Milestones in Analog and Digital Computing [3 ed.] 9783030409739, 9783030409746

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Herbert Bruderer

Milestones in Analog and Digital Computing Third Edition

Milestones in Analog and Digital Computing

Herbert Bruderer

Milestones in Analog and Digital Computing Third edition Translated from the German by John McMinn

Herbert Bruderer Rorschach, Switzerland

ISBN 978-3-030-40973-9    ISBN 978-3-030-40974-6 (eBook) https://doi.org/10.1007/978-3-030-40974-6 © Springer Nature Switzerland AG 2015, 2018, 2020 This work is subject to copyright. All rights reserved. The translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction as microfilm or by any other physical process, transmission, as well as information storage and retrieval, electronic modification or use of computer programs, or by any currently known or subsequently developed method requires the express permission of the publisher. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication, even in the absence of a specific context, does not imply that such names are exempt from relevant protective legislation and regulations, therefore precluding their free use. To the best of their knowledge, the publisher, the authors and the editors attest to the correctness and accuracy of the recommendations and information found in this book at the time of publication. However, neither the publisher, the authors, nor the editors are liable for any errors or omissions, either expressed or implied, with respect to the material of the book. The publisher remains neutral with regard to jurisdictional claims in relation to published maps and institutional affiliations. This Springer imprint is published by the Springer Nature AG registered company Registered company address: Gewerbestrasse 11, 6330 Cham, Switzerland

Preface As per the title of this book, this work presents selected masterpieces from the field of calculating and computing technology. It also includes related areas, such as historical automatons and scientific instruments (astronomy, land surveying, and time measurement). The book deals with contributions to the history of mathematics, with articles from the history of computer science. The objective is therefore not the complete documentation of historical developments. The focus is primarily on the technical achievements and not on their impact on the economy and society. The work contains no biographies. The history of mathematics and computer science constitutes a cultural-historical travel through time, a journey into the past. Two Volumes In view of the scope of this work, the book comprises two volumes. Some selected keywords relate to the following content: Volume 1 Basic Principles, Mechanical Calculating Devices, and Automatons • Basic principles (mechanical and electronic calculators, the digital transformation) • Global overview of early electronic digital computers • Development of arithmetic • Mechanical calculating machines • Classification of calculating aids • Museums and their collections • Famous replicas (Babbage, Pascal, Leibniz, Hollerith) • Slide rules (linear, circular, cylindrical, and pocket watch slide rules) • Roman hand abacus • Historical automatons and robots (automaton figures, musical automatons, Leonardo da Vinci’s robots) • Automaton clocks • Scientific instruments (mathematics, astronomy, surveying, time measurement) • Chronology • Technological, economic, social, and cultural history • Step-by-step instructions Volume 2 Electronic Computers, Glossaries, and Bibliographies • Invention of the computer (Babbage, Turing, Zuse, von Neumann) • Development in Germany (Zuse, Telefunken, Siemens)

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• Development in Great Britain (Enigma, Turing-Welchman Bombe, Colossus, Bletchley Park) • Development in Switzerland (Zuse Z4, Ermeth) • Original documents (Zuse Z4 and Ermeth) • Global development of the computing technology • German-English glossary of technical terms • English-German glossary of technical terms • Worldwide bibliography There are also hybrid forms between analog and digital calculating devices. The use of mechanical and electronic calculating devices is overlapping. The boundary between the two volumes is consequently somewhat fuzzy. Thus, for example, the chapter “Basic Principles” covers both older and newer calculating machines. The German-English and English-German glossaries and the bibliography include entries covering the entire history of computing technology. The 20 step-by-step instructions (including the Roman hand abacus and the pantograph) refer to both analog and digital calculating devices.

The Book in Numbers

The two volumes together encompass around 2000 pages, with more than 150 tables and more than 700 figures. Each of the two German-English and English-German glossaries of technical terms includes more than 5000 entries. The bibliography lists more than 6000 sources.

What Is New?

Compared with the award-winning first edition, the second edition has been thoroughly revised and considerably expanded. For the English version, the entire work has been revised and supplemented and errors corrected. Below are the most important changes of the second and third editions: • New findings: Multiple Curta (world’s smallest mechanical parallel calculator), circular slide rule of Weber, and Summus circular adding machine • Additional step-by-step operating instructions for especially instructive mechanical calculating devices: Millionaire, Madas, Simex, Summus, Brunsviga, and original Odhner • Significantly expanded global overview of the existing holdings of valuable historical objects in the most important museums • About 280 new figures (compared to the second edition) of rare analog and digital calculating devices and other scientific instruments (above all from time measurement and astronomy), as well as historically important automaton figures, musical automatons, Roman bead frames, Leonardo’s robots, and famous replicas • More detailed explanation of the finding of the century, the Antikythera mechanism (world’s first known astronomical calculating machine), in connection with a survey among internationally leading researchers

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• About 50 new tables (compared to the second edition) relating to different subjects • Comprehensive German-English and English-German glossaries of technical terms dealing with the history of computer science and related fields, each with more than 5000 entries • Greatly expanded and updated bibliography with more than 6000 entries, including selected publications about arithmetic teachers, history of technology, and history of science, together with history of astronomy, surveying, clocks, automatons, and the digital transformation • In general, greater consideration of related fields, such as scientific instruments (mathematics, astronomy, surveying, or measurement of time), typewriters, perforated tape controlled looms, and automatons: automaton figures (androids and animal figures), musical automatons (mechanical music instruments), picture clocks, chess automatons, automaton writers, automaton clocks, drawing automatons, and historical robots • Dealing with the basic questions of the history of science and technology and the preservation of the cultural heritage of technology • Additional definitions, such as algorithm, logarithm, and numerical and graphical computation (nomography) • Numerous new definitions relating to mechanical calculating devices, bookkeeping machines and punched card equipment • Expanded presentation of the differences between analog and digital • Details about the origin of the binary system before Leibniz • Overview of current developments, such as digitization, the digital transformation, artificial intelligence, machine learning, industrial revolutions, robotics, drones, social networks, electronic commerce, privacy protection, and data ownership • Reference to DNA and quantum computers • Detailed elaboration of controversial issues: Ada Lovelace (reputed to be first woman programmer), Alan Turing (universal computer, stored program, influence on computer design), Thales of Miletus (measurement of the height of the pyramids, intercept theorem), Heron of Alexandria (invention of the pantograph), and onset of artificial intelligence (international computing machinery conference, 1951 in Paris) • Additional documents from the first Great Exhibition of 1851 in London • Evaluation of exhibition catalogs (e.g., the Mustermesse Basel and the Bürofachmesse Zurich) and commercial journals • Determination of the age of Swiss calculating devices with the help of exhibition catalogs and entries in the Swiss Official Gazette of Commerce • Dating of the world-famous “Millionaire” direct multiplying machine based on the serial number (thanks to newly discovered findings of documents of the manufacturer and global inquiries, for example, with museums, collectors, and surveying offices)

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• Considerations for self-built analog devices (pantograph, pair of sector compasses, and proportional dividers) • Very detailed index of persons, places, and subjects.

Selected Milestones

This work presents a number of particularly sensational and surprising findings: • The world’s first (mechanical) astronomical calculating machine • The world’s largest and most accurate commercially available cylindrical slide rules • The world’s first (commercially) successful calculating machine • The world’s oldest known keyboard adding machine • The world’s first (mechanical) “process computer” • The world’s smallest mechanical calculating machine • The world’s smallest mechanical parallel calculating machine.

Global Surveys

This work includes numerous global surveys, such as concerning the first (electromechanical) relay and (electronic) vacuum tube computers, the pioneers of computer science and their inventions, and museum holdings. Furthermore, it conveys an overview of the mechanical calculating devices in Switzerland. Together with the extensive index of persons, places, and subjects, the book is therefore suitable as a reference work.  tep-by-Step Operating Instructions S Hard-to-find user instructions for historical analog and digital calculating devices are included in order to enhance the user value of this book. These make clear how cumbersome calculating once was.  reservation of the Cultural Heritage of Technology P It is my hope that this book will motivate readers to become interested in the cultural heritage of technology and the preservation of such treasures. Perhaps this publication will wrest some outstanding achievements in computer science from oblivion. It would be gratifying if this book is able to encourage young persons to take up a technical education and thus alleviate the shortage specialists in the next generation. A further important objective is the promotion of the history of technology. Digital Transformation Groundbreaking inventions, such as the wheel, the steam engine, letterpress, the current generator, the number zero, the computer, the transistor, the World Wide Web, and the robot, have led to a profound reshaping of the world. Many companies have fallen victim to the transition from mechanical systems to electronics. They failed to recognize the signs of the time and were left behind with this development. A similar rapid upheaval is apparent with the

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transition from analog technology to digital technology. In this connection, numerous companies have also perished. The upsurge of the global Internet has a far-reaching, many-faceted, and difficult-to-­foresee impact on politics, society, economics, science, and technology. The omnipresent informatics penetrates nearly all areas of life. The ongoing digital transformation is often described as the fourth industrial revolution. Fifty years ago, no one sensed the onset of this fundamental revolution in technology. The inexorable changes overwhelm many persons. Who recalls today how difficult it was to handle the slide rule and tables of logarithms or the typewriter? How will the world look in another 50 years? Will we still be able to read our electronic documents? How long will the lifespan of digital reference works be? Books and newspapers survive for centuries. Let us recall: Albert Einstein derived his groundbreaking insights with paper and pencil, without the help of electronic resources.

Regarding the Origins of This Book

The enormous work required to compile this book entailed negative as well as positive experiences.  bstacles O The many years of – exclusively unsalaried – researches were unfortunately complicated by the circumstance that the readiness for the support of these was often meager, in some cases because of narrow-minded jealousy. At times, the work was purposely hindered. Which historical calculating devices are found at which particular places? The most important museums were asked to check their holding lists for correctness and completeness. Unfortunately, some (repeated) questions remained unanswered. Considerable reluctance was also encountered regarding the willingness to deliver difficultly accessible documents. Further hurdles arose concerning the entry of the work in Wikipedia.  heft of Intellectual Property T With the discovery of theft or falsification of intellectual property, the victim is often penalized and not the offender. Almost worse than the faulty circumstances themselves is the behavior of the persons involved when this fraudulence comes to light: from resolute silence to intimidation with threatened legal actions. Instead of eliminating plagiarizations and falsifications from the market, these continue to be actively sold. Works from foreign sources are all too often kept quiet in order to exclude competition.

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 cquisition of Top-Quality Photographic Material A Acquiring high-resolution photographs of historical calculating devices was enormously time-consuming and in part very expensive. Initially, it was necessary to find the relevant contact partners. In some cases, it was necessary to open an online account with the related illustration database and examine the collections over many hours. Furthermore, the acquisition and use of these photographs required concluding agreements which, in some cases, could be delivered only by letter mail. Many museums demand exorbitant fees even for works relating to research, which, as experience shows, exist only in limited editions. Apart from one or more specimen copies, it is not at all rare that the cost of a single photograph is more than that of a 1000-page book, even though this provides cost-free transnational advertisement for the institutions in question. For financial reasons, in many cases, it was necessary to do without photographic material. In addition, photos are guarded as though they were state secrets. For copyright and quality reasons, no photographic material was taken from the Internet. In one particular case, concerning the illustration of the competition between American cyberneticist Norbert Wiener and chess-playing automaton of the Spaniard Leonardo Torres Quevedo (1951), it is not known who is entitled to the copyright. This is evidently a photograph taken from the press. The illustrations were taken from the following countries: Australia, Austria, Belgium, Canada, China, France, Germany, Greece, Italy, Liechtenstein, the Netherlands, Spain, Sweden, Switzerland, the UK, and the USA.  o Financial Support N The entire work was financed by the author alone, without any third-party funding. Consequently, there are no obligations and dependencies. The work originated single-handedly.  ulticolored Mixture M This work is a practice-oriented mixture of history book, informatics book, textbook, museum guide, instructions for use, glossary, bibliography, and reference work. It presents various outstanding achievements, discusses controversial issues, and defines core themes. Both digital and analog computers are considered, including ornate automatons. Understandably, this structure may be somewhat confusing. It is of course not easy to reconcile such diversity. One can say to the detriment of the book that it is “neither fish nor flesh” and that the common thread is not always immediately recognizable.  dditions and Improvements A Wherever possible, the correctness of all assertions was controlled on the basis of the original documents. In spite of great care, however, errors can unfortunately not be excluded. The author is therefore grateful for suggested improvements – calling attention to errors and additional information.

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 earch for Objects and Documents S I would be pleased to receive any information about rare and unknown historical calculating devices – mechanical calculating machines or slide rules of all types – and previously unknown documents.

English Edition

The tedious international search for the financial backing of the comprehensive English translation remained unsuccessful. The author himself therefore assumed the costs of the transcription. The search for a qualified native English translator also proved very time-consuming. The search was conducted above all in North America, Great Britain, Germany, and Switzerland. The database of the German Federal Association of Interpreters and Translators was especially helpful here. Ultimately, a good solution was found. It is not at all self-evident that a publishing house is prepared to publish such a large, four-colored work. Environmental Protection Although worldwide researches were carried out, not a single flight was necessary for the work. Public transport (train and bus) was used for all domestic and international travel to European museums, libraries, archives, conferences, etc.

Highlighting

Certain words and passages deserving particular emphasis are highlighted in italics. Herbert Bruderer

September 2020

Bruderer Informatik, Seehaldenstraße 26, Postfach 47, CH-9401 Rorschach, Switzerland, Telephone +41 71 855 77 11, Electronic mail: [email protected]; [email protected] http://orcid.org/0000-0001-9862-1910

Rorschach, Switzerland

Acknowledgments This book owes its origin to a great many persons. Without their very much appreciated help, this work would never have been possible. I would like to express my heartfelt thanks to all those who supported me during roughly 10 years of work. Because of the danger that I could forget to mention some of those who have helped me, with a few exceptions, I will not name these persons.

Libraries

First of all, I would like to mention the ETH (Swiss Federal Institute of Technology, Zurich) Library. I am very grateful to the staff of the different sections. Beatrice Ackermann, Ursula Albrecht, Manuela Christen, Aristidis Harissiadis, and Patricia Robertson were able to provide me with numerous, often difficult accessible, domestic and foreign documents.

Museums and Archives

Numerous domestic and international technical, scientific, and historical museums were helpful with the researches. Valuable information was obtained from a number of private and public archives.

Magnificent Fully Functional Androids from the Eighteenth Century

The three automaton figures of Jaquet Droz, the “Musician”, the “Writer”, and the “Draftsman”, first introduced in 1774, are regarded as the world’s finest examples of sophisticated androids. They are part of the holdings of the Musée d’art et d’histoire in Neuchâtel. In connection with a film for the American journal Communications of the ACM, Thierry Amstutz demonstrated this mechanical wonder for us.  rovision of Mechanical Calculating Machines and Cylindrical P Slide Rules Some collectors supported the investigations by providing analog and digital devices of historical importance: Heiri Hefti, Fritz Menzi, Niklaus Ragaz, and Urs Rüfenacht.

Scientific Journals and Conference Proceedings

The results of these time-consuming efforts have found international approval, not in the least thanks to the publications in the flagship magazine of the Association for Computing Machinery (ACM), New York. My special appreciation goes to the editors of the widely circulated Communications of the ACM: Moshe Y. Vardi, Andrew A. Chien, Andrew Rosenbloom, David Roman, Diane Crawford, and Lawrence Fisher. The ACM awards the Turing Prize, generally viewed as the Nobel Prize for informatics.

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Acknowledgments

Other articles (talks given in London and New York) are documented in the conference proceedings of the International Federation for Information Processing (IFIP, Laxenburg, Austria), the global parent organization of the national scientific informatics societies. Worthy of mention are also the IEEE Annals of the History of Computing (New York), the leading journal for the history of computer science, along with the Journal of the Oughtred Society (California), CBI Newsletter (Charles Babbage Institute, University of Minnesota, Minneapolis), and Resurrection, the newsletter of the British Computer Conservation Society (London).

Photographs

To their credit, many institutions made high-resolution black and white and color photographs of history-charged devices, machines, and documents available to me and granted permission to reproduce these. Further information can be found in connection with the respective photographs.

Award-Winning Book

The Oughtred Society conferred an award on the first edition of this work in 2016. This USA-based international association is concerned with the history of the slide rule and other mathematical instruments. The Briton William Oughtred was the inventor of the slide rule.

Book Reviews

I would like to express my gratitude to Thomas Sonar (Technische Universität Braunschweig), Steven Deckelman (University of Wisconsin-Stout, Menomonie, Wisconsin), Rainer Gebhardt (Adam-Ries-Bund, AnnabergBuchholz), and Maik Schmidt, as well as Peter Schmitz (Magazin für Computertechnik c’t, Hanover) for their outstanding reviews of the first edition. These were published by the Mathematical Association of America and in the Mathematische Semesterberichte (Springer Verlag) and reprinted in the Newsletter of the European Mathematical Society and the Deutsche Mathematiker-Vereinigung.

English Translation

The excellent English translation of this difficult and demanding undertaking by the American physicist Dr. John McMinn (Bamberg, Germany), delivered on schedule, deserves a commendation.

The Publisher

Finally, I would like to express my particular gratitude to the staff of Springer Nature Switzerland AG, Cham, for their support and realization of this book.

Contents Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .     v Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .   xiii Volume I 1 Introduction���������������������������������������������������������������������������������������     1 1.1 Objective ���������������������������������������������������������������������������������������     1 1.2 Target Groups�������������������������������������������������������������������������������     3 1.3 Period of Time�������������������������������������������������������������������������������     3 1.4 What Is Computing Technology? �����������������������������������������������    4 1.5 Spectacular Device and Document Findings ���������������������������    4 1.6 Most Frequently Asked Questions Regarding Unknown Calculating Devices ���������������������������������������������������������������������    9 1.7 Instructions for Operating Historic Calculating Aids���������������    10 1.8 In Regard to the Origin of This Book ������������������������������������������   13 1.9 In Regard to Language�����������������������������������������������������������������    16 1.10 In Regard to the Content �������������������������������������������������������������    18 1.11 Priorities ���������������������������������������������������������������������������������������    19 1.12 Oral History Interviews ���������������������������������������������������������������   20 1.13 Firsthand Accounts ����������������������������������������������������������������������   21 1.14 Approach���������������������������������������������������������������������������������������    22 1.15 Highlights of the Researches�������������������������������������������������������    29 1.16 Low Points of the Researches�����������������������������������������������������    31 1.17 Plagiarism of Intellectual Property���������������������������������������������    32 1.18 Publications ���������������������������������������������������������������������������������    32 1.19 Sources �����������������������������������������������������������������������������������������    33 1.20 Bibliography���������������������������������������������������������������������������������    33 1.21 Regarding the Title of the Book �������������������������������������������������   34 1.22 Instructions for Assembly�����������������������������������������������������������    35 2 Basic Principles���������������������������������������������������������������������������������    37 2.1 Analog and Digital Devices���������������������������������������������������������   38 2.1.1 Numerals or Physical Variables �������������������������������������������������   39 2.1.2 Numeration or Measurement �����������������������������������������������������   39 2.2 Parallel and Serial Machines�������������������������������������������������������   69 2.3 Decimal and Binary Machines ���������������������������������������������������    73 2.4 Fixed Point and Floating Point Computers�������������������������������   78 2.5 Special-Purpose and Universal Computers������������������������������    80 2.6 Interconnected Computers ���������������������������������������������������������    82 2.7 Conditional Commands���������������������������������������������������������������   84 2.8 Components of Relay and Vacuum Tube Computers���������������   86 2.9 Electronic Tubes���������������������������������������������������������������������������   90 2.10 Delay Line Memories and Electrostatic Memories �������������������   93 xv

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2.11 Main Memory �������������������������������������������������������������������������������   93 2.12 Magnetic Memory�������������������������������������������������������������������������    97 2.13 Hardware and Software���������������������������������������������������������������   99 2.14 Subtraction with Complements �������������������������������������������������   101 2.15 Direct and Indirect Multiplication ���������������������������������������������   103 2.16 Sequence Control and Program Control �����������������������������������  106 2.17 Automation�����������������������������������������������������������������������������������  108 2.18 Punched Card Machines �������������������������������������������������������������   110 2.19 Electronic Brains ��������������������������������������������������������������������������  113 2.20 Commercial Data Processing and Scientific Computation ������  114 2.21 Program-Controlled Digital Computers in the Year 1950����������   115 2.22 Mechanical Calculating Machines����������������������������������������������  118 2.23 Accounting Machines�������������������������������������������������������������������   128 2.24 Tabulators�������������������������������������������������������������������������������������   128 2.25 Diversity of Terms and Change of Meaning�������������������������������   129 2.26 Digitization and Artificial Intelligence���������������������������������������   138 2.26.1 Algorithms Are Nothing New �����������������������������������������������������   138 2.26.2 Artificial Intelligence Is Nothing New ���������������������������������������   139 2.26.3 Digitization Is Nothing New �������������������������������������������������������   139 2.26.4 Two Notable Phases of Digitization�������������������������������������������  140 2.26.5 Digital History?�����������������������������������������������������������������������������  140 2.26.6 Industrial Revolutions�����������������������������������������������������������������  140 2.26.7 The Digital Transformation����������������������������������������������������������  141 2.27 Quantum Computers �������������������������������������������������������������������   154 2.28 DNA Computers ���������������������������������������������������������������������������   156 3 The Coming of Age of Arithmetic ��������������������������������������������������  157 3.1 From Tally Stick Through Abacus to Smartphone �������������������   158 3.2 Counting with the Fingers�����������������������������������������������������������   164 3.3 Abacus Calculation ���������������������������������������������������������������������   165 3.3.1 Calculating with Roman Numbers Is Laborious�����������������������   176 3.3.2 Bead Frame Computation�����������������������������������������������������������   179 3.3.3 Russian Counting Frames and School Abacus�������������������������   182 3.4 Counting Tables, Counting Boards, and Counting Cloths�������   183 3.4.1 Line Computation/Calculating on Lines�����������������������������������   185 3.5 Pen and Paper Calculation ����������������������������������������������������������  191 3.6 Graphical Computation: Nomography����������������������������������������  191 3.7 Lines of Development ������������������������������������������������������������������  192 3.8 Many Technical Objects Are Also Magnificent Works of Art���   196 Classification of Calculating Aids and Related Instruments �   199 4 4.1 Calculating Devices and Calculating Machines �����������������������  200 4.2 Adding Machines and Calculating Machines ���������������������������   201 4.3 Mathematical Machines and Mathematical Instruments �������   201 4.4 Planimeters�����������������������������������������������������������������������������������   203 4.5 Pantographs ����������������������������������������������������������������������������������  211

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4.6 Intercept Theorems ���������������������������������������������������������������������   214 4.6.1 We Are Probably Indebted to Thales of Miletus for the Intercept Theorem ������������������������������������������������������������  215 4.6.2 The Pantograph: The Invention of Heron or Scheiner?������������  217 4.6.3 How Does a Pantograph Function? �������������������������������������������   218 4.7 Sectors�������������������������������������������������������������������������������������������   220 4.8 Proportional Dividers��������������������������������������������������������������������  221 4.9 Protractors and Clinometers�������������������������������������������������������   225 4.10 Coordinatographs�������������������������������������������������������������������������   227 4.11 Mathematical Tables �������������������������������������������������������������������   230 4.12 Astronomical instruments�����������������������������������������������������������   232 4.13 Mechanical and Electronic Calculators�������������������������������������   237 4.14 Classification Criteria�������������������������������������������������������������������   238 4.14.1 Types of Calculating and Computing Machines�����������������������   238 4.14.2 Computer Generations�����������������������������������������������������������������   238 4.14.3 Arithmetic Unit and Memory Unit ���������������������������������������������   239 5 Chronology�����������������������������������������������������������������������������������������   245 5.1 Pre- and Early History of Computer Technology and Automaton Construction�����������������������������������������������������   245 Pioneers in Calculating and Computing Technology���������������   255 6 6.1 From Which Countries Do the Inventors and Discoverers Come? �������������������������������������������������������������������������������������������   257 6.2 Who Invented Which Calculating Aid When?���������������������������   267 6.3 New Inventions of Fundamental Importance���������������������������   272 6.4 Manufacturers of Calculating Aids���������������������������������������������   272 7 Conferences and Institutes�������������������������������������������������������������   277 7.1 Early Conferences on Computer Science�����������������������������������   277 7.2 Early Institutes for Computing Technology�������������������������������   287 7.3 Universities with an Illustrious Past �����������������������������������������  290 7.4 Associations and Journals for the History of Computer Science�������������������������������������������������������������������������������������������   291 Global Overview of Early Digital Computers (Tables) �������������   293 8 8.1 Preliminary Remarks�������������������������������������������������������������������   293 8.2 Early Relay and Vacuum Tube Computers (In Alphabetical Order) ���������������������������������������������������������������   295 8.3 Early Relay and Vacuum Tube Computers (In Chronological Order)�������������������������������������������������������������  300 8.4 Commentary Regarding the Early Relay and Vacuum Tube Computers���������������������������������������������������������������������������   302 9 Museums and Collections���������������������������������������������������������������   307 9.1 Museums of Science and Technology ���������������������������������������  308 9.1.1 Collection Databases��������������������������������������������������������������������  312

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9.1.2 Early Exhibits of Calculating Aids ����������������������������������������������  313 9.2 Which Museum Has Which Historical Calculating Devices?���   316 9.3 Which Calculating Devices Are Among the Museum’s Holdings?����������������������������������������������������������������������������������������  317 9.3.1 Australia ����������������������������������������������������������������������������������������  317 9.3.2 Austria�������������������������������������������������������������������������������������������   318 9.3.3 Belgium�����������������������������������������������������������������������������������������   319 9.3.4 Canada�������������������������������������������������������������������������������������������   319 9.3.5 China���������������������������������������������������������������������������������������������   319 9.3.6 Czech Republic�����������������������������������������������������������������������������   319 9.3.7 France �������������������������������������������������������������������������������������������   319 9.3.8 Germany ����������������������������������������������������������������������������������������  321 9.3.9 Greece �������������������������������������������������������������������������������������������   328 9.3.10 Italy �����������������������������������������������������������������������������������������������   328 9.3.11 Japan ���������������������������������������������������������������������������������������������  330 9.3.12 The Netherlands���������������������������������������������������������������������������  330 9.3.13 New Zealand���������������������������������������������������������������������������������  330 9.3.14 Spain ���������������������������������������������������������������������������������������������  330 9.3.15 Sweden �����������������������������������������������������������������������������������������  330 9.3.16 Switzerland������������������������������������������������������������������������������������  331 9.3.17 UK���������������������������������������������������������������������������������������������������   333 9.3.18 USA�������������������������������������������������������������������������������������������������   336 9.4 Where Is a Particular Historical Calculating Device on Exhibit?�����������������������������������������������������������������������������������������   362 9.4.1 Analog Calculating Aids �������������������������������������������������������������   362 9.4.2 Digital Calculating Aids���������������������������������������������������������������   363 9.4.3 Counting Tables, Counting Boards, and Counting Cloths�������  364 9.4.4 Historical Calculating Aids and Their Exhibition Sites: Originals ���������������������������������������������������������������������������������������  366 9.4.5 Historical Calculating Aids and Their Exhibition Sites: Replicas and Reconstructions ��������������������������������������������������������������������  371 9.4.6 Programmable Historical Automaton Writers (Original Specimens) �����������������������������������������������������������������������������������   374 9.4.7 Why Reconstructions?������������������������������������������������������������������  375 9.4.8 Roberto Guatelli: Replicas of Machines from da Vinci, Pascal, Leibniz, Babbage, and Hollerith�������������������������������������������������   376 9.4.9 Resurrected Relay and Vacuum Tube Computers���������������������  389 9.5 Oldest Surviving Calculating Aids ���������������������������������������������  390 9.5.1 Early Four-Function Machines ���������������������������������������������������  390 9.5.2 Early One- and Two-Function Machines�����������������������������������   393 9.5.3 Schickard, Pascal, and Leibniz���������������������������������������������������  396 9.5.4 Cylindrical Calculating Machines�����������������������������������������������  407

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10 The Antikythera Mechanism��������������������������������������������������������   409 10.1 An Astronomical Calculating Machine ������������������������������������   409 10.2 The Astrolabe: Planetarium or Calendar Calculator?���������������   412 10.3 When Was the Astronomical Calculator Found? ���������������������   414 10.4 When Did the Ship Sink?�������������������������������������������������������������   415 10.5 When Was the Ship Built?�����������������������������������������������������������   415 10.6 When Was the Astronomical Calculator Built?�������������������������   416 10.7 Who Constructed the Mechanism?���������������������������������������������   418 10.8 Reconstructions ���������������������������������������������������������������������������  420 10.9 Conclusions�����������������������������������������������������������������������������������   425 11 Schwilgué’s Calculating Machines�����������������������������������������������   427 11.1 Schwilgué’s “Process” Calculator�����������������������������������������������   427 11.1.1 An Unconventional Special-Purpose Calculating Machine Without a Customary Setting Mechanism?���������������  428 11.1.2 The Peculiar Machine Proved to Be an Early “Process” Calculator �������������������������������������������������������������������   432 11.1.3 An Accompanying Document Reveals the First Indications About the Origin of the Calculating Machine �������������������������������������������������������������������   432 11.1.4 Purpose of the Calculating Machine: Calculation of Circle Partitioning Factors�������������������������������������������������������  434 11.1.5 The Results of the Calculating Machine Determine the Settings for the Gear Milling Machine���������������������������������  434 11.1.6 Controlling the Gear Milling Machine from a Paper Tape�������������������������������������������������������������������������������������   435 11.1.7 High-Precision Fine Mechanics �������������������������������������������������  437 11.1.8 Gear Milling Machine or Gear Partitioning Machine? �������������  437 11.1.9 A Tooling Machine Specifically Designed for the Astronomical Clock ���������������������������������������������������������  442 11.1.10 Dating the “Process” Calculator �����������������������������������������������  442 11.1.11 Was the Large Adding Machine Used for the Astronomical Clock?���������������������������������������������������������������������������������������������  443 11.1.12 The Calculating Machine Determines Number Trains for the Tape Controlled Milling Machine�����������������������  445 11.1.13 Machine Control by Paper Tape �������������������������������������������������  445 11.1.14 When Were Schwilgué’s Machines First Mentioned?��������������   446 11.1.15 Schwilgué’s Church Calculator���������������������������������������������������  449 11.2 Schwilgué’s Keyboard Adding Machine�������������������������������������   451 11.2.1 The World’s Oldest Surviving Keyboard Adding Machines�����   452 11.2.2 Technical Features�����������������������������������������������������������������������   452 11.2.3 Inputting Numbers via Keyboard�����������������������������������������������  456 11.2.4 Two Precursors and Two Finalized Devices �����������������������������   457 11.2.5 The Replica of a Solothurn Clockmaker�������������������������������������  459

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11.2.6 The World Exhibition of 1851 at the Crystal Palace in London ������������������������������������������������������������������������   460 12 The Thomas Arithmometer �����������������������������������������������������������  463 12.1 The Arithmometer: The First Industrially Produced Calculating Machine ������������������������������������������������������������������   464 12.2 The Stepped Drum Machine Is Capable of All Basic Arithmetic Operations�����������������������������������������������������������������  465 12.3 The World Exhibition of 1851 at the Crystal Palace in London �������������������������������������������������������������������������������������   473 12.4 What Was the Cost of an Arithmometer?�����������������������������������  479 12.5 A Wealth of Information About the History of Technology and Industry���������������������������������������������������������������������������������  482 13 The Curta �������������������������������������������������������������������������������������������  485 13.1 Preliminary Remarks�������������������������������������������������������������������  485 13.2 Development of the Curta����������������������������������������������������������   486 13.2.1 The First Patents for the Curta ��������������������������������������������������   488 13.2.2 Arrest and Deportation to the Buchenwald Concentration Camp ������������������������������������������������������������������   488 13.2.3 Curta, a Gift for the Führer for the Ultimate Victory?��������������   489 13.2.4 Design Drawings from the Buchenwald Concentration Camp ������������������������������������������������������������������   490 13.2.5 Contract for Work with Rheinmetall-Borsig in Sömmerda �����   491 13.2.6 Escape from Russian Persecutors in Thuringia�������������������������   491 13.2.7 The Crowning Achievement of 350 Years of Mechanical Calculating Machine Development �������������������������������������������  495 13.3 Description of the Curta���������������������������������������������������������������  495 13.3.1 Design Drawings���������������������������������������������������������������������������  498 13.3.2 Is the Curta the Smallest Mechanical Calculating Machine in the World?�����������������������������������������������������������������   502 13.4 The Founding of Contina in Liechtenstein �������������������������������   502 13.4.1 New Beginning in Liechtenstein�������������������������������������������������   502 13.4.2 Swindled Out of His Life’s Work�������������������������������������������������   503 13.4.3 Letters of Inquiry to Swiss Machine Builders for the Manufacture of the Curta�������������������������������������������������������������   503 13.4.4 Opposition from Switzerland �����������������������������������������������������   507 13.5 Mass Production of the Curta in Liechtenstein�������������������������   525 13.5.1 Piece Numbers �����������������������������������������������������������������������������   526 13.6 Global Sales of the Curta�������������������������������������������������������������   527 13.6.1 The Curta at the Schweizer Mustermesse in Basel�������������������   527 13.6.2 The Curta at the Bürofachausstellung in Zurich�����������������������   528 13.6.3 Who Used the Curta? �������������������������������������������������������������������   528 13.6.4 Prices���������������������������������������������������������������������������������������������   529 13.7 A Mechanical Parallel Calculator from Liechtenstein �������������  530

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13.7.1 Double, Quadruple, and Quintuple Curtas��������������������������������  531 13.7.2 Patent Specifications for the Multiple Calculating Machine���   536 13.7.3 The World’s Smallest Mechanical Parallel Calculator�������������   536 13.8 A British Mechanical Parallel Calculator�����������������������������������   537 13.8.1 The British 12-Fold Curta for Matrix Calculations���������������������   537 13.8.2 Independent Development of Two Mechanical Parallel Calculators?�����������������������������������������������������������������������������������   541 13.8.3 The UK Matrix Calculator Has Been Lost�����������������������������������   541 14 Slide Rules �����������������������������������������������������������������������������������������   543 14.1 Logarithms �����������������������������������������������������������������������������������   543 14.1.1 Graphical Calculation �����������������������������������������������������������������   543 14.1.2 Who Introduced Logarithms and the Slide Rule?���������������������  544 14.1.3 Addition and Subtraction with Slide Rules�������������������������������  546 14.2 Types ���������������������������������������������������������������������������������������������  548 14.2.1 Linear Slide Rules, Circular Slide Rules, and Cylindrical Slide Rules���������������������������������������������������������  548 14.2.2 Endless Scales and Double Scales���������������������������������������������  549 14.3 Classification of Slide Rules �������������������������������������������������������   550 14.3.1 Linear Slide Rules�������������������������������������������������������������������������   550 14.3.2 Circular Slide Rules ���������������������������������������������������������������������   550 14.3.3 Cylindrical Slide Rules������������������������������������������������������������������  551 14.4 Slide Rule Manufacturers �����������������������������������������������������������   558 14.5 Dating of Cylindrical Slide Rules �����������������������������������������������  560 14.6 Relationship Between the Serial Numbers and Scale Length �������������������������������������������������������������������������  564 14.7 The Weber Circular Slide Rule�����������������������������������������������������  569 14.7.1 A Circular Slide Rule of Unusual Design�����������������������������������  569 14.7.2 How Does the Device Function?�������������������������������������������������  570 14.7.3 Who Built the Circular Slide Rule?���������������������������������������������  570 14.7.4 Where Was the Circular Slide Rule Found?��������������������������������  571 14.8 Loga Cylindrical Slide Rules�������������������������������������������������������   572 14.8.1 The 24 Meter Cylindrical Slide Rule�������������������������������������������   572 14.8.2 Determination of Age��������������������������������������������������������������������  575 14.8.3 How Long Is the Scale? ���������������������������������������������������������������   576 14.8.4 Loga Cylindrical Slide Rules: Lists of Models and Price Lists�������������������������������������������������������������������������������   578 15 Historical Automatons and Robots�����������������������������������������������   593 15.1 Automaton Figures�����������������������������������������������������������������������  594 15.1.1 Programmed Cylinders ���������������������������������������������������������������   595 15.1.2 Famous Builders of Automatons�������������������������������������������������   595 15.1.3 Ornate Automaton Figures ���������������������������������������������������������  598 15.1.4 Jaquet-Droz�����������������������������������������������������������������������������������  602 15.1.5 Maillardet’s Automaton in Philadelphia�����������������������������������   613

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15.1.6 Programmable Automaton Writers���������������������������������������������   613 15.1.7 The World’s Most Magnificent Mechanical Androids Are from the Eighteenth Century �����������������������������������������������   614 15.1.8 The Mechanical Clock with a Writing Figure of the Beijing Palace Museum�����������������������������������������������������   616 15.1.9 Magnificent Human and Animal Automatons from Le Locle���������������������������������������������������������������������������������   623 15.1.10 The Tower and Ship Automatons and Chariots�������������������������  628 15.1.11 Leonardo da Vinci’s Automatons�����������������������������������������������  636 15.2 Musical Automatons �������������������������������������������������������������������  649 15.2.1 Mechanical Musical Instruments�����������������������������������������������  649 15.2.2 The Wide Variety of Instruments �����������������������������������������������  649 15.2.3 Music Boxes�����������������������������������������������������������������������������������  650 15.2.4 Singing Birds���������������������������������������������������������������������������������  656 15.2.5 Train Station and Chalet Automatons ���������������������������������������   661 15.2.6 Violin and Organ Automatons ���������������������������������������������������  662 15.2.7 Sound Recording Media��������������������������������������������������������������   664 15.2.8 Talking Machines������������������������������������������������������������������������   664 15.2.9 Automaton Figures and Musical Automatons in Museums�����  665 15.2.10 The Componium���������������������������������������������������������������������������  666 15.3 Chess Automatons �����������������������������������������������������������������������  666 15.3.1 The Niemecz Chess Automaton���������������������������������������������������   667 15.3.2 The End-Game Automaton of Torres Quevedo �������������������������   667 15.4 Typewriters����������������������������������������������������������������������������������   668 15.5 Clocks���������������������������������������������������������������������������������������������   672 15.5.1 An Enormous Range of Clocks ���������������������������������������������������   672 15.5.2 Clockmakers as the Inventors of Automatons and Calculating Machines�����������������������������������������������������������   729 15.6 Looms��������������������������������������������������������������������������������������������  730 16 Mechanical Calculating Aids���������������������������������������������������������   737 16.1 Counting Tables ���������������������������������������������������������������������������   737 16.2 Manufacturers of Mathematical Drawing, Measuring, and Calculating Devices �������������������������������������������������������������  740 16.3 Slide Bar Adders and Mechanical Calculating Machines �������   743 16.3.1 The Millionaire�����������������������������������������������������������������������������  744 16.3.2 The Madas�������������������������������������������������������������������������������������   783 16.3.3 The Precisa �����������������������������������������������������������������������������������  784 16.3.4 The Stima���������������������������������������������������������������������������������������  784 16.3.5 The Conto �������������������������������������������������������������������������������������  786 16.3.6 The Coréma�����������������������������������������������������������������������������������   787 16.3.7 The Correntator�����������������������������������������������������������������������������  788 16.3.8 The Demos�������������������������������������������������������������������������������������  789 16.3.9 The Direct �������������������������������������������������������������������������������������  790

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16.3.10 The Eos �����������������������������������������������������������������������������������������   791 16.3.11 The Heureka ���������������������������������������������������������������������������������   791 16.3.12 The St. Gotthard���������������������������������������������������������������������������   792 16.3.13 The Ultra ���������������������������������������������������������������������������������������   793 16.4 Prices of Calculating Aids�����������������������������������������������������������   793 16.5 Piece Numbers �����������������������������������������������������������������������������  798 16.6 Patents for Calculating Aids������������������������������������������������������   800 16.7 Mechanical Calculating Aids (Overview)�����������������������������������  801 16.8 Dating with the Help of Exhibition Catalogs����������������������������   808 16.8.1 Catalogs from the Schweizer Mustermesse, Basel ������������������   808 16.8.2 Presence of Manufacturers at the Mustermesse�����������������������   813 16.8.3 Manufacturers’ Presence at the Bürofachausstellung�������������  814 16.9 The Volksrechner�������������������������������������������������������������������������   816 16.10 Grunder’s Calculating Machine �������������������������������������������������  818 1 7 Technological, Economic, Social, and Cultural History�����������   823 17.1 The Rich Technical Cultural Heritage�����������������������������������������  824 17.2 Technology Is Part of Our Culture�����������������������������������������������   825 17.3 The History of Science and Technology�������������������������������������   825 17.3.1 What Do We Understand by the History of Science and Technology?���������������������������������������������������������������������������  826 17.3.2 Why Does One Pursue the Study of the History of Science and Technology ���������������������������������������������������������������������������  826 17.3.3 Presentation of Science and Technology in Museums�������������   827 17.4 The Transformation in the History of Technology �������������������   827 17.4.1 Does the History of Technology Fulfill the Expectations Placed in It?�����������������������������������������������������������������������������������  829 17.4.2 Technical History Without Relating to Science and Engineering?�������������������������������������������������������������������������   831 17.4.3 Combination of “Hard” and “Soft” Technological History �����  834 17.5 Lack of Appreciation for the History of Technology�����������������   835 17.6 Experiencing Technological History �����������������������������������������  836 17.7 Furthering of the Follow-On Generation of Technological Historians �������������������������������������������������������������������������������������   837 17.8 Computers Were Originally Humans �����������������������������������������  838 17.9 Patent Protection �������������������������������������������������������������������������   841 17.9.1 No Claim to the Protection of Inventions�����������������������������������   841 17.9.2 Had the Patent Protection for the Thomas Arithmometer Expired?�����������������������������������������������������������������������������������������  843 17.10 Discoveries and Inventions��������������������������������������������������������   844 17.10.1 Invention Priority�������������������������������������������������������������������������  845 17.10.2 Were Logarithms Discovered or Invented? ������������������������������   846 17.11 Patriotism and Hero Worship ����������������������������������������������������   846 17.12 Lifespan of Calculating Aids������������������������������������������������������   846

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18 Preserving the Technical Heritage�����������������������������������������������   851 18.1 Loss of Cultural Heritage�������������������������������������������������������������   851 18.2 Long-Duration Archiving�������������������������������������������������������������   852 18.3 Management of Object Collections���������������������������������������������   855 18.3.1 Building Up a Collection�������������������������������������������������������������   855 18.3.2 Breakup of a Collection���������������������������������������������������������������   855 18.3.3 Gloves �������������������������������������������������������������������������������������������  856 18.3.4 Functionality of Devices �������������������������������������������������������������  856 18.3.5 Improper Safekeeping of Cultural Heritage�������������������������������   857 18.3.6 Damage to Devices due to Nonuse���������������������������������������������   857 18.3.7 Reappraisal of Scientific Collections �����������������������������������������  858 19 Operating Instructions �������������������������������������������������������������������  859 19.1 The Abacus: Bead Frame�������������������������������������������������������������   861 19.2 The Aristo Slide Rule: Analog Computing Device��������������������   866 19.3 The Brunsviga: Pinwheel Machine���������������������������������������������  867 19.4 The Curta: Stepped Drum Machine �������������������������������������������   873 19.5 The Loga Circular Slide Rule: Analog Calculating Device������   880 19.6 The Loga Cylindrical Slide Rule: Analog Calculating Device �  882 19.7 The Madas: Stepped Drum Machine ����������������������������������������   884 19.8 The Millionaire: Direct Multiplying Machine ��������������������������   889 19.9 Napier’s Bones: Multiplication and Division Rods������������������   896 19.10 The Odhner: Pinwheel Machine������������������������������������������������   900 19.11 Schwilgué’s Keyboard Adding Machine/Single-Digit Adding Machine���������������������������������������������������������������������������  905 19.12 The Sector: Analog Calculating Device ������������������������������������   906 19.13 The Simex: Direct Adding Machine ������������������������������������������   909 19.14 The Stima: Three-Function Machine ������������������������������������������  911 19.15 The Summus: Disc Adding Machine �����������������������������������������   915 19.16 The Thomas Arithmometer: Stepped Drum Machine���������������   919 19.17 The Trebla: Slide Bar Adder/Stylus-Operated Calculator �������   921 19.18 The Volksrechner: Setting Wheel Machine/Stylus-Operated Calculator �������������������������������������������������������������������������������������   925 Volume II 2 0 Who Was the Inventor of the Computer? �����������������������������������   927 20.1 Preliminary Remarks�������������������������������������������������������������������  928 20.2 What Is a Computer? �������������������������������������������������������������������  929 20.3 What Is a Turing Machine? ���������������������������������������������������������  929 20.3.1 Design of the Turing Machine�����������������������������������������������������  930 20.3.2 Program Flow�������������������������������������������������������������������������������  930 20.3.3 Significance for Theoretical Computer Science �����������������������   931 20.3.4 Algorithms�������������������������������������������������������������������������������������   931 20.3.5 The Universal Machine ���������������������������������������������������������������   932 20.4 What Is a von Neumann Computer?�������������������������������������������  934

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20.4.1 Design of a von Neumann Computer�����������������������������������������  934 20.5 Is the von Neumann Computer a Serial or a Parallel Machine?���������������������������������������������������������������������������������������   935 20.6 Who Invented the von Neumann Computer? ���������������������������  936 20.7 What Does Stored Program Mean?���������������������������������������������   937 20.7.1 Stored Programs Are Nothing New���������������������������������������������   937 20.7.2 Data and Program in the Same Memory �����������������������������������   937 20.7.3 Computers with and Without a Program Memory �������������������  938 20.7.4 Prerequisites for Program Storage ���������������������������������������������  939 20.7.5 Faster Data Processing Thanks to Program Storage�����������������  939 20.7.6 What Is a Self-Modifying Program? ������������������������������������������   940 20.7.7 Is the Turing Machine Self-Modifying? �������������������������������������  942 20.7.8 Is the Turing Machine Stored Programmed?�����������������������������  943 20.7.9 The Turing Machine: Program and Data in the Same Memory? (Memory Tape as Program and Data Memory)��������   944 20.7.10 The Turing Machine: Program and Data on Different Memory Tapes?�����������������������������������������������������������������������������  945 20.7.11 Retrospective Firsthand Evidence ���������������������������������������������  945 20.8 The Universal Computer ≠ the Stored Program Computer ����   946 20.9 Who First Had the Idea of the Stored Program?�����������������������  947 20.9.1 Kurt Gödel as the Founding Father of the Stored Program �����  950 20.9.2 Zuse’s Approaches for the Stored Program�������������������������������   951 20.9.3 Mechanical Components Brake Electronics �����������������������������   952 20.9.4 The Breakthrough of the Stored Program Thanks to von Neumann���������������������������������������������������������������������������������������   953 20.9.5 Turing, von Neumann, or Eckert/Mauchly? �����������������������������   953 20.9.6 Conclusions�����������������������������������������������������������������������������������   955 20.10 Who First Introduced Automatic Programming? ���������������������  956 20.11 Who Created the First Compiler? �����������������������������������������������   957 20.12 The Early Days of Programming�������������������������������������������������  959 20.13 Open Questions Regarding the History of Computer Science ������������������������������������������������������������������   960 20.14 Where Did the Construction Knowledge Come From?�������������   961 20.14.1 Academic Lectures�����������������������������������������������������������������������  962 20.14.2 Publications ���������������������������������������������������������������������������������  963 20.14.3 The Construction of the First Computing Machines�����������������  965 20.14.4 Introduction to Computer Technology and Evaluation of the Situation (Overview)���������������������������������������������������������  966 20.15 Early Relay and Vacuum Tube Computers and Their Successors�������������������������������������������������������������������������������������   967 20.16 Motivations for the Building of Computers�������������������������������  969 20.17 Who Was Instrumental in the Development of the Computer? �������������������������������������������������������������������������   973 20.17.1 Charles Babbage���������������������������������������������������������������������������   973

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20.17.2 Alan Turing�����������������������������������������������������������������������������������   974 20.17.3 John von Neumann�����������������������������������������������������������������������   974 20.17.4 Konrad Zuse ���������������������������������������������������������������������������������   975 20.17.5 Other Possible Inventors�������������������������������������������������������������   975 20.17.6 Who Invented Which Computing Machine?�����������������������������  976 20.18 Where Is the Cradle of the Computer?���������������������������������������   977 20.19 What Point in Time Is Decisive for an Invention?���������������������   979 20.20 Who Won the Race Against Time? ��������������������������������������������   980 20.20.1 The Race to Develop the First Stored Program Computer �������  982 20.21 Which Was the First Stored Program Computer?���������������������  985 20.22 Who Influenced the Development of Computers and How Much? ��������������������������������������������������������������������������   989 20.22.1 The Institute for Advanced Study: A Magnet for Visiting Scholars��������������������������������������������������������������������   990 20.22.2 Who Set the Tone? �����������������������������������������������������������������������  993 20.22.3 Was Ada Lovelace Actually the First Programmer? �����������������  1002 20.22.4 The Opinions in Regard to Turing’s Influence on Computer Construction Differ Considerably�����������������������������  1003 20.23 Which Were the Most Influential Computers?��������������������������� 1009 20.23.1 Model Computer Designs�������������������������������������������������������������  1010 20.24 Which Computers Were the First Commercially Available? ���  1010 20.24.1 Ferranti Mark 1 and Univac 1�������������������������������������������������������� 1011 20.24.2 Leo 1 and IBM 701/650������������������������������������������������������������������ 1011 20.24.3 Zuse Z4�������������������������������������������������������������������������������������������� 1011 20.25 Where Did the Money Come from?���������������������������������������������� 1011 20.26 Setbacks with the Construction of Computers �������������������������  1014 20.27 Machines with Print Mechanism ������������������������������������������������ 1015 20.28 Chronology: Early Electromechanical and Electronic Digital Computers�������������������������������������������������������������������������  1019 20.29 Early Transistor Computers���������������������������������������������������������  1020 20.30 For Centuries Only a Limited Computational Need ������������������ 1021 20.31 Pioneers as ACM and IEEE Award Winners�������������������������������  1022 20.32 Relevant Anniversaries in the History of Computing���������������  1024 21 Computer Development in Germany�������������������������������������������  1025 21.1 Preliminary Remarks�������������������������������������������������������������������  1025 21.2 Plankalkül�������������������������������������������������������������������������������������  1026 21.3 Early German Relay and Vacuum Tube Computers �����������������  1026 21.3.1 The Computer Pioneer Konrad Zuse�������������������������������������������  1026 21.3.2 Zuse’s Process Computer�������������������������������������������������������������  1029 21.3.3 Zuse’s Logistics Machine and Chess�������������������������������������������  1030 21.3.4 Acquisition of the Zuse KG by BBC Mannheim with the Loss of Millions������������������������������������������������������������������������������ 1031 21.3.5 Other German Relay and Vacuum Tube Computers������������������ 1032 21.4 Early German Transistor Computers �����������������������������������������  1033

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21.5 The First German Digital Computers (Overview) ���������������������  1034 21.5.1 Telefunken GmbH, Berlin: Computer Manufacture in Konstanz�����������������������������������������������������������������������������������  1035 21.5.2 The Analog and Hybrid Computers of Dornier (Friedrichshafen) �������������������������������������������������������������������������  1036 2 2 Computer Development in the UK �����������������������������������������������  1037 22.1 Preliminary Remarks�������������������������������������������������������������������  1037 22.2 The Enigma�����������������������������������������������������������������������������������  1038 22.2.1 The Enigma, a True Puzzle ���������������������������������������������������������  1038 22.3 The Polish Bomba and the Turing-Welchman Bombe �������������  1042 22.3.1 The Polish Bomba�������������������������������������������������������������������������  1042 22.3.2 The Electromechanical Bombe���������������������������������������������������  1042 22.4 The Colossus���������������������������������������������������������������������������������  1045 22.4.1 The Lorenz SZ�������������������������������������������������������������������������������  1045 22.4.2 The Electronic Jumbo�������������������������������������������������������������������  1045 22.4.3 Did Turing Collaborate on the Colossus?����������������������������������� 1049 22.4.4 Did Churchill Command the Destruction of All Colossus Computers?������������������������������������������������������������������� 1049 22.5 The Tunny�������������������������������������������������������������������������������������  1050 22.6 Enigma and the Bombe, Lorenz and the Colossus�������������������� 1051 22.6.1 Selected Cryptographic Machines ���������������������������������������������� 1051 22.6.2 Bombes and Colossi���������������������������������������������������������������������  1052 22.7 Bletchley Park�������������������������������������������������������������������������������  1054 22.7.1 Code Names�����������������������������������������������������������������������������������  1054 22.7.2 Technical Terms���������������������������������������������������������������������������  1055 22.7.3 The Huts ���������������������������������������������������������������������������������������  1056 22.7.4 Regarding the History of Bletchley Park �����������������������������������  1057 22.8 Birkbeck College of the University of London���������������������������  1059 22.9 Imperial College, London ����������������������������������������������������������� 1060 22.10 The Harwell Computer����������������������������������������������������������������� 1060 22.10.1 The Harwell Computer: The Oldest Functional Relay Computer��������������������������������������������������������������������������������������� 1060 22.11 The First British Digital Computers (Overview) �����������������������  1062 23 Computer Development in Switzerland �������������������������������������  1065 23.1 Zuse’s Relay Computer and the ETH Zurich �����������������������������  1065 23.1.1 When Did the ETH Zurich Learn About the Zuse Machine?�����  1065 23.1.2 How Did the ETH Zurich Learn About the Zuse Machine?������� 1066 23.1.3 Zuse and Die ETH Zurich�������������������������������������������������������������  1070 23.1.4 Why Did Zuse Prepare to Flee to Switzerland in 1949?�������������� 1071 23.1.5 What Did the Z4 Cost? �����������������������������������������������������������������  1077 23.1.6 Who Paid for the Z4? �������������������������������������������������������������������  1079 23.1.7 How Was the Conditional Jump Implemented with the Z4?��� 1080 23.1.8 How Was the Z4 Utilized? ����������������������������������������������������������� 1080

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23.1.9 The Bark and the Z4���������������������������������������������������������������������  1083 23.2 Difficulties with the Construction of the First Swiss Computer���������������������������������������������������������������������������������������  1085 23.2.1 The Grueling Construction of the First Swiss Electronic Computer���������������������������������������������������������������������������������������  1085 23.2.2 Purchase or Self-Construction?��������������������������������������������������� 1088 23.2.3 Five Years for Construction Instead of Three����������������������������� 1090 23.2.4 Vacuum Tube Computer Instead of Relay Computer��������������� 1090 23.2.5 Vexation with the Magnetic Drum ���������������������������������������������  1091 23.2.6 The Chief Engineer Jumps Ship��������������������������������������������������  1093 23.2.7 Did IBM Want to Hinder the Ermeth?�����������������������������������������  1095 23.2.8 Conflicts with Remington Rand over Breach of Contract���������  1095 23.2.9 Negotiations with Industry��������������������������������������������������������� 1096 23.2.10 The Project Succeeds with the Support of the School Board President ��������������������������������������������������������������������������� 1096 23.2.11 Problems Abroad Also����������������������������������������������������������������� 1098 23.3 Why Did the Efforts to Establish a Swiss Computer Industry in the 1950s Fail?����������������������������������������������������������� 1098 23.3.1 Reproaches Against Swiss Industry������������������������������������������� 1099 23.3.2 Interest on the Part of Industry���������������������������������������������������  1100 23.3.3 Why Only the Drum Memory?������������������������������������������������������ 1101 23.3.4 Hasler’s Market Prospects������������������������������������������������������������ 1102 23.3.5 Did the Chief Engineer Prevent the Marketing of the Ermeth?�������������������������������������������������������������������������������� 1102 23.3.6 Consequences�������������������������������������������������������������������������������  1104 23.4 Construction of Magnetic Drum Memories in Zurich���������������  1106 23.4.1 The Z4: Experimental Drum �������������������������������������������������������  1106 23.4.2 The Ermeth: Experimental Drum������������������������������������������������ 1107 23.4.3 The Ermeth: Large Drum�������������������������������������������������������������  1108 23.5 The Ermeth’s Successor���������������������������������������������������������������  1109 23.5.1 In 1964, the ETH Zurich Was Without a Large-Scale Computer for Several Months�����������������������������������������������������  1109 23.5.2 The Purchase of the Large-Scale Computer Led to the Acquisition of Desktop Computing Machines���������������������������  1109 23.6 The Lilith, Ceres, Smaky, and Gigabooster ��������������������������������  1111 23.6.1 Lilith and Ceres������������������������������������������������������������������������������  1111 23.6.2 The Music and the Gigabooster����������������������������������������������������  1113 23.6.3 The Smaky��������������������������������������������������������������������������������������  1115 23.7 Zuse’s M9 Calculating Punch and Remington Rand�����������������  1116 23.7.1 The M9: The Journeyman Work ��������������������������������������������������  1121 23.8 The Cora Transistor Computer of Contraves������������������������������ 1128 23.9 Heinz Rutishauser: A Forgotten Pioneer������������������������������������ 1130 23.9.1 Rutishauser and the Universal Turing Machine������������������������  1132 23.9.2 A Fundamental Reference Work for Computer Construction����������������������������������������������������������������������������������  1133

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23.10 Who Was Involved in the Decisions for the Zuse Z4 and the Ermeth?���������������������������������������������������������������������������� 1134 23.11 Kommission zur Entwicklung von Rechengeräten in der Schweiz ������������������������������������������������������������������������������������������  1135 23.12 Who Took Part in the Meetings Concerning the Z4 and When? ������������������������������������������������������������������������������������ 1136 23.13 Who Took Part in the Meetings for the Ermeth?������������������������ 1138 2 4 Documents Relevant to the Z4 and Ermeth �������������������������������� 1139 24.1 Preliminary Remarks�������������������������������������������������������������������� 1139 24.2 Basic Contract for the Z4 Between Zuse and the ETH (1949)������������������������������������������������������������������������  1141 24.3 Supplementary Agreement for the Z4 Between Zuse and the ETH (1949)������������������������������������������������������������������������  1151 24.4 Contract Extension of the ETH for the Z4 (1950)������������������������  1155 24.5 Test Report of the ETH for the Z4 (1949)��������������������������������������  1157 24.6 Acceptance Certificate for the Z4 (1950)�������������������������������������� 1165 24.7 Final Bill of the Zuse KG for the Z4 (1950) ���������������������������������� 1167 24.8 Agreement for the Return of the Z4 to the Zuse KG (1955)�������  1168 24.9 Project Proposal for the Building of the Ermeth (1953) ������������ 1170 24.10 License Agreement for the Manufacture of the Magnetic Drum Memory (1955)���������������������������������������������������  1184 24.11 Research Contract Between Hasler und Paillard and the ETH (1957)�����������������������������������������������������������������������  1189 2 5 The Global Evolution of Computer Technology�������������������������� 1193 25.1 Preliminary Remarks�������������������������������������������������������������������� 1193 25.2 Argentina���������������������������������������������������������������������������������������� 1195 25.3 Australia ���������������������������������������������������������������������������������������� 1195 25.4 Austria�������������������������������������������������������������������������������������������� 1196 25.4.1 The Tauschek System�������������������������������������������������������������������� 1196 25.4.2 The Mailüfterl�������������������������������������������������������������������������������� 1196 25.5 Belgium������������������������������������������������������������������������������������������ 1197 25.6 Canada�������������������������������������������������������������������������������������������� 1198 25.7 China���������������������������������������������������������������������������������������������� 1199 25.8 France �������������������������������������������������������������������������������������������� 1199 25.8.1 Couffignal’s Failure ���������������������������������������������������������������������� 1199 25.8.2 SEA�������������������������������������������������������������������������������������������������  1200 25.8.3 Bull with Gamma �������������������������������������������������������������������������  1200 25.9 India�����������������������������������������������������������������������������������������������  1200 25.10 Israel ���������������������������������������������������������������������������������������������� 1201 25.11 Italy ������������������������������������������������������������������������������������������������ 1201 25.11.1 The UNESCO International Computation Center ���������������������� 1201 25.11.2 Milan and Pisa ������������������������������������������������������������������������������ 1203 25.12 Japan ���������������������������������������������������������������������������������������������� 1203

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25.13 Mexico�������������������������������������������������������������������������������������������� 1203 25.14 The Netherlands���������������������������������������������������������������������������  1204 25.15 Russia���������������������������������������������������������������������������������������������  1204 25.16 Spain ���������������������������������������������������������������������������������������������  1206 25.16.1 The Analog Calculating Machine of Torres Quevedo���������������� 1207 25.16.2 The Chess Automatons of Torres Quevedo �������������������������������� 1207 25.16.3 The Analytical Engine of Torres Quevedo���������������������������������� 1210 25.16.4 Formal Language ��������������������������������������������������������������������������  1212 25.17 Sweden ������������������������������������������������������������������������������������������  1213 25.17.1 The Bark Relay Computer ������������������������������������������������������������  1213 25.17.2 Who Operated the Bark? �������������������������������������������������������������� 1214 25.17.3 The Besk Electronic Computer ����������������������������������������������������  1215 25.18 USA�������������������������������������������������������������������������������������������������� 1216 25.18.1 The Patent and Copyright Dispute����������������������������������������������  1217 25.18.2 The First American Digital Computers (Overview)��������������������  1217 25.18.3 Eckert and Mauchly Were of Swiss Descent������������������������������� 1218 Glossary of the History of Technology������������������������������������������������������  1221 German-English���������������������������������������������������������������������������� 1222 Glossary of the History of Technology������������������������������������������������������ 1382 English-German���������������������������������������������������������������������������� 1382 Bibliography for the History of Science and Technology �������������������� 1547 Index of persons, places and subjects������������������������������������������������������ 2015

Chapter 1

Introduction

Abstract  The chapter “Introduction” describes the goal of the book and the period of time covered by the presentations. It conveys an overview of new and exciting findings of objects (above all calculating machines) and documents and provides insight into their origins. The book focuses on the history predating the emergence of analog and digital computer technology and the early history of their development, automaton construction (automaton figures and musical automatons), and selected scientific instruments from the areas of astronomy, surveying, and measurement of time. Special attention is given to the non-English-speaking countries. It is not the intention of the book to present the entire history without interruption. Instead, the emphasis is on the highlights and the most significant achievements. Overviews in the form of tables facilitate the study of the material. Lines of development depict coherent relationships. Instead of a treatment of the most recent era in computer science, the subjects of digital transformation and artificial intelligence are discussed at length. Numerous step-by-step operating instructions for analog and digital calculating devices round out the volume. Keywords  Analog technology · Artificial intelligence · Automaton construction · Automaton figures · Calculating technology · Digital technology · Digital transformation · Historical calculating aid findings · Historical robots · Musical automatons · Scientific instruments

1.1  Objective This compilation presents a broad-spectrum of outstanding masterworks from the history of computer technology and related fields. The objective is not to present a complete and comprehensive discourse on the development of computer science, but as well as possible to convey a general understanding of new knowledge. The milestones should be embedded in a global relationship,

© Springer Nature Switzerland AG 2020 H. Bruderer, Milestones in Analog and Digital Computing, https://doi.org/10.1007/978-3-030-40974-6_1

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1 Introduction

enabling their proper allocation and emphasizing their significance. The focus is on fascinating findings of rare analog and digital calculating devices along with important text documents, drawings, and images. Particularly the surprising findings were decisive for the choice of topics. There are no geographical limitations in this work; pioneering achievements are not bound to any borders. Nevertheless, the book attempts to especially consider the non-­English-­speaking region, which has been largely neglected in publications in the English language. Overall views are well suited as an introduction. They serve to convey an overview but owing to their nature only describe a limited part of the history. A weighting of the content is therefore essential. Some factual circumstances in this book are examined from different perspectives, inevitably resulting in repetitions. In addition, motives for the machine construction are interwoven. Furthermore, the influence of pioneers on further developments is also discussed. Lines of development are elaborated to show the historical evolution. This of course includes not only successes but also setbacks. Thus, disillusionment often follows exaltation. The data concerning the useful life of calculating aids reveal that their sustainability falls off rapidly in the course of time: a calculating board lasts longer than a cell phone. This work strives to achieve the greatest possible usefulness, for example, with numerous alphabetically or chronologically ordered lists, overview tables, a comprehensive bibliography, and an extensive index of persons, places, and subjects, so that the book can serve as a reference work. The present book attempts to bridge the gap between the analog and the digital computing device worlds and to place the counting boards, slide rules, drawing and measuring instruments, calculating tables, mechanical calculating machines, differential analyzers, and punched card equipment, along with analog and (early) digital electronic calculating machines. This compilation is intended to bring readers up to date with the most recent state of research. For a deeper examination of the individual areas, the reader is referred to the additional literature. Various anthologies exist with regard to mechanical calculating devices from Germany and the USA. However, comparable listings from Switzerland (and Austria) are not available. An attempt has therefore been made to compile a list of Swiss brands. Perhaps it will be possible to arouse enthusiasm on the part of laypersons and specialists for the preservation, or even the collection, of the technical heritage, such as calculating aids and the related instruction manuals, and encourage interest in dealing with these ingenious and astounding constructions. Maybe you should occasionally take the time to look for historically valuable objects in your attic or in the basement.

1.3  Period of Time

3

1.2  Target Groups This book addresses all those who would like to learn more about the history of computer technology. It is intended for laypersons as well as specialists and for all enthusiasts. The target groups include, for example, universities, universities of applied sciences, pedagogical colleges, secondary schools, vocational colleges, libraries, archives, museums, collectors of historical calculating devices, computer specialists, mathematicians, engineers, historians, archaeologists, and art historians.

1.3  Period of Time The book deals with global events from the prehistory and early history of computer science. It spans the time from the beginnings of computer technology in antiquity, through the middle ages, to modern times. A particularly masterful achievement was the more than 2000-year-old Antikythera mechanism. The emphasis is on slide rules, mechanical calculating machines, relay-based and vacuum tube computers, as well as punched card equipment. The period of time therefore ranges predominantly from the seventeenth century to the second half of the twentieth century. A prominent turning point is the replacement of mechanical calculating aids by digital electronic computers in the 1970s. This work primarily covers the pioneer era. It must be noted here that archives have a period of protection of several decades, so that as a rule the most recent documentation is not available. The most recent period is taken into account by fundamental considerations about the history of science and technology, reflections on the preservation of the technical heritage and observations regarding the digital transformation, artificial intelligence, machine learning, robotics, and drones. At the same time, the two technical glossaries and the bibliography reflect the developments up to the most recent times. For a number of reasons, an uninterrupted account of the history of computing up to today in the form presented here is not sensible: • Above all, this work would like to report on new, unknown aspects not treated in publications to date. Such events are of course rare and neither plannable nor predictable. • Since the end of twentieth century, the number of devices, programming languages, programs, technologies, processes, occurrences, achievements, companies, etc. has increased enormously, so that these can no longer be adequately described with the same approach. This would require a work of several volumes, which no publishing house would be willing to do and it would hardly sell.

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• Numerous newer monographs about the recent history of computer science (especially from the USA) already exist. It does not appear to be appropriate to repeat the contents of such publications. • A work about the newest, very short-lived time is already obsolete before publishing. • Compared with historical mechanical calculating devices, only relatively little (suitable) pictorial material exists for the new electronic digital computers. The situation is even more sparing, for example, with programming languages. The decorative calculating machines were often single objects, whereas today’s smartphones are mass merchandise. • The operation and demonstration of mysterious ancient calculating aids bring enormous pleasure and pose a challenge, because only a few specialists can operate them.

1.4  What Is Computing Technology? Computer technology is understood to mean the field of expertise concerned with computing aids. Numerous calculating aids exist: the fingers, the hands, pebble stones, tallying sticks, notched bones, shells, knotted cords, calculating boards, calculating tables, counting cloths, tokens, arithmetic textbooks, pens, stylus, paper, chalk, slate tablets, (linear) slide rules, circular slide rules, cylindrical slide rules, pocket watch slide rules, sliding bar calculators, punched card equipment, mechanical, electrical and electronic calculating machines, cell phones, quantum computers, etc. The subject of computer technology accordingly relates to technology and mathematics, informatics, mechanical and electrical engineering, physics and particularly clockmaking, goldsmithing, precision mechanics, automatization, and microelectronics. In addition to the equipment itself, computing technology is also understood as the method of manual and mechanical calculation, both oral and in writing. The present treatment is concerned with mechanical calculating and electronic computing technology.

1.5  Spectacular Device and Document Findings In the course of inquiries over the past 10 years (since 2009), rare historic calculating aids – analog (continuous) and digital (discrete) calculating devices – as well as previously unknown documents, drawings, and photographs came to light. The findings were made in the Swiss Cantons Aargau (AG), BaselStadt (BS), Bern (BE), St Gallen (SG), Vaud (VD), Valais (VS), and Zurich (ZH), as well as in France (Strasbourg) and in England (Birmingham).

1.5  Spectacular Device and Document Findings

5

Structure of the Descriptions The different findings (see box) are described as follows: • • • • •

Year of finding Name of the device (analog or digital computer, year of construction) Brief description (occurrence) Manufacturer Location (museum). Newly Found Historic Calculating Devices 2010 Zuse M9 (digital calculator, manufactured about 1953) Program-controlled calculating punch (only surviving specimen in the world) First mass-produced computer of the German computer inventor Konrad Zuse (Zuse KG, Neukirchen) Museum für Kommunikation, Bern 2011 Cora (digital computer, manufactured in 1963) First Swiss transistor computer (Cora 1, only surviving specimen in the world) First electronic digital computer of Contraves AG, Zurich Ecole polytechnique fédérale de Lausanne (EPFL), Bolo Museum (found by EPFL) 2013 24 m Loga cylindrical slide rule (analog calculator, year of manufacture unknown) World’s largest and most precise commercial cylindrical slide rule, with a scale length of 24 m (9 surviving specimens known until now) Loga-Calculator, Zurich ETH Zurich, Department of Computer Science 24 m Loga cylindrical slide rule (analog calculator, year of manufacture unknown) World’s largest and most precise commercial cylindrical slide rule, with a scale length of 24 m (9 surviving specimens known until now) Loga-Calculator, Zurich UBS Basel, corporate archives (UBS = major Swiss bank) 2014 Schwilgué keyboard adding machine (digital calculator, manufactured in 1851, patented in 1844) Best-preserved specimen of the world’s oldest known keyboard adding machine (continued)

6

1 Introduction

Jean-Baptiste Schwilgué, creator of the (currently) last astronomical clock of the Strasbourg cathedral ETH Zurich, Collection of astronomical instruments The Thomas arithmometer (digital calculator, manufactured about 1863) World’s first successful commercially produced calculating device (numerous surviving specimens) Charles Xavier Thomas (Colmar), insurance broker in Paris ETH Zurich, Collection of astronomical instruments Volksrechner (people’s calculator) (digital calculator, manufactured in 1930) Rare set wheel stylus adding machine with (indirect) subtraction (9 surviving specimens known until now) Manufacturer unknown (presumably Maschinen- und Werkzeugfabrik Paul Brüning, Berlin) Flea market in Rorschach SG, Switzerland (site of discovery) Schwilgué keyboard adding machine (digital calculator, manufactured in 1846) World’s oldest surviving keyboard adding machine (no longer functional) together with two earlier models Jean-Baptiste Schwilgué, creator of the (currently) last astronomical clock of the Strasbourg cathedral Musée historique, Strasbourg Schwilgué counting registers (digital counter, year of manufacture unknown, patented 1844) Several specimens Jean-Baptiste Schwilgué, creator of the (currently) last astronomical clock of the Strasbourg cathedral Musée historique, Strasbourg Summus circular adding machine (analog calculator, manufactured about 1906) Very rare circular cogged wheel adder (only a few surviving specimens) Max Eckelmann, Dresden Schreibmaschinenmuseum Beck, Pfäffikon ZH, Switzerland Schwilgué “process computer” (digital calculator, manufactured in the 1830s) World’s first (mechanical) “process computer” (numerical control of a gear cutting machine via a paper strip (only known specimen) Jean-Baptiste Schwilgué, creator of the (currently) last astronomical clock of the Strasbourg cathedral (continued)

1.5  Spectacular Device and Document Findings

7

Musée historique, Strasbourg (Finding: December 2014, determination as process computer: January 2015 24 m Loga cylindrical slide rule (analog calculator, year of manufacture unknown) World’s largest and most precise commercial cylindrical slide rule, with a scale length of 24 m (9 surviving specimens known until now) Loga-Calculator, Zurich Private collection, Windisch AG, Switzerland 2015 Multiple Curta (digital calculator, patented 1958) World’s smallest mechanical parallel computer (found in design drawings and patent documentation) Curt Herzstark, Contina AG, Mauren, Liechtenstein Schreibmaschinenmuseum Beck, Pfäffikon ZH, Switzerland 2016 Grunder’s calculating device (digital calculator, manufactured in 1945) Mechanical adder made of wood (one of a kind machine, no longer functional) Johannes Gottfried Grunder, Brienz BE, Switzerland Museum für Kommunikation, Bern 24 m Loga cylindrical slide rule (analog calculator, year of manufacture unknown) World’s largest and most precise commercial cylindrical slide rule, with a scale length of 24 m (9 surviving specimens known until now) Loga-Calculator, Zurich Komturei Tobel TG (Switzerland) 2017 Weber’s circular slide rule (analog calculator, year of manufacture unknown, around 1900) Very rare three-dimensional logarithmic circular slide rule (only surviving specimen) Georg Wilhelm Weber, Zurich ETH Library, Zurich Twelvefold Curta (digital calculator, manufactured in 1953) World’s smallest mechanical parallel calculator (matrix calculator) James Christie Robb, University of Birmingham, UK University of Birmingham, Department of Chemistry (device lost) (continued)

8

1 Introduction

2018 Millionaire: Replica of Roberto Guatelli (hybrid calculator, partial product multiplying machine) Direct multiplier (only known specimen) Roberto Guatelli, New York Carnegie Mellon University, Pittsburgh, Pennsylvania 2019 Replicas of Roberto Guatelli (calculating machines of Pascal, Leibniz, Webb, and Pallweber Mechanical calculating machines (only known specimens) Roberto Guatelli, New York Carnegie Mellon University, Pittsburgh, Pennsylvania 2020 24 m Loga cylindrical slide rule (analog calculator, year of manufacture unknown) World’s largest and most precise commercial cylindrical slide rule, with a scale length of 24 m (9 surviving specimens known until now) Loga-Calculator, Zurich Private collection, Bremgarten BE, Switzerland The Thomas arithmometer (digital calculator, manufactured about 1863) World’s first successful commercially produced calculating device (numerous surviving specimens) Charles Xavier Thomas (Colmar), insurance broker in Paris Schulmuseum Bern, Köniz BE Remarks The abbreviations ETH and ETHZ stand for the Eidgenössische Technische Hochschule and the Eidgenössische Technische Hochschule (Zürich), respectively. The English name is occasionally given as the Swiss Federal Institute of Technology. EPFL stands for Ecole polytechnique fédérale de Lausanne, with the German abbreviation ETHL.

Documents • In paper form (contracts, letters, annual reports, test reports, minutes, price lists, invoices, advertising, project descriptions, decrees, patent documentation, etc.) for the following devices: Cora, Curta, Ermeth, Loga calculator, Madas, Millionaire, the Thomas arithmometer, Zuse M9 (=Z9), Zuse Z4, Schwilgué “process computer,” and Multiple Curta • Drawings and photos for the following machines: Ermeth, Zuse M9, and the Thomas arithmometer, as well as the Schwilgué gear cutter and Multiple Curta.

1.6  Most Frequently Asked Questions Regarding Unknown Calculating Devices

9

In the spring of 2020, the ETH Zurich University archives received a donation from a private source (Hs 1517). The dossier (with records of calculations that were carried out by the Institut für Flugzeugstatik und Flugzeugbau for the Swiss P-16 jet aircraft on the Zuse Z4 computer) contained a typewritten copy of the instruction manual for the Z4, which had been missing for many years. The operating instructions, written in 1952 at the Institute for Applied Mathematics and labelled as No. 19, explain on 16 pages the organization of the machine, the commands and their effects, the programming and forbidden sequences of instructions and their remedies. In addition to previously unknown contracts between Zuse KG and the ETH Zurich, minutes concerning the escape of Curt Herzstark from Sömmerda (1945) and a letter of the Swiss School Board (now ETH Board) President to the border authorities (1949) with the request to allow Konrad Zuse to flee to Switzerland came to light. Illuminating are also reports about the Thomas arithmometer in the Bulletin de la société d’encouragement pour l’industrie nationale. As the catalog Great exhibition of the works of industry of all nations documents, the machine of Thomas and a copy of the Schwilgué adding machine by Schilt were exhibited in 1851 at the first world exhibition at the Crystal Palace in London. The most important sites of the findings were Zurich (ETH Library, University archives, Collection of astronomical instruments), Department of Computer Science, Schweizerisches Sozialarchiv), Pfäffikon ZH (Schreibmaschinen­ museum Beck), Winterthur ZH (Swiss Science Center Technorama), Bern (Museum für Kommunikation, with depot in Schwarzenburg BE), Köniz BE (Historisches Archiv und Bibliothek of the Post, Telephone and Telegraph (PTT), Dietfurt SG (site of the former spinning factory and weaving mill), Basel (UBS Historisches Archiv und Museum, along with the Schweizerisches Wirtschaftsarchiv), in addition to several locations in Liechtenstein, Feldkirch (firsthand witnesses of the former Contina AG), Strasbourg (depot of the Musée historique), and the University of Birmingham. Initial results were presented at the international conferences “Making the history of computing relevant” and “International communities of invention and innovation” of the International Federation for Information Processing (IFIP) at the London Science Museum (June 2013) and at New York University (May 2016). For more detailed information, see, e.g., the conference proceedings issued by Arthur Tatnall (University of Melbourne). The findings are described in the corresponding chapters.

1.6  M  ost Frequently Asked Questions Regarding Unknown Calculating Devices When unknown calculating devices come to light, the following questions arise: • What kind of device is it (classification)? • Where does the device come from (origin)?

10

• • • • • • • •

1 Introduction

Who invented the device (invention)? Who manufactured the device (manufacturer)? How old is the device (age)? How does one operate the device (operation)? How does the device function (technology)? Who used the device (user)? For what purpose was the device used (purpose of use)? How and when was the device found (discovery)?

For the mysterious Antikythera mechanism, for example, the answers would be as below: • • • • • • • •

Astronomical calculating machine Unknown (possibly from the island of Rhodes) Unknown (possibly Poseidonios) More than 2000 years (3rd to 1st century BC) By rotating a knob or a crank Extremely complex gear train with several dial plates and pointers Presumably used for teaching purposes Chance discovery from a shipwreck with the help of sponge divers (1901).

If a brand name is known (and also the model) reference works, such as the electronic calculator lexicon (http://www.rechnerlexikon.de), often help to determine the type of design and the origin. On the other hand, determining the age is often difficult. Occasionally, operating instructions can be found in the Internet. Otherwise, only trying out operating the device remains. In order to understand the principle of operation of the machines, profound technical expertise is usually required, and it may be necessary to dismantle the devices. In some cases, we even need to rebuild the machine. Findings cannot be planned. Often they are fortuitous. Nevertheless, one can systematically research books, journals, archives, and museums. With enough luck, findings are possible at flea markets, in antique trade, at auctions, in waste disposal, at collectors’ meetings (possibility of trading), in private collections, and in museums and their depots. In the Internet as well, devices are repeatedly offered (beware of fraudulent offers!). The rediscovery of devices and the building up of a collection with rare or precious objects demand many years of research.

1.7  Instructions for Operating Historic Calculating Aids Devices are often carelessly destroyed. Operating instructions and other documentation land mostly in recovered paper. Unfortunately there is hardly any documentation for the calculating aids in the collections of these objects. Because information about the operation is altogether scarce, brief comprehensible step-by-step instructions were prepared for important analog and digital calculating aids by trying out operating these:

1.7  Instructions for Operating Historic Calculating Aids

11

Analog Calculating Aids • Slide rule (any desired slide rule) • Circular slide rule (Loga disc) • Cylindrical slide rule (Loga drum) • Sector (general) • Circular cogged wheel adder (Summus). Digital Calculating Aids • Bead frame with manual tens carry (Chinese abacus) For the operation of Chinese, Japanese, and Russian bead frames and the use of school abaci and children’s counting frames derived from these three identical fundamental rules apply • Calculating tables (counting boards) The rules for bead frames are mostly applicable to calculating tables and counting cloths as well • Napier’s rods (Napier’s bones) • Slide bar adders with semiautomatic tens carry (Trebla) • One-function calculators (single digit adder of Schwilgué) • One-function calculators (Simex of Arvai) • Two-function calculator (“cash register” of Brüning) • Three-function calculators (Stima slide bar-type machine) • Four-function calculators (stepped drum machines the Thomas arithmometer, Madas, and Curta) • Four-function calculators (pinwheel machines of Odhner and Brunsviga) • Direct multiplying machine (Millionaire direct multiplier). The step-by-step instructions in this book can be used for the following calculating devices (source; arithmetic operations): • • • • • • • • • • • •

Chinese abacus (China; addition, subtraction, multiplication, division) Russian abacus and school abacus Napier’s rods (Scotland; multiplication, division) Calculating table Sector (Italy; addition, subtraction, multiplication, division) Loga circular slide rule of Daemen-Schmid (Switzerland; multiplication, division) Loga cylindrical slide rule of Daemen-Schmid (Switzerland; multiplication, division) Schwilgué keyboard adding machine (France; addition) The Thomas arithmometer (France; addition, subtraction, multiplication, division) Trebla slide bar adder (with crook tens carry) of Steinmann (Switzerland; addition, subtraction) Three-function calculator (with automatic tens carry) Stima of Steinmann (Switzerland; addition, subtraction, multiplication) Set wheel stylus machine with the name Volksrechner (people’s calculator) of Rutishauser and Brüning (Switzerland and Germany; addition and subtraction)

12

1 Introduction

• Simex desk calculating machine (Switzerland; addition) • Summus circular adding machine (Germany; addition) • Curta pocket calculating machine of Contina (Liechtenstein; addition, subtraction, multiplication, division) • Madas stepped drum machine of Egli (Switzerland; addition, subtraction, multiplication, division) • Pinwheel mechanical machine of Odhner (Sweden; addition, subtraction, multiplication, division) • Pinwheel mechanical machine of Brunsviga (Germany; addition, subtraction, multiplication, division) • Millionaire direct multiplying machine of Egli (Switzerland; addition, subtraction, multiplication, division). Remarks Contrary to French and Italian language use, in Germany and Great Britain, the bead frame is mostly referred to as abakus and abacus, respectively. See also Sect. 2.25. The one-, two-, three-, and four-function calculators feature automatic tens carry. For the examples given here, the subtraction is carried out partly with and partly without complements (complementary numbers) – i.e., as indirect and direct subtraction. Multiplication is always carried out as repeated addition (indirect multiplication). The numbers are entered with keys, setting levers, stylus, or wheels. The instructions cover only mechanical, but not electrical (electromechanical) or electronic calculating devices. In many cases, the operating instructions describe only a fraction of the diverse range of applications. They are intended as a point of entry and serve to give an overview of the principles of operation of these devices. Perhaps they also contribute to the preservation of the calculating aids. In fact, the instructions should also motivate technical curators to set instructive machines in motion. In order to prevent damage, it is necessary to carefully operate them occasionally. With the aid of the instructions, it is probably possible to carry out a number of similar calculating aids. Here it must be said that some curators are afraid of technology. Mathematical instruments, such as pantographs, planimeters, or coordinatographs, are treated only peripherally; these are not of primary interest in this book. Logarithmic slide rules are analog tools, while mechanical calculators are digital. Mixed forms exist as well (e.g., circular adding machines with regular scales and direct multipliers). The slide bar adder has a semiautomatic tens carry (crook tens carry), while mechanical calculating devices feature automatic tens carry. The Thomas machine, the Madas, the Curta, and the Millionaire are four-­ function machines, as are also the devices Odhner and Brunsviga. They master the four basic arithmetic operations: addition, subtraction, multiplication, and division. “Adders” are capable of one or two basic arithmetic operations.

1.8  In Regard to the Origin of This Book

13

Four-function calculators are fundamentally suited for exponentiation (repeated multiplication) and in part for extracting roots. In this book, addition-subtraction machines are considered two-function machines, regardless of whether subtraction takes place directly or indirectly (with complementary numbers). The same applies for four-function machines. If we do not view complementary addition (indirect subtraction) as a true arithmetic operation, then the Curta, for example, would be a three-function machine. From the point of view of the user, though, the calculating procedure is of no interest. All basic arithmetic operations lead back to addition, and modern program-controlled computers make use of this. Multiplication is usually carried out as a repeated addition and division as a repeated subtraction.

1.8  In Regard to the Origin of This Book My investigations into the history of computer science began in 2009, prompted by the 100th birthday of Konrad Zuse. 100th Birthday of Konrad Zuse  (co-inventor of the computer – see Fig. 1.1) What were the reasons for compiling this book and how did this work come about? 2010 celebrated the 100th birthday of the German computer pioneer Konrad Zuse. The German civil engineer is regarded as the creator of the world’s first programming language, Plankalkül, and as one of the inventors of the computer (the Z3 program-controlled digital computer). One year before the anniversary, the German “c’t Magazin für Computertechnik” called attention to this event in a brief communication. At that time, I was a university lecturer in the Department of Computer Science of the ETH Zurich. I was aware that in his time, there were close ties between Zuse and the ETH. In the meantime I have retired but remain active as a historian of technology. From 1950 to 1955, Zuse’s Z4 relay machine (originally named V4, V for Versuchsgerät (experimental device)) was located in Zurich. In 1950, the ETH was the first university in Central Europe with a functioning programmable computer. At this time, though, this term was not commonly used in the German-speaking region. The founding of the Institute for Applied Mathematics (Institut für Angewandte Mathematik) (1948) at the ETH Zurich and the use of Zuse’s numerical calculating machine marked the beginning of computer science in Switzerland, ample reason for a commemorative publication. Beginning with the centennial year, this was released in four increasingly more extensive editions, the first two under the title “Konrad Zuse und die ETH Zürich” (December 2010, 25 pages and February 2011, 40 pages), followed by “Konrad Zuse und die Schweiz” (July 2011, 92 pages and 2012 in book form). The investigations showed that the German pioneer had yet another foothold in Switzerland: the Zurich Remington Rand company commissioned him

14

1 Introduction

with the development of a program-controlled punched card calculating machine (M9) and with the manufacture of more than 20 such calculating punches. This was the first mass-produced Zuse machine. Since “Rem Rand” left its mark on these developments along with the ETH, the title of the publication was accordingly changed. These efforts ultimately led to the publication of the work “Konrad Zuse und die Schweiz. Wer hat den Computer erfunden?” (Oldenbourg Verlag, Munich/De Gruyter Oldenbourg, Berlin/Boston 2012, xxvi, 224 pages). In the following, this work is referred to as the “Zuse book.”

Fig. 1.1  Konrad Zuse. This acrylic painting shows one of the most important inventors of the program-controlled digital computer. The Z3 (1941) was a programmable punched tapecontrolled relay machine that functioned on the basis of binary numbers and floating point notation. The German civil engineer also created Plankalkül, considered to be the first programming language. The Z4 (1945), which has survived to the present time, was the world’s first commercial computer. The ETH Zurich utilized the leased expanded device from 1950 to 1955. (© Ingrid Zámečniková, Bratislava 2011)

100th Birthday of Alan Turing  (co-founder of computer science  – see Fig. 1.2) In 2012, there was a wealth of events all around the world celebrating the 100th birthday of Alan Turing, arguably the most important founder of theoretical computer science. The annually conferred Turing award (“Nobel Prize”

1.8  In Regard to the Origin of This Book

15

for informatics) of the American Association for Computing Machinery (ACM), named after him, is viewed as the most important distinction in this branch of science. The author was co-organizer of the international conference “Turing under discussion” at the ETH Zurich (October 26–27, 2012). The groundbreaking merits of the British mathematician are extensively acknowledged in the Zuse book and in the present work. Turing conceived the Turing machine (mathematical model of a universal calculating machine, 1936). During the Second World War, in the English mansion of Bletchley Park (Buckinghamshire, Southern England), he contributed significantly to the deciphering of the radio messages from the German Wehrmacht (armed forces). He developed the concept of the Turing Bombe, together with Gordon Welchman, based on the Polish “Bomba.” The coded messages from the enigma were regarded for a long time as undecipherable. In order to unravel the messages of the Lorenz cipher machine (SZ 42), until 1975, the highly secret Colossus digital electronic computer was used.

Fig. 1.2  Alan Turing. The acryl painting recalls Alan Turing. In 1936, he introduced the universal Turing machine in a seminal paper. This mathematical model of a program-controlled digital computer had an endless storage tape. Together with Gordon Welchman, the British mathematician also developed a relay machine at the beginning of the Second World War, with which the secret messages of the German enigma cryptographic device could be deciphered. (© Ingrid Zámečniková, Bratislava 2011)

16

1 Introduction

New Work in Place of an Improved Version of the Zuse Book The original intention was to issue a second, completely revised and greatly expanded version of the Zuse book. Due to the unexpected results of many years of investigations, however, the decision to compile a fundamentally new work (“Meilensteine der Rechentechnik,” 2015) (Milestones in Analog and Digital Computing) increasingly emerged. When meaningful, excerpts from the Zuse book are given in updated form and, in certain cases, references are made to the earlier work. Second Edition of the Meilensteine The first edition of “Meilensteine der Rechentechnik” was very well received, so that the work had to be reprinted shortly after its appearance. The book reviews in the German- and English-speaking regions (e.g., by Thomas Sonar and Steven Deckelman) were exceptionally positive. Recent knowledge and further surprising findings led to the publication of a completely revised and significantly expanded second edition (“Meilensteine der Rechentechnik,” 2018). The two volumes can be read independently. Third Edition and English Version of the Meilensteine In view of the numerous requests from the non-German-speaking regions for the publication of an English version (Milestones in Analog and Digital Computing, 2020), the need for a translation was evident. The present work is a revised and expanded version of the second edition of the German “Meilensteine.” In addition to the correction of errors, more than 280 additional high-resolution pictures have been included. The improvements and additions are primarily concerned with the chapters “Basic principles” (in the digitization and artificial intelligence sections), “The coming of age of arithmetic” (Roman hand abacus), “Museums and their collections,” “The Antikythera mechanism,” “Slide rules” (Loga calculator), “Historical automatons,” and “Mechanical calculating aids” (“Millionaire” calculating machine), the glossaries and the bibliography, as well as the index of persons, places, and subjects. Overview of the Different Editions 2015 Meilensteine der Rechentechnik, 1st edition (1 volume, 850 pages) 2018 Meilensteine der Rechentechnik, 2nd edition (2 volumes, 1600 pages) 2020 Milestones in Analog and Digital Computing, 3rd edition (2 volumes, about 2000 pages) 2020 Meilensteine der Rechentechnik, 3rd edition (2 volumes, about 2000 pages)

1.9  In Regard to Language Explanation of Computer Names ASCC: Automatic sequence-controlled calculator. “Sequence” is the command order or workflow. “Sequence controlled” can be understood

1.9  In Regard to Language

17

as command controlled or program controlled (program-controlled automatic calculator). CPC: Card-programmed electronic calculator. “Card programmed” has the meaning punched card controlled. The program instructions were recorded on punched cards and not on program plugboards (card-programmed electronic computer). Edsac:  Electronic delay storage automatic calculator. “Delay storage” refers to a delay line, delay line memory, or mercury delay line memory. Other devices employ electrostatic Williams tubes (electronic automatic computer with mercury storage). Edvac: Electronic discrete variable computer. “Discrete” expresses a difference compared with analog machines (e.g., differential analyzers) and means digital. “Variable” doubtlessly refers to the variable memory addresses or the variable instructions and thus the versatility (universal electronic digital computer). Eniac: Electronic numerical integrator and computer: “Numerical” (discrete) refers to a digital calculator (as opposed to analog devices). Regarding “integrated,” a digital differential analyzer was planned. Eniac is, so to speak, the successor of an analog differential analyzer, also built in Philadelphia (electronic numerical calculator, electronic digital computer). PSRC: Pluggable sequence relay calculator. “Pluggable sequence” has the meaning plugboard controlled (i.e., not punched tape controlled) (plugboard-controlled relay computer). SSEC:  Selective sequence electronic calculator. “Selective” stands for optional or alternative. “Selective sequence” refers to the conditional order or the conditional commands (electronic calculator with conditional commands). It follows from the names above “calculator” (Edsac) and “computer” (Edvac) were used then in the same sense. Abbreviations This work tries to avoid the use of abbreviations. Experience indicates that abbreviations are often not understood abroad or by non-native speakers. They quickly lead to misunderstandings for example in the case of dates (12.05.  =  December 5th!). Missing first names or merely initials complicate researching especially with frequently occurring names Abbreviations of brand names are often set exclusively in capital letters. In this book, the less insistent and less promotionally oriented spelling Csirac, Edsac, Edvac, Eniac, Leo, Sage, Univac, as well as Ermeth, is used when the abbreviation is spoken in syllables (as a word). When the abbreviation is spoken letterwise, only capital letters are used: ABC, ASCC, HP, IBM, etc. The two-letter abbreviations after the Swiss place names refer to the respective canton (see Table 1.1).

18

1 Introduction

Table 1.1  Abbreviations of the Swiss cantons Swiss cantons Abbreviation AG AI AR BE BL BS FR GE GL GR JU LU NE

Full name Aargau Appenzell Innerrhoden Appenzell Ausserrhoden Bern Basel-Landschaft Basel-Stadt Fribourg Geneva Glarus Graubünden Jura Lucerne Neuchâtel

Abbreviation NW OW SG SH SO SZ TG TI UR VD VS ZG ZH

Full name Nidwalden Obwalden St Gallen Schaffhausen Solothurn Schwyz Thurgau Ticino Uri Vaud Valais Zug Zurich

Reference Style guide. English. A handbook for authors and translators in the Federal Administration, Federal Chancellery, English language service, Bern 2016, 101 pages FL stands for Principality of Liechtenstein.

1.10  In Regard to the Content The birth of program-controlled mechanical and electronic digital computers took place in Germany (Konrad Zuse), England (Charles Babbage, Alan Turing, Max Newman, Thomas Flowers, Maurice Wilkes, Frederic Williams, John Pinkerton, Andrew Booth), and in the USA (John Atanasoff, George Stibitz, Howard Aiken, Clair Lake, Presper Eckert, John Mauchly, John von Neumann). However, groundbreaking machines were also built in Ukraine (Sergey Lebedev) and Australia (Trevor Pearcey, Maston Beard). In addition, the Mailüfterl transistor computer was developed by Heinz Zemanek in Austria. The birthplaces of mechanical calculating machines are predominantly Germany (Wilhelm Schickard, Gottfried Wilhelm Leibniz, Jacob Leupold), France (Blaise Pascal, Charles Xavier Thomas, Jean-Baptiste Schwilgué), and Italy (Giovanni Poleni). Also worthy of mention is Willgodt Theophil Odhner (Sweden). Leading manufacturers also existed in Switzerland (Hans W. Egli, Ernst Jost, Albert Steinmann). The crowning achievement is the Curta, the smallest mechanical four-­ function pocket calculator of Curt Herzstark (Austria/Liechtenstein).

1.11 Priorities

19

Great Britain is the home of the slide rule (scale of Edmund Gunter, 1620; William Oughtred, (linear) slide rule and circular slide rule, about 1622). The emergence of logarithms around 1600 is attributed to John Napier (Scotland) and Jost Bürgi (Switzerland). The English mathematician Henry Briggs introduced common (base 10) logarithms (1617). Other significant inventions were the pantograph of Christoph Scheiner (Germany, 1603) and the polar planimeter of Jakob Amsler (Switzerland, 1854). Also deserving mention are the sector and the adjustable proportional dividers, associated with Galileo Galilei (Italy) and Bürgi and, finally, the electronic analog computer (e.g., Helmut Hoelzer, Germany). Herman Hollerith (punched card equipment) is also of German descent. Presper Eckert and John Mauchly (originally Mauchle) have Swiss roots.

1.11  Priorities As a rule, investigations in archives require visits in person. The archive material, often encompassing several running meters or even running kilometers, is not always processed or only inadequately organized and can only be viewed on site. The objects cannot be lent out, are normally not digitized, and are only rarely accessible via the Internet. Investigations over many months entail high expenditures of time and money (such as travel expenses). Frequently, old printed matter and rare documents may be examined only in the reading room of the respective library. In order to prevent damage, photocopies are not allowed. Journals (individual issues and volumes) are generally excluded from inter-library loan. For these reasons, one is compelled to limit such searches to the nearby and wider surrounding area and to nearby libraries and archives. Consequently, the research concentrated on the German-speaking region, in particular Germany, Austria, Switzerland, Liechtenstein, and South Tyrol, along with the nearby areas of the Alsace. Since these countries belong to the birthplaces of European computer technology, informatics, typewriter construction, and automaton engineering and boast numerous illuminating developments (Schickard calculating clock, Leibniz calculating machine, Brunsviga, Zuse Z4, Millionaire, Madas, Precisa, Curta, Loga, logarithms, proportional dividers, polar planimeter, pantograph, analog computer, Kirchenkomput (church calculator), androids of Jaquet-­Droz, Mitterhofer-type machine, Algol, etc.) and the archives of the ETH Library in Zurich constitute a source of valuable findings, countless treasures could be discovered. In any case, in-depth investigations require a prior understanding of local, regional, and national relationships. In order to determine names and addresses of still living firsthand witnesses, descendants of pioneering persons and locations of objects and connections are of utmost importance.

20

1 Introduction

The researches focus on mechanical analog and digital calculating devices (e.g., slide rules, calculating tables, mechanical calculating machines, and punched card equipment) and early digital electronic computers. Because the number of program-­controlled and stored program machines soon increased dramatically, the investigations are restricted to the respective world’s first relay and vacuum tube machines. The development of programming languages is treated only peripherally. Particular emphasis is placed on historical automatons and robots, as well as scientific instruments from the areas of astronomy, surveying, and the measurement of time.

1.12  Oral History Interviews As the numerous errors in historical reports of the short-lived daily, Sunday, and weekly press show, printed sources are not always reliable. Due to lacking documentation, many questions relating to the history of technology can no longer be answered, even though the history of computer science is still young. Passing on information orally  – in discussions with firsthand witnesses – serves to fill out some gaps in knowledge. Over the last several years, numerous personal discussions, telephone conversations, and exchange of information by letter and email took place with domestic and international firsthand witnesses. These were concerned with the following devices: • • • • • • • • •

Cora (first Swiss transistorized computer) Curta (Austrian/Liechtenstein mechanical pocket calculator) Ermeth (first Swiss vacuum tube computer) GigaBooster (Swiss high-performance computer) Lilith (Swiss computer workstation) Mailüfterl (first Austrian transistorized computer) Smaky (Swiss electronic desktop computer) Zuse M9 (German calculating punch) Zuse Z4 (first commercial German relay computer).

The names of the firsthand witnesses for the Z4, Ermeth, and M9 calculating and computing machines are listed on page 204 and for the Cora on page 81 of the Zuse book. Curta Views were exchanged with a number of persons who had firsthand experience with the tiny Curta mechanical pocket calculator, e.g., Christine Holub (domestic partner of the inventor Curt Herzstark), Franz Oehry (head of production), and Elmar Maier (development engineer). Pioneers Particularly fascinating were the contacts to Alarich Baeumler (co-developer of the M9), Friedrich Bauer (co-creator of the Perm and Algol), Corrado Böhm (drafter of a compiler), Jean-Daniel Nicoud (developer of the Smaky), Niklaus

1.13  Firsthand Accounts

21

Wirth (creator of Pascal and Lilith), and Heinz Zemanek (builder of the Mailüfterl). Colleagues and Students Eduard Stiefel, founder of the Institute for Applied Mathematics of the ETH Zurich, had an impact on an entire generation of mathematicians. I had contact to his staff (mostly former doctoral students) and students. However, very few women were in this environment. Descendants The investigations also included a consideration of the descendants of JeanBaptiste Schwilgué (Brice d’Andlau), Konrad Zuse (Horst Zuse), Heinz Billing (Dorit Gronefeld), Curt Herzstark (Curt Herzstark Jr.), and the children of three Swiss informatics pioneers of the first hour: Eduard Stiefel (Eduard Stiefel Jr.), Heinz Rutishauser (Hanna Rutishauser), and Ambros Speiser (Christian and Michel Speiser). Contact was also taken up with the American descendants of Presper Eckert and John Mauchly.

1.13  Firsthand Accounts Unfortunately it was only possible in rare cases to convince former involved persons to write firsthand accounts. These were occasionally able to supplement the sometimes one-sided and incomplete written-form sources and correct erroneous statements. The firsthand accounts described below can be accessed via the Research Collection publication platform of the ETH Zurich (­ https://www.research-collection.ethz.ch/). The (long-term valid) reference sources for the reports are listed in the “Firsthand accounts” section of the bibliography. Zuse (Z4 and M9) The informative recollections of Urs Hochstrasser regarding his experiences with the Zuse machine (“Ein Zeitzeuge berichtet über seine Erlebnisse mit der Z4”) are altogether exemplary. These are reproduced in the Zuse book (Herbert Bruderer: Konrad Zuse und die Schweiz. Wer hat den Computer erfunden?, De Gruyter Oldenbourg-Verlag, Munich 2012, pages 19–27). The foreword by Peter Läuchli (pages v–vi) and the afterword by Heinz Waldburger (pages 205–207) in the same volume are derived from the writings of directly involved persons. In order to further the oral history, a video film with former service specialists for the M9 Zuse machine was produced together with the Museum für Kommunikation in Bern (Beatrice Tobler) (in Swiss German dialect). The Zuse book includes more detailed information about this event (page 128). Furthermore, the digitized diploma thesis “Relaisrechner mit Lochstreifeneingabe und -ausgabe” (relay computer with punched card input and output) of Ernst Inauen (former service technician for the Zuse M9 calculating punch) of 1962 should be mentioned here.

22

1 Introduction

Erwin Engeler wrote a revealing report about his acquaintance with Zuse, “Meine persönliche Beziehung zu Konrad Zuse.” Curta The extensive memoirs of Elmar Maier “Ein prägender Lebensabschnitt. Rechenmaschine Curta (Patent Herzstark)” regarding the further development of the “pepper mill” and (in this book) a contribution about the naming of the Curta are impressive. Cora Instructive firsthand articles regarding the Swiss Cora transistorized computer were contributed by Ernst Hutzler, “Programmierung des Coragraphen. Rückblick auf meine Tätigkeit bei der Firma Contraves AG” (Programming the Coragraph. Recollections of my work at Contraves AG) and François Nicolet, “Bau eines Fortran-IV-Compilers für die Cora 2” (Construction of a Fortran IV compiler for the Cora 2). The results of discussions with Peter Tóth, the constructor of the Cora, are documented in the Zuse book (pages 79–83).

1.14  Approach An important principle characterizes the work: as well as possible, all information was examined with a view to correctness. This of course cannot completely eliminate errors. For the first time, the holdings of the ETH Zurich archives were systematically examined in regard to the early years of informatics in Switzerland (1947–1964). Nevertheless, even with a systematic investigation of historical objects (artifacts) and documents (text, photo, audiovisual documents) and searching through published and unpublished writings, much remains left to chance. Evaluation of the Technical Literature The efforts required in the search for relevant writings; the procuring of domestic and international books, journals, and articles; and their evaluation were exceedingly high. Many reference sources were insufficient and inexact. Preference was given to the original publications of the pioneers of these times. Self-presentations and, above all, life memoirs are as a rule less critical and often fail to mention disadvantageous experiences. The same is true of most commemorative publications. Even in firsthand works, contradictions are occasionally found. Published and unpublished articles in German, English, French, Italian, and Spanish were taken into account. Journals from the disciplines computer science/data processing, mathematics, physics (especially mechanics), electrical engineering, and surveying were (retrospectively) searched. In some cases, these can be accessed via the Internet.

1.14 Approach

23

Commemorative Publications Anniversary publications exist for the Amsler (Schaffhausen), BBC (Baden, now ABB, Zurich Oerlikon), Coradi (Zurich), Gfeller (Bern), Hasler (Bern, now Ascom, Baar ZG), Kern (Aarau), Sulzer (Winterthur ZH), Wild (Heerbrugg SG), and Zellweger (Uster ZH) companies. Search for Persons, Companies, Patents, and Documents An important element of these researches was to find firsthand witnesses (Zuse Z4, Zuse M9, Ermeth, Curta, Cora), descendants (Schwilgué, Zuse, Billing, Herzstark, Stiefel, Rutishauser, Speiser, Grunder), devices (Schwilgué machines, the Thomas arithmometers, Multiple Curta, slide rules and mechanical calculating devices from Switzerland, e.g., the Loga cylindrical slide rules, Millionaire, as well as M9, Cora, Ermeth magnetic drum memories), companies (in the Swiss Official Gazette of Commerce, Schweizerisches Handelsamtsblatt), patents (inpatent databases), papers, drawings, and photos (and therefore archives and estates). Visits to Archives The following archives were visited, for example: • • • • • • • • • • •

Archives of the Deutsches Museum, Munich Archives of the Neue Zürcher Zeitung (NZZ), Zurich Archives of the Swiss Science Center (Technorama), Winterthur ZH Historical Archives ABB, Baden Historisches Archiv und Bibliothek PTT, Köniz BE/Museum für Kommunikation, Bern King’s College archives of the University of Cambridge Schreibmaschinenmuseum Beck, Pfäffikon ZH Schweizerisches Sozialarchiv, Zurich Schweizerisches Wirtschaftsarchiv, Basel Studiensammlung Kern, Aarau University archives and Archives of contemporary history of the ETH Zurich.

Researches were also carried out at the Schweizerisches Bundesarchiv (Swiss Federal Archives, Bern), the Staatsarchive (state archives) of the cantons Zurich, St Gallen, Bern, Vaud, and Neuchâtel, the Stadtarchive (municipal archives) of Winterthur, Zurich, and St Gallen, the Gemeindearchiv (communal archive) of Brienz BE and the Liechtensteinisches Landesarchiv in Vaduz, along with the archives of the University of Zurich (Zentralbibliothek, central library), the Eisenbibliothek (Iron library) in Schlatt TG, the Sulzer Management AG (Winterthur ZH), the Bibliothek am Guisanplatz (Bern), the Musée international d’horlogerie (La Chaux-de-Fonds NE), the National Archive for the History of Computing (Manchester, UK), the National Archives (Kew, Richmond, Surrey, UK), the Royal Society of Chemistry (London), US archives (IBM Corporate Archives, IBM Corporation, Poughkeepsie, New York; Hagley Library, Wilmington, Delaware; Charles Babbage Institute, Minneapolis, Minnesota), and the Albert Einstein Archive of the Hebrew University in Jerusalem.

24

1 Introduction

Patent, Library, Archive, and Museum Databases Patents are well accessed and can be examined via global databases, e.g., with the European Patent Register (European Patent Office, Munich, https:// www.epo.org, Espacenet). However, very early patents require, e.g., perusing through national registers (e.g., the Deutsches Patent- und Markenamt (German Patent and Trade Mark Office) or the Institut national de la propriété industrielle). With regard to the library holdings, countless international, national, regional, and local catalogs, for example, the world’s largest register WorldCat (https://www.worldcat.org), the Karlsruhe virtual catalog (KVK, http://kvk. bibliothek.kit.edu) or Swissbib (https://www.swissbib.ch), is accessible on the Internet. The search for archived documents requires considerably more time. The text, photo, and audio material is only partly listed in integrated databases. These provide information about which documents exist and where they can be found. Worth mentioning here is, for instance, the archive portal Archives online (http://archivesonline.org). It must be noted that only part of the archive material is available in electronic form, and the documents can usually not be sent out. Collection databases of museums are rarely linked to each other. However, an example of an interconnected system is the platform for museum collections (http://museums-online.org). The search for historical objects is thus very tedious, since it is necessary to inquire about each museum separately. In any event, the collection databases of technical and scientific museums can only be queried remotely in comparatively few cases. Mainly US and UK institutions offer access. In the German-­speaking region, access is sometimes restricted to use for internal purposes. For smaller collections, there are often no inventories. Online Journals and Newspapers The retrospective digitization of journals and other documents, often coupled with cost-free Internet access independently of place and time and a full-text search, greatly simplifies historical researching. However, in some cases, the quality of the digitized documents is unsatisfactory, for example, with old newspapers (e.g., with the archives of the Neue Zürcher Zeitung) and typewritten documents. Worth mention is the Swiss online journal platform E-Periodica (http://www.e-periodica.ch) of the ETH Library in Zurich, which also incorporates the Schweizerisches Handelsamtsblatt. Mathematical Tables and Other Aids to Computation A promising source of information for the early days of the history of global computer science is the newsletter Mathematical Tables and Other Aids to Computation (MTAC), founded in 1943. In the 1940s and 1950s, it was the leading international journal for computer technology. Since 1960, it is called Mathematics of computation.

1.14 Approach

25

Bulletin de la société d’encouragement pour l’industrie nationale Of particular advantage is an examination of the exemplary French journal Bulletin de la société d’encouragement pour l’industrie nationale, available via the Internet. Sites of Estates For many no longer existing or acquired manufacturers of calculating devices, the documentation is largely lost. Only in exceptional cases was it possible to find archives. Selected results are described below. • Germany The works of Konrad Zuse and Heinz Billing can be found in the Deutsches Museum, Munich. The Freie Universität Berlin has built up an (incomplete) digital archive about Zuse. On the other hand, in the company archives of Siemens, which acquired the Zuse KG, there is little to be found. • France Documents relating to Jean-Baptiste Schwilgué exist in the Strasbourg Departement archives (Archives départementales du Bas-Rhin). • Italy The Istituto per le Applicazioni del Calcolo (Rome) (computation center) is concerned with the global exchange of letters of its founder, Mauro Picone. • Liechtenstein The Museum Mura in Schaanwald FL harbors text, photo, and video documents about the Contina company and Curta. In Hilti (Schaan FL), however, there are no more documents referring to the acquired Contina company. • Switzerland The sites of the following company archives are indicated in parentheses: Amsler, Schaffhausen (Eisenbibliothek, Schlatt TG), Daemen Schmid/Loga calculator, Uster ZH (Schweizerisches Wirtschaftsarchiv, Basel), Hasler, Bern (now Ascom, Baar ZG: Historisches Archiv und Bibliothek of the PTT), Köniz BE), Kern, Aarau (Studiensammlung Kern, Stadtmuseum Schlössli Aarau), Paillard, and Yverdon VD/Sainte-Croix VD (Archives vaudoises cantonales, Lausanne). Unclear is the whereabouts of the documentation of the Coradi company (Zurich) and the Steinmann company (La Chaux-de-Fonds NE). Coradi was part of Amsler for a time. A successor company to the Precisa company (Zurich), which was acquired by Paillard, in fact exists, but operates in another field (Dietikon ZH, Präzisionswagen). Part of the Precisa documentation has been preserved in the Ortsmuseum Zurich Oerlikon. No company archives of Egli (Zurich) survive, although some documents can be found in the Ortsmuseum Zurich Wollishofen. The Num AG, Teufen, has only very limited documentation from its predecessor Güttinger, Teufen AR.  The archives of the (former) Contraves (Zurich) are private.

26

1 Introduction

Companies that have survived are Hasler, Bern (Ascom, Baar ZG), HaagStreit, Köniz BE, Crypto, Steinhausen ZG and Reuge, and Sainte-Croix VD. For the (at that time) Wild Heerbrugg SG (Leica), the surviving source material is very limited. The Schreibmaschinenmuseum Beck, Pfäffikon ZH, preserves the works of Curt Herzstark. The Federal Archives in Bern possess documents relating to the Contina and to Herzstark. The works of Eduard Stiefel and Heinz Rutishauser can be found in the archives of the ETH Library in Zurich. In individual instances, remnant documents still exist at the Winterthur Swiss Science Center (Technorama). Texts and photos can occasionally be found with the firsthand witnesses (former staff members) and descendants. • UK A promising source is the National Archive for the History of Computing, Manchester (holdings: Cambridge University computer laboratory, English Electric company Ltd., Ferranti Ltd., International Computers Ltd. (ICL), Leo Computers Ltd., Manchester University Department of Computer Science, National Physical Laboratory, as well as records of the innovators Douglas Hartree, Alan Turing, and Frederic Williams). The King’s College archives of the University of Cambridge house documents about Alan Turing. For this mathematician, papers can also be accessed from the University of Canterbury in Christchurch, New Zealand (http://www.alanturing.net). • USA Remington Rand and Univac are in the meantime part of Unisys. Documents can be accessed in the Sperry company archives of the Hagley Library, Wilmington, Delaware (https://www.hagley.org/research/collections). The IBM headquarters offer documents via the Internet (IBM Corporate Archives, Poughkeepsie, New York). Surveys Surveys were conducted in regard to calculator collections with banks, insurance companies, administrative institutions, schools (secondary schools, universities of applied science and universities), public transportation systems, industrial plants (mechanical and electrical engineering, chemistry, pharmaceuticals, foodstuffs, etc.), surveying offices, and the army. The inquiries included several large Swiss museums (Landesmuseum Zurich, Verkehrshaus der Schweiz, cantonal and municipal museums) and numerous museums in other countries. In connection with the Schwilgué keyboard adding machine and the Thomas arithmometer findings, inquiries were made with the world’s leading science museums and documentation centers, such as the: • Arithmeum, University of Bonn, Germany • Charles Babbage Institute, the University of Minnesota, Minneapolis, USA

1.14 Approach

• • • • • • • • • •

27

Computer History Museum, Mountain View, California, USA Deutsches Museum, Munich, Germany Heinz Nixdorf MuseumsForum, Paderborn, Germany History of Science Museum, Oxford, UK Musée des arts et métiers, Paris, France National Museum of American History, Washington, D.C., USA National Museum of Computing, Bletchley Park, UK Science and Industry Museum, Manchester, UK Science Museum, London, UK Technisches Museum Wien, Vienna, Austria.

Visits to Museums In order to obtain an overview, the author visited a number of domestic and international public and private calculator and computer collections as well as technical, scientific, clock, automation, and art museums. The museums visited are located in the following countries: Austria, England, France, Germany Italy, Liechtenstein, and Switzerland. The inventories of a number of important European museums are exemplary: • • • • • • • • • • • • • •

Arithmeum, Bonn, Germany Bletchley Park Trust, Bletchley Park, UK Deutsches Museum, Munich, Germany Hein Nixdorf MuseumsForum, Paderborn, Germany Kunsthistorisches Museum, Vienna, Austria (Kunstkammer) Mathematisch-physikalischer Salon, Dresden, Germany (Zwinger) Musée des arts et métiers, Paris, France Musée historique, Strasbourg, France Museo Galileo, Florence, Italy National Museum of Computing, Bletchley Park, UK Residenzschloss, Dresden, Germany (Grünes Gewölbe) Science Museum, London, UK Technische Sammlungen, Dresden, Germany Technisches Museum Wien, Vienna, Austria.

Excellent collections of mathematical instruments also exist in Switzerland, in particular in: • • • • • • • • •

Aarau (Studiensammlung Kern) Basel (Museum of the Swiss international UBS bank) Bern (Museum für Kommunikation) Dorénaz VS (patrimoine technologique) Geneva (Musée d’histoire des sciences) Lausanne (EPFL, Bolo Museum) Pfäffikon ZH (Schreibmaschinenmuseum Beck) Solothurn (Enter Museum) Zurich (ETH Library, Collection of astronomical instruments, and Schweizerisches Landesmuseum, Zurich)

28

1 Introduction

The author also visited the Schweizerisches Nationalmuseum in Affoltern am Albis ZH. Liechtenstein The following collections can be recommended: • Mauren (Museum Mura, Schaanwald) • Vaduz (Liechtensteinisches Landesmuseum). Other Collections of Historical Calculating Devices A multifaceted private collection exists in Gelterkinden BL (Schaub). Numerous other collections and repositories were visited, for example, at Roche and Novartis in Basel and Credit Suisse in Zurich. The Winterthur Technorama is no longer a museum in the traditional sense. At the present time, there is only very little about Amsler on exhibit at the Schaffhausen Museum zu Allerheiligen. In addition, flea markets and junk shops were occasionally closely scrutinized. Automaton Figures, Musical Automatons Clocks, and Watches Fascinating are the precious clocks of the Musée international d’horlogerie in La Chaux-de-Fonds NE (with reconstructions of the Antikythera mechanism and Dondi’s Astrarium) and the Musée international d’horlogerie in Le Locle NE (with androids and artificial animals). The mechanical music instruments in the Museum für Musikautomaten in Seewen SO (with a large nave organ), the automated figures and mechanical musicians in the Musée Cima (Centre international de la mécanique d’art, in the former Paillard factory SainteCroix (VD), and the Musée Baud, L’Auberson (VD), along with the collection of the Museum für Uhren und mechanische Musikinstrumente in Oberhofen BE, on Lake Thun. The famous triumvirate (musician, writer, and draftsman) of Pierre Jaquet-Droz and colleagues can be admired in the Musée d’art et d’histoire in Neuchâtel. One can also make astounding discoveries in historical museums. The museums below are among the most important Swiss museums for music boxes, musical automatons, automaton figures, and clocks and watches: • • • • • • • • •

Musée Baud, L’Auberson VD Musée Cima (Centre international de la mécanique d’art), Sainte-Croix VD Musée d’art et d’histoire, Neuchâtel Musée d’horlogerie, Le Locle NE Musée international d’horlogerie, La Chaux-de-Fonds NE Museum für Musikautomaten, Seewen SO Museum für Uhren und mechanische Musikinstrumente, Oberhofen BE Uhrenmuseum Beyer, Zurich Uhrenmuseum Winterthur ZH.

Organized Events Furthermore, a number of organized events were visited: the opening of the exhibit Genial und geheim (Genial and secret) commemorating the centenary

1.15  Highlights of the Researches

29

birthday of Alan Turing in Paderborn, Germany (Heinz Nixdorf MuseumsForum, January 2012). Also valuable was the participation in the international conference Making the History of Computing Relevant on the history of computer science in London (Science Museum, June 2013). Enlightening as well was the meeting of slide rule collectors at the University of Bonn (Arithmeum, March 2014). Finally, a conference concerned with Turing was held at the ETH Zurich. This led to encounters with leading international researchers on the subjects of Turing (Martin Davis, Andrew Hodges, Jack Copeland) and Zuse (Raúl Rojas, Ulf Hashagen), as well as to discussions with members of the British Computer Conservation Society. The conference presentation of the Zuse researcher Raúl Rojas (Freie Universität Berlin) on the subject “The architecture of Zuses’s Z1” was of considerable interest. This took place on December 18, 2013 in the colloquium of the Seminar for Applied Mathematics of the ETH Zurich. From May 2015 to January 2016, the Bonn Arithmeum exhibited devices of Jean-Baptiste Schwilgué discovered a few months earlier in Strasbourg (special “horologists and calculating machines” exhibit).

1.15  Highlights of the Researches The most gratifying moments during the many years invested in investigating the history of computer science were: • The rediscovery of numerous analog and digital calculating devices, for example, the world’s oldest well-preserved keyboard adding machine, the world’s largest commercial cylindrical slide rule, an early model of the world’s first commercially successful mechanical calculating machine, the world’s first mechanical “process computer” for the numerical control of a gear cutting machine for the astronomical clock of the Strasbourg cathedral, a three-dimensional logarithmic circular slide rule, and the world’s smallest mechanical parallel computer. • Finding drawings and photos of the Zuse M9 calculating punch in the Toggenburg valley near St Gallen (2011) • Finding papers and drawings in the French Bulletin de la société d’encouragement pour l’industrie nationale • Finding texts and drawings in the catalog of the first Great Exhibition of 1851 in London • The realization of a video conversation with former service technicians for the Zuse M9 calculating punch (first mass-produced Zuse calculating machine) in the Museum für Kommunikation in Bern (2011)

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1 Introduction

• The receipt of the firsthand accounts of Urs Hochstrasser about his experiences with the Zuse Z4 machine (2011) and of Elmar Maier about his further development of the Curta (2014) • Visiting object collections: Deutsches Museum (Munich), Heinz Nixdorf MuseumsForum (Paderborn), Arithmeum (Bonn), Science Museum (London), Bletchley Park Trust and National Museum of Computing (both Bletchley Park, UK), Musée des arts et métiers (Paris), Musée historique (Strasbourg), Technisches Museum Wien, (Vienna), Kunsthistorisches Museum (Vienna), Mathematisch-physikalischer Salon (Dresden), Residenzschloss Dresden, Museo Galileo (Florence, Italy), and also grandiose public and private collections in Switzerland and in Liechtenstein • The clarification of open questions and the rectification of mistakes (e.g., the reliability of the Zuse Z4, the conditional jump with the Z4, and the marketing of the Ermeth) • The organization of a public lecture about the Zuse Z1 machine at the ETH Zurich together with the Freie Universität Berlin (2013) • Realizing an international conference on the 100th birthday of the English mathematician Alan Turing at the ETH Zurich (2012) • Participating in the international conference on the history of informatics of the International Federation for Information Processing (IFIP) at the Science Museum in London (2013) • The presentations for the international conference on the history of informatics of the International Federation for Information Processing (IFIP) at New York University (2016) • The publication of the book Konrad Zuse und die Schweiz. Wer hat den Computer erfunden? with the Oldenbourg-Wissenschaftsverlag, Munich (2012) • The publication of the book Meilensteine der Rechentechnik. Zur Geschichte der Mathematik und der Informatik with De Gruyter Oldenbourg, Berlin/ Boston (2015) • The publication of the book Meilensteine der Rechentechnik (2nd edition, 2 volumes, 2018) with De Gruyter Oldenbourg, Berlin/Boston (2018) • The publication of the two-volume English edition Milestones in Analog and Digital Computing (2020). • Meeting Zuse Z4 firsthand witnesses at the ETH Zurich (2016) • The writing of peer reviews on the history of computer science for British and American scientific journals • The expert appraisal of applications for research projects for funding organizations • The publication of numerous papers relating to the results and findings of these investigations in domestic and international printed and electronic media • The publication of papers in the leading scientific journals Communications of the ACM (flagship magazine of the Association for Computing Machinery, New York, from 2017) and IEEE Annals of the History of Computing (2017)

1.16  Low Points of the Researches

31

• The publication of blog posts about the history of technology in the Communications of the ACM • The special exhibit “Uhrmacher und Rechenmaschinen” (Horologists and calculating machines) in the Arithmeum of the University of Bonn from May 2015 to January 2016, including machines of Jean-Baptiste Schwilgué found in December 2014 in Strasbourg • Public demonstration of historic calculating machines at Schloss Frauenfeld (Historisches Museum Thurgau, 2015) • Public demonstration “Rechnen ohne Strom” (Calculating without electricity) with historic calculating devices of the Collection of astronomical instruments in the ETH Library, Zurich (2017) • Named Fellow of the Oughtred Society, USA, in recognition of the work “Meilensteine der Rechentechnik” (2016) • The exchange of views with the authoritative international experts for research on the Antikythera mechanism (2017) • Finding the multiple Curta (drawings and patents, 2015; device, 2017) • Finding documents about the H.W. Egli AG company (Zurich) and about the world’s first successful direct multiplier, the “Millionaire” (2018) • Finding unknown documents on the calculating machines Millionaire and Madas in the Museum für Kommunikation, Bern, the Schweizerisches Sozialarchiv, Zurich, the University archives of the ETH Zurich, and in the Swiss Science Center, Winterthur ZH (2018) • Finding famous replicas of Pascal’s and Leibniz’s calculating machines in the Carnegie Mellon University, Pittsburgh, Pennsylvania (model maker: Roberto Guatelli, New York) (2019) • The news about a mysterious ivory Roman hand abacus in Paris (2019).

1.16  Low Points of the Researches There were also disappointments: • The discovery of a falsified firsthand account in a collected volume on the history of technology of a Swiss publisher and a quixotic, contrived (unpublished) eyewitness report about Alan Turing. • The discovery (during a book review) of the plagiarism of intellectual property in a multivolume work on the history of computing of a German publisher. The rectorate of the University of Münster confirmed this plagiarism in January 2015. • The confrontation with a historian of technology in Lorraine, who claimed exclusive research and publication rights with regard to the rediscovery of rare Schwilgué counting and calculating devices. Also to be mentioned is an article of Valéry Monnier about the auctioning of a Thomas arithmometer for more than 230,000 € by a German auction house. The device was tucked into a richly decorated, unsuited (too small) housing and bore an incorrect date. This was clearly a fraud.

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1 Introduction

1.17  Plagiarism of Intellectual Property Numerous inventions and discoveries have been made repeatedly, independently of each other (simultaneously or separated in time). Sometimes the knowledge and achievement are forgotten and emerge again at a later time. Conflicts concerning priority are documented; see Thomas Sonar: The history of the priority dispute between Leibniz and Newton, Mathematics in history and culture, Springer-Verlag GmbH, Berlin, Heidelberg 2016. Science is not immune to mistakes. Stealing ideas from others and plagiarizing date back to ancient times. In the history of technology as well, persons have adorned themselves with borrowed plumes, resulting in patent trial processes. Accusations of plagiarism were made, for example, with the sector (Galileo Galilei), see Ivo Schneider: Der Proportionalzirkel. Ein universelles Analogrecheninstrument der Vergangenheit, R. Oldenbourg Verlag, München 1971, and with the punched card-controlled loom (Falcon/Vaucanson versus Jacquard), see Jean Etènvenaux: Charles-Marie Jacquard (1752–1834) et la naissance de l’industrie textile moderne, Editions lyonnaises d’art et d’histoire, Lyon 1994. The invention of the electronic digital computer resulted in a patent trial (Atanasoff versus Mauchly). The creation of the stored program led to a dispute between Eckert/Mauchly and von Neumann. Furthermore, a conflict regarding the joint program-controlled relay machine flared up between IBM and Harvard University. And finally, Williams and Kilburn (University of Manchester) and Ferranti plagiarized the magnetic drum of Booth (London). Diverging views between Polish and British historians of technology are also seen with the breaking of the enigma radio messages.

1.18  Publications Media activities were accorded high priority. The objective is to make the public aware of the significance of the technical cultural heritage and acquaint people with the history of technology. Contributions also appeared in highcirculation influential German printed media (Frankfurter Allgemeine Zeitung, Süddeutsche Zeitung, Der Spiegel), in an Austrian newspaper (Der Standard), in Swiss daily newspapers (Neue Zürcher Zeitung, Tages-Anzeiger) and the Liechtenstein press (Vaterland, Volksblatt), as well as in numerous journals such as the German c’t Magazin für Computertechnik, in the Communications of the ACM, on radio and television, in the Internet, on ETH Zurich’s publication platform (Research Collection), and in the Researchgate social network. Nevertheless, it is not easy to win over editorial teams for such subjects. Since the demise of (printed) daily newspapers brought about by the Internet, the difficulties have increased dramatically.

1.20 Bibliography

33

Thanks to information from the reading public, the Zuse M9 calculating punch was (re)discovered. Furthermore, several Loga cylindrical slide rules, mechanical calculating machines, and sliding bar calculators came to light. Eyewitnesses and collectors came forward and requested information about the origin, meaning, and handling of devices or wanted to know what they should do with decommissioned machines. Certain sections of this book thus already appeared in older, abbreviated versions in newspaper and journal essays, in electronic media, and in the Internet. These publications provided new knowledge and clarified a number of open questions.

1.19  Sources Placing of Footnotes and Endnotes in the Running Text For historical works, exact references are essential. Endnotes at the end of the book or in the individual chapters are disliked and sometimes even an imposition. Looking these up requires repeatedly turning the pages and is exceedingly arduous. In addition, voluminous footnotes are deterring. They interrupt the flow of reading and, because of the small type size, are occasionally difficult to decipher. In order to take these into account, it is necessary to constantly page back and forth. On the other hand, neglecting these makes their value questionable. In the present compilation, the references are therefore inserted (with the indication “see”) directly in the running text. This work includes a very extensive bibliography: a detailed list of publications and an overview of the archive holdings. The bibliography therefore also constitutes a list of references. In this book, as a rule, only original texts and contributions of firsthand witnesses were used. Internet sources are given only in exceptional cases. References to websites often quickly become obsolete. Unambiguous and permanent web addresses (doi = digital object identifier) provide help here, so that documents can be cited over the long term.

1.20  Bibliography The list of publications encompasses more than 6000 entries in English, French, German, Italian, and Spanish. It comprises contributions from Europe, Africa, America, Asia, and Australia. The compilation includes as many detailed bibliographical information as possible in order to simplify the often tedious acquisition of such documents. All entries are in alphabetical order and, where necessary, arranged chronologically. In most scientific libraries, one searches for numerous works in vain. This is the case for many conference proceedings and exhibition catalogs. Meetings

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1 Introduction

dealing with mechanical calculating devices are organized by collectors. It would be of great help if the essays worth reading but difficult to access could be made permanently available in electronic form.

1.21  Regarding the Title of the Book A milestone is a significant event, a masterpiece, a historical highlight, a landmark, and a turning point in development. Originally, the title “Milestones in Analog and Digital Computing” was planned for the English edition. However, the book goes far beyond the history of computer science alone and deals with related areas, such as historical automatons and robots, as well as scientific instruments from the areas of mathematics, astronomy, time measurement, and surveying. A more appropriate name for the work is therefore “Milestones in Technology.” In the two volumes, however, only a very small part of the technology is covered. Consequently, the subtitle of the first volume refers to analog and digital calculating machines, historical automatons and robots, and scientific instruments from the areas of mathematics, astronomy, time measurement, and surveying. The second volume deals with the invention of the computer and the development of computer technology in Germany, Great Britain, Switzerland, and other countries and also contains a glossary and a global biography. The book can be regarded as a mathematical and informatics excursion through time. It is a chronicle of preeminent events in the history of mathematics, informatics/computing, and technology. They of course do not exclude steps backward. The history of science, a historico-cultural journey, is also a history of setbacks. Among the gems of calculating machine construction are the very rare, grandiose cylindrical machines. We owe these and many other jewels of technical artistry primarily to horologists and also to goldsmiths. Particularly outstanding as well are androids from the eighteenth century. A magnificent masterpiece is the decimal positional number system with the numeral 0. This work deals with the history of analog and digital calculating aids, which is with subareas of informatics and mathematics. It touches on related fields, such as astronomy, geodesy (surveying), navigation, horology (time measurement), scientific instruments and automatons (picture clocks, automated figures, musical automatons, calculating machines, chess automatons, automaton writers, automaton clocks, and drawing automatons), and typewriters. The excursions into related fields can be viewed as digressions.

1.22  Instructions for Assembly

35

1.22  Instructions for Assembly One can construct simple analog devices, such as pantographs, sectors, and proportional dividers (see Figs. 1.3, 1.4, 1.5, and 1.6) alone and use these, e.g., for instructional purposes. Their accuracy is in fact not very high, but they are adequate for explaining the functional principle and operation. However, the components of the common wood, metal, and plastic model kits are not always suitable. The Internet offers handicraft instructions, for example, for cardboard (paperboard) devices and also for folding templates.

Fig. 1.3  Pantograph, design form A. With such an instrument drawings can be enlarged. If one holds the leg (front left) firmly and moves the guide peg (metal screw, front middle) along the given figure, the drafting pen (front right) then transfers the contour of the figure in the chosen scale. (© Bruderer Informatik, CH-9401 Rorschach)

Fig. 1.4  Pantograph, design form B. With such an instrument drawings can be enlarged. If one wishes to decrease the size of the figure, it is necessary to reverse the positions of the drafting pen and the guide peg. With this model, both inner legs are arranged differently. (© Bruderer Informatik, CH-9401 Rorschach)

Fig. 1.5  Sector. With a sector (with linear scales on both legs and a pair of dividers, one can perform all four basic arithmetic operations. When these once widespread mathematical instruments are equipped, for example, with logarithmic or trigonometric scales, several different calculations are possible. (© Bruderer Informatik, CH-9401 Rorschach)

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Fig. 1.6  Proportional dividers. This instrument functions similarly to the sector. The divider tips are already incorporated in the legs. One can, for example, decrease the length of line segments in the specified ratio. It is useful to allow the pivot to shift freely. (© Bruderer Informatik, CH-9401 Rorschach)

Chapter 2

Basic Principles

Abstract  The chapter “Basic Principles” explains fundamental concepts, such as analog and digital computers, numerical and physical quantities, counting and measuring, conditional instructions, decimal and binary computers, parallel and serial computers, hybrid computers, special-purpose and universal computers, punched card machines, bookkeeping machines, mechanical calculating machines, adding machines, relay, vacuum tube, magnetic storage, direct and indirect subtraction, direct and indirect multiplication, sequence and program control, automation, commercial data processing, scientific computing, stepped drum, pinwheel, counting board, bead frame, slide rule, sector, curvimeter, planimeter, and pantograph. Numerous features serve to characterize analog and digital calculating devices in detail. The examples are taken from the fields of mathematics (difference engine), astronomy (armillary sphere, astrolabe, terrestrial globe, celestial globe, planisphere), geodesy (pedometer, odometer), and time measurement (planetarium clock). The evolution of the digital system is briefly described. The following topics are also discussed: algorithms, artificial intelligence, artificial neural networks, big data, blockchains, booking platforms, data privacy, the digital transformation, digitization, drones, electronic commerce, the Internet of Things, machine learning, quantum computers, ride-hailing services, robots, self-driving cars, smartphones, social networks, and voice assistants. Keywords  Analog computer · Automation · Binary computer · Decimal computer · Digital computer · Digital system · Digital transformation · Digitization · Magnetic storage · Parallel computer · Program control · Punched card machine · Serial computer · Special-­purpose computer · Universal computer · Vacuum tube

© Springer Nature Switzerland AG 2020 H. Bruderer, Milestones in Analog and Digital Computing, https://doi.org/10.1007/978-3-030-40974-6_2

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2.1  Analog and Digital Devices There is a fundamental, but not undisputed, difference between analog and digital computers. The time is displayed either analog by hour, minute, and second hand or digitally by numerals (18:35:29). With an analog display, the time is read out from the position of the hands, i.e., from the angle at a glance and, with a digital display, immediately from numerals, enabling greater accuracy. Here it must be noted: in contrast to the hour and minute hands, the second hand jumps from one position to the next. The demographic development can be represented in analog form as a graph, a curve, a bar diagram or (less descriptively) digitally by a pile of numbers, a list, or a table. The speed of a car is mainly indicated as an analog display. On the other hand, a kilometer counter functions digitally. The borderline between analog and digital technology is fuzzy (see Table 2.1). Even if the second hand moves in small steps, this is not continuous, and diagrams can be stepped. Staircase signals are analog since the analog voltage signal is displayed on the oscilloscope as a staircase graph (personal communication of Bruno Fricker). Table 2.1  Comparison of the terms analog and digital Differences between analog and digital Analog Physical quantities with arbitrarily (continuously) changing values Fluent transitions (e.g., for speed, temperature, pressure, frequency, sound level, or brightness) Representation of numerical values by analog quantities, e.g., diagrams, hand position, or water level) Analog computer with continuous representation of input values and results (as physical quantities, e.g., electrical voltages, electric currents, resistances, acoustic waves, light waves, pressure, distances, or angles) Determination by a measuring process, measurable Functions with analog displays (scale readings) without electric current

Digital Numerical magnitudes with definite (stepped) values (without intermediate values) Stepwise (discrete) transitions (e.g., yes or no, on or off, 0 or 1) Representation of numerical values by digital magnitudes, e.g., decimal or binary system, numerals Digital computer with numerical representation of input values and results by numerals (with mechanical, electromechanical, or electronic counters) Determination by a numerical process, discretely countable Functions with digital displays (numerical displays) with electric current

© Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020

Note The French word numérique has the meaning discrete or numerical on the one hand and digital (electronic, online) on the other hand.

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2.1.1  Numerals or Physical Variables Numbers can be represented by numerals (digitally) or by physical variables (analog). Accordingly, we distinguish between digital (discrete) and analog (continuous) computing devices. While digital machines function with numerals, mechanical analog calculating devices utilize, e.g., lengths (of distances) or angular rotation (of gear trains or shafts) and electronic analog computing devices mostly (time dependent) electrical voltages, current strengths, or also resistances. Gear wheels, relays, vacuum tubes, and transistors are examples of components for digital calculating and computing machines.

2.1.2  Numeration or Measurement With digital mathematical instruments, the result is determined by numeration (e.g., counting the beads with a bead frame) and with analog instruments by measuring (e.g., measuring the straight lengths with a slide rule). With mechanical desk calculating machines, the numerals are mostly represented by the number of teeth of stepped wheels and pinwheels, by toothed racks, or by toothed wheels. Electromechanical and electronic calculating devices function, for example, with pulse trains or magnetization states of electromagnetic relays (telecommunications relay), vacuum tubes, magnetic cores, or transistors. Digital devices utilize methods of calculation (algorithms). They are suited for numerical and nonnumerical tasks. Analog machines consist of components (modular principle) and are programmed, for example, via plugboards. In order to solve a problem using a differential analyzer, a schematic diagram is first generated. The basic drives (integral, sum, and function drives) are coupled in a specific way (see Figs. 2.1 and 2.2). Digital computers allow the permanent storage of large amounts of data. Internally, they function on the basis of binary system numbers, but input and output data are in the form of decimal numbers. During the conversion from decimal numbers to binary system numbers and back, round-off errors can occur. Analog computing devices were very fast and inexpensive and were employed especially for differential and integral calculus. Programming was relatively simple. Compared with digital computing devices, the level of technical complexity was relatively low.

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Fig. 2.1  Hartree’s differential analyzer (1935). The picture shows about one-half of the differential analyzer built by Douglas Hartree in Manchester. The antetype was the mechanical machine of Vannevar Bush, MIT, Cambridge, Massachusetts (1930). The mathematical instrument attempts to provide a numerical solution for differential equations on the basis of analog technology. (© Science Museum, London/Science & Society Picture Library)

Fig. 2.2  IBM-Ott differential analyzer (section). This differential analyzer with cutting wheel integrating gear mechanism dates from 1941–1944 by the Institut für praktische Mathematik of the Technische Hochschule Darmstadt in collaboration with the Albert Ott company in Kempten. (© Deutsches Museum, Munich)

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Analog and digital calculating devices can be characterized according to different attributes (see Table 2.2). Attributes of Digital Computers • Numerical notation by numerals (number of electric pulses, teeth of toothed wheels, or toothed racks) • Functional principle: non-continuous (stepwise, discrete, no intermediate values) • Performance of arithmetic operations on the basis of logical links • Basic arithmetic operations: addition, subtraction, multiplication, and division • High accuracy (depending on the number of places) • Floating point or fixed point notation • Program-controlled serial or parallel computer (arithmetic operations are processed mostly in succession according to the program; normally only one arithmetic unit) • Range of applications: very versatile (mostly universal computers). Attributes of Analog Computers • Numerical notation by physical variables (voltage curve) • Functional principle: continuous (stepless, fluent, with intermediate values) • Performance of arithmetic operations on the basis of physical variables • Basic arithmetic operations: addition, subtraction, multiplication, division, integration • Limited accuracy (depending on the accuracy of measurement) • Fixed point notation • Programmable parallel computer (arithmetic operations take place simultaneously according to the block diagram of the computational elements/ arithmetic circuit; several computational elements) • Range of applications: solution of differential equations, simulation of dynamic processes in real time (mostly special-purpose computers). Note Logical links are expressed by the Boolean operators “and”, “or”, and “not”. Table 2.2  Attributes of analog and digital computers Comparison of analog and digital computers Attribute Analog Numerical notation Physical variables Functional principle Continuous, stepless Accuracy Limited Speed Very high Type of computer Parallel computer Numerical format Fixed point Range of applications Special computer

Digital Numerals Discrete, stepwise Any desired High Serial or parallel computer Floating point or fixed point Universal computer

© Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020

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Examples of Analog and Digital Calculating Aids • Mechanical and electromechanical analog calculators/analog calculating aids, e.g., astrolabe, quadrant, sextant, octant, (linear) measuring rule, (logarithmic) slide rule, circular slide rule, cylindrical slide rule, pocketwatch slide rule, calculating wheel, grid slide rule, sector (pair of sector compasses), proportional dividers, planimeter, measuring square, nomogram, the Strasbourg astronomical clock (church calculator of JeanBaptiste Schwilgué), tide predictor (William Thomson), electromechanical differential analyzer (Vannevar Bush), electrical network • Electronic analog computers • Electronic differential analyzers • Mechanical and electromechanical digital computers/digital calculating aids, e.g., counting board; bead frame; counting table; counting cloth; Napier’s rods; calculating machines of Wilhelm Schickard, Blaise Pascal, Gottfried Wilhelm Leibniz, Charles Babbage (difference engine, analytical engine), Pehr Georg Scheutz/Edvard Raphael Scheutz (difference engine), Martin Wiberg (difference engine), Percy Edwin Ludgate (analytical machine), Charles Xavier Thomas (arithmometer), Jean-Baptiste Schwilgué (“process calculator”), Herman Hollerith (punched card equipment), Leonardo Torres (y) Quevedo (electromechanical calculating machines), George Stibitz (Bell relay calculators), Konrad Zuse (Z3, Z4, Z5, Z11), Howard Aiken (Harvard Mark 1/IBM ASCC), Conny Palm (Bark), Andrew Booth (ARC), Herbert Kortum/Wilhelm Kämmerer (Oprema), and Curt Herzstark (Curta); and cash register (James Ritty, 1879) • Electronic digital computers, e.g. ABC, Colossus, Eniac, Manchester Mark 1, Edsac, Pilot Ace, Univac 1, IBM 701 and 650, IAS computer, Whirlwind, Ape(x)c, Leo, Ermeth, Zuse Z22 and Z23, Tradic, Mailüfterl, Csirac, Besm, as well as calculating devices from Dresden (D1, D2, D4a, Cellatron), Göttingen (G1, G1a, G2, G3), Jena (ZRA 1), and Munich (Perm). Digital calculating aids also include the fingers, pebble stones, reckoning pennies, mathematical tables (e.g., logarithmic tables), slide bar adders, and mechanical calculating machines, as well as the (theoretical) Turing machine. Adding machines also function with numerals. Today’s computers are electronic digital computers. Mechanical and Electronic Pocket Calculators Pocket calculators include not only the electronic dwarfs of our time. They also comprise small bead frames (abacus), short slide rules, circular slide rules with small diameter, tin slide bar adders, and the Curta cylindrical calculating machine. Besides this cylindrical calculator, for a short time, a comparable small mechanical calculating device was manufactured, the German Alpina universal calculating machine (URM, 1960) from Kaufbeuren. The builder of this four-function pinwheel machine was Oskar Mildner, and the manufacturer was named Otto Rudolf Bovensiepen. However, the devices were not very widespread. The same is true for the Norwegian Multifix (1954). The adder (without automatic tens carry) of Morland was also a convenient device.

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Sectors and Proportional Dividers: Versatile Tools A popular mathematical tool was the sector. This had either a fixed or a variable pivot. The highly flexible calculating aid has, e.g., linear, logarithmic, or trigonometric scales on its legs. Paths are picked off with dividers. With the linear scales, one can add or subtract. Thanks to the (geometrical) intercept theorems, it is possible to solve proportional equations, so that multiplication and division are also made possible. Other calculations are concerned with distances, polygons, circles, and roots. All of these instruments have largely disappeared. Analog Logarithmic Slide Rules and Digital Mechanical Calculating Machines In simple terms it can be said: • Slide rules are inexpensive and lightweight but inaccurate. They function silently. • Mechanical calculators are heavy and expensive but also accurate. However, they are also noisy. Analog Computers Electronic analog computers were widespread in the 1950s and 1960s and still in use into the 1970s. At that time analog and digital machines were used alongside each other. Analogy: The solution to a problem is reduced to analog (similar, corresponding) physical processes, and the problem is simulated by a similar, corresponding physical system (model). At the end of the 1930s, George A. Philbrick (Boston) built a special-purpose electronic analog computer with the name Polyphemus. Helmut Hoelzer also worked on an electronic analog computer in the year 1941. Differential analyzers were developed, for example, at the Massachusetts Institute of Technology, Cambridge, Massachusetts, and at the University of Manchester (Meccano 1934). American and British manufacturers of electronic analog computers were, e.g., George A.  Philbrick Researches Inc. (Boston, Massachusetts), the Boeing airplane company (Seattle, Washington), English Electric (Stafford), Elliott Brothers (London) Ltd., Metropolitan-Vickers (Manchester), and EMI Electronics (London). In addition there were also hydraulic and optical analog computers. Sophisticated Integrators Only a few mechanical integrators (devices for the integration of differential equations) are known. Such drawing, measuring, and calculating instruments once abounded: • The curvimeter (curve measuring device) • The planimeter (area measuring device) • The pantograph (redrawing device for the enlargement or reduction of drawings) • The coordinatograph (cartographic device for the pointwise drawing of curves and measurement of the coordinates of individual points) • The harmonic analyzer (device for the examination – analysis – of a given curve; device for the determination of the Fourier coefficients for a given curve)

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• The harmonic synthesizer (device for plotting the curve corresponding to given values; device for the superpositioning of oscillations; for example, tide predictor) • The integraph (device for plotting the integral curve for a given curve or the integral curve for a differential equation). Harmonic analysis is the resolution of an oscillation into the fundamental oscillation and the harmonic components. Harmonic oscillations can be expressed as a sine function. Unfortunately, for lay people, all of these aids are accessible only with some difficulty. An understanding of these instruments requires a knowledge of higher mathematics. Differentiation and integration are complex (see box). Differentiation and Integration Infinitesimal calculus, as its name suggests, is concerned with arbitrarily (infinitely) small numerical values and with the calculation of the limit values for functions. The relevant mathematical operations are differentiation and integration. The differentiation of a function comprises the forming of a derivative, which can be best represented as a tangential slope. Integration defines the antiderivative of this derivative function. The result can be visualized as a surface area. Integration is the calculation of (definite and indefinite) integrals. Extracting roots and calculating logarithms are the opposite processes of raising to a power, and integration is the opposite process of differentiation. Differential and integral equations serve to describe natural processes. Differential and integral calculus are subareas of higher mathematics, more precisely of infinitesimal calculus.

Hybrid Computers Analog and digital computers can also be combined to hybrid computers. Examples are program-controlled analog computers, simulators, the magnetic drum digital differential analyzer (MADDIDA) (Northrop Aircraft Corporation, Hawthorne, California), the Integromat of Schoppe & Faeser (Minden), the Bendix D-12 and G-15 of the Bendix Aviation Corporation (Los Angeles), and the TRICE of Packard Bell. The Univac 1103A, IBM 704, and Era 1103 are further examples of hybrid computers. The partial products in the (only) multiplying block of the millionaire (four-­ fuction) machine are represented by sliding plates (stepped plates) of different lengths, that is, analog plates. However, the display is digital (see Peter Kradolfer: Einige Rosinen aus der Entwicklung der Rechenmaschinen, Sauerländer Verlag, Aarau 1988, pages 34–36). The Whirlwind was originally planned as the design of an analog flight simulator and was only later transformed into a digital computer.

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The Antikythera mechanism is an analog calculating machine that carries out numerical calculations. Sources Helmut Adler: Elektronische Analogrechner, VEB Deutscher Verlag der Wissenschaften, Berlin, 3rd edition 1970 Wolfgang Giloi; Rudolf Lauber: Analogrechnen. Programmierung, Arbeitsweise und Anwendung des elektronischen Analogrechners, Springer-Verlag, Berlin, Göttingen etc. 1963 Christine Krause: Die Analogrechentechnik unter besonderer Berück­ sichtigung der Entwicklung von Analogrechnern in Thüringen und Sachsen, in: Werner H.  Schmidt; Werner Girbardt (editors): Mitteilungen zur Geschichte der Rechentechnik, 2006, v 6, pages 121–133. Note The boundary between analog and digital computers is blurred. See, for example: Andreas Brennecke: Physikalische Analogien und Ziffernrechenmaschinen – Von mechanischen Rechengeräten zu Integrieranlagen und programmgesteuerten Maschinen, in: Werner H. Schmidt; Werner Girbardt (editors): 1. Greifswalder Symposium zur Entwicklung der Rechentechnik, September 15–17, 2000, Ernst Moritz Arndt Universität, Greifswald 2000, pages 89–111 Bernd Ulmann: Analogrechner. Wunderwerke der Technik  – Grundlagen, Geschichte und Anwendung, Oldenbourg-Verlag, Munich 2010 Horst Völz: Grundlagen der Information, Akademie Verlag GmbH, Berlin 1991 Other Hybrid Forms With the musical box, the rotating movement of the pinned barrel takes place analog, while the barrel pins themselves are digital. A combination is also found in jaquemarts (e.g., San Marco, Venice). Interchangeable cams control certain automaton figures (e.g., the handwriting automaton and the musician of Jaquet-Droz or the duck of Vaucanson). The difference between analog and digital is not always clear (see box). Are Gear Wheels Analog or Digital? Due to their construction, gear wheels are analog. They rotate constantly around their shafts. The operating principle of the gear wheel is digital when its rotary motion is subdivided into steps by an external control device. The steering ensures that the physical motion represents valid logic values (e.g., whole numbers) (communication of Doron Swade of May 16, 2017). A continuously intermeshed gear train is analog because there is no quantization. The angularity of the teeth must be expressed in real numbers (personal communication of Bruno Fricker of October 3, 2018).The tooth-equipped stepped drums and the pinwheels, with their retractable and extendable teeth function digitally.

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Fig. 2.3  Pedometer. With such devices distances were measured. The origin and age of this metal instrument (with analog display) are unknown. (© ETH Library Zurich, Collection of astronomical instruments)

Elaborations on Analog and Digital Devices The curve measuring device (opisometer, curvimeter) and area measuring device (planimeter) are analog devices. On the other hand, the step counter (pedometer) (see Fig. 2.3) and kilometer counter function stepwise (but partly with analog display). Position measuring devices (odometer) (see Fig.  2.4) employ mechanical counting wheels. Certain scientific instruments now forgotten were used in land surveying (see Figs. 2.5 and 2.6). The astrolabe (see Fig. 2.7) is, unlike the three-dimensional armillary sphere (see Figs.  2.8 and 2.9), a circular (two-dimensional) astronomical measuring instrument. It is comprised, e.g., of a bedplate (mother, mater), a fixed disc with the coordinates of the celestial sphere (tympano), a rotating perforated wickerform disc with celestial constellations (rete), an alignment device (sight), and a rotating hand (sighting ruler, alidade). The rotating arm of an angle measuring device outfitted with a readout device is called the alidade. The two planispheres (see Figs. 2.10 and 2.11) reveal the transition from the geocentric Copernican system to the heliocentric world view, with the Earth and the sun at the center. Among the most valuable astronomical instruments are planetary clocks (see Fig. 2.12). Not so well known is the torquetum (see Fig. 2.13). Several terrestrial and celestial globes have been preserved (see Figs. 2.14, 2.15, 2.16, 2.17, 2.18, and 2.19). Analog slide rules function with straight lengths. The sector and proportional dividers utilize lengths and angles. Pantographs are also constructed on the basis of geometrical relationships. The cam discs of automaton figures are analog. The water level of a lake rises and falls continuously: the speed of a car normally varies steplessly. This is also true for the liquid in a thermometer.

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Electrical signals can be represented, transmitted, stored, and processed as analog or digital. The pebble stones of a calculating table, the cylinder teeth of a stepped drum machine, and the variable teeth of a pinwheel machine are digital. The perforations of punched cards and punched tapes represent the values digitally, as also the insertion positions of toothed racks and slide bar adders. Braille and the Morse code are also based on two states, and music notes are digital as well. Braille (1–6 points) is digital. The Morse alphabet is based on three characters (dot, dash, pause or short signal, long signal, pause). Musical notation is also digital.

