Symbolizing Existence : Metalithikum III [1 ed.] 9783035603798, 9783035603781

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Applied Virtuality Book Series SYMBOLIZING EXISTENCE — Metalithikum III

Birkhäuser Basel

Applied Virtuality Book Series SYMBOLIZING EXISTENCE — Metalithikum III Edited by Vera Bühlmann, Ludger HovestadT

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SERIES EDITORS Prof. Dr. Ludger Hovestadt Chair for Computer Aided Architectural Design (CAAD), Institute for Technology in Architecture (ITA), Swiss Federal Institute of Technology (ETH), Zurich, Switzerland Dr. phil. Vera Bühlmann Laboratory for Applied Virtuality at the Chair for Computer Aided Architectural Design (CAAD), Institute for Technology in Architecture (ITA), Swiss Federal Institute of Technology (ETH), Zurich, Switzerland Layout and Cover Design: onlab, D-Berlin, www.onlab.ch Typeface: Korpus, binnenland (www.binnenland.ch) Translations: Reinhart R. Fischer (Tholen, Hovestadt), Cambridge-Editing (Harenberg) Copyediting: Max Bach (Tholen, Bühlmann, Schubring), Sebastian Michael (Hovestadt, Schildberger), Gordon C.F. Bearn (Introduction), Cambridge-Editing (Lambert, Bearn, Harenberg) Proofreading: Cambridge-Editing Printing and binding: Strauss GmbH, D-Mörlenbach

Library of Congress Cataloging-in-Publication data A CIP catalog record for this book has been applied for at the Library of Congress. Bibliographic information published by the German National Library The German National Library lists this publication in the Deutsche Nationalbibliografie; detailed bibliographic data are available on the Internet at http://dnb.dnb.de. This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, re-use of illustrations, recitation, broadcasting, reproduction on microfilms or in other ways, and storage in databases. For any kind of use, permission of the copyright owner must be obtained. This publication is also available as an e-book ISBN PDF 978-3-0356-0379-8 ISBN EPUB 978-3-0356-0389-7 © 2016 Birkhäuser Verlag GmbH, Basel P.O. Box 44, 4009 Basel, Switzerland Part of Walter de Gruyter GmbH, Berlin/Boston Printed on acid-free paper produced from chlorine-free pulp. TCF ∞ Printed in Germany

ISSN 2196-3118 ISBN 978-3-0356-0378-1 987654321 www.birkhauser.com

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Symbolizing existence — Metalithikum III

TABLE OF CONTENTS

on the book series  6 Introduction — Symbolizing Existence 14 I A Scheme for a Fantastic Genealogy of the Articulable 28 Ludger Hovestadt

I A Love Affair 32 — II Speech Exercises in the Third Infinity 36 — III A Genealogy of Learning to Speak 40 — IV Understanding One Another 41 — V The Algebraic Stage Schema 44 — VI The Whole Point, O1 > O2 49 — VII The Moving Point, I1 > I2 50 — VIII The Mensurated Point, S1 > S2 51 — IX The Rational Point, O2 > O3 53 — X The Moving Point, I2 > I3 55 — XI The Mensurated Point S2 < S3 58 — XII The Complex Point O3 > O4 65

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Topologies of an Aesthetics of the Virtual in Music 68 Michael Harenberg

I From Classical Composition to its Technical and Aesthetic Differentiation 70 — II Foundations of Pythagorean Space-Time Models in Music Theory 75 —  III The Mathematical Indexing of the World in Music 78 — IV On Digital Beauty 81 — V Hybrid Spheres—Between Analogue and Digital 83 — VI Real Virtuality of Digital Composition 87 — IV Non-Linear Structures in Musical Reality 93

III Media Metaphorology: 98 Irritations in the Epistemic Field of Media Studies Georg Christoph Tholen IV From Pebbles to Digital Signs. 114 The Joint Origin of Signs for Numbers and for Script —Their Intercultural Standardization and Their Renewed Conjunction in the Digital Era Gert Schubring

I Mesopotamia 116 — iI The Way to Effective Positional Systems 120 —  iII Introducing the Metric System - Resistance to Universalization 123 —  iV The Digital Era 125

V Foucault, Boole, And Our Deleuzean Century Gordon C.F. Bearn

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VI A Mathematical Drama Articulating a Thing Entirely in its Own Terms Vera Bühlmann

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VII ‘On the Baroque Line: the Mind-Body Problem’ and the Art of Cryptography Gregg Lambert VIII Nudged Viands David Schildberger

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I Limit-experiences in The Order of Things 131 — II Broaching Boole 135  — III George Boole (1815-1864) 139 — IV The Hapless Task (Continental and Analytical Philosophy) 146 — V Waking Up: Our Deleuzean Century 151

1 A Spectrograph 163— II The Spectrometer 163 — III The Generic 164 — IV Characterizations of The Generic 178 — v Falling in Love With the In-Sinuousness Proper to an Economy of Entropy 181  — vi The Master 184 —  viI Characterizations of The Master 189 — viIi Acquiring a Body-to-Think-In 202 — ix Masterpieces, and Why There Are so Few of Them 208

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I The Cosmos 236 — Ii The Realm 236 — Iii The Machine 236 — IV The Ecology 238 — v The Obstacle 240 — vI The Antenatal Prolific Mixture 242 — viI The Discovery of a Castoff Viand 246 — viiI The Quasi-Amalgamation of a Mob 252

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ON THE BOOK SERIES VERA BÜHLMANN, LUDGER HOVESTADT Only one hundred years ago, hardly any scientist of renown would have been unaware of philosophy, and hardly any artist or architect uninformed about up-to-date technology and mathematics. Today, our ability to explain and explicate our own work within a shared horizon of assumptions and values beyond our specific scientific community has, perhaps paradoxically, turned into an inability and resulted to some degree in a kind of speechlessness. Only rarely is it now thought important that we relate our work to, and integrate it with, an overall context that is in itself “on the table” and up for consideration. More and more, that kind of context is taken for granted, without any need for active articulation, refinement or development. At the same time, though, the media are full of news stories about catastrophes, crises, and an impending doom that cannot, it seems, be warded off. Climate change, a shortage of resources and population growth, urbanization and its political radicalization, in the course of globalization, and this is just naming a few of the critical issues today. Quite obviously, the notion of such an overall context, both implicit and assumed, is extremely strained, if not indeed overstretched today. This all is widely acknowledged—the UNESCO Division of Foresight, Philosophy and Human Sciences in Paris, for example, launched a discourse on this subject in their 21st-Century Talks and Dialogues under the heading The Future of Values. The companion book, published in several languages simultaneously in 2004,1 is structured in three parts, and includes one chapter on the ethical issues of values and nihilism lying ahead, another chapter on technological progress and globalization, as well as a third chapter on the future of science, knowledge, and future studies. What remains strangely implicit, and therefore ignored here, in a way that is typical of this inarticulacy with regard to the overall context mentioned above, is the societal, scientific and cultural role that inevitably is ascribed to technology against the backdrop of such discussions, along with the expectations that are associated with that role of technology. Giuseppe Longo, the current Directeur de Recherche CNRS at the Ecole Normale 1

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Jérôme Bindé, ed., The Future of Values: 21st-century Talks (New York: Berghahn Books, 2004).

Symbolizing existence — Metalithikum III

Supérieure in Paris has quite dryly put into a striking formulation the particular challenge this modernist inheritance of inarticulacy concerning technology imposes today: the systems most worth studying are dissipative systems, he maintains; we need to dare thinking “far away from the absurd theories of equilibrium. It does not exist in an ecosystem nor in a society, unless everybody is dead.” 2 In conflict with this, technology depends upon symmetries and balances in order to function. This can be seen as the logics of how to control equilibria. In the interview from which we quote here, Longo raises the question of how financial and scientific world views relate to each other, and he maintains that a technology orientated scientific world view cannot unproblematically be the basis for thinking about economics.3 Rather, he suggests, we must learn to consider a structural parallelism between the two. Longo maintains that mathematics is “a science of invariants and invariant preserving transformations, thus of symmetries.”  4 We consider the perspective suggested by Longo so interesting because it promises to perhaps show a way of thinking about economics in which the diverse economies would not have to impose scarcities as the basis for symmetry considerations in order to legitimate themselves. It is a core feature of something considered “invariant” that it must not be determined what in total it amounts to—thermodynamics’s first law formulates the invariance of energy in the universe, and it merely states that energy can neither be created nor destroyed. The amount of energy at stake does not have to be positively determined thereby; this is the key idea in the physics of heat. The concept of invariance is crucial for taking the step, in physics, from mechanical machines to dynamical apparatus. Mathematics, if related to invariances and the transformations that preserve it, needs no longer be troubled with definitions of the infinite—the infinite merely counts to 2 Giuseppe Longo, “Are Financial And Scientific Views Of the World Similar?”, http://www.npr.org/sections/13.7/2011/06/13/137154418/are-financial-and-scientific-views-of-the-world-similar; as well as the conversation with him by France Culture, entitled “Internet, Logique et Finance”, http://www.di.ens.fr/users/longo/ FranceCulture/archive-red/fr-culture-Internet-red-full.mp3. 3 Ibid. 4 Longo doesn’t shy away from considering that in parallel with the advent of a conceptual domain of abstraction around the 6th century BC, there was also the invention of money. Money, he suggests, can be seen as the enabler of a kind of geometry on the face value of the ruler, whose implicit and impersonated power was thereby rendered explicit and visible as the nominal value, in the coins that are being sent out to circulate through a kingdom or empire. This parallel structure of which Longo speaks conceives of mathematics as the science of symmetries and of finance as the symbolic corporealities of symmetries. It leads him to distinguish three revolutions of such “symbolic” script: (1) a kind of symbolic “writing” in the coined nominal values of a personal sovereign that emerges around the 6th century BC, then (2) a kind of symbolical “writing” in paper money covering for the nominal value of a bank that emerges in Renaissance times, and (3) most recently, a kind of symbolic “writing” in electronic money. Longo elaborates on how these paradigms can be seen to manifest in different notions of space, derived from mobility schemes afforded by money as “symbolical script”. We cannot in an adequate manner discuss here the depth or the extent of his argument, and instead point the reader to the original documents: Giuseppe Longo, ibid.

On The Book Series

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it as an indefiniteness that is intrinsic to all that mathematics can model and formulate. Mathematics, as the science of symmetries, knows that it is a science, that it deals with symmetry only insofar as symmetries are yet understood, just as physics knows that it deals with nature only insofar as nature has yet been understood. This understanding is crucial, for it delineates, via a measure of entropy, also spaces of probability: to say that mathematics is the science of invariances, rather than calling it the theory of invariances, for example, points to the crucial fact that an invariance has the elusive character of a rendered spectrality, like phenomena do, too. They can be grasped neither positively nor negatively, but only via a projective list that gathers all those transformations of which one knows that they actually preserve the invariance. An invariance, hence, different from its reification into invariants, can never be formulated exhaustively in what may be understood by it. Like the form of a circle, its scope and compass is of indefinite yet formulate-able extension. Projective lists of mastered possibilities provide the probabilistic alphabets in whose terms invariances can be addressed; but what is at stake in them is masked by the cipher that constitutes the probabilistic alphabet. The “eloquence” a thinking in terms of invariances affords can always be more or less. The mastership involved is not only one of either getting something right or wrong, bringing it to function or not. What we believe to understand from this is that postulating an identity between mathematics and symmetry would be as absurd (or violent) as postulating one between physics and nature, or between rationality and reality. In short, with Longo’s perspective there might be a way to think of economics as drawing from an indefiniteness that is not the quasi-infinite of a storage or a resource—just as life appears to draw from a source that would, doubtlessly, be inadequately conceived of as a resource or as a storage. In the Metalithicum Series, we tend to regard technology in the extended sense of technics at large. Along with its respective solution-oriented application to the sciences, culture, economics and politics, we think that technology needs to be considered more fundamentally, especially regarding the semiotic and mathematical-philosophical aspects it incorporates. From this perspective, we see in technology a common factor for facilitating a discourse that seems to have been largely lost from today’s discursive landscape, the degree of its disappearance inversely proportional to the increasingly central role technology plays in every domain of our lives. Such a discourse seems crucial if we are to develop adequate schemes for thinking through the potentials of today’s technology, something that is in turn essential for all planning. Our stance is an architectural and, in the philosophical sense, an architectonic one. Our main interest centers on the potentials of information technology, and how we can get used to the utterly changed infrastructures they have brought us.

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Symbolizing existence — Metalithikum III

But have our infrastructures really changed substantially? Or is it merely the case that a new level of media networks has emerged on top of technology with which we are already familiar? Are the “new” and digital media simply populating and exploiting, in a parasitic sense, the capacities of modern industrial infrastructures that have brought prosperity and wealth to so many? In his contribution to the UNESCO dialogues, Paul Kennedy was still convinced: “In the Arabic world, 3% of the population has access to the internet. In Africa, it’s less than 1%. This situation won’t improve as long as the infrastructures remain in their current state. It won’t change, as long as these countries lack electrification, telephone wiring and telephones, and as long as the people there can’t afford either computers or software. If knowledge is indeed power, then the developing countries today are more powerless than they were thirty years ago, before the advent of the internet.” 5 Our experience since then has allowed us to see things a little differently. There are meanwhile as many mobile phones in use worldwide as there are people living on the planet. Six billion people out of a seven billion world population can meanwhile read, write, and calculate (at least in some basic sense). Only three decades ago, this proportional measure was not 6/7th, but 2/5th! We have seen the “Arab Spring” that brought simultaneous political revolutions in several Arabic countries, giving facticity to the cultural impact of digital media, and this to a degree that was unexpected or previously deemed improbable by many. And the credence of this facticity is not harmed, we think, by the fact that since then we have had to witness ongoing fundamentalist reactions as in Syria, where the situation has meanwhile escalated into a veritable war. To say that the facticity of the cultural impact of digital media is not impaired in its credence thereby is not to down play the seriousness of these complex situations. We think, for example, that the falling energy prices we currently witness are (at least among other factors) also owed to the success of sustainable forms of cultivating energy, and crucially so also to photovoltaics—the only form of energy harvesting that draws from a (quasi-)infinite source, rather than from finite resources. This development, it is to be expected, will put territorially rooted forms of government, as the one in Saudi Arabia, under increasing pressure with the effect of severely challenging the existing political stabilities across the world. Thus, of course, in political, economical, religious reorientation all is at once at stake, and the idea that technological modernization be sufficient for consolidating the complex conflicts that arise in such phases of reorientation must strike one as quite naive. Even if technology affects how people live on the collectively existential level of infrastructure, it 5

Paul Kennedy, “Globalization and its Discontents” in Jérôme Bindé, ed., The Future of Values: 21st-century Talks (New York: Berghahn Books, 2004): 107-109.

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cannot do away with conflicting cultural values whose roots lie in different cultures. Modernization of technological infrastructure, as “democratizing” and empowering for the people it may be, might even have an infantilizing effect on societies who begin to depend on it, because it fosters the idea that all kinds of problems may be solved technically, and can in essence be taken care of by respective experts and specialists. The same must be observed with greatest prudence also on a global scope, where we cannot help but observe an increasingly tyrannical polarization of values into a crude and simple distinction of good and bad—orientated around the two poles of (1) sustainability or the collective care for the health of the larger whole (the climate), and (2) terrorism as a new, diffuse, form of violence. We call this polarization tyrannical because it refutes interpretative investigations into the nature of these complex issues and instead focuses on ‘objective’ measures like a numerical index for CO2 pollution or registered documentation of power abuse; interestingly, the same technology is used by military and intelligence agencies as by defenders of civil rights like Edward Snowden. Thus we see the same technological means instrumentalized sophistically from all sides. We read these constellations as strong indicators for just how limited the applicability of our noetic schemes is for thinking through longterm developments. These schemes have evolved from our experience of prosperity in times of strong modern nation states and industrial technology with matching economics. They go along with notions of centeredness for thinking about control, notions of linearity and nested recursion, of processes and grids, and of mechanical patterns of cause and effect used for planning. It is a truism, perhaps, to point out that these notions do not fit information technology very well. They are stressed and overstrained by the volatile associativity that emerges from logistic networks and disperses throughout user populations. Going by our inherited notions, industrial infrastructures appear to be used as a playground for what is called, somewhat helplessly, “consumer culture” or “the culture industry”. But in the case of India, for example, what came back as a result of the success of mobile telephony, astonishingly, were new infrastructural solutions. With no banks and no cash machines on hand, people simply invented the means to transfer money and pay by SMS. Yet the standards developed for micro-banking today can be referred to and linked up with solutions that exist for other areas, such as energy provision maintained by photovoltaics and micro-grids, for example. This is not the place to present scenarios. But let us remember that in India, Africa, Arabia, information technology has achieved what no administration, no mechanical infrastructure, no research and no aid has been capable of: enabling people in developing areas of the world to use standard, state-of-the-art, technological infrastructures, not state administered and directed for their own benefit. We would simply like

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Symbolizing existence — Metalithikum III

to invite you to consider the profound extent to which codes, protocols, or algorithms, standards such as ASCII, barcodes, MP3, or the Google and Facebook algorithms, have challenged our established economic, political and cultural infrastructures. From this we get a sense of the potentials that come with information technology, directly proportional to these challenges. We deliberately call them potentials, because we are interested in developing adequate noetic schemes for integrating them into thinking about information technology from an infrastructural perspective. We are interested in how these potentials and dynamics can be applied to finding ways of dealing with the great topics of our time. We are interested in how we could understand computing as a literacy that is at once more capacious and more demanding than the strict reduction of complex issues to simplified and mechanically treatable measures of truth values. As Marcel Niggli and Louis Frédéric Muskens wrote in their article on mechanization and justice for the second volume of this series: “We might advance with greater ease once we admit that law bears greater resemblance (and hence is linked more strongly) to quantum physics and its often perplexing complexities.” 6 Since information technology itself is constituted by quantum physics, this argument may well be extended to any field and domain that is organized today by this new form of technics. In another contribution to the UNESCO dialogues mentioned above, Michel Serres observed, somewhat emphatically: “Today’s science has nothing to do with the science that existed just a few decades ago.” 7 Computers and IT bring us the tools for statistical modeling, simulation and visualization techniques, and an immense increase in accessibility of data and literature beyond disciplinary boundaries. With the Colloquies that are documented in the Methalithicum book series, of which this is the fourth volume, our main interest lies in how to gain a methodological apparatus for getting familiar with the potentials and dynamics that are specific to information technology and applying them to dealing with the global challenges that are characteristic of our times, by referring them to a notion of reality we assume will never be “fully” understood. The prerequisite for making this possible is a regard for, and estimation of, the power of invention, abstraction and symbolization that we have been able to apply, in past centuries and millennia, in order to come up with ever evolving ways of looking at nature, cities, at trade and exchange, at knowledge and politics, the cosmos and matter, and increasingly reflected, at our ways of looking, speaking, representing. Rooted in 6 7

Marcel Niggli, Louis Frédéric Muskens, “Mechanical Justice” in Vera Bühlmann, Ludger Hovestadt, eds., Domesticating Symbols, Metalithicum II (Vienna: ambra, 2014): 20-44, here 30. Michel Serres, “Is Culture Threatened?” in Jérôme Bindé, ed., The Future of Values: 21st-century Talks (New York: Berghahn Books, 2004): 142-146.

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their respective historical cognitive frames of reference, we have been able to find ever new solutions for existential challenges. There has most likely never been any such thing as a prototype for coordinate systems: their detachment from substance-space and its formal symbolization result from acts of abstraction. Plato may have already considered the idea of a vacuum, yet he thought it “inconceivable”; nevertheless, this notion of the vacuum inspired abstract thought for ages, before Otto von Guericke invented the first vacuum pump as a technological device in 1654. Electricity was thought of as sent by the gods in thunderstorms before the algebraic mathematics of imaginary and complex numbers were developed along with the structures that allowed us to domesticate it. Today, we imagine the atomic structure of matter by means of orbital models gained from a better understanding of electricity. So, in short, we do not share the idea that characterizing our time as post-anything is very helpful. While we agree that we seem to be somewhat stuck within certain mindsets today, we do not consider it at all plausible that any kind of concept or model, political or otherwise, will ever come close to anything resembling a natural and objective closure. The concepts behind any assumption of an End to History—whether this be in the Hegelian, the Marxian, or the more recent Fukuyama sense—stem from the 19th century, when Europe was at its peak in terms of imperialist expansion. To resurrect them today, in the light of our demographic, climatic and resources-related problems, seems to us a romantically dangerous thing to do. By now it is safe to say that technology is not simply technology, but has changed character over time, perhaps even, as Martin Heidegger put it, it has changed “modalities in its essence”. In order to reflect this spectrum, we propose to engage with a twin story, which we postulate has always accompanied our technical evolution. Historically, the evolution of technics is commonly associated with the anthropological era called the Neolithic revolution, which marks the emergence of early settlements. We suggest calling our twin story Metalithicum. As the very means by which we have been able to articulate our historical accounts, metalithic technics have always accompanied Neolithic technics, yet in their symbolic character as both means and medium, they have remained largely invisible. The Metalithicum is ill suited for apostles of a new origin, nor is it a utopian projection of times to come. Rather, we wish to see in it a stance for engaging with the historicity of our culture. As such, it might help to bring onto the stage as a theme of its own an empirical approach to the symbolics of the forms and schemes that humans have always applied for the purpose of making sense. This certainly is what drives our interest in the Metalithicum Colloquies, which we organize once a year in a concentrated, semi-public setting. As participants, we invite people from very different backgrounds— architects and engineers, human and natural scientists, scholars of

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humanities, historians—or, to put it more generally and simply, people who are interested in better understanding the wide cultural implications and potentials of contemporary technology. This as well characterizes the audience for whom this book is written. We are very grateful for the opportunity of collaborating with the Werner Oechslin Library Foundation in Einsiedeln. The Library chiefly assembles source texts on architectural theory and related areas in original editions, extending from the 15th to the 20th century. Over 50,000 volumes document the development of theory and systematic attempts at comprehension and validation in the context of humanities and science. The core area of architecture is augmented, with stringent consistency, by related fields, ranging from art theory to cultural history, and from philosophy to mathematics. Thanks to the extraordinary range and completeness of relevant source texts and the academic and cultural projects based on them, the library is able to provide a comprehensive cultural history perspective. When we first talked to Werner Oechslin about the issue that troubled us most—the lost role of Euclidean geometry for our conceptions of knowledge, and the as yet philosophically unresolved concepts of imaginary and complex numbers and their algebraic modeling spaces—he immediately sensed an opportunity to pursue his passionate interest in what he calls “mental chin-ups” as a form of “mental workout”, if not some kind of “thought acrobatics”. We would like to express our thanks to him, Anja Buschow Oechslin, Bernd Kulawik and Monika Heinrich, for being such wonderful hosts. We would also like to thank the editors at Birkhäuser (Vienna), David Marold and Angelika Heller, for all the support we have received for our project, and for making this third volume a reality.