Fig. 2.4  Odometer. In 1584 Christoph Trechsler the Elder built this mechanical wagon odometer. The measuring mechanism of the fire-gilded brass scientific instrument consists of twelve toothed wheels. The distance traveled can be read from the dial (in rods and miles). The ratchet registers each revolution of the wheels and transmits this to the gear mechanism on the front. A sturdy link chain serves as the connection between the wheel axle and the trigger lever. The size of the wagon wheel was one rod (4.5  m). 2000 rods resulted in 1 mile (9  km). The odometer is equipped with a plotting table, onto which a wooden plate with clamped paper was placed. The aim points are marked with a moving needle. The wheel size is an analog variable (length), and the counting of the number of wheel revolutions is a digital process. The plotting table is also analog. The odometer is therefore a hybrid device. (© Mathematisch-physikalischer Salon, Dresden)

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Fig. 2.5  Land surveying 1. For the measurement of the terrestrial surface, a triangulated mesh is used. Mountain peaks and church spires serve, for example, as fixed points (high points and ground marks). Triangulation is a common method in geodesy (surveying). For this purpose a number of older and newer measuring instruments (e.g., theodolites for the determination of the horizontal and vertical angles) were used. This illustration is taken from the “Fabrica et usus instrumenti chorographici” of Leonhard Zubler (1607). (Source: ETH Library, Zurich, Rare books collection)

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Fig. 2.6  Land surveying 2. This drawing shows a trigonometric measurement dating from the seventeenth century (from Leonhard Zubler: Fabrica et usus instrumenti chorographici: quo mira facilitate describuntur regiones & singulae partes earum, veluti montes, urbes, castella, pagi, propugnacula, & similia [...], impensis Ludovici Regis [...], [Basel] 1607). (Source: ETH Library, Zurich, Rare books collection)

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Fig. 2.7  Astrolabe. This magnificent astrolabe of Erasmus Habermel (1588) is an analog astronomical instrument for the determination of the positions of celestial bodies. An astrolabe is a circular observational instrument with a sighting device invented by the Arabs. The circles of the celestial sphere are displayed in stereographic projection (imaging of spatial objects on a plane). These popular tools, which also served as nocturnal dials, were employed, for example, for seafaring navigation. (© Deutsches Museum, Munich)

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Fig. 2.8  Armillary sphere (1). This woodcut from the “Opera Mathematica” of Johannes Schöner (1551) represents the motions of the signs of the zodiac around the Earth. These form the central focus. An armillary sphere is a three-dimensional device in general use in antiquity and the Middle Ages for the representation of the main cosmic orbits. The concentric rings (Latin: armilla) are partly fixed and partly rotating. They are positioned according to the most important circles of the celestial sphere (horizon, celestial equator, meridian, and ecliptic). This astronomical instrument measures the hour angle and the declination of a star. (Source: ETH Library, Zurich, Rare books collection)

Fig. 2.9  Armillary sphere (2). This armillary sphere from the seventeenth century displays a zodiac sign (from Tycho Brahe: Tychonis Brahe Astronomiae instauratae mechanica, apud Levinum Hulsium Noribergae [Nuremberg] 1602). (Source: ETH Library, Zurich, Rare books collection)

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Fig. 2.10  Planisphere after Ptolemy. This two-dimensional representation shows the solar system according to the Ptolemaic (geocentric) model (Earth at the center) (from Andreas Cellarius: Harmonia macrocosmica, seu, Atlas universalis et novus, totius universi creati cosmographiam generalem, et novam exhibens (...), apud Gerardum Valk & Petrum Schenk, Amstelodami 1708). (Source: ETH Library, Zurich, Rare books collection)

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Fig. 2.11  Planisphere after Copernicus. Here the solar system is visualized on a plane according to the Copernican (heliocentric) model (from: Andreas Cellarius: Harmonia macrocosmica, seu, Atlas universalis et novus, totius universi creati cosmographiam generalem, et novam exhibens (...), apud Gerardum Valk & Petrum Schenk, Amstelodami: 1708). (Source: ETH Library, Zurich, Rare books collection)

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Fig. 2.12  Planetary clock. The astronomical art clock from 1563–1568 is a work of Eberhard Baldewein, Hans Bucher, and Hermann Diepel. On the upper hand, the disc for Mars and spandrel figures (combat rider and battle scenes) are depicted. The planet requires 1.881 years on the average to revolve about the Earth. In the small display at the center, a quarter hour and weekday dial (planetary gods as daily regents) can be seen. The lower display constitutes an astrolabe with 39 fixed star locations and ecliptic. The rete rotates in sidereal time. The hour hand rotates in mean solar time. The spandrel figures represent the four seasons. A celestial globe with magnitude 1 to 5 stars, the ecliptic of which passes through a small solar image in real solar time in 1 year rotates on the clock in sidereal time. (© Mathematisch-physikalischer Salon, Dresden)

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Fig. 2.13  The torquetum. This observation instrument, also called the turquet, was used to determine the position of the astronomical orbits (e.g., the equator or the ecliptic). (from: Petrus Apian: Astronomicum Caesareum [...], [Ingolstadt]; [s. n.], 1540. (Source: ETH Library, Zurich, Rare books collection)

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Fig. 2.14  Terrestrial globe (1). The continents and countries are depicted on a sphere (woodcut) (aus: Johannes Schoner: Opera mathematica Ioannis Schoneri (...), Impressa Norinbergae, in officina Ioannis Montani & Ulrici Neuberi, Norinberga 1551). (Source: ETH Library, Zurich, Rare books collection)

Fig. 2.15  Celestial globe (1). This drawing depicts the heavens on a celestial sphere (woodcut) (aus: Johannes Schoner: Opera mathematica Ioannis Schoneri (...), Impressa Norinbergae, in officina Ioannis Montani & Ulrici Neuberi, Norinberga 1551). (Source: ETH Library, Zurich, Rare books collection)

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Fig. 2.16  Terrestrial globe (2). This wooden sphere with the surface of the Earth (1613) is from Jodocus Hondius the Younger (Flanders) and Adriaen Veen (Amsterdam). (© ETH Library, Zurich, Collection of astronomical instruments)

Fig. 2.17  Celestial globe (2). This wooden globe (1613) was created by Jodocus Hondius the Younger and Adriaen Veen. (© ETH Library, Zurich, Collection of astronomical instruments)

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Fig. 2.18  Celestial globe (3). The Kassel 1 celestial globe clock (around 1580). The clockdriven moving (gold-plated) celestial globe of Jost Bürgi simulates the motions of the sun and the fixed stars with astonishing accuracy. The motion of the sun is however not constant. According to Kepler’s second law, it sometimes moves faster and sometimes slower through the ecliptic (apparent solar orbit). A sundial indicates the actual solar time. This deviates from the mean solar time of mechanical clocks. Bürgi took this equation of time into consideration. Five of his globes have survived, at the sites: Mathematischphysikalischer Salon, Dresden, Astronomisch-physikalisches Kabinett, Kassel (2 globes), Musée des arts et métiers, Paris, and Schweizerisches Landesmuseum, Zurich. (© Museumslandschaft Hessen Kassel, Astronomisch-physikalisches Kabinett)

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Fig. 2.19  Celestial globe (4). The German clockmaker Gerhard Emmoser created this celestial globe with clockwork (1579). The artwork of gilded silver, gilded brass, and steel (clockwork) with extremely complex mechanical action turned once and showed the signs of the zodiac. The Emperor Rudolf II exhibited it in his cabinet of curiosities in Prague. The winged horse Pegasus bears the seemingly weightless globe on its outspread wings. (© Metropolitan Museum of Art, New York)

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Fig. 2.20  Babbage’s difference engine no. 1. The highly gifted English mathematician Charles Babbage designed this automatic digital calculator from 1824 on. The toolmaker Joseph Clement built this functioning demonstration model, a small part of the unfinished machine, in 1832. The number values are represented by decimal numeral wheels. (© Science Museum, London/Science & Society Picture Library)

There were several difference engines (see box).

2.1  Analog and Digital Devices

What Is the Function of a Difference Engine? In earlier times, the mathematical tables prepared by human beings were altogether erroneous. This complicated working, e.g., in astronomy, navigation at sea and technology, as well as in the banking and insurance business. With the difference method it was possible to control the correctness of the existing tabulated data. In addition, one can calculate new tables and intermediate values by simple addition (interpolation). Difference engines (see Figs.  2.20, 2.21, 2.22, 2.23, 2.24, and 2.25) can assume this arduous and time-consuming task: they are capable of determining function values of polynomial mathematical expressions f(x). These systems are constructed of successively arranged adders with continuous tens carry. For logarithms and trigonometric tables, the values are approximated. Manual Calculation Nevil Maskelyne (1732–1811), an astronomer at the Greenwich Observatory, utilized the difference method to create nautical tables. A large number of persons calculated the “Nautical Almanac,” which first appeared in 1767, in home work. In France Gaspard de Prony (1755–1839) had a number of co-workers calculate differences in subordinated steps. Mechanical Calculation Already in 1784, the German engineer Johann Helfrich Müller (1746–1830) was working on a tabulating machine based on the difference method. In 1786 the British astronomer John Herschel translated a book of Müller that describes this device, in excerpt form, for Charles Babbage into English. Charles Babbage The planned (fix-programmed) difference engine no. 1 of Babbage is regarded as the first automatic calculating machine. Operation no longer requires human intervention in the arithmetical process. The machinist Joseph Clement built a demonstration machine based on this incomplete automaton in 1832. In 1991, the 200th birthday of Charles Babbage, the London Science Museum, under the direction of Doron Swade, exhibited a functional reconstruction of difference engine no. 2. Numerous difference engines were manufactured according to the prototype of Babbage, for example, those of Scheutz, Wiberg, Hamann, and Thompson. Sources Christine Krause: Das Positive von Differenzen. Die Rechenmaschinen von Müller, Babbage, Scheutz, Wiberg…, Technische Universität Ilmenau, year not given Doron D. Swade: Der mechanische Computer des Charles Babbage, in: Spektrum der Wissenschaft, 1993, volume 4, pages 78–84

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Fig. 2.21  Babbage’s difference engine no. 1. This figure shows a reconstructed section of Charles Babbage’s unfinished difference engine. Such (non-programmable) mechanical devices were intended to generate faultless mathematical tables. (© Museo nazionale della scienza e della tecnologia “Leonardo da Vinci”, Milan)

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Fig. 2.22  Babbage’s difference engine no. 2. The British computer pioneer designed this system, accurate to 31 places (seventh degree polynomial) between 1847 and 1849. However, it was not built during his lifetime. It has a two-stage tens carry (addition without carry, but with tensioning of a spring; release of the spring and carry). In 1991, on the occasion of the bicentennial birthday of Charles Babbage, the London Science Museum completed this 2.6 ton heavy functional reconstruction, comprising 4000 different parts. Measurements on the surviving parts of difference engine no. 1 showed that Joseph Clement adhered to a tolerance of 0.04 to 0.05 millimeters. This refutes the usual notion that the precision engineering of that time was not adequate for this construction. (© Science Museum, London/Science & Society Picture Library)

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Fig. 2.23  Scheutz difference engine no. 3 (1859). This picture illustrates a section from a system that had the goal of avoiding calculation, scribal and compositorial errors with the preparation and printing of logarithmic tables. The machine of the Swedish father and son Georg and Edvard Scheutz was inspired by the work of Charles Babbage. It was used in 1864 to generate life insurance tables in England. (© Science Museum, London/Science & Society Picture Library)

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Fig. 2.24  Wiberg’s difference engine 1. This machine served for the automatic calculation and printout of mathematical tables (logarithms, powers, square roots, and cube roots). It is constructed of a copper, brass, and bronze alloy. (© Peter Häll, Tekniska museet, Stockholm)

Fig. 2.25  Wiberg’s difference engine 2. This machine, dating from 1875, was based on the knowledge of Charles Babbage and was a successor to the difference engine of Scheutz. (© Peter Häll, Tekniska museet, Stockholm)

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Fig. 2.26  Babbage’s analytical engine (1834–1871). In 1834 the English mathematician Charles Babbage began with the development of this programmable, card-programmed calculating machine. Until his death in 1871, however, only a small part was realized. This figure shows a section of the digital calculating unit and the printer unit. The analytical engine, which already provided for conditional branching, is regarded as the ancestor of the modern-day computer. (© Science Museum, London/Science & Society Picture Library)

An analytical engine (Babbage, Ludgate, Torres) (see Fig. 2.26) is a numerical (program-controlled) machine. Which Calculating Aid for Which Purpose? Until the introduction of the electronic pocket calculator, calculating was rather laborious. This is especially true for division, raising to a power and extracting roots. The efforts to mechanize and automate arithmetic operations therefore stand to reason. The following overview (see Table 2.3) is restricted to inexpensive portable mathematical instruments. Electronic pocket calculators are available for all four basic arithmetic operations. Slide rules, mathematical tables, and electronic pocket calculators exist for more demanding calculations.

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Table 2.3  Which calculating aid for which arithmetic operation? Widespread calculating aids for basic arithmetic operations Basic arithmetic operation Analog and digital resources Addition Bead frame, slide bar adder, electronic pocket calculator Subtraction Bead frame, slide bar adder, electronic pocket calculator Multiplication Bead frame, mathematical tables, Napier’s rods, slide rules, electronic pocket calculator Division Bead frame, mathematical tables, Napier’s rods, slide rules, electronic pocket calculator © Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020

Only a few inventors of calculating aids are known to us (see Table 2.4). Table 2.4  Inventors of analog and digital calculating aids Who invented which calculating aid? Calculating aid Inventor (selection) Logarithms Jost Bürgi Slide rule William Oughtred Cylindrical slide rule Sector

George Fuller Guidobaldo del Monte

Proportional dividers Pantograph

Federico Commandino Heron of Alexandria

Planimeter Polar planimeter Tide predictor Differential analyzer Calculating rods Promptuary Punched card machine Slide bar adder Mechanical calculating machine Key-driven calculating machine Difference engine Program-controlled automatic calculating machine

Johann Martin Hermann Jakob Amsler William Thomson Vannevar Bush John Napier John Napier Herman Hollerith Heinrich Kummer Wilhelm Schickard Luigi Torchi Johann Helfrich Müller Charles Babbage

John Napier Edmund Gunter (scale) Edwin Thacher Fabrizio Mordente Jacques Besson Christoph Scheiner Tito Gonnella Albert Miller

Julius Billeter Michiel Coignet Jost Bürgi

James Powers Blaise Pascal

Gottfried Wilhelm Leibniz Du Bois Parmelee

Jean-Baptiste Schwilgué Charles Babbage Alan Turing Konrad Zuse

© Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020

Remarks The cylindrical slide rules of Fuller (Ireland, 1878), Thacher (USA, 1881) and Billeter (Switzerland, 1891) are structured differently. Slide rules are logarithmic tools. Tide predictors and differential analyzers were analog devices. Napier’s

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rods are digital by nature. A key-driven calculating machine is a mechanical calculating aid actuated from a keyboard and not by a crank. The sector is usually attributed to Galileo Galilei, even though he was not the original inventor. The Romans already knew simple proportional dividers in the 1st century, as excavations in Pompei show (Museo archeologico nazionale, Naples). Leonardo da Vinci designed such instruments (Codex Atlanticus, Codex Forster). In spite of electronics, we are still well away from the paperless office. Both printed and digital documents have their advantages (see Table 2.5). Table 2.5  Advantages and disadvantages of printed and electronic documents Comparison of printed and electronic documents Printed book Digital document Long lifespan Short lifespan Long-term archival guaranteed Long-term archival not guaranteed Available, tangible Not available, not tangible Quality partly better (e.g., encyclopedia) Quality partly worse (e.g., Wikipedia) Tracing tedious Tracing simple Unlimited citability Limited citability (e.g., Wikipedia) Use of text and illustrations overseeable Use of text, illustrations, sound, film less (overview) overseeable (only excerpts, e.g., from schedule or telephone book) Primarily internal references Internal and external references Readable without electric current Readable only with electric current Readable without technical aids Readable only with technical aids No zooming of text and illustrations Zooming of text and illustrations No speech output Speech output Insertion of notes and highlighting possible Insertion of notes and highlighting restricted Tedious searching (of subject index, lists of Full-text search with cues figures and tables) by paging Use subject to costs Use in part cost-free Wikipedia) Access partly place bound (e.g., archives) Access partly not place bound (e.g., globally via Internet Postal document exchange via global Electronic document exchange via internet interlibrary loan (library system) High space requirement Small space requirement High weight Negligible weight Data carrier: paper Data carrier: electronic storage medium High production costs (printing, binding) Lower production costs (no printing costs) Tedious reproduction Simple reproduction Tedious distribution (sending by mail) Simple distribution (sending via networks) No personalization Personalization possible Theft of intellectual property Theft of intellectual property (violation of (violation of copyright) more difficult copyright) simple Data security guaranteed (encyclopedia) Data security not guaranteed (Wikipedia) No internet criminality Internet criminality (e.g., danger of virus) © Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020

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Remarks Unlike Wikipedia, with a printed encyclopedia (free of advertising), the persons concerned (e.g., authors and editors) are usually explicitly named. In a printed work, the entries are systematic but in Wikipedia sooner by chance and of wavering quality. According to language edition, there are significant differences. Search engines frequently entail annoying advertising.

2.2  Parallel and Serial Machines Fundamental differences exist between parallel and serial machines (see Table 2.6).

Table 2.6  Characteristics of parallel and serial machines Comparison of parallel and serial machines Attribute Parallel operation Simultaneous processing of Processing in arithmetic operations for all digits of the arithmetic a number (of a word), simultaneous unit processing of all bits of a word Data exchange Simultaneous transfer of all digits of a number over several channels to and from (lines) memory Sequencing in Simultaneous reading and writing of memory all digits of a number Computing More complex, more expensive (more equipment lines and circuit elements) Programming More difficult Faster Computation speed Examples Vacuum tube computer with electrostatic memory

Serial operation Sequential processing of arithmetic operations for all places of a number (of a word), processing bit by bit Sequential transfer of all digits of a number (digit by digit) over a single channel (a single line) Sequential reading and writing of all digits of a number Simpler, less expensive (less lines and circuit elements) Simpler Slower Vacuum tube computer with mercury memory

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Remarks Serial machines are characterized by serial addition and parallel machines by parallel addition. Serial machines (e.g., Edvac) require less vacuum tubes than parallel machines (Eniac). Punched card machines have several counter registers and parallel machines several arithmetic units.

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Fig. 2.27  Computer construction. The work Programmgesteuerte digitale Rechengeräte (elektronische Rechenmaschinen) (Program-controlled digital calculating devices (electronic calculating machines)) by Heinz Rutishauser, Ambros Speiser, and Eduard Stiefel of the ETH Zurich, which appeared in 1951, was regarded at that time as the leading German language investigation of the construction of stored-­program electronic computers. The only comparable book was High-speed computing devices of the US company Engineering Research Associates (1950). (Source: ETH Library, Zurich)

Parallel or Serial? This most important German language treatment (see Fig. 2.27) dealing with the onset of the digital age at the beginning of the 1950s comes to the following conclusion: An arithmetic unit can function serially or in parallel. In the first case, the two addends are conducted through separate channels and added digit-wise in a single place adder. In the second case, all n digits of the addends are simultaneously conducted to the arithmetic unit and simultaneously added in n elementary adders. It is clear that a parallel adder functions much faster and requires much more  ­ material (see Heinz Rutishauser; Ambros Speiser; Eduard Stiefel: Programmgesteuerte digitale Rechengeräte (elektronische Rechenmaschinen), Birkhäuser Verlag, Basel 1951, page 77).

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The experiences of the three pioneers show that a parallel computer can be more easily controlled: It is a general fact that with machines that function in parallel the control unit is considerably simpler than with a serial machine. Consequently, this compensates partly for the additional complexity of the arithmetic unit. Furthermore, a parallel machine is easier to oversee and troubleshooting is made easier. When a suitable memory can be found the arithmetic unit functioning in parallel will be increasingly preferred (see Heinz Rutishauser; Ambros Speiser; Eduard Stiefel: Programmgesteuerte digitale Rechengeräte (elektronische Rechenmaschinen), Birkhäuser Verlag, Basel 1951, page 81).

The same conclusion was also reached with the Princeton machine (IAS computer): At the time the decision in favor of parallel over serial was made (1946) it was not at all obvious that the number of tubes would be smaller for the former than for the latter. Indeed, the a priori view was to the contrary, since a serial arithmetic unit contains much less equipment than a parallel one. The real saving occurred in the control, which was much more complex in the serial machine. This more than outweighed the savings in the arithmetical parts (see Herman Goldstine: The computer from Pascal to von Neumann, Princeton University Press, Princeton, New Jersey 1993, page 312).

Bit and Word A bit (binary digit) is the smallest possible information unit in a digital computing system. It assumes one of two values (0 and 1, O or L). Here 1 and 0 stand for opposite states or values, such as “on” and “off”, “closed” and “open”, “yes” and “no”, “true” and “false”, etc. The combination of eight bits gives one byte. A 32 bit processor can process 32 bits simultaneously (in parallel). A processor is understood as the central unit of a digital computer. It comprises a control unit and an arithmetic unit. A word is a character string processed as a unit by the computer. It is the largest amount of information that a processor can handle in a single (simultaneous) processing step. Computers have word lengths of, e.g., 8, 16, 32, 48, or 64 bits. Word lengths can be fixed or variable. Instead of bit-serial transfer and processing, today’s computing machines utilize bit-parallel transmission and processing (words consisting of 32 or 64 bits). Serial-Parallel Machines Series-parallel operation is a combination of serial and parallel operation. In this case the characters are transmitted successively but the bits within a word simultaneously. However, the characters are processed successively (serially), while the places of a number are processed simultaneously (in parallel). Examples of serial-parallel computers: Ermeth and Ural 1. The Sec (simple electronic computer, Birkbeck College) had a serial arithmetic unit and a serial-parallel control unit. Serial machines usually had mercury memories. On the other hand, parallel computers generally used cathode ray tubes. Eniac originally executed the programs in parallel. Later, following the conversion to a (partly) stored-program-controlled computer (with read-only memory), the device functioned serially.

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Numerous serial and parallel computers were built on the basis of relays and vacuum tubes (see Table 2.7). Table 2.7  Computers with parallel or serial processing Parallel and serial operation of early computers Name of computer ABC (USA) Ace (England) Analytical engine (England) Ape(x)c (England) ARC (England) Bark (Sweden) Bell 1 computer (USA) Bell 5 A/B computer (USA) Bell 6 computer (USA) Besk (Sweden) Besm 1 (Ukraine) Binac (USA) Colossus 2 (England) Csirac (Australia) Curta (Liechtenstein) Deuce (England) Edsac 1 (England) Edsac 2 (England) Edvac (USA) Eniac (USA) Era 1101 (USA) Ferranti Mark 1 (England) Harvard Mark 1/IBM ASCC (USA) Harvard Mark 2 (USA) Harvard Mark 3 (USA) Harwell Dekatron (England) IAS computer (USA) IBM 650 (USA) IBM 701 (USA) IBM SSEC (USA) Leibniz machine (Germany) Leo 1 (England) Punched card machine (USA) Manchester baby (England) Manchester Mark 1 (England) Mesm (Ukraine) Pascaline (France) Pilot Ace (England)

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Table 2.7 (continued) Parallel and serial operation of early computers Name of computer M9 calculating punch (Germany) Bead frame (abacus) Calculating table Schickard calculating clock (Germany) Seac (USA) Sec (England) Swac (USA) Thomas arithmometer (France) Turing machine (England) Univac 1 (USA) Whirlwind (USA) Slide bar adder Zuse Z3 (Germany) Zuse Z4 (Germany)

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Remarks The unfinished analytical engine of Charles Babbage (England) and the Turing Bombe, or Turing-Welchman Bombe, of Alan Turing and Gordon Welchman (England), as well as the Bell 5 computer, also belong to the parallel machines. The once common name Madm (Manchester automatic digital machine) is found in the professional journals for both the Manchester baby and the Manchester Mark 1. Swac was originally called Zephir. With mechanical calculating machines and slide bar adders, numbers are entered sequentially, usually from right to left (ones, tens, hundreds place, etc.). With four-­function machines operated by a hand crank, multi-digit numbers are transferred simultaneously to the accumulator mechanism. “Function” stands for basic arithmetic operation. With the Schickard and Pascal calculating devices, the individual digits of a number are transferred serially (sequentially) and with the Leibniz machine in parallel (simultaneously) to the arithmetic unit. Cylindrical machines are in general serial calculating devices.

2.3  Decimal and Binary Machines Mechanical calculating machines and early relay and vacuum tube computers were mostly decimal machines. They functioned internally with the decimal system, so that the conversion from and to the binary system no longer

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applied. Decimal machines often represented numbers with the Aiken code or the excess-3 code (Stibitz code). Vastly simpler for the construction of computers is, however, the binary system. Gottfried Wilhelm Leibniz (1679, Description of a binary calculating machine), Raymond Valtat (1936), and Louis Couffignal (1937) in France and William Phillips in England (1936, binary octal system) had already proposed this approach. In this case, it is necessary to convert numbers from the decimal system to the binary system and vice versa. Both decimal numbers and binary representation have their advantages (see Table 2.8). Table 2.8  Properties of decimal and binary machines Comparison of decimal and binary machines Attribute Decimal machine Arithmetic unit Utilizes the numerals 0 to 9 Configuration More complex Speed Requires no conversion between decimal and binary numbers Examples Relay computers, early vacuum tube computers, mechanical calculating machines

Binary machine Utilizes the numerals 0 and 1 Simpler Requires conversion between decimal and binary numbers Relay computers, vacuum tube computers, transistor computers

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Binary computers soon became the standard (see Table 2.9). Table 2.9  Computers with decimal or binary system Early decimal and binary computers Name of computer ABC (USA) Ace (England) Analytical engine (England) ARC (England) Bark (Sweden) Bell 1 computer (USA) Bell 3 computer (USA) Bell 5 A/B computer (USA) Besm 1 (Ukraine) Binac (USA) Colossus 2 (England) Csirac (Australia) Curta (Liechtenstein) Deuce (England) Edsac 1 (England)

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Table 2.9  (continued) Early decimal and binary computers Name of computer Edvac (USA) Eniac (USA) Era 1101 (USA) Ferranti Mark 1 (England) Harvard Mark 1/IBM ASCC (USA) Harvard Mark 2 (USA) Harvard Mark 3 (USA) Harwell Dekatron (England) IAS computer (USA) IBM 650 (USA) IBM 701 (USA) IBM SSEC (USA) Leibniz machine (Germany) Leo 1 (England) Manchester baby (England) Manchester Mark 1 (England) Mesm (Ukraine) Pascaline (France) Pilot Ace (England) Schickard calculating clock (Germany) Seac (USA) Swac (USA) Thomas arithmometer (France) Turing machine (England) Univac 1 (USA) Univac 2 (USA) Whirlwind (USA) Zuse Z3 (Germany) Zuse Z4 (Germany)

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Remark The Turing machine is not necessarily binary. Confusing: Digital – Electronic – Binary The counting board of antiquity was already digital, as was the calculating table of the Middle Ages. Digital does not always mean electronic: There are also mechanical digital calculating machines (e.g., stepped drum and pinwheel machines). With analog machines a distinction is also made between mechanical and electronic machines. Digital does not always mean binary. In earlier times digital computers were in fact often decimal. The binary system existed well before Leibniz (see box).

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The Binary System Already Originated Before Leibniz In numerous publications, including newer ones, the polymath, Gottfried Wilhelm Leibniz is always cited with having discovered or invented the binary system. During his lifetime there was in fact no application for the binary system, but since 1940 it constitutes an important basis for the digital computer. The researches of Shirley und Ineichen question the European origin of this place value system. Reports of very much older number systems based on two numerals indicate that this was developed above all in Asia. Of particular interest here are the developments in Polynesia and the Ethiopian multiplication method. The English Mathematician and Natural Scientist Thomas Harriot: Initial Investigations Already about 70  years ago, John W.  Shirley (North Carolina State College, Raleigh, North Carolina) pointed out that the binary system originated long before Leibniz: Though it is frequently stated that binary numeration was first formally proposed by Leibniz as an illustration of his dualistic philosophy, the mathematical papers of Thomas Harriot (1560–1621) show clearly that Harriot not only experimented with number systems, but also understood clearly the theory and practice of binary numeration nearly a century before Leibniz’s time (see John W.  Shirley: Binary numeration before Leibniz, in: American Journal of Physics, volume 19, 1951, no. 8, page 452).

It is frequently asserted that Leibniz expressly proposed the binary system for the first time with the exposition of his dualistic philosophy. However, as clearly emerges from the mathematical essays of Thomas Harriot (1560–1621), Harriot not only dealt with number systems but also fully understood the theory and practice of the binary system a century before Leibniz. Shirley rejects Leibniz as the originator of the binary system. The English mathematician and natural scientist Harriot also investigated the ternary, quaternary, and quinternary number systems, as well as higher number systems. In his time, though, he saw no applications for these. In regard to Thomas Harriot, Robert Ineichen of the Universität Freiburg (Switzerland) determined: He is arguably the creator of thebinary system, as several manuscripts that he left behind show. In thebinary system he uses the numerals 0 and 1 and gives examples showing how to convert from the decimal system to thebinary system and vice versa (Conversio and Reductio). In further examples he demonstrates the basic arithmetic operations (see Robert Ineichen: Leibniz, Caramuel, Harriot und das Dualsystem, in: Mitteilungen der deutschen Mathematiker-Vereinigung, volume 16, 2008, no. 1, page 14).

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Juan Caramuel y Lobkowitz: First Publication According to Ineichen, the two-volume work Mathesis biceps vetus et nova (Double-headed mathematics – old and new) of the Spanish priest Juan Caramuel y Lobkowitz (1606–1682) is probably the first European publication about the binary system (and other place value systems). Gottfried Wilhelm Leibniz (1646–1716) dealt, for example, with this subject in the Histoire de l’Académie royale des sciences (Paris 1705). John Napier discussed binary arithmetic (powers of two) on a chessboard (multiplication, division, square roots) in his Rabdologiæ (1617). And in De numeris multiplicibus (1654, 1665), Blaise Pascal recognized that the base 10 is not compulsory. Binary, Ternary, and Decimal Machines Leibniz built (mechanical) decimal calculating machines, a species of which has survived. But he also described a binary model that functioned with beads. Some early electromechanical or electronic relay and vacuum tube computers were decimal: Eniac, Harvard Mark/IBM ASCC, and Univac (all USA). Nevertheless, the binary representation prevailed: ABC (USA), Edsac (UK), Ferranti Mark (UK), IAS computer (USA), Pilot Ace (UK), and Zuse Z4 (Germany). Ternary computers, such as the Setun (Russia), were rare. An exception: Quantum computers can function simultaneously in two (or more) states. Multiplication in the Binary System Without a knowledge of multiplication tables, it is possible to perform multiplication in written form by halving, doubling, and adding. The procedure already described in the Rhind mathematical papyrus (around 1550  BC) is known by several names: Egyptian, Ethiopian, or Russian multiplication, as well as peasant multiplication. Sources Robert Ineichen: Leibniz, Caramuel, Harriot und das Dualsystem, in: Mitteilungen der deutschen Mathematiker-Vereinigung, volume 16, 2008, no. 1, pages 12–15 John W. Shirley: Binary numeration before Leibniz, in: American Journal of Physics, volume 19, 1951, no. 8, pages 452–454

Notes For more details on Egyptian, Ethiopian, and Russian multiplication, see: Otto Forster: Algorithmische Zahlentheorie, Springer Spektrum, Wiesbaden, 2nd revised edition 2015 (section “Die russische Bauernregel der Multiplikation“), pages 12–13)

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Jens Gallenbacher: Abenteuer Informatik. IT zum Anfassen für alle von 9 bis 99  – vom Navi bis Social Media, Springer-Verlag GmbH, Deutschland, Berlin, 4th edition 2017 (section “Die Äthiopische Multiplikation“), pages 123–127) CatherineStern; Margaret B. Stern: Comments on ancient Egyptian multiplication, in: The arithmetic teacher, volume 11, 1964, pages 254–257 and Egyptian multiplication, Wolfram demonstrations project, http://demonstrations.wolfram.com/EgyptianMultiplication/, https://rosettacode.org/wiki/ Ethiopian_multiplication Eric W. Weisstein; Dave Zobel: Russian multiplication, MathWorld – A Wolfram web resource, http://mathworld.wolfram.com/RussianMultiplication.html

2.4  Fixed Point and Floating Point Computers Fixed point and floating point had their drawbacks (see Table 2.10).

Table 2.10  Advantages and disadvantages of fixed point and floating point computers Comparison of fixed point and floating point computers Attribute Fixed point computer Numerical notation Fixed point Range of numbers Smaller Arithmetic unit Simpler Programming More difficult

Floating point computer Movable decimal point Larger More complex Simpler

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Explanations With fixed point representation, it is necessary to ensure that the permissible range of numbers is not exceeded during the entire computation process. Accordingly, restrictions are given for the input values. For example, the decimal point is positioned before the first digit (0.9999) or after the last digit (9999.). With the floating point representation, exponents are used, enabling a considerable expansion of the range of numbers. Examples (simplified): 345.67 = 0.34567 ∗ 103 or 0.009876 = 0.9876 ∗ 10−2. In the electronic computer, the values can be represented as 34567 + 3 or 98760 – 2. Early computers functioned primarily with fixed point notation (see Table 2.11).

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Table 2.11  Computers with fixed point or floating point Early fixed point and floating point computers Name of computer ABC (USA) Ace (England) Bark (Sweden) Bell 1 computer (USA) Bell 2 computer (USA) Bell 3 computer (USA) Bell 4 computer (USA) Bell 5 A/B computer (USA) Bell 6 computer (USA) Besk (Sweden) Besm 1 (Ukraine) Binac (USA) Curta (Liechtenstein) Edsac 1 (England) Edsac 2 (England) Edvac (USA) Eniac (USA) Era 1101 (USA) Ferranti Mark 1 (England) Harvard Mark 1/IBM ASCC (USA) Harvard Mark 2 (USA) Harvard Mark 3 (USA) IAS computer (USA) IBM 650 (USA) IBM 701 (USA) IBM SSEC (USA) Leo 1 (England) Manchester baby (England) Manchester Mark 1 (England) Mesm (Ukraine) Pilot Ace (England) Seac (USA) Swac (USA) Univac 1 (USA) Whirlwind (USA) Zuse Z3 (Germany) Zuse Z4 (Germany)

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Remarks Bead frames, mechanical calculating devices, slide bar adders, and punched card equipment were generally fixed point calculators in so far as they utilized decimal places at all. With analog devices (e.g., slide rules, sectors, proportional dividers, or planimeters), the accuracy was in any case limited. Colossus processed only whole numbers and is therefore neither a fixed point nor a floating point computer. Zuse referred to the floating point notation by the term “semilogarithmic representation.” Torres Quevedo had already dealt with floating point arithmetic. Comparison of Fixed Point and Floating Point In summary it can be said that the constraint of having to approximately determine the order of magnitude of the computational result formed in advance with a fixed point machine i9n order to work successfully represents a disadvantage, this is more than compensated by a number of advantages compared with floating point machines. Without a doubt future developments will attempt to combine the advantages of both systems in a single machine (see Heinz Rutishauser; Ambros Speiser; Eduard Stiefel: Programmgesteuerte digitale Rechengeräte (elektronische Rechenmaschinen), Birkhäuser Verlag, Basel 1951, page 27).

2.5  Special-Purpose and Universal Computers The term “universal computer” is not used consistently. Some persons regard only stored-program machines as (true) general-purpose computers. In any case we are still a long way from all-purpose computers. Mechanical calculating machines capable of all four basic arithmetic operations were viewed as universal machines, just as were program-controlled (punched tape controlled) devices. Even the plugboard-­controlled monster Eniac, which was programmed by replugging connecting cables and later by rotating switches, is regarded as a universal computer. In this book the term universal computer is used in a wider sense. Over a period of time, general-purpose machines replaced special computers (see Table 2.12). Table 2.12  Properties of digital special-purpose and universal computers Comparison of selected special-purpose and universal computers Attribute Special-purpose computer Universal computer Purpose Restricted General, unrestricted Device control Fixed program (rigid gear train, External program (on punched tape, plugboard control panel) hard wiring, microprogram) (relay and External program (on punched Internal program (stored program) vacuum tube tape, plugboard control panel) computers) Analytical engine, punched card Examples ABC, Bell 1–4 computers, equipment, calculating punch, Zuse Z4, Colossus 1 + 2, difference Bell 5 computer, Harvard Mark 1/IBM engine, Schwilgué “process ASCC, Edsac, Edvac, IAS computer, calculator,” Enigma Ferranti Mark, Univac, universal Turing cryptographic machine, machine (mathematical model) Antikythera mechanism © Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020

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Remarks Eniac and Binac were originally conceived as special-purpose computers but (later) used as general-purpose machines. Examples of calculating aids without program control (special-purpose calculators): • Digital single-purpose calculators (less than four basic arithmetic operations) Napier’s rods Slide bar adders Single-digit adders Adding machines • Digital general-purpose calculators (four basic arithmetic operations) Counting frames (bead frame) Four-function calculating machines • Analog single-purpose calculating devices Antikythera mechanism Church calculator of Jean-Baptiste Schwilgué (astronomical clock of the Strasbourg cathedral) Tide predicting machine of William Thomson Slide rule (2 basic arithmetic operations) Curvimeter Planimeter Pantograph Coordinatograph Analog fire control computer (Special-purpose) differential analyzers • Analog general-purpose calculating devices Sector Proportional dividers Mechanical differential analyzer of Vannevar Bush Electronic analog computer of Helmut Hoelzer. A sequence control is also found e.g. in automaton clocks, automaton figures, musical automatons and mechanical looms. Table 2.13 contrasts three historically important program-controlled digital computers: the Harvard Mark 1/IBM ASCC, Eniac, and Zuse Z4. Table 2.13  Comparison of three important early digital computers Attributes of three important digital automatic computers Name of computer Harvard Mark 1/IBM ASCC Year of manufacture 1943 Universal computer ■ Relay computer ■ Vacuum tube computer

Eniac 1945 ■ ■

Zuse Z4 1945 ■ ■ (continued)

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Table 2.13 (continued) Attributes of three important digital automatic computers Name of computer Harvard Mark 1/IBM ASCC Plugboard control Punched tape control ■ Stored program □ Parallel computer ■ Decimal computer ■ Binary computer Conditional branching □ Fixed point computer ■ Floating point computer

Eniac ■ □ ■ ■ ■ ■

Zuse Z4 ■ □ ■ ■ □ ■

© Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020 Explanation of symbols: ■ Yes □ No

Remarks The information above refers to the original configuration. In 1949/50, at the request of ETH Zurich, the Zuse Z4 was modified and equipped with conditional branching. The program control of the Eniac vacuum tube computer was subsequently simplified (switches in place of cables). All three computers differ in certain properties from modern digital computers: decimal number system (Harvard Mark 1/IBM ASCC, Eniac), no conditional branching (Harvard Mark 1/IBM ASCC, Z4), and in general without stored program. With respect to the binary system and floating point notation, the Z4 was more advanced than its American competitors but was less developed in terms of technology (relays) and conditional commands than Eniac. The two punched tape controlled Bell 5 computers (A: 1946, B: 1947) were also “universal computers” (parallel decimal relay machines with floating point notation and conditional branching) but without a stored program.

2.6  Interconnected Computers Different types of calculating aids can be coupled, in which case the components are mostly used independently of each other: • Digital slide bar adder (addition on the front side) and digital slide bar adder (subtraction on the rear side) • Digital slide bar adder (addition, subtraction) and analog slide rule (multiplication, division) (e.g., Faber Castell) • Digital slide bar adder (addition, subtraction) and printed tables (multiplication, division) • Digital slide bar adder (addition, subtraction) and digital multiplication and division cylinders • Digital calculating machine (addition and subtraction) and digital multiplication and division cylinders (e.g., the calculating clock of Schickard)

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• Digital electronic pocket calculator and digital bead frame (e.g., Sharp) • Digital electronic pocket calculator and analog slide rule (e.g., Faber Castell) • Digital differential analyzer (program-controlled analog computer) (e.g., Maddida) • Digital punched card machine and digital electronic calculating devices (e.g., card-programmed calculators). The combination of an analog slide rule and a digital slide bar adder proved to be successful. Equipping a slide bar adder with multiplication and division tables was also practical. On the other hand, the combination of a (high-performance) digital electronic pocket calculator with another calculating aid does not appear to be sensible, since this does not extend the functionality. In terms of construction there are also hybrid forms of the same device: mechanical and electrical components, relays and vacuum tubes, vacuum tubes and transistors, or fast vacuum tubes and slower drum memories. A hybrid between relay and vacuum tube computers was the IBM SSEC (selective sequence electronic calculator). The SSEC was primarily a relay computer. A rare combination comprises an abacus with (unusually) 4 and 2 beads and rotating Napier’s bones (see Figs. 2.28 and 2.29).

Fig. 2.28  Interconnected calculating device (1). This calculator of Michel Rous from Paris (1869) comprises eight rotating Napier’s bones and a nine-place Chinese abacus. (© Technisches Museum Wien, Vienna)

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Fig. 2.29  Interconnected calculating device (2). This rare mathematical instrument served for multiplication and division (at the top). For multiplication partial products were formed. The rods of the abacus (below) are equipped with a small numerical drum and a rotating knob, allowing the recording of the results of additions. (© Inria/picture: J.-M. Ramès)

2.7  Conditional Commands Programs fundamentally execute sequentially. However, in the event of repetitions (repeated execution of loops), omissions (skipping instructions), and calling subroutines, it is possible to deviate from the linear command

2.7  Conditional Commands

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sequence. Conditional commands (conditional instructions) make it possible to influence the program execution. Their execution depends on one or more prerequisites. With the instruction “if…then…otherwise,” only a single condition is queried and for case decisions several conditions. According to whether or not the condition is fulfilled or to the result of a calculation or comparison, the program execution can follow different paths. Conditions (conditional branching) occur with: • • • •

Loops Jumps Decisions (if…then…otherwise) Case differentiations.

Nested loops and above all jumps can lead to unclear and non-transparent programs. For this reason, subprograms are often written. These can be called with jump instructions and must be programmed and stored only once. Charles Babbage had already envisaged conditional commands and loops for the (unbuilt, steam drive planned) analytical engine (jumping out from and returning to the command sequence in the form of a program loop). Leonardo Torres Quevedo (also Torres y Quevedo) also planned such branching. Early machines with conditional commands included the Colossus (partly) and Eniac electronic computers. The conditional jump was an important feature of the von Neumann machines. However, some older automatic relay and vacuum tube machines did not offer conditional commands (see box). The Harvard Mark 1/IBM ASCC was equipped only later with conditional instructions. Konrad Zuse and Howard Aiken generated program loops by sticking together punched tapes. Early Machines Without Conditional Commands • ABC • Bell 1, 2, and 3 computers • Harvard Mark 1/IBM ASCC • Zuse Z3 Early Machines with Conditional Commands • Ace • Bark • Colossus 2 • Bell 5 A/B and 6 computers • Edsac • Eniac • IBM SSEC • Zuse Z4 (subsequent addition)

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In connection with Plankalkül, Konrad Zuse mentions flexible programs along with inflexible programs. von Neumann machines, for example, the Princeton machine (IAS computer) generally and devices built according to the Edvac concept, generally have conditional commands.

2.8  Components of Relay and Vacuum Tube Computers Table 2.14 gives an overview of a few common components used for the arithmetic unit and memory of early relay and vacuum tube computers.

Table 2.14  Switching and memory components of mechanical, electromechanical, and electronic computing machines Components of mechanical, electromechanical, and electronic computers Attribute Switching element Memory element Arithmetic unit Counter, counter wheel Ring counter Counting tube Gear wheel, toothed rack Step counter Relay Vacuum tube Gas-filled tube Transistor Germanium diode Memory Punched card, punched tape Counter, counter wheel Ring counter Gear wheel (Stepped drum, pinwheel) Relay Delay line Electrostatic memory tube Transistor Germanium diode Magnetic core (ring) Magnetic drum Magnetic tape Magnetic disc © Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020

Remarks Other components were, e.g., resistors and capacitors. Vacuum tubes and transistors were also utilized as control elements.

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Fig. 2.30  Hand counting system. Counting and calculating with the fingers was once common. These instructions are taken from the first part of the work Summa de arithmetica geometria of Luca Pacioli (1523). (Source: ETH Library, Zurich, Rare books collection)

Counters Counting and calculating are closely related. This is already made clear by counting with the fingers (see Fig.  2.30). With the bead frame, the result is found by counting the beads. This calculating aid is therefore described as a counting frame. On the calculating table, the result is also given by the number of tokens. Calculating can thus be reduced to counting. For multiplication mechanical calculating devices are often equipped with a revolution counter. This retains the number of times the multiplicand is multiplied by the multiplier. For division the number of times the divisor is contained in the dividend, i.e., the number of times the divisor can be subtracted from the dividend, is counted. The arithmetic unit, or result register, of mechanical calculating devices is also referred to as the accumulator or accumulator register.

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Counters (switching mechanisms) can be mechanical or electronic. We distinguish between decimal counters and binary counters. Ring counters were comprised, for example, of flip-flop tubes or flip-flop transistors. Cold cathode tubes (glow discharge tubes) and thyratron tubes were used. A circular shift register also came into question. Heinz Billing describes the process as follows: The ring counter is used almost exclusively as a decimal counter. Each decimal place is allocated to a counting ring with 10 memory locations. In each counting ring only one of the memory locations is occupied ("1"), marking which decimal numeral from 0 to 9 is stored in the ring. A counting pulse shifts the set position in the ring allocated to the lowest decimal place to the neighboring storage location, which is allocated to the next higher position, for example making a 6 out of a 5. When the ring has counted up to 9 the next counting pulse has two functions. First it shifts the lowest counting ring from 9 to 0. For this purpose location 9 is linked to location 0 to close the counting ring. Secondly, the transition from 9 to 0 triggers a new counting pulse that increases the next higher decimal place by one position (see Karl Steinbuch (editor): Taschenbuch der Nachrichtenverarbeitung, Springer-Verlag, Berlin, 2nd revised edition 1967, page 502).

Flip-Flops A flip-flop (bistable toggle switch, bistable trigger circuit) is a circuit with two stable states. With this toggle switch only one of the two triodes conducts current. A simple version of this is a light switch. For electronic flip-flops, vacuum tubes and transistors are used, for example. A flip-flop is capable of storing one bit. Memory registers and electronic counters, such as ring counters, are comprised of flip-flops. Vacuum tube flip-flops were also called trigger circuits. A (simple) trigger circuit consists of two triodes, with the anodes and grids cross-connected. Shift Registers Registers are small intermediate memories with short access times. They are usually comprised of flip-flops. With counter registers, one can count, while shift registers serve to shift data. A shift register is a linear or ringshaped arrangement of memory locations. It was made up of flip-flop tubes, flip-flop transistors, or magnetic cores. During shifting information is transferred to neighboring locations. Shift registers are utilized, e.g., for shifting place values.

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Fig. 2.31  Relay. The first program-controlled digital computers (e.g., Zuse, Bell and Harvard machines, calculating punch) utilized mostly electromagnetic relays for the arithmetic unit and partly also for the memory. They were regarded as reliable but were slow. (© HeinzNixdorf-­Museumsforum, Paderborn, Germany)

There are different types of relays (see box). What Is a Relay? The Brockhaus Computer und Informationstechnologie (F. A. Brockhaus GmbH, Leipzig, Mannheim 2003, page 766) defines the relay (see Fig. 2.31) as follows: “component that opens and closes a circuit when it registers a change in a physical variable. Such a change can occur in an electric pulse or also as pressure or temperature fluctuations. The most common form of the relay is the electromechanical relay. Here an electromagnet actuates the switch contact(s). Such a relay can be controlled with weak currents, but can switch much stronger currents.” There are different types of electromagnetic relays. The most common are the electromagnetic switching devices. In communications technology, telecommunications relays were used for automatic switching. Electromagnetic relays are found in punched card machines, calculating punches and some early automatic digital computers. One also speaks of electronic relays (vacuum tube relays). Relays enable the representation of all logical links.

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Lines of Development: Memories and Arithmetic Units (Early Times) Main Memory Relay ⇨ electronic tube (mercury tube, Williams -Kilburntube) ⇨ magnetic drum ⇨ magnetic core (ferrite core) ⇨ semiconductor Mass Storage Magnetic drum ⇨ magnetic disc (fast access) Punched card ⇨ magnetic tape (slow access) Arithmetic Unit Relay ⇨ electronic tube (vacuum tube) ⇨ transistor Relays and vacuum tubes were the forerunners of transistors (see Table 2.15). Table 2.15  Use of relays and vacuum tubes for computers in earlier times Who used relays and vacuum tubes for digital computers in the early days? Component Germany England USA Relays Konrad Zuse Andrew Booth George Stibitz Howard Aiken Vacuum Helmut Schreyer Thomas Flowers John Atanasoff tubes (experimental model) John Mauchly Presper Eckert

Ukraine

Sergey Lebedev

© Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020

2.9  Electronic Tubes Numerous vacuum tube types were utilized. Radio tubes were in widespread use. Electronic tubes (see Fig. 2.32) were usually divided into: • Vacuum tubes • Gas-filled tubes (thyratrons). Electronic tubes were used for the following units: • Control unit and arithmetic unit (logic) • Memory (main memory). As with relays electronic tubes had two functions. They served as switching elements and as memory components. The pistons were mostly of glass but also of ceramic or steel. For vacuum tubes (multi-electrode tubes, multigrid tubes), a distinction is made between several forms according to the number of electrodes (cathode (negative) and anode (positive)): • Diodes (two-terminal tubes) • Triodes (three-terminal tubes) • Tetrodes (four-terminal tubes)

2.9  Electronic Tubes

• • • •

91

Pentodes (five-terminal tubes) Hexodes (six-terminal tubes) Octodes (eight-terminal tubes) Enneodes (nine-terminal tubes).

Vacuum Tubes Thanks to experience with radar technology it was possible to modify cathode ray tubes (electron beam tubes) for storage purposes. Such electrostatic memory tubes are known as Williams tubes or Williams-Kilburn tubes. Older display screens were equipped with Braun tubes (picture tubes, cathode ray tubes, television tubes). In the English-speaking countries electronic tubes are described as thermionic valves (British English) or mostly vacuum tubes (American English).

Fig. 2.32  Electron tube. The arithmetic unit of early program-controlled digital computers consisted mostly of vacuum tubes. These were in fact much faster than electromechanical relays but much more susceptible to disturbances. Among the best known vacuum tube computers were the Colossus (England) and Eniac (USA). Later machines functioned with transistors. (© Heinz-­Nixdorf-­Museumsforum, Paderborn, Germany)

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Gas-Filled Electronic Tubes Gas-filled electronic tubes have a cold (unheated) cathode (cold cathode) or a heated cathode (hot cathode): • Cold cathode tubes, e.g., trigger tubes, have a glow discharge. • Thyratrons are gas-filled triodes or tetrodes (gas triodes, gas tetrodes). They have an unheated cathode (cold cathode thyratron) or a heated cathode and are employed as decimal thyratron counters. • Decatrons. Gas-filled tubes contained mercury vapor, hydrogen, or noble gas (argon, helium, neon, or xenon). Mercury tanks were used for delay lines. Decatrons found use in the Harwell computer as cold cathode counters. Thyratron tubes were used in the Colossus. Helmut Schreyer constructed tube circuits from vacuum tubes and glow discharge lamps, while Louis Couffignal wanted to use electrostatic neon lamps. A computer with neon tube memory was built in Belgium. Operational Reliability For the early electronic computers, mostly vacuum tubes were used. These electronic switches were considerably faster than mechanical switches (relays) but, for a long time, were regarded as unreliable. Frequent on and off switching reduced their lifespan significantly, as Thomas Flowers, the creator of the British Colossus, found out with the construction of telephone circuitry. Moreover, he let these devices run at less than the rated output. The builders of the giant American Eniac computer, John Mauchly and Presper Eckert, followed the same approach. Arithmetic Unit For numerical computation mostly common vacuum tubes found use. The massive Colossus and Eniac electronic computers utilized thousands of such tubes. Memory For numerical storage special memory tubes were used. Three types of such electronic tubes can be distinguished: • Flip-flop tubes • Delay lines, mostly mercury tubes • Cathode ray tubes, mostly Williams-Kilburn tubes. Delay Line The most common form of delay line was the mercury tube, i.e., metal or glass tubes filled with mercury. The proven tubes from radar technology were more reliable but slower than the Williams tubes. Presper Eckert of the University of Pennsylvania in Philadelphia was decisively involved with the development (patent application in 1947). Mercury tubes were used mostly in serial machines.

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Cathode Ray Tube The Williams-Kilburn tubes of Frederic Williams and Thomas Kilburn (University of Manchester) were the most important of the cathode ray tubes. Cathode ray tubes were found predominantly in parallel computers. For the Whirlwind real-time computer, Jay Forrester of the Massachusetts Institute of Technology (MIT, Cambridge) developed a further, improved version of the electrostatic memory tube. At that time the Radio Corporation of America ((RCA), Research laboratories, Princeton, New Jersey) wars the world’s largest manufacturer of electronic tubes. Jan Rajchman worked on the new Selectron (selective electronic storage tube) tube type. John von Neumann originally wanted to utilize this in his IAS machine. However, production was delayed, so that he had to revert to the Williams tubes. Selectron tubes were used in the Johnniac built by the Rand Corporation (1953).

2.10  Delay Line Memories and Electrostatic Memories The two most important types of electronic (main) memories before the onset of the magnetic drum memory were: • Delay Line Memory Numerous technical terms exist: electronic delay line memory and mercury (delay line) memory, as well as ultrasonic (delay) memory, sonic delay line memory, and acoustic (delay line) memory. The widespread mercury memory was comprised of a steel tube filled with mercury closed off at both ends with a piezo crystal (quartz). Less common were ultrasonic memories with nickel wire, so-called magnetostrictive memory (magnetic wire memory, e.g., Seac). • Electrostatic Memory Here as well there are numerous terms: electrostatic tube memory, Williams-­ Kilburn tube memory, and cathode ray tube memory. Mercury delay lines found use, for example, with the Edvac, Edsac, Binac, Univac 1, Pilot Ace, Deuce, Leo 1, Seac, and Csirac. The following machines were outfitted with electrostatic memories: Manchester Baby (small-scale experimental machine), IBM 701, Swac, IAS computer (Princeton machine), Whirlwind, and Besk. Initially the Besm had a delay line memory and later a cathode ray tube memory.

2.11  Main Memory In the early years electronic tubes were frequently used for the main memory (see Table 2.16).

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Table 2.16  Vacuum tube computers with delay line or electrostatic memory Which type of memory did the early electronic computers have? Electrostatic memory Cathode ray tubes Delay line memory Williams-Kilburn tubes Name of computer Mercury tanks Ace (England) ■ Besk (Sweden) ■ Besm 1 (Ukraine) ■ ■ Binac (USA) ■ Csirac (Australia) ■ Deuce (England) ■ Edsac 1 (England) ■ Edvac (USA) ■ Era 1103 (USA) ■ Ferranti Mark 1 (England) ■ IAS computer (USA) ■ IBM 701 (USA) ■ IBM 702 (USA) ■ Leo 1 (England) ■ Manchester Baby (England) ■ Manchester Mark 1 (England) ■ Pilot Ace (England) ■ Seac (USA) ■ Swac (USA) ■ Univac 1 (USA) ■ Whirlwind (1) (USA) ■ © Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020 Explanation of symbol: ■ = applicable

Remarks For storage early electronic computers were equipped with counting wheels, ring counters, relays, flip-flop tubes, and other similar components. • Electronic Computers ABC This vacuum tube computer had a revolving drum with capacitors. Colossus The memory of the Colossus was comprised of gas-filled tubes (thyratron tubes) and vacuum tubes (with trigger circuits). For the reconstruction of the machine pentodes, triodes, tetrodes, and thyratron tubes (binary counters) were used. Colossus functioned with ring counters.

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Eniac The massive Eniac vacuum tube computer was outfitted with 20 accumulators (memory registers for 10-place decimal numbers). It utilized vacuum double triode flip-flops. For a 10-place decimal number 100 such toggle switches were required. The electronic flip-flop rings (vacuum tube ring counters) replicated the decadic (decimal, 10-place) counting wheels of mechanical tabletop calculating machines. The accumulators were used for storage and for computation. 10-ring counters stored a 10-place decimal number. Eniac had around 18,000 electron tubes (16 different types). Punched cards were used for mass storage. Mesm and Besm The Ukrainian Mesm electronic computer had a flip-flop tube memory (with trigger circuits) and a magnetic drum. For the operation of the followon Besm 1, three memory types were tried out: mercury, electrostatic, and magnetic core memories. The machine, designed for an electrostatic memory, initially had a mercury memory. The Williams tubes were only added in 1955, because they were not available up to this time. The Seac had a magnetic wire memory (nickel wire with serial access) and was later equipped with an electrostatic memory. The Whirlwind was equipped with a magnetic core memory in 1953. The IBM 704 (1954) was one of the first marketable computers with core memory. The Era 1101 vacuum tube computer of Engineering Research Associates, IBM 650, Harvard Mark 3 and 4 had a magnetic drum, as did the Csirac, Manchester Mark 1, and Besk (as auxiliary storage). • Electromechanical Computers Complex Computer/Bell 1 Computer The first Bell computer had 450 relays and, as numeric data register, 10 crossbar switches. The second machine had 440 relays, 5 teleprinters, and 6 registers for the storage of numerical data. Model 3 was equipped with 1400 relays and 10 registers for numerical data. Zuse Z4 The Z4 functioned with mechanical switching elements. For a time a magnetic drum (developed at the ETH Zurich) was also installed. Harvard Mark 1/IBM ASCC The memory of the Harvard Mark 1/IBM ASCC consisted of mechanical counter registers (counting wheels and rotary counters) (mechanical register). The decimal counters also served as an adder. ARC The ARC relay computer (England) exhibited a magnetic drum.

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• Relay/Vacuum Tube Hybrid Computer IBM SSEC The punched card-controlled IBM SSEC hybrid computer had a small (electronic) flip-flop tube memory, a relay memory, and an extensive punched card memory (for data and programs). Different components were utilized for the memories (see Table 2.17). Table 2.17  Memory components of early relay and electronic computers Memory elements of the first relay and vacuum tube computers Relay computers Vacuum tube computers Computer Component Computer Component ARC Magnetic drum ABC Capacitor Bell 1 computer Crossbar switch Colossus Ring counter Harvard Ring counter Eniac Ring counter Zuse Z4 Mechanical switching element © Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020

Remarks Neither delay line memories (e.g., mercury tanks) nor electrostatic memories, such as Williams-Kilburn tubes, were yet available for the first vacuum tube computers. In place of the triode rings of the Colossus and Eniac, the ABC made use of capacitors. These were (nearly) evacuated or gas-filled electron tubes. The developers of memory components (see Table  2.18) are no longer familiar. Table 2.18  Developers of memory components for vacuum tube computers Who developed the early memory components? Type of storage Developer Delay line William Shockley, Presper Eckert, University memory Bell Labs, New York of Pennsylvania, Philadelphia Jay Forrester, MIT, Electrostatic Frederic Williams, Cambridge, MA memory tube University of Manchester Magnetic core Jay Forrester, MIT, Jan Rajchman, RCA, memory Cambridge, MA Princeton © Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020

Jan Rajchman, RCA, Princeton An Wang, Harvard University, Cambridge, MA

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Remarks MIT stands for Massachusetts Institute of Technology and RCA for Radio Corporation of America. The storage media are required both as a data carrier and as a program carrier. Special forms, such as wooden or brass pinned cylinders, metal perforated discs, and pinned boards, are found in musical automatons. The winding springs of mechanical clocks and music boxes also serve as memory. The melodies of mechanical musical instruments were often retained on punched tapes of folded (stacked) carton or paper. Core memories were developed at several locations at the end of the 1940s: Harvard University (An Wang) and MIT (Jay Forrester), both in Cambridge (Massachusetts), and Radio Corporation of America, Princeton (Jan Rajchman). Andrew Booth, Dudley Buch, William N.  Papian, and Frederick Viehe are mentioned as other developers of the magnetic core memory. The magnetic drum also has a number of fathers, e.g., Arnold Cohen (ERA, St. Paul, Minnesota), Heinz Billing (Göttingen), and Andrew Booth (London). There are several inventors of storage media and switching elements (see box). Inventors of Storage Media and Switching Elements Basile Bouchon created the punched tape and Jean-Baptiste Falcon the punched card. The relay was developed by Joseph Henry. The flip-flop is the work of William Henry Eccles and Frank Wilfred Jordan. We owe the magnetic tape to Fritz Pfleumer and the magnetic drum to Gustav Tauschek and Gerhard Dirks. Louis Stevens, John Lynott, and William Goddard patented the magnetic hard disc. Also worth mentioning is the gear wheel (e.g., the stepped drum and pinwheel of Gottfried Wilhelm Leibniz and the pinwheel of Giovanni Poleni).

2.12  Magnetic Memory Magnetic memories (see Fig.  2.33) served for both short-term and long-term storage. Below are the most important forms: • • • •

Magnetic drum memory (main memory and mass storage) Magnetic core memory (main memory with random access) Magnetic disc storage (main memory and mass storage) Magnetic tape storage (mass storage with serial (sequential) access).

Mass storage with slow access (external memory) • Magnetic tape. Mass storage with fast access (internal and external memory) • Magnetic drum • Magnetic disc.

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Fig. 2.33  Core memory. With magnetic cores (ferrite cores), the computation speed could be increased considerably. (© Deutsches Technikmuseum, Berlin)

Drum memories and core memories succeeded tube memories. Drum memories first served as main and later as external memories. Today’s computers are equipped with semiconductor memories and hard discs. Tape storage and hard discs provide data backup. Several memory types are often combined: small, fast, and expensive main memory with large, slow, inexpensive auxiliary storage devices. Early vacuum tube computers often had both a disc memory and a tape memory. Optical memories (compact disc (CD) and digital versatile disc (DVD) function as external memories. With optical media as well, the problem of longterm digital data storage remains unsolved. Since When Have Magnetic Drum, Magnetic Tape and Magnetic Core Memories Been in Use? • Magnetic drum memories were used for electromechanical and above all for electronic digital computers, partly for the main memory and partly for auxiliary storage. The term magnetic drum computer refers to machines with a drum memory as main memory. Examples of machines with drum memories are ABC (1942), Ape(x)c (1953), ARC2 (1947), Atlas 1/Era 1101 (1950), Besm 1 (1953), BTM Hec 2  M

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(1955), Csirac (drum 1951), Deuce (1955), Edvac (1952), Elliott 402 (1955), Era 1103 (1953), Ferranti Mark 1 (1951), G1 (Göttingen 1, 1952), Harvard Mark 3 (1950), Harvard Mark 4 (1952), Hec4 (1955), IAS computer (1952), IBM 650 (1953), IBM 701 (1952), IBM 704 (1954), Mailüfterl (1958), Manchester Mark 1 (1949), Mesm (1951), Pilot Ace (from 1954), Sec (1950), Strela (1953), and Z22 (1958). The ABC incorporated a capacitor drum. The ARC (automatic relay calculator, Birkbeck College) and the Demon and Goldberg special codebreaking computers of the Engineering Research Associates (ERA) (1948) are regarded as the first magnetic drum computers. Magnetic drum computers appeared around the end of the 1940s. • Magnetic tapes were utilized in the Ape(x)c (1953), Besm 1 (1953), Edvac (1952), Era 1103 (1953), Harvard Mark 3 (1950), IBM 650 (1953), IBM 701 (1952), IBM 704 (1954), Mesm (1951), and Univac 1 (1951) vacuum tube computers. Magnetic steel tapes were first used in computers around 1950. • Magnetic core memories appeared in the first half of the 1950s: Eniac (1953), Era 1103A (1956), Harvard Mark 4 (1952), IBM 650 (1953), IBM 704 (1954), Edsac 2 (1957/1958), Univac 2 (1957), and Whirlwind (1953). Notes Computers with magnetic discs were first offered from 1956/1957 (e.g., IBM 305 Ramac). The Elliott 403 also belongs to the early magnetic disc computers. The following article describes the memories of mechanical calculating machines: Harald Schmid: Speichervorrichtungen bei mechanischen Vierspezies-­Rechenmaschinen, 2006 (www.rechnerlexikon.de). The Schickard calculating clock already had a memory for intermediate results.

2.13  Hardware and Software In computer science a distinction is made between hardware and software. Hardware is understood to mean devices and components. Software refers to either programs and data or simply programs. Physical laws apply for the “hardware”. The “software” follows logical rules. However, the boundary between the (non-alterable) materials and the (alterable) immaterial goods is fuzzy. One can transform “mental” algorithms to “physical” material. Thus, for example, we can convert between the binary system and the decimal system or “hardwire” the floating point notation. Instructions that the manufacturer stores to a read-only memory are referred to as firmware, i.e., “permanent ware”. The user has only restricted possibilities to change these instructions. The multiplication table of direct multipliers can be seen as a read-only memory (or hardwired) program.

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Early calculating devices consisted of a single body, whereas the programmable digital computers of recent times have a body and a “soul”. More precisely: the “soul” was then carved in wood, chiseled in stone, or cast in iron. One advertised with a “brain of steel”. It is much easier to change abstract program commands to others than gear wheels of brass and bronze or the pinned cylinders of barrel organs (hurdy gurdies). Machines with a large amount of material, such as the giant Eniac of Mauchly/Eckert, are more cumbersome than machines with a high degree of logic (e.g., the Ace of Turing). A modern smartphone is far more versatile than a mechanical pocket calculator. The less hardware and the more software, the greater is the range of applications (see Table 2.19). However, software is always bound to hardware. Thus, for example, robots and drones must have a body. Table 2.19  The proportions of hardware and software determine the versatility of the device Relationship of hardware to software Component Hardware Scope of Single-purpose device applications (Non-alterable) Integrated algorithm hard-wired program (Alterable) external program

(Alterable) internal program Examples

Bead frame Slide rule Counting board Slide bar adder Mechanical calculating machine Chess-playing machine Antikythera mechanism Heron’s automatic theater

Hardware and software Single-purpose or multi-purpose device

Hardware and software General-purpose device

Interchangeable cam Interchangeable plugboard Punched card program Punched tape program

Automaton figure Musical automaton “Jacquard” loom Punched card machine Harvard Mark 1/IBM ASCC Eniac Zuse Z4

Interchangeable stored program Electronic digital computer Smartphone

© Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020

Remarks Examples of hybrid forms are the hard-wired ABC electronic computer, the early Bell relay computer, and the plug-programmed Colossus vacuum tube computer. As a rule, machines with artificial intelligence, robots, drones, and selfdriving cars can be used only for a single purpose.

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2.14  Subtraction with Complements With skillful techniques it is possible to simplify arithmetic operations with mechanical and electronic machines. The Pascaline already functioned with complements and thus employed indirect subtraction. The small Curta also drew upon this, as did the Harvard Mark 1/IBM ASCC. The complements also serve for the representation of whole negative numbers on mechanical and electronic digital machines. Direct and Indirect Subtraction With some mechanical calculating machines, it is possible to rotate the crank in the clockwise and the counterclockwise direction. For addition, for example, the crank is rotated to the right and for (direct) subtraction to the left, or one has to shift for subtraction. Direct Subtraction Direct subtraction means subtracting without complements. This requires that the machine is capable of tens carry in both directions and that the direction of rotation can be reversed. Indirect Subtraction With indirect subtraction one adds the complements. For devices such as the Thomas arithmometer or the Curta, the crank is always rotated in the same direction. With the Thomas machine, changing between addition and subtraction takes place with a lever and with the Curta by lifting the crank. This device utilizes a stepped complement cylinder for indirect subtraction. Complementation (see box) also plays an important role with electronic computers. It changes the sign of binary numbers, allowing binary subtraction to be performed as an addition.

Complementation In the decimal system (base-10 number system) a distinction is made between: • Nine’s complement • Ten’s complement. With nine’s complement the difference of a number from 9 is calculated. The complement of the number 456 (to 999) is 543. The value 123 corresponds to the nine’s complement 876 (123 + 876 = 999). Decimal starting number + nine’s complement = 9.99, 999, etc. (i.e., 101–1, 102–1, 103–1, etc.). The ten’s complement of 456 is 544 (456 + 544 = 1000), and the ten’s complement 123 is 877 (complement of 1000). Decimal starting number  +  ten’s complement  =  10, 100, 1000, etc. (i.e., 101, 102, 103, etc.). (continued)

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In the binary system (base-2 number system), we speak of: • One’s complement • Two’s complement. The one’s complement represents the difference from the binary value 1. The complement of the binary number 101 is, e.g., 010, or simply 10, that is the inverse (101 + 010 = 111, decimal 5 + 2 = 7). The one’s complement of (binary) 100110 is identical with the mirror image: 011001 (100110 + 011001 = 111111, decimal 38 + 25 = 63). One therefore replaces – place by place – each 1 by a 0 and each 0 by a 1, i.e., interchanges 0 and 1. Binary starting number + one’s complement = 1, 11, 111, 1111 (binary), etc. (i.e., 20, 20 + 21, 20 + 21 + 22, 20 + 21 + 22 + 23, etc.). The two’s complement represents the complement of binary 0. For the binary number 1010, the ones and zeroes are first interchanged, yielding the value 0101. Then 1 is added: 0110 (control: 1010 + 0110 = 10000, decimal 10  +  6  =  16). Converting the ones of the binary number 10101 to zeroes and the zeroes to ones leads to the numerical sequence 01010, adding the 1 to 01011 (10101 + 01011 = 100000, decimal 21 + 11 = 32). The two’s complement of the binary numbers 11111 and 00000 are 00001 and 100000. The sum of these binary numbers and their two’s complements is (binary) 100000 (decimal 31 + 1 = 32; 0 + 32 = 32). For the two’s complement, we form the one’s complement and add 1 to this. Binary starting number + two’s complement = 1, 10, 100, 1000 (binary), etc. (i.e., 20, 21, 22, 23, etc.).

The (decimal) nine’s and ten’s complements are of practical relevance for mechanical computing devices and the (binary) two’s complement for electronic computers. Subtraction = Addition with Complements With some mechanical calculating devices, subtraction is performed as an addition of complements (see box). For example, 345 is subtracted from 612. The nine’s complement of 345 is 654, and the individual numbers are all raised to 9 (3 + 6 = 9, 4 + 5 = 9, 5 + 4 = 9). Direct subtraction:   612–345 = 267. Indirect subtraction:  612 + 654 = 1266. The overflow, i.e., the number 1, is added to the remaining value 266, giving the result 267. Other examples of indirect subtraction: 3–0 = 3 3 + 9 = 12 1 + 2 = 3 The overflow (1) is added to the last digit (2). 3–1  = 2 3 + 8 = 11 1 + 1   = 2 The overflow (1) is added to the last digit (1). 3–2  = 1  3 + 7  = 10  1 + 0 = 1

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The overflow (1) is added to the last digit (0). 3–3 = 0   3 + 6 = 9    0 The result 9 corresponds to the value 0 (nine’s complement). 33–32 = 1    33 + 67 = 100     1 + 0 = 1 The overflow (1) is added to the value 00. 33–33 = 0  33 + 66 = 99     0 The result 99 corresponds to the value 0 (nine’s complement). 333–333 = 0 333 + 666 = 999 0 The result 999 corresponds to the value 0 (nine’s complement). Subtraction with Nine’s Complements Minuend – Subtrahend = Difference a – b = ? x = a – b x = 999 – [(999 – a) + b] Example x = 345 – 76 x = 999 – [(999–345) + 76] x = 999 – [654 + 76] x = 999 – 730 x = 269.

2.15  Direct and Indirect Multiplication As with complementation, shift processes in the decimal and binary system can simplify mechanical computation. Direct and Indirect Multiplication with Mechanical Calculating Machines Indirect Multiplication: Repeated Addition Indirect multiplication is on the basis of addition. With mechanical calculating devices, this method requires rotating the crank repeatedly. Different methods have been tried to simplify and accelerate handling. The number of revolutions can be reduced by abridged multiplication (from left to right) and by a moving carriage. The setting mechanism and accumulator register can be shifted relative to each other, enabling the correct positioning of the numbers for calculation. Shortcut Multiplication Abridged multiplication (abbreviated multiplication) requires a revolution counter with tens carry. With this method the number of crank revolutions can be reduced. For multiplication by nine, two revolutions are sufficient: initially multiplication by 10, carriage shift by one place from the tens to the ones, and (subtractive) crank rotation (according to the model in the clockwise or counterclockwise direction).

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Direct Multiplication Only a few mechanical calculating machines offer direct multiplication. The most successful of these was the Swiss “Millionaire.” A further example is the Moon-Hopkins bookkeeping machine (accounting and billing machine) of the Moon-Hopkins Billing Machine Company (Burroughs) (John C. Moon, Hubert Hopkins). Less fortunate was the Kuhrt calculating machine (with multiplication table, 1923). Multiplication Tables Thanks to a multiplication table or multiplication block, with this direct multiplying machine, only one revolution of the crank per decimal place suffices. Note: these machines are capable of all four basic arithmetic operations. Lazy Tongs The calculating machines of Eduard Selling (see Figs. 2.34 and 2.35) made use of toothed racks with lazy tongs (1886) but were unable to gain acceptance. These tongs were comprised of a series of parallelograms (a description of the operating principle is given by K. Hoecken: Die Rechenmaschinen von Pascal bis zur Gegenwart, unter besonderer Berücksichtigung der Multiplikations­ mechanismen, in: Sitzungsberichte der Berliner Mathematischen Gesellschaft, volume 13, 106th session, February 26, 1913, pages 16–17). Remark Division is performed as repeated subtraction.

Fig. 2.34  Selling’s direct multiplier (original). The direct multiplication machine of Eduard Selling (1906) functions according to the lazy tongs principle. Hermann Wetzer in Pfronten built two of these according to the second version. It eliminates wheels; however the tens carry is difficult. (© Deutsches Museum, Munich)

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Fig. 2.35  Selling’s direct multiplier (replica). With this machine, for direct multiplication toothed racks are shifted by lazy tongs. The invention achieved little commercial success. (© Braunschweigisches Landesmuseum, Braunschweig, picture: Anja Pröhle)

Place Value Shifting with Electronic Computers In the arithmetic unit of a computer, the basic arithmetic operations (addition, subtraction, multiplication, and division) and the logical operations (comparisons: and, or, not) are performed. Since the arithmetic operations can be reduced to addition, thanks to the forming of complements and place value shifting, the adder represents the heart of the calculating unit. It can be used for all four basic arithmetic operations. With electronic decimal computers, multiplication was executed as repeated addition or by searching a multiplication table. Shifting two places to the left with decimal numbers represents multiplication by 102  =  100. Shifting three places to the right executes a division by 103 = 1000. In the binary system, shifting a number by three places to the left represents multiplication by 23  =  8. Shifting four places to the right corresponds to division by 24 = 16.

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2.16  Sequence Control and Program Control Sometimes a distinction is made between sequence control and program control. However, the boundary between these terms is not altogether clear. Sequence control refers sooner to a fixed sequence, while program control is sooner understood as an adaptable sequence. There are numerous hybrid forms: hardwired programs can be interchanged in the form of plugboard control panels. Thanks to pinned cylinders, perforated discs, perforated cardboards, or phonograph records, for example, music programs can be interchanged. Recent digital computers usually have a stored program. In earlier times, these were hardwired, plugboard programmed, (punched) card programmed, or paper tape controlled. The expression “program control” is also used as a collective term: • External program control (switches, plugboard control panel, punched paper tape, chain of cards) • Internal program control (stored program). In this book control by an internal program is referred to as a stored program. Programming The meaning of the word “programming” has changed in keeping with technical advances. In earlier times one frequently programmed and controlled computers externally using pluggable connecting cables (plugwires) or plugboard control panels. Today, programming no longer requires such devices. Microprograms In addition to hardwired machines, there are also microprogrammed computers. As a rule, the design of a microprogram control is simpler than laying out hardwiring. However, such devices are slower. Charles Babbage already provided for microprogramming with his analytical engine. The development from the fixed program to the stored-program simplified machine control (see Table 2.20). Table 2.20  Relay and vacuum tube machines with fixed program, external plugboard or punched tape control, or internal stored program Program control with early relay and vacuum tube computers Fixed Plugboard-controlled Name of computer program program ABC (USA) ■ Bark (Sweden) ■ Bell 1 computer (USA) ■ Bell 2 computer (USA)

Taped program

Stored program

■ (continued)

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Table 2.20  (continued) Program control with early relay and vacuum tube computers Fixed Plugboard-controlled Name of computer program program Besm 1 (Ukraine) Colossus 1 + 2 (England) ■ Csirac (Australia) Edsac (England) Edvac (USA) Eniac (USA) ■ Ferranti Mark 1 (England) Harvard Mark 1/IBM ASCC (USA) IAS computer (USA) IBM SSEC (USA) Leo (England) Mesm (Ukraine) Pilot Ace (England) Univac (USA) Zuse Z4 (Germany)

Taped program

Stored program ■ ■ ■ ■

■ ■

■

■ ■ ■ ■ ■ ■

© Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020 Explanation of symbol: ■ = applicable

Fixed Preset Inflexible Control A few examples: • Machines with sequence control have been in existence since antiquity. The Antikythera mechanism (see Chap. 10) – an astronomical calculating machine  – and Heron’s automatic theater (with memory drum) were equipped with an inflexible sequence. • Astronomical clocks are fixed sequence controlled with gear wheels, levers, and cams. • Automaton figures are controlled by levers, cams, and pinned cylinders. The movements of human or animal figures are generally predefined. • Steam engines (James Watt) and windmills also have a sequence control. Remark The crowing rooster with its flapping wings on the first astronomical clock of the Strasbourg cathedral (around 1350) is regarded as the oldest known surviving automaton in the western world. Influenceable Selective Control A few examples: • Heron of Alexandria developed a freely programmable automatic door opener with cable operation and program cylinder already in the first century after Christ.

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• The handwriting automatons of Jaquet-Droz and Knaus allow freely selectable texts within certain limits. • The looms of Basile Bouchon, Jean-Baptiste Falcon, Joseph-Marie Jacquard, and Jacques Vaucanson were concerned with generating patterns. Such textile machines are sequence-controlled production machines. • Music boxes function with interchangeable pinned cylinders and interchangeable perforated discs. For many mechanical musical instruments, chains of cards and later with phonograph records were offered. Also worth mentioning are carillons with control drums. Some of these sophisticated devices utilized mechanical, hydraulic, and pneumatic components. • An ingenious control was also required for the chess-playing machine of Leonardo Torres Quevedo. • Numerical values determined the gear cutter of Jean-Baptiste Schwilgué. Accordingly, it was numerically controlled. His large mechanical calculating machine can be seen as an (early) “process calculator” (or as a forerunner). Hardwired and freely programmable machines with (mechanical) external or internal storage have therefore been known for a long time.

2.17  Automation With older mechanical  – analog and digital  – calculating devices (e.g., the slide rule, pair of sector compasses, bead frame, or slide bar adder), as a rule only single arithmetic operations were performed. With hand-operated calculators, several steps were always necessary: entering the input values, performing the calculation, and writing down the result (when no printing mechanism was available). Some electrical desk calculating machines were semiautomatic. The arithmetical process ran independently, with automatic place value shifting. Some devices had memory devices and printing mechanisms. With punched card equipment, a sequence of arithmetic operations could be generated (sequence control). The greater the level of automation (see Table 2.21), the less manual steps were necessary.

Table 2.21  Automation levels Degree of automation Attribute Description Manual All work steps by hand Semiautomatic Individual work steps automatic Fully automatic Entire work process automatic

Example Bead frame (abacus) Mechanical calculating machine Electronic digital computer

© Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020

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Thanks to the electric motor, there were already automatic mechanical calculating machines before the introduction of program-controlled automatic computers. Multiplication and division were automated. Stepped drum machines were better suited to this than pinwheel calculators. With the Curta pocket arithmometer, one strived for electrification. However, high-performance batteries were lacking. Fully automatic means that no human interventions take place between input (data entry) and output (exit). On the basis of intermediate results, with the help of conditional commands, the machine also makes decisions independently. When a person assumes this task, the arithmetical process is slowed down. Mathematical tasks require the greatest possible range of commands, with conditional branching and address modification. Calculating punches do not satisfy these requirements: Mostly though, the structure of complicated mathematical problems does not allow the use of this rather inflexible method of working [punched card machines controlled from a plugboard control panel], because the machine must also have the possibility to forget commands that no longer occur. This then led to the idea to write both the individual commands of the program and the numerical input in coded form (more precisely, as numerical sequences) and either feed these successively to the machine by one or more punched tapes (magnetic steel tape, etc.) or keep these in instructional storage, as with operands. Instructional storage (program memory) is often identical with the numerical storage [data memory], so that it is possible to calculate with commands [address conversion] (see Heinz Rutishauser, Ambros Speiser and Eduard Stiefel: Programmgesteuerte digitale Rechengeräte, Birkhäuser Verlag, Basel 1951, page 8).

Contrary to the electromechanical, tape-controlled Harvard Mark 1/IBM ASCC and the complex Bell 1 computer, the plugboard-controlled Eniac electronic computer offered conditional commands. For the Z4, Konrad Zuse originally had inflexible fixed programs (linear programs) that did not provide for conditional branching. This shortcoming was later eliminated with the installation of an additional punched tape reader. Program-controlled automatic computers are suited for general-purpose applications. For his analytical engine, Charles Babbage envisaged control by an external program on punched cards. John von Neumann realized a control in the form of an internal program in the main memory. Remarks Terms such as “automaton” and “machine” are not precise. One spoke of fully automatic calculating devices. The Swiss Madas desk calculating machine was advertised as semiautomatic or fully automatic device and as automatic machine with memory. One even spoke of automatic calculating machines with reference to bead frames or children’s counting frames. Automatons play an important role in theoretical informatics.

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2.18  Punched Card Machines Following their emergence at the end of the nineteenth century, punched card machines were globally in widespread use for several decades. Punched card machinery consisted of a number of devices (e.g., card punch, card reader, collator, sorter, and tabulator). The highest level was without doubt the mechanical and electronic calculating punch. A well-known punched card-controlled electronic computer was the card-­ programmed (electronic) calculator (CPC) of 1946. The parallel, decimal pluggable sequence relay calculator (PSRC) of Clair Lake and Benjamin Durfee (IBM) functioned with plugboards, as did the M9 electromechanical calculating punch of Zuse. Punched card equipment utilized (interchangeable) program plugboards as well as program punched cards. One could plug the program instructions manually into the plugboard control panels. Hub charts were provided for this purpose. The plugboards were adopted from communications technology (telephone exchange). Note When punched cards form a tape, we speak of a punched card tape or chain of cards (e.g., with historic looms). With and Without Branching With punched card machines, one speaks of a linear program that is either hardwired or on a plugboard control panel. Contrary to flexible programs, fixed programs do not accommodate conditional commands. Modifying the program sequence according to intermediate result (branching) was made possible by special perforations in the punched cards (control perforations). Intermediate results could be recorded onto result punched cards. The operator had to load the stack in the machine again manually. The transition between the different punched card machines (see Figs. 2.36, 2.37, and 2.38) also required manual intervention. Weaknesses of the Punched Card Machines Punched card machines were of great use especially for statistics, accounting, and administration. Tabulating machines provided fully automatic multiplication and division. However, punched card machines were not suited for the solution of complex mathematical problems. Programming with plugboards was cumbersome. Punched tapes were not practical with fast electronic computers, because the scanning of the instructions took too long. If necessary one could transfer their content to the main memory before processing. Furthermore, punched paper tapes were largely inflexible. The execution of conditional commands and address modifications (adaptation of memory addresses) were time-consuming. With punched cards it was not possible to delete the

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(punched) information and replace this with new values, as is possible with magnetic data carriers: they cannot be overwritten. A machine capable of completely solving a numerical problem must therefore be able to perform all basic arithmetic and logic operations which are required for the solution of the given problem. Furthermore, the machine must have adequate memory capacity for the storage of the input values and intermediate results and the capability to independently determine the subsequent execution of the program sequence in accordance with the results of intermediate calculations (see Anatoly Ivanovich Kitov; Nikolai Andreevich Krinitsky: Elektronische Digitalrechner und Programmierung, B. G. Teubner Verlagsgesellschaft, Leipzig 1962, page 8).

Fig. 2.36  Punched card machines (1). For the American census count (1890), Herman Hollerith developed counting and sorting machines. Punched card machines were widely used for several decades. The leading manufacturers were IBM and Remington Rand. Interchangeable plugboards were often used for program control. This illustration shows a replica of a Hollerith machine. (© Heinz-Nixdorf-Museumsforum, Paderborn, Germany)

A rebuilt Hollerith’s punched card machine can also be found, for example, in Milan.

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Fig. 2.37  Punched card machines (2). The system designed by Herman Hollerith, who was of German descent, consisted of three parts: a sorting machine, a counting machine, and a card punch (© Museo nazionale della scienza e della tecnologia “Leonardo da Vinci”, Milan)

Fig. 2.38  D11 tabulator machine (later: IBM 450, around 1950). This machine originated in the Berlin factory of the Deutsche-Hollerith-Maschinen-Gesellschaft, the forerunner of IBM Deutschland GmbH. Punched card systems often consisted of several devices, such as card punches, card readers, collators, card sorters, and tabulators. (© Deutsches Museum, Munich)

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2.19  Electronic Brains Computers were gladly compared with humans. The instruction and number storage was called the memory. One spoke of thinking machines and electronic brains or giant brains. And new fields of research emerged: cybernetics and artificial intelligence. For decades chess was considered a prime example of machine intelligence. Already in 1914 the Spaniard Leonardo Torres Quevedo introduced an electromechanical chess end game machine at the Paris Sorbonne. Within the scope of his Plankalkül (1945/1946), Konrad Zuse entertained considerations of an “artificial brain” and dealt with mechanical chess playing. His “logistics machine” was supposed to solve brainteasers. Babbage, Torres Quevedo, Turing, and Zuse Leonardo Torres Quevedo, Alan Turing, and Konrad Zuse are regarded as the founders of artificial intelligence. But Charles Babbage already gave thought to this: Babbage and his contemporaries did not let the opportunity to speculate on machine intelligence slip. Harry Wilmot Buxton, a younger colleague, to whom Babbage confided much of his work, wrote that “the wondrous medulla and fibers of the brain were replaced by brass and iron: He [Babbage] taught the gear train how to think” (see Doron D. Swade: Der mechanische Computer des Charles Babbage, in: Spektrum der Wissenschaft, 1993, volume 4, page 80).

For more detailed information on “thinking machines” see Herbert Bruderer: Nichtnumerische Datenverarbeitung. This book deals with the topics interactive databases and information networks, computer chess and machine-aided language translation, automation in libraries, artificial intelligence and computer art, data processing in medicine and chemistry, simulation of decision processes, and legal informatics, Bibliographisches Institut & F. A. Brockhaus AG, Wissenschaftsverlag, Mannheim, Leipzig etc. 1980, pages 72–156 and 225–237. According to Vardi, the philosopher Charles S.  Peirce was already concerned with artificial intelligence in 1887 (see Moshe Vardi: Who begat computing?, in: Communications of the ACM, volume 56, 2013, no. 1, page 5). Variants of the Turing Test: Automated Language Translation “Electronic brains” usually execute programs written by humans. In order to assess their ability to think, the Turing test was proposed. Whether a machine can be viewed as intelligent is a matter of judgment and the paraphrasing of terminology. Some even attribute feelings to the computer. One could then classify an automaton as intelligent when it is, for example, capable of understanding the content, i.e., the meaning of any exacting written or spoken texts and translating these in faultless quality into other languages. This entails high-quality text or speech recognition and text or speech output. In spite of decades of efforts, we are still well removed from such machine capabilities. Programs such as Google translate or DeepL are unable to really comprehend the meaning. The qualitative evaluation of an automatically translated text might be more informative than the traditional Turing test.

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2.20  C  ommercial Data Processing and Scientific Computation Commercial and administrative computational tasks usually require large amounts of data. On the other hand, the computer programs that process this data are comparatively simple. Sorting processes often occur, for example. High-performance input and output devices are important here. Commercial machines were mostly decimal computers. In earlier times, there were also calculators that printed out data and typewriters that performed calculations, posting machines, cash registers, and versatile punched card systems. By contrast, the computer programs for scientific and technical applications are often quite complex, while the extent of the input and output values is relatively small. In this case, a fast arithmetic unit is decisive. The demand was therefore predominantly for binary computers with floating point notation. Initially there were data processing systems, i.e., punched card machines, and later electronic digital computers. Ultimately, both areas merged. Single-Digit Adding Machines For commercial calculations, adding columns of numbers was everyday routine. The results were entered in account books. Special machines were developed for single-digit calculations, the single-digit adding machines. Keyboard adding machines were especially convenient. Simply pressing a key initiated the calculation. Rotating a crank was no longer required. On entering a number, this was simultaneously transferred to the accumulator register, so that a single step was sufficient. Keyboard control replaced crank operation. The oldest known single-digit adding machine is the keyboard adding machine of Jean-Baptiste Schwilgué. The existing models of Schwilgué accommodate only single-place values. The addition of longer numerical sequences with the four-­function machine of that time (the Thomas arithmometer) was cumbersome (slide setting and countless rotations of the crank). Keyboard adding machines were considerably faster. In addition, less input errors occur with keys than with slides. Compact Adders Above all in the USA, key-driven adders were later manufactured in high quantity. However, these were relatively expensive. Numerous inexpensive plate calculators, the slide bar adders, therefore appeared in retail trade. These usually had a semiautomatic tens carry (crook tens carry), and operation was with a stylus. Compact adders were also available that could be operated without a stylus. Input and arithmetic unit drives were with the finger (direct drive). Two types of keyboards were common (see box).

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Ten-Key Keyboard and Full Keyboard With many mechanical calculating machines, the numbers are entered via arrays of keys. A ten-key keyboard is an array of keys from 0 to 9. A full keyboard is an array of keys in which the numerals 1 to 9 are repeatedly present in adjacent key columns. For each decimal place (hundredth, tenth, ones, tens, hundreds, thousands, etc.), a vertically arranged sequence of numerals exists. Zero keys are missing, since zeroes do not have to be input: they are entered automatically. Pressing the key with the numeral 1  in the thousands column displays the value 1000.00. Several keys can be pressed simultaneously, speeding up the numerical input. A 10-place machine includes ten-key columns with the numerals 1 to 9 (in differently colored groups of three). Half keyboards, with only five numerals, also existed.

Initially, different computer designs existed for scientific and commercial applications. Later, these merged (see Table 2.22). Table 2.22  Characteristics of commercial and scientific computers Comparison of commercial and scientific computers Attribute Data processing computer Number system Decimal Design Serial or parallel Data Nonnumerical Numerical notation Fixed point Computational tasks Relatively simple Data volumes Very high Memory requirement High Input devices Fast Output devices Fast Programming Relatively simple Examples Univac 1 IBM 650 IBM 702 IBM 705

Scientific computer Predominantly binary Predominantly parallel Numerical (primarily numerals) Floating point Mostly complex Moderate Moderate Moderate Moderate Demanding Ferranti Mark 1 Era 1103 (Univac 1103) IBM 701 IBM 704

© Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020

2.21  P  rogram-Controlled Digital Computers in the Year 1950 How Many Computers Were There in 1950 in Europe? Today it is hardly imaginable that in 1950 there were less than a dozen functioning computers in Europe (see Table  2.23). To our knowledge there were two machines in actual use on the continent. In a few countries (e.g., the

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Soviet Union, England, the Netherlands, and Belgium), other digital computers were being built. John Coales of Elliott Brothers (London) Ltd., for example, developed a secret digital fire control computer, the Elliott 152, at the Borehamwood Laboratories (Hertfordshire, South England) for the British Royal Navy. 1951 then brought about dramatic changes. The Ferranti Mark 1 (UK) and Univac (USA) computers were now commercially available, although the piece numbers were of course initially rather low. Konrad Zuse propagated a number of myths, including the legend that the Z4 was the only working computer in Europe in 1950. One frequently read that this program-­controlled digital computer was the only automatic computer on the European continent at that time. These assertions are not correct. At the Royal Institute of Technology in Stockholm, a plugboard-controlled relay computer, the Bark, was commissioned and was inaugurated in April of the same year. This was also known in Zurich, as can be found in publications of Rutishauser, Speiser, and Stiefel. Table 2.23  How many relay and vacuum tube computers were there in 1950 in Europe? Program-controlled digital computers in 1950 in Europe Country England England England England England England England Sweden Switzerland Ukraine

Name of computer ARC (London) Colossus 1 (Bletchley Park) Colossus 2 (Bletchley Park) Edsac 1 (Cambridge) Elliott 152 (Borehamwood) Manchester Mark 1 (Manchester) Pilot Ace (London) Bark (Stockholm) Zuse Z4 (Zurich) Mesm (Kiev)

Design Relay computer Vacuum tube computer Vacuum tube computer Vacuum tube computer Vacuum tube computer Vacuum tube computer Vacuum tube computer Relay computer Relay computer Vacuum tube computer

Year of manufacture 1948 1943 1944 1949 1950 1949 1950 1950 1945 1950/51

© Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020

Remarks The Colossus electronic computer built by the Post Office Research Station (Dollis Hill, London) was operated by the Foreign Ministry at Bletchley Park intelligence service center. The Ukrainian Mesm vacuum tube computer (Kiev) of Sergey Lebedev operated for the first time in 1950. This experimental machine achieved its final form in December of 1951. What Happened to the Colossus? Shortly after the Second World War eight of the ten Colossus computers in Bletchley Park were dismantled. Two went to Eastcote in North London and later to the British Secret Service in Cheltenham, where they were destroyed in

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1960 (see Anthony Sale: The Colossus of Bletchley Park – The German cipher system, in: Raúl Rojas, Ulf Hashagen (editors): The first computers – history and architectures, MIT press, Cambridge, Massachusetts, London 2000, page 362). At the suggestion of Max Newman, the material from two complete Colossus machines was apparently brought from Bletchley Park to the University of Manchester in 1945 (see David Anderson: Contested histories: De-mythologising the early history of modern British computing, in: Arthur Tatnall (editor): History of computing. Learning from the past, IFIP WG 9.7 International conference, HC 2010, Brisbane, Australia, September 20–23, 2010, Springer, Berlin 2010, page 61). How Many Computers Were There in the USA in 1950? A reliable overview of North American computers during the early post-war years is made difficult by the secrecy of developments. Numerous machines were functional in 1950: for example, the large differential analyzer of Vannevar Bush (1942) and digital machines such as Eniac (1946), IBM SSEC (1948), Binac (1949), Seac (1950), Swac (1950), and Atlas 1/Era 1101 (1950). The Atanasoff-Berry computer (ABC, 1942) was no longer operating in 1950. A number of machines were developed for military purposes and were found in US military facilities. Still in development were the Edvac, die IAS machine, and Whirlwind. Binac was (like the Jena Oprema) a twin computer. In 1950 there were about a dozen functioning relay and vacuum tube computers, a few of which were no longer in operation. The best known early series of computers were those of Harvard and Bell (see Table 2.24).

Table 2.24  Bell and Harvard computer models Bell and Harvard computers Name of computer Bell 1 computer Bell 2 computer Bell 3 computer Bell 4 computer Bell 5 A computer Bell 5 B computer Bell 6 computer Harvard Mark 1/IBM ASCC Harvard Mark 2 Harvard Mark 3 Harvard Mark 4

Year of manufacture 1939 1943 1944 1945 1946 1947 1949 1944 1947 1950 1952

Design Relay Relay Relay Relay Relay Relay Relay Relay Relay Vacuum tube Vacuum tube

© Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020

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Remark The year refers to the date of completion of the computer. The first model of the Bell Telephone Laboratories (BTL) also had the name “complex computer”, model 2 “relay interpolator”, and model 3 “ballistic computer”. Two model 5 machines were built (1946 and 1947). The Bell 1 computer was completed at the end of 1939 and began operating at the beginning of 1940. The Harvard Mark 1 was already completed in 1943 but did not come to Harvard University until 1944. How Many Computers Were There Worldwide in 1950? Assuming that the listed machines were not yet scrapped and were still functioning, worldwide around 20 digital relay and vacuum tube computers can be identified in 1950. The Australian Csirac electronic computer (1949) can be mentioned here. From 1951 on, the number of program-controlled computers increased dramatically in North America and Europe.

2.22  Mechanical Calculating Machines Adding and Calculating Machines In earlier times a distinction was made between adding machines (one- and two-­function machines) and calculating machines (three- and four-function machines). Devices without crank or without lift lever were referred to as highspeed calculators (direct adders). One or More Counter Registers and Memory Units The machines function in a single step (input of values and processing in a single work step) or in two steps (with the entry of the numbers and processing each requiring one step). They had one or more counter registers and one or more accumulators (memory units). Four-function machines normally had no printing mechanism, while adding machines were with or without printing mechanism. Direction of Rotation For addition, with pinwheel calculating machine, the hand crank is rotated forward and for subtraction backward. Contrary to the Thomas arithmometer (stepped drum machine), the gear train does not have to be repositioned. No Zeroes The numerical values were entered by means of stylus, lever, or keys. With some machines (e.g., mechanical calculating machines with full-keyboard and manual operation), the zeroes were automatically printed, so that these keys are missing.

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Balancing Balancing is the determination of the account balance (the amount by which the debit side and the credit side of an account differ). The debit balance (also known as credit balance) was indicated (directly) by numerals and minus sign or (indirectly) by complements. Bells Certain machines have a bell that sounds, for example, in the event of a revolution counter register or accumulator (place value) overflow or at the end of a division (when the crank is rotated too far). With the Schickard calculating clock, a signal according to Bruno von Freytag Löringhoff probably indicated that one million was exceeded during addition or a value less than zero resulted during subtraction. Calculating machines capable of one or more basic arithmetic operations are described by several attributes (see box). Characteristics of Mechanical One-Function and Multi-purpose Machines • One, two, three, or four basic arithmetic operations (functions) • Without automatic tens carry/with semiautomatic tens carry/with automatic tens carry • Operation by finger, stylus, setting lever (setting slide), or keys • Ten-key keyboard or full keyboard • Without/with direct addition (two-step or one-step process) • Indirect or direct subtraction • Debit side with complements/debit side with direct display • Without or with printing mechanism • One or more arithmetic units • One or more memory units. Stepped Drums and Pinwheels Primarily stepped drums and pinwheels were used with mechanical calculating machines. These two devices for mechanical numerical notation were invented by Gottfried Wilhelm Leibniz and the pinwheel also (probably independently) designed by Giovanni Poleni. Stepped Drums A stepped drum (see Fig. 2.39) is a (broad metal) drum with teeth of different length. The teeth, with staggered length and parallel to the axis of the drum, represent the numerical values 1 to 9. No tooth has the value zero, and all teeth correspond to the number 9. The numeral 1, for example, is represented by one (the longest) tooth and the number 2 by two (the longest and the second longest) teeth. 3 is composed of the longest, the second longest, and the third longest teeth.

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Length of teeth

Numeral 3 (= longest, second longest and third longest tooth)

Numeral 5 (= five longest teeth)

Numeral 7 (= seven longest teeth)

© Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020

Numeral 1 (= longest tooth)

Numeral 9 (= all teeth) Numerical values 1 (single = longest tooth) to 9 (all teeth)

Fig. 2.39  Stepped drum. A complete revolution of Gottfried Wilhelm Leibniz’s stepped drum drives a gear wheel of the calculating unit further according to its position, e.g., at zero (top line in the drawing) or at nine teeth (lowest line). (Source: Albert Rohrberg: Theorie und Praxis der Rechenmaschinen, page 6). (© Bruderer Informatik, CH-9401 Rorschach, Switzerland)

Pinwheels A pinwheel (see Fig. 2.40) is a (narrow disc-shaped) gear wheel with nine movable and adjustable pins. The teeth, arranged perpendicular to the shell, can be individually extended or retracted or folded inward and outward. If no pins extend from the wheel rim, this represents the number 0. Nine extended teeth correspond to the value 9. Five extended pins give the value 5.

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Pins in different positions © Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020

Fig. 2.40 Pinwheel (schematic diagram). With the pinwheel of Gottfried Wilhelm Leibniz and Giovanni Poleni 0–9 teeth protrude from the wheel rim. These represent the numerals 0–9 and engage in a gear wheel of the accumulator register. The three pins drive the gear wheel three teeth further when the crank is rotated through a complete revolution. In this schematic diagram (with only six pins), two pins are fully retracted and three fully extended. One is in an intermediate position. (© Bruderer Informatik, CH-9401 Rorschach, Switzerland)

Remark The stepped drum is also described as a stepped wheel or a Leibniz wheel and the pinwheel as a variable toothed wheel or an Odhner wheel. Poleni invented a pinwheel machine (see Fig. 2.41). One fine example of an Odhner device was dedicated to the Swedish King (see Fig. 2.42).

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Fig. 2.41  Poleni’s pinwheel machine. The two most important forms of four-function calculating machines were the stepped drum machine and the pinwheel machine. With the pinwheel machine, the numbers are represented by moving teeth arranged on the perimeter of the wheel in and out. The original machine of Poleni has not survived. (© Museo nazionale della scienza e della tecnologia “Leonardo da Vinci”, Milan)

Fig. 2.42  The Odhner pinwheel machine for the Swedish King Gustav V.  This elaborate design dates from the year 1892. The machines of Willgodt Theophil Odhner were widely used. (© Peter Häll, Tekniska museet, Stockholm)

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Many mechanical calculating machines followed similar designs (see Table 2.25). Table 2.25  Components of mechanical calculating machines A mechanical calculating machine comprises these components Component Purpose Setting mechanism Input of numerical values Control mechanism Controls numerical values entered Counter register Displays number of revolutions, displays result of division Accumulator Displays the result of addition, subtraction, and multiplication and the remainder for division Memory Stores intermediate results Printing mechanism Prints out the results © Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020

Remark The switching mechanism transfers the numbers from the setting mechanism to the accumulator. The values set are then displayed in a horizontal line on the setting dial. Setting Mechanism, Accumulator and Counter Register One distinguishes between three basic parts of mechanical calculating machines: • The setting mechanism (entry register) • The accumulator (result register) • The revolution counter (counter register). With some older devices, the counter register, which simplifies multiplication and division, is missing. The term “counter” is used for both the accumulator (result mechanism) and the counter register. In general, “arithmetic unit” is identical with the term accumulator. Capacity The number of places (capacity) is expressed as follows: 8 × 1 × 12 i.e., 8 setting counters, 1 revolution counter, 12 result counters (8 places in the entry register, 1 place in the revolution counter, 12 places in the accumulator) Carriage and Shifting of the Carriage For (place aligned) multiplication and division, mechanical calculating machines require a moving carriage. This allows shifting the entry register and accumulator/revolution counter or switching mechanism (carrying mechanism) and counter register relative to each other.

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Different forms exist: • As a rule, the carriage incorporates the accumulator (and usually the revolution counter as well). In this case the entry register is fixed (immovable). • The carriage accommodates the entry register (and the switching mechanism). In this case the accumulator is fixed. The carriage thus incorporates either the result mechanism (accumulator) or the result mechanism and the revolution counter. Early Thomas arithmometers had no revolution counter. The handling of the calculating machines depends on the direction of rotation (see box). Bidirectional and Unidirectional According to the design, the crank or the toothed rack can be rotated or shifted in one or in two directions: • Unidirectional (in only one shifting or rotational direction) Examples: stepped drum machines, proportional rod calculating  machines, ratchet machines, slide bar adders • Bidirectional or both directions (in both shifting and rotational directions) Examples: pinwheel machines, toothed segment machines. Pinwheels are bidirectional (forward rotation = addition, backward rotation = subtraction), and, as a rule, stepped drums are unidirectional. The Leibniz machine was bidirectional, and the stepped drum calculating machine of Hahn (Stuttgart) was unidirectional.

Single- or Double-Step Tens Carry Tens carry is executed in one or two steps: • Phase-shifted (time staggered, two-step, two-stage) • Non-phase-shifted (simultaneous, single-step, single-stage). The machines of Leibniz, Hahn, Thomas, Baldwin, Odhner, and Herzstark have a two-step tens carry, i.e., this takes place in two stages (standby p ­ osition/ preparation and execution). First all numerals of a number are simultaneously added. The required tens carries are stored by a wheel or level position, for example. The earmarked carries are then added from right (ones) to left (tens, hundreds, etc.) to the intermediate sums. The tens carry is not executed together with the addition or subtraction. Accordingly, the carry does not take  place simultaneously with the processing of the numerical places, but afterwards. The Schickard calculating clock, Pascaline, and Poleni’s pinwheel machine had a single-step tens carry.

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Serial or Parallel Tens Carry When the tens carry takes place simultaneously over all numerals of a multidigit number (e.g., 9999 + 1 = 10,000), this constitutes a parallel carry. Leibniz dared to choose the demanding parallel method, with its difficult implementation. Schickard, Pascal, Thomas, and Hahn realized a serial tens carry. Over-Rotation The operation of mechanical calculating machines (crank rotations) entails the risk of over-rotation (overthrow) of components (e.g., shafts of the result mechanism or number drums). This leads to centrifugal errors. To prevent these, arresting devices (e.g., catch springs (leaf springs), safety catches, lock washers, full stroke lock-outs, or recoil dampers) are installed. These reduce the intrinsic movement and guard against further rotation. Numerous safety mechanisms also exist against faulty operation. Back Transfer Back transfer describes the transfer of intermediate results from the accumulator to the entry register, e.g., for multiplication with several factors, or from the accumulator to the counter register, e.g., when raising to a power. Arithmetic Underflow When negative numbers occur during subtraction (values less than zero), one speaks of arithmetic underflow. With some machines, a warning bell then sounds. The underflow can be eliminated by a compensating addition. For division (see Sect. 19.4), repeated alternation takes place between subtraction and compensating addition, which entails carriage shifting. Display of the Results The accumulator displays the sum (addition), the difference (subtraction), or the product (multiplication). For division the quotient is shown in the counter register and the remainder in the accumulator. If no counter register is present, it is necessary to count the number of revolutions and write down the result. If a series of nines is displayed, this indicates that the crank was rotated through too many revolutions during the division. Drive Systems Mechanical and electromechanical calculating machines are mostly operated by a hand crank or an electric motor. A combination of manual and electrical drive is also known. In rare instances an (additional) weight drive was used, as for the large Schwilgué machine. Giovanni Poleni’s pinwheel machine was also driven by a weight. With his (unfinished) analytical engine, Babbage considered the use of a steam engine. With some calculating machines (e.g., keydriven adding machines) and slide bar adders, the fingers are sufficient.

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Other (Selected) Definitions Balancing Non-balancing Printing Non-printing Displaying Displaying and printing Manual Electric Adding machine Adder Adding/ subtracting mechanism Balancing machine Balance register Carriage Counter Accumulator Counter register Revolution counter register Simplex machine Duplex machine Triplex machine Capacity Decimal point pin (decimal point shifter) Result window Setting dial Full keyboard

With (direct) display of the debit side (values less than zero), with a negative sign With (indirect) display of the debit side (values less than zero) by complements With printing mechanism Without printing mechanism With display of results in result windows (without printing mechanism) With display of results in result windows and with printing mechanism With manual drive With electric drive, motor drive Calculating machine that displays complements for values less than zero (no debit side) Arithmetic unit with indirect subtraction (no debit side: display of negative values as complements) Arithmetic unit with direct subtraction (no (direct) debit side: display of negative values as complements) Calculating machine capable of addition and subtraction and displaying negative results (values less than zero) with a minus sign Calculating machine capable of addition and subtraction and displaying negative results (values less than zero) (direct subtraction; debit page: direct display of negative values with minus sign) Carriage for place value shifting; moving part that usually bears the accumulator and the counter register Accumulator or counter register Result mechanism Revolution counter (displays the number of revolutions with multiplication and the quotient with division) Counter register (displays the quotient with division) Machine with one counter register, single calculating machine Machine with two counter registers, twofold calculating machine Machine with three counter registers, threefold calculating machine Number of places in the entry register, counter register, and accumulator Adjustable device for the display of decimal places Display window, viewing window (for displaying the result and as a control display) Linear display (in the input control device) Array of keys with numerous columns of numerals (for two-handed operation, one numeral column for each decimal place, numerals 1 to 9, with automatic entry of zeroes) (continued)

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(continued) Half keyboard

Multi-column array of keys with the numerals 1 to 5 (values greater than 5 are pieced together with double entry, e.g., 9 = 4 + 5 or 6 + 3) Ten-key keyboard Array of keys with 10 numerals (numerals 0 to 9) Tens carry Tens transmission, single- or double-step switching mechanism for transfer from a lower to a higher decimal place, with transfer in one or two steps: continuous (over all places, sequentially or staggered) Machine Calculation with mechanical calculating machines or mechanical and calculation electronic calculation Mechanical Calculation with mechanical aids (slide bar adder, mechanical calculation calculating machine, punched card machine, slide rule) Manual Calculation by hand (written calculation)/calculation with a manual calculation calculating machine (e.g., without power) Column Addition of an array of values in perpendicular arrangement under calculation each other (e.g., with single-digit adder)

Remark The ten-key keyboard gradually replaced the full keyboard. A well-known duplex calculating machine was this Brunsviga (see Fig. 2.43).

Fig. 2.43  Duplex Brunsviga (1952). Some manufacturers offered duplex machines in order to accelerate the calculation process. The German Brunsviga pinwheel machine was one of the best. (© Heinrich Heidersberger, Institut Heidersberger GmbH, Wolfsburg, Germany)

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2.23  Accounting Machines The terms used to describe these machines are confusing and contradictory: • Accounting machines • Bookkeeping machines • Billing machines. There were combinations of typewriters and calculating machines: • Typewriter calculators (calculating machines that typed the results) • Calculating typewriters (typewriters capable of performing calculations). Moreover, there were calculating and non-calculating accounting machines. Remarks Leslie John Comrie discovered that Burroughs accounting machines can be used as difference engines. This enabled the Nautical Almanac Office to simplify the time-­consuming and error-prone calculations for the British observatory in Greenwich. In 1928 the New Zealander Comrie utilized Hollerith punched card machines for the first time for scientific applications. The collective terms mécanographie and meccanografia do not always cover the same devices. These refer basically to (mechanical) office machines, calculating machines, accounting machines, and punched card machines.

2.24  Tabulators For tabulators as well, the terminology is not altogether uniform: • Punched card machine (see Fig.  2.44) for the evaluation of a pre-sorted stack of punched cards (printout of the results, e.g., in the form of tables, lists or punching the results in punched cards) • Printing statistical and calculating automaton that processes the punched cards sorted by the sorter according to particular instructions, executes calculations, and prints out the results in tabular form. Certain models sort, add, create tables, and print lists. However, one also speaks of printing and non-printing tabulating machines. For more information, see Sect. 2.18.

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Fig. 2.44  Sorting machine of Tauschek. From 1926 on the Austrian Gustav Tauschek designed a punched card-controlled accounting system (the Tauschek system). This system incorporated, e.g., punched card, sorting, collator, accounting, and calculating machines, but was never manufactured in quantity. (© Technisches Museum Wien, Vienna)

2.25  Diversity of Terms and Change of Meaning In this book the terms calculating aids and calculating devices are used in the sense of collective terms. The terms calculating machine and calculating device have the same meaning for electronic, but not for mechanical, calculating machines. The slide rule (particularly the linear slide rule) and bead frame (abacus) belong to the calculating devices, but not to the calculating machines. Historical calculating machines include analog and digital, mechanical, electromechnical, and electronic calculating devices. In computer science the devices were originally in the foreground. However, the emphasis shifted more and more to programs. The discipline took on a new orientation. Some technical terms are rather vague. The use of language is contradictory: for example, robot, Turing machine, von Neumann computer, analog and digital, stored program, musical automaton, or mechanical musical instrument. Robots are sometimes understood to mean not only machines but also (allegedly) “clever” programs. What Is a Computer, and What Is the Meaning of “Process Computer”? The answer to the question of the origin of the computer is not entirely clear. Opinions depend to a large extent on the respective definition, which is easily tailored to one’s one requirements. It must be noted that such definitions can change with time. For the continuous changes in the meaning of the term digital computer, no end is in sight.

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Computers were originally calculating persons (see Sect. 17.8). Then came plugboard-­controlled, program-controlled, and later stored-program computers. Today, tiny digital computers are unobtrusively embedded in countless devices. Modern-day digital computers function on the basis of stored programs. This was not the case with the first programmable automatic computers (Zuse Z3, Harvard Mark 1, and Eniac). In spite of this, since the definitions must reflect the particular state of technology, these early machines are regarded as computers. The exact form of the definition must be consistent with technical advances or when referring to the state of knowledge of the time in question. Process Computers A process computer is a machine that controls technical and scientific or industrial process flow (e.g., production processes). Different perceptions exist with regard to its features. There is no generally accepted definition. Of course it is not possible to place the same demands on the nearly 200-year-old Schwilgué “process calculator” as on a process computer of our time. As elaborated above, the first programmable automatic computers do not satisfy the requirements that we place on today’s electronic digital computers. Machine Control The Viennese computer pioneer Zemanek mentions a weaving machine from the year 1740, now in the Webereimuseum Haslach (near the Bavaria-Czech Republic-­Upper Austria border triangle, in the Mühlviertel district). However, the invention of the automatic loom is thought to be much older. The “Bröselmachine” machine is probably named after its creator. The device is a loom [...] with a process control device comprising a cloth binding about 50  cm wide to which small wooden blocks were fixed. These blocks are the program record: they determine the weaving process and therefore the woven pattern (see Heinz Zemanek: Weltmacht Computer. Weltreich der Information, Bechtle Verlag, Esslingen, Munich 1991, page 47).

As with the looms of Jacquard and his predecessors (Bouchon, Falcon, Vaucanson) and Babbage, this had card or tape control, but did not function with numbers, i.e., not as a numerical process calculator. Zemanek also refers to a lens calculation for photography (portrait and landscape lens) that Josef Petzval realized with the aid of form sheets at the middle of the nineteenth century. The model was the program-controlled calculation by persons used since the Renaissance for ballistics tables for artillery (see Heinz Zemanek: Weltmacht Computer. Weltreich der Information, Bechtle Verlag, Esslingen, Munich 1991, pages 48–50). There was a change in the meaning of the term compiler (see box). Compilers A change in the definition can also be seen with the term compiler. Today, a compiler is a translator that converts the instructions of a highlevel programming language to machine language. Grace Hopper understood this as a program part that manipulated subprograms (e.g., floating point notation) filed in libraries.

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The Abacus: Calculating Board and Bead Frame The term abacus is confusing. It has two meanings, either calculating board (counting board, reckoning board) or bead frame (counting frame, arithmetical frame). The origin and age of this calculating aid are not clear. The abacus is regarded as the first digital calculator. The bead frame allows all four arithmetic operations. Tens carry takes place manually. In regard to classification: • The calculating board (device with line grid or columns for numerical values): The ancient Greeks already had such counting boards. Well-known is the Salamis tablet (found on the Isle of Salamis). A calculating board is pictured on the Darius vase. Line elements can be drawn in the sand. Pebbles (Latin: calculi) were used for calculating. On calculating tables reckoning coins (jetons, tokens) were used. These were placed on or between the lines. Reckoning pennies did not serve as a means of payment. The Salamis tablet also has the name Salamis counting table. • The bead frame (device with movable beads arranged on staffs): Such bead frames were very popular (see box). Examples: Chinese, Japanese, and Russian abacus (suanpan, soroban, stchoty). The Romans knew a hand abacus (a device with grooves/slits for moving the ball knobs). The term “abacus” is also used for medieval calculating tables and calculating cloths. Calculation fields can also be depicted on a slate tablet. In French and Italian, a distinction is made between abaque and abaco, respectively (calculating board), and boulier and pallottoliere, respectively (bead frame). However, abaque also means a graphic chart, a nomogram. The German term Abakus stands for the calculating board as well as the bead frame. Several terms are in use for the abacus in the English-speaking countries: calculating board, counting board, reckoning board, calculating table, counting table, reckoning table, counter, etc.

Calculating Frame or Counting Frame? People have always struggled with calculations. In order to simplify this task, a wealth of calculating aids has therefore been developed. The Roman number system (without zero), which was in use from antiquity up to the early modern era, considerably complicated arithmetic. HinduArabic numerals (with zero) gained acceptance only slowly. With the bead frame and the calculating board, together with the calculating table and the calculating cloth, it became possible to simplify calculations and use Roman numerals primarily to represent the results. Addition and subtraction calculations could be reduced to counting. However, for multiplication and division, a knowledge of multiplication tables was helpful. (continued)

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Shouldn’t we then rather speak of a “counting frame” and “counting board”? It is sufficient to shift beads, add or take away pebbles, and finally count the number of beads or reckoning pennies. But this requires a command of the fives or tens carry. Since one can also perform calculations with the counting frame and counting board, the terms calculating frame and calculating board are justified. In this book the terms bead frame and counting frame are used in the same sense. Calculating Tables Two types of calculating tables exist, the calculating table in the stricter sense (French: “table à calculer”) for calculations of a general nature and the counting table (French: “table de compte”) with horizontal coin strip, vertical coin columns, or other measures. These served for the calculation of sums of money (e.g., currency conversion) and quantities of goods.

Fig. 2.45  Napier’s rods. The set consists of 25 wooden rods. They were used primarily for multiplication and for calculating square and cube numbers. (© Nisse Cronestrand, Tekniska museet, Stockholm)

Napier’s Rods Linear slide rules are the most important slide rule design. These are analog (logarithmic) calculating aids. By comparison with these, the calculating rods of John Napier (see Fig. 2.45), Henri Genaille, and Edouard Lucas, as well as

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the calculating box of Kaspar Schott, were digital calculating aids (for multiplication and division). In somewhat modified form, these also found use in the Schickard calculating clock and René Grillet’s four-function device, as well as in “Burattini’s” addition and multiplication device and in Kaspar Schott’s calculating box (see Figs. 2.46 and 2.47).

Fig. 2.46  Schott’s calculating box (1) (1668). The German Kaspar Schott transformed Napier’s bones into 12 rotatable cylinders that include multiplication tables with the numerals 1 to 9 and thus build upon the Pythagorean table. This instrument also enables division and extracting roots. The device is a replica. (© Science Museum, London/Science & Society Picture Library)

Napier’s bones (multiplication table rods) were inspired by the lattice multiplication known for many centuries by the name gelosia. With this approach, dating back to Middle Ages, as Luca Pacioli describes in 1494, for example, multiplication is reduced to an addition.

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Fig. 2.47  Schott’s calculating box (2) dating from 1668–1764. The cabinet has nine cylinders. The casing is made of leather. (© Museumslandschaft Hessen Kassel, Astronomischphysikalisches Kabinett)

The multiplication table is also called the “Pythagorean table” (see Fig. 2.48). This calculating aid is commercially available to this day. The multiplication table up to 100 includes the factors 1 to 10 (maximum value 100) and the multiplication table up to 400 includes the products of the factors 11 to 20 (maximum value 400). The illustration shows only the factors 1 to 9.

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Fig. 2.48  Pythagorean table. The multiplication table up to 100 is engraved on this tablet. The illustration is taken from the work Ein newü Rechenpüchlein of Jacob Koebel (1522). (Source: ETH Library, Zurich, Rare books collection)

Napier’s Promptuary Napier also developed another, but little known, calculating aid for multiplication and division, the promptuary (see Fig.  2.49). Instead of rods he used strips (see Erwin Tomash: The Madrid promptuary, in: Annals of the history of computing, volume 10, 1988, no. 1, pages 52–67, and Stephan Weiß: Die Rechenstäbe von Neper, ihre Varianten und Nachfolger. Ein Beitrag zur Geschichte des instrumentalen Rechnens, April 2007).

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Fig. 2.49  Napier’s promptuary. Napier’s bones were widespread, but his promptuary was very rare. Garry Tee of the University of Auckland in New Zealand built another (differently designed) reconstruction of the calculating instrument that is now in Edinburgh. (© Museo Arqueológico Nacional, Madrid)

Mathematical Machines and Mathematical Instruments Older books have headings such as “mathematical machines” and “mathematical instruments”. Mathematical machines include digital mechanical and electronic calculating machines, slide bar adders, and bookkeeping machines. Analog calculating tools, such as sector compasses, proportional dividers, planimeters, slide rules, and mechanical differential analyzers are allocated to the mathematical instruments. The use of these terms is contradictory. Calculating Machines and Calculating Devices Some specialists distinguish between calculating machines and calculating devices. Mechanical calculating aids without automatic tens carry belong to the calculating devices. Calculating aids with automatic tens carry are regarded as calculating machines. Slide bar adders with semiautomatic crook tens carry also belong to the calculating devices. Calculating boards and bead frames have a manual tens carry. Classification according to (mechanical) calculating devices and calculating machines may be practical, but this is not always sensible. Thus, for relay and vacuum tube computers, the terms “calculating device” and “calculating machine” are used synonymously.

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The term “arithmometer” was used for a time not only for the Thomas machines but also for other stepped drum machines and even for pinwheel machines. Terms such as “Thomas machine” and “Odhner machine” were also in common use as generic terms. Calculating Machines, Adding Machines, and Adders For decades a distinction (owing to their design) has been made between adding machines and calculating machines. Nevertheless, this is questionable, since adding machines are also calculating machines. Adders or adding machines are expected to total numerical values. In keeping with their name, they are able to perform (only) one arithmetic operation, namely addition. Many of these calculating aids are however also capable of subtraction and, in some cases, of multiplication and even division as well. Multiplication is in fact repeated addition. In these cases the names “adder” and “adding machines” are misleading. More appropriate names would be one-function and multifunction or one-, two-, three-, and four-function calculating machines. In Europe the four-function machines (Thomas arithmometer) were the first commercially successful, mass-produced calculating machines, and in the USA keyboard machines (comptometer of Dorr Eugene Felt) first led the way. Slide Rules The term slide rule usually refers to a linear slide rule. In a broader sense, however, this also includes circular slide rules, cylindrical slide rules, calculating wheels, pocket-watch slide rules, and (logarithmic) calculating tables. With the slide rule, multiplication and division are reduced to the vastly simpler addition and subtraction. According to their scale layout, various systems were commonly found with slide rules (see Table 2.26). The Mannheim system greatly facilitated the spreading of slide rules. Table 2.26  Arrangement of scales on slide rules Scale systems for linear slide rules Name of system Creator Soho slide rule James Watt and James Boulton (site Soho near Birmingham) Mannheim slide rule Victor Mayer Amédée Mannheim Rietz slide rule Max Rietz Darmstadt slide rule Alwin Walther (Technische Hochschule Darmstadt)

Year 1790 1851 1902 1934

© Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020

The most important scale systems for slide rules were the systems of Victor Mayer Amédée Mannheim (Mannheim system), Max Rietz (Rietz system), and Alwin Walther (Darmstadt system).

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The usual scale lengths ranged from 12.5 cm up to 24 m (see Table 2.27). Table 2.27  Prevalent scale lengths of linear, circular, and cylindrical slide rules Usual scale lengths of slide rules Type of slide rule Linear slide rule Circular slide rule Cylindrical slide rule

Scale lengths 12.5 and 25 cm 30 and 75 cm 1 to 24 m

© Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020

Remarks Linear slide rules with a scale length of 50 cm are rare. They are unwieldly and buckle. Circular slide rules with scale lengths of 30 and 75 cm have diameters of 12 and 30 cm, respectively. Sectors and Proportional Compasses Sectors and proportional compasses (proportional dividers) may not be confused with each other. Sectors have a fixed pivot. Proportional compasses have an adjustable pivot. Proportional dividers were used, e.g., for the true-toscale reduction and enlargement of polygons, circles, drawings, and plans. The use of the terms “sectors”, “proportional compasses”, and “proportional dividers” is contradictory. Both types of instruments are based on the intercept theorems and function with proportions. The French terms for these are compas de proportion (pair of sector compasses) and compas de réduction (pair of proportional dividers).

2.26  Digitization and Artificial Intelligence For a number of years, such terms as “algorithm”, “digitization”, “artificial intelligence”, “machine learning”, “robots”, and “Industry 4” have appeared in the media.

2.26.1  Algorithms Are Nothing New Already around 2000  BC, the first known written algorithms (formulas for extracting roots) originated in Mesopotamia. Such algorithms are therefore already more than 4000 years old. Classical algorithms were also known in ancient Greece (instructions for the determination of the greatest common divisor of Euclid and for the determination of prime numbers of Eratosthenes and the algorithm for the approximation of the constant π of Archimedes) and in Egypt (Heron’s method).

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2.26.2  Artificial Intelligence Is Nothing New Since its emergence in the 1950s, artificial intelligence has experienced several high points and low points. Ostensible breakthroughs, always connected with exaggerated expectations, have repeatedly been reported with great clamor. Setbacks and disappointments were inevitable. To this day, in spite of commotion in the media, programs and machines are not truly intelligent. Weak artificial intelligence (AI) exists when a program learns to solve a single problem (mostly) from training data (e.g., playing chess, natural language translation, diagnosis, image recognition, handwriting recognition, speech recognition, or face recognition). Face recognition should supplement or replace the comparison of fingerprints, finger vanes and hand vanes, the retina, or the iris. It is not possible to exclude errors and misuse for the measurement of (biometric) data with persons. This is also true of voice recordings, electronic patient dossiers, and electronic identification cards. In all of these cases, the machine supports the intellectual capabilities of humans. By comparison, strong artificial intelligence is capable of solving any desired problems. Thanks to its “understanding,” the computer is then able to independently generate high-quality brainpower. But we are still a long way from this.

2.26.3  Digitization Is Nothing New The 20,000-year-old Ishango bone from Africa has digital notches. The millennium-­old abacus, to this day occasionally used in China, is digital. And the mechanical calculating machines of the seventeenth century (Schickard, Pascal, Leibniz) functioned with numerals. Several steps can be identified in the development of digital computers: • Counting and calculating with the fingers (finger calculation) • Calculating with pebbles (abacus calculation, line reckoning with the counting board) • Calculating with beads (bead calculation with the bead frame) • Calculating with toothed racks (mechanical calculation with the slide bar adder) • Calculating with wheels (mechanical calculation with mechanical and electromechanical calculating machines) • Calculating with punched cards or punched tapes (mechanical calculation with punched card equipment) • Calculating with relay, vacuum tube, transistor, or integrated circuits (program-­controlled mechanical or electronic computation).

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An ancient form of digital memory is the tally stick. Tally sheets record numerical values as well. The ongoing replacement of mechanical systems by electronic equipment has accelerated the digitization process. Many analog devices have given way to digital machines: the analog camera has been largely replaced by the digital camera, and the digital telephone has succeeded the analog telephone. Digital radio and digital television are replacing analog radio and analog television. Music and video can be streamed from the Internet. The flat TV screen has replaced the older CRT screens.

2.26.4  Two Notable Phases of Digitization The first far-reaching phase of digitization began with the development of program-­controlled electronic computers (from around 1940) and expanded further with the emergence of the Internet (since about 1970), microelectronics (from about 1970), and the World Wide Web (since 1990). The second fundamental phase of digitization began with the advent of the new millennium (around 2000) and – e.g., due to the emergence of the smartphones (2007), social networks, and artificial intelligence – has experienced a rapid upswing in recent years. The (current) digitization is thus more than 70 years old. Today, this focuses on networking (Internet of Things). If one considers the introduction of punched card machines (around 1890), we can say that digitization began already 130 years ago.

2.26.5  Digital History? Strictly speaking no digital history and no digital humanities exist. The descriptions computer-aided history and humanities would be more accurate here.

2.26.6  Industrial Revolutions One often reads about the Fourth Industrial Revolution. However, this term is debatable, because it looks to the future and not to the past. The revolution began namely only recently, and the impact, e.g., of artificial intelligence, is difficult to predict. The first revolution began around 1760  in Great Britain. Opinions differ regarding the classification into three or four eras (see Table 2.28).

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Table 2.28  Industrial revolutions (classification) Features of the industrial revolutions Phase Characterization Achievements 1 Mechanization Steam engine, spinning machine, mechanical loom, railroad, mining 2 Automation Electrification, electric motor, production line, mass production 3 Informatization Microelectronics, miniaturization, informatics, robotics, internet, and World Wide Web 4 Digitization Nanotechnology, networking via Internet (internet of things), smartphone, artificial intelligence © Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020

Remark With the omnipresent smartphone, networking has increased dramatically. Where do the names of Internet companies come from (see box)? Origin of Proper Names • “Airbnb” is derived from air mattress and bed and breakfast. • “Alibaba”, in the fable “Ali Baba and the forty thieves” from the Arabian Nights, Ali Baba discovers the treasure of a band of brigands (Open Sesame). • “Amazon” derives from the South American river. • “Facebook” was originally an illustrated student directory. • “Google”: Googol is the English term for the number 10100. • “Netflix” is a composite of net (network, Internet) and flick(s) (film, movie). • “Twitter” means chirping. • “Uber” stands for Mega. • “YouTube” is deduced from tube (slang for television).

2.26.7  The Digital Transformation Industrial revolutions up to now have generally brought about greater prosperity. However, they have also brought disadvantages, e.g., in terms of environmental pollution. The often feared mass unemployment has largely not materialized. Countless jobs were lost, but at the same time new professions arose. The digital revolution has simplified and, at the same time, complicated our lives. In many ways, it asks too much of the older generation. Established services, such as with the post office and railroads, have disappeared. Digitization cannot be held back but can be (within reason) controlled and shaped. Under discussion are an unconditional basic income and a digital services tax.

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Below are a few selected (partly overlapping) keywords relating to the contemporary historical development, together with a brief description of each term. 2.26.7.1  The Internet and World Wide Web The World Wide Web, invented in 1989 at the CERN (European Laboratory for Elementary Particle Physics) in Geneva, has dramatically changed our lives. The Internet and the World Wide Web (WWW) are frequently confused. The Internet, which originated in the USA, is much older (Arpanet, 1969). Electronic mail and the WWW utilize the Internet. The term “cyber” refers to the Internet. In addition to the Web covered by search engines, there is also an invisible concealed Web (the deep web). This region contains some library catalogs. Furthermore, there is also a secret, coded Internet (the darknet), where the black market thrives and where, for example, drug, pornography, and weapon traffic exist. 2.26.7.2  Internet Giants Today, the Internet giants belong to the world’s most valuable companies: • • • • • • • • •

Alibaba Alphabet Amazon Apple Baidu Facebook IBM Microsoft Tencent.

GAFA is an abbreviation for the US companies Google, Amazon, Facebook, and Apple. BAT stands for the Chinese giants Baidu, Alibaba, and Tencent. Alphabet has several subsidiaries, e.g., Google (search engine), YouTube (video-sharing website), and Waymo (self-driving cars). The Facebook social network also offers a number of platforms: Facebook messenger (social network), WhatsApp (instant messaging platform), and Instagram (photo and video service). The company has in mind the merging of the three services Messenger, WhatsApp, and Instagram. Uber and the electric vehicles manufacturer Tesla, for example, are concerned with self-­driving cars. Massive Chinese competitors are Alibaba (electronic commerce), Baidu (search engine), and Tencent (social network) with the versatile platform WeChat, along with the Huawei technology company. In many areas a transition from machines (hardware) through programs (software) to services can be seen.

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2.26.7.3  Search Engines Powerful (commercially financed) Web-based search engines (such as Google, Bing, and Baidu) simplify researching. Nevertheless, the hit rate leaves something to be desired, and one also acquires much material of little or no interest. Moreover, the databases are rather incomplete. 2.26.7.4  Digital Reference Works Reference works, such as electronic encyclopedias (e.g., Wikipedia), telephone books, timetables, and guidebooks, are increasingly supplanting printed books. Searching is in fact simpler; however the overview is lacking. Wikis are shared platforms to which users can also contribute. 2.26.7.5  Localization Thanks to satellite navigation systems like GPS (global positioning system) and Galileo, positions can be determined (nearly) anywhere. On the one hand, continuous localization violates personal privacy. On the other hand, it can also facilitate searches for missing persons and combating crime. With the help of location data, this application enables, e.g., the generation of movement profiles and thus allows getting on and off public traffic at will. Smartphones can also be used as navigation devices. 2.26.7.6  Smartphones Since their introduction in 2007 (Apple’s iPhone), versatile smartphones have experienced an unparalleled triumph. Applications (apps) exist for virtually every conceivable purpose. Also popular are self-pictures (selfies). However, this development has its drawbacks: exposure to radiation from the cellular network of the fifth-generation 5G or the regional WLAN radio network, obsession with the Internet, permanent accessibility, total surveillance, and tracking. 2.26.7.7  Social Networks (Social Media) The exchange of information, thoughts, and documents via social networks (social media) such as Facebook, WhatsApp, Instagram, Snapchat, and Tiktok (in China: Douyin) can significantly influence society and politics. Countless fully automatic interactive computer programs operate on such platforms. These attempt to simulate human behavior and can influence democratic

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processes (e.g., elections and voting) and ultimately lead to the abuse of power (misuse of market power). The automatic selection of news can sometimes lead to fake news. Via social networks fellow human beings can also be annoyed, denounced, and tortured with malicious intent (trolling or mobbing). Profession-­oriented social networks are LinkedIn (Microsoft) and Xing, while ResearchGate and Academia belong to the scientific platforms. Deep fakes may be dangerous. Also worth mentioning are tweet services, such as SMS (short message service), Twitter, and Weibo (China) along with the communication service Skype (Microsoft) and the multimedia messaging app Snapchat. The definitions are not altogether clear. The boundaries between social networks, platforms (Internet platforms), portals (Internet portals), Internet services, and placing and distribution services are fuzzy. 2.26.7.8  Electronic Commerce Trans-border electronic commerce (e.g., Amazon or Alibaba) is suppressing stationary retail trade. This is also suited to second-hand goods. Digital platforms facilitate the exchange of goods and services and constitute an electronic marketplace. Less favorable is the ecologically harmful package traffic resulting from online trade. Shipments can be traced. Among the best known payment services is PayPal. Alipay (Alibaba) and TenPay and WeChat Pay (Tencent) are Chinese payment systems. Apple Pay, Google Pay, Samsung Pay, and Facebook Pay are other services. 2.26.7.9  Sharing Economy Ride-hailing companies (e.g., Uber or Lyft) and accommodation services (e.g., Airbnb) simplify travel planning. One speaks of the sharing economy. Freelance service providers, such as car drivers, are paid on a per commission basis. Legally disputed is whether this constitutes work assigned to employees or self-­employment. Widespread, for example, are courier delivery services, home meal services, bicycle renting services, partner contact agencies, and online auction websites, such as eBay and Taobao (China). Booking platforms exist for hotels (e.g. Booking or Expedia). The dependence of the catering and hotel industry on such Internet portals is sometimes not without risks. Furthermore, there are also Internet comparison services and recommendation services. A widespread video-sharing website is YouTube, and a well-known audio platform has the name Spotify. Videos can be obtained via film services, such as Netflix (video on demand). These and other subscription-based services of Amazon, Apple, Disney, and Warner Media lend out pieces of music and films (music and video streaming). Libraries offer similar services for books (ebook

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lending). Photos are transmitted, for example, via the photo- and video-­ sharing service Instagram. With crowdfunding, thanks to micropayment, funds can be raised. The knowledge of volunteers can be tapped via the Internet (crowdsourcing). 2.26.7.10  Open Access to Economic Information Government-financed research results will no longer be circulated (exclusively) by expensive subscriptions to academic journals. Instead, these will be available on the document platforms of universities and as cost-free scientific journals (open access) and as open data. Prominent academic publishing houses, such as Elsevier, Springer, and Wiley, reap substantial earnings from external services. For some time predatory journals have published numerous articles without proper peer reviews for high fees. Furthermore, many pseudo-scientific congresses are announced that profit from the global competition prevailing in research (publish or perish). 2.26.7.11  Digitization of Libraries and Archives Many library and archive sites are retroactively digitizing books (e.g., old and rare printings and handwriting), newspapers, maps, archive material, and illustrations. These can then be accessed online at different sites worldwide at any time. This represents an enormous help for research in the history of science and technology. Copyright law must of course be respected here. 2.26.7.12  Citizen Science With the participation of the public in research (e.g., by observations, the collection and evaluation of data, or the imparting of ideas), the amount of available data is increasing. The term “citizen science” has therefore been coined to describe this. Gathering data on the weather, climatic change, and biological diversity, for example, provides the basis for an inexhaustible data source. 2.26.7.13  Virtual Reality We distinguish between the actual real (physical) world and the artificial (virtual) world. This refers to virtual and augmented (mixed) reality. The virtual world allows spatial presentations unknown until now. For three-dimensional visualization data, virtual-reality headsets are necessary.

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2.26.7.14  Devices for Three-Dimensional Input and Output A further new achievement is the production of three-dimensional objects with 3D printers. This leads to a multitude of potential uses. Complementing this is the 3D scanner (e.g., a tomograph). Digital production in the building industry is based on three-dimensional printing. 2.26.7.15  Fitness In order to monitor and improve the physical condition fitness trackers, sports watches and smartwatches are worn. These display numerous values and pass on the data. 2.26.7.16  Cyborgs The implantation of artificial objects (implants, e.g., artificial joints) in the human body is commonplace in medicine. Persons with technical (predominantly electronic) devices implanted are referred to as cyborgs. However, this does not mean that human and machine merge to a single entity. 2.26.7.17  Cybercrime The cyberspace encourages criminal activities of all kinds, such as cyberattacks, blackmail (Trojans), sabotage, terrorism, and espionage. Commonplace Internet-­connected devices (Internet of Things), cardiac pacemakers, navis, drones, cars, and robots, for example, can be victimized by hackers. Falsified ratings of hotels and fabricated book reviews are also made possible. On the other hand, via the World Wide Web, abuses can be identified faster (e.g., WikiLeaks, phone bugging scandals). Vigilance (caution with attachments and links in electronic mail), coding, data backup, and separation of the computer from the Internet provide a certain degree of protection against such offenses. 2.26.7.18  Cloud Computing Internet enables the provision of multifaceted services. Thus, one can utilize large amounts of memory space in the “digital cloud” as required and access extensive computing power, as well as make use of external programs. A “cloud” is a (terrestrial) data and computer center. Thanks to distributed computing, it is possible to solve problems that overwhelm even large computing centers. Research is therefore extended to include a third pillar, simulation in addition to theory and experiment. Questions of data privacy and data security (digital preservation) are of central importance. Many Internet companies

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(e.g., Alibaba, Alphabet (Google), Amazon, Apple, IBM, and Microsoft) provide cloud computing services. In the mobile communications network, a contrary trend can be observed, namely, the transfer of information to peripheral computers (edge computing). 2.26.7.19  Blockchains Thanks to blockchains, a central processing site is not required for payments through the Internet. Consequently, financial institutions, such as commercial banks, are not (absolutely) necessary for this purpose. The distributed database is augmented by one member (block), as with a chain, for these processes. The data blocks are copied to the computers participating in the network (network nodes). The transactions can therefore be traced and controlled, making falsifications difficult. Subsequent changes and deletions are thus hardly possible. The blockchain technique is a prerequisite for (the not always stable) digital money (e.g., Bitcoin). In addition to bank notes, central banks could also create book money (electronic bank notes). Several other applications come into question, such as for entries in medical case histories, bookings, and the processing of digital contracts of all kinds (e.g., for power distribution). Blockchains play an important role in the Internet of Things. With the help of sensor technology, they enable the end-toend monitoring of supply chains (logistics chains). This allows one, e.g., to determine the origin of food stuffs and, e.g., luxury watches and works of art (forgeries). As with other innovations and misuse by criminals, with digital money, the danger of complete interception by other persons exists. The lacking public supervision of monetary circulation for cryptocurrencies entails risks. As with hard cash, one can pay (anonymously) with digital money (e.g., commerce with illegal money or money laundering). There are private and public blockchains. To what extent this technique will become established is open. At the present time, it requires a high level of computer processing power for control purposes and therefore (often) consumes significant amounts of electrical energy. The “mining” process (processing of money transfers) is anything but environmentally friendly. The (stable) Libra global currency (or possibly global payment network) proposed by Facebook is based on an entirely different model than the previous cryptocurrencies. With this closed centralized network, the power demand is much lower, and the users do not remain anonymous. 2.26.7.20  Internet of Things The Internet of Things refers to the linking of devices at will via the Internet. This allows the (independent) remote control and monitoring of processes via the World Wide Web and therefore a broad range of applications. Inexpensive sensors and wireless data transmission are available for this.

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One reads about the “smart home”, the “smart city”, and the “smart factory”. With Internet-connected objects (e.g., a networked car with smartphone connection), data is often sent to the manufacturer and the Internet companies without the knowledge and without the permission of the user. The greater the degree of networking, the greater is the danger of hacking attacks (e.g., cracking nuclear power plants, interrupting the provision of water and electricity, paralyzing hospitals, or deactivating traffic control systems). 2.26.7.21  Mobile Communications Standard 5G On the heels of 2G, 3G, and 4G, the high-speed fifth-generation 5G will now follow. Above all, this will support Industry 4.0. Nevertheless, there is opposition to the non-ionizing electromagnetic mobile communications radiation. Worldwide satellite-supported Internet services, such as Starlink, enable wideband access. Nevertheless, the vast number of satellites increases the amount of hazardous space debris. The Wi-Fi 6 standard applies for the wireless Internet (WLAN). 2.26.7.22  Big Data The evaluation of big data serves to provide new knowledge, for example, about user behavior. The personal profiles can be used as the basis for targeted (personalized) advertising. These are also able to influence the listed results from the search engines and the newsfeed in social networks (filter bubble, echo chamber). For this purpose cookies are planted on personal computers and smartphones. These snooping files serve for recognition. For tracking, monitoring programs are utilized. Other uses are concerned, e.g., with personalized healthcare. Saleable personal data are regarded as a resource serving as the basis for certain business models. Alphabet (Google, YouTube), Facebook (Messenger, WhatsApp, Instagram), Amazon, and Twitter reap substantial profits from advertising. Health insurances and other insurances employ risk profiles. Based on the analysis of buying behavior, ecommerce companies can even specify personalized prices. Big data also serves for climate research, genetic engineering, elementary particle physics, and modeling. Data science and data analysis are concerned with such datasets. However, the size of the data mass says nothing about the quality of the information. The analysis of big data entails the risk that many absurd, alleged relationships are found along with genuine ones. If the given (retrospective, historical) training material is inadequate, obsolete, biased, unjust, insufficiently conclusive, or even racist, this can result in false conclusions. Bias and partiality are propagated further. As a result of unequal treatment, women, blacks, homosexuals, disabled persons, persons of other faiths, and foreigners can be disadvantaged.

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The mania for collecting data has its drawbacks: seeing through people (transparent citizens), ­privacy violations, and misuse of personal data. Face recognition is a delicate matter. Data scandals are on the increase. Especially pronounced is the exhaustive continuous monitoring (and the related evaluation of persons with behavioral profiles) with omnipresent surveillance cameras in China, reminiscent of George Orwell’s novel “1984” (big brother is watching you). In some countries Internet censorship and network blocking exist. The collection of extensive datasets and their evaluation are nothing new, but their size and speed have increased dramatically. 2.26.7.23  Data Ownership Who does the data belong to? In connection with the unfathomable, difficultto-­comprehend use of personal data by Internet giants, the fundamental question of data ownership arises. Why is it that the appropriation of such data is not subject to costs, especially considering that Google, Facebook, and Amazon & Co. reap enormous profits with this data? Do these data hydra have the right to pass on and to sell the data of other persons without their knowledge and permission? It must be possible for the users themselves and not the Internet companies to control their own data (proprietary rights). This is true particularly for health data. 2.26.7.24  Artificial Intelligence In recent years artificial intelligence has undergone a significant new upsurge. This can be largely attributed to the following developments: • Computing power has rapidly and significantly increased in recent times. • Big data is available as a result of the unending collecting activities. • Better programs, i.e., sophisticated algorithms, are well suited for the processing of the flood of data. In addition this is supported by the widespread use of artificial neural networks. Current key areas of artificial intelligence are: • Machine learning • Pattern recognition. In medicine substantial progress has been made as a result of artificial intelligence in the diagnosis, early detection, and therapy of diseases and the prognosis of their clinical course. Robots are able to operate gently and precisely 7  days a week around the clock without tiring and without hunger. Nevertheless, machines cannot replace doctors. For robots, drones, and self-driving cars, the recognition of the surroundings (in real time) plays an essential role. The prerequisite for machine vision is the presence of sensors.

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The improvements have led to systems that have less effort in dealing with the natural language, facilitating voice control. This is seen with digital bots (virtual voice assistants). Voice control is based on speech recognition. Writing programs automatically generate simple texts (e.g., weather forecasts, traffic volumes, or stock market quotations). In the area of automatic language translation, depending on the language pair, considerable progress has been made. However, machines are lacking in the profound understanding of the content. Artificial neural networks, machine learning, and big data have changed nothing in this regard. A command of the ambiguity of words is achieved only with difficulty. Complex texts are beyond the capabilities of artificial intelligence. There are limits to statistical probability. The development of viable practical automatic interpreters is especially full of thorns. With older documents, even text recognition is often wanting. Sobering is that until now no faultless spelling programs and hyphenation programs exist. With many texts, the spelling program of Microsoft fails to recognize the relevant language and in some cases is therefore useless. Some (older) chess programs make use of “brute force” in searching for plausible chess moves. By comparison, humans have the ability to correctly comprehend complicated circumstances and processes immediately and see through relationships (intuition). Under the term singularity, we understand the point in time at which artificial intelligence overshadows human intelligence. The machine is then superior to humans. Many humans tend to ascribe too much intelligence to narrowly focused AI systems (see Alan Bundy: Smart machines are not a threat to humanity, in: Communications of the ACM, volume 60, 2017, no. 2, page 41).

The capability and the power of artificial intelligence are often overestimated. In many fields, research is only in the beginning stage and lags far behind what is generally assumed. Machine-based systems cannot actually think. Far more, they only possess apparent intelligence. Machines have no creative powers (creativity). They have neither will, curiosity, fantasy, feelings (emotions), empathy, conscience, nor awareness and are unable to assume responsibility for faulty performance. One can only feign feelings. Many apparently intelligent achievements have little to do with intelligence. In spite of artificial neural networks, the usefulness of bots and other interactive programs (social bots, chatbots, or bots) is distinctly limited for sophisticated tasks. The computer does not understand what it does. During a game it doesn’t even know that it is playing. A robot does not know who it is. Furthermore, such descriptions as “artificially intelligent machine” or “artificially intelligent robot” make little sense, namely, because there are no naturally reasonable machines.

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2.26.7.25  Voice Assistants Interactive programs with speech recognition and speech output give information in certain areas. Speech recognition is concerned with spoken utterances (contrary to text recognition, which implies machine-written or printed text material). Familiar voice assistants (virtual assistants or digital assistants) are, e.g.: • • • •

Alexa (Amazon) Cortana (Microsoft) Google Assistant (Google) Siri (Apple).

The constant eavesdropping by smart loudspeakers (bugs) is dubious from the standpoint of personal privacy. 2.26.7.26  Machine Learning and Artificial Neural Networks Advances in artificial intelligence are based to a large extent on machine learning aided by artificial neural networks. Neurons and nerve cells (in the human brain) are utilized primarily for pattern recognition (e.g., object, image, speech, and voice recognition). A further area is emotion recognition. Such programs attempt to identify patterns in the enormous datasets and allocate these to object classes. Persons label the data sets and define the categories. In general, machine learning requires large quantities of labeled data. With recourse to multilayer artificial neural networks, one speaks of deep learning. The learning capability of neural networks serves to simplify programming. Today’s networks are tailored to particular applications and are thus not universal. Furthermore, there is no guarantee that the computer recognizes the essential features. Only the future will show whether self-learning systems achieve the breakthrough for any desired spheres of life. Until now how the brain learns is still unknown. The machine must, for example, be fed with countless images of cats before it is capable of recognizing such a living being. And even then, it still does not know what a cat is. On the other hand, for children a single cat is usually enough. Humans learn quite differently than machines. A program “learns” by a statistical process of pattern matching and, in doing so, develops no deeper understanding. Reference is often made to black boxes. It is difficult to understand how and why the artificial neural network finds certain solutions. In any case, only explainable and justifiable decisions (such as with regard to jurisdiction, granting of credit, job applications, approval of travel, or the determination and therapy of diseases) are credible. Systems are thus only able to provide support to expert persons.

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A fundamental weak point of machine learning is the poor efficiency. The learning process requires huge amounts of high-quality training data and a great deal of electrical power. The opposite of a learning system is a rulebased system. Artificial neural networks already appeared in the 1940s and 1950s (Warren S. McCulloch and Walter H. Pitts, 1943; Frank Rosenblatt, Perceptron 1958). Arthur L. Samuel coined the term machine learning in 1959. 2.26.7.27  Machine Vision Fundamental meaning is ascribed to machine vision. This requires a vast array of sensors. Examples are cameras (stereo cameras or infrared cameras), laser (scanners), ultrasound, radar, and Lidar (scanners). Lidar enables the calculation of a three-dimensional model of the ambient. The sensors communicate the contact to the external world and are employed in robots, drones, and self-driving cars. In addition, prestored maps are accessed. Machine vision is also a basis for cashless stores. Several terms are used in machine vision (see box). What Does That Mean? Infrared Laser Lidar Radar Scanner Stereo camera Ultrasound

Invisible thermal radiation Device for the generation of a sharply focused light beam Light wave-based positioning system Electromagnetic wave-based positioning system Sensing device, text reader Camera for spatial imaging Sound not perceived by humans

2.26.7.28  Robots and Drones Robots have long since taken over monotonous, strenuous, dirt-stained, unhealthy and dangerous, as well as poorly paid tasks. They operate not only in industry but increasingly in the household. Furthermore, they are active in the service industry. They perform surgical tasks on humans and execute courier services (delivery robots and delivery drones), such as for medicines, food, meals, spare parts, or luggage). The machines are endowed with “eyes” and “ears” and attempt to perceive the surroundings with these. The electrical energy is taken from the power grid or from storage batteries. Solar energy is also suited for operation.

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Robots have difficulty becoming oriented to continuously changing or entirely new surroundings and correctly perceiving the environment. They must adapt to the particular situation in real time. Automatic lawn mowers and vacuum cleaners are available commercially. They can be controlled with voice commands via smartphone. Remotecontrolled flying objects, namely, drones (multicopters, quadrocopters, hexacopters), are widespread. Agriculture also works with robots (e.g., milking robots) and drones. 2.26.7.29  Self-Driving Cars Future self-driving (electrically driven) cars show promise for improving safety in private and public traffic. At the present time, difficult situations overwhelm the autopilots. Autonomous vehicles have been known for a longer time. Nevertheless, a number of hurdles must be overcome before they are suitable for everyday use. 2.26.7.30  Who Is Responsible? Automatic machines pose delicate legal questions. Examples: Who is liable for a robotic nurse that causes harm to patients? Who is liable for deficient computer-­based diagnoses? Who is to blame when a self-driving car causes an accident (the manufacturer, the leaser, the programmer, or the user)? Why are the platform operators (e.g., Google, YouTube, Facebook, WhatsApp, Instagram, or Twitter) not liable for the contents propagated with their websites as is the case for the press, radio, and television? 2.26.7.31  Superiority of Machines Many animals and machines are stronger or faster and therefore physically superior, to humans. Examples are bears, birds, cars, and robots. There are also devices and programs that are cognitively superior to humans, such as the Deep Blue chess-­playing computer of IBM, its successor Stockfish, or the AlphaGo game-playing program of the Google subsidiary DeepMind. The further developments AlphaGo Zero and Alpha Zero acquire the necessary knowledge in a short time by playing against themselves, without recourse to previously stored data. This represents a remarkable new approach. In 1997 the former world chess champion Garry Kasparov lost against the IBM program (Deep Blue), which did not employ a neural network. Unlike the general, universal, intelligence of humans, these technical masterpieces are characterized by a special form of intelligence tailored to a particular purpose. As a rule, the machine can only execute a task that has been

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previously programmed (and has been trained) to deal with these. The learning system Watson of IBM, for example, suggests a course of therapy based on a medical diagnosis. Incidentally not only modern electronic computers but also many timehonored mathematical instruments without power can provide support for intellectual work. Program-controlled machines have long since made decisions independently. Worth noting, the brain requires far less energy than the computer. 2.26.7.32  Will Robots Dominate the World? The fear of robots dominating the world is absurd. Smart machines do not threaten mankind: far more we should utilize the chances that they offer. However, as with all technical achievements, misuse can hardly be avoided. Some people fear the end of the world, a destructive war between robots and attacks by autonomous weapon systems (e.g., autonomous drones and tanks) against humans. Mobile devices do not function without energy. They require long-life storage batteries and, for radio communication, good network coverage. 2.26.7.33  What Does the Future Have in Store? Since time immemorial man has tried to predict the future, but even the near future with only very limited success. The uncertainty creates fear, especially when profound changes transpire. As shown in the past, history does not repeat itself, but we can of course learn from this. No one could foresee the digital revolution. Nor do we know what awaits us in the future. Many questions are still open: What will prevail? What will disappear? Futurology is not the job of historical scholarship. For commerce, administration, society, and science, basic programming capabilities are indispensable. Mere knowledge of applications is not enough for either work or spare time. Whoever does not take part in this development will remain behind, lose continuity, and no longer be competitive. Informatics is increasingly embedded in goods and services as an essential component.

2.27  Quantum Computers Quantum computers utilize the laws of quantum mechanics. The bits (smallest units of information) of conventional digital computers possess only two states, 0 or 1. However, as a result of superposition, the electrons, atoms,

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molecules, and light particles can exist simultaneously in both basic states 0 and 1. Photons (the smallest unit of light) have both particle and wave character. As the smallest information carriers, one can use the spin of elementary particles such as electrons, for example. Arithmetic operations with quantum bits (qubits) act on all states simultaneously. Enormous amounts of data can therefore be processes in parallel. Spatially separated but quantum mechanically coupled quantum particles can be linked. Thanks to this interleaving, a change in the state of one quantum bit immediately changes another bit, independently of the distance separating the two qubits. Interleaved particles assume the same state. This so-called teleportation enables the transmission of data. The extremely high-performance quantum computers can, for example, crack the usual code systems and resolve virtually endless numbers into their prime factors. Some code systems are based on resolution into prime numbers. Conversely, (at least theoretically) quantum cryptography enables the bugproof transmission of messages (only a single use of qubit-based codes exchanged by interleaving). The quantum code, comprised of an arbitrary sequence of zeroes and ones (random generator), can be transmitted with quantum amplifiers (signal amplifiers) via fiber optic cable or satellites. Other conceivable potential applications for quantum computation are pattern recognition (pattern matching) and searching databases. With superpositioning and interleaving, one strives to achieve unimaginably high speeds. Thanks to parallel processing, in the future it will be possible to solve problems that completely overwhelm today’s electronic computers. Research in this area is currently being conducted in universities and industry around the world. When high-performance quantum computers will become available is not clear (see Der Brockhaus. Computer und Informationstechnologie, F.  A. Brockhaus GmbH, Leipzig, Mannheim 2003, page 746; Dossier Quantencomputer: Rechner der Zukunft, in: Uni nova, no. 130, November 2017, pages 14–33 (scientific magazin of the University of Basel)). P and NP Problems A distinction is made between P problems and NP problems. Simple tasks (class P) can be solved in polynomial time. Difficult tasks (class NP) cannot be solved in polynomial time. A polynomial is a multi-term mathematical expression in which the individual terms are separated by a plus or minus sign, e.g., (3x – 4y) or (a + b)2. The resolution of numbers into their prime factors, an NP problem, rapidly increases the computing time with increasing capacity; the time increases exponentially.

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2.28  DNA Computers The molecules of the genetic material DNA (deoxyribonucleic acid) can store enormous amounts of genetic information that can be processed in parallel. However, there are many obstacles in the way of developing practically usable, freely programmable biocomputers. DNA molecules require very little memory space and are extremely long-lived. DNA data centers (biological data storage) are in the planning stage. Artificial DNA is machine-produced (chemically): DNA is a macromolecule comprised of the components phosphoric acid residues, the sugar desoxyribose and the [nitrogeous] organic bases adenine (A), thymine (T), guanine (G) and cytosine (C). the structure of the DNA is determined by the specific sequence of desoxyribose, phosphoric acid residues and bases, that is the sequence of nucleotides (see Duden, Basiswissen Schule. Biology, Bibliographisches Institut and F. A. Brockhaus AG, Mannheim/Duden Paetec GmbH, Berlin 2005, page 261).

Chapter 3

The Coming of Age of Arithmetic

Abstract  This chapter “The Coming of Age of Arithmetic” traces the tedious journey from the tally stick, through the bead frame, to the smartphone. To this day the importance of the Ishango bone discovered in Africa is puzzling. The tally stick was a digital memory with which falsification was hardly possible. Among popular calculating aids was also the (digital) quipu. Since time immemorial the fingers have served for counting and calculating. An (digital) abacus utilizes either lines and counters (counting board) or staffs with beads (bead frame). Unlike the Roman number system, the use of the Roman hand abacus is simple. Although there was no symbol for zero, one could represent this number on the “pocket calculator” along with ones, tens, hundreds, etc. Once widespread logarithmic analog calculating devices, such as the slide rule, circular slide rule, and cylindrical slide rule, disappeared 50 years ago, as did mechanical desktop calculators. The difference between numerical and graphical computation is also described. A special form is nomography. The omnipresent portable smartphone is regarded as an extremely versatile tool. The evolution of certain mathematical instruments is illustrated in the form of lines of development. Keywords  Abacus · Arithmetic · Bead frame · Counting board · Graphical computation · Lines of development · Graphical computation · Ishango bone · Nomography · Numerical calculation · Quipu · Roman hand abacus · Slide rule · Smartphone · Tally stick The millennium-old history of the development of arithmetic includes many stages. Some of these were in use simultaneously: • • • • • • •

Counting and calculating with fingers. Calculating on the lines (calculating with counters). Calculation with bead frames. Pen and paper calculation. Calculation with slide rules. Calculation with Napier’s rods. Machine calculation.

© Springer Nature Switzerland AG 2020 H. Bruderer, Milestones in Analog and Digital Computing, https://doi.org/10.1007/978-3-030-40974-6_3

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Remarks Abacus calculation comprises calculation with counters and with bead frames. Calculating with mechanical calculating machines was quite demanding.

3.1  From Tally Stick Through Abacus to Smartphone As with reading and writing, calculating is a fundamental human cultural technique. In the course of the millennia, different methods were developed: counting with the fingers, line computation with calculating tables, and ­calculating with the stylus on the slate or with the pen on paper. Even today strokes are a still common practice, for example, with card games. The purpose of mathematical instruments was and is to spare humans arduous calculating. To this day, mental calculation and calculating with pencil and paper are distressful for many people. The history of computing technology is closely bound to the history of astronomy, mathematics, geodesy, seafaring (navigation), precision mechanics (precision engineering), clockmaking, instrument making, and automaton construction. In addition, machine engineering, physics, electrical engineering and microelectronics play an important role. Some institutes for computer science have emerged from applied or numerical mathematics. Many computing professionals were formerly mathematicians. Widespread calculating aids and data storage devices were  – apart from the fingers – tally sticks, knotted cords (quipus) (Chinese and Peruvian), pebble stones, counting boards, and counting frames. The abacus is regarded as the oldest digital calculating device and is found in two different forms: as a counting board (calculating table) and as a counting frame (bead frame). After the computists (devotees of bead computation) came the abacists (proponents of line computation). These were in turn superseded by the algorists (supporters of pen and paper calculation). The Roman arithmeticians belong to the computists. Arithmetic was taught in reckoning schools. Among the earliest analog computing devices are the astrolabes (two-­ dimensional devices for the observation and determination of the position of stars, a navigation aid for sea travel) and the mysterious Antikythera mechanism. Other significant landmarks were, e.g., the calculating church clock of the Strasbourg cathedral. In the seventeenth century, the (logarithmic) slide rule, a portable, inexpensive, and silent calculating aid, was invented. The first mechanical calculating machines also appeared at this time. However, these loud instruments were useful in practice only from the middle of the nineteenth century. Numbers were entered directly with the fingers or by means of setting levers, setting wheels, styluses, or keys. An important forerunner of the modern computer was the (program controlled) analytical engine of Charles Babbage. This was never completed. A

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sequence control already existed by the way with antique automatons, church clocks dating from the Middle Ages and modern times, automaton figures, music boxes, and looms. After the American census of 1890, a diversity of useful punched card equipment gradually came about. In 1931 the first report of a powerful (electro) mechanical differential analyzer for the analog solution of differential equations appeared. Programmable mechanical digital computers (relay machines) first appeared at the beginning of the 1940s. For many years (analog) slide rules, (digital) mechanical desk calculating machines and pocket calculators, mechanical and electronic analog computers, as well as (digital) mechanical and electronic calculating machines existed alongside each other. Electronic analog computers and electronic digital computers were in direct competition with each other. As the computation speed and memory capacity of digital computers increased, digital computers ultimately replaced analog computers. Vacuum tube computers were mostly equipped with delay line memories, electrostatic memories, or magnetic drums. Core memories and transistors then followed. In 1946 the first publications about the giant American Eniac electronic computer came to light in Europe. In the same year, a series of lectures on the design of programmable computing machines took place in Philadelphia, and the influential paper about the von Neumann computer architecture was in circulation. Numerous conferences on computer technology were convened to still the hunger for information. In England, the first two stored-program digital computers appeared in 1948 in Manchester and in 1949 in Cambridge and were in competition with each other. At the same time, a New  York machine (1948) also laid claim to this honor. Moreover, the first Australian computer (Csirac) was in operation from 1949. In 1950, a mere two automatic relay computers were operating continuously in continental Europe, the tape controlled Zuse Z4 in Switzerland and the plugboard controlled Bark in Sweden. Stored program implies that data and instructions can be held in the same form in the same (internal) memory. In this case, the machine is controlled by an internal program. The first vacuum tube computers appeared on the market in 1951 (Ferranti Mark 1 in England and Univac in the USA), and the first stored-program computer in continental Europe, the Ukrainian Mesm, was built. UNESCO planned a European computing center, which was finally realized in Rome after considerable delay and which served a different purpose. Large-scale American businesses established research centers near Zurich (International Business Machines and Radio Corporation of America) and in Geneva (Battelle Memorial Institute). No one was aware that the top secret British Colossus electronic computer began operating at the beginning of 1944. Only more than 30 years (or over 30 years) later did we learn of its existence and of the grueling battle between the Turing-Welchman Bombe and the Enigma cipher machine. At that time one spoke of mathematical machines. Until the middle of the 20th century, computers were viewed as humans. One referred for example to a “female computer” or to “women computers”. Later, a distinction was made between “human computers” and “digital computers”.

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Since they did not want to be left behind in the face of the developments in England and the USA, in the 1950s, many universities and technological universities built programmable automatic computers. Evidently there was little trust in the machines on the market. There were different reasons for this: the machines were not tailored to individual requirements, they were too prone to failure or too expensive, or their operation and maintenance were too ­laborious. Furthermore, one was dependent on foreign sources. In-house activities also served in support of teaching and research. The commercialization of the early electronic computers was successful only in a few locations, such as in Manchester, Cambridge, London, or Philadelphia, as well as in Delft and Dresden. But this was not provided for everywhere. In the 1960s, the importance of homemade stored-program computers decreased significantly. By this time industry was able to supply mass-produced systems. The main emphasis at universities turned from machine development to programming and to the creation of programming languages. This signaled a new orientation, a transition from computer design to the utilization of information technology. However, in many places the need for the early introduction of study paths in computer science was not recognized. In the 1970s, electronic machines suddenly replaced mechanical calculating devices – both slide rules and calculating machines. The first signs of this development were seen in 1961 with the Anita desk computer. About 10 years later, battery-driven electronic pocket calculators from Canon, Hewlett-Packard, Sanyo, Sharp, and Texas Instruments became available. Not only slide rules but also many other analog devices, namely, sectors, proportional dividers, planimeters, pantographs, and coordinatographs, were soon forgotten. Electromechanical and electronic digital computers originally performed primarily calculations. In spite of their name, however, computers can do far more than calculate. They are also able to handle letters and special characters. Texts are coded in the form of numbers. This is also true for still images and moving images (drawings, photos, videos, and films) and for sound. One speaks of nonnumerical data. And the machine is also in command of playing chess. Business data processing, tailor-made for administrative activities, merged with scientific computation. This development continues with increasing turbulence, while the lifespan of the machines is continuously decreasing. General-purpose devices are gradually replacing single-purpose instruments and are becoming more compact, lighter, more capable, and less expensive, but at the same time more sensitive. Information technology, telecommunications, and electronic audiovisual media (radio and television) are growing together. The typewriter has also disappeared. The global Internet now links people. The World Wide Web is undergoing an enormous upsurge. Risks and breakdowns are on the increase. Privacy, copyright, and data ownership are disregarded far too often. The ever present hope of finding solutions for the problems of manhood now places its expectations in artificial intelligence. But we are still far away from a clever all-purpose robot. As theoretical computer science shows, not all mathematical problems can be solved with digital computers even if these are

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endowed with infinite memory capacity and are available for an unlimited time. Digitization is spreading, and social networks link people. Electronic commerce, the Internet of Things, the sharing economy, and the blockchain technique necessitate new business models. The print media are struggling to survive. The quantum computer is waiting in the wings. The smartphone is omnipresent. With this device a virtually inexhaustible range of applications is available underway, such as: altimeter, camera (photo, video), compass, dictating machine, dictionary, electronic commerce, electronic mail, electronic purse, flashlight, language translation, mobile radio, movies, navigational device, newspaper, notepad, playback devices (sound and image), pocket calculator, pocket diary, pulse monitor, radio, road map, route planner, scanner, search engine, social networks, sonar, teaching materials, (visual) telephone, telephone book, television, textbook, ticket machine, timetable, toys, watch, and weather report. The way from the tally stick, through the abacus, to the decimal place-value system with the number zero and the modern computer was a rocky path and required millennia. Today, we can hardly imagine anymore how our ancestors had to struggle with calculating. Nor can we even begin to imagine where we are heading with the rapid, relentless developments of our time. Although computer science is still young compared with mathematics and physics, the beginnings already lie in the dark. Firsthand witnesses have largely died out, important devices have long since been scrapped, and documents thrown out. It is often difficult to piece together an overall picture from the few existing fragments, the mosaic pieces. Some descriptions for time-honored calculating aids have remained part of our language: digital derives from the Latin “digitus” (finger). The term “calculate” is taken from the Latin “calculus” (pebble stone).

Fig. 3.1  Tally stick. Tally sticks and notched bones are among the oldest methods of numerical storage. The values were carved or cut in (notched). The piece of wood was split along its length. Such data carriers were, e.g., used as forgery-proof evidence for the creditor and debtor. Placing the two parts together enables one to determine whether they fit together. (© Heinz-Nixdorf Museumsforum, Paderborn)

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Fig. 3.2  The Ishango bone (viewed from four sides). The 10 cm long, 20,000-year-old bone was found in 1950 during excavations along the Congolese bank of Lake Edward. A sharp piece of quartz is affixed to one end (at the top). The bone is of mammalian origin. The grip of the tool exhibits 168 parallel notches in all, engraved on three sides, arranged in groups. (© Institut royal des Sciences naturelles de Belgique, Brussels)

Note To this day the meaning of the notches is not clear, although several explanations have been attempted (see Have you heard of Ishango?, Association pour la diffusion de l’information archéologique, Royal Belgian instititute of natural sciences, Brussels, year not given, 21 pages).

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Fig. 3.3  Knotted cords (1). In South America and Asia, knotted cords were an aid for the storage of numbers. Groups of thinner cords with different colors, which can also have subordinate cords, are fastened to the main horizontally running cord. The knots represent numerical values according to their arrangement. The knotted cord (quipu) of the Incas even made use of the number zero. (© Heinz-Nixdorf Museumsforum, Paderborn)

Notes For numerical notation the colors and the arrangement of the knotted cords and the type of cord all play a role (see Marcia Ascher: Ethnomathematics. A multicultural view of mathematical ideas, Brooks/Cole Publishing Company, Pacific Grove, California 1991, pages 16–26, and Marcia Ascher: Mathématiques d’ailleurs. Nombres, formes et jeux dans les sociétés traditionnelles, Editions du Seuil, Paris 1998, pages 28–44). According to Gary Urton (see Khipu database project of Harvard University, Cambridge, MA, “http://khipukamayuq. fas.harvard.edu/”), the material (cotton or wool) is also decisive. Furthermore, the numerical value presumably depends on the length of the cord and the position of the knots as well. Knotted cords were used in the time from around 1400–1500. Fig. 3.4  Knotted cords (2). Overall view with main and secondary cords (Inca, Peru). (© Inria/picture: J.-M. Ramès)

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Fig. 3.5  Knotted cords (3). Section with different cords. (© Inria/picture: J.-M. Ramès)

Fig. 3.6  Knotted cords (4). Section with hanging cord (light-colored) and subordinate cord (dark). (© Inria/picture: J.-M. Ramès)

3.2  Counting with the Fingers Counting and calculating with the fingers is probably as old as manhood and remains in various forms to this day. According to Jacob Leupold (Theatrum arithmetico-­geometricum, edition “libri rari”, Th. Schäfer GmbH, Hanover 1982), numbers up to one million could be represented with the fingers, hands, and arms. One can count from 1 to 99 on one hand, from 1 to 9999 on two hands (see Jérôme Gavin; Alain Schärlig: Sur les doigts, jusqu’à 9999, Presses polytechniques et universitaires romandes, Lausanne, 2014). Numerous other aids also existed: counting rods, pebble stones, and mussel shells, for example. And already in earlier times, the results of calculations were retained on tally sticks (e.g., counting sticks, wooden picks, milk rods, or notched bones) (see Figs.  3.1 and 3.2) or with knots (knotted cords, calculating cords, and Miller’s knots) (see Figs. 3.3, 3.4, 3.5, and 3.6). With the fingers it was not only possible to count but also to calculate. Above all, simple multiplications could be carried out (see David Eugene Smith: History of Mathematics, volume 2, Dover publications, Inc., New York 1958, pages 201–202, and Michael Roy Williams: A history of computing technology, IEEE Computer society press, Los Alamitos, California 1997, pages 47–53).

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3.3  Abacus Calculation Two forms of abacus computation have to be distinguished: • Line computation, e.g., in sand with freely movable (loose) stones or on counting tablets, calculating slates, counting boards, calculating tables, and counting cloths. • Bead computation with bead frames (counting frames) (see Figs. 3.7, 3.8, and 3.9). In French, a distinction is made between abaque (counting board, calculating board, calculating slab, calculating table) and boulier (bead frame, counting frame). According to the material, one could speak of a sand, wood, stone, metal, ivory, or cloth abacus.

Fig. 3.7  Roman hand abacus (1) (replica). Calculating with the Roman number system is arduous. With the hand abacus, calculating is reduced to counting. The device utilizes the decimal system (lower field) and the quinternary system (upper field). It has seven decimal columns. The ones (I), tens (X), hundreds (C), etc. are represented below. For the thousands, the symbol ɸ was originally used. The numeral M was only introduced in the Middle Ages. The upper buttons have the fivefold value. For these there are special numerals (V  =  5, L = 50, D = 500). The highest (whole number) value that this device can display is 9,999,999, that is ten million minus 1. The slot marked with a sphere ○ is used for the Roman ounces. Since one as (monetary unit) was 12 ounces, this column includes five ones buttons below and one six button above, enabling the representation of 5  +  6  =  11 Roman ounces. The groove at the far right possibly serves for the representation of half, quarter, and third Roman ounces. The Roman hand abacus is regarded as the first “pocket calculator”. This example shows the value 5,555,555 as and 7 ounces. (© Braunschweigisches Landesmuseum, Braunschweig, picture: Anja Pröhle)

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Fig. 3.8  Roman hand abacus (2) (replica). The reconstruction is based on two drawings from the seventeenth century, originating in Augsburg and in Rome. The originals have vanished. The copy differs due to the different representation of the fractional ounces in the groove at the right from three of the four (known) surviving original specimens. With this button device, the groove at the right is divided into three parts. According to Alain Schärlig, the half ounces (S, semiuncia) are entered at the top, the quarter ounces (Ɔ, sicilicus) in the middle, and the third ounces (2, duella) below. (© Adam Ries Museum, Annaberg-Buchholz)

Fig. 3.9  Roman hand abacus (3) (replica). Numerous reconstructions of the Roman hand abacus exist. Who built them is, however, mostly not known. (© Adam Ries Museum, Annaberg-Buchholz)

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Fig. 3.10  Front side of a Roman abacus, Aosta (original). The numerical symbols are missing. This object stems from a gravesite, from which the other objects allow dating to the first century AD. (© Regione Autonoma Valle d’Aosta, Assessorato del Turismo, Sport, Commercio, Agricoltura e Beni culturali, Dipartimento soprintendenza per i beni e le attività culturali, Archivi Patrimonio archeologico. Picture: L. Berriat)

Fig. 3.11  Rear side of a Roman abacus, Aosta (original). With one exception (at the far right) all beads remain. (© Regione Autonoma Valle d’Aosta, Assessorato del Turismo, Sport, Commercio, Agricoltura e Beni culturali, Dipartimento soprintendenza per i beni e le attività culturali, Archivi Patrimonio archeologico. Picture: L. Berriat)

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Fig. 3.12  Front side of a Roman abacus, Paris (original). The numerical symbols are difficult to recognize. The slot at the far right consists of a single piece. (© Bibliothèque nationale de France)

Fig. 3.13  Rear side of a Roman abacus, Paris (original). Several beads are missing from this pocket calculator. (© Bibliothèque nationale de France)

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Fig. 3.14  Front side of a Roman abacus, Rome (original). This pocket calculator is made of bronze. The slot at the far right consists of a single piece. (© Museo nazionale romano, Palazzo Massimo alle Terme, Rome)

Fig. 3.15  Rear side of a Roman abacus, Rome (original). Several beads are missing from this pocket calculator. (© Museo nazionale romano, Palazzo Massimo alle Terme, Rome)

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Fig. 3.16  Roman hand abacus from the second to the fifth century. The Italian ivory pocket calculator is lost. There were fixed (stationary) and portable (mobile) devices. They were made of sand, wood, stone, metal, ivory, or cloth. (© Inria/picture: J.-M. Ramès)

The Lost Ivory Roman Pocket Calculator As far as we know, only three or four original specimens of the Roman hand abacus have survived. They are made of bronze and are now in Aosta (Musée archéologique régional) (see Figs. 3.10 and 3.11), Paris (Bibliothèque nationale de France) (see Figs.  3.12 and 3.13), and Rome (Palazzo Massimo alle Terme) (see Figs. 3.14 and 3.15). A fourth device is known to exist, but no one knows where this is. On March 2, 2019, Jérôme Gavin in Geneva sent me an inquiry about the whereabouts of the magnificent ivory Roman hand abacus (see Fig. 3.16). The device belonged to the collection of IBM Europe in Paris. It was displayed at the exhibition “The wonder of numbers”, which took place in Paris from December 1986 to May 1987 (Tour Pascal, Cité Galilée) and for a time was also exhibited in Sophia Antipolis (France). The Amisa (Association pour le musée international du calcul de l’informatique et de l’automatique de Valbonne Sophia Antipolis) was responsible for a part of the IBM collection on loan from 1991 to 2008. Since its return to the owner, the location is unknown. IBM Europe no longer exists. The collection was allegedly dispersed and possibly auctioned. In 1984 IBM Europe acquired a large part of the (former) collection of Lucien Malassis. The Roman hand abacus in the British Museum in London is not original.

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IBM Lost Interest in the History of Computing For many years, I have tried to find out more about the IBM collection of historical calculating devices, especially in France, Germany, and the USA. In the Stuttgart area, there was a “Haus der Geschichte”, but the blue giant gave this up. With regard to the whereabouts of the Paris collection, one can only grope in the dark. The corporate archives are in the vicinity of New York. However, the collection is no longer accessible to the public. Note There is no connection between the collection of IBM Europe (Paris La Défense) and the Musée de l’informatique (Paris, La Défense), opened in 2007 and closed in 2010. Numerical Notation With the Roman calculating device, the numerical notation was similar to that with the Chinese and Japanese models (see Fig. 3.17).

Numerical notation with the Roman hand abacus

Heaven

(((I))) ((I))

(I)

C

X

I

Hell

1 850 296 as and 11 ounces © Bruderer Informatik, CH-9401 Rorschach, Switzerland

Fig. 3.17  Numerical notation. The Romans in fact had no numeral for zero, but could represent the zero (= nothing) on the abacus. The place value system can also be depicted on the bead frame. With the Roman currency, 1 as was 12 ounces (second column from right). (© Bruderer Informatik, CH-9401 Rorschach, Switzerland)

It is generally assumed that the buttons in the column at the far right have the values 1/2 (top), 1/4 (middle) and 1/3 each (below) (see Fig.  3.18). If the right column is a single piece, this makes handling confusing. With sections, this is simpler.

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Fractions with the Roman hand abacus 0

1/2

1/4

1/3

2/3

3/4

5/6

7/12

11/12

½

¼

⅓ © Bruderer Informatik, CH-9401 Rorschach, Switzerland

Fig. 3.18  Fractions on the Roman hand abacus. This drawing shows three separate vertical grooves. However, these values can be represented on a single-piece groove. (© Bruderer Informatik, CH-9401 Rorschach, Switzerland)

From today’s perspective, the assumption that the two buttons at the bottom both have the value 1/3 means that: • The following fractions could not be represented: 1/12, 2/12, and 5/12. • The following fractions greater than 12/12 could be represented: 13/12, 14/12, and 17/12 (see Fig. 3.19).

Fig. 3.19  Values greater than 1. Do the two lower buttons really have the value 1/3?. (© Bruderer Informatik, CH-9401 Rorschach, Switzerland)

Fractions with the Roman hand abacus 13/12

14/12

17/12

6/12

½

3/12

¼

4/12

⅓

© Bruderer Informatik, CH-9401 Rorschach, Switzerland

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If we assign the value 1/12 to the buttons at the bottom, this appears to give a rational solution (see Fig. 3.20). This allows the representation of all fractions from 1/12 to 11/12.

Notation of fractions with the Roman hand abacus 0

1/12

2/12

3/12

4/12

5/12 6/12

7/12

8/12

9/12

10/12 11/12

½

¼

1/12

© Bruderer Informatik, CH-9401 Rorschach, Switzerland

Fig. 3.20  Representation of all fractions from 1/12 to 11/12. Assuming that the two lowest buttons have the value 1/12, one can effortlessly enter the fractions. However this solution only appears to be correct. (© Bruderer Informatik, CH-9401 Rorschach, Switzerland)

What if the Buttons at the Bottom Do Not Have the Value 1/12? For the fractional ounces (last slot), one could have repeated the ounce slot (next to last slot), since this would (much more easily) reproduce all fractions from 1/12 to 11/12. One must therefore conclude that the buttons at the bottom do not have the value 1/12. In fact fractions can be represented on the Roman hand abacus, but they are not very compatible with the system of Roman numerals. The Reason for the Last Column Remains a Mystery The mathematical historians Alain Schärlig and Jérôme Gavin view the solution described in Wikipedia as false. The meaning of the symbols next to the last slot is uncertain. After all, the Roman currency embraced only half ounces. As a result of the currency devaluation, a twelfth ounce would have had only very little value.

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How Did the Romans Calculate with Their Numeral System? I assume that the Romans performed calculations with the abacus and used the Roman numerals only to document the results. Experience with the Chinese, Japanese, and Russian bead frames, as well as the teaching abacus, shows that one can calculate very fast with these devices. Addition and subtraction are simple, but multiplication and division are more demanding (see Fig. 3.21). Sources Herbert Bruderer: Zeitrechnung. Wie genau ist unser Kalender? Warum gibt es in der christlichen Zeitrechnung kein Jahr Null? 2011, https://doi. org/10.3929/ethz-a-006450534 Jérôme Gavin, personal communication from February 18 2019 Yoshihide Igarashi et al.: Computing. A historical and technical perspective, CRC press, Boca Raton 2014 Hermann Karcher: Konnten die Römer wirklich nicht rechnen?, Mitteilungen der DMV, 2014|, No. 22, pages 140–141, https://www.degruyter.com/ d o w n l o a d p d f / j / d m v m . 2 0 1 4 . 2 2 . i s s u e - 3 / d m v m -2 0 1 4 - 0 0 5 6 / dmvm-2014-0056.pdf Hermann Karcher; Heidrun Gansohr-Meinel: Der Abakus–völlig unterschätzt, in: epoc, 2012, No. 1, page 77, https://www.spektrum.de/pdf/77-77-epoc -01-2012-pdf/1142345?file Alain Schärlig: Compter avec des cailloux. Le calcul élémentaire sur l’abaque chez les anciens Grecs, Presses polytechniques et universitaires romandes, Lausanne 2001 Alain Schärlig: Compter avec des jetons. Tables à calculer et tables de compte du Moyen Age à la Révolution, Presses polytechniques et universitaires romandes, Lausanne 2003 Alain Schärlig, personal communication from February 18 2019 https://en.wikipedia.org/wiki/Roman_abacus

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Fig. 3.21  Roman numerals. This text (see translation) explains the origin and notation of Roman numerals. (Source: Max Hartmuth: Vom Abakus zum Rechenschieber, Verlag Boysen & Maasch, Hamburg 1942, page 14)

Roman Numerals Originated with the Tally Stick For the origin of the familiar Roman numerals I, II, III, V, X, etc. there is hardly a better explanation than that these symbols emerged from the notches on tally sticks. Referring again to the picture of the split (lengthwise) tally stick

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(on page 13) allows us to recognize essentially how closely related these symbols are with the runes and notches. Originally one represented the numbers 1–9 by the same number of vertical notches or strokes, while the tenfold value was indicated by a horizontal line: (10) (20) (30). The symbol X for 10 derived for example from these. Halving the X led to the symbol V for 5, whereby the Romans decided on the upper half and the Etruscans for the lower half (). Striking through once again led to the symbol () for 100, which later changed to (). For reasons of convenience, one then used only the right part (C), especially since this corresponded to the word centrum = hundred. M = 1000 originated with the word mille = thousand, but only in the Middle Ages; the Romans represented this number by setting the I or X in parentheses, i.e., (I) or (X). Rounding out the parentheses resulted in the symbol ∞ for 1000. However, this was replaced just as often by a simple stroke (Latin: vinculum). Thus, for example, we find an inscription with () for the number 7350. However, this notation must be strictly distinguished from the strokes with which the numerals were “covered” (to distinguish them from the letters). The symbol D = 500 is in fact the right half of (│) = 1000. Doubling and tripling the parentheses led to the symbols () for 10,000 and – for 100,000. For still higher numbers one again used the lower numerical symbols in combination with strokes and such symbols. For example, one then wrote the number 1,000,000 as () and the number 1,170,600 as (). By its very nature, this notation easily led to errors or falsifications. As an example, the report of the Roman author Suetonius, who lived around 200 BC, can be mentioned here. On the basis of his written notation, the wife of the Emperor Augustus, Livia, bequeathed 50 million sesterces to a deserving person with the name Galba and wrote this figure in the certificate as (). Her stepson, the future Emperor Tiberius, who as her principal heir was responsible for paying out this sum, deleted one part of the framing, so that ()  =  500,000 resulted. Thus, Tiberius arbitrarily and deceitfully reduced the sum to one hundredth of its value, an act in which the faultiness of the large Roman numerals came to his aid. Caption: Galba complaining to Emperor Tiberius about the injustice that happened to him

3.3.1  Calculating with Roman Numbers Is Laborious We calculate in the decimal place-value system using Hindu-Arabic numerals. But how did one handle Roman numbers with no zero in an additive number system when no hand abacus was available?

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Preliminary Remark For calculating with Roman numbers, the sequence of the numerals does not play any role. Exception: when a smaller numerical unit is placed to the left of a larger numerical unit, it is subtracted from the larger unit: IV, IX, IL, IC, ID, IM; VL, VC, VD, VM; XL, XC, XD, XM; LD, LM, and CD and CM. Addition The summands are added together as with the abacus (see Tables 3.1 and 3.2). The symbols must be bundled when required. Table 3.1  Addition in the Roman number system (1) 2 +3 =5

II III IIIII V

6 +4 =10

VI IV VV X

4 +12 =16

IV XII XVI

13 +9 22

XIII IX XXII

50 +40 90

L XL XLL XC

Table 3.2  Addition in the Roman number system (2) 160 +44 =204

CLX XLIV CLLIV CCIV

280 +370 =650

CCLXXX LXX CCC CCCCCLLXXXXX DCL

888 +449 =1337

DCCCLXXXVIII CDIL DDCCLLXXXVII MCCCXXXVII

Subtraction The subtrahends are subtracted from the minuends as with the abacus (see Table  3.3). The symbols must be separated (unbundled) when required. Numerals occurring in both the minuends and the subtrahends can be canceled. Table 3.3  Subtraction in the Roman number system 2345 -678

=1667

MM D MM M M

DD D

CCC C CC C C

L LL L

XXXX XX XX X X

V V

III

V V

IIIII II

– D L III – D L III

Multiplication Multiplication is a repeated addition. The factor 23 is added six times (see Table 3.4). This is how one calculates with the abacus, and most calculating machines operate in a similar way. In antiquity and in the Middle Ages, there were also other techniques, such as doubling (duplation), the lattice method (gelosia), and Egyptian (Abyssinian multiplication).

178 Table 3.4 Multiplication in the Roman number system

3  The Coming of Age of Arithmetic 23 +23 =46 +23 =69 +23 =92 +23 =115 +23 138

XXIII XXIII XL VI XXIII LX IX XXIII XCII XXIII CXV XXIII CXXXVIII

Division Division is a repeated subtraction. The divisor 7 can be subtracted eight times from the dividend 56 (see Table 3.5). This is how one calculates with the abacus, and most calculating machines operate in a similar way. In the Middle Ages, there were also other techniques, such as halving.

Table 3.5  Division in the Roman number system

56 −7 =49 −7 =42 −7 =35 −7 =28 −7 =21 −7 =14 −7 =7 −7 0

XXXX VV V I V II XXXX V IIII V II XXX VV II V II XX VV V V II XX V III V II X VV I V II VV IIII V II V II V II –

Shannon’s Roman Desktop Calculator The MIT Museum in Cambridge, Massachusetts, is in possession of a relay computer of Claude Shannon that calculates in the Roman number system (see Fig. 3.22).

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Fig. 3.22  The Throbac relay computer. The tabletop computer of Claude Shannon functions in the Roman number system. (© MIT Museum, Cambridge, Massachusetts MA)

Throbac (Thrifty Roman-numeral backward looking computer) is a tabletop computer that calculates entirely in the Roman number system. It is capable of the four basic arithmetic operations addition, subtraction, multiplication, and division and works just like an electromechanical tabletop machine typical of that time. The machine accepts different notations (IV or IIII, IL or XLIX). IIIIIV therefore has the meaning of zero. Multiplication is performed as a repeated addition and division as a repeated subtraction. To multiply 7 x 8, the multiplicand VII is entered first and then the multiplier 8 numeral by numeral I, I, I, and V. References Claude Elwood Shannon.: Throbac I, Bell Laboratories Memorandum, April 9, 1953 (Claude Elwood Shannon: collected papers, edited by N.  J. A.  Sloane, Aaron D.  Wyner, Piscataway, NJ: IEEE Press 1993, pages 695–698) Michael Roy Williams: A history of computing technology, IEEE Computer society press, Los Alamitos, California 1997, pages 7–8

3.3.2  Bead Frame Computation The widespread bead frames are characterized by beads or pearls arranged on vertical or horizontal slider rods. Because one basically does not need to calculate (for addition and subtraction), they are also known as counting frames.

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Bead computation was commonplace in Russia and Eastern Asia up to recent times but is evidently now dying out (see Fig. 3.23). Counting frames have different forms: abacus (Roman), soroban (Japanese) (see Fig.  3.24), stchoty (Russian) (see Fig. 3.25), or suanpan (Chinese). In China the Abacus Has Long Since Disappeared A survey of three lecturers teaching at Chinese universities (Pong Chi Yuen, China; Chris Leslie, USA; Walter Gander, Switzerland) and Chinese students makes clear that in China the abacus has long since disappeared: You may be disappointed to hear that romantic visions of old Canton are just a memory. I have never seen anyone using an abacus – my students tell me that maybe their grandparents could do it, but not them or their parents. Today, the Chinese use cash registers or solar calculators like everyone else – and when they pay they use their mobile phones instead of cash or cards. In that way they are far ahead of the US. (personal communication of Chris Leslie from January 17 2018)

Fig. 3.23  Abacus in a Chinese bakery. This photo may well have rarity value. (© Jiang Yi Geiger, Qingdao 2015)

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Fig. 3.24  Japanese bead frame (soroban). Such counting frames were widely used for centuries. Bead frames belong to the oldest (digital) calculating aids. They are capable of all four basic arithmetic operations, and the tens carry is implemented manually. A forerunner is the Roman hand abacus. (© Deutsches Technikmuseum, Berlin)

With the two-piece counting frame, the beads above the dividing bar have the fivefold value. For calculating the beads are moved toward or away from the dividing bar. The upper section of the bead frame is called “heaven” and the lower section “hell”. The abacus was followed by the (related) line computation, i.e., computation on (the) lines. According to their construction, counting frames have different numbers of beads at each position (see Table 3.6). Table 3.6  Overview of the common bead frames Comparison of counting frames Name Origin Form Abacus Roman Two-piece Soroban Japanese Two-piece Stchoty Russian One-piece Suanpan Chinese Two-piece

Rods Vertical Vertical Horizontal Vertical

Number of beads per position 4 + 1 4 + 1, 5 + 1,0.5 + 2 10 5 + 2

© Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020

Remarks The designations 4 + 1 and 5 + 2 mean 4 or 5 (lower) beads with simple value (hell beads or unit beads) and one or two (upper) beads (heaven beads or heaven units) with fivefold value. The magnitudes apply accordingly for the ones, tens, hundreds, etc. The usual arrangement with the soroban is 4 + 1. The Russian counting frames have no dividing bar and therefore have only one field. In order to simplify handling, the two middle beads have different colors. The rods with four beads served for the representation of quarter rubels and, when necessary, quarter kopecks. Counting frames are capable of performing all four basic arithmetic operations. The rules for calculation are similar to those for the calculating table.

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3.3.3  Russian Counting Frames and School Abacus The Russian counting board and the pupil’s counting board usually have 10 horizontal rods with 10 beads each. This allows the representation of numbers from zero to 10 billion. These decimal bead frames have no dividing bar; no difference is made between heaven and hell The fives carry is missing. This makes calculating faster, especially for multiplication (repeated addition) and division (repeated subtraction). Thus, for example, for the most difficult basic arithmetic operation, namely, division, one can simply subtract the divisor repeatedly. The tens carry takes place as usual. For the arithmetic operation, the multiplier and divisor are not required. However, it is meaningful to use these as a memory aid and for control purposes In the basic position (zero position), all beads are either to the left or to the right, and the result is displayed to the right or to the left, respectively. When calculating or counting, they are moved primarily from the right (ones) to the left (tens, hundreds, etc.). In certain cases this simplifies the tens carry Counting frames are an excellent learning aid for counting and calculating. With enough experience in their use, these devices enable calculating with high speed

Fig. 3.25  Russian bead frame (stchoty). With the Russian abacus, the wooden beads are arranged horizontally in rows of ten. In order to simplify handling, the two middle beads have different colors. Rods with four beads signify either the decimal point or represent quarter values (e.g., ¼ rubel). Sometimes the beads of the thousands rod also have a different color. The manufacturer and year of manufacture of this abacus are unknown. (© ETH Zurich, Collection of astronomical instruments)

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183

3.4  C  ounting Tables, Counting Boards, and Counting Cloths For calculating and counting on the calculating table (see Fig. 3.26) and comparable calculating aids, such as the counting board and the counting cloth, fundamentally, the same rules apply as for bead frame computation. Instead of metal rods, the calculating table has horizontal lines. Jetons (tokens, counters, reckoning coins, or reckoning pennies) replace the beads. They must not be slid over rods and are simply placed on or removed from the table. Lines and intermediate spaces assume the roles of heaven and hell. On the lines, the tokens (jetons) have a simple value, and in the spaces, the jetons have fivefold value. The line pattern simplifies the overview. Five tokens on a line are – for the example of addition – consolidated to a single jeton in the next higher space. Two jetons in a space are combined to one token on the next higher line. Conversely, above all with subtraction, resolution takes place when required, i.e., resolution into reckoning pennies with less value (see box). Calculating tables have one or more calculation fields. With several calculation fields, the two summands or the minuend and subtrahend can be placed in different fields.

Elevation and Resolution of Tokens (Jetons, Counters) For line computation on the calculating table, the terms below were used: • Elevation Bundling, grouping, consolidation, clearing up: Example: For addition five one’s tokens (on the line) are replaced by one five’s token (in the space); they were placed higher, i.e., combined. • Resolution Unbundling, segmentation, decomposition: Example: For subtraction one five’s token (in the space) is resolved into five one’s tokens (on the line); this was placed deeper, i.e., resolved. • Duplation or doubling • Mediation or halving

Additions With the arithmetical frame, beads (on rods) are moved. With the line board (line abacus), jetons are placed (on lines). Is the bead frame then a calculating machine? Here the opinions diverge (see box).

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184 Numerical notation on the calculating table

Ten thousands

Thousands

Hundreds

Tens Ones

Number 8765

Number 1234

© Bruderer Informatik, CH-9401 Rorschach, Switzerland

Fig. 3.26  Numerical notation on a calculating table. The tokens are either placed on the lines, where they have simple value, or in the spaces, where they have fivefold value. Maximum four jetons may be placed on a line. Only one jeton is allowed in a space. When this number is exceeded, the tokens (calculi) are consolidated (allocated to a higher unit). Fundamentally the same rules apply as for the bead frame (abacus). x indicates the thousands line. (© Bruderer Informatik, CH-9401 Rorschach, Switzerland)

Is the Bead Frame a Calculating Machine? The lack of clarity in terms of definitions is made clear by the term “machine”. Should we distinguish between a calculating device (calculating aid without automatic tens carry) and a calculating machine (calculating aid with automatic tens carry), as is usual in Germany for mechanical digital calculators? And what about mechanical analog calculators? For the once widely used slide rule, such a classification is superfluous. The widely held opinion is that a calculating machine has a more sophisticated construction than a calculating device and incorporates, for example, a gearwork mechanism. Electronic calculators are very complex and require less and less mechanical parts. Electronic calculators are viewed as either calculating devices or calculating machines, regardless of their size. These terms are mostly used in the same sense. With mechanical calculating aids, a calculating device is simpler than a calculating machine. The bead frame (counting frame) with horizontal rods is occasionally referred to as a children’s calculating machine. The construction of the “bead calculating machine” is very simple, and the tens carry is performed manually. The “abacus” is therefore not considered to be a machine here. Such distinctions are fuzzy, somewhat arbitrary, and a matter of discretion.

3.4  Counting Tables, Counting Boards, and Counting Cloths

185

3.4.1  Line Computation/Calculating on Lines Already in antiquity calculating took place with pebbles (calculi) on slates with line systems. The Romans already utilized line computation. The line fields on the calculating tables are inscribed with Roman numerals (I  =  1, V = 5, X = 10, L = 50, C = 100, D = 500, M = 1000) and with abbreviations for currencies, weights, measures of capacity, etc. The lowest horizontal line is allocated to the ones and the second lowest to the tens. The next parallel lines are for hundreds and thousands. The space between the two lowest lines has the value 5, the next space the value 50, and the third space the value 500. Calculations are performed with coins. These reckoning pennies (jetons) originally came from France and were later produced in Nuremberg in large amounts. Maximum four jetons may be placed on a line (values: 4, 40, 400, 4000), and only one jeton is allowed in the spaces (values: 5, 50, 500, 5000). These requirements apply for the final results, but not for intermediate results. The jetons were richly ornamented, but had no value as a means of payment. The calculating tables (counting boards) are capable of performing all four arithmetic operations (addition, subtraction, multiplication, and division). For calculating with jetons (line computation) and calculating with pencil and paper, Adam Ries (1492–1559) and others wrote numerous (handwritten and printed) arithmetic textbooks. A particularly valuable textbook on arithmetic and mensuration appeared in 1727: Jacob Leupold, Theatrum arithmetico-geometricum, Christoph Zunkel, Leipzig. According to a personal communication of Rainer Gebhardt of October 2, 2017, Adam Ries issued his first arithmetic textbook, “Rechnung auff der Linien”, in Erfurt in 1518. When it was printed is not known. Three further editions appeared in 1525, 1527, and 1530. The second computation textbook, “Rechnung auff der Linien und Federn” (see Fig.  3.27), belongs to the year 1522, and the third computation textbook, “Practica”, followed in 1550. Another work, “Rechenbuch/Uff Linien unnd Ziphren” appeared in 1565 (see Fig. 3.28). For more than 20 years, the Berg- und Adam-Ries-Stadt Annaberg-Buchholz has hosted events relating to the history of calculating (see box).

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Fig. 3.27  Adam Ries. Arithmetic textbook “Rechnung auff der Linien und Federn, auff allerley hantierung gemacht durch Adam Risen”, Wittenberg 1558. Ries was the best known German arithmetic teacher. (Source: ETH Library, Zurich, Rare books collection)

Annaberg Colloquia on the History of Mathematics Since 1992 the Adam-Ries-Bund e. V. has been tirelessly dedicated to the presentation of the early mathematical history in numerous events, including the following colloquia: 1996 Rechenmeister und Cossisten der frühen Neuzeit (Arithmeticians and algebraists of the early modern era) 1999 Rechenbücher und mathematische Texte der frühen Neuzeit  (Arithmetic textbooks and mathematical texts of the early modern era) 2002  Verfasser und Herausgeber mathematischer Texte der frühen Neuzeit  (Authors and publishers of mathematical texts in the early modern era) 2005 Arithmetische und algebraische Schriften der frühen Neuzeit (Arithmetic and algebraic literature of the early modern era) (continued)

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187

2008 Visier- und Rechenbücher der frühen Neuzeit  (Volume measurement and arithmetic textbooks of the early modern era) 2011  aufmanns-Rechenbücher und mathematische Schriften der frühen Neuzeit (Merchant’s arithmetic textbooks and mathematical literature of the early modern era) 2014 Arithmetik, Geometrie und Algebra der frühen Neuzeit (Arithmetic, geometry, and algebra of the early modern era) 2017 Rechenmeister und Mathematiker der frühen Neuzeit (Arithmeticians and mathematicians of the early modern era) 2021 Die Entwicklung der Mathematik in der frühen Neuzeit (The development of mathematics in the early modern era) These colloquia have been documented in conference proceedings (editor: Rainer Gebhardt).

Remarks The arithmetic books (e.g., of Adam Ries) were textbooks. Volume measurement is the determination of wine barrel capacities. Fig. 3.28  Adam Ries. Here you see the title page of the work “Rechenbuch/ […]” of Adam Ries (Helm: Rechenbuch/Uff Linien unnd Ziphren […],Chr. [istian] Egen.[olff] Erben, Franck[furt] 1565). (Source: ETH Library, Zurich, Rare books collection)

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In Thun BE an especially fine calculating table (see Fig. 3.29) has survived. A calculation table stemming from Basel has three sides, each with one calculation field (see Fig.  3.30). Calculating boards simplify monetary exchange (see Fig. 3.31).

Fig. 3.29  Calculating table with coin stripes. This jewel dates from around 1700 and was used for calculations with the pound currency. Calculating tables were once found in many town halls, but only a few have survived to this day, mostly in Switzerland. (© Historisches Museum Schloss Thun)

Explanation of symbols M = 1000 pounds, D = 500 pounds, C = 100 pounds, L = 50 pounds, X = 10 pounds, V = 5 pounds, lb. = 1 lb (= 20 Schillings), x = 10 Schillings (½ pound), v  =  5 Schillings (¼ pound), ß  =  1 Schilling (=  12 pence), 6  =  6 pence (½ Schilling), d = 1 pence. (Source: Museum Schloss Thun) Fig. 3.30  Basel counting board. The table plate has three single-column fields, one on each side. (© Historisches Museum, Basel, picture: Maurice Babey)

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189

Fig. 3.31  Counting board for monetary exchange. The wooden slate dates from 1536 and was used in the town hall in Thun BE. (© Historisches Museum Schloss Thun)

How does line computation function? For addition the two numbers (summands) are placed next to each other in the same column (or in adjacent columns) and reduced (combined according to the rules described above for the number of coins permitted on the lines and in the spaces) (see Figs. 3.32 and 3.33). Adding several numbers takes place stepwise. After simplifying the first intermediate result, the third number is added, the result simplified, and so forth. Subtraction is somewhat more complicated. The first number must first be resolved. Multiplication and division are much more difficult. From today’s perspective, such calculations appear to be quite laborious. The transition to paper and pencil calculation – the relearning process – was of course difficult for people. In addition to the calculating table, other calculating aids were used for line computation: the counting board and the (portable) counting cloth, as well as the (rare) counting hat. A few texts also refer to the reckoning bench and the reckoning leather.

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Fig. 3.32  Line computation. Jetons were not a means of payment but were used as tokens (counters). We owe the photograph to the work “Deutsche Arithmetica” of Michael Stifel (1545). (Source: ETH Library, Zurich, Rare books collection)

Fig. 3.33  Jeton. Richly decorated reckoning coins (jetons) were a popular calculating aid, but were not a means of payment. They were frequently minted in Nuremberg. Coin collections were kept in coin cabinets. The forerunners were the Roman pebbles, the “calculi”. (© Historisches Museum, Basel)

3.6  Graphical Computation: Nomography

191

3.5  Pen and Paper Calculation Complicated calculations with Roman numerals were cumbersome. There was no zero (and thus no year zero) and no decimal place value. Line computation was gradually replaced by “pen and paper calculation” (numerical calculation), i.e., the “written calculation” with Hindu-Arabic numerals practiced throughout the world today.

3.6  Graphical Computation: Nomography One can calculate not only with numerals, numbers, and letters but also, e.g., with drawings and line segments (see box).

Numerical and Graphical Computation A distinction is made between two methods of calculation: • Numerical computation • Graphical computation or nomography Numerical calculation (arithmetic, written calculation, pen and paper calculation) is regarded as the counterpart of line computation (abacus calculation). Algebraic calculation (algebra, cossic arithmetic) uses letters in place of numbers. On the one hand, Coss represents an unknown variable (x) to be determined and, on the other hand, an early form of algebraic calculation (algebra of the Middle Ages and early modern era, theory of equations). In ancient Greece the Greek alphabet was used for the representation of numbers (alphabetic numeration). Numerical tables include, e.g., multiplication or product tables (also known as Pythagorean tables), division or quotient tables, tables of squares and cubes, tables of square roots and cube roots, and reciprocal, logarithmic, and trigonometric tables. Nomography is based on graphic charts (nomograms), which represent functions graphically. There are also graphical logarithmic tables (with the values plotted on a scale and not in a table). Graphical computation represents numerical values in the form of lines (line sections), angles, ratios, or functions. Examples are slide rules, sectors, or proportional dividers. A conventional measuring rule with uniform divisions is suitable for graphical addition and subtraction. Numerical calculation permits greater accuracy, while graphical computation is more descriptive.

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3.7  Lines of Development The course of the historical development of computer technology has been characterized by numerous lines of development. The autonomous or networked currents flow successively or in parallel, simultaneously or chronologically shifted. Lines of development are often not linear. They can overlap and branch out and do not exclude disappointments. For centuries progress was comparatively slow and can be quantified as reasonably assessable. Since the 1970s, developments have been increasingly turbulent. New knowledge and the results of research follow in rapid succession. Commercially viable products are succeeded by newer products in ever shorter intervals of time. Many directions of flow lead to the haven of universal electronic digital computers and the global Internet. The far-reaching upheaval continues unremittingly – and overwhelms many, especially older people. The most important prerequisite for success in mathematics, the sciences, and technology was arguably the introduction of the number zero and the decimal place value system. A few selected examples will serve to illustrate the multifaceted developments. Here it should be noted that some achievements came about independently of preliminary work and without the knowledge of predecessors. Number Systems • From the Roman numeral system to the Hindu-Arabic place value system with zero Calculating Aids • From the fingers through pebbles and reckoning pennies to pen and paper • From the Egyptian and Greek counting board to the Roman bead frame and the calculating table of the Middle Ages • From the Chinese to the Japanese and Russian bead frames • From the multiplication table to the logarithm table and to printed tables • From the gelosia method through Napier’s rods to the mechanical calculating machine with cylinders for multiplication and division and calculating machines with multiplying block • From logarithms through the slide rule to the programmable electronic pocket calculator • From the slide rule and the circular slide rule to the cylindrical slide rule • From counting with the fingers through line computation, bead computation, pen and paper calculation, and slide rule calculation to machine calculation • From the mechanical slide bar adder with crook tens carry to the programmable electronic pocket calculator • From the mechanical calculating device with slide setting to the electromechanical calculating machine with ten-key or full keyboard

3.7  Lines of Development

193

• From the mechanical calculating device without automatic tens carry through the mechanical calculating machine with automatic tens carry to the electromechanical calculating machine with printout and memory • From the two-function calculator (addition and subtraction) to the fourfunction calculator (all basic arithmetic operations) • From the difference engine through the analytical engine to the mechanical decimal and binary computer • From the tabulator through the calculating punch to the punched tape controlled digital computer • From room-sized relay and vacuum tube machines to electronic desk and pocket calculators and embedded computers • From the human computer (female computer) with mechanical desk calculator to the electronic digital computer • From the relay through the vacuum tube and the transistor to the integrated circuit • From the mechanical through the electromechanical to the electronic computer • From the automatic bookkeeping machine to the bookkeeping program • From the cash register to the electronic payment system • From the desk calculator through the pocket calculator to the mobile telephone • From number crunching to non-numerical computing (for text, pictures, sound, and video) • From the decimal calculator to the binary computer • From the special-purpose machine to the automatic universal machine Memories • From the notched bone, the tally stick, and the knotted cord (quipu) through the slate to the gear wheel and paper • From the mechanical counter through electromagnetic relays, mercury delay lines, and electrostatic William-Kilburn tubes and magnetic drums to magnetic core memories and semiconductor memories (main memories) • From the punched card and the punched tape through magnetic drums and magnetic tapes to magnetic discs and optical discs (mass storage) • From microfilm to magnetic disc • From internal to external data storage via the Internet cloud Analog and Digital Technology • From the astrolabe and quadrants, sextants, and octants to digital measuring instruments • From the ruler and compass to the plotting and computing program • From the analog planimeter, sector, and proportional divider to the digital measuring and computing machine • From the gear train and the mechanical differential analyzer through the analog electronic computer to the universal digital computer • From the analog mechanical to the digital electronic fire control computer

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• From letterpress with movable metal letters (lead typesetting) through automatic typesetting to program controlled printing • From the printed book to the electronic book • From the printed reference work to Wikipedia and Google search • From the printed telephone book to the Internet query • From the printed schedule to search for connections in the Internet • From the printed magazine subscription to the open access publication • From the printed road map to digital map service • From the printed press to the social media • From the magnetic compass to global positioning system • From the sundial through the geared clock to the electronic wristwatch • From the analog clock to the digital watch • From musical automatons, the phonograph record, the audio tape, and the optical memory (CD, DVD) through exchange platforms (MP3, Napster) to music streaming • From the analog silent film to the digital sound film • From the analog camera to the digital camera • From the analog to the digital communications network • From analog to digital radio (broadcasting) • From analog to digital television • From the electric vacuum cleaner to the robotic housecleaner • From the mechanical bicycle to the self-driving electric car • From medical diagnosis to pattern recognition with artificial neural networks • From booking at the counter to the use of travel portals • From the printed ticket to electronic travel expense reports • From (stationary) brick and mortar store to (online) electronic commerce • From cash payment to payment by smartphone • From centralized to decentralized processing with blockchains • From conventional to digital money Communications Technology • From the Morse technique through operator-assisted communication with telephone relay and pluggable connecting cable to the global cellular network • From the post office through telegraphy and telephony to wireless communication • From the mailman to the drone • From letter mail and teleprinter through the fax machine to electronic mail and the social network Printing Technology • From the mechanical to the electromechanical typewriter to text processing systems and the universal computer with printout • From the spirit duplicator through the photocopier to the multifunction printer

3.7  Lines of Development

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Oral and Written Inputs • From the transcript to the photocopy and text and speech recognition • From keyboard input to text and speech recognition • From keyboard control to virtual voice assistant control Output • From the cathode ray screen to the flat screen Encryption • From mechanical code systems to the electromechanical cipher device to the electronic encoding program Automaton Writers • From the programmable mechanical handwriting automaton to the electronic text system Automaton Games • From the electromechanical chess automaton through the electronic chess program to the self-learning game-playing program Automaton Figures • From the mechanical android and automated animal figure to the “intelligent” electronic robot Musical Automatons • From the mechanical and pneumatic musical automaton to the electronic musical instrument • From the punched card controlled loom to the pneumatic piano and dance organ with punched tape roll and punched card chain control • From the cylinder musical box and the disc-type musical box through the gramophone (mechanical record player) and the phonograph (device for the recording of sound on wax discs) to the jukebox (musical automaton with audio records) • From the pinned drum and perforated disc through the long-playing record to the compact disc (CD) and to music streaming via the Internet Looms • From the punched tape controlled mechanical loom to the punched card controlled analytical engine and the electromechanical punched card machine Program Control and Programming • From sequence control to the process computer • From the punched tape and punched card controlled loom and the analytical engine to the punched card machine • From sequence controlled automaton figures and musical automatons to the program controlled automatic computer • From external punched card and punched tape control and plugboard control to internal program control (stored-program control)

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• From the plugged or punched program to the stored program • From the programming device to automatic programming • From Algol to Pascal and many other programming languages Data Privacy • From personal privacy to permanent surveillance • From data security to the data leak. Energy From antiquity through the Middle Ages to the modern era, several types of drives have been developed. These range from human and animal muscle power through the utilization of wind and water to the generation of hot air, steam, and electricity. Weights were also used (such as with clocks, musical automatons, phonographs, or calculating machines) and turbines. Springs and cranks (hand cranks and foot treadles) were widely used. Steam power and electrical power contributed significantly to the triggering of the first and second industrial revolutions. Mills Water power and wind power are the respective driving mechanisms for watermills and windmills. In earlier times saws (sawmills) were mostly located on water. The same was true of grain mills, and combined paper mills and sawmills. Along with the waterwheel and windmill, other driving mechanisms and aids were the treadmill, the horse capstan, animals, as well as the hands. Overshot and undershot waterwheels were controlled by limiting the water throughput and by shutting down.

3.8  M  any Technical Objects Are Also Magnificent Works of Art Technology and culture and technology and art are no contradictions. Technology is an integral part of culture and is a prerequisite for works of art. Magnificent technical works (churches, town halls, palaces, castles, half-timbered houses, mills, towers, bridges, fountains, paddle steamers, steam locomotives, etc.) are in abundance. Many technical objects not only have utilitarian value but are also genuine works of art (artifacts). Some devices were not intended primarily for practical use, but far more as gifts for dynasties and richly ornamented. These are often found in art history museums (and cabinets of curiosities). Clock and watch, musical instrument, and automaton museums occupy a special place here. Countless technical masterpieces can be admired in collections of scientific instruments.

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Grandiose cultural heritage can be found in the following areas: • Astronomy: armillary spheres, astrolabes, astronomical clocks, and earth and celestial globes • Automaton design: automaton figures (e.g., androids and animal automatons) and mechanical pictures (picture clocks) • Calculator technology: mechanical calculating machines (above all cylindrical calculators) • Mathematics: bead frames and slide rules • Measurement of time: sundials, longcase clocks, wall clocks, table clocks, and pocket watches • Music: mechanical musical instruments and musical automatons • Seafaring: navigation instruments, such as the compass • Surveying: pedometers and hodometers. One speaks rightly of the art of clockmaking and material culture. Technical achievements are often unjustly not recognized as part of our cultural heritage. Remarks Artful creations, such as automaton clocks, musical automatons, and automaton figures, are relatively well documented and in many cases preserved. On the contrary purely utilitarian objects, such as mathematical instruments, were often consigned to waste disposal. With an astrolabe one can determine the state of a star at a particular location and at a particular time. Mechanical celestial globes are controlled by clockwork. With the aid of earth and celestial globes, one can, e.g., determine the rising and setting times for the sun and the heavenly bodies.

Chapter 4

Classification of Calculating Aids and Related Instruments

Abstract The chapter “Classification of Calculating Aids and Related Instruments” elaborates a classification of analog and digital mechanical and electronic calculating devices and machines that eliminates contradictions as well as possible. This also considers plotting and measuring devices, as well as astronomical instruments. Calculations are performed with all of these tools. The chapter describes the differences between calculating aids and calculating machines, adding and calculating machines, and mathematical machines and mathematical instruments. Planimeters, pantographs, sectors, proportional compasses, protractors, clinometers, coordinatographs, quadrants, sextants, and octants are introduced. Furthermore, the intercept theorems are explained. Among the popular calculating aids are also mathematical tables. Finally, the classification is recapitulated in the form of a list and a table. Keywords  Analog calculating aids · Astronomical instruments · Classification of calculating aids · Digital calculating aids · Electronic calculating machines · Intercept theorem · Mathematical instruments · Mathematical machines · Mathematical tables · Measuring instruments · Mechanical calculating machines · Plotting devices · Surveying instruments There are several proposals for the classification of calculating aids, most of which are not satisfactory. Consequently, in this chapter, I will try to offer new definitions as free of contradictions as possible. This book is limited to mechanical, electromechanical, and electronic devices. For computation and modeling mechanisms that function with pneumatic, hydraulic, and optical techniques also exists. Pneumatics is concerned with air pressure, hydraulics with fluid pressure, and optics with light.

© Springer Nature Switzerland AG 2020 H. Bruderer, Milestones in Analog and Digital Computing, https://doi.org/10.1007/978-3-030-40974-6_4

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4.1  Calculating Devices and Calculating Machines In this book, the collective term calculating aid (also calculation aid) is used. This includes natural parts of the body, such as the fingers, hands, and arms. Man-made calculating aids are summarized under the term calculating devices. “Devices” usually refer to tools, instruments, mechanisms, and, in part, also machines. Electromechanical relay computers and electronic vacuum tube computers are described as calculating machines, calculating devices, and also computing systems. The restriction of the term “calculating devices” to mechanical calculating aids without automatic tens carry is therefore not always justified. Nevertheless, the allocation of mechanical calculating aids with automatic tens carry to the mechanical calculating machines is sensible, because one generally makes higher demands on a (mechanical) machine than on a device. The automatic tens carry in the accumulator register and the counter register posed great difficulties for the builders. Slide bar adders with semiautomatic tens carry (crook tens carry) (see Fig.  4.1) are considered (mechanical) calculating devices. There are also machines without tens carry (see Fig. 4.2).

Fig. 4.1  Slide bar adder of Troncet. The once widely used mathematical instrument belongs to the Collection of astronomical instruments of the ETH Zurich. This calculating (1889) of the French inventor Louis Troncet with semiautomatic crook tens carry was still in use until the 1970s. Occasionally it also incorporated a collection of tables, including multiplication tables. (© Herbert Spühler, Stallikon)

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Fig. 4.2  Slide bar adder of Caze. This abacus-like French stylus operated calculating device from the year 1720 has no tens carry. (© Inria/picture: J.-M. Ramès)

4.2  Adding Machines and Calculating Machines The distinction between (mechanical) adding machines and mechanical calculating machines is widespread. While this may be helpful, it is not altogether convincing. Addition is a (the most important) basic arithmetic operation, so that adding machines are also calculating machines. Furthermore, many adding machines are capable of other arithmetic operations, such as subtraction. Here it should be noted that multiplication can be realized as a repeated addition and division as a repeated subtraction. According to the machine, multiplication and especially division can be very cumbersome. Digital calculators also include bookkeeping machines. Adders and Multipliers Expressions such as “adder” and “multiplier” encompass adding devices and adding machines and multiplication devices and multiplication machines.

4.3  Mathematical Machines and Mathematical Instruments The term mathematical machines refers especially to program-controlled digital computers. The term mathematical instruments refers above all to analog drawing, measuring, and calculating devices. There were many geometrical drawing and measuring devices (see Fig. 4.3).

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Fig. 4.3  Geometrical instruments. These encompass a wide range of instruments: the ruler (Fig. 1), composing stick (2), parallel ruler (3), triangles (4 + 5), dividers (6), inserts for the drawing compass (7 + 8), protractor (9), measuring cord (10), surveyor’s chain (11), astrolabe (12), protractor (13), Zubler instrument (14), tripod (15), sundials (16), and plumb level (17). (From: Tobias Mayer: Mathematischer Atlas, in welchem auf 60 Tabellen alle Theile der Mathematic vorgestellet und nicht allein überhaupt zu bequemer Wiederholung, sondern auch den Anfängern besonders zur Aufmunterung durch deutliche Beschreibung und Figuren entworfen werden, Pfeffel, Augspurg 1745; Source: ETH Library, Zurich, Rare books collection)

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203

Mechanical integrators include, e.g., curvimeters, planimeters, harmonic analyzers, integraphs, and integrimeters. Also popular were pantographs. A special case is the little known logarithmic calculating machine of Fuß (Askania-Werke). In addition, there was a broad range of differentiators, e.g., tangent plotters and mirror rulers.

4.4  Planimeters The planimeter (see Figs. 4.4, 4.5, 4.6, 4.7, 4.8, 4.9, 4.10, 4.11, 4.12, 4.13, 4.14, 4.15, 4.16, 4.17, 4.18, and 4.19) was of great importance in land surveying.

Fig. 4.4  Planimeter (1). The planimeter, developed between 1851 and 1854 by Kaspar Wetli and Georg Christoph Starke, is comprised of brass and porcelain. The Swiss device was patented in 1849  in Austria and was later improved by Georg Christoph Starke (Vienna). It was awarded a prize in 1851 at the World Exhibition in London. (© Division of medicine & science, National Museum of American History, Smithsonian Institution, Washington, D.C.)

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Fig. 4.5  Planimeter (2). The disc planimeter after Wetli and Starke for rectangular coordinates was built in 1849. (© Geodätisches Institut der Leibniz-Universität Hannover)

Fig. 4.6  Planimeter (3).This planimeter of Coradi measures surface area by moving around the surface. The inventor of the polar planimeter (1854) was the Swiss mathematician Jakob Amsler. (© Vermessungsamt, Aarau)

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Fig. 4.7  Planimeter (4). Planimeters were widely used in land surveying offices. (© Vermessungsamt, Aarau)

Fig. 4.8  Planimeter (5). Among the world’s leading manufacturers of such mathematically sophisticated integrators were Amsler (Schaffhausen, Switzerland), Coradi (Zurich, Switzerland), and Ott (Kempten, Germany). (© Vermessungsamt, Aarau)

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Fig. 4.9 Planimeter (6). This analog instrument measures surface area. (© Vermessungsamt, Aarau)

Fig. 4.10  Planimeter (7). Gottlieb Coradi (Zurich) manufactured a range of planimeters. (© Vermessungsamt, Aarau)

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Fig. 4.11  Rolling disc planimeter (1). As can be seen from the gauging table (in the cover of the case), this analog tool of Coradi dates from 1956. In 1985 it was updated. (© Historisches Museum Thurgau, Schloss Frauenfeld)

Fig. 4.12  Rolling disc planimeter (2). This measuring calculator of G. Conradi AG, Zurich, was still in use a few decades ago. (© Historisches Museum Thurgau, Schloss Frauenfeld)

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Fig. 4.13  Rolling disc planimeter (3). Scales of 1:200 to 1:5000 are shown on the gauging table. (© Historisches Museum Thurgau, Schloss Frauenfeld)

Fig. 4.14  Linear planimeter (1). This analog calculator is from the Ott workshops in Kempten. (© Geodätisches Institut der Leibniz-Universität Hannover)

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Fig. 4.15  Linear planimeter (2). This photograph shows a section of the instrument of Ott. (© Geodätisches Institut der Leibniz-Universität Hannover)

Fig. 4.16  Haff planimeter (1). The manufacturers of this polar planimeter were the Gebrüder Haff in Pfronten, Germany. (© Geodätisches Institut der Leibniz-Universität Hannover)

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Fig. 4.17  Haff planimeter (2). The Allgäu Haff company manufactures mechanical planimeters (with vernier readout) to this day. Each of these three devices has a pole plate (upper right), a traveling magnifier (lower right), and – according to model – fixed or sliding pole arms. The middle point of the traveling magnifier traces the perimeter of an area. The traveling magnifier can be replaced by a tracer point. At the left is the measuring element. (© Gebrüder Haff GmbH, Pfronten)

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Fig. 4.18  Haff planimeter (3). At the upper right is the pole with the pole arm. Below is the tracer point with magnifier and travel arm and the measuring element. (© Gebrüder Haff GmbH, Pfronten)

Fig. 4.19  Haff planimeter (4). With the electronic digital planimeter of the Haff precision mechanics company, it is possible to measure volumes and lengths as well as areas. (© Gebrüder Haff GmbH, Pfronten)

4.5  Pantographs Pantographs (see Figs. 4.20, 4.21, 4.22, 4.23, and 4.24) enable the enlargement and reduction of drawings.

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Fig. 4.20  Pantograph (1). This brass pantograph (around 1860) was manufactured by Jakob Goldschmid (Zurich). (© ETH Zurich, Collection of astronomical instruments)

Fig. 4.21  Pantograph (2). The floating pantograph of the mechanic Jakob Goldschmid (Zurich) was described in 1864 by J.H. Kronauer in the Swiss journal Schweizerische polytechnische Zeitschrift. This ingenious design was new at the time. (© Martin Wagener, Frankfurt am Main)

Fig. 4.22  Pantograph (3). With the pantograph design of the German physicist and astronomer Christoph Scheiner, dating from 1603, one can enlarge and reduce drawings, plans, and maps. The movable linkage forms a parallelogram with the fixed pivot (pole), tracer point, and drawing pen with a fixed, in some cases adjustable, spacing ratio. (© Historisches Museum Thurgau, Schloss Frauenfeld)

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213

Fig. 4.23  Pantograph (4). With the traveling stylus, one traces the perimeter of a drawing. The drawing pen reproduces the figure simultaneously. (© Historisches Museum Thurgau, Schloss Frauenfeld)

Fig. 4.24  Pantograph (5). The Allgäu company Ott in Kempten was one of the most important manufacturers of such mathematical instruments. (© Vermessungsamt, Aarau)

Who is familiar today with the once widespread pantograph, sector, and planimeter or the proportional dividers? Pantographs were a popular tool in embroidering for the transfer of patterns.

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4.6  Intercept Theorems

Fig. 4.25  Intercept theorem. The intercept theorems are utilized with the sector and the proportional dividers. Thanks to the proportions, it is possible to carry out a wide range of calculations. P stands for pivot. (© Bruderer Informatik, CH-9401 Rorschach)

The relationships (see Fig. 4.25)



PA : AC = PB : BD ( read : PA is to ACas PBis to BD ) PA : PC = PB : PD PC : AC = PD : BD

follow from the first intercept theorem. The relationships



PA : PC = AB : CD PB : PD = AB : CD

follow from the second intercept theorem.

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The equations PA : PC = AB : CD and PA : PC = AB : x



apply for multiplication. For PA an arbitrary (suitable) value is chosen. For division the permutations PC : PA = CD : AB and PC : PA = CD : x apply.



For PC an arbitrary value is chosen. Proportions A proportion has the form:

= a : b c= : d or a / b c / d. It can be rewritten as the product equation:



a · d = b · c.

The product of the means is equal to the product of the extremes. Proportions are commonly found, for example, in percent calculations. Three values are given, and the fourth, the unknown, has to be found.

4.6.1  W  e Are Probably Indebted to Thales of Miletus for the Intercept Theorem Below are a few contradictory opinions about the work of Thales (seventh/ sixth century BC): Diogenes Laertius reports that Thales [of Miletus] measured the height of the pyramids in Egypt from their shadows, allowing the conclusion that he was familiar with the most important propositions relating to the similarity of triangles and proportions (see Matthäus Sterner: Principielle Darstellung des Rechenunterrichtes auf historischer Grundlage, 1st part, Druck und Verlag von R.  Oldenbourg, Munich and Leipzig 1891, page 43).

Similarly, in the work of Heath, Diogenes Laertius quotes Hieronymus, a student of Aristoteles, regarding the calculation of the height measurement of the pyramids: Hieronymus says that he [Thales] even succeeded in measuring the pyramids by observation of the length of their shadow at the moment when our shadows are equal to our own height (see Thomas Heath: A history of Greek mathematics, volume 1, Clarendon press, Oxford 1921, page 129).

216

4  Classification of Calculating Aids and Related Instruments Hieronymus also says that he measured the pyramids, making an observation on our shadows when they are of the same length as ourselves, and applying it to the pyramids (see George Johnston Allman: Greek geometry from Thales to Euclid, Hodges, Figgis, & Co., Dublin 1889, pages 8–9). Third inference. – Thales discovered the theorem that the sides of equiangular triangles are proportional. The knowledge of this theorem is distinctly attributed to Thales by Plutarch. […] Hieronymus of Rhodes, a pupil of Aristotle, according to the testimony of Diogenes Laertius, says that Thales measured the height of the pyramids by watching when bodies cast shadows of their own length […] (see George Johnston Allman: Greek geometry from Thales to Euclid, Hodges, Figgis, & Co., Dublin 1889, page 14). Statement of Thales: The proportionality of the sides intersected by parallel lines across both legs of an angle […] (see Wilhelm Franz Meyer; Hans Mohrmann (editors): Geometrie, Encyklopädie der mathematischen Wissenschaften mit Einschluss ihrer Anwendungen, Verlag und Druck von B. G. Teubner, Leipzig 1907–1910, volume 3, part 1, first half, page 53). The sides of similar triangles are proportional. He [Thales] used this proposition in measuring the height of a pyramid by means of the shadow of the pyramid and that of a staff (see David Eugene Smith: History of mathematics, volume 1, Dover publications, Inc., New York 1958, page 68).

Von Braunmühl concurs: In fact Thales was undoubtedly familiar with the method making use of similar triangles. Otherwise, he could not have determined the distance of ships from the port of Miletus as Proclus reports. […] and Thales certainly learned this [the measurement] from these [the Egyptians] and thus made the beginnings of proportion theory known in Greece (see Anton von Braunmühl: Vorlesungen über Geschichte der Trigonometrie, part 1, Druck und Verlag von B. G. Teubner, Leipzig 1900, page 6).

The Authorship of Thales is Doubtful: However, whether the intercept theorem really derives from Thales is disputed. Carl Anton Bretschneider argues that Thales and also Pythagoras obtained certain knowledge from Egyptian priests and that Thales was not familiar with the laws of geometric similarity: If Thales actually used this method for the measurement of an unknown distance, this leads us to the suspicion that this was not his invention but that of Egyptian geometricians long before his time who applied this theory to right-angled triangles. […]. We obtain exactly the same final result with the second practical exercise, the solution of which is attributed to Thales, namely the height of the pyramid determined from the length of its shadow. […]. Hieronymus reports that he [Thales] measured the pyramids ‘by observation of the length of their shadow at the moment when our shadows are equal to (our own) height’. […]. The method mentioned here is a very simple application of the main property of right-angled isosceles triangles and requires so little ingenuity that one can be firmly convinced that this was not an invention of Thales, but far more an ancient method of Egyptian geometricians for the measurement of heights. […]. The application of this type of height measurement with the pyramids is however either a later embellishment or mistakes the identity of these world famous structures with the far less known obelisks. […]. That this approach functions very well with a body of only small floor area, such as a tree or an obelisk, is evident and, at the same time, that it is totally unsuited for a pyramid because such a structure possesses a deep root point [of the height per-

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pendicular] in its underground structure, making this measurement inaccessible (see Carl Anton Bretschneider: Geometrie und die Geometer vor Euklides, Dr. Martin Sändig oHG, Wiesbaden 1968, pages 44–45 (reprint from 1870)).

According to Bretschneider, Thales was unaware of proportion theory: “In arithmetic the introduction of proportion theory, in particular in connection with geometrical, arithmetic and so-called harmonic theory […]” (ibid., page 74). Thales did not determine “the height of an object using the theory of the similarity of figures” (ibid., page 75). For further details see Carl Anton Bretschneider: Beiträge zur Geschichte der griechischen Geometrie, Engelhard-Reyher’sche Hofbuchdruckerei, Gotha 1869, pages 11–12, section: Die von Thales bewirkte Höhenmessung der Pyramiden, and Dietmar Herrmann: Die antike Mathematik, Springer-Verlag, Berlin, Heidelberg 2014, pages 19–22.

4.6.2  T  he Pantograph: The Invention of Heron or Scheiner? The pantograph is usually credited to Christoph Scheiner (1603). However, in his work about mechanics (first book), Heron of Alexandria (first century AD) already describes a pantograph with toothed rack and gear wheels. This enabled the enlargement and reduction of drawings according to the gear ratio of the gear wheels (see Kostas Kotsanas: Ancient Greek technology, Pyrgos 2014, page 47). The pantograph of Heron (see Fig. 4.26) has a rack and pinion with a fixed ratio. Thanks to Heron, even three-dimensional objects can be enlarged or reduced.

Fig. 4.26  Heron’s pantograph. This drawing tool is not a pantograph with a linkage. It functions with a gear wheel drive (two concentric gear wheels). (Source: Héron d’Alexandrie: Les mécaniques ou l’élévateur des corps lourds, Société d’édition Les belles lettres, Paris 1988; Reprint from 1894) (see pages 228–231 for pictures of pantographs)).

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Heron describes the pantograph as follows: Let us now show how we can find a figure similar to a given plane figure and having a given relationship to the plane figure with the help of an instrument. We fix two identically toothed round discs (ac, ab) around the same midpoint (a) and move both about the same axis in the same plane in the figure that we want to reconstruct in a similar form. Let the relationship of the discs to each other be a known ratio. A ruler with teeth (pr, lo) is attached to each of the discs in this direction (a) and the teeth engage in the teeth of the discs. Let these rulers move in the groove of another ruler (a h k) that moves along the axis of the discs by means of a round hole. Let the edges of the toothed rulers be provided with markings (m, n) for the outlines of the similar figures and run along a straight line (a m n) passing through the midpoint of the discs. However, in order that both always move so that the movement takes place along a straight line passing through the midpoint and the three points always execute the same motion and remain on the same straight line we must place the markings on the toothed rulers as far away from the midpoint as the shortest distance of the midpoint of both discs from the edges of the rulers. We then move these so that we reach the plane in which we want to draw the similar figures. We then stretch a marking so that it comes to rest on the perimeter of the original figure, while the other is so far removed that the space between the first and the midpoint of the discs is in the same ratio to the distance between this and the other marking as the diameters of the toothed discs (one leaves the ruler with the groove somewhat bent so that the marking on the line already mentioned runs along this line). The other marking then describes the figure similar to the original figure in the given relation defined by the ratio of the toothed discs to each other (see Leo Michael Ludwig Nix; Wilhelm Schmidt (editors): Herons von Alexandria Mechanik und Katoptrik, Druck und Verlag von B. G. Teubner, Leipzig 1900, pages 30–34, section 15 “Instrument zur Konstruktion ähnlicher ebener Figuren”).

In Section 18, “Instrument zur Konstruktion ähnlicher körperlicher Figuren” (pages 36–44), a three-dimensional pantograph is introduced. The original Greek work “Mechanica” of Heron of Alexandria has been lost and has survived only in an Arabic translation from the ninth century.

4.6.3  How Does a Pantograph Function? The pantograph (see Fig. 4.27) is a centuries old tool. It enables the enlargement and reduction of drawings. The device is comprised of a movable linkage of wood, metal (e.g., brass), or plastic. It embodies a parallelogram, i.e., a quadrilateral with two pairs of equally long opposite (parallel) sides. The opposite interior angles are equal, and the sum of two adjacent interior angles is 180°. The two diagonals are halved. The rods are connected via articulated joints. The pole (fixed pivot), tracer point, and drawing pen all lie on a straight line.

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Fig. 4.27  Pantograph. To reduce drawing A (original drawing), the pantograph is fixed at the pole P. With the adjustable bars (legs), the given ratio is defined. With the tracer point T, the perimeter (outline) of drawing A is traced. The drawing pen D produces a similar figure in the chosen scale. Exchanging the drawing pen and the tracer point enlarges the figure. (© Bruderer Informatik, CH-9401 Rorschach)

Explanation It follows from the first intercept theorem that: PJ1 : PJ 2 PJ 2 : PJ1 PJ1 : J1J 2 PJ 2 : J1J 2



= = = =

PD : PT : PD : PT :

PT PD DT DT

Example



PJ1 : PJ 2 = 6 : 12 enlargement by the factor two ( to 200% ) PJ 2 : PJ1 = 12 : 6 reduction by the factor two ( to 50% )



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Note The pantograph of Coradi with a scale length of 65 cm provides for enlargement and reduction ratios from 0.05 to 0.8:



1 / 20, 1 / 12, 1 / 10, 1 / 8, 1 / 6, 1 / 5, 1 / 4, 1 / 3, 2 / 5, 2 / 3, 3 / 4, 4 / 5, 1 / 2, 1 / 1, 5 / 4, 4 / 3, 3 / 5, 3 / 8, and 2 / 3.



4.7  Sectors A sector (see Figs. 4.28, 4.29, 4.30, and 4.31) is comprised of two rulers (legs, arms) and an articulated joint (pivot, hinge). It can be opened up to 180 degrees and in this state has a length of about 1 foot. Calculations are performed by measuring line lengths and utilizing the relationships between the lengths. Thanks to the geometrical intercept theorems, it is possible to solve proportions by picking off line segments (lengths) with dividers. The versatile calculating aid, which was widespread in the seventeenth and eighteenth centuries, is suited to all four basic arithmetic operations, the calculation of circles, areas (polygons), volumes, etc. The scales are also referred to as functional scales.

Fig. 4.28  Galileo’s sector. The invention of the “compasso di proporzione” is (wrongfully) attributed to Galileo Galilei. In fact there were a number of forerunners. From 1597 Galileo manufactured many sectors. These served for numerous geometrical and arithmetic tasks. This example of brass (around 1606) is provided with many scales. The quarter circle is fastened with screws. (© Museo Galileo, Florence)

4.8  Proportional Dividers

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Fig. 4.29  French sector of Michael Butterfield. The English instrument builder was active in France. A linear scale can be seen on this side of the brass calculating device (around 1700). The polygon scale indicates the side length of inscribed equilateral polygons. (© ETH Zurich, Collection of astronomical instruments)

Fig. 4.30  French sector of Jacques Canivet. This brass calculating device dates from around 1760. Here we see a sine scale. The solid object scale is used to determine the specific weight of certain metals. (© ETH Zurich, Collection of astronomical instruments)

Fig. 4.31  Sector of Andr. Alexandri. Some of these versatile mathematical tools also have scales for square roots and cube roots. (© ETH Zurich, Collection of astronomical instruments)

4.8  Proportional Dividers Proportional dividers (see Figs. 4.32, 4.33, 4.34, and 4.35) are comprised of two legs, each having a long and a short tip. The adjustable pivot can be moved in the slot. Operation is based on the same rules as for the sector.

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Fig. 4.32  Sector of Bürgi (around 1587). The pivot of this four-point calculating device is adjustable. With this versatile instrument, line segments, areas, and volumes can be measured and reduced or enlarged in any proportion. Plane figures can be transformed into each other keeping the surface area constant (e.g., a circle to a square or an isosceles triangle to a circle or a square). Furthermore, one obtains the ratio π between the diameter and the circumference. Likewise, the five Platonic bodies – cubes, three-sided pyramids (tetrahedrons), and eight-, twelve-, and twenty-­faced bodies (octahedrons, dodecahedrons, and icosahedrons) – and a sphere can be transformed into each other. We owe the first known drawing of a sector to Leonardo da Vinci (Codex Atlanticus, around 1500). Already before Bürgi, Federico Commandino, Christoph Schissler the Elder, and Wenzel Jamnitzer built simple sectors. (© Museumslandschaft Hessen Kassel, Astronomisch-­ physikalisches Kabinett)

4.8  Proportional Dividers

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Fig. 4.33  Sundial dividers of Schissler (divider pair instrument) (1555). The pair of dividers of the instrument maker Christoph Schissler the Elder has two recessible transverse struts. At the top is a closable compass. The versatile tool not only was a device for measuring lengths and angles but also served as a sundial and leveling instrument. (© Museumslandschaft Hessen Kassel, Astronomisch-physikalisches Kabinett)

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Fig. 4.34  Proportional dividers (Kern). The Swiss Kern company manufactured proportional dividers for 150 years. Above is a model dating from 1964 with millimeter graduations and a vernier setting. Thanks to proportions, the tool simplified dealing with lines, areas, bodies, circles, and the golden ratio and was of help with the conversion of units of measure. Below is a model from 1880 showing the ratio scales. Proportional dividers are equipped with an adjustable pivot. (© Aldo Lardelli, Studiensammlung Kern, Aarau)

Fig. 4.35  Proportional dividers (Haff). With this mathematical instrument offered by Haff, one can divide lengths and circumferences into equal parts and enlarge or reduce lengths in different ratios. (© Gebrüder Haff GmbH, Pfronten)

With this versatile tool, a straight line or a circle can, for example, be resolved into equal parts. Drawings can be enlarged and reduced. It is suited to rules of three. The “instructions for using the proportional dividers 1091–1095” of Kern are still valid (slightly adapted version): Line sectioning: When the mark of the runner is set exactly to a mark of the line divisions, the spacing of the small tips corresponds to the spacing of the large tips in the relationship described by the number set [ratio]. Example: When the runner is set to 6, the spacing of the small tips is one sixth that of the large tips.

4.9  Protractors and Clinometers

225

Circle sectioning: This serves for the determination of the side of any regular polygon when the diameter of the circle circumscribed about the polygon is known. The mark of the runner is set to the number of the circle sectioning that gives the number of sides of the polygon desired. The opening of the small tips then gives the length of the desired side when the diameter of the circle circumscribed about the polygon is represented by the opening of the large tips. Example: The slide is set to 11. The opening of the small tips is equal to the side of a regular 11-sided figure, which is circumscribed by a circle having a diameter equal to the opening of the large tips. Golden ratio: The mark of the runner is set to the golden ratio. This divides the opening of the small tips and that of the large tips according to the socalled golden ratio, i.e., the opening of the large tips is set by the opening of the small tips, so that the ratio of the smaller section of a straight line sectioned according to the golden ratio to the larger section is the same as the ratio of the larger section to the entire length. Example: a : b = b : c (with drawing) Area sectioning: The opening of the small tips gives the side of a square that is smaller than the square for which the length of the sides is given by the ratio set according to the opening of the large tips. Example: The slide is set to 7. The opening of the small tips gives the side of a square which is smaller by a factor of 7 than the side of the original square, given by the opening of the large tips. Sectioning of physical objects: The opening of the small tips gives the side of a cube that is smaller than that of the cube whose side length is given by the opening of the large tips by the ratio set. Example: The slide is set to 9. The opening of the small tips gives the side of a cube nine times smaller than the side of the cube given by the opening of the large tips. Remarks Proportional compasses are calculational compasses, whereas dividers are measuring compasses. Common compasses are drawing compasses. Proportional dividers were originally called a pair of sector compasses.

4.9  Protractors and Clinometers Protractors were available in several forms (see Figs. 4.36 and 4.37). Clinometers were also artistically manufactured (see Fig. 4.38).

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Fig. 4.36  Semicircular protractor. This brass protractor (from about 1700) was manufactured by the English engineer and mathematician Michael Butterfield. (© ETH Zurich, Collection of astronomical instruments)

Fig. 4.37  Circular protractor. The manufacturer of this brass protractor (from the first half of the eighteenth century) is unknown. (© ETH Zurich, Collection of astronomical instruments)

4.10 Coordinatographs

227

Fig. 4.38  Clinometer. The clockmaker Jacob Ochsner built this brass clinometer around 1800. It is equipped with a pendulum, allowing the determination of ascents and descents. Such devices were found, e.g., in civil engineering and seafaring. (©ETH Zurich, Collection of astronomical instruments)

4.10  Coordinatographs The distinction between drawing instruments, e.g., pantographs or coordinatographs (see Figs. 4.39, 4.40, and 4.41), and measuring instruments – e.g., protractors, curvimeters, or planimeters – on the one hand and calculating devices (mathematical instruments) on the other hand is fuzzy. With a planimeter one determines areas by tracing and therefore calculates. Analog devices measure, and digital devices count. Nevertheless, the analog slide rule is a calculating aid. Calculations were also performed with quadrants, sextants, octants, sectors, and proportional dividers. Dividers supported calculations, and coordinate calculators served for conversion between rectangular coordinates and polar coordinates. A distinction was made between arithmetic (numerical) and geometric (graphical) calculation.

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Fig. 4.39  Orthocoordinatograph (1). These drawing tools date from the nineteenth century and served for the production of exact plans and maps. The point source microscope (observation microscope with point indicators for marking points) of the land register geometrician Rudolf Bosshardt (St. Gallen) is mounted on the moving carriage. Such drawing devices were used, e.g., in the watchmaking industry. Circular polar coordinatographs were also available commercially. A leading manufacturer was the Haag-Streit AG in Köniz near Bern. (© Vermessungsamt, Aarau)

4.10 Coordinatographs

229

Fig. 4.40  Orthocoordinatograph (2). The photo shows ordinate and abscissa carriages and microscope and vernier. The Haag-Streit AG emerged from the Haag-Streit mathematicalphysical workshops. The manufacturer writes for maintenance: “Keep the blank tracks and the external roller surface of the ball bearings clean by periodically rubbing with a cloth moistened with oil or vaseline. Before using the instrument remove dust from the celluloid scales and underneath the vernier”. (© Vermessungsamt, Aarau)

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Fig. 4.41  Polar coordinatograph. The movable retaining ring is arranged on a ring-shaped bedplate. The instrument can be centered exactly over a point. The quad spacer with the point source microscope and the glass vernier plate rolls over the spacer track. The circle and length sections are (as with the slide rule) read from celluloid. According to the model, the radius of action is up to 20 cm. (© Vermessungsamt, Aarau)

4.11  Mathematical Tables Already in antiquity tables (see Fig. 4.42) were used: tables for all four basic arithmetic operations, above all multiplication tables (product tables), division tables (quotient tables), tables with squares and cubes, square roots and cube roots, reciprocals, trigonometric and logarithmic tables, collections of formulas, and reference works for commercial calculations (currency, interest, etc.). Finally, pen, pencil and paper, chalk, and slate can be seen as calculating aids. A unique analog tool is the Messknecht (measuring servant) (see Fig. 4.43) of Maximilian Robert Pressler.

4.11  Mathematical Tables

231

Fig. 4.42  Compilation of mathematical tables. The figures show tables for addition (Fig. 1), subtraction (Fig. 2), multiplication and division (Fig. 3 (Pythagorean table) and Fig. 4), and extracted roots (Fig. 5). The factoring of the (uneven) natural numbers from 1 to 1599 into their prime factors and the prime numbers can be seen in the large table (Fig. 6). (From: Tobias Mayer: Mathematischer Atlas, in welchem auf 60 Tabellen alle Theile der Mathematic vorgestellet und nicht allein überhaupt zu bequemer Wiederholung, sondern auch den Anfängern besonders zur Aufmunterung durch deutliche Beschreibung und Figuren entworfen werden, Pfeffel, Augspurg 1745; Source: ETH Library, Zurich, Rare books collection)

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Fig. 4.43  Messknecht. The folding graphical logarithmic table of the German engineer and inventor Maximilian Robert Pressler (1852) was intended, e.g., for forestry. This paperboard measuring instrument, which also includes trigonometric tables, was used, for example, as a protractor and thus for the determination of tree height. (© Aldo Lardelli, Studiensammlung Kern, Aarau)

4.12  Astronomical instruments The quadrant, sextant, and octant are sector instruments (see Figs.  4.44, 4.45, 4.46, 4.47, 4.48, 4.49, and 4.50). They were also used in land surveying.

4.12  Astronomical instruments

233

Fig. 4.44  Quadrant. This astronomical instrument is comprised of a quarter circle with degree divisions and a swiveling rod. The inclination of the rod indicates the height of the star observed. The origin of this brass tool (from around 1750) is unknown. (© ETH Zurich, Collection of astronomical instruments)

Fig. 4.45  Mural quadrant. Large quarter circles were attached to walls. (From: Denis Diderot; M. d’Alembert: Encyclopédie, ou dictionnaire raisonné des sciences, des arts et des métiers, Pellet, Geneva, 1778; Source: ETH Library, Zurich, Rare books collection)

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Fig. 4.46  Wilhelm quadrant (azimuthal quadrant) (before 1570). This oldest surviving metal quadrant is attributed to Eberhard Baldewein. The rotatable astronomical measuring instrument enables the determination of stellar passage heights and their azimuths (angle between the vertical plane of a celestial body and the southern half of the meridian plane). The instrument was commissioned by Landgrave Wilhelm IV of Hessen-Kassel. (© Museumslandschaft Hessen Kassel, Astronomisch-physikalisches Kabinett)

4.12  Astronomical instruments Fig. 4.47  Sextant. This angular measurement instrument (sixth of a circle) served especially in seafaring for the determination of the height of a star. (From Tycho Brahe: Tychonis Brahe Astronomiae instauratae mechanica, apud Levinum Hulsium, Noribergae [Nuremberg] 1602; Source: ETH Library, Zurich, Rare books collection)

Fig. 4.48  Octant (1). The eighth of a circle of John Haley (about 1750) was utilized as a nautical protractor. (From: Denis Diderot; M. d’Alembert: Encyclopédie, ou dictionnaire raisonné des sciences, des arts et des métiers, Pellet, Geneva, 1778; Source: ETH Library, Zurich, Rare books collection)

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Fig. 4.49  Octant (2). This Haley octant was built by Bushey around 1750. No further details are available. (© ETH Zurich, Collection of astronomical instruments)

Fig. 4.50  Desk turquet of Habermel (around 1590). The observation instrument from the workshop of Erasmus Habermel allows the simultaneous measurement of the positions (length and width) of celestial bodies in the ecliptic and the equatorial coordinate systems. The base plate is equipped with a compass and a plumb bob. It bears the equator plate (plane of the celestial equator) with the ecliptic ring. (© Museumslandschaft Hessen Kassel, Astronomisch-physikalisches Kabinett)

4.13  Mechanical and Electronic Calculators

237

4.13  Mechanical and Electronic Calculators Below are two examples from the wide range of mechanical calculating machines and electronic pocket calculators (see Figs. 4.51 and 4.52).

Fig. 4.51  Mercedes-Euklid (Model 21). This electric proportional lever machine of Christel Hamann (1947) is suited to all four basic arithmetic operations. (© Geodätisches Institut der Leibniz-Universität Hannover) Fig. 4.52 Electronic pocket calculator. The first programmable electronic pocket calculator, the HewlettPackard 65, from the year 1974. (© Geodätisches Institut der LeibnizUniversität Hannover)

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4.14  Classification Criteria In addition to the characteristic switchgear chosen here, other classifications are also possible for mechanical calculating machines. Other attributes are numerical input (setting: disc, slide, stylus, wheel, keyboard/ ten-key keyboard/full keyboard), drive (direct drive, key drive, manual lever drive, hand crank drive, or electric drive), and output (with printout, without printout). This book refers to a writing mechanism for handwritten output (handwriting automaton) and a printing mechanism for machinedriven output.

4.14.1  Types of Calculating and Computing Machines According to design, we distinguish between the following machine classes: • • • •

Mechanical calculators Electromechanical calculators Electronic computers Quantum computers

as well as • Relay computers • Vacuum tube computers • Transistor computers. Mechanical devices incorporate, e.g., joints, gear wheels, and gear trains, while electromechanical machines usually utilize relays. In electronic machines one finds, e.g., vacuum tubes, transistors, and integrated circuits. Differential analyzers may be mechanical, electromechanical, or electronic. Furthermore, mechanical counter registers (with automatic tens carry) can be mentioned here. Cryptographic machines (e.g., Enigma) and deciphering machines (e.g., Colossus) occupy a special position.

4.14.2  Computer Generations According to the design of the arithmetic unit, the early fix-programmed and program controlled machines were allocated to three generations: • 0th generation:  relay computers, e.g., Zuse Z4, Harvard Mark 1/IBM ASCC, and Complex computer/Bell 1 computer • 1st generation:   vacuum tube computers, e.g., ABC, Colossus, and Eniac • 2nd generation: transistor computers, e.g., Tradic and Mailüfterl

4.14  Classification Criteria

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4.14.3  Arithmetic Unit and Memory Unit Some aids, such as tally sticks and knotted cords, served above all for the storage of numerical values. For a long time, high-capacity memories were a problem child with relay and vacuum tube computers. Initially, relays, counter wheels, and ring counters, and then punched cards, were used. These were followed by flip-flops (switching between two stable states, i.e., electronic toggle switches), capacitors (electronic components for short-term storage), and vacuum tubes. Flip-flops are used, for example, for registers (small memories with fast access times). The fast registers provide data and instructions for immediate processing. An accumulator is a high-speed memory (register) of the central processing unit in which the results of arithmetic and logical operations are stored. Accumulators were mechanical or electrical devices for the storage and addition of numbers. Electromagnetic relays were regarded as altogether reliable but were slow. By comparison, the much faster vacuum tubes led to the pronounced evolution of heat. Furthermore, their lifespan was rather short. However, it was possible to prolong the lifespan and reduce burnout by operating vacuum tubes at less than the rated power and (almost) never shutting down the computer. Trends with Collected Objects It is apparent that the collection of historical office equipment generally falls into a number of groupings: they are limited either to typewriters, mechanical calculating machines, or slide rules. Only a few of these can be classified according to all three areas and still fewer to the remaining mathematical instruments, such as the sector, proportional dividers, pantographs, coordinatographs, curvimeters, planimeters, or integrators. This splitting can also be observed with some museums. Counting boards, counting cloths, and mathematically sophisticated analog drawing and measuring devices are found relatively seldom in holdings. There are numerous calculating aids (see box).

Classification of Calculating Aids (overview) 1. Analog calculating aids 1.1 Natural analog calculating aids (natural measurements) Examples: Fingertips (pinch), handful Finger width, span, ell, fathom, foot, and step 1.2 Man-made analog calculating aids (analog calculating devices, analog calculators) (continued)

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1.2.1. Mechanical analog calculators Examples: Astrolabe (device for determining the position of stars) Antikythera mechanism (astronomical calculating  machine) Quadrant (instrument for measuring the height of stars) Sextant (instrument for measuring the height of stars) Octant (instrument for measuring the height of stars) (Linear) measuring rule (addition and subtraction rule) (Logarithmic) slide rule (Logarithmic) circular slide rule (Logarithmic) pocket watch slide rule (Logarithmic) grid slide rule (Logarithmic) cylindrical slide rule Parallel slide rule Spiral slide rule Sector Proportional dividers Curvimeter Planimeter Coordinatograph Integraph Astronomical clock Strasbourg cathedral calculating clock (Jean-Baptiste  Schwilgué) Harmonic analyzer Tide predictor (William Thomson) Mechanical differential analyzer Nomogram (diagram for graphical calculation) 1.2.2. Electromechanical analog calculators Example: Electromechanical differential analyzer (Vannevar Bush) 1.2.3. Electronic analog computers Examples: Electronic analog computer Electronic differential analyzer (continued)

4.14  Classification Criteria

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2. Digital calculating aids (and printed mathematical tables) 2.1 Natural digital calculating aids Examples: Finger, hand, arm Stone (pebble), shell, nut 2.2 Man-made digital calculating aids (digital calculating devices, digital calculators) 2.2.1 Numerical storage Examples: Tally stick Knotted cord (quipu), miller’s knot 2.2.2 Mathematical tables Examples: Product table, logarithm table 2.2.3 Mechanical digital calculating aids 2.2.3.1 Mechanical digital calculators without automatic tens carry Examples: Counting board, counting table, counting cloth Pebble, jeton, reckoning penny Bead frame Numbering rods (multiplications and division  sticks with multiplication columns) Calculating box (cabinet) 2.2.3.2 Mechanical digital calculators with semiautomatic tens carry (toothed racks with crook tens carry) Example: Slide bar adder 2.2.3.3 Mechanical digital calculators with automatic tens carry Examples: Mechanical calculating machines (desk calculators and pocket calculators) One-function calculator (adding machine) Multifunction machine Stepped drum machine Pinwheel machine Mercedes machine (proportional rod calculating machine) (continued)

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Proportional gear machine Ratchet machine Adapting segment machine Direct multiplication machines: Partial product multiplying machine Multiplication machine with lazy tongs Slide bar-type machine Cogged chain machine Cogged disc machine Difference engine Analytical engine (Charles Babbage) 2.2.4 Electromechanical digital calculators Examples: Punched card calculator Relay calculator (Electromechanical) desk calculator 2.2.5 Electronic digital computers Examples: Vacuum tube computers Program controlled vacuum tube computer Stored-program vacuum tube computer Transistor computer (Electronic) desk computer (Electronic) pocket computer Smartphone 3. Hybrid calculating aids Example: Digital differential analyzer

Remarks Finger width, span, ell, fathom, foot, and step are all length units: Ell = length of the lower arm (including the hand) Fathom = span width of the laterally stretched arm of an adult Span = distance between the tip of the thumb and the tip of the middle finger or the little finger (with the hand spread) The compass, protractor, and sundial also served for (analog) calculation. Pedometers and hodometers were used as distance measuring devices. The classification of calculating aids is illustrated in an overview table (see Fig. 4.53).

4.14  Classification Criteria

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Fig. 4.53  Classification of calculating aids. This diagram attempts to give an overview as free of contradictions as possible of the diverse and difficult to assess range of natural and artificial (historical) calculating aids. (© Bruderer Informatik, Rorschach, Switzerland)

Chapter 5

Chronology

Abstract  The chapter “Chronology” describes selected pivotal achievements from the pre- and early history of computer science and automaton construction. The history of computing technology begins with counting on the fingers, the notched bone, the tally stick, the quipu, and the abacus and ranges from the slide rule and the mechanical calculating machine to the stored program electronic computer, the Internet, the World Wide Web, the smartphone, and the quantum computer. The earliest known calculating aids were already digital: fingers, the tally stick, the quipu, and the abacus. The most important analog device was the (logarithmic) slide rule. Keywords  Abacus · Automaton construction · Chronology · Computing technology · Early history · Internet · Number system · Prehistory · Smartphone · Tally stick · Time line · World Wide Web · Zero

5.1  P  re- and Early History of Computer Technology and Automaton Construction Because the relevant information is often contradictory, chronological tables (see Table 5.1) are awkward and error-prone. Furthermore, the origin of many pioneering inventions lies in the dark. This is true not only for the wheel but also for the origin of the number system and the zero. Without these two groundbreaking achievements, the introduction of which took place over centuries, program controlled computers would be unthinkable. The way from the inspiration, the first thoughts, to an ironclad understanding or a product useful in everyday life is often rocky. What is decisive: the point in time of the discovery, the data of publication, the commissioning or marketing, or the beginning or conclusion of research work? Between patent applications and the issuing of patents, many years often elapse. Patents are sometimes granted before and sometimes after production has begun. The development of computing devices and their © Springer Nature Switzerland AG 2020 H. Bruderer, Milestones in Analog and Digital Computing, https://doi.org/10.1007/978-3-030-40974-6_5

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components frequently entails several stages and degrees of maturity. For relay and vacuum tube computers, for (patriotic) priority reasons, the data of the first run is mostly given, even though a longer time is usually required from test operation to permanent operation. In some cases, the date refers to the first demonstration or the dedication. The years given are based on inconsistent data and must therefore be understood only as approximate values. The information about the time and place for the bead frame varies considerably. The Chinese abacus probably originated in the twelfth century and the Japanese in the sixteenth century. Calculating boxes, which later led to counting frames, appeared in Russia around the seventeenth century. The Russian abacus came to light in Western Europe at the beginning of the nineteenth century and became established as a teaching abacus. The counting board occurred in some (Greek) findings. The original forms of these aids probably go back to the gray past. In many cases, different years are cited, for example, for the differential analyzer of Vannevar Bush (completed in 1930, published in 1931), the paper on the universal Turing machine (submitted in 1936 and published in 1937), and the Plankalkül (1945 and 1946). There are also deviations regarding the allocation to countries. Thus, for example, the German inventor Emil(e) Berliner developed the gramophone in the USA. As a rule, the information refers to the country of birth. Key inventions in the history of computing technology and computer science include the: • • • • • • • • • • • • • • • • • • •

Number zero Place value system Binary system Abacus Automaton Logarithm Stepped drum Pinwheel Punched card Telephone Relay Vacuum tube Transistor Universal computer Stored program Robot Internet World Wide Web and Smartphone.

Other outstanding masterpieces include the clock, letterpress, the loom, the steam engine, and the generation of electrical power. In this connection, one should also call attention to the achievements of Leonardo da Vinci.

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Table 5.1  Chronology: Milestones in the pre- and early history of computing technology and automaton construction Highlights of the pre- and early history of computing technology and automaton construction Time Place Event 20,000 BC Congo Ishango bone Greece Intercept theorem of Thales of Miletus Seventh/ sixth century BC Sixth China Knotted cord century BC Fourth Greece Darius vase with counting table century BC Fourth Greece Salaminian table (counting board) century BC 300 BC Italy Roman hand abacus Greece Water organ of Ktesibios of Alexandria Third century BC Greece Astrolabe (Hipparchus) Second century BC First Greece Antikythera mechanism (astronomical calculating machine) century BC Greece Automatic puppet theater and pantograph of Heron of First century BC Alexandria 700 AD England Finger counting record of the monk Beda Venerabilis Eighth India Numeral 0 (inscription of Gwalior) century AD Ninth Persia Textbook of Muhammad ibn Musa al-Khwarizmi on century AD calculating with Indian numerals France Monastic abacus of Gerbert of Aurillac (Pope Silvester II) with Tenth apices with number symbols century (980) 1202 Italy Book of calculation (Liber Abaci) of Leonardo Fibonacci (Leonardo da Pisa) 1494 Italy Finger numeral table of Luca Pacioli 1503 Germany Woodcut with Pythagoras (line computation, board calculation) and Anicius Manlius Severinus Boethius (pen and paper calculation, numerical calculation) of Gregor Reisch (Margarita Philosophica) (erroneous allocation of inventor) Around Germany First arithmetic textbook of Adam Ries 1520 1544 Germany Arithmetic textbook of Michael Stifel 1568 Germany Planetary clock of Eberhard Baldewein 1584 Germany Hodometer of Christoph Trechsler 1585 Germany Mechanical galleon of Hans Schlottheim 1588 Czech Astrolabe of Erasmus Habermel Republic (continued)

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Table 5.1 (continued) Highlights of the pre- and early history of computing technology and automaton construction Time Place Event 1592 Switzerland “Kunstweg” (calculation of sine values) of Jost Bürgi 1597 Italy Sector of Galileo Galilei 1603 Germany Pantograph of Christoph Scheiner 1604 Switzerland Proportional dividers of Jost Bürgi 1614 Scotland Logarithms of John Napier 1615 France Water organ and pinned drum of Salomon de Caus 1617 England Common logarithms of Henry Briggs 1617 Scotland Napier’s bones for multiplication and division and promptuary of John Napier 1620 England Logarithmic scale of Edmund Gunter (Gunter scale) 1620 Switzerland Logarithms of Jost Bürgi 1622 England Logarithmic slide rule of William Oughtred 1623 Germany Addition and subtraction machine with rotatable multiplication and division drums of Wilhelm Schickard 1627 Switzerland Vienna crystal clock of Jost Bürgi 1630 England Logarithmic circular slide rule of William Oughtred 1633 Netherlands Logarithm tables of Adriaan Vlacq and Henry Briggs 1642 France Addition and subtraction machine of Blaise Pascal 1666 England Multiplication and division device (mechanical Napier’s bones) of Samuel Morland 1670 Spain Binary system of Juan Caramuel y Lobkowitz 1673 Germany Four-function pinwheel machine of Gottfried Wilhelm Leibniz 1679 Germany Binary numbers for machine calculation of Gottfried Wilhelm Leibniz 1688 Germany Mathematical cabinet of Athanasius Kircher (publication) 1709 Italy Pinwheel machine of Giovanni Poleni 1725 France Punched card controlled semiautomatic loom of Basile Bouchon 1727 Germany History of calculating machines of Jacob Leupold 1728 France Punched card controlled semiautomatic loom of Jean-Baptiste Falcon 1738 France Mechanical automatons of Jacques Vaucanson (duck, transverse flute player, drummer) 1745 France Punched card controlled semiautomatic loom of Jacques Vaucanson 1760 Germany Universal miracle writing machine (programmable writing automaton) of Friedrich Knaus 1770 England Musical writing automaton of Timothy Williamson (authorship disputed) 1772 Switzerland Programmable writing automaton (L’écrivain) of Pierre Jaquet-Droz (continued)

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Table 5.1 (continued) Highlights of the pre- and early history of computing technology and automaton construction Time Place Event 1774 Switzerland Mechanical automatons of Pierre Jaquet-Droz, Henri-Louis Jaquet-Droz, and Jean-Frédéric Leschot (writer, draftsman, musician) (presentation) 1774 Germany Four-function stepped drum machine of Philipp Matthäus Hahn 1780 Switzerland Singing bird of Pierre Jaquet-Droz and Henri-Louis Jaquet-Droz 1784 Germany Mechanical dulcimer player of Peter Kintzing and David Roentgen 1796 Switzerland Vibrating steel lamella (music box) of Antoine Favre-Salomon 1804 France Improved fully automatic punched card controlled loom of Joseph-Marie Jacquard (patent 1801) 1812 Germany Mechanical trumpet player of Friedrich Kaufmann 1814 Germany Planimeter of Johann Martin Hermann 1820 France Mechanical four-function calculating machine with movable carriage of Charles-Xavier Thomas 1822 England Difference engine of Charles Babbage (beginning of construction, remained uncompleted) 1824 Italy Planimeter of Tito Gonnella (invention/publication) around France “Process” calculator for the digital control of a gear cutter of 1830 Jean-Baptiste Schwilgué 1834 England Design of an analytical engine of Charles Babbage (remained uncompleted) 1834 Italy Keyboard adding machine of Luigi Torchi 1835 USA Electromechanical relay of Joseph Henry 1842 France Church calculator for the astronomical clock of the Strasbourg cathedral of Jean-Baptiste Schwilgué 1843 England Description of the mathematical principles of the analytical engine of Charles Babbage by Ada Lovelace 1844 France Keyboard adding machine of Jean-Baptiste Schwilgué 1847 Germany Slide bar adder (with crook tens carry) of Heinrich Kummer 1850 USA Keyboard adding device (column adder) of Du Bois D. Parmelee 1853 Sweden Printing difference engine of Georg and Edvard Scheutz 1854 Ireland Boolean algebra of George Boole 1854 Switzerland Polar planimeter of Jakob Amsler 1860 Sweden Printing difference engine of Martin Wiberg 1861 Germany Telephone of Johann Philipp Reis 1864 Italy Typewriter of Peter Mitterhofer 1865 Denmark Typewriter of Rasmus Malling-Hansen 1868 USA Typewriter of Christopher Latham Sholes, Carlos Glidden, and Samuel W. Soulé (patent) (continued)

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Table 5.1 (continued) Highlights of the pre- and early history of computing technology and automaton construction Time Place Event 1873 USA Diode electronic transmission of Thomas Edison 1876 Northern Tide predictor of William Thomson (Lord Kelvin)/feedback Ireland principle 1876 USA Telephone of Alexander Graham Bell 1877 USA Phonograph of Thomas Edison 1878 Germany Arithmometer of Arthur Burkhardt (mass produced) 1878 Ireland Logarithmic spiral scale cylindrical slide rule of George Fuller 1878 Poland Integraph of Bruno Abdank-Abakanowicz 1878 Sweden Pinwheel machine of Willgodt Odhner (patent) Harmonic analyzer of William Thomson (Lord Kelvin) 1879 Northern Ireland 1879 USA Cash register of James and John Ritty 1881 USA Logarithmic parallel cylindrical slide rule of Edwin Thacher 1884 USA Non-printing keyboard adding machine (macaroni box, later comptometer) of Dorr Felt 1885 Germany Perforated disc of Oscar Paul Lochmann 1885 England Perforated disc of Ellis Parr 1888 France Direct multiplication machine of Léon Bollée 1888 USA Printing segment adding machine of William Burroughs 1887 Germany Gramophone with gramophone record of Emil Berliner 1889 France Slide bar adder of Louis Troncet 1890 USA Tabulating and sorting machine with punched card technology of Herman Hollerith (used for the American census) 1893 Switzerland Direct multiplication machine of Otto Steiger and Hans W. Egli 1895 Spain Treatise on the (analog) algebraic machine for the solution of equations of Leonardo Torres Quevedo 1897 Germany Cathode ray tube of Karl Ferdinand Braun 1898 Denmark Magnetic sound recording onto steel tape of Valdemar Poulsen 1900 Germany Mathematical theses of David Hilbert 1906 Austria Hot cathode gas discharge tube (cathode ray relay, mercury vapor-filled amplifier tube) of Robert von Lieben 1906 USA Hot cathode gas discharge tube (triode, vacuum tube) of Lee de Forest 1909 Ireland Analytical (program controlled) engine of Percy Ludgate 1911 USA Punched card machines of James Powers 1914 Spain Demonstration of chess endgame machine of Leonardo Torres Quevedo at the Sorbonne in Paris (year of manufacture: 1912) 1914 Spain Decimal point notation of Leonardo Torres Quevedo (continued)

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Table 5.1 (continued) Highlights of the pre- and early history of computing technology and automaton construction Time Place Event 1917 Russia Electronic flip flop switch (trigger circuit, cathode relay) of Mikhail Alexandrovich Bonch-Brujevich 1919 England Electronic flip flop switch (toggle switch with vacuum tubes) of William Henry Eccles and Frank Wilfred Jordan 1920 Spain Demonstration in Paris of an electromechanical calculating machine with automatic multiplication and division and typewriter input/output by Leonardo Torres Quevedo 1923 Germany Enigma cryptographic machine of Arthur Scherbius 1926 Austria System of punched card controlled bookkeeping machines of Gustav Tauschek 1928 Austria Magnetic tape (paper audio tape) of Fritz Pfleumer 1930 USA Electromechanical differential analyzer of Vannevar Bush (Massachusetts Institute of Technology, Cambridge, MA) 1931 Austria Incompleteness theorems of Kurt Gödel 1932 Austria Magnetic drum memory of Gustav Tauschek (patent) 1932 Poland Bomba decoding machine of Marian Rejewski 1932 England Thyratron counter of Charles Eryl Wynn-Williams (Cambridge University) 1935 England Mechanical differential analyzer with Meccano components of Douglas Hartree (University of Manchester) 1936 Germany Mechanical switching element (memory element) of Konrad Zuse 1936 England Universal Turing machine (mathematical model) of Alan Turing (Cambridge University) 1936 USA Mathematical model of a computing machine by Emil Post 1936 USA Lambda calculus of Alonzo Church 1938 USA Electronic analog computer of George A. Philbrick 1938 Germany Electronic vacuum tube relay (vacuum tubes and neon lamps) of Helmut Schreyer 1938 Austria Curta four-function pocket calculator of Curt Herzstark (patents) 1938 USA Delay line of William Shockley (Bell Labs, New York) 1938 USA Switching algebra (1) of Claude Shannon (Bell Labs, New York) 1940 England Bombe relay calculator of Alan Turing and Gordon Welchman (Bletchley Park, England) 1940 USA Fixed program decimal relay complex computer with decimal point notation of George Stibitz (Bell Labs, New York) 1941 Germany Z3 punched tape controlled binary relay computer with decimal point notation of Konrad Zuse 1941 Germany Universal electronic analog computer of Helmut Hoelzer (continued)

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Table 5.1 (continued) Highlights of the pre- and early history of computing technology and automaton construction Time Place Event 1942 USA ABC fixed program binary vacuum tube computer with capacitor memory and fixed point notation of John Atanasoff and Clifford Berry (Iowa State University, Ames, IA) 1943 Germany Magnetic drum memory of Gerhard Dirks 1943 England Colossus plugboard controlled binary vacuum tube computer of Thomas Flowers 1943 USA Harvard Mark 1/IBM ASCC program controlled relay computer without conditional instructions of Howard Aiken and Clair Lake 1944 Germany Process computer of Konrad Zuse (S2 special computer for the Henschel aircraft factory for the automatic wing measurement of remotely controlled glider bombs) 1945 USA Von Neumann architecture with stored program (Edvac report) 1946 Germany Plankalkül programming language of Konrad Zuse 1946 USA Eniac plugboard controlled decimal vacuum tube computer with fixed point notation and conditional instructions of Presper Eckert and John Mauchly (University of Pennsylvania, Philadelphia) 1946 USA Lecture series on the design of stored program digital computers at the University of Pennsylvania, Philadelphia 1946 USA Treatise on the logical design of an electronic computer of Arthur Burks, Herman Goldstine, and John von Neumann (Institute for Advanced Study, Princeton University, Princeton, NJ) 1946 England Electrostatic memory of Frederic Williams and Thomas Kilburn (University of Manchester) 1947 England Magnetic drum memory of Andrew Booth (University of London) 1947 USA Mercury delay line memory of Presper Eckert (University of Pennsylvania, Philadelphia) 1947 USA Transistor of John Bardeen, Walter Brattain, and William Shockley (Bell Labs, New York) 1948 England Small-scale experimental stored program binary electronic computer with fixed point notation of Frederic Williams and Thomas Kilburn (University of Manchester) 1948 USA Switching algebra (2) of Claude Shannon (Bell Labs, New York) 1948 USA Magnetic core memory of An Wang (Harvard University, Cambridge, MA) 1948 USA Cybernetics of Norbert Wiener (Massachusetts Institute of Technology, Cambridge, MA) 1948 USA Information theory of Norbert Wiener (Massachusetts Institute of Technology, Cambridge, MA) (continued)

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Table 5.1 (continued) Highlights of the pre- and early history of computing technology and automaton construction Time Place Event 1949 England Index register of Max Newman, Frederic Williams, Thomas Kilburn, and Geoff Tootill (University of Manchester) 1949 England Edsac stored program binary electronic computer with fixed point notation and conditional instructions of Maurice Wilkes and William Renwick (Cambridge University) 1949 Australia Csirac stored program binary vacuum tube computer of Trevor Pearcey and Maston Beard (University of Sydney) 1949 USA Magnetic core memory of Jay Forrester (Massachusetts Institute of Technology, Cambridge MA) 1950 England Pilot Ace stored program electronic computer of Alan Turing and James Wilkinson 1950 Sweden Bark plugboard panel controlled binary relay computer with floating point notation of Conny Palm (Royal Institute of Technology, Stockholm) 1950 Switzerland Z4 program controlled binary relay computer with floating point notation of Konrad Zuse (operational) (ETH Zurich) 1951 England Leo stored program vacuum tube computer for commercial purposes 1951 England Harwell Dekatron (stored program) relay computer 1951 England Ferranti Mark 1 stored program binary electronic computer available commercially 1951 England Programming textbook of Maurice Wilkes, David Wheeler, and Stanley Gill (Cambridge University) 1951 England Microprogramming of Maurice Wilkes (Cambridge University) 1951 Ukraine Mesm stored program binary electronic computer with fixed point notation of Sergey Lebedev 1951 Switzerland Global overview of program controlled digital computing devices of Heinz Rutishauser, Ambros Speiser, and Eduard Stiefel (ETH Zurich) 1951 Switzerland Automatic programming of Heinz Rutishauser (ETH Zurich) 1951 USA Univac 1 stored program decimal electronic computer available commercially 1952 England Compiler of Alick Glennie 1952 USA Compiler of Grace Hopper 1952 USA IBM 701 stored program binary scientific electronic computer with fixed point notation available commercially 1953 USA IBM 650 commercial stored program decimal electronic computer with fixed point notation available commercially 1954 England Mark 1 autocode compiler of Ralph Anthony Brooker 1954 Italy Compiler in his own language of Corrado Böhm 1955 USA Tradic transistor computer of Jean Howard Felker (Bell Labs, New York) 1956 USA Hard disc of Louis D. Stevens, John Lynott, and William A. Goddard (IBM Research Laboratory, San José, California), patent application, 1954 (continued)

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Table 5.1 (continued) Highlights of the pre- and early history of computing technology and automaton construction Time Place Event 1958 Austria Mailüfterl transistor computer of Heinz Zemanek (Vienna University of Technology) 1959 USA Integrated circuit of Jack Kilby (Texas Instruments) and Robert Noyce (Fairchild) 1961 England Anita electronic desk calculating machine of Norman Kitz (Bell Punch company, London) 1968 USA Program controlled electronic pocket calculator of Hewlett-Packard 1969 USA Arpanet (Internet forerunner) 1973 USA Revocation of Eniac patent of Presper Eckert and John Mauchly in Honeywell versus Sperry Rand patent dispute and recognition of John Atanasoff as the inventor of the automatic electronic digital computer 1975 England Disclosure of details about the top secret British Colossus vacuum tube computer 1989 Switzerland World Wide Web of Tim Berners-Lee 2007 USA iPhone (Apple) (smartphone) © Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020

Remarks In 1950, Norbert Kitz (later Norman Kitz) built the SEC (simple electronic computer) vacuum tube computer according to the design of Andrew Booth (Birkbeck College, University of London). He also collaborated in the development of the Deuce, which the English Electric Company Ltd. built at the National Physical Laboratory (Teddington, London) in 1955. At Bell Punch, he built the first electronic pocket calculator, Anita (with glow lamp numeral display and thyratron tube ring decimal counters). Note Section 2.26 discusses fundamental considerations in regard to the newest developments  – the digital transformation, the Fourth Industrial Revolution, robotics, drones, smartphones, World Wide Web, electronic commerce, Internet of Things, artificial intelligence, machine learning, quantum computers, social networks, etc.

Chapter 6

Pioneers in Calculating and Computing Technology

Abstract  This chapter deals with the question who invented or discovered what and when. Important contributions of women (e.g., Ada Lovelace and Grace Hopper) are included. The achievements of women during the Second World War (e.g., cracking the Enigma ciphertexts in Bletchley Park, UK, and programming the giant Eniac computer in Philadelphia) were of great importance. The global overview by country traces the pre- and early history of calculating and computing technology. A number of unrecognized and unknown visionaries are mentioned as well. Along with analog and digital mathematical aids, numerous drawing and measuring devices and (partly programmable) automaton figures are described. Selected manufacturers of calculating and computing devices are also mentioned. A chronological table summarizes pathbreaking accomplishments. Keywords  Calculating and computing technology · Chronology · Discoveries · Inventions · Pioneers · Time lines · Women The following compilation gives a country-related overview of selected pioneers from the pre- and early history of computer science and does not claim to be complete. The allocation to countries is not always unambiguous (birthplace, citizenship, place of work, demise of old and arising of new countries, changes to international boundaries). Unrecognized and Unknown Innovators Some forward thinkers are little known and deserve greater recognition. Among those worth mentioning are, for example, Sergey Lebedev (Russia), Heinz Rutishauser (Switzerland), and Leonardo Torres Quevedo (Spain). For many years Alan Turing (England), whose achievements can be credited with saving the lives of ten thousands, was ostracized. In computer science there were also achievements of considerable importance by women (see box).

© Springer Nature Switzerland AG 2020 H. Bruderer, Milestones in Analog and Digital Computing, https://doi.org/10.1007/978-3-030-40974-6_6

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Pioneering Women in Informatics Only a few women have gone down in the history of early computer science. Those who made valuable contributions include, for example, Ada Lovelace (description of the analytical engine of Charles Babbage, Cambridge University) and Grace Hopper (“compiler”, programming languages, Harvard University, Cambridge MA, Remington Rand, Philadelphia). Lovelace is regarded (probably incorrectly) as the first woman programmer, and the programming language Ada is named for her. The collaboration of women programmers for the giant Eniac computer (University of Pennsylvania, Philadelphia) was commendable. Adele Goldstine (together with Harry Huskey) authored the multivolume user manual for Eniac. Also impressive is the devotion of countless women operating the decryption machines (Robinson, Turing-Welchman Bombe, Colossi) during the Second World War in the English Bletchley Park. They were known as “wrens” (WRNS, Women’s Royal Naval Service). The woman logician Rózsa Péter (Eötvös Loránd University, Budapest) is regarded as the founder of the theory of recursive functions (theoretical computer science). The work of Jean Sammet (IBM, New York) focused on programming and programming languages. And not to be forgotten, the first “computers” were women. They had to perform monotonous calculations with mechanical table calculating machines. Further Reading Janet Abbate: Recoding gender, MIT press, Cambridge, Massachusetts, London 2012 William Aspray: Women and underrepresented minorities in computing. A historical and social study, Springer international publishing AG Switzerland, Cham 2016 Claire Lisa Evans: Broad band. The untold story of the women who made the internet, Penguin Random House LLC, New York 2018 Jason Fagone: The woman who smashed codes. A true story of love, spies, and the unlikely heroine who outwitted America’s enemies, Harper Collins publishers, New York 2017 Marie Hicks: Programmed inequality. How Britains discarded women technologists and lost its edge in computing, MIT press, Cambridge, Massachusetts, London 2017 Ute Hoffmann: Computerfrauen, Rainer Hampp Verlag, Munich 1987 Sinclair McKay: The secret life of Bletchley Park. The WWII codebreaking centre and the men and women who worked there, Aurum press Ltd., London 2011 (continued)

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Liza Mundy: Code girls. The untold story of the American women code breakers of world war II, Hachette book group, Inc., New York 2017 Veronika Oechtering (editor): www.frauen-informatik-geschichte.de, Kompetenzzentrum Frauen in Informationsgesellschaft und Technologie, Bielefeld 2001 Jon T. Rickman, Kim D. Todd (editor): Pioneer programmer. Jean Jennings Bartik and the computer that changed the world, Truman State University Press, Kirksville, Missouri 2013 Valérie Schafer, Benjamin G.  Thierry (editor): Connecting women. Women, gender and ICT in Europe in the nineteenth and twentieth century, Springer, Cham, Heidelberg etc. 2015

American Pioneers with a European Background Many pioneers in the USA had European roots (see Table 6.1). Table 6.1  American computer pioneers with European roots Birthplace of American pioneers Name John Atanasoff Presper Eckert Herman Hollerith John Mauchly Emil Post James Powers John von Neumann

Birthplace Bulgaria Switzerland Germany Switzerland Poland Russia Hungary

Invention Atanasoff-Berry computer Eniac, Binac, Univac Punched card machines Eniac, Binac, Univac Mathematical machine model Punched card machines Von Neumann architecture

© Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020

6.1  F  rom Which Countries Do the Inventors and Discoverers Come? The pioneers and their countries are listed below in alphabetical order. As a rule, the place of birth is decisive. Australia Differential analyzer • David M. Myers (electromagnetic analog computer, integraph)

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Programmable computer • Maston Beard (Csirac electronic computer) Austria Mathematical plotting, measuring, and calculating devices • Albert Miller, Ritter von Hauenfels (polar planimeter) Punched card machines • Otto Schäffler (tabulator) • Gustav Tauschek (bookkeeping system with punched card machines, magnetic drum memory) (place of work Germany) Mechanical calculating machines • Hugo Bunzel (Bunzel-Delton calculating machine) • Curt Herzstark (Curta pocket calculating machine, place of work Liechtenstein) • Samuel Jacob Herzstark (Austria calculating machine with automatic keydriven carriage movement) • Joseph Gräber (stepped drum machine) • Alexander Rechnitzer (Autarith electromechanical calculating machine with automatic multiplication and division) Programmable computers • Kurt Gödel (incompleteness theorems) • Heinz Zemanek (Mailüfterl transistor computer) Belgium Mathematical plotting, measuring, and calculating devices • Michiel Coignet (sector) Czech Republic Programmable computer Antonín Svoboda (Sapo relay computer) France Slide rule • Amédée Mannheim (“Mannheim” system) Nomography • Maurice d’Ocagne (nomogram) Mathematical plotting, measuring, and calculating devices • Jacques Besson (proportional dividers) • Gaspard-Gustave Coriolis (integraph) Automaton figures • Jacques Vaucanson

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Bead frame • Gerbert of Aurillac (monastic abacus) (place of work Italy) Punched card and punched tape control/looms • Basile Bouchon (punched tape controlled semiautomatic loom with paper roll) • Jean-Baptiste Falcon (punched tape controlled semiautomatic loom with punched cards bound together (perforated wooden tablets)) • Joseph-Marie Jacquard (punched tape control, improvement of fully automatic loom, concatenated punched cards) • Jacques Vaucanson (automaton figures: punched card controlled fully automatic loom). Note In the professional literature, one sometimes speaks of punched cards and sometimes of punched tapes in connection with early French looms. This confusion probably arises from the fact that punched cards were often bound together to punched tapes. This permitted the exchanging of faulty punched cards. With punched tapes, on the other hand, the entire tape or the entire roll of paper had to be replaced. Later, musical automatons made use of folded carton and paper tapes. Rulers • Henri Genaille • Edouard Lucas Slide bar adder • Louis Troncet Mechanical calculating machines • Léon Bollée (direct multiplication machine) • Jean Lépine (addition and subtraction device) • Blaise Pascal (adding machine with indirect subtraction with setting wheels (numeral dials) and pin dials for the transfer of numerical values from the entry register to the arithmetic unit (Pascaline)) • Jean-Baptiste Schwilgué (“process” calculator, keyboard adding machine, church calculator) • Charles-Xavier Thomas (arithmometer) Programmable computers • Louis Couffignal (proposal for an unrealized punched card controlled relay machine, experimental model of a binary parallel vacuum tube computer with floating point notation, unsuccessful computer construction) • Raymond André Valtat (proposal for a binary computer)

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Germany Logarithms • Michael Stifel (forerunner of logarithms) Slide rule • Alwin Walther (“Darmstadt” system) Mathematical plotting, measuring, and calculating devices • Johann Martin Hermann (planimeter) • Christoph Scheiner (pantograph) Automaton figures • Friedrich Kaufmann • Peter Kintzing (place of work France) • Friedrich Knaus (place of work Austria) Differential analyzers • Hans Bückner (Askania-Werke, Berlin) • Wilfried de Beauclair (Institut für praktische Mathematik, Technische Hochschule Darmstadt) • Friedrich Wilhelm Gundlach (Institut für praktische Mathematik, Technische Hochschule Darmstadt, Elrad electronic analog computer) • Helmut Hoelzer (electronic analog computer, Heeresversuchsanstalt, Peenemünde) • Udo Knorr (Fahrdiagraph mechanical differential analyzer) • Albert Ott (Kempten) • Heinrich Pösch (Institut für praktische Mathematik, Technische Hoch­ schule Aachen) • Robert Sauer (Institut für praktische Mathematik, Technische Hoch­ schule Aachen) • Alwin Walther (Institut für praktische Mathematik, Technische Hoch­ schule Aachen) • Günter Weidenmüller (VEB Archimedes Rechenmaschinenfabrik, Glashütte, endim 2000 electronic long-term analog computer) • Ernst Weinel (Institut für angewandte Mathematik und Mechanik, Friedrich-­Schiller-­Universität Jena, mechanical differential analyzer) • Helmut Winkler (Institut für Physik, Technische Hochschule Ilmenau, Eari electronic short-term analog computer). Differential analyzers were very high-performance analog computers (see box).

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What Is a Differential Analyzer? Here are two descriptions of an informatics pioneer: “In the 20th century large-scale differential analyzers for the plotting of solution curves for differential equations represented the crowning development in mechanical analog computing devices.” (see Friedrich Bauer: Informatik. Führer durch die Ausstellung, Deutsches Museum, Munich 2004, page 52). “Differential analyzers are constructed by the coupling of differential gear trains with variators [...].” “Closing the coupling circuit by ‘feedback’ from the output of one differential gear train to the input of another reproduces a differential equation. Lord Kelvin already recognized the possibility for solving differential equations mechanically in 1876 [...].” “A universally utilizable mechanical differential analyzer includes the freely engageable elements: differential gear train, function generating mechanism, multiplication gear mechanism, addition gear mechanism, and proportional gear mechanism. The interconnection of these elements for a particular task is predefined in a ‘coupling plan.’ The implementation of the mechanical couplings by means of shafts and toothed gears is not easy to realize. Forces and torques must nearly always be reinforced [...].” (see Friedrich Bauer: Informatik. Führer durch die Ausstellung, Deutsches Museum, Munich 2004, pages 69–70).

Arithmetic textbooks • Adam Ries Slide bar adder • Heinrich Kummer (crook tens carry) (place of work Russia) Mechanical calculating machines • Anton Braun (pinwheel machine) (place of work Austria) • Curt Dietzschold (ratchet machine) • Christian Ludwig Gersten (addition and subtraction machine) • Philipp Matthäus Hahn (stepped drum machine) • Christel Hamann (proportional rod calculating machine, ratchet machine, difference engine, Mercedes machine with automatic multiplication and division) • Gottfried Wilhelm Leibniz (binary system, stepped drum, pinwheel, four-­ function machine) • Jacob Leupold/Anton Braun/Philippe Vayringe (toothed segment machine) • Johann Helfrich Müller (stepped drum machine) • Johann Jacob Sauter (pinwheel machine) • Arthur Scherbius (enigma cryptographic machine)

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• Wilhelm Schickard (addition and subtraction machine with rotatable cylinders for multiplication and division) • Kaspar Schott (calculating box with rotatable multiplication and division drums) • Johann Christoph Schuster (stepped drum machine) • Eduard Selling (direct multiplication machine with lazy tongs) Programmable computers • Heinz Billing (magnetic drum memory) • Gerhard Dirks (magnetic drum memory) • David Hilbert (Hilbert program, coherent mathematics) • Helmut Schreyer (vacuum tube circuits: electronic vacuum tube relay with neon lamps) • Konrad Zuse (Z3 program controlled relay computer) Programming language • Konrad Zuse (Plankalkül) Note For descriptions of the life and work of numerous German computing pioneers, see Friedrich Genser: Hommage an Konrad Zuse, Superbrain-Verlag, Düsseldorf, Balje 2013. Great Britain; see UK Greece Astrolabe • Hipparchus Astronomical calculating machine • Antikythera mechanism (inventor unknown) Abacus • Greek counting board (inventor unknown) Pantograph (with gear train) • Heron of Alexandria (place of work Egypt) Automatons • Heron of Alexandria (automatic puppet theater) Hungary Mechanical calculating machine • Ferdinand Hebentanz (adding machine) Programmable computer • John von Neumann (computer architecture and flow diagram, place of work USA) Ireland Cylindrical slide rules • George Fuller (spiral cylindrical slide rule)

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Mechanical calculating device • Percy Ludgate (analytical engine: program controlled calculator with forward and0 backward jump instruction) Programmable computer • George Boole (Boolean algebra) Italy Counting with the fingers • Luca Pacioli (finger numbers) Mathematical plotting, measuring, and calculating devices • Federico Commandino (proportional dividers) • Guidobaldo del Monte (sector) • Galileo Galilei (sector) • Tito Gonnella (wheel and disc planimeter) • Fabrizio Mordente (sector) Automaton figures (robots) • Leonardo da Vinci (mechanical knight, mechanical lion) Self-propelled cart • Leonardo da Vinci (programmable spring-driven vehicle for demon­strations) Mechanical calculating devices • Tito Livio Burattini (addition and multiplication device) • Tito Gonnella (keyboard adding machine) • Roberto Piscicelli (electromechanical pinwheel machine) • Giovanni Poleni (pinwheel machine) • Luigi Torchi (keyboard calculating machine) Programming • Corrado Böhm (compiler) (place of work Switzerland) Typewriters • Peter Mitterhofer (place of work South Tyrol) Japan Programmable computers • Motinori Goto (ETL Mark 1 and 2 relay computers) • Jasuo Komamija (ETL Mark 1 and 2 relay computers) Lithuania Mechanical calculating machines • Jevno Jacobson (addition and subtraction device with multiplication table) New Zealand Difference engine • Leslie John Comrie (use of a bookkeeping machine as difference engine, place of work England)

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Norway Differential analyzer • Svein Rosseland Poland Mathematical plotting, measuring, and calculating devices • Bruno Abdank-Abakanowicz (integraph) Mechanical calculating machines • Israel Abraham Staffel (four-function machine) Decryption device • Marian Rejewski (bomba) Russia Mechanical calculating machines • Pafnuty Lvovich Chebyshev (four-function machine) • Zinovy (Zelg) J. Slonimsky (adding machine, multiplication machine) Programmable computers • Yuri Y. Basilevsky (Strela vacuum tube computer) • Isaac Semenovich Bruk (differential analyzer, M-2 and M-3 vacuum tube computers) • Sergey Alexeyevich Lebedev (Mesm electronic computer, Besm vacuum tube computer, stored program) (place of work Ukraine) • Bashir Iskandarovich Rameyev (Strela and Ural vacuum tube computers) Programming • Alexander Mikhailovich Lyapunov (automatic programming, programming course) Slovakia Mechanical calculating machines • Didier Roth (adding machine, multiplication machine (pinwheel machine)) (place of work France) Spain Mechanical calculating machines • Leonardo Torres Quevedo (analog algebraic machine for the solution of equations, digital electromechanical (arithmetic) calculating machine with automatic multiplication and division and linking to a typewriter by cable connections, chess endgame machine, treatise on floating point notation) • Ramón Verea (direct multiplier) Sweden Mechanical calculating machines • Willgodt Theophil Odhner (pinwheel machine, place of work Russia) • Edvard Raphael Scheutz (difference engines with printout) • Pehr Georg Scheutz (difference engines with printout) • Martin Wiberg (difference engine with printout)

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Programmable computers • Conny Palm (Bark relay computer) Switzerland Logarithms • Jost Bürgi (logarithms, variable proportional dividers, places of work Germany and Czech Republic) Slide rules • Heinrich Daemen Schmid (cylindrical slide rule) Mathematical plotting, measuring, and calculating devices • Jakob Amsler (polar planimeter) • Gottlieb Coradi (manufacturer, builder) • Heinrich Rudolf Ernst (mechanic) • Jakob Goldschmid (mechanic, pantograph) • Johannes Oppikofer (planimeter) • Kaspar Wetli (planimeter) Automaton figures • Pierre Jaquet-Droz (father) • Henri-Louis Jaquet-Droz (son) • Jean-Frédéric Leschot • Henri Maillardet Mechanical calculating machines • Victor Schilt (keyboard adding machine, replica of Schwilgué machine) • Otto Steiger (Millionaire direct multiplier) Turing machine • Paul Bernays (principles of mathematics) Programming • Heinz Rutishauser (automatic programming, Algol programming language) • Niklaus Wirth (Pascal programming language) UK Logarithms • Henry Briggs (decadic or common logarithms) • John Napier (logarithms, Napier’s bones) Slide rules • Edmund Gunter (Gunter logarithmic scale (Gunter’s line)) • William Oughtred (slide rule, circular slide rule) Mathematical plotting, measuring, and calculating devices • Thomas Hood (sector) • James Thomson (planimeter, integrator) • William Thomson/Lord Kelvin (feedback principle, tide predictor, harmonic analyzer)

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Automaton figure • Timothy Williamson Integrating machines • Douglas Hartree (differential analyzer) • Arthur Porter (differential analyzer) Mechanical totalizer (counter register for wagers) • George Julius (places of work New Zealand and Australia) Mechanical calculating machines • Charles Babbage (difference engine) • Samuel Morland (cogged disc adding machine without tens carry and without subtraction, device with multiplication and division drums) • Charles Stanhope (stepped drum and toothed segment machine, cogged disc adding machine) Programmable computers • Charles Babbage (analytical engine, subprogram, program loop, conditional jump) • Andrew Donald Booth (magnetic drum memory) • Thomas Flowers (Colossus) • Thomas Kilburn (memory tube, Manchester Baby small-scale experimental machine) • Trevor Pearcey (Csirac electronic computer, place of work Australia) • Alan Turing (Pilot Ace with microprogramming) • Maurice Wilkes (Edsac with microprogramming) • Frederic Williams (memory tube, Manchester Baby small-scale experimental machine) Turing machine • Alan Turing (universal Turing machine) Programming • Alick E.  Glennie (autocode compiler, Royal Armaments Research Establishment, Fort Halstead) • Ada Lovelace (ostensibly Bernoulli numbers) • Maurice Wilkes (microprogramming, subprograms, programming manual) USA Cylindrical slide rule • Edwin Thacher (parallel cylindrical slide rule) Differential analyzers • Vannevar Bush • George A. Philbrick (electronic analog computer) Punched card machines • Herman Hollerith (punched card machine) • James Legrand Powers (punched card machine)

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Mechanical calculating machines • Harold T. Avery (proportional gear machine) • Frank Stephen Baldwin (pinwheel machine) • William Seward Burroughs (key-driven segment adding machine with printout) • Dorr Eugene Felt (macaroni box: key-driven comptometer without printout • George Barnard Grant (difference engine) • Du Bois D. Parmelee (single-column key-driven adding machine) Programmable computers • Howard Aiken/IBM (Harvard Mark relay computer) • John Atanasoff (ABC electronic computer) • Presper Eckert (Eniac electronic computer and computer design) • Herman Goldstine (flow diagram) • John Mauchly (Eniac electronic computer) • Claude Elwood Shannon (information theory, switching algebra) • George Stibitz (Bell relay computers) Remark The ABC electronic computer of John Atanasoff was fix-programmed. Turing machine • Alonzo Church (Lambda delta calculus, Church-Turing thesis) • Emil Post (mathematical computer model) Programming • Grace Hopper (compiler). What Were the Professions of the Pioneers? We have mostly philosophers, polymaths, and astronomers for the early inventions and discoveries of computing. In addition, engineers, technicians, clockmakers, and instrument and automaton builders played a decisive role. Goldsmiths also manufactured automatons.

6.2  Who Invented Which Calculating Aid When? The following list gives selected masterpieces of computing technology (in alphabetical order in the individual areas because the times cited are sometimes uncertain). Inventors of Calculating Aids Logarithms Henry Briggs (England, common logarithms)...................................... 1617 Jost Bürgi (Switzerland)....................................................................... 1620 1) John Napier (Scotland)......................................................................... 1614

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Slide rule Edmund Gunter (England, Gunter logarithmic scale (Gunter’s line)).... 1620 William Oughtred (England)................................................................ 1622 Circular slide rule William Oughtred (England)................................................................ 1630 Napier’s bones (Napier’s rods) John Napier (Scotland)......................................................................... 1617 Cylindrical slide rule George Fuller (Ireland, spiral cylindrical slide rule)............................ 1878 Edwin Thacher (USA, parallel cylindrical slide rule)........................... 1881 Pantograph Christoph Scheiner (Germany)............................................................. 1603 Sector Michiel Coignet (Belgium), around...................................................... 1580 2) Humphrey Cole (England)................................................................... 1576 2) Guidobaldo del Monte (Italy), around.................................................. 1569 2) Galileo Galilei (Italy)............................................................................ 1598 2) Fabrizio Mordente (Italy), around........................................................ 1560 2) Proportional dividers Jacques Besson (France)...................................................................... 1571 3) Jost Bürgi (Switzerland), around.......................................................... 1600 3) Federico Commandino (Italy).............................................................. 1568 3) Planimeter Tito Gonnella (Italy)............................................................................. 1824 Johann Martin Hermann (Germany).................................................... 1814 Johannes Oppikofer (Switzerland)....................................................... 1827 Kaspar Wetli (Switzerland).................................................................. 1849 Polar planimeter Jakob Amsler (Switzerland)................................................................. 1854 Albert Miller, Ritter von Hauenfels (Leoben, Austria).......................... 1855 Tide predictor/feedback principle William Thomson/Lord Kelvin (Northern Ireland)............................... 1876

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Analog mechanical (algebraic) calculating machine Leonardo Torres Quevedo (Spain)........................................................ 1893 Universal mechanical integrating machine Vannevar Bush (USA)........................................................................... 1930 Universal electronic analog computer Helmut Hoelzer (Germany).................................................................. 1941 Mechanical calculating machine • Proportional rod Christel Hamann (Germany)........................................................... 1905 • Proportional wheel Harold T. Avery (USA)..................................................................... 1932 • Ratchet Christel Hamann (Germany)........................................................... 1925 • Pinwheel Gottfried Wilhelm Leibniz (Germany)............................................. 1673 Giovanni Poleni (Italy).................................................................... 1709 • Stepped drum Gottfried Wilhelm Leibniz (Germany)............................................. 1682 • Toothed segment Carl Mauritz Friden (Sweden, place of work USA)........................... 1921 Electromechanical calculating machine with typewriter (remote control) Leonardo Torres Quevedo (Spain, experimental device)...................... 1920 4) Slide bar adder Heinrich Kummer (Germany)............................................................... 1847 Louis Troncet (France)......................................................................... 1889 Addition and subtraction machine Blaise Pascal (France).......................................................................... 1642 Addition and subtraction machine with multiplication and division device Wilhelm Schickard (Germany)............................................................. 1623 Four-function machine Gottfried Wilhelm Leibniz (Germany).................................................. 1673 Charles-Xavier Thomas (France).......................................................... 1820 5)

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Keyboard calculating machine Du Bois D. Parmelee (USA)................................................................... 1850 Victor Schilt (Switzerland, replica)...................................................... 1850 Jean-Baptiste Schwilgué (France)........................................................ 1844 Luigi Torchi (Italy)............................................................................... 1834 Automaton figure (human, animal) Leonardo da Vinci (Italy)..................................................................... 1495 Henri-Louis Jaquet-Droz, Pierre Jaquet-Droz (Switzerland).................. 1774 Peter Kintzing (Germany)..................................................................... 1784 Friedrich Knaus (Germany).................................................................. 1760 Jacques Vaucanson (France)................................................................ 1738 Punched card and punched tape control (loom) Basile Bouchon (France)...................................................................... 1725 Jean-Baptiste Falcon (France).............................................................. 1728 Joseph-Marie Jacquard (France)........................................................... 1805 6) Jacques Vaucanson (France)................................................................ 1745 Difference engine Charles Babbage (England, uncompleted)........................................... 1832 Edvard Scheutz, Pehr Georg Scheutz (Sweden).................................... 1853 Martin Wiberg (Sweden)...................................................................... 1860 Analytical engine (program controlled calculating machine) Charles Babbage (England, uncompleted)........................................... 1834 Percy Ludgate (Ireland)........................................................................ 1909 Leonardo Torres Quevedo (Spain, experimental device)...................... 1920 4) Punched card machine Herman Hollerith (USA)....................................................................... 1890 7) James Powers (USA)............................................................................. 1911 Remote controlled fix-programmed digital computer (relay computer) George Stibitz (USA)............................................................................. 1940 Fix-programmed digital computer (vacuum tube computer) John Atanasoff, Clifford Berry (USA).................................................... 1942 Tape controlled digital computer (relay computers) Howard Aiken, Clair Lake (USA).......................................................... 1944 Konrad Zuse (Germany)....................................................................... 1941

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Plugboard controlled digital computer (electronic computers) Presper Eckert, John Mauchly (USA).................................................... 1946 Thomas Flowers (England).................................................................. 1943 Stored-program digital computer (vacuum tube computers) Maurice Wilkes (England).................................................................... 1949 Frederic Williams, Thomas Kilburn (England)..................................... 1948 Universal Turing machine Alan Turing (England)......................................................................... 1936 8) Stored program Alan Turing (England)......................................................................... 1936 John von Neumann (Hungary)............................................................. 1945 Konrad Zuse (Germany)....................................................................... 1936 Von Neumann architecture John von Neumann (Hungary)............................................................. 1945 Programming language (Plankalkül) Konrad Zuse (Germany)....................................................................... 1946 Automatic programming Heinz Rutishauser (Switzerland)......................................................... 1951 Compiler Alick Glennie (England)....................................................................... 1952 Grace Hopper (USA)............................................................................. 1952 Remarks In regard to the time of the invention of the slide rule and the circular slide rule by William Oughtred, there are conflicting views. The publication of the invention only appeared at a later date. (1) 1620 = year of publication; the development of logarithms by Jost Bürgi was already before 1600. (2) Galileo Galilei claimed to be the inventor of the sector, but he was not the first designer. The original form probably derives from Guidobaldo del Monte (around 1569). Fabrizio Mordente developed an intermediate stage (around 1560). An important precursor was Michiel Coignet (around 1580) (see Ivo Schneider: Der Proportionalzirkel, R. Oldenbourg Verlag, Munich 1971, pages 17–49).

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(3) Pairs of compasses with fixed pivot (proportional dividers) were already in existence in antiquity. Leonardo da Vinci considered designs for this instrument; Jost Bürgi built a form with tips at all four ends (see Ivo Schneider: Der Proportionalzirkel, R.  Oldenbourg Verlag, Munich 1971, pages 17–49). (4) Year in which the machine was exhibited in Paris. In 1914 Leonardo Torres Quevedo already introduced an automatic chess machine in Paris. (5) Commercially available calculating machine (mass production of the arithmometer from around 1850). (6) The year of the patent was 1801. Joseph-Marie Jacquard was not the inventor of the loom; the first inventor was Basile Bouchon. In addition to 1805, the year 1804 is also mentioned. (7) Year in which the Hollerith punched card machines were used for the American census. (8) Equivalent developments by Emil Post and Alonzo Church (both USA, both 1936). Note Heron of Alexandria had already invented a pantograph (with gear train). See Sect. 4.6.2. Section 15.1.2 discusses the automaton builders at greater length. The opinions in regard to the originators of the stored program differ considerably. Presper Eckert and John Mauchly must also be mentioned.

6.3  New Inventions of Fundamental Importance Two inventions with global impact should be mentioned here: • The World Wide Web: Tim Berners-Lee, Cern, Geneva, 1989 • The Smartphone (iPhone): Steve Jobs, Apple, Cupertino, California, 2007.

6.4  Manufacturers of Calculating Aids Below is a brief selection of leading manufacturers in the German-speaking countries: Slide rules (linear slide rules, circular slide rules, cylindrical slide rules) • Heinrich Daemen Schmid, Zurich and Uster ZH • Johann Christian Dennert/Hans Dennert (Dennert & Pape, Aristo, Hamburg-­ Altona, Germany) • Lothar Faber (Faber-Castell, Stein near Nuremberg, Germany) • Albert Nestler (Lahr, Baden/Black Forest, Germany)

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Mechanical calculating machines • Arthur Burkhardt, Glashütte, Germany (arithmometers) • Hans W. Egli, Zurich (Millionaire, Madas) • Curt Herzstark, Mauren, Liechtenstein (Contina: Curta) • Samuel Jacob Herzstark, Vienna (Austria) • Ernst Jost, Zurich (Precisa) • Albert Natalis, Braunschweig (Brunsviga-Maschinenwerke, Grimme, Natalis: Brunsviga) Note Besides the Burkhardt arithmometer and the Brunsviga, above all in Germany, there was a wide-ranging offering of mechanical calculating machines, such as Archimedes, Astra, Badenia, Diehl, Hamann, Lipsia, Mercedes-Euklid, Olympia, Rheinmetall, Saxonia, Thales, Tim, Triumphator, Unitas, and Walther. Mathematical plotting and measuring devices • Jakob Amsler, Schaffhausen SH • Gottlieb Coradi, Zurich • Gebrüder Haff, Pfronten, Germany • Jakob Kern, Aarau AG • Albert Ott, Kempten, Germany Differential analyzers, electromechanical, and electronic analog computers • Amsler, Schaffhausen SH • Contraves, Zurich • Güttinger, Teufen AR • Hasler, Bern, Switzerland • Schoppe & Faeser, Minden (Hermann Schoppe, Hugo Faeser) (Germany) • Telefunken, Ulm, Germany Also: Brown, Boveri & Cie. Boveri (BBC, Baden, Switzerland), Dornier (Friedrichshafen, Germany), Siemens & Halske (Berlin/Munich) The Electronic Associates, Inc., Long Branch, New Jersey, is considered the market leader for analog computers. Another important manufacturer was the Japanese Hitachi company. Cryptographic machines • Crypto, Steinhausen ZG • Gretag, Regensdorf ZH. The following illustrations show two electronic analog computers (see Figs. 6.1 and 6.2) and a cipher machine (see Fig. 6.3).

Fig. 6.1  Electronic analog computer (1). This first product of the Güttinger engineering office, the analog computer AR-2, was equipped with 12 operational amplifiers. A further analog computing device was the AR-3. For many years there was competition between analog and digital computers. Swiss manufacturers of mechanical or (less commonly) electronic analog computers were Amsler, BBC, Contraves, Güttinger, and Hasler (© NUM, Teufen)

Fig. 6.2  Electronic analog computer 2. The analog computers of the former Güttinger AG in Teufen AR are long since only history (© NUM, Teufen)

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Fig. 6.3  Cipher machine. The C-52 mechanical cryptographic machine (1952) with six rotors was the first coding machine built by the former Crypto AG. This model, with rod wheel technology, proved to be especially successful. The Swedish engineer Boris Hagelin founded the Swiss Zug company (© Crypto AG)

The Calculator and Computer Industry The manufacturers of calculating aids came from different fields: clockmaking, precision mechanics, optics, surveying, office machines, machine tool construction, sewing machines, insurances, electrical engineering, communications technology, aircraft manufacturing, etc. In some cases these were (former) armorers: examples are Contraves (Zurich), Mercedes Büromaschinenund Waffenfabrik (Zella-Mehlis, Germany), Rheinmetall (Sömmerda, Germany), and Waffenfabrik Mauser (Oberndorf am Neckar, Germany). The mass production of mechanical calculating machines began in Paris around 1850 with the stepped drum machines of Thomas (patenting of the arithmometer in 1820). The first German calculating machine factory was founded in 1878  in Glashütte (Saxony) by Arthur Burkhardt (copy of the Thomas arithmometer). The mass production of the pinwheel machine of the Swedish engineer Willgodt Theophil Odhner began in 1886 in the Russian city of St. Petersburg. Grimme, Natalis & Co. (GNC) from Braunschweig (Germany) acquired a license from Odhner (Brunsviga machines). Hans W. Egli began with the mass production of the Millionaire direct multiplying machine in Munich in the 1890s. He soon moved on to Zurich. Adding machines, e.g., from Burroughs and Felt and Tarrant were at first in high demand above all in North America. Addiator was the leading German manufacturer of slide bar adders. The best known supplier of mechanical pocket calculating machines was the Liechtenstein Contina company (Curta). Among the global market leaders for mathematical instruments (plotting, measuring, and calculating devices) were Amsler (Schaffhausen), Coradi (Zurich), and Ott (Kempten). The Haff company has survived to this day. The mathematical-mechanical institute G(ottlieb) Coradi in Zurich offered, e.g., pantographs, affinographs, planimeters, integrators, integraphs, curvimeters, harmonic analyzers, and coordinatographs. In addition to the pioneering mathematical instruments, Alfred J.  Amsler & Co., Schaffhausen, manufactured numerous other devices (such as measuring instruments). The most important manufacturers of punched card machines were International Business Machines (Hollerith) and Remington Rand (Powers).