On The Book Series

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INTRODUCTION— SYMBOLIZING EXISTENCE VERA BÜHLMANN, LUDGER HOVESTADT “The most revolutionary event in human history, and perhaps in the history of hominids, was less, I believe, the accession to the abstract or to generality in and through language, than an uprooting from the whole of the relations that we maintain in the family, the group, etc., and which concern only us and them, leading to an accord, perhaps unclear, but sudden and specific, to something external to this whole. Before this event, there was only a network of relationships into which we were plunged without appeal. And, suddenly, a thing, something appeared, outside of the network. The messages exchanged no longer said: I, you, he, we, etc., but this, here. Ecce. Here is the thing itself.” 1 “Can one conceive of an object outside of the relationships of forces?” 2 I

INFORMATION AND OBJECT: A PUZZLE

When one listens to the talk today about the role of “information,” in its broadest sense,3 there is a particular idea that appears to underlie the expectations of laypeople just as much as the many differently specialized experts: the intuition that “information” is a kind of “elementary patch”—not really an element and not really a particle either, more like a mixture of both, pieces of an enormous puzzle perhaps—patches that one can expect to fit together neatly and smoothly and with no need to apply force, if only enough care is invested in figuring out how the patches must be arranged so as to continue and complement each other. These patches of information are to show the 1 2 3

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Michel Serres, The Birth of Physics (Manchester UK: Clinamen Press, 2001 [1977]): 132. Ibid., 133. Cf. for example James Gleick, The Information: A History, a Theory, a Flood (New York: Vintage, 2012).

Symbolizing existence — Metalithikum III

way things fall into place “just as they ought to,” naturally. Associations that go together with this intuition include that information, as is often said, bears the unique quality that it is “recordable” “immediately”. The journalist doesn’t tell a story when she reports news, the laboratory scientist is not a dramatist, and neither is the empirically working field researcher nor the carefully working historian. This is because, so understood, there is an objectivity to information that originates in its quantitative aspects. In this way, information is often associated with something like the very “stuff” of what can be known, the pure content of what is known, as well as of what is not yet known. We cannot deny that this particular idea of information is accompanied by a certain sense of unease, of embarrassment even, that goes together with a sense of sudden and surprising vulnerability. For haven’t we already seen decades of critical discourse demystifying exactly this very idea? Haven’t we all learned that journalists never just record, but inevitably also introduce a certain bias (choice of theme, location, decision to give the floor, et cetera), haven’t we come to accept that science in the laboratory is science in action,4 that the historian cannot help but make the absence of verifiable data, of which he cannot even know that it is absent, a relevant factor in his accounts, and so on? Haven’t we absorbed the fact that power and knowledge go together, that science involves, just like culture at large, and economy, and theology, issues that are ultimately and irreducibly political issues? And doesn’t this urge us to foreground an interest in subjectivity, and not to go along with this idea, that all the incrementally small patches of what can be known, delivered and stored as information, will eventually link up to display a full picture of all affairs insofar as they exist objectively? Our intent is far from either ridiculing, or otherwise stigmatizing, this familiar, as well as doubtlessly naive, idea of information as patches of a puzzle. We actually think this idea is quite admirable for the very sense of vulnerability it transmits to everyone who in principle praises its simplicity, its abstractness, and desires the sobriety that goes with a pursuit of intellection worked out in the face of a socially shared inclination to consent to something that is “merely an intuition”. It is this sense of vulnerability we want to bring to the fore by putting this idea of patches of information into focus, and it is in the zone of its imposed need for diligence and care that we want to see how well it lends itself to actually clarifying what is the concern of this book—Symbolizing Existence. II

DOPING AND DATA—MYTHOLOGY OF THE GIVEN

With this third volume of the metalithicum series, we again want to select one particular concept from the torrid wasteland of purely 4

Bruno Latour, Science in Action: How to Follow Scientists and Engineers Through Society (Cambride MA: Harvard University Press, 1987).

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technical language, and consider its larger philosophical implications: electro-chemical doping in semi-conductor technology. The word “doping” derives from Latin dotare, for to endow, or to bestow. How to think of this strange practice, which is the giving of dispositions that condition what will be recorded as data? If we think of information as data that can be recorded, then doping introduces something like the reversibility of the happenings that can be so recorded. This focus both continues and differentiates the first and the second of the metalithicum colloquies, both of which also focused on semiconductor technology and its role in how we can think about materiality and meaningfulness in the age of electricity. The first one, Printed Physics, took as its starting point that materials can have their physical characteristics formally analyzed, technologically constructed and (bio-)chemically synthesized on a symbolic level, and—hence the wording of the title—that doped materials can be produced industrially, using printing technologies. Doped materials can be manufactured using a process that bears striking similarities to the printing technologies we are familiar with from the past. The manufacture of digital processors and memory chips for example is in fact reminiscent of lithography, copper etching, and the chemical printing of photographs, and thus continues a line of earlier forms of analogue relief printing methods. In the case of printable solar cells, it can be said that instead of ink on paper, ions are literally being “imprinted” on silicon. Yet there is one important difference, which becomes apparent in the respective notions of “imprinting” and “doping”. Unlike any other print product, the manufacturing of doped materials in printed physics relies less on a referential expertise about how to record the physical characteristics of materials, that would permit us to duplicate and perfect or purify them and their constellations. With printed physics, we are maximizing generic polyvalency, physical indeterminateness. Pursuant to the first colloquy, the second one was called “domesticating symbols,” and it focused not on the conditions of production, but on how to think of the electro-chemical “substrates” on which today’s data-processing-machines operate. Information-technological media and apparatus no longer operate primarily on the substrate of physical forces and their mechanical principles. Rather, their effectiveness is deployed on a quasi-immaterial bed made of probabilistic signal horizons of symbolic codings, through which the erstwhile physical substrate is now formally getting rendered, as a given substrate (“data”) in the sense of “informational constellation”. In this regard, it is important to stress that information technology today is no longer simply confined to elaborately controlling and investigating processes that may already be accessed through a mechanical apparatus. Indeed, we maintained that a movement is underway towards learning how to grant the quantum-energetic constitution of our world its own right, and form of address, amidst its dynamical constraints. This form of right and this form of address ought

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Symbolizing existence — Metalithikum III

to take into account that for the first time, photovoltaics succeeds in harvesting energy, as electricity, straight from sunlight, and, to boot, completely without recourse to any of the ever-dwindling tangible energy resources that planet Earth (still) holds in store. Domesticating Symbols implicitly tries to consider a notion of capital that is not wrested from accumulation and the centralizing control of equilibria and controlled balances, but one that views capital, ultimately, as an abundantly streaming source, the sun, which due to the original blankness of its value (solar radiation as white light) is, per se, namely without a symmetrybreaking play through obstacles that reflect light, entirely bare of value. Domestication, then, would not be “appropriation” and “purification”, but the anonymous collectivization of “sourcing” and “doping”. While Printed Physics focused on how semi-conductor technology changes the conditions of manufacturing, by maximizing generic polyvalency and physical indeterminism, and while Domesticating Symbols focused on an alphabetization of nature in its probabilistic givenness, Symbolizing Existence foregrounds a perspective regarding how we deal with data in a rational way. To put it somewhat drastically, it looks out for how one might think about the axiomatization of what we suggest to call “existential contingency.” We want to foreground that from the point of view of quantum physics (which is mandatory for addressing electronics), we are ill advised if we assume a symmetry between technographic “reading” and “writing” practices. This indeed distinguishes digital code and its electro-magnetic, physical substrate, from manners of coding with respect to classical (Newtonian) physics of forces: for the Newtonian physicist, in her paradigm of temporal reversibility, “reading” is the playing of recorded data while “writing” is the recording of data that can be “read” (played). For her, the two are strictly symmetrical (this is what grants the reversibility of time). But this is not so for the quantum physicist, who is concerned with energy rather than forces, on a macroscale (heat, thermodynamics) and on a microscale (information, molecular biology, communication). For her, there is only the symmetry of a translation between “reading” and “writing,” with which comes a certain irreversibility as to how the two are brought to relate. For the quantum physicist, code can be of diverse “character” (the probabilistic alphabets). The manufacturing of doped materials in printed physics relies on a kind of “literacy” in “articulating” the “characteristics” proper to code (the characters encrypted in probabilistic alphabets): for any signal to be recorded, a channel must first be established that can filter a coherent message against a background noise. To consider a veritable alphabeticity of nature is not merely a metaphorical manner of speaking: what is needed to dope materials is a certain rationality of characteristics, such that the characters are transformable into each other. We are used to referring this transformability to a calculus, to numbers and signifiers. But what is at stake is the symbolicity of both, a literacy

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and a calculus. We suggest to address the literacy through so-called probabilistic alphabets, the alphabets of code (ciphers) that render a certain number of possibilities finite and countable, and that are constitutive for probabilisitics (and that distinguish it from stochastics). This is for writing. For reading, we suggest, it is the calculus that ought to be seen as encrypted, and the reader is to specify the characters from a without to the characteristics of the signifiers in whose terms what she reads has been written. This “without” is what we suggest to call “existential contingency”. Such an encrypted calculus is also at the core of every technological communication channel: it defines the “entropy,” the background noise against which the message and its transmission is being profiled and foregrounded.5 These alphabets are literally stocks of contingency, resources of existentiality. It is the quanta of this stock, as the elementarized blankness of entropic (polyvalent, indetermined) existentiality, elements of the probabilistic alphabets, that is the concern of the articles collected in Symbolizing Existence. How are we to grasp the philosophical implications of this gesture? The path we chose in the 2011 conference “Symbolizing Existence,” which this book documents but also builds on (by including articles that were not part of the conference 5 years ago), was to dare considering a philosophical notion of existence—pure contingency—but without linking existence to any notion of a neutral individual, without even linking it to a form of subjectivity. Our challenge then was how one might speak of a pureness of the contingent, meaning its entropicness (against the negentropicness of organized orders). We were seeking a notion of purity bare of reference to a certain something that, supposedly capable of entirely resting in itself, could be the addressee of such “purity.” If there were such an addressee, then existential contingency would merely be an attribute, something that happens to it and tears it apart from a genuine existence resting entirely within itself. When putting together this collection of articles, this was still our concern: What can we possibly make of pure contingency, how can we give priority to a notion of the possible, without attaching it to something like an abstract point, or a supposedly concrete being of a particular magnitude, or, more critically, a given case of such magnitude—however singular and incomparable this point, this magnitude, this case might be conceived? To consider such a notion of existence—and this is how we can only now, five years after the conference, return to these questions—entails questioning the moral and/or ethical investment of the very notion “existence”. To consider its pure contingency means to consider that existence is not 5

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Cf. Vera Bühlmann, “Generic Mediality: Post-Alphabetical?” forthcoming 2016 in the proceedings to the joint annual conference of the Society for European Philosophy and the Forum for European Philosophy, September 3-5 2014 at Utrecht University, with the annual theme: Philosophy after Nature (http://philosophyafternature.org), edited by Rosi Braidotti and Rick Dolphijn.

Symbolizing existence — Metalithikum III

an intuitive, immediate referent for a notion of justice, that it is not a guarantor for a kind of equivalence. Existence as pure contingency means that existence is not gratuitous after all—it entails to deal with the important findings of Leon Brillouin 6 and others, that information not only maintains relations to entropy but also to negative entropy, that it has its price, that “[we] cannot get anything for nothing, not even an observation”, as Dennis Gabor famously maintained,7 and hence the impossibility, in principle, of a perfect experiment—whether that experiment be carried out by a human or an artificial, non-anthropocentric kind of agency. Existence as pure contingency would once again have to be conceived of in terms of a “first philosophy,” reconciled with the enlightenment tradition of relating politics and economy. Existence as pure contingency would have to be conceived of as the indefinite equality pole underneath economical and political dealings, an asymmetric “equilibri-ality” (rather than an equilibrium) because it doesn’t rest in communication; communication is where it struggles for balance. Existence, as pure contingency, pertains to the “order-ability” incorporated in generalizations. Existence as pure contingency, hence, must be addressed through orders of objectivity derived from generalizations of particular cases. Thus, existence as pure contingency must be addressed in terms of “objects”, not those of “subjects”. Yet as opposed to its Cartesian conception, “the object” in its existential contingency must be considered as the totality of all possible inclinations in the path which a particular case (the subjectivity determined by such objectivity) might take during the time of its actual duration. In other words, the notion of the object needs to be reconciled with both the first and the second law of thermodynamics, that is, with reversible (negentropic) as well as with irreversible (entropic) time. Quantum Physics, its electric energy and the semiconductor technology it has brought us, permits the relation of each to the other without subjecting one to the other: an object, existing in its pure contingency, at once has a singular duration (negentropy) and is of all time (entropy). In other words, if contingency can exist “purely,” then an object never can. For its particular existence is an articulation of both, contingency and necessity, entropy and negentropy. When we now come back to the particular vulnerability zone of the idea with which we started, that information is something like elementary patches of a puzzle, we no longer need to feel embarrassed about the naivety of the idea. It all depends on how we think about “the puzzle”—there is indeed something to be learnt from Sisyphus, the classic existentialist figure in literature. We want to bring it on stage in this introduction before going on to present the contents of this book. In Michel Serres reconsideration of the classic figure of Sisyphus, we can get a glimpse of how to use 6 7

Leon Brillouin, Science and Information Theory (New York: Academic Press, 1956). Dennis Gabor, MIT Lectures, 1951 cited in Léon Brillouin, Science and Information Theory, Dover, New York 2013 [1956], here referred to in the kindle edition, position 3805.

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prisms to decipher the spectrality of all this “stuff” that is being recorded, an ever increasing flood of information about which we may often feel inclined to complain. We don’t expect that all of these past and future lines of thought in relation to Sisyphus have been entirely clear during our confrontation with them here. But we certainly hope to have raised curiosity for some of its aspects, and it is in this sense that before moving on to Sisyphus and to introducing the different articles collected in this book, we would like to give a more extensive excerpt from one of the key texts that has inspired us to begin speaking of Symbolizing Existence: “All I know, but of this I am certain, is that they are all structured around the information-background-noise couple, the changeprogram couple or the entropy-negentropy couple. And this holds true whether I describe the system in terms of chemistry, physics, thermodynamics, or information theory, and whether I situate myself as the final receptor of an integrated apparatus. By reversing the ambiguity function, things naturally converge. Either I am submerged in signal exchanges or I observe the global set of exchanges. But from now on I understand and can explain what happens when the observer changes his point of view, when the subject becomes object, and the obstacle becomes a piece of information, or when introspection veers off into experience, and psychology flows into physics. Inversely, when the object becomes subject, it temporarily increases its autonomy. […] The realms of the subjective and of the objective are no longer at odds. The observer as object, the subject as the observed, are affected by a division more stable and potent than their antique separation: they are both order and disorder. From this moment on I do not need to know who or what the first dispatcher is: whatever it is, it is an island in an ocean of noise, just like me, no matter where I am. It is the genetic information, the molecules or crystals of the world, the interior as one used to say, or the exterior – none of this is important any longer. A macro-molecule, or any given crystallized solid, or the system of the world, or ultimately what I call “me”—we are all in the same boat. All dispatchers and all receivers are structured similarly. It is no longer incomprehensible that the world is comprehensible. The real produces the conditions and the means for its self-knowledge. The “rational” is a tiny island of reality, a rare summit, exceptional, as miraculous as the complex system that produces it, by a slow conquest of the surf’s randomness along the coast. All knowledge is bordered by that about which we have no information.” 8 8 Michel Serres, “The Origin of Language: Biology, Information Theory, & Thermodynamics” in Josue V. Harari & David F. Bell, eds., Hermes: Literature, Science, Philosophy (Baltimore: the Johns Hopkins University Press, 1982): 71-83, here 82/83.

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III SISYPHUS. his prismatic communication and his dealings with what is puzzling “From the darkness of times, out of the hollows of the underworld, from an abyss of pain, a report recurs that some thing keeps returning here—and all we do is talk about the man who keeps taking it away from there, we Narcisses,” Michel Serres exclaims.9 All existentialist praise of Sisyphus has neglected, he maintains, that there can be no reckoning about Sisyphus without his host; and his host, so Serres tells us, is the stone. It is the object that determines Sisyphus as a subject. Sisyphus is not the modern hero, a hero whitewashed, and emancipated, from power and ambition. He is not the hero who, stripped from the burden of ever effecting anything at all, exists face-to-face with pure necessity and can therefore guard, in the manner of a bureaucrat, a notion of righteousness that rests in the sheer repetition of routine. The myth’s character does not become a modern hero because he has been punished and corrected by the Gods for the cunning, ruse and mischief, with which Sisyphus had challenged them in ever new attempts to reconcile transcendence and immanence; he is not a post-Christian crucified, without resurrection, he is not a modern savior.10 To Serres, Sisyphus is the personification of someone who values the object as the reception of news, neither good nor corrupt, simply as the appearance of something extrinsic to the heretofore manifest wholeness of the web of relations. Sisyphus plays a central role in Serres’ novel humanism, because he renders novelty communicable. This communication is the contribution of the excluded third to the bipolar idea of communication between sender and receiver, between origin and destination, between source and reception. Sisyphus crosses, always anew, their impossible falling-together in an identity. As a parasite depending on the stone as his host, Sisyphus is the instructed rather than the excluded third. He is instructed by the thalweg of the stone that comes to rest after falling down again every morning at a novel point. After being sentenced by the Gods, Sisyphus is not any less mischievous or cunning. But he invests his ambition and powers in localizing the new location, and in making the path communicable that has led him to do so. The messages exchanged in Sisyphus’ communication of news extrapolate speculatively indexes from the object, markings of a this, a here. These messages dope the manifestly existing web or relations with novel conduct-ability. His role is not the 9

“Du fond des âges, du creux des enfers, d’un abîme de douleur, le récit répère qu’une chose revient là et nous ne parlons que de celui qui l’ évacue, narcisses.” Michel Serres, Statues (Paris: Flammarion, 1987): 302. 10 Cf. Anton Schütz, “Sisyphos und das Problem”, in Gralf-Peter Callies, Andreas FischerLescano, Dan Wielsch and Peer Zumbansen, eds., Soziologische Jurisprudenz: Festschrift für Gunther Teubner zum 65. Geburtstag (Berlin: De Gruyter, 2009): 165-178.

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impossible task to evacuate, to save the stone as object. He is not a hero fulfilling his mission, he is a scientist concerned with semiconduction. He is concerned with exposing objectivity symbolically, from within the entropic play of forces. Serres also calls the symbolic function the “ambiguity function,” because it “mobilizes information and produces background noise”.11 Serres captures the symbolical exposition of objectivity as a function, and hence hands such symbolical exposition over to a notion of system; but it is a notion of system that is interlocked, a system where levels have to be integrated by protocols, rules that have neither origin nor reference outside of the consistency they need to contract. Every “next level in the interlocking series receives, manipulates, and generally integrates the information-background noise couple that was given off at the preceding level.” 12 By tracing the thalweg of his object, Sisyphus the scientist casts off from the particular level he is submerged in when he localizes the positions where his stone has previously come to rest. His struggle is not that of carrying weight indifferently, every day until the end of times. His struggle is to learn to cope with the amount of ambiguity that keeps growing from day to day, as he looks anew for his object. Sisyphus is a hero, perhaps, but not because he fulfills what he is meant to do— whether by a logic of the negative or the positive. Rather he is a hero because he endows the gates that interlock the levels of the symbolic function with keys that fit. The keys are not for unlocking sight upon a secret that was hidden within, but for granting access and passage to the novelty of the day; so that it can circulate also within the heretofore manifest web of relations, into which every day inevitably introduces additional noise, but which every day also endows with a certain excess in polyvalency. To Serres, the symbolic function performed by Sisyphus adds meaning and presents obstacles: he adds meaning because he present obstacles. Sisyphus filters packages of chance, from level to level, from day to day. And thus, because his symbolic function is an ambiguity function, his capacity to hold in restraint grows with the increasing amount of ambiguity, and in parallel to the increasing power he acquires from finding his stone and tracing its thalweg. The scientist of semiconducting acts to lesser and lesser degrees in extensio, and to greater and greater degrees of virtu. IV

THE CONTENTS OF THIS BOOK

Ludger Hovestadt, an architect and information scientist, invents “A Scheme for a Fantastic Genealogy of the Articulable.” Hovestadt maintains that a genealogy, if it is fantastic, is as real as it is made up, 11 Serres, “The Origin of Language,” ibid., 77. 12 Ibid.

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and he suggests that we think of genealogy as a confluence of several geneses by considering differently masked infinities. Today, in the era of digital code, we can think of the encryption of numbers as providing such masks. But what would be the body behind such masks? Hovestadt devises the notion of a body of thinking as the very subject of such a fantastic genealogy. Such bodies of thinking are tyrannic if their sovereignty is not shared, if they don’t live amidst populations. For such a notion of a collective body to engage with others of its kind, it is crucial that each instance can come forward with articulations of the worlds in which they live. They can do so on a stage that is algebraic, so Hovestadt maintains, a stage that is political in its algebraic capacity to host the happenings of vulnerable and fragile love affairs—that articulate rather than represent tragic or comic plots, lonely odysseys across the seas, or odes to life or death itself. Such stages are capable of displaying action that takes place amidst all the institutional infrastructures, the dependabilities, availabilities, reassurances, stabilities, which ultimately collectivize (either as private or public) technical elements of infrastructures like cables, pylons, pumps, pipes, tanks, machines, sensors, displays, actuators. This collectivization is being media-ized and embedded in the schemata of formats like news, photography, telephony, music, cinematography, teaching programs, cleaning programs, foodstuffs, control systems, research programs, production schemes, politics, jurisdiction… schemata, in short, which are precious not despite but because they are lacking, in the sense of a sieve. The observation of such love affairs, hence, present us with things that are open, that unexpectedly burst into being amidst the most ordinary, that surprise in banality and delicacy. Things that are brought about by humor, through know-how, through affection, through concentration. Central to Hovestadt’s article hence is the introduction of exercises for such bodies of thinking, to develop proprioception so that they can learn how to talk in and about the worlds that they shape and in which they evolve. Michael Harenberg, a composer and media theorist, draws in his article “Topologies of an Aesthetics of the Virtual in Music” genealogical maps of what he calls “the mediality” that underlies the aesthetics of musical composition—as an art and as a theory. All the elementarization of music’s key notions are rooted in this mediality, he maintains, in varying ways whose dispositions change with the very nature of this mediality. The genealogy in which Harenberg addresses varying compositional topologies from Wagner and Busoni to the electroacoustic and computer generated spheres of Xenakis and Luigi Nono, among many others, relates them back, iteratively and in a discontinuous manner, to the Pythagorean idea of a universality of proportion and partition. Harenberg discusses the topologies in their intimate entanglement with technics on the one hand, and with ideational notions of cosmic beauty, harmony and spiritedness on the other hand. He thereby depicts,

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indexically, a profile that might lend itself to feature also outside the field of music proper, as a kind of diffractive prism, in other fields of the creative expression of knowledge.  Georg Christoph Tholen, a scholar in media and cultural studies, introduces in his article “Media Metaphorology: Irritations in the Epistemic Field of Media Studies” a theoretical stance that promises to guard what he calls “the a-teleological openness of digital code” against any particular anthropological, ideological or straightforward technocratic instrumentalization. This stance, Tholen holds, must count as a principled stance, and he recognizes the field of digital media studies as an epistemic field only in the commitment to just this role. The mediality induced by digital code, by the computer considered as a universal medium, ranges beyond mechanic and organic models of how to think about the power brought by technology. According to Tholen’s critique, these models all open up particular economies of augmentation only to restrain and control the proliferation of the media induced as-ifs within political frames of compensation, however differently weighted (culturally colored) these frames might be. We need to conceive a non-concept based metaphorology, he maintains, that we are capable of addressing the continuous transmissibility of mediated communication—without forgetting about the unsteady and discrete conditions of mediacy that grant the extent in differentiation and scope of just such transmissibility. In his article “From Pebbles to Digital Signs. The Joint Origin of Signs for Numbers and for Script—Their Intercultural Standardization and Their Renewed Conjunction in the Digital Era,” Gert Schubring, a historian of mathematics and the sciences, gives insights into the historical development of the encoding of information. Encodings began as concrete materializations, he argues, and they were intimately tied to specific social and cultural forms of living. Next to identifying characteristic stages of encodings and patterns of their transformation, from highly differentiated material sign systems to abstract and globally used symbols, Schubring is especially interested in how the two encoding systems—numbers and script, or numeracy and literacy, which developed separately over millennia—were and are related to each other. In his article “Foucault, Boole, And Our Deleuzean Century,” Gordon C.F. Bearn, a philosophy scholar, sets out with celebrating Borges laughter Michel Foucault hears bursting through the former’s famous classificatory order of animals, on which Foucault reports at the beginning of The Order of Things, his book devoted to an archaeology of the Human Sciences. The shattering of orders that bursts forth from Borges’ laughter not only prepared Foucault for making an experience of raw, naked being, so Bearn; it can also be epitomized as a welcome greeting to “our Deleuzian Century”—an era in which the experience of difference must no longer count as a formal, logical impossibility. An archaeology of the human sciences is also an archaeology of the formal sciences, Bearn

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argues in his reading of Foucault, and as long as we don’t recognize this double articulation, we are captured in what he calls “the algebraic-anthropological sleep.” On his walks through different manners of sleeping algebraico-anthropologically, Bearn follows up on one particular sentence that had taken hold of his mind when reading Foucault: “It was inevitable that a symbolic logic should come into being, with Boole, at precisely that period when languages were becoming philological objects.” It is this bifurcation of thinking about “roots” in devising, on the one hand, a framework of variation (philology), and on the other hand calculi of variation (algebra), that has, over the decades and after the fierce battles of the so-called foundational crisis, lulled us into the said sleep in the first place, so Bearn argues. In her article “A Mathematical Drama: Articulating a Thing Entirely in its Own Terms,” Vera Bühlmann, whose work is in media theory, philosophy and architectural theory, gives a tentative account of a particular drama she has been witnessing ever since she developed an interest in engineering, design, computation and programming: The competing coexistence of two conceptual persona, whom she calls The Generic and The Master, both raising claims as to how the authority of Sovereign Knowledge, of which they both claim to be the true face, ought to be addressed. Hence, Bühlmann’s article dramatizes the role of knowledge in a manner that seeks its politicization. Bühlmann holds that this is a politicization we can find neither in the urbanity of modern and postmodern societies, nor in any nomadic forms of dwelling. It is a politicization, she holds, that is driven by a different kind of economy—one that is abundant and entropic, self-engendering, because its source is of time (rather than in time), and which radiates, in-sinuously and incandescently, in all that is. It is an economy, so Bühlmann, whose principle unity is, paradoxically, one consisting in its own partition-ability (the staggering insight that the universe actually expands). The principle of such unity must come to terms, must contract, two competing forces: life and death, conservation and dissipation, the first law of thermodynamics and the second one. Information, in its quasi-thermodynamic physicality, thwarts and articulates any interplay of these two “forces,” this is the mathematical drama which Buehlmann addresses in her article. Her account of this drama involves discussions of and commentary on contemporary positions in political philosophy (as for example Jacques Rancière and Quentin Meillassoux), which seek ways of coming to terms with the mathematics of chance and the power for prediction proper to its probability calculi. Gregg Lambert, a philosophy and literature scholar, explores Gilles Deleuze’s presentation of a new materialist method for addressing the formal difference between matter and expression. Deleuze calls this method “the art of cryptography”, and Lambert discusses the relation of this art to Leibniz’ philosophy, from whom Deleuze largely derives

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his method. Lambert argues that with this method, Deleuze generalizes what we usually tend to associate with the Baroque: his article “‘On the Baroque Line: The Mind-Body Problem’ and the Art of Cryptography” argues that what we tend to associate with the Baroque as an epochal, historical concepts actually characterizes the operation of processes in general, independent of the historical situations in which these processes might actually happen. In every operation, there are enfoldings and unfoldings of two infinities involved (one of matter and one of expression), which conserve the circulation of a third infinity which Deleuze, in Lambert’s reading, associates to the Leibnizian concept of the monad. David Schildberger, an architect and architectural theorist, opens up in his article “Nugged Viands” a view upon our most recent cultural heritage, the modern utopia of living in a lap of luxury, expressed and formalized in an urbanized land- and cityscape relation. Schildberger’s view looks at this utopia as a myth articulated as a machine: a mythic machine dealing with foundations, orders, and architectonics of value, substantialized in matter, energy and information. A mythic machine as an artificial umbilical cord, affording the supply with energy-in-general, energy collected by artifical photosynthesis, a mythic machine as nature in action, learning to care for the birth of life in its most vulnerable sta­ges. Can we conceive of this artificial nature as frameworks for the characterization of a congregation of the civic and the rural, he asks, and suggests to multiply its legends, each as presenting facts, each as function that works, but none of them as exhausting the abounding originality the mythic machine bears in stock. Schildberger hence presents a cataract of thoughts, indexing concepts in a manner that scaffolds them such as to host, in staging, characterizations yet to come. The effectiveness of such scaffolding is proportional, in its capacity to act as such hosts, to how much and how diverse of a castoff “characteristicality” those indexical scaffolds are capable of interiorizing and organizing. Schildberger’s article invests in the daring idea that the affirmation of luxuration, in its full decadence and decoupledness from an original nature, might actually be an eminently political gesture—and, perhaps, the most authentic form of provocation today.

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I A Scheme for a Fantastic Genealogy of the Articulable Ludger Hovestadt I A Love Affair 32 — II Speech Exercises in the Third Infinity 36 — III A Genealogy of Learning to Speak 40 — IV Understanding One Another 41 — V The Algebraic Stage Schema 44 — VI The Whole Point, O1 > O2 49 — VII The Moving Point, I1 > I2 50 — VIII The Mensurated Point, S1 > S2 51 — IX The Rational Point, O2 > O3 53 — X The Moving Point, I2 > I3 55 — XI The Mensurated Point S2 < S3 58 — XII The Complex Point O3 > O4 65

Ludger Hovestadt is Professor for Computer Aided Architectural Design (CAAD) at the Swiss Federal Institute of Technology (ETH) in Zurich. His approach, broadly speaking, is to look for a new relationship between architecture and information technology. He aims at developing a global perspective that relates to and integrates with developments in different fields such as politics and demographics, as well as technology, in a postindustrial era. He is the inventor of the digitalSTROM® chip and founder of several related companies in the fields of smart building technology and digital design and fabrication. A showcase of his recent work can be found in Beyond the Grid – Architecture and Information Technology: Applications of a Digital Architectonic (Birkhäuser, 2009). www.caad.arch.ethz.ch

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In the first volume of this series I introduced a ‘fantastic genealogy of the printable’: today we print not just written or drawn material, today we print all things that are, in a machinic and analytical way, depictable. And of course, every new abstraction of the technics of writing—and we understand printing as just such an abstraction—engenders a new kind of language. Therefore we shall here, in a next step, attempt to raise the question of the articulable on a new plateau. That’s no easy job, of course. And I am far from pretending that I have fully understood it, or that I’m able to embrace it in its totality. I am an architect and computer scientist who chafes against the limits of his disciplines. Nevertheless, A Scheme for a Fantastic Genealogy of the Articulable

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a promising body of thinking is shaping up and this is the second part of its presentation. The first one, Towards a Fantastic Genealogy of the Articulable, 1 served to prepare the ground for this second one now, entitled A Scheme for a Fantastic Genealogy of the Articulable. A first draft of this text origina­ ted two years ago, and as I now go over it and complete it, I cannot help but realize that it is taxing: it comes as an incredibly large gesture –something I still treasure, and so often and acutely miss in the texts of others—, but at the same time it is, for my own taste today, too impulsive, too activistic and too engaged. Finding the right balance, though, is demanding: not 1

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Vera Bühlmann and Ludger Hovestadt, eds., Domesticating Symbols, Metalithikum II (Vienna: ambra, 2014).

Symbolizing existence — Metalithikum III

to be aloof and neutral, but neither to come across as over-committed and agitated. Stirred might perhaps be the word. Stirred up by the beauty of contemporary forms of thinking, by the terror of their technical might and by the abys­ ses of their thoughtless exalta­ tions and damnations. How do you take a position in the technical performance of computers without becoming part of a technocratic game that accelerates at an alarming rate? Hence my focus on the intellect, hence also my impatience with the intelligible, and at the same time my avoidance of clearly defined problems, but above all my rejection of concrete solutions and conclusions. It is, then, an intellectual exercise. But in spite of these reservations about A Scheme for a Fantastic Genealogy of the Articulable

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the text, I have decided to make only minimal modifications. After two years of involvement with it, there are now mainly compositional inconsistencies that jump out at me, as there forever will be. If you juggle a bunch of balls in the air, then every so often you will drop one. But, short of restarting the game, it’s difficult to pick up and reintegrate the drop-outs. So let us consider this text an exercise, a workout: live and evolving, rather than serene and final. I A Love Affair Let’s get stuck in, right in the middle. On the one hand, there are today’s institutional infrastructures, the dependabilities, availabilities, reassurances, stabilities, references of the ‘second nature’ described in Part I. We are used to them, in the form of technical infrastructures, cables, pylons, pumps, pipes, tanks, machines, sensors, displays, actuators. And we know them as standardized global media-izations, embedded in the schemata of formats like news, photography, telephony, music, cinematography, teaching programs, cleaning programs, foodstuffs, control systems, research programs, production schemes, politics, jurisdiction… —in fact in all those things on which we can depend. With these, we described technology as deceleration. On the other hand, there are things that are open, that unexpectedly burst into being, that surprise. Things that we may bring about through humor, know-how, affection,

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concentration. Things that never were, and things that always have been, but that suddenly appear in a new light. An affair: possible any time, anywhere; possibly right here, right now. Beauty, fascination, love, elegance. Out of the blue. The immanence of its possibility, by removing the tiniest part, by adding the slightest nuance, by just nudging, touching, briefly arresting it: a bated breath, merely. Perhaps. These immanences throw wide open the reference system, give birth to new things. Create new references, sometime… Things around us are, on the one hand, referenced, secured. On the other hand, they are indexed, open to any new reference. Our second natures are endowed with liveliness and animated within the secured schemata. As human beings we can be ingenious by indexing and cultivating these natures. Let’s pick up from our discussion, in Part I, of Dedekind, his cut, and the notion of continuity, and turn now to the mathematician Andrei Andreyevich Markov.2 In 1913 he grabbed the first 20,000 characters of Eugene Onegin, Alexander Pushkin’s novel in verse, and mechanically counted off the alternations of vowels and consonants. Imagine: simply counts off the characters of this famous Russian poem, mechanically puts these numbers in relation to each other, pulls up a probabilistic structure, and in doing so is able to show that there is no need to analyze a text, or to fully comprehend it, in order to synthesize from it the next characters, the most obvious next steps in Pushkin’s vein, for any given position in the text. It means there is no need to have a precise notion of a text in order to find your way around it. For Markov, the spirit of the text lies not with the letters, and not within the relations or references. It resides in the immanences. And with his schematic indexing system, he demonstrates for the first time that it is possible to operate with immanences. All we need is a fragment, a hint of an idea; and a system made of indexes begins to gleam. Abstraction from analysis and synthesis. That’s Markov. Fabulous. And by now it has become commonplace. Any blurred technical picture,3 any phone call beset by noise interference: we recognize the person, recall the mood, hear the intonation. It does not take many fragments of our analytical reference systems for situations to become rich. This is a challenge to any supposedly intuitive immediacy, to analytical care, to the scientific method, to enthusiasts of analogue hi-fi recordings, even to statistics: they have all been relegated to the status of trivial functionality. Flushed out. Analytics cannot succeed where Markov does. Not through care, not through orderliness, not through hygiene. 2 3

Philipp von Hilgers and Wladimir Velminski, ed., Andrej A. Markov – Berechenbare Künste. Mathematik, Poesie, Moderne (Berlin: Diaphanes, 2007). Vilém Flusser, Into the Universe of Technical Images (Minneapolis: University of Minnesota Press, 2011 [1985]).

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Nor through real or metaphorical psycho-technology or bio-technology. Those are but lesser or higher degrees of complications of the trivial. Let’s look at an example to demonstrate the confusion Markov ought to create. This one from medicine: certain diseases can be diagnosed by their symptoms. That’s how we diagnosed and treated ailments in the Middle Ages. Others are predictable through stochastics. That’s how we’ve identified them since the modern age, and fought them with hygiene, or controlled them through vaccination. And then there are diseases that defy these methods, that are unpredictable, and therefore beyond hygiene and control. Yet they exist, such as cancer. Markov, we assume, ought to be able to deal with them, because he no longer tries to understand Pushkin’s poem, and correspondingly desists from any attempt at describing what cancer is, which is precisely what makes it possible for him to handle it—by ‘diagnosing’ it based on attributed ‘predictions’. That’s putting it maybe a bit imprecisely. More adequate would be to speak in terms of a coexistence with cancer, as something that actually can’t be ‘named’ in a definitive way: it would be a case of living with cancer, in order to avoid it. Science fiction? Not really. This is exactly how Google’s PageRank algorithm works. It meets the fragment that is our search term with an ordered list of useful documents. No analysis, no comprehension on Google’s part: just near-infinite lists, indexes, and probabilities. It is us users who, in our coexistence with the medium, set the links, the frequencies, the probabilities. Google, just as Markov, doesn’t care one bit about the why or how. No settlement on any particular set of assumptions is required by the Markov way of proceeding. And it is because of this that its ‘indexical system’ is so fantastic: not in our wildest dreams could we have imagined anything so multifarious, just 20 years ago: adaptable, fast, stimulating; movement within movements, an intellectual propellant; intentionalities… it’s liberating because it’s ungraspable. Not a machine. Not stochastics, not hygiene. Not multitude, but rather ‘potentude’. Therefore we had better examine, alongside oft-misinterpreted Deleuze, the conditionalities for the faculties of reason that are at work within the differences.4 In contrast to Deleuze, however, we want to reflect on ways in which we might familiarize ourselves with such a notion of reason, how to ‘manage’ such wealth; how to economize those riches, which Deleuze still tends to naturalize as abilities. Does that sound adventurous? We have been used to it for a long time! For more than 100 years Boole, Dedekind, Peirce, Wittgenstein, Turing, Gödel, Markov, and then Foucault, Deleuze and Guattari, have been playing within this orthogonality. 4 Gilles Deleuze, Difference and Repetition, translated by Paul Patton (London: Continuum, 1994 [1968]).

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Today, on the new stage of intentional quantities, we may—in the metaphor of running, channelled, and retained water—let the water come. Because we don’t have to hold on to it in one particular way, but are able, on this new orthogonal stage, to hold it any way we like. Because computers are not machines; or rather, in keeping with Michel Serres,5 a computer is not an apparatus, but an abstract apparatus. We are no longer being talked to via channel systems, addressed by some nature, some machine, some bureaucracy, some technocracy; we now place these as algebraic bodies orthogonally on stage, and simply let them do the talking. Now the general apparatus are speaking; the processors are able to decelerate applicatively, analytically, vividly that which is being attributed to them. We assemble them on stage, appreciatively. This is what we shall call ‘articulating’. In this interplay— electro-magnetic, quantum-mechanical, for example—we ‘pump’ water, energies, currents, data, telephone calls; and they no longer run off, instead they congregate, concentrate, narrate, crack jokes, turn cunning and perfidious, get excited, tense and fall in love, they have affairs…as long as we appreciate them. To illustrate, we can draw a simple, functional image of an inverted channel system: the quantum-mechanical effects of a solar tree conduct electro-magnetic effects—electrical current—through a cable to the sea. There, now once again in way we can readily visualize, a pump presses water through a membrane to desalinate it, and a pipe then leads the desalinated water back to the solar tree. Thus the one solar tree delivers enough water for twenty natural trees, simply because we are able to articulate it, and because we appreciate having water for our trees in the desert, for example. Nothing, in this staging, is used up, and very little is used. The scenario is pure intellect. But if we wanted to express this in physically descriptive (rather than physically articulatory) terms, something or other would forever have to be held up, channelled, consumed. In the world of our intuitive expectations, water doesn’t just ‘arrive’ like that: water—in fact, everything—always runs out. A purely intellectual scenario, by contrast, is abstract, and so we can relax. In valuative terms we inspect from the outside the many things that talk intuitively to each other. There are many of them. We can hear them talk, noisily: they are all intent upon ‘withholding’. No longer can we take analyses seriously, but populations of analyses. Not models, but that which is model-like in kind. Not generalizations, but abstractions. No longer the functions, causes and signs. In our linguistic handling of symbols of code, we are able to create stabilities on the level of symmetries and invariances, of trusting in symbolic algebra in lieu of arithmetics and analytical geometry; in articulations instead of linear, structural or post-structural constructs or historical accounts. We may become operational from within the universal flow of a generic richness. 5

Michel Serres, Verteilung, Hermes IV (Berlin: Merve, 1993 [1977]).

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II

Speech Exercises in the Third Infinity

Here we propose to delve into a closer examination of the invariances and symmetries of our bodies of thinking, and to understand the inversion of those bodies, so as to acquire a notion of the ways in which they may cross-fertilize one another, and how we can move about within a cultural richness without being retentive and impervious to new things. In so doing, we hope to overcome the ravages and blockages imposed on us by the conception of cultural and technological progress. We trust in mathematics, which, literally translated, and to the surprise of many, means ‘the art of learning’. So let me, as an architect, devise a body of thinking that is at once comprehensive and beautiful. I hope you will indulge me by overlooking some imprecisions in the detail. We know three infinities: the space of whole numbers, the space of rational numbers, the space of complex numbers.