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The first important suppliers of stored-program electronic computers were Ferranti (England) and Remington Rand (Univac, USA). The most successful supplier of electronic analog computers in the German-­ speaking countries was probably Telefunken. In Switzerland, BBC, Contraves, and Güttinger, for example, offered analog machines. Further Reading Arithmeum (editor): Arithmeum, Rechnen einst und heute, Universität Bonn, Bonn 1999 Friedrich Ludwig Bauer: Kurze Geschichte der Informatik, Wilhelm Fink Verlag, Munich 2007 Joachim Fischer: Instrumente zur mechanischen Integration, in: Hans Werner Schütt, Burghard Weiß (editors): Brückenschläge, Verlag für Wissenschaftsund Regionalgeschichte Dr. Michael Engel, Berlin 1995, pages 111–156 Joachim Fischer: Instrumente zur mechanischen Integration II, in: Astrid Schürmann, Burghard Weiß (editors): Chemie – Kultur – Geschichte, GNT Verlag, Berlin 2002, pages 143–156 Andreas Wilhelm Gottfried Galle: Mathematische Instrumente, B. G. Teubner, Leipzig, Berlin 1912 Peter Haertel: Die Klassifikation mechanischer Rechenmaschinen, in: Historische Bürowelt, March 1996, volume 45, pages 6–43 Peter Haertel: Die Klassifizierung mechanischer Rechenmaschinen, in: Historische Bürowelt, December 2011, volume 86, pages 12–24 Annegret Kehrbaum; Bernhard Korte: Historische Rechenmaschinen im Forschungsinstitut für diskrete Mathematik Bonn, in: DMV Mitteilungen, 1993, volume 1, pages 18–31 and 33 and volume 2, pages 8–20 Bernhard Korte: Zur Geschichte des maschinellen Rechnens, Bouvier Verlag Herbert Grundmann, Bonn 1981 Peter Kradolfer: Einige Rosinen aus der Entwicklung der Rechenmaschinen, Verlag Sauerländer, Aarau 1988 Walther Meyer zur Capellen: Mathematische Instrumente, Akademische Verlagsgesellschaft Geest und Portig KG, Leipzig 1949 Francis J.  Murray: Mathematical machines, Columbia university press, New York 1961 (2 volumes) Hansjörg Nipp: Curta, Carena & Co. Geschichte der Contina in Mauren, Alpenland Verlag AG, Schaan FL 2017 Hartmut Petzold: Rechnende Maschinen, VDI Verlag, Düsseldorf 1985 Hartmut Petzold: Moderne Rechenkünstler, Verlag C.H. Beck, Munich 1992 Gérald Saudan: Swiss calculating machines, Yens sur Morges VD 2017 (self-published) Ivo Schneider: Der Proportionalzirkel, R. Oldenbourg Verlag, Munich 1971 Hans-Joachim Vollrath: Verborgene Ideen, Springer Fachmedien, Wiesbaden 2013 Friedrich Adolf Willers: Mathematische Instrumente, R.  Oldenbourg Verlag, Munich, Berlin 1943 Friedrich Adolf Willers: Mathematische Maschinen und Instrumente, Akademie Verlag, Berlin 1951 Michael Roy Williams: A history of computing technology, IEEE Computer society press, Los Alamitos NM 1997

Chapter 7

Conferences and Institutes

Abstract  This chapter presents a global overview of important conferences in the early days of computer science. From 1945 on, these were held mostly in the USA. In 1951 a large international conference took place in Paris which, in spite of comprehensive documentation (however in French), remains virtually unknown. The first significant conference on the history of computer science was organized in 1976. In 2012 numerous events commemorated the 100th birthday of Alan Turing. The first institutes for computing technology, which arose especially in the USA and the UK, are listed as well. Worldwide, there are several associations focusing on the history of calculating and computing technology. Keywords  Associations for the history of computer science · Associations for the history of computing technology · Early institutes of computer science · First conferences on computer science

7.1  Early Conferences on Computer Science The first conferences on digital computers were held in the 1940s. There was a substantial backlog in the postwar years. USA 1945 1947 1949

Conference on advanced computation techniques, Massachusetts Institute of Technology (MIT), Cambridge, Massachusetts (October) Symposium on large-scale digital calculating machinery, Harvard University, Cambridge, Massachusetts (January) Second symposium on large-scale digital calculating machinery, Harvard University, Cambridge, Massachusetts (September)

© Springer Nature Switzerland AG 2020 H. Bruderer, Milestones in Analog and Digital Computing, https://doi.org/10.1007/978-3-030-40974-6_7

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Joint AIEE-IRE computer conference: “Review of electronic digital computers,” Philadelphia, Pennsylvania (AIEE = American Institute of Electrical Engineers, IRE = Institute of Radio Engineers) (December) Joint AIEE-IRE computer conference: “Review of input and output equipment used in computing systems,” New York (American Institute of Electrical Engineers, Institute of Radio Engineers, Association for Computing Machinery) (December) Symposium on automatic programming for digital computers, Office of Naval Research (ONR), Department of the Navy, Washington, D.C. (May) Symposium on “automatic coding,” Franklin Institute, Philadelphia, Pennsylvania, Pennsylvania (January)

Alan Turing was the only British participant at the Harvard University symposium in 1947. Of considerable importance was a series of lectures at the University of Pennsylvania in Philadelphia, in which specialists from Europe also took part: Seminar 1946 Moore School lectures “Theory and techniques for design of electronic digital computers,” University of Pennsylvania, Philadelphia (July/August) In 1946/1947 Wallace Eckert and Herbert Griosch offered a computer seminar at Columbia University in New  York. In 1947/1948 Harvard University in Cambridge, Massachusetts, introduced a master’s program in computer science. W. Gordon Welchman (originally of Bletchley Park) is said to have held the first series of lectures about digital computers within the scope of his activities for the large-scale Whirlwind computer in the Electrical Engineering Department of MIT. The IBM Scientific Computation Forum was held in 1940, 1946, 1947, 1948, 1949, and three times in the 1950s in New York. Topics: processes for the solution of scientific problems with IBM punched card machines. (IBM stands for International Business Machines.) In place of the joint AIEE-IRE computer conference, from 1953 to 1961, a Western joint computer conference (west coast) and an Eastern joint computer conference (east coast) took place on a yearly basis. From 1962 to 1972, a spring joint computer conference and a fall joint computer conference were held every year. From 1973 to 1987, there was a (single) national computer conference each year in an American city (see Heinz Zemanek: Weltmacht Computer, Bechtle Verlag, Esslingen, Munich 1991, pages 447–448).

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The First Important Conference on the History of Computer Science 1976 International Research Conference on the History of Computing, Los Alamos Scientific Laboratory, Los Alamos, New Mexico (June) Australia 1951 Conference on automatic computing machines, University of Sydney (August) Canada 1945 First Canadian mathematical congress, Montreal, McGill University/ University of Montreal (June) France 1951 Colloque international du CNRS “Les machines à calculer et la pensée humaine,” Paris (January) (CNRS = Centre national de la recherche scientifique) Germany 1952 Kolloquium über programmgesteuerte Rechengeräte und Integrier­ anlagen, Rheinisch-westfälische Technische Hochschule, Aachen (July) 1953 Kolloquium über Rechenanlagen, Max-Planck-Institut für Physik, Göttingen (March) 1955 Symposium “Elektronische Rechenmaschinen und Information­ sverarbeitung,” Technische Hochschule, Darmstadt (October) 1955 Internationales Mathematiker-Kolloquium über aktuelle Probleme der Rechentechnik, Technische Hochschule, Dresden (November) Russia 1956 All-union conference: Prospects for the development of Soviet mathematical machinery and instrumentation, Moscow State University (March) The first global computer congress took place in June 1959 under the sponsorship of UNESCO in Paris. This led to the beginning of the International Federation for Information Processing (IFIP) conferences in 1960. UK 1949 1951

Conference on high-speed automatic calculating machines, Cambridge University (June) Manchester University computer, inaugural conference (July)

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International symposium on automatic digital computation, National Physical Laboratory, Teddington (March) Symposium on the “Mechanisation of thought “processes”, National Physical Laboratory, Teddington (November)

Lecture Series 1946/1947 Lectures by James Wilkinson and Alan Turing regarding the design of the Ace electronic computer, Ministry of Supply, London The first large European conference on computer science took place in Paris (see box).

Paris: International Conference “Computing Machines and Human Thought Processes” In 1951 the most important early European conference on computer science was held in Paris. As the title and the program suggest, one could regard this well-documented event as the first significant conference on artificial intelligence. 15 of the 38 presentations were devoted to the subject “large-scale computers, logic and physiology of the nerve system.” The occasion was supported by The Rockefeller Foundation. Both analog and digital machines were dealt with. In 1950 the first ten program controlled relay and vacuum tube computers appeared in Europe. 268 professionals, including 10 women (mostly “calculatrices”, i.e., female calculating specialists), from 12 countries are documented in an 11-page list of participants. 190 were from the host country France and 41 from England, where several electronic digital computers had already been built or were being built. Similar projects were also underway in Sweden (four participants), the Netherlands (nine), and Belgium (six) (see Fig. 7.1). In consideration of the devastating damage inflicted by the war in Europe, travel restrictions, and lack of money, the degree of participation was remarkably high. All important British research centers were represented. However, Alan Turing did not take part. Instead his colleague Francis Colebrook, head of the Electronics Department of the Londoner National Physical Laboratory, and Frederic Williams of the University of Manchester were present. The computer industry was also in attendance: the British Tabulating Machine Co. (London and Letchworth), Compagnie des machines Bull (Paris), Société d’électronique et d’automatisme (Paris and Courbevoie, France), Elliott Brothers Research Laboratories (Borehamwood, (continued)

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England), Messrs. Ferranti Ltd. (Manchester), International Business Machine Co. (Paris), Société Logabax Audibel (Paris and Malakoff, France), Société anonyme Philips (Paris and Hilversum, Netherlands), Société anonyme des machines à statistiques Powers (Paris), PowersSamas Accounting Machines (London), and Powers Tabulating Remington Rand (Brussels). The goal of the conference was without doubt the exchange of knowledge, experience, and opinions. Some speakers were already familiar with programmable, i.e., program controlled, and stored-program relay and vacuum tube computers, e.g., Aiken, Booth, Colebrook, Hartree, Kilburn, Stiefel, Wilkes, and Williams. Several cyberneticists and neurologists visited the event, including Ashby, McCulloch, Walter, and Wiener. In the 1950s numerous European universities began to build their own large-scale computers. During this time the first attempts were made to develop machine language translation systems. Although the computing power and the memory capacity were still rather limited, soon there were many such systems around the world (see Herbert Bruderer: Handbuch der maschinellen und maschinenunterstützten Sprachübersetzung. Automatische Übersetzung natürlicher Sprachen und mehrsprachige Terminologiedatenbanken, K.  G. Saur Verlag, Munich/Walter de Gruyter, Berlin etc. 1978). Functional machines were exhibited in Paris: • A chess-playing automaton, Telekino, as well as an analog calculating machine with endless spindle of Leonardo Torres Quevedo • Artificial animals of W. Grey Walter • The homeostat of William Ross Ashby On the 12th or 13th of January 1951, the North American cyberneticist Norbert Wiener played chess against the chess-playing automaton of Leonardo Torres Quevedo, operated by the inventor’s son. Eduard Stiefel of the ETH Zurich presented the first experiences with the Zuse Z4. All lectures were translated into French by the Centre national de la recherche scientifique. The extensive conference proceedings (see Fig. 7.2) exist only in French. This is probably the reason why this conference of major importance for the early period in the history of computer science is unjustly hardly known in the Anglo-American world. Conference Proceedings Joseph Pérès (editor): Les machines à calculer et la pensée humaine, Paris, January 8–13 1951, Editions du Centre national de la recherche scientifique (CNRS), Paris 1953.

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7  Conferences and Institutes Belgium; 6; 2% Spain; 5; 2% Brazil; 1; 1% Switzerland; 1; 0% USA, 5, 2% Sweden; 4; 2% Germany; 1; 0% Netherlands; 9; 3% Yugoslavia; 1; 0% Italy; 4; 2%

United Kingdom; 41; 15%

France; 190; 71% Internationalconference "Les machines à calculer et la pensée humaine" Paris, January 1951 268 participants from 12 countries © Bruderer Informatik,CH-9401 Rorschach, Switzerland 2020 Source: Proceedings, CNRS, Paris 1953

Fig. 7.1  Participants at the Paris conference in 1951. 268 persons attended the conference, 41 of these from England. (© Bruderer Informatik, CH-9401 Rorschach, Switzerland)

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Fig. 7.2  Proceedings of the 1951 conference in Paris. The papers of the Paris computer science conference were reproduced in French translations in 1953 in a comprehensive book. (Source: ETH Library, Zurich)

Among the prominent persons taking part in the Paris conference were: • • • • • • • • • • • • •

Howard Hathaway Aiken (Harvard University, Cambridge, Massachusetts) William Ross Ashby (Barnwood House Hospital, Gloucester, England) Andrew Donald Booth (Birkbeck College, University of London) Bertram Vivian Bowden (Ferranti Ltd., Manchester, England) Francis Morley Colebrook (National Physical Laboratory, Teddington, Middlesex, England) Louis Couffignal (Institut Blaise Pascal, Paris) Stig Ekelöf (Chalmers University of Technology, Gothenburg, Sweden) Douglas Rayner Hartree (Cavendish Laboratory, Cambridge University, England) Thomas Kilburn (University of Manchester, England) Warren Sturgis McCulloch (Medical School, University of Illinois, Chicago) Mauro Picone (University of Rome) Eduard Stiefel (ETH Zurich) Gonzales Torres Quevedo (Madrid)

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• Albert M.  Uttley (Telecommunications Research Establishment, Great Malvern, England) • Adriaan van Wijngaarden (Mathematisch Centrum, Amsterdam) • W. Grey Walter (Burden Neurological Institute, Bristol, England) • Alwin Walther (Institut für Praktische Mathematik, University of Applied Sciences, Darmstadt, Germany) • Norbert Wiener (Massachusetts Institute of Technology, Cambridge, Massachusetts) • Maurice Vincent Wilkes (Mathematical Laboratory, Cambridge University, England) • Frederic Calland Williams (University of Manchester, England) • John Ronald Womersley (British Tabulating Machine Co, Letchworth, England). Source List of participants, pages IX–XIX of the conference proceedings Man Versus Machine: Wiener Versus a Chess-Playing Automaton According to the report of Brian Carpenter (see references below), one of those taking part was the scientific editor of Le Figaro. He was the author of a book about artificial thought processes that appeared in several editions and was also translated into English: Pierre de Latil: La pensée artificielle, Librairie Gallimard, Paris 1953 / Thinking by machine. A study of cybernetics, Houghton Mifflin company, Sidgwick and Jackson, Boston 1957. The book includes eight black and white photos. These showed, e.g., the four leading cyberneticists (William Ross Ashby, Warren Sturgis McCulloch, W. Grey Walter, and Norbert Wiener), a conversation between Louis Couffignal and Howard Aiken, the Elsie electronic turtle (“premier animal artificiel au monde”, [allegedly] the world’s first artificial animal), the homeostat (“la plus révolutionnaire machine du monde”, the world’s most revolutionary machine), and the chess-playing automaton of Leonardo Torres Quevedo. The text accompanying the last of these photos was (citing extracts): Le match de la mécanique classique contre la cybernétique […]. Au Congrès cybernétique de Paris 1951, G. Torrès-Quevedo, fils du grand automatiste qui construisit le célèbre joueur d’échecs électro-magnétique (à gauche), se mesure sur l’échiquier magique avec Norbert Wiener, le pape de la cybernétique. Ici, la mécanique classique gagne toujours. Partout ailleurs, elle perd (see Pierre de Latil: La pensée artificielle, Librairie Gallimard, Paris 1953, next to page 160).

Competition between classical mechanics and cybernetics […]. At the Cybernetics conference of 1951 in Paris, G. Torres Quevedo (left), the son of the great engineer who built the famous electromagnetic chess-playing automaton, pits himself against Norbert Wiener, the cyberneticist, on the magic chessboard (see Fig. 7.3). Here classical mechanics always wins, although this loses anywhere else.

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Fig. 7.3  Norbert Wiener and the chess automaton. In 1951 the American cyberneticist (at the right) at the Cybernetics conference in Paris against the chess automaton of Leonardo Torres Quevedo, operated by the son of the inventor (at the left). The machine (white, with king and rook) plays against the human chess player (black, with king). (© Studio Constantin, Paris)

[...] Torres y Quevedo had demonstrated a very impressive device in 1914, which played a king and a rook against an opponent’s king (Wiener played against a later version at the 1951 Cybernetic Conference in Paris.) (see Heinz Zemanek: Central European prehistory of computing, in: Nicholas Constantine Metropolis; Jack Howlett and Gian-Carlo Rota (editors): A history of computing in the twentieth century, Academic press, New York, London etc. 1980, pages 587–609).

In his memoirs Norbert Wiener speaks about his participation at the conference in Paris: These [duties] had become arduous because I was also to participate in a congress on high-­speed computing machines and automatization which was to take place in Paris in January 1951 (see Norbert Wiener: I am a mathematician, MIT press, Cambridge, Massachusetts, London 1973, pages 333–334).

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References Herbert Bruderer: The birth of artificial intelligence, in: Arthur Tatnall; Christopher Leslie (editor): International communities of invention and innovation, Springer international publishing AG Switzerland, Cham 2016, pages 181–185 Herbert Bruderer: Computing history beyond the U.K. and U.S.: Selected landmarks from Continental Europe, in: Communications of the ACM, volume 60, 2017, number2, pages 76–84 Herbert Bruderer: The birthplace of artificial intelligence?, https://cacm. acm.org/blogs/blog-cacm/222486-the-birthplace-of-artificial-intelligence/ fulltext Brian E. Carpenter: A meeting that missed its mark: the Paris conference of 1951, http://www.rutherfordjournal.org/article050103.html. Macy Conferences From 1946 to 1953, ten Macy conferences were convened (see Table 7.1). The Josiah Macy Foundation (New York) sponsored these events on the subject of cybernetics. In the years 1946 and 1947, a conference was held in March and also in October. From 1948 on there was only one conference, which took place in the spring. No conference proceedings exist for the first five conferences. Among those attending in 1949–1953 were, e.g.: Table 7.1  The Macy conferences Relatively few persons took part in the Macy conferences Year Month/day Place 1949 March 24–25 New York 1950 March 23–24 New York 1951 March 15–16 New York 1952 March 20–21 New York 1953 April 20–24 Princeton

Number of participants 25 26 25 29 28

© Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020

• • • • • • • •

W. Ross Ashby (Gloucester, England) Julian H. Bigelow (Princeton, New Jersey) Warren S. McCulloch (Chicago) Walter Pitts (Cambridge, Massachusetts) Claude E. Shannon (Murray Hill, New Jersey) John von Neumann (Princeton, New Jersey) W. Grey Walter (Bristol, England) Norbert Wiener (Cambridge, Massachusetts).

Alan Turing did not participate in 1949–1953. Source Claus Pias (editor): Cybernetics. The Macy conferences 1946–1953, Diaphanes, Zurich, Berlin 2016

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287

In the winter of 1943/1944, Herman Goldstine, Warren McCulloch, Walter Pitts, John von Neumann, and Norbert Wiener all attended a meeting in Princeton, for which no further details are known. Symposium on Artificial Intelligence From November 24 to 27, 1958, a symposium “Mechanisation of thought processes” took place at the National Physical Laboratory in Teddington, UK.  Among the topics were artificial intelligence in general, automatic programming, machine language translation, voice recognition, and machine learning. The speakers included William Ross Ashby, Grace Murray Hopper, John McCarthy, Warren Sturgis McCulloch, Marvin L.  Minsky, and Albert M. Uttley. Also present was W. Grey Walter. Source National Physical Laboratory (editor) Mechanisation of thought processes, Her Majesty’s stationery office, London 1959 (2 volumes) More Recent Conferences on the History of Computer Science International conferences on the global history of computer science are organized above all by the International Federation for Information Processing (IFIP). In recent years several conferences took place, e.g.: 2010 History of computing. Learning from the past, Brisbane, Australia 2013 Making the history of computing relevant, London, England 2016 International communities of invention and innovation, Brooklyn, New York, USA

7.2  Early Institutes for Computing Technology The first center for applied/practical mathematics was probably the Istituto per le Applicazioni del Calcolo of Mauro Picone, founded in 1927  in Naples (relocated to Rome in 1932). Below is an overview of selected institutions in alphabetical order of their countries, with the institutes in alphabetical order according to their locations. Australia • Division of Radiophysics, Commonwealth Scientific and Industrial Research Organization (CSIRO), Sydney (Trevor Pearcey and Maston Beard) Austria • Institut für Niederfrequenztechnik, Technische Hochschule Wien (now Technische Universität Wien) (Heinz Zemanek) France • Laboratoire de calcul mécanique de l’Institut Blaise Pascal of the Centre national de la recherche scientifique (CNRS), Paris/Châtillon-sous-Bagneux (Louis Couffignal)

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Germany • Institut für praktische Mathematik, Technische Hochschule Aachen (now Rheinisch-­westfälische Technische Hochschule) (Robert Sauer) • Mathematisches Institut, Technische Hochschule Aachen (now Rheinisch-­ westfälische Technische Hochschule) (Hubert Cremer) • Institut für praktische Mathematik (IPM), Technische Hochschule Darmstadt (now Technische Universität) (Alwin Oswald Walther, HansJoachim Dreyer) • Institut für maschinelle Rechentechnik, Technische Hochschule Dresden (now Technische Universität) (Friedrich Adolf Willers, Nikolaus Joachim Lehmann) • Institut für Instrumentenkunde, Max-Planck-Gesellschaft (later: MaxPlanck-­Institut für Physik), Göttingen (Ludwig Biermann, Heinz Billing) • Institut für elektrische Nachrichtentechnik und Messtechnik, Technische Hochschule München (now Technische Universität) (Hans Piloty (father), Robert Piloty (son)), and Mathematisches Institut, Technische Hochschule München (now Technische Universität) (Robert Sauer) Remark Technische Hochschule can be understood as Polytechnic. Italy • Istituto nazionale per le applicazioni del calcolo (Inac), since 1975 Istituto per le Applicazioni del Calcolo (IAC) “Mauro Picone,” Rome (Mauro Picone) • Centro internazionale di calcolo dell’Unesco (only much later UNESCO computing center with another purpose) Japan • Electrotechnical Laboratory of the Ministry for International Commerce and Industry, Tokyo (Motinori Goto, Yasuo Komamiya) The Netherlands • Mathematisch Centrum (MC), Amsterdam (Adriaan van Wijngaarden) • Optics Laboratory of the Delft Technical University (Willem Louis van der Pool) Russia • Institute for Precision Mechanics and Computer Technology of the Soviet Academy of Sciences, Moscow (Sergey Alexeyevich Lebedev) Spain • Laboratorio de mecánica aplicada (later: Laboratorio de automática), Madrid (Leonardo Torres Quevedo) Sweden • Matematikmaskinnämnden (Office of Computational Machinery), Stock­ holm (Conny Palm, Royal Institute of Technology (KTH), Stockholm)

7.2  Early Institutes for Computing Technology

289

Switzerland • Institut für angewandte Mathematik (IaM), ETH Zurich (Eduard Stiefel) Ukraine • Institute of Electrical Engineering of the Ukrainian Academy of Sciences, Kiev (Sergey Alexeyevich Lebedev) UK • Government Code and Cypher School (GC&CS), Bletchley Park (Max Newman, Alan Turing) • Cavendish Laboratory, Cambridge University (Charles Eryl Wynn-Williams, Douglas Rayner Hartree, John Pinkerton) • Mathematical Laboratory (later: Computer Laboratory), Cambridge University (Maurice Vincent Wilkes) • Electronic Computation Laboratory, Birkbeck College, University of London (Andrew Donald Booth) • Department of Mathematics, Imperial College of Science and Technology, London (Keith Tocher) • Post Office Research Station, Dollis Hill, London (Thomas Flowers) • Department of Electrotechnics (later: Department of Electrical Engineering), Royal Society Computing (Machine) Laboratory (later: Computing Machine Laboratory), University of Manchester (Frederic Calland Williams, Thomas Kilburn) • Physics Laboratory, University of Manchester (Douglas Rayner Hartree, Arthur Porter) • Mathematics Division, National Physical Laboratory (NPL), Teddington, Middlesex (John Womersley, Alan Turing) USA • Physics Department, Iowa State College, Ames (now Iowa State University) (John Atanasoff, Clifford Berry) • Cruft Laboratory (later Computation Laboratory) of Harvard University, Cambridge, Massachusetts (Howard Hathaway Aiken) • Lincoln Laboratory, Massachusetts Institute of Technology (MIT), Cambridge, Massachusetts (Kenneth Olsen) • Servomechanisms Laboratory (later: Digital Computer Laboratory), Massachusetts Institute of Technology (MIT), Cambridge , Massachusetts (Jay Wright Forrester, Robert Rivers Everett) • Bell Telephone Laboratories (BTL), New York (following the Second World War Murray Hill, New Jersey) (George Stibitz) • IBM Watson Scientific Computing Laboratory, Columbia University, New York (Wallace John Eckert) • Moore School of Electrical Engineering, University of Pennsylvania, Philadelphia (John William Mauchly, John Presper Eckert) • Institute for Advanced Study (IAS), Princeton, New Jersey (John von Neumann).

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7.3  Universities with an Illustrious Past Who had the most illustrious past in the early history of computer technology? At the top of the list is arguably the English Cambridge University, with Charles Babbage and Alan Turing. The following list is a selection of universities and does not claim to be complete. Europe Cambridge University • Digital mechanical analytical engine (Charles Babbage) • Universal Turing machine (Alan Turing) • Edsac stored-program digital electronic vacuum tube computer (Maurice Wilkes) University of Manchester • An0alog mechanical differential analyzer (Douglas Hartree) • Manchester Mark stored-program digital electronic vacuum tube computer (Frederic Williams, Thomas Kilburn) ETH Zurich • Automatic programming (Heinz Rutishauser) • Algol (Heinz Rutishauser and colleagues) Remark In earlier times famous scholars were often in the service of royal houses. In our summary, for example, Jost Bürgi (logarithms) and Gottfried Wilhelm Leibniz (digital mechanical four-function calculating machine) can be mentioned here. North America • Whirlwind digital electronic vacuum tube computer (Jay Forrester, Robert Everett) Iowa State University, Ames • ABC digital electronic vacuum tube computer (John Atanasoff, Clifford Berry) Harvard University, Cambridge, Massachusetts • Harvard Mark 1/IBM ASCC digital electromechanical relay computer (Howard Aiken/Clair Lake) Massachusetts Institute of Technology, Cambridge, Massachusetts • Analog mechanical differential analyzer (Vannevar Bush) University of Pennsylvania, Philadelphia • Eniac digital electronic vacuum tube computer (John Mauchly, Presper Eckert) • Edvac stored-program digital electronic vacuum tube computer (John Mauchly, Presper Eckert)

7.4  Associations and Journals for the History of Computer Science

291

Institute for Advanced Study (IAS), Princeton, New Jersey • Stored-program digital von Neumann computer (John von Neumann).

7.4  A  ssociations and Journals for the History of Computer Science A number of associations for the history of computing and the history of technology exist that deal with these fields regionally or internationally. The globally authoritative parent organization International Federation for Information Processing (IFIP), founded by UNESCO, organizes international conferences on the history of computer science, such as 2013  in London, 2016 in New York, and 2018 in Poland, and publishes the conference proceedings for these. The responsibility for these lies with Technical Committee TC 9 (“ICT and society”), or more exactly with the work group WG 9.7 “History of computing.” Below is an overview of selected institutions. Austria Here the Österreichische Gesellschaft für Informatikgeschichte addresses historically oriented topics. Germany The Deutsche Gesellschaft für Informatik (GI) was active in connection with the 100th birthday of Konrad Zuse. Within the GI is a Fachgruppe Informatikund Computergeschichte. The German Konrad-Zuse-Gesellschaft also deserves mention here. The Internationales Forum Historische Bürowelt (IFHB) is devoted to the preservation of mechanical calculating aids and typewriters and publishes the journal Historische Bürowelt. The Rechenschiebersammlertreff (RST) group occasionally organizes gatherings. The Netherlands The Kring Historische Rekeninstrumenten group is primarily concerned with slide rules. Switzerland The Sammlerclub historische Büromaschinen Schweiz (SHBS), disbanded in 2019 but still active, deals primarily with calculating machines and typewriters. Together with the Club der Radio- und Grammophon-Sammler, the Förderverein Enter issues the Histec Journal (Swiss journal for the history of technology). UK The activities of the British Computer Conservation Society (CCS) are exemplary. The society regularly sponsors events and publishes a newsletter,

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Resurrection. The society reconstructs computing devices of historical interest which have been destroyed and repairs no longer functioning devices, as well as maintaining these machines. The masterpieces are found in Bletchley Park, London, and Manchester. The members of the UK Slide Rule Circle (UKSRC) are dedicated to the preservation of slide rules. One of the few journals dealing with the history of mathematics is the Journal of the British Society for the History of Mathematics (BSHM). In 2012 a veritable flood of events around the world commemorated the 100th birthday of Alan Turing. In 2014 400 years of logarithms (John Napier, Edinburgh) were the occasion of celebration. USA The Special Interest Group on Computers, Information, and Society (Sigcis) of the Society for the History of Technology (Shot) is a globally active and highly committed institution. Another society is the IT History Society (ITHS). The Oughtred Society (OS) publishes a journal, the Journal of the Oughtred Society, which focuses on slide rules. The Charles Babbage Institute (CBI) of the University of Minnesota, Minneapolis, issues the CBI Newsletter. The internationally leading journal for the history of computer science is the IEEE Annals of the History of Computing. It is reviewed and appears quarterly. IEEE is the abbreviation for Institute of Electrical and Electronics Engineers. The association maintains an IEEE history center and a work group named the IEEE Computer Society History Committee, similar to the Association for Computing Machinery (ACM) with the ACM History Committee.

Chapter 8

Global Overview of Early Digital Computers (Tables)

Abstract  The chapter “Global Overview of Early Digital Computers (Tables)” gives an overview of the first (mechanical) relay and (electronic) vacuum tube computers. These are presented in alphabetical order and (in abbreviated form) in chronological order (1939–1953), together with the most important attributes and detailed descriptions. Examples are the Bell Labs mechanical relay computer (USA), the Harvard Mark perforated tape controlled relay machine (USA), the ABC special-purpose electronic computer (USA), the giant Eniac plug-­programmed vacuum tube computer (USA), the stored program Edvac (USA) and Edsac (UK) computers, the Princeton IAS computer (USA), which served as a model for many replicas, the decade-long top secret Colossus (UK), used for the deciphering of coded messages, the Ace machine, built according to the designs of Alan Turing (UK), the Zuse Z3 binary computer with floating point notation (Germany), and the mass-produced Ferranti Mark (UK), as well as the Univac (USA), IBM 650 and 701 (USA), and Leo (UK). Keywords  Bell computer · Colossus · Early digital computer · Electronic vacuum tube computer · Eniac · Ferranti · Harvard Mark · IBM · Leo · Mechanical relay computer · Princeton machine · Univac · Zuse Z3

8.1  Preliminary Remarks This compilation, based on surveys in the corresponding countries, is intended to convey an overview of the first digital automatic computers and simplify comparisons (see Tables 8.1, 8.2, and 8.3). The available primary literature and also the secondary literature were evaluated. Nevertheless, in the publications, contradictions and errors can be recognized. The information from the original texts was used in spite of occasional inconsistencies – especially in regard to the designated dates. The overview encompasses the early relay and vacuum tube computers and, as a rule, includes only the initial computers and initial models. ARC

© Springer Nature Switzerland AG 2020 H. Bruderer, Milestones in Analog and Digital Computing, https://doi.org/10.1007/978-3-030-40974-6_8

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8  Global Overview of Early Digital Computers (Tables)

(England), Bark (Sweden), Csirac (Australia), Mesm (Ukraine), and later ­versions for example of the Bell and Harvard machines are therefore missing. In the UK, there was also a series of computers: Manchester Baby, Manchester Mark, and Ferranti Mark. Without this restriction, the list would get out of hand, because the number of new machines increased enormously. Below is a brief description of their different properties. The allocation to these properties is however not always unambiguous. • Many machines, such as the IBM SSEC, had both electromechanical and electronic components (relays and vacuum tubes). • The early digital computers often employed decimal and, then later, binary numerical notation. The Stibitz and the Aiken codes (binary-coded decimal numerals) were also known. • There were special forms of fixed point and floating point notation. The Edsac had subprograms for floating point arithmetic, slowing down processing significantly. The IBM 650 was optionally available with floating point processing. • Along with purely parallel and purely serial machines, hybrid serial-parallel computers were also developed. The arithmetic operation or the data transfer took place simultaneously (in parallel) or sequentially (serially). • The borderline between special-purpose machines (machines that served one or only a few purposes) is fuzzy. Some computers were originally designed as special-­purpose computers but then used as general-purpose systems (e.g., Binac and Eniac). • A fixed program (hardwired program) greatly restricted the possibilities for applications. External program control was by means of (interchangeable) plugboard panels, rotary switches, punched tapes, or punched cards. By far the most advantageous were internally stored instructions (stored programs). In the following tables, the expression “program controlled” refers only to external control, in most cases via plugboard panels and punched tapes: Colossus and Eniac were plugboard controlled, while the Zuse Z4 and Harvard Mark 1/IBM ASCC were punched tape controlled. The IBM SSEC (electromechanical) hybrid computer was to some extent program controlled (with punched card control). • In the beginning, the computers that were controlled by an external or an internal program were usually one-of-a-kind machines. Later the industry entered the scene and produced them in quantity.

8.2  Early Relay and Vacuum Tube Computers (In Alphabetical Order)

295

8.2  E  arly Relay and Vacuum Tube Computers (In Alphabetical Order) Table 8.1  The first electromechanical and electronic digital computers (in alphabetical order)

American Telephone & Telegraph Company (AT&T), Bell Telephone Laboratories, New York City John William Eckert-­Mauchly computer Mauchly, John Presper corporation, Philadelphia Eckert

Country Year Electromechanical Electronic Decimal Binary Fixed point Floating point Parallel computer Serial computer Special-purpose computer Universal computer Fix-­programmed Program controlled Stored program One-­of-­a-­kind Mass-­produced USA 1942

National Physical Laboratory, Teddington, London

□ ■ □ ■ ■ □ ■ □ ■ □ ■ □ □ ■ □

UK 1950

Implementation Iowa State College, Ames, Iowa

□ ■ □ ■ ■ □ □ ■ □ ■ □ □ ■ ■ □

USA 1939

Builder John Vincent Atanasoff, Clifford Edward Berry Alan Mathison Turing, James H. Wilkinson, Edward A. Newman, Harry Douglas Huskey George Robert Stibitz, Samuel B. Williams

■ □ ■ □ ■ □ ■ □ ■ □ ■ □ □ ■ □

USA 1949

Binac

Bell 1 computer

Ace

ABC

Name of computer

Selected early relay and vacuum tube computers (in alphabetical order)

□ ■ □ ■ ■ □ □ ■ □ ■ □ □ ■ ■ □ (continued)

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8  Global Overview of Early Digital Computers (Tables)

Table 8.1 (continued)

Country Year Electromechanical Electronic Decimal Binary Fixed point Floating point Parallel computer Serial computer Special-purpose computer Universal computer Fix-­programmed Program controlled Stored program One-­of-­a-­kind Mass-­produced UK 1943

Implementation Post Office Research Station, Dollis Hill, London

□ ■ □ ■ □ □ ■ □ ■ □ □ ■ □ □ ■

UK 1949

Builder Maxwell (Max) Herman Alexander Newman (Bletchley Park)/ Thomas H. Flowers, W. W. (Bill) Chandler, Sid W. Broadhurst (Dollis Hill), Colossus 2: Allen W. M. Coombs (Dollis Hill) Maurice Vincent Wilkes, William Renwick, Tom Gold; David John Wheeler (Cambridge)/ Ernest H. Lenaerts (Leo) John Presper Eckert, John William Mauchly, Thomas Kite Sharpless, Herman Lukoff, Richard L. Snyder

□ ■ □ ■ ■ □ □ ■ □ ■ □ □ ■ ■ □

USA 1952

Edvac

Edsac 1

Colossus 1

Name of computer

Selected early relay and vacuum tube computers (in alphabetical order)

□ ■ □ ■ ■ □ □ ■ □ ■ □ □ ■ ■ □

Cambridge University

University of Pennsylvania, Philadelphia

(continued)

8.2  Early Relay and Vacuum Tube Computers (In Alphabetical Order)

297

Table 8.1 (continued)

University of Manchester/ Ferranti Ltd., Manchester

Harvard University, Cambridge, Massachusetts/ North street engineering laboratory, IBM, Endicott, New York

Country Year Electromechanical Electronic Decimal Binary Fixed point Floating point Parallel computer Serial computer Special-purpose computer Universal computer Fix-­programmed Program controlled Stored program One-­of-­a-­kind Mass-­produced USA 1946

Engineering Research Associates, Inc., St. Paul, Minnesota

□ ■ ■ □ ■ □ ■ □ □ ■ □ ■ □ ■ □

USA 1950

Implementation University of Pennsylvania, Philadelphia

□ ■ □ ■ ■ □ ■ □ □ ■ □ □ ■ □ ■

UK 1951

Builder John Presper Eckert, John William Mauchly, Joseph Chedaker, Arthur Walter Burks Howard T. Engstrom, William C. Norris, Arnold A. Cohen, Charles Brown Tompkins Frederic Calland Williams, Thomas Kilburn, Geoff C. Tootill (Cambridge) Howard Hathaway Aiken (Harvard)/ Clair D. Lake, Francis E. Hamilton, Benjamin M. Durfee (IBM)

□ ■ □ ■ ■ □ □ ■ □ ■ □ □ ■ □ ■

USA 1944

Harvard Mark 1/IBM ASCC

Ferranti Mark 1

Era 1101

Eniac

Name of computer

Selected early relay and vacuum tube computers (in alphabetical order)

■ □ ■ □ ■ □ ■ □ □ ■ □ ■ □ ■ □

(continued)

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8  Global Overview of Early Digital Computers (Tables)

Table 8.1 (continued)

Country Year Electromechanical Electronic Decimal Binary Fixed point Floating point Parallel computer Serial computer Special-purpose computer Universal computer Fix-­programmed Program controlled Stored program One-­of-­a-­kind Mass-­produced USA 1952 USA 1953

International Business Machines Corporation, Endicott, New York International Business Machines Corporation, Poughkeepsie, New York Wallace John International Business Eckert Machines (Columbia University)/ Corporation, Endicott, Francis E. New York/ Hamilton, Columbia Robert R. University, Seeber New York (IBM) John Maurice J. Lyons and Co. Ltd, Pinkerton, London/Leo David Computers Ltd., Tresman London Caminer, Ernest Henry Lenaerts, Derek Hemy

□ ■ □ ■ ■ □ ■ □ □ ■ □ □ ■ ■ □

□ ■ ■ □ ■ □ □ ■ □ ■ □ □ ■ □ ■

USA 1952

Implementation Institute for Advanced Study, Princeton, New Jersey

□ ■ □ ■ ■ □ ■ □ □ ■ □ □ ■ □ ■

USA 1948

Builder John von Neumann, Julian Himely Bigelow, James H. Pomerene, Arthur Walter Burks, Herman Heine Goldstine Francis E. Hamilton, Ernest S. Hughes, James J. Troy Jerrier A. Haddad, Nathaniel Rochester

■ ■ ■ □ ■ □ ■ □ □ ■ □ ■ ■ ■ □

UK 1951

Leo 1

IBM SSEC

IBM 701

IBM 650

IAS computer

Name of computer

Selected early relay and vacuum tube computers (in alphabetical order)

□ ■ □ ■ ■ □ □ ■ □ ■ □ □ ■ □ ■

(continued)

8.2  Early Relay and Vacuum Tube Computers (In Alphabetical Order)

299

Table 8.1 (continued)

Konrad Zuse – (Berlin)

Country Year Electromechanical Electronic Decimal Binary Fixed point Floating point Parallel computer Serial computer Special-purpose computer Universal computer Fix-­programmed Program controlled Stored program One-­of-­a-­kind Mass-­produced UK 1948 USA 1950

□ ■ □ ■ ■ □ □ ■ □ ■ □ □ ■ ■ □

USA 1950

US Bureau of Standards East, Washington, D.C. US Bureau of Harry Standards West/ Douglas University of Huskey California, Los Angeles John Presper Remington Rand, Eckert, John William Philadelphia Mauchly Massachusetts Jay Wright Institute of Forrester, Technology, Robert Cambridge, Rivers Massachusetts Everett, Perry O. Crawford Konrad Zuse – (Berlin)

□ ■ □ ■ ■ □ □ ■ □ ■ □ □ ■ ■ □

□ ■ □ ■ ■ □ ■ □ □ ■ □ □ ■ ■ □

USA 1951

Implementation University of Manchester

□ ■ ■ □ ■ □ □ ■ □ ■ □ □ ■ □ ■

USA 1951

Builder Frederic Calland Williams, Thomas Kilburn, Geoff C. Tootill Samuel N. Alexander, Ralph Slutz

□ ■ □ ■ ■ □ ■ □ □ ■ □ □ ■ ■ □

Germany Germany 1945 1941

Zuse Z4

Zuse Z3

Whirlwind

Univac 1

Swac

Seac

Manchester Baby

Name of computer

Selected early relay and vacuum tube computers (in alphabetical order)

■ □ □ ■ □ ■ ■ □ □ ■ □ ■ □ ■ □

■ □ □ ■ □ ■ ■ □ □ ■ □ ■ □ ■ □

© Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020 Explanation of symbols ■ Yes □ No UK = United Kingdom, USA = United States of America

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8  Global Overview of Early Digital Computers (Tables)

Remarks The abbreviations of the computer names are explained in Sect. 8.4. The dates given (point in time of the first operational run, the first demonstration, commissioning, advertisement, delivery, deployment, beginning of permanent operation, etc.) can be compared only to a limited extent. The first Bell computer model was originally called the Complex computer. Colossus 1 was a one-of-a-kind computer. Nine Colossus 2 computers were completed. Iowa State College is now a state university. A lengthy patent dispute involving Honeywell versus Sperry Rand took place before the Federal Court in Minneapolis (June 1, 1971–March 13, 1972). On October 19, 1973, Judge Earl Richard Larson returned the verdict: The Eniac patent (application submitted on June 26, 1947, granted on February 4, 1964) was declared invalid. Presper Eckert and John Mauchly were no longer recognized as the inventors of the “automatic electronic digital computer.” Instead this was attributed to John Atanasoff. The controversial decision was not contested. Zuse’s colleague Helmut Schreyer had built a test model with vacuum tubes, but this was lost during the war. The Zuse Z4 was (to a large extent) operational in March of 1945 and was commercially available in July 1950.

8.3  E  arly Relay and Vacuum Tube Computers (In Chronological Order) Table 8.2  The first electromechanical and electronic digital computers (in chronological order)

Mass-­produced

One-­of-­a-­kind

Stored program

Program controlled

Fix-­programmed

Universal computer

Special-purpose computer

Serial computer

Parallel computer

Floating point

Fixed point

Binary

Decimal

Electronic

Electromechanical

Name of Year computer 1939 Bell 1 computer 1941 Zuse Z3 1942 ABC 1943 Colossus 1 1944 Harvard Mark 1/IBM ASCC

Country

Selected early relay and vacuum tube computers (in chronological order)

USA ■ □ ■ □ ■ □ ■ □ ■ □ ■ □ □ ■ □ D USA UK USA

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(continued)

8.4  Commentary Regarding the Early Relay and Vacuum Tube Computers

301

Table 8.2 (continued)

Electronic

Decimal

Binary

Fixed point

Floating point

Parallel computer

Serial computer

Special-purpose computer

Universal computer

Fix-­programmed

Program controlled

Stored program

One-­of-­a-­kind

Mass-­produced

1949 1949 1950 1950 1950 1950 1951 1951 1951 1951 1952 1952 1952 1953

Name of computer Zuse Z4 Eniac IBM SSEC Manchester Baby Edsac 1 Binac Ace Seac Swac Era 1101 Ferranti Mark 1 Univac 1 Whirlwind Leo 1 Edvac IAS computer IBM 701 IBM 650

D USA USA UK

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UK USA UK USA USA USA UK USA USA UK USA USA USA USA

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Country

Year 1945 1946 1948 1948

Electromechanical

Selected early relay and vacuum tube computers (in chronological order)

© Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020 Explanation of symbols ■ Yes □ No D (Deutschland) = Germany, UK = United Kingdom, USA = United States of America

Remarks Mass production refers to Colossus Model 2.

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8  Global Overview of Early Digital Computers (Tables)

8.4  C  ommentary Regarding the Early Relay and Vacuum Tube Computers Table 8.3  Selected properties of the first relay and vacuum tube computers Detailed remarks regarding the first relay and vacuum tube computers Name of computer Remarks Period of construction: 1937–1942 ABC Demonstration of test version: October 1939 (Atanasoff Berry Operational: May 1942 Computer) (because of the war) interruption of further development: June 1942 Binary card punch and punched card reader Manual sequence control Period of construction for Pilot Ace: beginning of 1949 to end of 1951 Ace First operational run: May 10, 1950 (Automatic Public demonstration: December 1950 Computing Completed: end of 1951 Engine) Continuous operation: from beginning of 1952 In spite of the name “Pilot Ace” or “Ace pilot model” digital computer for use in practice (large-scale) Ace computer, 1 machine: end of 1958 Marketed under the name Deuce (Digital Electronic Universal Computing Engine) by the English Electric Company Ltd., Stafford March 1955: 33 machines Further models: Deuce 2 (1955) and Deuce 2A (1957) Follow-on machine: Mosaic (Ministry of Supply Automatic Integrator and Computer, built by the British Post Office Research Station) Period of construction: 1938–1939 Bell 1 computer Completed: October 1939 or Commissioned: January 8, 1940 Complex Demonstration before the American Mathematical Society with computer remote control via a telegraph line from Dartmouth College, Hanover, New Hampshire, to New York City: September 11, 1940 (participants included John Mauchly and Norbert Wiener) Later models: Bell 2 to Bell 6 computers (model 5 – two machines) Model 1: special-purpose computer for complex numbers (all four basic arithmetic operations) Model 2: completion: September 1943 program control with punched tapes, access via teleprinter Models 2–6: programmable, Stibitz code All 7 Bell computers were relay machines without stored program Period of construction: 1947–1949 Binac (Binary Automatic First operational run and public demonstration: August 1949 Available from: September 1949 Computer) Designed as special-purpose computer, used as universal computer Partly unreliable in operation (problems with dismantling and reassembling) (continued)

8.4  Commentary Regarding the Early Relay and Vacuum Tube Computers

303

Table 8.3 (continued) Detailed remarks regarding the first relay and vacuum tube computers Name of computer Remarks Colossus Period of construction: 1943 (11 months) First operational run of Colossus 1: December 8, 1943, in Dollis Hill, London Commissioned: January 18, 1944, in Bletchley Park, Buckinghamshire Later model: Colossus Mark 2 (from 1944); Total of 10 machines built: 1 Colossus Mark 1 and 9 Colossus (Mark) 2 Processed only whole numbers (neither fixed point nor floating point) The existence of the Colossus computer was kept secret until October 20, 1975 Period of construction: 1946–1949 Edsac 1 (Electronic Delay First operational run: May 6, 1949 Storage Automatic Continuous operation from beginning of 1950 Later model: Edsac 2 (1958) Calculator) Marketed as Leo 1 commercial computer Subprogram for floating point processing Period of construction: 1945–1952 Edvac Limited operation from end of 1951 (Electronic Discrete Variable Unlimited operation: beginning of 1952 Fixed point and floating point capability Arithmetic Computer) Period of construction: 1943–1945 Eniac Commissioned: November 1945 (Electronic Demonstration: February 14, 1946 Numerical Originally parallel computer, from April 1948 serial computer with Integrator and limited stored program capability (use of function tables) Computer) Aiken code Period of construction: 1948–1950 (Era 1101, original name: Atlas) Era 1101 Atlas 1 (noncommercial, completion in October 1950, available from (Engineering December 1950, 2 machines) Research Atlas 2 (noncommercial, available from 1953, 1 machine) Associates) Era 1101 (commercial version of Atlas 1, 3 machines built, available from 1951) Era 1102 (3 machines built, available 1954–1956) Era 1103 (commercial version of Atlas 2, scientific computer, advertised 1953, delayed availability, 19 machines built) Era 1103A (core memory, available from 1956) Later models: 1103 AF, 1104 Era 1101 was later called Univac 1101 Era 1103 was renamed to Univac 1103 Ferranti Mark 1 Period of construction: 1949–1951 Available from: February 1951 9 machines built (Mark 1 and Mark 1 star (Mark 1*)) Ferranti Mark is a further development of the Manchester Mark 1 Later models: Ferranti Mark 1 star (1953), Pegasus 1 (1956), Pegasus 2 (1959), Mercury (1957), Perseus (1959), etc. (continued)

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Table 8.3 (continued) Detailed remarks regarding the first relay and vacuum tube computers Name of computer Remarks Period of construction: 1939–1944 Harvard Mark 1 Completion of the machine in Endicott: January 1943 or Demonstration for Harvard staff: December 1943 IBM ASCC Assembled in Cambridge, Massachusetts: from February 1944 (Automatic Commissioned: May 1944 Sequence Dedicated: August 7, 1944 Controlled Later models: Mark 2 (relay computer), Mark 3, and Mark 4 Calculator) (both vacuum tube computers) Machine designed by Harvard, built by IBM Period of construction: 1947–1952 IAS computer Operational June 10, 1952 (Institute for Advanced Study)/ Numerous replicas around the world Princeton machine IBM 650 Period of construction: 1953–1954 Advertised: July 2, 1953 Available from: December 1954 More than 1800 machines built up to 1962 Optionally with floating point processing Digital computer produced in large numbers for commercial-­ industrial and scientific-technical purposes Most widely found computing system of the 1950s IBM 701 Period of construction: 1951–1952 Dedicated: April 7, 1953 First installation in New York: December 20, 1952 Available from: spring 1953 19 machines built Later models: 702, 704, 705, 709 First mass-produced IBM digital computer (for scientific and technical purposes) Period of construction: 1946–1947 IBM SSEC Experimental version: 1947 (Selective Dedicated: January 27, 1948 Sequence Electronic Calculator) Period of construction: 1949–1953 Leo 1 (Lyons Electronic First operational run: February 1951; First complete run: September 5, 1951 Office 1) Continuous operation: from beginning of 1953 Completion: December 24, 1953 at first in use at Lyons Full operation: 1954 Public demonstration: February 16, 1954 Dedicated: May 27, 1954 Leo Computers Ltd., London, founded November 4, 1954 First delivery of Leo 2: May 1957 Commissioned: July 1957 Later model: Leo 3 (completed: 1961, available from: April 1962) Leo is a further development of the Edsac (Cambridge University) (continued)

Table 8.3 (continued) Detailed remarks regarding the first relay and vacuum tube computers Name of computer Remarks Manchester Baby Period of construction: 1946–1948 First run: June 21, 1948 (trial model) or Follow-on machine: Manchester Mark 1 SSEM Period of construction: 1948–1949 (completed: October 1949) (small-scale Marketed as Ferranti Mark 1, Ferranti Mark 1∗, and Ferranti Mark 2 experimental Additional name for the first Manchester computer: machine) Madm (Manchester Automatic Digital Machine) Period of construction: 1948–1950 Seac Demonstration: April 1950 (Standards Eastern Automatic Commissioned: June 20, 1950 Later model: Dyseac (1954) Computer) Period of construction: 1949–1950 Swac Operational: July 1950 (Standards Western Automatic Dedicated: August 17–19, 1950 Fully operational: from mid-1953 Computer) Period of construction: 1946–1951 Univac 1 Available from: March 31, 1951 (Universal 46 machines built Automatic Stibitz code Computer) Subprogram for floating point processing Later models: Univac 2 (1957) and 3 (1962) Whirlwind Period of construction: 1945–1951 Completed: April 1951 Fully operational: from 1953 Real-time processing Zuse Z3 Period of construction: 1940–1941 Demonstration: May 12, 1941 Z1 (1938, mechanical arithmetic unit and memory, floating point) Z2 (1939, electromechanical arithmetic unit, mechanical memory, fixed point) Z3 (1941, electromechanical arithmetic unit and memory, floating point) Z4 (1945, electromechanical arithmetic unit, mechanical memory, floating point) Later models: Z5 relay computer (completed 1952, delivered to the Leitz-­Werke, Wetzlar, Germany, July 7, 1953) Z11 relay computer (from 1956) Z22 vacuum tube computer (first delivery: December 1957 Commissioned: March 1958) Z23 transistor computer (from 1961), etc. M9 calculating punch (from 1953) Special-purpose computers: S1 (1942, electromechanical arithmetic unit and memory, fixed point) S2 (1944, electromechanical arithmetic unit and memory, fixed point, process computer) Logistics device (1944, electromechanical arithmetic unit and memory) Electronic computer of Helmut Schreyer (1938 and 1944) Zuse Z4 Period of construction: 1942–1945 Demonstration: March 29, 1945 Continuous operation: August 1950 (installed July 11, 1950) to April 1955 at the ETH Zurich © Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020

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Remarks In the specialized literature, different computer names are sometimes used. The words calculator and computer are often confused. For the Complex computer (first Bell computer), the names complex calculator, complex number computer, and complex number calculator are all used. For the a in Edvac, the words automatic and arithmetic are (additionally) cited. Thus John Mauchly writes: The initials [Edvac] stand for “Electronic Discrete Variable Arithmetic Computer” (see John William Mauchly, Preparation of problems for Edvactype machines, in Brian Randell (editor), The origins of digital computers, Springer-Verlag, Berlin, Heidelberg, etc., third edition 1982, page 393). For Swac the Institute for Numerical Analysis, Los Angeles, is also given as a site. The Whirlwind was originally an analog computer.

Chapter 9

Museums and Collections

Abstract  The chapter “Museums and Collections” gives the reader detailed information about the collections of important museums (e.g., in Athens, Beijing, Berlin, Bletchley Park, Bonn, Clermont-Ferrand, Dresden, Florence, Kassel, London, Madrid, Manchester, Melbourne, Milan, Mountain View, Munich, Neuchâtel, Ottawa, Oxford, Paderborn, Paris, Stockholm, Strasbourg, Vienna, and Washington). Most of these are museums of science, technology, and art. The chapter examines analog and digital calculating aids, historical automatons, and robots, as well as scientific instruments. The first mechanical calculating aids (Schickard, Pascal, Morland, and Leibniz) date from the seventeenth century. The chapter also describes where originals and reconstructions of famous objects (e.g., the Antikythera mechanism, Babbage’s difference engine, the Colossus, the Csirac, Hollerith’s punched card equipment, the Johnniac, the Leibniz machine, the Pascaline, the Pilot Ace, the Roman hand abacus, Schickard’s calculating clock, the Thomas arithmometer, the Turing-Welchman Bombe, and the Zuse Z4) are found. Furthermore, the question of which are the oldest surviving mechanical and electronic computers is addressed. The early one-, two-, and four-­function machines are summarized in overview tables. The world’s most magnificent calculating machines, including the replicas of Roberto Guatelli, are described. The oldest large museums of technology (Dresden and Paris) date from the eighteenth century. Their forerunners were often royal wonder and curiosity cabinets from the early modern era. Scientific societies were founded as early as the seventeenth century and mathematical associations from the nineteenth century. The first world exhibition was the Great Exhibition, which took place in London in 1851. Today, the most important collections, and in part also object databases, are accessible on the Internet. Keywords  Calculating machines · Calculator collections · Computer museums · Historical calculating machines · Museums of technology · Object databases · Originals · Reconstructions · Replicas · Science museums · Wonder cabinets

© Springer Nature Switzerland AG 2020 H. Bruderer, Milestones in Analog and Digital Computing, https://doi.org/10.1007/978-3-030-40974-6_9

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9.1  Museums of Science and Technology The few surviving masterpieces of calculating technology are mostly found in museums of technology, natural science and history, in computer and local history museums, and in private collections inaccessible to the public. They are widely scattered. Where is one then most likely to find them? The two leading European museums of technology are the Science Museum in London and the Deutsches Museum in Munich. As large, educational universal museums, they cover (nearly) the entire spectrum of engineering and the natural sciences. For computing technology and informatics, there are two important special museums, the Heinz Nixdorf  Museumsforum in Paderborn and the Arithmeum of the University of Bonn. The most important museums of computer technology in the USA are (in alphabetical order): • The Computer History Museum, Mountain View, California • The National Museum of American History, Washington, D.C. In Europe there are several important museums of computing technology (see box).

Important European Museums of Computing Technology • Arithmeum, Bonn Main emphasis: mechanical calculating machines, slide rules, many replicas and models • Bletchley Park Trust, Bletchley Park, Bletchley, England Main emphasis: coding and decoding (Enigma) • Deutsches Museum, Munich Overview; e.g., analog and digital mechanical, electromechanical, and electronic calculating devices, numerous original machines • Heinz Nixdorf  Museumsforum, Paderborn, Germany Overview: e.g., mechanical, electromechanical, and electronic calculating devices • Musée des arts et métiers, Paris Overview: e.g., mechanical, electromechanical, and electronic calculating devices, mechanical looms • National Museum of Computing, Bletchley Park, Bletchley, England Overview: e.g., reconstructions and functional machines, such as Turing-­ Welchman Bombe, Colossus, Harwell-Dekatron computer, and Edsac • Science Museum, London Overview: e.g., mechanical, electromechanical, and electronic calculating devices, numerous originals

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Worldwide only a few museums are specialized in computing technology: • Germany: Heinz Nixdorf  Museumsforum, Paderborn • USA: Computer History Museum, Mountain View, California • UK: National Museum of Computing, Bletchley Park In France a museum for computer science has been planned for several years, and in Switzerland the Museum Enter (Solothurn) plans to construct a new building for this purpose. Other well-known museums of science and technology in the UK: • History of Science Museum, Oxford • Science and Industry Museum, Manchester • Whipple Museum of the History of Science, Cambridge Other important museums of science and technology in Germany and Austria: • • • •

Deutsches Technikmuseum, Berlin Technische Sammlungen, Dresden Technisches Museum Wien, Vienna Technoseum, Mannheim

Magnificent technical masterpieces are on exhibit, for example, in the following sites: • Astronomisch-physikalisches Kabinett, Kassel • British Museum, London • Kunsthistorisches Museum Wien (particularly the Kunstkammer Wien), Vienna • Mathematisch-physikalischer Salon, Dresden (Zwinger Gallery) • Metropolitan Museum of Art, New York • Museo Galileo, Florence • Museo Nazionale della Scienza e della Tecnologia “Leonardo da Vinci”, Milan • Residenzschloss Dresden (historical grünes Gewölbe and new grünes Gewölbe; grünes Gewölbe = treasure chamber) The two largest Swiss museums for computer technology are the: • Museum Enter, Solothurn • Museum für Kommunikation, Bern Other fascinating collections of mathematical devices in Switzerland are the: • • • • • • •

Historisches Archiv und Museum of the UBS, Basel Musée Bolo, EPF Lausanne (Ecole polytechnique fédérale) Musée d’histoire des sciences, Geneva Patrimoine technologique, Dorénaz VS Sammlung Sternwarte (Collection of astronomical instruments), ETH Zurich Schreibmaschinenmuseum (typewriter museum), Pfäffikon ZH Studiensammlung Kern, Aarau

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The following collections in Liechtenstein are also of interest: • Liechtensteinisches Landesmuseum, Vaduz (Curta) • Museum Mura, Schaanwald (Curta) Probably the best known typewriter museum is the Schreibmaschinenmuseum in Partschins, South Tyrol. Remarks The computer collection of the Winterthur Technorama no longer exists, as is the case with the Collection Lucien Malassis (IBM Europe). In 2011 IBM exhibited old calculating devices in commemoration of its 100th birthday. Most large museums of science and technology were founded in the twentieth century (see Tables 9.1 and 9.2). Table 9.1  Year of founding of selected museums (in alphabetical order according to name of museum) When were important museums founded? Name City Arithmeum Bonn Astronomisch-physikalisches Kabinett Kassel British Museum London Computer History Museum Mountain View, CA Deutsches Museum Munich Heinz Nixdorf  Museumsforum Paderborn History of Science Museum Oxford Kunsthistorisches Museum Wien Vienna Mathematisch-physikalischer Salon Dresden Metropolitan Museum of Art New York Musée des arts et métiers Paris Museo Galileo Florence National Museum of American History Washington, D.C. National Museum of Computing Bletchley Park Palastmuseum Beijing Science Museum London Technisches Museum Wien Vienna © Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020

Country Germany Germany England USA Germany Germany England Austria Germany USA France Italy USA England China England Austria

Year 1999 1992 1753 1979 1903 1996 1924 1891 1728 1870 1794 1930 1964 2007 1925 1853 1909

Remark Electoral Prince August of Saxony had already founded the treasure chamber (grünes Gewölbe in the Dresden Castle, Dresden) in 1560.

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Table 9.2  Year of founding of selected museums (in chronological order) When were the major museums founded? Year Name City 1728 Mathematisch-physikalischer Salon Dresden 1753 British Museum London 1794 Musée des arts et métiers Paris 1853 Science Museum London 1870 Metropolitan Museum of Art New York 1891 Kunsthistorisches Museum Wien Vienna 1903 Deutsches Museum Munich 1909 Technisches Museum Wien Vienna 1924 History of Science Museum Oxford 1925 Palace Museum Beijing 1930 Museo Galileo Florence 1964 National Museum of American History Washington, D.C. 1979 Computer History Museum Mountain View, CA 1992 Astronomisch-physikalisches Kabinett Kassel 1996 Heinz Nixdorf  Museumsforum Paderborn 2007 National Museum of Computing Bletchley Park © Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020

Country Germany England France England USA Austria Germany Austria England China Italy USA USA Germany Germany England

Learned societies were founded in the seventeenth century, followed by mathematical societies in the second half of the nineteenth century and the first half of the twentieth century (see Tables 9.3 and 9.4). Table 9.3  Founding of scientific societies Scientific societies already arose in Europe in the seventeenth century Year Name 1603 Accademia nazionale dei lincei 1652 Leopoldina – National Academy of Sciences 1660 Royal Society 1666 Académie des sciences © Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020

Country Italy Germany UK France

Table 9.4  Founding of mathematical societies Mathematical societies from 1850 on Year Name 1865 London Mathematical Society 1872 Société mathématique de France 1883 Edinburgh Mathematical Society 1888 American Mathematical Society 1890 Deutsche Mathematiker-Vereinigung 1911 Real sociedad matemática española 1915 Mathematical Association of America

Country England France Scotland USA Germany Spain USA

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9.1.1  Collection Databases The databases of many museums of science and technology (object databases, archive databases, and in part picture libraries) are accessible online. However, searching in the sometimes imperfect and incomplete data records is very tedious. Museums with freely accessible databases (selection) • Bayerisches Nationalmuseum, Munich • British Museum, London • Canada Science and Technology Museum/Musée des sciences et de la technologie du Canada, Ottawa • Computer History Museum, Mountain View, California • ETH Zurich, Sammlung Sternwarte (Collection of astronomical instruments) • Germanisches Nationalmuseum, Nuremberg • Grünes Gewölbe, Dresden (treasure chamber) • History of Science Museum, Oxford • Kunsthistorisches Museum Wien (treasure chamber), Vienna • Louvre, Paris • Mathematisch-physikalischer Salon, Dresden • Metropolitan Museum of Art, New York • Musée des arts et métiers, Paris • Museen der Stadt Dresden • Museo Galileo, Florence • Museo Nazionale della Scienza e della Tecnologia “Leonardo da Vinci”, Milan • Museum für Kommunikation, Bern • Museum of Applied Arts and Science, Sydney • Museum of Transport and Technology, Auckland • Museums Victoria, Melbourne • National Museum of American History, Washington, D.C. • National Museum of Scotland, Edinburgh • Rijksmuseum Boerhaave, Leiden, Netherlands • Science and Industry Museum, Manchester • Science Museum, London • Technische Sammlungen, Dresden • Technisches Museum Wien, Vienna • Technoseum, Mannheim • Tekniska museet (National Museum of Science and Technology), Stockholm Notes The collection database of the Staatliche Kunstsammlungen Dresden covers the salon in the Zwinger Gallery and the grünes Gewölbe. For the database of the Bonn Arithmeum, a search function is missing.

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9.1.2  Early Exhibits of Calculating Aids At the Great Exhibition of the works of industry of all nations (= first world exhibition) at the Crystal Palace in London in 1851, one could admire mechanical calculating machines, e.g., the Thomas arithmometer and the copy of a Schwilgué keyboard adding machine by Victor Schilt. Exhibition catalogs and reports are good sources of information about historical calculating devices (and dating). Sources Anonymous: Great exhibition of the works of industry of all nations, 1851. Official descriptive and illustrated catalogue, Spicer brothers, London 1851 (4 volumes) Authority of the royal commission: Official catalogue of the great exhibition of the works of industry of all nations, 1851, Spicer brothers, London 1851 Rudolf Biedermann: Bericht über die Ausstellung wissenschaftlicher Apparate im South Kensington Museum zu London 1876, London 1877 Walter Dyck: Katalog mathematischer und mathematisch-physikalischer Modelle, Apparate und Instrumente, Georg Olms Verlag, Hildesheim, Zurich 1994 (first published in 1892, followup 1893) Wilhelm Jordan: Internationale Ausstellung wissenschaftlicher Apparate im South-­Kensington-­Museum in London im Sommer 1876, in: Zeitschrift für Vermessungswesen, volume 5, 1876, no. 9, pages 449–461 Eugène Lemaire: Exposition publique de machines à calculer anciennes et modernes. Catalogue explicatif des objets exposés, exposition organisée par la société d’encouragement à Paris du 5 au 13 juin 1920 Eugène Lemaire: Exposition publique de machines à calculer anciennes et modernes, organisée par la société d’encouragement à Paris, 44, rue de Rennes, du 5 au 13 juin 1920. Catalogue explicatif des objets exposés 1920, in: Bulletin de la société d’encouragement pour l’industrie nationale, volume 119, September/October 1920, pages 608–644. At the end of the nineteenth century and the beginning of the twentieth century, a number of special exhibitions took place (see Table 9.5). Table 9.5  Important exhibitions of historical calculating devices Exhibitions of calculating devices Year City Details of the exhibition 1876 London Exhibition of scientific apparatus (South Kensington Museum) 1893 Munich Mathematische und mathematisch-physikalische Modelle (Deutsche Mathematiker-Vereinigung, Technische Universität München) 1911 Zurich Ausstellung Konkordatsgeometer (Helmhaus) 1920 Paris Exposition publique de machines à calculer anciennes et modernes (Société d’encouragement pour l’industrie nationale) © Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020

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World Exhibitions Mathematical instruments were presented at the major national and international events, such as the following world exhibitions (see Table  9.6) and awarded prizes: 1851 (London), 1855 (Paris), 1867 (Paris), 1873 (Vienna), 1880 (Melbourne), 1889 (Paris), 1893 (Chicago), and 1900 (Paris). Later mostly industrial trade fairs took place.

Table 9.6  Early world exhibitions The first world exhibitions Year City Year 1851 London 1880 1855 Paris 1888 1862 London 1889 1867 Paris 1893 1873 Vienna 1897 1876 Philadelphia 1900 1878 Paris © Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020

City Melbourne Barcelona Paris Chicago Brussels Paris

Source Bureau international des expositions, Paris Remark The earliest world exhibitions were characterized by competition between France and the UK. Symbolic for the world exhibition in Paris in 1889 was the Eiffel Tower. Today the International Bureau of Exhibitions is responsible for determining the venue. 9.1.2.1  Exhibition at the Helmhaus, Zurich According to the “Verzeichnis der Aussteller und Ausstellungsgegenstände”, from May 13 to May 15, 1911, the following companies took part in the presentation at the Helmhaus in Zurich: • Amsler-Laffon & Sohn, Schaffhausen Planimeter • Billeter, Julius, Zurich Cylindrical slide rule, grid slide rule, and circular slide rule • Coradi, G. [Gottlieb], Zurich Planimeter, pantograph, and coordinatograph

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• Daemen-Schmid, Oerlikon-Zurich Loga cylindrical slide rule • Egli, Hans W. [Walter], Zurich Millionaire • Kern & Co. AG, Aarau Theodolite, leveling instrument, set of drawing instruments • Landolt, Karl, Thalwil Conto B. Source Anonymous: Generalversammlung des Vereins schweizerischer Konkordatsgeometer, 14. und 15. Mai 1911 in Zürich. Ausstellung im Helmhaus vom 13. bis 15. Mai. Verzeichnis der Aussteller und Ausstellungsgegenstände, in: Schweizerische Geometer-Zeitung, volume 9, 1911, pages 105–131. Remarks The Julius Billeter company in Zurich was listed from 1893 to 1895 in the Swiss Official Gazette of Commerce and the successor Julius Billeter’s Söhne in Zurich from 1895 to 1897. The exhibitor was possibly a trading company or a successor company. The “Loga” brand existed already before the founding of the Loga-­Calculator AG, Uster ZH (1915). In Zurich there was also a chamber of wonders (see Fig. 9.1). For this curiosity cabinet, there were several names (see box).

Fig. 9.1  Treasure chamber. This sketch offers a view into a curiosity cabinet. Johann Meyer: Sketch of the treasure chamber at the Wasserkirche in Zurich. Draft for the New Year’s magazine of the Stadtbibliothek Zurich from 1687. (© Zentralbibliothek Zurich)

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Cabinet, Treasure Chamber, and Salon A cabinet is a collection or a room for the safekeeping of a collection. Rare, valuable, and extraordinary objects were exhibited in ecclesiastic or secular cabinets, treasure rooms, or salons The museums or exhibition rooms are described differently, e.g., curiosity cabinet, acoustical cabinet, arts cabinet, astronomical cabinet, mathematical cabinet, music cabinet, physical cabinet, as well as panopticum, numismatical collection, chamber of horrors, gallery of prints, natural history treasure chamber, armory, vault, and wax figure cabinet. Such treasure chambers have existed since the sixteenth century and in part already since the fourteenth century.

9.2  W  hich Museum Has Which Historical Calculating Devices? In the following a number of important historical calculating aids, selected historical automatons and robots, mechanical looms, and scientific instruments are listed, together with their current locations. Only the milestones from the early days of computer science are considered here. This list does not claim to be complete. Two questions are of primary concern here: • Which masterpieces are exhibited in a particular museum? Which rare devices from the early days of computer science can I, for example, view in Munich, Vienna, Paris, London, or Washington, D.C.? This overview is intended as an aid for reaching decisions regarding travel. It provides information about what is exhibited, for example, in Dresden, Florence, Madrid, Bletchley Park, Mountain View, Ottawa, or Melbourne. This involves searching for museum holdings. • In which museum will I find a particular masterpiece? Where is the original Leibniz machine? Which institutions have devices of Pascal and Schickard? Are there works of Babbage in England? Has the census machine of Hollerith survived? Where are there reconstructions of the Turing-­Welchman Bombe and the secretive Colossus? Is Amsler’s polar planimeter extant somewhere? Where can one view analog differential analyzers? This involves searching for a specific object. This compilation is not intended as an evaluation of individual holdings. To be sure, it comprises only a small part of the respective collections. Note: only a fraction of the objects is exhibited, while the rest is kept in repository. In spite of great care with regard to the following lists, their accuracy cannot be guaranteed. Some museums were not prepared to verify the enumerations (e.g., the Bonn Arithmeum), or they were not willing to make the effort (e.g., the IBM Corporate Archives in Poughkeepsie, New York).

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Notes Napier’s bones (Scotland), sectors (Italy), cylindrical slide rules (England), and such calculating machines as the Thomas arithmometer (France), the Millionaire (Switzerland), the comptometer (USA), the Curta (Liechtenstein), and the encryption machine (Germany) are largely missing in this compilation because numerous specimens have survived. This also applies for the first electronic pocket calculator Anita (England), which can be found, e.g., in Berlin, Bonn, Vienna, London, Washington, D.C., and Mountain View, California. The Enigma rotary cipher machine is found at the following locations: Deutsches Museum, Munich; Technisches Museum Wien, Vienna; Museo Nazionale della Scienza e della Tecnologia “Leonardo da Vinci”, Milan; Bletchley Park Trust, Bletchley; Science Museum, London; Tekniska museet, Stockholm; Computer History Museum, Mountain View, California; Carnegie Mellon University, Pittsburgh, Pennsylvania; and Museum of Applied Arts and Sciences, Sydney. Replicas can be found, for example, at the following sites: National Museum of Computing, Bletchley Park (UK), and the Mathematikum der Universität Gießen.

9.3  W  hich Calculating Devices Are Among the Museum’s Holdings? The following overview is restricted to selected rare masterpieces from the history of computing and related areas. The list considers the world’s leading museums (in alphabetical order by country and place). In order to simplify comparisons between the different museums, as a rule the numerous mechanical calculating machines and devices are listed according to the name of the inventor (e.g., Hollerith’s punched card system, Leibniz’s calculating machine, Babbage’s analytical engine, or Thomas arithmometer) and the remaining objects according to the category or manufacturer’s name (e.g., astrolabe, hodometer, loom, planetary clock, typewriter, IBM, or Siemens).

9.3.1  Australia 9.3.1.1  Melbourne Museum, Carlton, Victoria • Csirac (Trevor Pearcey, Maston Beard) 9.3.1.2  Museum of Applied Arts and Sciences, Sydney • Antikythera mechanism (model of Allan Bromley)

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9.3.2  Austria 9.3.2.1  Kunsthistorisches Museum Wien, Vienna (Kunstkammer) • • • • • • • • • • • • • • • • •

Automaton figure with Diana on a centaur of Hans Jakob Bachmann Automaton with the triumph of Bacchus by Hans Schlottheim Bell tower automaton of Hans Schlottheim Braun’s pinwheel machine First ball clock of Christoph Margraf Mechanical celestial globe of Georg Roll and Johannes Reinhold Mercenary’s beret (calculating hat) Sun quadrant of Johann von Gmunden Table automaton in the form of a ship of Hans Schlottheim (sail boat with musical puppets) Table sundial with time conversion diagram of Erasmus Habermel Triumph carriage with Minerva of Achilles Langenbucher Trumpeter automaton of Hans Schlottheim Vienna crystal clock of Jost Bürgi Vienna flute playing clock of Helmut Kowar Vienna planetary clock of Jost Bürgi Wooden box clock (with astrolabe) of Jan Táborský Zither player

Kunsthistorisches Museum Wien (Münzkabinett) • Coins 9.3.2.2  Technisches Museum Wien, Vienna • • • • • • • • •

Anita (first electronic desk calculator) Handwriting automaton of Friedrich Knaus Hebentanz’s totalizer (pointer adding machine) (Ferdinand Hebentanz) Musical automatons Roth’s cogged disc adding machine Tauschek’s bookkeeping machines (Gustav Tauschek) Telefunken electronic analog computer Typewriter of Peter Mitterhofer Zemanek’s Mailüfterl (Heinz Zemanek)

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9.3.3  Belgium 9.3.3.1  Institut royal des sciences naturelles de Belgique, Brussels • Ishango bone

9.3.4  Canada 9.3.4.1  C  anada Science and Technology Museum, Ottawa/ Musée des sciences et de la technologie du Canada, Ottawa • Babbage’s difference engine 1 (replica of Roberto Guatelli) • Pascaline (replica of Roberto Guatelli)

9.3.5  China 9.3.5.1  故  宫博物院 Palace Museum, Beijing (Museum of the Forbidden City) • Musical automaton clocks • Musical clock with handwriting automaton of Timothy Williamson

9.3.6  Czech Republic The Czech National Museum in Prague exhibits, e.g., astronomical instruments of Jost Bürgi, Erasmus Habermel, and Engelbert Seige.

9.3.7  France 9.3.7.1  Château du Clos Lucé, Amboise, Val de Loire • Collection of models (reconstructions) of Leonardo da Vinci 9.3.7.2  Muséum Henri-Lecoq, Clermont-Ferrand • Pascaline (machine of Marguerite Périer) • Pascaline (machine of the nobleman Durant-Pascal)

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9.3.7.3  Musée des arts et métiers, Paris • Amslers polar planimeter (Jakob Amsler) • Arithmaurel (calculating machine of Maurel/Jayet) • Bollée’s direct multiplication machine (partial-product multiplying machine) • Bollée’s multiplication and division device (arithmograph with Napier’s bones) • Celestial globe/globe clock of Jost Bürgi • Chebyshev’s calculating machine • Couffignal’s calculating machine (experimental piece) (Louis Couffignal) • Ernst’s planimeter (Heinrich Rudolf Ernst) • Felt’s comptometer • Genaille/Lucas counting rods • Grillet’s four-function device (Napier’s bones with cogged wheel adder) • Hollerith’s punched card equipment (counting and sorting machine, tabulator, pantograph card punch (census machine)) • Joueuse de tympanon (dulcimer player) of Peter Kintzing • Lépine’s adding and subtracting machine (Jean Lépine) • Loom with punched card control of Jean-Baptiste Falcon (replica) • Loom with punched card control of Joseph-Marie Jacquard (replica) • Loom with punched tape control of Basile Bouchon (replica) • Loom with punched tape control of Jacques Vaucanson • Pascaline (4-place, with sous and deniers, i.e., 6-place) (replica from the eighteenth century with original parts) • Pascaline (6-place, with sous and deniers, i.e., 8-place) • Pascaline (6-place, with sous und deniers, i.e., 8-place) • Pascaline (6-place, without sous and without deniers, i.e., 6-place) • Roth’s addition and subtraction machine • Roth’s cogged disc adding machine • Roth’s multiplication and division rods • Roth’s pinwheel machine • Thomas arithmometer (stepped drum machine, 12-, 16-, 20-place, early model, decorative gift for a prince) • Thomson’s tide predictor (William Thomson) Remark Former French currency: 1 livre = 20 sols, 1 sol = 12 deniers. The sol later became the sou. 9.3.7.4  B  ibliothèque nationale de France, Paris (Cabinet des médailles) • Roman hand abacus

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Note The French National Library also possesses astrolabes, armillary spheres, planispheres, and monetary exchange balances. 9.3.7.5  Cathédrale Notre Dame de Strasbourg • Astronomical clock with church calculator of Jean-Baptiste Schwilgué 9.3.7.6  Musée de l’œuvre Notre-Dame, Strasbourg • Calculating table 9.3.7.7  Musée historique, Strasbourg • Schwilgué’s “process” calculator • Schwilgué’s keyboard adding machine • Schwilgué’s mechanical counter

9.3.8  Germany 9.3.8.1  Philipp-Matthäus-Hahn-Museum, Albstadt-Onstmettingen • Hahn’s stepped drum machine (replica) 9.3.8.2  Deutsches Technikmuseum, Berlin • • • • • • • • •

Anita (first electronic desk computer) Hoelzer’s electronic analog computer (replica of Helmut Hoelzer) Leibniz’s calculating machine (binary, reconstruction) Leibniz’s calculating machine (decimal, replica) Pascaline (replica) Roman hand abacus (replica) Schickard’s calculating clock (reconstruction) Telefunken RA 463/2, electronic analog computer Zuse Z1 (replica of Konrad Zuse)

9.3.8.3  Arithmeum, Bonn • Anita (first electronic desk computer) • Arithmaurel (calculating machine of Maurel/Jayet) • Auch’s cogged disc addition and subtraction machine (replica)

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Babbage’s difference engine 1 (reconstruction) Baldwin’s pinwheel machine (replica) Billeter’s (logarithmic) grid slide rule Bollée’s direct multiplication machine (replica) Braun’s pinwheel machine (replica) Burroughs calculator (William Seward) Dietzschold’s ratchet machine (Curt Dietzschold) Dinkelsbühl calculating table (replica) Gonnella’s cogged disc adding machine Grillet’s four-function device (Napier’s bones with cogged wheel adder) (replica) Guinigi’s adding machine (Niccola Guinigi) Hahn’s cogged disc adding machine (possibly from Auch) Hahn’s stepped drum machine (replica) Herzstark’s Contina (prototype of the Curta 1) Hollerith’s punched card equipment (counting and sorting machine, tabulator, pantograph cardpunch (census machine)) (replica) (Herman Hollerith) Leibniz’s calculating machine (decimal, replica) Leupold/Braun/Vayringe toothed segment machine (replica) Morland’s cogged disc adding machine (replica) Morland’s multiplication and division device (replica) Müller’s stepped drum machine (replica) Pascaline (6- and 8-place, replicas) Poleni’s pinwheel machine (replica) Roth’s cogged disc adding machine Roth’s pinwheel machine (replica) Sauter’s pinwheel machine (replica) Schickard’s calculating clock (reconstruction) Schuster’s stepped drum machine (1820, 9-place, replica) Schuster’s stepped drum machine (1822, 10-place, original and replica) Stanhope’s calculating machine (replica) Stanhope’s cogged disc adding machine (replica) Stanhope’s stepped drum machine (replica) Thomas arithmometer (early model, decorative gift for a prince) Verea’s direct multiplier (replica) Warazan (Japanese straw knotted cord)

Remark In spite of repeated inquiries, the Arithmeum in Bonn provided no information about its holdings and made no illustrations available. The above information derives from publications and from the museum’s website. Calculating machines (e.g., Pascaline, piano arithmometer of Charles Xavier Thomas) on permanent loan from the IBM collection, New York

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9.3.8.4  Braunschweigisches Landesmuseum, Braunschweig • • • • • • • • • • • •

Arithmaurel (calculating machine of Maurel/Jayet) Brunsviga calculating machines Gersten’s addition and subtraction machine (replica) Grillet’s four-function device (Napier’s bones with cogged wheel adder) (replica) Hahn’s stepped drum machine (replica) Leibniz’s calculating machine (decimal, replica) Müller’s stepped drum machine (replica) Pascaline (replica) Roman hand abacus (replica) Schickard’s calculating clock (reconstruction) Selling’s direct multiplication machine (replica) Staffel’s addition and subtraction machine (Israel Abraham Staffel)

9.3.8.5  Hessisches Landesmuseum, Darmstadt • Gersten’s addition and subtraction machine (replica) • Leibniz’s calculating machine (binary, reconstruction) • Müller’s stepped drum machine 9.3.8.6  Historisches Museum, Dinkelsbühl • Calculating tables 9.3.8.7  Grünes Gewölbe, Dresden • Automaton figure with Diana on a centaur of Hans Jakob Bachmann • Rolling ball clock of Hans Schlottheim (musical automaton clock) 9.3.8.8  Mathematisch-physikalischer Salon, Dresden • • • • • • • • • •

“Hottentot dance” musical automaton of Matthäus Rungel “Topsy-turvy world” of Hans Schlottheim Astrolabe of Erasmus Habermel Astronomical-geographical bracket clock of Johannes Klein Auch’s cogged disc addition and subtraction machine Celestial globe of Georg Roll and Johannes Reinhold Celestial globe of Jost Bürgi Cross-beat escapement clock of Jost Bürgi Dietzschold’s ratchet machine (Curt Dietzschold) Napier’s bones

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Observational cross-beat escapement clock of Jost Bürgi Odometer of Christoph Schissler Pascaline Planetary clock of Eberhard Baldewein, Hans Bucher, and Hermann Diepel Wagon odometer of Christoph Trechsler World time clock of Andreas Gärtner

Remark In the exhibition guide of Wolfram Dolz, Joachim Schardin, Klaus Schillinger, and Helmut Schramm: Uhren  – Globen, wissenschaftliche Instrumente, Mathematisch-physikalischer Salon, Dresden Zwinger, Karl M.  Lipp Verlag, Dresden 1993, page 103, Auch’s cogged disc addition and subtraction machine (1790) is erroneously described as a four-function machine. 9.3.8.9  Technische Sammlungen, Dresden • D4a (transistor computer) • Leibniz’s calculating machine (decimal, replica, on loan from the Technische Universität Dresden) • Schickard’s calculating clock (reconstruction) • Typewriter of Peter Mitterhofer 9.3.8.10  Gottfried Wilhelm Leibniz Bibliothek, Hanover • Leibniz’s stepped drum machine (original and replica) 9.3.8.11  Leibniz Universität Hannover (Leibniz Exhibit) • Leibniz’s calculating machine (binary, four-function geared machine) (reconstruction) • Leibniz’s calculating machine (binary, functional model, ball machine) (machina arithmetica dyadica) • Leibniz’s calculating machine (decimal, functional model) • Leibniz’s coding and decoding machine (machina deciphratoria) (reconstruction) 9.3.8.12  L  eibniz Universität Hannover (Sammlung historischer geodätischer Instrumente und historischer Rechenhilfsmittel) • • • • •

Beyerlen’s calculating wheel (Angelo Beyerlen) Haff’s polar planimeter Ott’s linear planimeter (Albert Ott) Sonne’s calculating disc (Eduard Sonne) Wetli’s disc planimeter (Kaspar Wetli and Georg Christoph Starke)

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9.3.8.13  Astronomisch-physikalisches Kabinett, Kassel • • • • • • • • • • • •

Compass instrument (sundial compass) of Christoph Schissler Equation clock (astronomical bracket clock) of Jost Bürgi Kassel 1 celestial globe clock of Jost Bürgi Kassel 2 celestial globe clock of Jost Bürgi Observational clock 1 of Jost Bürgi Observational clock 2 of Jost Bürgi Pedometer of Thomas Rückert Proportional dividers of Jost Bürgi Schott’s calculating box (Napier’s bones) (Kaspar Schott) Table torquetum (turquet) of Erasmus Habermel Triangulation instrument of Jost Bürgi Wilhelm’s clock (planetary clock) of Eberhard Baldewein Hermann Diepel • Wilhelm’s quadrant (azimuthal quadrant) of Eberhard Baldewein

and

Remarks A torquetum is an astronomical observational and demonstration device. Celestial globes and armillary spheres with astronomical clocks of Jost Bürgi are found, e.g., in the Klassik-Stiftung Weimar and the Nordiska museet (Nordic Museum) in Stockholm. 9.3.8.14  Technoseum, Mannheim • Hahn’s stepped drum machine (Urach specimen, on loan from the House of Württemberg) 9.3.8.15  Bayerisches Nationalmuseum, Munich • Armillary sphere of Christoph Schissler • Counting cloths • Organum mathematicum of Athanasius Kircher 9.3.8.16  Deutsches Museum, Munich • “Stanislaus” relay calculating machine for propositional logic (formula controlled logic computer) • Amsler’s polar planimeter (Jakob Amsler) • Astrolabe of Erasmus Habermel • Beyerlen’s calculating wheel (Angelo Beyerlen) • Bollée’s direct multiplication machine (partial-product multiplying machine) • Dehomag D11 tabulator

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Felt’s comptometer Haff’s digital planimeter Henrici-Coradi’s harmonic analyzer IPM-Ott differential analyzer (parts) Leibniz’s calculating machine (binary, reconstruction) Leibniz’s calculating machine (decimal, replica) Leupold/Braun/Vayringe toothed segment machine (original and replica) Loom of Joseph-Marie Jacquard (replica) Lorenz SZ 42 cipher attachment (cipher teleprinter) LRR1 relay calculating machine for propositional logic Mechanical trumpeter (trumpeter automaton) of Friedrich Kaufmann Müller’s stepped drum machine (replica of a section) Pascaline (replica) Perm (program controlled elctronic computer) Praying monk (automaton figure) Roman hand abacus (replica) Schickard’s calculating clock (reconstruction) Schuster’s stepped drum machine (1792, 11-place) Schuster’s stepped drum machine (1820, 9-place) Selling’s direct multiplication machine Siemens 2002 transistor computer Telefunken RA 463/2 electronic analog computer Telefunken TR4 transistor computer Zuse Z3 relay computer (reconsruction of Konrad Zuse) Zuse Z4 relay computer

Remark IPM stands for the Institut für praktische Mathematik (Technische Hochschule, Darmstadt). 9.3.8.17  Münchner Stadtmuseum, Munich • Counting cloths 9.3.8.18  Heinz Nixdorf  Museumsforum, Paderborn • Astrolabe of Erasmus Habermel • Babbage’s analytical engine (multimedia presentation of the functional principle) • Babbage’s difference engine 2 (demonstration model, reconstruction) • Calculating cloth (replica) • Calculating hat (calculating beret, replica) • Chinese bamboo counting sticks (replica) • Dinkelsbühl calculating table (replica)

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• Edmondson’s cylindrical stepped drum calculating machine ( J o s e p h Edmondson) • Eniac (components) • Eniac (functional model) • Fuller’s cylindrical slide rule • Grillet’s four-function device (Napier’s bones with cogged wheel adder) • Harvard Mark 1/IBM ASCC, control unit (on loan from the Smithsonian Institution, Washington, D.C.) • Harvard Mark 1/IBM ASCC, function counter (on loan from the Smithsonian Institution, Washington, D.C.) • Harvard Mark 1/IBM ASCC, punched card reader (on loan from the Smithsonian Institution, Washington, D.C.) • Hines’ patent computer (cylindrical slide rule) (James Hines) • Hollerith’s punched card equipment (counting and sorting machine, tabulator, pantograph card punch (census machine)) (replica) • Knotted cord (replica) • Leibniz’s calculating machine (binary, reconstruction) • Leibniz’s calculating machine (decimal, replica) • Leupold/Braun/Vayringe toothed segment machine with functional model (replica) • Monastic abacus (Gerbert of Aurillac) (replica) • Müller’s stepped drum machine (replica) • Pascaline with demonstration model for addition and indirect subtraction (replica) • Roman hand abacus (replica) • Roth’s cogged disc adding machine • Schickard’s astronomical counting sticks (replica) • Schickard’s calculating clock with demonstration model for tens carry (reconstruction) • Schickard’s hand planetarium (replica) • Schott’s calculating box (Napier’s bones) (Kaspar Schott) • Spalding’s adding machine (Cyrus G. Spalding) • Thomas arithmometer (early model, decorative gift for a prince) • Webb’s cogged disc adding machine (Charles Henry Webb) • Zuse Z3 addition circuit (replica) 9.3.8.19  Landesmuseum Württemberg, Stuttgart • Auch’s cogged disc addition and subtraction machine • Hahn’s cylindrical slide rule (Napier’s bones) • Hahn’s stepped drum machine (Stuttgart specimen)

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9.3.8.20  Museum Tuttlingen-Möhringen • Leupold/Braun/Vayringe toothed segment machine (replica) Note Significant collections can also be found at the Germanisches Nationalmuseum in Nuremberg (e.g., astrolabes and coin cabinet) and the Sächsisches Industriemuseum in Chemnitz (analog and digital, mechanical and electromechanical calculating aids, bookkeeping machines, and typewriters).

9.3.9  Greece 9.3.9.1  Επιγραφικό Μουσείο, Athens (Epigraphic Museum) • Salamis counting board 9.3.9.2  Ε  θνικό Αρχαιολογικό Μουσείο, Athens (National Archaeological Museum) • Antikythera mechanism Remark In addition to the original Antikythera mechanism, the Athens museum maintains several reconstructions, e.g., the reconstructions of Derek de Solla Price and Michael Wright.

9.3.10  Italy 9.3.10.1  Musée archéologique régional, Aosta • Roman hand abacus 9.3.10.2  Museo Galileo, Florence • Burattini’s addition and multiplication device (without tens carry, with Napier’s bones) • Galileo Galilei’s sector • Gonnella’s keyboard adding machine • Handwriting automaton of Friedrich Knaus • Hodometer of Christoph Schissler • Leonardo da Vinci’s mechanical lion (reconstruction) • Leonardo da Vinci’s self-propelled cart (reconstruction) • Mathematical compendium of Christoph Schissler

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• • • •

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Military instrument of Jost Bürgi Morland’s multiplication and division device Morland’s trigonometric calculator Organum mathematicum of Athanasius Kircher

Notes It is not clear who invented the device attributed to Burattini. The Florence museum also maintains numerous scientific instruments (partly from the collection of the Medici family). 9.3.10.3  M  useo Nazionale della Scienza e della Tecnologia “Leonardo da Vinci”, Milan • Babbage’s difference engine 1 (demonstration model, reconstruction) • Hollerith’s punched card equipment (counting and sorting machine, tabulator, pantograph card punch (census machine)) (replica) • Leibniz’s calculating machine (decimal, replica of Roberto Guatelli) • Leonardo da Vinci’s self-propelled cart (reconstruction) • Pascaline (replica of Roberto Guatelli) • Poleni’s pinwheel machine (replica) • Typewriter (cembalo scrivano) of Giuseppe Ravizza 9.3.10.4  Palais-Mamming-Museum, Meran • Typewriter of Peter Mitterhofer 9.3.10.5  Museo archeologico nazionale, Naples • Darius vase 9.3.10.6  Palazzo reale, Reggia di Caserta • Thomas arithmometer (early model, decorative gift for a prince) 9.3.10.7  M  useo nazionale romano (Palazzo Massimo alle Terme), Rome • Roman hand abacus Note Other Italian museums with models (reconstructions) of Leonardo da Vinci: • Leonardo3 Museum, Milan • Museo Leonardiano, Vinci • Museo Leonardo da Vinci, Florence

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9.3.11  Japan In the National Museum of Nature and Science in Tokyo is a replica of the mechanical analog computer of John B. Wilbur (MIT, 1936). It served for the solution of (nine) linear equations.

9.3.12  The Netherlands 9.3.12.1  Rijksmuseum Boerhaave, Leiden • Auch’s cogged disc addition and subtraction machine

9.3.13  New Zealand 9.3.13.1  Museum of Transport and Technology, Auckland • Lennard-Jones’ differential analyzer (John Edward Lennard-Jones/J. B. Bratt) (Cambridge Meccano differential analyzer)

9.3.14  Spain 9.3.14.1  M  useo “Torres Quevedo,” Madrid (Universidad politecnica de Madrid) • Torres Quevedo’s mechanical calculating machines • Torres Quevedo’s chess automaton 9.3.14.2  Museo arqueológico nacional, Madrid • Napier’s promptuary (John Napier) Note The builder of this cabinet calculator is not known.

9.3.15  Sweden 9.3.15.1  Stadsmuseum, Gothenburg • Sauter’s pinwheel machine (Johann Jacob Sauter) Arithmeum, Bonn.

9.3  Which Calculating Devices Are Among the Museum’s Holdings?

9.3.15.2  T  ekniska museet, Stockholm (National Museum of Science and Technology) • • • •

Odhner’s pinwheel machine for the Swedish King Gustav V Pascaline (replica) Wiberg’s difference engine (Martin Wiberg) Writing ball of Rasmus Malling-Hansen

9.3.16  Switzerland 9.3.16.1  Historisches Museum, Basel • Calculating tables 9.3.16.2  Museum für Kommunikation, Bern • • • • • • •

Ermeth (vacuum tube computer) Hermes C-3 of Paillard IA 58 differential analyzer of Contraves Nema (cipher machine) Pascaline (demonstration model, replica) Schickard’s calculating clock (reconstruction) Zuse M9 (calculating punch)

9.3.16.3  Musée d’art et d’histoire, Geneva • Calculating table 9.3.16.4  Museum Rosenegg, Kreuzlingen TG • Stöckle’s polymeter 9.3.16.5  Musée international d'horlogerie, La Chaux-de-Fonds NE • Astrarium of Giovanni Dondi (reconstruction) 9.3.16.6  Musée d’horlogerie, Le Locle NE • Fée carabosse (old humpbacked witch) • Silkworm of Henri Maillardet

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9.3.16.7  Musée d’art et d’histoire, Neuchâtel • The draftsman (Le dessinateur) of Henri-Louis Jaquet-Droz • The musician (La musicienne) of Henri-Louis Jaquet-Droz • The writer (L’écrivain) of Pierre Jaquet-Droz 9.3.16.8  Museum Allerheiligen, Schaffhausen • Amsler’s integration instruments (Jakob Amsler) 9.3.16.9  Museum für Musikautomaten, Seewen SO • Britannic philharmonic organ 9.3.16.10  Museum Enter, Solothurn • • • • •

Alpina Atlas (disc adder) Nema (cipher machine) Pascaline (replica) Schickard’s calculating clock (reconstruction)

9.3.16.11  Historisches Museum, Schloss Thun BE • Calculating table • Counting board 9.3.16.12  ETH Zurich • Schwilgué’s keyboard adding machine (Jean-Baptiste Schwilgué) 9.3.16.13  Schweizerisches Landesmuseum, Zurich • Calculating tables • Celestial globe of Jost Bürgi • St. Gallen Globe of Tilemann Stella 9.3.16.14  Uhrenmuseum Beyer, Zurich • Astrarium of Giovanni Dondi (reconstruction) • Pagoda church tower clock

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Note Other excellent museums for musical automatons and automaton figures are the: • • • •

Musée Baud, L’Auberson VD Musée Cima (Centre international de la mécanique d’art), Sainte-Croix VD Museum für Uhren und mechanische Musikinstrumente, Oberhofen BE Uhrenmuseum, Winterthur ZH.

9.3.17  UK 9.3.17.1  Bletchley Park Trust, Bletchley Park • Enigma 9.3.17.2  National Museum of Computing, Bletchley Park • • • • • •

Colossus (functional reconstruction) Edsac (functional reconstruction) Harwell-Dekatron relay computer (functional original) Hec 1 (Hollerith electronic computer) (original) Tunny (reconstruction of the Lorenz SZ42 cipher machine) Turing-Welchman Bombe (functional reconstruction)

9.3.17.3  Centre for Computing History, Cambridge • Collection of machines, software packages, manuals, and magazines 9.3.17.4  Edinburgh Napier University • Napier’s promptuary (reconstruction) Napier’s promptuary has disappeared into oblivion (see box).

Napier’s Promptuary In his work Rabdologiæ (1617, in Latin), along with the decimal Napier’s bones, John Napier describes the promptuary, which has largely fallen into oblivion. Garry Tee considers the promptuary to be the first calculating machine (= mechanical lattice multiplication, or gelosia). The school of engineering of the University of Auckland reconstructed the (continued)

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promptuary on the basis of the Rabdologiæ translation of William Francis Hawkins. Hawkins demonstrated the device for the first time in 1979 at the University of Waikato in New Zealand. In commemoration of the 400th anniversary of John Napier’s death in 2017, the University of Auckland presented the reconstruction to the Napier University in Edinburgh. Napier’s writing also includes an elaboration of binary arithmetic. For further details see William Francis Hawkins: The first calculating machine (John Napier, 1617), in: The New Zealand mathematics society Newsletter 1979, volume 16, appendix, pages 1–23 William Francis Hawkins: The first calculating machine (John Napier, 1617), in: Annals of the history of computing, volume 10, 1988, no. 1, pages 37–51 Garry J.  Tee: The Auckland promptuary, in: The New Zealand mathematics society newsletter, December 2017, volume 131, 3 pages Erwin Tomash: The Madrid promptuary, in: Annals of the history of computing, volume 10, 1988, no. 1, pages 52–67.

9.3.17.5  British Museum, London • • • • •

Astrolabes Mechanical ship automaton (with musical puppets) of Hans Schlottheim Papyrus Rhind Roman hand abacus Sundials

9.3.17.6  Science Museum, London • • • • • • • • • • • • •

Arithmaurel (calculating machine of Maurel/Jayet) Babbage’s analytical engine (section, original and reconstruction) Babbage’s difference engine 1 (section of the original machine) Babbage’s difference engine 1 (section, functional reconstruction, demonstration model) Babbage’s difference engine 2 (functional reconstruction) Bavarian counting cloth (replica) Besm 6 BriCal disc adder CDC 6600 Colossus (components) Edsac (component: mercury delay line memory) Elliott/NRDC 401 Mark 1 (NRDC = National Research Development Corporation) Eniac (component)

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• • • • • • • • • • • • • • • • • • • • • • • • • • • •

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Enigma Felt’s comptometer Ferranti Mark 1 (components: Williams memory tubes) Ferranti Pegasus Hand loom of Joseph-Marie Jacquard (replica) Hartree’s differential analyzer (Meccano model) Hartree’s differential analyzer (original, half section) Harvard Mark 1/IBM ASCC (electromagnetic decimal counter, relay) Henrici’s harmonic analyzer Julius’ totalizator Kelvin’s tide predictor (William Thomson) Leibniz’s calculating machine (decimal, replica) Leo 1 (component: mercury delay line memory) Morland’s cogged disc adding machine (original and replica) Morland’s trigonometric calculator Napier’s bones Pascaline (replica) Pilot Ace Roman hand abacus (replica) Roth’s cogged disc adding machine Sauter’s stylus-type adder (Johann Jacob Sauter) Scheutz’s difference engine 3 Schickard’s calculating clock (reconstruction) Schott’s calculating box (Napier’s bones) (replica) Stanhope’s cogged disc adding machine Stanhope’s stepped drum machine Stanhope’s toothed segment machine Stanhope’s toothed segment machine (experimental piece)

9.3.17.7  Science and Industry Museum, Manchester • Hartree’s (analog) differential analyzer (Douglas Rayner Hartree) • Manchester Baby (small-scale experimental machine) (functional recon­struction) 9.3.17.8  History of Science Museum, Oxford • • • • • • •

Astrolabe of Erasmus Habermel Astronomical compendium of Christoph Schissler BriCal disc adder Morland’s cogged disc adding machine Stanhope’s cogged disc adding machine Stanhope’s logic calculator Sundials

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9.3.18  USA 9.3.18.1  Intellectual Ventures Laboratories, Bellevue, Washington • Babbage’s difference engine 2 (functional reconstruction) 9.3.18.2  Harvard University, Cambridge, Massachusetts • Harvard Mark 1/IBM ASCC (section) 9.3.18.3  M  IT Museum, Cambridge, Massachusetts (Massachusetts Institute of Technology) • Bush’s mechanical differential analyzer (component: integration element) (Vannevar Bush) • TX-0 transistor computer (component: terminal) • Whirlwind (component: core memory unit) 9.3.18.4  N  ational Cryptologic Museum, Fort George G.Meade, Maryland • Cryptanalytical Bombe of the US Navy 9.3.18.5  Computer History Museum, Mountain View, California • Amsler’s integrator (Jakob Amsler) • Amsler’s polar planimeter (Jakob Amsler) • Atanasoff-Berry computer (addition and subtraction mechanism, reconstruction) (John Vincent Atanasoff) • Atanasoff-Berry computer (operational reconstruction, on loan from Iowa State University, Ames) • Babbage’s difference engine 1 (demonstration model, replica of Roberto Guatelli) • Bendix G-15 • Dyseac (components) • Harvard Mark 2–4 (components) • Hollerith’s pantograph card punch (original and replica) (Herman Hollerith) • Hollerith’s punched card equipment (counting and sorting machine, tabulator, pantograph card punch (census machine)) (replica of Roberto Guatelli) • IBM 650 (components) • IBM 701 (components) • IBM 7030 (Stretch) (components)

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• • • • • • • • • • •

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IBM 305 Ramac (magnetic disc) Illiac 1 (components) Johnniac Maddida digital differential analyzer (experimental piece, original) Pascaline (replica of Roberto Guatelli) Sage (semiautomatic ground environment antiaircraft defense system) (component) Schickard’s calculating clock (reconstruction) Stibitz’ Model K addition device (K= kitchen) (replica) (George Robert Stibitz) Univac 1 (components) Univac Larc (components) Whirlwind (components)

Remark Johnniac is the only still intact surviving early large-scale American computer. 9.3.18.6  U  niversity of Pennsylvania, Philadelphia (School of Engineering and Applied Science) • Eniac (components: e.g., 4 of the original 40 control cabinets with plugboards) 9.3.18.7  C  arnegie Mellon University, Pittsburgh, Pennsylvania (Traub-McCorduck Collection) • Adix keyboard adding machine (replica of Roberto Guatelli) • Leibniz’s calculating machine (decimal, replica of Roberto Guatelli) • Millionär of Otto Steiger and Hans W. Egli (direct multiplication machine) (replica of Roberto Guatelli) • Pascaline (replica of Roberto Guatelli) • Webb’s adding machine (Charles Henry Webb) (replica of Roberto Guatelli) 9.3.18.8  Living Computers: Museum + Labs, Seattle, Washington • Collection of fully restored and usable supercomputers, mainframes, minicomputers, and microcomputers 9.3.18.9  I BM Corporate Archives, IBM Corporation, Poughkeepsie, New York • Arithmaurel (calculating machine of Maurel/Jayet) • Babbage’s analytical engine (section, reconstruction)

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• Bollée’s direct multiplication machine (partial-product multiplying machine) • Bollée’s multiplication and division device (arithmograph with Napier’s bones) • Edmondson’s cylindrical stepped drum calculating machine (Joseph Edmondson) • Grant’s difference engine (George Barnard Grant) • Hahn’s stepped drum machine • Hand loom (model) of Joseph-Marie Jacquard • Hill’s keyboard calculating machine (four-function calculator, Thomas Hill) • Hollerith’s punched card equipment (counting and sorting machine, tabulator, pantograph card punch (census machine)) • Leibniz’s calculating machine (decimal, replica) • Leupold/Braun/Vayringe toothed segment machine (replica) • Michelson/Stratton harmonic analyzer (Albert A.  Michelson, Samuel W. Stratton) • Morland’s trigonometric calculator • Pascaline (original and replica) • Galileo Galilei’s sector (replica) • Roth’s cogged disc adding machine • Sage (semiautomatic ground environment, antiaircraft defense system) (magnetic core arrangement) • Scheutz’s difference engine 2 (replica) • SSEC (selective sequence electronic calculator) (control console) • Thomas’ piano arithmometer (Charles Xavier Thomas) • Verea’s direct multiplier (Ramón Verea) • Webb’s adding machine (Charles Henry Webb) Notes The following website provides information about the IBM collection of historical instruments: https://www-03.ibm.com/ibm/history/exhibits. According to the personal communication of Jamie Martin of August 31, 2017, the collection of the IBM Corporate Archives is not open to the public. Max Campbell writes in his email of November 18, 2018 that the cost of making inquiries is too high. In some cases it is not clear whether an original or a replica is present. The book of Herman Goldstine: The computer from Pascal to von Neumann, Princeton University Press, Princeton, New Jersey 1993, includes photos (page 120 ff.) of IBM of rebuilds of Babbage’s difference engine (1) and the Leibniz (decimal) calculating machine, as well as Schickard’s calculating clock. Whether these objects are still part of the collection is not clear. See also the Arithmeum in Bonn (calculating machines on permanent loan)

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9.3.18.10  National Museum of American History, Washington, D.C. • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • • •

Amsler’s polar planimeter (Jakob Amsler) Babbage’s difference engine 1 (section, reconstruction) Babylonian clay tablet (replica) Baldwin’s pinwheel machine (Frank Stephen Baldwin) Barbour’s direct multiplier (Edmund D. Barbour) Bell 5 relay computer (section: control unit) Bollé’s direct multiplication machine (partial-product multiplying machine) Bush’s differential analyzer (several components) Coradi’s planimeter (Gottlieb Coradi) Edvac (components) Eniac (several parts: accumulator) Felt’s comptometer (macaroni box) Harvard Mark 1/IBM ASCC (section) Hollerith’s punched equipment (counting and sorting machine, tabulator, pantograph card punch (census machine)) IAS computer (large part) Kern’s circular protractor Lépine’s addition and subtraction machine Odhner’s pinwheel machine (very early model) Pascaline (demonstration model, replica) Ramminger’s pedometer (Jacob Ramminger) Salamis counting board (replica) Scheutz’s difference engine 1 Schilt’s keyboard adding machine (original, copy of the Schwilgué machine) Seac (sections) Swac (small components) Thomas arithmometer (stepped drum machine) (oldest surviving model) Univac 1 (several components) Verea’s direct multiplier (Ramón Verea) Webb’s adding machine (Charles Henry Webb) Wetli’s planimeter (Kaspar Wetli) Whirlwind (numerous parts) Wright’s arithmeter (cylindrical slide rule) (Elizur Wright)

Note The Long Island Science Center in Riverhead, New York, has a collection of models of Leonardo da Vinci (reconstructions of Roberto Guatelli). The Metroplitan Museum of Art, New York houses rare figure automatons. Sources The information regarding the details of the collections is taken from visits to museums, museum guides, exhibition catalogs, email correspondence, collection databases, and the websites of the museums. Note: the object databases are often incomplete and sometimes of only limited informational value.

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Illustrations The following pages depict the precious cylindrical machines of Braun, Hahn, Müller, Schuster, and Sauter. They are capable of performing all four basic arithmetic operations (see Figs. 9.2, 9.3, 9.4, 9.5, 9.6, 9.7, 9.8, 9.9, 9.10, 9.11, 9.12, 9.13, and 9.14). Following these are the one-function and multifunction calculating machines of Auch, Bollée, Felt, Gersten, Gonnella, Grillet, Lépine, Maurel, Morland, Roth, and Staffel. The objects are from England, France, Germany, Italy, Poland, and the USA (see Figs. 9.15, 9.16, 9.17, 9.18, 9.19, 9.20, 9.21, 9.22, 9.23, 9.24, 9.25, 9.26, 9.27, 9.28, 9.29, 9.30, and 9.31). They include adding machines (with ten-key and full keyboards), multiplication devices with Napierian cylinders, partial-product multiplying machines, and trigonometric calculators. Drawings from an influential contemporary reference work convey an overview of the selected calculating devices from France, Germany, Switzerland, and the USA (see Figs. 9.32 and 9.33). Finally, another illustration depicts an attractive combination of Jacob Leupold’s machine book, a cylindrical calculating machine, and a pinwheel calculating machine (see Fig. 9.34).

Fig. 9.2  Braun’s pinwheel machine (1727). This scientific instrument of Anton Braun is made of brass and is gold-plated and partly tin-plated. (© Kunsthistorisches Museum Wien, Vienna, KHM-Museumsverband)

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Fig. 9.3  Leupold/Braun/Vayringe toothed segment machine (1735). Anton Braun designed this cylindrical four-function machine from the unfinished plans of Jacob Leupold (built by Philippe Vayringe). A similar machine is in the i Wiener Kunstkammer. (© Deutsches Museum, Munich)

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Fig. 9.4  Hahn’s stepped drum machine (1) (1774). This cylindrical machine of Philipp Matthäus Hahn is considered the first mechanical four-function machine to be useful in practice. (© Landesmuseum Württemberg, Stuttgart, picture: P. Frankenstein, H. Zwietasch)

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Fig. 9.5  Hahn’s stepped drum machine (2) (1774). This magnificent cylindrical machine functions with 11 places. (© Landesmuseum Württemberg, Stuttgart, picture: P. Frankenstein, H. Zwietasch)

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Fig. 9.6  Hahn’s stepped drum machine (1) (1776). The machine of Philipp Matthäus Hahn functions with 12 places. (© Technoseum, Mannheim, picture: Klaus Luginsland)

Fig. 9.7  Hahn’s stepped drum machine (2) (1776). Only a few of Hahn’s calculating machines have survived. (© Technoseum, Mannheim, picture: Klaus Luginsland)

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Fig. 9.8  Hahn’s stepped drum machine (3) (1776). Calculating machines were often masterpieces of art as well. (© Technoseum, Mannheim, picture: Klaus Luginsland)

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Fig. 9.9  Müller’s stepped drum machine (1) (1784). This cylindrical 14-place four-function machine of Johann Helfrich Müller enables calculations in different number systems (base-2 to base-12 number system) by changing the numeral discs. (© Hessisches Landesmuseum, Darmstadt)

Fig. 9.10  Müller’s stepped drum machine (2) (1784). Mechanical devices protect against operating errors. In 1786 Müller was thinking of building a difference engine with printout. (© Hessisches Landesmuseum, Darmstadt)

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Fig. 9.11  Schuster’s stepped drum machine (1792). The cylindrical four-function machine of Johann Christoph Schuster functions with 12 places. (© Deutsches Museum, Munich)

Fig. 9.12  Schuster’s stepped drum machine (1820). Johann Christoph Schuster completed his 9-place cylindrical four-function machine only after 15 years construction time. (© Deutsches Museum, Munich)

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Fig. 9.13  Sauter’s pinwheel machine (1) (1796). Johann Jacob Sauter created one of the most magnificent four-function machines. Experts only learned of its existence a few years ago. (© Stadsmuseum Gothenburg)

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Fig. 9.14  Sauter’s pinwheel machine (2) (1796). The cylindrical machine of Johann Jacob Sauter functions with 9 places. Exceeding the calculating capacity causes a bell to ring. (© Stadsmuseum Gothenburg)

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Fig. 9.15  Arithmaurel (1849). The stepped drum machine of Timoléon Maurel and Jean Jayet is capable of all four basic arithmetic operations. No carriage shifting is required. (© Braunschweigisches Landesmuseum, Braunschweig, picture: Ingeborg Simon)

Fig. 9.16  Morland’s calculating machine (1664). This 10-place device of Samuel Morland is suitable for multiplication and division. At the top are the numeral discs (circular dials) of the setting mechanism (Napierian cylinders) and at the bottom the 11 display windows of the calculating unit. In the middle is the mechanical memory. (© Museo Galileo, Florence)

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Fig. 9.17 Morland’s cogged disc addition device (1666). Together with Schickard, Pascal, and Leibniz, Samuel Morland belongs to the few builders of calculating aids of the seventeenth century. The case is of leather. (© Science Museum, London/Science & society picture library)

Fig. 9.18  Cogged disc addition and subtraction machine (1789). Only three specimens of this fine addition machine of the clockmaker Jacob Auch have survived (1789, 1790, and 1800). The dials are operated with a stylus. (© Landesmuseum Württemberg, Stuttgart, picture: P. Frankenstein, H. Zwietasch)

Fig. 9.19  Roth’s cogged disc adding machine (1843). This calculating aid was intended for the English currency. Didier Roth also built a circular pinwheel calculator (1841) for the four basic arithmetic operations (© Science Museum, London/Science & society picture library)

Fig. 9.20  Staffels’s addition and subtraction machine (1845). This calculating aid of the Warsaw inventor Israel Abraham Staffel functioned with toothed racks. (© Braunschweigisches Landesmuseum, Braunschweig. picture: Ingeborg Simon)

Fig. 9.21  Grillet’s four-function device. The cogged disc adder (before 1678) of René Grillet utilizes Napierian cylinders for multiplication and division. It has no tens carry. (© Musée des arts et métiers-Cnam, Paris/picture: Sylvain Pelly)

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Fig. 9.22  Lépine’s addition and subtraction machine (1725). The calculating aid of the clockmaker Jean Lépine in the leather-lined wooden casing is equipped with 10 rows of 5 circles. Each circle has a viewing window. The machine is operated with a stylus. (© Division of medicine & science, National Museum of American History, Smithsonian Institution, Washington, D.C.)

Fig. 9.23  Gersten’s addition and subtraction machine (1722). This calculating aid of Christian Ludwig Gersten (replica) utilizes complements for subtraction (© Braunschweigisches Landesmuseum, Braunschweig, picture: Ingeborg Simon)

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Fig. 9.24  Gonnella’s keyboard adding machine (1858). This brass and iron calculating aid of Tito Gonnella belongs to the few early key-driven column adders. Below are the keys for the numerals 1–5 and above the keys for the numerals 6–9. (© Museo Galileo, Florence)

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Fig. 9.25  Morland’s trigonometric calculator (1670). Samuel Morland built this rare device for trigonometric calculations. (© Museo Galileo, Florence)

Fig. 9.26  Morland’s trigonometric calculator (1664). Samuel Morland invented this brass, iron, and wooden device for trigonometric calculations. (© Science Museum, London/ Science & society picture library)

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Fig. 9.27  Macaroni box (1884). For his prototype Dorr E. Felt utilized a wooden macaroni box. This 5-place device was the forerunner of the comptometer, a keyboard adding machine. (© Division of medicine & science, National Museum of American History, Smithsonian Institution, Washington, D.C.)

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Fig. 9.28  Comptometer of Felt and Tarrant (1887). This early adding machine with full keyboard was mass-produced by the Felt and Tarrant manufacturing company in Chicago, Illinois. (© Deutsches Museum, Munich)

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Fig. 9.29  Verea’s direct multiplier (1878). The inventor was the Spanish-born Ramón Verea. Two vertical brass prisms can be seen on the front side of the open model. Each of these has ten sides, and each side has two rows of ten holes. The holes have different sizes, with the largest hole representing the numeral 0 and the smallest the numeral 9. The cylinders are rotated with the two knobs (on the top). (© Division of medicine & science, National Museum of American History, Smithsonian Institution, Washington, D.C.)

Fig. 9.30  Bollée’s direct multiplier (1889). This heavy calculating machine was not successful commercially, but it inspired the production of the Swiss four-function Millionaire machine. (© Musée des arts et métiers-Cnam, Paris, picture: studio Cnam)

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Fig. 9.31  Arithmographe of Léon Bollée. The 14-place portable French multifunction calculator (1889) is comprised of a slide bar adder with semiautomatic crook tens carry and Genaille-Lucas rulers in the form of superimposed lamellae. The stylus-operated slide bar adder performs addition and subtraction. The rulers are for multiplication and division. The two horizontal levers (below) reset all values to zero. Thanks to a movable rack, the GenailleLucas rulers can be positioned to the left and right, showing the partial products directly. This avoids forming products as repeated additions. The carriage serves for shifting. The frame has six bundled groups of nine rotatable rods. This device is an ingenious combination of two digital calculators. (© Inria/picture: J.-M. Rames)

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Fig. 9.32  Calculating machines described in a reference work (1). Shown here are (from above to below) the Pascaline addition and subtraction machine, Leibniz’s stepped drum calculator, and the Millionaire direct multiplier. (Source: Meyers Großes KonversationsLexikon, Bibliographisches Institut, Leipzig, Vienna, 6th completely revised and expanded edition of 1908, 16th volume: heading Rechenmaschinen, in the public domain)

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Fig. 9.33  Calculating machines described in a reference work (2). Shown here in addition to a calculating stylus are Müller’s cylindrical stepped drum machine, Selling’s direct multiplier, the Burroughs full-keyboard adder, the Brunsviga pinwheel machine, and Burkhardt’s stepped drum machine. (Source: Meyers Großes Konversations-Lexikon, Bibliographisches Institut, Leipzig, Vienna, 6th completely revised and expanded edition of 1908, 16th volume: heading Rechenmaschinen, in the public domain)

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Fig. 9.34 Brunsviga, cylindrical calculator, and textbook. The Brunsviga is a pinwheel machine, and the cylindrical machine has 12 places. Jacob Leupold designed a toothed segment machine that was built by Anton Braun and Philippe Vayringe. (© Heinrich Heidersberger, Institut Heidersberger GmbH, Wolfsburg, Germany)

9.4  W  here Is a Particular Historical Calculating Device on Exhibit? 9.4.1  Analog Calculating Aids Antikythera mechanism (builder unknown) National Archaeological Museum/Εθνικό Αρχαιολογικό Μουσείο, Athens Remark Reconstructions exist in several countries (e.g., Australia, England, Germany, Greece, and Switzerland). Schwilgué’s church calculator (Jean-Baptiste Schwilgué) Strasbourg cathedral Loga cylindrical slide rule, 24 m (Heinrich Daemen Schmid) Numerous collections (nine surviving specimens), e.g., ETH Zurich, UBS Basel, and Universität Greifswald, as well as private collections Armillary spheres Numerous museums

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Astrolabes Numerous museums Globes Numerous museums Sundials Numerous museums Slide rules Numerous museums Sectors Numerous museums Proportional dividers Numerous museums Curvimeters Numerous museums Planimeters Numerous museums Differential analyzers • Hartree’s differential analyzer (Douglas Hartree/Arthur Porter) Science Museum, London (Meccano demonstration model) • Differential analyzer of Lennard-Jones (John Edward Lennard-Jones/J. B. Bratt) Museum of Transport and Technology, Auckland, New Zealand • IPM-Ott differential analyzer Deutsches Museum, Munich • Contraves IA 58 Museum für Kommunikation, Bern.

9.4.2  Digital Calculating Aids Counting boards (marble calculating boards) See Alain Schärlig: Compter avec des cailloux, Presses polytechniques et universitaires romandes, Lausanne, 2nd revised edition 2001 Bead frames (counting frames) Numerous museums Counting sticks (e.g., Napier, Genaille/Lucas) Numerous museums Sliding bar calculators Numerous museums

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Difference engines • Scheutz’s difference engine 1 (Pehr Georg Scheutz, father; Edvard Raphael Scheutz, son) National Museum of American History, Washington, D.C. • Scheutz’s difference engine 3 (Pehr Georg Scheutz, Edvard Raphael Scheutz) Science Museum, London Punched card equipment • Numerous museums • Tauschek’s bookkeeping machine (Gustav Tauschek) Technisches Museum Wien, Vienna Programmable automatic computers • Csirac vacuum tube computer (Trevor Pearcey, Maston Beard) Melbourne Museum, Carlton, Victoria • Harwell-Dekatron relay computer (Edward Cooke-Yarborough, Robert Barnes) National Museum of Computing, Bletchley Park (functional) • Hec 1 (Hollerith electronic computer, Raymond Bird) National Museum of Computing, Bletchley Park • Mailüfterl transistor computer (Heinz Zemanek) Technisches Museum Wien, Vienna • Pilot Ace vacuum tube computer (Alan Turing, James Wilkinson) Science Museum, London • Zuse Z4 relay computer (Konrad Zuse) Deutsches Museum, Munich Cipher machines • Enigma (Arthur Scherbius) Numerous museums

9.4.3  C  ounting Tables, Counting Boards, and Counting Cloths Counting tables/calculating tables Australia • Renmark (private ownership, table originally from French-speaking Switzerland) Austria (seventeenth century) • Innsbruck (Schloss Ambras)

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Denmark (seventeenth century) • Copenhagen (Rosenborg castle) France (around 1600) • Strasbourg (Musée de l'Oeuvre Notre-Dame) Germany (nine specimens, sixteenth century) • • • • • •

Berlin (Jüdisches Museum, on permanent loan from Dinkelsbühl) Dinkelsbühl (Haus der Geschichte) Goslar (Museum Goslar) Lüneburg (Rathaus, two specimens) Münster Nuremberg (Germanisches Nationalmuseum, on permanent loan from Dinkelsbühl) • Volkach (Museum Barockscheune) • Wittenberg (Ordinandenstube of the St. Marien Church) Switzerland (18 specimens, sixteenth and seventeenth centuries) • • • • • • • • • •

Basel (Historisches Museum, two specimens) Basel (Staatsarchiv) Bremgarten AG (Stadthaus) Château d’Œx VD (Musée du Vieux Pays-d’Enhaut, two specimens) Geneva (Musée d’art et d’histoire) Sembrancher VS (Maison communale) Sierre VS (Château Muzot) Thun BE (Historisches Museum Schloss Thun) Veytaux VD (Château de Chillon) Zurich (Schweizerisches Landesmuseum, two specimens)

Further calculating tables are in private ownership in cantons Vaud (four specimens) and Neuchâtel (one specimen). Counting boards (wooden tablets) Switzerland (three specimens) • Château d’Œx VD (Musée du Vieux Pays-d’Enhaut) • Thun BE (Historisches Museum Schloss Thun) A further counting board is in private ownership in Rossinière VD. Counting cloths Germany (eight specimens) • • • •

Munich (Bayerisches Hauptstaatsarchiv, two specimens) Munich (Bayerisches Nationalmuseum, three specimens) Munich (Stadtmuseum, two specimens) Überlingen (Städtisches Heimatmuseum)

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Calculating hat • Vienna (Kunsthistorisches Museum Wien, mercenary’s beret) Remark Numerous replicas of calculating tables exist (e.g., at the Adam-Ries-Museum in Annaberg-Buchholz, the Heimatmuseum in Bad Staffelstein, the Arithmeum in Bonn, the Heinz Nixdorf  Museumsforum in Paderborn, the Heimatverein Wittenberg und Umgebung, the Stadtmuseum Ingolstadt, and Schloss Vianden in Luxembourg) and replicas of counting cloths (e.g., in AnnabergBuchholz, Bad Staffelstein, and Erfurt). Source Ulrich Reich: Rechentische, -bretter und -tücher. Originale und Nachbauten, in: Rainer Gebhardt (Hg.): 500 Jahre erstes Rechenbuch von Adam Ries, Adam-Ries-­Bund, Annaberg-Buchholz 2018, pages 57–64 For further information see Alain Schärlig: Compter avec des jetons. Tables à calculer et tables de compte du Moyen Age à la Révolution, Presses polytechniques et universitaires romandes, Lausanne 2003. The following is divided into a description of original and rebuilt devices. It covers only rare devices from the early history of calculating technology.

9.4.4  H  istorical Calculating Aids and Their Exhibition Sites: Originals • Amsler’s integrators (polar planimeter of Jakob Amsler) Museum Allerheiligen, Schaffhausen; v Museum, Munich; Musée des arts et métiers, Paris; National Museum of American History, Washington, D.C., Computer History Museum, Mountain View, California • Antikythera mechanism (astronomical calculating machine) National Archaeological Museum/Εθνικό Αρχαιολογικό Μουσείο, Athens • Arithmaurel (calculating machine of Timoléon Maurel and Jean Jayet) Musée des arts et métiers, Paris; Braunschweigisches Landesmuseum, Braunschweig; Arithmeum, Bonn; Science Museum, London; IBM Corporate Archives, Poughkeepsie, New York • Arithmometer (stepped drum machine) (Charles Xavier Thomas) Numerous museums; see www.arithmometre.org, e.g., National Museum of American History, Washington, D.C.; Musée des arts et métiers, Paris; Arithmeum, Bonn; Reggia di Caserta (Palazzo reale); Heinz Nixdorf ­ Museumsforum, Paderborn • Auch’s cogged wheel addition and subtraction machine (Jacob Auch) Landesmuseum Württemberg, Stuttgart; Mathematisch-physikalischer Salon, Dresden; Rijksmuseum Boerhaave, Leiden

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• Babbage’s analytical engine (section) (Charles Babbage) Science Museum, London • Babbage’s difference engine 1 (section) (Charles Babbage) Science Museum, London • Baldwin’s pinwheel machine (Frank Stephen Baldwin) Numerous museums, e.g., National Museum of American History, Washington, D.C. • Beyerlen’s calculating wheel (Angelo Beyerlen) Deutsches Museum, Munich; Leibniz Universität Hannover (Sammlung historischer geodätischer Instrumente und historischer Rechenhilfsmittel) • Bollée’s direct multiplication machine (Léon Bollée) Musée des arts et métiers, Paris; Deutsches Museum, Munich; National Museum of American History, Washington, D.C.; IBM Corporate Archives, Poughkeepsie, New York • Bollée’s multiplication and division device (arithmograph with Napier’s bones) Musée des arts et métiers, Paris; IBM Corporate Archives, Poughkeepsie, New York • Braun’s pinwheel machine (Anton Braun) Kunsthistorisches Museum Wien, Vienna • Bürgi’s proportional dividers (Jost Bürgi) Astronomisch-physikalisches Kabinett, Kassel • Csirac stored program vacuum tube computer (Trevor Pearcey, Maston Beard) Melbourne Museum, Carlton, Victoria • Curta (stepped drum machine) (Curt Herzstark) Numerous museums, original model in the Liechtensteinisches Landes­ museum, Vaduz • Darius vase with calculating table (Apulia) Museo archeologico nazionale, Naples • Dietzschold’s ratchet machine (Curt Dietzschold) Arithmeum, Bonn; Mathematisch-physikalischer Salon, Dresden; Uhrenmuseum, Vienna • Felt’s comptometer (Dorr Eugene Felt) Deutsches Museum, Munich; Science Museum, London; Musée des arts et métiers, Paris; National Museum of American History, Washington, D.C. (macaroni box) • Galileo’s sector (Galileo Galilei) Museo Galileo, Florence • Gonnella’s keyboard adding machine (Tito Gonnella) Museo Galileo, Florence

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• Gonnella’s cogged disc adding machine (Tito Gonnella) Arithmeum, Bonn • Grillet’s four-function device (Napier’s bones with cogged disc adder of René Grillet) Musée des arts et métiers, Paris; Heinz Nixdorf  Museumsforum, Paderborn • Hahn’s cylindrical calculating drum Landesmuseum Württemberg, Stuttgart • Hahn’s stepped drum machine (Philipp Matthäus Hahn) Landesmuseum Württemberg, Stuttgart; Technoseum, Mannheim; IBM Corporate archives, Poughkeepsie, New York • Hartree’s differential analyzer (Douglas Rayner Hartree) Science Museum, London; Science and Industry Museum, Manchester • Harwell Dekatron stored program relay computer (Edward CookeYarborough, Robert Barnes) National Museum of Computing, Bletchley Park • Hec 1 (Hollerith electronic computer) National Museum of Computing, Bletchley Park • Hollerith’s punched card equipment (counting and sorting machine, tabulator, pantograph card punch (census machine)) (Herman Hollerith) National Museum of American History, Washington, D.C.; IBM Corporate Archives, Poughkeepsie, New York; Musée des arts et métiers, Paris • Kircher’s organum mathematicum (Athanasius Kircher) Bayerisches Nationalmuseum, Munich; Museo Galileo, Florence • Johnniac (vacuum tube computer) Computer History Museum, Mountain View, California • Leibniz’s stepped drum machine (Gottfried Wilhelm Leibniz) Gottfried Wilhelm Leibniz Bibliothek, Hanover • Lépine’s addition and subtraction machine (Jean Lépine) Musée des arts et métiers, Paris; National Museum of American History, Washington, D.C. • Leupold/Braun/Vayringe toothed segment machine (Jacob Leupold/Anton Braun/Philippe Vayringe) Deutsches Museum, Munich • Mailüfterl transistor computer (Heinz Zemanek) Technisches Museum Wien, Vienna • Millionaire direct multiplication machine (Otto Steiger) Numerous museums • Morland’s multiplication and division device (Samuel Morland) Museo Galileo, Florence

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• Morland’s trigonometric calculator (Samuel Morland) Science Museum, London; Museo Galileo, Florence; IBM Corporate Archives, Poughkeepsie, New York • Morland’s cogged disc adding machine (Samuel Morland) Science Museum, London; History of Science Museum, Oxford • Müller’s stepped drum machine (Johann Helfrich Müller) Hessisches Landesmuseum, Darmstadt • Napier’s promptuary (John Napier) Museo arqueológico nacional, Madrid • Odhner’s pinwheel machine (Willgodt Theophil Odhner) Numerous museums, e.g., Deutsches Museum, Munich; National Museum of American History, Washington, D.C. • Pascaline addition and subtraction machine (Blaise Pascal) Numerous museums (eight surviving specimens and one later replica with original parts), e.g., Musée des arts et métiers, Paris (three specimens); Mathematisch-physikalischer Salon, Dresden (one specimen); Muséum ­Henri-Lecoq, Clermont-Ferrand (two specimens), IBM Corporate Archives, Poughkeepsie, New  York (one specimen); and private collection (Léon Poncé collection) (one specimen). The later ninth specimen (also in Paris) dates from the eighteenth century. • Pilot Ace stored program vacuum tube computer (Alan Turing, James Wilkinson) Science Museum, London • Roman hand abacus Museo nazionale romano (Palazzo Massimo alle Terme), Rome, Bibliothèque nationale de France (Cabinet des médailles), Paris; Musée archéologique régional, Aosta • Roth’s addition and subtraction machine (Didier Roth) Musée des arts et métiers, Paris; Heinz Nixdorf  Museumsforum, Paderborn • Roth’s multiplication and division rods (Didier Roth) Musée des arts et métiers, Paris • Roth’s pinwheel machine (Didier Roth) Musée des arts et métiers, Paris • Roth’s cogged disc adding machine (Didier Roth) Musée des arts et métiers, Paris; Heinz Nixdorf  Museumsforum, Paderborn; Arithmeum, Bonn; Technisches Museum Wien, Vienna; Science Museum, London; IBM Corporate Archives, Poughkeepsie, New York • Salamis counting board (island of Salamis) Epigraphic Museum/Επιγραφικό Μουσείο, Athens

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• Sauter’s pinwheel machine (Johann Jacob Sauter) Stadsmuseum, Gothenburg • Sauter’s stylus-type adder (Johann Jacob Sauter) Science Museum, London • Scheutz’s difference engine 1 (Pehr Georg Scheutz) National Museum of American History, Washington, D.C. • Scheutz’s difference engine 3 (Pehr Georg Scheutz) Science Museum, London • Schilt’s keyboard adding machine (Victor Schilt, copy of the Schwilgué machine) National Museum of American History, Washington, D.C. • Schuster’ pinwheel machine (Johann Christoph Schuster) Deutsches Museum, Munich; Arithmeum, Bonn • Schwilgué’s keyboard adding machine (Jean-Baptiste Schwilgué) ETH Zurich; Musée historique, Strasbourg • Schwilgué’s “process” calculator (Jean-Baptiste Schwilgué) Musée historique, Strasbourg • Selling’s direct multiplication machine (Eduard Selling) Deutsches Museum, Munich • Staffel’s addition and subtraction machine (Israel Abraham Staffel) Braunschweigisches Landesmuseum, Braunschweig • Stanhope’s logic calculator (Charles Stanhope) History of Science Museum, Oxford • Stanhope’s stepped drum machine (Charles Stanhope) Science Museum, London • Stanhope’s toothed segment machine (Charles Stanhope) Science Museum, London • Stanhope’s cogged disc adding machine (Charles Stanhope) Science Museum, London; History of Science Museum, Oxford • Torres Quevedo’s mechanical calculating machine (Leonardo Torres Quevedo) Museo “Torres Quevedo”, Madrid • Verea’s direct multiplier (Ramón Verea) National Museum of American History, Washington, D.C.; IBM Corporate Archives, Poughkeepsie, New York • Wetli’s planimeter (Kaspar Wetli) Leibniz Universität Hannover (Sammlung historischer geodätischer Instrumente und historischer Rechenhilfsmittel); National Museum of American History, Washington, D.C.

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• Wiberg’s difference engine (Martin Wiberg) Tekniska museet, Stockholm • Zuse M9 plugboard controlled calculating punch (Konrad Zuse) Museum für Kommunikation, Bern • Zuse Z4 program controlled relay computer (Konrad Zuse) Deutsches Museum, Munich

9.4.5  H  istorical Calculating Aids and Their Exhibition Sites: Replicas and Reconstructions • Atanasoff-Berry computer (ABC, John Atanasoff) Computer History Museum, Mountain View, California (on loan) • Auch’s cogged disc addition and subtraction machine (Jacob Auch) Arithmeum, Bonn • Babbage’s analytical engine (section) (Charles Babbage) Science Museum, London; IBM Corporate Archives, Poughkeepsie, New York • Babbage’s difference engine 1 (Charles Babbage) Science Museum, London; Arithmeum, Bonn; Museo Nazionale della Scienza e della Tecnologia “Leonardo da Vinci”, Milan; National Museum of American History, Washington, D.C.; Computer History Museum, Mountain View, California (replica of Roberto Guatelli); Canada Science and Technology Museum, Ottawa (replica of Roberto Guatelli) • Babbage’s difference engine 2 (Charles Babbage) Science Museum, London; Heinz Nixdorf Museumsforum, Paderborn; Intellectual Ventures Laboratories, Bellevue, Washington • Bollée’s direct multiplication machine (Léon Bollée) Arithmeum, Bonn • Braun’s pinwheel machine (Anton Braun) Arithmeum, Bonn • Colossus plugboard controlled vacuum tube computer (Thomas Flowers) National Museum of Computing, Bletchley Park • Edsac stored program vacuum tube computer (Maurice Wilkes) National Museum of Computing, Bletchley Park • Galileo’s sector (Galileo Galilei) IBM Corporate Archives, Poughkeepsie, New York • Gersten’s addition and subtraction machine (Christian Ludwig Gersten) Braunschweigisches Landesmuseum, Braunschweig; Hessisches Landes­ museum, Darmstadt

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• Grillet’s four-function device (Napier’s bones with cogged disc adder) (René Grillet) Braunschweigisches Landesmuseum, Braunschweig; Arithmeum, Bonn • Hahn’s stepped drum machine (Philipp Matthäus Hahn) Braunschweigisches Landesmuseum, Braunschweig; Philipp-MatthäusHahn-­Museum, Albstadt-Onstmettingen; Arithmeum, Bonn • Hoelzer’s electronic analog computer (Helmut Hoelzer) Deutsches Technikmuseum, Berlin • Hollerith’s punched card equipment (counting and sorting machine, tabulator, pantograph card punch (census machine)) (Herman Hollerith) Heinz Nixdorf Museumsforum, Paderborn; Arithmeum, Bonn; Museo Nazionale della Scienza e della Tecnologia “Leonardo da Vinci”, Milan; Computer History Museum, Mountain View, California (replica of Roberto Guatelli) • Leibniz’s calculating machine (binary, Gottfried Wilhelm Leibniz) Deutsches Museum, Munich; Deutsches Technikmuseum, Berlin; Hessisches Landesmuseum, Darmstadt; Heinz Nixdorf Museumsforum, Paderborn, Leibniz Universität Hannover (Leibniz exhibition) • Leibniz’s calculating machine (decimal, Gottfried Wilhelm Leibniz) Leibniz Universität Hannover (Leibniz exhibit)/Gottfried Wilhelm Leibniz Bibliothek Hanover; Deutsches Museum, Munich; Deutsches Technikmuseum, Berlin; Berlin-brandenburgische Akademie der Wissenschaften, Berlin; Heinz Nixdorf Museumsforum, Paderborn; Arithmeum, Bonn; Braunschweigisches Landesmuseum, Braunschweig; Technische Universität Dresden/Technische Sammlungen, Dresden; Museum für Astronomie und Technikgeschichte, Kassel; Museo Nazionale della Scienza e della Tecnologia “Leonardo da Vinci”, Milan (replica of Roberto Guatelli); Science Museum, London; Carnegie Mellon University, Pittsburgh, Pennsylvania (replica of Roberto Guatelli); IBM Corporate Archives, Poughkeepsie, New York • Leupold/Braun/Vayringe toothed segment machine (Jacob Leupold/Anton Braun/Philippe Vayringe) Deutsches Museum, Munich; Heinz Nixdorf Museumsforum, Paderborn; Arithmeum, Bonn; Museum Tuttlingen-Möhringen; IBM Corporate Archives, Poughkeepsie, New York • Manchester Baby stored program vacuum tube computer (Frederic Williams) Science and Industry Museum, Manchester • Millionaire (direct multiplication machine) (Otto Steiger, Hans W. Egli) Carnegie Mellon University, Pittsburgh, Pennsylvania (replica of Roberto Guatelli)

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• Morland’s multiplication and division device (Samuel Morland) Arithmeum, Bonn • Morland’s cogged disc adding machine (Samuel Morland) Science Museum, London; Arithmeum, Bonn • Müller’s stepped drum machine (Johann Helfrich Müller) Braunschweigisches Landesmuseum, Braunschweig; Hessisches Landes­ museum, Darmstadt; Heinz Nixdorf Museumsforum, Paderborn; Arithmeum, Bonn; Deutsches Museum, Munich (section) • Napier’s promptuary (John Napier) University of Edinburgh • Pascaline (Blaise Pascal) Deutsches Museum, Munich; Deutsches Technikmuseum, Berlin; Heinz Nixdorf Museumsforum, Paderborn; Braunschweigisches Landesmuseum, Braunschweig; Arithmeum, Bonn; Museum für Kommunikation, Bern; Museum Enter, Solothurn; Museo Nazionale della Scienza e della Tecnologia “Leonardo da Vinci”, Milan (replica of Roberto Guatelli); Science Museum, London; Tekniska museet, Stockholm; National Museum of American History, Washington, D.C.; Computer History Museum, Mountain View, California; Carnegie Mellon University, Pittsburgh, Pennsylvania (replica of Roberto Guatelli); IBM Corporate Archives, Poughkeepsie, New  York; Canada Science and Technology Museum, Ottawa (replica of Roberto Guatelli) • Poleni’s pinwheel machine (Giovanni Poleni) Museo Nazionale della Scienza e della Tecnologia “Leonardo da Vinci”, Milan; Arithmeum, Bonn • Roman hand abacus Deutsches Museum, Munich; Deutsches Technikmuseum, Berlin; Braunschweigisches Landesmuseum, Braunschweig; Heinz Nixdorf Museumsforum, Paderborn; Science Museum, London • Roth’s pinwheel machine (Didier Roth) Arithmeum, Bonn • Sauter’s pinwheel machine (Johann Jacob Sauter) Arithmeum, Bonn • Scheutz’s difference engine 2 (Pehr Georg Scheutz) IBM Corporate ArchivesPoughkeepsie, New York • Schickard’s calculating clock (addition and subtraction machine with (independent) multiplication and division rods on rotatable vertical drums (Wilhelm Schickard) (reconstruction)

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Deutsches Museum, Munich; Deutsches Technikmuseum, Berlin; Heinz Nixdorf Museumsforum, Paderborn; Technische Sammlungen, Dresden; Braunschweigisches Landesmuseum, Braunschweig; Arithmeum, Bonn; Stadtmuseum im Kornhaus, Tübingen; Computermuseum des WilhelmSchickard-Instituts für Informatik der Universität Tübingen; Rechen­ technische Sammlung des Instituts für Mathematik und Informatik der Universität Greifswald; Kepler-Museum, Weil der Stadt; Computermuseum Aachen; Universität Linz (archive); Museum für Kommunikation, Bern; Museum Enter, Solothurn; Science Museum, London; Computer History Museum, Mountain View, California • Schuster’s stepped drum machine (Johann Christoph Schuster) Arithmeum, Bonn • Selling’s direct multiplication machine (Eduard Selling) Braunschweigisches Landesmuseum, Braunschweig • Stanhope’s stepped drum machine (Charles Stanhope) Arithmeum, Bonn • Stanhope’s toothed segment machine (Charles Stanhope) Arithmeum, Bonn • Stanhope’s cogged disc adding machine (Charles Stanhope) Arithmeum, Bonn • Tunny machine (reconstruction of the Lorenz SZ42 cipher machine) National Museum of Computing, Bletchley Park • Turing-Welchman Bombe electromechanical decoding machine (Alan Turing) National Museum of Computing, Bletchley Park • Verea’s direct multiplier (Ramón Verea) Arithmeum, Bonn • Zuse Z1 mechanical computer (Konrad Zuse) Deutsches Technikmuseum, Berlin • Zuse Z3 program controlled relay computer (Konrad Zuse) Deutsches Museum, Munich; Konrad Zuse Museum, Hünfeld

9.4.6  P  rogrammable Historical Automaton Writers (Original Specimens) • Knaus’s allesschreibende Wundermaschine (universal writing machine) (Friedrich Knaus) Technisches Museum Wien, Vienna

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• L’écrivain (writer) (Pierre Jaquet-Droz) Musée d’art et d’histoire, Neuchâtel Remarks The Rheinisches Landesmuseum in Trier is in possession of a Roman relief fragment which possibly displays an abacus. There are two spellings for the name of the inventor of the friction wheel drive: Gonella and Gonnella. In the case of Roth, who came from Hungary originally, one finds two different first names: Didier and David – he had two forenames. Sources Erhard Anthes; Rose Vogel: Rechnende Räder, Verlag der Studiengalerie, Pädagogische Hochschule Ludwigsburg 2001 Friedrich Ludwig Bauer: Informatik. Führer durch die Ausstellung. Deutsches Museum, Munich 2004 Richard Hergenhahn, Ulrich Reich, Peter Rochhaus: “Mache für dich Linihen …“. Katalog der erhaltenen originalen Rechentische, Rechenbretter und -tücher der frühen Neuzeit, Adam-Ries-Bund, Annaberg-Buchholz 1999 Jacques Payen: Les exemplaires conservés de la machine Pascal, in: Revue d’histoire des sciences et de leurs applications, volume 16, 1963, no. 2, pages 161–178 Ulrich Reich: Rechentische, -bretter und -tücher. Originale und Nachbauten, in: Rainer Gebhardt (editor): 500 Jahre erstes Rechenbuch von Adam Ries, Adam-­Ries-­Bund, Annaberg-Buchholz 2018, pages 57–64 Alain Schärlig: Compter avec des jetons. Tables à calculer et tables de compte du Moyen Age à la Révolution, Presses polytechniques et universitaires romandes, Lausanne 2003 Alain Schärlig: Compter du bout des doigts. Cailloux, jetons et bouliers, de Périclès à nos jours, Presses polytechniques et universitaires romandes, Lausanne 2006 Collection databases (e.g. Science Museum, London; Musée des arts et métiers, Paris; National Museum of American History, Washington, D.C.; Computer History Museum, Mountain View, California) and international survey of the leading museums.

9.4.7  Why Reconstructions? Reconstructions (see Fig.  9.35) of valuable rare calculating aids are made when no specimens have survived, when machines existed only on paper or when these have been lost or are in poor condition, when one wants to understand the functioning of a puzzling device, or in order to investigate whether a historical machine actually ran flawlessly. Since many devices were individually produced, replicas also serve to fill gaps in collections. Along with the specialized technical knowledge and the required skilled craftsmanship, the available drawings, descriptions, and suitable components

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are prerequisites for the manufacture of copies true to the original. Numerous calculating machines have been rebuilt throughout the world, above all in England and in Germany (e.g., at the Arithmeum in Bonn). The mysterious Antikythera mechanism has encouraged many reconstructions. In regard to the decimal and binary four-function calculating machines of Leibniz, several reconstructions and functional models have been produced at the Leibniz Universität Hannover (see Erwin Stein: Die LeibnizDauerausstellung der Gottfried-Wilhelm-Leibniz-Universität, Leibniz-Uni­ versität, Hanover, undated). Repairing historical devices may require patching, replacing, or adding on to damaged or missing parts. An open question: What is better from the point of view of historical scholarship: a defective, nonfunctional original in its original state or a reconstructed functioning original that incorporates parts of other origin or has been changed internally? In place of reconstructions, simulations are often programmed.

Fig. 9.35  The Atanasoff-Berry computer (ABC). The binary vacuum tube computer of John Vincent Atanasoff and Clifford Edward Berry (1942) from Ames (Iowa) was reconstructed in 1996. The ABC is regarded as the world’s first digital electronic computer. The fix-programmed, comparatively small special-purpose machine was designed to solve systems of equations. It clearly influenced the design of the giant Eniac computer. The ABC utilized a capacitor memory drum. (© Computer History Museum, Mountain View, California/picture: Mark Richards)

9.4.8  R  oberto Guatelli: Replicas of Machines from da Vinci, Pascal, Leibniz, Babbage, and Hollerith Leonardo da Vinci (1452–1519) prepared numerous technical drawings (Codex Atlanticus, Codex Madrid). He was already familiar, for example, with the gear train, the cogged slide bar, the cam, the lazy tongs, the sector, and the odometer and is said to have designed a calculating machine as well. The scholar and artist conceived models for machines and instruments (e.g., an

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odometer in the form of a wheelbarrow, a loom, and a compass), flying devices, ships, bridges, churches, for city planning and for the military (e.g. fortresses, a cable-operated knight). However, the interpretation of the sketches is not always unproblematic. The once world famous but now largely forgotten Italian engineer Roberto A.  Guatelli (1904–1993), who spent a long time in a Japanese concentration camp during the Second World War, not only built numerous models of devices from Leonardo da Vinci but also a number of replicas of calculating machines, such as the addition and subtraction machine of Blaise Pascal, the four-function calculating machine of Gottfried Wilhelm Leibniz, the difference engine of Charles Babbage, and the census machine of Herman Hollerith. In 1968 Guatelli rebuilt Leonardo da Vinci’s “calculating machine.” Whether or not this was actually a calculator, however, remains a matter of dispute. These excellent replicas can often not be distinguished from the original devices. 9.4.8.1  F  ive Guatelli Replicas at the Carnegie Mellon University, Pittsburgh It only became known in December 2018 that Guatelli also rebuilt the Millionaire direct multiplication machine from Zurich. Further masterpieces came to light in January 2019, including the calculating machines of Pascal, Leibniz, Pallweber, and Webb. In 2018 the firsthand witness Pamela McCorduck donated the calculating machine collection, which included an early Thomas arithmometer and two Enigmas with three and four rotors, respectively, to the Carnegie Mellon University in Pittsburgh, Pennsylvania. In honor of her deceased husband, the computer pioneer Joseph Traub, the collection bears the name Traub-McCorduck Collection. They had bought the five replicas from Guatelli in 1988. Guatelli replicas can also be found in Milan, Mountain View, New York, and Ottawa (see Figs. 9.36, 9.37, 9.38, 9.39, 9.40, 9.41, 9.42, 9.43, 9.44, 9.45, 9.46, 9.47, 9.48, 9.49, 9.50, and 9.51).

Fig. 9.36  Roberto Guatelli’s replica (1) of the Pascaline. The Italian model builder replicated s number of Pascal machines true to the original devices. (© University Libraries, Carnegie Mellon University, Pittsburgh, picture: Heidi Wiren Bartlett)

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Fig. 9.37  Roberto Guatelli’s replica (2) of the Pascaline. The addition and subtraction machine of Blaise Pascal (1623–1662) can represent values up to 999 999 livres. 1 livre has 20 sols and 1 sol 12 deniers. (© Museo nazionale della scienza e della tecnologia “Leonardo da Vinci”, Milan)

Fig. 9.38  Roberto Guatelli’s replica (2) of the Pascaline. Eight original machines of Blaise Pascal have survived, for example, in Paris, Clermont-Ferrand, Dresden, and New  York. Pascal built the first machine in 1642. (© Canada Science and Technology Museum, Ottawa, object number 1979.0568.001)

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Fig. 9.39  Guatelli’s replica (1) of Leibniz’s calculating machine. Gottfried Wilhelm Leibniz (1646–1716) built his first calculating machine in 1673. The sole surviving specimen dates from the 1690s and is kept in Hanover. It is the world’s first mechanical calculating machine capable of executing all four basic arithmetic operations. (© Museo nazionale della scienza e della tecnologia “Leonardo da Vinci”, Milan)

Fig. 9.40  Rear side of Guatelli’s replica (2) of Leibniz’s calculating machine. (© University Libraries, Carnegie Mellon University, Pittsburgh, picture: Heidi Wiren Bartlett)

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Fig. 9.41  Section of Guatelli’s replica (3) of Leibniz’s calculating machine. (© University Libraries, Carnegie Mellon University, Pittsburgh, picture: Heidi Wiren Bartlett)

Fig. 9.42  Section of Guatelli’s replica (4) of Leibniz’s calculating machine. (© University Libraries, Carnegie Mellon University, Pittsburgh, picture: Heidi Wiren Bartlett)

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Fig. 9.43  Guatelli’s replica of Babbage’s difference engine. Charles Babbage (1792–1871) worked from 1822 on his first difference engine, which however remained uncompleted. It was intended to enable the error-free generation of mathematical tables. The original machine is located in London. (© Canada Science and Technology Museum, Ottawa, object number 2011.0022.001)

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Fig. 9.44  Replica of the Hollerith census machine by Roberto Guatelli. Hermann Hollerith (1860–1929), of German descent, built this punched card machine (counting and sorting machine, tabulator, and pantograph card punch) for the American census in 1890. (© Computer History Museum, Mountain View, California)

9.4.8.2  H  ow Many da Vinci Models and Replicas of Calculating Machines Have Survived? To my knowledge there is no list of models that Roberto Guatelli built based on the drawings of Leonardo da Vinci. It is also not clear which and how many calculating machines he rebuilt for IBM New York and other clients and which of these have survived and where. From 1951 to 1961, Guatelli worked for Thomas Watson, the founder of IBM. A year later he opened a workshop in New  York. According to Jim Strickland, Guatelli’s nephew, Joseph Mirabella, worked with him from 1964. Following Guatelli’s death, he continued their work until 2005. Mirabella donated the da Vinci models to the Long Island Science Center in Riverhead, New York. Nathan Myhrvold  – Intellectual Ventures (formerly Microsoft Corporation)  – is supposed to have purchased the remaining replicas of calculating machines. 9.4.8.3  The Millionaire Direct Multiplier The location of the original Millionaire machine (maker number 2380), which Guatelli rebuilt, is not known. It is not listed in the Australian “Register of Millionaire calculators” of John Wolff. The Millionaire in the collection of the IBM Corporate Archives in Poughkeepsie, New York, has the number 403. The four specimens of Harvard University in Cambridge, Massachusetts, which

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had worked together with IBM, bear other serial numbers. The Millionaire of the H.W. Egli AG in Zurich was for many years the world’s fastest multiplication machine.

Fig. 9.45  Guatelli’s replica (1) of the Millionaire direct multiplier. The numerals are entered with the setting levers. With the crank (upper right) the values are transferred to the arithmetic unit. At the upper left is the multiplication lever, which greatly accelerates multiplication. (© University Libraries, Carnegie Mellon University, Pittsburgh, picture: Heidi Wiren Bartlett)

Fig. 9.46  Guatelli’s replica (2) of the Millionaire direct multiplier. At the top is the input unit with the slides and the revolution counter register and result register in the middle and at the bottom. The very heavy machine is capable of all four basic arithmetic operations. (© University Libraries, Carnegie Mellon University, Pittsburgh, picture: Heidi Wiren Bartlett)

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Fig. 9.47  Side view of Guatelli’s replica (3) of the Millionaire direct multiplier. (© University Libraries, Carnegie Mellon University, Pittsburgh, picture: Heidi Wiren Bartlett)

At the present time, the following Guatelli replicas of calculating machines are known to exist: Guatelli Replicas of Calculating Machines Known Until Now Museo Nazionale della Scienza e della Tecnologia “Leonardo da Vinci”, Milan • Pascaline Replica. Several different original specimens (1642 ff.) have survived (e.g., in Paris, Clermont-Ferrand, Dresden, and New York). • Calculating machine of Gottfried Wilhelm Leibniz (around 1694) The only surviving original machine is in the Gottfried Wilhelm Leibniz Bibliothek in Hanover. Computer History Museum, Mountain View, California • Pascaline Replica (1981). Several different original specimens (1645) have survived (e.g., in Clermont-Ferrand, Paris, Dresden, and New York). • Difference engine no. 1 (demonstration piece) of Charles Babbage Replica (1972) of the original from 1833, located in the Science Museum in London (continued)

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• Census machine of Herman Hollerith (counting and sorting machine, tabulator, pantograph card punch) • Electrical tabulating system of Herman Hollerith Canada Science and Technology Museum, Ottawa • Pascaline Replica (around 1978). Several different original specimens (1642 ff.) have survived (e.g., in Clermont-Ferrand, Paris, Dresden, and New York). • Difference engine no. 1 (demonstration piece) of Charles Babbage Replica (1972) of the original from 1833, located in the Science Museum in London Carnegie Mellon University, Pittsburgh, Pennsylvania (Traub-McCorduck Collection) • Pascaline Replica. Several different original specimens (1642 ff.) have survived (e.g., in Paris, Clermont-Ferrand, Dresden, and New York). • Calculating machine of Gottfried Wilhelm Leibniz (around 1694) The only surviving original machine is in the Gottfried Wilhelm Leibniz Bibliothek in Hanover. • Counter dial adding machine of Charles Henry Webb, New  York (Webb’s adding machine) Webb patented this machine in 1868. It was operated with a stylus. • Keyboard adding machine of the Adix Company, Mannheim This 3-place column adder was invented by Josef Pallweber in Mannheim (patent 1904). The portable ratchet machine was manufactured by the Adolf Bordt company in Mannheim. • Millionaire The first Millionaire of the H.W. Egli AG company in Zurich appeared in 1893. The existing machine with serial number 2380 was manufactured around 1916. The inventor of this machine was Otto Steiger. IBM Corporate Archives, Poughkeepsie, New York In addition to the Pascaline, there are also other replicas of Guatelli in the IBM archives (https://www.ibm.com/ibm/history/). It is not known who has the proprietary rights for the calculating machines of Leibniz, Leupold/Braun/Vayringe, Morland, the analytical and difference engines of Charles Babbage, and difference engine 2 of Edvard and Pehr Scheutz. Unfortunately no information could be obtained.

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9.4.8.4  Models of Leonardo da Vinci Museums with models of Leonardo da Vinci exist, for example, in Vinci, Florence, and Milan. Handcrafted replicas of Roberto Guatelli and Joe Mirabella are exhibited in the Long Island Science Center in Riverhead, New York (https://www.sciencecenterli.org/davinciexhibition). The following Guatelli models of devices from Leonardo da Vinci are on hand in the IBM Corporate Archives: mobile mechanical musical drum, flying machine, helicopter, odometer, paddlewheel ship, and scaling ladder. For further reconstructions of Leonardo’s inventions (mechanical lion, mechanical knight, and self-propelled cart), see Sect. 15.1.11.

Fig. 9.48  Webb’s adding machine (1). The large disc of this circular calculator (1889) of Charles Henry Webb registers the values 1 to 99 and the small disc the hundreds. The American stylus-­operated calculator has an automatic tens carry and allows addition up to 4999. The result is displayed in a window at the point where the two discs are closest together. © University Libraries, Carnegie Mellon University, Pittsburgh, picture: Heidi Wiren Bartlett)

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Fig. 9.49  Webb’s adding machine (2). This illustration shows a well-preserved original. It was evidently manufactured later than the model specimen available to Guatelli (© Inria/ picture: J.-M. Rames)

Fig. 9.50  The Austrian engineer Josef Pallweber invented the column adder. (© University Libraries, Carnegie Mellon University, Pittsburgh, picture: Heidi Wiren Bartlett)

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Fig. 9.51  The Adix keyboard adding machine (replica of Roberto Guatelli) (2). The arithmetic unit of the ratchet machine is removable. (© University Libraries, Carnegie Mellon University, Pittsburgh, picture: Heidi Wiren Bartlett)

9.4.8.5  Excerpts from Two American Publications Francis C. Moon of Cornell University, Ithaca, New York, writes: One of the most famous sets of Leonardo models was commissioned by the Italian dictator Mussolini for an exhibition in 1939 in Milan as a part of an effort to build national pride in Italian history. The 200 models were built by an Italian engineer, Roberto A. Guatelli at a cost of $250,000 (Time Magazine, May 29, 1939, p. 39). These models went on tour and ended up in Japan where they were destroyed during World War II. After the War, Guatelli was commissioned to make a smaller set of 66 models for an exhibition at IBM headquarters in New York City in 1951. With the recent demise of the IBM museum in New York, these models have been dispersed and are on occasional tour in various exhibitions (see Francis C. Moon: The machines of Leonardo da Vinci and Franz Reuleaux, Springer, Dordrecht 2007, page 201).

David Pantalony of the Canada Science and Technology Museum, Ottawa, attempts to investigate the origin of models: Since the 1930s, IBM’s founder, Thomas Watson Sr. had been collecting antiques and books related to the history of calculating and computing. They were first exhibited at the 1939 World’s Fair […]. In 1951, Watson channeled this interest toward Leonardo

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da Vinci and a travelling exhibition of his machines. A few years earlier, Watson had seen an exhibit of replicas made by the Italian artisan and scholar Roberto Guatelli; he subsequently bought the collection and hired Guatelli. Thus began a long relationship between Guatelli and IBM. Roberto Guatelli (1904–1993), a science and engineering graduate from the University of Milan, developed his reputation by building and exhibiting interpretations based on the work of Leonardo da Vinci. In 1939, fitting the nationalist context of the time, the Italian government sponsored a major exhibition of Leonardo da Vinci models at the Palazzo dell’arte Milan. […]. The Italian ministry of culture then sponsored a travelling version for the United States. In 1940 Guatelli, emerging as one of the leading model makers, travelled to New York for an exhibition at the Museum of Science and Industry in the Rockefeller Center […]. Guatelli and his models were a travelling sensation in post-World War II America (see David Pantalony: Collectors, displays and replicas in context, in: Jed Buchwald; Larry Stewart (editors): The romance of science, Springer international publishing AG, Cham 2017, pages 271–272).

Sources Jed Buchwald; Larry Stewart (editors): The romance of science: Essays in honour of Trevor H. Levere, Springer international publishing AG, Cham 2017 Erez Kaplan: The controversial replica of Leonardo da Vinci’s adding machine, in: IEEE Annals of the history of computing, volume 19, 1997, no. 2, pages 62–63 Francis Charles Moon: The machines of Leonardo da Vinci and Franz Reuleaux. Kinematics of machines from the Renaissance to the 20th century, Springer, Dordrecht 2007, pages 107–115 and 199–211 David Pantalony: Collectors, displays and replicas in context: What we can learn from provenance research in science museums, in: Jed Buchwald; Larry Stewart (editors): The romance of science: Essays in honour of Trevor H. Levere, Springer international publishing AG, Cham 2017, pages 268–274 Jum Strickland: Who was that guy? Roberto Guatelli, in: Computer History Museum, Mountain View, California, volunteer information exchange, volume 2, February 15th 2012, no. 3.

9.4.9  Resurrected Relay and Vacuum Tube Computers Only machines for which no (functional) original specimen exists any longer are mentioned here (the list does not claim to be complete): • ABC electronic computer (John Atanasoff) Computer History Museum, Mountain View, California • Bell Model K (kitchen, experimental machine) (George Stibitz) Denison University, Granville, Ohio (William Howard Doane Library) • Colossus electronic computer (Thomas Flowers) National Museum of Computing, Bletchley Park • Edsac electronic computer (Maurice Wilkes) National Museum of Computing, Bletchley Park • Manchester Baby (small-scale experimental machine) electronic computer (Frederic Williams, Thomas Kilburn, Geoff Tootill) Science and Industry Museum, Manchester

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• Turing-Welchman Bombe relay computer (Alan Turing, Gordon Welchman) National Museum of Computing, Bletchley Park • Zuse Z1 relay computer (Konrad Zuse) Deutsches Technikmuseum, Berlin • Zuse Z3 relay computer (Konrad Zuse) Deutsches Museum, Munich; Konrad Zuse Museum, Hünfeld

9.5  Oldest Surviving Calculating Aids Among the oldest still existing calculating aids are the Greek calculating boards, the Roman hand abacus (bead frame), the Antikythera mechanism, and astrolabes. The devices of Blaise Pascal, Gottfried Wilhelm Leibniz, Samuel Morland, René Grillet, Charles Xavier Thomas, and Jean-Baptiste Schwilgué, for example, belong to the oldest preserved mechanical calculating machines.

9.5.1  Early Four-Function Machines The following tables provide an overview of early four-function machines (see Tables 9.7, 9.8, 9.9, and 9.10) that have survived. Table 9.7  Early four-function machines that have been preserved (1) (selection, in order of the year built) The early mechanical calculating machines were above all ornamental objects Year built Inventor Site (original) 1694 Gottfried Wilhelm Leibniz Gottfried Wilhelm Leibniz Bibliothek, Hanover 1727 Anton Braun Kunsthistorisches Museum Wien, Vienna 1735 Jacob Leupold; Anton Braun; Deutsches Museum, Munich Philippe Vayringe 1774 Philipp Matthäus Hahn Landesmuseum Württemberg, Stuttgart (Stuttgart specimen) 1775 Charles Stanhope Science Museum, London (stepped drum machine) 1776 Philipp Matthäus Hahn Technoseum, Mannheim (Urach specimen) 1777 Charles Stanhope Science Museum, London (toothed segment machine) 1784 Johann Helfrich Müller Hessisches Landesmuseum, Darmstadt 1792 Johann Christoph Schuster Deutsches Museum, Munich (12-place) 1796 Johann Jacob Sauter Stadsmuseum, Gothenburg 1820 Johann Christoph Schuster Deutsches Museum, Munich (9-place) 1820 Charles Xavier Thomas National Museum of American History, Washington, D.C. 1822 Johann Christoph Schuster Arithmeum, Bonn (10-place) 1841 Didier Roth Musée des arts et métiers, Paris © Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020

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Remarks The frequently mentioned year 1694 (Leibniz machine) is not certain. The full name of Didier Roth was David Didier Roth. Table 9.8  Early four-function machines that have been preserved (2) (selection, in alphabetical order of the inventors) The most important inventors include Braun, Hahn, Leibniz, Müller, Sauter, Schuster, and Stanhope Year Inventor built Site (original) Braun, Anton 1727 Kunsthistorisches Museum Wien, Vienna Hahn, Philipp Matthäus 1774 Landesmuseum Württemberg, Stuttgart (Stuttgart specimen) Hahn, Philipp Matthäus 1776 Technoseum, Mannheim (Urach specimen) Leibniz, Gottfried Wilhelm 1694 Gottfried Wilhelm Leibniz Bibliothek, Hanover Leupold, Jacob; Braun, Anton; 1735 Deutsches Museum, Munich Vayringe, Philippe Müller, Johann Helfrich 1784 Hessisches Landesmuseum, Darmstadt Roth, Didier 1841 Musée des arts et métiers, Paris Sauter, Johann Jacob 1796 Stadsmuseum, Gothenburg Schuster, Johann Christoph 1792 Deutsches Museum, Munich (12-place) Schuster, Johann Christoph 1820 Deutsches Museum, Munich (9-place) Schuster, Johann Christoph 1822 Arithmeum, Bonn (10-place) Stanhope, Charles 1775 Science Museum, London (stepped drum machine) Stanhope, Charles 1777 Science Museum, London (toothed segment machine) Thomas, Charles-Xavier 1820 National Museum of American History, Washington, D.C. © Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020

Table 9.9  Early four-function machines that have been preserved (3) (selection, in alphabetical order of the sites) The Deutsches Museum and the Science Museum have several four-function machines Year Site (original) built Inventor Bonn: Arithmeum (10-place) 1822 Johann Christoph Schuster Darmstadt: Hessisches Landesmuseum 1784 Johann Helfrich Müller Gothenburg: Stadsmuseum 1796 Johann Jacob Sauter Hanover: Gottfried Wilhelm Leibniz 1694 Gottfried Wilhelm Leibniz Bibliothek London: Science Museum (stepped drum 1775 Charles Stanhope machine) (continued)

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Table 9.9 (continued) The Deutsches Museum and the Science Museum have several four-function machines Year Site (original) built Inventor London: Science Museum (toothed segment 1777 Charles Stanhope machine) Mannheim: Technoseum (Urach specimen) 1776 Philipp Matthäus Hahn Munich: Deutsches Museum 1735 Jacob Leupold; Anton Braun; Philippe Vayringe Munich: Deutsches Museum (12-place) 1792 Johann Christoph Schuster Munich: Deutsches Museum (9-place) 1820 Johann Christoph Schuster Paris: Musée des arts et métiers 1841 Didier Roth 1774 Philipp Matthäus Hahn Stuttgart: Landesmuseum Württemberg 1727 Anton Braun (Stuttgart specimen) Vienna: Kunsthistorisches Museum Wien Washington, D.C.: National Museum of 1820 Charles Xavier Thomas American History © Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020 Table 9.10  Early four-function machines that have been preserved – with design (selection, in alphabetical order of the inventors) Nine stepped drum, three pinwheel, and two toothed segment machines Year Inventor built Design Braun, Anton 1727 Pinwheel machine Hahn, Philipp Matthäus 1774 Stepped drum machine Hahn, Philipp Matthäus 1776 Stepped drum machine Leibniz, Gottfried Wilhelm 1694 Stepped drum machine Leupold, Jacob; Braun, Anton; 1735 Toothed segment machine Vayringe, Philippe Müller, Johann Helfrich 1784 Stepped drum machine Roth, Didier 1841 Pinwheel machine Sauter, Johann Jacob 1796 Pinwheel machine Schuster, Johann Christoph 1792 Stepped drum machine Schuster, Johann Christoph 1820 Stepped drum machine Schuster, Johann Christoph 1822 Stepped drum machine Stanhope, Charles 1775 Stepped drum machine Stanhope, Charles 1777 Toothed segment machine Thomas, Charles-Xavier 1820 Stepped drum machine © Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020

Form Circular Circular Circular Rectangular Circular Circular Circular Circular Circular Circular Circular Rectangular Rectangular Rectangular

Remarks The four-function machines of Hahn, Leibniz, Müller, and Schuster are stepped drum machines. Those of Braun, Roth, and Sauter are pinwheel machines, while the Leupold/Braun/Vayringe device is a toothed segment

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machine. The first four-­function calculator of Stanhope is a stepped drum machine (1775) and the second a toothed segment (1777). With the exception of Leibniz, Stanhope, and Thomas, all calculating machines described are circular (cylindrical) machines. The last machine of Hahn was built by Schuster. Schuster’s circular device of 1792 is a reconstruction of a Hahn machine and is therefore referred to as the Schuster-Hahn machine. Grillet’s calculating device (before 1678), designed for all four arithmetic operations (as well as squares and cubes), has no tens carry. The numeral discs have no mechanical wheelwork and provide the addition of partial products. Multiplication and division are on the basis of Napier’s bones. Unique: Müller’s calculating machine is able to calculate with different number systems (base-2, base-3, base-4, base-5, and base-12 system). As a rule, the year built is given as the time of completion (e.g., for Leupold and Schuster). According to information of Jane Desborough of the Science Museum (personal communication of August 29, 2017), there are three calculating machines of Charles Stanhope in London: A four-function stepped drum machine (1775) A four-function toothed segment machine (1777) An experimental model of a toothed segment calculating machine (1777) Stanhope’s cogged disc adding machine is in Oxford. Among the most important makers of one- and two-function machines are Morland, Pascal, Roth, and Stanhope (see Tables 9.11, 9.12, and 9.13).

9.5.2  Early One- and Two-Function Machines Table 9.11  Early one- and two-function calculating machines that have been preserved (1) (selection, in order of the year built) The following calculating machines were mostly built in the seventeenth, eighteenth, and nineteenth centuries Year built Inventor Site (original) Design type Addition and subtraction 1642 ff. Blaise Pascal Musée des arts et métiers, machine Paris Muséum Henri-Lecoq, Clermont-Ferrand Mathematisch-physikalischer Salon, Dresden, etc. 1664 Samuel Science Museum, London Trigonometric calculator Morland 1664 Samuel Museo Galileo, Florence Multiplication and division Morland machine Cogged disc adding 1666 Samuel Science Museum, London machine Morland History of Science Museum, Oxford (continued)

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Table 9.11 (continued) The following calculating machines were mostly built in the seventeenth, eighteenth, and nineteenth centuries Year built Inventor Site (original) Design type 1670 Samuel Museo Galileo, Florence Trigonometric calculator Morland Addition and subtraction 1725 Jean Lépine Musée des arts et métiers, machine Paris National Museum of American History, Washington, D.C. 1780 Charles History of Science Museum, Cogged disc adding Stanhope Oxford machine 1789 Jacob Auch Landesmuseum Württemberg, Cogged discaddition and subtraction machine Stuttgart Mathematisch-physikalischer Salon, Dresden Rijksmuseum Boerhaave, Leiden 1790 Johann Jacob Science Museum, London Stylus-type adder Sauter Cogged disc adding 1842 Didier Roth Musée des arts et métiers, machine Paris Arithmeum, Bonn 1859 Tito Gonnella Museo Galileo, Florence Keyboard adding machine Arithmeum, Bonn Cogged disc adding machine © Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020 Table 9.12  Early one- and two-function calculating machines that have been preserved (2) (selection, in alphabetical order of the inventors) The inventors of calculating machines came from England, France, Germany, and Italy Year Inventor built Site (original) Design type Cogged disc addition and Auch, Jacob 1789 Landesmuseum Württemberg, subtraction machine Stuttgart Mathematisch-physikalischer Salon, Dresden Rijksmuseum Boerhaave, Leiden Gonnella, Tito 1859 Museo Galileo, Florence Keyboard adding machine Arithmeum, Bonn Cogged disc addition and subtraction machine Addition and subtraction Lépine, Jean 1725 Musée des arts et métiers, Paris machine National Museum of American History, Washington, D.C. Morland, 1664 Science Museum, London Trigonometric calculator Samuel Morland, 1664 Museo Galileo, Florence Multiplication and division Samuel machine (continued)

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Table 9.12 (continued) The inventors of calculating machines came from England, France, Germany, and Italy Year Inventor built Site (original) Design type Cogged disc adding Morland, 1666 Science Museum, London machine Samuel History of Science Museum, Oxford Morland, 1670 Museo Galileo, Florence Trigonometric calculator Samuel Addition and subtraction Pascal, Blaise 1642 ff. Musée des arts et métiers, Paris machine Muséum Henri-Lecoq, Clermont-Ferrand Mathematisch-physikalischer Salon, Dresden, etc. Roth, Didier 1842 Musée des arts et métiers, Paris Cogged disc adding Arithmeum, Bonn machine 1790 Science Museum, London Stylus-type adder Sauter, Johann Jacob Stanhope, 1780 History of Science Museum, Cogged disc adding Charles Oxford machine © Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020 Table 9.13  Early one- and two-function calculating machines that have been preserved (3) (selection, in alphabetical order of the sites) Machines dating from the seventeenth, eighteenth, and nineteenth centuries from Dresden, Florence, London, Oxford, and Paris Site Museum Year built Inventor Bonn Arithmeum 1842 Didier Roth 1859 Tito Gonnella Clermont-Ferrand Muséum Henri-Lecoq 1642 ff. Blaise Pascal Dresden Mathematisch-physikalischer 1642 ff. Blaise Pascal Salon 1790 Jacob Auch Florence Museo Galileo 1664 Samuel Morland 1670 Samuel Morland 1859 Tito Gonnella Leiden Rijksmuseum Boerhaave 1790 Jacob Auch London Science Museum 1664 Samuel Morland 1666 Samuel Morland 1790 Johann Jacob Sauter Oxford History of Science Museum 1666 Samuel Morland 1780 Charles Stanhope Paris Musée des arts et métiers 1642 ff. Blaise Pascal 1725 Jean Lépine 1842 Didier Roth Stuttgart Landesmuseum Württemberg 1789 Jacob Auch Washington, D.C. National Museum of American 1725 Jean Lépine History © Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020

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Remarks The Paris Musée des arts et métiers houses an addition and subtraction machine of Roth, as well as several of Roth’s adding machines, his multiplication and division rods, and a cylindrical pinwheel machine (all from around 1840). The Bonn Arithmeum is in possession of an adding machine (around 1790) that was possibly built by Hahn or Auch. Only reconstructions exist for Schickard’s calculating clock (1623) and Gersten’s addition and subtraction machine (1722).

9.5.3  Schickard, Pascal, and Leibniz The development of mechanical calculating machines began in the seventeenth century in France, Germany, and the UK with Schickard, Pascal, Leibniz, and Morland. From the early days, three masterpieces (see Table 9.14) stand out, all of which have automatic tens carry (see Figs.  9.52, 9.53, 9.54, 9.55, 9.56, 9.57, 9.58, 9.59, 9.60, 9.61, 9.62, and 9.63): • Schickard’s calculating clock Two-function machine: addition and subtraction, as well as (without linking) rotatable cylinders for multiplication and division (following the principle of Napier’s bones • Pascaline Two-function machine: addition and indirect subtraction with complements, a machine with pinwheels and counter wheels • Leibniz’s calculating machine Four-function machine for all basic arithmetic operations, a (decimal) stepped drum machine (as well as a pinwheel machine). Leibniz also described a binary calculating machine. If the tens carry is not possible in both directions of rotation (clockwise and counterclockwise), the subtraction is carried out instead as an addition with complements (nine’s complement: difference from nine). The (no longer existing) Leibniz calculating machine from the year 1673 had pinwheels. However, the only surviving device (dating from about 1692 or between 1695 and 1698) utilized stepped drums (see Erwin Stein; Franz-Otto Kopp: Konstruktion und Theorie der leibnizschen Rechenmaschinen im Kontext der Vorläufer, in: studia leibnitiana, volume 42, 2010, no. 1, pages 35–37). In many publications the device of 1673 is described  – to be sure erroneously  – as a stepped drum machine. With suitable approaches (e.g., the methods of Töpler, Hermann, Collatz, and Lambacher, continued fractions) it is also possible to extract square roots with certain machines.

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Table 9.14  Properties of the three most important early (mechanical) calculating machines Comparison of the calculating machines of Schickard, Pascal, and Leibniz Name of the machine Year Features Schickard’s 1623 Addition and subtraction mechanism with counter wheels, multiplication and division device with rotatable drums (with calculating multiplication columns), tens carry for addition and (direct) clock subtraction in both directions of rotation; serial calculator, monophase arithmetic operation (no separation of input and arithmetic units), numerical storage 1642 Addition and subtraction mechanism with toothed stylus wheels, Pascal’s (indirect) subtraction with complements (nine’s complements), tens calculating carry in one direction of rotation (addition); serial calculator, machine monophase arithmetic operation (no separation of input and (Pascaline) arithmetic units) 1673 Arithmetic unit with pinwheels for addition, (direct) subtraction, Leibniz’s multiplication, and division (four-function machine); biphase tens calculating carry in both directions of rotation; parallel calculator; biphase machine arithmetic operation (separation of input and arithmetic units), movable counter mechanism carriage for multiplication and division, revolution counter © Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020

Remarks Since 1957 it is known that in 1623, Wilhelm Schickard built a calculating machine which he called “calculating clock,” which the Kepler researcher Franz Hammer rediscovered. The machines of Schickard and Leibniz featured direct subtraction and the Pascaline indirect subtraction. Schickard’s calculating clock is not a genuine four-function machine. Addition/subtraction and multiplication/division were separated. For addition ten-toothed gear wheels and numeral cylinders were used, and a multiplication table is served for multiplication. Eight calculating machines of Pascal have survived (see box). Surviving Pascalines The Paris Musée des arts et métiers houses a 6-place and two 8-place Pascalines. The Clermont-Ferrand machines are 5-place and 8-place. The Dresden specimen exhibits 10 places, and the IBM devices in New York and in a private collection (Collection Léon Poncé) each have 8 places. A further (6-place) machine is preserved in Paris which was only built (with original parts) in the eighteenth century, i.e., after Pascal’s death. This is therefore not considered to be original. The Muséum Henri-Lecoq has rebuilt a 5-place machine. IBM is in possession of an original machine and a (6-place) replica. (continued)

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The French terms inscripteur and totalisateur refer to the input unit and the result mechanism, respectively. The term fenêtre refers to the viewing window, and remise à zero has the meaning resetting to zero, i.e., deleting. Source Nathalie Vidal; Dominique Vogt: Les machines arithmétiques de Blaise Pascal, Muséum Henri-Lecoq, Clermont-Ferrand 2011.

Fig. 9.52  Schickard’s calculating clock (1) (1623). The “calculating clock” of Wilhelm Schickard is considered to be the first mechanical calculating machine. It comprises two separate sections, an arithmetic unit for addition and subtraction (below) and cylinders for multiplication and division (above) that function similarly to Napier’s bones. The six rotating knobs (at the top) serve for inputting up to 6-place multiplicands. The six (vertically mounted) dials (below) acquire the values for the addition and subtraction mechanism. The numerals are represented by counter wheels. This machine exists only as reconstructions. (© Deutsches Technikmuseum, Berlin)

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Fig. 9.53  Schickard’s calculating clock (2) (1623). The eight horizontal slides (for the numerals 2 to 9) allow inputting (multi-digit) multipliers. The two- to ninefold values of the multiplicands are displayed in the windows. The Napierian cylinders are inscribed with simple multiplication. The six knobs in the base (at the front) are reminder discs with which one can retain the individual places of quotients (© Deutsches Technikmuseum, Berlin)

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Fig. 9.54  Schickard’s calculating clock (3) (1623). The vertically arranged rotating cylinders (numeral drums) are reminiscent of Napier’s bones with simple multiplication. Because these cylinders function independently of the remaining part of the arithmetic unit (addition and subtraction), Schickard’s calculating clock is not a genuine four-function machine. A special feature: the device has a numerical storage. The tens carry takes place in both directions of rotation (addition and subtraction). (© Deutsches Technikmuseum, Berlin)

Fig. 9.55  Schickard’s calculating clock (4) (1623). The six (vertical) setting dials are intended for inputting numerals. For addition these are rotated to the right and for subtraction to the left. The corresponding viewing windows serve also for the addition of intermediate products. The setting dial at the far right represents the one’s digit, the next dial to the left the ten’s digit, etc. (© Deutsches Technikmuseum, Berlin)

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Fig. 9.56  Pascaline (1) (original). Five-place machine of the nobleman Durant-Pascal. (© Muséum Henri-Lecoq, Ville de Clermont-Ferrand, picture: Adeline Girard)

Fig. 9.57  Pascaline (2) (original). Five-place machine of the nobleman Durant-Pascal. (© Muséum Henri-Lecoq, Ville de Clermont-Ferrand, picture: Stéphane Vidal)

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Fig. 9.58  Pascaline (3) (original). Eight-place machine for Marguerite Périer. (© Muséum Henri-­Lecoq, Ville de Clermont-Ferrand, picture: Nathalie Vidal)

Fig. 9.59  Pascaline (4) (original). Eight-place machine for Marguerite Périer. (© Muséum Henri-­Lecoq, Ville de Clermont-Ferrand, picture: Stéphane Vidal)

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Fig. 9.60  Pascaline (replica). Until the discovery of Schickard’s calculating clock, the Pascaline (1642 ff.) was regarded as the first (mechanical) calculating machine. It is capable of two basic arithmetic operations, addition and indirect subtraction (with complements). With this 6-place model, numerals are entered via the rotating discs with a stylus. Addition and subtraction take place in the same direction of rotation. (© Deutsches Technik­ museum, Berlin)

Fig. 9.61  Leibniz’s calculating machine (1) (around 1700). Only a single calculating machine of Gottfried Wilhelm Leibniz has survived. The (lockable) stepped drum construction is viewed as the first four-function machine. The implementation of the tens carry proved to be difficult. (© Gottfried-Wilhelm-Leibniz-Bibliothek – Niedersächsische Landes­ bibliothek, Hanover, picture 3, 65, 12)

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Fig. 9.62  Leibniz’s calculating machine (2) (around 1700). On the right side is the movable carriage with the 8-place input unit. The numerals are entered with the eight numeral wheels (at the top of the input unit) and transferred to the arithmetic unit with the crank at the right. The stepped drums (not seen in the illustration) are in the input unit. At the left the result mechanism with the pentagonal discs, which display the uncomplete tens carries, can be seen. With the crank at the left – for multiplication and division – the input unit (setting mechanism) is shifted in relation to the result mechanism (carriage shift). (© GottfriedWilhelm-Leibniz-Bibliothek  – Niedersächsische Landesbibliothek, Hanover, picture 3, 65, 555)

Fig. 9.63  Calculating machine of Leibniz (reconstruction). The performance features of the stepped drum machine are 8 x 1 x 16, i.e., 16 places in the input unit, 1-place in the revolution counter, and 16 places in the result mechanism. Both cranks can be rotated in both directions. Revolving in the counterclockwise direction with the crank at the right (front side) carries out an addition, and revolving in the clockwise direction realizes a subtraction. The revolution counter can be seen on the top at the right. The polymath built his first (no longer surviving) calculating machine, designed for all four basic arithmetic operations, already in 1673. Leibniz invented both the stepped drum and the pinwheel. These switching elements constitute the basis for numerous subsequent calculating machines. (© Heinz Nixdorf  Museumsforum, Paderborn)

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The first relay and vacuum tube computers were largely disposed of. The room-­sized machines were scrapped (e.g., the ABC), destroyed during the war (the Z3), or dismantled for reasons of secrecy (Colossus). They were no longer of use, there was not enough space, or their historical significance was not recognized. Very little of the large-scale American computers has survived. Components still exist, deriving, for example, from the following machines: Bell 5 computer, Bush’s differential analyzer, Eniac, Harvard Mark 1/IBM ASCC, IAS computer, Univac 1, and Whirlwind. However, the Zuse Z4 (Deutsches Museum, Munich), Csirac (Melbourne Museum, Carlton, Victoria), Pilot Ace and Elliott 401 (Science Museum, London), as well as the Harwell-Dekatron and Hec 1 computers (National Museum of Computing, Bletchley Park) are preserved (see Table  9.15). The builder of the Hec 1 was Raymond Bird, and evidently two specimens were constructed. The difference engines of Pehr Georg and Edvard Scheutz (National Museum of American History, Washington, D.C.; Science Museum, London) and Martin Wiberg (Tekniska museet, Stockholm) have survived, along with the analog differential analyzers of Douglas Hartree/Arthur Porter (Manchester 1935; Science Museum, London), and John Edward Lennard-Jones/J.B. Bratt (Museum of Transport and Technology, Auckland, New Zealand). Historically significant machines such as the Manchester Baby (Manchester), the Turing-Welchman-Bombe, Colossus, and Edsac (all in Bletchley Park), as well as the Atanasoff-Berry Computer (Computer History Museum, Mountain View, California, on loan), were reconstructed. To the best of my knowledge, only one single early American pioneer computer has survived: Johnniac, named after John von Neumann (see Fig. 9.64). The Rand Corporation in Santa Monica, California had made this vacuum tube computer according to the example of the Institute for Advanced Study, Princeton (RAND stands for “research and development”). The machine was in operation from 1953 to 1966 and is no longer functional. The parallel device is now in the Computer History Museum in Mountain View.

Table 9.15  Surviving early electromechanical and electronic computers Oldest surviving relay and vacuum tube computers Year Name Design type 1945 Zuse Z4 Relay computer 1949 Csirac Vacuum tube computer 1950 Pilot Ace Vacuum tube computer 1951 Harwell computer Relay computer 1951 Hec 1 (Hollerith electronic computer) Vacuum tube computer 1953 Johnniac Vacuum tube computer 1953 Elliott 401 Vacuum tube computer © Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020

Country Germany Australia England England England USA England

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Remarks Spared from scrapping were, e.g., the punched card machines of Herman Hollerith (National Museum of American History, Washington, D.C.; Musée des arts et métiers, Paris) and the Zuse M9 calculating punch (Museum für Kommunikation, Bern).

Fig. 9.64  The Johnniac (central processing unit). This electronic vacuum tube machine (about 1953) is the only still fully intact early large-scale American computer. It was manufactured by the Rand Corporation in Santa Monica, California. (© Computer History Museum, Mountain View, California/picture: Mark Richards)

9.5.3.1  Operability Many mechanical calculating aids are still functional. With the exception of the Harwell-Dekatron computer, the early elctromechanical relay and electronic computers are no longer running. Reconstructions of old computers are as a rule functional: Turing Bombe (Turing-Welchman Bombe), Colossus, as well as the Heath Robinson and Lorenz coding machines. The oldest still working automatons are most likely the automaton clocks, musical automatons, and automaton figures, such as the handwriting automaton of Pierre Jaquet-Droz.

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9.5.4  Cylindrical Calculating Machines The Curta pocket calculating machine is fondly described as the “pepper mill.” It is a fine-mechanical marvel and is considered the crowning achievement of centuries of technical development (see Chap. 13). The Curta was never surpassed, but the mechanics was soon supplanted by electronics. The tiny device represents the high point of an impressive series of cylindrical calculating devices going back to the eighteenth century, which also includes magnificent ornamental devices such as those of Jacob Leupold/Anton Braun/ Philippe Vayringe, Anton Braun, Philipp Matthäus Hahn, Johann Helfrich Müller, Johann Jacob Sauter, Johann Christoph Schuster, Didier Roth, and Christel Hamann (Gauß/Mercedes models). Curt Herzstark did not create his masterpiece out of nowhere. Just as Charles Xavier Thomas, Jean-Baptiste Schwilgué, Konrad Zuse, and many others, he was able to further develop earlier technology. However, it is often not clear whether the inventors knew about their predecessors (see Erhard Antes: Rechenmaschinen mit kreisförmiger Anordnung der Zählwerke, in: Jochen Konrad-Klein; Klaus Kühn; Hartmut Petzold (editors): 7. Internationales Treffen für Rechenschieber- und Rechenmaschinensammler, Deutsches Museum, Munich 2001, pages 85–94).

Chapter 10

The Antikythera Mechanism

Abstract  The chapter “The Antikythera mechanism” describes an astronomical calculating machine discovered in Greece in 1901. The sensational finding only gradually revealed its secrets in recent decades. Some consider this technical marvel to be the first (analog) computer. Where it was built and who invented it remain a mystery. Numerous material and virtual reconstructions have been made in an attempt to explain the functioning of the device. Keywords  Analog calculator · Antikythera mechanism · Astronomical calculating machine

10.1  An Astronomical Calculating Machine The Antikythera mechanism (see Figs.  10.1, 10.2, 10.3, 10.4, 10.5, 10.6, 10.7, 10.8, 10.9, 10.10, 10.11, 10.12, 10.13, and 10.14) – an astronomical calculating machine – is considered by some to be the earliest analog computer.

© Springer Nature Switzerland AG 2020 H. Bruderer, Milestones in Analog and Digital Computing, https://doi.org/10.1007/978-3-030-40974-6_10

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Fig. 10.1  The Antikythera mechanism (1). The more than 2000  year old, complex astronomical calculator was discovered in 1901  in the Mediterranean before the Greek island Antikythera. The finding of this mysterious technical marvel was an enormous surprise. Until today, it is not known where the device was built and who the inventor was. The opinions regarding its age differ by at least 120 years. Numerous physical and virtual reconstructions exist. Research groups from Greece, the UK, and the USA are endeavoring to elicit the last secrets that the mechanism conceals. (© National Archaeological Museum, Athens/ Costas Xenikakis)

How was the mechanism constructed (see box)?

Design Principle of the Antikythera Mechanism Astronomical calculating machine Front side Middle Two dials with a common center Sun pointer for the motions of the sun Moon pointer for the motions of the moon and for the lunar phases Very likely five planet pointers Outer dial Egyptian calendar 365 days +1 leap year’s day 12 (Egyptian) 30-day months +5 extra days +1 leap year’s day Inner dial Zodiac (continued)

Rear side Above Dial with the Metonic cycle (19 years) (Metonic spiral) 235 lunar months: 125 30-day months and 110 29-day months Inside this dial: Probably a dial with the Callippic cycle (76 years) Dial with the Panhellenic and the Naa and Halieian games (four quadrants) Below Dial with the Saros cycle 223 lunar months (around 18 years) Sculptures representing solar and lunar eclipses Inside this dial: Exeligmos cycle (54 years) 669 lunar months Remarks The concentric dial on the front side had several pointers. Each of the four or five dials on the rear side had a pointer. The Antikythera mechanism very skillfully determines which months have 29 and which months have 30 days. The star calendar is drawn on the front side of the housing. The dial with the Callippic cycle is not actually preserved. The version of the Egyptian calendar represented on this dial assumed a uniform calendar year of 365  days. There were no leap days. For this reason, the Egyptian calendar scale could be manually adjusted in order to allow different alignments with the apparent motion of the sun through the zodiac. It is difficult for laypersons to comprehend the functioning of the mechanism. The structure of the Metonic cycle was in fact very unusual, because this had two different centers. Fig. 10.2 The Antikythera mechanism (2). The front side of the mechanism exhibits seven pointers (sun, moon, and five planets) and a double ring scale (outer ring: Egyptian calendar, inner ring: zodiac). In the digital model, inscriptions can be seen above and below (star calendar). (© Hublot model with data derived from the Antikythera mechanism research project)

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Fig. 10.3 The Antikythera mechanism (3). The rear side of the digital reconstruction of the mechanism shows two spiral-shaped scales. Above: the Metonic cycle, with display of the (reconstructed) Callippic cycle and the Panhellenic games. Below: the Saros cycle for eclipses and the Exeligmos cycle. (© Hublot model with data derived from the Antikythera mechanism research project)

10.2  The Astrolabe: Planetarium or Calendar Calculator? For a long time, the purpose of the Antikythera mechanism, a bronze gear train in a wooden housing, remained a puzzle. Was the roughly 32–33  cm high, 17–18 cm wide, and at least 8 cm deep shoe box size object an astrolabe, a planetarium, or a calculating device? Contrary to many other questions, this has been clarified in our time. The mechanism is in fact an astronomical calculating machine. It represents the approximate position of the sun, the moon, and – as can be inferred from the texts on the mechanism – possibly the five planets then known and also serves as a calendar. The machine predicted or described solar and lunar eclipse possibilities and calculated the lunar phases on the basis of the Saros cycle. Furthermore, it displayed the data for the four Panhellenic games (Isthmian, Olympic, Nemean, and Pythian games), as well as the lesser known Naa games (Dodona) and Halieian games (Rhodes). The scales on the front side are circular (concentric). The main scales on the rear side (Metonic and Saros cycles) were spiral shaped, and the remaining cycles on the rear side are circular. Greek (astronomical and technical) texts were found on the covers of both sides of the device. The machine almost certainly incorporates more than 40 different gears (including any plausible reconstructions of the lost planetary gearwork). The fix-programmed calculator was presumably operated with a laterally mounted knob or a crank. The development of such astronomical instruments evidently began in the third century BC. The degree of sophistication of the mechanism suggests that it can hardly be a one-of-a-kind device? In view of the fact that such complex constructions appeared in Europe only with the astronomical church tower

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clocks in the fourteenth century, more than 1000 years later, the mechanism occupies a position of exceptional importance in cultural, technological, and scientific history. The Antikythera mechanism is regarded as the world’s first analog calculator. The astrolabes also belong to the early analog calculating devices. Alexander Jones of New  York University believes that the machine was designed primarily for philosophical and educational purposes. It was certainly suited to demonstrations. It was probably too inaccurate for astronomers and was not suitable for navigation. Fig. 10.4 The Antikythera mechanism (4). Computer-­based reconstruction of the front side of Tony Freeth. (© 2012 Tony Freeth, Images First Ltd., London)

Why Have No Astronomical Calculators Survived? The bronze gearwheels of the Antikythera mechanism were only 2 mm thin. This fine, delicate construction may well explain why no such devices have survived. Metal was valuable and was consequently recycled. Since they were not gilded works of art decorated with gemstones, they have not been preserved. The Antikythera Mechanism Research Project In 2005, an international research collective with the name Antikythera mechanism research project was founded. It is comprised primarily specialists from the areas of astronomy, physics, astrophysics, mathematics, engineering, technological and scientific history, archaeology, and classics. For further details, see http://antikythera-mechanism.gr.

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10.3  When Was the Astronomical Calculator Found? The Ionic island Antikythera originally called Aigila is situated between the Peloponnesian peninsula and the island of Crete, opposite Kythera (hence Antikythera). The shipwreck was found by sponge divers during Easter 1900. The mechanism was then discovered in the summer of 1901 (presumably in July). Divers also carried out searches in the years 1953, 1972, and from 2012 until today. The mechanism is only incompletely preserved and consists of 82 (damaged and corroded) fragments. Fundamental investigations, including tomographic analyses, began only in the 1950s.

Fig. 10.5  The Antikythera mechanism (5). Reconstruction of the clockmaker Ludwig Oechslin with sun and moon pointers but without the presumed planetary pointers. (© ochs und junior ag, Lucerne)

10.5  When Was the Ship Built?

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10.4  When Did the Ship Sink? As can be deduced from the coin and amphora (two-handled vessels) findings, the ship sank between 70 and 50  BC.  This time window is generally accepted as correct. The ship may have been underway from Asia Minor to the western Mediterranean Sea and was probably a large cargo vessel. It was probably about 40 m long and 10 m wide and could load around 250 tons of cargo. The cargo embraced, e.g., silver and bronze coins minted in the years between 85 and 60 BC.

10.5  When Was the Ship Built? The radiocarbon analyses of Andrew Wilson (Oxford University) from 2010 indicate that the wood used for building the ship can be dated with a probability of 84.8% to the period between 211 and 40 BC. This conclusion is based on the new calibration curves for radiocarbon dating (C-14 dating, 14C method, radiocarbon method) (see Michael G. Edmunds: The Antikythera mechanism and the mechanical universe, in: Contemporary physics, volume 55, 2014, no. 4, page 263). Since wooden ships remain seaworthy for a limited time, the ship must have been built at the earliest a few centuries before this time.

Fig. 10.6  The Antikythera mechanism (6). Computer-based reconstruction of Tony Freeth. At the left, the front side with the two concentric scales and seven pointers, at the right the rear side with the spiral scales, e.g., for indicating solar and lunar eclipses. (© 2012 Tony Freeth, Images First Ltd., London)

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10.6  When Was the Astronomical Calculator Built? The opinions regarding the year in which the astronomical calculating machine was built differ considerably. The estimates range from 205  BC to 50 BC. Christián Carman, James Evans, and Tony Freeth assume that it was built around 205 BC. Michael Edmunds, Paul Iversen, Alexander Jones, and Michael Wright are of the opinion that it was built much later, at a time much closer to the time at which the ship sank. Michael Edmunds of Cardiff University in Wales writes: The present best estimate of its construction date is around the middle of the range 150–60 BC  – although a date as early as 220 BC is not completely ruled out (see Michael G. Edmunds: The Antikythera mechanism and the mechanical universe, in: Contemporary physics, volume 55, 2014, no. 4, page 263).

The astrophysicist continues: My preferred period is 140–70 BC. But there must have been earlier, probably simpler versions. So one would guess that similar mechanical devices might date from 200, or maybe 250 BC (personal communication of November 22, 2017).

According to Edmunds, there are indications in the literature that astronomical instruments were built or were at least known from 250  BC until at least 500 AD. In this regard, the science historian and classicist Jones writes: We are obviously a long way from being able to put together a coherent story of the evolution and eventual degeneration of the ancient tradition of astronomical mechanisms, but there is enough evidence to suggest that complex and scientifically ambitious mechanisms were being made at least through the three centuries from about 100 BC to AD 200, and that the people who were most likely to encounter them were mechanicians, philosophers, and scientists (see Alexander R. Jones: A portable cosmos. Revealing the Antikythera mechanism, scientific wonder of the ancient world, Oxford University Press, New York 2017, page 242).

Paul Iversen of Case Western University, Cleveland (Ohio), believes that the mechanism was built at a later time: I would say the Mechanism was manufactured soon before the shipwreck ca. 70–50 BC, but in any case probably not more than one generation, or ca. 100 BC at the earliest (personal communication of November 20, 2017).

Jones concurs largely with this view: A far simpler hypothesis, however, is that the Mechanism was made somewhere around the Aegean not long before the shipwreck and was on its way to its intended home by a route that would next have proceeded up the Adriatic toward, say, Brundisium, stopping somewhere along the way to deliver part of the cargo. Occam’s razor thus makes it probable that the Mechanism was commissioned by someone who lived in or near Epirus in the first half of the first century BC (see Alexander R. Jones: A portable cosmos. Revealing the Antikythera mechanism, scientific wonder of the ancient world, Oxford University Press, New York 2017, page 93).

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Jones continues: […] I argued that the archeological context favors the hypothesis that the Mechanism was new when it was lost in the wreck, because otherwise it becomes difficult to account for the presence of an antique object that was manifestly made for a locality west of the Aegean in a cargo originating in the Aegean and destined for points west (see Alexander R. Jones: A portable cosmos. Revealing the Antikythera mechanism, scientific wonder of the ancient world, Oxford University Press, New  York 2017, page 157).

Michael Wright (London, former Science Museum) remarks: There is, however, no good argument for suggesting that the instrument was designed that early [205 BC], and there is a counter-argument that the several displays were adjusted to mutual agreement in a way that could not have been done before the latter half of the second century BC. The most likely explanation is that the designer of these displays drew on old information (personal communication of November 22, 2017)

However, since part of the device was in fact mechanically in disorder, the physicist Wright rejects the assumption that the instrument was new when the ship went down. He writes: I think it very unlikely that the instrument was very old at the time because I think it simply would not have lasted very long without being destroyed by use and handling. I suggest that it was probably built with a generation or so of its loss; that is, within a few decades of 100 BC.

The physicist James Evans of the University of Puget Sound in Tacoma (Washington) thinks the mechanism was built earlier: The eclipse predictor best fits an 18-year Saros cycle that started in 205 BC. One or two Saros cycles later would also work, though with somewhat larger errors. Of course, we cannot rule out the possibility that it was built considerably later but using an out of date eclipse cycle (personal communication of November 21, 2017).

Tony Freeth in London, on the other hand, believes in a construction dating from the time 205 BC: the prediction of the solar and lunar eclipses is based on the Saros cycle. The indication on the rear side of the mechanism is intended to enable an age determination (personal communication of November 6, 2017). According to Christián Carman and James Evans, the eclipse predictor functions best when the full moon of the first month in the Saros cycle falls on May 12, 205 BC (see Christián Carlos Carman; James Evans: On the epoch of the Antikythera mechanism and its eclipse predictor, in: Archive for history of exact sciences, volume 68, November 2014, no. 6, page 693). If the astronomical calculating machine was built during Archimedes’ lifetime, it would have been about 150  years old when the ship sank. Such an early date for the manufacture of the mechanism is therefore hardly credible. When did the Greek and Roman scholars live (see box)?

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Lifetimes Archimedes  Greek mathematician and physicist Hipparchos  Greek astronomer Posidonius  Greek philosopher Marcus Tullius Cicero  Roman statesman

285–211 BC 190–125 BC 135–51 BC 106–43 BC

10.7  Who Constructed the Mechanism? The origin of the mechanism is unknown. While Sicily was once assumed to be the site of its manufacture, today, Rhodes is considered more likely. Where was the Mechanism made? Possibilities include Alexandria, Pergamon, Syracuse and Rhodes. Syracuse had the advantage of any heritage left by Archimedes, but the problem that it was sacked in at the time of his death in 211 BC, although something may have remained. The best candidate must be Rhodes, a port at which the Antikythera ship had called (judged by some of its cargo) not long before its wreck. Rhodes was a highly technological naval centre around 100 BC with a fine bronze industry and an astronomical tradition. It is also one place where we know that a similar contemporary device was reputedly made and seen (see Michael G.  Edmunds: The Antikythera mechanism and the mechanical universe, in: Contemporary physics, volume 55, 2014, no. 4, page 282).

In his personal communication of November 22, 2017, Edmunds adds that the star calendar preserved on the mechanism (parapegma) coincides with the geographical latitude of Rhodes and Cicero is said to have seen a comparable device in the first century BC. For a number of reasons, the classicist and epigrapher Iversen believes that the calculator was most likely manufactured in Rhodes: • The Halieian games held in honor of the sun god are depicted together with the Panhellenic games on the rear side of the device. The Halieian events are attested only on Rhodes or the territory under its control on the mainland opposite the island known as the Rhodian Peraia. They are mentioned in the Dorian dialect, but not in the Attic-Ionian dialect otherwise found on the mechanism. In the Dorian dialect, helios means sun. • Based on literary sources (dating from around the time of the shipwreck), we know that such devices were manufactured in Rhodes around the time of the shipwreck. Our closest literary description of such a device is mentioned by Cicero and was built by his teacher Posidonius, who lived on

10.7  Who Constructed the Mechanism?

• •

•

•

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Rhodes. Around this time, Geminos, who formulated the astronomical theory on which the mechanism was based, may also have been working on this island. The theory elaborated in Book 8 of his treatise is the best commentary on the astronomical basis for the gearwork of the mechanism. In the first century BC, around the time of the shipwreck, the island of Rhodes was a center for astronomy. In the first century BC, the astronomers of Rhodes spoke Attic-Ionian dialect, the language of science. In fact, an astronomical inscription written in the Attic-­Ionian dialect was found on Rhodes – the only inscription found on Rhodes known to me in the Attic-Ionic dialect. The most recent research on the rising and setting of various constellations on the parapegma inscription allow the conclusion that the alphabetical lists with the annual astronomical events (e.g., solstice, the solar equinoxes) for the sun and the fixed stars fit best to the northern latitude of 33.3 to 37.0 degrees, that is, to Rhodes. On the other hand, they do not apply for Epirus (Western Greece) or Alexandria. Objects of Rhodian origin were found in the cargo of the shipwreck, including amphorae dating from ca. 100 to 50 BC.

Iversen considers it improbable that Archimedes built the device, because it utilizes certain knowledge about the motion of the sun and moon attributed to Hipparchus (around 150 BC). Posidonius or one of his followers, for example, comes into question as the creator. In view of the Epirotic calendar (Metonic spiral), the customer probably came from Epirus (personal communication of November 20, 2017). In De Natura Deorum, volume 2, paragraph 88 (45 BC, About Godly beings) Cicero mentions the “sphaera” of Posidonius. The word “sphaera” (Greek: sphaira) has several meanings: We need to be careful to distinguish mechanized planetaria from certain other concepts and categories of objects that may be described in similar language. The Greek word sphaira (or Latin sphaera) may refer to an astronomical mechanism but was also appropriate for a simple globe […] (see Alexander R. Jones: A portable cosmos. Revealing the Antikythera mechanism, scientific wonder of the ancient world, Oxford University Press, New York 2017, page 239).

The star calendar is also associated with the Greek book author Geminos (Geminus), who presumably lived in the first century BC. Archimedes, who died in 211  BC, was active in the Corinthian colony in Syracuse. According to Cicero, the great Greek scientist built such an instrument. Freeth writes: I personally think it is likely that the original design came from Archimedes and he started the tradition of making these devices. The Antikythera Mechanism is simply a later version of the Archimedes design. But there is little hard evidence.[…]. The sophistication of the mechanism, when uncovered by Price, was astonishing, given what had previously been known about ancient Greek technology (personal communication of November 6, 2017).

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Wright is of the opinion that the device of Archimedes was very different, namely, a mechanical celestial globe. The English physicist reconstructed this device. Cicero, who reported on the “sphaera” of Archimedes in De re publica, volume 1, section 14 (54–51 BC), and in Tusculanae disputationes, volume 1, section 36 (45 BC), lived however more than 100 years later than the eminent Sicilian researcher. Kyriakos Efstathiou (Aristotle University of Thessaloniki) points out that one of the most important Greek astronomers, Hipparchus, was also living on Rhodes at this time. Many researchers believe that he, his pupil Posidonius, or someone else from the astronomy school there comes into question (personal communication of November 23, 2017). The most convincing assumption is that the Antikythera mechanism originated with the followers of Posidonius. It is unlikely that this stoic philosopher had the astronomical or the artisanal knowledge. Evidently, the work of Hipparchus and Geminos bears a close relationship to the mechanism.

10.8  Reconstructions Numerous material reconstructions and a number of virtual models of the Antikythera mechanism exist. Among the best known physical reconstructions are the devices of Ioannis Theofanidis (Greece, 1934), Derek de Solla Price and Robert Deroski (USA), Allan Bromley and Frank Percival (Australia), John Gleave (UK), Michael Wright (UK), and John Seiradakis and Kyriakos Efstathiou (Greece). Dionysios Kriaris (Greece), Massimo Vicentini (Italy), and Tatjana van Vark (The Netherlands), for example, have also built reconstructions. However, some reconstructions are not functional and deviate from the original design. 3D Solidforms, Thessaloniki, sells such devices, developed in collaboration with the Aristotle University of Thessaloniki. Markos Skoulatos and Georg Brandl (Germany) have created new physical and virtual reconstructions. Digital reconstructions also exist, for example, that of Tony Freeth (UK). The mechanism has also been rebuilt in Switzerland, for example, by Ludwig Oechslin (Lucerne and the Musée international d’horlogerie in La Chaux-deFonds). Mathias Buttet created a clock for Hublot SA, Nyon VD, incorporating the functions of the Antikythera mechanism. The most important reconstructions are regarded as those of Wright and those of the Antikythera mechanism research project team (2006).

10.8 Reconstructions

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Fig. 10.7  Antikythera mechanism (7). Contrary to other real and digital models, the reconstruction from Thessaloniki is equipped with a protective cover on both sides. (© 3D Solidforms, Thessaloniki)

There are real and virtual reconstructions (see box). “Hard” and “Soft” Reconstructions Michael Wright, the leading model builder for the Antikythera mechanism, rightly points out that a computer-based three-dimensional image is not as convincing as a physical model. In the virtual world, there is no mass, inertia, force, friction, or elastic or inelastic bending. Questions relating to the material strength are thus disregarded.

Fig. 10.8 The Antikythera mechanism (8). View into the complex gearwork of the Thessaloniki reconstruction. (© 3D Solidforms, Thessaloniki)

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The physicist Markos Skoulatos of the Technische Universität München designed a real reconstruction and then followed with a digital model, developed together with the physicist Georg Brandl. The mechanical reconstruction exhibits less friction and the virtual model high accuracy. Fig. 10.9 The Antikythera mechanism (9). The illustration shows the front side of the reconstruction by Markos Skoulatos and is fully functional. (© Markos Skoulatos)

Fig. 10.10 The Antikythera mechanism (10). The illustration shows the rear side of Skoulatos’ model. The transparent model allows one to follow the functioning of the mechanism. (© Markos Skoulatos)

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Fig. 10.11  The Antikythera mechanism (11). Markos Skoulatos and Georg Brandl also created a digital model, which can be controlled from a portable computer or a smartphone. (© Markos Skoulatos and Georg Brandl)

Fig. 10.12  The Antikythera mechanism (12). This picture shows the Help menu for the front side. (© Markos Skoulatos und Georg Brandl)

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Fig. 10.13  The Antikythera mechanism (13). This picture shows the Help menu for the rear side. (© Markos Skoulatos und Georg Brandl)

The mechanism is generally regarded as an analog device (see box). Is the Antikythera Mechanism an Analog Calculator? As mentioned earlier, the (non-programmable) Antikythera mechanism is considered the world’s oldest analog calculator. The gearwork is designed to describe the orbits of the planets. Because of this similarity, the mechanical calendar calculator is regarded as an analog device. With this machine, both the input and the output are analog: the dials (scales) and the continuously rotatable pointers. However, the calendrical calculations are carried out digitally. The number of teeth for the gear wheels is always a whole number. The gear ratio between two toothed wheels is always a rational number. These relationships reflect the celestial motion, e.g., in the Metonic cycle (x cycles in y years, with x and y whole numbers). Rational numbers are numbers which can be represented as the quotient of two whole numbers. Together with the number zero, this includes all (positive and negative) whole and fractional numbers. The display is in fact analog, but the gearwork functions digitally. Nevertheless, most researchers consider the astronomical marvel to be an analog calculator. One can also view it as a hybrid calculator. Similarly, astronomical clocks as well as digital watches with analog display are hybrid devices. Eine numerische Anzeige ist genauer als analoge Zeiger, das Ablesen ist aber beschwerlicher. For further explanations, see Paul Cockshott, Lewis M.  Mackenzie, and Greg Michaelson: Computation and its limits, Oxford University Press, Oxford 2012 (section “Was the Antikythera device an analogue computer?” pages 34–35).

10.9 Conclusions

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Fig. 10.14  The Antikythera mechanism (14). One of the 48 models that two Chinese researchers designed for the construction of the gearwork. At the top, the pointers for the sun, moon, and five planets are seen, and at the bottom, four astronomical cycles and the course of the Panhellenic games. (© Jian-Liang Lin and Hong-Sen Yan)

10.9  Conclusions The current state of research can be summarized as follows: the Antikythera mechanism discovered in 1901 was lost around 60 BC when a Roman cargo ship sank in the Mediterranean Sea. The complex astronomical calculator was possibly built shortly before by followers of the Greek philosopher Posidonius on the island of Rhodes. The intended customer for the educational device was probably a person in northwestern Greece. Sources Andrea Bignasca; Maria Lagogianni-Georgakarakos; Nikolaos Kaltsas; Elena Vlachogianni (editors): Der versunkene Schatz. Das Schiffswrack von Antikythera, Antikenmuseum Basel und Sammlung Ludwig, Basel 2015 Yanis Bitsakis: Ein antiker mechanischer Kosmos, in: Antike Welt 2015, volume 5, pages 27–32

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Christián Carlos Carman; James C.  Evans: On the epoch of the Antikythera mechanism and its eclipse predictor, in: Archive for history of exact sciences, volume 68, November 2014, no. 6, pages 693–774 Michael G. Edmunds: The Antikythera mechanism and the mechanical universe, in: Contemporary physics, volume 55, 2014, no. 4, pages 263–285 Michael G. Edmunds (Wales), personal communication of November 22nd 2017 Michael G.  Edmunds; Tony Freeth: Using computation to decode the first known computer, in: Computer, volume 44, July 2011, pages 32–39 Kyriakos Efstathiou (Greece), personal communication of November 23rd 2017 James C. Evans (USA), personal communication of November 21st 2017 Tony Freeth: Eclipse prediction on the ancient Greek astronomical calculating machine known as the Antikythera mechanism, July 30th 2014, https://doi. org/10.1371/journal.pone.0103275 (Plos one 9(7): e103275) Tony Freeth (UK), personal communications of November 6th and 7th 2017 Paul A.  Iversen: The calendar on the Antikythera mechanism and the Corinthian family of calendars, in: Hesperia, volume 86, 2017, pages 129–203 Paul A. Iversen (USA), personal communication of November 20th 2017 Alexander R.  Jones: A portable cosmos. Revealing the Antikythera mechanism, scientific wonder of the ancient world, Oxford University Press, New York 2017 Alexander R. Jones: The Antikythera mechanism and the public face of Greek science, presentation at the conference “From Antikythera to the square kilometre array: Lessons from the ancients”, June 12th to 15th 2012  in Kerastari, Greece, 23 pages Alexander R. Jones (USA), personal communication of November 14th 2017 John H.  Seiradakis; Michael G.  Edmunds: Our current knowledge of the Antikythera mechanism, in: Nature Astronomy, volume 2, January 2018, pages 35–42 Michael T. Wright (UK), personal communication of November 22nd 2017.

Chapter 11

Schwilgué’s Calculating Machines

Abstract  The chapter “Schwilgué’s Calculating Machines” deals with the largely unknown mathematical machines of Jean-Baptiste Schwilgué, the creator of the present astronomical clock of the Strasbourg cathedral. We have him to thank for the earliest surviving keyboard adding machine (patented in 1844) and a mechanical “process” calculator. Keywords  Astronomical clock · Church calculator · Keyboard adding machine · Milling machine · Process calculator · Victor Schilt · Jean-Baptiste Schwilgué · Strasbourg cathedral · World Exhibition (1851) Jean-Baptiste Schwilgué (1776–1856) is the creator of the famous (last) astronomical clock of the Strasbourg cathedral. The clock is still running to this day and is wound every 8 days. Schwilgué invented numerous devices, but the astronomical clock is regarded as his masterpiece. He was a clockmaker, calibrator, and teacher of mathematics, and his (small) calculating machine is considered to be the world’s oldest keyboard adding machine. For a long time, mathematical instruments had lever-controlled numerical input.

11.1  Schwilgué’s “Process” Calculator Following further investigations, an extraordinary (large) mechanical calculating machine that came to light on December 9, 2014, in Strasbourg proved to be the world’s oldest “process” calculator. The adding machine built in the 1830s by Jean-­Baptiste Schwilgué numerically controlled from a paper tape an extremely precise milling machine with which gear wheels could be cut with a large number of teeth. Restructuring of the Astronomical Clock from 1838 to 1842 According to the source of information, the cathedral clock stood still from 1786 or 1788 due to insufficient maintenance. The restoration took place from June 24, 1838, to October 2, 1842, and the clock was then dedicated on © Springer Nature Switzerland AG 2020 H. Bruderer, Milestones in Analog and Digital Computing, https://doi.org/10.1007/978-3-030-40974-6_11

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December 31, 1842. The rediscovered adding machine therefore probably dates from before 1838 and is accordingly at least 180 years old. The thorough restructuring of the astronomical clock required profound mathematical, astronomical, and technical knowledge, as well as a knowledge of clockmaking.

11.1.1  A  n Unconventional Special-Purpose Calculating Machine Without a Customary Setting Mechanism? As a rule mechanical calculating machines are comprised, e.g., of an input unit, a result mechanism (accumulator), and possibly a revolution counter (for multiplication and division). However, with this crank-operated device, one searches in vain for setting levers or keys. This leads to the conclusion that the system functioned with fixed values. It has three rows of 12 decagonal brass numeral dials (for the numerical values 0 to 9), allowing the representation of three 12-place numbers. There are two possible ways to attach the crank. Schwilgué’s machines feature automatic tens carry, with which Schickard, Pascal, and Leibniz all experienced problems. This device, as well as a number of counters and keyboard adders discovered in Strasbourg, bears no nameplate of Schwilgué. This suggests that these models were prototypes or that they were intended for his own use.

Fig. 11.1  Schwilgué’s large adding machine (total view). This remarkable large calculating machine, on which neither setting levers nor keys for inputting numerals are to be found, was discovered in the Strasbourg Musée historique in December 2014. (© Musées de la Ville de Strasbourg, picture: Mathieu Bertola)

11.1  Schwilgué’s “Process” Calculator

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Operating the  – in its closed state  – unimposing calculating machine (see Figs. 11.1, 11.2, 11.3, 11.4, and 11.5) was facilitated using weights. By comparison: mechanical clocks have to be wound (tensioning a spring), as do music boxes. Hurdy-gurdies have a hand crank. Punched tape controlled pianos were operated, for example, via pedals, whereas some musical automatons had a weight-driven mechanism. Later designs were outfitted with an electric motor.

Fig. 11.2  Schwilgué’s large adding machine – display windows. With this device comprehensive calculations were performed for constructing the present-day astronomical clock of the Strasbourg cathedral. (© Musées de la Ville de Strasbourg, picture: Mathieu Bertola)

The display windows allow the viewing of the results. The three 12-place numerals probably represent the three successive numbers displayed in the glass-enclosed control box of the milling machine.

Fig. 11.3  Schwilgué’s large adding machine – dials. The mechanical calculating machine from the 1830s has three rows of 12 brass dials. (© Musées de la Ville de Strasbourg, picture: Mathieu Bertola)

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As a rule, with mechanical calculating machines, numbers are entered with setting levers, keys, stylus, wheels, or setting dials, all of which are missing from this device.

Fig. 11.4  Schwilgué’s large adding machine – drive. A hand crank served as the drive for the calculator. This can be attached at two different points. The machine determines circle partitioning factors. These were then transferred manually to a paper tape. One placed the paper roll into a box on the milling machine. (© Musées de la Ville de Strasbourg, picture: Mathieu Bertola)

In this picture the weights which, according to a description facilitated the operation of the machine, are missing.

11.1  Schwilgué’s “Process” Calculator

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Fig. 11.5  Schwilgué’s large adding machine – closeup view. This picture shows the decagonal brass numeral dials with the numerals 0 to 9. The results were intended for the control of the milling machine, with which the very exacting gear wheels of the Strasbourg astronomical clock were manufactured. (© Musées de la Ville de Strasbourg, picture: Mathieu Bertola)

Note According to a personal communication of Sylviane Hatterer of the Musée historique in Strasbourg from May 9, 2019, Schwilgué’s “process” calculator has been reconditioned. It is now in the museum’s repository (see box). How Did the Finding of the “Process” Calculator Come About? My goal was to shed light on the background of the very rare Schwilgué keyboard adding machine rediscovered in Zurich. This necessitated time-­consuming researches. In this connection, I learned about the existence of a second specimen in the Alsace. The Strasbourg Musée historique restored the device outwardly and sent me two pictures of the machine. In order to carefully examine the internal workings of this machine and clarify open questions, I traveled to Strasbourg. During my visit to the museum repository, much to my surprise, a strange, nameless calculating machine unknown to me, and, as far as I know, for which no publications and no pictures then existed, came to light on December 9, 2014. In addition, other inventions of the highly talented clockmaker emerged: several mechanical counters, partly with and partly without a clock, and two prototypes of the adding machine.

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11.1.2  T  he Peculiar Machine Proved to Be an Early “Process” Calculator Extensive investigations showed that this machine was very likely the world’s first and oldest “process” calculator. A process computer is a device that controls technical or scientific processes (such as production). Until this discovery the (lost) S2 special-purpose computer of Konrad Zuse (1944) had been considered the first process computer. The Schwilgué “process” calculator is more than 100 years older. The interpretation as a process calculator is in fact a subjective matter, and there is no generally valid definition for this type of device.

11.1.3  A  n Accompanying Document Reveals the First Indications About the Origin of the Calculating Machine As can be gathered from an old accompanying document (see Fig. 11.6), this heavy unmarked apparatus was designed to perform calculations relating to the restructuring of Schwilgué’s astronomical clock. It is not clear who penned this note and when. At first it was also not certain whether this loose piece of paper belonged to the case at all. Its wording was as follows: Machine à Additionner construite par J.-B.  Schwilgué vers 1830, pour réaliser les nombres nécessaires à la confection des roues d’engrenage à grand nombre de dents, à l’aide de la machine à tailler construite également par Schwilgué pour l’exécution des mécanismes de l’Horloge Astronomique de la Cathédrale de Strasbourg.

Adding machine of J.-B. Schwilgué from around 1830 for the calculation of the numerical data required to manufacture the multi-tooth gear wheels; manufacture of the gearwork for the astronomical clock of the Strasbourg cathedral with the aid of a milling machine also built by Schwilgué. What numerical values were meant and how were they transferred to the gear cutter.

11.1  Schwilgué’s “Process” Calculator

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Fig. 11.6  Document accompanying Schwilgué’s adding machine. This note of unknown origin gives the first indications about the possible usage of the calculating machine. (© Musée historique, Strasbourg, December 9, 2014)

High Computational Effort for the Construction of the Gearwork

Fig. 11.7  Computational effort for the Strasbourg astronomical clock. The difficult to comprehend celestial motions require extensive calculations. (© Charles Schwilgué: Kurze Beschreibung der astronomischen Uhr des Straßburger Münsters, 1858, page 68)

According to the son of the creator, the astronomical clock of the Strasbourg cathedral was the result of immense calculations and laborious investigations (see Fig. 11.7). Difficult questions had to be answered. Consequently, the work was not a mere renovation as many believe, but an entirely new invention and design (see Charles Schwilgué: Description abrégée de l'horloge astronomique de la cathédrale de Strasbourg), Ph.-Alb. Dannbach, Strasbourg, 3rd edition 1847, page 65, and Charles Schwilgué: Kurze Beschreibung der astronomischen Uhr des Straßburger Münsters, Adolphe Christophe, Strasbourg, 5th edition 1858, page 68).

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11.1.4  P  urpose of the Calculating Machine: Calculation of Circle Partitioning Factors Information about the purpose of the calculating machine was first found in a  document of Théodore Ungerer (a pupil, colleague, and successor of Schwilgué): Parmi les machines spéciales que Schwilgué inventa pour l’horloge astronomique, il faut encore citer une fraiseuse à roues dentées sur laquelle on peut enregistrer la dixmillionème partie du cercle et qui permet ainsi d’opérer toutes les divisions, même avec des nombres premiers élevés. Pour le calcul des facteurs partiels, Schwilgué construisit une machine à calculer qui, elle aussi, est remarquable (see Théodore Ungerer: L’horloge astronomique de la cathédrale de Strasbourg. Historique – description – fonctionnement, Société d’édition de la Basse-Alsace, Strasbourg, 12th revised and improved edition of Charles Ungerer in collaboration with Léon Leclerc, 1976, page 12).

Among the special machines that Schwilgué invented for the realization of the cathedral clock a gear milling machine on which the ten millionth part of a circle can be read out, allowing any partitioning  – even with higher prime numbers – deserves particular mention. For the calculation of the partitioning factors, Schwilgué built an interesting calculating machine. Remark A prime number is a number that can be factored only into 1 and itself, for example, 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, and 97 (italicized texts by the author).

11.1.5  T  he Results of the Calculating Machine Determine the Settings for the Gear Milling Machine In a technical description of the Strasbourg cathedral astronomical clock, Alfred and Théodore Ungerer give a brief discussion of the calculating machine: Une grande machine à additionner, construite dans le but d’obtenir automatiquement les nombres diviseurs auxquels la machine à diviser déjà mentionnée doit être placée, pour exécuter des roues ayant un nombre de dents très élevé. Le principe en est le suivant: On obtient un nombre de dents N à l’aide du quotient q provenant de la division 10,000,000 / N en additionnant successivement N fois ce quotient (q, 2 q, 3 q … N x q), on obtient les nombres correspondant aux différentes positions du tambour diviseur, afin de réaliser N dents. Il faut donc consécutivement additionner N fois le quotient q, ce qui, lorsqu’il s’agit de nombres de dents très élevés, est un calcul fort long (see Alfred Ungerer; Théodore Ungerer: L’horloge astronomique de la cathédrale de Strasbourg, Imprimerie Alsacienne, Straßburg 1922, page 136).

A large adding machine was built for the automatic calculation of circle partitioning factors. The results were utilized for the settings of the milling machine already mentioned in order to manufacture gear wheels with a very large number of teeth. The method is as follows: With the aid of the quotient q

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resulting from the division 10,000,000/n, the number of teeth n is found by adding n such quotients (q, 2 q, 3 q … n∗q). This gives the numbers corresponding to the respective positions of the partial drum in order to produce n teeth. Thus, one must count the quotients q n times in succession. For very large numbers of teeth, this leads to tedious calculations. Example of a Number Train In a paper Alfred Ungerer gives an example of a calculation: If one wishes to obtain arbitrary partitioning with this worm gear, one must calculate the coefficients [characteristic values] for this partitioning in ten millionths and string together as many values as there are partitions. For example, if a gear wheel is to have 199 teeth, then 10,000,000/199 = 50 251 partitioning coefficients are required. To mill the first tooth one sets the drum to 50 251; to mill the second tooth one sets 2 x 50 251 (= 100 502), to mill the third tooth one sets 3 x 50 251 (= 150 753), etc. If we continue in this way, for the last tooth we obtain the number 199 x 50 251 = 9,999,949 instead of 10,000,000, which of course would be erroneous. One avoids this error by adding one or two decimals and appropriately rounding the numbers to which the partitioning drum is set (see Alfred Ungerer: Eine schwilguésche Räderteilmaschine, in: Deutsche Uhrmacher-Zeitung, volume 34, 1910, no. 7, page 114).

Below is an overview of the numerical settings (see Table 11.1). Table 11.1  The calculation of the circle partitioning factors requires 9 or 10 places Partitioning coefficient for a gear wheel with 199 teeth One decimal place 10,000,000 199 50,251.3 100,502.5 150,753.8 10,000,000.0

Two decimal places 10,000,000 199 50,251.26 100,502.51 150,753.77 10,000,000.00

© Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020

Remarks 199 = number of teeth (=n). 10,000,000 divided by 199 yields 50,251.2563 (=q). Multiplying by 2, 3, n gives the values above.

11.1.6  C  ontrolling the Gear Milling Machine from a Paper Tape Ungerer continues in his paper: Such number trains must be calculated for all partitions with high partitioning numbers. This is realized with paper tapes inserted in a special box (Fig. 3) with two rollers in order that one roller takes up the tape and the other unwinds the tape. The

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number in question can be viewed behind a small glass pane. Fig. 4 shows the first eleven numbers of such a paper tape required for partitioning into 199 pieces. Column a gives the successive numbers for the individual partitions, column b the hundredths marked on the large partitioning drum, column c the thousandths marked on the large partitioning drum, column d the hundredths marked on the small partitioning drum, and column e the thousandths on the same disc with a decimal place corresponding to the information for the Vernier. Since numerous gear wheels with a large number of teeth were required for the Strasbourg astronomical clock, for which Schwilgué accordingly built a special addition machine, a great many such number train calculations would have been necessary in order not to have to write down these coefficient additions. As soon as this adding machine is set to the relevant coefficients (with decimal places) one only has to turn a crank to successively add the coefficients. In this way the machine generates the numbers required for partitioning with the gear milling machine (see Alfred Ungerer: Eine schwilguésche Räderteilmaschine, in: Deutsche Uhrmacher-­Zeitung, volume 34, 1910, no. 7, page 114).

Operating the Calculating Machine First one calculates the quotients q by hand. The number q is equal to 10,000,000 divided by the number of teeth (n). One then sets the quotient q onto the first row of the numeral wheels (by manually rotating the wheels). The numbers 2q, 3q, 4q, etc. up to nq are then calculated by turning the crank through a corresponding number of rotations. 2q is displayed on the second and 3q on the third number wheel row, 4q on the first, 5q on the second, 6q on the third row, etc. Weights facilitate operation. Multiplication is carried out as a repeated addition. The values required for controlling the milling machine are recorded on the paper tape (see Table 11.2). Table 11.2  Paper tape with values for controlling the gear milling machine for a gear wheel with 199 teeth Controlling the gear milling machine Paper tapes a b c 1 5 2 1 0 3 1 5 4 2 0 5 2 5 6 3 0 7 3 5 8 4 0 9 4 5 10 5 0 11 5 5

d 02 05 07 10 12 15 17 20 22 25 27

© Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020

e 5.1 0.2 5.4 0.5 5.6 0.7 5.9 1.0 6.1 1.3 6.4

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11.1.7  High-Precision Fine Mechanics The following example illustrates the extraordinary precision of the gearwork for the celestial globe of the Strasbourg astronomical clock: under the influence of the sun and moon, the Earth’s axis executes precession. Consequently, in around 25,800 years, this results in a return travel movement of the point of intersection between the celestial equator and the ecliptic (great celestial circle, in which the plane of the Earth’s equator intersects the celestial globe envisaged around the sun). A complete revolution of the Earth’s axis about the normal to the orbital plane therefore takes about 25,800 years. The uppermost wheel of the gearwork for this so-called (lunisolar) precession of the equinox requires 25,806 years for one revolution. The reduction gear ratio for the precession cycle is 1:9 451 512. This enormous slowdown of the daily motion was realized with the aid of the following eight gear wheel pairs:



1 36 12 12 12 12 12 12 12 = x x x x x x x 9 451 512 81 84 94 96 108 115 126 128



(see Alfred Ungerer; Théodore Ungerer: L’horloge astronomique de la cathédrale de Strasbourg, Imprimerie Alsacienne, Strasbourg 1922, page 136). According to information of the expert Walter Schiesser, today at most the following gear ratios are possible in a single step: worm gear 1:60, spur gear 1:100. In earlier times, however, these upper limits were exceeded, particularly with church tower clocks.

11.1.8  G  ear Milling Machine or Gear Partitioning Machine? The church tower clock manufacturer and successor to Schwilgué Alfred Ungerer published a picture of the gear milling machine referred to on the label in several books about the astronomical clock and church tower clocks (see Figs. 11.8, 11.9, 11.10, 11.11, and 11.12).

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Fig. 11.8  The gear milling machine for the astronomical clock (historical picture). Contrary to Schwilgué’s “process” calculator, a few historical pictures of the gear partitioning machine have survived. At the right next to the drum was the box with the paper tape for controlling the milling machine. (© Alfred Ungerer; Théodore Ungerer: L’horloge astronomique de la cathédrale de Strasbourg, Imprimerie Alsacienne, Strasbourg 1922, page 27)

No historical illustrations of Schwilgué’s “process” calculator are known to exist. However, there are references in contemporary writings.

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Fig. 11.9  The front side of the gear milling machine for the astronomical clock. The box with the paper roll on which the circle partitioning factors calculated with the large adding machine are entered is missing. The numerical values were used for the wheel partitioning machine settings. The horizontal drum enabled the manufacture of high-quality gear wheels with a large number of teeth. (© Musées de la Ville de Strasbourg, picture: Mathieu Bertola)

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Fig. 11.10  The rear side of the gear milling machine for the astronomical clock. JeanBaptiste Schwilgué developed this device for his own use in connection with the construction of the astronomical clock of the Strasbourg cathedral. (© Musées de la Ville de Strasbourg, picture: Mathieu Bertola)

Numerous inventions of the famous Strasbourg clockmaker are preserved. However, little has been handed down about the operation of these devices.

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Fig. 11.11  Total view of the gear milling machine for the astronomical clock. Until 2015 this device lay forgotten in the repository of the Musée historique in Strasbourg. Along with the astronomical clock, Jean-Baptiste Schwilgué created a number of other showpieces, including counters, calculating machines, and church tower clocks. (© Musées de la Ville de Strasbourg, picture: Mathieu Bertola)

The  – for laypersons  – difficult to comprehend celestial motions compelled the builders of precise astronomical clocks to utilize complex multi-toothed gearworks.

Fig. 11.12  Closeup view of the gear milling machine for the astronomical clock. The bronze drum has a diameter of 46 cm. Thanks to an ingenious concept, it was possible to read out one ten millionth of its circumference, allowing the milling of, for example, 167, 179, 181, 197, 269, 281, and 307 teeth (prime numbers). (© Musées de la Ville de Strasbourg, picture: Mathieu Bertola)

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11.1.9  A  Tooling Machine Specifically Designed for the Astronomical Clock Schwilgué built an entirely new type of gear milling machine or gear partitioning machine, on which the most demanding gear wheels could be manufactured for the astronomical clock. These are the gear wheels having a number of teeth equal to a large prime number. The partitions required for the manufacture of these brass or bronze gear wheels are entered on the cylindrical lateral surface of a (horizontal) bronze drum with a diameter of 46 cm. The upper edge of the drum incorporates a screw thread with 1000 screw channels. A (horizontal) worm gear outfitted with a tiny (vertical) drum meshes as required into this thread. The circumference of this disc is also provided with 1000 graduation marks, and the circumference has a silver belt. Furthermore, the zero mark pointing to this partition is equipped with an addition (vernier). With the aid of a strong magnifying glass one can then read out the ten millionth part of the large drum’s circumference. This device allows the extremely precise graduation of a gear wheel with any number of teeth. The lateral surface of the drum incorporates a number of circles, the partitioning of which enables the manufacture of gears with up to 100 teeth. Larger numbers of teeth utilize the screw thread mentioned above, with partitioning up to 1000 teeth. With this machine it was possible to mill even spur gears, bevel gears, and also worm gears (gears with helical teeth). Contrary to other gear partitioning machines with a flat (horizontal) circle partitioning disc, the indentations of the partitions are not soiled with dust and cuttings. Thanks to an ingenious device underneath the drum, it was not necessary to count the partitions during milling. The tooling machine was originally provided with a large cast iron hand disc flywheel (about 1.80 m in diameter), driven by the operator with a hand crank. This enabled fast rotation by belt transfer from the cutting element. Later, the machine was equipped with a small electric motor. Schwilgué’s successors made further use of the machine for smaller individual tasks in their Strasbourg church clock factory. Conflicting information exists regarding the time when the gear partitioning machine was built: around 1827 (see Alfred Ungerer: Les horloges d’édifice, Gauthier-Villars, Paris 1926, page 32) and around 1830 (see Alfred Ungerer: Eine Schwilguésche Räderteilmaschine, in: Deutsche Uhrmacher-Zeitung, volume 34, 1910, no. 7, page 115).

11.1.10  Dating the “Process” Calculator There is no indication on the large adding machine regarding the year when it was built. The milling machine, which we know served for the manufacture of the gearwork for the Strasbourg astronomical clock, originated in the second

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half of the 1820s. This follows from the publications of Alfred Ungerer, a successor of Schwilgué. In order to calculate the circle partitioning factors for the milling machine, Schwilgué built his own calculating machine: Since many gears with very large number of teeth were now required for the Strasbourg astronomical clock, this made an enormous amount of number train calculations necessary. Schwilgué therefore built a special adding machine in order to avoid having to write down these long coefficient additions (see Alfred Ungerer: Eine Schwilguésche Räderteilmaschine, in: Deutsche Uhrmacher-Zeitung, volume 34, 1910, no. 7, page 114).

According to this and other reports (see the following section “Was the Large Adding Machine Used for the Astronomical Clock?”), the calculating machine was available for the reconstruction of the Strasbourg clock (1838–1842). The device was also listed in an 1844 exhibition report “Rapport du jury central” (report of the main board) on the “grande exposition des produits de l’industrie française” (large-­scale exhibit of products from French industry). The milling machine was already functional about 10 years before the reconstruction of the clock. The large adding machine was probably built after the milling machine. One can assume that the calculating machine originated during the first half of the 1830s. It was probably finished by 1838 at the latest. The maintenance of the astronomical clock was Schwilgué’s lifelong goal. It is known that he began with the time-consuming preparations long before he was awarded the contract. This imposed itself when it became clear that this delicate undertaking posed considerable technical difficulties. The clock had not functioned for about 50 years. The nameless special-purpose calculating machine was matched to the milling machine, and its use was therefore severely limited. Without the milling machine, it served no useful purpose and could not be sold alone. The Strasbourg city council first addressed the restoration of the astronomical clock in 1833 and 3 years later constituted a corresponding committee which presented its report in the same year. In 1837 Schwilgué did not renew his collaboration with his business partner Frédéric Rollé in order to devote himself entirely to the astronomical clock. In 1821 he had already made different suggestions to the city for the clock’s restoration. At the time the work began, he was already more than 60 years old.

11.1.11  W  as the Large Adding Machine Used for the Astronomical Clock? Documents of Alfred and Théodore Ungerer show that the large adding machine was used for calculating the gearwork of the Strasbourg ­astronomical clock:

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Since many gears with very large number of teeth were now required for the Strasbourg astronomical clock, this made an enormous amount of number train calculations necessary. Schwilgué therefore built a special adding machine in order to avoid having to write down these long coefficient additions (see Alfred Ungerer: Eine Schwilguésche Räderteilmaschine, in: Deutsche Uhrmacher-Zeitung, volume 34, 1910, no. 7, page 114). Among the special machines that Schwilgué invented for the realization of the cathedral clock a gear milling machine on which the ten millionth part of a circle can be read out, allowing any partitioning – even with higher prime numbers – deserves particular mention. For the calculation of the partitioning factors Schwilgué built an interesting calculating machine (see Théodore Ungerer: L’horloge astronomique de la cathédrale de Strasbourg. Historique  – description  – fonctionnement, Société d’édition de la Basse-Alsace, Strasbourg, 12th revised and improved edition of Charles Ungerer in cooperation with Léon Leclerc, 1965, page 11).

These assertions are confirmed in Schwilgué’s biography: Schwilgué “inventa son multiplicateur, qui est d’une utilité non moins grande, non-­ seulement pour obtenir les résultats des calculs dans lesquels l’opération de la multiplication devient indispensable, quelques grandes que soient ces multiplications, mais encore pour les calculs de séries (footnote: Les séries dont nous parlons ici, se rapportent principalement à celles dont mon père a eu besoin pour calculer les nombreux engrenages des mécanismes divers de la partie astronomique de l’horloge de la cathédrale.)” (see Charles Schwilgué: Notice sur la vie, les travaux et les ouvrages de mon père J.  B. Schwilgué, Imprimerie de G.  Silbermann, Strasbourg 1857, pages 119–120).

Schwilgué invented his multiplication machine, which was used as much [as the keyboard adding machine] not only to perform calculations for which multiplication is indispensable, however extensive these multiplications may be, but also to determine number trains (footnote: the number trains referred to here are largely concerned with the calculations that my father needed for the numerous gears in the different components of the astronomical clock of the cathedral). Difficult Gear Ratios: Prime Number Gears For the simulation of the exceedingly complex celestial motions, the mysterious Antikythera mechanism discovered in 1901 (see Chap. 10) embodies numerous gear trains. Their gears exhibit greatly different numbers of teeth, allowing the realization of numerous gear ratios. If the number of teeth is a (non-factorable) prime number, such as 53, 127, or 223, this complicates the manufacture of gears considerably. With the Strasbourg astronomical clock, many gears also had a large number of teeth. Often these were prime numbers, e.g., 167, 179, 181, 197, 269, 281, and 307. The very high gear ratios could be implemented only by several gear steps.

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11.1.12  T  he Calculating Machine Determines Number Trains for the Tape Controlled Milling Machine The clockmaker Alfred Ungerer describes Schwilgué’s milling machine (see Alfred Ungerer: Les horloges d’édifice, Gauthier-Villars, Paris 1926, pages 32–34). In this book one reads, for example, in order to mill a gear with n teeth, one calculates the quotient q = 10,000,000/n and then carries out: • • • •

The first milling by setting the drum to partition 0 The second milling by setting the drum to the partition equal to q The third milling by setting the drum to the partition equal to 2q The fourth milling by setting the drum to the partition equal to 3q

and so forth, so that with the nth milling – n∗q = 10,000,000 – the drum returns to the zero point. Schwilgué built this milling machine primarily for the realization of his plan to carry out the manufacture of the new gearwork for the astronomical clock of the Strasbourg cathedral. For this he had to utilize a large number of gears with many teeth.

11.1.13  Machine Control by Paper Tape In order to simplify manufacturing, Schwilgué wrote the number train q, 2q, 3q, etc. on a paper tape wound around two rollers. These are placed in a box on the right side of the machine. The rollers are outfitted with handles, so that the paper tapes can be moved forward after each milling step. Thanks to a glass pane on the top of the box, one can read out three successive numerals from the paper tape. According to a footnote, Schwilgué himself built a calculating machine that served to mechanically retain the numbers 2q, 3q, 4q, etc. up to n times q. This machine was preserved in the [former] Musée d’horlogerie of Strasbourg. Here the wording of the French footnote: Schwilgué a même construit une machine à calculer servant à obtenir mécaniquement les nombres 2q, 3q, 4q, etc., jusqu’à n x q. Cette machine est déposée au Musée d’Horlogerie de la Ville de Strasbourg (see Alfred Ungerer: Les horloges d’édifice, Gauthier-Villars, Paris 1926, page 34).

On page 37 of the above work, Alfred Ungerer states that a collection of Schwilgué’s machines and devices was also preserved in the city’s Musée d’horlogerie. In the Strasbourg Musée des arts décoratifs, there is in fact a clock exhibit.

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11.1.14  W  hen Were Schwilgué’s Machines First Mentioned? Schwilgué’s biography, written by his son (see Charles Schwilgué: Notice sur la vie, les travaux et les ouvrages de mon père J.-B. Schwilgué, G. Silbermann, Strasbourg 1857), mentions the machines additionneur (pages 117–119), multiplicateur (pages 119–120), and compteur industriel (pages 120–121). This elaboration indicates that Schwilgué invented numerous precision machines and devices between 1818 and 1851. Keyboard Adding Machine The easy to operate adding machine was designed to avoid the erroneous addition of many values and simplify the controlling of calculations. Schwilgué “a inventé une machine qui diffère de toutes celles du même genre qui avaient été établies jusqu’alors, autant par la simplicité du mécanisme que par la facilité avec laquelle on emploie l’instrument. En effet, pour faire fonctionner l’additionneur, il suffit de connaître la valeur des chiffres; aussi la personne la moins exercée dans les calculs peut-elle obtenir, sans crainte d’erreur, les résultats des additions les plus longues” (see Charles Schwilgué: Notice sur la vie, les travaux et les ouvrages de mon père J.  B. Schwilgué, G.  Silbermann, Strasbourg 1857, pages 118–119).

Schwilgué accordingly invented a machine that differed from all conventional devices of this type both by its simple design and by its simple operation. In order to use the adding machine, one only had to know the numerical values. Even an inexperienced person could perform very long additions without fear of errors. This description indicates that Schwilgué also built adders with more than three places in the result mechanism. Multiplication Machine (“Process” Calculator) Schwilgué “inventa son multiplicateur, qui est d’une utilité non moins grande, non-­ seulement pour obtenir les résultats des calculs dans lesquels l’opération de la multiplication devient indispensable, quelques grandes que soient ces multiplications, mais encore pour les calculs de séries (footnote: Les séries dont nous parlons ici, se rapportent principalement à celles dont mon père a eu besoin pour calculer les nombreux engrenages des mécanismes divers de la partie astronomique de l’horloge de la cathédrale.). Le mécanisme de cet instrument est renfermé dans une boîte de 70 centimètres de long sur 40 de large et 20 de hauteur; il peut être posé sur le bord d’une table, afin que les poids qui y sont adhérents puissent monter et descendre à volonté, et mieux encore sur les quatre pieds qui peuvent s’y adapter et qui lui donnent ainsi la forme d’un petit meuble” (see Charles Schwilgué: Notice sur la vie, les travaux et les ouvrages de mon père J.  B. Schwilgué, G.  Silbermann, Strasbourg 1857, pages 119–120).

Schwilgué invented his multiplication machine, which was used as much [as the keyboard adding machine] not only to perform calculations for which multiplication is indispensable, however extensive these multiplications may be, but also to determine number trains (footnote: the number trains referred to here are largely concerned with the calculations that my father needed for

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the numerous gears in the different components of the astronomical clock of the cathedral). This device is housed in a box 70 cm wide, 40 cm deep, and 20 cm high. It can be placed at the edge of a table plate, so that the accompanying weights can be freely moved up and down. Still better is placing the machine on a frame with 4 feet. It then has the form of a small piece of furniture. Industrial Counter Construit sur un système nouveau, cet instrument sert principalement à constater la quantité de fonctions du moteur d’une machine ou d’une opération quelconque dans un temps déterminé, tel que le nombre de coups de piston d’une machine à vapeur ou le nombre de révolutions d’une roue. On lui a donné le nom du compteur industriel, parce qu’il sert principalement à compter. Sa construction est des plus simples. Il a, en outre, l’avantage d’être d’un usage très-facile, en ce que, d’un coup d’œil, on peut juger du résultat d’une expérience. Mon père a donné à son compteur industriel la forme d’une boîte dont la partie supérieure, garnie d’une ouverture recouverte d’un verre, permet de voir la série de chiffres qui indique le résultat. Cette série, qui se compose le plus ordinairement de cinq ou six chiffres, peut atteindre le nombre de 99 999 ou celui de 999 999 (see Charles Schwilgué: Notice sur la vie, les travaux et les ouvrages de mon père J.  B. Schwilgué, G.  Silbermann, Strasbourg 1857, pages 120–121).

This tool, designed on the basis of a new method, was intended above all to determine the number of operational cycles of a motor or any process during a defined period of time, e.g., the number of piston thrusts of a steam engine or the rotational speed of a wheel. The device is known as the industrial counter. Its design is exceedingly simple. Furthermore, the operation of the counting mechanism is very simple. One can read out the test result without effort. The industrial counter is in the form of a box. The number train of the result can be viewed through a glass pane in the cover and normally comprises five or six numerals. The upper limit is 99 999 or 999 999, respectively. Industrial Exhibition of 1844 in Paris In his work Notice sur la vie, les travaux et les ouvrages de mon père, J.  B. Schwilgué, Charles Schwilgué gives a “rapport du jury central” on the “grande exposition des produits de l’industrie française.” On page 223 of this report about a large industrial exhibition that took place in Paris in 1844, he refers to the “inventeur du multiplicateur” (inventor of the multiplication machine) and on pages 224–225 to a “machine dite épicycloïdale, pour donner aux roues d’engrenage, par le fait seul de l’exécution mécanique de leur denture, les courbes théoriques qui leur conviennent, et sa machine à pignon jouissant des mêmes propriétés” (machine called “epicycloidal” for producing gear wheels solely for the mechanical execution of the gear teeth, the curves relating to these, and his pinion machine exhibiting the same properties). An epicycloid is a plane curve produced by tracing the path of a chosen point on the circumference of a circle – called an epicycle – which rolls without slipping around a fixed circle. The report of the exhibition in 1844 also helps with dating.

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At the “exposition générale des produits de l’industrie française” (general exhibition of products from French industry) in 1834, Schwilgué – still under the company name “Rollé et Schwilgué” – exhibited “un instrument désigné sous le nom de compteur marqueur” (an instrument designed under the name marking counter) and a “calendrier perpétuel” (perpetual calendar), that is a counter and a perpetual, everlasting calendar (see Charles Schwilgué: Notice sur la vie, les travaux et les ouvrages de mon père J. B. Schwilgué, G. Silbermann, Strasbourg 1857, pages 104 and 105). From April 1, 1827, to March 31 1837, Schwilgué had a company together with Frédéric Rollé. Page 35 of Alfred Ungerer’s work “Les horloges d’édifices” shows an illustration of Schwilgué’s “machine à raboter les pignons en acier” (steel gear milling machine), built around 1825, and page 36 an illustration of the same inventor's “machine servant à friser les courbes épicycloidales dans les gabarits d’engrenages” (milling machine for cycloid-shaped gear tooth surfaces of gear train patterns), built around 1830. For more information on the milling machine, see Alfred Ungerer: Eine Schwilgué’sche Räderteilmaschine mit Cycloïden-Trassierapparat und Additionsmaschine (Regional association of German engineers in Alsace-­Lothringen, invitation to the 130th meeting on March 23, 1909, Strasbourg 1909, pages 2–3). Schwilgué’s large adding machine was already mentioned in publications more than 170 years ago, at the latest in 1844. It was then forgotten and is missing from the leading international works about the history of computing. Schwilgué applied for two patents together in 1844 (see box). Two Patents from the Year 1844 On December 24, 1844, Schwilgué submitted patent applications for a mechanical adding machine and a general-purpose mechanical counter to the French Ministry of Agriculture and Commerce. The patents, granted on March 1, 1845, were in force for 15 years. The patent is concerned with the keyboard adding machine, but not with the large adding machine discovered in December 2014. The counter served to determine the rotational speed of motors and machines. In the collection of the Strasbourg Musée historique, there are several manually operated counting mechanisms. These are operated with an extractable metal rod which, thanks to a spring, springs back. With each movement the number increases by one. The heavy metal boxes can be opened with a key, and the front face is folded down towards the front. The devices incorporate four or five brass gears, each with the numerals 0 to 9.

Remark The French patent office is named the Institut de la propriété industrielle (www.inpi.fr).

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11.1.15  Schwilgué’s Church Calculator Already in 1821 Schwilgué built a small mechanical church calculator (church calendar) with the dimensions 15 x 20 cm. He demonstrated the device for the French King Louis XVIII and the Paris Academy of Sciences. The model had been in the possession of a great grandchild of Schwilgué and was lost in the Second World War. Today’s large analog church calculator, which sets the astronomical clock in motion every year at midnight on December 31, has the following features: • • • • • • •

The four-place year The solar cycle The lunar cycle (golden number) The indiction (Roman interest number) The dominical letter The epacts The Easter festival.

Explanations • Each numeral of the year is comprised of a special ring with the numerals 0 to 9. For a complete revolution, the ones ring requires 10 years, the tens ring 100 years, the hundreds ring 1000 years, and the thousands ring 10,000 years. Following the year 9999, one places the numeral 1 before the thousands ring, following another 10,000 years, the numeral 2, etc. • The solar cycle comprises 28 years. After this time the weekdays again fall on the same monthly date. • The lunar cycle (Metonic cycle) comprises 19 years. Nineteen solar years correspond to around 235 lunar months. After this time the times of full moon and new moon again fall on the same day of the year. • The indiction period is 15 years and began 3 years before the birth of Christ. This period of time was important for courts of law and the collection of taxes. • The dominical letters designate the Sundays in the perpetual calendar. For the weekdays the letters A–G were used. • The epacts give the number of days elapsed between the last new moon of the old year and the beginning of the new year. A lunar year has 354 days. • The date of Easter Sunday and the other movable holidays changes every year. The decrees of the (first) Council of Nicaea (325) are authoritative. With the exception of the church calculator functioning according to the Gregorian calendar, the astronomical clock embodies, e.g., a celestial globe, a perpetual calendar, solar and lunar equations, and also a planetarium. Who Took Care of the Astronomical Clock After Schwilgué’s Death? Jean-Baptiste Schwilgué (1776–1856) was succeeded by Schwilgué’s pupils and colleagues, the brothers Albert Ungerer (1813–1879) and Théodore Ungerer (1822–1885). The clock factory remained in the Ungerer family for many

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generations (partly with the same first names): Alfred Ungerer, Théodore Ungerer (2), Charles Ungerer (2), Jean Boutry (died in 1995, married to Edith Ungerer, the daughter of Théodore). Schwilgué had three sons and five daughters. The sons had no children, and two sons (Jean-Baptiste and Alexandre) died before Schwilgué (1855 and 1836, respectively). One son, CharlesMaximilien, was also involved with patents. He was incurably ill and paralyzed as the result of a stroke in 1858. He died in 1861. The highly indebted company had to discontinue operation in 1989. The breakup took place over the years 1989 to 1991. In 1989 the reserve storage became the property of the Bodet SA, the company which maintains the astronomical clock to this day. Note In 2015 the Strasbourg cathedral celebrated the “millénaire des fondations de la cathédrale de Strasbourg” (laying of the cornerstone for the predecessor church 1000 years ago). The precision mechanics was already very highly developed in the nineteenth century (see box). Charles Babbage and Jean-Baptiste Schwilgué In numerous publications, one finds the opinion that some inventors of mechanical calculating machines were unsuccessful due to inadequate fine mechanics. Their machines did not run without problems or were not completed. Tens carry over several places, for example, posed difficulties. In this context one can mention, e.g., Blaise Pascal, Gottfried Wilhelm Leibniz, and Charles Babbage. The English mathematician Babbage was a contemporary of Schwilgué. He was not able to complete either his difference engine or the pioneering analytical engine, the ancestor of today’s electronic digital computers. Babbage began with the difference engine in the 1820s and with his analytical engine in the 1830s. As measurements show, however, the cause of failure was not a lack of precision (see Doron D.  Swade: Der mechanische Computer des Charles Babbage, in: Spektrum der Wissenschaft, 1993, volume 4, pages 78–84). Schwilgué’s inventions constitute proof that the fine mechanics of that time was sufficient for the manufacture of precise gear trains. Sources Without the publications of Schwilgué and Ungerer, it would not have been possible to understand the significance and purpose of the extraordinary calculating machine. Herbert Bruderer: Fund einer seltsamen mechanischen Rechenmaschine für die Konstruktion der astronomischen Uhr des Straßburger Münsters, https://doi.org/10.3929/ethz-a-010345595 (2015) Herbert Bruderer: Mechanische Rechenmaschine für den Bau der astronomischen Uhr des Straßburger Münsters, https://doi.org/10.3929/ethza-010428857 (2015)

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Herbert Bruderer: Erster Prozessrechner der Welt, https://doi.org/10.3929/ ethz-a-010352586 (2015) Denis Roegel: A mechanical calculator for arithmetic sequences (1844–1852), in: IEEE Annals of the history of computing, volume 37, 2015, no. 4, pages 90–96 and volume 38, 2016, no. 1, pages 80–96 Charles Schwilgué: Notice sur la vie, les travaux et les ouvrages de mon père J. B. Schwilgué, G. Silbermann, Strasbourg 1857 Andreas Stiller: Der erste Prozessrechner, in: Magazin für Computertechnik, c’t, 2015, no. 4, January 24th 2015, pages 20–21 Alfred Ungerer: Eine Schwilguésche Räderteilmaschine, in: Deutsche Uhrmacher-­Zeitung, volume 34, 1910, no. 7, pages 113–115 Alfred Ungerer: Les horloges d’édifice, Gauthier-Villars, Paris 1926 Alfred Ungerer; Théodore Ungerer: L’horloge astronomique de la cathédrale de Strasbourg, Imprimerie Alsacienne, Strasbourg 1922 Theodor Ungerer: Die astronomische Uhr des Straßburger Münsters, Société d’édition de la Basse-Alsace, Strasbourg 1965.

11.2  Schwilgué’s Keyboard Adding Machine On January 28, 2014, an extremely rare, more than 160-year-old mechanical keyboard adding machine of Jean-Baptiste Schwilgué came to light in the Collection of astronomical instruments of the ETH Zurich. Apart from precursors, at the present time, only two specimens are known, one from Strasbourg (1846) and one from Zurich (1851). Inquiries involving Schwilgué’s descendants in regard to other devices proved to be unsuccessful. The Alsatian specimen was restored externally in 2014 but is otherwise in defective condition. The keys for numeral input are unusable; the register clearing mechanism (knobs for resetting the result mechanism) functions only partly. The machine bears the number 15. The Zurich device has no serial number and is in vastly better condition. It is possible that a several dozen key-driven adders were manufactured. Schwilgué’s calculating machine is largely unknown among experts. Until today the device is missing from important books about the history of technology. It is mentioned in Rudolf Wolf’s Verzeichnis der Sammlungen der Sternwarte as a handwritten addition on page 187, but without any additional information. Johann Rudolf Wolf (1816–1893) was an astronomer and chief librarian at the ETH Zurich. Neither operating instructions nor other relevant documents exist. No documentation relating to Schwilgué’s calculating machine exists in the library of the museums of Strasbourg or in the state archives of Strasbourg. How Did the Finding Come About? In connection with the discovery of two large Loga cylindrical slide rules (at the end of 2013) from Yvonne Voegeli of the ETH Library, Zurich, I learned about the existence of a mysterious cultural heritage treasure hidden in the main building of the ETH Zurich. Heinz Joss, a specialist for cylindrical slide

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rules, and I were searching for the long-lost slide rule of Privy Councilor Johann Caspar Horner from Zurich. The photographer Herbert Spühler was also with us. In the database of the cultural heritage collection of that time, we found a rather uninformative entry “calculating machine.” The surprise was all the greater when a historically valuable device emerged.

11.2.1  T  he World’s Oldest Surviving Keyboard Adding Machines On December 24, 1844, Jean-Baptiste Schwilgué and his son CharlesMaximilien applied for a patent for their “additionneur mécanique” (adding machine), which was granted on March 1, 1845. This device was a column adder (see Figs. 11.13, 11.14, 11.15, 11.16, and 11.17). In the second half of the nineteenth century, numerous inventors built similar devices. Above all the comptometer, invented by the American Dorr E. Felt in 1887, was by far the most successful commercially. Schwilgué’s device is presumably the world’s second keyboard adding machine, after the full-keyboard calculating machine with direct multiplication of the cabinetmaker Luigi Torchi (Milan, 1834). Torchi’s wooden trial device has probably not survived. How reliable it was is not clear. Until 1950 only a few keyboard adders were known (see Table 11.3). Table 11.3  The oldest known keyboard adding machines The earliest (known) keyboard adding machines Inventor Country Year Remarks/site Luigi Torchi Italy 1834 Lost Jean-Baptiste France 1844 ETH Zurich and Musée historique, Schwilgué Strasbourg Victor Schilt Switzerland 1850 National Museum of American History, Washington, D.C. (replica) Du Bois Parmelee USA 1850 Lost © Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020

11.2.2  Technical Features The heavy metal machine from the year 1851 has keys for the numerals 1 to 9. The calculated result is read out from a display window between the two rotating knobs. These serve to set the starting value (with the ones and tens wheels) and for resetting to zero. The device adds numerals from 0 to 299. No key is required for the numeral zero, because adding the numerical value zero does

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not change the sum. With this device, then, only single-place numerals can be entered. The low number of places can be explained by the intended purpose, namely, the adding of long number trains (columns). From 1 to 9, the stroke depth of the keys increases stepwise, and the toothed racks or gears of the counting mechanism move accordingly. The dimensions of the housing are width 25.3 cm, depth 13.5 cm, and height 9.5 cm, with a weight of 3336 g. A number of features of the keyboard adding machine are summarized below (see box).

Schwilgué’s Keyboard Adding Machine Attributes: One-function machine, single-digit adding machine Numerical input: Nine-digit keyboard Inventor: Jean-Baptiste Schwilgué, Strasbourg clockmaker Patent: 1844 Significance: World’s oldest surviving, very rare keyboard adding machine (column adder) Year built: 1851 (ETH Zurich device) Replica: Machine of Victor Schilt

Functioning of keyboard adding machines • Single step, i.e., the number is immediately added when entered • Two-step, i.e., the number is held (preset) when entered, so that the addition can be repeated.

Fig. 11.13  Front view of Schwilgué’s keyboard adding machine (Zurich). The nine numeral keys, with increasing stroke height (slit length) from 1 (left) to 9 (right), can be seen on the front face. (© ETH Zurich, Collection of astronomical instruments)

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Fig. 11.14  Top view of Schwilgué’s keyboard adding machine (Zurich). The two buttons next to the display window are for entering the starting value and clearing the result. (© ETH Zurich, Collection of astronomical instruments)

Fig. 11.15  Interior of Schwilgué’s keyboard adding machine (Zurich), right side. Entering numbers from a keyboard entailed considerable technical difficulties. From the first mechanical calculating machine to a workable adding device, more than 200 years were required. (© ETH Zurich, Collection of astronomical instruments)

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Fig. 11.16  Interior of Schwilgué’s keyboard adding machine (Zurich), left side. Keyboard adding machines are fast calculating devices: with the Thomas arithmometer, one has to first set the numerical values with levers and then transfer these to the calculating mechanism by turning a crank. By contrast, with Schwilgué’s keyboard adding machine, there is only one work step. The values entered are simultaneously transferred to the calculating mechanism. Operating is therefore simpler and faster. (© ETH Zurich, Collection of astronomical instruments)

The Zurich specimen is still more or less functioning.

Fig. 11.17  Schwilgué’s keyboard adding machine (Strasbourg). This specimen of the Musée historique in Strasbourg is older than the ETH Zurich device, but no longer working. (© Musées de la Ville de Strasbourg, picture: Mathieu Bertola)

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11.2.3  Inputting Numbers via Keyboard Schwilgué’s machine is considerably simpler than the much older Thomas arithmometer. It was designed for the fast and simple addition of columns of numbers. By comparison, the high-performance Thomas machines were of little use for everyday accounting. For this they were too cumbersome and in any case rather expensive. Entering numbers via keyboard, and not by setting levers, stylus, setting dial, or rotating wheel, was a significant step forward. Since this greatly increased the speed of adding billing amounts, the later widespread keyboard adding machines were especially well suited to accounting. The Schwilgué machine immediately adds the single-place numbers entered, and a plus sign is not necessary. Crank rotations are no longer required. The tens carry always takes place automatically. Above the number 299, the result mechanism is reset to zero. Entering numbers from the keyboard was very demanding (see box). 200 Years for Keyboard Input From the invention of the first mechanical calculating machine by Wilhelm Schickard (1623) to the development of today’s self-evident keyboard, more than 200 years were required. We owe the first key-driven calculating machines to Luigi Torchi (1834) and Jean-Baptiste Schwilgué (1844). Keyboard calculating machines became widely available to the public only in the 1880s. No information exists about the capabilities of the no longer preserved device of Torchi and the prevalence of Schwilgué’s operational adder. The construction of working sophisticated calculating machines is technically very demanding. The switching elements must function smoothly and allow disengaging, and the drive must run as shock-free and jolt-free as possible. Over-rotation (unwanted further rotation of gears due to inertia) must be avoided, since this can lead to incorrect results. Old musical instruments, such as the clavichord of the fourteenth century, were outfitted with keys. Keyboard instruments, such as the piano, harpsichord, and organ, became increasingly popular beginning in the sixteenth century. It is not surprising that a clockmaker brought about the world’s first (surviving) truly useful keyboard adding machine, Clockmakers belonged to the most talented inventors and builders, not only of timekeepers but also of calculating machines, scientific instruments, musical automatons, and automaton figures. These include artificial persons (androids) and artificial animals. Terrestrial and celestial globes can be mentioned here as well.

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11.2.4  Two Precursors and Two Finalized Devices In the 1840s Schwilgué built at least two trial versions of his keyboard adding machine (see Figs. 11.18, 11.19, and 11.20).

Fig. 11.18  Prototype (A) of Schwilgué’s keyboard adding machine. The oldest and smallest trial model was probably built before 1844 (date of patenting). It has no indication of its origin, but its design allows us to attribute it without doubt to Schwilgué. The corrugated sheet is missing, and the numerals are arranged on the top of the housing. (© Musée historique, Strasbourg, December 9, 2014)

Fig. 11.19  Interior of prototype (A) of Schwilgué’s keyboard adding machine, showing the calculating mechanism. (© Musée historique, Strasbourg, December 9, 2014)

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The trial models convey an impression of the development of the column adder.

Fig. 11.20  Prototype (B) of Schwilgué’s keyboard adding machine. This trial device has a corrugated sheet, presumably a decorative or protective strip. (© Musée historique, Strasbourg, December 9, 2014)

The existing finalized device (see Fig. 11.21) is the world’s oldest known surviving keyboard adding machine.

Fig. 11.21  Final model of Schwilgué’s keyboard adding machine. The machine dating from 1846 bears a Schwilgué label and the serial number 15. It was cleaned up externally only recently. As with prototypes (A) and (B), it no longer functions flawlessly. (© Musées de la Ville de Strasbourg, picture: Mathieu Bertola)

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Note According to a personal communication of Sylviane Hatterer of the Musée historique in Strasbourg from May 9, 2019, Schwilgué’s keyboard adder has been reconditioned. It is on permanent loan to the Arithmeum in Bonn. How Did the Keyboard Adding Machine of 1846 Come to the Musée Historique? According to a personal communication of Brice d’Andlau (Strasbourg) of November 14, 2014, her family donated Schwilgué’s keyboard adding machine of 1846 several years ago to the Musée des arts décoratifs in Strasbourg. The device stemmed from the collection of her father, Jean Boutry, who was married to Edith Ungerer. The machine only came to the Musée historique in Strasbourg in 2014. The large mechanical adding machine and the gear milling machine also belong to the holdings of the Musée historique in Strasbourg. We have clockmakers to thank for many magnificent calculating machines (see box).

Special Exhibit “Clockmakers and Calculating Machines” Schwilgué’s calculating machines from the Musée historique in Strasbourg were the subject of the special exhibit “clockmakers and calculating machines” at the Arithmeum in Bonn (May 2015 to January 2016). On display were magnificent masterpieces from clockmakers of the eighteenth century: Jacob Auch, Anton Braun, Philipp Matthäus Hahn, Johann Jakob Sauter, and Johann Christoph Schuster. In addition, there were further developments of Curt Dietzschold, Ferdinand Hebentanz, François Timoléon Maurel, Jean-Baptiste Schwilgué, and Friedrich Weiss.

11.2.5  The Replica of a Solothurn Clockmaker In 1850 Victor Schilt, a clockmaker from Grenchen (near Solothurn, Switzerland), built a replica of the Schwilgué machine (see Fig. 11.22).

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Fig. 11.22  Schilt’s keyboard adding machine (1850). This device of Victor Schilt was on display at the first World Exhibition in London in 1851. It is evidently a copy of Schwilgué’s keyboard adding machine. Probably only one specimen has survived. (© Division of Medicine & Science, National Museum of American History, Smithsonian Institution, Washington, D.C.)

11.2.6  T  he World Exhibition of 1851 at the Crystal Palace in London The first World Exhibition – “The great exhibition of the works of industry of all nations, 1851” – took place from May 1 to October 11, 1851, at the Crystal Palace in Hyde Park in London. The exhibition attracted more than six million visitors. According to the exhibition catalog, calculating machines from four countries were exhibited: France, Poland, Switzerland, and the UK. Schilt’s calculating machine (see Figs. 11.23 and 11.24) was described as follows:

Fig. 11.23  Schilt’s keyboard adding machine at the World Exhibition in London. (Source: Great exhibition of the works of industry of all nations, 1851. Official descriptive and ­illustrated catalogue, Spicer Brothers, London 1851, volume 3 (Foreign states), page 1270)

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In the book of Kidwell and Ceruzzi, we find the following text: Victor Schilt (1822–1880), a little-known clockmaker from the Swiss canton of Solothurn, sent the adding machine […] to the first of the great world’s fairs, the Crystal palace exposition held in London in 1851. This machine is the oldest extant adding machine driven directly by pushing keys. Earlier machines required a stylus to rotate wheels (as in Lepine’s machine) or had numbers set with levers (as in Thomas’s machine). The device added numbers up to a sum of 299. Schilt won an honorable mention at the fair. He also reportedly received an order for 100 adding machines but refused to fill it (see Peggy Aldrich Kidwell and Paul E.  Ceruzzi: Landmarks in digital computing, Smithsonian Institution press, Washington, London 1994, page 33).

The order indicates that the keyboard adding machine functioned flawlessly and fulfilled a particular requirement. Schilt did not respond to the request, possibly because his device was an illegal copy. Schilt worked about 2 years in Schwilgué’s Strasbourg workshop.

Fig. 11.24  Schilt’s accolade. (Source: H. Canning; Edgar A. Bowring (editor): Exhibition of the works of industry of all nations, 1851, William Clowes and sons, London 1852, page 311)

Below are two descriptions of Schilt’s machine: According to C.  Dietzschold (Die Rechenmaschine, Leipzig 1882, page 19) an outstanding adding machine of V.  Schilt that was accorded honorable mention at the World Exhibition of 1851 in London had keys: the author is not aware of any older examples of such machines (see Rudolf Mehmke: Numerisches Rechnen, in: Akademien der Wissenschaften zu Göttingen, Leipzig, München und Wien (editors): Encyklopädie der mathematischen Wissenschaften mit Einschluss ihrer Anwendungen, B. G. Teubner, Leipzig 1900–1904, volume 1, part 2, page 962). Since it is very easy with the introduction of a stylus to inadvertently access a wrong tooth gap, the newer constructions, such as that of Schilt, which was awarded a prize at the London World Exhibition in 1851, are outfitted with keys (see Curt Dietschold: Die Rechenmaschine, reprint from: Allgemeines Journal der Uhrmacherkunst, Druck und Verlag von Hermann Schlag, Leipzig 1882, page 19).

Chapter 12

The Thomas Arithmometer

Abstract  The chapter “The Thomas Arithmometer” describes the world’s first successful, industrially manufactured calculating machine. The mechanical stepped drum machine of Charles Xavier Thomas is capable of all four basic arithmetic operations. It was exhibited at the Great Exhibition of 1851 in London. Keywords  Bulletin de la société d’encouragement pour l’industrie nationale · Carriage shifting · Four-function calculating machine · Great Exhibition of 1851 · Mechanical digital calculator · Stepped drum calculating machine · Charles Xavier Thomas · Thomas arithmometer On January 28, 2014, a more than 150-year-old mechanical calculating machine came to light in the Collection of astronomical instruments of the ETH Zurich: a Thomas arithmometer from Paris. Operating instructions and other documentation were missing. However, there are numerous publications about the Thomas arithmometer. How Did the Finding Come About? Following the “discovery” of two massive Loga cylindrical slide rules (see Chap. 14 for more details), I was informed by Yvonne Voegeli of the ETH Library, Zurich, about a well-guarded cultural heritage treasure hardly known even among experts in the main building of the ETH. Heinz Joss, a specialist for cylindrical slide rules, and I were searching for the long-lost slide rule of Privy Councilor Johann Caspar Horner from Zurich. In the database of the cultural heritage collection of that time, we found a rather uninformative entry “calculating machine.” The surprise was all the greater when a rare historical device emerged.

© Springer Nature Switzerland AG 2020 H. Bruderer, Milestones in Analog and Digital Computing, https://doi.org/10.1007/978-3-030-40974-6_12

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12.1  T  he Arithmometer: The First Industrially Produced Calculating Machine The first calculating machines were invented by Wilhelm Schickard (1623), Blaise Pascal (1642), and Gottfried Wilhelm Leibniz (1673). Magnificent devices followed, often in the form of cylindrical machines. However, the first calculating machines suitable for everyday use were not able to assert themselves on the market until the nineteenth century. For Charles Xavier Thomas from Colmar (1785–1870), the path to success was stony and tedious. Thomas was the director of two insurance companies in Paris. On November 18, 1820, he was granted a first patent for his arithmometer, a “machine appelée arithmomètre, propre à suppléer à la mémoire et à l'intelligence dans toutes les opérations d'arithmétique” (a machine called the arithmometer with a memory and the capability to perform all arithmetic operations). The Thomas machine is a milestone in the history of computing. The arithmometer is the world’s first commercially successful (mechanical) calculating machine. Until then there were only one-of-a-kind machines or machines produced in small numbers. Numerous clones followed, e.g., by Arthur Burkhardt in Glashütte (Saxony, 1878). The ETH Zurich specimen (see Fig. 12.1) is considered unique, because the devices were continuously improved in mass production. Sales of 1500 Machines by 1878 Several different models were available commercially. Regular production began around 1850 and continued into the twentieth century. According to a report of A. Sebert (1878), 1500 machines were sold by 1878. The mass production of mechanical calculating machines began with the Thomas arithmometer (see box).

The Thomas Arithmometer Attributes: Four-function stepped drum calculating machine Numerical input: By setting levers Inventor: Charles Xavier Thomas from Colmar, insurance broker in Paris Patents: 1820 (first patent), 1850 (new patent, renewed 1865 and 1880) Significance:  World’s first successful industrially produced mechanical calculating machine Year built: Around 1863 (ETH Zurich device) Clones:  Machines of Arthur Burkhardt and other manufacturers

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12.2  T  he Stepped Drum Machine Is Capable of All Basic Arithmetic Operations The Thomas arithmometer is capable of all four basic arithmetic operations, addition, subtraction, multiplication, and division, and is therefore described as a four-­function machine. It is a stepped drum machine (by contrast to pinwheel machines). With the present device, the stepped drums are mounted horizontally. The stepped drum and pinwheel components invented by Gottfried Wilhelm Leibniz were the most common switching elements in mechanical calculating machines. The numerals are entered via setting levers (for the ones, tens, hundreds, etc.). A crank drive operates the machine. The changeover from addition/multiplication to subtraction/ division and back is implemented with a reversing lever (multiplication = repeated addition and division = repeated subtraction). The white clearing button serves to reset the entire result mechanism to zero. Individual numerical values can be altered with the rotatable knobs next to the display windows. The result mechanism can be shifted in relation to the input mechanism. The movable carriage enables calculations with the numbers placed correctly and therefore greatly simplifies multiplication and division. The basic design of stepped drum machines changed very little over many decades. Later constructions also included a revolution counter (for multiplication and division), an electric motor drive, keys instead of levers for entering numerical values, versatile memory devices, and a printing mechanism.

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Fig. 12.1  The Thomas arithmometer (1). The four-function calculating machine has five places in the entry register (front right, with setting levers) and ten in the result register (top, with display windows). A revolution counter is missing. The selector switch (middle left) changes between addition/multiplication and subtraction/division. The individual places of the result register are deleted with the rotatable knobs beneath the display windows. The brass plate at the top can be hinged upward. The carriage with the accumulator is shifted back and forth for multiplication and division. The crank (at the right) serves to operate the machine. The housing can be locked. (© ETH Zurich, Collection of astronomical instruments)

Dating The four-function machine discovered at the ETH Zurich is 38.2 cm (with base 39 cm) wide, 16.7 cm (17.6 cm) deep, and 10.5 cm high. It weighs 5200 g. The inscription reads “Thomas, de Colmar à Paris inventeur, No 507” (Thomas of Colmar, inventor in Paris). In the Bonn Arithmeum, there is a similar machine without revolution counter from the year 1865 with the serial number 528. However, the allocation of the machine numbers was confusing. The ETH device was built around 1863. According to Valéry Monnier (www.arithmometre.org), the production of this model began in this year. Among other devices, the Arithmeum exhibits a Thomas arithmometer dated around 1853. This calculating machine has a locking compartment on the left side (with inscribable slate cover) for accessories, such as tools, machine oil, and cleaning rags. This compartment is missing from the specimen in Zurich. Such compartments were common with the later Thomas machines. The oldest surviving specimen is in Washington, D.C. (see Fig.  12.2). The machine at the Schweizerisches Landesmuseum in Zurich (see Fig.  12.3) is much newer.

Fig. 12.2  The Thomas arithmometer (2). This oldest surviving Thomas machine (with brass stepped drums) was built around 1820 in Paris. With the three setting levers (at the bottom), ones, tens, and hundreds are entered. The fourth lever (at the far left) served for direct multiplication. The movable carriage (at the top) incorporates six pairs of display windows. The selector switch on the right side of the carriage opens six display windows to indicate the results of additions and multiplications (in black numerals) and subtraction and division (in red numerals). Beneath the display windows, one sees six buttons, which served to clear the individual digits. The machine has no revolution counter. The capacity is 3 x 0 x 6 (3 places in the setting mechanism, no revolution counter, and 6 places in the result mechanism). The calculating machine is operated from a tape and not by means of a crank. (© Division of medicine & science, National Museum of American History, Smithsonian Institution, Washington, D.C.)

Fig. 12.3  The Thomas arithmometer (3). This four-function machine of the Paris machinist Louis Payen (a successor of Thomas) has 6 places in the setting mechanism, 7 in the revolution counter, and 12 in the result (capacity: 6 × 7 × 12). The serial number 2683 indicates that the machine was built in 1892 (Source: www.arithmometre.org). The rotatable knobs next to the display windows served to clear the individual digits. The machine is operated with the crank (at the right). (© Schweizerisches Landesmuseum, Zurich)

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Shortly before Easter 2019, a well-preserved Thomas arithmometer came to light at the Schulmuseum Bern, Köniz. It bears the factory number 560 and was probably manufactured in 1863 (see Figs. 12.4, 12.5, and 12.6).

Fig. 12.4  The Thomas arithmometer (4). This specimen has four places in the setting mechanism and ten places in the result mechanism. A revolution counter is missing. (© Schulmuseum Bern, picture: Mark Kohler)

Fig. 12.5  The Thomas arithmometer (5). The carriage is movable and can be shifted to the right or left by one decimal place. (© Schulmuseum Bern, picture: Mark Kohler)

12.2  The Stepped Drum Machine Is Capable of All Basic Arithmetic Operations

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Fig. 12.6  The Thomas arithmometer (6). This picture provides a view into the inner workings. The carriage can be folded up. (© Schulmuseum Bern, picture: Mark Kohler)

Gifts for Royals In order to promote the sales of his calculating machines, at the beginning of the 1850s, Charles Xavier Thomas presented royal courts and the Pope with magnificently decorated devices, for which he was accorded a number of awards. According to a press release of the Ministry of Culture and Science in the German state of North Rhine-Westphalia of October 25, 2017, only three Thomas arithmometers with 8 places in the setting mechanism and 16 places in the result mechanism are known: one each for Czar Nikolaus I., for Ferdinand II., King of both Sicilies, and for Louis-Napoleon Bonaparte. The Czar’s specimen, built in 1851, is now in the Arithmeum, and the machine of Ferdinand II in the Palazzo Reale of Caserta (Reggia di Caserta) near Naples. The device intended for Napoleon is in the Paris Musée des arts et métiers. The Heinz Nixdorf Museumsforum in Paderborn also has such an early princely specimen, however with fewer places. These machines from the early 1850s were not yet equipped with a revolution counter. Artistically designed mechanical calculating machines, especially circular machines, and automatons with very imaginative opulence served not only as utilitarian objects. Today, for example, the Reuge company (Sainte-Croix VD) still manufactures luxurious music boxes that find use as gifts for persons of power and high officials all around the world.

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To my knowledge, in Switzerland there are only a few collections with Thomas machines: the Musée d’histoire des sciences, Geneva, the Museum Enter in Solothurn, the Collection of astronomical instruments of the ETH Library, Zurich, the Schweizerisches Landesmuseum (Zurich), and the Schulmuseum Bern. Thomas arithmometers are found in several museums of technology around the world, for example, the Heinz Nixdorf Museumsforum (Paderborn) and the Deutsches Museum (Munich). The three following drawings (see Figs. 12.7, 12.8, and 12.9) are taken from a French technological journal. For further information see http://www.arithmometre.org. Fig. 12.7  Drawing of the Thomas arithmometer dating from 1822. The journal Bulletin de la société d’encouragement pour l’industrie nationale has published excellent articles about a number of technical achievements. This drawing of November 1822 conveys an insight into the design of the Thomas machine patented in 1820. Its capabilities: 4 x 0 x 6 places in the setting mechanism and the result mechanism, no revolution counter. (© Conservatoire national des arts et métiers, Cnam, Paris)

12.2  The Stepped Drum Machine Is Capable of All Basic Arithmetic Operations

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Fig. 12.8  Drawing of the Thomas arithmometer dating from 1879 – stepped drums. This drawing from the Bulletin de la société d’encouragement pour l’industrie nationale of August 1879 shows six stepped drums next to each other for the ones, tens, hundreds, thousands, etc., with (stepped) teeth of different lengths. These represent the numerals 0 to 9. At the top is the result mechanism with the movable carriage. The stepped drum was invented by Gottfried Wilhelm Leibniz. (© Conservatoire national des arts et métiers, Cnam, Paris)

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Fig. 12.9  Drawing of the Thomas arithmometer dating from 1879  – overview. Top left: 6-place setting mechanism with levers for numerical input, as well as the display windows for the 7-place revolution counter and the 12-place result mechanism. Alongside: cross section with stepped drum and the half-open movable carriage. Bottom left: Longitudinal view of the tens carry. Alongside: Drive with crank (Bulletin de la société d’encouragement pour l’industrie nationale, August 1879). (© Conservatoire national des arts et métiers, Cnam, Paris)

12.3  The World Exhibition of 1851 at the Crystal Palace in London

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12.3  T  he World Exhibition of 1851 at the Crystal Palace in London Along with Schilt’s keyboard adding machine, some other calculating machines were also exhibited at the World Exhibition in London (see Fig. 12.10):

Fig. 12.10  Calculating machines in London. In the catalog of the World Exhibition in 1851, six calculating aids are listed. (Source: H. Canning; Edgar A. Bowring (editor): Exhibition of the works of industry of all nations, 1851, William Clowes and sons, London 1852, page 323)

The Thomas arithmometer is described and illustrated in volume 3 of the exhibition catalog on page 1196 (see Figs. 12.11 and 12.12). Remark See Sect. 9.1.2 for further information about exhibits.

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Fig. 12.11  The text for the Thomas arithmometer in the catalog of the World Exhibition. The first World Exhibition took place in London in 1851. (Source: Great exhibition of the works of industry of all nations, 1851. Official descriptive and illustrated catalogue, Spicer Brothers, London 1851, volume 3 (Foreign states), page 1196)

Remark The reference to Napier’s bones and logarithms is evidently an error: Napier’s bones are a digital aid for multiplication and division. Logarithm-based calculating devices function analog. The Thomas arithmometer has no Napier’s rods.

12.3  The World Exhibition of 1851 at the Crystal Palace in London

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Fig. 12.12  Drawing of the Thomas arithmometer in the catalog of the World Exhibition. The sketch illustrates an early design of the arithmometer without accessory compartment. Features: 5 × 0 × 10 (5-place setting mechanism, no revolution counter, 10-place result mechanism. (Source: Great exhibition of the works of industry of all nations, 1851. Official descriptive and illustrated catalogue, Spicer Brothers, London 1851, volume 3 (Foreign states), page 1196)

Awards at the World Exhibition in London Numerous awards were conferred at the World Exhibition in London in 1851. Detailed information can be found in the report of the prize jury. As can be seen from the overview of class 10 (“philosophical instruments,” i.e., scientific instruments), compared with astronomical, meteorological, musical, nautical, optical, surveying instruments, clocks, and drawing tools, only a few calculating machines were exhibited (see H. Canning; Edgar A. Bowring (editor): Exhibition of the works of industry of all nations, 1851, William Clowes and sons, London 1852, pages 317–323). A table of medals for the scientific instruments is given on pages 63–65. A distinction was made between four types of awards: general council medal (~ gold medal), council medal (~ silver medal), prize medal (~ bronze medal), and honorable mention (~ recognition prize). Among the members of the prize jury for device class 10 were, e.g., the Geneva physicist Jean-Daniel Colladon and the Berlin chemist Schubarth from the Customs Union (Zollverein). The German Customs Union, founded in 1834, was a commercial consolidation of the German federal states (Bavaria, Hesse, Prussia, Saxony, Thuringia, and Württemberg). No top accolades were accorded for the calculating machines. The calculating machine of the Polish clockmaker Israel Abraham Staffel (Russia) and the Thomas arithmometer (France) were each awarded a bronze medal, and Schilt’s keyboard adding machine (Switzerland), D. J. Wertheimer’s calculating machine (UK), and Léon Lalanne’s nomogram (France) were distinguished with recognition awards (see Figs. 12.13 and 12.14).

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Fig. 12.13  Award conferred for Staffel’s machine. The reception of calculating machines was indifferent. There were in fact numerous attempts to solve numerical problems by mechanical means, but most of these devices were only able to add and subtract and were of little practical value. They were slow and in some cases yielded incorrect results. In the estimation of the prize jury, the best machine was that of Israel Abraham Staffel (Russia). This machine was capable of all four basic arithmetic operations and extracting roots. (Source: H. Canning; Edgar A. Bowring (editor): Exhibition of the works of industry of all nations, 1851, William Clowes and sons, London 1852, page 310, excerpt)

12.3  The World Exhibition of 1851 at the Crystal Palace in London

Fig. 12.13 (continued)

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Fig. 12.14  Award conferred for the Thomas machine. In the estimation of the prize jury, the arithmometer of Charles Xavier Thomas was the second best machine. It combines the two essential properties of time savings and correctness of the results and is suitable for all four basic arithmetic operations. (Source: H. Canning; Edgar A. Bowring (editor): Exhibition of the works of industry of all nations, 1851, William Clowes and sons, London 1852, page 310, continuation)

Remark The catalog numbers refer to the corresponding numbers in the official exhibition catalog (see the Great exhibition of the works of industry of all nations, 1851. Official descriptive and illustrated catalogue, Spicer Brothers, London 1851, volume 3: Foreign states). Dietzschold also mentions the distinction: In the same year [1851] the London prize jury awarded him [Thomas of Colmar] a (simple) prize medal (see Curt Dietzschold: Die Rechenmaschine, reprint from: Allgemeines Journal der Uhrmacherkunst, Druck und Verlag von Hermann Schlag, Leipzig 1882, page 37).

12.4  What Was the Cost of an Arithmometer?

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Industrial exhibitions were a good platform for the presentation of calculating machines (see box).

Industrial Exhibitions and Books About Machines World exhibitions, national industrial exhibitions, and (later) also trade fairs were vitally important for commercial manufacturers. At these platforms they were able to make their calculating machines, musical automatons, etc. known. The exhibition catalogs also simplify the dating of these machines. In the course of time, the role of world exhibitions took on other forms. According to a press release of the Deutsche Messe AG of November 28, 2018, due to declining interest, the Cebit Hanover will no longer be held from 2019. This was regarded as the world’s largest trade fair for information technology and took place for 33 years, from 1986 to 2018. Another popular aid for the announcement of inventions was the machine books, e.g., Jacob Leupold’s “Theatrum arithmetico-geometricum” (see Helmut Hilz: Theatrum machinarum. Das technische Schaubuch der frühen Neuzeit, Deutsches Museum, Munich 2008, 143 pages). Such illustrative technical books appeared especially in the time from the sixteenth to the eighteenth century.

12.4  What Was the Cost of an Arithmometer? In the catalog of the World Exhibition of 1862, the Thomas arithmometer is shown as a full-page advertisement (see Fig.  12.15). At that time a 10-place arithmometer cost 6 pounds. As well as is known, that was the least expensive and most widespread model. In France it was available for 150 francs. Dingler’s polytechnisches Journal (see Fig.  12.16) cites a price range from 150 to 400 (French) francs. For the calculating machines of Arthur Burkhardt from Glashütte (clones of the Thomas arithmometer) in 1880, the following prices were quoted: 350 marks for a 6-place machine, 450 marks for an 8-place machine, and 600 marks for a 10-place machine. This was in good agreement with the prices in Paris (see Wilhelm Jordan: Eine deutsche Fabrik für Rechenmaschinen, in: Zeitschrift für Vermessungswesen, volume 9, 1880, no. 11, pages 441). In 1892 the outlays for these machines looked like this: 6-place machine 375 marks, 8-place machine 475 marks, and 10-place machine 675 marks (see Walter Dyck: Katalog mathematischer und mathematisch-­physikalischer Modelle, Apparate und Instrumente, Georg Olms Verlag, Hildesheim, Zurich, New York 1994, page 150) (first published in 1892).

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Fig. 12.15  Price list for the Thomas arithmometer (1) from 1862 from the catalog of the World Exhibition of 1862 in London. (Source: The international exhibition of 1862. The illustrated catalogue of the industrial department, British division, volume 2, Her majesty’s commissioners, London 1862 (Official illustrated catalogue advertiser, part 7, page 2))

12.4  What Was the Cost of an Arithmometer?

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Fig. 12.16  Price list for the Thomas arithmometer (2). (Source: Franz Reuleaux: Die Thomas’sche Rechenmaschine, in: Dingler’s polytechnisches Journal, volume 165, 1862, no. 83, page 362)

Auctioning of an Extraordinary Thomas Machine for 233,000 Euros In November 2013 the well-known Cologne Breker auction house sold a Thomas arithmometer for the incredible price of 233,000 Euros. The auctioned specimen was a treasure and was housed in a magnificent wooden casing. Ostensibly it was manufactured in 1835. This would make it one of the oldest surviving arithmometers. At the time the Breker (Cologne) text read: “Arithmomètre” de Thomas de Colmar, 1860s World’s first calculating machine produced in series Sold on 16 November 2013: Euro 233.600,- / US$ 315,400.- / £ 195,500.- / ¥ 32.000.000.

An Error with Serious Consequences? Valéry Monnier of Osny (France) pointed out that the dating was erroneous and that the machine and casing did not match (see Valéry Monnier: Mademoiselle Renauds Arithmometer, in: Historische Bürowelt, 2014, no. 541, pages 19–26). In his investigation, the arguably best expert on Thomas stepped drum machines comes to the conclusion that the device was manufactured in 1863. This is consistent with the date of origin of the specimen belonging to the Collection of astronomical instruments of the ETH Library, Zurich. Both have five places in the setting mechanism, no revolution counter, ten places in the result mechanism, and bear the same stamp. An accessory compartment is missing. The ETH Zurich device bears the serial number 507 and is therefore somewhat older than the “Cologne” model, with the number 541. According to Monnier, the year of manufacture was subsequently changed on the Breker website. The wooden casing with Boulle’s inlay was probably intended for the 1850/1852 models. It is too small for the model of 1863, so that the machine had to be trimmed to size. Why, how, and when it came to this curious combination between the unsuited casing and the calculating machine remains unexplained. The age of many mechanical calculating machines is difficult to determine. According to Monnier, important features of the arithmometer are the form of the stamp and the tens carry mechanism. Properties such as the form of the reversing lever (for changing between the basic arithmetic operations), the missing revolution counter, or an accessory compartment are not always unambiguous and can lead to false assumptions.

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Note Section 17.9.2 gives further information in regard to the question, whether Arthur Burkhardt violated the patent of Thomas and his successors with his clone in 1878.

12.5  A  Wealth of Information About the History of Technology and Industry On June 27, and July 8, 2014, a number of publications and tables with excellent technical drawings (both copper engravings and woodcuts) came to light in the Bulletin de la société d’encouragement pour l’industrie nationale (BSEIN) in the course of researching the arithmometer at the ETH Library, Zurich. In four contributions, Francœur, Hoyau (both 1822), Benoît (1851), and Sebert (1879) report on the successful stepped drum machine. The illustrations of 1822 and 1879 convey an impression of the device’s inner workings. The figure of 1822 shows a very early model, shortly after patenting in 1820, and the drawings of 1879 demonstrate an improved model of one of the inventor’s sons (Thomas of Bojano). The Bulletin de la société d’encouragement pour l’industrie nationale is an excellent source for industrial history (see box). Bulletin de la société d’encouragement pour l’industrie nationale No well-sounding name like Science or Nature. Inconspicuous, largely unknown, but still high-quality. A veritable treasure chest with diverse technical texts and superb drawings of machines and tools of all kinds. The journal appeared for 142 years, without interruption form 1802 to 1943. Only a few Swiss scientific libraries carried the rare publication from Paris: Bulletin de la société d’encouragement pour l’industrie nationale. Individual references in French publications and books about the history of mathematics led to the awareness of the Bulletin, published by the first French nonprofit society, founded in 1801 and still in existence today: the Société d’encouragement pour l’industrie nationale (SEIN). It’s goal is the promotion of economic development through technical innovation. All volumes of the journal were digitized and are accessible cost-free online. The author is not aware of any German or English language magazine of comparable value dealing with the history of technology. It contains an enormous number of historical contributions, covering all kinds of subjects. Some examples from the earliest decades are agriculture, chemistry, clocks, coin mintage, fire departments, foods, light, looms, machine construction, measuring instruments, musical instruments, patents, the printing industry, potteries, sawmills, steam engines, steam locomotives, steamships, tools, traffic systems, and windmills.

12.5  A Wealth of Information About the History of Technology and Industry

483

Rudolf Mehmke mentions the Bulletin de la société d’encouragement pour l’industrie nationale in his treatise “Numerisches Rechnen” (see Akademien der Wissenschaften zu Göttingen, Leipzig, München und Wien (editors): Encyklopädie der mathematischen Wissenschaften mit Einschluss ihrer Anwendungen, B.  G. Teubner, Leipzig 1900–1904, volume 1, part 2, pages 938–1079) in several footnotes.

Chapter 13

The Curta

Abstract  The chapter “The Curta” introduces still another technical marvel. The highly gifted Austrian engineer Curt Herzstark created a picture-perfect “pepper mill,” the tiniest mechanical calculating machine in the world. The design drawings were drafted in the Buchenwald concentration camp. The round-shaped calculator was manufactured in high numbers in Liechtenstein until the beginning of the 1970s. However, the inventor was cheated out of his life’s work. Only recently, high-quality drawings for the Multiple Curta, the world’s smallest mechanical parallel calculator, came to light. The University of Birmingham constructed a 12-fold Curta in 1953. The Curta is considered the crowning achievement of the 350-year history of mechanical calculating machines. The stepped drum devices remain completely functional to this day. Keywords  Buchenwald concentration camp · Circular calculating machine · Curta · Curt Herzstark · Cylindrical calculating machine · Four-function calculating machine · Mechanical parallel calculating machine · Multiple Curta · Round-shaped calculator · Stepped drum calculating machine

13.1  Preliminary Remarks From the point of view of technological history, the most significant event in Liechtenstein was without doubt the mass production of the Curta, the world’s smallest mechanical calculating machine. In recent years surprising documents have been discovered (see box).

© Springer Nature Switzerland AG 2020 H. Bruderer, Milestones in Analog and Digital Computing, https://doi.org/10.1007/978-3-030-40974-6_13

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New Documents for the Curta from Austria, Germany, and Switzerland In the course of researching the history of computing, on November 25, 2014, drawings of the Curta calculating machine, originally called the “Liliput,” were discovered at the Schreibmaschinenmuseum Beck Beck in Pfäffikon ZH. They were prepared in the Buchenwald concentration camp by the inventor Curt Herzstark. The legacy, which Herzstark’s partner in life Christine Holub donated to the museum’s owner Stefan Beck, included letter correspondence with long since vanished well-known Swiss calculating machine manufacturers as well as lists of customers. Furthermore, of particular interest is a marketing contract with the Rheinmetall-Borsig company in Sömmerda (Thuringia), concluded shortly before Herzstark’s dramatic escape from Thuringia, for which a previously unknown transcript came to light. New is also an informative authentic account of Herzstark’s colleague Elmar Maier on the further development of the Curta (Curta 1a, 2a and electrification). Further documents exist in the Swiss Federal Archives in Bern.

The Multiple Curta as the World’s Smallest Mechanical Parallel Calculator In 2015 previously unknown design drawings and patent documents relating to a multiple calculator of Curt Herzstark came to light in Switzerland. In 2017 a paper concerning a mechanical parallel calculator with 12 Curtas dating from 1953 in England was discovered.

13.2  Development of the Curta The life of the Austrian inventor Curt Herzstark (1902–1988) (see Fig.  13.1) was overshadowed by tragic events: prevention from taking over his parents’s calculating machine factory because of the “annexation” of Austria, prisoner in the Buchenwald concentration camp, escape from Soviet persecutors in Thuringia, defrauding with the buildup of mass production for the Curta by the Prince of Liechtenstein, and the resistance of certain Swiss competitors.

13.2  Development of the Curta

487

Fig. 13.1  Curt Herzstark. The inventor of the world’s smallest mechanical pocket calculating machine spent several years in the Buchenwald concentration camp. Although the inventor was Austrian, the Curta was manufactured in Liechtenstein. (© Liechtensteinisches Landesmuseum, picture: Sven Beham)

Below are some of the landmarks on the rocky road to the Curta. 1928: Demonstration of an automatic calculator in Berlin The first pioneering invention of the Austrian engineer was the Multimator, exhibited in 1928 in Berlin. That was an automatic calculator unique worldwide, which stored the typed inputs in up to 30 columns, added these horizontally and vertically according to requirement, printed out subtotals at any arbitrary point or all final sums at the end of a form including cross-­matching, with the single press of a button, and even gave the carry (see Curt Herzstark: Kein Geschenk für den Führer, Books on demand GmbH, Norderstedt 2005, page 123).

The company brochure spoke of an automatic crosswise adding machine with multiple accumulators. By 1937 around 400 machines had been sold. Traditional calculating machines weighed several kilograms, so that customers increasingly wanted lightweight, easy-to-operate devices. Slide rules were inaccurate and not suited for all basic arithmetic operations. For a long time, there were only heavy or inaccurate calculating aids (see box). Heavy, Inaccurate, or Unsuitable Calculating Aids Today electronic pocket calculators are commonplace. However, until the 1970s there were practically only: • Portable bead frames, which in fact enabled all four basic arithmetic operations but had no automatic tens carry (continued)

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• Lightweight, easy-to-use (logarithmic) slide rules, which were incapable of addition and subtraction and inaccurate • Mechanical pocket calculators, such as the sliding bar calculator, which was incapable of multiplication and division and exhibited only semiautomatic tens carry • Heavy mechanical desktop calculating machines, which were capable of all four basic arithmetic operations and had automatic tens carry, but could not be easily transported.

13.2.1  The First Patents for the Curta From 1928 Herzstark was concerned with the development of a small fourfunction pocket calculating machine, that is, a device for addition, subtraction, multiplication, and division. The basic design was completed around 1930. However, subtraction and division posed sheer unsolvable problems for the installation of conventional stepped drums in a cylindrical form. “The solution didn’t want and didn’t want to come to me,” wrote Herzstark in his memoirs (see Curt Herzstark: Kein Geschenk für den Führer, Books on demand GmbH, Norderstedt 2005, page 178). On Lake Constance, near Lindau, the long-sought flash of inspiration for the Curta suddenly came: While returning home from the Black Forest in the express train I had time to think about my small calculating machine. On Lake Constance, near Lindau, the thought suddenly occurred to me that I could perform subtraction as a pure addition by simulation. […]. And so I thought that it must be possible to structure the stepped drums so as to carry out normal calculations in one position and, by axial shifting to a second position, add the complements, which are then displayed as the subtraction or division result in the result mechanism. If I'm able to solve this technically, the fourfunction pocket calculating machine would be reality (see Curt Herzstark: Kein Geschenk für den Führer, Books on demand GmbH, Norderstedt 2005, page 178).

In Vienna, Herzstark had a first trial four-function pocket calculating machine device built in his parents’ factory. Since it was functional, in February 1938 he applied to the Vienna patent office for patents on his two fundamental inventions. However, because of the uncertain political situation (Hitler‘s invasion of Austria), he did not reveal all his secrets.

13.2.2  A  rrest and Deportation to the Buchenwald Concentration Camp At the behest of the Nazis, the “half-Jew” Curt Herzstark from Vienna, arrested on spurious pretexts in 1943, drafted the design drawings for the Curta while in the Buchenwald concentration camp.

13.2  Development of the Curta

489

In his memoirs Herzstark describes the gruesome, inhuman conditions in the large concentration camp near Weimar. That he survived the labor camp is undoubtedly not in the least due to his creative genius, which the Nazis were acutely aware of. In the Wilhelm-Gustloff-Werk, an arms factory, he was compelled to draw sketches for his pocket calculating machine in pencil.

13.2.3  C  urta, a Gift for the Führer for the Ultimate Victory? The Curta was supposed to be a “gift for the Führer.” Christine Holub (the daughter of Rudolf Holub, who suggested the Multimator calculating machine) was Herzstark’s longtime partner in life. The memoirs of Curt Herzstark which she co-­edited with great care are based on discussions, tape recordings, and the written legacy (see Fig. 13.2).

Fig. 13.2  Kein Geschenk für den Führer. Curt Herzstark’s memoirs describe the fate of the highly gifted inventor. The book was issued by Christine Holub in collaboration with Heinz Joss and Ute and Bernd Schröder. (Source: Books on demand GmbH, Norderstedt)

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13.2.4  D  esign Drawings from the Buchenwald Concentration Camp In the Buchenwald concentration camp, the Curta was still called the Liliput (see Figs. 13.3 and 13.4). Fig. 13.3  The front side of the Liliput (1944). Curt Herzstark drafted the design drawings in the Buchenwald concentration camp. (Source: Schreibmaschinenmuseum Beck, Pfäffikon ZH)

Fig. 13.4  Total view of the Liliput (1944). Curt Herzstark prepared the first drawings for the Curta in Buchenwald. The machine was later renamed the “Curta”. (Source: Schreibmaschinenmuseum Beck, Pfäffikon ZH)

13.2  Development of the Curta

491

13.2.5  C  ontract for Work with Rheinmetall-Borsig in Sömmerda Following his liberation from the Buchenwald concentration camp, Herzstark was named Technical Director of the Sömmerda branch of the Berlin Rheinmetall-­Borsig AG. There he had trial models built at his own cost. Wilma Scherer (later Wilma Riegel) produced final drawings from the pencil sketches made in Buchenwald. Among the papers found in Pfäffikon ZH was a contract dated October 16, 1945, for work between the Rheinmetall-Borsig AG, Sömmerda, and its Technical Director Curt Herzstark. The 5-year agreement for the exclusive marketing rights of all products from the Sömmerda calculating machine factory would have taken effect on January 1, 1946. But fate was to will otherwise.

13.2.6  Escape from Russian Persecutors in Thuringia After the turnover of the American zone to the Russian occupational zone, Herzstark was spied on. The situation became increasingly dangerous. He was threatened with deportation to Russia. The handwritten minutes of the 12th meeting of the works council on December 4, 1945 (page 2), include the text (see Figs. 13.5 and 13.6): Hereupon colleague Wittig [First Chairman of the works council) announced that the technical director Herzstark disappeared unnoticedly. Up to now no exact information is available. (Source: Historisch-technisches Museum of Sömmerda)

The highly dangerous escape with three prototypes and the design drawings in a small carrying case led Herzstark by way of Prague to Vienna. In Weimar, with caution and luck, he narrowly avoided the Soviet persecutors.

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Fig. 13.5  Escape from Sömmerda. First minutes of the works council meeting of December 4, 1945, page 1. The works council is informed of Herzstark’s disappearance. (Source: City of Sömmerda, Historisch-technisches Museum im Dreyse-Haus)

13.2  Development of the Curta

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Fig. 13.6  Escape from Sömmerda. First minutes of the works council meeting of December 4, 1945, page 2. The works council is informed of Herzstark’s disappearance. (Source: City of Sömmerda, Historisch-technisches Museum im Dreyse-Haus)

In Vienna he was aware that the inheritance of his father’s Rechenmaschinenwerk Austria Herzstark & Co. was denied. Before the War it had been agreed that he would take over the company, entered in the commercial register in 1906. Curt Herzstark’s life was characterized by tragedy (see box).

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Curt Herzstark January 26, 1902 August 19, 1938 April 13, 1939 October 27, 1988 1921 1921

1927 1928 1938 1938 1943 1945 1945 1945 1945 1945 1946 1946 1946 1948 1949 1950 1951 1971

Born in Vienna Granting of the main patent (DRP no. 747 073) Complementation gearwork (complementation stepped drum) Granting of the main patent (DRP no. 747 074) for the reduction Death in Nendeln, Liechtenstein Conclusion of studies at the Higher State Technical School, Vienna Employment at the Austria Herzstark & Co. calculating machine factory in Vienna and further education in precision mechanics and tool construction companies in Germany Invention of the Multimator (Multisummator) automatic calculator and numerous patent applications Presentation of the Multimator at the international office machine exhibition in Berlin Construction of an initial trial model of the Curta Invasion of Hitler in Austria Arrest and deportation to the Buchenwald concentration camp Liberation from the Buchenwald concentration camp Final drawing of the engineering documents Technical Director of the Sömmerda branch of the Berlin Rheinmetall-Borsig AG Construction of three Curta prototypes at the Sömmerda factory Escape from Russian persecutors in Thuringia and return to Vienna Invitation of Prince Franz Josef II of Liechtenstein to come to Vaduz Founding of the Contina Büro- und Rechenmaschinenfabrik AG, Vaduz FL (later in Mauren FL) Curt Herzstark, Technical Director of Contina AG Beginning of mass production of Curta in Mauren (Plant I) and the Eschen branch (Plant II) Presentation of the Curta 1 at the Basler Mustermesse and the Frankfurt trade fair Presentation of the Curta 1 at the technical trade fair in Hanover Resigning of Curt Herzstark from Contina Cessation of the Curta production

13.3  Description of the Curta

495

13.2.7  T  he Crowning Achievement of 350 Years of Mechanical Calculating Machine Development The circular, exceedingly attractive Curta, which reminds one of a pepper mill, is a lightweight, full-fledged “universal” calculating machine in pocket format. It was the most successful mechanical four-function pocket calculating machine. The – until today – unrivaled calculating aid is viewed as the crowning achievement of the 350-year development of mechanical calculating machines. The diminutive, still fully functional devices enthrall the experts to this day. The fine mechanical marvel was manufactured in Liechtenstein from 1948 to 1971 and in use until it was replaced by inexpensive electronic devices. The Curta is the forerunner of today’s electronic pocket calculators, which appeared on the market in the 1970s. The early providers included Canon, Hewlett-Packard, Sanyo, Sharp, Olivetti, and Texas Instruments. A meeting came about between Herzstark and Zuse (see box).

Meeting Between Konrad Zuse and Curt Herzstark “At a conference on precision mechanics in October 1958 I was impressed by a talk of Professor Konrad Zuse on electromechanical and electronic calculating machines” (see Curt Herzstark: Kein Geschenk für den Führer, Books on demand GmbH, Norderstedt 2005, page 286). The meeting with Konrad Zuse took place on October 31st 1958 in the Institut für Feinwerktechnik und Regelungstechnik of the Technische Hochschule Braunschweig. The expert committee for precision mechanics of the German Association of Engineers (VDI) held the 10th precision mechanics convention, with the title “Interrelationships between mechanics and electronics” on October 30 and 31. (Source: Konrad Zuse Internet archive, zuse.zib.de).

13.3  Description of the Curta

Fig. 13.7  The Curta 1. The smaller of the two models differs from the larger version mainly by the number of places in the setting mechanism, revolution counter, and result mechanism. Even after decades the attractive devices still function flawlessly. (© Liechtensteinisches Landesmuseum, Vaduz, picture: Sven Beham)

Fig. 13.8  Sectional view of the Curta. Section of the technical marvel (Model 1). The tiny “pepper mill” is characterized by high mechanical precision. Lay persons also admire the ingenious calculating machine. (© Liechtensteinisches Landesmuseum, Vaduz, Sven Beham)

13.3  Description of the Curta

497

The Curta (see Figs. 13.7, 13.8, and 13.9) is a circular digital calculating machine capable of all four basic arithmetic operations. Contina manufactured two models, a smaller and a larger version: Curta 1 (features) • 8 places in the setting mechanism, 6 places in the revolution counter, and 11 places in the result mechanism, i.e., 8 × 6 × 11. • 53  mm diameter, 85  mm high, 230  g weight without sleeve, 330  g with sleeve. • The manufacture and assembly of a Curta 1 took 9–10 hours. Curta 2 (features) • 11 places in the setting mechanism, 8 places in the revolution counter, and 15 places in the result mechanism, i.e., 11 × 8 × 15 • 65 mm diameter, 90 mm high, and 360 g weight.

Fig. 13.9  The Curta cylindrical calculating machine. The very attractive “pepper mill” is on view in numerous museums around the (© Nisse Cronestrand, Tekniska museet, Stockholm)

A virtually unknown forerunner of the Curta came to light in Sweden (see Fig. 13.10).

498

13  The Curta

Fig. 13.10 Petersson’s calculator. This very rare stepped drum machine with a weight 6.6 kg (1873) of Axel Jacob Petersson is designed for all four basic arithmetic operations. The crank, which can be rotated in both directions, is not shown. (© Okänd, Tekniska museet, Stockholm)

A Coveted Collector’s Object The Curta, a coveted devotee object, is undoubtedly the most often found mechanical calculating machine in museums of science and technology around the world. Examples of places are the Deutsches Museum (Munich), Heinz Nixdorf M ­ useumsforum (Paderborn), Arithmeum (Bonn), Deutsches Technikmuseum (Berlin), Technisches Museum Wien, Vienna, Museum für Kommunikation (Bern), Museum Enter (Solothurn), Schreibmaschinen­ museum Beck (Pfäffikon ZH), Science Museum (London), National Museum of Computing (Bletchley Park, UK), Musée des arts et métiers (Paris), Museo nazionale della scienza e della tecnologia “Leonardo da Vinci” (Milan), Tekniska museet (Stockholm), Rijksmuseum Boerhaave (Leiden), National Museum of American History (Washington, D.C.), Computer History Museum (Mountain View, California), Harvard University (Cambridge, Massachusetts), Canada Science and Technology Museum (Ottawa), or the Museum of Applied Arts and Sciences/Powerhouse Museum (Sydney). The original model can be admired in the Liechtensteinisches Landesmuseum (Vaduz). The MuseumMura, Schaanwald FL, is particularly committed to the preservation of this cultural heritage.