We also know that there are definitions of further number spaces, and we know that the concept of the number space, and indeed of the number itself, is fairly recent. We further know that rational numbers possess the same cardinality 6 as natural numbers. Nevertheless, we find this trisection useful for our purposes. So let’s proceed as follows: whole numbers – x: numbers are brought in relation to things — they determine the body of thinking of antiquity and medieval scholasticism rational numbers – x/y or dx: two whole numbers are brought into functional difference — they determine the body of thinking of the modern era complex numbers – x+iy: two rational numbers are put into an operation — they determine the body of thinking of the present era (we cautiously suggest since 1890, although we still tend to perceive ourselves within the rational-number body of thinking)

Our assumption is not that rational numbers will replace whole ones, or complex numbers rational ones. It is rather a question of specificity.7 In the rationality of the rational-number space, design takes place before things are realized in the whole-number space. We’re used to that. However: accordingly, in the complex-number space operation takes place prior to design in the rational-number space. In the rational think space real things are pre-specific. In the complex think space rational designs are pre-specific. Georg Cantor, Contributions to the Founding of the Theory of Transfinite Numbers (Chicago: Open Court, 1915) 7 Vera Bühlmann and Martin Wiedmer, eds., Pre-specifics. Some Comparatistic Investigations on Research in Art and Design (Zurich: JRP|Ringier, 2008). 6

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In this text, our interest turns mainly to the Third Infinity, the body of thinking in the complex-number space. We want to cultivate operation and, in doing so, treat rationality as pre-specific. The familiar differentials, functions, transformations, probabilities, eigenvectors, Möbius strips; the fascination of fractals, grammars and their nestings, non-linearities: they are all logical systems, flawless and consistent, and for this very reason incomplete.8 Systems clearly delimitate what they can integrate from what they cannot. That is why we speak of bodies that we can inspect from without or from within. To look at them from within we can use logic, geometry, and arithmetic: means that for an outside inspection are unfit. But we have algebra. More precisely, we speak, in line with Peacock,9 De Morgan,10 Boole,11 Babbage and Peirce,12 of a symbolic algebra (exterior view), as clearly distinct from a logical algebra (interior view) around Frege 13 or Russell.14 Only symbolic algebra allows us to operate with algebraic bodies before having symbolically determined them to the extent where design within this constitution, rationally and logically—that is with logical algebra, from an interior view—is possible. Too abstract? Too complex? Actually, we experience this all the time: it has become commonplace. Only 20 generations ago, our medieval ancestors, within the rational, geometric body of thinking of natural numbers, built gigantic aqueducts to channel water to their cities. This was necessary because water, within animistic thinking, flows downward, without question. Today, in the analytical thinking of the rationalist body of thinking, we build pumps, and water flows wherever we want it to. No more aqueducts, and running water in every house: wizardry. Demoniac, to the eyes of the Middle Ages. People were burnt at the stake for much less, as late as 20 generations ago, three of which I personally knew (my grandfather was born 1890). So: not long ago, really. Today we are in a situation where water does indeed flow wherever we want it to go, but it still has to come from somewhere, always: we consider it a scarce resource, and in the end it always drains away. We imagine that we use up water, and so we mean to use it sparingly. But 8 9 10 11 12 13

14

Kurt Gödel, On formally undecidable propositions of Principia Mathematica and related systems I, in Solomon Feferman, ed., Kurt Gödel Collected works, vol. I. (London: Oxford University Press, 1986 [1931]): 144-195. George Peacock, A Treatise on Algebra (Cambridge: J.&J.J. Deighton, 1830). Augustus De Morgan, Formal Logic (London: Taylor & Walton, 1847). George Boole, An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities (London: Walton & Maberly, 1854). Charles Sanders Peirce, On the Algebra of Logic, A Contribution to The Philosophy of Notation, in American Journal of Mathematics, 3.1 (1880): 15–57. Gottlob Frege, Basic Laws of Arithmetic: An Exposition of the System (Berkeley: University of California Press, 1964). The original full title in German is: Die Grundlagen der Arithmetik. Eine logisch mathematische Untersuchung über den Begriff der Zahl (1884). Alfred North Whitehead and Bertrand Russell, Principia Mathematica (Cambridge: University Press, 1910-1913).

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what if today someone were to claim that water does not come from rain, or from storing it up, but is where it is simply because we know how to express it, how to encode it? No more dearth. Water is, because we know how to express it. This is the magic of algebra seen from the perspective of rationality. Magic that is the same as an electric current, as mobile telephony, or the Internet. Not really abstract or complex, just from a different world. Everybody uses it. Everybody likes it. It’s been with us for a good one hundred years now. We are just loath to admit that it’s from a different world. So let us differentiate: We argue in the whole think space. We narrate in the rational think space. We articulate in the complex think space.

Also: We move in a natural place, or in a rational space, or in a complex universe.

And: We argue substantively, we narrate functionally, we articulate valuatively.

And: In argumentative speech the noun is primary. In narrative speech the attribute is primary. In articulative speech the verb is primary.

Accordingly we speak of the: epistemic locus, diastemic space, and choreostemic universe.

And: Epistemically loci are being encapsulated on the stage of space. Diastemically spaces are being encapsulated on the stage of time. Choreostemically times are being encapsulated on the stage of values.

And the: choice of ratios or proportions, bundle of functions or potentials, displacement of concentrations or intentions.

So much for now on the mutual delimitation of the various stages. To gain a better understanding of today’s discursive landscape, we shall briefly compare these exhilarating vistas with the more sobering dayto-day business on the analytical stage. We turn, for example, to the notion of ‘construction’, for it says a lot about our self-image as architects and engineers, and the image we present to others. And the way it is worded is remarkably weak: under ‘technical construction’, for

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example, we find in Wikipedia (August 2011, German version, translated here): “A construction, e.g. a building or a machine, is the material result of preceding constructive activity.” Or: “Just as technology developed at breathtaking speed over the last 150 years, the construction process changed comparably over the same period.” And: “Around 1850, construction was workshop-oriented. T. Edison, for example, is known for his intensive laboratory work, following the trial-anderror principle.” As a performance, this is incredibly slow, incredibly dull. How is that possible! ‘Construction in mathematics’ yields a bit more: “In geometry, construction, in particular with compass and ruler, means development of the precise graphic representation of a figure based on given variables, whereby, as a rule, a restriction to the use of exclusively ʻEuclidean toolsʼ—compass and ruler—is required.” This, too, is extremely sparse, seeing that there is only so much construction you can do with a compass and ruler, and it wasn’t that simple even with the Ancient Greeks. What is missing is any reference to ‘understanding’ or ‘skill’, or particularly to ‘artifice’ with which ‘technics’ and ‘mechanics’ are normally associated. For example, there were levers—strong physical lines—by means of which Archimedes claimed he could dislodge Earth from its axis, if only he had a fixed anchor point. Similarly, there were circular lines arranged around points in the form of strong winches and worm gears. There was a comfortable, free and easy, urban lifestyle of ‘friends’ who were expected to hold their own in oratory, and, in case of a dispute, be capable of defending themselves in court. Sophists were concerned with ‘persuasiveness’: they were crafty persuaders, masters at applying their levers of argument to great effect, and whose art could be bought by whoever had need of it. And of course there were political, military quarrels. How do you trust words, when anything can be said and anything may be believed? Plato set up a school of dialectics to educate roaming strays in friendship by Dialogue, Eros and ideals. Homer’s Odyssey. Aristotle’s ethos, pathos and logos. Tragedies, comedies on the strident stages of the amphitheater… Life in those days wasn’t any less rich, nor were people more stupid, nor were the personal differentiations in the world’s currents any less considerable than they are today. It is a poor advisor who, like the dike watchman standing high and dry upon his levee, assesses the power of the water masses that are being channeled, the dike’s construction, and takes this as the measure of all things. History may be channeled, but our languages are rich. Our languages provide the indexes for what we’ve so far learnt to articulate and treasure in our world’s currents. With them, we want to learn to speak on the new stage of the Third Infinity. We don’t want to build any new canals, write down history, work on our progress, or suchlike. We don’t want to hold back. All that would be acting the play on the Second Infinity stage. Here it is about letting analytical persons

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interact, setting indexes and working out invariances on which the many analyses—which are now the characters—may cross-fertilize one another. Hence our predilection for abstraction. This is why we take concepts seriously and want to challenge the engineers, because too often they say: ‘Come on, you know what I mean.’ Hence also our predilection for populations, taking numbers seriously—not common in the humanities—seeing that all too often we hear: ‘What does it matter, really, whether we are talking about 10 or 100.’ And in consequence, therefore, also our predilection for operations. It’s on their behalf that we do the staging, which to us is fascinating: based on the variety of differences and repetitions,15 we may concentrate, form notions, without losing stability in the currents. From dike watchmen we turn into surfers. We want to learn how to articulate on the new stage. That’s no less than cultivating our cultural history, which from our old stage we remember as the prudent analytical assembling of potentials into ‘resources’. So let’s take a step back in abstraction and consider what a cultural history based on an algebraic shift of concentrations would look like. We hope we have piqued your curiosity, and not made too many mistakes on the way. Let us begin our Speech Exercises in the Third Infinity, in a valuative discourse, especially about architecture. There are precedents for using this procedure. Alfred North Whitehead,16 for example, faced with an at the time largely encyclopedic mathematical interest, conceives exactly this new algebraic stage,17 but later composes a Greek play with an ontic, organistic philosophy,18 writing the very shadow of the Third Infinity into the First one. We may be better off emulating Michel Serres 19 or Jules Vuillemins.20 They populate a vivid stage with encyclopedic interest and mathematical, technical curiosity, thus setting a valuable basis for a new, valuative stage. III A Genealogy of Learning to Speak Let us proceed one step further into detail. Let us characterize the first stage—that of the Greek sophists—in a way that lets us build the algebraic symmetries, invariances, concentrations that are needed for the subsequent stages of this text. 15 Gilles Deleuze, Difference and Repetition, translated by Paul Patton (London: Continuum, 1994 [1968]). 16 Alfred North Whitehead, Process and Reality: An Essay in Cosmology (New York: Prentice-Hall, 1929). 17 Alfred North Whitehead, A Treatise on Universal Algebra: With Applications (Cambridge: University Press, 1898). 18 Alfred North Whitehead, Process and Reality. 19 Michel Serres, Hermes I – IV (Paris: Éditions de Minuit, 1968 -1980). 20 Jules Vuillemin, La philosophie de l’algèbre. Recherche sur quelques concepts et méthodes de l’algèbre moderne (Paris: Presse Universitaire de France, 1962).

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Learning how to Speak Mythically The clauses / gods / loci / media are sacred. They ordain the significance of words. In the interplay of spoken clauses / gods / loci / media, with the stability of words (for example by practicing Homer’s Odyssey), new clauses are being generated through new word combinations – rhetoric / didactics / topic… Divinity is the (one) clause. Diabolic are the (many) words.

And let us straight away shift our concentration along algebraic symmetries, onto the next, rational stage of the Greek idealists and empiricists, as well as medieval scholastics: Learning Corporeal Speech The words / forms / personae become sacred. They ordain the significance of the properties / phonemes / figures / numbers, in the interplay of written words, with the stability of properties (such as the mores in Ovid’s Amores). The erstwhile sacred clauses have become a chorus of words (syllogistic), so as to influence the property of another word, through two properties / propositions (categories) – Organon: deduction – God is the (one) word / being – diabolic are the (many) properties / phonemes – eroticism, friends, insemination, ethos, pathos, logos. Heraclitus the word mover, Aristotle the word creator.

And on we move, onto the next analytical stage, that of the modern age: Learning Ostensive Speech The properties / figures / numbers now turn sacred. They ordain the significance of the modi, in the interplay of narrated properties (logic, analytics) with the stability of modi (such as the drama in Shakespeare’s Hamlet). The erstwhile sacred word has become a co-narration of properties, so as to influence, through its modi, the modi of other properties – God is now the (one) property / becoming / life / nature – analysis, construction – diabolic are the (many) modi – Leibniz the generator of properties, Kant the gatherer, Hegel the doer.

And—anticipating somewhat—on to the next, the algebraic stage of the 20th century: Learning Valuative Speech The modi / imagination / intellect now turn sacred. They ordain the significance of the values, in the interplay of the articulated modi (logic)… The erstwhile sacred properties have become the co-articulation of modi, so as to influence, through its values, the values of other properties – God now is the (one) modus – diabolic are the (many) values – Nietzsche the modalizer…

IV Understanding One Another Even after this brief, diagrammatic outline we sense that it will not be easy to find stabilities, if we are to refocus not only the actors and plays, but the stage sets as well with our pieces. On the stage of

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talking bodies, we see the performances of the thoroughly differentiated Greek buildings, for example; or, with barely changed sets, of the successful megalopolis Rome, of the pragmatically controlled orations of free Roman citizens, or of late medieval scholasticism. The word is ever sacred, and ever are the properties that are not enshrined in words diabolic: elementary, contemplative motions of man on the scholastic stage of geometric, syllogistic rules. We suspect that it will be impossible to replicate these performances on the sets of the era, because we no longer have these sets. Today we find ourselves on a new stage, slightly blind to the productions of days gone by. We watch their relics and think them a little gauche as they move about on our present-day stage. Their richness does not lie in some objective reference, some precise analysis. Those are the sets, the personae and the plays of the analytical stage that were unknown then. All of them schemata of our contemporary, or rather of yesterday’s stage, clouding our view to the abundance of our cultures. That makes us like the dike watchman who doesn’t want to get wet, who isn’t even able to swim, but who’ll talk about anything and everything. Then again, if all you can do is swim, and, while unwilling to step out of the water, are still prepared to talk about everything, you won’t be able to appreciate the richness of the dike-builders’ art either. These small overlaps of various bodies of thinking: we may be able to call out to each other in the storm. But talk about what? The riches of different worlds encapsulated. Nearly speechless. A system of coordinates, for example, like the one by which today we so easily map movements, did not exist in antiquity (it took Descartes to formulate it in 1637), which is why drawings of a Greek temple, or a Roman house, or a Romanesque church are all at least as much instances of self-staging as of third-party staging. If we take these mappings as references, we decelerate the irritations of our own flickering past, channeling them, literally petrifying them, self-analytically tracing, as archeologies, our throttled infrastructures. The same applies to the prominent grammars of William J. Mitchell in his book The Logic of Architecture (1990): 21 of course we can reproduce existing architectures! But designing them is a whole different ball game. Christopher Alexander does better in his Pattern Language,22 but he, too, has analysis precede synthesis, in order to avoid inventing new truths. Every snapshot reflects the same game: we stage nature and ourselves on the setting of analytical, throttled projections. The photographic images, which today we see as so natural, veracious—innate, as it were—did not exist 200, let alone 500 years ago. It’s almost unimaginable now that the photographic view is an 21 William J. Mitchell, The Logic of Architecture: Design, Computation, and Cognition (Cambridge, MA: MIT Press, 1990). 22 Christopher Alexander, A Pattern Language. Towns, Buildings, Construction (New York: Oxford University Press, 1977).

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invention of ours: cultivated by us; a convention, a highly regarded staging. As a student I heard an impressive story (whether it is true or not I can no longer verify): in some jungle, ethnologists filmed some natives that had never seen a photographic or technical picture in their lives, and now beheld themselves as tiny manikins on a monitor. They viewed those figures with great interest and, after a while, went looking round the monitor in order to watch themselves from behind. When they found there was nothing to see, they laughed and walked away. The idea that a person has a face, a mask, that is capable of expressing different things, the idea that you can peel a figure off a thing, but still be able to talk about the thing itself, or even just the idea that you can talk as a friend to friends, were all unknown to them. They did not know anything of such an explicit nature, and so they didn’t trust it, were unable to appreciate it. They will have had other sets of values on their stages. Indeed, Vitruvius’ ten treatises about architecture contain exclusively text, just as Euclid’s geometry manages practically without illustrations. To us it’s hard to imagine how that could have worked. It’s even less imaginable that people were not in the habit, then, to conceive of graphic, geometric representations of architecture, or use draughtsmanship to visualize geometric problems, or consider drawings or diagrams as helpful in the construction of their buildings. Just as to us it is hardly conceivable that scale drawings, or indeed every word of our language, are not natural, but in fact complex inventions: we developed them, because we experienced them as useful and were able to enter a cultural compact about them. Now they have become internalized, second nature: innate movements and well practiced speech; like swimming or riding a bicycle: once you’ve learnt it, you don’t ever lose it; it’s impossible to lose it, you don’t even have to think about it any more. How then do we overcome the mutual speechlessness of our encapsulated worlds? How avoid the reductionisms of too-tiny overlaps? Michel Foucault may be able to help.23 With his notion of ‘device’ or ‘apparatus’ (‘dispositif’), he densifies every cultural articulation and frees the discourse from the powerful constraints of script. Habermas, by contrast, locks them up in idealistic ‘rational discourses’.24 Lyotard, too —to give just a couple of indexes to today’s discourses—dissolves this openness into melancholy-tainted multitudinosities.25 What we are looking for, however, is a self-confident, open, purposeful, masterly quest for invariances that corresponds most closely to Foucault’s approach. Thanks to these invariances, we are able to let the encapsulated riches compete on the algebraic stage and produce, in the theatrical, performative sense, new abundances. 23 Michel Foucault, Archaeology of Knowledge (New York: Vintage, 1982 [1969]). 24 Jürgen Habermas, Theory of Communicative Action, transl. by Thomas A. McCarthy (Boston, Mass.: Beacon Press, 1984 [1981]). 25 Jean-François Lyotard, Les Immatériaux, Paris, Centre Georges-Pompidou, 1985.

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V

The Algebraic Stage Schema

Let us now describe in more detail the concept of the stage that is so central to our text. For us as architects, Vitruvius 26 is the reference. Come the Renaissance, Alberti translated Vitruvius’ texts for a fresh, urban public,27 expanding/reducing them with drawings and graphic representations. Thus, the 15th century reenacted the ancients. Vitruvius had authored a tractate, a text whose purpose was to didactically, dogmatically stabilize and popularize institutional Roman power, as we might put it today. Alberti, too, calls his Vitruvius text a tractate. In so doing, he deliberately places it in the traditional line of religiousdogmatic scholastic treatises. The perspectives, constructions, architecture models that make their first appearance in the 15th century are thus part of a tradition of teaching, persuasion and rhetoric, but now addressing an affluent, urban ‘public’. Thus we get to the first assumed invariance on our stage. Vitruvius, in the language game of rhetoric/didactics/poetics, distinguishes between orthographía (ὀρθός orthós, ‘upright, right’ – the ‘performer’), ichnographía (τό ἴχνος, íchnos, ‘track, footprints’ – the ‘play’ ) and skenographía (ἡ σκηνή, skēné, ‘every covered, shadowy place; tent; stage, scene’ – the ‘stage’). We shall label them O, I, and S.

We shall then follow Aristotle’s logic. It, and in particular his syllogistic, has an exceptional influence upon the history of Western thinking. In his Categories, the first book of writings later gathered in the Organon,28 he regulates free-standing linguistic expressions with two so-called essential (primary) properties: exists in an inherent (Z) and is being expressed by an inherent (A).

Therefore a ‘word’ is always either (ontological square): ( ¬Z, ¬A) e.g. the individual, Socrates, the first substance, ( ¬Z, A) e.g. the species ‘man’, the second substance, ( Z, ¬A), e.g. individual property ‘white’, or ( Z, A) e.g. property as species ‘whites’.

Additionally, a ‘word’ has other, accidental (secondary) properties: quantity, relation, quality, plus another few that are subordinate: place, time, situation (or position), action and passion (‘being acted on’). 26 There are 73 editions of Vitruvius’ Ten Books of Architecture (1497 and 1909) available at the Stiftungsbibliothek Werner Oechslin in Einsiedeln: http://echo.mpiwg-berlin. mpg.de/content/florentinecathedral/oechslin. 27 Leon Battista Alberti, De re aedificatoria libri decem, 1452, 1485. 28 Robin Smith, “Aristotle’s Logic,” in The Stanford Encyclopedia of Philosophy (Fall 2011 Edition), Edward N. Zalta, ed., http://plato.stanford.edu/archives/fall2011/entries/ aristotle-logic.

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In Organon’s second book, De Interpretatione (Περί Ἑρμηνείας, Perí Hermeneías), Aristotle defines as proposition a word structure that may be either true or false. In the third book, Prior Analytics ( Ἀναλυτικά Πρότερα; Latin: Analytica Priora), the doctrine of deductive reasoning, he discusses how, from two propositions or observations, a new proposition may be deduced (syllogism). Then the outlines of this procedure are drawn and good examples of scholars’ disputes are given (Topics; τά τοπικά; Latin: ‘Topica’ – written by Aristotle first, in fact, but later treated as an appendix, especially in the Middle Ages), as well as examples of fallacies. So let us put Aristotle’s Organon upon the Vitruvian stage, proceeding quite schematically, and see what happens. The words, then, are staged as substances (¬Z), attributive of properties/propositions (Z) to another substantial word (A); with the purpose of his language game being the enacting of clauses, topoi; in Vitruvius’ case in order to guide the erection of buildings in accordance with the speech modes of the scholars. In the enactment, the words correspond to orthographia (O1), syllogistic to skenographia (S1), and the proposition to ichnographia (I1). We shall call this constellation (S1, O1, I1). To be sure, anchoring these so readily may give rise to some justified criticism. But let us demonstrate how well the invariances thus positioned can describe the shift of concentration in relation to Vitruvius with Alberti. So what does change, with Alberti and the Renaissance, in respect of Vitruvius? According to our thesis, all we have to do is switch one position within the vector (S1, O1, I1): during the Renaissance, properties— as we have shown—become substantial (Z > ¬Z) and start assuming the part of substantives. Now adjectives stand as upright persona on stage; now properties (which, recast in the orthographic role, we shall call O2) attribute values to other properties (O2). This shift in concentration becomes apparent everywhere in the comparison of Vitruvius’ and Alberti’s texts. (Owing to my lack of knowledge of Latin and Greek, I’m afraid I have to rely on the available, idealistically and analytically distorted modern language translations). Properties become substantial, values specific, topoi pre-specific. Therefore, the shift of concentration in the Renaissance shall be called (S1, O1, I1) > (S1, O2, I1). It will take some time and a few further shifts before we will be able to find a consistent (S2, O2, I1). But more of this later. Now, notions such as property, value, substance, role, concentration, etc., are highly abstract. And our perception of the Renaissance or of antiquity does not yet gain much differentiation from the schema as presented here. But before we continue to elaborate on this thought game, a couple of brief remarks about our use of language in our algebraic body of thinking: within it, notions have lost their specific meaning. While it is convenient to have a definition for a specific term, we

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soon find that there are many definitions. We may refer to conceptual histories, encyclopedias, discourses, etc, but the closer we look, the more complex, more sluggish and more contradictory things become. We get stuck. If we are curious and take pleasure in our abilities, then, try as we might, this is not how we are going to discover any stabilities, unless we trivialize the stage on which the play is supposed to happen, and follow boring rules. So on the specific stage, we can only either move slowly and be interesting, or move fast and be boring. But what we want to do on our algebraic stage is to grant constitutive agility to our concepts, which we shall not quantify, but quantize. We know they can have many meanings, it just depends. But if we place three of them onto the stage, they start stabilizing each other, even though individually they are ungraspable. Then add a fourth one. It’s a different kind of play! The identities of these concepts show a different characteristic. How thrilling! Thus we are, in our descriptions, not looking for definitions or clarities, but for agilities in which may develop rich stabilities, in which, in turn, the concepts involved may enrich each other as much as possible, may cross-fertilize each other, may show us just what they’re capable of. A brief demonstration may be of help. Kruft, the German architecture theorist, for example, writes about Vitruvius: “Although proportion is the precondition for ordinatio, eurhythmia and symmetria, it is not defined as these concepts are introduced; it is not, for Vitruvius, an aesthetic term. For Vitruvius, proportion is purely the relationship of numbers, not the effect brought about by its application.” 29 There are many such passages, by many such authors. And of course, this is not wrong; but with its funneling, it does not get us very far. We would call this kind of writing and thinking functionalist, perhaps even minimalist or existentialist. It’s too easy to interpret the ‘missing definition’ of ‘proportion’ as a failing. We believe that it in fact enhances the role of proportion within Vitruvius. To suggest that Vitruvius reduces proportion to “purely the relationship of numbers” is inappropriate and tells us more about Kruft’s idealization of numbers than it contributes to Vitruvius. Even more drastic is the effective short-circuiting of the concepts ‘effect’ and ‘application’: a curious, slap-dash jumble of concepts held together in a minimalistic corset. What a strange cast for our stage. What a strange interplay that yields so little about Vitruvius, but so much about Kruft and his time. From today’s perspective, it is tempting to cast the Vitruvian concepts as somewhat authoritarian personae: grown up, educated, fully formed figures, resembling, perhaps, the architect that Vitruvius outlines in his first book: an architect who he demands should have a 29 Hanno-Walter Kruft, Geschichte der Architekturtheorie (München: C.H. Beck, 1985): pp. 28.

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comprehensive education, be a competent craftsman and specialist expert, an eloquent speaker and skillful writer, familiar with geometry and optics, as well as arithmetics (so as to be able to calculate project costs and master proportion), historical learning (to appreciate ornamentation and understand its meaning), philosophy (to shape character), music, medicine, law, astronomy. And then some. Of particular interest though is what he does not demand. He does not demand a personality. His concepts have no facial expression, no personal names, no history of their own, no political position. I would suggest that concepts and figures are not specifically distinguished, that in Vitruvius’ time they were typified. I’d be inclined, therefore, to cast Vitruvian concepts as authorities, and have them exchange carefully proportionately stabilized properties, after the speaking manner of wise men. So our personae are: Firmitas, Utilitas, Venustas, Eurythmia, Symmetria, Distributio… Orthographia, Skenographia, Ichnographia… They all perform a complex play upon Vitruvius’ stage and demonstrate, among friends, what they are capable of. In the construction of a building, a temple, the play of these authorities is being re-enacted. That’s how it might happen: that’s how we might attain the riches of these texts. Kruft, however, differentiates much too much between subject and object, cause and effect… Proportion is to be understood as 1) the relation of the parts to each other, 2) the relation of all measurements in respect of an underlying modulus, 3) analogy to the proportions of man.30 How weak all this is. These are all unnecessary reductions, impoverishments. So let our concepts play on the algebraic stage: Vitruvius has substantial (Z, ¬Z) words (O1) attribute properties (A, ¬A) to other words (O1). Alberti, however, has substantial (Z, ¬Z) properties (O2) attribute values (A, ¬A) to other properties (O2). The ancient stage (S1, O1, I1) in the Renaissance mutates to (S1, O2, I1).

And let’s see what this can contribute to architectural representation: On the Renaissance stage, we find the special properties (O2) of place, situation, and quantities cast as substances. Lines (O2) are now attributing points to one another in order to specify themselves. Euclid’s geometry still performed clauses, i.e. specific motional figures (O1). They attributed elements, for example lines, to one another, so as to generate new motional figures. With Euclid, it was still “a point is that which has no part.” 31 Now, lines are attributing values to one another, calculating them rationally, utilizing the particular motility of numbers against magnitudes,32 to test the ratio, the proportions of the old 30 Kruft, ibid., 28. 31 Euclid, The Elements: Books I–XIII – Complete and Unabridged, translated by Sir Thomas Heath (New York: Dover, 1956): Book I, Postulate I 32 Augustus De Morgan, The Elements of Algebra (London: Taylor & Walton, 1837).

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authorities, prior to acting, to building. The topoi of antiquity, the proportions, the buildings become pre-specific. They become negotiable, so as to enable the enactment of new stage plays. Thus originates the architectural model, thus representation in perspective. Thus beckons Descartes’ analytical geometry; thus the bourgeoisie supplants the guilds; the clergy, aristocracy; thus the theoretical planner disunites from practical execution. And so on. It is striking, for example, how Palladio in his Villa Rotonda adopts the geometrical motions and symmetries of the scholastic models in the mounting of his figures (O2) and through his Ichnographia (I)—we’ll grant him an ‘I1’ for this projected imitation—and how, in the gap of the new figurativeness of Orthographia (O2), he sets up urban Roman figures of power as upright persona. These Roman figures are no longer words, but they embody the virtuality of word generation. Talking figures. They are no longer articulated by the scholastic order, but impersonate it; they have ingested scholasticism, as it were. And now they stand on stage, projecting the old scholastic order into the world with their scholastic linguistic apparatus. An unfriendly take-over of the old feudal and clerical order by the new urban one. We’ve met this shift in focus of concentration before, and called it (S1, O1, I1) > (S1, O2, I1). We can observe many such shifts in our culture. If we look at the plans of St. Gallen monastery of the late 11th century, or indeed the drawings of Honnecourt in the early 13th century: what a difference from Palladio. Although here, too, there are only lines and circles, these are contemplations, rather than projections. What then makes medieval monks on their stage copy books over and over again, build quadrate cloisters, and amble round well-tended gardens for centuries? We don’t know. We just note: they built cloisters. Sediments, today. We don’t know how they talked, we don’t know how they read, we just know how they wrote. Sediments, today. We can only bring these sediments back to life in a very limited way on our stage. We can perambulate around the cloisters, for example. But today, after the third lap at the latest, we get bored. Yet if we put the cloisters and their bodies of thinking on stage and let them converse with a Palladian body of thinking, the whole thing gets vastly more interesting. It’s unthinkable that Palladio would just keep on walking about that paradise. He wraps it up into the explicit interior of his villas, he takes it along in his projects and projections, he expresses it in his facades. Thus, if Palladio draws a square, he draws a different square from the monks before him. If Palladio writes a word, he writes a different word from the monks before him. Different worlds. There’s no chance of enacting them together on an analytical stage. The Cantor set would be approaching zero. On the analytical stage, we wouldn’t perform common roots, etymologies, epistemologies, lest we should fall into a mute aestheticized contemplation. Some are content to wander round the

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quadrangle forever. Others sit down right in the middle of it. A square is not a square, a word is not a word. Conversely, the logical quantifiers of Boole, Dedekind, or Peirce open up the situation on the algebraic stage. What we, in common with them, suggest is to take specifically positioned invariances and let the riches of our world talk on the algebraic stage. This approach is neither analytically rational, nor arbitrary, opportunistic, positivistic, or aestheticizing. It means to be challenging, fast, masterly. It demands charm, wit, ambition, skill, responsibility. This is how we can put worlds on stage, enrich our world. What we want to avoid, however, are generalizations. They reduce the one world as a quantitative picture into the accelerations of the channel systems of a projective world. Furthermore, we shall pay particular attention to the notion of abstraction. Abstraction is to mean that a notion stands in a concentrated relationship with a population of other notions. In terms of a counter concept, we shall promote that of concretion and take it to mean the transformation of a notion into a population of other notions. We shall call the corresponding processes ‘symbolizing’ and ‘articulating’. They shall be our means to assess abundances. So much about the algebraical approach, and the symmetries and invariances we posed. Now we are going to let our cultural history rotate. Spin at high speed, in fact, and see what happens. In a subsequent text, we will have space and time for more detail. VI

The Whole Point, O1 > O2

Let us begin (S1, O1, I1) with the perfused, mystical, very early representations of the visions of Hildegard von Bingen in the 12th century: the properties have not yet found a form, are not yet substantial, but they offer the fascination of meditation. In contrast to this the institutionalized, as we might say today, scholastic ‘mappings’ of about 100 years later: the myths are signified, for example by way of the square intertwined with the circle. Also, man no longer perceives himself as a second substance (¬Z, A), as unfounded and unexpressed, but is being extracted from the representation and replaced by the interplay of symbolized properties: founded and expressed (Z, A) without a symbolized external onlooker, who has obviously been moved from the pictorial plane to the reality in front of the picture. The skill of contemporary Honnecourt in dealing with properties (Z, A) might be of a similar nature. He draws labyrinths, perpetuum mobiles, as well as many useful machines. And he is involved in building gothic cathedrals. Their medialization of substance is not far from that of the Renaissance discussed above, not least because in the gothic period, too, it was the cities and townspeople who, during the long boom years of the 12th– 14th centuries, took position opposite the contemplative, epistemic

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order. A period that comes to an abrupt end in the second half of the 14th century with a catastrophe that wipes out swathes of the European population, while the orthodox order faces a crisis so real that it bears no comparison to anything we can imagine, or bemoan, today: in the North, the Reformation, and in Italy, the Renaissance. Leonardo now takes the human form and with it casts the old divine order, takes it over, as described above. With the massive successes of the great merchants, the Reconquista-induced sense of liberation and self-assurance—the crusades were ritualistic by comparison— and Columbus’ hoards of gold that represent a projective potential that doesn’t originate from the ancestral lands and that consequently leads to the abolition of the ban on usury, comes a boom in projective, increasingly descriptive modes of speech. This is the climate in which Alberti experiments (1477), in which Michelangelo articulates (1512; he uses the means of the corporeal order for articulating the phantasm of representation) that which Palladio will be able to stabilize architectonically (1577; he develops the vocabulary and the grammar for the visual architectonic order, which will swiftly differentiate through to our present day) and which Machiavelli, for instance, will stabilize politically (S1, O2, I1). VII

The Moving Point, I1 > I2

The counter-reformation, of course, is not long in coming and plays a virtuoso piece on the new stage. While Palladio’s figures still cast very simple geometrical movements on an epistemological ground, that ground itself now turns into a project —the Tractatus, the Ichnographia, this ground is re-written in the counter-reformation. Pope Sixtus V (1521-1590) rebuilds Rome in just five years, 15851590, by not only constructing a new church or some new compound, but by projecting axes and erecting obelisks at strategic points. Thus Sixtus, the gardener, folds and wraps Rome into a new order, cleanses the city for the first time, provides it with water again and, taking off from these strategic points, lets it grow into the planned directions. While the Renaissance was about making the subject O2 ‘mobilized’ by S1 along I1, now I2 is being made ‘mobilized’ by S1 on the moving O2. The epistemological Renaissance interplay I1 is being projected into the moving O2. The point turns into a baroque pearl. The natural-number space, the epistemological, geometrical interplay of I1, is being turned by I on O into an upright rule, is being orthogonalized, becomes I2.

And a supremacy over the figurality of the interplay is what baroque is about: individual faces enigmatically distorted, individual motions focused, from the dark, mysterious ground, onto one sole, vertical, bright, central vector. The folds of the garments detach from the figures. The

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motion of the medium explodes the frame 33… Who yields power over the properties, their potentialities? On the one hand the power of wild speculation (tulip mania 1637), on the other hand the concentrated baroque interplays—concentration/inclusion, expansion/explosion. The skills and the might, the ‘management’—of multiplication, integration, differentiation under projective, illustrative control—that they generate become extraordinary: a self-projective orchestration of the projective subjects into ever diminishing size. The point turns into a baroque pearl. And at the end of that era, there is no outcome in the exhausting power play between the cities, the church, and the aristocracy. Just productivities and differences. The Peace of Westphalia, 1648: pragmatism from the projective difference of baroque pearls. An open contest over the most attractive performance, in front of the unchanged scenery (S1, O2, I2). VIII

The Mensurated Point, S1 > S2

Only now, during this phase of the expansion of language games that exhaust themselves in an open contest, do we get, in 1637, along with Descartes’ offensive counter-reformation, analytical geometry, the succession of the primacy of epistemological geometry by the new primacy of the difference of numbers (pure formality with Leibniz, pure functionality with Spinoza), rational numbers, a modified Skenographia (S2). Now a number is the difference of two baroque pearls, and no longer a contemplative circularity. In 1673, Leibniz develops an angled line into a sprocket wheel, to execute calculations based on the interacting movements of such wheels. The stage has changed. The mutually stable epistemological reflection of Ichnographia (interplay) and Orthographia (upright rule) allows us now to abstract Skenographia (S) from the geometrically skillful perspective (S1) into the perspectivity of two numbers (S2). And here we are, with two infinities: the arithmetical infinity in the coordinate system, the rational-number space (I2), and orthogonally the geometrical, upright projection into the infinity of the natural-number space (O2).

Now the object of mensuration is no longer perspective. It is the perspectival possibility that is now being measured. And it is termed ‘function’. Louis XIV (1638-1715) dismisses Bernini, the papal builder of St. Peter’s Square, gently but firmly, because he is not up to meeting the demands of the court ladies’ functional requirements and the standards of comfort expected at Versailles. Inwardly, perspectivity is in demand; outwardly its possibilities are measured in absolute terms. Which is why, in such a unique gesture and in the face of Parisians’ 33 Gilles Deleuze, The Fold: Leibniz and the Baroque (Minneapolis: University of Michigan Press, 1993 [1988]): pp. 197.

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resistance, the young king builds Versailles on the interface between city and countryside, as an abstraction from everything. It proclaims power over the differences of the pearls and their ability to express themselves. Therefore, too, is the Würzburg residence (1719-1744) by Neumann inwardly ‘perspectivistic’, and outwardly ‘mensurative’. Kant’s transcendental reason (1781) is measured in an idealized space and time. Numbers, things, persons become alive, and this aliveness is being measured. The stage is rebuilt. Skenographia is no longer perspective, it is analytics. In 1702, wheat prices are released from the aristocratic, territorially defined order, and a series of rampant famines can finally be brought to an end. In the medical field, vaccinations bring the plague under lasting control by measuring it before a new outbreak…—invisibilities in the old epistemic orders. Witchcraft, and the basis for the new, much more powerful diastemic orders. Perspectivity becomes a comfort system, in the difference of numbers. They measure comfort, becoming its infrastructure. The numbers are pre-specific, a not yet perspectively projected geometry: potential geometry. The potential of comfort. That’s how we want to see analytics, and arithmetic. Quite contrary to today’s view: analytical geometry is not geometry. Analytical geometry is calculating with numbers, is arithmetic, is mensuration, is infrastructure for the co-ordination of rendering into geometrical movements, i.e. putting it into difference, in specific places. For the first time calculus as we know it today becomes possible. We are becoming very fast: emerging along the orthogonal vector from the baroque pearl of the one point (integration), gaining an overview over the other pearls that are abstracted into numbers, while swiftly reaching another place through calculations (diastemic order), now differentiating again into epistemic differentiation of the baroque pearl at the other place. Hence the performance of diastemic arithmetic and analytics—finding shortcuts between A and B, as channels in the epistemically invisible. We easily forget these two planes, treating numbers as geometries on the same stage, and squander the potentials, the rationality of this difference. A natural number is part of the epistemic order, a rational number of the diastemic one. These are the first two infinities. Our concept today of construction takes place on the level of rational numbers and therefore is infrastructure, orthogonal to the perspectival epistemic concept of space. Perspectival space conception is rendering a body, comfort, a baroque pearl. Natural numbers are orthogonal to rational numbers. It is too simplistic to view numbers as equal to numbers, to treat 3.0 (diastemic) as equal to 3 (epistemic). 3.0 is a channel, 3 is a thing. I like these symmetries of abstract notions. Now, we can look further. What then did happen during that time? Euclid’s first axiom still says: “a point is that which has no part.” Now, the difference between two numbers is understood as elementary.

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Points, lines, circles are now being ‘recounted’, for staging. Monads (Leibniz) or modi (Spinoza) now become elementary. New forms develop on the new stage. Visibilities emancipate from Plato’s elements and Euclid’s motions. In the visibilities of difference we can now talk about, and deal with, things that formerly were fantastic, that now can be turned into a project: Locke (separation of powers), Hume (empiricism—world and perception), Newton (new pragmatism in the old order), Leibniz (idealism in the figurative order), Spinoza (idealism in the functional order): this new, enlightened order abstracts from city/estates, and land/gentry. What we now have are planned, mapped projects that are calculable, ‘recountable’. And now publicity-minded groups make their entrance: scientists, journalists, authors; critical ‘regents’. Disputes are located in the scientific area. We have a bourgeoisie, the economy, medicine, comfort. Comfort systems. Networking. Gabrielle Émilie Le Tonnelier de Breteuil, Marchioness of ChâteletLaumont (Paris 1706–1749 Lunéville) translates Newton. While Rome formulates, with St. Peter’s Square, the absolute urban claim to power (people, bodies), Versailles formulates the absolute, elementary interface between town and countryside (all things are being put into difference, Versailles as controller of that difference, the absolute measure. Resources – lines – infrastructures). Meanwhile in a leafy Bath, a club of moneyed Englishmen who have grown globally rich a in worldwide competition, meet and spur each other on in their dealings (values) in a landscape that is considered to be motile. During that time, competing systems of measuring visibility are being developed that are highly efficient thanks to their claim to absoluteness. Equality. Fraternity. These are Euler’s new lines. Kant’s transcendentia. Ichnography rewritten. Skenographia is no longer the subject in Euclid’s space; skenographia is now analytics. IX

The Rational Point, O2 > O3

Whither now? Let’s start with the hot air balloon of the Montgolfier brothers, on 19th October 1783. Let us imagine that everything we just discussed regarding Versailles, or Rome, or Bath— all the mensurations and encapsulations—that all of it got encapsulated in the balloon and forced from the horizontal into the vertical direction. A vertical rocket-Versailles, the palace in the blast-pipe, the intersection between the measured within and without, town and countryside. Town and countryside no longer: the words, analytically, geometrically measured, or indeed re-counted, are now single properties, temperatures, densities, measured and set into the perspective of difference, into speed. Steam into motion, coal into energy. Watt the rocket-builder; Durand develops ground-breaking (I) rocket buildings (each knot of the typologies/genealogies a measured baroque pearl of

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double perspectivity), Schinkel conceives idealistic upright (O) rocket buildings, the encyclopedists provide the rocket fuel; Boullée designs rocket arsenals. Lagrange supplies the mathematics for motility, for the fuse, shakes the rocket until it ignites. Fichte is a self-igniter, with Kant as the blast-pipe, Pestalozzi the flying instructor, Goethe and Schiller brilliant flying champions, Mozart the pushed prodigy with his jet music. Popular, vulgar, speedy, breathtaking… For the first time, the Montgolfier flight displays this world from above. Properties pervade the words, numbers the figures, steam the machines (they mutate into apparatus), knowledge the people (they turn into citizens), the balloon flies over cities (they turn into states) and countrysides (they turn into landscapes). Then, a few years later, in 1789, the revolution of the rocket men. Every upright citizen (O) a rocket-Versailles. A legal system. Liberty. Equality. Fraternity. While in England rocket men start their industrialization with rocket machines, Napoleon conducts rocket men all over the continent from above. Until the self-sustaining fuel runs out and he has his budgets cut: he loses steam and the bubble bursts—wonderfully described by Thomas Robert Malthus in An Essay on the Principle of Population (1798), and re-edited, along a largely unchanged frame of thinking, in the Club of Rome’s The Limits to Growth, in 1972. What just happened? It is important to me that we find the invariances in abundance. If we were in pursuit of forms, such representations would be boundless and presumptuous, reductionist in their perception and unrestrained in the speed channelled by that reduction. A rocket embodiment, what else. And that’s precisely what we don’t want. Which is why I emphasize again the mutual orthogonality of our phases of the genealogy of the articulable. The traces of the properties, of the ‘rockets’, precisely aren’t traces of numbers any longer, of baroque pearls on the coordinate system of the analytical scenery. We are going to call the rocket-points on the coordinate system ‘substantial’ because, in the sense of the primary Aristotelian categories, they belong ‘not to the underlying’. They are ‘expressed’ or ‘non-expressed’ upright individuals or species. In accordance with Vitruvius/Alberti, we called this invariance by which we focus our interest ‘orthography’ (O). The columns, facades, windows, doors of a building in this sense are substantial and are, in classicism, indeed reformulated with great precision. Because the new points are ‘not underlying’, their driving force is not visible in Ichnographia (I), in front of the Skenographia (S) of analytics. These special constellations of (S2 | O3 | I2) describe classical phases, such as we were already able to describe in the Renaissance (S1 | O2 | I1) in front of the syllogistical Skenographia (S1). Yet, the driving forces are still analytically visible (I1), they are still represented in the interplay (I2) in front of an analytical scenery (S2). We shall call this special constellation (S2 | O3 | I3) ‘manneristic’. We already met