13.3.1  Design Drawings The large-format design drawings for the Curta are extremely complex. Since they would no longer be readable following reduction in size, it is unfortunately not possible to reproduce them here. The two following illustrations (see Figs. 13.11 and 13.12) serve only to convey an initial impression.

13.3  Description of the Curta

499

Fig. 13.11  Design drawing for the Curta 1, step 1. This drawing depicts the base body (step 1) of the calculating machine manufactured in Mauren. (Source: MuseumMura, Schaanwald FL)

500

13  The Curta

Fig. 13.12  Design drawing for the Curta 1, step 2. This drawing depicts the base body (step 2) of the high-precision calculating machine. (Source: MuseumMura, Schaanwald FL)

Remarks The counting mechanism carriage is comprised of the result mechanism and the revolution counter. The machine originally had the name “Liliput” and later “Contina.” The final name soon became Curta. A firsthand witness tells how the name Curta came about (see box).

How the Name “Curta” Came About A firsthand account by Elmar Maier This is a short but a nice story. At the very beginning, when Herzstark’s first ideas for the pocket calculating machine had already been documented in design drawings (this was shortly after the Second World War), the first samples were constructed. The separate parts illustrated in these drawings were manufactured at the Rheinmetall-Borsig company in Sömmerda. Following his insanely dangerous escape from the Russians in Thuringia, Mr. Herzstark ultimately reached his native city Vienna, naturally with the Curta parts he had secretly smuggled. These were then assembled in the still existing Herzstark company of his (continued)

13.3  Description of the Curta

501

father. There were only a few construction models. At that time Mr. Herzstark appropriately called this tiny calculating machine “Liliput,” which can still be seen on old drawings. In 1947, as is known, production began in the Contina company, founded jointly with the Prince of Liechtenstein. In 1948 I had my first interview with Mr. Herzstark for a position as development engineer. This took place in Mr. Herzstark’s office in Mauren (Liechtenstein). I can still remember that one of three prototypes of the calculating machine was on his desk. The name “Contina” was engraved on this device. The name “Liliput” was therefore already no longer current. But one was also not very happy with this name for the small calculating machine, because it was rather long-drawn and sounded a little like “Continental” (another calculating machine). Moreover, the name was probably patent protected. Due to lack of space, at that time Contina transferred the patent office to a private house in the Binsen district of Mauren. We were invited to take part in a patent meeting there. Those present were Mr. von Gerliczy from Sales, a Mr. Mark “from Vienna,” as he always gladly introduced himself (he was a patent expert), and also a graduate engineer Emil Eckstein, a patent engineer at Contina, with his secretary Ms. Ramakers from Holland, and my humble self. Mr. Eckstein was a dyed-in-the-wool Berliner with a humor that was drier than the sand in the desert. In addition – when no one was listening – he often referred to Mr. Herzstark as a “carpet dealer.” Why I was never able to find out. As planned, first patent topics were discussed. Somehow – entirely unforeseen – the name of the calculating machine was mentioned. So behind the scenes, one was still searching for a name for the tiny calculating machine. A few names were suggested, some good and some not so good, and our guessing game continued. Ms. Ramakers, who was standing somewhat aside and until then had hardly participated in the discussions, suddenly said: “Oh, that’s all so complicated. Look. We have our boss – the inventor of the calculating machine  – whose name is Curt, and the calculating machine is in fact his child. So why can’t we christen this “Curta?” At first they were taken aback in silence. They all looked to Ms. Ramakers, partly amazed, partly ironically, and partly incredulously – but not as pleasantly as Ms. Ramakers would have liked. She ducked her head and expected everything possible. Then Emil Eckstein, the dry-humored one: “Ms. Ramakers, you’ve just given birth to a child, and that in the midst of men – my secretary – congratulations!” The spell was now broken. Unfortunately, I don’t know how and by whom the name “Curta” was conveyed to Mr. Herzstark and how he reacted. But apparently it pleased him, because there was no further debating of this issue. The name was immediately implemented and to this day remains a firmly established term globally for all fans of this tiny calculating marvel. Feldkirch, November 2014

502

13  The Curta

13.3.2  I s the Curta the Smallest Mechanical Calculating Machine in the World? Experts consider the Curta to be the world’s smallest mechanical calculating machine, and this is hardly disputed. However, tiny bead frames also exist. But the dimensions of the smallest of these abacuses are unknown. If we regard the bead frame as a machine, should we view the Curta with some reservation (e.g., apart from the abacus/with the exception of the bead frame) as the world’s smallest mechanical calculating machine? Such a restriction would appear to be unpractical, because – in contrast to the two Curtas – bead frames come in several different sizes, making meaningful comparisons impossible. The assertion that the bead frame is the smallest mechanical calculating device is true only in certain cases. Furthermore, because of the lack of a tens carry, the bead frame is generally not considered a calculating machine. From a technical standpoint, the “pepper mill” is a highly sophisticated device capable of performing difficult calculations. Multiplication is effortless, and division is relatively easy. The bead frame is amazingly simple. While it has no automatic tens carry, especially in the Russian version, it is capable of all four basic arithmetic operations. Sliding bar calculators are usually only able to perform two basic arithmetic operations and have no automatic tens carry.

13.4  The Founding of Contina in Liechtenstein 13.4.1  New Beginning in Liechtenstein The founding of a company for the manufacture of the Curta was extremely arduous. Herzstark declared equity requirements of 3½–4 million Swiss francs in order to begin production (without the property and buildings). The prince created a financial company that was responsible for establishing industrial companies. The Contina Büro- und Rechenmaschinenfabrik AG was founded in Vaduz in 1946. The available capital stock was however only 1 million francs. “It was as though the Devil had a hand in this,” lamented the destitute Herzstark (see Curt Herzstark: Kein Geschenk für den Führer, Books on demand GmbH, Norderstedt 2005, page 245). The princely house played a nebulous, nontransparent role, and the promises were not kept. The authority to decide lay with the deceitful administrative office. This led to vicious intrigues. And money was constantly lacking.

13.4  The Founding of Contina in Liechtenstein

503

13.4.2  Swindled Out of His Life’s Work In 1951 the defrauded Herzstark already resigned from the debt-ridden company. Already from the end of 1950, as the result of a serious patent dispute, he was no longer allowed to set foot in the company, and he was certified sick. The inventor was thus swindled out of his life’s work by the avaricious, Nazioriented Board of Directors. Until the end of 1956, Herzstark remained active in an advisory capacity (for the most part in Sales). The mass production of the Curta 2 began only following Herzstark’s suppression. Due to the poorly organized marketing, in total only 140,000 Curtas 1 and 2 were sold, predominantly in Western Europe but also outside of Europe. In 1965 the Contina AG was acquired by Hilti (Schaan FL). In his private life as well, things went wrong. His marriage was rather unhappy, and his wife and children returned to Vienna. For the connections of Martin Hilti with the Third Reich, see the book of Franco Ruault: Geschäftsmodell Judenhass (Verlag Peter Lang, Frankfurt am Main, 2017).

13.4.3  L  etters of Inquiry to Swiss Machine Builders for the Manufacture of the Curta The letters that Herzstark sent to various Swiss companies from Vienna in February 1946 are impressive (see Figs. 13.13, 13.14, and 13.15). He asked for the support of a number of companies: Christen & Cie., Bern, H. W. Egli AG, Zurich, Eterna SA, Grenchen, Landis & Gyr AG, Zug, Theo Muggli AG, Zurich, E. Paillard & Cie. SA, Yverdon VD, and Precisa AG, Zurich. Egli, Muggli, and Precisa were manufacturers of calculating machines. The Egli AG was the manufacturer of the well-known “Millionaire” direct multiplying machine and the popular Madas calculating machine. The Precisa AG (Zurich), a leading supplier of desk calculating machines (Precisa brand), would have gladly taken over the manufacture and sales of the Curta. Ernst Jost, the Director of Precisa, made him an exceedingly attractive offer: a permanent position as technical director, in addition 6 or 7 francs royalty per machine, with a planned annual sales volume of 100,000 devices. But Herzstark preferred to form a company from the very beginning according to his own visions, which he would later bitterly regret. The response of the Theo Muggli AG, Zurich was likewise positive. By contrast, the answer of the Paillard SA, Yverdon, was altogether humiliating.

504

13  The Curta

The agriculturally characterized Liechtenstein was in search of lucrative innovations. Herzstark was therefore received in 1946 at the Vaduz Castle by Prince Franz Josef II, who persuaded him to relocate to the Rhine Valley.

Fig. 13.13  The envelope of Herzstark’s letter to Egli. In February 1946 Curt Herzstark appealed to a number of Swiss manufacturers of calculating machines, including the Egli company in Zurich. Egli manufactured the high-performance Madas and had acquired a reputation with the Millionaire direct multiplier. (Source: Schreibmaschinenmuseum Beck, Pfäffikon ZH)

13.4  The Founding of Contina in Liechtenstein

505

Fig. 13.14  Page 1 of Herzstark’s letter to Egli. Here, the inventor of the entirely new small calculating machine later named the Curta is in search of a producer. (Source: Schreibmaschinenmuseum Beck, Pfäffikon ZH)

506

13  The Curta

Fig. 13.15  Page 2 of Herzstark’s letter to Egli. Herzstark describes the difficult situation during and after the War. He expects sales of at least 3–4 million Curtas. (Source: Schreibmaschinenmuseum Beck, Pfäffikon ZH)

13.4  The Founding of Contina in Liechtenstein

507

13.4.4  Opposition from Switzerland No answer from the Egli AG to Herzstark has survived. However, in the meantime a letter of rejection from the Zurich company to the Federal Office for Industry and Labour in Bern has come to light. Nor was there interest on the part of Steinmann in La Chaux-de-Fonds, the manufacturer of the Stima, and just as little on the part of Bührle. Apparently these were afraid of competition and enticing away valued specialists. They maintained that a small calculating machine would not meet the needs of the domestic economy. The Swiss Federal Immigration Authority was then responsible for issuing residence and work permits in Liechtenstein. Consequently, the relevant documents regarding Contina and Herzstark are in the Swiss Federal Archives in Bern. For more information see Hansjörg Nipp: Curta, Carena & Co., Alpenland-Verlag AG, Schaan FL 2017, pages 30–35. Ultimately, the Swiss Federal Department of Foreign Affairs prevented the Immigration Authority from acting: […] on the part of Liechtenstein, i.e. on the part of the princely house of Liechtenstein, there is still great interest in the presence of Mr. Herzstark […]. This is not only because the Prince himself is especially interested in the presence of these persons […]. The Federal Department of Foreign Affairs will therefore no longer be able to take responsibility in the future in relation to the Liechtenstein government for refusing the extension of the residence permits for Mr. Herzstark […] (see the letter of March 22nd 1949 of Minister A.  Zehnder to P.  Baechtold, Director of the Swiss Federal Immigration Authority in Bern).

As the following letters show, the Swiss authorities laid numerous obstacles in Herzstark’s path (see Figs.  13.16, 13.17, 13.18, 13.19, 13.20, 13.21, 13.22, 13.23, 13.24, 13.25, 13.26, 13.27, 13.28, 13.29, 13.30, 13.31, and 13.32):

508

13  The Curta

Fig. 13.16  Page 1 of the letter from the Federal Office for Industry and Labour, dated May 14, 1947. (Source: Swiss Federal Archives, Bern)

13.4  The Founding of Contina in Liechtenstein

509

Fig. 13.17  Page 2 of the letter from the Federal Office for Industry and Labour, dated May 14, 1947. (Source: Swiss Federal Archives, Bern)

510

13  The Curta

Fig. 13.18  Page 3 of the letter from the Federal Office for Industry and Labour, dated May 14, 1947. (Source: Swiss Federal Archives, Bern)

13.4  The Founding of Contina in Liechtenstein

511

Fig. 13.19  Page 4 of the letter from the Federal Office for Industry and Labour, dated May 14, 1947. (Source: Swiss Federal Archives, Bern)

512

13  The Curta

Fig. 13.20  Page 5 of the letter from the Federal Office for Industry and Labour, dated May 14, 1947. (Source: Swiss Federal Archives, Bern)

13.4  The Founding of Contina in Liechtenstein

513

Fig. 13.21  Page 1 of the letter from the Federal Immigration Authority of June 12, 1947. (Source: Swiss Federal Archives, Bern)

514

13  The Curta

Fig. 13.22  Page 2 of the letter from the Federal Immigration Authority of June 12, 1947. (Source: Swiss Federal Archives, Bern)

13.4  The Founding of Contina in Liechtenstein

515

Fig. 13.23  Page 3 of the letter from the Federal Immigration Authority of June 12, 1947. (Source: Swiss Federal Archives, Bern)

516

13  The Curta

Fig. 13.24  Page 4 of the letter from the Federal Immigration Authority of June 12, 1947. (Source: Swiss Federal Archives, Bern)

13.4  The Founding of Contina in Liechtenstein

517

Fig. 13.25  Page 5 of the letter from the Federal Immigration Authority of June 12, 1947. (Source: Swiss Federal Archives, Bern)

518

13  The Curta

Fig. 13.26  Letter from the Swiss Federal Department of Justice and Police of July 30, 1947. (Source: Swiss Federal Archives, Bern)

13.4  The Founding of Contina in Liechtenstein

519

Fig. 13.27  Page 1 of the letter from the Swiss Federal Department of Foreign Affairs of August 7, 1947. (Source: Swiss Federal Archives, Bern)

520

13  The Curta

Fig. 13.28  Page 2 of the letter from the Swiss Federal Department of Foreign Affairs of August 7, 1947. (Source: Swiss Federal Archives, Bern)

13.4  The Founding of Contina in Liechtenstein

521

Fig. 13.29  Page 1 of the letter from the Swiss Federal Department of Foreign Affairs of August 13, 1947. The Foreign Ministry was responsible for the relationships with the Principality of Liechtenstein. (Source: Swiss Federal Archives, Bern)

522

13  The Curta

Fig. 13.30  Page 2 of the letter from the Swiss Federal Department of Foreign Affairs of August 13, 1947. (Source: Swiss Federal Archives, Bern)

13.4  The Founding of Contina in Liechtenstein

523

Fig. 13.31  Page 3 of the letter from the Swiss Federal Department of Foreign Affairs of August 13, 1947. (Source: Swiss Federal Archives, Bern)

524

13  The Curta

Fig. 13.32  Contina AG.  Small calculating machine and gauge manufacture. Record of January 28, 1949. At the beginning of 1949, the Curta was not yet on the market and was introduced at the Schweizer Mustermesse (Swiss Sample Fair) in Basel in May. (Source: Swiss Federal Archives, Bern)

13.5  Mass Production of the Curta in Liechtenstein

525

13.5  Mass Production of the Curta in Liechtenstein

8,100

The first devices were manufactured in 1948. The three diagrams below (see Figs. 13.33, 13.34, and 13.35) illustrate the development of mass production.

4,200

100

300

1,000

1,910

2,450

2,647

3,000

3,600

3,600

3,710

3,250

4,160

3,060

3,240

3,800

3,800

3,800

3,800

4,700

4,800

5,700

8,100 7,900 Curta 1 calculating machine 7,700 Inventor: Curt Herzstark 7,500 Quantitative development 1948–1970 7,300 Total number manufactured 7,100 Curta 1: around 78,700 6,900 6,700 Curta 1 and Curta 2: around 140,400 6,500 6,300 6,100 5,900 5,700 5,500 5,300 5,100 4,900 4,700 4,500 4,300 4,100 3,900 3,700 3,500 3,300 3,100 2,900 2,700 2,500 2,300 2,100 1,900 1,700 1,500 1,300 Sources 1,100 Service department of Contina AG and 900 Hansjörg Nipp: Curta, Carena & Co., Alpenland-Verlag, Schaan 2017 700 © Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020 500 300 100 1948 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970

5400

3600

3000

2000

2000

2500

2900

2920

3500

3600

4200

4800

5400

Inventor: Curt Herzstark Quantitative development 1953–1971 Total number manufactured Curta 2: around 61,700 Curta 1 and Curta 2: around 140,400

5400

Curta 2 calculating machine

2200

Sources Service department of Contina AG and

1000

Hansjörg Nipp: Curta, Carena & Co., Alpenland-Verlag, Schaan 2017 © Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020

500

740

6,100 5,900 5,700 5,500 5,300 5,100 4,900 4,700 4,500 4,300 4,100 3,900 3,700 3,500 3,300 3,100 2,900 2,700 2,500 2,300 2,100 1,900 1,700 1,500 1,300 1,100 900 700 500 300 1953

6000

Fig. 13.33  Manufacture of the Curta 1 from 1948 to 1970. A pronounced drop production occurred in 1953. (© Bruderer Informatik, CH-9401 Rorschach, Switzerland)

1954

1955

1956

1957

1958

1959

1960

1961

1962

1963

1964

1965

1966

1967

1968

1969

1970

1971

Fig. 13.34  Manufacture of the Curta 2 from 1953 to 1971. The number built dropped dramatically in 1957 and especially in 1971. (© Bruderer Informatik, CH-9401 Rorschach, Switzerland)

526

13  The Curta

8,647

9,600

7,200

6,650

7,210

6,850

6,660

6,240

6,700

5,800

6,000

300

100

740

3,000

2,910

3,560

4,700

5,700

6,720

8,100

8,400

9,000

9,600

10,000 9,800 Curta 1 und 2 calculating machines 9,600 9,400 Inventor: Curt Herzstark 9,200 9,000 Quantitative development 1948–1971 8,800 Curta 1 and Curta 2: around 140,400 8,600 8,400 8,200 8,000 7,800 7,600 7,400 7,200 7,000 6,800 6,600 6,400 6,200 6,000 5,800 5,600 5,400 5,200 5,000 4,800 4,600 4,400 4,200 4,000 3,800 3,600 3,400 3,200 3,000 2,800 2,600 2,400 2,200 2,000 1,800 1,600 Sources 1,400 Service department of Contina AG and 1,200 Hansjörg Nipp: Curta, Carena & Co., Alpenland-Verlag, Schaan 2017 1,000 © Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020 800 600 400 200 0 1948 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 1971

Fig. 13.35  Manufacture of the Curta 1 and 2 from 1948 to 1971. In 1953, 1957, and especially in 1971, the number manufactured dropped considerably. (© Bruderer Informatik, CH-9401 Rorschach, Switzerland)

13.5.1  Piece Numbers As shown by recent findings, the piece numbers known up to now (Source: Gerhard Kleinecke, Ruggell FL, last head of service and repair for the Curta), epecially the numbers for the first year, are not correct. In 1947 only trial samples were built. In 1948 around 100 machines were built for demonstration and learning purposes. For 1949 around 300 devices are reported. From 1948 to 1971, around 140,400 Curtas (Curta 1, around 78,700; Curta 2, around 61,700) were manufactured, and mass production began in 1949–1950 (see Hansjörg Nipp: Curta, Carena & Co., Alpenland-Verlag AG, Schaan FL 2017, pages 95–97 and 165–166). Around the turn of the year 1948/1949 the mass production of the calculating machine finally began. The first 200 or 300 machines still had the originally conceived setting stylus, which I soon replaced by grooved sliding levers (see Curt Herzstark: Kein Geschenk für den Führer, Books on demand GmbH, Norderstedt 2005, page 261). At the Mustermesse (Swiss sample fair) in Basel from May 7th to 17th 1949 the tiny universal calculating machine was first presented before a broad public. A series of 100 machines was manufactured specifically for this purpose (see Curt Herzstark: Kein Geschenk für den Führer, Books on demand GmbH, Norderstedt 2005, pages 262–263).

13.6  Global Sales of the Curta

527

The information on the number of machines built is contradictory to what the taped discussion of September 11, 1987, with Erwin Tomash shows (German version, page 76, English translation, page 60). Tomash: Part five, side five of the interview with Curt Herzstark in Nendeln, Liechtenstein, Friday morning, September 11. Mr. Herzstark, do you have any idea what the total production was for the Curta? Herzstark: Yes, the numbers that I had heard vary somewhat. There were at least 150–160,000 units made. Some people state that there were somewhat more manufactured. But it was somewhere in this range. And the opinion of marketing people I have consulted with was that, for this machine, one should have been able to sell at least 2–3  million in the world market and that very easily. Remark For the next question, “Did you continue to design more calculating machines?”, Herzstark did not mention the Multiple Curtas.

13.6  Global Sales of the Curta 13.6.1  The Curta at the Schweizer Mustermesse in Basel The Curta (no. 1) was first presented before a broad public in May 1949 at the Schweizer Mustermesse in Basel (Muba) (Swiss Sample Fair). Until 1954 the Ernst Jost AG, Zurich, had the exclusive marketing rights in Switzerland. The first advertisement appeared on November 28, 1949, in the Neue Zürcher Zeitung. Widely acclaimed was the new tiny calculating machine of the Contina AG in Mauren (Liechtenstein).The Contina [later: Curta] (builder Curt Herzstark), with a weight of barely 250 g, is a full-fledged precision instrument for all four basic arithmetic operations held in the left hand while operating. Both the result mechanism and the revolution counter have a continuous tens carry. In principle, the machine is operated in the same way as large machines (see Hermann Spindler: Einige bürotechnische Neuheiten an der Schweizer Mustermesse 1949, in: Büro und Verkauf, volume 18, no. 9, June 1949, page 253). Whoever is looking for a portable but very high-performance calculating device is well advised to consider the two models of the Curta calculating machine for all four basic arithmetic operations (Manufacturer: Contina AG, Vaduz). One model has an 11-place and the other a 15-place result mechanism. The entire machine, in all respects a precision mechanism, is held in one hand. In spite of its tiny dimensions the Curta is wear-resistant and stands up to heavy stress (see Hermann Spindler: Die Gruppe "Bürofach" an der Schweizer Mustermesse 1963, in: Büro und Verkauf, volume 32, no. 8, May 1963, page 228).

Beginning with the Mustermesse of 1952, the Curta 2 was offered. The Contina Bureaux- und Rechenmaschinenfabrik AG, Mauren/Vaduz, was exhibited in Basel every year for 20 years, from 1949 to 1968.

528

13  The Curta

13.6.2  The Curta at the Bürofachausstellung in Zurich In 1950 and 1952, the Ernst Jost AG, Zurich, exhibited the Curta at the Bürofachausstellung (Büfa) (Office Trade Fair) in Zurich (then held every 2 years). Jost advertised the Curta in the journal Büro und Verkauf only in the two volumes 1950–1951 and 1951–1952. In 1948 the Contina was not yet exhibited at the Büfa (Source: Kataloge der Bürofach-Ausstellung (Büfa), Zurich). In 1954 my old friend [Ernst[ Jost from the Precisa company in Zurich resigned as the Swiss chief representative after conflicts with Vaduz over matters about which I had no further knowledge […] (see Curt Herzstark: Kein Geschenk für den Führer, Books on demand GmbH, Norderstedt 2005, page 283).

13.6.3  Who Used the Curta? In Pfäffikon ZH there are (undated) customer lists of the Contina AG, Vaduz FL.  These verify that the calculating machine was sold around the world. Among Swiss customers were, for example, the Swiss Federal Government, the Institutes for Applied Mathematics and Technical Physics of the ETH Zurich, the Eidgenössische Anstalt für Wasserversorgung, the Eidgenössische Materialprüfungsanstalt (Empa), Swissair, the Aluminium-Industrie AG, AG Brown Boveri & Cie., Maschinenfabrik Oerlikon, Escher-Wyss AG, the Schweizerische Kreditanstalt, the Schweizerische RückversicherungsGesellschaft, and the Schweizerische Unfallversicherungs-Gesellschaft. German customers included regional finance departments; gas, water, and electricity providers; universities; surveying offices; the Deutsche Bundesbahn; mining operations; chemical and machinery factories; banks; insurance companies; and publishers. In Austria the Postdirektion, textile and trade companies, the Nationalbank, and agricultural and forestry offices, for example, acquired the valuable calculating device. 1957: Exercises for mathematics teachers with the Curta at the ETH Zurich As a document from the ETH Zurich University archives shows, from November 7 to December 14, 1957, 3-day courses for mathematics teachers from Swiss high schools and polytechnics took place in the main building of the ETH Zurich. Due to the overwhelming demand, this event had to be offered four times. The founder and director of the Institute for Applied Mathematics, Eduard Stiefel, had invited the schools. In addition to lectures of the computer science pioneers Eduard Stiefel and Heinz Rutishauser, the comprehensive program offered exercises with the handheld Curta calculating machine, visits to the analog differential analyzers of Contraves (Zurich) and Amsler (Schaffhausen), and a demonstration of the first Swiss computer, the Ermeth vacuum tube computer. At the Institute for Applied Mathematics (now Seminar for Applied Mathematics), founded in 1948, mechanical desk calculating machines also found use: the Madas calculating machine (Madas = multiplication, automatic division, addition, and subtraction) from Zurich and the

13.6  Global Sales of the Curta

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Loga cylindrical slide rule from Uster ZH. The ETH Zurich was also in possession of Millionaire machines.

13.6.4  Prices In the issue of January 2, 1954 (volume 72, no. 1, page 4 of the advertisements), the Schweizerische Bauzeitung, a weekly publication for architecture, engineering, and machine technology, gave the following description: Curta Model 1 (8 × 6 × 11 places) 400 Swiss francs and Curta Model 2 (11 × 8 × 15 places) 495 francs. According to the assembly manager Franz Oehry, at that time a Curta cost more than the month’s wages of a precision mechanic. In 1963 the Büromaschinen-Lexikon gave the prices for the Curta 1 as 425 DM and for the Curta 2 as 535 DM (see Paul Greiner: Büromaschinen-Lexikon, Robert Göller Verlag, Baden-Baden, 7th edition 1963/64). In the North American magazine Popular Mechanics of May 1952, a price of 134 dollars and 70 cents is listed for the Curta 1. In the June 1968 issue of Scientific American, this device is offered for 128 dollars. For the Curta 2, a price of 165 dollars is cited in 1971. Sources Documents of the Museum Mura, Schaanwald FL (Hansjörg Nipp) (e.g. technical drawings on the Website) and Franz Oehry ETH Zurich University archives: Schulratsakten (School board’s records), SR 3: 1957, systematic number 509.203 Films and videos of Kuno Bont, Hansjörg Nipp and Karl Lüthi Oral history interviews with Elmar Maier (development engineer) and Franz Oehry (head of assembly and service), as well as with Curt Herzstark Junior, Christine Holub, Arnold Kessler, Helmut Waldbauer, and others Erwin Tomash: An interview with Curt Herzstark, Nendeln, Liechtenstein, September 10th–11th 1987, Charles Babbage Institute, University of Minnesota, Minneapolis. Further Reading Erhard Anthes: Die Wiener Ingenieurfamilie Herzstark und die Erfindung der Rechenmaschine Curta, in: Blätter für Technikgeschichte, 1984/85, volume 46/47, pages 115–137 H.  Beyer: Die rechnerischen Vorteile der Curta“-Rechenmaschine, in: Österreichisches Ingenieur-Archiv, volume 9, 1955, no. 1, pages 31–37 Karl Holecek: Neue konstruktive Wege im Rechenmaschinenbau, in: Feinwerktechnik, volume 55, 1951, no. 6, pages 129–136 Karl Holecek: Eine neuartige Rechenmaschine – eine interessante feinmechanische Konstruktion, in: Maschinenbau und Wärmewirtschaft, volume 9, 1954, no. 6, pages 155–162 Elmar Maier: Ein prägender Lebensabschnitt. Rechenmaschine Curta (Patent Herzstark),2014, https://doi.org/10.3929/ethz-a-010345785

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Peter Kradolfer: Die Curta und ihr Erfinder Curt Herzstark, in: Historische Bürowelt, October 1993, volume 35, pages 19–31 Hansjörg Nipp: Curta, Carena & Co. Geschichte der Contina in Mauren, ­Alpenland-­Verlag AG, Schaan FL 2017 Walter Sigrist: Die Curta-Rechenmaschine– eine Legende, in: Vermessung, Photogrammetrie, Kulturtechnik, volume 90, 1992, no. 3, pages 138–142 Clifford Stoll: Rechnen mit der Kurbel, in: Spektrum der Wissenschaft, 2004, volume 4, pages 87–94 Ernst Trost: Aufbau und Wirkungsweise einer Taschenrechenmaschine, in: Technische Rundschau, volume 49, 1957, no. 50, pages 21–23.

13.7  A Mechanical Parallel Calculator from Liechtenstein On November 14, 2015, the investigation of Curt Herzstark’s estate brought to light exceptionally interesting original drawings and patent documents at the Schreibmaschinenmuseum Beck Beck in Pfäffikon ZH (see Figs. 13.36, 13.37, 13.38, 13.39, 13.40, and 13.41) for a previously unknown multiple calculating machine, the world’s smallest mechanical parallel calculator. According to the newly discovered patent documents, any number of circular machines can be coupled. In particular, Herzstark describes the following configurations: • • • •

Two Curtas standing next to each other Three Curtas stacked over each other Four Curtas standing next to each other Five Curtas in a circular arrangement.

How Did the Multiple Curta Function (see box)? Features of the Multiple Calculating Machine The parallel calculator is distinguished by the following features: • All machines are driven simultaneously by a single hand crank. • All devices can be (by axially shifting the drive shafts) changed jointly or individually to another basic arithmetic operation. This is possible even when the individual calculating machines are set to different arithmetic operations. • All counting mechanisms can be simultaneously or individually advanced with the correct number of places (decade-wise) in both directions of rotation. • All result mechanisms and/or all revolution counters can be reset to zero jointly or individually. Curt Herzstark adds: “In addition, the multiple calculating machine can also be operated with an electric drive” (see patent specification no. 195 147, page 5).

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13.7.1  Double, Quadruple, and Quintuple Curtas The entirely surprising findings show that the Viennese inventor designed not only individual devices but also Multiple Curtas. Calculating machines with several counting mechanisms were known from earlier times, for example, the double or triple Brunsviga, Marchant, Millionaire, Monroe, Thales, and Triumphator machines. They accelerate the calculation process and were used for surveying and liquidation calculations. The following illustrations are concerned with the Curta 1.

Fig. 13.36  The Double Curta (1). As the drawing shows, Herzstark arranged the two machines rodlike over each other with a rigid coupling. According to the patent application, more than two devices can be stacked. (© Austrian patent office, Vienna, basic patent 1954/57)

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Fig. 13.37  The Double Curta (2). The original drawing shows two stacked mechanical calculating machines. (Source: Schreibmaschinenmuseum Beck Beck, Pfäffikon ZH) In order to simplify operation, Herzstark designed a further form of the Double Curta with a base plate (additional patent).

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Fig. 13.38  The Double Curta (3). The original drawing shows two mechanical pocket ­calculating machines arranged next to each other. The drive crank activates the main drive  shafts via bevel gears and spur gears. A chain drive is also possible. (Source: Schreibmaschinenmuseum Beck Beck, Pfäffikon ZH) The following variant with four cylindrical machines is missing from the patent application:

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Fig. 13.39  The Quadruple Curta (1). This original drawing shows four Curtas removably attached to a socket, which is equipped with coupling, drive, and control elements. The joint drive crank is connected to the stepped drum shafts by a chain drive. (Source: Schreibmaschinenmuseum Beck Beck, Pfäffikon ZH)

Fig. 13.40  The Quadruple Curta (2). This drawing shows the plan for the mechanical parallel calculator. (Source: Schreibmaschinenmuseum Beck Beck, Pfäffikon ZH)

13.7  A Mechanical Parallel Calculator from Liechtenstein

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Fig. 13.41  The Quintuple Curta. The five calculating machines stand on a socket, which can be rotated and attached to a circular base plate. This allows the convenient operation of the five devices. The main shaft drive (middle) with the crank is coupled to the five stepped drum shafts via spur gears. (© Austrian patent office, Vienna, basic patent 1954/57)

Acceleration of the Arithmetic Operation The high-precision Curta is capable of all four basic arithmetic operations. The coupling of several devices accelerates arithmetic operations considerably. For example, with a Quadruple Curta, one enters the values (multiplicands) 137, 263, 389, and 491 and multiplies these by the number 7 (multiplier). The four multiplications are then performed simultaneously (in this case with seven rotations of the crank). One can simultaneously divide the numbers 623, 511, 301, and 259 (dividends) by 7 (divisor). Possible applications were, for example, the simultaneous conversion of a price list to several currencies, the simultaneous calculation of piece prices for goods, or the simultaneous determination of the x and y coordinates in surveying.

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13.7.2  P  atent Specifications for the Multiple Calculating Machine The following Austrian patents are known for the multiple calculating machine of Curt Herzstark: • Patent specification no. 195 147 of January 25, 1958 (basic patent): Submitted: October 19, 1954 Granted: May 15, 1957 • Patent specification no. 205 775 of October 10, 1959 (additional patent): Submitted: December 15, 1954 Granted: March 15, 1959. The first application for a multiple calculating machine patent in Austria was already submitted on December 20, 1949. Efforts were also made to patent the device in America. Earlier Austrian patents for the customary Curta bear the numbers 747 073/192, 747 074/191, and 166 581, 163 380.

13.7.3  T  he World’s Smallest Mechanical Parallel Calculator According to our present knowledge, the Multiple Curta is the world’s smallest mechanical parallel calculator and the world’s first mechanical parallel calculator in pocket format. Herzstark’s preoccupation with the Multiple Curta is largely unknown (see box). Thoughts Regarding the Multiple Calculating Machine In the section “Weiterentwicklung der Curta” (further development of the Curta), Herzstark writes: “In my thoughts I came upon the idea of a ‘multiple calculating machine’ for coordinated arithmetic operations. My conception was so: Either two machines over each other with a common axis or up to four machines arranged next to each other. At the end of 1954, now only remotely connected with the Contina AG, I applied for a patent on both versions. But the idea remained an experiment on paper” (see Curt Herzstark: Kein Geschenk für den Führer, Books on demand GmbH, Norderstedt 2005, page 268). […] I also resubmitted the idea of a multiple calculating machine (two or more Curtas next to or over each other) for a new patent. Following the issuing of these patents in the years 1954–1955 […] (see Curt Herzstark: Kein Geschenk für den Führer, Books on demand GmbH, Norderstedt 2005, page 284).

13.8  A British Mechanical Parallel Calculator

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Curt Herzstark probably did not build a trial sample. Six elderly firsthand witnesses in Liechtenstein, Austria, Germany, and Switzerland could not recall any prototypes. The multiple calculating machine was not mass produced. By this time the inventor, who was deprived of his life’s work by the Nazis, was no longer employed at Contina. Curt Herzstark left his position as Technical Director of the Contina AG on December 31 (siehe Curt Herzstark: Kein Geschenk für den Führer, Books on demand GmbH, Norderstedt 2005, page 276) and was then only active as a consultant for technical questions and for sales. On December 31, 1956, he severed all connections with the company permanently (ibid, page 286).

13.8  A British Mechanical Parallel Calculator Since November 2015 it is known that, from the end of the 1940s, Curt Herzstark was intensively concerned with multiple calculating machines. His mechanical parallel calculator was patented, and excellent design drawings have survived. However, the Multiple Curta never appeared on the market. In the summer of 2017, I was made aware that a 12-fold Curta was built at the University of Birmingham (UK) for matrix calculations.

13.8.1  T  he British 12-Fold Curta for Matrix Calculations In the 1940s and 1950s, the periodical Mathematical Tables and Other Aids to Computation, founded in 1943, was the leading international journal for computer technology. Since 1960 it has the title Mathematics of Computation. In the issue of July 1954, see Fig. 13.42. A. Opler called attention to the 12-fold Curta in the section “Other aids to computation”:

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Fig. 13.42  The mechanical parallel calculator. Review of the article of James Robb in the journal Mathematical Tables and Other Aids to Computation (1954). (© MTAC)

James Christie Robb (1924–1999), of the Chemistry Department of the University of Birmingham, had submitted an article about a 12-fold Curta to the Transactions of the Faraday Society (see Fig. 13.43) that was received on July 20, 1953. The journal was published from 1905 to 1971. Robb was active at the University of Birmingham from 1948. In 1956 he was appointed Professor for Physical Chemistry and in 1983 became the Head of the Department of Chemistry. The parallel calculator designed by Robb was built by S. Traver, with the support of J. Harcourt. The 12 Curtas (Model 1) are mounted in a circle on a dural aluminum alloy octagonal base provided with two handles. Each cylindrical calculator has 8 places in the setting mechanism, 6  in the revolution counter, and 11  in the result mechanism. The base plate has three levers (from left to right), one for shifting the carriage (six different decimal places), one for resetting to zero, and one for multiplication. The lever at the left raises the carriage and rotates it to one of the six positions (ones, tens, hundreds, thousands, etc.). According to the description, there is in principle no limit to the number of Curtas that can be combined. In this contribution the Curta and the Contina are mentioned, but not Curt Herzstark. The Liechtenstein Contina AG donated the 12 Curtas. The device simplified the solution of linear simultaneous equations. It served for the calculation of inverse matrices. One could multiply 12 arbitrary (1- to 8-place) values by the same (positive or negative) factor simultaneously.

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The article refers to a patent application no. 10993/53 with the British patent office. However, whether a patent was granted is not known. There is no corresponding entry in the European patent database. Herzstark already submitted the first patent application for the multiple calculating machine to the Austrian patent office in Vienna on December 20, 1949, and in 1953 he had already left the manufacturer Contina.

Fig. 13.43  The 12-fold Curta (1). The world’s smallest mechanical parallel calculator was built at the University of Birmingham in 1953 and comprises 12 Curtas (Model 1). (© Royal Society of Chemistry, London)

The English multiple calculating machine was introduced in the Curta-News (1957) (see Figs. 13.44 and 13.45):

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Fig. 13.44  The 12-fold Curta (2). With a delay of several years, the British matrix calculator was described in the Curta-News. (Source: Curta AG, Vaduz/Schreibmaschinenmuseum Beck Beck, Pfäffikon ZH)

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Fig. 13.45  The 12-fold Curta (3). The section with the parallel calculator is enlarged here. (Source: Curta AG, Vaduz/Schreibmaschinenmuseum Beck Beck, Pfäffikon ZH)

13.8.2  I ndependent Development of Two Mechanical Parallel Calculators? It is fair to assume that the two mechanical parallel calculators, both of which are based on the Curta, came about independently of each other: Robb was evidently not aware of Herzstark’s patent, and, in fact, even close colleagues in Liechtenstein were unaware of Herzstark’s efforts to build a multiple calculator. It is also possible that the inventor of the Curta knew nothing about the matrix calculator in Birmingham, UK. In his memoirs Kein Geschenk für den Führer and in the conversation with Erwin Tomash of the Charles Babbage Institute, the multiple calculating machine in Birmingham is not even mentioned, in spite of the fact that the Curta-­News had reported on this in 1957. Robb‘s matrix machine was presumably not patented.

13.8.3  The UK Matrix Calculator Has Been Lost The mechanical parallel calculator has probably not been preserved. Research inquiries with the University of Birmingham (presidency, Department of Chemistry, library/archives), the Birmingham Museums Trust, the Royal Society of Chemistry (London), the Science Museum (London), the National Museum of Computing (Bletchley Park, UK), and the British Computer Conservation Society (London) brought no results. Jim Burdon of the University of Birmingham roughly recollects the device: “I vaguely remember the device. It was purely mechanical. I do not know if the device still exists” (personal communication of June 30, 2017). Nor were

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Jo-Ann Curtis, the Curator for history of the Birmingham Museums Trust (communication of July 6, 2017), and David Allen, the librarian of the Royal Society of Chemistry, London (email of July 10, 2017), able to help. References Herbert Bruderer: The world’s smallest mechanical parallel calculator, in: Arthur Tatnall; Christopher Leslie (editor): International communities of invention and innovation, Springer international publishing AG Switzerland, Cham 2016, pages 186–192 Herbert Bruderer: Multiple Curtas. Discovery of original drawings and patent documents of an unknown parallel mechanical pocket calculator in Switzerland, in: Charles Babbage Institute, Center for the history of information technology, Newsletter, volume 38, 2016, no. 1, pages 21–23 Herbert Bruderer: Finding the world’s smallest mechanical parallel calculator. Discovery of a 12-fold Curta in Britain, in: Communications of the ACM, blog post of September 12th 2017, https://cacm.acm.org/blogs/blogcacm/220968-finding-the-worlds-smallest-mechanical-parallel-calculator/ fulltext Curt Herzstark: Kein Geschenk für den Führer, Books on demand GmbH, Norderstedt 2005 Roy S. Lehrle: James C. Robb 1924–1999, in: Chemistry in Britain, volume 37, 2001, no. 1, page 57 Opler: 1143. James C.  Robb, “A calculator for aiding matrix calculations”, Faraday Soc. Trans., Volume 50, 1954, pp.  8–12, in: Mathematical tables and other aids to computation, volume 8, July 1954, no. 47, page 181 James C. Robb: A calculator for aiding matrix calculations, in: Transactions of the Faraday society, volume 50, 1954, pages 8–12 Erwin Tomash: An interview with Curt Herzstark, Nendeln, Liechtenstein, September 10th–11th 1987, Charles Babbage Institute, University of Minnesota, Minneapolis.

Chapter 14

Slide Rules

Abstract  The chapter “Slide Rules” describes once widespread mathematical instruments designed on the basis of the logarithms discovered by Jost Bürgi (Switzerland) and John Napier (Scotland). These instruments reduce multiplication to the addition and division to the subtraction of line segments. One also speaks of nomography. There are different types of instruments: linear slide rules, circular slide rules, cylindrical slide rules, and pocket-­watch slide rules. Cylindrical slide rules have scale sections arranged parallel to each other or in a helical arrangement. This analog calculating instrument dates from the seventeenth century and was in use until the 1970s. The English mathematician William Oughtred is considered the inventor of the slide rule. The largest mass-produced cylindrical slide rule, the Loga calculator, has a scale length of 24  m. The longer the scale, the greater the accuracy of the instrument. For the Swiss-made Loga cylindrical slide rules, the serial numbers are related to the scale length. Keywords  Analog calculating instrument · Jost Bürgi · Circular slide rule · Cylindrical slide rule · Loga calculator · Logarithms · Mathematical instrument · John Napier · Linear slide rule · Nomography · William Oughtred · Pocket-watch slide rule · Slide rule

14.1  Logarithms 14.1.1  Graphical Calculation The calculation of logarithms is the inverse of raising to a power. On the basis of the laws of logarithms, multiplication is reduced to addition, division to subtraction, raising to a power to multiplication, and extracting roots to

© Springer Nature Switzerland AG 2020 H. Bruderer, Milestones in Analog and Digital Computing, https://doi.org/10.1007/978-3-030-40974-6_14

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division. This simplifies calculations considerably. On the logarithmic scales, the arithmetic (numerical) multiplication becomes a geometric (graphical) addition of two sections. One therefore speaks of graphical calculation. Linear scales (with uniform partitioning) begin with 0 (addition scales). Logarithmic scales (with nonuniform partitioning) begin with 1 (multiplication scales). Slide rules utilize logarithmic scales. Logarithms greatly simplify calculation (see box).

What Is a Logarithm? In the equation ab = c, the given number a (base, radix) is raised to the number b sought (exponent, superscript, logarithm) in order to obtain the given number c (antilogarithm, potentiated value). The logarithm is an exponent. Thus, b is the logarithm of c to the base a (b = loga c). Until the introduction of the electronic pocket calculator in the 1970s, tables of logarithms and logarithmic slide rules were used alongside mechanical desk calculating machines for complex calculations. Widely used are decadic, or decimal, logarithms with base 10. Instead of b = log10 c, one writes the shorter form b = lg c. Examples: lg 1 = lg 100 = 0, lg 10 = lg 101  = 1, lg 100 = lg 102  = 2, lg 1000 = lg  103  = 3,

since  since  since  since 

100 = 1 101 = 10 102 = 100 103 = 1000.

14.1.2  Who Introduced Logarithms and the Slide Rule? Logarithms were discovered by the Scottish mathematician John Napier and the Swiss clockmaker and mathematician Jost Bürgi (around 1700). It is generally believed that Bürgi first invented logarithms, while Napier was the first to publish these. The dispute of many decades continues to this day: It seems a fair conclusion that Napier has both the priority in the invention of the logarithms as well as the priority in publication (see Brian Rice; Enrique GonzálezVelasco; Alexander Corrigan: The life and works of John Napier, Springer international publishing AG Switzerland, Cham 2017, page 431).

The English mathematician William Oughtred is regarded as the creator of the slide rule and the circular slide rule. The Oughtred Society, an international association for the history of computing technology, is consequently named after him. The cylindrical slide rule appeared somewhat later.

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Remarks There were several forerunners with the development of logarithms, e.g., Michael Stifel and Archimedes. It should be noted that Napier’s bones, which simplify multiplication and division, are digital instruments and are not logarithmic. For a long time Bürgi’s sine calculations remained a mystery (see box).

Bürgi’s Kunstweg As indicated in a personal communication of October 2, 2017, Menso Folkerts already found the handwritten documents of Bürgi in 1991  in the library of the University of Breslau (Poland). In 2013 he investigated the work in greater detail and thereby discovered Jost Bürgi’s method for the calculation of sine values, the Kunstweg (1592). Further Reading Menso Folkerts: Eine bisher unbekannte Schrift von Jost Bürgi zur Trigonometrie, in: Rainer Gebhardt (editor): Arithmetik, Geometrie und Algebra der frühen Neuzeit, Adam-Ries-Bund, AnnabergBuchholz 2014, pages 107–114 Menso Folkerts; Dieter Launert; Andreas Thom: Jost Bürgi’s method for calculating sines, in: Historia mathematica, volume 43, 2016, no. 2, pages 133–147 Dieter Launert: Bürgis Kunstweg im Fundamentum astronomiae. Entschlüsselung eines Rätsels, Bayerische Akademie der Wissenschaften, Munich 2015 Dieter Launert: Sinustafel wiederentdeckt  – Bürgis "Kunstweg" entschlüsselt, in: Mitteilungen der deutschen MathematikerVereinigung, volume 24, 2016, no. 2, pages 89–94 Grégoire Nicollier: How Bürgi computed the sines of all integer angles simultaneously in 1586, in: Mathematische Semesterberichte, volume 65, 2018, no. 1, pages 15–34 Jörg Waldvogel: Jost Bürgi’s artificium of 1586 in modern view, an ingenious algorithm for calculating tables of the sine function, in: Elemente der Mathematik, volume 71, 2016, no. 3, pages 89–99.

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14.1.3  Addition and Subtraction with Slide Rules By their nature, logarithmic slide rules are not suited for addition and subtraction. This requires measuring rules with a uniform scale (customary rulers). Nevertheless, by roundabout ways (see Figs. 14.1 and 14.2), these two basic arithmetic operations are possible (addition and subtraction logarithms of Z. Leonelli).

Fig. 14.1  Addition and subtraction (1). One can also add and subtract with the slide rule, but this is cumbersome. (Source: Max Hartmuth: Vom Abakus zum Rechenschieber, Verlag Boysen & Maasch, Hamburg 1942, pages 131–132)

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Fig. 14.2  Addition and subtraction (2). One can also add and subtract with the slide rule, but this is cumbersome. (Source: Max Hartmuth: Vom Abakus zum Rechenschieber, Verlag Boysen & Maasch, Hamburg 1942, pages 131–132)

Explanation A short exam question: Who even of us old “experts” knows that one can also add and subtract with the logarithmic slide rule? Because normally we are told that one can only multiply, divide, extract roots, and calculate squares with this device! So what is the truth?

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Yes, it really does work  – in fact without tricks or deception. This only requires converting the expression according to the formula (see Fig. 14.1). For example, to add 472 and 183, one calculates: (see Fig. 14.2). (As the factor before the parentheses – for both addition and subtraction – it is expedient to always choose the smaller of the two numbers). We (see Fig. 14.2) calculate on the lower scale and set the value 1 at the left end of the slide over 1-8-3 on the body. We then move the runner to 4-7-2 on the body and read out the value 2-5-8. Since the quotient 472/183 is in the range 1–10, we must interpret the result as 2.58 and mentally add the value “1,” giving 3.58. Under 3-5-8 on the slide, we read out 6-5-5, and the result of the calculation is 655. Describing the procedure is more complicated than actually executing (see setting illustration!). If we want to subtract 183 from 472, we then proceed as above up to reading out the value 2-5-8. The 1 is now no longer added, but subtracted mentally, giving the value 1-5-8. And on the scale under this value, the required difference 289 is read off the body. Note: Set both numbers on the body and then read the result from the body. Only the intermediate readout takes place on the slide. Whoever carries out any arbitrary example according to this procedure is delightfully surprised that this really “works.” One can in fact claim that for such calculations, pencil and paper provide the answer faster, but the fact remains that the slide rule does not fail here either – quod erat demonstrandum! – important is, however, that the entire expression can be solved with only a single movement of the slide, and even this is a remarkable achievement with a simple slide rule.

14.2  Types 14.2.1  L  inear Slide Rules, Circular Slide Rules, and Cylindrical Slide Rules There are several types of slide rules: • • • • • •

Linear slide rules (straight slide rules) Circular slide rules Cylindrical slide rules Logarithmic calculating wheels Pocket-watch slide rules Grid slide rules (grid-iron slide rules)

The (tripartite) slide rules are comprised of a (fixed) body, a (movable) slide, and a (movable) runner (cursor). With linear slide rules, the numerous scales

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are on the front face and the reverse face of the body and the slide. Sometimes the scales are widely separated, so that a runner is required. Display windows facilitate using. For historical reasons, the square and square root scales are designated A and B and the fundamental scales C and D. These designations were adopted for the Soho, Mannheim, and Rietz slide rules. The (tripartite) circular slide rules exhibit outer (fixed) and inner (movable) circular scales and a rotatable pointer, similar to calculating wheels. The (bipartite) cylindrical slide rules are comprised of a drum (cylinder, barrel, tube) and a rotatable and laterally displaceable sleeve (slide, cage, basket). Cylindrical slide rules generally have two (adjacent) scales, one on the drum and one (in the form of stripes) on the slide. There were numerous books about linear slide rules, but hardly any about the other types of slide rules. Some of these include instructions for using slide rules. On the other hand, instructions for using circular slide rules and, above all, cylindrical slide rules are difficult to find.

14.2.2  Endless Scales and Double Scales Endless scales, i.e., the circular scales of circular slide rules, eliminate inconvenient shifting (off the end problem). Simple scales are sufficient. The beginning and the end of the scales coincide. With other types of slide rules, it is necessary to either move the slide through (shift) (C and D scales of the slide rule) or print the scale sections doubly – either directly after each other (A and B scales of the slide rule) or overlapping, as with many cylindrical slide rules. If one only wants a simple spiral scale (helical scale), this requires a multiple pointer. Pushing the slide through the body (frame) is not necessary (see Max Hartmuth: Vom Abakus zum Rechenschieber, Verlag Boysen & Maasch, Hamburg 1942, page 136). Why Do the Scales of a Cylindrical Slide Rule Overlap? The slide of a slide rule can be pulled out from either side. However, due to the design of the cylindrical slide rule, the sleeve can only be moved to the left and right ends of the drum. This makes the overlapping of successive scale sections on the drum necessary. Where Is the Beginning of the Scale on a Cylindrical Slide Rule? The beginning of the scale is in the middle of the drum surface and is marked, e.g., with a red circular ring or a red double bar.

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14.3  Classification of Slide Rules The term slide rule is in use not only as a collective term but usually also in the meaning of a linear slide rule. The following explanations refer to the three most common forms: linear slide rules, circular slide rules, and cylindrical slide rules.

14.3.1  Linear Slide Rules There are two basic forms of linear slide rules: • The simplex slide rule (single slide rule): This slide rule has a continuous baseplate (without divider bars). The scales are printed on both the upper side of the body and the upper and lower sides of the slide. The upper side of the body is outfitted with a runner (cursor), for example, slide rules of older design. • The duplex slide rule (double slid rule): This slide rule has two body slats, fixed to each other by divider bars at both ends. The scales are printed on the upper and lower side of the body and on both sides of the slide. The runner envelops both sides, for example, slide rules of newer design. Duplex slide enjoyed great popularity.

14.3.2  Circular Slide Rules There are several circular slide rule designs: • Calculating devices with a circular area and a ring: The inner (movable) circular area and the outer (fixed) ring are in the same plane. The scales are printed on the front face or on both faces. There are normally one or two rotating pointers, for example, the Loga circular slide rule. Most circular slide rules are of this design. However, there are also circular slide rules with a movable ring and a fixed inner disc, for example, the circular slide rule of Eduard Sonne. • Calculating devices with two discs: the two circular discs are arranged over/under each other. The top disc is either smaller than the bottom plate or transparent. According to the model, there are one or two rotating pointers, for example, the Weber circular slide rule with fixed plates. • Calculating devices with one disc and two rotating pointers: All scales are printed on the fundamental (fixed) disc. Two rotating pointers allow calculations. One can move these separately or together and thus set a fixed angle (circular segment) and transfer sections as with a standard pair of dividers, for example, Nystrom’s circular slide rule.

14.3  Classification of Slide Rules

551

Remark With the closely related (logarithmic) pocket-watch slide rules, the circular scales are rotated with set screws.

14.3.3  Cylindrical Slide Rules In this book the terms cylindrical slide rule, spiral slide rule, slide rule drum, and tubular slide rule refer to the same type of slide rule: • Cylindrical slide rules with a movable sleeve (parallel scale cylindrical slide rules): The scale sections are printed (doubly) parallel to each other on the rotating cylinder as surface lines in the longitudinal direction. A rotating and laterally movable sleeve (transparent or with slots and slats) with the second (simple) scale surrounds the cylinder, for example, the Billeter, Loga, Nestler, and Tröger cylindrical slide rules. Cylindrical slide rules with a movable basket are especially common. • Cylindrical slide rules with a fixed sleeve (parallel scale cylindrical slide rules): The scale sections are printed parallel to each other on the rotating cylinder as surface lines in the longitudinal direction. The second scale is printed on an outer, laterally fixed cylinder of the same width (with recesses), for example, the Thacher cylindrical slide rule. • Cylindrical slide rules with spiral lines (spiral slide rules, spiral scale slide rules): The scales are in the form of helical lines on two rotating cylinders (on the same axis) that can be slid into each other (the inner and outer cylinders), for example, the Fuller and Otis King cylindrical slide rules. Spiral Scale Slide Rules Spiral scale slide rules have one or two helical lines: The Fuller has (only) a single, continuous serpentine line on the outer cylinder but several metal pointers: a fixed runner and a runner attached to the upper and lower movable runners on the inner cylinder. Since this pointer has a double marking in intervals of a decade (the section between the beginning and end of the scale), there is no need for overlapping. The helical line of the Fuller cylindrical slide rule has 50 convolutions and a diameter of 8.1 cm. This represents a scale length of 50 × 8.1 cm × π = 12.72 m. The Otis King pocket calculator (tubular slide rule) has two helical lines and one pointer (runner), while the upper logarithmic scale, with two decades, is twice as long as the lower. Remarks Ernst Hammer mentions a cylindrical slide rule of Edwin Thacher (USA, patented in 1881) with scale sections arranged in parallel and a double division of 18.287 m (see Ernst Hammer: Über einige neue Formen des logarithmischen Rechenschiebers, in: Zeitschrift für Vermessungswesen, volume 20, 1891, no. 16, pages 438 ff.). This device is the equivalent of a 9.144-m-long linear slide rule.

552

14  Slide Rules

The scales can also be printed on several cylinders that rotate together or in opposite directions about the same axis. The following pages illustrate slide rules of different designs: linear slide rules, circular slide rules, cylindrical slide rules, and calculating wheels (see Figs. 14.3, 14.4, 14.5, 14.6, 14.7, 14.8, 14.9, 14.10, 14.11, and 14.12).

Fig. 14.3  The Aristo linear slide rule. These relatively inexpensive mathematical instruments were popular over a longer period of time. Compared with mechanical desk calculating machines, their operation is virtually silent. (© Geodätisches Institut of the Leibniz University Hanover)

Fig. 14.4  The Faber-Castell linear slide rule. Slide rules were designed for all conceivable applications. This teaching slide rule could be used while underway. (© Geodätisches Institut of the Leibniz University Hanover) Fig. 14.5 Billeter’s circular slide rule. Julius Billeter was the first Swiss manufacturer of circular slide rules and cylindrical slide rules. The company existed only from 1893 to 1895. The term “Blitzrechner” (lightning-­speed calculator) was used for various calculating aids, including calculating tables. (© Inria/picture: J.-M. Ramès)

14.3  Classification of Slide Rules

553

Fig. 14.6  The Loga circular slide rule with stand. There were numerous handy slide rules. Their scales were mostly tailored to the particular purpose. However, with the popular and equally widespread expensive circular slide rules, there was considerably less variety. Daemen-Schmid (Loga, Zurich) was an important manufacturer. (© Schweizerisches Landesmuseum, Zurich)

Fig. 14.7  The circular slide rule of Eduard Sonne (Darmstadt). This analog calculating device was built by Landsberg in Hanover. (© Geodätisches Institut of the Leibniz University Hanover)

554

14  Slide Rules

Fig. 14.8 Beyerlen’s calculating wheel (1). Angelo Beyerlen, from Stuttgart, invented this logarithmic calculator (around 1893). The two wheels can be rotated in opposite directions. On the perimeters of both wheels are circular scales. The instrument is operated as with common slide rules. (© Deutsches Museum, Munich)

Fig. 14.9  Beyerlen’s calculating wheel (2). The impressive analog calculator of Angelo Beyerlen (1885) belongs to the rarities of our engineering heritage. (© Geodätisches Institut of the Leibniz University Hanover)

14.3  Classification of Slide Rules

555

Fig. 14.10  The Fuller spiral cylindrical slide rule (1878). Cylindrical slide rules appeared on the market in the second half of the nineteenth century. The Irish engineer George Fuller was one of the first to offer such instruments. The surface lines are arranged helically. More often there were parallel scale sections. Stanley, London, offered this slide rule. (© Javier Salvador Pelay)

Fig. 14.11  The Thacher cylindrical slide rule (1881). This cylindrical slide rule was very popular. It was sold by Keuffel and Esser (K&E), New York. (© Javier Salvador Pelay)

Fig. 14.12  Billeter’s cylindrical slide rule. There were a number of slide rule manufacturers in Zurich with similar company names: Ernst Billeter, Ernst Billeter & Co., Ernst BilleterBossert, Julius Billeter, and Julius Billeter’s Söhne. The oldest of these companies was Julius Billeter. (© Technisches Museum Wien, Vienna)

556

14  Slide Rules

Fuller’s Spiral Cylindrical Slide Rule with a Scale Length of 25.4 m? In a contribution on slide rules, Ernst Hammer mentions an expensive cylindrical slide rule, with a price of 60 German marks, of the Irish George Fuller (British patent: 1878; US-patent: 1879) with helical surface lines and a scale length of 25.4 m (see Ernst Hammer: Über einige neue Formen des logarithmischen Rechenschiebers, in: Zeitschrift für Vermessungswesen, volume 20, 1891, no. 16, pages 434 ff.). However, the actual scale length of 500 inches (one inch  =  2.54  cm) is equivalent to a length of 12.7  m (= 41 2/3  feet, with 1 foot  =  30.48  cm; 41 feet, 8 inches  =  12.70  m, with 1 foot  =  12 inches) (see Fig. 14.13).

Fig. 14.13  Scale length of cylindrical slide rules. The details of the scale length, such as for the Fuller spiral cylindrical slide rule, are ambiguous. Evidently there are discrepancies between the Anglo-Saxon and the German language regions. (© Zeitschrift für Vermessungswesen, 1891)

In his paper Hammer quotes Fuller’s assertion that his spiral scale slide rule is the equivalent of a linear slide rule with a length of 83 feet and 4 inches or a circular slide rule with a diameter of 13 feet and 3 (see Ernst Hammer: Der logarithmische Rechenschieber und sein Gebrauch, Verlag von Konrad Wittwer, Stuttgart, 6th edition of 1923, page 9). In the English-speaking regions, comparisons are made with linear slide rules (addition of the body length and the slide moved out to its limit), but not the circular slide rules, other than in Germany. The Deutsches Museum describes its exhibited specimen as follows: Fuller’s invention from 1878 serves to enhance the accuracy by arranging the logarithmic scales on a helical line. This gives a scale length of around 12.7 m, far more than the otherwise normal lengths of 25 cm (see Friedrich Bauer: Informatik. Führer durch die Ausstellung, Deutsches Museum, Munich 2004, page 50).

The Fuller spiral cylindrical slide rule is comprised of three extendible concentric cylinders (as with a telescope), with a total length of 67 cm. This is the equivalent of a circular slide rule with a diameter of 4.04 m.

14.3  Classification of Slide Rules

557

Logarithmic pocket-watch slide rules are relatively rare (see Figs. 14.14, 14.15, and 14.16).

Fig. 14.14  Pocket-watch slide rule (1). This calculator has a logarithmic scale. Pocket-watch slide rules are much less common than circular slide rules. Operation is by means of a set screw. (© Okänd, Tekniska museet, Stockholm)

Fig. 14.15  Pocket-watch slide rule (2).The brand name Calculigraphe von Chatelain indicates that this is a graphical calculating device, which measures instead of counting. (© Okänd, Tekniska museet, Stockholm)

558

14  Slide Rules

Fig. 14.16 Pocket-watch slide rule (3). Boucher was a well-known manufacturer of analog circular calculators. These are comprised of a copper alloy (copper, brass, and bronze) and lightweight metal (aluminum). (© Okänd, Tekniska museet, Stockholm)

14.4  Slide Rule Manufacturers Slide rules were manufactured in numerous countries, e.g., France, Germany, Japan, the UK, and the USA. Familiar German suppliers were Dennert & Pape, Hamburg-­Altona (Aristo), Faber-Castell, Stein near Nuremberg, and Albert Nestler, Lahr, and Baden/Black Forest. An important American supplier was Keuffel and Esser Co., New York. The leading Swiss manufacturer of circular slide rules and cylindrical slide rules was the Loga-Calculator AG. The company’s owner, Heinrich Daemen Schmid, established a workshop in 1900 in Zurich. In 1903 this relocated to Oerlikon and in 1911 moved to Uster ZH. Other well-known Swiss brands were Billeter and National (see Table 14.1). The legacy of the Loga-Calculator AG is now in the Schweizerisches Wirtschaftsarchiv in Basel. Table 14.1  Leading Swiss manufacturers of cylindrical slide rules The leading Swiss manufacturers of cylindrical slide rules Company name Julius Billeter, Zurich Julius Billeter’s Söhne, Zurich Ernst Billeter & Co., Zurich Ernst Billeter-Bossert, Zurich National Rechenwalzen AG, Zurich National Rechenwalzen AG, Küsnacht Daemen-Schmid, Zurich Daemen-Schmid & Cie., Uster ZH Loga-Calculator AG, Uster ZH © Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020 Source: Swiss Official Gazette of Commerce

Period 1893–1895 1895–1897 1912–1917 1921–1934 1916–1925 1925–1934 1900–1911 1911–1915 1915–2018

14.4  Slide Rule Manufacturers

559

Remarks • It follows from the article “Julius Billeters Rechenapparate” in the Neue Zürcher Zeitung of April 24, 1886 that Billeter began manufacturing slide rules already before founding the company (Source: Schweizerisches Wirtschaftsarchiv, Basel, Dossier 1918). The Paris Musée des arts et métiers has a cylindrical slide rule of Julius Billeter, acquired in 1895. In addition to cylindrical slide rules, Billeter also offered circular slide rules and logarithmic tablets. The Ernst Billeter-­Bossert company, Zurich, was renamed in 1934 to Ernst Billeter, Zurich. The existence of this company can be verified up to 1938. A company with the name Ernst Billeter was already operating from June to October 1912. • It follows from patent documents that the company founder, Heinrich Daemen-­Schmid from Nieukerk (Prussia), was a Swiss citizen. Loga cylindrical calculators were first marketed under the name “Heinrich DaemenSchmid.” The joint-stock company Daemen-Schmid & Cie., Uster, was founded in 1911. In 1912 a branch of Daemen-Schmid & Cie. was established in Zurich. In 1915 Daemen-Schmid & Cie. became the Loga-Calculator AG (Uster). In 1947 the Loga-Calculator AG was renamed the Loga-Calculator Aktiengesellschaft. When the company discontinued, the manufacture of cylindrical slide rules and circular slide rules is not clear. In a two-page leaflet with the annotation “50 Jahre Loga” (50  years Loga) of the LogaCalculator AG, Uster, three cylindrical slide rules are described: 2.4 m (195 Swiss francs), 7.5 m (345 Swiss francs), and 15 m (685 Swiss francs). The document most likely dates from 1950. In a sales document from 1953 with the 15 m cylindrical slide rule, the swivel arm, and the tilting mechanism, we find: “Fabrikat der Loga-Calculator AG, Uster (Schweiz)” and “Vertrieb durch Heinrich Daemen Zürich”. These documents show that the Loga cylindrical slide rules were produced and/or marketed at least up to the 1950s (see also Sects. 16.4 and 16.8.1). From 1972 to 1976, numerous ­advertisements for circular slide rules appeared in the Schweizerische Lehrerzeitung. The Loga-Calculator Aktiengesellschaft discontinued the production of calculating aids in Uster ZH in 1978 and was thereafter active, e.g., in property management. The company was by far the longest on the market and also had a site in Germany: the Loga-Calculator Fabrikationsund Vertriebs-Ges. mbH, Berlin (see Ludwig Brauner, Victor Vogt (editors): Illustriertes Orga-Handbuch erprobter Büromaschinen, Verlag für SammlerLiteratur Dingwerth GmbH, Delbrück 2003 (reprint of excerpts from 1921)). • Jakob Kern (Aarau) manufactured linear slide rules for surveying. See the following works for the history of Swiss cylindrical slide rules manufacturers: Heinz Joss: Messrechnen: 350 Jahre Rechenschieber, in: Elemente der Mathematik, volume 53, 1998, no. 2, pages 73–78 Heinz Joss: Der Rechenschieber. Gestern alltäglich, heute vergessen, in: Schweizer Ingenieur und Architekt, volume 118, April 2000, no. 16, pages 356–363 Heinz Joss: 350 Jahre Rechenschieber, und was die Region Zürich dazu beigetragen hat, in: Vierteljahrsschrift der Naturforschenden Gesellschaft Zürich, volume 146, 2001, no. 2/3, pages 75–82.

560

14  Slide Rules

14.5  Dating of Cylindrical Slide Rules A few rules of thumb apply for dating Swiss cylindrical slide rules: Daemen-Schmid • With the company name “Daemen-Schmid & Cie., Uster,” manufactured from 1911 to 1915 • With the company name “Daemen-Schmid & Cie., Zürich,” manufactured from 1912 to 1915 • With the company name “H. Daemen-Schmid” (Uster), manufactured from 1916 to 1924 • With the company name “Heinrich Daemen” (Zurich), manufactured from 1900 to 1911 Billeter • With the company name “Ernst Billeter & Co.” (Zurich), manufactured from 1912 to 1917 • With the company name “Ernst Billeter” (Zurich), manufactured either in 1912 or from 1934 • With the company name “Ernst Billeter-Bossert” (Zurich), manufactured from 1921 to 1934 • With the company name “Julius Billeter’s Söhne” (Zurich), manufactured from 1895 to 1897 • With the company name “Julius Billeter” (Zurich), manufactured from 1893 to 1895 Loga-Calculator AG • With the company name “Loga-Calculator AG” (Uster), manufactured from 1915 to 1947 • With the company name “Loga-Calculator Aktiengesellschaft” (Uster), manufactured from 1947 National Rechenwalzen • With the company name “National Rechenwalzen Aktien-Gesellschaft (Küsnacht),” manufactured from 1925 to 1934 • With the company name “National Rechenwalzen Aktien-Gesellschaft (Zürich),” manufactured from 1916 to 1925 Place Name • With the place name “Küsnacht,” manufactured from 1925 to 1934 • With the place name “Uster,” according to company name manufactured from 1911, 1915, 1916, or 1947 Notes For the periods from 1898 to 1911 and 1918 to 1920, no entries for Billeter were found in the commercial register. Especially the first gap is surprising. Julius Billeter died in 1895, and in 1897 the subsequent joint-stock company of his sons was bankrupt. In 1911 at the exhibition in the Helmhaus Zurich (see Sect. 9.1.2), slide rules from Julius Billeter were on display. In 1905 a report of the

14.5  Dating of Cylindrical Slide Rules

561

Vermessungsamt Zürich mentioned five “Billeter cylindrical slide rules” (see J.  Etter etc.: Die Rechenmaschine im Dienste städtischer Kataster­ vermessungen, in: Zeitschrift des Vereins Schweizerischer Konkordats­ geometer, volume 3, 1905, no. 11, pages 131–137). There were also cylindrical slide rules of Ernest Billeter-Surber, Zurich. This company apparently had no entry in the commercial register. The brand name “Loga” was already in use (at the latest) in 1911. On some cylindrical slide rules, there is no manufacturer’s information. Patents The (German) Imperial Patent Office granted Julius Billeter a patent for a logarithmic calculating board (no. 43463, March 25, 1887) and a cylindrical slide rule (no. 71715, February 21, 1893). For his cylindrical slide rule, there is also a French patent (no. 217367, November 10, 1891) and a US patent (no. 513172, January 1894). Max Billeter (National Rechenwalzen Aktien-Gesellschaft, in Zurich) had a Swiss patent (no. 80250, February 17, 1919). In the European patent database, there are numerous entries for Heinrich Daemen-Schmid from 1907 to 1926 in several different countries. Individual Patents Heinrich Daemen-Schmid Viktor Daemen Walter Daemen Loga-Calculator

1907, 1908, 1911, 1912, 1915, 1917, 1922, 1923 1922 1935, 1938, 1939 1949

Materials For dating slide rules, the design can also be of help (see Table 14.2). • Originally, linear slide rules were mostly of boxwood. According to maker, other types of wood (e.g., bamboo) followed. Such slide rules were (from 1900) mostly coated with celluloid. From the 1940s, plastics (polyvinyl chloride (PVC) and polystyrene) increasingly replaced wood. • Circular slide rules were made of cardboard, sheet metal, or plastic. • Cylindrical slide rules originally had a wooden, and later a cast iron, frame. Already from about 1900 aluminum drums were used. From around the 1930s, the frame and drum were then made of plastic (in certain cases Bakelite). Table 14.2  Design and dating of slide rules Frequently used materials for slide rules Material Boxwood Pear wood (with celluloid surface) Mahogany (with celluloid surface) Laminated wood with synthetic resin Plastic

Period (estimated) Seventeenth century to 1925 1920 to 1975 1900 to 1975 1940 to 1975 1940 to 1975

© Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020 Source Manufacturers’ and collectors’ catalogs

562

14  Slide Rules

Remarks There are deviations according to the manufacturer. In general, the production of slide rules came to an end in the 1970s. Many Swiss makers of cylindrical slide rules experienced ups and downs. Some companies were unable to survive (see Fig. 14.17).

1924

1925

1937

1961

1973

1960

1972

1963

1951

1939

1927

1974 1975 Loga-Calculator Aktiengesellschaft, Uster

1962

1950

1938

1926

1976

1964

1952

1940

1928

1916

1904

1897

1899

1918

H. Daemen-Schmid, Uster

1931

1978

1965 1966 Loga-Calculator Aktiengesellschaft, Uster

1953 1954 Loga-Calculator Aktiengesellschaft, Uster

1941 1942 Loga-Calculator AG, Uster

1979

1967

1955

1943

Ernst Billeter-Bossert, Zürich National Rechenwalzen Aktien-Gesellschaft, Küsnacht

1977

1908

1919 1920 Loga-Calculator AG, Uster

1907

1980

1968

1956

1944

1932

National Rechenwalzen Aktien-Gesellschaft, Zürich

1929 1930 Loga-Calculator AG, Uster

1917

1905 1906 Heinrich Daemen, Zürich

1898

1981

1969

1957

1945

1933

1921

1909

1982

1970

1958

1946

1934

1911

1983

1971

1959

1947

Ernst Billeter, Zürich

1935

1923

Daemen-Schmid & Cie., Uster

Ernst Billeter-Bossert, Zürich

1922

1910

Fig. 14.17  Swiss cylindrical slide rule manufacturers. Some companies sprouted out of nowhere and quickly disappeared. (© Bruderer Informatik, CH-9401 Rorschach)

© Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020

Source: Swiss Official Gazette of Commerce (1893–2018)

1949

Ernst Billeter, Zürich

1948

1936

National Rechenwalzen AG, Zürich

H. Daemen-Schmid, Uster

1915

1903

Ernst Billeter & Co., Zürich

1913 1914 Daemen-Schmid & Cie., Uster Daemen-Schmid & Cie., Zürich

1912

1902

1896

Julius Billeter's Söhne, Zürich

1901

1895

1900

1894 Julius Billeter, Zürich

Dating of Swiss cylindrical slide rules (1890–1980)

1893

14.5  Dating of Cylindrical Slide Rules 563

564

14  Slide Rules

Comments • The three most important Swiss manufacturers of cylindrical slide rules were the Daemen-Schmid/Loga-Calculator, Billeter, and National Rechenwalzen companies • The Heinrich Daemen company (“Spezialgeschäft für Rechenapparate und Rechenmaschinen”) was founded in Zurich in 1890, and the production of Loga cylindrical slide rules began (according to information from the company) in 1900. For 1890 no entry was found in the commercial register. • The joint-stock company Daemen-Schmid & Cie., Uster, was founded in 1911 and abolished in 1915. From 1912 to 1915, there was a branch in Zurich. • The company H. Daemen-Schmid, Uster, existed from 1916 to 1924. • The company Loga-Calculator AG, Uster, was founded in 1915. • In 1947 the company Loga-Calculator AG, Uster, was renamed the Loga-­ Calculator Aktiengesellschaft, Uster. • In 1977 the company Loga-Calculator AG, Uster, changed its statutes, and in 1978 its pension fund, founded in 1976, was abolished. • The company Loga-Calculator AG, Uster, was in existence until 2018, but over the last 40 years, no longer manufactured slide rules. • In advertisements (e.g., Schweizerische Bauzeitung, volume 74, no. 20, November 15, 1919), one finds the company name Loga-Calculator, Zurich, even after the move to Uster. • The company Ernst Billeter, Zurich, was founded in June 1912 and abolished in October 1912. The successor was the Ernst Billeter & Co., Zurich, which existed from 1912 to 1917. • The company Ernst Billeter-Bossert, Zurich, was founded in 1921 and in 1934 renamed Ernst Billeter, Zurich. How long this company survived is not clear. It is mentioned in the Swiss Official Gazette of Commerce in 1938. • The National Rechenwalzen Aktien-Gesellschaft, Zurich, relocated in 1925 to Küsnacht ZH.  The company manufactured cylindrical slide rules with the “System Billeter.” • The production of cylindrical slide rules began partly before the founding of the company. This follows, for example, from the article “Julius Billeters Rechenapparate” in the Neue Zürcher Zeitung of April 24, 1886. • Past issues of the Swiss Official Gazette of Commerce were examined (digitized). Because of errors with automatic text recognition, all entries could not always be found. • The company founders and their oldest sons often have the same first name (e.g., Ernst Billeter and Heinrich Daemen), which is sometimes confusing. Source: Swiss Official Gazette of Commerce (1893–2018)

14.6  R  elationship Between the Serial Numbers and Scale Length For the Loga cylindrical slide rules, there is evidently a relationship between the scale length and the serial numbers (see Table 14.3).

14.6  Relationship Between the Serial Numbers and Scale Length

565

Table 14.3  Relationship between scale length and serial numbers The serial number provides information about the number manufactured of each model Collection Serial no. Scale length Schaub collection, Gelterkinden BL 50 1,2 m Schaub collection, Gelterkinden BL 2,4 70 2,4 m Museum of UBS, Basel 2,482 2,4 m Rudowski collection, Bochum (Germany) 2,4 150 2,4 m Brüngger collection, Bremgarten BE 1,2459 1,2 m Schreibmaschinenmuseum Beck, Pfäffikon ZH 1,2499 1,2 m Brüngger collection, Bremgarten BE (297) 24 m Bethmann collection, Celle (Germany) 24/1138 2,4 m ETH Zurich R-1179 24 m Museum für Kommunikation, Bern 1501 15 m Geppert collection, Göttingen (Germany) 1731 2,4 m Denz collection, Münster (Germany) 1837 2,4 m Brüngger collection, Bremgarten BE 2097 2,4 m Smallenburg collection, RS Meppel, Netherlands 2123 2,4 m Narr collection, Windisch AG 2238 2,4 m Schweizerisches Nationalmuseum, Affoltern am Albis ZH 2256 2,4 m Stiftung Komturei Tobel TG 2413 24 m Rechentechnische Sammlung, Universität Greifswald (Germany) 2443 24 m Museum of UBS, Basel 2499/8199 24 m Narr collection, Windisch AG 02841 2,4 m Kordetzky collection, Cham ZG 5538 10 m Kordetzky collection, Cham ZG 5739 10 m Narr collection, Windisch AG 6741 10 m Bruderer collection, Rorschach SG 6919 10 m Schreibmaschinenmuseum Beck, Pfäffikon ZH 6992 10 m Denz collection, Münster (Germany) 7002 10 m Schaub collection, Gelterkinden BL 7145 2,4 m Narr collection, Windisch AG 7146 10 m Museum für Kommunikation, Bern 7531 10 m Kantonsschule Freudenberg, Zurich 7642 10 m Narr collection, Windisch AG Narr collection, Windisch AG Museum of UBS, Basel Schreibmaschinenmuseum Beck, Pfäffikon ZH ETH Zurich Schaub collection, Gelterkinden BL Anthes collection, Markgröningen (Germany) Narr collection, Windisch AG ETH Zurich Smallenburg collection, RS Meppel, Netherlands Narr collection, Windisch AG

750321 750397 750431 750446 750454 750479 750506 750811 750828 750837 108302

7,5 m 7,5 m 7,5 m 7,5 m 7,5 m 7,5 m 7,5 m 7,5 m 7,5 m 7,5 m 10 m

(continued)

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14  Slide Rules

Table 14.3 (continued) Kordetzky collection, Cham ZG Schaub collection, Gelterkinden BL Schreibmaschinenmuseum Beck, Pfäffikon ZH ETH Zurich Museum of UBS, Basel Narr collection, Windisch AG Museum of UBS, Basel Museum of UBS, Basel Technisches Museum Wien, Vienna Museum für Kommunikation, Bern Schreibmaschinenmuseum Beck, Pfäffikon ZH ETH Zurich Narr collection, Windisch AG Musée d’histoire des sciences, Geneva Schaub collection, Gelterkinden BL Kordetzky collection, Cham ZG Anthes collection, Markgröningen (Germany) Deutsches Museum, Munich Kordetzky collection, Cham ZG Narr collection, Windisch AG Museum für Kommunikation, Bern Museum of UBS, Basel Smallenburg collection, RS Meppel, Netherlands Schaub collection, Gelterkinden BL Studiensammlung Kern, Aarau AG Denz collection, Münster (Germany) Schaub collection, Gelterkinden BL Brefka collection, Stuhr (Germany) Museum of UBS, Basel Smallenburg collection, RS Meppel, Netherlands Museum of UBS, Basel Museum of UBS, Basel Smallenburg collection, RS Meppel, Netherlands Geppert collection, Göttingen (Germany) Wiesbauer collection, Michelsdorf (Austria) Narr collection, Windisch AG Narr collection, Windisch AG Mathematikum, Gießen (Germany) Schweizerisches Nationalmuseum, Affoltern am Albis ZH Schaub collection, Gelterkinden BL Narr collection, Windisch AG Museum für Kommunikation, Bern © Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020 Source: Survey of museums and collectors

109487 109531 15136/8456 15469 15514/8814 15515 15720/9320 151367 151899 152004 152194 152641 153561 153580 153761 153852 154085 154306 154316 154389 154568 155065 155068 155125 155294 155613 155738 155778 155834 155910 156005 156026 156033 156034 156239 15428720 151578457 152578557 153118611 24100 24102 24163

10 m 10 m 15 m 15 m 15 m 15 m 15 m 15 m 15 m 15 m 15 m 15 m 15 m 15 m 15 m 15 m 15 m 15 m 15 m 15 m 15 m 15 m 15 m 15 m 15 m 15 m 15 m 15 m 15 m 15 m 15 m 15 m 15 m 15 m 15 m 15 m 15 m 15 m 15 m 24 m 24 m 24 m

14.6  Relationship Between the Serial Numbers and Scale Length

567

Explanation of Symbols Meaning of the colors in green: Obvious relationship between scale length and serial number in blue:  No relationship between scale length and number manufactured in red:  Deviation/interpretation not certain Remark The serial number 2499 is on the axis at the left. At the right is the number 8199. The meaning of the second numeral is not clear. This may be in connection with a modification of the drum. For R-1179, R apparently indicates reciprocal values. Comments With the exception of two specimens with numbers greater than 15 million, the 7.5 m cylindrical slide rules have the highest numbers. To my knowledge, however, the Loga-Calculator AG manufactured nowhere near 750,000 cylindrical slide rules. This fact was cause enough for me to examine the assigning of serial numbers more closely. The table shows that the company used two different numbering systems: (a) In the beginning the Loga cylindrical slide rules were probably numbered consecutively, without regard to the scale length. (b) With increasing demand, from around 10,000 specimens, the numbering system was changed, after which the serial numbers took the scale length into account. The devices with the numbers 50, 1731, 1837, and 2238, for example, were apparently numbered consecutively, without regard to the scale length. Nos. 7145 and 7146 have scales of 2.4 m and 10 m, respectively. Cylindrical slide rule no. 50 is probably very old and was presumably manufactured shortly after 1900. Numbers 70, 1501, 1731, 1837, 2413, and 5538 have a cast iron frame, while numbers 6919 and 7002 have wooden frames and number 7145 a plastic frame. Cast iron was used quite early. Loga cylindrical slide rules up to about serial number 9999 presumably belong to the oldest (earliest) company products. It appears that from 1900 predominantly cylindrical slide rules with scale lengths of 2.4 m and 10 m were made. Originally, the cylindrical slide rules had, at the highest, 4-place and later at least 5-place numbers. For Loga cylindrical slide rules having 5-place serial numbers, the first two numerals are related to the scale length. Most 15  m cylindrical slide rules mostly have 4- to 6-place values. After the first 4-place series (99 specimens), the 5-place series (999) followed and then the 6-place series (9999). When this number was exceeded, additional places were added. It is conceivable that the third numeral, around the 15,000 numbers, has a special meaning (e.g., reference to a certain type of cylinder). However, this is unlikely, because all the company produced very high numbers. No. 155738 is probably the 5738th specimen of the 15 m cylindrical slide rule (second series).

568

14  Slide Rules

Nevertheless, the two 8- and 9-place numbers for the 15  m cylindrical slide rules stand out. Such production numbers were certainly not achieved. There are no 7-place values. For 9-place values, the last four numerals may have a different meaning (possibly the date of manufacture). 24  m drums generally have 5-place numbers, i.e., at the most 999 specimens. Evidently this was enough, as the few surviving specimens show. No. 24100 is possibly the 100th specimen of the 24 m cylindrical slide rule (second series). 15 m cylindrical slide rules were very common, but the most precise and most expensive 24 m cylindrical slide rules and the 1.2 m cylindrical slide rules were relatively rare. Cylindrical slide rules with scale lengths of 1.2 and 2.4 m were probably manufactured only in the beginning. Notes As a rule the serial numbers are engraved on the axis of the drum. Sometimes there are no numbers. Conclusions • Beginning with the 5-place serial numbers, the first two numerals relate to the scale length (e.g., no. 75xyz, 7.5 m; no. 24xyz, 24 m). For the 24 m cylindrical slide rules preserved, even with 4-place numbers, the serial number begins with 24 (with the exception of R-1179). This is also true of the 15 m cylindrical slide rules. • From the maker numbers, one can conclude what the (planned) production numbers were per model and in some cases recognize the age (e.g., 109531: ­maximum 9999 specimens, highest 6-place number 109999, accordingly a late 10 m cylindrical slide rule). • Before the change in the numbering system, predominantly 2.4 m and 10 m cylindrical slide rules were manufactured and, after the change, mostly 7.5 m and 15 m cylindrical slide rules. Assumptions • The change in the numbering system may have coincided with the move to Uster ZH (new, greater capability production site). • Cylindrical slide rules with 1- to 4-place serial numbers possibly derive predominantly from the period 1900 to 1911 (company name probably mostly Heinrich Daemen, Zurich). • Cylindrical slide rules with 5-place serial numbers sooner derive from 1912 (company name: Daemen-Schmid & Cie.) and later from 1915 (company name: Loga-Calculator AG). Note A reference work of 1921 mentions Loga drums with scale lengths of 2.4, 15, and 24  m (see Ludwig Brauner, Victor Vogt (editor): Illustriertes OrgaHandbuch erprobter Büromaschinen, Verlag für Sammler-Literatur Dingwerth GmbH, Delbrück 2003 (reprint of excerpts from 1921)).

14.7  The Weber Circular Slide Rule

569

14.7  The Weber Circular Slide Rule On January 26, 2017, the ETH Library in Zurich came into possession of a previously unknown logarithmic circular slide rule (see Figs.  14.18, 14.19, and 14.20). Its age was estimated to be about 100 years. The base plate of the brass device, with the inscription “Re Ma.3”, has a diameter of nearly 25 cm. The logarithmic calculator, with a weight of 2.45 kg, exhibits a logarithmic scale (with values from 1 to 10). The scale length measures about 77  cm that is roughly three times as long as a common linear slide rule and is therefore significantly more accurate. It was apparently intended for mass multiplication and division.

14.7.1  A Circular Slide Rule of Unusual Design As a rule, a circular slide rule has a fixed outer scale ring and a rotating inner circular area with several scales and a movable pointer. The recently discovered circular slide rule exhibits an unusual design. The (only) scale of the analog calculating device is fixed. Instead, there are two narrow rotating steel pointers. The upper pointer is attached to a metal wheel and the lower pointer to a brass disc. The wheel and the disc are concentric, i.e., they have a common center. With the wheel the angle between the two pointers is set. Rotating the (upper) metal disc moves the two coupled pointers simultaneously. The angle between these remains unchanged. This special calculating device is distinguished by simple operation and high precision (approximately three places), but its use is limited to mass multiplication and division with a constant factor or divisor. Fig. 14.18  The Weber circular slide rule (1). This device has a (single) logarithmic scale with two pointers. It is a special calculating device for mass multiplications and divisions. (© ETH Zurich, Image Archive)

570

14  Slide Rules

14.7.2  How Does the Device Function? To divide 2 by 3 with a conventional circular slide rule, one rotates the inner scale so that the 3 of the inner scale is positioned exactly under the 2 of the outer scale. The value 6.67 is then read out on the outer scale above the number 1 on the inner scale, i.e., the result 0.667. Inversely, setting the 2 of the inner scale under the 3 of the outer scale gives the value 6.67 under the number 1 of the outer scale (on the inner scale). As usual with linear and circular slide rules, the decimal point is calculated mentally. By way of example, with the Weber circular slide rule, one sets the left pointer to 2 and the right pointer to 3 (ratio 2:3). Then one rotates the two pointers together in the clockwise direction. With the left pointer on 4, the value 6 is read out with the right pointer. According to the direction of rotation, a multiplication or a division is performed. The pointers function essentially like a pair of dividers.

Fig. 14.19  The Weber circular slide rule (2). The base plate is fixed, and the ring and disc can be rotated. (© ETH Zurich, Image Archive)

14.7.3  Who Built the Circular Slide Rule? There is no documentation concerning this calculating aid. As manufacturer one finds the name “G. Weber, Zürich”, with no indication of the year built. According to information from Karin Huser of the Staatsarchiv Zurich, Georg Wilhelm Weber, a machinist from Dresden, was born in 1862 and, together with his family, acquired Swiss citizenship in 1908. “The land rights of Canton Zurich, and therefore Swiss citizenship, were granted to these persons” (government decision no. 2424 of December 12, 1908).

14.7  The Weber Circular Slide Rule

571

In the European patent database, there are two patents of Wilhelm-Georg Weber from Zurich for measuring instruments (1895 and 1896). But these bear no reference to the circular slide rule. The Kern collection of the Stadtmuseum Aarau is in possession of a topographic slide rule (Hofer & Brönnimann system), built by “Wilh. GG. Weber Zürich”. In the database of the Stadtarchiv Zurich, the Schweizerisches Wirtschaftsarchiv in Basel, the archives of the Neue Zürcher Zeitung, and in the School Board records of the ETH Zurich, there are no entries regarding the manufacturer or the device. One also searches in vain in the Swiss Official Gazette of Commerce. Fig. 14.20  The Weber circular slide rule (3). The upper pointer is attached to the metal wheel and the lower pointer to the shaft of the brass disc. Rotating the (upper) metal disc moves the two coupled pointers simultaneously. (© ETH Zurich, Image Archive)

14.7.4  Where Was the Circular Slide Rule Found? In the middle of the 1970s, the equipment of the Institute for Physics of the ETH Zurich was moved from the old building in Gloriastraße to a new building on the Hönggerberg. “In the course of many years, mountains of old devices had collected which we were ordered to dispose of as metal scrap. In fact, though, there were several treasures of precision mechanics among these, such as goniometers, telescopes for reading scales, and barometers that we would only reluctantly throw out. Those involved with the move rescued individual devices”, wrote Robert Hofmann from Wallisellen in a letter to the author on January 20, 2017. At that time he was an assistant in the laboratory for solid-state physics and took part in the removal. The physicist, born in 1934, carefully preserved the precision mechanical device for nearly 50 years. Hofmann believes that the circular slide rule was used for the evaluation of film strips resulting from the structural analysis of crystals according to the

572

14  Slide Rules

Debye-Scherrer method. This method was developed around 1915 at the ETH Zurich. The inscription “Re Ma. 3” (Rechenmaschine = calculating machine no. 3) is painted on the underside of the disc. The Institute for Physics had several calculating devices. One of these, designated “Re Ma. 4”, is a 7.5 m Loga cylindrical slide rule (serial number 750454), partly made of plastic. This material indicates that the device was acquired after 1915. The Weber circular slide rule was probably a one-­of-­a-kind device. Note The Weber circular slide rule should not be confused with Weber’s Rechenkreis. This logarithmic device, built by R.  Weber (Forstakademie Aschaffenburg) was on view in 1893 in Munich. The scale divisions of circular slide rules become smaller toward the inside. As with circular calculating machines (e.g., the Curta) the numerals are arranged radially, making reading out somewhat complicated. The more scales a circular slide rule has, the more confusing it becomes.

14.8  Loga Cylindrical Slide Rules 14.8.1  The 24 Meter Cylindrical Slide Rule At the end of 2013, two very rare Loga cylindrical slide rules with a scale length of 24 m were found at the ETH Zurich and the UBS bank in Basel. According to present knowledge, these are the world’s largest and most accurate mass-produced cylindrical slide rules. The linear slide rule was invented about 400 years ago and was in wide use until the 1970s. It was abruptly replaced by the electronic pocket calculator and has been largely forgotten. Cylindrical slide rules were popular from the second half of the nineteenth century and found in large numbers. There was a wide range of linear slide rule and circular slide rule models, in general tailored to particular applications. Cylindrical slide rules were used for a number of purposes, including banks, insurance companies, the textile industry, public transport, research, and in the army.

14.8  Loga Cylindrical Slide Rules

573

Fig. 14.21  The Loga cylindrical slide rule (1). The internationally most important manufacturer of cylindrical slide rules was certainly the Loga-Calculator AG in Uster ZH. The impressive cylindrical slide rules were produced in large numbers and sold around the world. (© UBS)

High accuracy was, for example, indispensable for currency conversions in banks. In addition to linear slide rules and logarithmic tablets, Loga-Calculator manufactured primarily circular slide rules and cylindrical slide rules (see Figs. 14.21, 14.22, and 14.23).

574

14  Slide Rules

Fig. 14.22  The Loga cylindrical slide rule (2). Because of their accuracy, the massive 24 m cylindrical calculators were especially popular with banks, such as for currency conversions. (© UBS)

Fig. 14.23  Loga cylindrical slide rule assortment. The Loga-Calculator company in Uster ZH produced cylindrical slide rules in six different sizes (1.2 m to 24 m). The larger the diameter and length of the cylinders, the greater the accuracy of the slide rules. (© Bruno Narr, Windisch AG)

14.8  Loga Cylindrical Slide Rules

575

Only a Few Surviving 24 m Cylindrical Slide Rules According to information from the manufacturer, the 24  m Loga cylindrical slide rules are accurate to five or six places. Together with the frame, they are nearly 70 cm long. The useful length of the cylinder is 60 cm. The cylindrical slide rules have a diameter of about 25 cm and a circumference of 80 cm. These are very rare. Until the summer of 2013, only three specimens (Dällikon ZH, Gelterkinden BL, Greifswald, Germany) were known. As chance would have it, at the end of November and the beginning of December 2013, two further specimens were discovered within a short time, one in the Department of Computer Science at the ETH Zurich and one in the Historisches Archiv & Museum of the UBS major bank in Basel. In February 2014 another cylindrical slide rule came to light in Windisch AG, and in September 2016 yet another in the (former) Komturei Tobel. In connection with an examination of the serial numbers, it emerged on March 1, 2019, that the Museum für Kommunikation in Bern also has a 24 m Loga cylindrical slide rule. In 2020 another specimen came to light in a museum in Zug. It is now in Bremgarten BE. At present, nine 24 m cylindrical slide rules are therefore known. 15 m cylinders are far more common. There are also a few much longer cylindrical slide rules. However, these are individual specimens and were evidently built above all to justify an entry in the Guinness Book of Records. The “Eximius Diu 6” spiral slide rule, built by Dave Hoyer in 2012 (Encore consulting Pty Ltd., Sydney, http://www. encoreconsulting.com.au), has a scale length of 318 m. It is 175 m long and has a diameter of 7.5 cm and 135 spiral windings. The accuracy is given as six places.

14.8.2  Determination of Age The Loga cylindrical slide rules of the ETH Zurich and the UBS Basel bear the inscription “Zürich (Schweiz)”. In 1911 the company relocated to Uster ZH. The two cylindrical slide rules were possibly built at the latest in this year. In the journal Der Organisator, for example, advertisements were published in 1922 and 1925 with the company name “Loga-Calculator, Zürich”. On July 19, 1919, an offer of the Loga-Calculator AG, Zurich appeared in the Schweizerische Bauzeitung. The production site was in fact in Uster, but the sales (Daemen Schmid) remained in Zurich. It is not certain whether there were still cylindrical slide rules with the place name Zurich after the relocation to the Zurich Oberland. The material (wood, metal, or plastic) also gives clues about the difficult dating.

576

14  Slide Rules

14.8.3  How Long Is the Scale? The Longer the Scale, the Greater the Accuracy The longer the scale of a slide rule, the greater the accuracy. In practice, linear slide rules prevailed. Nevertheless, circular slide rules and, above all, cylindrical slide rules allow accuracy to more places. The longest scales, and therefore the greatest accuracy, was with cylindrical slide rules. Linear slide rules usually have a scale length of 25 cm (less frequently 12.5 cm and 50 cm) and circular slide rules 30  cm. Circular slide rules and cylindrical slide rules accommodate long scales in a small space. No documentation giving information about their acquisition, price, and use exists for the two cylindrical slide rules referred to at the ETH Zurich and in the corporate archives of the UBS Basel. An important feature of cylindrical slide rules is the scale length. Especially for the early devices, however, it is often not possible to find such information. With the help of measurements and a list of Loga cylindrical slide rule models, one can unambiguously determine the scale length. Loga-Calculator manufactured cylindrical slide rules with scale lengths from 1.2 to 24 m (models: 1.2 m, 2.4 m, 7.5 m, 10 m, 15 m, and 24 m). A circular slide rule with a 24-m-long scale would have a diameter of 7.64 m (24 m/π)! The scale length can be calculated as described below (see box). Scale Length A Loga cylindrical slide rule with a scale length of 24 m has 80 parallel subdivisions (sections) of 60 cm, giving a total length of 48 m. However, the scale is not 48  m long. Since the successive scales overlap (up to 50%), the scale measures (only) 24 m. The scale is printed doubly. 15 m Loga cylindrical slide rules have 60 subdivisions of 50 cm, giving a scale length of (60 × 50 cm)/2, i.e., 15 m.

What Does the Type Designation 24/48 m Mean? In lists of models and price lists, the Loga-Calculator AG, Uster, used type designations such as 10 m, 15 m, 24 m or the (confusing) 10/20 m, 15/30 m, and 24/48 m. For example, what does the type 24/48 m mean? This model is not a device with a scale length of 48  m. Instead, this describes a 24  m cylindrical slide rule. The numerical sequence 24/48  m can be understood as follows: The sleeve has a scale length of 24 m, and on the drum is a doubly (offset) printed 24 m scale, i.e., 2 × 24 m. The double application of the scale does not increase

14.8  Loga Cylindrical Slide Rules

577

the accuracy of the cylindrical slide rule. Without the overlapping scale sections, it would not be possible to use the slide rule at all. The misleading description “48 m” apparently served only for advertising purposes. This also follows from the statement: “According to its size (length and diameter), the Loga calculator has a scale length of 10 to 200 times that of a 25-cm-long linear slide rule” in the article “Die logarithmisch-graphischen Rechenapparate” (see Verlag Organisator AG (editor): Maschinen und Hülfsmittel für das Büro, Verlag Organisator AG, Zurich 1932, page 35). An advertisement of the Loga-Calculator AG, Uster, in the same issue (page 8) shows that “Loga-­Calculatoren” (“Loga” cylindrical slide rules) were offered in different sizes and models, with prices ranging from 100 to 800 Swiss francs and scale lengths from 2.4 to 48 m. The Ferrol Calculation Method In the user manual for the 10 m cylindrical slide rules, Loga-Calculator refers to a new method of calculation. The author was Fritz Ferrol (a pseudonym for Jakob Schmitt). This work appeared at least since 1907 in several places and in numerous editions. The eight guideline documents are traceable back to 1910 (Berlin), and in 1913 the fifth edition was published. Tips for the Care of Cylindrical Slide Rules Protect the surfaces of the cylinders with the subdivisions against scratches, and remove the dust daily with a fine brush. Rub the surface weekly with cotton and talcum. Thoroughly clean the device every 2 months as described in the following: Lift the cylinder out of the bearings and remove the slide. Wash the surface of the cylinder with a soft sponge and lukewarm water, not wetting excessively. Dry completely with a clean cloth and then rub in talcum powder thoroughly with the cotton wad supplied. Brush the slide upholstery clean. Then insert the slide again and set the drum onto the bearings. (© Schweizerische Armee, Artillerie-Reglement IX, Artillerie-Beobachtungsdienst 1935, pages 48–49)

Calculator Inventory: One Loga Cylindrical Slide Rule and One Mechanical Calculating Machine A Loga cylindrical slide rule was in use in the Institute for Applied Mathematics of the ETH Zurich. This is mentioned in a handwritten document of August 11, 1949 (estate of Eduard Stiefel in the University archives of the ETH Zurich). At that time the institute was in possession of an electrical calculating machine and a Loga cylindrical slide rule. A Madas desk calculating machine from the H.  W. Egli AG company, Zurich, was acquired in 1948. When and how the cylindrical slide rule came to the Institute for Applied Mathematics is not known. As a label indicates, the 24-m-long Loga cylindrical slide rule came by way of the Institute for Telecommunications to the computer center of the ETH. From 1951 to 1953, Heinz Weber of the Institute for Telecommunications was a member of the Kommission zur Entwicklung von Rechengeräten in der Schweiz.

578

14  Slide Rules

14.8.4  L  oga Cylindrical Slide Rules: Lists of Models and Price Lists Overviews of the models offered by the Loga-Calculator AG are hard to find and not easily accessible. In general, the dating of cylindrical slide rules is difficult. The following three multipage documents are known: • List of the Loga-Calculator models • An undated price list for “Loga” calculators • A dated price list of the Loga-Calculator AG, Uster (1921) The first two documents are not dated. They date at the earliest from the year 1915, since the Loga-Calculator AG was founded at this point in time. Sources (a) List of models (see Figs. 14.24 and 14.25) Schweizerisches Wirtschaftsarchiv (SWA), Basel, Loga AG private archives, Dossier K 9, List of the Loga calculator models (undated) (b) Price list without date (see Figs.  14.26, 14.27, 14.28, 14.29, 14.30, 14.31, 14.32, and 14.33) UBS AG, Historisches Archiv & Museum (Basel) (c) Price list from 1921 (see Figs. 14.34, 14.35, 14.36, and 14.37) Alte Kantonsschule Aarau, school collection. Determination of the Scale Length With many Loga cylindrical slide rules, there is no information about the scale length. Thanks to the overview of the models, this can be determined with certainty.

14.8  Loga Cylindrical Slide Rules

579

Fig. 14.24  List of Loga cylindrical slide rule models, page 1. The accuracy varies between three and six places according to the scale length. (Source: Schweizerisches Wirtschaftsarchiv, Basel)

580

14  Slide Rules

Fig. 14.25  List of Loga cylindrical slide rule models, page 2. The same numbers occur repeatedly because of the overlapping, which can cause confusion. (Source: Schweizerisches Wirtschaftsarchiv, Basel)

14.8  Loga Cylindrical Slide Rules

581

Fig. 14.26  Undated price list for Loga cylindrical slide rules, page 1. (Source: UBS AG, Historisches Archiv & Museum, Basel)

582

14  Slide Rules

Fig. 14.27  Undated price list for Loga cylindrical slide rules, page 2. (Source: UBS AG, Historisches Archiv & Museum, Basel)

14.8  Loga Cylindrical Slide Rules

583

Fig. 14.28  Undated price list for Loga cylindrical slide rules, page 3. (Source: UBS AG, Historisches Archiv & Museum, Basel)

584

14  Slide Rules

Fig. 14.29  Undated price list for Loga cylindrical slide rules, page 4. (Source: UBS AG, Historisches Archiv & Museum, Basel)

14.8  Loga Cylindrical Slide Rules

585

Fig. 14.30  Undated price list for Loga cylindrical slide rules, page 5. (Source: UBS AG, Historisches Archiv & Museum, Basel)

586

14  Slide Rules

Fig. 14.31  Undated price list for Loga cylindrical slide rules, page 6. (Source: UBS AG, Historisches Archiv & Museum, Basel)

14.8  Loga Cylindrical Slide Rules

587

Fig. 14.32  Undated price list for Loga cylindrical slide rules, page 7. (Source: UBS AG, Historisches Archiv & Museum, Basel)

588

14  Slide Rules

Fig. 14.33  Undated price list for Loga cylindrical slide rules, page 8. (Source: UBS AG, Historisches Archiv & Museum, Basel)

14.8  Loga Cylindrical Slide Rules

589

Fig. 14.34  Loga cylindrical slide rule price list from 1921, page 1. (Source: Alte Kantonsschule Aarau, school collection)

590

14  Slide Rules

Fig. 14.35  Loga cylindrical slide rule price list from 1921, page 2. (Source: Alte Kantonsschule Aarau, school collection)

14.8  Loga Cylindrical Slide Rules

591

Fig. 14.36  Loga cylindrical slide rule price list from 1921, page 3. (Source: Alte Kantonsschule Aarau, school collection)

592

14  Slide Rules

Fig. 14.37  Loga cylindrical slide rule price list from 1921, page 4. (Source: Alte Kantonsschule Aarau, school collection)

Chapter 15

Historical Automatons and Robots

Abstract  The chapter “Historical Automatons and Robots” depicts a wealth of magnificent mechanical automatons. Of particular interest are automaton figures (human or animal automatons), musical automatons (mechanical musical instruments), handwriting automatons, drawing automatons, chess automatons, mechanical robots, and punched card controlled looms. Included are clocks (sand glasses, sundials, night clocks, longcase clocks, pendulum clocks, tabernacle clocks, table clocks, pocket watches, astronomical clocks, picture clocks, and automaton clocks) and early typewriting machines. Some of these objects were programmable (e.g., with perforated tapes, program cylinders, and cams). Among the best known automaton builders are James Cox, Pierre and Henri-Louis Jaquet-Droz, Peter Kintzing, Friedrich Knaus, Hans Schlottheim, and Jacques Vaucanson. The origin of a musical automaton figure in the Beijing Palace Museum attributed to Timothy Williamson is unclear. More than 500  years ago, Leonardo da Vinci designed several “robots” (a mechanical knight, a mechanical lion, and a self-propelled cart). Numerous reconstructions of these have been made. Some automaton figures dating from the eighteenth century are still fully functional. Keywords  Androids · Astrarium · Automaton clocks · Automaton figures · Chess automaton · Clocks · Drawing automatons · Elephant clock · Handwriting automaton · Historical automatons · Mechanical looms · Mechanical musical instruments · Mechanical robots · Musical automatons · Music boxes · Philharmonic organ · Planetarium · Self-­playing violin · Singing bird boxes · Singing bird cages · Typewriting machines · Zeitglockenturm · Eberhard Baldewein · Basile Bouchon · Abraham-Louis Breguet · Jost Bürgi · James Cox · Leonardo da Vinci · Giovanni Dondi · Eise Eisinga · Jean-Baptiste Falcon · Joseph-Marie Jacquard · Henri-Louis JaquetDroz · Pierre Jaquet-Droz · Peter Kintzing · Friedrich Knaus · Jean-Frédéric Leschot · Henri Maillardet · Rasmus Malling-­Hansen · Jeremias Metzger · Peter Mitterhofer · David Röentgen · Hans Schlottheim · Christopher Latham Sholes · Leonardo Torres Quevedo · Jacques Vaucanson · Timothy Williamson

© Springer Nature Switzerland AG 2020 H. Bruderer, Milestones in Analog and Digital Computing, https://doi.org/10.1007/978-3-030-40974-6_15

593

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15  Historical Automatons and Robots

This chapter deals primarily with mechanical automatons. Of particular interest are automaton figures (human and animal automatons), e.g., drawing automatons and (programmable) automaton writers (handwriting automatons). Also worth mention are musical automatons and chess automatons, along with automaton clocks and mechanical looms (weaving machines). Furthermore, a brief description of writing machines is also included. Some machines execute diverse movements and are often coupled with a musical mechanism or a clock, which, e.g., controls a globe. Such automatons have much in common with mechanical calculating machines (such as gear wheels, programmed drums, or punched card control. Chapter 2 describes globes in greater detail, and Chapter 9 gives detailed information about automatic calculating machines.

15.1  Automaton Figures Automatons cover a wide range and depict, for example, humans, animals, vehicles, buildings, or landscapes. The mechanical figures (human and animal figures) were also called automaton figures. Automatons are known to exist since antiquity. An important pioneer was Hero(n) of Alexandria. The machines served for science, entertainment, or also practical purposes. Water clocks (complex water-driven devices) (clepsydras) and jaquemarts (hourly chiming clock) were already developed very early. Highly gifted automaton builders, who were often in the service of royal houses, e.g., in Germany, Austria, France, and Spain, have left behind significant legacies in calculating technology. They were often originally clockmakers. Their most important creations include androids (cyborgs, human-like automatons), animal automatons, music boxes or more precisely cylinderoperated music boxes (musical boxes with pinned cylinders), disc-type music boxes (disc-playing boxes, music boxes with perforated discs), orchestrions, self-playing pianos and organs, flute-playing clocks, musical clocks (clocks with musical mechanisms), trinket boxes (with clock, singing bird or carillon), and pocket watches (with musical mechanism and automaton figures). They came, for example, from Geneva, the Swiss Jura, or the Black Forest in Germany. The (poorly paid) home-based work in rural regions played an important role in the manufacture of these devices. The golden age of automaton building was in the eighteenth century. The most entertaining machines were very popular with the populace. Their makers enjoyed great respect, and some were even wealthy. Many of these magnificent, more than 200-year-old extremely complex precision mechanical marvels have been maintained with great care and are still fully functional. The semiautomatic and fully automatic looms were often hated, since these led to the fear of job losses. The successors to the androids are the program controlled robots. With the aid of mechanical gripping and rotating devices, together with sensors, they

15.1  Automaton Figures

595

are capable of carrying out difficult and dangerous work procedures. Robots can adapt to their environment (interaction) and to some extent change their operating site. Instruction Storage With automatons the programs are stored on cylinders, drums, discs, punched cards, or punched tapes. Pins, cams, and perforations served for this purpose. Note François Junod (www.francoisjunod.com) and Nicolas Court (www.mec-art. ch/nicolas-court), both in Sainte-Croix VD, are still producing automaton figures today.

15.1.1  Programmed Cylinders Programmed cylinders occur in different forms in many devices. They are found already in antiquity, in the middle ages, and in the early modern era (see Table 15.1). Table 15.1  Rotating programmed cylinders Programmable cylinders already appearing in antiquity Creator Period Device Ktesibios of Third century BC Water organ Alexandria Heron of Alexandria First century AD Theater automaton: rotating drum with pegs and cord winding Ibn al Razzāz al-Jazarī Around 1200 Rotating drum with bolts/pins Salomon de Caus 1615 Pinned cylinder, water organ Athanasius Kircher Seventeenth Pinned cylinder century © Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020

Remarks The pinned cylinder is much older than the music box. Programmed cylinders can be seen as early forerunners of magnetic drum memories. Playing cylinders were also installed in carillons. Works of Salomon de Caus are preserved in the park of Hellbrunn Castle (near Salzburg). In the water organ of de Caus, a water wheel drives a pinned cylinder which in turn controls organ pipes.

15.1.2  Famous Builders of Automatons Among the leading builders of automatons were (in alphabetical order): Ibn al Razzāz al-Jazarī, James Cox, Salomon de Caus, Heron of Alexandria, Pierre Jaquet-­Droz, Athanasius Kircher, Friedrich Knaus, Ktesibios of Alexandria,

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Henri Maillardet, Mical, Philo of Byzantium, Jacques Vaucanson, and Wolfgang von Kempelen. We are indebted to Marcus Vitruvius Pollio for some reports. Ktesibios is regarded as the inventor of the water clock (clepsydra) and the pinned cylinder. These were used repeatedly in water organs. Heron was extraordinarily creative: reaction steam turbine (forerunner of the steam engine, also described as aeolipile), a musical machine, a theater automaton, and a pantograph (with toothed gear drive). Al-Jazarī is, e.g., known for his elephant clock. Mical built speaking heads (1783). Salomon de Caus also constructed a musical machine. Several famous builders of automatons were active in the eighteenth century (see Table 15.2). Table 15.2  Creators of figure automatons The most important builders of automatons in the eighteenth century Name Country Work Switzerland The musician (1774) Pierre Jaquet-Droz The writer (1772) Henri-Louis Jaquet-Droz The draughtsman (1774) Jean-Frédéric Leschot Friedrich Kaufmann Germany The trumpet player (1810) Peter Kintzing Germany The harpsichord player David Roentgen (The dulcimer player) (1784) Friedrich Knaus Germany Miraculous writing machine (1760) Jacques Vaucanson France The flute player (1738) The shepherd’s pipe player/drummer (Tambourine player) (1738) Timothy Williamson England The writer (1770)

Site Neuchâtel Munich Paris Vienna Not preserved

Beijing

© Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020

Remarks This overview is limited to musical automatons, automaton writers, and drawing automatons. It does not include animal automatons, such as the duck of Vaucanson, automaton clocks, or textile automatons. Knaus is usually allocated to the eighteenth century. His flute player (1757) has been lost. The automaton writers make use of a quill pen. With the miraculous writing machine (see Fig. 15.1), a tiny writing figure sits on top of a globe in which the mechanism is located. The organ player of Jaquet-Droz is referred to as a harpsichord player or clavichord player. In fact this is a flute-playing organ. The androids of JaquetDroz and Leschot (see Fig. 15.2) are in Neuchâtel.

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Fig. 15.1  The miraculous writing machine (1760). With this handwriting automaton of Friedrich Knaus, the control mechanism is located in the (here open) globe. A very small brass figure with a mechanical quill sits on top of this. With the aid of a pinned cylinder, one can define any arbitrary text up to 68 characters long within certain limits. The form of the letters is determined by cams, which function as templates. Knaus headed the Physical and Mathematical Cabinet of the Viennese court. The miraculous machine is not demonstrated, but its functional principle is explained in a video film. (© Technisches Museum Wien, Vienna)

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Fig. 15.2  Automaton figures of Jaquet-Droz (1774).The three grandiose Neuchâtel androids are regarded as the world’s most magnificent and technically most sophisticated automaton figures. In spite of their high age, they are still completely functional. The tripartite group is made up of a draughtsman (at the left), a musician (in the middle), and a writer (at the right). (© Musée d’art et d’histoire, Neuchâtel)

15.1.3  Ornate Automaton Figures Automated figures, mechanical pictures, musical automatons, clocks, globes, and cylindrical calculating machines were not only technical masterpieces but often eye-catching works of art as well. Some outstanding automaton figures are still working today (see Table 15.3). Table 15.3  Famous historically important automatons (selection) Still functioning historical automatons Automaton Inventor Country Year Switzerland 1772 L’écrivain Pierre (The writer) Jaquet-­ Droz Le dessinateur (The draughtsman)

Henri-­ Louis Jaquet-­ Droz, Jean-­ Frédéric Leschot

Switzerland 1774

Site Musée d’art et d’histoire, Neuchâtel Musée d’art et d’histoire, Neuchâtel

Attributes Oldest programmable writing automaton (with internal precision mechanics) Drawing automaton with internal precision mechanics

(continued)

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Table 15.3 (continued) Still functioning historical automatons Automaton Inventor Country Switzerland La musicienne Henri-­ (The musician) Louis Jaquet-­ Droz Germany Peter La joueuse Kintzing, de tympanon (The cimbalom David Roentgen player) The miraculous Friedrich Germany Knaus writing machine

Year 1774

Site Musée d’art et d’histoire, Neuchâtel

Attributes Very fine musical figure automaton

1784

Musée des arts et métiers, Paris Technisches Museum Wien, Vienna

Very fine musical figure automaton

1760

Oldest programmable writing automaton (with external precision mechanics)

© Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020

Remarks At the present time, the mechanical trumpeter of Friedrich Kaufmann (Germany, built: 1810–1812), on display at the Deutsches Museum (Munich) (see Fig. 15.3), is not functional. This has a wooden pinned cylinder and wire pins and wire bridges, as well as two brass cylinders. The automaton trumpeter (dating from 1808) of the German mechanician Johann Nepomuk Mälzel has been lost. No information is available regarding the whereabouts of the trumpeter automaton of the Belgian Etienne-Gaspard Robertson. The development of automatic textile equipment began with the punched tape controlled loom of Basile Bouchon (1725).

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Fig. 15.3  Mechanical trumpeter (1812). The trumpeter automaton of the Dresden instrument maker Friedrich Kaufmann is controlled by two pinned cylinder systems. One of these determines the melody, and the other determines the rhythm. The tones are produced by 12 metal tongues and 2 leather bellows. Each of the two rotating brass cylinders has six beating metal tongues. The program is stored on a wooden cylinder with metal pins and wire bridges. A hand crank winds two spiral springs, which drive the wooden pinned cylinders and the bellows. (© Deutsches Museum, Munich)

Peter Kintzing created his dulcimer player (see Fig. 15.4) together with David Roentgen. The name Kintzing is sometimes written without a t: Kinzing.

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Fig. 15.4  The dulcimer player (1784). The captivating dulcimer player of Peter Kintzing utilizes tiny hammers for the dulcimer. The head and eyes move, but not the upper body. The control mechanism is not in the automaton figure but underneath this. In contrast to the musician of Henri-­Louis Jaquet-Droz, sophisticated finger mechanics is missing. (© Musée des arts et métiers/Cnam, Paris, picture: Pascal Faligot)

Musical automatons, automaton writers, and drawing automatons (see Table 15.4) fascinate people to this day. Table 15.4  Important automatons from the eighteenth century Musical and drawing automatons and automaton writers in chronological order (selection) Year Builder Work 1738 Jacques Vaucanson The flute player, the shepherd’s pipe player/ drummer 1757 Friedrich Knaus The flute player 1760 Friedrich Knaus The miraculous writing machine (continued)

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Table 15.4 (continued) Musical and drawing automatons and automaton writers in chronological order (selection) Year Builder Work 1770 Timothy Williamson The writer/musical clock The musician, the writer, the draughtsman 1774 Pierre Jaquet-Droz Henri-Louis Jaquet-Droz Jean-Frédéric Leschot 1784 Peter Kintzing The dulcimer player David Roentgen © Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020

Remarks The “writer” of Jaquet-Droz was completed in 1772 and introduced together with the other two machines in 1774. Vaucanson also built a mechanical animal, a duck.

15.1.4  Jaquet-Droz Among the leading automaton builders were Jacques Vaucanson (France) as well as Pierre (father) and Henri-Louis (son) Jaquet-Droz and Jean-Frédéric Leschot (Switzerland). These automatons mostly depict humans or animals. Examples are a lovestruck pair writing letters and persons making music and performing gymnastics. Especially well-known were the flute player (transverse flute player), the tambourine player, and the digesting duck (Le canard digérateur) of Jacques Vaucanson (France, around 1738). His two music-making androids have been lost and were probably destroyed during the French revolution. The duck, which was equipped with a program cylinder and cams, burned. A reconstruction exists that was exhibited at the Musée dauphinois in Grenoble. Each of the three wonderful figure automatons of Jaquet-Droz is shown below in three pictures, two from the front and one from the rear (see Figs. 15.5, 15.6, 15.7, 15.8, 15.9, 15.10, 15.11, 15.12, and 15.13).

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Fig. 15.5  The musician (1774) (1). The ravishing automaton figure of Henri-Louis JaquetDroz is a masterpiece without equal. It incorporates numerous moving parts (head, eyes, upper body, breast, arms, fingers). (© Musée d’art et d’histoire, Neuchâtel)

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Fig. 15.6  The musician (1774) (2). The automaton figure of Henri-Louis Jaquet-Droz actuates the keys of the flute-playing organ with its fingers. It is capable of five pieces of music, probably composed by the clockmaker himself. (© Musée d’art et d’histoire, Neuchâtel)

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Fig. 15.7  The musician (1774) (3). The complex mechanism of the diminutive artificial person is housed in the footstool, as is the pinned drum. (© Musée d’art et d’histoire, Neuchâtel)

The La Chaux-de-Fonds clockmakers Pierre Jaquet-Droz, Henri-Louis Jaquet-­ Droz, and Jean-Frédéric Leschot (with subsidiaries in Geneva, Paris, and London) built three automatons from 1768 to 1774 that were demonstrated for many years all over Europe. They were first introduced in 1774. Pierre JaquetDroz once studied with the mathematician Daniel Bernoulli in Basel. The dulcimer player of Peter Kintzing and the musician of Henri-Louis Jaquet-­Droz belong to the most esthetic of all automatons.

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Fig. 15.8  The draughtsman (1774) (1). The automaton figure of Henri-Louis Jaquet-Droz and Jean-Frédéric Leschot produces four different drawings with pencil. (© Musée d’art et d’histoire, Neuchâtel)

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Fig. 15.9  The draughtsman (1774) (2). While drawing not only the hands move but also the eyes. The automaton is driven by a spring winding. (© Musée d’art et d’histoire, Neuchâtel)

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Fig. 15.10  The draughtsman (1774) (3). The entire mechanism is built into the body of the child. The cams (in the middle) determine the shaping. (© Musée d’art et d’histoire, Neuchâtel)

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Fig. 15.11  The writer (1772) (1). The android of Pierre Jaquet-Droz, completed in 1772 and first demonstrated together with the other two automaton figures in 1774, is the technically most sophisticated automaton figure. It is still completely functional today and is regularly demonstrated. (© Musée d’art et d’histoire, Neuchâtel)

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Fig. 15.12  The writer (1772) (2). The spring-wound machine figure dips the goose quill into the ink well, shakes the ink from the quill, and writes up to 37 characters on four lines of a paper sheet. This technical marvel is regarded as the world’s most sophisticated and magnificent handwriting automaton. (© Musée d’art et d’histoire, Neuchâtel)

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Fig. 15.13  The writer (1772) (3). The entire highly complex control mechanism of the programmable handwriting automaton is located in the body of the child. The (horizontal) cams in the middle column ensure the flawless form of the letters. The text content is defined with the (vertical) cam wheel and stored to the cams. (© Musée d’art et d’histoire, Neuchâtel)

Henri-Louis Jaquet-Droz came to London at the end of 1775, followed by his father Pierre Jaquet-Droz in 1776. They displayed four automatons in King Street, Covent Garden. The incredibly multifaceted craggy landscape automaton with the name “Grotto” (see Fig. 15.14) has been lost. This accommodated a hut, a mill, an aviary (bird house), sheep, goats, and music makers. The automaton theater also featured a brook, waterfalls, and fountains.

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Fig. 15.14  Grotto. Only the above illustration of this Jaquet-Droz automaton has survived. At the upper left, one can see the musician and at the upper right the writer and (underneath) the draughtsman. Etching and engraving of Balthasar Anton Dunker, completed by François Guillaume Lardy (1775). (© Trustees of the British Museum, London)

Below is an excerpt from the leaflet for the automaton exhibit of father and son Jaquet-Droz in London (Bodleian Library, Oxford: John Johnson collection): Second peace presents a contrast of art and nature, an assemblage of rocks, parterres, cottages, and pieces of architecture. This work, immense by the multitude and variety of objects therein and its operations, is only four feet and a half square, and about three feet in height. In the forepart of this piece is an elegant parterre terminated by the front of a building: further back is a landscape in Switzerland surrounded by rocks, behind which a sun rises, arrives at the meridian, and sets exactly agreeable with the revolutions of the sun on our horizon, according to the different seasons of the year. The landscape interspersed with plants, bushes and some shrubs, represents a cottage, mill, rivulet, and flock feeding. The farthest part is terminated by a chain of craggy rocks in which are caves and grottos, and on the summit goats are seen feeding. The pastoral part consists of a Shepherd and Shepherdess; sheep and goats are seen feeding or heard bleating; a cow chewing the cud, a calf sucking, and a dog guarding the sheep. The action of this piece begins by a countryman coming out of his cottage, mounted on an ass, he crosses the scene in that manner, passes the bridge over the rivulet, and carries his corn to the mill while he passes before the flock, the shepherd dog barks at him several times, and so naturally that many dogs have been deceived by its voice. Soon after the shepherd appears coming

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out of the cave in the rock; he stops, puts his flute to his mouth, and plays some preludes, which an echo repeats; afterwards he resumes his walks, and perceives the Shepherdess asleep near her sheep, her head leaning on her arm; he approaches her and plays a tender air. The Shepherdess wakes, sit up, looks at him, takes her guitar (sic) and joins in a duet with the Shepherd, till interrupted by the unexpected return of the countryman: the Shepherd thereupon retires into the Shepherdess’s grotto, who immediately resumes her former attitude; at the same time the countryman is seen walking back to his cottage, driving before him the ass laden with flour. The parterre is surrounded with a railing, and has in its enclosure a regular arrangement of vases, statues, jets-d’eau, and several orange trees, on which are seen flowers in bud, which soon expand, and are at length succeeded by the fruit. The piece of architecture is also adorned with fine statues, two fountains which seem to play very naturally and an aviary, where several birds fly about, and whistle with their natural notes. In the middle of the edifice is a portal, above which is a clock and bas reliefs: at the entrance to the portal is seen a country girl playing on a dulcimer several ­minuets, which two young ladies dance with great regularity and grace.

15.1.5  Maillardet’s Automaton in Philadelphia In 1928 the Franklin Institute science museum in Philadelphia came into possession of an automaton that had been destroyed by fire and consequently no longer functioned. Following restoration, the unusual machine proved to be a work of the Swiss clockmaker Henri Maillardet. According to information from the museum, the “draughtsman-writer,” built before 1800, has the largest (mechanical) memory (cams and brass discs) ever found in such devices. The figure creates four drawings and three poems, two in French and one in English. Maillardet worked for Pierre Jaquet-Droz. He is said to have constructed an automaton for the Emperor of China that wrote in Chinese – a gift of the English King Georg III.  The still operational draughtsman-writer of Maillardet was most recently improved and restored in 2007.

15.1.6  Programmable Automaton Writers Most mechanical automatons function according to a fixed, predefined program. With many mechanical musical instruments, it is possible to replace the acoustical memory, just as one can replace the punched tapes of looms. Handwriting a ­ utomatons, on the other hand, enable freely chosen texts within a limited scope. Cams The term cam is understood to mean a cam disc with a precisely cut profile. The ridges and indentations of these elements control the movement sequences, and the movements can be stopped in any position. One can quickly change the direction of the individual movements and modify their speed. The movements can be defined with camshafts.

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The Oldest Programmable Automaton Writers Two automaton figures from the eighteenth century are regarded as the first programmable automaton writers: The miraculous writing machine of Friedrich Knaus and The Writer (L’écrivain) of Pierre Jaquet-Droz. These devices are now in Vienna and Neuchâtel, respectively. Both automaton writers allow the programming and storing of texts. The character set of the self-writing miraculous machine, dating from 1760, is comprised of all small letters, four large letters (F, M, T, and V), punctuation marks (comma and period), and blank spaces. The maximum length of the written text is 68 characters, and the text is defined by means of a pinned cylinder (perforated drum) with the insertion of tiny iron pins. For each letter there are three gliding combs which control the movements to the left and right, up and down, and to and from the paper. Lever sensors transfer this information to the quill pen. The girl writer sits on a globe that houses the mechanism. By contrast, with the writer, built from 1768 to 1772 and introduced together with other automaton figures in 1774, the entire complex mechanism is housed inside the child itself. The little boy dips the goose quill into the ink well and writes nearly any arbitrary texts up to 37 letters (small and large letters), spread over four lines. The following characters are arranged in this order on the vertical wheel: A, a, b, C, [c], D, d, E, e, F, f, z, G, g, h, I, i (without period), · (i with period, 38th character), k, L, l, M, m, y, n, o, P, p, q, R, r, S, s, t, u, V, v, and x. The reasons for the choice of letters and the order are not known. The following characters are missing: B, H, J, j, K, N, O, Q, T, U, X, Y, and Z und therefore N for Neuchâtel (see Charles Perregaux; F.-Louis Perrot: Les Jaquet-Droz et Leschot, Attinger frères, editors, Neuchâtel 1916, pages 184 and 220–221). In the report the small letter c is missing. The eyes follow the movements, and the wording is stored on a camshaft (wheel on which replaceable cams are inserted) to nearly 40 discs. The miraculous writing machine is presumed to be the first programmable handwriting automaton with an external mechanism and the writer the first programmable automaton writer with an internal mechanism. The machines incorporate devices for input, storage, control, and output. The individual letters are written as analog, while the programming of the text is digital.

15.1.7  T  he World’s Most Magnificent Mechanical Androids Are from the Eighteenth Century Below are some commentaries about the automatons of Jaquet-Droz and Leschot: But the most magnificent and technically most sophisticated androids were those of the three Swiss mechanicians Pierre Jaquet-Droz (1721–1790), his son Henri-Louis (1752–1791), and Jean-Frédéric Leschot (1746–1824), from Neuchâtel, which they

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introduced in 1774 and which fascinated the public in Paris and London and then in other European cities. These comprised three life-like figures: a harpsichord player, a handwriting child, and a child draughtsman, in which especially the coordination of the hand, head and eye movements fascinates the viewer to this day while experiencing the demonstration of the androids in Neuchâtel. The mechanical repertoire is comparable with that of the machine of Knaus, that is it includes levers, cams, camshafts, rods, gear wheels, springs, and wire cables so that the respective mechanisms fit precisely into the body and are constructed still more precisely (see Akos Paulinyi; Ulrich Troitzsch: Mechanisierung und Maschinisierung: 1600 bis 1840, Ullstein Buchverlage GmbH, Berlin 1997, page 214). The French mechanic Jacques de Vaucanson presented three automata – a flute player, a galoubet player, and a duck – to the Académie des sciences in Paris in 1738. He set the standard for mechanical androids for the following decades and continues to this day to be the best known and most-often-cited eighteenth-century automaton maker. In 1760, Friedrich von Knaus, a mechanic employed at the imperial court in Vienna, built a writing machine […]. It was the first mechanical device to implement the process of writing. Father and son Jaquet-Droz introduced in 1774 three android automata often considered to be the most spectacular and appealing of the entire period: a writer, a draftsman [draughtsman], and the harpsichord player (see Adelheid Voskuhl: Androids in the enlightenment, University of Chicago press, Chicago, London 2013, page 5). This automaton [“miracle writing machine”] is not an android automaton, strictly speaking, since the writing mechanism is not located in the body of the writing figure […] (see Adelheid Voskuhl: Androids in the enlightenment, University of Chicago press, Chicago, London 2013, page 31). The harpsichord player is technically and artistically more sophisticated than the dulcimer player. She is bigger, has more movable parts, and has a larger gestural and musical repertoire. The hammer-wielding dulcimer player does not require the same minute technical detail, since she needs no finger-moving mechanics. She also does not move her upper body. The most distinct moving parts apart from her arms […] are her head and eyes (see Adelheid Voskuhl: Androids in the enlightenment, University of Chicago press, Chicago, London 2013, page 132).

With the dulcimer player and the organist, the mechanism is outside of the figure (underneath the footstool): The most spectacular of all automata that have survived are the writer, the artist [draughtsman], and the musician produced by Pierre Jaquet-Droz (1721–1790) and his son Henri-­Louis (1752–1791) of Geneva. Father and son combined all the technical developments known in their time in an effort to produce a machine that faithfully imitated a human being, and their efforts were as successful as any have ever been (see Silvio A. Bedini: The role of automata in the history of technology, in: Technology and culture, volume 5, 1964, no 1, page 39).

The works of Jaquet-Droz belong to the best known automaton figures: Automaton writers and keyboard players were made by a number of craftsmen, but none achieved the fame of the three made by Jaquet-Droz father and son and extant today in Switzerland (see Arthur W. J. G. Ord-Hume: Clockwork music, George Allen & Unwin Ltd., London 1973, page 18). The automatons of Neuchâtel represent an enormous step forward in automaton technology. One has to have seen the roughly 70  cm high figures in order to fully appreciate this achievement of the eighteenth century. The writer can be programmed to produce any arbitrary text up to 40 characters long. The machinery is housed entirely in the body and thus several orders of magnitude more reliable than the work

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of von Knaus (see Heinz Zemanek: Schweizer Automaten, in: Elektronische Rechenanlagen, volume 8, 1966, no. 5, page 214). Les chefs-d’œuvre de l’horlogerie sont sans conteste les automates androides du XVIIIe siecle, notamment ceux des Jaquet-Droz qu’on peut voir au musée de Neuchâtel (see Pierre de Latil: L’homme et la machine, Librairie Hachette, Paris 1965, page 23). The greatest clockwork creations are without doubt the automaton androids of the eighteenth century, especially those of Jaquet-Droz, on view in the Musée de Neuchâtel.

15.1.8  T  he Mechanical Clock with a Writing Figure of the Beijing Palace Museum In the history of technology in the West, the Chinese mechanical “writer” (see Figs. 15.15, 15.16, 15.17, 15.18, 15.19, 15.20, 15.21, 15.22, 15.23, 15.24, and 15.25) is virtually unknown. Obtaining illustrative material from the museum of the Forbidden City proved to be extremely costly and time-consuming. The 231 cm high, still functional musical figure automaton of Timothy Williamson is comprised of a carved wooden coffee table, on which a gold-plated copper fourstorey tower rests. The four storeys accommodate (from top to bottom) dancing figures with a scroll, a jaquemart (bell ringer), a clock, and a writer, which composes a predefined, unchanging text consisting of eight Chinese characters with a brush on paper. The device is not programmable. The movements are controlled from three round gear wheels (see Laurence Bodenmann; Morghan Mootoosamy (editor): Automates et merveilles, Editions Alphil, Neuchâtel 2012, pages 49–50). Such devices, called singsongs, were very expensive. Horloge de l’écrivain, en cuivre doré. Fabriquée en Angleterre au 18e siècle. Avec une hauteur de 231  cm et la base d’un diamètre de 77  cm. Au moment de sonner 3h-6h-8h-12h, la musique fonctionne, un automate agenouillé écrit la phrase suivante: “Que les rois de tous les pays viennent rendre hommage à notre empereur.” L’horloge est signée par le maître anglais Williamson, mais c’est en fait on ouvrage de l’horloger suisse Jaquet-Droz (see Pu Zhang; Fuxiang Guo: L’art de l’horlogerie occidentale et la Chine, China international press, Peking 2005, pages 90–91).

Automaton clock with writer, made of gold-plated copper. Manufactured in England in the eighteenth century. The clock is 231 cm high, with a base 77 cm in diameter. When the clock strikes 3, 6, 8, and 12 o’clock, a melody sounds and a [half-]kneeling automaton figure write the following sentence: “May the Kings of all lands come and pay homage to our emperor.” The clock is signed by the English master clockmaker Williamson but is actually the work of the Swiss watchmaker Jaquet-Droz. The Palace Museum is in possession of 13 works of Jaquet-Droz, for example, a gold-plated copper clock incorporating a singing bird with moving beak, wings, and tail, as well as other table clocks and pocket watches (see Fu Xiang Guo; Xue Ling Guan: Les collections de Jaquet-Droz au musée de la Cité interdite, in: Nicole Bosshart (editor): Automates et merveilles. Merveilleux mouvements... surprenantes mécaniques, Editions Alphil, Neuchâtel 2012, pages 45–49).

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Fig. 15.15  Hall of clocks and watches of the Beijing Palace Museum. Table at the entrance. (© Peter Geiger 2019)

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Fig. 15.16  Gilt bronze clock with writing figure (Williamson, London 1780) (1). This very rare picture shows the “writer” of Timothy Williamson, which composes a predefined short Chinese text with a brush. A clock is also built into the multistorey tower, and a bell ringer announces each hour. (© Palace Museum, Beijing)

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Fig. 15.17  Gilt bronze clock with writing figure (Williamson, London 1780) (2). The paper is clamped under a frame. On the bottom is a blank sheet of paper. The automaton is still working. (© Peter Geiger 2019)

Fig. 15.18  Gilt bronze clock with writing figure (Williamson, London 1780) (3). Side view of the writer (1). (© Peter Geiger 2019)

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Fig. 15.19  Gilt bronze clock with writing figure (Williamson, London 1780) (4). Side view of the writer (2). (© Peter Geiger 2019)

Fig. 15.20  Gilt bronze clock with writing figure (Williamson, London 1780) (5). The creator of the clock was apparently Timothy Williamson. (© Peter Geiger 2019)

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Fig. 15.21  Gilt bronze clock with writing figure (Williamson, London 1780) (6). Jaquemart (1). (© Peter Geiger 2019)

Fig. 15.22  Gilt bronze clock with writing figure (Williamson, London 1780) (7). Jaquemart (2). (© Peter Geiger 2019)

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Fig. 15.23  Gilt bronze clock with writing figure (Williamson, London 1780) (8). Dancing figures with a scroll (1). (© Peter Geiger 2019)

Fig. 15.24  Gilt bronze clock with writing figure (Williamson, London 1780) (9). Dancing figures with a scroll (1). (© Peter Geiger 2019)

Who Created the Chinese Musical Clock Automaton Figure? The Swiss clockmaker Thierry Amstutz is currently the best authority on the three automaton figures of Jaquet-Droz. He looks after the trio and regularly

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demonstrates them. On November 11, 2018, he visited the automaton on exhibit in Beijing. The Chinese clockmaker has opened a covering of a few cm2 over the left foot. However, due to the difficulty of accessing the construction of the automaton, it was not possible to see the entire inner mechanism. It is therefore not possible to completely assess the mechanism. It is not clear who built the writer (personal communications of November 9 and November 10, 2019). A further automaton of Timothy Williamson, a mechanical clock with a peacock and a jaquemart, is also in possession of the Beijing Palace Museum.

Fig. 15.25  Palace Museum Beijing, collection catalog. The authorship of the Chinese musical clock automaton has been disputed for decades. (Source: Simon Harcourt-Smith: A catalog of various clocks, watches, automata, and other miscellaneous objects of European workmanship dating from the eighteenth and the early nineteenth centuries, in the Palace Museum and the Wu Ying Tien, Peiping, Palace Museum, Peiping 1933, page 31)

15.1.9  M  agnificent Human and Animal Automatons from Le Locle Robots able to execute movements on their own existed as long ago as Leonardo da Vinci (mechanical lion) and Jacques Vaucanson (duck). Other magnificent examples are the “fée carabosse”, the old humpbacked witch, and the Ethiopian caterpillar automaton (see Figs.  15.26, 15.27, 15.28, 15.29, and 15.30).

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Fig. 15.26  The “old humpbacked witch” automaton (1). This android (from the beginning of the nineteenth century) depicts an old woman who moves with the help of two wooden walking sticks. (© Musée d’horlogerie du Locle, Château des Monts, Le Locle NE, picture: Renaud Sterchi)

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Fig. 15.27  The “old humpbacked witch” automaton (2). The figure is made of fire-gilded copper and the mechanism of brass. The creator of the “fée carabosse” is not known. (© Musée d’horlogerie du Locle, Château des Monts, Le Locle NE, picture: Renaud Sterchi)

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Fig. 15.28  The “old humpbacked witch” automaton (3). Functioning walking robots existed already 200 years ago. (© Musée d’horlogerie du Locle, Château des Monts, Le Locle NE, picture: Renaud Sterchi)

15.1  Automaton Figures

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Fig. 15.29  Silk caterpillar (1). The animal automaton is attributed to Henri Maillardet or Piguet & Capt (Geneva or London, beginning of the nineteenth century). It consists of gold rings, semi-­pearls, translucent red enamel, gemstones, and emerald stones. (© Musée d’horlogerie du Locle, Château des Monts, Le Locle NE, picture: Renaud Sterchi)

Fig. 15.30  Silk caterpillar (2). The artificial Ethiopian animal is in the possession of Fondation Edouard et Maurice Sandoz, Pully VD. (© Musée d’horlogerie du Locle, Château des Monts, Le Locle NE, picture: Renaud Sterchi)

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15.1.10  The Tower and Ship Automatons and Chariots For automaton figures there are no limits to creativity. In the following a few examples are introduced. In the Kunstkammer Wien, in Vienna, there are numerous precious, still functional automatons, many of which incorporate a musical mechanism (see Figs. 15.31, 15.32, 15.33, 15.34, 15.35, 15.36, 15.37, 15.38, and 15.39). Fig. 15.31  Bell tower automaton (around 1580). This fire-gilded automaton, attributed to Hans Schlottheim, is made of bronze. The painted figures of glass, metal, and wood are partly clothed. (© Kunsthistorisches Museum Wien/ KHM-Museumsverband)

15.1  Automaton Figures

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Fig. 15.32  Automaton in the form of a ship (1585). This gold-plated table automaton of Hans Schlottheim is made of silver, a copper alloy, and cold glaze, as well as oil paintings. The drive mechanism rolls over the table and plays music. The cannons can be loaded with black powder. (© Kunsthistorisches Museum Wien/KHM-Museumsverband)

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Fig. 15.33  Automaton in the form of a ship (1580–1590) (2). The mechanical galleon (battleship) of the Augsburg clockmaker Hans Schlottheim has three masts. Ten cannons are arranged around the hull. The seamen on the masts rotate and function as hourly chimes. The Musée national de la renaissance in Ecouen (France) possesses a similar ship automaton. (© Trustees of the British Museum, London)

15.1  Automaton Figures

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Fig. 15.34  Automaton in the form of a ship (1580–1590) (3). This view shows part of the mechanism. On the main deck are eight figures armed with swords. (© Trustees of the British Museum, London)

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Fig. 15.35  Automaton in the form of a ship (1580–1590) (4). Spring-driven clock mechanisms controlled the figures (e.g., the German Emperor Rudolf II on the throne, seven electoral princes, heralds, trumpeters, and drummers). (© Trustees of the British Museum, London)

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Fig. 15.36  Automaton in the form of a ship (1580–1590) (5). The analog automaton clock had gear wheels and cams. (© Trustees of the British Museum, London)

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Fig. 15.37  Automaton in the form of a chariot (1766). The English clockmaker James Cox built this “toy” for trade with Asia. A Chinese companion moves the clock-controlled vehicle. A spring drives the wheels, and the objects in the two hands of the woman are set into motion by tiny levers. The ornamental piece made use of gold, silver, diamonds, and pearls. (© Metropolitan Museum of Art, New York)

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635

Fig. 15.38  Automaton in the form of a triumphal chariot (about 1760–1770). Four horses draw the carriage. The British author is unknown. A spring-like device over the right front wheel drives this wheel and two interconnected shafts under the horses. The carriage can be controlled to the left and right. (© Metropolitan Museum of Art, New York)

Fig. 15.39  Escritoire with clock (about 1766–1772). This secretaire, borne by four bulls, stems from the Londoner James Cox. The butterflies are adorned with gemstones. A built-in, spring-driven music box plays melodies. (© Metropolitan Museum of Art, New York)

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15.1.11  Leonardo da Vinci’s Automatons Leonardo da Vinci (1452–1519) conceived, e.g., a self-propelled cart (1478), a mechanical knight controlled by cables (1495), and a mechanical lion (1515) more than 500 years ago. Furthermore, he designed a mechanical bird, a mechanical dragonfly, a mechanical drum, a hydraulic clock, a derrick, and a flying machine. In thousands of drawings scattered over Italy, France, England, and Spain, the polymath depicted a wide range of machines and instruments: shovel excavators (dredgers), paddlewheel boats, submarines, propellers, parachutes, printing presses, water-driven saws, grinding machines for concave mirrors, hodometers, clinometers, hygrometers, wind gages, military machines (e.g., tanks), and more. Leonardo was familiar with structural elements and devices, such as ball bearings, belt transmissions, cams, chains, connecting rods, crank drives, flywheels, gear drives, inclined planes, levers, pendulums, pulleys (rope hoists), ratchet pawls, screws, spiral spring drives, and trammels. According to information from Andrea Bernardoni (Florence), there is evidence that the highly gifted engineer from Vinci in fact did build the animal automaton (see Figs.  15.40, 15.41, 15.42, 15.43, and 15.44). It is not clear whether Leonardo made the knight (see Figs. 15.45, 15.46, 15.47, 15.48, 15.49, and 15.50). On the other hand, Claudio Giorgione (Milan) doubts that the vehicle (see Figs. 15.51, 15.52, 15.53, 15.54, 15.55, 15.56, 15.57, and 15.58) was actually constructed (as of May 2019). Note Certain automatons of Leonardo were referred to in the literature as robots. With the technically highly developed machines of Vaucanson and JaquetDroz (eighteenth century), however, one normally speaks of automaton figures and not of robots.

15.1  Automaton Figures

637

Fig. 15.40  The mechanical lion (1). A single spring controls several movements. The animal executes a few steps, sits onto its back legs, and moves its tail. The lion then opens its breast and shows a bouquet of flowers. Lilies adorn the coat of arms of the Medicis. Leonardo is said to have developed the artificial creature in 1515 for the visit of the French King in Milan. (© Museo Galileo, Florence)

Fig. 15.41  The mechanical lion (2). This model of Luca Garai (Opera laboratori fiorentini) gives an insight into the complex gearwork of the automaton figure. (© Museo Galileo, Florence)

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Fig. 15.42  The mechanical lion (3). The exploded drawing of Luca Garai (Bologna) shows the internal workings of the lion. (© Museo Galileo, Florence)

Fig. 15.43  The mechanical lion (4). The model is from Amboise, where Leonardo died (4). (© Château du Clos Lucé, Amboise)

15.1  Automaton Figures

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Fig. 15.44  The mechanical lion (5) . The Italian research center Leonardo3 constructed a functional wooden model of the animal with cable pulleys. (© Leonardo3 Museum, Milan)

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Fig. 15.45  The mechanical knight (1). The automaton depicts a mechanical model of the human body. (© Museo Leonardo da Vinci, Florence)

15.1  Automaton Figures

641

Fig. 15.46  The mechanical knight (2). The warrior, described in the Codice Atlantico, was intended for celebrations at the court of the Duke of Milan. (© Museo Leonardo da Vinci, Florence)

Fig. 15.47  The mechanical knight (3). Section of the warrior conceived in 1495. (© Museo Leonardo da Vinci, Florence)

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Fig. 15.48  The mechanical knight (4). The model of the medieval warrior is comprised, e.g., of wood, metal, and wire rope hoists, plastic, and glass. (© Leonardo3 Museum, Milan)

15.1  Automaton Figures

643

Fig. 15.49  The mechanical knight (5). The cables depict the muscles and nerves and the rollers the joints. (© Mark Rosheim: Leonardo’s lost robots, Springer-Verlag Berlin, Heidelberg 2006)

Fig. 15.50  The mechanical knight (6). The two arms are positioned differently. (© Mark Rosheim: Leonardo’s lost robots, Springer-Verlag Berlin, Heidelberg 2006)

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Fig. 15.51  The self-propelled cart (1). As the Codice Atlantico (Biblioteca Ambrosiana, Milan, foglio 812r) indicates, Leonardo designed this vehicle in 1478. (© Museo Galileo, Florence)

Fig. 15.52  The self-propelled cart (2). Model with spring drive of Leonardo. Some erroneously saw this as the precursor of today’s cars. (© Museo Galileo, Florence)

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645

Fig. 15.53  The self-propelled cart (3). Giorgio Canestrini constructed this model of the “carro automotore” from 1952 to 1955. Presumably the vehicle was intended for the theatrical stage. (© Museo Nazionale Scienza e Tecnologia “Leonardo da Vinci”, Milan, picture: Alessandro Nassiri 2009)

Fig. 15.54  The self-propelled cart (4). Functional models demonstrate that the vehicle could move about independently. (© Museo nazionale della scienza e della tecnologia “Leonardo da Vinci”, Milan, picture: Alessandro Nassiri 2009)

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Museo Leonardiano di Vinci There are two reconstructions of the self-propelled cart in the Museo Leonardiano di Vinci, Castello dei Conti Guidi. Roberto Antonio Guatelli manufactured a wooden model in 1952 based on a project of Giovanni Canestrini. It was donated to the museum by IBM Italy. Creator of another rebuild (2010) is the Etruria Musei based on a project of the Università degli studi di Firenze, facoltà di ingegneria, dipartimento di meccanica e tecnologie industriali.

Fig. 15.55  The self-propelled cart (5). This reconstruction can be seen in the Loire Valley. (© Château du Clos Lucé, Amboise)

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Fig. 15.56  The self-propelled cart (6). This model makes the complexity of the vehicle clear. (© Leonardo3 Museum, Milan)

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Fig. 15.57  The self-propelled cart (7). The programmable vehicle can drive straight ahead, to the right or to the left. Control is by means of interchangeable banana-shaped cams. The speed can be varied as well. (© Mark Rosheim: Leonardo’s lost robots, Springer-Verlag Berlin, Heidelberg 2006)

Fig. 15.58  The self-­propelled cart (8). The vehicle was driven with spiral springs. (© Mark Rosheim: Leonardo’s lost robots, Springer-Verlag Berlin, Heidelberg 2006)

15.2  Musical Automatons

649

15.2  Musical Automatons 15.2.1  Mechanical Musical Instruments Mechanical musical instruments are autonomous (self-playing) musical instruments. The sequence of notes is defined with the help of a memory, which includes control instructions for the notes (pitch and tone duration, i.e., tone beginning and end). The terms “mechanical musical instrument” and “musical automaton” are used mostly in the same sense (as a collective term). Common, manually operated and manually played musical devices constitute the opposite of mechanical musical instruments.

15.2.2  The Wide Variety of Instruments The mechanical musical instruments include, for example, the following (partly) spring-wound devices: • • • • • • • • • • •

Aeolian harps Carillons Disc music boxes/gramophones/phonographs Mechanical accordions (concertinas) Mechanical harpsichords and grand harpsichords Mechanical organs (barrel organs, flute-playing organs) Mechanical reed organs Mechanical violins Mechanical zithers Music boxes (cylinder musical boxes) Musical clocks (carillon clocks, flute-playing clocks, harp-playing clocks, dulcimer clocks, organ clocks, trumpeter clocks) • Musical snuffboxes (singing bird boxes) • Orchestrions • Serinettes (bird organs, small barrel organs). Also popular were music-making bird cages and horse carousels. Later there were vending machines (e.g., coin-operated phonographs). Mechanical musical instruments were found nearly everywhere, in waiting rooms of train stations, in restaurants, in dance halls, on steamships, and at county fairs.

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15.2.3  Music Boxes Antoine Favre-Salomon (Geneva, 1796) is considered the inventor of the steel rib. This is the prerequisite for the music box. The Leipzig instrument maker Paul Lochmann and the English inventor Ellis Parr are credited with the invention of the perforated plate and the disc music box (around 1885). Music boxes and magnificent musical instruments, such as the violin automaton and philharmonic organ, thrill specialists and lay persons to this day (see Figs.  15.59, 15.60, 15.61, 15.62, 15.63, 15.64, 15.65, 15.66, 15.67, 15.68, 15.69, 15.70, 15.71, 15.72, 15.73, 15.74, 15.75, 15.76, 15.77, 15.78, 15.79, 15.80, and 15.81).

Fig. 15.59  The Voix céleste (heavenly voice) cylinder-operated music box. This music box with swing-through tongues from Ste-Croix VD (around 1870) is capable of eight melodies. The pinned cylinder is made of brass and the sound ribs of steel. The most important Swiss music box builders were Mermod, Paillard, and Thorens. (© Museum für Musikautomaten, Seewen SO)

15.2  Musical Automatons

651

Fig. 15.60  The duplex cylinder-operated music box. This music box of Ami Rivenc, from Geneva (around 1890), is capable of ten melodies. It has two coupled half-cylinders and two sound combs, increasing the playing time. (© Museum für Musikautomaten, Seewen SO)

Fig. 15.61  The tambour timbres vue cylinder-operated music box, with a selection of eight melodies (Sainte-Croix VD, around 1895). The bells and drum enhance the range of sounds. (© Museum für Musikautomaten, Seewen SO)

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Fig. 15.62  The Sublime Harmonie Zither cylinder-operated music box. Music boxes were often lovingly designed, for example, with butterflies. This example of Karrer, from Teufenthal AH (around 1890), had eight melodies. (© Museum für Musikautomaten, Seewen SO)

Fig. 15.63  The Voix céleste cylinder-operated music box. The music box has swing-through tongues. This section shows the brass cylinders and the two sound combs. The Geneva clockmaker Antoine Favre invented the steel rib in 1796. (© Museum für Musikautomaten, Seewen SO)

15.2  Musical Automatons

653

Fig. 15.64  The Reuge music box (1). This picture shows the attachment of a spring to a high-­ precision music box. The once widespread music-playing devices are comprised, among other components, of a pinned cylinder and a sound comb. The melodies are stored on the cylinder. Disc-­type music boxes came later. The manufacturing of perforated discs (metal plates with nubs) was less demanding and therefore less expensive. The phonograph record (shellac disc and later the vinyl record) increasingly suppressed the music box. Nevertheless, the music box remains a popular gift and ornamental object. The Reuge SA in Sainte-Croix, in the Swiss Jura, is considered the world’s leading manufacturer. (© Reuge SA, SainteCroix VD)

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Fig. 15.65  The Reuge music box (2). The high-quality music boxes are comprised of four components. At the upper left is the sound comb with the steel ribs, which must be tuned to the correct pitch. At the right is the pinned cylinder. The uniformly long steel wire pins are pressed into the holes of the cylinder. The pins pluck the sound ribs, and the oscillations of the steel comb produce the sounds. The device is spring-wound. With some music boxes, it is possible to replace the cylinder. The metal pins of the sound recording medium control the presentation of the music. Many mechanical musical instruments had a spring drive. However, there were also automatons, such as clock towers, that were outfitted with a weight drive. (© Reuge SA, Sainte-Croix VD)

15.2  Musical Automatons

655

Fig. 15.66  The Harmonia disc-type music box. With this model, patented in 1895, the pegs in the steel disc were replaced by perforations. The inventor of the steel disc as the sound recording medium was the Leipzig instrument maker Paul Lochmann (1885). (© Museum für Musikautomaten, Seewen SO)

Fig. 15.67  The Edelweiss disc-type music box. This device from the Thorens company (Sainte-Croix VD) is equipped with a coin slot. The sound recording medium is a steel plate. (© Museum für Musikautomaten, Seewen SO)

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Fig. 15.68  The Ariston. Organette with perforated cardboard disc. Organettes are tonguedriven barrel organs (desk organs with hand crank). The manufacturer was the Leipziger Musikwerke, formerly the Paul Ehrlich & Co AG, Leipzig-Gohlis (patented 1882). (© Technisches Museum Wien, Vienna)

15.2.4  Singing Birds

Fig. 15.69  Singing birds. The Swiss clockmakers Pierre Jaquet-Droz and Henri-Louis Jaquet-­ Droz are considered the creators of this musical device (1780). Tiny precision mechanical song birds once decorated many snuffboxes. Luckily these magnificent birds of paradise, with colorful feathers and long tail feathers, still exist today. (© Reuge SA, Sainte-Croix VD)

15.2  Musical Automatons

657

Fig. 15.70  Mirror with singing bird (1). The Rochat brothers in Geneva manufactured this artistic mirror (around 1820). The fantasy in the styling of mechanical musical instruments was almost unlimited. (© Musée d’horlogerie du Locle, Château des Monts, Le Locle NE (picture: Renaud Sterchi))

Fig. 15.71  Mirror with singing bird (2). This section shows the singing bird. (© Musée d’horlogerie du Locle, Château des Monts, Le Locle NE (picture: Renaud Sterchi))

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Fig. 15.72  Singing bird music box (1). The Rochat brothers in Geneva manufactured this music box in the first quarter of the nineteenth century. (© Musée d’horlogerie du Locle, Château des Monts, Le Locle NE (picture: Renaud Sterchi))

Fig. 15.73  Singing bird music box (2). The “snuffbox” conceals a musical mechanism. (© Musée d’horlogerie du Locle, Château des Monts, Le Locle NE (picture: Renaud Sterchi))

15.2  Musical Automatons

659

Fig. 15.74  Singing bird music box (3). The popular musical automatons were richly decorated. (© Musée d’horlogerie du Locle, Château des Monts, Le Locle NE (picture: Renaud Sterchi))

Fig. 15.75  Singing bird cage (1). This anteroom clock (around 1790) is attributed to Pierre Jaquet-Droz, from La Chaux-de-Fonds. (© Musée d’horlogerie du Locle, Château des Monts, Le Locle NE (picture: Renaud Sterchi))

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Fig. 15.76  Singing bird cage (2). This clock (around 1790) with three singing birds, a striking mechanism, and a bird organ with seven melodies is attributed to Jaquet-Droz, from Geneva or Bienne BE. It was intended for the market in Constantinople and was comprised of brass, enamel, and glass. (© Museum für Musikautomaten, Seewen SO)

15.2  Musical Automatons

661

15.2.5  Train Station and Chalet Automatons

Fig. 15.77  The “Sissach BL” train station automaton. This entertainment machine of the Sainte-Croix VD music box manufacturer Auguste Lassueur (from 1898) embodies dancing dolls and a carousel. Such coin-operated automatons were once found in the waiting rooms of train stations. The music boxes were manufactured primarily in Geneva and in the Vaud Jura. (© Museum für Musikautomaten, Seewen SO)

Fig. 15.78  Chalet with clock and musical mechanism. Such rural houses were popular souvenirs (Switzerland, around 1900). (© Museum für Musikautomaten, Seewen SO)

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15.2.6  Violin and Organ Automatons

Fig. 15.79  The Phonoliszt Violina (self-playing violin) (1). The pneumatic violin automaton of the Leipzig company Ludwig Hupfeld AG is comprised of a piano and three violins. A paper note roll controls the Hupfeld Violina. These magnificent instruments (dating from 1908) are still functional today. (© Technisches Museum Wien, Vienna)

15.2  Musical Automatons

663

Fig. 15.80  The Phonoliszt Violina (self-playing violin) (2). Even today these violin automatons fascinate both young and old. (© Museum für Musikautomaten, Seewen SO)

Fig. 15.81  The Mortier organ (around 1915). The builder of this dance organ (serial no. 1010) was the Antwerp organ maker Theophile Mortier. (© Museum für Musikautomaten, Seewen SO)

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15.2.7  Sound Recording Media For the musical program, there were different sound recording media: • • • •

Pinned cylinder (wood or brass) Perforated disc (steel, sheet iron, tin plates, cardboard) Perforated cardboard tape Perforated paper roll.