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it when talking about baroque (S1 | O2 | I2). We’ll separate it neatly from the classicistic (S2 | O3 | I2) previously referred to. Against the security of analytics (S2) and of the substantial point (O3) we’ll find it easy to formulate new interplays (I2 > I3). Now the substantial points are no longer geometrical elements (O1) or baroque pearls (O2), but energetic propelling charges (O3). And the interplay (I) is no longer one of differential logic (syllogistic – I1), or of differential calculation (I2), but one of differential transformation (I3). In the 19th century, this transformative interplay of driving forces (I3) becomes familiar and is exercised in its innumerable forms. X

The Moving Point, I2 > I3

Everything wants to fly. William Turner paints, a thousandfold and almost journalistically, the dream of a weightless energetic fusion. And as in his pictures, steam engines waft about the land. Not thresholds, not projects, not motion: energetic streaming becomes the dominant feature. In the fast-expanding grid of these transforming energetic streams, the old territory gets potentialized into a resource. Industrial cities give root to these potentialities. Nation-states stake out the fields of potentialities. The Panic of 1857: The first great blowout of global potentialities. The British in particular suddenly show up in the oddest places. As if from another planet, they arrive and do strange things; look on, slightly bored and aloof, observe what’s there, and ponder what could be done about it. And then do nothing. At first. Tourists. The rich daughters of British ‘mighties’, in particular, turn their backs on marriage and discover the Alps in winter. Lying out on the terrace surrounded by the snowy peaks, they bask in the sunshine, doing nothing. At least for the time being. On the continent, priorities differ only slightly. As Wilhelm von Humboldt puts it: “Transforming as much of the world as possible into your own person is, in the highest sense, living.” Or: “The true purpose of man—not that prescribed by ever shifting inclinations, but by eternally immutable reason—is the highest and most proportionate development of his powers toward one whole. First and indispensable prerequisite to this end is liberty.” His brother Alexander, meanwhile, gathers and examines meticulously anything he can get his hands on during his extensive travels. Wilhelm, in turn, examines with committed self-transformation his own language in On Language: the Diversity of Human Language-Structure and Its Influence on the Mental Development of Mankind. Darwin, through population-related dynamics, examines species that do not exist. Medicine fights diseases whose existence is only probable. Hygiene, travel agencies, kindergartens. It really gets quite breezy, when we all fly: Joseph Paxton, with his Crystal Palace, manages to put up, at vertiginous speed and in luminous boundlessness, a no-longer-building, a climatic mega-space for negotiating

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industrial potentials. Eiffel and Boileau, in Paris, build the first department store, Le Bon Marché. In a combination of bright skylights, light iron gangways, slim girders and ornamental forms, the architectural bodies dissolve in airy logistics. “The 19th century turned bold while nobody was watching,” Giedion writes about construction behind this scenery of a dissolution into light. Eiffel builds, without scaffolding, a free-standing tower such as the world has never seen before. Up into the air. Without any tangible purpose. Whereas for Hegel, weaver of transformations, things are getting more serious: “The State is the reality of concrete liberty.” Cantor packages the infinities, Marx dispenses them. Meanwhile in Chicago, Sullivan takes the Midwestern wheat glut as his cue to pile stores on top of each other and turn them into skyscrapers. Gaudí naturalizes emoted potentials as a suspended model into the Catalan ground, by way of elementary, mythically transformed figures. Ludwig II of Bavaria dreams up Neuschwanstein; his father creates, against massive resistance from the city’s population, the Technical University of Munich. His friend Richard Wagner, in Tristan und Isolde, lets harmonics explode in such a way that nothing can ever be the same again… Fourier the transformer; Maxwell thinks up a fantastic 20th century infrastructure, Werner von Siemens builds it; Boole amalgamates analytics into 0 and 1, Hilbert symbolizes the extant mathematical world into algebraics; modern chemistry symbolizes matter that is not yet there… Things threaten to dissolve, in accelerating self-transformation, towards entropy. Everything flies, anything can transform itself into anything else. The world is detached from its ground, has become atmospheric, climatic. The analytic double points, the self-projective pearls, the linear analytic opening-up of the point with Descartes, Newton, Leibniz…—they all dissolve in diffractive patterns. Analytics and numbers have exhausted their possibilities. Symbolic algebra integrates logic, analytic algebra, and arithmetics. Points are being renewed: non-linear probabilistic openings. (S2, O3, I3). Impressionism. The time is ripe for the next transformation. But before we proceed into our own era, S2 > S3, let us briefly summarize. We described the stage thus: O : Orthographia – Elevation – The Actors I : Ichnographia – Ground Plan – The Play S : Skenographia – Perspective – The Scenery.

We ranged the times into: 0 : Sophists 1: Antiquity and Scholasticism 2: Modern Age 3: Enlightenment 4: Today

And we repeatedly cautioned against the view of linear-energetic sequences, stories, figures, or reduced series. We much prefer the idea

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of diverse stages relating to different times. The actors have different identities in different eras: Settlers (O0) – Merchants (O1) – Seafarers (O2) – Pilots (O3) – Astronauts (O4)

Or: Friend (O1) – Person (O2) – Individual (O3) – Identity (O4)

The play, too, receives different identities in different eras: to talk (I0) – to order (I1) – to move (I2) – to balance (I3) – to appraise (I4)

As does the scenery: myth (S0 – syllogistic/order (S1) – analytics/motion (S2) – logic algebra/balance (S3) – symbolic algebra/constitution (S4)

To exemplify what is being generated with the help of the stages, the simple case of the line: A line as a friend (O1) is the way covered (I1) between two points on the ordered earth (S1). Merchant. A line as a person (O2) is calculated motion (I2) on moving water (S2). Seafarer. A line as an individual (O3) is a balanced, energetic tension (I3) in the climate of the (interliked) air (S3). Pilot.

And what about the next step? A line as an identity (O4) is a fertile constitution of indexes in the available universe (S4). Astronaut.

And: An identity (O4) becomes, via a fertility in the availabilities (I4), an individual (O3). The individual (O3) becomes, via an equilibrium in an energetic field (I3), a person (O2). The person (O2) becomes, via a position in a motional system (I2), a friend (O1). The friend (O1), via a position in a topos (I1), is real.

It would be reckless to permit shortcuts here: it’s a long way, across the various stages, from a friend to a person to an individual to an identity; or from symbolic algebra (S4), via logic algebra (S3), via analytics (S2) and syllogistic (S1) to myth (S0), and back. Or more directly: the steam engine cannot be described syllogistically, in the orders of friends. Protective vaccination cannot be narrated analytically, in a person’s motions. Mobile telephony cannot be comprehended logically-algebraically, in individuals’ balances. It’s a long way, out and back, and shortcuts must be avoided. It’s not about progress: it’s about different worlds. An everyday example to show how ingrained these reductionist and impoverishing patterns have become today: National Geographic’s films on mega-factories. ‘Behind the scenes at Coca-Cola’. We’re shown fast, massive machines. We come face to face with a ‘natural

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phenomenon’ called Coca-Cola. Untold numbers of bottles, dizzying speeds. Impotent, we gape, as at the Niagara Falls. The might of Coca-Cola is visualized through technics, and technics through nature. Outrageously totalitarian and outrageously boring. And all the while Coca-Cola is about our idea of food, and food about our idea of our body. Here, Coca-Cola is a genuine pioneer. For Coca-Cola is no invention, no design. Just as mobile telephony is not design. Pasteurized milk would be a designed product: milk that keeps is balanced, hygienic, healthy, functional. Coca-Cola, however, was created as a brand. Coca-Cola is an identity. Its objective is not to be healthy or to function. That objective (equal to logic algebra) is being taken for granted and translated into the negative. Coca-Cola is neither toxic, nor spoilt, nor immediately unhealthy. That’s why Coca-Cola is neither healthy nor unhealthy. Coca-Cola was created as a brand, which holds out the promise of an identity. An identity that is welcome amidst the global mess: a welcome identity that is helpful in medializing the totalities of the functions and machines so lionized in National Geographic. With Coca-Cola we learn to play the machines. This is Coca-Cola, not a shortcut to plant engineering (which indeed would also have to be introduced as an identity and as a brand, so as to liberate it from logic algebra). Returning to our summary: we described our cultural history as an overlap of stages in which Skenographia, Orthographia and Ichnographia develop in a staggered relay, drive each other mutually and amalgamate their respective know-hows and riches, comparable to an Archimedean pump or to the phase delay of electro-magnetic waves. Sophists (S0 | O0 | I0) The settlers talk to each other within the myths Idealists (S0 | O1 | I0) The merchants talk to each other within the myths (Plato) Empiricists (S0 | O1 | I1) The merchants self-organize within the myths (Aristotle) Scholasticism (S1 | O1 | I1) The merchants self-organize within the order Renaissance (S1 | O2 | I1) The seafarers self-organize within the order Baroque (S1 | O2 | I2) The seafarers move within the order Absolutism (S2 | O2 | I2) The seafarers move within the motion Classicism (S2 | O3 | I2) The pilots move within the motion Romanticism (S2 | O3 | I3) The pilots equilibrate within the motion Generalism (S3 | O3 | I3) The pilots equilibrate within the balance Redesire (S3 | O4 | I3) The astronauts equilibrate within the balance

Xi

The Mensurated Point (S2 < S3)

Shall we explicate our own era in this schema? We want to break open the shortenings of our time, cultivate them. It was easy enough to

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confront bygone eras with our alien body of thinking. Very few people are informed enough to feel challenged or concerned. But after having given our new body of thinking stability within the past, we shall now let it speak in our present time. And yet, we find ourselves immediately startled and challenged by its unfamiliar view. Let us be good hosts, and see what this stranger has to tell us. But first, let’s have a look at the symmetries-deduced 20th century schema: The mutually stable diastemic reflection of Ichnographia (Interplay) and Orthographia (upright rule) allows us now to abstract Skenographia (S) from the perspectivity of two numbers (S2) into the probabilistics of four numbers (S3). And we now deal with three infinities: the arithmetical infinity in the coordinate system, the rational number space (I2); orthogonally to it the geometric upright projection into the natural number space (O2); and the balanced algebraic infinity of the complex number space (S2).

And: The modi / imagination / intellect now become sacred. They rule the significance of the values. Interplaying with the articulate modi (logic)… The erstwhile sacred property now turns into an inter-articulation of modi, so as to influence, through their values, the values of other properties – god is now modus – diabolic are the values – Nietzsche the modalizer…

For example, economy: Adam Smith writes about wealth (S1), Stuart Mill about political economy (S2), Keynes about employment (quantity of work), and Friedman about money supply (S3). Money supply, or rather money supply policy or, actually, the politics of money supplies (S3), provides more political leeway in a secure economic framework (S2), generates economic wealth, and thereby generates greater individual freedom of movement for people. This is how we would view liberalism (S2) and the somewhat unfortunate notion of neo-liberalism (S3). Unfortunate, because neo-liberalism ought to be about labor and money-supply politics rather than economics of capital (S2). ‘This conceptual shortcut of 19th century economics and 20th century capital produces the unspeakably corrupt and tyrannical—not to say fascistoid—conditions found in so many parts of the world,’ says our guest. Accordingly, the energy question: energy is either possessed in the form of wood (S1), generated from resources in the form of coal or petrol (S2), or produced through photovoltaics (S3). Therefore, energy is a rare resource and capitalizable merely in the diastemic body of thinking (S2). Today (S3) it shouldn’t be all about capitalized and fair energy distribution, but about energy supply politics in an environment of basic abundance. And that’s where today’s Greens and ecologists, referencing their work to the scarce resources typical of the 19th century diastemic body of thinking, turn up in uneasy symmetry with

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Fig. 1 Oskar Schlemmer, The Triadic Ballet 1916.

Fig. 2 Busby Berkeley, Footlight Parade, 1933.

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Fig. 3 Jaques Tati, Playtime, 1967.

Fig. 4 Quentin Tarantino, Pulp Fiction, 1994.

Fig. 5 James Cameron, Avatar, 2009.

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those neo-liberal excesses that they so rightfully bemoan. ‘Yet, caught up in this symmetry they aren’t providing a solution, they are part of the problem,’ says our guest. Or the media: Marshall McLuhan who, contrary to general perception, does not conjure up the ‘Global Village’ of cybernetics, but much rather uses this term to strongly and very clearly warn against dumbing down, and dumbing down in the media, calls the media the Fourth Estate, which by necessity can only deal with bad things and therefore must be diabolic. Because, according to McLuhan, their power cannot be accommodated within the nation-state’s trinities of liberty, fraternity and equality; or executive, legislative and judicial powers. Only bad news is ‘good’ news. It is an inversion from the shadows of the enlightenment. No longer outgrowth of the refinements of the enlightenment, of scientific analyses, of artfully developed styles or industrial production. Devilish 34 stuff that upsets the make-up of classic modern times. For Immanuel Kant it was still about a Critique of Pure Reason (1781); for Georg Friedrich Hegel about the Science of Logic (1812-16), and for David Ricardo about the Principles of Political Economy and Taxation (1817). It was always about systematic procedures towards answerable refinement within a frame-setting stability, just as in Mary Shelley’s Frankenstein or The Modern Prometheus (1818). But already with Karl Marx, the pitch changes: A Contribution to the Critique of Political Economy (1857-58). Here the framework itself is being differentiated, and mapped for greater clarity. These ground plans reek of the mental maps of a dark and damp London, with which the ingenious Sherlock Holmes chases criminals, or which journalists use to sniff out bad news and—hiding behind their professional ethos—protect their sources. Bram Stoker’s blood-sucking Dracula (1897) as an inversion of Shelley’s apparatus Frankenstein. These mappings are not part of the nation-state framework, they are maps, reports, technical illustrations about the nature of the prevailing order, a psychoanalysis of nationstate-ism, a portrait of naturalness. By this inversion of nature Nietzsche generates tragedy from the spirit of music (1872); now the exiled Zarathustra speaks to us (1883), and there arises before our eyes a Genealogy of Morality (1887); all of it driven by our technical know-how: electric power, photography, telegraphy, radio, cinemas… Soon a startled Europe, and particularly Germany, tries to fold it all back into the old order. To territorialize 34 The English expression ‘symbol’ goes back to the Greek word σύμβολον (sýmbolon), a derivative from συμβάλλω (symbállō ‘join together’). The sýmbolon was a token by which two parties (friends, business partners) made sure they were able to recognize each other, or representatives of each other’s party. To that end, a bone or earthenware object was broken in half, and each of the partners kept one of the parts. When meeting again, the legitimacy of the parties could be verified by joining the fragments. From which there evolved the notions of ‘sign’, ‘mark’, ‘tag’, ‘proof’, ‘agreement’, ‘identification’, ‘password’, ‘code’.

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it, in the orthodox, nationalistic way. Thus driving themselves and the world into the great wars. And only thereafter, cleansed as it were and somewhat naïve at first glance, McLuhan’s The Medium is the Message (1967), or Ernest Bloch’s Grundrisse einer besseren Welt (1954–58). And what about architecture? The architect turns into a world builder, into a stage designer (S3). Le Corbusier’s Plan Voisin for Paris, Buckminster Fuller’s Dymaxion domes, and his Operation Manual for Spaceship Earth (1968), Oscar Niemeyer’s draft for Brasilia in the middle of the jungle: the all-potent—world builder—breaking open the old order, diabolically negating, positively articulating the diabolical. Carried by the media, expelled from the old order. How else is one to globalize technical know-how without becoming definite, imperial, or capitalistic, as determined by the old systems? One answer is the International Style, an architecture that makes it possible not to be directly concerned by these world designs. An architecture in which I can breathe, in which I don’t have to deal existentially with the Irishman, the Russian, the Catalan, the Japanese, the Chinese, the Nigerian…— and yet am still able to live on the same, interlinked planet. How else would it work, initially? Without these abstractions? Without the battle of an Adolf Loos against ornament in all its refinement? And then, barely 100 years later, towards the end of the 20th century, the mannerisms of the international, on the technically and culturally secure basis of a planet that by now, in terms of media, is thoroughly globalized. What else? Architecture has become decadent: a non-standard architecture,35 parametrism,36 geometrical nodes,37 the ‘chancelike nature of city life’ 38… In the post-modern age in particular did we learn explicitly to symbolize everything: the old worlds have directly become the new stage sets (S3). Diastemical settings for a choreostemical play. And this is how our guest describes the various phases of stage design in the course of the 20th century: Agility. The experimental phase. The Renaissance as the setting. Picasso, Gris, Delaunay… Gropius, Moser, May, Melnikov, Le Corbusier, Mies van der Rohe… They operate with elementary symbols as negations of the diabolic. The components of their architecture are elemental and friendly. They encapsulate and mark naturalities and perform them on the new stage. Analyzing them from an old world point of view would always be a diabolic investigation. But they are ousted 35 Non-standard Architectures, Exhibition, Centre Pompidou, Paris, December 10th to March 1st 2004. 36 Patrik Schumacher, Parametricism as Style – Parametricist Manifesto (London, 2008), www.patrikschumacher.com/Texts/Parametricism%20as%20Style.htm. 37 e.g. UN Studio, Mercedes Museum, Stuttgart, 2006. 38 Rem Koolhaas, Delirious New York: A Retroactive Manifesto of Manhattan (London: Academy Editions, 1978).

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↖  [Fig. 1]

P. 60 Oskar Schlemmer, The Triadic Ballet, 1916.

↖  [Fig. 2] P. 60 Busby Berkeley, Footlight Parade, 1933.

↖  [Fig. 3] P. 61 Jaques Tati, Playtime, 1967.

↖  [Fig. 4]

P. 61 Quentin Tarantino, Pulp Fiction, 1994.

and concentrate on elemental properties: coloration, figurativeness, materiality, motility… —these abilities are being directly articulated. They are no longer products, but articles. That’s why the simplicity of Sullivan’s “form follows function” is deceptive and must be read with caution: the articulate form is cleansed of all the rigors of functional production. Forms are driven out of functionality, are being born from functionality. Ornaments are still being produced and consumed. The forms of the Weissenhof Estate (1927), on the other hand, are pure articulations beyond the adversities of industrialization and capitalism. They are socialized in a new world. Dynability. The test phase. Baroque as the setting. The energies of the elemental articulations are being mutually measured and socially bundled. Unfortunately, these social bundles are all too often tied back into the diastemical and nation-state-like, into the familiar nationalsocialistic—and with catastrophic consequences. The notion of national socialism is a contradiction in terms: the choreostemically social cannot be bound up as though diastemically national. Whatever is not part of the order, is devilish. In the 20th century there is no way around dancing with the devil; but if—as in the illustration above—we trust the functions instead of the cleansed, abstract forms, things get really messy. Substantiability. The cultivation phase. Enlightenment, classicism as a symbolic setting. Something like a measuring system for the development of social sheafing of symbols is being articulated. The talk is of structuralism, existentialism, or a ‘linguistic turnaround’. The quasi homoerotic movements of Fellini’s figures in Rome. Konrad Wachsmann’s or Fritz Haller’s lonely general nodes that, while all-powerful, are nothing because they have not yet managed to find themselves. Andy Warhol’s “everybody’s always creative”, drugs, music, cybernetics. Sowing the seeds of globalization. Generability. The harvest phase. Romanticism as the setting. Energized nodes grow along coded structures. Noam Chomsky’s cybernetically linguistic anchorages proliferate everywhere. The Greens. Material, form, facade, nature. Imaginations turning explicit. Creativities dreamt in the 19th century explicating themselves in applications. The power of marketing, of brands. Hadid’s brachialia. Green megacities. The post-oil city. The symbolizing of natures so as to be able to speak of new, artificial natures. Globalized markets. Containers. Logistics. NGOs. Empathy. Sustainability… Everything being symbolized with everything. Symbolized catastrophes. Unattainable luxury goods. The new high rises de-materialized. Trees. In Singapore, a gigantic pool 200 meters up, on top of a casino. Hubs of global networks made of indexes growing on the energetic generic nodes of nation-state infrastructures. Agility, dynability, substantiability, generability. These notions outline the 20th century vocabulary of the contemporary scenery, of our

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Skenographia (S3). They delineate the Third Infinity of the complex numbers that has synchronized with the infinities of Ichnographia (I3) and Orthographia (O3). In the laboratory, symbolizing the Renaissance, 1900-1930; in field tests of social bundling, symbolizing baroque, 19301950; in terror of oneself, symbolizing the infrastructures and the genealogies of the enlightenment that relieve us of our pains, 1950-1980; and in the general vaporizing and the didactics of the balanced global networks, symbolizing romanticism, 1980–2000. (S1 | O1 | I1) ( ¬Z, ¬A) e.g. individual man Socrates, the first substance ( ¬Z, A) e.g. the species man, the second substance ( Z, ¬A), e.g. individual property ‘white’ or ( Z, A) e.g. property as species ‘whites’.

↖  [Fig. 5]

P. 61 James Cameron, Avatar, 2009.

(S2 | O2 | I2) ( ¬Z, ¬A) e.g. the individual property ‘Celsius’, the first substance ( ¬Z, A) e.g. the species property ‘temperature’, the second substance ( Z, ¬A), e.g. individual value ’26’ or ( Z, A) e.g. value as species ‘dx | 26.0’. differential, integral.

(S3 | O3 | I3) ( ¬Z, ¬A) e.g. the individual value ‘Switzerland’, the first substance ( ¬Z, A) e.g. the species value ‘Swissness’, the second substance ( Z, ¬A), e.g. the individual index ‘http://www…’ or ( Z, A) e.g. index as species ‘URL’. Universal Resource Locator.

XII

The Complex Point (O3 > O4)

Now that everything and nothing is sophistically articulable, it is time to find stabilities, form identities in these basic riches and this symbolic force. It is time for a new literacy. Now that we stand on this new choreostemical stage, how do we talk, how do we act? What is an actor to say, if they can say anything, talk to any master, yet don’t know what to say? When the symbolism of joining the broken rods as a reductional sign in its logical possibilities (Frege) in the trivial (Gödel) is exhausted, has become barren? When we don’t know how to join up the many rods of possible links in the internet? When everybody can be everybody’s friend? When our cosmic, analytical, scientific order is diabolically exploded? How to move in this disposability? When no longer things and properties, but values are substantial. When modalities are being attributed. When properties, potentials, territories, balances, powers are pre-specific. Just as when, in the Renaissance, nouns, things, topoi turned pre-deterministic. So we are no longer free to decide our actions. Nor to find out what we

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ought to do. When no longer nouns, nor adverbs, but—we suspect— verbs are at the core of our thoughts?… This text is a showpiece of this kind. As an architect, I have tied some rods into a fugue: an architectural example of building an identity. I have wrapped up indexes in a way that something interesting may result. With great respect, and with great impatience, I have bundled indexes from our world. That’s new in itself. It cultivates the generically available. It provokes speaking out in front of a socialized generic monotony and an authoritarian specific speechlessness. It’s a text for the cultivation of the articulable on a choreostemic stage.

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II Topologies of an Aesthetics of the Virtual in Music Michael Harenberg

I From Classical Composition to its Technical and Aesthetic Differentiation 70 — II Foundations of Pythagorean Space-Time Models in Music Theory 75 — III The Mathematical Indexing of the World in Music 78 — IV On Digital Beauty 81 — V Hybrid Spheres—Between Analogue and Digital 83 — VI Real Virtuality of Digital Composition 87 — IV Non-Linear Structures in Musical Reality 93

Michael Harenberg studied Systematic Musicology at Justus-Liebig University in Giessen, Germany, and Composition with Toni Völker at the Akademie für Tonkunst in Darmstadt, Germany. He earned his PhD in media studies from Basle University. Together with Daniel Weissberg, Harenberg is founder of the Bachelor Course “Music and Media Art” as well as the Master Course “Contemporary Arts Practice” at Berne University of the Arts, Switzerland (www. medien-kunst.ch). His theoretical and practical work focuses on digital soundcultures, experimental interfaces, compositional models of the virtual, the embodiment of electro-acoustic music in instrumental and installational settings. Harenberg is an internationally renowned musician, and plays in several musical ensembles. Among his publications are Virtuelle Instrumente im akustischen Cyberspace (transcript, 2012), and, together with Daniel Weissberg, Klang (ohne) Körper: Spuren und Potenziale des Körpers in der elektronischen Musik (transcript, 2013).

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Not just specific genres or styles, but music in general, is in the midst of a period of change that affects all areas. From fundamental questions of musical aesthetics— forms and structures, as well as production conditions, reception and distribution—all aspects are in motion, and thus in the process of departing from historical standards and rituals. One of the central causes is the crisis of the Late Romantic Period, in which the 350-year artistic era of classical composition began to stagger and be replaced by a new era of technical and aesthetic differentiation.

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I From Classical Composition to its Technical and Aesthetic Differentiation The systemic crisis that revealed itself in the Late Romantic Period had at its core the strict linearity of the one-dimensional, hierarchically-organized tonal system, which called for a new quality of material homogeneity beyond binary harmonic thinking in major and minor, consonance and dissonance, tonal and atonal, and so forth. The underlying paradigm of a teleologically understood time-linearity could not be overcome within the context of traditional tonal music, but only continually differentiated for 350 years 1. With Richard Wagner’s Tristan chord and its utilization, it became perceptible with a shock on June 10th, 1865, that the system of tonal functional harmony was formally collapsing. Similar systemic conflicts could already be seen in Hector Berlioz’ “Symphonie Fantastique,” in Scriabin’s Prometheus chord, and in the impressionistic polytonality and the new sound-dispositive of Debussy. This corresponds to Friedrich Nietzsche’s analysis regarding the transition from symbolic traditional composition techniques to compositional reference of real physical sound systems in Richard Wagner 2, who uses Herrmann von Helmholtz’s “Lehre von den Tonempfindungen” (On the Sensations of Tone) 3 for the material organization of his prelude to “Das Rheingold.” 4 During his political exile in Zurich, Wagner read of the harmonic laws as Helmholtz describes them, and decided to use this structure for the wave motif in the opening of Das Rheingold. Along with the ambiguous, functional-harmonic classification of the Tristan chord, the historical foundation of the structure of musical theory based on the functional harmony model in the Late Romantic Period was thus called into question as a whole 5. In the search for alternatives, an expansion of indirect parameters, such as tuning systems, sound, timbre and acoustics, were connected. Composers and musicians perceived this systematic break with tradition, beginning to seek new dispositifs of spatial forms of organization of time in the late 19th century that would be able to escape the aesthetic narrative of tonal linearity. This development was intensified by the crisis of the physical notion of space, and the associated successive separation of linear space-time 1

Cf. Michael Harenberg, “Von der Reihe zum Loop. Zur Aktualität des Serialismus in der Musik,” in Christine Blaettler, ed., Kunst der Serie. Die Serie in den Künsten (München: Wilhelm Fink, 2010): 115 – 142. 2 Friedrich Nietzsche, “Der Fall Wagner,” in Mazzino Montinari, ed., Kritische Studienausgabe, Vol. 6 (München: dtv, 2005), 24. 3 Herrmann von Helmholtz, Die Lehre von den Tonempfindungen als physiologische Grundlage für die Theorie der Musik (Braunschweig: Vieweg, 1865). 4 Friedrich Kittler, Grammophon, Film, Typewriter (Berlin: Brinkmann und Bose, 1986). 5 Cf. Konrad Boehmer, “Das Prinzip der Determination,” in Armin Köhler, Rolf W. Stoll, eds., Vom Innen und Außen der Klänge: Die Hörgeschichte der Musik des 20. Jahrhunderts (Mainz: Schott, 2004).

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concepts. In music, this question of modernity in accordance with the musical space of a work seemed to lead back to the symbolic space of the theoretical. Through new technological possibilities of recording sound and the synthetic creation of sound, the crisis of Euclidian, three-dimensional space led to a relative, multi-dimensional concept of space, as well as to artificial, composable acoustic spaces. Influenced by new perceptual qualities in the course of the development of media technologies such as the telephone and radio, as well as the new aesthetic techniques of photography, and especially film, the new conceptions of space fostered the notion of abstract space far beyond any physical existence, to the virtual, topological and topophonic acoustic spaces with which we operate today.6 In reference to these fundamental shocks, the Italian-German piano virtuoso, composer and theorist living in Berlin, Ferruccio Busoni, called most enduringly for new theoretical, instrumental and musical-aesthetic approaches in the early 20th century in his text, “Entwurf einer neuen Ästhetik der Tonkunst” (Sketch of a New Aesthetic of Music), which was dedicated to Rainer Maria Rilke and first published in 1907.7 First becoming famous as a child prodigy, Busoni was regarded worldwide as a cool and intellectual piano virtuoso, who as a composer reckoning with arrangements and transcriptions of Johann Sebastian Bach, sought a new music of boundless abstraction of sound and an uninhibited piano technique. In his comic-fantastic opera, “Die Brautwahl” (The Bridal Choice), after E.T.A. Hoffmann and “Doktor Faust,” he had already experimented with atonal systems that brought him to musical boundaries that were only to be overcome by Schönberg in the Second Viennese School. In his work, he analyses from his musical practice all the conditions that had impeded an adequate evolution of music in the Late Romantic Period. He includes among these the limitations of instrumental timbres above all, along with the harmonic and melodic tonal systems that could scarcely be further differentiated from an evolutionary view, as well as the limited complexity of Western rhythms. Widely discussed topics that Busoni takes up are the absence of microtonal systems and corresponding polyrhythms, and the overcoming of functional harmonic tonality. The demand for progress in instrumentation, on the other hand, was unusual, and described by his colleague, Hans Pfizner, with the premonitory dictum, “futurist threat.” Fifty years later, with the establishment of the electronic studio at WDR in Cologne, Herbert Eimert wrote retrospectively: “The idea of infinite sound material is an ancient dream of musicians. At the beginning of this century, Busoni and Schönberg 6 7

Cf. Michael Harenberg, Virtuelle Instrumente im akustischen Cyberspace. Zur musikalischen Ästhetik des digitalen Zeitalters (Bielefeld: Transcript, 2012). Ferruccio Busoni, Entwurf einer neuen Ästhetik der Tonkunst (Leipzig: Insel Verlag, 1983 [1907/1911]).

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occupied themselves with ‘free composition flight tests’—they collapsed at the bounds of instrumental mechanics.” 8 This is a rather one-sided analysis, which can only be understood before the backdrop of technological inventions with regard to music production and distribution. For Eimert, electronic music resolves serial, compositional-structural questions and makes available new sound generation methods that allow exact technical access to timbre parameters. For Busoni, novel electric instruments represent modern artistic concepts of form that should be drawn only from the sound itself, the sounding “material.” The inspiration for this analysis was an American’s electric play instrument that he had read about in a newspaper, and which he described as a “machine room.” The article, about a “New Music for an Old World.” Dr. Thaddeus Cahill’s “Dynamophone, an extraordinary electrical invention for producing scientifically perfect music,” from 1906, is remarkable in several respects. Using varying sizes of gears spinning over solid magnets, the 200-ton machine that the inventor Thaddeus Cahill had built in 1890 produced pure tones by simple induction that, as per Helmholtz, could freely be combined as fundamental tones and harmonics into pitches and timbres. The sound of this rather rough tone-generating model, as later refined by Hammond for his organ, could, however, not be amplified, and, with respect to the noisy steam engine mechanism, could scarcely be heard. The businessman, Cahill, made the best of it, and he played his instrument—also known as the telharmonium—over the telephone network, where he offered remote concerts for a fee. In the process, he was very successful commercially—after all the machinery had been transported by special train to New York—in the remote public address systems of hotels, bars and restaurants, to whom he offered an early variant of muzak. The attraction lay in the strange, never-before-heard sounds of this sophisticated electronic organ, which were supplemented by live performances and recordings. As a result of the technically-optimistic fantasies of early modernism and the imagination of Busoni (who was never able to hear this first electric instrument himself), it is the perfect instrument-machine that would have been able to satisfy all of his requirements in “scientific perfection.” “The connected space [by means of telephone cables] is magically met with sound; a scientifically complete, never failing sound; invisibly, effortlessly and tirelessly.” 9 In the process, Busoni fails to recognize the complex, early media network of the entertainment industry, consisting of electrical sound generation—broadcast via telephone—vocal and instrumental voices 8 9

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Herbert Eimert, “Elektronische Musik—eine neue Klangwelt,” lecture held at the Darmstädter summer school Music and Technics, Darmstadt 1951. Ferruccio Busoni, Entwurf einer neuen Ästhetik der Tonkunst, ibid., pp. 49.

Symbolizing existence — Metalithikum III

complementing the sound recordings that are transmitted with it, as a subset and constituent part from which the instrument is actually constructed. Fully in the European tradition, Busoni interprets the electric instrument paradigm in its potential for a new, progressive musical aesthetic, something which it never was in the USA or for Cahill. Nonetheless, Busoni unites two discourses with his proposition that had hitherto been strictly separated from each other. The physical and technical fundamentals of instruments and classification systems were long treated as strictly separated from aesthetic matters. As music was interpreted as a movement of the soul well into the Romantic period, there exist only scarce points of contact with technology and acoustics, as explored by Athanasius Kircher in relation to music. Until the 19th century, it was even overtly negated that the material side of music theory might have something to do with the genius of the artist whom the music first inspired, as it did not wish to remain a mechanical, dead construct. “If mathematics provides an indispensable key for the exploration of the physical part of musical art, then its significance may, on the other hand, not be overestimated in the completed work. In a tone poem, whether the most beautiful or the worst, nothing is mathematically calculated. Creations of the imagination are not arithmetic. All monochord experiments, sound figures, interval proportions and the like do not belong here; the aesthetic field first begins where the elemental relations have given up their significance. Mathematics only governs elementary matter for intellectual treatment, and acts hidden in the most ordinary of conditions. But musical thought is brought to light without it. When Oerstedt asks: ‘Should the lives of several mathematicians be enough to calculate all the beauties of a Mozart symphony?’ I admit that I do not understand. What, then, ought or can be calculated? Perhaps the vibration ratios of each tone to the next, or the lengths of the individual periods against each other? What makes a piece of music into a tone poem and raises it from a series of physical experiments, is free, spiritual, and thus incalculable…”.10 At the same time, there was a sophisticated technical understanding of a sonorous, parallel history. It is the long-unrecognized history of the ancient tradition of the automaton and instrument-machines. Ontologically, they were not brought into connection with the history and paradigms of classical music until well into the 20th century.11 10 Christian Friedrich Daniel Schubart, Ideen zu einer Ästhetik der Tonkunst (Leipzig: Reclam, 1977 [1806]). Especially interesting is the question of music’s formalizable elements, which the author deems absurd, yet which describes quite aptly our contemporary manner of working, with digital media. 11 Cf. Friedrich Kittler, “Der lange Weg zur Compact Disc,” in Sigrit Fleiß, Ina Gayed, Amor vincit omnia. Karajan, Monteverdi und die Entwicklung der neuen Medien (Wien: Paul Zsolney Verlag, 2000): 215-232.

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This knowledge of sophisticated mechanics was the result of a first Renaissance that took place not in Europe, but in Mesopotamia. Between the 9th and 12th centuries, Arab-Islamic scholars built machines in the tradition of Greco-Alexandrian and Byzantine culture that were artful, but above all, ingenious and even programmable.12 The mastery of Arabic engineers and scholars expressed itself in the forms of automatic calendar-watches and self-playing instruments as examples of universal and programmable machines. With knowledge of the original Arabic culture and writings, Athanasius Kircher wrote the celebrated “Musurgia Universalis” in Rome in 1650. In it, he describes, among others, the principles of universal-mechanical control and drive types in automated music machines—be it using water, air, steam or muscle power—as well as the sound generation of chimes, organs, imitations of animal sounds, etc., and mechanical programming and symbolic storage of sound via clockworks and rollers.13 Although he provides a perfect outline in the Islamic tradition of the mediality of the devices as energetic machines, mechanical media instruments and symbolic storage media, including musical aesthetics and compositional theory, the work remained largely ignored, especially in neighboring disciplines. Kirchers interdisciplinary writing, with the aim of a comprehensive treatment of the subject in all the realms of knowledge known to him, demonstrates the significance of music machines in connection with the changing understanding of artistic time and space relations in Early Baroque Europe, which in the process is impressively illustrated. “To be sure, the knowledge incorporated by rollers and pins, notches and springs into the music- and figure-machines of the manors and churches was not recognized as such; it was just music and sound, one of the liberal arts, from the quadrivium of arithmetic, geometry, astronomy and music, a building block of the Baroque world view. … But because the history of music machines in the 17th and 18th century remained in an almost pre-Copernican universality concept of classical cosmology, it is explicable that the famous calculators of Pascal (1644) or Leibniz (1673), with their invariable mechanical control techniques, never came into contact with Athanasius Kirchner’s ‘Musurgia Universalis,’ which had already formulated the principles of universal mechanical control of music machines in 1650.” 14 12 Siegfried Zielinski et al., eds., Allah’s Automata: Artifacts of the Arab-Islamic Renaissance (800-1200) (Ostfildern: Hatje Cantz, 2015). 13 Cf. Athanasius Kircher, Musurgia Universalis (Rome, 1662). 14 Wolfgang Hagen, “Die verlorene Schrift. Skizzen zu einer Theorie der Computer” in Friedrich Kittler, Georg Christoph Tholen, eds., Arsenale der Seele: Literatur- und Medienanalyse seit 1870 (Munich: Wilhelm Fink, 2001 [1989]), pp. 212.

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II Foundations of Pythagorean Space-Time Models in Music Theory With the evolution between 800 and 1200 CE from monophony to polyphony, music theory, in addition to ideological interpretations, also included aspects of a musical doctrine of artisanry. Polyphony brought a new complexity in the coordinating structuring of horizontally-temporal and vertically-harmonic developments, including all the consequences for the underlying compositional theories and tonal systems, as well as for the evolving instrument families and corresponding performance practices. For this purpose, symbolic memory systems had to be invented, which enable a written construction and handing-down of these new, diverse overlays of a structural and artistic poetics. The symbolic representation of storages, such as mechanical pin rollers, and especially in musical notation, was so strong that, from then on, these types of written music were considered works, even if they were not at all heard. Only now are these relationships in the exchange from the symbolic to the real—in the face of fundamental changes through digital technical notation systems—beginning to fundamentally change. With the differentiation of technology and music theory as an aesthetic foundation for material organization in three-dimensionallyconceived musical structures, the status of composition is also changing. With all distinctions and reinterpretations of different eras, styles and genres, theory has long remained in the status of an artistic propaedeutic. It gained a fundamentally new constitution first in 1914, with Hugo Riemann’s fragmentary “Ideen zu einer Lehre von den Tonvorstellungen” (Ideas on a Doctrine of How to Think about Sound) which, in recourse to Descartes’ 1618 “Musicae Compendium,” attempts to substantiate music theory through the structures of musical listening.15 According to Riemann, a theory of music is primarily a theory of musical consciousness—that is, a doctrine of the meanings of tones, which we actively interpret and grasp when listening. He is concerned with a musical epistemology, which does not accept any musical object as given, but understands it as a product of a subjective activity of cate­ gorical formations. Thus, one must inspect and understand the activity, from whose results a musical phenomenon arises. “It is not the actual, sounding music that is the alpha and omega of musical art, but rather, the novel presentation of the tonal relationships living in the musical imagination of the artist before recording, and arising again in the musical imagination of the listener.” 16 15 Carl Dahlhaus, ed., Einführung in die systematische Musikwissenschaft (Cologne: Gerig, 1971), pp. 107. 16 Ibid., 108.

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This called for a radical break with the prevailing understanding of theory in relation to aesthetic concepts, which thus far had sufficed for the pure conception and reproduction of a structural and tonal ideal. With the loss of certainties shaped by religion and the church, concrete models have been elaborated since the Middle Ages, which had to prove themselves in and to the newly-reorganized sound material. In order to be able to describe and store these models, the writing and experimental design environment of modern notation developed little by little. Further were abstract, but musical descriptions of form-algorithms, whose intervals, rules and codes had to be obeyed exactly with discipline, and at the same time artistically designed. In the process, the prevailing linear historical consciousness shifts—along with the role and function of composition and music theory—in favor of structural, multi-dimensional relations, as they were first heard in the masterwork of Claudio Monteverdi and Josquin Desprez. The written structures of aesthetic models are thus comparable to today’s algorithmic forms, as they are no longer just mappings of givens, but drafts for not-yet-realized projections of possible alternate versions. This great utopian potential was the basis for the turbulent development of theoretical forms and structures in music, until its systematic implosion in the late 19th century. The universality of proportions and division ratios mark the beginning of the attempt, attributed to Pythagoras, at extracting the vibration ratios and resonances of an entire cosmology from the string of a monochord, and to bring these sonorously into the world. With only the numbers one and two, the fundamental musical intervals may be ascribed in their pure pitches: octave (frequency ratio 1:2), fifth (2:3=(1+2):2) and fourth (3:4=(2x(1x2):(1+2)). The octave resonates at a division of the string in half; the fifth at 2/3 of the vibrating string, which corresponds to the arithmetic mean; and the fourth, in the golden ratio, corresponds to the harmonic mean at a vibration of 3/4 of the total length. At the very start, the physical reality legitimizes an idealized, generalized model of philosophical, aesthetic and ideological attitudes, before these become independent of the physical reality of the material world. The result of the proportions extrapolated and heard—1, 2, 3 and 4—depicts the central arithmetic space of Pythagorean theory: the Tetractys, which also symbolizes Euclidian geometry, and, for the Greeks, makes the entire space of the world represented in music able to be described, and thus conceived. Johannes Kepler deduces from this a universal Pythagorean character of world harmony, which formulates the entire cosmos as an ideal symbolic system oscillating in musical proportions, in which the planets represent the pitches, and their distances the meta­ phorically-interpreted intervals. In the much older myth of the marriage of Harmonia—the daughter of Aries and Aphrodite—to Cadmus/Cosmos, the singing Muses first

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appear in the persona and function of a “background choir.” They are daughters of Zeus and Mnemosyne, the goddess of memory, and serve as protective goddesses of the arts. This is the symbolic heart of the oldest known proclamation of the Pythagorean worldview, which, as a scientific ethos, led to Johannes Kepler, and reached at least as far into the history of composition as Hindemith’s opera, “Harmonie der Welt” (Harmony of the World) (1957). At the same time, this myth is among the most extraordinary ever. The mathematically-ascertainable octave—here conceived spatially—is defined both rationally and poetically with Harmonia, whose consonance is raised to a global principle and transfigured by the musical idea into aesthetic beauty. The strange tale is thus only told with the close interaction of scientific precision and artistic interpretation. The musical number systems and proportional relationships form the elementary basis in the Renaissance for novel abstractions, as they can be intellectually quantified and formalized. The sensual aspect of this process takes place in an idealized geometric space, to which an equally-idealized, “pure” time is given. The “counting” and “recounting” immanently describes a logic of linear temporality, which Leibniz defines absolutely, as the “order of succession,” and which Aristotle had defined even more fundamentally as the “measure of motion” itself. Every sequence is not necessarily bound to a temporal nature. But time without linear sequence is, by the same token, inconceivable. In music, one speaks of rhythm if materially-extensive and regularly recurring sequences are present. A series of notes that yield a coherent whole is perceived more as a musical theme or figure than as a melody composed of individual events. And after all, works exist in their own temporality, where they become able to be experienced by our perception. The subjective perceptual time of a work can differ vastly from the measurable time of Chronos, which allows time to become a central, artisticallymalleable parameter in music.17 A basic condition is the recognition of a differential as a global engine of formalizing strategies of becoming and creating, as they can be written using notation symbols and numbers. Even the numerical series, one and two, can be read both discretely and as a continuous process, which, in Renaissance mathematics, also constituted a first space in which formal appearances became conceivable. This allowed the Pythagorean formalization strategies to be viewed in the Renaissance as a discrete universal motor of an ideal world mechanism that continually generated differentiations. The results are the structures, related to the cosmos, of homogenous harmony and the semantics of classification systems, which are developed aesthetically, philosophically and in practice, 17 Cf. Karlheinz Stockhausen, “… wie die Zeit vergeht,” in Herbert Eimert, ed., Musikalisches Handwerk (Wien: Universal edition, 1957): 13 - 43.