Pegged cylinders, perforated discs, and perforated tapes were widely used sound recording media. Besides wire pins, wire bridges were also employed for the cylinders. Contrary to these, on phonograph records, magnetic tapes, and optical discs (CD and DVD), sound waves are recorded. Many mechanical musical instruments function as if by magic, and some have a treadle drive (pedal). Various methods existed for sound recording and sound reproduction. With the emergence of the phonograph record and the gramophone (mechanical record player), punched paper and cardboard tapes, brass cylinders, cardboard, and sheet metal discs disappeared as the sound recording media.

15.2.8  Talking Machines A distinction is made between two types of “talking” machines: • Phonographs (tinfoils, wax cylinders) • Gramophones (shellac discs). Remarks “Talking” machines were originally devices for the simulation of the human voice. Horns were used for certain gramophones. Shellac is a tree resin. The Slovakian baron Wolfgang von Kempelen, the inventor of the chessplaying turk, built a “talkin” machine as early as 1791. Inventions 1877 The phonograph of Thomas Edison 1887 The gramophone with shellac disc of Emile Berliner Remarks Phonographs, gramophones, magnetic audio devices, and radios belong to the devices for the reproduction of music. Important Swiss manufacturers of mechanical musical instruments were E.  Paillard & Cie., Hermann Thorens, and Mermod frères, all in SainteCroix VD.

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665

Drive Mechanisms Numerous types of drives were conceived for mechanical musical instruments: springs, hand cranks, weights, water (turbines), hot air, pressurized air, and current (electric motors). Along with manual drives, treadle drives (pedals) also exist.

15.2.9  A  utomaton Figures and Musical Automatons in Museums Switzerland A visit to informative Swiss collections can be highly recommended: these include the Museum für Musikautomaten in Seewen SO, Musée Cima (Centre international de la mécanique d’art), Sainte-Croix (VD), Musée Baud, L’Auberson (VD), Museum für Uhren und mechanische Musikinstrumente, Oberhofen BE, and the Musée d’art et d’histoire, Neuchâtel. In Sainte-Croix the manufacture of mechanical musical instruments is also described. The Musée des arts et sciences von Sainte-Croix is also joined to a historical workshop, the “Atelier de mécanique ancienne du Dr Wyss,” with tooling machines for the manufacturing of music boxes. A new museum is planned, which will combine the two museums in the center of Sainte-Croix and in L’Auberson VD. The exhibit in Seewen houses a huge, self-playing philharmonic organ built around 1913 by M. Welte & Söhne, Freiburg im Breisgau, for the ocean liner Britannic. The Britannic was built in Belfast, Ireland, and was the sister ship of the Titanic, which sunk in 1912. The pneumatic organ plays from music rolls (paper rolls). Note The Reuge SA company (Sainte-Croix) still manufactures music boxes, singing birds, and clocks today. The Ed. Jobin AG in Brienz BE also makes music boxes. Other Countries (Selection) Mechanical music instruments can, for example, also be admired at the following sites: in the Auto- und Technikmuseum, Sinsheim; the Deutsches Musikautomatenmuseum, Bruchsal; the Deutsches Phonomuseum, St. Georgen; the Elztalmuseum, Waldkirch; the Museum mechanischer Musikinstrumente, Königslutter; the Schwarzwald-Museum, Triberg; Siegfrieds mechanisches Musikkabinett, Rüdesheim am Rhein; the Technikmuseum Speyer with the Museum Wilhelmsbau, the Deutsches Museum, Munich; as well as the Technisches Museum Wien, Vienna; the Musée des arts et métiers, Paris; and the Nationalmuseum in Utrecht, Netherlands. The Deutsches Musikautomaten-Museum in Bruchsal (near Karlsruhe) is in possession of a Titanic organ. Other collections of musical instruments with musical automatons include the Muziekinstrumentenmuseum (Musée des instruments de musique) in

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Brussels, Museum für Musikinstrumente in Leipzig, and the Musée de la musique der Philharmonie de Paris in Paris.

15.2.10  The Componium Johann Nepomuk Mälzel, who also traveled around with the chess-playing turk of Wolfgang von Kempelen, in fact invented the panharmonicon (1805) and not the metronome with which he is generally credited, which is actually the work of Diederich Nikolaus Winkel (1814), who created a musical composing automaton, a componium with random generator (today in the Musikinstrumentenmuseum of the Royal Belgian Conservatory in Brussels) in 1821 (see Heinz Zemanek: Geschichte des Automaten: Das Componium von Winkel, in: Elektronische Rechenanlagen, volume 8, 1966, no. 2, pages 61–62, as well as Renße Lyr: Une merveille de mécanisme... Le componium de T. N. Winkel, in: Alfred Chapuis (editor): Histoire de la boîte à musique et de la musique mécanique, Edition Scriptar SA, Lausanne 1955, pages 113–122). The full name of the inventor was Thierry Nicolas Winkel). Athanasius Kircher also designed a mechanical composing machine. Famous composers have dealt with mechanical music (see box). Composers Several classical composers wrote music for mechanical musical instruments, for example, Carl Philipp Emanuel Bach, Johann Sebastian Bach, Ludwig van Beethoven, George Frideric Handel, Franz Joseph Haydn, Leopold Mozart, and Wolfgang Amadeus Mozart (see Wolfram Metzger: Musikautomaten, Info Verlagsgesellschaft, Karlsruhe 1995, page 30; Arthur W. J. G. Ord-­Hume: The musical clock, Mayfield books, Ashbourne, Derbyshire 1995, pages 102–118; and Alexander Buchner: Mechanische Musikinstrumente, Verlag Werner Dausien, Hanau/Main 1992, pages 225–226).

15.3  Chess Automatons In addition to genuine automatons, there were also sham automatons. The best known example was probably the chess-playing turk (1770) of Wolfgang von Kempelen. A human player was hidden inside the machine. Charles Babbage is said to have lost a game of chess against the “automatic” chess machine in 1819. The machine was later destroyed in a fire.

15.3  Chess Automatons

667

15.3.1  The Niemecz Chess Automaton In Bohemia Joseph Niemecz (1750–1806) (Pater Primitivus Niemecz), court chaplain and librarian of the Esterhazy court and builder of mechanical musical instruments, is said to have made a chess automaton, which has however not been preserved. Niemecz was probably the author of the book “Beschreibung des Schlosses Esterhäz,” which appeared in Bratislava in 1784. And so there were a number of ornate musical automatons in the princely castles in Eisenstadt and Esterhäza, partly of his work. Among these were a music-making spinning wheel, a music-making armchair, a sounding pocket watch, and a chess automaton. The most grotesque were the naked figures of Adam and Eva, coupled with waterworks in the large hall of the castle in Eisenstadt (see Ernst Fritz Schmid: Joseph Haydn und die Flötenuhr, in: Zeitschrift für Musikwissenschaft, volume 14, 1932, no. 4, page 198).

15.3.2  The End-Game Automaton of Torres Quevedo The Spanish engineer Leonardo Torres Quevedo, who also constructed an aerial cableway across the Niagara Falls, created two chess automatons (see Table 15.5). The first of these, dating from 1912, was demonstrated in Paris in 1914. The machine plays with a king and rook (white) against a king (black). The second model dates from 1920 (see Fig. 15.82). Both machines have survived (in Madrid). Fig. 15.82  The second chess automaton of Torres Quevedo. The first chess program did not originate with Konrad Zuse or Alan Turing, as one often reads. The machine of Torres Quevedo is more than 30 years older. (© Museo Leonardo Torres Quevedo, Escuela técnica superior de ingenieros de caminos, canales y puertos. Universidad politécnica de Madrid)

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Table 15.5  Early (genuine) chess automatons Historical chess automatons Inventor Automaton Leonardo El ajedrecista (The chess player) Torres Quevedo Leonardo El ajedrecista (The chess player) Torres Quevedo

Country Spain

Year 1912

Spain

1920

Site Museo “Torres Quevedo”, Madrid Museo “Torres Quevedo”, Madrid

Attributes Oldest (genuine) Chess automaton Second oldest (Genuine) Chess automaton

© Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020

Note Electronic chess computers and chess programs experienced an upswing in the 1970s (see Herbert Bruderer: Nichtnumerische Datenverarbeitung, Bibliographisches Institut & F.  A. Brockhaus AG, Wissenschaftsverlag, Mannheim, Leipzig, etc., 1980, section “Computerschach”, pages 119–136 and 227–231).

15.4  Typewriters Two different types of writing machines must be distinguished: machines for handwriting and printing, on the one hand and ornate androids and practical tools for daily use on the other hand. As with the calculating machine, there were many inventors and precursors of the typewriter (see Table 15.6). Below are a few milestones along the way.

Table 15.6  Early development of the mechanical typewriter (selection) The origin of the typewriter Inventor Henry Mill Pellegrino Turri Karl Drais Giuseppe Ravizza Peter Mitterhofer Rasmus Malling-Hansen Christopher Latham Sholes Carlos Glidden Samuel W. Soulé

Country England Italy Germany Italy Italy Denmark USA USA USA

© Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020

Year 1714 1808 1821 1855 1864 1865 1868 1868 1868

15.4 Typewriters

669

The development of the typewriter is described in the following (see box). The History of the Typewriter 1714 1749 1760 1762 1770 1772 1823 1829 1832 1833 1843 1844 1850 1850 1851 1852 1854 1855 1856 1857 1863 1864 1865 1868 1872

Patent for a typewriting machine by Henry Mill (England) “Writing harpsichord” of Pierre Carmien (France) “Miraculous writing machine” handwriting automaton of Friedrich Knaus (Germany) “Copiste secret” of Leopold Neipperg (Austria) Handwriting automaton of Timothy Williamson (England) Handwriting automaton “L’écrivain” von Pierre Jaquet-Droz (Switzerland) “Tachigrafo” or “tachitipo” of Pietro Conti (Italy) Patent for the “typographer” of William Austin Burt (USA) Typewriting machine of Karl Drais (Germany) Patent for the “plume typographique” of Xavier Progin (France) Patent for the “mechanical chirographer” of Charles Thurber (USA) Patent for the “stéréographe” of Gérard Labrunie (France) Typewriting machine of Oliver T. Eddy (USA) “Clavier imprimeur” of Pierre Foucauld (France) “Typographer” of Charles Wheatstone (England) Patent for the “mechanical typographer” of John M. Jones (USA) Patent for the “typograph” of Robert S. Thomas (USA) Patent for the “cembalo scrivano” of Giuseppe Ravizza (Italy) Typewriting machine of John H. Cooper (USA) Patent for the typewriting machine of Samuel William Francis (USA) Patent for the “pterotype” typewriting machine of John Pratt (USA) Typewriter of Peter Mitterhofer (Italy) “Skrivekugle” (writing ball) of Rasmus Malling-Hansen (Denmark) Patent for the “typewriter” of Christopher Latham Sholes, Carlos Glidden, and Samuel W. Soulé (USA) Takygraf of Rasmus Malling-Hansen (Denmark).

Sources August Baggenstos: Von der Bilderschrift zur Schreibmaschine, Zurich, Herrliberg 1977, pages 19–52 Ralph-Helmut Kwauka; Roland Schwarz: Die Schreibmaschinen, Technische Sammlungen der Stadt Dresden, Dresden 2001 Ernst Martin: Die Schreibmaschine und ihre Entwicklungsgeschichte, Verlag Peter Basten, Aachen 1949, pages 5–64

670

15  Historical Automatons and Robots

Technisches Museum Wien (editor): Schreiben wie gedruckt, Technisches Museum Wien, Vienna 2005/2006, Alfred Waize: Peter Mitterhofer und seine fünf Schreibmaschinenmodelle, Desotron Verlagsgesellschaft, Erfurt, 2nd edition 2003 International Rasmus Malling-Hansen society Schreibmaschinenmuseum, Partschins (South Tyrol, Italy). Notes Among the most important inventors of the typewriter are Giuseppe Ravizza, Peter Mitterhofer, Rasmus Malling-Hansen, and the trio of Christopher Latham Sholes, Carlos Glidden, and Samuel W.  Soulé. Particularly noteworthy are cryptographic, stenographic, music note, and Braille typewriters. There were even models for syllabic writing. From South Tyrol come the typewriting machines of Peter Mitterhofer (see Figs. 15.83, 15.84, and 15.85). Four (different) models have been preserved at the following sites: • Dresden model: Technische Sammlungen, Dresden • Meran model: Palais-Mamming-Museum, Meran (1866) • Vienna model: Technisches Museum Wien, Vienna (two specimens, 1864 and 1869). The writing ball of the Danish inventor and pastor Rasmus Malling Hansen (see Fig. 15.86) has gone down in history.

Fig. 15.83  Mitterhofer’s typewriting machine (1). This picture shows the Vienna model of 1869. In Vienna there is also a second model (1864). (© Technisches Museum Wien, Vienna)

15.4 Typewriters

671

Fig. 15.84  Mitterhofer’s typewriting machine (2). An important but neglected inventor of the typewriter comes from South Tyrol: Peter Mitterhofer. This photograph shows a reconstruction of the first model (1864). (© Schreibmaschinenmuseum, Partschins)

Fig. 15.85  Mitterhofer’s typewriting machine (3). The completed Meran model (1866) is comprised largely of metal. Thanks to its case shift, it can write both capital and small letters, as well as numerals. At the left are the typebars, and on top is the typing cylinder. (© Palais Mamming Museum, Meran)

672

15  Historical Automatons and Robots

Fig. 15.86 The typewriting machine of Rasmus Malling Hansen. The keys of the writing ball have only capital letters and numerals. (© Tekniska museet, Stockholm)

15.5  Clocks 15.5.1  An Enormous Range of Clocks The development of the clock goes back to antiquity. Among the early forms were the sundial, water clock, sand glass, and geared clock. The stationary mechanical clocks (e.g., church tower clocks, wall clocks, and pedestal clocks) and the portable mechanical clocks (e.g., wristwatches, pocket watches, and neck watches) are usually driven by a weight or a wound spring. Clocks exist in many forms (see box). Clocks Numerous primitive clocks and art clocks are known, for example: • Primitive clocks Sundials, water clocks (clepsydras), fire clocks (candle, slow match, oil), and sand glasses (e.g., hourglasses) • Geared clocks (stationary and portable) Astronomical clocks, church clocks, city hall clocks, longcase clocks, wall clocks, table clocks, pocket watches, wristwatches, and automaton clocks: picture clocks (partly with music-playing mechanism) and musical clocks (continued)

15.5 Clocks

673

Different drive types must be distinguished: • Weight drives • Spring drives • Electrical drives. A further classification distinguishes between foliot clocks and pendulum clocks. Especially for geared clocks, many different forms exist: altar clocks, box clocks, bracket clocks (clocks with truncated, i.e., shortened, pendulum), cartel clocks (French wall clocks), chair clocks, chronometers (marine chronometers), column clocks, console clocks, flute-playing clocks, framed clocks, iron chamber clocks, lantern clocks, mantlepiece clocks, mirror clocks, neck watches, onions (pocket watches in onion form), pendant watches, pendulum clocks, plate clocks, rolling ball clocks, saw blade clocks (toothed rack clocks), skeleton clocks, tabernacle clocks, time stamp clocks, and wooden wheel clocks. A special case is the night dial (nocturnal, moondial). Newer developments include quartz, atomic, and digital clocks. From 1792 to 1806, decimal clocks were made (during the French revolution). These were based on the (unpopular) decimal time. A day had 10 h, each 100 min long, and each minute was comprised of 100 s. Time clocks were used to record working time. Around 1880, there were also pocket watches in Switzerland with a mechanical digital display (numerals instead of watch hands).

In scientific applications, particularly in astronomical instruments, clocks played a major role (see Figs. 15.87, 15.88, 15.89, 15.90, 15.91, 15.92, 15.93, 15.94, 15.95, 15.96, 15.97, 15.98, 15.99, 15.100, 15.101, 15.102, 15.103, 15.104, 15.105, 15.106, 15.107, 15.108, 15.109, 15.110, 15.111, 15.112, 15.113, 15.114, 15.115, 15.116, 15.117, 15.118, 15.119, 15.120, 15.121, 15.122, 15.123, 15.124, 15.125, 15.126, 15.127, 15.128, 15.129, 15.130, 15.131, 15.132, 15.133, 15.134, 15.135, 15.136, 15.137, 15.138, 15.139, 15.140, 15.141, 15.142, 15.143, 15.144, 15.145, 15.146, 15.147, 15.148, 15.149, 15.150, 15.151, 15.152, 15.153, 15.154, and 15.155), for example, they controlled globes. Planetariums should also be mentioned here.

674

15  Historical Automatons and Robots

Fig. 15.87  Elephant clock. This unusual device was invented by Ibn al Razzāz al-Jazarī (1136–1206).The bird on the dome chirped every half hour. The man (at the top) lets a ball fall into the mouth of the dragon, and the driver beats the elephant with his whip. The book is of Syrian origin. (© Metropolitan Museum of Art, New York)

15.5 Clocks

675

Fig. 15.88  Sand glass (1). This sand glass dates from the sixteenth century (from: Pierre Dubois: Histoire de l’horlogerie depuis son origine jusqu’à nos jours: précédée de recherches sur la mesure du temps dans l’antiquité et suvie de la biographie des horlogers les plus célèbres de l’Europe, Administration du Moyen Age et la Renaissance, Paris 1849). (Source: ETH Library, Zurich, Rare books collection)

Fig. 15.89  Sand glass (2). The origin and year built of this wood and glass timepiece are unknown. (© ETH Zurich, Collection of astronomical instruments)

676

15  Historical Automatons and Robots

Fig. 15.90  Quadruple hour glass of the bell ringer of St. Thomas, Leipzig (seventeenth century). Johann Sebastian Bach was active in this church. The clock, created by Christian Heining, has a spruce frame with engravings pasted on. Each glass bears the time figures 1/4, 2/4, 3/4, and 4/4 (with a running time of 1 h) painted in red. (© Historisches Museum Basel, picture: Peter Portner)

15.5 Clocks

677

Fig. 15.91  Nocturnal. Leonhard Hartmann built this brass night dial (1648). The clock time was determined from the positions of the stars. (© ETH Zurich, Collection of astronomical instruments)

Fig. 15.92  Day and night clock. David Georg Polykarp Hahn from Kornwestheim, Germany, the younger brother of Philipp Matthäus Hahn, built this clock in 1776. The Roman numerals on the outer ring and the pointing hand above are cut through the brass face and backed with red silk so that when a burning candle is placed behind them they are visible at night. The ring rotates anticlockwise, and the pointing finger indicates the time. For the daytime the hours are indicated on the enamel dial in Roman numerals and 5-min intervals in Arabic numerals. (© Historisches Museum Basel, Bild: Maurice Babey)

678

15  Historical Automatons and Robots

Fig. 15.93  Ring dial. The age of this brass clock by Christian Jenderich and J.  Linzner is unknown. Sundials allow the determination of the local time based on the position of the rod’s shadow. According to the position of the dial plate, a distinction is made between horizontal, vertical, and equatorial sundials. (© ETH Zurich, Collection of astronomical instruments)

15.5 Clocks

679

Fig. 15.94  Universal ring dial. Georg Friedrich Brander built this brass astronomical instrument around 1760. Thanks to the cogged wheel, one can rotate the ring dial with the screws. A pointer (on the cogged wheel) indicates the alignment of the ring dial in relation to the bedplate, which has a circle graduation with four quadrants. The dial plate is divided into two 12-h parts (each in steps of 3  min). A decorative curved disc is attached to the inner meridian ring and bears the swiveling alhidade (the rotating arm of an angle measuring apparatus, with readout device) and can be rotated about the world axis. On both sides of the alhidade is a sighting device. The solar declination (angular distance from the celestial equator) can be set for each individual day, either in 12 signs of the zodiac or in a calendar divided into 12 months. (© ETH Zurich, Collection of astronomical instruments)

680

15  Historical Automatons and Robots

Fig. 15.95  Equatorial sundial (1782) of Philipp Matthäus Hahn from Echterdingen (Baden-­ Württemberg). The brass ring is calibrated to set the latitude of the particular location. The socket disc has a degree scale and a wind rose. The focused sunlight passes through two tiny apertures in the wall parallel to the axis and strikes the time scale on the inside of the box, so that either the mean time or the real local time can be read off the dial. Two hands indicate the hours in Roman numerals (I–XII) and the 5-min intervals in Arabic numerals. (© Historisches Museum Basel, picture: Maurice Babey)

15.5 Clocks

681

Fig. 15.96  Horizontal sundial (1). This brass sundial with compass dating from around 1700 is a work of Michael Butterfield. (© ETH Zurich, Collection of astronomical instruments)

Fig. 15.97  Horizontal sundial (2). J. C. Bartenschlager (Schaffhausen) built this brass table sundial around 1760. (© ETH Zurich, Collection of astronomical instruments)

682

15  Historical Automatons and Robots

Fig. 15.98  Box sundial (set of astronomical instruments) in the form of a pendant (1). The famous instrument builder Christoph Schissler the Elder from Augsburg constructed this threefold timekeeper (lid, plate, and base) of gilded bronze in 1580. (© Historisches Museum Basel, picture: Maurice Babey)

Fig. 15.99  Box sundial (set of astronomical instruments) in the form of a pendant (2). On the upper side of the plate is an engraved sundial with Roman numerals for a 16-h day (IV XII - VIII) and a folding gnomon. The compass in the bottom part of the box has a round opening cut out. The inside of the cover depicts a wind rose. (© Historisches Museum Basel, picture: Peter Portner)

15.5 Clocks

683

Fig. 15.100  Box sundial (set of astronomical instruments) in the form of a pendant (3). In the lower part is an equinoctial sundial with a folding gnomon and a concave sunken dial with engraved lines for the hours (9–24), the tropics, and the equator, together with the latitude at 45°. (© Historisches Museum Basel, picture: Peter Portner)

684

15  Historical Automatons and Robots

Fig. 15.101  Equatorial sundial. This portable brass and marble sundial with telescope were built around 1780 by Brander & Höschel (Augsburg). (© ETH Zurich, Collection of astronomical instruments)

Fig. 15.102  Sundial. This portable ivory sundial of Hans Troschel (Nuremberg, 1631) incorporates a compass. (© Musée international d’horlogerie, La Chaux-de-­Fonds NE/ picture: MIH)

15.5 Clocks

685

Fig. 15.103  The astrarium of Giovanni Dondi (Padua) (1). This marvel is a reconstruction of an astronomical clock from the second half of the fourteenth century. The seven dial plates represent the orbits of the sun, moon, and the five planets known at that time (Mars, Mercury, Venus, Jupiter, and Saturn). The Earth is at the center (in the geocentric system of Ptolemaeus from the second century). The clock is comprised in part of brass and is weightdriven. The reconstruction was made by Luigi Pippa (1985). (© Musée international d’horlogerie, La Chaux-de-Fonds NE/ picture: MIH)

686

15  Historical Automatons and Robots

Fig. 15.104  The astrarium of Giovanni Dondi (2). The weight-driven planetarium is equipped with a verge escapement. It was built from 1348 to 1364  in Padua, Italy. (© Uhrenmuseum Beyer, Zurich, picture: Dany Schulthess, Emmen)

15.5 Clocks

687

Fig. 15.105  The astrarium of Giovanni Dondi (3). The large astronomical clock also indicated the length of the individual days in hours and minutes. Alan Lloyd (UK) built this reconstruction in 1960. (© Uhrenmuseum Beyer, Zurich, picture: Dany Schulthess, Emmen)

688

15  Historical Automatons and Robots

Fig. 15.106  Frisian orrery (1). On the living room ceiling of a canal house in the Dutch town of Franeker is the world’s oldest functional planetarium. (© Koninklijk Eise Eisinga Planetarium, KE Franeker)

15.5 Clocks

689

Fig. 15.107  Frisian orrery (2). The precise moving model of the solar system with six planets was built between 1774 and 1781. (© Koninklijk Eise Eisinga Planetarium, KE Franeker)

690

15  Historical Automatons and Robots

Fig. 15.108  Frisian orrery (3). The central section of the wheelwork can be seen here. (© Koninklijk Eise Eisinga Planetarium, KE Franeker)

Fig. 15.109  Frisian orrery (4). The model was built by the Frisian carder Eise Eisinga. (© Koninklijk Eise Eisinga Planetarium, KE Franeker)

15.5 Clocks

691

Fig. 15.110  Zeitglockenturm (clock tower) in Bern (1). The tower clock (above), the astrolabe (below), and the tower figures (right) characterize the structure in the center of the city of Bern. The tower clock was once the city’s main timekeeper. It determined the time long before the introduction of a railway time. Travel times were measured from the clock tower. (© Markus Marti)

692

15  Historical Automatons and Robots

Fig. 15.111  Zeitglockenturm in Bern (2). The astrolabe was built with the original tower clock of 1405. The celestial bodies orbit the earth, which is at the center. Five planetary gods (Saturn, Jupiter, Mars, Venus, and Mercury) can be seen above the astrolabe. (© Markus Marti)

Fig. 15.112  Zeitglockenturm in Bern (3). The black-gold sphere of the moon pointer shows the respective lunar phase. Twelve zodiac symbols represent the stars. (© Markus Marti)

15.5 Clocks

693

Fig. 15.113 Zeitglockenturm in Bern (4). This view shows the lunar gear train. (© Markus Marti)

Fig. 15.114  Zeitglockenturm in Bern (5). The astrolabe also has a zodiac gearing mechanism. (© Markus Marti)

694

15  Historical Automatons and Robots

Fig. 15.115  Zeitglockenturm in Bern (6). Kaspar Brunner completed the main clockwork of the mechanical wheel clock in 1530. The five separate mechanisms are driven by a stone weight. The weights, which weight about 400 kg together, must be pulled up daily in the 20 m high cable shaft. The movement constitutes the central part of the monumental clock. The pointers on the large dials and on the astrolabe are driven from the hour wheel, which also controls the tripping of the two striking mechanisms and the moving clock figures. The 149 kg heavy pendulum ball was installed between 1690 and 1712 and replaced the original balance beam. The hour striking mechanism serves for the large bell, and the quarter-hour striking mechanism serves for the small bell. The animated figures comprise a mechanical rooster, as well as a moving bear and a mechanical jester (hour striking mechanism).The complex figure animation takes place hourly. (© Markus Marti)

15.5 Clocks

695

Fig. 15.116  Decorative astronomical clock monstrance. This clock dates from around 1600  in Augsburg. (© Uhrenmuseum Winterthur, Sammlungsausstellung Konrad Kellenberger, picture: Michael Lio)

696

15  Historical Automatons and Robots

Fig. 15.117  Pendulum clock. This drawing represents a trial arrangement of Christiaan Huygens (from: Christiaan Huygens: Christiani Hugenii [...] horologium oscillatorium sive de motu pendulorum ad horologia aptato demonstrationes geometricae, apud F. Muguet, Parisiis 1673). (Source: ETH Library, Zurich)

15.5 Clocks

697

Fig. 15.118  Clock tower. This gearwork mechanism is part of a mechanical church tower clock that strikes hourly and quarter-hourly on three bells. The tripartite drive was manufactured in 1925 by the Ecole de mécanique, Neuchâtel. (© Musée international d’horlogerie, La Chaux-de-Fonds NE/ picture: J. Hoffman)

698

15  Historical Automatons and Robots

Fig. 15.119  Appenzell wooden wheel clock in Teufen AR from 1767. In some rural areas (such as Appenzell, Bern, Jura, Schwyz, Sertigtal GR, or Toggenburg SG), peasant artisans made such clocks from the seventeenth to the nineteenth century. (© Uhrenmuseum Winterthur, Sammlungsausstellung Konrad Kellenberger, picture: Michael Lio)

15.5 Clocks

699

Fig. 15.120  Longcase clock with flute and harp mechanism. Peter Kintzing and David Roentgen from Neuwied (Germany) built this clock around 1800. (© Museum für Musikautomaten, Seewen SO)

700 Fig. 15.121 Astronomical longcase clock (1). Philipp Matthäus Hahn from Kornwestheim created this clock in 1775 for the Basel silk manufacturer Wilhelm Brenner. The housing is made of massive walnut wood. The painted dial plates are attached with screws to a brass plate. (© Historisches Museum Basel, picture: Maurice Babey)

15  Historical Automatons and Robots

15.5 Clocks

701

Fig. 15.122  Astronomical longcase clock (2). The display system of Philipp Matthäus Hahn’s clock is complex: a main dial plate in the middle for minutes in mean time and two secondary dial plates for minutes in solar time (below) and seconds (above) in real local time. At the left: hours (below) and lunar displays with adjustable horizon (above), in the middle at the top: starlit sky over a fixed horizon, and at the right: sun displays with adjustable horizon (above) and calendar with month and day of the week (below). (© Historisches Museum Basel, picture: Maurice Babey)

702

15  Historical Automatons and Robots

Fig. 15.123  Calendar clock of the State Chancellery in Fribourg (1). The builder of this representative equipment object from 1747 is unknown. The clock has five dials, a central main dial and four planetary dials. In the middle of the clock is the earth, and not the sun. The two red pointers of the main dial give the hours and minutes. The hour ring comprises two times 12 h. The numerals XII correspond to noon (above) and midnight (below). The pointed double pointer enables reading solar and lunar eclipses. The open-head pointer gives zodiacal information (position of the sun in the zodiac) and the lunar phases. (© Museum für Kunst und Geschichte, Fribourg/Brigitte Vinzens)

15.5 Clocks

703

Fig. 15.124  Calendar clock of the State Chancellery in Fribourg (2). In addition to the clock time, the main dial shows the zodiacs, the lunar phases, and solar and lunar eclipses. The four small dials indicate the positions of the five planets known at that time (top left Jupiter, top right Saturn, below left Venus and Mercury, and below right Mars). The month and day, day of the week, fixed and variable holidays, sunrise and sunset, and solar and lunar cycles (28 and 19 years) can be read from the nine small windows. The planetary dial at the lower left originally had two pointers. (© Museum für Kunst und Geschichte, Fribourg/Brigitte Vinzens)

704

15  Historical Automatons and Robots

Fig. 15.125  The pendule sympathique (1). The creator of this masterpiece was the world famous Neuchâtel watchmaker Abraham-Louis Breguet (1747–1823). At the top a pocket watch can be attached. After wearing, at 12 o’clock, the position of its minute hand is made to coincide with that of the table clock. (© Uhrenmuseum Beyer, Zurich, picture: Lucas Peters, Zurich, and Thierry Bösiger, Winterthur)

15.5 Clocks

705

Fig. 15.126  The pendule sympathique (2). This view shows the inner mechanism of the clock, which was manufactured 1808/1830 in Paris. (© Uhrenmuseum Beyer, Zurich, picture: Lucas Peters, Zurich, and Thierry Bösiger, Winterthur)

706

15  Historical Automatons and Robots

Fig. 15.127  The pendule of Albert Baillon (Paris). The rich ornamentation is possibly the work of André-Charles Boulle. The magnificent clock, dating from around 1715, is comprised of copper, bronze, enamel, and wood. (© Musée international d’horlogerie, La Chaux-deFonds NE/picture: MIH)

15.5 Clocks

707

Fig. 15.128  Pendule with organ mechanism of Pierre Jaquet-Droz. This magnificent clock with hourly and quarter-hourly striking on three bells dates from 1760 in La Chaux-de-­Fonds NE.  The organ mechanism comprises 13 metal pipes and has 8 melodies. On the white enamel dial plate, the hours are shown in Roman numerals and 5-min intervals in Arabic numerals, while the individual minutes are marked with strokes. A world famous pendule of this clockmaker designated “Le berger” is in the Palacio real in Madrid. (© Historisches Museum Basel, picture: Maurice Babey)

708

15  Historical Automatons and Robots

Fig. 15.129  The “Empire” pedestal clock (1). We have Pierre Jaquet-Droz from La Chaux-de-­ Fonds to thank for this emperor’s clock. (© Musée d’horlogerie du Locle, Château des Monts, Le Locle NE (picture: Renaud Sterchi))

15.5 Clocks

709

Fig. 15.130  The “Empire” pedestal clock (2). Here you see the rear face and the bird cage. (© Musée d’horlogerie du Locle, Château des Monts, Le Locle NE (picture: Renaud Sterchi))

Fig. 15.131  The “Empire” pedestal clock (3). This is how Pierre Jaquet-Droz from La Chauxde-­Fonds signed his work. (© Musée d’horlogerie du Locle, Château des Monts, Le Locle NE (picture: Renaud Sterchi))

710

15  Historical Automatons and Robots

Fig. 15.132  Renaissance table clock (1). Jeremias Metzger (1525–ca. 1599) created this marvelous work. (© Uhrenmuseum Beyer, Zurich, picture: Dominique Cohas, Paris)

15.5 Clocks

711

Fig. 15.133  Renaissance table clock (2). This clock dates from 1573 in Augsburg, Germany. (© Uhrenmuseum Beyer, Zurich, picture: Dominique Cohas, Paris)

712

15  Historical Automatons and Robots

Fig. 15.134  Ornate table clock (1). Jeremias Metzger from Augsburg created this table clock of fire-gilded bronze in 1570. The front side shows dials for hours, minutes, cardinal directions, signs of the zodiac, the position of the sun in the zodiac, and a calendar disc. (© Historisches Museum Basel, picture: Peter Portner)

15.5 Clocks

713

Fig. 15.135  Ornate table clock (2). This view shows the rear face with astrolabe (rete with 22 stars and sun and moon pointers) and underneath a dial showing the days of the week. On the side of the casing are six setting dials. (© Historisches Museum Basel, picture: Peter Portner)

714

15  Historical Automatons and Robots

Fig. 15.136  Astronomical table clock (1568). The clock mechanism is probably from the Augsburg clockmaker Jeremias Metzger. The clock shows the positions of the stars, the days of the week, the time with Roman and Arabic numerals, day and night hours, and the date. (© Metropolitan Museum of Art, New York)

15.5 Clocks

715

Fig. 15.137  English table clock (around 1600). This brass clock is equipped with a bell and an alarm clock and is the work of John or Nicolas Vallin (London). The horizontal dial plate incorporates a silver ring with Roman numerals. (© Musée international d’horlogerie, La Chaux-de-Fonds NE/ picture: MIH)

Fig. 15.138  German table clock with hourly striking and alarm (around 1670). The creator of this fire-gilded decagonal clock was Samuel Berckmann from Augsburg. Each side allows a view through small apertures of the mechanism, which is mounted on spiral pillars. The full hours are indicated in Roman numerals (I–XII), and there are pointers for the half- and quarter-hours (innermost). The alarum disc has Arabic numerals (1–12), and the bell is mounted on the bottom of the casing. (© Historisches Museum Basel, picture: Maurice Babey)

716

15  Historical Automatons and Robots

Fig. 15.139  “Cherry harvest” table clock (1). This clock dates from the beginning of the nineteenth century in Geneva. (© Musée d’horlogerie du Locle, Château des Monts, Le Locle NE (picture: Renaud Sterchi))

Fig. 15.140  “Cherry harvest” table clock (2). Lateral view. (© Musée d’horlogerie du Locle, Château des Monts, Le Locle NE (picture: Renaud Sterchi))

15.5 Clocks

717

Fig. 15.141  “Cherry harvest” table clock (3). The inside of the automaton clock conceals a striking mechanism. (© Musée d’horlogerie du Locle, Château des Monts, Le Locle NE (picture: Renaud Sterchi))

718

15  Historical Automatons and Robots

Fig. 15.142  Enameled gold clock with automaton and musical mechanism with the name “theater,” Geneva (around 1805). The musical clock employs a pinned cylinder. (© Uhrenmuseum Winterthur, Sammlungsausstellung Oscar Schwank, picture: Michael Lio)

15.5 Clocks

719

Fig. 15.143  Automaton clock with double shell casing (around 1770). The creator of this gold and gemstone work of art was James Cox (London). The eight rosettes (stars) rotate within the rotating frame. (© Metropolitan Museum of Art, New York)

720

15  Historical Automatons and Robots

Mechanical picture clocks were very popular (see box). Picture Clocks (Mechanical Pictures) In the nineteenth century, fantasy knew no limits. Pictures were coupled with mechanical equipment. On spring-wound moving images, for example, landscapes were depicted with waterfalls, windmills, sailboats, railroads, or lighthouses, always together with a clock.

Fig. 15.144  Picture clock (1). This clock depicts a sailboat, a tower, a windmill, and a suspension bridge. (© Musée Baud, L’Auberson VD)

Fig. 15.145  Picture clock (2). The painting on this clock portrays a blacksmith, a horse, and a church tower. (© Musée Baud, L’Auberson VD)

15.5 Clocks

721

Fig. 15.146  Picture clock (3). This moving image depicts children playing in front of a windmill. (© Musée Baud, L’Auberson VD)

Fig. 15.147  Picture clock (4). Spring-driven musical clocks with three-dimensional portraits were popular. (© Musée Baud, L’Auberson VD)

722

15  Historical Automatons and Robots

Fig. 15.148  Picture clock (5). The author of this painting, depicting a village with a clock tower, is unknown (first third of the nineteenth century). (© Museum für Kunst und Geschichte, Fribourg)

15.5 Clocks

723

Fig. 15.149  Pagoda automaton clock. This gilded bronze tower clock, built in 1780  in London, is probably the work of James Cox. The musical clock has a striking mechanism, together with dancing signs of the zodiac. Rolling glass rods convey the impression of flowing water. An East Asian pagoda is a Buddhist multistorey tower-like temple. (© Uhrenmuseum Beyer, Zurich, picture: Thierry Bösiger, Winterthur)

724

15  Historical Automatons and Robots

Fig. 15.150  Viennese crystal clock (1622/1627). The gold-plated table clock of Jost Bürgi has a mechanical globe and is comprised of copper alloy, silver, and mountain crystal, and the mechanism is made of brass. (© Kunsthistorisches Museum Wien / KHM-Museumsverband)

15.5 Clocks

725

Fig. 15.151  Viennese astronomical clock (around 1605). This gold-plated table clock, attributed to Jost Bürgi, is comprised of a copper alloy, silver, quartz, and glass, as well as topcoat painting. The mechanism is made of iron and brass. The (larger) dial plate for the first time includes a mechanical depiction of the heliocentric planetary system (at the top) with five pointers for the planets Mercury, Venus, Mars, Saturn, and Jupiter. Below a geocentric world view can be seen. The dragon hand requires nearly 19 years for one revolution. The device was designed for the prediction of solar and lunar eclipses. (© Kunsthistorisches Museum Wien /KHM-Museumsverband)

726

15  Historical Automatons and Robots

Fig. 15.152  The Wilhelmsuhr (1560–1561). With the aid of a complex clockwork, the planetary (orbit) clock of the clockmaker Eberhard Baldewein simulates all celestial movements in the sky. The four removable lateral walls each have two planetary discs with pointers, representing the planetary deities. The solar disc is designed as an astrolabe. A clock is fixed to the celestial globe (at the top) which shows the actual solar time. Baldewein’s artistic astronomical clock simulates the motions of the moon according to the classical Ptolemaean (geocentric) orbital theory. The goldsmith work and the engravings are from Hermann Diepel. (© Museumslandschaft Hessen Kassel, Astronomisch-physikalisches Kabinett)

15.5 Clocks

727

Fig. 15.153  Equatorial clock with cover lifted up (1591). The complex astronomical bracket clock of the clockmaker Jost Bürgi indicates the difference between the mean and the true movements of the sun and moon (so-called equation). The instrument maker utilizes the Copernican lunar orbit theory. The upper side of the cover houses an astrolabe. The circular dials on the lateral walls serve the following purposes: alarm mechanism, simulation of the lengths of day and night, indication of the day, and time display. Eight famous natural scientists are represented next to these, including Thales, Euclid, Archimedes, Hipparchus, Ptolemaeus, and Copernicus. The relief work is that of the goldsmith Hans Jacob Emck. In the four corners, feminine figures embody the most important virtues: righteousness, wisdom, prudence, and bravery. (© Museumslandschaft Hessen Kassel, Astronomischphysikalisches Kabinett)

728

15  Historical Automatons and Robots

Fig. 15.154  Tabernacle clock, Innsbruck (1547). This column clock stems from Niklaus Lants. (© Uhrenmuseum Winterthur, Sammlungsausstellung Konrad Kellenberger, picture: Michael Lio)

15.5 Clocks

729

Fig. 15.155  Tabernacle clock, Baden AG (around 1630), of George Strässler. (© Uhrenmuseum Winterthur, Sammlungsausstellung Konrad Kellenberger, picture: Michael Lio)

15.5.2  C  lockmakers as the Inventors of Automatons and Calculating Machines Many gifted scholars were unable to realize their ingenious ideas. Either they lacked the craftsmanship, or the required precision mechanics was (ostensibly) not yet adequately developed. Charles Babbage and Gottfried Wilhelm Leibniz completed their calculating machines only with great effort or not at all. The manufacture of practicable mechanical calculators became possible only with the clockmaker Philipp Matthäus Hahn. We are indebted to

730

15  Historical Automatons and Robots

ingenious clockmakers for magnificent cylindrical calculating machines: Jacob Auch, Anton Braun, Philipp Matthäus Hahn, Johann Jacob Sauter, and Johann Christoph Schuster. Clockmaker inventors also included, for example, Curt Dietzschold and Jean-Baptiste Schwilgué. The clockmaker Albert Steinmann from La Chaux-de-Fonds NE also built calculating aids. Furthermore, clockmakers such as Jacques Vaucanson, Friedrich Knaus, and Pierre Jaquet-Droz are the fathers of multifaceted automaton figures.

15.6  Looms Semiautomatic and Fully Automatic Looms Punched tapes or punched cards joined to tapes simplify work on looms (pattern control). Among the pioneers were Basile Bouchon (see Fig. 15.156), JeanBaptiste Falcon (see Fig.  15.157), Jacques Vaucanson, and Joseph-Marie Jacquard (see Fig. 15.158), all from France. Their achievements are on view in the Musée des arts et métiers in Paris. A working loom can be admired, for example, in the Appenzeller Volkskunde-Museum in Stein AR (see Figs. 15.159 and 15.160). Note The loom was already invented before Joseph-Marie Jacquard and punched card control before Charles Babbage and Herman Hollerith.

15.6 Looms

731

Fig. 15.156  The loom of Basile Bouchon (1725). This semiautomatic loom (functional model) is punched tape controlled. (© Musée des arts et métiers/Cnam, Paris, picture: Sylvain Pelly)

732

15  Historical Automatons and Robots

Fig. 15.157  The loom of Jean-Baptiste Falcon (1728). This semiautomatic loom (functional model) is punched card controlled, and the punched cards are bound together. (© Musée des arts et métiers/Cnam, Paris, picture: Sylvain Pelly)

15.6 Looms

733

Fig. 15.158  The loom of Joseph-Marie Jacquard (1804). This fully automatic loom is punched card controlled. In 1855 the mechanician Jean Marin built this functional model of the mechanical loom which was further developed by the silk weaver Joseph-Marie Jacquard. The concatenated cardboard cards were punched according to the required pattern. Charles Babbage also wanted to control his programmable analytical engine with punched cards. The upsurge of punched card machines began in 1890 with the American census (Herman Hollerith). (© Musée des arts et métiers/Cnam, Paris, picture: Studio Cnam)

734

15  Historical Automatons and Robots

Fig. 15.159  Satin stitch loom (1). In 1804 Joseph-Marie Jacquard from Lyon developed a system that was capable of weaving a pattern together with the simple weaving process. Thanks to punched cards, it was now possible to control the warps individually. In 1823 Conrad Altherr from Teufen AR improved this machine with the addition of a satin stitch plate, so that the pattern appeared to be hand-knitted. (© Appenzeller Volkskunde-Museum, Stein AR)

15.6 Looms

735

Fig. 15.160  Satin stitch loom (2). The more than 100-year-old loom in the Appenzeller Volkskunde-Museum is one of only a few still operational satin stitch looms in the Appenzellerland. In its heyday from 1820 to 1860, mostly men sat at the loom. The machines were controlled by concatenated punched cards. In former times a significant textile industry with weaving, spinning, and embroidery existed in Eastern Switzerland. (© Appenzeller Volkskunde-Museum, Stein AR)

Chapter 16

Mechanical Calculating Aids

Abstract  Since overviews regarding other manufacturing countries such as the USA and Germany are already available, the chapter “Mechanical Calculating Aids” is essentially limited to Switzerland. This chapter describes calculating tables, slide bar adders, and mechanical calculating machines, for example, the Millionaire, Madas, Precisa, and Stima brands. A tabular overview lists the attributes of all known products from Switzerland. The legendary Millionaire, a partial-product multiplying machine, was the first commercially successful direct multiplying machine. On the basis of serial numbers and previously unknown documentation from the H.W.  Egli AG, Zurich, an attempt is made to date this four-function calculating machine. A global survey reveals information about the known Millionaire machines, and the catalog of the Schweizer Mustermesse Basel, which was issued every year from 1917 (founding) to 2019 (final year), was evaluated. Little information is available in regard to piece numbers, prices, and patents. Keywords  Calculating tables · Counting tables · Curta · H.W. Egli SA · Madas · Mechanical calculating machines · Millionaire · Precisa · Slide bar adders · Stima This chapter focuses on mechanical calculating machines. Since – compared with Germany and the USA – no comprehensive overview of Swiss products exists, the discussion is limited to these products. The presentation examines calculating boards, as well as calculating aids without automatic tens carry, such as slide bar adders.

16.1  Counting Tables Counting tables (calculating tables) and counting cloths have long since vanished into thin air. For centuries they were widely used in administrations and commerce. According to our present knowledge, only 31 counting tables have © Springer Nature Switzerland AG 2020 H. Bruderer, Milestones in Analog and Digital Computing, https://doi.org/10.1007/978-3-030-40974-6_16

737

738

16  Mechanical Calculating Aids

survived, 18 of these in Switzerland, for example, in Basel, Bremgarten AG, Château-d’Œx VD, Geneva, Sembrancher VS, Thun BE, Veytaux VD, and Zurich. Wooden counting boards (e.g., of the Historisches Museum, Thun) are very rare. For more detailed information, see Sect. 9.4.3. The counting tables of the early modern era are the descendants of the counting boards of antiquity and the middle ages. The best known predecessor is the Salamis tablet. Most still existing counting tables derive from the sixteenth century, although a few can be dated to the seventeenth or eighteenth century. As a rule they have horizontal jeton strips (jeton rows) and occasionally vertical jeton columns. Some counting tables had several line fields, enabling simultaneous calculations in different currencies. See Sect. 3.4 for a more detailed discussion of line computation. Note Along with arithmeticians there were also calligraphers. The Example of Basel The two well-preserved counting tables (see Figs.  16.1 and 16.2) of the Historisches Museums Basel were originally used in the city hall of Basel. Presumably the so-called triple office utilized the tables for accounting purposes. This body, dating from 1453, consisted of three members of the small council (government of the city of Basel) and oversaw the entire state payment transactions and thus played a key role. In Basel, around 1600 a change took place from line computation with Roman numerals to written computation with Hindu-Arabic numerals. With this change, the traditional task of the counting table was then lost. Both counting tables from the sixteenth century are characterized by three calculating fields. Three arithmeticians (probably two treasurers and the chamberlain scribe) processed the same invoice simultaneously in order to control each other and prevent fraud. The letters on the fields have the meanings: d (denarius) = Pfennig, s (solidus) = Schilling, and lb or lib (libra) = Pound. X, C, and M stand for 10, 100, and 1000 Pounds, respectively. For the four basic arithmetic operations, one must use the pound line under X for ones (I). As a rule, arithmeticians were civil servants. One of the tables has simple single-column calculating fields. Two of these are arranged on the transverse side, and the third is on the long side. With the single-­column tables, the numbers (e.g., both summands) must be entered in the same column. Two double-columned calculating fields are arranged next to each other on the long side of the second table, and the third is on the transverse side. On the double-columned tables, the numbers (e.g., minuend and subtrahend) can be entered in adjacent columns. The jetons (tokens) were kept in the drawers of the table.

Fig. 16.1  Basel counting table with double-columned calculating fields. The rectangular tabletop is made of walnut tree wood, and the supporting structure adorned with Gothic leafwork of beechwood. Two (difficult to recognize) double-columned calculating fields are printed on the long side and the third on the transverse side. (© Historisches Museum Basel, picture: Peter Portner)

Fig. 16.2  Basel counting table with single-column calculating fields. The well-preserved counting table from the sixteenth century has three single-column calculating fields. The jetons were kept in the drawer. (© Historisches Museum Basel, picture: Maurice Babey)

740

16  Mechanical Calculating Aids

Sites of counting tables, counting boards, and counting cloths Richard Hergenhahn; Ulrich Reich; Peter Rochhaus: “Mache für dich Linihen …”. Katalog der erhaltenen originalen Rechentische, Rechenbretter und -tücher der frühen Neuzeit, Adam-Ries-Bund, Annaberg-Buchholz 1999 Ulrich Reich: Rechentische, -bretter und -tücher. Originale und Nachbauten, in: Rainer Gebhardt (editor): 500 Jahre erstes Rechenbuch von Adam Ries, Adam-­Ries-­Bund, Annaberg-Buchholz 2018, pages 57–64.

16.2  M  anufacturers of Mathematical Drawing, Measuring, and Calculating Devices With the exception of the Vaud accessory provider Logitech, the Swiss IT industry had little success in the field of equipment. The marketing of their homemade computers, such as the Ermeth, the Lilith (Diser), the Gigabooster, Smaky, and Cora could not be successfully sustained. At the same time, however, some of the world’s leading manufacturers of integrating instrument (e.g., planimeters), important suppliers of cylindrical slide rules, and wellknown builders of mechanical calculating machines were found here. Below is an overview of selected specialties and predominant manufacturers: • Cylindrical slide rules and circular slide rules Loga-Calculator AG, Uster ZH Ernst Billeter & Co. Zurich • Mechanical and electromechanical calculating machines H.W. Egli AG, Zurich (Millionaire and Madas desk calculating machines) Precisa AG, Zurich (Precisa desk calculating machines, now Precisa  Gravimetrics AG, Dietikon ZH) Albert Steinmann, La Chaux-de-Fonds NE (pocket and desktop calculators, slide bar adders) • Mathematical tools (e.g., integrators) Alfred J. Amsler & Co., Schaffhausen G. Coradi AG, Zurich • Differential analyzers Alfred J. Amsler & Co., Schaffhausen Contraves AG, Zurich (now Rheinmetall Air Defence AG) BBC Baden AG (now ABB, Zurich Oerlikon) • Analog calculating devices Güttinger AG, Teufen AR (now NUM AG, Lustmühle AR) • Coordinatographs Haag-Streit AG, Köniz BE Wild Heerbrugg AG, Heerbrugg SG (now Leica Geosystems AG) • Telecommunications Hasler AG, Bern (now Ascom, Baar ZG, in the health informatics sector)

16.2  Manufacturers of Mathematical Drawing, Measuring, and Calculating Devices 741

• Surveying instruments Kern & Co. AG, Aarau • Cipher devices Crypto AG (since 2018: Crypto International and CyOne Security AG),  Steinhausen ZG (founded by the Swedish inventor Boris Hagelin) Gretag, Regensdorf ZH (founded by Edgar Gretener, later Omnisec AG, Dällikon ZH, closed in 2019) Zellweger AG, Uster ZH (now Uster technologies). It was not possible to determine the year of founding for all of these companies (see Table 16.1). Table 16.1  Dates for the founding of Swiss manufacturers Selected manufacturers Company name Alfred J. Amsler & Co., Schaffhausen Ernst Billeter & Co., Zurich Contraves AG, Zurich G. Coradi AG, Zurich H.W. Egli AG, Zurich Güttinger AG, Teufen Hasler AG, Bern Haag-Streit AG, Köniz BE Kern & Co. AG, Aarau Loga-Calculator AG, Uster ZH National-Rechenwalzen AG, Zurich Precisa AG, Zurich

Founded 1854 1888 1936 1880 1893 1957 1852 1858 1819 1900 1916 1935

Paillard SA, Sainte-Croix VD Thorens SA, Sainte-Croix VD

1814 1881

© Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020

Remarks The Güttinger AG in Teufen AR delivered its first electronic analog computer (AR 2) to the Maschinenfabrik Oerlikon in 1958. Its predecessor, the AR 1, was operational in 1957, but was not mass produced. The largest analog computer built by Güttinger was supplied to the RWE utility company (formerly the Rheinisch-­Westfälisches Elektrizitätswerk) in Essen in 1960 and was installed in the Kahl Nuclear Power Plant. IA 55 and IA 58 were electromechanical differential analyzers from Contraves. These universal analog computing machines were employed, for example, for the solution of systems of linear and nonlinear differential equations and for the recording of algebraic and trigonometric functions. 55 and 58 presumably stand for the years in which they were built: 1955 and 1958. In the 1950s Amsler also manufactured mechanical differential analyzers.

742

16  Mechanical Calculating Aids

The most important manufacturers of mechanical music-playing devices in Sainte-Croix VD and in the neighboring village L’Auberson VD were Moïse Paillard, Ernest Paillard, Hermann Thorens, Philippe Mermod, Louis-Philippe Mermod, and Jules Cuendet. In 1890 Paillard manufactured more than 100,000 music boxes and in 1929 more than 220,000 gramophone devices (see Anonymous: Paillard 1814–1939, E. Paillard & Cie. SA, Sainte-Croix, Yverdon VD 1940). The predecessors of Haag-Streit were Herrmann and Pfister and Pfister & Streit (Bern) (see Simon Wernly; Chris Haag: 1858–2008. 150 Jahre Haag-Streit. 150 years of Haag-Streit, Haag-Streit AG, Köniz BE 2008). Jakob Goldschmid was a well-known mechanician during his lifetime (see box). Jakob Goldschmid, Zurich The mechanician Jakob Goldschmid (1815–1876) built several different devices: a pantograph, a measuring table, a double-angle mirror, an aneroid barometer (for height measurements), and a circular diastimeter. His son, Jakob Kaspar Albert Goldschmid (1843–1918), and his grandson, Jonas Eugen Goldschmid (1877–1972), also worked as a mechanician and optician in Zurich. According to information from Martin Wagener (Frankfurt am Main, personal communication of April 11, 2017), they were probably not related to J. Goldschmidt, Paris, who, e.g., offered a pinwheel machine. For further information see J.  H. Kronauer: Goldschmid’s schwebender Pantograph, in: Schweiz­ erische polytechnische Zeitschrift, volume 9, 1864, no. 5, pages 157–158 Mario von Moos: Genealogie eines Zweiges der Familie Goldschmid von Winterthur unter besonderer Berücksichtigung von Jakob Goldschmid (1815–1876), Mechaniker in Zürich, Forschungsbericht vom 12. August 2016, Fehraltorf ZH 2016, Fehraltorf 2016 (self-publisher).

Most of the companies mentioned above have disappeared and were taken over by other companies and have long since been forgotten. Until today still there is no (comprehensive) history of Swiss calculating aids and their inventors. Sources of information are altogether scanty and little is available in archives. As a countrywide survey showed, only a few historical calculating devices have survived. Furthermore, only a few specimens of the Nema cryptographic machine (see Fig. 16.3) are extant.

16.3  Slide Bar Adders and Mechanical Calculating Machines

743

Fig. 16.3  The Nema cryptographic machine. The “new machine” (Nema) was manufactured by the then existing Zellweger Uster company and was created by Arthur Alder, Hugo Hadwiger, Heinrich Emil Weber, and Paul Glur. (© Heinz Nixdorf Museumsforum, Paderborn)

16.3  S  lide Bar Adders and Mechanical Calculating Machines Who can imagine today how tedious calculating was 50 years ago? In the nineteenth and particularly in the twentieth century, numerous mechanical aids were built in Switzerland. With the emergence of the electronic computer in the 1970s, the more than 300-yearlong development of calculating devices – (analog) slide rules and (digital) mechanical calculating machines – came to an abrupt end. A few decades ago, complex calculations were still carried out in reckoning centers or computing factories with mechanical desktop calculating machines. Slide rules (especially linear slide rules) belonged to the few portable and inexpensive mathematical instruments. The mass production of mechanical calculating machines began in the middle of the nineteenth century with the French Thomas arithmometer. The

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16  Mechanical Calculating Aids

most important suppliers came especially from Germany and the USA. Among the most capable Swiss models were the Millionaire, Madas, Precisa, and Stima. There were many excellent, extremely ingenious constructions for mechanical calculating machines. Two methods for the mechanical representation of numerals predominated: the stepped drum and the pinwheel. The stepped drum is a cylinder with ribs of different lengths (graduated along the length of the cylinder). The pinwheel is a disc with movable teeth that can be driven in and out. A distinction was made between calculating machines, capable of executing all four basic arithmetic operations, and adding machines. The numerals were mostly entered via wheels, setting dials, levers, keyboard, or stylus. The devices were operated by a crank, pressing keys, or later by an electric motor. Some models also allowed printout.

16.3.1  The Millionaire The Millionaire direct multiplying machine developed by Otto Steiger (1893) (see Figs.  16.4 and 16.5) attracted considerable attention. The calculating machines of that time normally performed a multiplication as a repeated addition, requiring innumerable crank rotations. The short-cut multiplication greatly accelerated calculations. The so-called multiplying block, incorporating the simple multiplication table (1×1–9×9), made the calculation process considerably faster. The Millionaire built by the H.W.  Egli AG in ZurichWollishofen was the first commercially successful multiplication machine. The direct multiplying machine was also able to perform the other three basic arithmetic operations. However, it had a weight of several kilograms and was not low-priced. Forerunners of the Millionaire were the machines of Edmund Barbour (Boston, 1872), Ramón Verea (New York, 1878), and Léon Bollée (Le Mans, 1888). The origin of the brand name Millionaire is not known (see box). Why Was Egli’s Early Four-Function Machine Called the “Millionaire”? The reason for the peculiar choice of name remains somewhat unclear to this day. Nevertheless, there are some indications regarding the origin of the brand name. Initially, the Stolzenberg Büroeinrichtungs-A.-G. factory in Oos (Baden) was the sales agency in Germany. This “biggest and oldest office equipment factory in Europe,” with 30 domestic and international branch offices, also manufactured its own products. According to Gérald Saudan, the sales agency proposed this name. At the head of this vast operation was Gustav Mez, the founder of Mercedes Büromaschinen GmbH in Berlin (see Gérald Saudan: Swiss calculating machines, Yens sur Morges VD 2017, pages 14, 44 and 53–54 (self-publisher)).

16.3  Slide Bar Adders and Mechanical Calculating Machines

745

Fig. 16.4  The Millionaire direct multiplying machine, drawing 1. In his article H. Sossna describes the invention from 1893 as a very fast calculating machine in use around the world. At the right (below) is the extremely versatile multiplication block. (Source: Zeitschrift für Vermessungswesen, volume 28, 1899, no. 24, page 690)

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Fig. 16.5  The Millionaire direct multiplying machine, drawing 2. At the lower left, one can see the setting lever for numerical input and at the right the viewing windows. (Source: Zeitschrift für Vermessungswesen, volume 28, 1899, no. 24, page 675)

Egli built several prototypes and demonstration models (see Figs. 16.6, 16.7, and 16.8).

16.3  Slide Bar Adders and Mechanical Calculating Machines

747

Fig. 16.6  Millionaire prototype (about 1893). At the upper left the (initially) round multiplication block can be seen, and at the right the setting levers. (© Museum für Kommunikation, Bern)

Fig. 16.7  Millionaire demonstration model (1). At the top left, one sees the multiplication block. The lever for selecting multiplication or division is at the lower left. The model dates from the 1890s. (© Museum für Kommunikation, Bern)

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Fig. 16.8  Millionaire demonstration model (2). This machine was built at the earliest in 1898 (relocation to Zurich). (© Deutsches Museum, Munich)

With the Millionaire the numerals were entered either by setting levers or from a keyboard (see Figs.  16.9, 16.10, and 16.11). In the Orga-Handbuch (1921), Millionaires are pictured with levers and with keyboard. Older machines function with a crank, and newer ones are equipped with an electric motor. Nameplates provide information about the manufacturer or sales agency (see Figs. 16.12 and 16.13).

16.3  Slide Bar Adders and Mechanical Calculating Machines

749

Fig. 16.9  Millionaire with setting levers. This model has a 4-place setting mechanism (above, in the middle), and the numerical input is by means of setting levers. The crank at the right transfers the input to the calculating unit. The pivoted lever for multiplication is at the left. The result mechanism (at the bottom) has ten places. The cover piece includes instructions for use and pictures the setting levers (upper left). (© Museum für Kommunikation, Bern)

Fig. 16.10  Millionaire with full keyboard. The setting mechanism features eight places. The rotary knobs beneath the individual numeral columns serve for clearing these. The very heavy, manually operated machine is fully functional. (© Historisches Museum Thurgau, Schloss Frauenfeld)

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Fig. 16.11  Lateral view of the Millionaire. Roberto Guatelli built this replica. (© University Libraries, Carnegie Mellon University, Pittsburgh, picture: Heidi Wiren Bartlett)

Fig. 16.12  Millionaire nameplate and serial number. In 1918 the company was renamed H.W. Egli AG, Zurich. The original of this replica with the maker number 2380 was therefore manufactured at the latest in 1918. (© University Libraries, Carnegie Mellon University, Pittsburgh, picture: Heidi Wiren Bartlett)

Fig. 16.13  Millionaire of the American marketing partner. Morschhauser in New  York acquired exclusive sales rights in the USA. (© University Libraries, Carnegie Mellon University, Pittsburgh, picture: Heidi Wiren Bartlett)

16.3  Slide Bar Adders and Mechanical Calculating Machines

751

16.3.1.1  The Development of the Egli Company in Zurich In 1897 the ETH Was the World’s First University in Possession of a Direct Multiplier As only became known in July 2018, in 1897 the ETH Zurich (at that time the Federal Polytechnic School) became the first university in the world to have the legendary Millionaire four-function machine (see Figs.  16.14 and 16.15). The first commercial production series of 12 machines was manufactured in 1896 at Maistraße 4 in Munich, where Egli had its own workshop. In 1898 he returned to Switzerland and opened a workshop in Zurich. Sales of the Millionaire

Fig. 16.14  Sales of the Millionaire (1). In 1897 the ETH Zurich acquired a Millionaire. (Source: H.W.  Egli AG (Hbt./hh): 50 Jahre Egli-Rechenmaschinen, draft of an anniversary publication, Zurich 1943, page 4)

In 1897 interested customers were finally found for the first specimens of the machine manufactured in Munich. The first buyers were the Bayerische Hypotheken- und Wechsel-Bank in Munich and the Material management of the Federal Polytechnic School in Zurich.

Fig. 16.15  Sales of the Millionaire (2).The purchase of the Millionaire is confirmed in another document (possibly a press release). (Source: 50 Jahre Egli RechenmaschinenFabrik AG, Zurich, October 1943, page 1)

The first machines were sold to the Bayerische Hypotheken- und WechselBank in Munich and the material management of the Federal Polytechnic School in Zurich. In the School Board minutes of the ETH Zurich, there is no indication of having purchased a Millionaire. This is surprising, since at that time such machines were very expensive. The Federal Polytechnic School was then using primarily slide rules. The records, which were retroactively digitized,

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may not be complete. The quality of the more than 100-year-old original may be faulty, which would cause difficulties with the recognition of the text. Reference List from 1904 As the reference list in the operating instructions for the Millionaire shows, the life insurance department of the Bayerische Hypotheken- und WechselBank AG (later the Bayerische Hypo- und Vereinsbank AG, HypoVereinsbank, from 2009 Unicredit Bank AG, Munich) had two machines in 1904. In this year the Swiss Federal Laboratories for Materials Science and Technology (Empa), founded in 1880, and the agricultural chemistry laboratory of the Federal Polytechnic School each had a machine. The “material management” of the Federal Polytechnic School (1897) evidently refers to the Empa. The owner of the operating instructions for the Millionaire in the computer science library of the ETH was the “Institut für Fernmeldetechnik of the ETH” (Sternwartestraße 7, Zurich, today the Institute for signal and information processing). This shows that such a machine was in use here as well. Anniversary Celebration on the Bürgenstock In October 1943 the entire work force of the manufacturer was present at an anniversary celebration on the Bürgenstock NW (central Switzerland). In its article “50 Jahre Egli-Rechenmaschinen-Fabrik AG” of October 14, 1943, the “Volksrecht” reported this event. The Metallarbeiter-Zeitung also paid tribute to this occasion. On November 20, 1943, the director of H.W. Egli AG, Zurich (-Wollishofen), Oscar Bannwart, sent two group photographs from the Bürgenstock celebration to the Schweizerischer Metall- und Uhrenarbeiter­ verband. (Source: letters from the Schweizerisches Sozialarchiv, Zurich) The World’s First Successful Direct Multiplying Machine The Millionaire was a fast partial-product multiplying machine. Compared with the conventional mechanical calculating machines of that time, only a single rotation of the crank was needed for multiplying with a single-digit multiplier. A number of specimens of this toothed rack calculating machine have survived and still function to this day. A trading partnership in Baden (Germany) proposed the rather peculiar name “Millionaire,” as the draft of the anniversary publication (page 4) makes clear. The Millionaire is regarded as an extremely complex calculating machine. In fact, even today engineers have difficulty understanding it. Empa Machine in the Schweizer Nationalmuseum On September 12, 2018, during a visit to the collection center of the Schweizer Nationalmuseum in Affoltern ZH, I came across a completely functional Millionaire direct multiplying machine. However, this was not the device acquired by the Empa in 1897, but  – according to the serial number  – a machine manufactured around 1907. This is probably the only surviving specimen of the machines used at the ETH Zurich. It was apparently used for instruction purposes. All four lateral walls consist of plexiglass, allowing a view of the inside.

16.3  Slide Bar Adders and Mechanical Calculating Machines

753

Did Einstein Perform Calculations with the Millionaire? From 1896 to 1900, Albert Einstein was enrolled in the course of studies “specialist teacher in the field of mathematics and the natural sciences.” In 1901 he became a Swiss citizen. From 1909 to 1911, he was an associate professor at the University of Zurich and from 1912 to 1914 full professor for theoretical physics at the ETH Zurich. Whether the Nobel Prize laureate utilized the Millionaire for calculations is not known. In the holdings of the Bernisches Historisches Museum (Einstein Museum), the Albert Einstein archives of the Hebrew University in Jerusalem, the School Board records of the ETH Zurich, and in Einstein’s collected writings, there is no mention of the machine. For decades the H.W. Egli AG left its mark on the calculating machine market (see box). The Development of H.W. Egli AG and the Millionaire and Madas Machines 1893 Founding of the company: Millionaire with setting levers (three trial models of Otto Steiger built in the precision mechanics workshops of Falter & Sohn, Munich) 1894 First Excelsior (later renamed Millionaire) 1895 Millionaire: Manufacture of four machines by the Württembergische Uhrenfabrik Bürk & Söhne in Schwenningen am Neckar 1896 Manufacture of 12 Millionaires in Munich in the company’s own workshops (Maistraße 4) 1897 Beginning of sales activities 1898 Entry of the Hans W.  Egli, Ingr., Zurich company in the Swiss commercial register (Gotthardstraße 32, Zurich 2) 1903 Gold medal at the Deutsche Städte-Ausstellung in Dresden 1904 Relocation to Albisstraße 2 in Zurich-Wollishofen (Zurich 2) 1911 Millionaire with setting levers and electric motor 1913 Millionaire with (full) keyboard 1913 Madas (stepped drum machine) with setting levers and automatic division 1914 Millionaire with double counting mechanism 1918 Founding of the H.W. Egli AG, Zurich(-Wollishofen) 1922 Madas with keyboard for manual or electric drive 1927 Millionaire with multiplication keyboard (instead of multiplication lever) 1927 Millionaire with manually operated constant panel (especially for surveying) 1927 Madas with keyboard presetting of multiplier and multiplicand 1931 Portable Madas (continued)

754

16  Mechanical Calculating Aids

1936 Madas with double counting mechanism 1938 Millionaire exhibited at the Schweizer Mustermesse (Muba) in Basel for the last time 1952 Opening of a branch in Kreuzlingen TG 1968 Madas exhibited at the Schweizer Mustermesse (Muba) in Basel for the last time 1968 Participation of the H.W.  Egli AG in exhibits at the Schweizer Mustermesse (Muba) in Basel for the last time 1968 Cessation of company activities and therefore of Madas production 1972 Disbandment of the H.W. Egli AG, Zurich.

Sources H.W. Egli AG: 50 Jahre Egli-Rechenmaschinen, draft of an anniversary publication Zurich 1943/catalogs of the Messe Basel, Swiss Official Gazette of Commerce Notes A distinction is made between the long Madas (from 1913 on) and the portable Madas (from 1931 on). In 1975 the pension fund for the employees of the H.W. Egli AG, Zurich, was abolished. Company sites 1896 Munich, Maistraße 4 1898 Hans W. Egli, Ingr., Gotthardstraße 39, Zurich 2 1906 Hans W. Egli, Ingr., Albisstraße 2, Zurich 2 (Zurich-Wollishofen) 1918 H.W. Egli A.-G., Albisstraße 2, Zurich 2 (Zurich-Wollishofen) Note Beginning in the 1940s, the address Seestraße 356 appears instead, and the name Albisstraße is no longer used. However, nothing changed at the company site (formerly the crossing Albisstraße and Seestraße). Entries in the Swiss Official Gazette of Commerce (SHAB) No. 247, August 31, 1898, page 1034 August 27. Owner of the company Hans W.  Egli, Ingr. in Zurich II is Hans Walter Egli of Kirchberg (St. Gallen), in Zurich II.  Workshops for precision mechanics; specialty: manufacture of calculating machines, patent Steiger. Gotthardstrasse 39. No. 464, November 15 1906, page 1854 November 13. The Hans W. Egli, Ingr. company in Zurich II (S.H.A.B. no. 247 of August 31, 1898, page 1034) hereby indicates a change of address to the business premises: Albisstrasse 2, Zurich II.

16.3  Slide Bar Adders and Mechanical Calculating Machines

755

No. 78, April 3, 1918, pages 534–535 Calculating machines and other high-precision articles  – March 30. A joint stock company of unlimited duration has been established on March 30, 1918, under the company name H.W. Egli A.G. (H.W. Egli S.A.), with headquarters in Zurich. The purpose of the company is the production and sales of calculating machines and other high-precision articles. In particular, this company takes over and continues the activities of the business conducted until now under the company Hans W. Egli in Zurich (S.H.A.B. no. 464 of November 15, 1906, page 1854). […]. Business premises: Albisstrasse 2, Zurich 2. No. 92, April 19, 1918, page 638 Workshops for precision mechanics, calculating machines  – April 15. As a result of the transfer of the company to the H.W. Egli, A.-G. company in Zurich, the entry for the Hans W. Egli, Ingr. company in Zurich 2 (S.H.A.B. no. 464 of November 15, 1906, page 1854), Workshops for precision mechanics; specialty: manufacture of calculating machines, patent Steiger has been deleted. No. 305, December 29, 1961, page 3774 December 20, 1961. Office machines etc. H.W.  Egli A.-G. (H.W.  Egli S.A.) (H.W.  Egli Ltd.), in Zurich. […]. Business premises: Seestrasse 356  in Zurich 2. No. 22, January 28, 1971, page 221 January 15, 1971. The H.W.  Egli Holding A.-G. in Zurich 2 (SHAB no. 305 of December 29, 1961, page 3774), with holdings in other domestic and foreign companies, etc. As a result of the decision of the general meeting of December 23, 1970, the company has been abolished. No. 171, July 24, 1972, page 1958 July 11, 1972. Office machines. The H.W. Egli A.-G. in Zurich 2 (SHAB no. 305 of December 29, 1961, page 3774), manufacture and sales of office machines etc. As a result of the decision of the general meeting of March 7, 1972, the company will be disbanded. According to the partners, the capital has been liquidated. Due to the lack of approval of the Federal Tax Administration the entry for the company cannot be deleted. No. 183, August 7, 1972, page 2084 July 26, 1972. The H.W. Egli A.-G. in Zurich 2 (SHAB no. 171 of July 24, 1972, page 1958). The Federal Tax Administration has issued approval for the disbandment of the company. The company entry has been deleted. No. 58, March 11, 1974, page 663 February 28, 1974. The H.W. Egli Holding A.-G- in liquidation, in Zurich 2 (SHAB no. 22 of January 28, 1971, page 221), with holdings in other companies, etc. The liquidation has been consummated. The company entry has been deleted.

756

16  Mechanical Calculating Aids

Prototypes and Demonstration Models According to Michael Lewin, two trial pieces and three demonstration models of the Millionaire were built. All five machines are preserved and are now in the Museum für Kommunikation in Bern (the second trial machine and a demonstration model), the Deutsches Museum in Munich (a demonstration model) and the Bonn Arithmeum (the first trial machine, a demonstration model; a replica of the second trial machine, and also a production machine 10). The earliest mass-produced machines are now in a private collection. Lewin and Ullrich Wolff built two replicas of the second trial machine, requiring several years, in order to clarify whether the machine was in fact capable of performing calculations. The first trial machine dates from 1893 in Munich. According to Saudan, the Württembergische Uhrenfabrik Bürk & Söhne in Schwenningen (Black Forest) built four machines in 1895. Adolf Haarpaintner constructed calculating machines for Egli at Falter & Sohn in Munich. Some details are contradictory, such as the beginning of mass production. Swiss Machine Engineers The inventor of the Millionaire was the St. Gallen machine builder Johann Otto Steiger (1858–1923, born in Flawil SG), and the manufacturer was Hans Walter Egli (1862–1925) from Kirchberg SG. Where Is the Anniversary Publication? The Egli company was the only Swiss manufacturer exhibiting (without interruption) for 52 years – from 1917 to 1968 – at the Schweizer Mustermesse in Basel. The company missed its chance to enter the world of electronics and disappeared a few years later. The inglorious demise may explain that, apart from patent documents, there are hardly any documents in the archives. Subsequent researches for the anniversary publication in domestic and foreign library catalogs and archive holdings were without result. Relevant databases of leading technical museums possessing Egli machines show no such entries: London (Science Museum), Mountain View, California (Computer History Museum), Paris (Musée des arts et métiers), and Washington (National Museum of American History). Inquiries with the archives in Zurich (Stadtarchiv, Staatsarchiv, Archiv für Zeitgeschichte, Schweizerisches Sozialarchiv), Basel (Schweizerisches Wirtschaftsarchiv), Köniz BE (PTT-Archiv), and Munich (Deutsches Museum) also led nowhere. The draft of the anniversary publication is therefore a rarity. A document that came to light on September 13, 2018, during a visit to the Museum für Kommunikation in Bern reveals that the anniversary publication was never issued. Possible reasons for this are the high additional load due to the Second World War, the construction of a new factory building, and the death of a director (1942).

16.3  Slide Bar Adders and Mechanical Calculating Machines

757

Dating of the Two Operating Instructions for the Millionaire In both operating instructions, there is a reference on page 13 to the year of publication (around 1905 and 1908, respectively): • Several machines have been in constant use for more than seven years (1897) without requiring even the slightest repairs. • Several machines have been in constant use for more than ten years (1897) without requiring even the slightest repairs.

16.3.1.2  R  egarding the Dating of the Millionaire Direct Multiplying Machine The discovery of new documents about the H.W.  Egli AG (Zurich) in the Museum für Kommunikation, Bern, provides new indications in regard to the dating. A Machine Full of Mysteries Due to its construction, the Millionaire occupies a unique position in the history of mechanical calculating machines. Until today this machine has still not yet revealed all its secrets. The origin of its peculiar name is still not clear, nor is it known until when it was manufactured. Furthermore, the allocation of the serial numbers and their correlation with the years of manufacture remains open. The determination of the age therefore entails considerable uncertainties, as a survey of international museums shows. Engineers still have difficulties understanding the functional principle of the highly complex multiplication block. Only since the discovery of new documents in the Museum für Kommunikation in Bern in September 2018 is it clear, how many specimens were manufactured. Neither Year of Manufacture Nor Model Designation When no year of manufacture is engraved on the calculating machines and no documents (such as proofs of purchase) exist, dating is often very difficult. This also applies for the Swiss Millionaire direct multiplying machine, which was famous the world over in its time. This very heavy machine manufactured by the H.W. Egli AG in Zurich from 1893 was capable of performing all four basic arithmetic operations. On the basis of the (not very transparent) serial numbers, an attempt is made to approximately determine the years of manufacture. As a rule, the surviving Millionaire machines have no model designations, complicating their dating even more. There were 21 different types of the Millionaire (including the Excelsior model). The Excelsior was a (pure) multiplication machine. Besides the Millionaire direct multiplying machine, Egli manufactured another successful stepped drum machine, the Madas.

758

16  Mechanical Calculating Aids

Obsolete Operating Instructions The company – possibly for economic reasons – sometimes provided obsolete operating instructions. As a result there are keyboard machines with operating instructions for setting lever machines in the cover. Around 1930, for example, operating instructions more than 20 years old for a machine with setting levers, multiplication lever, and hand crank were provided for a machine with keyboard, multiplication keys, and electric motor. Here, for example, important information about the crank locking mechanism was missing. Remark There are Millionaire machines with a keyboard. However, the operating instructions in the cover refer to setting levers. In such cases it is possible that a keyboard replaced the setting levers later. Documents with Information About the Number of Units Have Come to Light New documents which came to light on September 13, 2018, in the Museum für Kommunikation in Bern simplify the allocation of the year of manufacture. For the first time since the disbandment of the company around 50 years ago, exact piece numbers are now known for all Millionaire and Madas calculating machines manufactured by Egli. In all, 5074 Millionaire machines (and also 25 Excelsior machines) were produced (see Fig. 16.16). The reason for this investigation was an indication that the first machines were sold in 1897 (e.g., to ETH Zurich) and the erroneous dating (by the Empa, Dübendorf ZH, and the collection center of the Schweizerisches Nationalmuseum, Affoltern ZH) of a machine as from 1895. On November 6, 2018, I again examined the existing documentation for calculating machines closely at the Swiss Science Center (Technorama) in Winterthur ZH.  This reveals that the museum  – at that time in the buildup phase – acquired the entire collection of historical calculating machines from the H.W. Egli AG on October 29, 1969. Two new machines followed on June 17, 1970. In the meantime the company had discontinued production. In addition to numerous machines of its own, the collection also included many machines of other manufacturers. In a letter of January 5, 1989, to the Technorama, Andreas Lanz mentions, e.g., six Millionaire machines in wooden casings belonging to the holdings of the museum.

1941

1940

1939

1938

1937

1936

1935

1934

1933

1932

1931

1930

1929

1928

1927

1926

1925

1924

1923

1922

1921

1920

1919

1918

1917

1916

1915

1914

1913

1912

1911

1910

1909

1905

1904

1903

1902

1901

1900

1899

1898

1897

1896

Fig. 16.16  Development of the piece numbers for the Millionaire. The number of machines sold each year was estimated on the basis of information from the H.W. Egli AG, Zurich. (© Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020)

1906

Millionaire+ Excelsior: 5099 specimens

1908

Not included: 25 specimens of the Excelsior

5074 specimens

1896 to 1941

ofthe Millionaire calculatingmachine

Mass production and/or sales

1907

5200 5100 5000 4900 4800 4700 4600 4500 4400 4300 4200 4100 4000 3900 3800 3700 3600 3500 3400 3300 3200 3100 3000 2900 2800 2700 2600 2500 2400 2300 2200 2100 2000 1900 1800 1700 1600 1500 1400 1300 1200 1100 1000 900 800 700 600 500 400 300 200 100 0

16.3  Slide Bar Adders and Mechanical Calculating Machines 759

760

16  Mechanical Calculating Aids

Hans W.  Egli manufactured mechanical calculating machines for several decades (see box). H.W. Egli AG, Zurich: The Millionaire and Madas Mass production and/or sales Millionaire 1896–1941 Madas 1913–1968 Remark The Millionaire was sold at least until 1941. Production ceased in the 1930s. Piece numbers Millionaire 5099 Madas 93,964 Eos (license) 1250 Total 100,313 The figure 93,964 is comprised of 9339 “long” Madas and 84,625 portable Madas. After January 15, 1931, the number of long Madas manufactured (9339) no longer changed. Remarks The figure 5099 includes 25 specimens of the Excelsior. Due to a transfer error (3339 instead of 9339), 6000 machines are missing from the compilation of the H.W. Egli AG of 1972. As a result, the company erroneously reports 94,313 piece numbers (instead of 100,313). Lifetime of the company Founding of the company: Disbandment of the company:

1893 1972

Notes The Madas was manufactured from 1913 to 1968 and sales began in 1914. Until this time all serial numbers therefore refer to the Millionaire. 1935 is often cited as the end of Millionaire production, but this date is not substantiated. A letter of November 20, 1967, from the H.W. Egli AG to a customer indicates that the production of the Millionaire was discontinued 40 years before, that is, in1927 (see Gérald Saudan: Swiss calculating machines. H.W. Egli AG, Yens sur Morges VD 2017, page 70). This statement is probably an error. The model with multiplication keyboard was in fact only introduced in 1927. The installation instructions for no. 17523 bear the date March 10, 1930. Furthermore, the catalogs of the Schweizer Mustermesse show that this machine was on view in Basel until 1938 (see Sect. 16.7). According to an unpublished compilation of the company, five Millionaires were sold by the end of 1941 (i.e., 66 since October 6, 1933). In the technical literature, one often finds 4655 Millionaire machines manufactured. This value is however incorrect.

16.3  Slide Bar Adders and Mechanical Calculating Machines

761

With the appearance of the sister machine Madas, with automatic multiplication (1927), and the portable Madas (1931), the sales figures for the Millionaire evidently sank drastically, especially considering that division with this machine was rather cumbersome. On June 17, 1970, the H.W. Egli AG donated two new Madas machines, model BTR, no. 104929, and model BTRZ, no. 103329, to the Technorama. The year of manufacture is given as 1969 (in the Technorama file 1968), contradicting the asserted end of production. These were apparently the last machines that the company produced. The Technorama file lists a Millionaire VIII eTMD with multiplication keyboard, no. 15075, for which the year of manufacture is given as 1940. But this is clearly incorrect, since it was certainly manufactured before no. 17523 (around 1930). The Millionaire was still in use until the 1950s. In 1949 Alex Aregger, the cadaster surveyor in Beromünster LU, bought a Millionaire, no. 3529, from Faigle in Zurich for 750 Swiss francs (personal communication of Adrian Bläuenstein of January 6, 2019). Millionaire machines were still advertised in the 1940s (e.g., in the Schweizerische Zeitschrift für Vermessungswesen und Kulturtechnik, volume 38, 1940, pages 152–153: for sale or for leasing, for manual and electrical drive, and in the Schweizerische Bauzeitung, volume 67, December 3, 1949, no. 49, page 9; used machine with electrical drive). Differences from Earlier Investigations Lewin assumes a common numbering of the Millionaire and the Madas. According to his diagram of 1992, which covers the period from 1895 to 1931, the serial number 500 corresponds to the year of manufacture 1900. However, until this time only 150 machines had been built (see Michael Lewin: Entwicklungsgeschichte der Rechenmaschinen der Firma H.W. Egli bis 1931, in: Typenkorb 1992, no. 49, page 11). For 1905 he mentions more than 1500 pieces, but up to this time, only around 400 specimens had been manufactured. With the introduction of the Madas (1913), the machines were numbered from 3500 on. But, according to the documents from Egli, there were only approximately 2200 specimens (of the Millionaire). Saudan believes that the maker numbers for the two products must be considered separately. His line graph (2017) covers the years 1893 to 1924. For 1905 and 1910, he calculates 500 and 1500 machines, respectively, which agrees well with the values of the manufacturer (around 400 and 1600, respectively) (see Gérald Saudan: Swiss calculating machines. H.W.  Egli AG, Yens sur Morges VD 2017, page 73). At the time of the beginning of sales for the Madas (1914), he estimates the serial numbers of the Millionaire to be around 2400 (according to the author’s calculations around 2300). For 1918 he arrives at no. 3500 (around 3000). For 1918 and 1921, he indicates a numbering gap of 500 (from 3500 to 4000) and 1500 numbers (from 4500 to 6000), respectively.

762

16  Mechanical Calculating Aids

According to Saudan the numbers 3500 and 4000 (gap) derive from 1918 and the numbers 4500 and 6000 (gap) from 1921. No. 6500 belongs to the year 1924. Owing to the lack of data, whether there are contradictions in regard to the years of manufacture of the different types and models cannot be determined. Allocation of the Serial Numbers to the Years of Manufacture The following tables attempt to relate the serial number to the years of manufacture and to the legal form of the manufacturer (sole proprietorship or jointstock company) (see Tables 16.2, 16.3, 16.4, 16.5, 16.6, 16.7, and 16.8). Note: above all with the later machines, there are considerable uncertainties. The Millionaire Direct Multiplying Machine Table 16.2  Dating on the basis of the serial numbers (1896–1916) Period 1896–1916 Serial numbers 1–12 13–300 301–410 411–600 601–830 831–1050 1051–1350 1351–1634 1635–1911 1912–2237 2238–2369 2370–2537 Total

Year of manufacture 1896 1897–1904 1905 1906 1907 1908 1909 1910 1911 1913 1915 1916

Year’s production 12 288 110 190 230 220 300 284 277 326 132 168 2537

© Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020 Table 16.3  Allocation to the years 1897 to 1904 (estimated) Period 1897–1904 Serial numbers 13–48 49–84 85–120 121–156 157–192 193–228 229–264 265–300

Year of manufacture 1897 1898 1899 1900 1901 1902 1903 1904

© Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020

Total

288

16.3  Slide Bar Adders and Mechanical Calculating Machines

763

Remark The operating instructions for the Millionaire direct multiplying machine of Hans W. Egli, Zurich, includes a five-page list “references, April 1904”. This shows that, up to this time, 277 machines were supplied worldwide. Table 16.4  Allocation to the years 1912 to 1915 (estimated) Period 1912–1915 Serial numbers 1912–2074 2075–2237 2238–2303 2304–2369 Total

Year of manufacture 1912 1913 1914 1915

Total 163 163 66 66 458

© Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020

Remarks The information about the number of calculating machines manufactured each year allows an approximate estimate of the years of manufacture. Nevertheless, these are only approximations. For the years 1912, 1914, and 1917 and the following years, no piece numbers are available. No. 7 is said to be dated to 1898. This contradicts other documents (issued later). According to the list of John Wolff’s Web Museum, Millionaire no. 1079 was used for the first Australian census (1911), but the date of purchase is unclear. The Shawmut Mining Co., St. Mary’s, Pennsylvania, is said to have acquired no. 1338 in 1909. From around 1910, no. 1829 stood in the Sydney Observatory. One of the machines used by the New York Central Railroad Co., with the number 2015, was manufactured in 1912. These four examples verify that the allocation to 1912 as the year of manufacture is more or less correct. As a survey from fall 2018 shows, the “Register of Millionaire calculators” of John Wolff’s Web Museum is incomplete. For the different models, this states: number of places (6, 8, 10, 12), numerical input with setting levers or keys, wooden or metal casing, and manual or electric drive. Website: http:// johnwolff.id.au/calculators/Egli/Register/MillionaireRegister.htm. Table 16.5  Uncertain allocation to the years 1917 to 1933 (estimate) Period 1917–1933 Serial numbers 2538–3020 3021–3500 4001–4200 4201–4400 6001–6180

Year of manufacture 1917 1918 1919 1920 1921

Total 963 400

Allocation 483 pieces/year 480 pieces/year 200 pieces/year 200 pieces/year 180 pieces/year (continued)

764

16  Mechanical Calculating Aids

Table 16.5 (continued) Period 1917–1933 Serial numbers 6181–6350 6351–6510 6511–6650 6651–6770 6771–6870 6871–6950 6951–7020 7021–7080 7081–7100 7101–7108 – – Total Mean value/year

Year of manufacture 1922 1923 1924? 1925? 1926? 1927? 1928? 1929? 1930? 1931? 1932 1933

Total

1108 2471

Allocation 170 pieces/year 160 pieces/year 140 pieces/year 120 pieces/year 100 pieces/year 80 pieces/year 70 pieces/year 60 pieces/year 20 pieces/year 8 pieces/year 0 pieces/year 0 pieces/year 145.353

© Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020

Note From 1924 on the years of manufacture are no longer traceable. The machines were probably manufactured several years earlier than as described here. Remarks From 1917 to 1933 2471, machines (5008 minus 2537) were manufactured, corresponding to a mean yearly production of 145.35 pieces. With the emergence of electrical four-function machines around 1930, the yearly production fell off drastically. This allocation is based on the production of 145 pieces per year. It is assumed that all mass-produced machines (and models) were numbered from number 1 on. It is apparent that there were large gaps. Gaps in the numbering (such as new counting from certain models) and the common numbering including the Madas (from around 1924) result in a forward shift of the year of manufacture, i.e., the machines are in fact several years older than the serial number would suggest. The determination of the year of manufacture (after number 6500) therefore becomes increasingly uncertain. Gaps in the numbering and a common numbering benefit marketing, but complicate dating. Such methods can deceive the competition. Up to October 1933, 5008 Millionaire machines (+ 25 Excelsiors) were built and by the end of 1941 an additional 66 machines. On the average, this corresponds to 8.25 pieces per year. The list of John Wolff provides the following information: The US Department of Agriculture purchased no. 2372, supposedly around 1911. From 1917 on, no. 2566 was in use from 1917 with the Metropolitan Gas Co. in Melbourne. Millionaire no. 4307 was acquired by Rothamsted Research in

16.3  Slide Bar Adders and Mechanical Calculating Machines

765

Harpenden, Herts. (UK) in 1919 for statistical purposes. Furthermore, no. 6338 was purchased in 1923. The Musée de la machine à écrire in Lausanne is in possession of a Millionaire with the no. 6443. This device is equipped with a multiplication keyboard, which was introduced in 1927. Since machines with multiplication keys also bear the numbers 10193, 10852, 15075, and 17523, the machine was probably already manufactured in 1923 and later retrofitted. The collection of Fritz Rusterholz in Herrliberg ZH includes a Millionaire with the number 10852, equipped with multiplication keys. It was apparently supplied to the power plant in Laufenburg AG. A postcard documents the notification of a technician for the first overhaul in October 1940. The same collection also includes a Madas, with the number 11154, which – on the basis of the external motor and the division stop key – can be dated to around 1927. Since the Millionaire had a lower number, it was probably manufactured in 1927 (but presumably sold at a later time) (personal communication of Fritz Rusterholz of January 28, 2019). The possibilities for verifying the reliability of Wolff’s lists are rather limited. Particularly the date of purchase by the Department of Agriculture seems to be uncertain. The determination of the years of manufacture on the basis of the serial numbers appears to be more or less accurate until 1927. The Millionaire (replica) of the Carnegie Mellon University in Pittsburgh bears the factory number 2380. The National Museum of American History in Washington, D.C., has two machines, with the numbers 2432 and 2609. In all three cases, Hans W.  Egli is given as the manufacturer, indicating that they were manufactured before 1918. This is also true for machine no. 2505 of the Heinz Nixdorf Museumsforum in Paderborn (Germany) and no. 2770 of the Canada Science and Technology Museum in Ottawa. The machines 3044 and 4062 of the Museum für Kommunikation in Bern, no. 3260 of the Abteilung Amtliche Vermessung der Stadt Zürich, and no. 3282 from the Collection of Historical Scientific Instruments of Harvard University bear a nameplate with the company name H.W. Egli SA. Accordingly, they were probably manufactured in or shortly after 1918. Table 16.6  The borderline between sole proprietorship and joint-stock company Form of company Serial numbers 2359 2372 2380 2432 2505 2547

Manufacturer Hans W. Egli Hans W. Egli Hans W. Egli Hans W. Egli Hans W. Egli Hans W. Egli (continued)

766

16  Mechanical Calculating Aids Table 16.6 (continued) Form of company Serial numbers 2597 2598 2609 2637 2653 2741 2770 2851 2910 2918 3035 3044 3055 3066 3177 3230 3260 3262 3282 3357 3376 4007 4062 4089 4108 4321 4361 4372

Manufacturer Hans W. Egli Hans W. Egli Hans W. Egli H.W. Egli AG Hans W. Egli H.W. Egli AG Hans W. Egli H.W. Egli AG Hans W. Egli H.W. Egli AG H.W. Egli AG H.W. Egli AG Hans W. Egli Hans W. Egli Hans W. Egli Hans W. Egli H.W. Egli AG H.W. Egli AG H.W. Egli AG H.W. Egli AG Hans W. Egli Hans W. Egli H.W. Egli AG Hans W. Egli Hans W. Egli H.W. Egli AG H.W. Egli AG H.W. Egli AG

© Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020

Remarks As a rule, machines with the nameplate Hans W.  Egli were manufactured before 1918. The designations “H.W. Egli AG” and “H.W. Egli SA” usually indicate a date of manufacture from 1918. From about number 3000, the Millionaire machine nameplates bear the name H.W. Egli AG. However, there are numerous exceptions: numbers 2637, 2741, 2851, 2918, 3055, 3066, 3177, 3230, 3376, 4007, 4089, and 4108. The numbering is sometimes nontransparent. Saudan assumes that the H.W. Egli AG nameplate replaced the original Hans W. Egli nameplates in the course of overhauling (retrofitting), reconditioning, repair, or modification. These machines may stem from older stocks and returned

16.3  Slide Bar Adders and Mechanical Calculating Machines

767

machines or were second-hand articles. In some cases the manufacturer’s information is missing, and in some cases, the sales agencies replaced the original nameplates with their own. More than 10,000 Serial Numbers Are Missing for the Millionaire About 5100 Millionaire machines were produced, but the serial numbers run up to over 17,000. Consequently, more than 10,000 serial numbers are missing. Most of these numbers were apparently allocated to the Madas. From the founding of the company (1893) to the disbanding of the company (1972), the H.W.  Egli AG produced 100,313 calculating machines: 5099 Millionaires (including the Excelsior), 93,964 Madas, and 1250 Eos. Table 16.7  Dating on the basis of the serial numbers (summarizing estimate: 1896–1924) Period 1896–1924 Serial numbers 1–12 13–48 49–84 85–120 121–156 157–192 193–228 229–264 265–300 301–410 411–600 601–830 831–1050 1051–1350 1351–1634 1635–1911 1912–2074 2075–2237 2238–2303 2304–2369 2370–2537 2538–3020 3021–3500 4001–4200 4201–4400 6001–6180 6181–6350 6351–6510 6511 ff.

Year of manufacture 1896 1897 1898 1899 1900 1901 1902 1903 1904 1905 1906 1907 1908 1909 1910 1911 1912 1913 1914 1915 1916 1917 1918 1919 1920 1921 1922 1923 ab 1924

© Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020

768

16  Mechanical Calculating Aids

Remarks According to Gérald Saudan, the serial numbers 3501–4000 and 4501–6000 were allocated to the Madas. The numbers from 6501 to (ostensibly) 14,000 were used for the Madas and occasionally also for the Millionaire (see Gérald Saudan: Swiss calculating machines. H.W. Egli AG, Yens sur Morges VD 2017, page 71). The numbers 14382, 15007, 15075, and 15125 (University of Melbourne) and 17523 are likewise documented as Millionaire machines. The numbers 4401–4500 are allocated to the year 1920. A closer examination reveals that the following numbers were allocated to the Madas machines: 3512 (Museum für Kommunikation, Bern), 3527 (Wolff, Belgrave, Australia), 3533 (National Museum of American History, Washington, D.C.), 3691 (Narr, Windisch AG), 3775 (Wolff, Belgrave, Australia), 3992 (Narr, Windisch AG), and 3997 (Denz, Münster VS), as well as 4540 (Museum Enter, Solothurn SO), 4571 (National Museum of American History, Washington, D.C.), 4650 (Museum Enter, Solothurn SO), 4757 (Science Museum, London), 5095 (National Museum of American History, Washington, D.C.), 5460 (Museum für Kommunikation, Bern), 5836 (Barbian, Düsseldorf), 5920 and 5951 (both Museum Enter, Solothurn SO), in addition to no. 6518 (Historische Bürowelt aktuell 2019, volume 1), 6595 (Museum Enter, Solothurn SO), and 6875 (Technische Sammlungen, Dresden). Numbers 3055, 3066, 3086, 3177, 3253, 3260, 3265, 3282, 3285, 3347, 3357, 3376, and 3431, as well as 4007, 4022, 4062, 4089, 4154, 4321, and 4493 as well as 6082, 6290, 6443, and 6455, are Millionaire machines. Numbers 3285 and 6455 are mentioned in the German Rechnerlexikon (www.rechnerlexikon.de). The relationships between the serial numbers and the year of manufacture are illustrated in the diagram below (see Fig. 16.17).

1

4001 4000

3500 3501

Dating of the Millionaire machines difficult

4500 4501

1913

6001 6000

Fig. 16.17  Dating of the Millionaire machines. The serial numbers of the Millionaire conform to three different schemes. Particularly after 1924 the allocation is not clear. (© Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020)

As the installation instructions indicate, the Millionaire with the number 17523 was probably manufactured in 1930. © Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020

5099 Millionaire machines were produced. These numbers were not allocated consecutively (without gaps), but together with the Madas.

The 4500 numbers (3500 + 500 + 500) were not enough, so that beginning with 6501 another 599 numbers were allocated to the Millionaire.

The 4000 numbers (3500 + 500) were not enough for the Millionaire, so that another 500 numbers were allocated to the Millionaire.

The 3500 numbers were not enough for the Millionaire, so that another 500 numbers were allocated to the Millionaire.

be allocated to a later time than no. 3600 (Madas).

At this time the first 3500 numbers for the Millionaire were not yet exhausted. No. 3400 (Millionaire) could therefore

The Madas was introduced in 1913. These machines were given serial numbers beginning with 3501.

The first mass produced Millionaire machines were manufactured in 1896. They were assigned the numbers 1 to 3500.

Explanations

Common serial numbers

Serial numbers for the Madas

Serial numbers for the Millionaire

Explanation of symbols

1896

Madas + Millionaire

Madas 6501 1924

Millionaire

18000 1930

6500

Allocation of serial numbers to the year of manufacture 16.3  Slide Bar Adders and Mechanical Calculating Machines 769

770

16  Mechanical Calculating Aids

Until the beginning of the common numbering, 4500 numbers had to be allocated to the Millionaire. This interpretation does not rule out the possibility that additional Millionaire machines were manufactured after 1930. Table 16.8  Serial numbers according to type Serial numbers and type Type Manually operated machines Machines with electric motor Machines with setting levers Machines with keyboard

Serial numbers From 1 to about 7000 From about 2000 to about 17000 From 1 to about 7000 From about 2000 to about 17000

© Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020

Note These values agree largely with the allocation to the years of manufacture elaborated above. The manufacturer’s name and the models allow initial conclusions about the date of manufacture (see box). Dating on the Basis of the Type and Manufacturer’s Name The Millionaire type and manufacturer’s name provide useful information for dating: • • • • • • • • •

Models with setting levers Models with keyboard Manually operated models Models with electric drive Models with double counting mechanism Manufacturer’s name: Hans W. Egli, Zurich 2 Manufacturer’s name: H.W. Egli AG, Zurich 2 Setting check dial with keyboard machines Models with multiplication keyboard

From 1896 From 1913 From 1896 From 1911 From 1914 Until 1918 From 1918 From 1924 From 1927.

Remarks The existing documents from the H.W. Egli AG provide information about the introduction of certain models, but not about the end of production. Further information about the periods of production for different types (wooden or metal casing, setting levers, manual operation, and the number of places in the setting mechanism, result mechanism, and revolution counter) would simplify dating. The introduction of the full keyboard (1913) enabled the development of a constant apparatus (trademark protection in 1914). This accessory unit, which F. Bühlmann describes in 1915 in an article, considerably simplified surveying

16.3  Slide Bar Adders and Mechanical Calculating Machines

771

(see F. Bühlmann: Die Berechnung der Koordinaten der Grenzpunkte mit der Rechenmaschine “Millionär”, in: Schweizerische Geometer-Zeitung, volume 13, 1915, no. 6, pages 154–164). In the price list of Hans W. Egli of 1914, Millionaire machines are offered with setting levers and keyboard, with manual and electric drive, and with double counting mechanism, as well as a machine with setting levers in a wooden cabinet. The following machines have a wooden casing: 1464, 2702, and 4089. Entry in the Commercial Register According to the Swiss Official Gazette of Commerce no. 78 of April 3 (pages 534–535), the H.W. Egli AG was entered in the commercial register on March 30, 1918. As a rule, then, it can be assumed that machines with the nameplate Hans W. Egli were manufactured at the latest by March 29, 1918, and machines with the nameplate H.W.  Egli AG or H.W.  Egli SA were manufactured at the earliest from March 30, 1918. The use of a false company name is illegal. Dating on the Basis of Selected Collections In the following (see Tables 16.9, 16.10, 16.11, 16.12, 16.13, 16.14, 16.15, 16.17, 16.18, 16.19, 16.20, 16.21, 16.22, 16.23, 16.24, 16.25, 16.26, 16.27, 16.28, 16.29, 16.30, 16.31, 16.32, 16.33, 16.34, 16.35, 16.36, 16.37, 16.38, and 16.39), an attempt is made to determine the year of manufacture. Since not all collection databases are accessible to the public or serial numbers and years of manufacture are missing, a further control, a global survey, focusing primarily on Europe, North America, and Australia, was carried out. In some cases no answers were received by the editorial deadline, for example, from Bletchley Park (National Museum of Computing) or Bonn (Arithmeum). Preliminary Remark In many cases the year of manufacture is given as 1895. The reason for this erroneous dating derives from a comment found on certain machines: PTD May 7TH 1895. Sept. 17TH 1895 (ptd = patented). These misleading comments refer to two US patents of Otto Steiger and have nothing to do with the year of manufacture. The museums and collections are listed in alphabetical order by country and, within the countries, alphabetically by site. Australia Table 16.9  Museums Victoria, Melbourne Number 625 1693

Year of manufacture 1907 1911

772

16  Mechanical Calculating Aids Table 16.10  Powerhouse Museum, Sydney (Museum of Applied Arts & Sciences) Number 212 960 1077 1385 1392 1829

Year of manufacture 1902 1908 1909 1910 1910 1911

Remark Henry Ferdinand Halloran reportedly used machine no. 1077 from 1899 to 1950. This assertion is not correct. Table 16.11  John Wolff’s Web Museum, Belgrave, Victoria Number Year of manufacture 2789 1917 2968 1917

Remark No. 2789 is a setting lever machine and no. 2968 has a keyboard and an electric motor. Austria Table 16.12 Technisches Museum Wien, Vienna Number 1314 6480 9129

Year of manufacture 1909 1923 After 1924

Remark The setting lever machine, no. 1314, was manufactured by the sole proprietary company Hans W. Egli and the other machines from H.W. Egli AG. No. 6480 has a keyboard. Table 16.13  Private collection of Franz Pehmer, Markersdorf Number Year of manufacture 479 1906 15007 After 1924

Remark No. 479 is a setting lever machine. No. 15007 has a keyboard and an electric motor.

16.3  Slide Bar Adders and Mechanical Calculating Machines

773

Belgium Table 16.14 Private collection of Cris Vande Velde, Berendrecht Number 1515 9244

Year of manufacture 1910 After 1924

Remark No. 1515 has setting levers, and no. 9244 is an electric keyboard machine with double counting mechanism. Canada Table 16.15  Canada Science and Technology Museum/Musée des sciences et de la technologie du Canada, Ottawa Number 1902 2770

Year of manufacture 1911 1917

Remark Both machines utilize setting levers for numerical input. Czech Republic Table 16.16  Národní technické muzeum (National Technical Museum), Prague Number 791 7558

Year of manufacture 1907 After 1924

Remark No. 791 functions with setting levers, and no. 7558 offers a keyboard. France Table 16.17  Musée des arts et métiers, Paris Number Year of manufacture 2169 1913 10823 After 1924

774

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Remark No. 10823 has a second counting mechanism. Such machines were offered beginning in 1914. Germany Table 16.18  Deutsches Technikmuseum, Berlin Number 310 9176

Year of manufacture 1905 After 1924

Remark The setting lever machine, no. 310, bears the manufacturer’s name Hans. W. Egli. In 1918 the sole proprietary company became the H.W. Egli AG. No. 9176 has a keyboard and was manufactured by the H.W. Egli AG. Table 16.19  Arithmeum, Bonn Number 10 73 1402 1846 2564 2633 2950 7565 9211

Year of manufacture 1896 1898 1910 1911 1917 1917 1917 After 1924 After 1924

Remark No. 73 is an Excelsior. No. 1402 utilizes setting levers and is installed in a metal casing. Table 16.20  Private collection of Michael Lewin, Darmstadt Number 6 7 26 3431 9136 10193

Year of manufacture 1896 1896 1897 1918 After 1924 After 1924

Remark No. 10193 (VIII eT) has a multiplication keyboard.

16.3  Slide Bar Adders and Mechanical Calculating Machines

775

Table 16.21  Private collection of Hans Barbian, Düsseldorf Number Year of manufacture 2367 1915 6279 1922

Remark No. 2367 is an electric setting lever machine. The side walls are covered with plexiglass. No. 6279 has a keyboard and, strangely, two nameplates (Hans W. Egli and H.W. Egli SA). Table 16.22  Deutsches Museum, Munich Number 1115 1160 10248

Year of manufacture 1909 1909 After 1924

Remark Models with keyboard (no. 10248) were manufactured from 1913 on. Table 16.23 Heinz Nixdorf Museumsforum, Paderborn Number 1712 2505 6046 6151

Year of manufacture 1911 1916 1921 1921

Italy Table 16.24 Museo Nazionale della Scienza e della Tecnologia “Leonardo da Vinci”, Milan Number 2851 3347

Year of manufacture 1917 1918

Remark No. 2851 is a setting lever machine and no. 3347 has a keyboard. The Netherlands Table 16.25 Rijksmuseum Boerhaave, Leiden Number Year of manufacture 4089 1919

776

16  Mechanical Calculating Aids

Remarks Rijksmuseum means national museum. This machine was encased in a wooden frame. Egli’s price list of 1914 mentions a setting lever machine in wooden frame. Hermann Moos & Co., Löwenstraße 61, Zurich 1, a “specialty store for modern office equipment and office machines”, supplied “one Millionaire calculating machine, no. 4089, with setting lever operation, 8  ×  8=16-place” for 2100 Swiss francs and a matching stand for 200 Swiss francs, as well as a certificate of guarantee (for 2 years) to the Dutch astronomer Willem de Sitter, as a “faktura” (invoice) of October 5, 1920, shows. These documents are now in the archives of Leiden University. In a personal communication of November 18, 2018, Andries de Man writes: According to T. van Helvoort in “Een verborgen revolutie: de computerisering van de Rijksuniversiteit Groningen” (A veiled revolution: the computerization of the University of Groningen), publishing house Verloren, 2012, page 65, this was a “tweedehands” (secondhand) machine, but this was not confirmed”. The Handbuch der Büromaschinen (Verlag für Sammler-Literatur Dingwerth GmbH, Delbruck 2003, reprint) gives a price of 1750 to 4600 Swiss francs, according to model, for the Millionaire in 1927. Sweden Table 16.26  Tekniska museet (National Museum of Science and Technology), Stockholm Number Year of manufacture 1323 1909 6346 1922

Remark No. 6346 is a setting lever machine. Switzerland Table 16.27 Museum Kommunikation, Bern Number 240 1520 3044 4062

für

Year of manufacture 1903 1910 1918 1919

Remarks No. 4062 is a keyboard machine. A machine with the number 240 is also preserved in the collection of Harvard University. This is evidently an error on the part of the manufacturer.

16.3  Slide Bar Adders and Mechanical Calculating Machines

777

Table 16.28  Private collection of Hans Peter Schaub, Gelterkinden BL Number 2547 4007

Year of manufacture 1916 1919

Remark Machine no. 2547 has setting levers and no. 4007 keys. Table 16.29  Private collection of Fritz Rusterholz, Herrliberg ZH Number 125 2910 3262 4361 10852

Year of manufacture 1900 1917 1918 1920 After 1924

Remark Machine no. 125 is in a wooden casing and no. 10852 has a multiplication keyboard. No. 4361 was resold by Hermann Moos & Co. in Zurich. The Swiss Official Gazette of Commerce (SHAB), volume 38, no. 283, of November 9, 1920, page 2113, states: “November 6. As a result of the transfer of business assets and liabilities to the collective proprietorship under the company ‘Pfeiffer & Brendle’, in Zurich 1 […], and the resulting disbandment of this collective proprietorship, the entry Hermann Moos & Co. has been deleted.” Hermann Moos & Co was founded on January 1, 1914 (SHAB, volume 32, no. 2, January 5, 1914, page 9), and the company Pfeiffer & Brendle on November 1, 1920 (SHAB, volume 38, no. 275, October 30, 1920, page 2059). Herrmann Moos & Co. existed from January 1914 to November 1920. No. 4361 was therefore manufactured at the latest in 1920. Table 16.30 Musée de la machine à écrire, Lausanne Number Year of manufacture 3230 1918 6443 1923

Remark No. 6443 has a multiplication keyboard, which was introduced in 1927 and possibly retrofitted to this specimen.

778

16  Mechanical Calculating Aids Table 16.31 Museum Enter, Solothurn Number 1169 1680 2905 3066 4321

Year of manufacture 1909 1911 1917 1918 1920

Remark No. 1680 is a setting lever machine in a wooden casing. No. 3066 has setting levers, and no. 4321 is equipped with a keyboard. The two machines with the numbers 1169 and 2905 are not on display. Table 16.32  Private collection of Bruno Narr, Windisch AG Number 1834 2637 6203

Year of manufacture 1911 1917 1922

Remark No. 1834 is in a wooden casing and the other machines in a metal casing. No. 6203 has a keyboard, and the others have setting levers. Table 16.33 Schweizerisches Nationalmuseum, Zurich Number Year of manufacture 784 1907 1377 1910

UK Table 16.34  Science Museum, London Number 1382 2741 2918

Year of manufacture 1910 1917 1917

USA Table 16.35  Harvard University, Cambridge, Massachusetts Number 240 704 3282 6215

Year of manufacture 1903 1907 1918 1922

16.3  Slide Bar Adders and Mechanical Calculating Machines

779

Remarks No. 240 and no. 704 have setting levers and nameplates bearing the name Hans W. Egli. No. 3282 and no. 6215 have keyboards and nameplates bearing the name H.W. Egli AG (SA.). A machine with the number 240 is also preserved in the Museum für Kommunikation in Bern. This is evidently an error on the part of the manufacturer. Table 16.36 MIT Museum, Cambridge, Massachusetts Number 1030 1637 2653 3177

Year of manufacture 1908 1911 1917 1918

Remarks No. 3177 has a keyboard and the other machines utilize setting levers. No. 2653 is equipped with a motor. Table 16.37 Yale University, New Haven, Connecticut Number Year of manufacture 3086 1918 9104 After 1924 Table 16.38  Computer History Museum, Mountain View, California Number 272 488 539 990 1073 1523 4493 6417

Year of manufacture 1904 1906 1906 1908 1909 1910 1920 1923

Remark The museum has acquired the Gwen Bell artifact and book collection. With numbers 272, 539, and 1073, the numerals are entered with setting levers. The setting lever machines with the numbers 4493 and 6417 are electromech anical machines. Such models with electric motor were introduced in 1911. However, on the website of Gordon Bell, the following years of manufacture are given: 1900 (no. 272), 1903 (no. 539), and 1920 (no. 4493).

780

16  Mechanical Calculating Aids Table 16.39 National Museum of American History, Washington, D.C. Number 809 821 832 837 1132 2432 2609 4154 9123 14382

Year of manufacture 1907 1907 1908 1908 1909 1916 1917 1919 After 1924 After 1924

Other Collections The years cited are approximate dates. The machines are listed in alphabetical order by country and site. Australia • Machine no. 2702 from the Computing and Information Systems Collection of the University of Melbourne is a setting lever machine in a wooden casing (dating from around 1917). Germany • A Millionaire with the number 1455 with wooding casing (dating from around 1910) is preserved in the Deutsches Bergbau-Museum in Bochum. • The Mathematisch-physikalischer Salon in Dresden is in possession of Millionaire no. 889 (dating from around 1909). • The holdings of the Technische Sammlungen Dresden include a Millionaire with serial number 959 (from around 1908). • The Millionaire with factory number 964 of the Göttinger Sammlung mathematischer Modelle und Instrumente (University of Göttingen) is a setting lever machine in a wooden casing. It was manufactured around 1908. • The factory number of the setting lever machine in wooden casing of the Geodätisches Institut of the Leibniz University in Hanover is 245 (from 1903). • The setting lever machine of the Technoseum in Mannheim, no. 3376, was probably manufactured in 1918. The museum gives the date as 1927. • Several “Millionaires” are found in German private collections: in Altdorf (Eggebrecht) no. 2597 (1917), Berlin (Bertelmann) no. 1629 (1910), Göttingen (Geppert) no. 1330 (1909, metal casing), Hohenstein (Atzbach) no. 803 (1907), Kerpen-Sindorf (Doose) no. 185 (1901), Lilienthal (Haertel) no. 2598 (1917), Münster (Denz) no. 3055 (1918), and Usingen (Hagenah) no. 3357 (1918).

16.3  Slide Bar Adders and Mechanical Calculating Machines

781

Switzerland • The Kantonales Vermessungsamt in Aarau has a setting lever machine in wooden casing with the number 1464. This dates roughly from the year 1910. • The Millionaire of the Vermessungsamt of the city of Bern has the number 17523. It was probably manufactured around 1930, as the installation instructions of March 10, 1930, indicate. • The keyboard machine of the Amt für Landwirtschaft und Geomatik in Chur GR bears the serial number 12989. It was probably manufactured after 1924. • The Historisches Museum Thurgau (Schloss Frauenfeld) has a mechanical Millionaire with full keyboard. It bears the number 3265 and was therefore probably manufactured around 1918. • The Millionaire no. 14356 of the Historisches Museum, Lucerne, was manufactured after 1924. • The machine of the Schreibmaschinenmuseum Beck in Pfäffikon ZH, with serial no. 1379, was manufactured around 1910. • Millionaire no. 2261 of the Abteilung Vermessung of the city of St. Gallen was manufactured around 1914. • The Abteilung Amtliche Vermessung of the city of Zurich has a keyboard machine with the number 3260 (from around 1918), equipped with a constant apparatus. • The following machines, for example, belong to Swiss private collections: in Bremgarten BE (Brüngger) no. 2171 (1913), Buchs SG (Erne) no. 3253 (1918), Bülach ZH (Schwarz) no. 4022 (1919), Davos GR (Darnuzer) no. 6082 (1921), Kienberg SO (Schmid) no. 6290 (1922), Lenzerheide GR (Strässler) no. 4372 (1920), Männedorf ZH (Weiss) no. 915 (1908), Sattel SZ (Schwegler) no. 3035 (1918), Würenlos AG (Möckel) no. 2648 (1917), and Yens VD (Saudan) no. 2943 (around 1917). For the abbreviations for the Swiss cantons, see Sect. 1.9. USA • The Museum of Science and Industry in Chicago has a machine with the number 10240 that was probably marketed after 1924. • The Traub-McCorduck Collection of the Carnegie Mellon University in Pittsburgh, Pennsylvania, includes a Millionaire with the number 2380 (around 1916). This machine is a replica by Roberto Guatelli. • The Millionaire of the IBM Corporate Archives in Poughkeepsie, New York, with the number 403, can be dated to the year 1905. Sources Anonymous: 50 Jahre Egli Rechenmaschinen Fabrik AG, Zurich, October 1943, 2 pages (typewritten). (Source: Schweizerisches Sozialarchiv, Zurich, Ar 422.73.1: Hans W. Egli Rechenmaschinen Zurich 1914-1948) Anonymous: Daten aus der Geschichte der Firmen Hans W. Egli und H.W. Egli A.G., Zurich-Wollishofen, undated (around 1961) (abbreviation 11/10/611 RK-; copy of Hbt), 2 pages (typewritten), Museum für Kommunikation, Bern, Pap 1734

782

16  Mechanical Calculating Aids

Anonymous: Gebrauchs-Anleitung für die Rechenmaschine "Millionär". Patent Otto Steiger, Hans W.  Egli, Ingenieur, Zurich 2, undated (around 1905), 36 pages (with references from April 1904). (Source: Schweizerisches Sozialarchiv, Zurich, Ar 422.73.1: Hans W.  Egli Rechenmaschinen Zurich 1914-1948) Anonymous: Gebrauchs-Anleitung für die Rechenmaschine "Millionär". Patent Otto Steiger, Hans W.  Egli, Ingenieur, Zurich 2, Fabrikation von Rechenmaschinen, undated (around 1908), 31 pages. (Source: ETH Zurich computer science library) Anonymous: H.W.  Egli AG.  Rechenmaschinenfabrik, Seestraße 356/358, Zurich-­Wollishofen, gegründet 1893, 2 pages, around 1943, Museum für Kommunikation, Bern, Pap 1734 Anonymous: untitled, "Total v. H.W.  Egli AG produzierte Rechenmaschinen (vom Anfang bis zur Liquidation), around 1972, 1 page (handwritten), Museum für Kommunikation, Bern, Pap 1734 Anonymous: Rechenmaschinen geliefert bis Jan. 1942, 1 page (handwritten), Museum für Kommunikation, Bern, Pap 1734 Archiv des Swiss science center Technorama, Winterthur ("Rechenmaschinen und Rechengeräte" file with corresponding dossiers) F.  Bühlmann: Die Berechnung der Koordinaten der Grenzpunkte mit der Rechenmaschine "Millionär", in: Schweizerische Geometer-Zeitung, volume 13, 1915, no. 6, pages 154–164 H.W.  Egli AG (Hbt./hh): 50 Jahre Egli-Rechenmaschinen. Entwurf zu einer Jubiläumsschrift, Zurich 1943, 13 pages (typewritten, Hbt. possibly stands for Herbert Bannwart), Museum für Kommunikation, Bern, Pap 1734 H.W.  Egli AG (Hbt./hh): 50 Jahre Egli-Rechenmaschinen. Entwurf zu einer Jubiläumsschrift, Zurich 1943, 13 pages (biographical dossier, ETH Zurich, University archives, typewritten (Hbt. possibly stands for Herbert Bannwart) H.W.  Egli AG: 50 Jahre schweizerische Rechenmaschinenindustrie, Zurich 1943, 32 pages (Madas product overview, Rechnerlexikon, www. rechnerlexikon,de) ETH Library Zurich: Albert Einstein’s Zurich, ETH Zurich 2016, 6 pages (folded brochure in English) ETH Library Zurich: Albert Einsteins Zürich, ETH Zurich 2016, 6 pages (folded brochure in German) Adolf Haarpaintner: Entwicklungsgang der Rechenmaschine "Millionär", Zurich, October 7th 1933, 15 pages (handwritten), Museum für Kommunikation, Bern, Pap 1734 Adolf Haarpaintner: Zusammenstellung aller Sorten der fabrizierten "Millionär", October 7th 1933, 1 page (handwritten), Museum für Kommunikation, Bern, Pap 1734 Michael Lewin: Entwicklungsgeschichte der Rechenmaschinen der Firma H.W. Egli bis 1931, in: Typenkorb 1992, volume 48, pages 15–20 Michael Lewin: Entwicklungsgeschichte der Rechenmaschinen der Firma H.W. Egli bis 1931, in: Typenkorb 1992, volume 49, pages 6–12

16.3  Slide Bar Adders and Mechanical Calculating Machines

783

Michael Lewin; Ullrich Wolff: Die Entwicklung der "Millionär"Rechenmaschine, in: Historische Bürowelt, December 2014, volume 98, pages 3–11 Martin Reese: 55 erfolgreiche Jahre: Madas-Rechenautomaten aus der Schweiz 1913–1968, in: Historische Bürowelt, June 2010, volume 82, pages 15–22 Register of Millionaire calculators, John Wolff’s web museum (http://johnwolff.id.au/calculators/Egli/Register/MillionaireRegister.htm) Gérald Saudan: Swiss calculating machines. H.W. Egli A.-G. – A success story, Yens sur Morges VD 2017, 147 pages (published by the author) Gérard Schmid; Michael Lewin: Die Millionär Nr. 10, in: Historische Bürowelt, 2017, volume 108, pages 20–23 H.  Sossna: Auflösung der Aufgabe des Einkettens mittelst Maschine und numerisch-­ trigonometrischer Tafel. Die neue Multiplicationsmaschine von Otto Steiger und Hans W.  Egli in Zurich, in: Zeitschrift für Vermessungswesen, volume 28, 1899, no. 24, pages 665–696

16.3.2  The Madas In 1913 the Zurich company brought out the first calculating machine with automatic division, the Madas (an acronym for multiplication, automatic division, addition, and subtraction), designed by Erwin Jahnz (see Fig. 16.18). The Madas belonged to the internationally most capable desk calculating machines. Both the Millionaire and the Madas were offered with manual or electric drive.

Fig. 16.18  The Madas four-function machine with full keyboard. The expensive, widely used Madas was one of the most highly capable calculating machines on the market. This model is equipped with a full keyboard and an electric drive. (© Museum für Kommunikation, Bern)

784

16  Mechanical Calculating Aids

16.3.3  The Precisa Another important Swiss machine builder was Ernst Jost of the Precisa AG, in Zurich-Oerlikon. This company marketed numerous addition and four-function machines under the brand name Precisa, with and without printing mechanism (see Figs. 16.19 and 16.20).

Fig. 16.19  Precisa with printing mechanism and manual drive. The Precisa company offered a variety of models. This model features a ten-key keyboard and a hand crank. (© Museum für Kommunikation, Bern)

Fig. 16.20  Precisa with printing mechanism and electric drive. The Precisa was one of the best known Swiss calculating machine brands. Here a model with ten-key keyboard and electric drive. (© Museum für Kommunikation, Bern)

16.3.4  The Stima The clockmaker Albert Steinmann of La Chaux-de-Fonds NE developed, e.g., the Stima calculating machine (see Figs. 16.21 and 16.22).

16.3  Slide Bar Adders and Mechanical Calculating Machines

785

Fig. 16.21  The Stima multifunction calculating machine (1). The Albert Steinmann clock factory in La Chaux-de-Fonds NE, about which little is known, built numerous calculating machines with automatic tens carry. This model is operated with a stylus. (© Museum für Kommunikation, Bern)

Fig. 16.22  The Stima multifunction calculating machine (2). The machine reminds one of a slide bar adder, but has no crook tens carry. (© Schweizerisches Landesmuseum, Zurich)

“A New Branch of the Clock Industry” One writes us: After more than 20 years of technical work, one of the best still existing clock factories, in La Chaux-de-Fonds, has created a new industry, namely, in the field of calculating machines. The basic idea was to build an apparatus suitable for modern accounting and calculation methods that is wieldy, practical, solidly built and offers high performance. The first machines appeared on the market at the end of December 1930 and immediately proved to be popular. Today, it must be said that the sales figures exceeded expectations. In fact, more than 1000 of these machines were sold in Switzerland. For many years now, the market is flooded with inferior foreign calculating devices which

786

16  Mechanical Calculating Aids

are hardly more than toys. The tiny “Stima” calculating machine is a precision instrument that can only be constructed with suitable fine tools, such as the clockmaker uses. The size of 8 x 14.5 x 1.5 cm incorporates around 500 components, all of which are machined to a hundredth of a millimeter. As the first of their kind, this calculating machine is able to control every numeral entered, has a fully automatic tens carry, allows the correction of any input errors, and quickly clears to zero […]. Together with the case, it weighs 740 grams. With these properties the apparatus, which costs not even 100 Swiss francs, and in many cases, performs the function of a large machine could be sold wherever one is hesitant to invest in an expensive machine. The factory now employs a respectable number of workers. (Source: Neue Zürcher Zeitung, March 2, 1932).

Remark The dimension 1.5 cm refers to the flat model and not to the stand model. The following pages illustrate selected mechanical calculating aids in alphabetical order (see Figs. 16.23, 16.24, 16.25, 16.26, 16.27, 16.28, 16.29, 16.30, 16.31, 16.32, 16.33, 16.34, 16.35, and 16.36).

16.3.5  The Conto Much less common was the unconventional Conto of Carl Landolt & Co. in Thalwil ZH with rotatable indicators for numerical input.

Fig. 16.23  The Conto (1). With this adding machine, offered in models A, B, and C, numerical input is via the pointers of the eight numeral circles. The sickle-shaped lever (top left) transfers the input values to the result mechanism. The round knob (at the left) deletes the results. (© Daniel Maurer, Vienna)

16.3  Slide Bar Adders and Mechanical Calculating Machines

787

Fig. 16.24  The Conto (2). Model A is ascribed to Johannes Aumund (patent 1905). The device provides for six places before and two places after the decimal point. (© Schweizerisches Landesmuseum, Zurich)

16.3.6  The Coréma The Coréma was from the French-speaking region of Switzerland.

Fig. 16.25  The Coréma addition and subtraction machine. This Geneva machine is characterized by its full keyboard. (© Museum für Kommunikation, Bern)

788

16  Mechanical Calculating Aids

16.3.7  The Correntator In connection with the slide bar adder, Bergmann also offered ready reckoners.

Fig. 16.26  Desk model of the Correntator slide bar adder. The developer of this calculating machine, Jean Bergmann, apparently fled from Berlin to Switzerland. The device requires a stylus and utilizes the crook tens carry. (© Museum für Kommunikation, Bern)

Fig. 16.27  Pocket model of the Correntator slide bar adder (1). With this pocket calculator numerals are entered with a stylus. The plate enables changing between addition and subtraction. Such stylus-operated calculating devices were once widespread. (© Historisches Museum Thurgau, Schloss Frauenfeld)

16.3  Slide Bar Adders and Mechanical Calculating Machines

789

Fig. 16.28  Pocket model of the Correntator slide bar adder (2). In columns 1 to 9, the crook for semiautomatic tens carry can be seen at the top. The metal bow (at the top) serves for clearing the device. (© Historisches Museum Thurgau, Schloss Frauenfeld)

16.3.8  The Demos The Theo Muggli AG in Zurich brought the Demos calculating machine to the market.

Fig. 16.29  The Demos four-function machine. With this manually operated machine, numerical input is via setting wheels. (© Museum für Kommunikation, Bern)

790

16  Mechanical Calculating Aids

16.3.9  The Direct The Muggli product line also included the Direct keyboard adding machine.

Fig. 16.30  The Direct multifunction machine (1). This calculating aid of Carl Moesch is characterized by the full keyboard, the hand crank, and the printing mechanism. (© Museum für Kommunikation, Bern)

Fig. 16.31  The Direct multifunction machine (2). Several models of this calculating machine were on the market. (© Schweizerisches Landesmuseum, Zurich)

16.3  Slide Bar Adders and Mechanical Calculating Machines

791

16.3.10  The Eos The Eos was a replica of the German Hannovera CK.

Fig. 16.32  The Eos four-function machine. This calculating machine was a replica of the German Hannovera. (© Schweizerisches Landesmuseum, Zurich)

16.3.11  The Heureka The Heureka was among the early single-digit adding machines.

Fig. 16.33  The Heureka adding machine (1). This calculating machine with nine keys is viewed as rare. The result mechanism allows 10-place values. (© Heinz Nixdorf Museumsforum, Paderborn)

792

16  Mechanical Calculating Aids

Fig. 16.34  The Heureka adding machine (2). No information is available about the popularity of this calculating device. (© Heinz Nixdorf Museumsforum, Paderborn)

16.3.12  The St. Gotthard The St. Gotthard, from Northern Switzerland, was probably not very popular.

Fig. 16.35  The St. Gotthard two-function machine. The calculating device from Basel-­ Landschaft was capable of addition and subtraction with complements. (© Museum für Kommunikation, Bern)

16.4  Prices of Calculating Aids

793

16.3.13  The Ultra In the 1950s the Werkzeugmaschinenfabrik Oerlikon manufactured several calculating machines called the Ultra.

Fig. 16.36  The Ultra multifunction machine, an electric calculator featuring a ten-key keyboard and printing mechanism. (© Museum für Kommunikation, Bern)

16.4  Prices of Calculating Aids Determining the prices retroactively is often very difficult (see box). Slide Rules Slide rules were manufactured in numerous countries, e.g., the UK, France, the USA, Germany, and Japan. The most important Swiss slide rule producer was the Loga-Calculator AG of Heinrich Daemen Schmid. Other well-known producers were Billeter and National. The Kern company in Aarau offered slide rules for surveying purposes. Prices for slide rules Loga slide rules 15 and 30 cm Loga circular slide rules 30–150 cm Loga circular slide rules Loga cylindrical slide rules 1.2–24 m Loga cylindrical slide rules Loga cylindrical slide rules

1932 8–12 Swiss francs 1932 20–70 Swiss francs 1941 from 15 Swiss francs 1932 100–800 Swiss francs 1941 up to 670 Swiss francs 1942 150, 300, 420, 600 Swiss francs (continued)

794

16  Mechanical Calculating Aids

Sources Der Organisator and advertisements in the Neue Zürcher Zeitung. Calculating Machines The following compilations provide an impression of the prices for calculating devices (see Table 16.40). Model Conto, 8-place Conto, 10-place Coréma portative Coréma portative Demos Direct Direct Eos Madas (electric) Oxner Baby Precisa Rapida 8 Rapida 8 Simex Caroline Stima 7-, 8-, 9-place Stima Trebla Volksrechner

Year 1932 1932 1949 1952 1923 1932 1936 1930 1958/1959 1952/1954 1937 1946 1947/1948 1960 1932 1940/1941/1944/1948 1941 1930

Price 320 Swiss francs 420 Swiss francs 385 Swiss francs 415 Swiss francs 500 Swiss francs from 600 Swiss francs from 350 Swiss francs 525, 575 Swiss francs from 1540 Swiss francs 435 Swiss francs 800 Swiss francs 200 Swiss francs 220 Swiss francs 100 Swiss francs 85, 98, 115 Swiss francs 155, 185, 145 Swiss francs 22, 50 Swiss francs 95 Swiss francs

Remark When more than one price is quoted: cost according to model. Sources Der Organisator as well as Büro und Verkauf and advertisements in the Neue Zürcher Zeitung. Table 16.40  Price development for mechanical calculating machines Prices for well-known calculating aids (Switzerland and Liechtenstein) Device Date Price Source Conto October 1932 320 SFr. (8-place), Der Organisator, no. 163 420 SFr. (10-place) Coréma portative September 1949 385 SFr. Der Organisator, no. 366 Correntator January/February 22 to 88 SFr. Der Organisator, (slide bar adder) 1946 no. 322 and no. 323 Curta 1 1963 425 DM Büromaschinen-Lexikon Curta 2 1963 535 DM Büromaschinen-Lexikon (continued)

16.4  Prices of Calculating Aids

795

Table 16.40 (continued) Prices for well-known calculating aids (Switzerland and Liechtenstein) Device Date Price Source Demos June 1923 480 SFr. Der Organisator, no. 51 Demos January 1925 500 SFr. Der Organisator, no. 70 Demos 3 July 1925 600 SFr. Der Organisator, no. 76 Demos 1927 600 SFr. Handbuch der Büromaschinen Demos 1930 300 to 600 SFr. Der Organisator: Moderne Büro-Maschinen Direct 1930 750 SFr. Der Organisator: Moderne Büro-Maschinen Direct 2 April 1937 345 SFr. Der Organisator, no. 217 Direct A 1927 125 Dollars Handbuch der Büromaschinen Direct B 1927 175 Dollars Handbuch der Büromaschinen Direct L April 1932 650 SFr. Büro und Verkauf, no. 4 Direct L November 1937 650 SFr. (8-place), Der Organisator, no. 224 850 SFr. (10-place) Eos 1927 600 SFr. Handbuch der Büromaschinen Eos February 1927 600 and 780 SFr. Der Organisator, no. 95 Eos 1930 525 and 575 SFr. Der Organisator: Moderne Büro-Maschinen Loga circular slide September 1937 60 SFr. Der Organisator, no. 222 rule Loga circular slide April 1945 18 to 100 SFr. Büro und Verkauf, no. 7 rule Loga circular slide January 1946 35 to 100 SFr. Der Organisator, no. 322 rule Loga cylindrical slide 1930 100 to 800 SFr. Der Organisator: rule Moderne Büro-Maschinen Loga cylindrical slide June 1943 95 to 700 SFr. Büro und Verkauf, no. 9 rule Loga cylindrical slide January 1946 300 to 750 SFr. Der Organisator, no. 322 rule Loga cylindrical slide February 1948 170 to 600 SFr. Der Organisator, no. 347 rule Madas 1930 1400 to 3600 SFr. Der Organisator: Moderne Büro-Maschinen Madas 10 R 1963 1660 DM Büromaschinen-Lexikon (continued)

796

16  Mechanical Calculating Aids

Table 16.40 (continued) Prices for well-known calculating aids (Switzerland and Liechtenstein) Device Date Price Source Madas 12 e N 1963 1230 DM Büromaschinen-Lexikon Madas 16 L August 1949 2400 SFr. Der Organisator, no. 365 Madas 16 LG March 1956 2600 SFr. Büro und Verkauf, no. 6 Madas 16 LG 1963 2290 DM Büromaschinen-Lexikon Madas 16 LS 1963 2875 DM Büromaschinen-Lexikon Madas 16 e August 1949 1600 SFr. Der Organisator, no. 365 Madas 16 e March 1956 1750 Fr. Büro und Verkauf, no. 6 Madas 16 e N 1963 1595 DM Büromaschinen-Lexikon Madas 20 AT August 1949 4400 SFr. Der Organisator, no. 365 Madas 20 AT March 1956 5450 SFr. Büro und Verkauf, no. 6 Madas 20 AV August 1949 3800 SFr. Der Organisator, no. 365 Madas 20 BG 1963 3870 DM Büromaschinen-Lexikon Madas 20 BS 1963 4715 DM Büromaschinen-Lexikon Madas 20 BTG 1963 5560 DM Büromaschinen-Lexikon Madas 20 BTZG 1963 6100 DM Büromaschinen-Lexikon Madas 20 BVG 1963 3990 DM Büromaschinen-Lexikon Madas 20 BZS 1963 4915 DM Büromaschinen-Lexikon Madas 20 e 1963 1895 DM Büromaschinen-Lexikon Madas 20 LS 1963 3275 DM Büromaschinen-Lexikon Madas IX 1927 1700 SFr. Handbuch der Büromaschinen Madas IX e 1927 2300 SFr. Handbuch der Büromaschinen Madas IX e T 1927 2800 SFr. Handbuch der Büromaschinen Madas IX T 1927 2200 SFr. Handbuch der Büromaschinen Madas VII 1927 1350 SFr. Handbuch der Büromaschinen Madas VII e 1927 2100 SFr. Handbuch der Büromaschinen Madas VII e T 1927 2500 SFr. Handbuch der Büromaschinen Madas VII T 1927 1900 SFr. Handbuch der Büromaschinen Madas XX A June 1937 3600 SFr. Büro und Verkauf, no. 9 Millionaire VI 1927 1750 SFr. Handbuch der Büromaschinen Millionaire VI T 1927 1900 SFr. Handbuch der Büromaschinen Millionaire VIII 1927 2100 SFr. Handbuch der Büromaschinen Millionaire VIII e 1927 3400 SFr. Handbuch der Büromaschinen (continued)

16.4  Prices of Calculating Aids

797

Table 16.40 (continued) Prices for well-known calculating aids (Switzerland and Liechtenstein) Device Date Price Source Millionaire VIII eT 1927 3600 SFr. Handbuch der Büromaschinen Millionaire VIII T 1927 2350 SFr. Handbuch der Büromaschinen Millionaire X 1927 2700 SFr. Handbuch der Büromaschinen Millionaire X e 1927 4000 SFr. Handbuch der Büromaschinen Millionaire X eT 1927 4300 SFr. Handbuch der Büromaschinen Millionaire X T 1927 3000 SFr. Handbuch der Büromaschinen Millionaire XII eT 1927 4600 SFr. Handbuch der Büromaschinen Precisa 108-8 1963 398 DM Büromaschinen-Lexikon Precisa 108-10 1963 450 DM Büromaschinen-Lexikon Precisa 117 1963 665 DM Büromaschinen-Lexikon Precisa 160 December 1961 850 SFr. Büro und Verkauf, no. 3 1963 665 DM Büromaschinen-Lexikon Precisa 160-8 (black printout) Precisa 160-8 1963 798 DM Büromaschinen-Lexikon (red-black printout) Precisa 160-12 1963 898 DM Büromaschinen-Lexikon (black printout) Precisa 160-12 1963 1100 DM Büromaschinen-Lexikon (red-black printout) 1963 1550 DM Büromaschinen-Lexikon Precisa Electric 110-11-10 with sliding carriage 1963 1855 DM Büromaschinen-Lexikon Precisa Electric 110-11-10 with shuttle carriage Precisa Triomatic 176 1963 2650 DM Büromaschinen-Lexikon Precisa Virtuosa 170 1963 3950 DM Büromaschinen-Lexikon Stima November 1937 60 to 165 SFr. Der Organisator, no. 224 Stima March 1947 128, 145, 185, 750 Der Organisator, no. 336 SFr. Trebla April 1937 18 SFr. Der Organisator, no. 217 Trebla September 1937 18 SFr. Büro und Verkauf, no. 12 Trebla November 1937 22.50 SFr. Der Organisator, no. 224 Ultra Electric September 1950 1250 SFr. Büro und Verkauf, no. 12 Ultra Electric November 1957 980 SFr. Der Organisator, no. 464 Büro und Verkauf, no. 2 Ultra Electric April 1959 1070 SFr. Büro und Verkauf, no. 7 © Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020

798

16  Mechanical Calculating Aids

Abbreviations DM German mark SFr. Swiss franc Sources Paul Greiner: Büromaschinen-Lexikon, Robert Göller Verlag, Baden-Baden, 7th edition 1963/64, 608 pages Handbuch der Büro-Maschinen, Verlag für Sammler-Literatur Dingwerth GmbH, Delbrück 2003 (reprint from 1927). Remarks Millionaire and Madas: The numerals VI, VIII, X, and XII refer to the number of decimal places. E stands for electric and T for Tastatur (keyboard). When the symbols e and T are missing, the machines are operated manually and have setting levers. The sales prices for calculating machines often remained unchanged over a longer time. The issue number refers to the relevant volume (year). At the time, calculating machines were regarded as expensive. Converting to today’s conditions to account for rising prices is not very meaningful. More revealing is a comparison with the respective daily wages and monthly salaries (see Table 16.41). Table 16.41  Mean wages from 1918 to 1970 Mean hourly wages in Swiss Rappen (all industries) Year Skilled and semiskilled workers Unskilled workers 1918 108 86 1921 162 126 1929 148 114 1939 140 108 1950 262 220 1959 355 294 1960 375 309 1969 686 581 1970 738 631

Women 51 83 77 73 163 212 222 404 439

Adolescents 54 77 64 52 131 176 191 348 353

© Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020

Source Eidgenössisches Statistisches Amt (editor.): Statistisches Jahrbuch der Schweiz, Birkhäuser Verlag, Basel, volumes 1920–1970

16.5  Piece Numbers Information about the sales of calculating aids is very scarce: When the visitor enters the “Modern office” hall a graphical presentation on the wall opposite the entrance informs him or her that Switzerland occupies third place among the countries exporting office machines, after the United States of America and Germany (see Hermann Spindler: Das moderne Büro an der Schweizerischen Landesausstellung, in: Büro und Verkauf, volume 8, no. 9, June 1939, page 2).

16.5  Piece Numbers

799

For skilled workers and technical staff, slide rules were routine daily tools. They caught on with commercial employees much slower: For some time commercial employees in Switzerland have used logarithmic-graphical calculating aids (linear slide rules, circular slide rules, cylindrical slide rules) more than before, now that wide circles have recognized the versatility and the many advantages of these instruments (see Hermann Spindler: Die Gruppe “Büro und Geschäft” an der Mustermesse 1944, in: Büro und Verkauf, volume 13, no. 8, May 1944, page 21). The great interest of commercial personnel in calculating with slide rules is reflected in the pronounced visiting of courses serving to explain the use of these instruments (see Hermann Spindler: Die Gruppe “Büro und Geschäft” an der Mustermesse 1945, in: Büro und Verkauf, volume 14, no. 8, May 1945, page 212). “More than 100,000 pieces in use” stated an advertisement for Loga calculators (circular slide rules and cylindrical slide rules) in the journal Organisator (volume 27, no. 323, February 1946, page 39). The technician and the engineer have long since made use of these high-performance calculating aids, and now the logarithmically constructed calculating devices (linear slide rules, circular slide rules and cylindrical slide rules) are generating increasing interest in the commercial office. Particularly circular slide rules and linear slide rules with corresponding special partitioning are well suited for commercial calculations (see Hermann Spindler: "Büfa", schweizerische Bürofachausstellung in Zürich, in: Büro und Verkauf, volume 20, no. 1, October 1950, page 17). We consider it necessary to call attention to logarithmic-graphical calculating aids (linear slide rules, circular slide rules and cylindrical slide rules). A Swiss factory manufactures circular and cylindrical slide rules in very precise and solid design. Much too little is known about the vast usefulness of these instruments for practical calculations in the office and how quickly and reliably they can be used to solve extensive calculations. Furthermore, they constitute an enormous advantage when one is traveling and always has a circular or cylindrical slide rule at hand while telephoning and can confidently calculate with such an instrument (see Hermann Spindler: Bürotechnik heute  – Beobachtungen an der Büfa 1952, in: Büro und Verkauf, volume 22, no. 1, October 1952, page 21). Among the calculating aids, in addition to calculating machines there are also the Loga circular and cylindrical slide rules. In many circles too little is known about the capabilities of these simple and noiseless calculating instruments or that there are special models for commercial calculations (see Hermann Spindler: Bürotechnik an der 40. Schweizer Mustermesse, in: Büro und Verkauf, volume 25, no. 9, June 1956, page 234).

Trebla and Stima Year Machine Number 1941 (fall) Trebla 9000 machines 1942 (fall) Stima 13,000 machines The Millionaire According to an undated reference list of the Schweizer Wirtschaftsarchiv in Basel, the Millionaire was marketed worldwide. Thus, for example, the US Department of Commerce and Labor in Washington, D.C., purchased 11 machines, the Badische Anilin- und Sodafabrik (BASF) in Ludwigshafen,

800

16  Mechanical Calculating Aids

Germany, acquired 15 machines, and the Prudential insurance company in Newark, New Jersey, even purchased 34 machines.

16.6  Patents for Calculating Aids The search for patents relating to calculating devices from Switzerland and Liechtenstein reveals the following picture (without claiming to be complete): Patents for mechanical calculating machines Arvai, Tibor 1946, 1952, 1958, etc. Aumund, Johannes 1905, 1906 Benninger, Eugen 1947 Bergmann, Jean 1922, 1923, 1925, 1926, 1927, 1928 Brüning, Paul 1931, 1937, 1952, 1955, 1956, 1957 Chlouba, Adolf 1951 Cho, Chi Liang 1944, 1947, 1955 Coréma, A. 1947 Diethelm, Eugen 1945 Egli, Hans W. 1912 Gabler, Gerhard 1978 Gelling, Helmut 1960, 1963, 1977 Heinze, Werner 1954, 1955 Herzstark, Curt 1938, 1939, 1942, 1946, 1947, 1948, 1949, 1950, 1951, 1952, 1953 Jahnz, Erwin 1912, 1913, 1925, 1930, 1934, 1935, 1942 Janno, Pietro 1952, 1953 Jost, Ernst 1926, 1928 Jülich, Werner 1954, 1955 Karasek, Karl 1905, 1906 Landolt, Carl 1912 Mauch, Julius Hermann 1925 Moesch, Carl 1942 Precisa 1943, 1945, 1949, 1950, 1951, 1952, 1953, 1954, 1955, 1956, 1962, 1963 Schenk, Gustav 1954, 1956, 1958, 1959, 1962 Schubode, Albert 1922, 1924 Steiger, Otto 1892, 1893, 1910 Steinmann, Albert 1930, 1946 Source European patent database, Munich Since the manufacturers of these mechanical calculating devices have long since disappeared, it is difficult to obtain a reliable overview of the calculating aids (see Tables 16.42 and 16.43).

16.7  Mechanical Calculating Aids (Overview)

801

16.7  Mechanical Calculating Aids (Overview) Table 16.42  Digital mechanical calculating aids from Switzerland and Liechtenstein (1)

Inventor/ Manufacturer/ builder site Tibor Arvai Arva SA, Geneva Zurich Atlas Julius Hermann Mauch Carl Landolt Conto A: Karl & Co, Karasek, Johannes Thalwil ZH; successor: Aumund Alfred Müller, B and C: Thalwil ZH Carl Landolt Coréma A. Coréma, Coréma SA, Geneva Chi Liang Cho Corren­tator Jean Unical AG, Bergmann Frauenfeld TG Contina AG, Curta Curt Herzstark Mauren FL Theo Muggli Demos Hans AG, Zurich; Huber, Carl Carl Moesch, Moesch Würenlos AG Direct Carl Theo Muggli Moesch AG, Zurich; Carl Moesch, Würenlos AG Eos Albert EOS-­ Schubode Genossen­ schaft für Fabrikation und Vertrieb von Rechen­ masch­inen, Zurich Device Arva

Adding machine Calculating machine∗ Stepped drum Pinwheel Multiplying block Rocker arm Toothed rack Cogged disc Numeral cylinder Toothed segment Setting wheel Slide bar adder Manual drive Electric drive Without printer With printer Basic arithmetic operations

Slide bar adders and mechanical calculating machines from Switzerland and Liechtenstein 1

■■■□2 4 ■□□□□□□■□□□□■□■□1 ■

■□□□□□□■□□□□■□■□1

■

□□□□■□□□□□■□■

■□□□□□

2

□□□□■■□■□2

□■■□□□□□□□□□■□■□4 □■□□□□□□□■□□■□■□4

■ □ □ □ □ ■ ■ □ □ □ □ □ ■ ■ ■ ■ 2–3

□■□

□□□□□■□□■□■□4

(continued)

802

16  Mechanical Calculating Aids

Table 16.42 (continued)

Device Grunder adding machine Heureka

Inventor/ builder Johannes Gottfried Grunder

Adding machine Calculating machine∗ Stepped drum Pinwheel Multiplying block Rocker arm Toothed rack Cogged disc Numeral cylinder Toothed segment Setting wheel Slide bar adder Manual drive Electric drive Without printer With printer Basic arithmetic operations

Slide bar adders and mechanical calculating machines from Switzerland and Liechtenstein 1

Manufacturer/ site Brienz BE ■

AG für technische Industrie, Zurich Madas Erwin H.W. Egli AG, Jahnz Zurich (Hans Walter Egli) Millionaire Otto H.W. Egli AG, Steiger Zurich (Hans Walter Egli) Minimath Sylvania, Geneva Ochsner Oxner Cyrill Ochsner Rechen­ maschin­en­ fabrik, St. Gallen Precisa Ernst Jost, Precisa Reche­n-­ Eugen Benninger mas­chinen­ fabrik AG, (Werner ZurichHeinze, Oerlikon Helmut Gelling, Pietro Janno, Werner Jülich et al.)

■□□□□□

■

■

1

□□□□□■□■□1

□■■□□□□□□□□□■■■□4

□■□□■□□□□□□□■■■□4

■□■□□□□□□□□□■□■□2 ■□□□□□■□□□□□■□■■2

■■□■□□■□□

□ □ ■ ■ □ ■ 2–4

(continued)

16.7  Mechanical Calculating Aids (Overview)

803

Table 16.42 (continued)

Device Rapida

Schilt Signal

Simex

St. Gotthard

Stima

Summa­ meter Trebla

Inventor/ builder Paul Brüning

Manufacturer/ site W. HäuslerZepf, Olten SO/ Injecta Druckguss AG, Teufental AG/ Henri Zepf, Lausanne (sales agency) Victor Victor Schilt, Schilt Grenchen SO Albert Albert Steinmann Steinmann, La Chaux-de-­ Fonds NE Tibor Arvai Société industrielle des métaux manufacturés SA, Nyon VD Rudolf Rudolf Schweizer Schweizer & Cie., Neu-Allschwil BL Albert Albert Steinmann Steinmann, La Chaux-de-­ Fonds NE Uhrenfabrik, Johann Sumiswald BE Leuen­ berger (?) Albert Albert Steinmann Steinmann, La Chaux-de-­ Fonds NE

Adding machine Calculating machine∗ Stepped drum Pinwheel Multiplying block Rocker arm Toothed rack Cogged disc Numeral cylinder Toothed segment Setting wheel Slide bar adder Manual drive Electric drive Without printer With printer Basic arithmetic operations

Slide bar adders and mechanical calculating machines from Switzerland and Liechtenstein 1

■□□□□□□□□■□□■□■□2

■□□□□■□□□□□□■□■□1 □■■□□□□□□□□□■□■□4

■□□□□□□■

□□□■□■□1

■□□□□□□□■□□□■□■□2

■ ■ ■ □ □ □ ■ □ □ □ □ □ ■ □ ■ □ 1–4

■

■

1

■□□□□□□□□□□■■□■□2

(continued)

804

16  Mechanical Calculating Aids

Table 16.42 (continued)

Device Ultra

Uto

Volks­ rechner (people’s calculator)

Inventor/ builder Gustav Schenk

Carl Moesch, Hans Huber Maschinenund Werk­zeug­ fabrik Paul Brüning, Berlin

Adding machine Calculating machine∗ Stepped drum Pinwheel Multiplying block Rocker arm Toothed rack Cogged disc Numeral cylinder Toothed segment Setting wheel Slide bar adder Manual drive Electric drive Without printer With printer Basic arithmetic operations

Slide bar adders and mechanical calculating machines from Switzerland and Liechtenstein 1

Manufacturer/ site ■■□■□ ■ □ □ □ □ □ ■ ■ □ ■ 2, 4 Werkzeug­ maschin­en­ fabrik Oerlikon, Bührle & Co., Zurich Theo Muggli □ ■ □ □ □ □ □ □ □ ■ □ □ ■ □ ■ □ 4 AG, Zurich ■□□□□□□□□□■□■□■□2 Edgar Rutishauser, St. Gallen (sales agency)

© Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020 Explanation of symbols ∗In the strict sense

Remarks In some cases the information is uncertain. There are contradictions, e.g., with the classification of the design, such as with the Heureka (proportional lever). Information regarding the number of basic arithmetic operations, manual or electric drive, and whether a printing mechanism is incorporated depends on the particular model. The best known machines were the Curta, Madas, Millionaire, Precisa, and Stima. A multiplication table in cylinder form with the name Säntis presumably stems from Eastern Switzerland. A cash register machine was called the Prema. This overview does not claim to be complete. This compilation does not include the Swiss slide rules (linear, circular, and cylindrical slide rules).

16.7  Mechanical Calculating Aids (Overview)

805

Other Swiss Calculating Machines? The following sources refer to calculating machines (without further information): A. Hennemann: Die technische Entwicklung der Rechenmaschine, Verlag Peter Basten, Aachen, 1953, page 23 (Arva) A. Hennemann: Die technische Entwicklung der Rechenmaschine, Verlag Peter Basten, Aachen, 1953, page 24 (adding machines from Winterthur). Table 16.43  Digital mechanical calculating aids from Switzerland and Liechtenstein (2) Slide bar adders and mechanical calculating machines from Switzerland and Liechtenstein 2 Numerical Drive Device Models Year input type Remarks Arva 1952 (?) Ten-key keyboard Atlas 1925 Setting Setting Concentric cogged discs, levers lever ratchets Conto A, B, C 1908 Pointer Direct Numeral circle with rotatable pointer, ratchet drive; cogged disc adder Coréma MC-15, 1949 Full Key (Names in Germany: portative keyboard Corexa and Simeca) Correntator Few 1936 Stylus Direct The universal calculator was a ready reckoner Curta 1, 2 1947 Sliding Crank Desk calculating levers machine, earlier names: Liliput, Contina Crank Setting cogged wheel Demos 1, 2 1920 Setting wheel Direct A, B, EL, 1920 Full Direct, Keyboard adding machine L, LL, 2 keyboard crank, motor Eos CK 1926 Setting Crank Replica of the Hannovera levers CK (Peine, 1923) from remaining stocks 1945 Wooden Lever, One-of-a-kind machine, Grunder wheels pedal clearing with weights adding machine Heureka 1906 Nine keys Key Single-digit adding machine with 10-place result mechanism: sector gear drive Crank, Automatic multiplication Madas Several 1913 Sliding and automatic division levers, full motor keyboard (continued)

806

16  Mechanical Calculating Aids

Table 16.43 (continued) Slide bar adders and mechanical calculating machines from Switzerland and Liechtenstein 2 Numerical Drive Device Models Year input type Remarks Crank, Fast direct multiplier with Millionaire Several 1893 Sliding multiplying block, Setting levers, full motor lever or full keyboard keyboard Minimath 1965 Sliding Crank Extricable sliding levers; levers plastic Oxner Numerous 1950 Full Setting keyboard lever, crank Precisa Several 1935 Ten-key Setting keyboard lever, motor Rapida Rapida 8 1948 Stylus Direct Presumably replica of the Résulta BS 7 Schilt 1850 Nine keys Key Single-digit adder, replica after Schwilgué, displayed at the World exhibition in London, 1851 Signal 1952 Full Crank keyboard Direct Numeral cylinder, roller Simex Caroline 1955 Setting wheels counting mechanism St. Gotthard NS 1936 Setting Direct levers Stima Numerous 1930 Stylus, full Direct, Slide bar adder with keyboard setting automatic tens carry, keyboard adding lever machine; four-function stepped drum machine with full keyboard Summameter Nineteenth century Trebla 1937 Stylus Direct Ultra Numerous 1947 Ten-key Setting keyboard lever, motor Uto 1921 Setting Crank levers Volksrechner 1930 Stylus Direct Equivalent to the Minerva/Résulta 7 © Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020

16.7  Mechanical Calculating Aids (Overview)

807

Remarks • The “year” refers to the beginning of production. However, some information is uncertain or contradictory. • Carl Moesch (Demos, Direct, Uto) had an electromechanical workshop. • Arva: The portable ten-key calculating machine of Arva could be operated manually or electrically. In manual operation it was well suited to addition and subtraction and in electrical operation for all four basic arithmetic operations. • Conto: Carl Landolt, Thalwil (the manufacturer), is already listed in the Swiss Official Gazette of Commerce in 1910. Karl Karasek was a businessman and Johannes Aumund an engineer. In 1906 they were granted a patent for an adding machine. Carl Landolt, Rechenmaschinen, in Thalwil near Zurich, Basel, and Stuttgart, offered the Conto manual adding machine, model B, of his own manufacture in three capacity levels (8/10/11 places) in 1911 (see Anonymous: Generalversammlung des Vereins schweizerischer Konkordatsgeometer, May 14 and 15, 1911, in Zurich, in: Schweizerische Geometer-Zeitung, volume 9, 1911, page 113). • Coréma: According to the Swiss Official Gazette of Commerce, the Coréma SA, Chézard NE (later relocated to Geneva) was founded in 1945. • Correntator: The Correntator slide bar adder of Jean Bergmann was offered in Berlin at the beginning of the 1920s. The Unical multiplication table (1935) was designed by Jean Bergmann and manufactured by P. Baumer in Frauenfeld TG. Unical stands for universal calculator (book of tables, partly in combination with the slide bar adder). • Curta: Regular production began in 1948. • Direct: Direct drive means the transfer of numerical values from the setting mechanism to the counting mechanism (i.e., without a crank). One also speaks of high-speed adding machines. • Hannovera: Dates for the Hannovera: model A 1923, models B and CK 192. • Minimath: This was a machine for instructional purposes. • Precisa: A first prototype was fit for production in 1933. The Precisa AG, Rechenmaschinenfabrik, was founded in Seengen AG in 1935 and had different production sites (1935–1940: Seengen AG, 1941–1944: Winterthur ZH, from 1944: Zurich Oerlikon). In 1934 Oerlikon became a district of Zurich. In 1941 the company name Rechenmaschinen “Precisa” Aktiengesellschaft was changed to Precisa AG Rechenmaschinenfabrik. The Swiss Official Gazette of Commerce, volume 62, no. 56 of March 7, 1944, page 553, has the following entry: “On the basis of the decision of the general assembly of February 17, 1944 the site of the company was moved to Zurich. […]. The location is [in] Wallisellenstrasse 333, in Zurich 11.” Sources Handbuch der Büro-Maschinen, Verlag für Sammler-Literatur Dingwerth GmbH, Delbrück 2003 (reprint from 1927) Anonymous: Brunsviga Rechenmaschinen-Museum. Katalog, Braunschweig, undated Swiss Official Gazette of Commerce.

808

16  Mechanical Calculating Aids

16.8  Dating with the Help of Exhibition Catalogs Only a few documents about Swiss manufacturers of analog and digital calculating aids have survived. An attempt was therefore made to find information on dating, popularity (piece numbers), store prices, and lifetimes of these machines in the exhibition catalogs and exhibition guides (Schweizer Mustermesse, Basel and Büfa, Zurich), reports of exhibitions, and advertisements in professional journals (Der Organisator and Büro und Verkauf). Due to the enormous effort that this required, such evaluations were only possible on a national scale, and the difficult to access publications could mostly only be viewed at the sites of their holding. A further useful source for researching companies, persons, and patents (but not the products themselves) is the Swiss Official Gazette of Commerce (Swiss journals online: https://www.eperiodica.ch).

16.8.1  Catalogs from the Schweizer Mustermesse, Basel The Schweizer Mustermesse first took place in 1917. It is regarded as the oldest and largest Swiss exhibition open to the public. All the catalogs from more than 100 years of exhibitions are available. The annual event was even held during the Second World War without interruption. The Schweizer Mustermesse took place for the last time in 2019. Cebit (Hannover), once the world’s biggest computer fair, first took place in 1986 and was held for the last time in 2018. There are many reasons for presence or absence at public and expert trade fairs (see Fig. 16.37), and these are not known in detail. In the second half of the 1960s, electronic pocket and desktop computers began to appear, and mechanical calculating machines were no longer on display at trade fairs. The last three remaining manufacturers – Contina, Egli, and Precisa – were present at the Mustermesse for the last time in 1968. Source Schweizer Mustermesse Basel: Offizieller Katalog, Verlag der Schweizer Mustermesse, Basel

16.8  Dating with the Help of Exhibition Catalogs

809

Slide rules, mechanical calculating machines and sliding bar calculators at the Schweizer Mustermesse, Basel (selection) Manufacturers from Switzerland and Liechtenstein Year

Bührle

Contina

Coréma

Egli

Eos

Loga

Muggli

National

Ochsner

Precisa

Zurich

Mauren/

Geneva

Zurich

Zurich

Uster ZH

Zurich

Zurich

St. Gallen

Zurich

Coréma

Millionär

Eos

Loga

Direct

Billeter

Oxner

Precisa

Vaduz FL Ultra

Curta

Schweizer

Steinmann

Tesa

Neu-

La Chaux-

Renens VD

Allschwil BL de-Fonds NE St. Gotthard Stima

Madas

Unical Frauenfeld TG

Maximatic

Signal

Unical Correntator

1917 1918 1919 1920 1921 1922 1923 1924 1925 1926 1927 1928 1929 1930 1931 1932 1933 1934 1935 1936 1937 1938 1939 1940 1941 1942 1943 1944 1945 1946 1947 1948 1949 1950 1951 1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963 1964 1965 1966 1967 1968 1969 1970 Year

14 years

20 years

5 years

52 years

3 years

8 years

20 years

5 years

4 years

34 years

1 year

30 years

1 year

7 years

Bührle

Contina

Coréma

Egli

Eos

Loga

Muggli

National

Ochsner

Precisa

Schweizer

Steinmann

Tesa

Unical

Zurich

Mauren/

Geneva

Zurich

Zurich

Uster ZH

Zurich

Zurich

St. Gallen

Zurich

Neu-

La Chaux-

Renens VD

Vaduz FL Ultra

Curta

Allschwil BL de-Fonds NE Coréma

Millionär

Eos

Madas

Loga

Direct

Billeter

Oxner

Precisa

St. Gotthard Stima Signal

Frauenfeld TG

Maximatic

Unical Correntator

Source: Catalogs of the Schweizer Mustermesse, Basel, 1917–1970 © Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020

Fig. 16.37  Manufacturers of calculating machines exhibiting at the Schweizer Mustermesse in Basel 1917–1968. Egli (brand names: Millionaire, Madas) exhibited the longest (52years), Precisa (Precisa) was present for 34 years, Steinmann (Stima, Trebla, Signal) 30 years, and Contina (Curta) 20 years. In 1968 their participation suddenly ended, since the demand for these machines had collapsed. (© Bruderer Informatik, CH-9401 Rorschach, Switzerland)

Company Abbreviations Bührle Werkzeugmaschinenfabrik Oerlikon, Bührle & Co., Zurich-Oerlikon Contina  Contina, Bureaux- und Rechenmaschinenfabrik AG, Mauren/ Vaduz FL Coréma Coréma SA, Geneva Egli H.W. Egli AG, Zurich Eos  Eos Genossenschaft für Fabrikation und Vertrieb von Rechenmaschinen, Zurich Loga Loga-Calculator AG, Uster ZH Muggli Theo Muggli AG, Zurich

810

National Ochsner Precisa Schweizer Steinmann Tesa Unical

16  Mechanical Calculating Aids

National Rechenwalzen AG, Zurich Ochsner Büromaschinen AG, St. Gallen Precisa AG, Zurich Rudolf Schweizer & Co., Neu-Allschwil-Basel Albert Steinmann, La Chaux-de-Fonds NE Tesa SA, Renens-Lausanne VD Unical AG, Frauenfeld TG

Remarks This overview is limited to manufacturers from Switzerland and Liechtenstein. The Millionaire and Madas and the Stima and Signal brands were partly exhibited at the same time. The Correntator was a slide bar adder and the Unical a multiplication table. The exhibit report of Hermann Spindler indicates that the Maximatic circular slide rule was on view at the Muba in 1949. Suppliers of slide rules, especially circular and cylindrical slide rules (e.g., Heinrich Daemen, Zurich: Loga-Calculator), were only rarely present at the Mustermesse. In the 1970s, the advent of electronic digital computers soon suppressed the analog logarithmic slide rules and digital mechanical and electromechanical calculating machines. Explanations Below is a summary of information collected from trade fair catalogs and advertisements. • The H.W. Egli AG, which supplied calculating machines beginning in the 1890s, took part in the Mustermesse for decades without interruption. As a rule, the Additions- und Rechenmaschinen AG, Zurich, was in charge of the stand. Egli exhibited the Millionaire until 1938. In 1932, 26 Madas models were mentioned. From 1957, 20 Madas models were still exhibited. The Madas portable is first mentioned in 1932. That the company last participated in the Mustermesse in 1968 was not by chance. In the 1960s the competition from Japan increasingly drove the Zurich-Wollishofen company, which also had a production site in Kreuzlingen TG, from the market. Egli was unable to develop a commercially successful electronic calculating machine, and the company was no longer c­ ompetitive. The incorporation into the Compagnie des Machines Bull SA in Paris was also a financial fiasco. In 1968 the Precisa AG in Zurich pledged to offer spare parts for the Madas for a period of 10 years. Only a few years later, the Egli AG was disbanded and deleted from the commercial register (see Gérald Saudan: Swiss calculating machines, Yens sur Morges VD 2017, pages 39–40). • The Precisa adding machines, balancing calculators, and calculating machines (ten-key machines) with printout marketed by the Ernst Jost AG, Zurich, offered direct subtraction and a negative account balance. In 1946 the Precisa Electra appeared. These machines were in part capable of per-

16.8  Dating with the Help of Exhibition Catalogs

•

• •

•

• •

811

forming all four basic arithmetic operations. From the 1960s, the company also produced cash registers and independent adding machines, installed in cash registers. In 1948 the following prices were given for the Precisa, Model 102; 880 Swiss francs, Model 103; 690 Swiss francs, and Model 110; 1550 Swiss francs. Small Precisa models for all four basic arithmetic operations were sold in 1955 for 715 Swiss francs. In 1962/1963 the Precisa 160 cost 850 Swiss francs and the manual model 480 Swiss francs. In 1964 the Precisa 162 electric three-function machine brought a price of 1125 Swiss francs, and the Precisa 164 was offered for 1875 Swiss francs. Albert Steinmann exhibited the Stima from 1931 and from 1954 also the Signal, a four-function machine with negative account balance and full keyboard. The Trebla slide bar adder only appeared in 1941 but was already offered in the journal Büro und Verkauf in 1937 (volume 12, page 19) as an “addition apparatus with direct subtraction” and was described in 1939 in the Büfa catalog with the property “direct subtraction and negative account balance.” In the November 1937, issue of the Organisator mention was made of 36 different Stima models. From time to time, a pocket-watch slide rule (Calculigraphe or graphical calculator) was presented, probably a foreign product. In 1947 the Stima Universal 4, a keyboard calculating machine for all four basic arithmetic operations, appeared on the market. The Swiss Official Gazette of Commerce listed an “Alpha” calculating machine of Albert Steinmann (trademark protection from July 12, 1930). The “Stima” brand was first registered on January 1931 and the “Trebla” on August 10, 1929. At the Mustermesse in 1945, a logarithmic pocket-watch slide rule of the Juvenia Montres SA watch factory in La Chaux-de-Fonds NE with the name Arithmo was on view. However, no further information could be obtained. According to the advertisement, the Direct keyboard machine of the Theo Muggli AG was capable of addition, direct subtraction, balancing, and multiplication and was offered in manual and electrical models. The Direct L calculating machine with printout and direct subtraction was first mentioned in 1932. The Direct 2 three-function machine no longer requires a crank, but has no printout. The Direct EL was equipped with an electric drive. According to the Büfa catalog, in 1948 thousands of Direct calculating machines were in use around the world. The Ultra, with manual or electric drive, was an adding machine and balancing calculator with direct subtraction and also supported multiplication. The manufacturer was the Werkzeugmaschinenfabrik Oerlikon, Bührle & Co. The machine appeared on the market in 1947. An Ultra automatic printing calculator (Ultra 804) was available in 1960. The Oxner of the Ochsner Büromaschinen AG promised addition, direct subtraction, and multiplication. The same applies for the Oxner Baby miniature adding machine. Rudolf Schweizer & Co. sold adding and subtraction machines.

812

16  Mechanical Calculating Aids

• The Coréma portative of the Coréma SA in Geneva was a portable adding and subtraction machine with full keyboard and was a high-speed calculating machine. • The Curta, manufactured by the Contina AG in Mauren FL, appeared in 1950 (Der Organisator, no. 379, October 1950, page 618). However, it was already on display at the Muba in 1949. • The Correntator of the Unical AG was a slide bar adder. It was advertised with direct subtraction by switchover. In 1947 the six models cost between 22 and 88 Swiss francs (highest numerical value: 99,999,999.99). • Beginning in 1959, the product range of the Hasler AG in Bern included cash registers and independent adding machines, installed in cash registers. • In the 1960s the Yverdon VD company E.  Paillard & Cie. SA produced accounting typewriters (account front-feed device, Hermes-Monoguide, automatic feed/form front-feed device, Hermes-Monomatic, HermesBimatic), full-text automatic accounting machine (Hermes C-3), and automatic invoice accounting machine (Hermes F-3), in addition to typewriters (Hermes). From 1963, the Hermes C-3 was exhibited for many years at the Mustermesse in Basel. The first Swiss automatic accounting machine was the Hermes F-3 and was first on view at the Muba in 1966. This automatic mechanical invoicing and accounting machine was described in the journal Büro und Verkauf (volume 36, January 1967, no. 424, page 112; volume 36, September 1967, no. 432, pages 328–329; price: 24,900 – 27,700 Swiss francs, depending on the number of counting mechanisms). • In the 1960s the Schaffhausen company Alfred J. Amsler & Co. was represented with mathematical instruments (planimeters, integrators) in Basel. • In the 1960s the Zurich company G.  Coradi AG offered coordinatographs and planimeters. • Contraves AG, in Zurich, sold analog computers. The IA 55 differential analyzer was the first Swiss electronic analog computer. It is immortalized in the trade fair catalog of 1955. Other Exhibitors Furthermore, versatile slide rules, such as the Maximatic circular slide rule of the Tesa SA in Renens-Lausanne, the circular slide rules of the Mikron AG in Bienne BE, the Loga-Calculator AG in Uster ZH, and the National-Rechenwalzen AG in Zurich (later Goldbach-Zurich and Küsnacht ZH), were commercially available. In 1945 a Loga slide rule sold for 18 to 100 Swiss francs and a Loga cylindrical slide rule for 150 to 740 or 750 Swiss francs. From 1948 LogaCalculator offered a cylindrical slide rule on a swiveling arm. In 1932 the LogaCalculator AG had more than 30 models in seven sizes in the form of circular, cylindrical, and linear slide rules and in panel form in its program (Büro und Verkauf, May 1932, page 24). In addition, planimeters manufactured by Karl Murbach in Zurich were mentioned. In 1946 a company with the name Addimult AG in Schaan FL/ Rheintal (factory for calculating machines, slide rules, and ready reckoners)

16.8  Dating with the Help of Exhibition Catalogs

813

was mentioned as well. The company originated in Berlin and essentially manufactured slide bar adders. In the 1940s a sliding table of the Pronto AG in Zurich was on the market. The inventor was Fritz Isler (application for patent in 1932, patent entered in 1934). The sliding table had the form of a linear or rotating table. Together with these devices, in 1945 a Hämmerle-Kalkulator of the Gebrüder Scholl AG in Zurich (calculating aid for the calculation of prices) was also listed. The Hermann Thorens SA in Sainte-Croix VD manufactured gramophones and music boxes. And finally, Edgar Rutishauser in Zurich, originally Multor (St. Gallen), supplied duplicating machines (Print-Fix). Dealers and Manufacturers at the Same Time Heinrich Daemen (Zurich), as well as Ernst Jost (Zurich) and Theo Muggli (Zurich), offered other brands along with their own.

16.8.2  Presence of Manufacturers at the Mustermesse The longest-living Swiss manufacturer of mechanical calculating machines was the H.W. Egli AG in Zurich. The company is listed in the trade fair catalog from 1917 to 1968. The Albert Steinmann clock factory in La Chaux-de-Fonds NE was present (with two short interruptions) from 1931 to 1963, and the Rechenmaschinenfabrik Precisa AG in Zurich was represented from 1935 to 1968. The Werkzeugmaschinenfabrik Oerlikon, Bührle & Co. in Zurich-Oerlikon took part from 1947 to 1961, and the Theo Muggli AG in Zurich was (mostly) in attendance in 1923 and from 1931 to 1951. The Contina Bureaux- und Rechenmaschinenfabrik AG in Mauren/Vaduz FL exhibited in Basel from 1949 to 1968. The Unical AG in Frauenfeld TG and the Coréma SA in Geneva were listed for 7and 5 years, respectively (1943–1949 and 1946–1950). As the journal Büro und Verkauf indicates, Jean Bergmann was already present with the Unical universal calculator in 1937. The Orga handbook (1921) lists the Berlin company Jean Bergmann GmbH with a universal calculator (ready reckoner). The Ochsner Büromaschinen AG in St. Gallen exhibited for 4 years (1951–1954), and the Eos Genossenschaft für Fabrikation und Vertrieb von Rechenmaschinen in Zurich took part from 1926 to 1928. The Rudolf Schweizer & Co. in Neu-Allschwil BL was present only once with the St. Gotthard fast adding and subtraction machine (1936) and Tesa SA in Renens VD only once (1946). The Loga-Calculator AG in Uster ZH was present (with longer interruptions) from 1917 to 1920, 1944 to 1946 and 1956, and the National-Rechenwalzen AG in Zurich from 1918 to 1922. In the Orga handbook (1921), the subsidiary Loga-­ Calculator, Fabrikations- und Vertriebs-GmbH, Berlin, is listed. The entries in the Mustermesse catalogs are apparently not always complete. The calculating machine dealers usually offered the products of several manufacturers and probably did not always report all brands. The Direct L

814

16  Mechanical Calculating Aids

and Unical calculating machines are missing from the Muba catalogs of 1936 and 1937, even though the journal Büro und Verkauf states that they were on display in these years. The same applies for the Ultra in 1959. The trade fair catalogs also include advertisements from manufacturers that did not exhibit. It is clearly evident that from 1969, the last three surviving manufacturers of mechanical and electromechanical calculating devices (Contina, Egli and Precisa) abruptly discontinued their presence at the Mustermesse.

16.8.3  Manufacturers’ Presence at the Bürofachausstellung The Bürofachausstellung (Büfa) was held for the first time in 1928 in Basel and later moved to Zurich. The 24th Büfa took place in 1982 in Geneva. The event was sometimes held annually, sometimes every 2 years, or sometimes less often. To my knowledge, not all catalogs are still available. The following overview (see Table 16.44) lists the manufacturers participating from 1948 to 1963. Table 16.44  Exhibitors at the Büfa in Zurich from 1948 to 1963 Bürofachausstellung in Zurich (1948–1963: Offering of calculating machines and slide rules Manufacturer 1948 1950 1952 1954 1956 1958 1960 1963 Curta Curta – – – – – Contina, Bureaux- – und Rechen­ maschinen­fabrik AG, Mauren FL H.W. Egli AG, Madas Madas Madas Madas Madas Madas Madas Madas Zurich Loga Loga Loga – – – – – Loga-Calculator AG, Uster ZH (Heinrich Daemen) Theo Muggli AG, Direct Direct Direct Direct Direct Direct – – Zurich – – Oxner Oxner Oxner Oxner Oxner – Ochsner Baby Baby Baby Baby Baby Büromaschinen AG, St. Gallen Precisa AG, Zurich Precisa Precisa Precisa Precisa Precisa Precisa Precisa Precisa Stima, – Albert Steinmann, Stima Stima Stima Stima, Stima, Stima, Signal Signal Signal Signal Univer­ La Chaux-desal 4 Fonds NE Ultra – – Ultra Ultra Ultra Ultra Ultra, Werk­zeug­ Ultra maschinen­fabrik automatic Oerlikon, calculator Bührle & Co., Zurich-Oerlikon © Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020 Source: Catalogs of the Bürofach-Ausstellung (Büfa), Zurich

16.8  Dating with the Help of Exhibition Catalogs

815

Remarks During this period of 16 years, only the Madas, and not the Millionaire, was exhibited at the Bürofachausstellung in Zurich. The Ernst Jost AG was responsible for the Curta and the Precisa from 1950 to 1952 and, from 1954, only the Precisa. Jost advertised the Curta in the journal Büro und Verkauf only in the years 1950/1951 and 1951/1952. From the Mustermesse of 1952, the Curta 2 was offered. The miniature calculator, which was on the market into the 1970s, apparently disappeared from the exhibition in Zurich in 1954. E.  V. Parisod (Zurich, Kilchberg, and later Aran-Grandvaux VD) marketed the Stima/Signal. Several companies (e.g., Bull, IBM, Remington Rand, and Samas) continued selling punched card machines. In 1937 the cost of a Trebla was 18 Swiss francs, and a Direct 2 was available for a price of 345 Swiss francs. In 1948 the Stima Universal 4 sold for 800 Swiss francs. Because of the War, in 1939 there was no Büfa. However, the Schweizerischer Büro-Fachverband (Zurich) issued a 192-page exhibition guide including illuminating information about the Egli company (pages 24–26), which simplifies dating. In the catalog of 1939, the Direct, Loga, Madas, Precisa, Stima, and Trebla machines are presented. On pages 22–24, we also learn that more than 30,000 Loga cylindrical slide rules were in use in industry, commerce, business, banks, and insurance companies, as well as in transportation. According to the manufacturer, these machines were suitable for multiplication, division, rule of three, proportional calculations, concatenation, bulk multiplication (with constant multiplier), and bulk division (with constant divisor). There were 30 different models of the Loga calculator. Regarding the Stima (pages 33–34), in 1930 the flat model A Stima appeared. In 1939, 29 flat models and 21 desk models were offered. Some models were capable of all four basic arithmetic operations. Exhibitors of calculating and accounting machines at the Büfa in 1933: • Additions- und Rechenmaschinen AG, Zurich (e.g., Madas calculating machines) • Ernst Jost, Zurich (e.g., Brunsviga calculating machines) • Theo Muggli, Zurich (e.g., Direct calculating machines) • Anton Waltisbühl & Co., Zurich (e.g., Remington accounting and invoicing machines). The exhibition guide of 1933 represents the H.W. Egli AG in Zurich and Paris as the manufacturer of Bull punched card machines (page 43). Edgar Rutishauser in Zurich (supplier of the Volksrechner) presents himself as the manufacturer of duplicating machines (Print-Fix) (pages 64–66 and 108). The Direct calculating machine (addition, direct subtraction, multiplication) with printout was offered at that time for at least 600 Swiss francs (page 45). Source Schweizerischer Büro-Fachverband (editor): Die Technik des modernen Büros, Zurich 1933.

816

16  Mechanical Calculating Aids

The Most Important Manufacturers The most important manufacturers of analog slide rules, digital mechanical calculating machines, and slide bar adders in Switzerland and Liechtenstein were (in alphabetical order) Bührle, Contina, Egli, Loga, Muggli, Precisa, and Steinmann. Among the leading suppliers of cash registers were Hasler and Precisa. Globally successful builders of analog mathematical instruments were Amsler and Coradi. Source H.W.  Egli AG (Rechenmaschinenfabrik), Zurich, 1919–1925, Schweizerisches Wirtschaftsarchiv, Basel New Findings Two reports regarding calculating machines unknown until recently follow.

16.9  The Volksrechner The first specimen of this machine came to light on May 1, 2014, in the collection of technical devices (“Patrimoine technologique”) of Jean-Marie Rouiller in Dorénaz VS. Inquiries regarding the mystifying Volksrechner (people’s calculator) were unsuccessful. On August 9, 2014, the miniature “cash register” (see Fig. 16.38) then turned up on the flea market in Rorschach SG, on Lake Constance. Until now, two surviving specimens are known. The nameplate from Edgar Rutishauser in St. Gallen on the unimposing black metal casing indicates that this company marketed the device. As usual, there was no documentation whatever. Who manufactured the tiny calculating machine? And how did one carry out calculations with this device? The Volksrechner was manufactured at the beginning of the 1930s. The number 33 is engraved on the reverse side of the aluminum cover. This device is badly worn, suggesting that it was in heavy demand. The specimen exhibited in Dorénaz VS is in vastly better condition and, after 80 years, still functional. In both cases, the stylus for the clearing crank is missing. No sales figures are available. The serial numbers are 10014 (Rorschach) and 10046 (Dorénaz). Edgar Rutishauser’s Activities Edgar Rutishauser, born in 1901  in Amriswil TG, was an inventor. For the period from 1939 to 1964, the international patent database lists 11 patents for duplicating machines. In 1930 Rutishauser was in in St. Gallen, where he sold the Volksrechner for 95 Swiss francs, as documented by advertisements in the Neue Zürcher Zeitung (NZZ, 04.02, 04.09, 06.25, and 07.02.1930). In 1931 the businessman moved to Zurich, at first at the address alte Beckenhofstraße 59 and later the address Tödistraße 1. From 1937 to 1962/63, the company that he founded, Schweizerische Spezialfabrik für Vervielfältigungsmaschinen (NZZ), was entered under the name Edgar

16.9  The Volksrechner

817

Rutishauser AG, Zurich, in the Schweizerisches Ragionenbuch (official guide to Swiss companies) and in the Swiss Official Gazette of Commerce (SHAB) and from 1963 to 1980 as Print-Fix Edgar Rutishauser AG.  According to the reference work Kompass (no. 3, 1951/52, page 610), the company had 60 employees and a capital of 300,000 Swiss francs. He had the Maschinenfabrik Otto Weibel in Rapperswil SG manufacture his “Print-Fix” duplicating machine. Before, he sold the Multor duplicating machine (probably named after the Multertor in St. Gallen). According to the Neue Zürcher Zeitung (09.09.1954), in 1954 Rutishauser was president of the Schweizerischer Büro-Fachverband (founded in 1940, today Swico), at that time in charge of the Schweizerische Bürofachausstellung Büfa. Rutishauser died in Ascona in 1978. Where Does This Calculating Machine Come from? In the professional literature, there is no mention of the Volksrechner, and it was also missing from the German Rechnerlexikon (www.rechnerlexikon.de). Together with Wolf-G, Blümich in Berlin and Wilfried Denz in Münster, the mystery of its origin could be solved. The calculating device was produced by the Maschinen- und Werkzeugfabrik Paul Brüning in Berlin and sold under the names Minerva and Résulta 7. The design of the Volksrechner is identical with that of these early devices of Brüning. However, with the two surviving specimens, Rutishauser ground away the name “Minerva” underneath the nameplate. It is also odd that the otherwise usual manufacturer’s information (month and year of manufacture and abbreviated symbol of the maker) is missing from these two specimens. Later models have a lever for switching between addition and subtraction. In this case, the second row of numerals with the nines complements is superfluous. In addition, the setting mechanism is provided with viewing windows at the bottom for checking the input values. Both the result mechanism and the setting mechanism have a clearing crank. These machines were offered by W. Häusler-Zepf in Olten SO (Rapida 8 brand, 1948) and Henri Zepf in Lausanne (Résulta BS). Fig. 16.38  Lateral view of the Volksrechner. The stylus serves for numerical input. The clearing crank (handle missing) sets the result mechanism to zero. (© Bruderer Informatik, Rorschach)

818

16  Mechanical Calculating Aids

What Can the Volksrechner Do? The heavy, metal device with a weight of around 1 kilogram – a setting wheel calculating machine with automatic tens carry – is 9 cm wide, 15 cm deep, and 10 cm high. It is suited for the addition and subtraction of numbers up to seven places. Accordingly, the highest value is 99,999.99. The numbers are entered with a stylus and rotated with large gears downward (for addition) or upward (for subtraction), transferring the numbers directly from the setting mechanism to the result mechanism. Rotating a crank for the calculation is no longer necessary. Rutishauser praised the device as the “smallest, handiest, and fastest calculating machine”. A crank was provided for clearing the result mechanism.

16.10  Grunder’s Calculating Machine The unusual wooden calculating machine of the Brienz secondary school teacher Johannes Gottfried Grunder (1892–1979) (see Figs. 16.39 and 16.40) is a one-of-a-­kind calculator. The heavy machine stems from 1945 and has been in the Bern Museum für Kommunikation since 2010. It was acquired from the Winterthur Technorama) (personal communication of Karl Kronig, head of collections). In October 2016, in the course of querying the new inter-museum search portal w ­ ww.museums-online.ch, the author came upon this strange object. I investigated the forgotten calculating aid – unknown in professional circles  – on November 8, 2016, in the museum’s main repository in Schwarzenburg BE.  No more detailed information about the device exists. There is no entry in the European patent database. Knowledge to date indicates that the machine is capable of only one, the most important and most frequent arithmetic operation, addition.

16.10  Grunder’s Calculating Machine

819

Fig. 16.39 Grunder’s calculating machine (1). Full view of the adder (1945) of Johannes Gottfried Grunder. Components (from top to bottom): Clearing bar, result mechanism with viewing window, setting mechanism, clearing weights, and pedal. Dimensions: 124 × 55 × 50 cm. (© Museum für Kommunikation, Bern)

In What Condition Is the Wooden Machine? Grunder’s calculating apparatus, with a weight of 28 kg and a height of 124 cm, is still partly functional. Only a few gears move, which greatly restricts trial calculations. Nevertheless, it was possible to reveal some of the wooden construction’s secrets. The roles of the pedal and the lever on the left side of the machine, both of which interact with the rear face of the result mechanism, remain unclear. The question of whether certain parts are missing is open. How Are Numerical Values Entered? The numerals are set by rotating digit wheels in the counterclockwise direction. The wheels are pushed downward to the stop, and the values are transferred directly to the result mechanism (i.e., without turning a crank). The machine is therefore a direct adder. The setting wheels have nine teeth. The zero is not required, since it has no influence on the addition process. The numeral 9 is (contrary to custom) is not inscribed between or before the movable teeth, but on a fixed bar above the setting wheels – at first confusing. To enter the numeral 8, one sets the finger in the gap before the 8 and to set the numeral 9 behind the numeral 8.

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Where Are the Results Displayed? The viewing window, which serves for the control of the numerical input and the display of the results, is located above the setting mechanism. It is divided into four sections, each with three numerals. Decimal places for currencies (Swiss francs/Rappen) are not separately marked. Fig. 16.40 Grunder’s calculating machine (2). Sectional view: 12-place setting mechanism (below) with clearing weights, 12-place result mechanism (above) with four-part viewing window and clearing comb with metal tongues. (© Museum für Kommunikation, Bern)

Clearing the Setting Mechanism Following the numerical input, thanks to the metal weights suspended on a cord, the numeral wheels automatically spring back to the zero position. Manual clearing is therefore unnecessary. This design is probably rare. Clearing the Result Mechanism The individual numeral wheels of the result mechanism can be manually reset to zero (by rotating in the clockwise direction). Rotating the comb with the 12 metal tongues, attached above the result mechanism, in the counterclockwise direction brings about total clearing. For this purpose, it must be pressed downward. All numeral wheels incorporate four numeral sequences of 0–9, which is unusual. Each of the four segments is equipped with a metal piece (between the numerals 7 and 8) which touches the corresponding metal tongue. For clearing, a quarter rotation is sufficient. This is evidently the reason for the fourfold application of the ten numerals, requiring 40 teeth instead of only 10. Automatic Tens Carry An important feature of mechanical calculating machines is the automatic tens carry. If one tries to add the numbers 44 and 77 with the fully functional left gears, the value 21 appears, and the 1 is missing. Whether one actually had to carry out the important tens carry manually is not clear, because not all parts of the machines are still functioning. However, for a 12-place calculating machine manual tens carry is unlikely. This would seriously limit the use of the invention.

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Restoration Restoring the device would possibly allow the clarification of the purpose of the pedal. It is conceivable that this enabled the reversal of the direction of rotation for the result mechanism (e.g., for total clearing). With pinwheel machines, reversing the direction of rotation changes between addition and subtraction. Certain machines utilize complements (nines complements), missing with Grunder, for subtraction. Why Is an Adding Machine from the 1940s Made of Wood? The wear (e.g., the missing setting wheel for the seventh place and damaged metal weights for clearing the setting mechanism) clearly shows that this calculating aid was used often. Numerals are missing from the setting wheels for the highest places, which may never have been attached. It is also possible that the storage was not technically correct. With the 12 places for numerical input and results, numbers up to nearly one trillion can be represented. Grunder did not contrive the machine for instruction purposes. He is said to have controlled the finances of the community of Brienz BE over many years. This suggests an automatic tens carry. In the 1940s, there were numerous wellengineered, high-performance mechanical calculating machines capable of executing one or more basic arithmetic operations. For a tiny mountain village, a sophisticated mass-­produced machine was probably unaffordable. Wood simplified the assembly of the unconventional gear wheel construction, but this also lowered the durability. Compared with the better known Zurich calculating machines, the Millionaire and the Madas, and the Curta cylindrical calculator from Liechtenstein (not yet commercially available in 1945), Grunder’s calculator is in fact no technical masterpiece, but more a product of his spare time in his Brienz workshop. In those days, logarithmic slide rules suited above all for multiplication and division were widespread. Furthermore, there were inexpensive slide bar adders for addition and subtraction. These had a semiautomatic tens carry. According to a personal communication of Vinzenz Bartlome of the Staatsarchiv in Bern of November 11, 2016, Hans Grunder grew up in Oberdiessbach BE. After attending the teachers’ college, he first held the position of a primary school teacher at Wichtrach BE and later continued his studies in Bern to become a secondary school teacher and was a secondary school teacher from 1923 to 1962 (and later also principal of the secondary school) in Brienz. A survey of the population revealed that the tinkerer taught humanities, built, e.g., a typewriter, and painted a relief. The author held telephone conversations with the grandchildren, Hans Grunder and Peter Grunder. However, the technical questions remained unanswered. According to information from Karl Kronig, Grunder built the calculating machine during the Second World War. Survey Zora Herren: Nachkommen des Erfinders gesucht, in: Jungfrauzeitung, November 15, 2016, page 17 Zora Herren: Wundermaschine des Lehrers weckt Erinnerungen, in: Jungfrauzeitung, November 25, 2016, page 15.

Chapter 17

Technological, Economic, Social, and Cultural History

Abstract The chapter “Technological, Economic, Social, and Cultural History” illustrates the role and the transformation of technological and scientific history. The history of science and technology is now mostly presented within the scope of the humanities, frequently with emphasis on the economic and social aspects and consequently not able to satisfy a number of requirements. Although technology and science greatly influence our lives, very few academic chairs and courses of study are concerned with their history. In spite of this, deeper specialized scientific and technical knowledge is decisive for museums and other collections, especially for preserving the cultural heritage. For some time, there has been a renewed revival of interest in material history. Patent protection is treated as well. Furthermore, information is given about the lifespan of analog and digital calculating aids. Keywords  Cultural history · Economic history · History of science · History of technology · Lifespan of calculating aids · Material history · Patent protection · Preservation of the technical cultural heritage · Social history Especially in the fields of electronics and informatics, technology penetrates our everyday life. Information technology (IT) destroys time-honored jobs and creates new work areas. It influences both working conditions and leisure time. Knowledge gained from research and technical inventions is transformed into marketable products, which should have the greatest possible utility value for the customer. Since the introduction of the electronic digital computer, countless companies have been founded and later disappeared. The history of computer science is therefore often closely related to industrial and corporate history as well. Information technology is present in devices of all kinds, mostly embedded and thus concealed. Today’s electronic computers are tiny, lightweight, fast, web-­enabled, versatile, high-powered, simple-to-use, and inexpensive – and sometimes sensitive and prone to breakdowns. Today, the terrestrial network, mobile communications, the Internet, and the social media guarantee that we can be reached nearly everywhere around © Springer Nature Switzerland AG 2020 H. Bruderer, Milestones in Analog and Digital Computing, https://doi.org/10.1007/978-3-030-40974-6_17

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the clock. This of course has its drawbacks. What is mostly ignored: in the event of a current blackout, everything comes to a halt. If the network breaks down and the Internet connection is interrupted, we’re left stranded. Technology, especially electronics and informatics, are a blessing and a curse at the same time. Contrary to mechanical equipment, with electronics we are often helpless. Within a short time, information and communications technology (ICT) have fundamentally changed our lives. Constant surveillance, in part coupled with face recognition, leads to transparent citizens. This can be linked to a social credit system. With data harvesters, such as Alphabet (Google, YouTube) and Facebook (WhatsApp, Instagram), data leaks that violate our privacy occur repeatedly. Networking (the Internet of things) paves the way for crimes of all kinds, sabotage, espionage, and extortion. Cyberattacks and drone invasions are becoming increasingly frequent. Their targets include water supplies, power plants, and hospitals. An end to this profound transformation is not in sight. The consequences of this upheaval can be estimated only with difficulty. Online shopping bestows us with a veritable flood of packages. Whether the electromagnetic radiation caused by mobile communication waves (mobile communications standard 5G) causes damage to health over a longer time is not known. However, it must be said that some aspects of technological advances have devastating consequences for the environment, climate change, and biodiversity (loss of species). Handwritten and typewritten letters are an ideal source for history writing. It is hardly possible to manage the colossal flood of emails and exchange of views in the social networks. Where can one access such information in the future? And is it even worth saving this information?

17.1  The Rich Technical Cultural Heritage Technical heritage is enormously rich and includes the aqueduct (e.g., the Pont du Gard), the bridge (e.g., the Landwasser Viaduct), the tower (e.g., the Eiffel Tower), the hot air balloon (Montgolfier), the loom (Vaucanson, Jacquard), the letterpress printing machine (Gutenberg), the sky disc (Nebra), the celestial globe (Bürgi), the robot (Leonardo da Vinci), the planetarium (provision for representing the motion, position, and size of celestial bodies, especially the planets), the wheel, the steam engine, the paddle steamer, the water mill and windmill, the musical automaton, the clock, and the typewriter. A distinction is made between material (physical) and immaterial (intellectual) cultural heritage. Calculating technology has brought forth a flood of excellent objects, such as the mysterious Antikythera mechanism, lovingly forged astrolabes and odometers, fascinating astronomical clocks, cleverly designed Nuremberg jetons,

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and carved counting tables. Several magnificent cylindrical calculating machines are preserved: the toothed segment machine of Jacob Leupold/Anton Braun/Philippe Vayringe, the pinwheel machines of Anton Braun and Johann Jacob Sauter, and also the stepped drum calculating machines of Philipp Matthäus Hahn, Johann Christoph Schuster, and Johann Helfrich Müller. Also not to be forgotten are the impressive large cylindrical slide rules and the finely designed Curta cylindrical calculator of Curt Herzstark, the versatile sector, and the widely used polar planimeter for the determination of area, and the pantograph. And let us not forget today’s versatile electronic devices.

17.2  Technology Is Part of Our Culture Technological history and cultural history are not contradictory. Technology is a part of our culture, and today’s culture would not be possible without technical breakthroughs. Culture embraces not only literature, music, painting, sculpture, and architecture. Technological history is closely related to political, economic, social, and cultural history. Historical research and historiography that are limited to political, economic, social, and cultural happenings without consideration of significant technical achievements do not adequately cover a decisive part of our environment. This is not understandable, especially considering that there has long been a shortage of the follow-on generation in the natural sciences and technical professions.

17.3  The History of Science and Technology What Is Technology? Below are some comments from a textbook: Nature, society and technology all belong to our world. Technology is an important sphere of life. […]. Man himself has created technology in order to shape life, and this has a profound impact on the way of life. Without technology, life in nature and society would be inconceivable. Technology is many-faceted (see Duden, Basiswissen Schule. Technik, Paetec Gesellschaft für Bildung und Technik mbH, Berlin/ Bibliographisches Institut & F. A. Brockhaus AG, Mannheim 2001, page 6). Technology has a long history. […]. Technology is as old as man. It began with the development of the first tools and the building of primitive huts by our remote ancestors. However, it was only about 200 years ago that man developed technology to the point that the industrial age was launched. Today, automation has an all-embracing impact on many areas of life. […]. Technological developments occur with increasing rapidity. […]. Improvements to existing technology and the invention of new technology take place in ever shorter time (see Duden, Basiswissen Schule. Technik, Paetec Gesellschaft für Bildung und Technik mbH, Berlin/Bibliographisches Institut & F. A. Brockhaus AG, Mannheim 2001, page 7).

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17.3.1  W  hat Do We Understand by the History of Science and Technology? The cross-disciplinary history of engineering and the natural sciences describes and elaborates the inventions of engineering and the natural sciences (objects, processes, and procedures), discoveries, and acquired knowledge. Furthermore, this includes reports on their creators and is concerned with the prerequisites for innovations and their impact on society, the economy, culture, and politics. It represents the course, underlying causes, and consequences of scientific and technical changes and deals with the origin and utility of innovations. A comprehensive history of engineering and the natural sciences must consider both the important achievements of engineering and the natural sciences and the interrelations between technology and manhood. The boundaries between the history of knowledge, the history of science, the history of mathematics, the history of engineering, the history of the natural sciences, and the history of philosophy are blurred. In addition, the history of medicine is also of great importance. For the sake of simplicity, the term “history of technology” is often used in the broader sense of the history of engineering and the (natural) sciences. As a rule, this also includes the history of mathematics.

17.3.2  W  hy Does One Pursue the Study of the History of Science and Technology The confrontation with the past helps us to (better) understand the present. The study of history enables us to recognize technical changes, their underlying reasons, and their interrelationships. This helps us with the allocation of events and occurrences and also with the assessment of technical and scientific successes and failures. Furthermore, it simplifies the understanding of important achievements. To a certain extent, this knowledge allows the prognosis and evaluation of the consequences of technical developments (e.g., the impact of the digital transformation). The consideration of earlier times enables us to recognize lines of development and sometimes to find more reasonable problem solutions. This also serves for the preparation of patent applications. Technology (e.g., industrial revolutions, the World Wide Web, the smartphone, and social networks) shapes and changes our lives dramatically. Benefits of Studying the History of Engineering and the Natural Sciences In retrospect, we can learn from accidents at nuclear power plants and, as well as possible, prevent their recurrence. We broaden our knowledge of the

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big bang and are able to predict previously unknown elementary particles. We are in a position to interpret surprising discoveries (e.g., the Antikythera mechanism or the iceman Ötzi) and to resurrect forgotten masterstrokes (e.g., the analytical engine of Babbage or the chess automaton of Torres Quevedo). Earlier developments also encourage the creation of (mass produced) innovations, such as the Curta pocket calculating machine.

17.3.3  P  resentation of Science and Technology in Museums Different approaches exist for the presentation of the history of engineering and the natural sciences: • Museums of science and technology (universal and special museums): Exposition of (partly still functional) masterstrokes of engineering and the natural sciences (originals, reconstructions, replicas, demonstration pieces, videos), in some cases embedded in economic, societal, and political developments • Museums of industry: Presentation of the relationship between technology and the workplace • Science centers (hands-on museums): Experimental laboratory for the solution of scientific problems from the fields of mathematics, physics, chemistry, biology, computer science, engineering, etc. (experiments, simulations, and animations) • Combined museums: Linking of milestones, industrial culture, and experiments • knowledge allows the prognosis and Historical and art history museums: Consideration of engineering and the natural sciences, art chambers, numismatic collections, collections of clocks, musical instruments, automatons, and scientific instruments Many museums offer media stations (interactive stations).

17.4  The Transformation in the History of Technology The “hard” history of technology was originally indigenous to the engineers. For around 50 years, the “soft” history of technology has taken its place in the historical departments of (technical) universities. Nevertheless, the classical history of engineering and the natural sciences in the hands of mathematicians, engineers, computer scientists, and natural scientists has not vanished,

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as the abundance of newer scientific publications by German-, English-, and French-speaking scientists underscores. This continues within and outside of the academic world (mostly within the relevant faculties). However, many of these adherents are retired or work on an unpaid basis. Below are a few selected accounts of the transformation in the history of technology (shift toward economic and social history): Today, clarity consists essentially of allocating the modern history of technology to the historical sciences and no longer to the technical sciences. Undisputed is also that this represents a specialized field of its own, a field that requires especially well educated, full-time specialists and can no longer be based on the mere secondary activities of the active technical staff or natural science historians (see Karin Hausen, Reinhard Rürup (editors): Moderne Technikgeschichte, Verlag Kiepenheuer & Witsch, Cologne 1975, pages 18–19). In the 1960s the engineer’s history of technology gave way to the historians’ history of technology (see Reinhold Bauer; James Williams; Wolfhard Weber (editors): Technik zwischen artes und arts, Waxmann Verlag GmbH, Münster 2008, page 169). During the period following the First World War, the history of technology of the engineers was extended only minimally, but dominated up to the 1960s. Thereafter, a history of technology ensued that is largely in the hands of historians (see Wolfgang König: Technikgeschichte, Franz Steiner Verlag, Stuttgart 2009, page 46). Since the 1960s the history of engineering technology has been replaced by a history of technology that is largely in the hands of historians. The new generation of technological historians was endeavored to characterize the subject and the image of the history of technology as a separate branch of history independent of the traditional history of technology. In particular, they sought the connection with historical subjects of a general nature. The older history of technology concentrated on individual technical events  – on persons, inventions, and other acquired knowledge. On the other hand, the new history of technology sought to explain the structural transformation of technology and found the answers in numerous socioeconomic contexts (see Wolfgang König: Technikgeschichte, Franz Steiner Verlag, Stuttgart 2009, pages 54–55). Following an in part heated and lengthy discussion of the method, in the 1970s the concept of the modern history of technology, with its structured and social-historical focus, which is distinguished from historical traditional scholarship prevailed in the Federal Republic of Germany (see Rolf-Jürgen Gleitsmann; Rolf-Ulrich Kunze; Günther Oetzel: Technikgeschichte, UVK Verlagsgesellschaft, Konstanz mbH 2009, page 165). The history of technology is pursued by both specialists having a scientific and technical (basic) education and by those from the humanities and the social sciences. Due to the anchoring of the history of technology in the historical sciences and the image as a historical discipline, however, current historiography is primarily the realm of historians (see Rolf-Jürgen Gleitsmann; Rolf-Ulrich Kunze; Günther Oetzel: Technikgeschichte, UVK Verlagsgesellschaft, Konstanz mbH 2009, page 166). This lack of consideration of the history of technology in overviews of general historical character was one of the reasons for the constituting and professionalization as an independent historical discipline since the 1960s in the Federal Republic of Germany (see Rolf-­ Jürgen Gleitsmann; Rolf-Ulrich Kunze; Günther Oetzel: Technikgeschichte, UVK Verlagsgesellschaft, Konstanz mbH 2009, page 178).

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17.4.1  D  oes the History of Technology Fulfill the Expectations Placed in It? Here are a few opinions: A historian should have far more knowledge, or – still better – understanding, of the evolution of the natural sciences and engineering in order to be able to accurately classify or properly present historical material (see Albrecht Timm: Kleine Geschichte der Technologie, W. Kohlhammer GmbH, Stuttgart 1964, page 7). In addition, specialized technical knowledge is an indispensable prerequisite for historical work – a problem also posed very similarly for other special historical disciplines, if not always with the same severity (see Karin Hausen, Reinhard Rürup (editors): Moderne Technikgeschichte, Verlag Kiepenheuer & Witsch, Cologne 1975, page 19). In the further course of the 19th century one could hardly speak of a scientific confrontation with the history of technology. In spite of the increasing importance of technology, historians did not view its history as a subject worthy of their attention (see Karin Hausen, Reinhard Rürup (editors): Moderne Technikgeschichte, Verlag Kiepenheuer & Witsch, Cologne 1975,page 11). In fact it was the technical experts that, in view of the failure of historians, came to their own aid and now began to write “their” history, i.e. the contribution of technology to the evolution of human culture, the history of their respective fields, and ultimately also the history of the status of their profession (see Karin Hausen, Reinhard Rürup (editors): Moderne Technikgeschichte, Verlag Kiepenheuer & Witsch, Cologne 1975, pages 11–12). For decades, the history of technology was almost exclusively pursued by technical persons for technical persons. Until beyond the middle of this century [the 20th century] neither Great Britain nor Germany had a professorship for the history of technology. Problems relating to the history of technology were dealt with outside of universities and academic institutions, largely without contact to other historical sciences (see Karin Hausen, Reinhard Rürup (editors): Moderne Technikgeschichte, Verlag Kiepenheuer & Witsch, Cologne 1975, page 12). For decades the history of technology […] was only a secondary preoccupation or old-­ age activity of technical practitioners […]. Precisely in the narrower fields of the history of inventions and constructions, a wealth of knowledge of lasting value has been compiled in authoritative studies rich in material. Even today, this knowledge constitutes a solid foundation for all far-reaching historical research (see Karin Hausen, Reinhard Rürup (editors): Moderne Technikgeschichte, Verlag Kiepenheuer & Witsch, Cologne 1975, page 13). In the absence of adequate knowledge about the evolution of today’s natural sciences and engineering it is not possible to completely analyze and accurately describe the course of European history. At the same time, without such knowledge it is hardly possible to comprehend and assess the causes, motives and tendencies of today’s political and economic happenings (see Deutsche Forschungsgemeinschaft (editor): Die Geschichte der Medizin, der Naturwissenschaft und der Technik, Bad Godesberg 1959, page 43).

The Propyläen Technikgeschichte represents the first “multivolume popular German-language history of technology.” It encompasses five volumes and

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has been published in several issues. The goal of this undertaking was the “description and explanation of the functioning of historical technology, the emergence and benefits of technical innovations, and the conditions and consequences of innovations – all of this integrated in the totality of a spatiotemporal network of relationships between economic, social, and cultural factors. The editor of this compilation, Wolfgang König, states in the introduction: In contrast to political events, technical changes are generally effective over the middle and long term. Since their further development up to the beginning of production demands patience and often swallows immense sums of money. The importance of inventions frequently becomes clear only after a longer time. New technology has to establish and assert itself against widespread competition before new solutions begin to prevail in the market. The history of technology not only poses the […] question how, but also the question why technical changes have occurred. It is not satisfied with the mere description of new technology, its functions, and its social impact, but also attempts to understand and explain the technical and non-technical circumstances of the development process. Neither the traditional history of inventions nor modern social and economic history possesses the requisite understanding of technology for meeting this need. With the exponential growth of technological knowledge in the 19th and 20th centuries, we are increasingly often confronted with the phenomenon of simultaneous inventions: several inventors arrive at similar results independently and practically simultaneously. Economic and social history are no more useful than contributions dealing with the history of inventions for a sufficient description and explanation of the emergence of technology. Considerations of technology from the point of view of economic history are generally limited to the proliferation and impact of the technology on the market and neglect the invention, development up to the point of production, or the relationship between commercial success and technical modifications. Some contributions to social history describe technology entirely from the point of view of social needs and interests, while completely ignoring the analysis of the state of technical knowledge and capability, together with demand on the part of the consumer the second prerequisite for successful technical development. Demand on the part of the consumer alone does not create technology, as the largely unsuccessful hundred year long search for a technical solution for the cost-efficient storage of large amounts of electrical energy makes clear. The emergence and benefits of technology are not two separate phenomena, but are intimately related. As with history in general, the history of technology cannot deliver guidelines for the solution of current problems. Nevertheless, it can certainly provide orientation in the jungle of proposed technical solutions, in the maze of condemnations and glorifications of technology and in the network of interrelationships between technology, economics and society. The history of technology does not give us certainty about the path that we should follow, but without this we would certainly be blind in dealing with our decisions relating to technology (see Wolfgang König: Introduction to “Propyläen Technikgeschichte”, in: Dieter Hägermann; Helmuth Schneider (editors): Landbau und Handwerk. 750 v. bis 1000 n. Chr, Propyläen-Verlag, Berlin 2003, pages 11–16, reproduction of the citations with permission of Wolfgang König, Berlin, of October 13, 2017).

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Leading young Anglo-American experts reject the “soft” history of technology: We see this as a part of a broader re-engagement of historians with the specifics of computer technology and the concerns of computer science. The history of science as a whole made a turn toward social and cultural analysis a generation ago, influenced by the emergence of science studies. Since then the wisdom of attempting to pry open the black boxes of technical knowledge and peer inside has been much debated. [...]. Within the history of computing, a relatively new and rather insecure subfield of the history of science and technology, the process of scholarly professionalization has been marked by a fairly uniform disengagement with technical detail in favor of stories about institutions, ideology, and occupations. Early historical work on computing, like early historical work on many other topics, was done by pioneers and other participants. They tended to produce detailed technical stories about particular computers, pioneering institutions, and the proper allocation of “firsts”. Most of those entering the field as graduate students in history programs and science studies programs have lacked the technical background to appreciate or produce such stories, and have in any event sought instead to increase the scholarly respectability of the history of computing and their own potential employability by patterning their work on established models in better-developed historical fields. The development of the history of computing in a more scholarly direction has also been defined largely as a move away from technical history and technical details. [...]. For a long while now, detailed examination of computer code or programming practice has been almost unknown in scholarly history of computing, seen at best as a guilty pleasure (see Thomas Haigh; Mark Priestley; Crispin Rope: Eniac in action, MIT press, Cambridge, Massachusetts, London 2016, page 13).

Multivolume Surveys Large-scale, multivolume compilations of the general history of technology are a deserving undertaking. Such editions exist in German, English, and French. Unfortunately (as expected) these are unable to formulate a coherent history, e.g., of machine engineering, electrical engineering, or computer science. They unavoidably cover only a small part of all happenings, from the point of view of the individual disciplines a sooner unsatisfactory and arbitrary part. In view of the sheer enormous dimensions, today it is hardly possible to address the entire history of technology. Consequently, the available multivolume surveys are also rather incomplete.

17.4.2  T  echnical History Without Relating to Science and Engineering? In most domestic and foreign universities and technical colleges, the history of mathematics, engineering, and the natural sciences is relegated to a shadowy existence. Its importance is not recognized. The majority of the few professorships around the world belongs to historians. The history of technology, which belongs to the historical sciences, often lacks any semblance of proximity to engineering and the natural sciences. By way of comparison: Experience shows that, because of the relevance to

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practice, the interdisciplinary didactics of computer science must be allocated to engineering and not to the educational sciences. The management  – repair, maintenance, and upkeep  – of technical and scientific collections urgently requires relevant expertise. This is especially true for reconstructions and simulations. An authentic history of technology requires profound technical knowledge (see box).

History of Technology Without an Understanding of Technology? Who should deal with the history of technology? Historians or engineers? Is it possible to write a credible history of technology without a well-founded knowledge of the given discipline and the historical research? What is more suitable, a view from within or from outside of the field? Is informative and reliable historiography feasible, for example, with regard to questions of computer science, mathematics, physics, astronomy, surveying, nautical science, chemistry, biology, medicine, or public transport possible without deeper mathematical, scientific, and technical knowledge? And what about horology, instrument making, and automaton construction? Is economic or social history of technology enough here? Unfortunately, a widespread (understandable) shyness of technological historians educated in history in relation to engineering and the natural sciences is evident. In practice, some adherents of the history of technology tend to gloss over a lack of technical expertise with a superficial presentation in intentionally difficult to understand or, in part, even pretentious language. For the history of technology, engineers (with additional training in history) are surely better suited than historians (with additional technical training). An interdisciplinary collaboration is not only meaningful but mandatory. The history of technology is in fact enriched by the consideration of different points of view, both from within and from outside. Questions • What can the economic and social history of technology contribute to the maintenance and explanation of technological cultural heritage collections? • Is it reasonable that professorships for the history of technology are not involved with collections? • What happens when the curators of technical collections are educated in history alone and have no adequate knowledge of the particular specialized field? (continued)

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Consequences • Failure to recognize the significance of valuable objects of technical cultural heritage and understand their essential character. • Many curators are unable to cope with this situation. • New findings cannot be sufficiently interpreted or cannot be interpreted at all. In some cases (for reasons of space as well), collections cannot be properly augmented and broadened. • Valuable objects are disposed of and not kept, destroying part of the technical heritage. • Outstanding museum objects often disappear to the museum repository. • Pioneering technical achievements are not adequately exhibited or not exhibited at all. • Exhibits without functioning devices give a lifeless impression. • One doesn’t dare to touch the objects and put them into operation (fear of contact, damage resulting from nonuse). • Improper care of the objects or neglect of care. • Damaged objects are never or almost never repaired. • Defective or incomplete masterpieces are not reconstructed. • Neither demonstration models nor simulations are made. • Collection databases are incorrect and of little informational value and can therefore not be linked unproblematically to other databases. Furthermore, the recall ratio for queries is unsatisfactory. • The furthering of the follow-on generation in the fields of mathematics, computer science, the natural sciences, and engineering with hands-on exhibits is virtually nonexistent. • Bridging the gap between economic and social history and the history of the technology itself fails to materialize. • Biographies of universal scholars, such as Leonardo da Vinci, are mostly limited to their lives and works of art and, for the most part, neglect their technical masterstrokes. • Many university professorships are unable to issue expert opinions relating to the history of technology or answer questions dealing with technical subjects for the media. It should be noted that: ( a) Museums of (general) history also possess various technical objects. (b) In fact very few natural scientists and engineers are well versed in the history of their particular field. (c) There is not only one technology but many branches of engineering and the natural sciences.

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17.4.3  C  ombination of “Hard” and “Soft” Technological History For decades there was a (not very fruitful) factional dispute between “hard” and “soft” technological history. Even today, a strained relationship is still apparent between the representatives of these two “camps.” A purely economically and socially oriented history of technology does not adequately meet the demands of mathematics, computer science, the natural sciences, engineering, and medicine. The authentic history of technology (technological history in the strict sense, or “old” technological history) and the social and economic history of technology (technological history in the broader sense, or “new” technological history) cannot simply replace each other but must complement each other. The efforts of professional and spare-time historians are not mutually exclusive. The history of technology is more than a history of inventions and discoveries, masterstrokes, and their creators (material history). An uncritical (profession-based, nationalistic) hero’s history is just as unsatisfactory as a history lacking in practical relevance that is not concerned with the preservation of valuable objects. The documentation, research, and explanation of technical milestones form the basis for embedding these in social and economic history. The Antikythera mechanism is a good example of this. Traditional historical scholarship is not capable of elucidating the significance of this finding of a century. The knowledge of mathematics, engineering, the natural sciences, and medicine is a prerequisite, for example, for the interpretation of archeological excavations (e.g., in Egypt) and maritime archeology. Only thanks to international collaboration was it possible to reveal so many secrets about the iceman “Ötzi”. The following overview (see Table 17.1) compares the history of the technology itself with the economic and social history of technology. Table 17.1  Attributes of internal and external technological history The history of technology can be viewed from within or from outside History of the technology itself Economic and social history of technology “Older” technological history “Newer” technological history “Hard” technological history “Soft” technological history Classical technological history Lack of classical technological history Technological history in the strict Technological history in the broader sense sense Technological history from within Technical history from outside Internal technological history External technological history (continued)

17.5  Lack of Appreciation for the History of Technology

835

Table 17.1 (continued) The history of technology can be viewed from within or from outside History of the technology itself Economic and social history of technology Technological history depicted by Technological history of (professional) historians engineers (engineering historians) (general) historians Anchoring in engineering, Anchoring in historical scholarship, complementary to engineering discipline of historical scholarship Engineering-oriented technological Social science-oriented technological history history History of the emergence of technology and History of technical achievements manufacturing and use of technology, as well as (inventions, discoveries, the impact of technology on politics, society, developments, masterpieces, economics, and culture processes, innovations) History of engineering achievements Profession-based history Maintenance of the technical cultural Causes and effects of technical change (immaterial culture) heritage (material culture) Deeper understanding of history Deeper technical understanding as a prerequisite as a prerequisite © Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020

Sources Rolf-Jürgen Gleitsmann; Rolf-Ulrich Kunze; Günther Oetzel: Technikgeschichte, UVK Verlagsgesellschaft, Konstanz mbH 2009 Karin Hausen, Reinhard Rürup (editors): Moderne Technikgeschichte, Verlag Kiepenheuer & Witsch, Cologne 1975 Wolfgang König: Technikgeschichte. Eine Einführung in ihre Konzepte und Forschungsergebnisse, Franz Steiner Verlag, Stuttgart 2009 Wolfgang König (editor): Technikgeschichte, Franz Steiner Verlag, Stuttgart 2010 Wolfhard Weber; Lutz Engelskirchen: Streit um die Technikgeschichte in Deutschland 1945–1975, Waxmann-Verlag GmbH, Münster 2000.

17.5  Lack of Appreciation for the History of Technology The slashing of university professorships for the history of technology results in the suffering of research, teaching, and service provisions. The neglect of this field can lead to the disappearance of fundamental knowledge that is sometimes rediscovered only decades later (e.g., Leibniz or Babbage). Outstanding, amazing ideas, such as for the design of mechanical calculating machines, can by all means prove to be of use for future technical achievements. One reason for the lack of appreciation of technological historical research is probably its highly interdisciplinary requirements. Who is equally well versed in historical scholarship, mathematics, earth science, the natural

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sciences, or engineering? In some courses for the study of technological history, the focus is on the usual issues of economic and social history. Unfortunately, curators with a background in history often lack the required specialized technical knowledge. This is reflected, e.g., in erroneous entries in various collection databases. Since it is difficult to obtain reliable data for old devices, the verification of such contributions is, to be sure, time-consuming. Many persons have a fear of technology or have an aversion to this and make no attempt to open machines. When the significance of technical treasures is unappreciated, experience shows that such objects are soon consigned to a museum repository. Object collections require considerable space, and archives cause substantial costs. In general, there are only a few active technological historians, and many of these are retired. Many  – often outstanding persons  – are passionately devoted to the reconstruction, maintenance, care, and use of artifacts. The work of collectors’ associations (slide rules, mechanical calculating machines, typewriters, etc.), which however is often plagued by a lack of younger persons, is also deserving. The members become older and die off. For posterity, this means an unavoidable loss of knowledge. We live in a world that is decisively characterized by engineering, mathematics, and the natural sciences. In the long term, these will have far more impact on the course of things than politics. Nevertheless, compared with the history of politics, the history of technology plays only a minor role, and technology is only held in very low esteem by the authorities responsible for the advancement of culture.

17.6  Experiencing Technological History On Lake Lucerne, Lake Geneva, and Lake Thun, as well as other Swiss bodies of water, exceedingly popular scheduled excursions are offered with luxuriant paddle wheel steamers. The impressive steam engines, the mighty paddle wheels, and the elegant salons restored in the original style enable the immediate experiencing of technical culture. Likewise, a substantial demand exists for train rides with smoking steam locomotives and vintage rail wagons. The enthusiasm is all the more when the untiring efforts of volunteer workers reactivate a no longer operative railway section, such as the mountainous route over the Furka Pass, or a railway line such as the Albula-Bernina-Bahn is declared a UNESCO World Heritage Site. With ancient calculating machines, one can demonstrate their functioning to the public. This assumes that they are still working and that one can operate them. It is important to preserve not only sensational historical objects but also particularly significant inconspicuous achievements. However, the media have little interest in publications of historical documents and objects.

17.7  Furthering of the Follow-On Generation of Technological Historians

837

Everyday equipment that is hardly valued and thoughtlessly disposed of can be regarded in a few decades as historically valuable. Treasures may be lying dormant in some attics. Only a short time ago, imposing looms were found in a number of basements but have now disappeared entirely. This is especially the fate of bulky equipment with high space requirements.

17.7  F  urthering of the Follow-On Generation of Technological Historians One repeatedly speaks of a shortage of specialists. Experience shows that the effective furthering of follow-on experts must begin well enough in advance, because the stage must be set early. This also applies for the history of technology. Thus, for example, demonstrations of historical calculating machines show that it is possible not only to awake the interest of adults and adolescents, but especially of young children, for mechanical objects and calculating aids. With the help of the digital abacus  – as in earlier times in elementary school – the tens carry can be practiced, e.g., with addition and subtraction. Thanks to analog devices, such as sectors, proportional dividers, and pantographs, one can apply the geometric intercept theorems. Simulation programs enable insight into the functioning of mechanical calculating machines. Graphical addition and subtraction are made simple with two ordinary yardsticks (with linear scale). Coding represents another starting point for mathematical and computer experiments. Light houses and role models serve to support the imparting of knowledge. Numerous technical and natural science museums have devised hands-on exhibitions, with which old and young can touch the objects and try them out. One wants to offer an experience and encourage brainteasers and tinkering. The visitors are supposed to become immersed in a mysterious world of games. However, daily routine shows that unaccompanied and unsupervised experiments can degenerate into total confusion and often damage to the stations. Technological History in the Historical Dictionary of Switzerland In October 2014 the last volume of the trilingual Historisches Lexikon der Schweiz was issued. Following 25 years of work, this now comprises 41 volumes (13 each in German, French, and Italian and further two volumes in Romansh), as well as an open-access online edition. Random samples indicate that technical subjects are in fact treated, but looking up often leads nowhere. Overview articles exist for the history of technology, computer science, mathematics, informatization, and astronomy and to related fields, such as mechanization, electrical engineering, physics, telecommunications, and office.

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Native pioneers, such as Jost Bürgi (logarithms, variable proportional compasses), Jakob Amsler (polar planimeter), Heinz Rutishauser (automatic programming, Algol programming language), and Niklaus Wirth (Pascal) are mentioned briefly, as are Eduard Stiefel, Ambros Speiser or also the Ermeth vacuum tube computer. Separate entries are also found for the Kern, Paillard, and Ascom (formerly Hasler) companies. However, one finds (almost) nothing about the leading manufacturers, such as Coradi, Loga, Egli, and Precisa or about popular mathematical instruments, for example, pantographs, pairs of sector compasses, proportional dividers, planimeters, differential analyzers, slide rules, or mechanical calculating machines (e.g., the Millionaire or the Madas).

17.8  Computers Were Originally Humans As a rule, the English term “computer” and the equivalent German term “Rechner” describe calculating machines. But until the middle of the twentieth-century computers were in fact humans who performed calculations. This is shown in older specialized books and numerous printed reference works. For complex calculations, the assistance of reckoning centers was required. In calculation halls human computers worked with mechanical desk calculating machines. This was often the work of women. Until the 1950s, in the English-speaking countries, computers were humans and not machines. One spoke of human computers and female computers, of a “human computer with a desk calculator.” This was the term for the first female programmers who worked with the monstrous Eniac. The title of a book by David Alan Grier makes this clear: “When computers were human” (Princeton University Press, Princeton 2005). To distinguish them from human computers, the terms digital computer and electronic digital computer were widely used. In these days, the spelling computor (with o) was also occasionally found. Expressions such as calculator (English), calculateur, calculatrice (French), calcolatore, calcolatrice (Italian), and calculador(a) (Spanish) were originally reserved for calculating persons. Later came the terms ordinateur (French), elaboratore (Italian), and ordenador/computador(a) (Spanish), which generally referred to electronic computers. A (German speaking) “Rechnerin” is always a person. On the other hand, “calculatrice” and “calcolatrice” describe both humans and machines. Other French names are machine à calculer (calculating machine) and calculette (pocket calculator). Other than in English with the words “computer,” “calculator,” and “reckoner,” in German – apart from compound names – only the term “Rechner” is common.

17.8  Computers Were Originally Humans

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The two quotations below underscore this: “The labour which is involved in computing astronomical data of this kind is very great, and for many years was undertaken by highly skilled computers, most of them elderly Cornish clergymen, who lived on seven figure logarithms, did all their work by hand, and were only too apt to make mistakes.” and “Today no logarithms are needed. About one-third of the staff are astronomers, and the rest computers, many of them young girls who can successfully operate their desk calculating machines but who may be quite unable to explain the complicated functions which they are computing. The complete mechanization of these computations cannot be long delayed.” (see Bertram Vivian Bowden: A brief history of computation, in: Bertram Vivian Bowden (editor): Faster than thought, Pitman publishing, London 1953, reprinted 1971, page 25).

The following article also touches on this subject: Mary Croarken: Human computers in eighteenth- and nineteenth-century Britain, in: Eleanor Robson; Jacqueline Stedall (editors): The Oxford handbook of the history of mathematics, Oxford University Press, Oxford 2009, pages 375–403. The original meaning of the English term “computer” can be seen from the following entries in British and US reference works: computer a person who did computations The New Encyclopaedia Britannica, volume 16, Encyclopaedia Britannica, Inc., Chicago, London, 15th edition 2007, page 630 computer, also computor one who computes; a calculator, reckoner; specifically a person employed to make calculations in an observatory, in surveying, etc. The Oxford English Dictionary, volume 3, Clarendon Press, Oxford, 1989, page 640 computer, also computor a person who makes calculations; specifically a person employed for this in an observatory, etc. (age of the word: 1630–1669) The New Shorter Oxford English Dictionary on Historical Principles, Clarendon Press, Oxford 1993, volume 1, page 464 computer a person who computes or makes calculations The Concise Oxford English Dictionary of Current English, Clarenden Press, Oxford, 9th edition 1995, page 274, as well as the Oxford English Reference Dictionary, Oxford University Press, Oxford, 2nd revised edition 2003, page 298 computer a person who makes calculations, especially with a calculating machine The New Oxford Dictionary of English, Clarenden Press, Oxford 1998, page 379

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computer, also computor one that computes, a person who calculates (as latitudes, longitudes, and areas) for map making from notes provided by engineering survey parties Webster’s Third New International Dictionary of the English Language, volume 1, G.  Bell & sons, Ltd., London/G. & C.  Merriam Co., Springfield, Massachusetts 1961, page 468 computer a person who computes Webster’s New Dictionary and Roget’s Thesaurus, Thomas Nelson publishers, Nashville, Tennessee 1984, page 149 computer a person who computes or calculates Collins English Dictionary 21st Century Edition, Harper Collins publishers, Glasgow, 4th edition 2000, page 330 computer any device or person that computes Collier’s Dictionary, volume 1, Macmillan Publishing Company, New  York 1986, pages 206 f. computer a person who computes The Chambers Dictionary, Chambers Harrap Publishers Ltd., London, 12th edition 2011, page 323 computer one who or that which computes Funk & Wagnalls New international Dictionary of the English Language, comprehensive edition, Library Guild Word Publishers, New York 1987, volume 1, page 269 computer a person who computes; computist (1640–1650) The Random House Dictionary of the English Language, Random House Inc., New York, 2nd edition 1987, page 421 computer somebody who computes; a person who calculates figures or amounts using a machine Encarta World English Dictionary, Bloomsbury Publishing Plc. London 1999, page 391 Oxford English Dictionary (online) Definition of computer noun

17.9  Patent Protection

841

• an electronic device which is capable of receiving information (data) in a particular form and of performing a sequence of operations in accordance with a predetermined but variable set of procedural instructions (program) to produce a result in the form of information or signals, • a person who makes calculations, especially with a calculating machine. Encyclopaedia Britannica (online) computer, device for processing, storing, and displaying information. Computer once meant a person who did computations, but now the term almost universally refers to automated electronic machinery.

17.9  Patent Protection The fear of plagiarizers is said to have influenced Jost Bürgi to publish his table of logarithms only many years after John Napier. The entirely justified fear of pirate copies can be seen with other pioneers, for example, Wilhelm Schickard, Blaise Pascal, Gottfried Wilhelm Leibniz, and Philipp Matthäus Hahn. Descriptions in articles were therefore sometimes reduced to a minimum. Pascal was accorded a royal privilege for the manufacture of his machines. Due to a fear of plagiarism, some instrument manufacturers in the sixteenth century did not publish drawings for their machines (e.g., for the sector and proportional dividers).

17.9.1  No Claim to the Protection of Inventions Up to the second half of the nineteenth century – with the exception of the industrial power Great Britain – the protection of inventions was inadequate and strongly disputed. In 1869, the Netherlands even repealed patent protection. On the other hand, Venice introduced a patent law as early as 1474. The protection of inventions was based on privileges and monopolies. There were invention privileges, introduction privileges, commercial monopoly privileges, and factory privileges. Until the advent of patent protection, the protection was on the basis of the power of pardon (see Marcel Silberstein: Erfindungsschutz und merkantilistische Gewerbeprivilegien, Polygraphischer Verlag AG, Zurich 1961). Before the introduction of patent law (see Table  17.2), protection against plagiarism consisted of a royal act of grace. There was no legal claim. From 1815, Prussia had protection for inventions. In the sixteenth century, secrecy was common. In his memoirs, the inventor of the Curta relates that, because of the threats of the Nazis, he refrained from very much detail in his patent application:

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In the Spring of 1938 I applied to the Patent Office in Vienna for patents on the two most important inventions. I only described the stepped drum exactly and illustrated the rest in drawings, so that the matter remained largely unclear (see Curt Herzstark: Kein Geschenk für den Führer, Books on demand GmbH, Norderstedt 2005, page 179).

The patent was granted two months after Hitler invaded Austria. Table 17.2  Patent protection in the nineteenth century Patent laws (in force in 1899) Country Austria Belgium France Germany Great Britain Italy Russia Spain Sweden Switzerland

Patent law 1852 1854 1844 1891 1623 1864 1896 1878 1884 1888

Term of protection 15 years 20 years 5, 10, 15 years 15 years 14 years 15 years 15 years 20 years 15 years 15 years

© Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020

Source L.  Glaser: Patentschutz im In- und Auslande, 1. Theil (Domestic and international patent protection, Part 1): Europa, Verlag von Georg Siemens, Berlin 1899. Remarks The above years refer to the patent laws in force in 1899. This overview gives the maximum term of protection. Exemplary is especially the UK, which introduced protection of inventions already in 1623. In France patent protection existed from 1791. Thomas had his arithmometer patented in 1820, and Schwilgué followed in 1844 with his keyboard adding machine (patent law of July 5, 1844). From 1877, Germany had a Reich patent law, which was changed in 1891. The German Reich therefore introduced uniform patent law only in 1877. Until this time, the individual regions (e.g., Bavaria, Prussia, or Saxony) were responsible for issuing patents (see Rudolf Boch (editor): Patentschutz und Innovation in Geschichte und Gegenwart, Peter Lang, Frankfurt am Main, Berlin, etc. 1999, pages 71–84). As shown by the patent statistics of the German Reich, in 1877 (in accordance with the Reich patent law of May 25, 1877), 190 patents were granted (with 3212 patent applications). In 1878 there were 4200 patents (5982 patent applications) (see Alfred Heggen: Erfindungsschutz und Industrialisierung in Preußen 1793–1877, Vandenhoeck & Ruprecht, Göttingen 1975, page 137). At that time there was no international agreement with France with respect to patent protection in the German Reich (however in any case with Austria

17.9  Patent Protection

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and Switzerland). In 1873, a patent protection conference took place in Vienna during the world exhibition. On March 20, 1883, an international treaty for the protection of industrial property rights was concluded in Paris. Initially the following countries, for example, were party to this contract: Belgium, France, Italy, the Netherlands, Spain, and Switzerland. Great Britain and Sweden joined them later. Germany did not take part.

17.9.2  H  ad the Patent Protection for the Thomas Arithmometer Expired? Kehrbaum and Korte write: “Competition for the Thomas arithmometer only appeared from 1878, following the expiration of patent protection, in Glashütte (Saxony)” (see Annegret Kehrbaum; Bernhard Korte: Historische Rechenmaschinen im Forschungsinstitut für diskrete Mathematik Bonn, in: DMV Mitteilungen, 1993, volume 2, page 10). Gerd Biegel gives this account: “Since there was no longer patent protection for the Thomas arithmometer, he [Arthur Burkhardt] built an improved, further developed version of this stepped drum machine and is therefore regarded as the founder of the German calculating machine industry” (see Gerd Biegel: Von der Erfindung der Zahl zum Computer, in: Matthias Puhle (editor): Von der Erfindung der Zahl zum Computer, Magdeburger Museen, Magdeburg 1992, page 44). Wilhelm Jordan, the author of an essential handbook of surveying, points out that the acquisition of a Thomas arithmometer from Paris and sending back and forth for repairs were cumbersome: Mr. Burkhardt essentially copied the construction of Thomas (which was not forbidden by patent laws), and his machines look just like those from Paris (see Wilhelm Jordan: Eine deutsche Fabrik für Rechenmaschinen, in: Zeitschrift für Vermessungswesen, volume 9, 1880, no. 11, page 439).

The inventor of the lazy tongs gives a similar explanation: Since the expiration of the original patents, such machines – with minor, in part patented modifications – have also been manufactured in Germany, with better workmanship but also with higher prices (see Eduard Selling: Eine neue Rechenmaschine, Verlag von Julius Springer, Berlin 1887, page 8).

On the other hand, the section “Geschäftssinn und Organisationstalent” in the loose leaf collection of the Bonn Arithmeum indicates: Immediately after his arrival in Glashütte in October 1878 Burkhardt cold-bloodedly delivered two original Thomas machines with changed engraving and minor improvements (engraved numerals, convenient clearing mechanisms) to the Prussian State Office of Statistics, and: Within a few months Burkhardt had already succeeded in establishing a factory for calculating machines in Glashütte and made initial contacts to important customers. The key for this success was, on the one hand, his sense

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of reality and, on the other hand, his unscrupulous use of the Thomas arithmometer, for which patent protection had become vulnerable following the death of the inventor (1870) (see Arithmeum (editor): Arithmeum  – Rechnen einst und heute  – im Forschungsinstitut für diskrete Mathematik, Texte, Universität Bonn 1999,no page numbers).

For decades, there was only one supplier of mechanical calculating machines in the world, the Paris insurance broker Charles Xavier Thomas. From 1878 Arthur Burkhardt in Glashütte began with the mass production of his stepped drum machine. It was a copy of the French arithmometer. In the time following, the German industrialist evidently made only minor improvements to the machine and hardly brought any creative innovations to the market. The first patent for the Thomas arithmometer dates from the year 1820. A further patent was granted in 1850 and was renewed in 1865 and 1880. In France, then, the patent was still in force in 1878. As the catalog of the world exhibition in London shows, in 1851 there were patents for the arithmometer in France and Great Britain. However, patent protection may not have existed in the German regions: The tedious process of the emergence of a widespread demand for calculating machines was just around the corner, and Thomas financed the calculating machine production until his death from his private assets. Thanks to these investments in the future, in the last third of the 19th century there was a fully developed [Thomas arithmometer] calculating machine available with expired patent protection, known to a small group of interested persons around the world, and: since the Thomas machine was no longer subject to patent protection and [Ernst] Engel [director of the Prussian State Office of Statistics] saw possibilities for improvement, as a result of which he commissioned Burkhardt with the construction of two new machines of this type (see Hartmut Petzold: Moderne Rechenkünstler, Verlag C.H. Beck, Munich 1992, pages 64 and 67).

Dietzschold reprimands Arthur Burkhardt’s behavior sharply: To this day, improvements [to the machines of Thomas from Colmar] are still being developed, as a patent of the company on September 29th 1880 shows. Since August 1st 1879, “a young German A.B.” has begun manufacturing calculating machines on the basis of the Thomas drum principle […]. We would not be concerned any further with the “young German” if it were not for his total lack of respect for the 50 years of work by Thomas and his blatantly pretentious reference to him, as well as the flagrant manner in which he vied for the commercial heritage. In fact the production of Thomas’ arithmometers is certainly not unprofitable […]. An extremely disrespectful behavior in view of the fact that the Paris company is still committed to the further development of the Thomas arithmometer and spares no patent costs! (see Curt Dietzschold: Die Rechenmaschine, reprint from: Allgemeines Journal der Uhrmacherkunst, Druck und Verlag von Hermann Schlag, Leipzig 1882, pages 38–39.

17.10  Discoveries and Inventions As the history of technology indicates, independently of each other, many achievements were simultaneously invented or multiply invented over a period of time. The same is true for discoveries.

17.10  Discoveries and Inventions

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One can systematically track down historical objects, for example, in private collections, museums, archives, on flea markets, in the professional literature, in excavations, or by diving. Nevertheless, many findings are accidental. One often discovers valuable artifacts without specifically searching for them. Thus, while on a mountain hike, a married couple discovered the famous icebound corpse Ötzi the iceman. Furthermore, we are indebted to sponge divers for the discovery of the mysterious Antikythera mechanism. The first large Loga cylindrical slide rule came to my attention in the office of a colleague in the Department of Computer Science at the ETH Zurich with whom I wanted to arrange a meeting. Another example is we searched for long gone slide rules in the Collection of astronomical instruments of the ETH Library. This led to the discovery of rare mechanical calculating machines. Or in the course of additional investigations of Schwilgué’s keyboard adding machine, a unique mechanical adding machine, used for the Strasbourg cathedral astronomical clock calculations, came to light in the Strasbourg Musée historique. Time and again, persons and their creations sink into oblivion. In many cases, it is not known whether the inventors were aware of the achievements of predecessors or contemporaries or their developments were entirely new. In some cases, preliminary work is only made clear in patent applications. Many “discoveries” are, strictly speaking, rediscoveries.

17.10.1  Invention Priority Of course the history of technology may not be limited to the question of who invented or discovered what. However, questions of priority are of importance for the patenting and marketing of innovations. Only original inventions can be registered. The use of such patents entails license fees. Priority disputes frequently result in legal processes. Research into priority rights is often fruitless. The search leads quickly to a dead end. In many cases, the origin can no longer be clarified with certainty. Even the determination of the relevant point in time is often difficult. Developments may require many years and pass through different stages of maturity. For historical scholarship there are more important and more fascinating subjects than confronting the question of priority, “who invented the computer?” Here there are different opinions. Answers to questions of priority depend significantly on the particular definition, and in any event, this can be tailored to one’s own requirements and also misused. What was the first pocket calculator? The hand abacus (bead frame), slide rule, slide bar adder, Curta, or some other device? Which definition does one take as a basis?

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Far more illuminating are formulations such as “How does the machine function?”, “How does one operate the device?”, or “Who used the device when and for what purpose?”

17.10.2  Were Logarithms Discovered or Invented? With regard to the emergence of logarithms (John Napier and Jost Bürgi), according to the source, one speaks of discovery or invention. Both views can be justified. Here it should be noted: inventions can be patented, but discoveries cannot.

17.11  Patriotism and Hero Worship The often one-sided, distorted point of view in English and American works dealing with the history of computing is often disappointing. The content of some books ends with the national border or, at the latest, with the language border. Breakthroughs in non-English-speaking countries are often not taken notice of or intentionally ignored, so that misunderstandings cannot be excluded (see Herbert Bruderer: Computing history beyond the U.K. and U.S.: Selected landmarks from Continental Europe, in: Communications of the ACM, volume 60, 2017, no. 2, pages 76–84). Certain historical treatments, such as regarding Alan Turing, read almost like “party opinions.” The answers are mostly clear from the very beginning. The long-­winded, obstinate argumentation of prejudiced experts sometimes comes across as dogmatic. In the history of technology, a nationalistic, uncritical hero worship, such as in favor of Charles Babbage, Jost Bürgi, Leonardo da Vinci, Ada Lovelace, John Napier, Adam Ries, Leonardo Torres Quevedo, Alan Turing, John von Neumann, and Konrad Zuse, is prevalent. Biographies are experiencing an upturn. The recognition of pioneers naturally harbors the danger of hero worship. Memoirs are unsatisfactory when these are the only sources and cannot be verified. These are sometimes published only after a delay of several decades. In this book, the focus is on the particular achievement and not on the lives of the relevant persons.

17.12  Lifespan of Calculating Aids Since time immemorial the fingers have been a popular aid for counting and calculating. In addition, mathematical tables were widespread.

17.12  Lifespan of Calculating Aids

847

The ancient Greeks had counting boards, while The Romans used bead frames. The line abacus lived on in the form of checker boards, counting tables, and counting cloths. The best known examples to date derive from the sixteenth to the eighteenth century. Until recently, the abacus was routinely used in countries of the East (e.g., China, Japan, and Russia). No substantiated times exist for the Roman hand abacus. Logarithms emerged in the seventeenth century. The linear slide rule and the circular slide rule were invented in the seventeenth century, but the slide rules (Mannheim system) only became widespread from the middle of the nineteenth century. Large numbers of circular slide rules and cylindrical slide rules were commercially available from the end of the nineteenth century. The first mechanical calculating machines were built in the seventeenth century but were not yet suitable for daily use. From around the middle of the nineteenth century, their production figures increased. Furthermore, for decades or even centuries, there was an abundance of analog drawing, measuring, and calculating instruments, such as pantographs, pairs of sector compasses, proportional dividers, planimeters, coordinatographs, and differential analyzers. Slide rules and tables of logarithms, along with mechanical calculating machines, were widely used mathematical instruments until the introduction of electronic pocket calculators. The lifespans of calculating aids differ greatly (see box). Lifespan of Calculating Aids The following information is only approximate. Some machines only caught on gradually. Many old (mechanical) calculating aids disappeared in the last quarter of the twentieth century due to the flourishing of microelectronics. • Fingers from time immemorial to the present day • Mathematical tables from antiquity to the present day • Astrolabe from antiquity to the seventeenth century • Bead frame (abacus) from around the twelfth century up to the twenty-first century • Calculating board (counting table) from the thirteenth century into the eighteenth century (jetons from the thirteenth century) • Linear slide rule from around 1620 until the 1970s • Circular slide rule from around 1620 until the 1970s (continued)

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• Mechanical calculating machine from around 1650 (Pascaline, two-function machine), more popular from around 1850 (Thomas arithmometer, four-function machine) until the 1970s • Napier’s bones from the seventeenth century into the nineteenth century (partly into the twentieth century) • Sector from the seventeenth century to the end of the nineteenth century • Pair of proportional dividers from the seventeenth century to the second half of the twentieth century (partly until today) • Pantograph from the seventeenth century until the 1980s • Planimeter from around 1820, increasingly popular from around 1855 (polar planimeter of Amsler) up to the 1980s • Difference engine from around 1850 up to the first half of the twentieth century • Keyboard adding machine from around 1850, more popular from around 1890 (comptometer) up to the 1970s • Cylindrical slide rule from around 1880 up to the 1970s • Slide bar adder from around 1890 (Troncet) up to the 1970s • Punched card machine from around 1890 up to the 1980s • Direct multiplying machine (Millionaire) from around 1890 until the 1940s • Mechanical differential analyzer from around 1930 until the 1950s • Relay computer from around 1940 until the 1950s • Vacuum tube computer from around 1950 until the 1960s • Electronic analog computer from around 1950 until the 1970s • Transistor computer from around 1960 until the 1970s • Stored program electronic universal computer from around 1950 until today The typewriter became established from around 1870 and was gradually replaced by the computer in the 1980s.

17.12  Lifespan of Calculating Aids

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Remarks Most manufacturers of historical calculating machines have not survived. Nevertheless, such devices are still produced, for example, bead frames (abacus) and slide rules. Haff in Pfronten (Bavaria) offers mechanical (and digital) planimeters, proportional compasses, and spacing dividers in addition to sets of drawing instruments. Mechanical musical instruments were in operation from the Middle Ages until the twentieth century. Music boxes are still popular gifts today, and barrel organs continue to provide entertainment. Reuge in Sainte-Croix VD still produces music boxes and singing birds. Today, automaton figures are still built in Switzerland, especially in canton Jura.

Chapter 18

Preserving the Technical Heritage

Abstract  It follows from chapter “Preserving the Technical Heritage” that much material and immaterial cultural heritage has been lost in the wake of rapid technical developments. The lifespan of objects decreases. Museums are bursting at the seams. When documentation is missing, it is not always known which objects are of relevance. At some sites a reevaluation of often neglected scientific collections is in progress. Maintaining the functionality of mechanical automatons and electronic computers is extremely time-consuming. The associations committed to the preservation of the technical cultural heritage have difficulty finding younger persons to carry on their work. Thanks to digitization many old and rare books, journals, maps, and plans are globally accessible online. However, since the lifespans of currently available electronic data carriers are short, the problems of long-duration digital archival remain. Furthermore, programs and operating systems, as well as document formats, continuously change. Due to the immense amounts of data, it is not possible to save all meaningful Internet-based information for posterity. The deluge of data leaks shows that external data keeping (clouds) is unreliable. Keywords  Digital permanence · Digitization of documents · Loss of cultural heritage · Material culture

18.1  Loss of Cultural Heritage Countless valuable machines have long since been disposed of due to lack of space, because they were not in working order, no one wanted to have them, or their value was not recognized. Now and then apart from patent specifications, nothing more exists. These can be traced in patent databases. Even devices and machines that were still widely used up to the 1970s have now been forgotten. Only a few of the original manufacturers have survived, e.g., International Business Machines (IBM) and Remington Rand (now Unisys). © Springer Nature Switzerland AG 2020 H. Bruderer, Milestones in Analog and Digital Computing, https://doi.org/10.1007/978-3-030-40974-6_18

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Estates are only the exception and historical archives are sooner rare, so that considerable technical heritage has disappeared. This is all the more regrettable in view of the fact that computer science and electronics are young disciplines and their development is also extremely fast. Illuminating documents and apparatus are sometimes in private hands, such as with former employees. The rapid and fundamental technical transformation detracts from preoccupation with the past. In the course of centuries, marvelous and magnificent calculating machines were built. Unfortunately, many objects and descriptions have been lost. The bronze Antikythera mechanism sank into the Mediterranean Sea during a storm. It was discovered in 1901 and is now in the National Museum of Archaeology in Athens. This represents one of the most significant findings in the history of technology. Only a few ancient Greek stone calculating tablets are preserved. Only a few species of the Roman hand abacus survived. The once popular calculating tables and calculating cloths of the middle ages and the early modern era have nearly died out. Overviews of the still existing mathematical instruments can be found in several books. Sources Alain Schärlig: Compter avec des cailloux, Presses polytechniques et universitaires romandes, Lausanne, 2nd revised edition 2001 Alain Schärlig: Compter avec des jetons, Presses polytechniques et universitaires romandes, Lausanne 2003 Richard Hergenhahn et al.: "Mache für dich Linihen …". Katalog der erhaltenen originalen Rechentische, Rechenbretter und -tücher der frühen Neuzeit, Adam-­Ries-­Bund, Annaberg-Buchholz 1999 Ulrich Reich: Rechentische, -bretter und -tücher. Originale und Nachbauten, in: Rainer Gebhardt (editor): 500 Jahre erstes Rechenbuch von Adam Ries, Adam-­Ries-­Bund, Annaberg-Buchholz 2018, pages 57–64. In antiquity presumably there were also portable wooden calculating boards and bead frames, but they have apparently decomposed. Slide rules, mechanical calculating machines, and other calculating aids are found in many museums. Mechanical integrating instruments (e.g., planimeters), pantographs, sectors, and proportional dividers are found less often in collections.

18.2  Long-Duration Archiving According to our present state of knowledge, the reliable long-duration archiving of electronic documents requires regular copying to the respective current high-quality storage media. When texts, tables, drawings, and diagrams are to be processed subsequently or multimedia documents access

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applications, the relevant programs must be available. These must be continuously installed and matched to the respective environment (platform, operating system, and device). Present-day electronic storage media, such as magnetic, optical, and semiconductor storage, are not at all suitable for longduration archiving. The two most important methods for long-term archiving are migration (transfer to new file formats, new storage media, a new operating system, or a new programming language) and emulation (simulation of devices and programs). A further, but very complex, method uses deoxyribonucleic acid (DNA) as a storage medium for preservation. Operating Systems, Programs, and File Formats Museums of technology collect primarily tangible objects (hardware). The long-­term preservation of programs (software) is more difficult: operating systems, application programs, utilities, drivers, and programming languages. Furthermore, file formats (e.g., for texts, still images, moving images, or sound) are short-lived. Older documents can often not be opened, because the original application programs are no longer available. Document formats independent of manufacturer, platform, and program are therefore important. Causes of Data Loss The most frequent cause for the loss of electronic documents is inadequate or lacking data backup. However, there are several other reasons as well: damage to digital storage media or the files themselves, nonexistence of suitable drives, incompatibility of interfaces and cables, or lacking drivers. According to the German Magazin für Computertechnik (see c’t, 2018, no. 10, page 156), three processes pose risks for data stored to hard disc: demagnetization, corrosion of the discs and the read/write head, and decomposition of lubricant in the bearings. For long-duration archiving, a temperature below 30 °C and a humidity of less than 50 % are recommended. Who still has functioning playback devices for old analog sound and image carriers (gramophone and phonograph records, audio tapes, video cassettes, film cartridge spools, or microfilms)? In any event, most erstwhile suppliers have long since disappeared. In order to prevent the loss of recorded data, it makes sense to keep old playback devices as well as magnetic disc drives. Only a few silent films have survived. And what about emails available only digitally? Who ensures that online journals, electronic books, digital reference works, databases, and websites will still be accessible decades later? There are excellent (often private) Internet pages for the history of technology that are available only electronically. What will become of this invaluable knowledge when these websites are no longer maintained? For documents available only in digital form, a massive data loss threatens. Sometimes printing out important documents on paper does no harm.

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Life Expectancy Data storage media, such as stone, clay, bone, parchment, or paper, have a high life expectancy of  – in part  – more than 1000 years. Cuneiform documents on clay tablets have survived over centuries. Books with acid-free paper have existed for centuries. In some ways, this material is still second to none. Contrary to electronic media, printed works such as books and journals can be read for centuries without (technical) resources and without electric current. The same applies for drawings and maps. Digitization of Historical Documents The digitization of historical manuscripts and old and rare printed material enables worldwide online access to documents at all times. This greatly simplifies historical scholarship. However, the volume of archive material is so large that probably only a fraction of this will be available electronically in the future. Sources for Digital Documents Ongoing changes to electronic reference works complicate referral to sources. Surveys at a particular time are difficult. Especially annoying is the rapid obsolescence of website addresses. In this book electronic references are therefore given only as exceptions. The Internet Archive (https://archive.org) in San Francisco tries to permanently store documents (and also websites) around the world. Nevertheless, because of the huge volume, it can only cover a part of this. Even after death many digital footprints remain online (see box).

Digital Estates Whoever has set up accounts for electronic mail, social networks (profiles), short message (tweet) services, banks, payment services, online retailers, auction services, search engines, reference works, news services, accommodation services, ride-hailing services, food delivery services, online research platforms, etc. or digital subscriptions (apps, games, streaming services, mobile communications services, music, videos, books, newspapers, magazines, etc.) or stores documents (e.g., photos) in external data centers (cloud computing) should regulate while still alive (in the will) what is to become of the digital legacy. In addition, there are insurance, electricity, and gas contracts. One can provide the login credentials (user name and password) and determine who obtains access to the accounts. We leave behind a wealth of tracks (digital footprint) in the cyberspace.

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18.3  Management of Object Collections The economic and social history of technology too often fails to answer many everyday questions: • • • • • • • • • • • • • • • • •

What is that? (determination) Where does it come from? (origin) Who conceived it? (invention) Who built it? (manufacturing) When was it built? (dating) Who made use of it? (usage) What does it do? (purpose) How is it operated? (handling) How does it function? (explanation) How important is it? (classification) How does it compare with similar objects? (comparison) Why is it constructed in this way? (design) How is it stored? (care) How can it be preserved? (preservation) How can it be patched? (repair) How can one maintain its functioning? (functionality) How can one rebuild or simulate it? (reconstruction, simulation)

18.3.1  Building Up a Collection As a rule, amassing a valuable collection requires decades of work: visiting flea markets and auctions, taking part in collectors’ meetings, or acquiring via electronic commerce.

18.3.2  Breakup of a Collection When one has to break up a high-quality collection due to age, health, or other reasons or dispose of individual objects, it is necessary to find interested persons. Descendants often show little interest. Many museums have no more space. For the takeover, for instance, museums of technology or history come into question. However, most objects end up in reserve storage, and only a very small part is exhibited. One can also offer devices in the Internet (e.g., via eBay). The breakup of a collection can lead to the separation of the various objects. This is not necessarily a disadvantage, since the individual items can also supplement other collections.

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Lacking documentation hampers the preservation of cultural heritage (see box). Technical Collections Without Documentation For some private and public collections, descriptions and identification labels are missing in the displays and stands, as is any other written documentation. Often only the collectors themselves are aware of the nature of a given device and ideally can still operate the calculating aid. Later owners are practically helpless. Often there are neither (high-quality) photos nor stocktaking. Even less common are (informative) object databases accessible to the public.

18.3.3  Gloves Historians generally handle sensitive old and rare documents with white cloth gloves in order to prevent damaging them. The same applies for other valuable objects, such as calculating devices. On the other hand, engineers, technicians, mechanicians, clockmakers, and the builders of these machines usually dispense with such a protective measure. They have no fear of touching. In their view, it is irrelevant whether one once again touches objects (without gloves) that have already been handled a hundred or a thousand times.

18.3.4  Functionality of Devices Many historical calculating machines still work perfectly even after decades. As expected, devices which function without electricity, such as calculating tables, bead frames, slide rules, slide bar adders, mechanical calculating machines, sectors, proportional dividers, planimeters and pantographs, as well as other measuring and drawing instruments, have the longest life expectancy. However, they can eventually stick together (e.g., the legs of a sector). Operating instructions are a help for using the devices. However, in most museums electromechanical and electronic relay, vacuum tube, and transistor computers are mostly standing still. The effort to restore their functionality is very considerable. Who can imagine how a dead machine standing idle once functioned? Here, films, such as describing the Enigma cipher machine, and interactive simulations, for example, for the Curta mechanical pocket calculator, are instructive. Hands-on demonstration models also further technical understanding.

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The National Museum of Computing in Bletchley Park, UK, where enthusiastic volunteers repaired the Harwell Dekatron computer and maintain its functionality, is altogether unique. In the former British secret service center, a number of important calculating machines (e.g., the Turing-Welchman Bombe, Colossus, and Edsac) have been reconstructed and are fully operational. The Manchester’s Science and Industry Museum regularly demonstrates the resurrected Manchester Baby (stored program electronic computer). The computers of Living Computers: Museum + Labs in Seattle, Washington, are also functional. Similarly, the Bonn Arithmeum maintains its treasures. In addition, volunteers are at work with the Studiensammlung Kern in Aarau. And the Solothurn Museum Enter endeavors to show many machines in a working state. This is also true of numerous museums for automaton clocks, musical automatons, and automaton figures.

18.3.5  Improper Safekeeping of Cultural Heritage Visits to museum repositories and to private and public collections, as well as an examination of company archives, reveal that irreplaceable historical documents and objects are sometimes improperly stored. Not only old paintings but also mathematical instruments suffer from these circumstances. It is important to protect calculating machines from dust, humidity, fluctuating temperatures, sunlight, water ingress, fire, and theft. The neglected objects of a former technological museum were in such a bad state (e.g., rusting) that they had to be either scrapped or with considerable effort restored. For the safekeeping of documents, there are recommendations, for example, by the Schweizerisches Wirtschaftsarchiv (Basel).

18.3.6  Damage to Devices due to Nonuse What is often disregarded, components of mechanical machines, clocks, music boxes, gramophones, and calculating aids, may stick together when not used over a longer period of time. The pivot joints of sectors can no longer be opened. Levers, keys, buttons, switches, cranks, and gearwork mechanisms no longer function. On the other hand, the permanent use of such devices is a delicate matter due to the wear that this entails. An old piece of advice regarding the care of mechanical calculating machines: A very good way is to immerse the entire mechanism, which can be very easily taken out of the casing, up to the cover plate in a suitable fine oil and allow it to drip one day long before using (see Franz Reuleaux: Die sogenannte Thomas’sche Rechenmaschine, Verlag von Arthur Felix, Leipzig, 2nd revised and expanded edition 1892, page 45).

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Recommendation To avoid damage due to nonuse, mechanical devices should be used in regular intervals (operation of the moving parts). Operating instructions are advisable here.

18.3.7  Reappraisal of Scientific Collections For several years a reappraisal of scientific collections at universities is apparent. Collection and object research is gaining in importance, as conferences on material culture make clear. Here, the efforts of the Koordinierungsstelle für wissenschaftliche Universitätssammlungen in Deutschland (Humboldt University of Berlin) deserve to be mentioned. Sources Cornelia Weber, Sarah Elena Link, Martin Stricker, Oliver Zauzig (editors): Objekte wissenschaftlicher Sammlungen in der universitären Lehre. Praxis, Erfahrungen, Perspektiven, Hermann von Helmholtz-Zentrum für Kulturtechnik, Humboldt-­Universität zu Berlin 2016, v, 104 pages Ernst Seidl, Frank Steinheimer, Cornelia Weber (editors): Materielle Kultur in universitären und außeruniversitären Sammlungen, Gesellschaft für Universitätssammlungen e.V., Berlin 2017, 123 pages.

Chapter 19

Operating Instructions

Abstract Chapter “Operating Instructions” gives detailed step-by-step instructions for the most important analog and digital calculating devices and mechanical calculating machines, making it possible to operate historical mathematical aids once again. In many cases, no operating instructions have been preserved. Failure to use such instruments can result in damage. The operating instructions range from heavy stationary desktop machines to lightweight portable pocket calculators, from the abacus (bead frame) through Napier’s bones and slide rules (linear, circular, and cylindrical slide rules), sectors, disc adding machines, and slide bar adders to keyboard adding machines (Schwilgué single-digit adding machine), stepped drum machines (Thomas arithmometer, Madas, Curta), pinwheel machines (Odhner, Brunsviga), and direct multiplying machines (The Millionaire). According to the model, numerical input is by wheels, stylus, setting levers, or keys. The use of the Chinese, Japanese, and Russian bead frames differs only slightly. This is also true for the children’s counting frame. Details for the use of the Roman hand abacus are given in Sect. 3.3. The numerical notation with the calculating table is described in Sect. 3.4. Section 4.6 explains the pantograph. Instructions for the use of proportional compasses are given in Sect. 4.8. All instructions are derived from trying out. These make very clear how arduous computation was for thousands of years. Keywords  Abacus · Analog calculator · Bead frame · Circular slide rule · Cylindrical slide rule · Digital calculator · Keyboard adding machine · Mechanical calculating machine · Napier’s bones · Napier’s rods · Operating instruction · Pinwheel machine · Sector · Slide bar adder · Slide rule · Stepped drum machine Calculating without electricity is fun, both with analog slide rules and with digital slide bar adders and calculating machines. But operating instructions are rare. This chapter therefore compiles step-by-step instructions in

© Springer Nature Switzerland AG 2020 H. Bruderer, Milestones in Analog and Digital Computing, https://doi.org/10.1007/978-3-030-40974-6_19

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alphabetical order according to the calculating device name for the most important types of calculators. Each set of operating instructions begins with one or more pictures (see Figs. 19.1, 19.2, 19.3, 19.4, 19.5, 19.6, 19.7, 19.8, 19.9, 19.10, 19.11, 19.12, 19.13, 19.14, 19.15, 19.16, 19.17, 19.18, 19.19, 19.20, 19.21, 19.22, 19.23, 19.24, 19.25, 19.26, 19.27, 19.28, 19.29, 19.30). Additional operating instructions are found as indicated below: • • • •

Calculating table, see Sect. 3.4 Pantograph, see Sect. 4.6 Proportional compass, see Sect. 4.8 Roman hand abacus, see Sect. 3.3

Calculating is possible not only with arithmetic but also with geometric calculating aids, for example, sectors and proportional dividers. The description of the “recipes” for analog instruments differs slightly from the instructions for digital machines. Mechanical calculating machines have blocking mechanisms (see box).

Blockage with Mechanical Calculating Machines Many mechanical calculating devices still function perfectly after more than 100 years. Nevertheless, they have their pitfalls. Often, machine parts are immobilized. The operating instructions – if these exist at all – give mostly no or only inadequate information about the blockage. In order to override the blockage, one then has no choice but to try different methods. When the carriage does not move, • This can be due to the transport locking screw. Remove this before use, and screw into an empty drilling on the panel or in the cover (transport lock). The screw prevents shifting of the carriage. • The crank is not in the basic position. The crank (according to brand and model) cannot be rotated when • The carriage is not correctly positioned or not in the basic position. • The reversing lever for the different arithmetic operations is not exactly positioned. When the crank is not in the basic position, • The (digit-by-digit and full) carriage shifting and switching between the four basic arithmetic operations is blocked. Furthermore, • Settings in the counting mechanism are sometimes blocked when the crank is not in the basic position. • The reversing lever for the different arithmetic operations is blocked when the crank is not in the basic position. • The clearing mechanisms may be blocked unless the crank is in the basic position.

19.1 The Abacus: Bead Frame

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19.1  The Abacus: Bead Frame

Fig. 19.1  Chinese abacus (suanpan). This abacus, acquired in Beijing in 1983, was still in use at that time at the checkout counters of department stores. As the 50-page instruction manual (in English) indicates, it is suited to the four basic arithmetic operations, as well as for square roots and cube. (© Aldo Lardelli, Studiensammlung Kern, Aarau 2020)

Operating Instructions for the Chinese Abacus Five beads per decimal place (ones, tens, hundreds, etc.) suffice for the numerical notation of the numerals 0 to 9 on the abacus: 4 hell beads and 1 heaven bead. This is the usual form of the Japanese soroban. By comparison, the older Chinese suanpan has 7 beads: 5 hell beads and 2 heaven beads. The additional beads serve as memory aids. In the zero position (basic position), all beads are moved out, in the lower part downwards and in the upper part upwards. Calculations are generally performed from left to right. As with the tokens of the calculating table, the beads are bundled (combined, with five beads forming a quinary bead) or unbundled (resolving a quinary bead into five separate beads) as required. This makes use of fives and tens complements. Ones, tens, hundreds, thousands, etc. beads are always hell beads (with a simple value). Five, fifty, five hundred, and five thousand beads are positioned in heaven, where they have a fivefold value. The ones position is the rod all the way to the right, the tens position immediately to the left of this, etc. Intermediate results can be controlled at any time. The procedure for multiplication and division is similar to that for calculations with pencil and paper. Remark Mechanical calculating machines utilize complements (nines or tens complements) for indirect subtraction.

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Heaven

Hell

Zero position Fig. 19.2  Chinese abacus in the zero position. All beads are at the upper edge of heaven and the lower edge of hell, moved away from the divider bar. The Japanese abacus has four hell beads and a single heaven bead. The Russian abacus and the school abacus deriving from it are equipped with horizontal rods with ten beads each. The Chinese and Japanese abacus forms have a fives carry and a tens carry. In certain cases, both are required (e.g., + 6 = (+ 10 - 5 + 1)) together. The Russian abacus only has a tens carry. (© Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020)

Addition Example: 936 + 487 = 1423 From Right to Left 1. Set all beads to the zero position. In the upper section (heaven), move them upward and in the lower section (hell) downward, that is, move them away from the divider bar. 2. Set in the number 936: Move one ones (hell) bead, one fivefold ones (heaven) bead, three tens (hell) beads, four hundreds (hell) beads, and one fivefold hundreds (heaven) bead toward the divider bar. 3. Add the number 487: To add the number 7, move the fivefold bead away from the divider bar, and move two ones beds and one tens bead toward the divider bar. Add the value 480 by moving two tens beads and one 500 bead away from the divider bar and moving a 1000 bead toward the divider bar. Counting the beads then gives the value 1423. From Left to Right 1. Set all beads to the zero position. In the upper section (heaven), move them upward and in the lower section (hell) downward, that is, move them away from the divider bar. 2. Set in the number 936: Move one 500 s bead, four 100 s beads, three 10s beads, one 5 s bead, and one 1 s bead toward the divider bar. 3. Add the number 487: To add the number 400, move one 1000s bead toward the divider bar, and move one 500  s and one 100  s bead away from the divider bar. Move a 100 s bead toward the divider bar and two 10s beads away from the divider bar. + 7 takes the form +10 + 2 – 5. Counting the beads then gives the value 1423.

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Heaven

Hell

Number 123 Fig. 19.3  Chinese abacus, showing the value 123. The rod all the way to the right gives the ones position; the second rod from the right, the tens position; and the third vertical rod, the hundreds position. The beads are moved toward the divider bar (transverse bar). With the Chinese abacus, contrary to the Japanese and Russian abacus, the numbers 10, 100, 1000, etc. can be represented in three ways (e.g., 1 × 10, 2 × 5, 1 × 5, and 5 × 1) and the 5, 50, 500 etc. in two ways (e.g., 1 × 5, 5 × 1). In certain cases, this simplifies carries. (© Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020)

Subtraction Example: 1234 – 789 = 445 1. Set all beads to the zero position. In the upper section (heaven), move them upward and in the lower section (hell) downward, that is, move them away from the divider bar. 2. Set in the number 1234 (as for addition). 3. Method A: – 1000 + 200, + 10 + 1; result: 445 (from left to right). 4. Method B: – 10 + 1 – 100 + 20 – 1000 + 300; result: 445 (from right to left). 5. Method C: – 100 + 10 + 1 + 300–1000; result: 445 (from right to left).

Heaven

Hell

Number 555 Fig. 19.4  Chinese abacus, showing the value 555. In each of the three positions, a heaven bead is moved to the divider bar. Hell beads have a simple value (1, 10, 100, etc.). Heaven beads are counted five times (5, 50, 500 etc.). For the Chinese abacus with 7 beads, each position can represent 16 values (0–15); for the Japanese abacus, with 5 beads, 10 values (0–9); and for the Russian abacus, with 10 beads, 11 values (0–10). (© Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020)

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Multiplication Example: 234 × 67 = 15,678 Set both factors, the multiplicand and the multiplier, and the intermediate result simultaneously on the abacus. This requires an abacus with the greatest possible number of positions. 1. Set all beads to the zero position. In the upper section (heaven), move them upward and in the lower section (hell) downward, that is, move them away from the divider bar. 2. Set the numerical value 234 on the left side of the abacus. 3. Set the numerical value 67 in the middle of the abacus. 4. Multiply the hundreds position (2) of factor 1 by the ones position (7) of factor 2. Enter the result (1400) on the right side of the abacus. 5. Multiply the tens position (3) of factor 1 by the ones position (7) of factor 2. Add the result (210) on the right side of the abacus. 6. Multiply the ones position (4) of factor 1 by the ones position (7) of factor 2. Add the result (28) on the right side of the abacus. 7. Multiply the hundreds position (2) of factor 1 by the tens position (6) of factor 2. Add the result (12,000) on the right side of the abacus. 8. Multiply the tens position (3) of factor 1 by the tens position of factor 2 (6). Add the result (1800) on the right side of the abacus. 9. Multiply the ones position (4) of factor 1 by the tens position of factor 2 (6). Add the result (240) on the right side of the abacus. 10. Read off the final result: 15,678.

Heaven

Hell

Number 987 Fig. 19.5  Chinese abacus, showing the value 987. The number is made up of 1 × 500 + 4 × 100; 1 × 50 + 3 × 10; and 1 × 5 + 2 × 1. For calculating, the beads are bundled (combined to a higher value) or unbundled (resolving a quinary bead into five separate beads) as required. If not enough beads are available, the values 5, 50, 500, etc. and 10, 100, 1000, etc. (fives complement, tens complement) can supplement these. Minus 30 is the same as minus 50 plus 20. Plus 90 can be entered as plus 100 minus 10. The procedures for calculating are the same as for calculations with pencil and paper. (© Bruderer Informatik, CH-9401 Rorschach, Switzerland 2020)

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Division Example: 4823: 7 = 689 1. Set all beads to the zero position. In the upper section (heaven), move them upward and in the lower section (hell) downward, that is, move them away from the divider bar. 2. Enter the divisor (7) on the left side of the abacus as a memory aid. 3. Set in the dividend (4823) on the right side of the abacus. 4. Work out how many times the divisor (7) goes into the first two positions of the dividend (48). Result: 6. 5. Enter the 6 in the middle of the abacus. 6. Multiply the divisor (7) by the number 6. 7. Subtract the result (42) from the dividend, i.e., 48, on the right side of the abacus (48 represents 4800 and 42 the value 4200). Remainder: 6 (i.e., 600). 8. Work out how many times the divisor (7) goes into 62 (= remainder 6 plus third digit of the dividend 4823). Result: 8. 9. Enter the 8 in the middle of the abacus (to the right of the 6). 10. Multiply the divisor (7) by the number 8. 11. Subtract the result (56) from 62 (56 represents the number 560 and 62 the value 620). Remainder: 6 (i.e., 60). 12. Work out how many times the divisor (7) goes into 63 (= remainder plus the last digit of the dividend 4823). Result: 9. 13. Enter the 9 in the middle of the abacus (to the right of the 8). 14. Multiply the divisor (7) by the number 9. 15. Subtract the result (63) from 63. Remainder: 0. 16. The final result is 689. Division by a multi-digit divisor is similar to division with pencil and paper. Remark Multiplication and division with the abacus assume a knowledge of the basic multiplication table. With the abacus, it is possible to not only carry out all four basic arithmetic operations but also extract square roots and cube roots and even solve equations (see Alfred Westphal: Über die chinesisch-japanische Rechenmaschine, in: Mittheilungen der deutschen Gesellschaft für Natur- und Völkerkunde Ostsiens, volume 1, 1873–1876, no. 8, pages 27–35, and Über die chinesische Swan-Pan, in: Mitteilungen der deutschen Gesellschaft für Natur- und Völkerkunde Ostasiens, volume 1, 1873–1876, no. 9, pages 43–53).

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19.2  The Aristo Slide Rule: Analog Computing Device

Fig. 19.6  The slide rules of Aristo, Faber-Castell, and Nestler were well-known German slide rule brands. Special models existed for every conceivable purpose. Slide rules are lightweight, portable, and inexpensive and function noiselessly. (© Michel Viredaz, Epalinges VD 2020)

Operating Instructions for the Slide Rule Notes As a rule, the logarithmic slide rule is not used for either addition or subtraction. The squares scale on the body is labeled with A and the squares scale on the slide with B. The two basic scales are designated C (on the slide) and D (on the body). C is the movable scale of the slide and D the fixed scale of the body. Using the end of the slide (the number 10) instead of the beginning (the number 1) is referred to as shifting (off the end problem). This entails shifting the slide to the far left. One normally uses the C and D scales for multiplication and division, but one can also use the A and B scales. Multiplication: 2 × 3 = 6 1. Move the beginning (the number 1) of the movable scale (slide) over the number 2 (multiplicand, first factor) of the fixed scale. 2. Move the cursor to the number 3 (multiplier, second factor) on the movable scale, and read off the result (6) on the fixed scale. Multiplication: 4 × 5 = 20 1. Move the end (the number 10) of the movable scale over the number 4 on the fixed scale.

19.3 The Brunsviga: Pinwheel Machine

867

2. Move the cursor to the number 5 on the movable scale, and read off the result (2, i.e., 20) on the fixed scale. Division: 9: 2 = 4.5 1. Move the number 2 (divisor) on the movable scale (slide) over the number 9 (dividend) on the fixed scale. 2. Move the cursor to the beginning (the number 1) on the movable scale, and read off the result (4.5) on the fixed scale. Division: 56: 7 = 8 1. Move the number 7 (divisor) on the movable scale over the number 5.6 (dividend) on the fixed scale. 2. Move the cursor to the end (the number 10) on the movable scale, and read off the result (8) on the fixed scale. With the slide rule, it is necessary to roughly estimate the result as a check (see box). Rough Calculation for the Determination of the Numerical Value When calculating with logarithmic scales, one leaves out the zeroes before and after the numbers, but not between the numbers. For the examples 3 × 4, 3 × 40, 3 × 400, 3 × 4000, 30 × 4, 300 × 4, 3000 × 4, 30 × 40, 30  ×  400, 30  ×  4000, 300  ×  400, and 3000  ×  4000, and also 0.3  ×  0.4, 0.03  ×  0.04, 0.003  ×  0.004, etc., one always calculates 3  ×  4 and then determines the number of places before the decimal point, i.e., the position of the decimal point, by a rough calculation. A 1 on the scale can represent the values 1000, 100, 10, 1, 0.1, 0.01, 0.001, etc. 9.9 stands for 0.099, 0.99, 9.9, 99, 990, 9900, 99,000, etc. The slide rule shows the sequence of numbers, but not the numerical value.

19.3  The Brunsviga: Pinwheel Machine In Germany, there were numerous manufacturers of mechanical calculating machines. One of the most important was the Brunsviga-Maschinenwerke, Grimme, Natalis & Co. AG in Braunschweig. Their pinwheel machines were very popular. Note Blockage: See the box at the beginning of this chapter.

868

19  Operating Instructions

Fig. 19.7  Brunsviga (1). The pinwheel machine from Braunschweig has its roots in Sweden (Odhner). It was widely used internationally. Pinwheel and stepped drum machines were the two main types of mechanical calculating machines. (© Heinrich Heidersberger, Institut Heidersberger GmbH, Wolfsburg, Germany 2020)

Fig. 19.8  Brunsviga (2). There were many different models and types. With a pinwheel, for example, the number 5 was represented by pressing five teeth outward. They were then retracted again as required. (© Heinrich Heidersberger, Institut Heidersberger GmbH, Wolfsburg, Germany 2020)

19.3 The Brunsviga: Pinwheel Machine

869

Fig. 19.9  Brunsviga (3). The heavy, portable desk machine was capable of all four basic arithmetic operations. For addition and multiplication, the crank is turned in the clockwise direction and for subtraction and division in the counterclockwise direction. (© Heinrich Heidersberger, Institut Heidersberger GmbH, Wolfsburg, Germany 2020)

Operating Instructions for the Brunsviga Pinwheel machine Model 13 RK General Hand crank • Pull out the handle, rotate it, and lock it in place. • Rotating in the clockwise direction: addition, multiplication. • Rotating in the counterclockwise direction: subtraction, division. Rotating the crank in the clockwise direction transfers a value from the setting mechanism to the result mechanism. Carriage shift • Shifting to the right: Press back the metal bracket (double grip, outer right side) repeatedly. • Shifting to the left: Pull the metal bracket forward (double grip, outer right side) repeatedly. Carriage shift is also possible with the handle on the (lower) front face. Clearing • Setting mechanism: Pull the metal lever on the left side of the machine forward. • Result mechanism: Pull the short metal lever on the lower front of the right side of the machine (lower front) forward.

870

19  Operating Instructions

• Revolution counter: Pull the metal lever on the upper rear face of the right side of the machine forward. • Clearing completely: Push the small lever on the (right) front face to the rear (position with two points), and pull the long metal lever on the lower front of the right side of the machine forward. When the small lever at the right of the front face (combined clearing lever) is in the forward position (position with one point), the result mechanism and the revolution counter can be cleared simultaneously with the long metal lever. In this position, the setting mechanism is also cleared with the clearing lever for the revolution counter (right rear side of the machine). Back transfer Back transfer enables the transfer of values from the result mechanism back to the setting mechanism. The clearing lever for the setting mechanism (on the left side of the machine) is pulled forward to the end stop and held fast. The lever for complete clearing is then pulled forward. Remark When the machine is blocked, rotate the hand crank to the zero position, and lock in place. Addition Example: 123,456 + 7890 = 131,346 1. Set the small lever (middle right) to the rear position (two points). Then clear all mechanisms with the long metal lever (right front). 2. Control the clearing of the three mechanisms. 3. Move the carriage all the way to the left to the end stop (press the metal bracket at the lower right forward several times or the lower lever in the middle to the left several times). 4. Enter the number 123,456  in the setting mechanism with the levers at the right. 5. Control the value 123,456 in the viewing windows of the setting mechanism (input accuracy control). 6. Rotate the crank once in the clockwise direction (pull out the handle to the right, hold fast, and then lock in place again). 7. Clear the setting mechanism with the lever at the left. 8. Control the clearing of the setting mechanism. 9. Enter the number 7890  in the setting mechanism with the levers at the right. 10. Control the value 7890 in the viewing windows of the setting mechanism. 11. Rotate the crank once in the clockwise direction. 12. Read out the value 131,346 in the result mechanism (below).

19.3 The Brunsviga: Pinwheel Machine

871

Subtraction Example: 123,456 − 7890 = 115,566 1. Set the small lever (middle right) to the rear position (two points). Then clear all mechanisms with the long metal lever (right front). 2. Control the clearing of the three mechanisms. 3. Move the carriage all the way to the left to the end stop (press the metal bracket at the lower right forward several times or the lower lever in the middle to the left several times). 4. Enter the number 123,456  in the setting mechanism with the levers at the right. 5. Control the value 123,456 in the viewing windows of the setting mechanism (input accuracy control). 6. Rotate the crank once in the clockwise direction (pull out the handle to the right, hold fast, and then lock in place again). 7. Clear the setting mechanism with the lever at the left. 8. Control the clearing of the setting mechanism. 9. Enter the number 7890  in the setting mechanism with the levers at the right. 10. Control the value 7890 in the viewing windows of the setting mechanism. 11. Rotate the crank once in the counterclockwise direction. 12. Read out the value 115,566 in the result mechanism (below). Remark Subtracting the number 89 from the number 67 gives a negative value (−22). This is represented in the result mechanism by the complement 9,999,999,999,978 (alarm signal). Multiplication Example: 4567 × 890 = 4,064,630 1. Set the small lever (middle right) to the rear position (two points). Then clear all mechanisms with the long metal lever (right front). 2. Control the clearing of the three mechanisms. 3. Move the carriage all the way to the left to the end stop (press the metal bracket at the lower right forward several times or the lower lever in the middle to the left several times). 4. Enter the number 4567  in the setting mechanism with the levers at the right. 5. Control the value 4567 in the viewing windows of the setting mechanism (input accuracy control). 6. Shift the carriage to the right by one tens place (press the metal bracket at the lower right toward the rear). 7. Control the place value 2 (tens) in the revolution counter (at the top) (parenthesis around the number 2).

872

19  Operating Instructions

8. Rotate crank nine times in the clockwise direction (pull the handle out to the right, hold fast, and then lock in place again). 9. The revolution counter (at the top) displays the value 90. 10. The result mechanism (below) shows the value 411,030. 11. Shift the carriage to the right by one tens place. 12. Control the place value 3 (hundreds) in the revolution counter (at the top) (parenthesis around the number 3). 13. Rotate crank eight times in the clockwise direction. 14. The revolution counter displays the value 890. 15. Read out the result 4,064,630 from the result mechanism. Remarks For multiplication, the factors can be permuted at will. If we choose 890 as the multiplier in our example, 17 revolutions of the crank are required (checksum 8 + 9) and 22 revolutions for 4567 (checksum 4 + 5 + 6 + 7). Shortcut multiplication eliminates several rotations of the crank (e.g., multiplication by 900 minus multiplication by 10 – this requires carriage shifting). For repeated multiplication, the intermediate results are transferred back to the setting mechanism, so that they do not have to be entered again. Division Example: 516,006: 789 = 654 1. Set the small lever (middle right) to the rear position (two points). Then clear all mechanisms with the long metal lever (right front). 2. Control the clearing of the three mechanisms. 3. Move the carriage all the way to the right to the end stop (press the metal bracket at the lower right to the rear several times or the lower lever in the middle to the right several times). 4. Control the place value 8 in the revolution counter (at the top) (parenthesis around the number 8). 5. Enter the number 516,006 (dividend) in the setting mechanism with the levers at the right. 6. Control the value 516,006 in the viewing windows of the setting mechanism (input accuracy control). 7. Rotate the crank once in the clockwise direction (pull the handle out to the right, hold fast, and then lock in place again). 8. Control the value 516,006 in the viewing windows of the result mechanism (below). 9. Clear the setting mechanism with the lever at the left. 10. Control the clearing of the setting mechanism. 11. Clear the revolution counter with the lever at the right. 12. Control the clearing of the revolution counter (at the top).

19.4 The Curta: Stepped Drum Machine

873

13. Enter the number 789 (divisor) in the setting mechanism with the levers (in this case, the first digit (7) of the divisor (789) must be positioned over the second digit (1) of the dividend (516,006) in order to subtract 789 from 5160; 789 cannot be subtracted from 516 since 789 > 516). 14. Control the value 789 and its position in the viewing windows of the setting mechanism. 15. Rotate the crank (seven times) in the counterclockwise direction until an alarm signal sounds. 16. Rotate the crank once in the clockwise direction. 17. Shift the carriage to the left by one tens place (press the metal bracket at the lower right forward once). 18. Control the place value 7 in the revolution counter (at the top) (parenthesis around the number 7). 19. Rotate the crank (six times) in the counterclockwise direction until an alarm signal sounds. 20. Rotate the crank once in the clockwise direction. 21. Shift the carriage to the left by one tens place. 22. Control the place value 6 in the revolution counter. 23. Rotate the crank (five times) in the counterclockwise direction until an alarm signal sounds. 24. Rotate the crank once in the clockwise direction. 25. Shift the carriage to the left by one tens place. 26. Control the place value 5 in the revolution counter. 27. Rotate the crank (once) in the counterclockwise direction until an alarm signal sounds. 28. Rotate the crank once in the clockwise direction. 29. The result mechanism (below) displays the remainder 0. 30. The revolution counter shows the result (quotient) 654 (with red numerals). Remark The divisor must be entered so that it can be subtracted from the first digits of the dividend. For example, the 3-place divisor 456 is less than the first three places of the dividend 9870 but more than the first three places of the dividend 3210. In the first case, the numeral 4 of the divisor is positioned over the numeral 9 of the dividend and in the second case over the numeral 2 of the dividend. 456 can be subtracted from 987 and 3210, but not from 321.

19.4  The Curta: Stepped Drum Machine The Curta is a precision mechanical marvel. Please handle the “peppermill” with great care! Addition, subtraction, and multiplication are simple. By its nature, division is somewhat more complicated. Shortcut multiplication is also possible. The Curta is even capable of extracting square roots.

874

19  Operating Instructions

Fig. 19.10  The Curta. The Curta pocket calculator is a full-fledged four-function calculating machine. (© Liechtensteinisches Landesmuseum, Vaduz, picture: Sven Beham 2020)

Operating Instructions for the Curta Basic Settings Before beginning calculations, the Curta must be in the basic state: • Crank in the basic position (i.e., in the down position, latched). • Revolution counter and result mechanism be cleared (clearing lever swiveled out and latched. To clear, lift the circular carriage (upper ring), and rotate the clearing lever once up to the end stop in the clockwise or counterclockwise direction. • Position all setting levers (i.e., on top) to zero. • Circular carriage (upper ring) in the basic position (i.e., in the down position, latched, in position 1: vertical place value arrow next to the ones lever). • Selection lever (on the rear face of the device) in the up position. Note To rotate the clearing lever to the rest position, press the button down. Addition Example: 123 + 456 + 789 = 1368 1. Control the basic settings for the device. 2. Enter the first number (123) with the setting levers (with ones, tens, and hundreds in any order). 3. Control the value (123) in the setting mechanism. 4. Rotate the crank through one complete movement (up to the end stop) in the clockwise direction. 5. The result mechanism (black circular display at the top) displays the value 123.

19.4 The Curta: Stepped Drum Machine

875

6. Enter the second number (456) with the setting levers. 7. Control the value (456) in the setting mechanism. 8. Rotate the crank through one complete movement (up to the end stop) in the clockwise direction. 9. The result mechanism (black circular display at the top) displays the value 579. 10. Enter the third number (789) with the setting levers. 11. Control the value (789) in the setting mechanism. 12. Rotate the crank through one complete movement (up to the end stop) in the clockwise direction. 13. The result mechanism (black circular display at the top) displays the value 1368. Note Erroneous entries can be corrected in the setting mechanism before beginning calculations. Subtraction Example 1: 3456–987 – 12 = 2457 1. Control the basic settings for the device. 2. Enter the first number (3456) with the setting levers (with ones, tens, hundreds, and thousands in any order). 3. Control the value (3456) in the setting mechanism. 4. Rotate the crank through one complete movement (up to the end stop) in the clockwise direction. 5. The result mechanism (black circular display at the top) displays the value 3456. 6. Enter the second number (987) with the setting levers. 7. Control the value (987) in the setting mechanism (at the top). 8. Lift the crank, and rotate through one complete movement (up to the end stop) in the clockwise direction. 9. The result mechanism (black circular display at the top) displays the value 2469. 10. Press the crank down. 11. Enter the third number (12) with the setting levers. 12. Control the value (12) in the setting mechanism (at the top). 13. Lift the crank, and rotate through one complete movement (up to the end stop) in the clockwise direction. 14. Press the crank down. 15. The result mechanism (black circular display at the top) displays the value 2457. Notes Erroneous entries can be corrected in the setting mechanism before beginning calculations. For a continuing subtraction, the crank can remain in the up position.

876

19  Operating Instructions

Example 2: 456–789 = −333 Negative numbers 1. Control the basic settings for the device. 2. Enter the first number (456) with the setting levers. 3. Control the value (456) in the setting mechanism (at the top). 4. Rotate the crank through one complete movement (up to the end stop) in the clockwise direction. 5. The result mechanism (black circular display at the top) displays the value 456. 6. Enter the second number (789) with the setting levers. 7. Control the value (789) in the setting mechanism (at the top). 8. Lift the crank, and rotate through one complete movement (up to the end stop) in the clockwise direction. 9. Press the crank down. 10. The result mechanism (black circular display at the top) displays the value 99,999,999,667 (Curta 1, 11 places) or 999,999,999,999,667 (Curta 2, 15 places). Notes The result mechanism does not use (negative) signs. Therefore, the value 333, which could be understood as positive, is not displayed. Instead, its tens complement is shown. 667 is the complement of 333 (667 + 333 = 1000). Entering the number 99,999,999,667 (Curta 1) or 999,999,999,999,667 (Curta 2) in the setting mechanism (and rotating the crank once), lifting the crank, and rotating twice give the result 333. Multiplication Multiplication is a repeated addition with stepwise place value shifting of the circular carriage. Example 1: 789 × 456 = 359,784 1. Control the basic settings for the device. 2. Enter the first number (789) with the setting levers. 3. Control the value (789) in the setting mechanism (at the top). 4. Rotate the crank six times in the counterclockwise direction (up to the end stop). 5. The revolution counter (white circular display at the top) displays the value 6 in the ones position. 6. Lift the circular carriage (upper ring), and rotate in the counterclockwise direction up to position 2 (tens). 7. Rotate the crank five times in the clockwise direction (up to the end stop). 8. The revolution counter (white circular display at the top) displays the value 5 in the tens position. 9. Lift the circular carriage (upper ring), and rotate in the counterclockwise direction up to position 3 (hundreds).

19.4 The Curta: Stepped Drum Machine

877

10. Rotate the crank four times in the clockwise direction (up to the end stop). 11. The revolution counter (white circular display at the top) displays the value 4 in the hundreds position. 12. The result mechanism (black circular display at the top) displays the value 359,784. 13. The revolution counter (white circular display at the top) shows the value 456. Example 2: 987.6 × 12.345 = 12,191.9220 1. Control the basic settings for the device. 2. Set a decimal point button at the bottom of the machine (at the lower ring) between the ones and tens positions. 3. Enter the first number (987.6) with the setting levers. 4. Control the value (987.6) in the setting mechanism (at the top). 5. Set a decimal point button in the revolution counter (white circular display at the top) between the hundreds and thousands windows. 6. Set a decimal point button in the result mechanism (black circular display at the top) between the thousands and ten thousands windows. 7. Rotate the crank five times in the clockwise direction (up to the end stop). 8. The revolution counter (white circular display at the top) displays the value 0.005. 9. Lift the circular carriage (upper ring), and rotate in the counterclockwise direction up to position 2. 10. Rotate the crank four times in the clockwise direction (up to the end stop). 11. The revolution counter (white circular display at the top) displays the value 0.045. 12. Lift the circular carriage (upper ring), and rotate in the counterclockwise direction up to position 3. 13. Rotate the crank three times in the clockwise direction (up to the end stop). 14. The revolution counter (white circular display at the top) displays the value 0.345. 15. Lift the circular carriage (upper ring), and rotate in the counterclockwise direction up to position 4. 16. Rotate the crank twice in the clockwise direction (up to the end stop). 17. The revolution counter (white circular display at the top) displays the value 2.345. 18. Lift the circular carriage (upper ring), and rotate in the counterclockwise direction up to position 5. 19. Rotate the crank once in the clockwise direction (up to the end stop). 20. The revolution counter (white circular display at the top) displays the value 12.345. 21. The result mechanism (black circular display at the top) shows the value 12,191.9220.

878

19  Operating Instructions

Shortcut multiplication Example: 567 × 89 = 50,463 1. Control the basic settings for the device. 2. Enter the first number (567) with the setting levers. 3. Control the value (567) in the setting mechanism (at the top). 4. Lift the circular carriage (upper ring), and rotate in the counterclockwise direction up to position 3 (hundreds). 5. Rotate the crank through one complete movement (up to the end stop) in the clockwise direction. 6. The revolution counter (white circular display at the top) displays the value 100. 7. Lift the circular carriage (upper ring), and rotate in the counterclockwise direction up to position 2 (tens). 8. Lift the crank, and rotate through one complete movement (up to the end stop) in the clockwise direction. 9. Lift the circular carriage (upper ring), and rotate in the counterclockwise direction up to position 1 (ones). 10. Rotate the crank (in the upper position) through one complete movement (up to the end stop) in the clockwise direction. 11. The result mechanism (black circular display at the top) displays the value 50,463. 12. The revolution counter (white circular display at the top) shows the value 89. Note Instead of 8 + 9 = 17 rotations, now only 3 rotations are required. Division Example 1 (without remainder): 51,102: 5678 = 9 1. Control the basic settings for the device. 2. Lift the circular carriage (upper ring), and rotate in the counterclockwise direction up to the highest position (6 with the Curta 1, 8 with the Curta 2). 3. Enter the divisor (5678) with the setting levers. 4. Control the value (5678) in the setting mechanism (at the top). 5. Rotate the crank in the clockwise direction until the dividend (51,102) is ­displayed in the result mechanism (black circular display at the top). 6. The revolution counter (white circular display at the top) shows the value 9 (quotient). Example 2 (with remainder): 230: 17 = 13.5300 (4 places after the decimal point) 1. Control the basic settings for the device. 2. Lift the circular carriage (upper ring), and rotate in the counterclockwise direction up to the second highest position (5 with the Curta 1 or 7 with the Curta 2). 3. Enter the divisor (17) with the setting levers. 4. Control the value (17) in the setting mechanism (at the top).

19.4 The Curta: Stepped Drum Machine

879

5. Rotate the crank in the clockwise direction until the dividend (230) is exceeded in the result mechanism (black circular display at the top) (value 238). 6. Lift the crank, and rotate through one complete movement (up to the end stop) in the clockwise direction (new value: 221). 7. Press the crank down. 8. Lift the circular carriage (upper ring), and rotate in the clockwise direction up to the next lowest position (4 with the Curta 1 or 6 with the Curta 2). 9. Rotate the crank in the clockwise direction until the dividend (230) is exceeded in the result mechanism (black circular display at the top) (value 231.2). 10. Lift the crank, and rotate through one complete movement (up to the end stop) in the clockwise direction (new value: 229.5). 11. Press the crank down. 12. Lift the circular carriage (upper ring), and rotate in the clockwise direction up to the next lowest position (3 with the Curta 1 or 5 with the Curta 2). 13. Rotate the crank in the clockwise direction until the dividend (230) is exceeded in the result mechanism (black circular display at the top) (value 230.01). 14. Lift the crank, and rotate through one complete movement (up to the end stop) in the clockwise direction (new value: 229.84). 15. Press the crank down. 16. Lift the circular carriage (upper ring), and rotate in the clockwise direction up to the next lowest position (2 with the Curta 1 or 4 with the Curta 2). 17. Rotate the crank in the clockwise direction until the dividend (230) is exceeded in the result mechanism (black circular display at the top) (value 230.01). 18. The revolution counter (white circular display at the top) shows the value 13.5300. Notes Decimal point: The number of places after the decimal point in the result mechanism (dividend: 230, here 4 with the Curta 1 or 6 with the Curta 2) minus the number of places in the setting mechanism (divisor: 17, here 0) gives the number of places after the decimal point in the revolution counter (quotient: 4–0 = 4 with the Curta 1 or 6 − 0 = 6 with the Curta 2). The decimal point is therefore positioned after 13 (4 or 6 places from right to left in the revolution counter). With additive and subtractive rotations of the crank, one approaches the solution stepwise. Important: If one begins with the highest value place (6 with the Curta 1 or 8 with the Curta 2), the revolution counter shows the result 3.53000 with the Curta 1 and 3.5300000 with the Curta 2. The foremost numeral can no longer be displayed, because too few places are available. As Karl Holecek shows in his examination, the quotient can be determined  to any number of places (see Karl Holecek: Ein Beitrag zum Maschinenrechnen, in: Österreichisches Ingenieur-Archiv, volume 7, 1953, no. 4, pages 331–337).

880

19  Operating Instructions

19.5  T  he Loga Circular Slide Rule: Analog Calculating Device

Fig. 19.11  Front side of the Loga circular slide rule. Circular slide rules have longer scales than linear slide rules and are therefore more accurate. They have an ideal design, and their scales are endless, so that the shifting required with a linear slide rules and overlapping scales, as with cylindrical slide rules, are no longer necessary. (© Schweizerisches Landesmuseum, Zurich 2020)

Operating Instructions for the Circular Slide Rule Notes These step-by-step instructions were derived from the Loga Model 30 Th circular slide rule. The inner circular scales and the pointer (cursor, runner) can be rotated in the clockwise or the counterclockwise direction, and the outer scales are fixed. Thanks to the circular form, the beginning and end of the scales coincide, and the scales are endless. This Loga instrument has (apart from the edge) a diameter of 12 cm. The main scales have a diameter of 9.5 cm. The handy circular slide rule therefore corresponds to a linear slide rule with a length of nearly 30  cm (perimeter  =  diameter  ×  π; circle constant π or Ludolph’s constant = 3.14159…).

19.5 The Loga Circular Slide Rule: Analog Calculating Device

881

The slide rule has the following scales from the outside to the inside: • Outer ring: first square root range (square root of x, range of values: 1–3.16), second square root range (square root of 10x, range of values: 3.16–10), basic A (x) scale. • Inner ring: basic B (x) scale, reciprocal R (1/x), cube (x3), and logarithm (log2 x, logarithm of x to the base 2). The same scales are on the front side of the Model 30 Tt, but this model also has additional (fixed) scales on the reverse side (e.g., sine and tangent trigonometric functions and Euler’s number), with increasing values in the counterclockwise direction. Multiplication: 2 × 3 = 6 1. Move the beginning (the number 1) on the movable scale (inner circular scale) under the number 2 (multiplicand, first factor) on the fixed scale (outer circular scale). 2. Rotate the pointer to the number 3 (multiplier, second factor) on the movable scale, and read off the result (6) on the fixed scale. Multiplication: 4 × 5 = 20 1. Move the beginning (the number 1) on the movable scale (inner circular scale) under the number 4 on the fixed scale (outer circular scale). 2. Rotate the pointer to the number 5 on the movable scale, and read off the result (2, i.e., 20) on the fixed scale. Division: 9: 2 = 4.5 1. Move the number 2 (divisor) on the movable scale (inner circular scale) under the number 9 (dividend) on the fixed scale (outer circular scale). 2. Rotate the pointer to the beginning (the number 1) on the movable scale, and read off the result (4.5) on the fixed scale. Division: 56: 7 = 8 1. Move the number 7 (divisor) on the movable scale (inner circular scale) under the number 5.6 (dividend) on the fixed scale (outer circular scale). 2. Rotate the pointer to the beginning (the number 1) on the movable scale, and read off the result (8) on the fixed scale.

882

19  Operating Instructions

19.6  T  he Loga Cylindrical Slide Rule: Analog Calculating Device

Fig. 19.12  The Loga cylindrical slide rule. The 24-meter Loga cylindrical slide rule is regarded as the world’s longest and most accurate commercially available cylindrical slide rule. It has 80 parallel 60-cm-long scale sections. Since successive sections overlap due to the design, this results in a scale length of 24 m. (© UBS 2020)

Operating Instructions for the Cylindrical Slide Rule Note The scale values described below apply for the world’s most accurate cylindrical slide rule, the 24-meter Loga-Calculator cylindrical slide rule. For smaller models, these values must be adjusted accordingly. Introduction Usually, there are multi-digit numbers at the left edge of the drum and sleeve. These guide numbers simplify locating numerical values. The number 200 (i.e., 2, 20, etc.), for example, is located in the scale section with the guide number 19,952, and the number 400 is located to the right of the value 39,810. The guide number 10,000 highlighted in white on the edge of the drum indicates the beginning of the scale. A red square or a plastic triangle, for example, serves the same purpose on the sleeve. According to the model, the scale on the drum begins with the value 1, 10, 100, or 1000. The scale begins in the

19.6 The Loga Cylindrical Slide Rule: Analog Calculating Device

883

middle of the drum. With some models, the beginning is marked with a red double circle in the middle of the drum. The beginning and end of the scales on the drum and sleeve are also highlighted by a vertical stroke. Depending on the model, the end of the scale is marked with the numbers 1, 10, 100, or 1000. The scale on the sleeve is positioned on the cardboard strips. The two halves of the drum are marked with a dotted line around the entire perimeter. The values are entered doubly on the drum scale, which is somewhat confusing. Since a numerical value at the far right on the sleeve can no longer be shifted to the far left on the drum, the number ranges overlap partly, with successive parallel sections. This overlapping is required by the design, because the sleeve cannot be moved beyond the edge of the drum. A scale section includes, for example, the numbers 47,315–5012 and the next section the values 48,695–51,585. In the first case, the number 500 is in the right half and in the second case in the left half of the drum. Displaced scale sections are not required on the sleeve. The overlapping is minimal with these four successive lines: 100–10,294, 10,292–10,593, 10,592–10,902, and 10,901–11,221. The ranges 86,595–9173 (with the number 900  in the right half) and 89,125–9441 (with the number 900 in the left half), for example, are adjacent scale lines. In our case, three successive scale sections around the middle of the drum are marked: from the value 94,405 to 1000 (end of the scale), from 9716 through the middle point of the scale 100 or 1000 up to the value 10,293, and from the beginning of the scale with the value 100 up to the value 10,593. Note: The numbers 100 and 1000 can have the same place value. The end of the scale in the middle of the drum is also the beginning of the scale. Remarks Only the scale on the drum is printed twice (with displaced sections), and overlapping scale sections are only on the drum. The drum and the sleeve can be rotated separately or together. Rotating the drum rotates the sleeve at the same time (for the same setting). By holding the sleeve, the drum rotates alone. Multiplication: 2 × 3 = 6 1. Rotate the drum (together with the sleeve) forward or backward up to the beginning of the sleeve scale (according to the model, marked differently, e.g., with the number 100 on the left side and a vertical red stroke, a plastic triangle, or a brass button on the sleeve ring). 2. Hold the sleeve fast. 3. Rotate the drum (without the sleeve) to the number 200 (multiplicand, first factor) on the drum scale (i.e., to the next lower guide number, here 19,952). 4. Slide the beginning of the sleeve scale to the number 200 on the drum. 5. Let go of the sleeve. 6. Rotate the drum (together with the sleeve) to the number 300 (multiplier, second factor) on the sleeve strip (i.e., to the next lower guide number, here 29,852). 7. Read off the result (600) at the number 300 on the drum.

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Division: 56: 7 = 8 1. Rotate the drum (together with the sleeve) forward or backward up to the number 700 (divisor) on the sleeve scale (i.e., to the next lower guide number, here 68,785). 2. Hold the sleeve fast. 3. Rotate the drum (without the sleeve) to the number 560 (dividend) on the drum scale (i.e., to the next lower guide number, here 54,635). 4. Slide the number 700 on the sleeve strip to the number 560 on the drum. 5. Let go of the sleeve. 6. Rotate the drum (together with the sleeve) to the end of the sleeve scale (according to the model, marked differently, e.g., with the number 100 or 1000 on the right side and a vertical red stroke, a plastic triangle, or a toggle on the right sleeve ring). 7. Read off the result (800) on the drum at the end of the sleeve scale. Note See Herbert Bruderer, Gebrauchsanweisung für Loga-Rechenwalzen (Operating Instructions for Loga Cylindrical Slide Rules), https://doi.org/10.3929/ ethz-b-000306665

19.7  The Madas: Stepped Drum Machine The Madas belongs to the long-lasting and high-performance calculating machines.

Fig. 19.13  The Madas four-function machine with setting levers. This early Madas from the collection of the Credit Suisse in Zurich is provided with setting levers, a signal bell, and a hand crank. (© Credit Suisse, Zurich 2020)

Operating Instructions for the Madas Preliminary Remarks These operating instructions refer to the hand-operated calculator (without electric motor). According to model, there are certain differences.

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Blockage When the hand crank is not in the basic position (rest position), the (partial and complete) carriage shifting, selection of the four basic arithmetic operations, and the button for automatic division are blocked. In this case, press down the crank or pull it upward and rotate it once to the initial position. However, if one of these functions is not adjusted correctly, it is not possible to rotate the crank. Certain models are blocked when a two or a one is displayed in the “automatic division” viewing window. To override the blockage, rotate the crank in the clockwise direction until a zero is displayed in the viewing window. Note Blockage: See the box at the beginning of this chapter. Operating 1. Lock the hand crank (right) in the initial position (before rotating, pull up or press down the handle), and rotate the crank in the clockwise direction. 2. Clear the setting mechanism (below). (Press down the zero key (at the lower left): complete clearing). 3. Clear the result mechanism (at the top) (slide the metal button to the right and back: complete clearing). 4. Clear the revolution counter (in the middle) (slide the metal button to the right and back: complete clearing). 5. Carriage shift (metal lever at top): Entire width or digit by digit (press the metal lever together) in both directions. 6. Carriage shift (metal lever below): Digit by digit in both directions. 7. Shift the carriage all the way to the left for addition, subtraction, and multiplication. 8. Shift the carriage all the way to the right for division. 9. Addition: Set the metal selection lever to the upper position. 10. Subtraction: Set the metal selection lever to the lower position. 11. Multiplication: Set the metal selection lever to the upper position. 12. Division: Set the metal selection lever to the lower position. 13. Disengage the repetition key (left) for addition and subtraction and pull upward. 14. Press down the repetition key (left) for multiplication and division and lock in place. 15. Correction key (Corr): Press the red plastic key if one revolution too many was executed (additional metal lever for the correction key, right). Addition Example: 2345 + 6789 = 9134 1. Clear the setting mechanism, result mechanism, and revolution counter. 2. Define the arithmetic operation: Set the selection lever to addition. 3. Disengage the repetition key and pull upward. 4. Shift the carriage to the left. 5. Enter the number 2345 at the right in the setting mechanism. 6. Control the number 2345 in the viewing windows. 7. Rotate the crank once.

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8. Enter the number 6789 at the right in the setting mechanism. 9. Control the number 6789 in the viewing windows. 10. Rotate the crank once. 11. Read out the result (9134) in the result mechanism. Subtraction Example: 3456 − 789 = 2667 1. Clear the setting mechanism, result mechanism, and revolution counter. 2. Define the arithmetic operation: Set the selection lever to subtraction. 3. Disengage the repetition key and pull upward. 4. Shift the carriage to the left. 5. Enter the number 3456 in the counterclockwise direction with the rotating knobs into the result mechanism. 6. Control the number 3456 in the viewing windows. 7. Enter the number 789 at the right in the setting mechanism. 8. Control the number 789 in the viewing windows. 9. Rotate the crank once. 10. Read out the result (2667) in the result mechanism. Multiplication Example: 765 × 432 = 330,480 1. Clear the setting mechanism, result mechanism, and revolution counter. 2. Define the arithmetic operation: Set the selection lever to addition (= multiplication). 3. Press down the repetition key and lock in place. 4. Shift the carriage all the way to the left. 5. Enter the number 765 at the right in the setting mechanism. 6. Control the number 765 in the viewing windows. 7. Rotate the crank twice. 8. Shift the carriage one place to the right. 9. Rotate the crank three times. 10. Shift the carriage one place to the right. 11. Rotate the crank four times. 12. Read out the result (330,480) in the result mechanism. Automatic Division Example 1: 1 963,025,363: 56,789 = 34,567 1. Clear the setting mechanism, result mechanism, and revolution counter. 2. Define the arithmetic operation: Set the selection lever to subtraction (= division) (with some models, the selection lever for the arithmetic operation and the lever for automatic division are necessarily at the left). 3. Press down the repetition key and lock in place or position the lever to the left (automatic division). 4. Shift the carriage all the way to the right. 5. Enter the number 1,963,025,363 in the counterclockwise direction with the rotating knobs to the left into the result mechanism (from the second viewing window, leave the first viewing window free).

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6. Control the number 1,963,025,363 in the viewing windows. 7. Enter the number 56,789  in the setting mechanism so that the highest place value of the divisor (5) is under the highest place value of the dividend (1). 8. Control the number 56,789 in the viewing windows. 9. Rotate the crank several times until the value 0000 (or a remainder) is displayed (with some models, a bell sounds). 10. Read out the result (34,567) in the revolution counter. Remarks In our example, 40 rotations of the crank are necessary. After the second, eighth, 15th, 23rd, and 32nd revolution, the carriage is automatically shifted one place to the left. For the calculation 17,353: 37 = 469, 469 revolutions, for instance, are not necessary. 28 revolutions are sufficient. What must be taken into account for inputting the divisor (see box)? Rules for Inputting the Divisor • If the first digit of the dividend is larger than the first digit of the divisor, enter the divisor all the way to the left in the setting mechanism, i.e., from the first position at the left. • If the first digit of the dividend is smaller than the first digit of the divisor, enter the divisor at the second position from the left in the setting mechanism.

Examples Entering the divisor all the way to the left in the setting mechanism (from the first position at the left) 9 :   3 The first digit of the dividend (9) > the first digit of the divisor (3) Enter the number 3 under the number 9. 78 :  13 The first digit of the dividend (7) > the first digit of the divisor (1) Enter the number 1 under the number 7. Entering the divisor at the second position from the left in the setting mechanism. 12 :  3 The first digit of the dividend (1)   the first digit of the divisor (1) Enter the number 1 under the number 7. Entering the divisor at the second position from the left in the setting mechanism. 12 :  3 The first digit of the dividend (1)