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musically. The numeric differences—which present the unifying cosmos of the beautiful appearance of these orders as a prerequisite to any harmony—were reduced by Leibniz in 1700 to a binary system of “0” and “1.” All numbers can be written in binary form, which, for artists of the time, symbolized both creation from nothing and the complete order of the world in such a universal system. The difference thus coming to appearance also possesses an order which preserves the unity of the divorced parts. This positively cast orderfunction is the ideal harmony, as a semantic abstraction of a structure of the experience of beauty. The model and overarching structure for this is the cosmos, which appears as a naturally-given harmony, just as do the acoustic harmonic series of complex sounds, which constantly resonate and are heard in the identity of timbre. From this point on, the formalization history can be recounted in a number of parallel strands, which all lead to various aspects of the digital. On one side, the Pythagorean tradition of musical interpretation and physical metaphor can be found, as in acoustics or in the history of musical machines. On the other side, there is the traditional history of music: as an aesthetic history of epoch-specific harmony as ordering systems for the appearance of beauty—for which it is not numerical categories, but artistic expression and perceptual experience that serve as a basis. All of these discourses led to a new stage of their categorical meaning in the late 19th century. With sound recordings and the electronic sound-synthesis, the media status of the representation of sound and music changes fundamentally. Music is no longer just emotional arousal, and thus only in the aesthetic realm; rather, it is also perceived as a material-physical phenomenon, to which technical “discourse networks” (Kittler’s “Aufschreibesysteme”) and writing systems can be addressed. The real representation of sound replaces symbolic representation media—with far-reaching consequences that also include digitalization phenomena. III

The Mathematical Indexing of the World in Music

Acoustically-perceptible harmonious sound was evidence for the Pythagoreans that music is essentially a mathematical phenomenon—the acoustic appearance of arithmetic difference, which formal processes make acoustically and sensorily perceptible. The theory of musical ratios is understood everywhere there is not a practical theory of composition as a universal set of rules for recognizing and representing inherent cosmic configurations. Figuratively, these theoretical approaches appeared in the early 16th century, in the works of Robert Fludd. His “Monochordon Mundi,” tuned by a single divine hand, represents the intervals of the harmony of the spheres, proportions and relationships of meaning. In his “Templum Musicae,” he portrays a

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house that is full of symbolic meanings, spheres of influence and relations from the forge of Pythagoras to the hexachord tonal system of Guido of Arezzo. The harmony of the cohesion-creating universal concept in Aristotle and Plato is ideological. In “Timaeus,” Plato describes the harmony of the number system as a creation of the soul of the world, which forms God according to the ideal numbers of the famous “Timaeus Scale.” The ideal numbers correspond to the musical consonances, which become a model for an absolute harmony, as they are also reflected in the individual human soul. Every individual human is thereby endowed with a sense of order, measure, proportion and harmony. The expanded Roman concept of harmony includes the notion of geometric symmetry as a component of a comprehensive theory of beauty, which only to be displaced in medieval mysticism entirely by the subjective sensitivity of a non-specific soul. For the ingenious machinist, polymath and composer, Athanasius Kircher, God in the mid-17th century is both an organ builder and an organist, who essentially created the world according to mathematical laws and proportions in six days—corresponding to the six registers of Kircher’s world-organ. Kircher also organizes the harmonious relationship of the differing zones of Heaven and Earth into octaves in his major work, “Musurgia Universalis Sive Ars Magna Consoni et Dissoni,” in which he depicts his own composing machine, along with the physical basis of acoustics and mechanics already mentioned.18 Even these few aspects demonstrate how strongly the settlements emanating from music are inscribed into the formation of theories of the respective eras. Thus, music theory is a comprehensive model for explaining the world up to the distinct harmony of the spheres of location and representation area, through the relationships, proportions and meanings of macro- and micro-spatial constellations, and on the basis of the principle of consonance in the system of musical intervals and tonal relationships abstracted in number theory. This fascinates through the surprising correspondences between simple, musical and physicalmathematical phenomena. As far as the interval proportions as spatial presentations of serialism after the Second World War and in contemporary music, numerological and Kabbalistic strategies—along with mathematical and number-theoretical compositional practices, as in the Fibonacci sequence, representative of the golden ratio—have been increasingly demonstrated, which continue to model in music theory, and, in the status of their first experimental, formal algorithmization, have led to often-criticized exaggerations.19 18 Athanasius Kircher, Musurgia Universalis, ibid. 19 Cf. Konrad Boehmer, Das böse Ohr: Texte zur Musik 1961-1991 (Cologne: DuMont, 1993).

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The development of theory takes proceeds in a collective musical consciousness of a system experience between reflective listening and the explicit knowledge of a “second immediacy” (Hegel) of theoretical foundations, which allows music theory to appear as a musical logic of a categorically-formed perception. Both planes influence each other, and are inextricably linked via the culture of common aesthetic ideals. That which was viewed as the “nature” of certain musical phenomena is thus able to be qualified as the interpretation of various approaches (mathematical, physical, aesthetic, as in the case of the Baroque doctrine of affections), which can be taken in depending on the issue and the different perspectives. The respective musical phenomena allow them to appear in the social structures of musical activity as “material capable of mentality” (Hanslick’s “geistfähiges Material”). Thus, the theory space is analogous to the social interaction with musicians and composers, who are directly dependent on the degree to which socialized work is developed within a social order. 20 But spatially-defined two- (Max Weber) and three-dimensional (Curt Sachs) structures also dissolve in favor of the function of their relationality, and become systematic materials that—depending on musical interest—can be playfully or categorically reconfigured. With regard to composition theory, the hollowing out of tonal frameworks in the first half of the 20th century proceeded between free material expression and structural determinism of the systems. This enabled the generation of composers after the Second World War, including Pierre Boulez, Karlheinz Stockhausen, Luigi Nono, György Ligeti and Iannis Xenakis, after the phase of a deterministic serialism of the 1950s, to increasingly watch out for extra-musical order principles. As described above, such principles have always played an important role in the use of algorithms, numerical systems and mathematical abstraction relationships in proportions and forms; now it seemed possible to directly generate, formalise and transform them in electronic and computer music into musical structures and sounds— without detours through symbolic representation systems. In the tradition of self-playing, mechanical instruments and music machines, technical and aesthetic discourses, as with the methods for sound recording, come together. The physical principles of Joseph Fourier and James Clerk Maxwell play an equally central role in the electronic music of Karlheinz Stockhausen in Cologne as they do in the musique concréte of Pierre Schaeffer in Paris and the early attempts of Max Mathews and Iannis Xenakis at digital sound synthesis. With the famous St. Petersburg call for the invention of a talking machine in 1780, these two hitherto separate discourses overlapped for 20 Cf. Kurt Blaukopf, Musik im Wandel der Gesellschaft. Grundzüge der Musiksoziologie (Kassel: DTV, 1986).

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the first time.21 Provided with a large cash prize and the prestige of the St. Petersburg Academy of Sciences, international inventors and scientists began to search for mechanical voice- and speech instruments.22 In addressing the voice as the most fundamental refuge of the self and of immediate vocal expression, concepts took hold in the tradition of mechanical birdsongs and organ pipe simulations. At this point, it becomes an epochal upheaval of recording sound, in which it was possible for the first time to directly address the audible sound of voices and instruments in the reality of oscillating soundwaves. In the real domain of technologically-recorded sound, concrete voices and sounds reveal themselves—not just rules, scores and playing instructions. This represents such a fundamental shift in paradigm that we are only gradually beginning to understand it in all of its consequences, as in digital techniques. Musical notation, as a “discourse network” (“Aufschreibesystem”) of musical structure using symbols, was originally conceived of primarily as a tool for musicians, and long not publically accessible in monas­ teries. The machine, the music-making device, could no longer guarantee this exclusivity. And what it can and does do—the conversion into other medial qualities and new medial phenotypes—it cannot hide. In its mechanical, strictly formalized programming, it is evident—unless one assumes an intent of deception attributed to a mechanical “self-ness” (Hans-Dieter Bahr’s “Selbstigkeit”)—that there is no transcendence in its soulless transience, and no mirrored desires can exist. Thomas Alva Edison’s talking machine, which he gave to his parents for Christmas, says “mama” and “papa” using a sooty roller.23 However, he does not come to think of the recording of music before other companies of music entertainment have already had great success with coin-operated phonographs. IV

On Digital Beauty

After all the media revolutions—rollers; mechanical reproduction instruments; the technical system of recording as storage in the real; analogue control possibilities and their programmable circuit logic—all of these strategies, techniques, technologies and functions finally come together in the universal medium of the digital. Both those of aesthetic semantics and of the mechanical (re-)production sphere 21 Fabian Brackhane, “Die Sprechmaschine Wolfgang von Kempelens – Von den Originalen bis zu den Nachbauten”, in Phonus 16 (Saarbrücken: Institute of Phonetics, Saarland University, 2011): 49–148. 22 Cf. Bernhard Serexhe, Peter Weibel, eds., Mensch in der Maschine (Berlin: Matthes & Seitz, 2007). 23 Cf. Friedrich Kittler, Gramophone, Film, Typewriter (Stanford: Stanford University Press, 1999 [1986]).

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enable complex aesthetic interactions of the most diverse of agents, in heterogeneous instances of historical and mechanical backgrounds in the “real virtual” (Gilles Deleuze) of a thusly-constructed acoustic cyberspace. In the evolution of electronic music after Busoni, it was not a contradiction prior to the Second World War to play the classical salon music of the 19th century with the newly-invented play instruments. This applied as well for the Russian inventor Lev Thermen’s “Theremin,” with a user interface of touchless manipulation of capacitive fields, that to this day remains experimental. In 1920, the sound of the new instrument, summoned as an “etherophone,” was praised as “soulful.” The sound alternates between high soprano voices and stringed instruments, but with exaggerated forms of glissando and vibrato, which may be intonated by gesture in the air. Until the Second World War, however, it largely failed to provoke aesthetic irritations. Medial radiophonic strategies, as well, stand within this aesthetic tradition that can be found in the further development of electric and electronic playing instruments from the Hellertion to Mager’s Trautonium. Conceived as broadcasting instruments, they were employed as a part of a complex multimedia system. Without recourse to inadequate microphones, amplifiers and loudspeakers, they were, following Cahill’s example, to be played live on the radio and heard directly through the listeners’ receivers. The question of an appropriate new aesthetic paradigm was posed at first only in a few experimental attempts—e.g., with Olivier Messiaen, Paul Hindemith, Kurth Weill and Edgar Varèse. Nevertheless, it was already clear with the Theremin that the new music machines, just like their mechanical player-piano precursors, abstracted the question of musical interpretation on a higher level, and thus could be viewed as such. With the disembodied, yet bodysimulating presentation of the machine, interpretation is itself able to be experienced as artwork. Secondly, it is clear that the music-making and -playing body is up for discussion, whereby the status of technology in general is changing. With recordings and synthetic sound synthesis, the interpreter, which Edgar Varèse perceives as a “distorting prism” between the composer and listener, becomes simply super­ fluous. In the electroacoustic arts, the composer can directly capture his or her ideas on record and tape in an electronic studio, and can generate or play his or her own instruments and timbres. In the process, the compulsion for a relationship between bodily action on a musical instrument or the voice and the resulting sound is forever eliminated. The idea for a sonorous structure and a technical understanding of the methods and tools is sufficient to be able to potentially produce any music. The new limits are merely our own imaginations and our abilities to conceive.

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V

Hybrid Spheres—Between Analogue and Digital

Particular aesthetic approaches, strategies and methods for music with synthetic sounds, first developed after 1945 with the serial music in the tradition of Arnold Schönberg and Anton Webern, the electronic music in Cologne of Herbert Eimert and Karlheinz Stockhausen, and the musique concrète in Paris of Pierre Schaeffer. For the first time, as well, large computer systems came into use at universities and in commercial installations in hybrid settings, where they initially accepted control tasks predominantly via analogue synthesizers, which, due to their sheer number and their precision, could no longer be carried out by hand. With his assistants, Edgar Varèse and Iannis Xenakis, Le Corbusier built the Philips Pavilion for the 1958 World’s Fair in Brussels. It can be regarded today as a multimedia space: in its spectacular hyperbolic forms, it integrated light, image- and video-projections with 350 loudspeakers, with which computer-controlled sound movements could be executed. Xenakis’ composition from manipulated recordings of glowing charcoal, “Concrète P.H.,” and Edgar Varèse’s analogue electronic work, “Poème électronique,” were both played. For the 1970 World’s Fair in Osaka, an ideal, spherical auditorium was built according to the conceptions of Karlheinz Stockhausen, which also operated with a computer-managed, 360 degree control of the sounds in the room. In addition, there have been fundamental reflections on the application of the computer as a universal sound-generator since the 1950s. The notion was bold: there existed hardly any concept of what it meant to formalize a complex sound with its strongly-interacting, complex overtone structures, with sensitivity to value and time. And thus, the first results ringing in the late 1950s were also quite devastating. When Max Mathews began at Bell Labs with the programming work for “Music I,” the first program for the generation and arrangement of sounds with a computer, the paradigm shift was also clear in terms of existing fundamental physical understanding. The sobering results of the first examples, including “The Silver Scale” and “Pitch Variations,” along with Norman Guttman, pointed not just to technical shortcomings like digital/analogue conversion technology, but far more fundamentally to the insufficient understanding of the “essence” of sound. It was recognized that even the purely quantitatively-formulated physical knowledge available since Fourier, Maxwell and Helmholtz, was obviously insufficient for describing the now technologically-presentable parameter of timbre with the desired details and subtleties. “The most apparent limitation in the field of computer music results from the lack of adequate knowledge of the sound of a given Pressure wave. The computer sounds are described in terms of the wave shapes produced by the unit generators in the instrument units. This method for describing sound is quite different

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from the method of ordinary music, in which the sound is specified by the instrument which produces it, when certain instructions have been received by the performer. […] An example of a psychoacoustic surprise is the dominance of the rates of attack and decay in determining the character of a sound. […] Another unexpected result is the importance of suitable random variations in almost all parameters of a note for introducing richness and interest. […] Our experience has shown how little we now know about the relation of the quality of sound to various features of waveform. A new body of psychoacoustics is necessary. […] An increase in knowledge in this field is bound to be of value and interest in other fields including those of speech and hearing.” 24 In the course of his research, Mathews developed the basic software solutions for all the sound-generation techniques commonly used today, which he referred to in his early sketches as “instruments.” With the exceptions of temporally-defined granular synthesis (based on Dennis Gábor’s theory of “quanta of sound”), as well as the genuinely-digital generation of sound using virtualized instrument models in physi­cal modeling, all methods of digital sound synthesis are based on the unidimensional principle, which reaches back to Fourier, of “snapshots” removed from time, of a spatially, statically conceived sound spectrum. According to Fourier, this is representable through a finite number of overlapping pure tones—which means, conversely, that even the most complex spectrum of pure tones can be resynthesized. This physical-technical determination of a method, originally rooted in analogue 18th and 19th century thinking, also served electronic music at the material level in the audiotape montage techniques of the Cologne studios (as an appropriate technical equivalent to the aesthetic counterpart of serial composition techniques). It met a fundamentally different space and time paradigm in the digital realm when confronted with the Shannon/Nyquist sampling theorem. The temporally-discrete rasterization of individual values, by a scanning operation that is clocked depending on the pitches to be represented, obeys a different logic than the modulation of sine waves. From analogue oscillations comes numerically-described information, after its analogue-digital conversion. Information, just as digitality at large, however, is an abstracted description of a universal medium, whose forms may appear as sounds. For this reason, no “digital music,” no “digital sound” exists by itself. What is perceived as the digital-analogue conversion are sounds that represent data that is present digitally. The medial forms thus remain observable to us, in which the sonorous results of our manipulations 24 Max Mathews, “The Digital Computer as a Musical Instrument, Science 1963”, in Johannes Goebel, ed., Computer Music Currents 13. The Historical CD of Digital Sound Synthesis (Mainz: Wergo, 1995), pp. 63.

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appear to us on the other side of the A / D converter. Due to the storied indifference of information with respect to its form, we are unable to distinguish whether what we hear was originally a result of an arithmetic operation, the transformed information of a digitized image or text, or a manipulated, multiplied, digitized sound (e.g., with the color values of video data). The price of the new freedom of being able to transversally move to forms in a transdisciplinary, universal medium is the loss of historical-aesthetic connotations, as well as a Shannonical prohibition on discourse for all sound components beneath the digital screening. But in this pragmatic obscurity, there is a systemic surplus value, as Claus Pias describes it: “From this direction, the digital appears as a methodical or systematic instrument of forgetting. Digital is something that knows no intermediates and grey zones between its elements, as we have no finger between our ring and middle fingers (digitus), or as we have no letters in our alphabet between ‘A’ and ‘B’. In this determinedness of the digital lies its forgetting-force. From the seventeen-million colour gradations of a scan, and from a sound beyond half the sampling rate, the forgotten continents of the real begin; and between two scans, a discourse prohibition prevails. And this discourse prohibition, or non-knowledge, is extraordinarily productive.” 25 Through this discourse prohibition, the universal, program-controlled and operably-formalized access to the material and its manipulation is possible. Through the intermedial interchangeability of non-specific, neutral information after analogue-to-digital conversion, the computer becomes a program-controlled, automated “hyper instrument,” as it was employed by Gottfried Michael Koenig, Iannis Xenakis and many others at MIT under Tod Machover. At the level of digital sound synthesis, these changes remain mere approximate solutions for a problem that is no longer fully representable mathematically and numerically. In the context of this musical-aesthetic search for artistically interesting solutions, compositional, unpredictable and intuitive experiments will further play a decisive role. This especially applies for the findings of media science: that the selected media processes do not neutrally produce results, and thus must be thought of artistically and strategically. Independent of our conscious relationship with technical processes, it generally remains hidden what they provide to epistemic knowledge by their nature. “Thus the nature of technics is absolutely nothing technical. We therefore never experience our relationship to the nature of technics, as long as we only imagine and operate the technical, 25 Claus Pias, “Ästhetik als Strategie,” unpublished manuscript of a lecture held at Hyperkult 11, Juy 4–7 2002, at Leuphana University in Lüneburg.

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come to terms with it or avoid it. Everywhere, we remain unfreely chained to technics, whether we passionately deny or affirm it. At worst, however, we are surrendered to technics when we view it as something neutral; for, this conception, which is particularly popular today, makes us completely blind to the nature of technics.” 26 Heidegger formulated that the object of technology is not determined by ideologically-cast actions towards it—stronger yet, he made clear that, beyond agreeing or disagreeing attitudes towards technics, access to the nature of technics and its epistemic power for humans and for knowledge of it, remains constitutively blind. Rieger cites in this context the shorter and more pragmatic version of Max Bense: “One does not escape technology by unlearning physics.” 27 In the interplay of musical-artistic concepts and mathematical-physical blurs in the generation of sound-structural artifacts in the digital medium, technical questions and methods gain a new meaning, which bring about a shift from the register of textuality and symbolic memory to a register of virtuality and creative manipulation in the domain of the real. Once the virtual is regarded not as a contradiction, but as a component of the real, it may then be more appropriate to speak of a real virtuality, instead of a virtual reality.28 What we already are seeing with complex computer simulations is the need for a new kind of media literacy, not just in the ever more dominant machine-machine communication. The presentation and manipulation of data structures in numerical simulations, like the methods of D/A-A/D conversion, is based on time-discrete sampling. From discrete points in time, real numbers are produced, which are defined only through infinitesimal approximation processes. The approximate model formations in the digital medium result, analogous to the universe of technical images (Vilém Flusser), which exist outside of real space in a new time dimension as “dialectics standing still,” that digitally generated sounds become perceptible outside real time in a new, virtual time and space environment, in a “dialectic in motion.” In the process, a new quality of referentiality is created that opens a possible 26 Martin Heidegger, “Die Frage nach der Technik,” in Vorträge und Aufsätze (Pfullingen: Günter Neske, 1985), 9. We opted for the translation of the German “Technik” as “technics,” against the more common convention of rendering it as “technology.” We want to preserve a distinction that is central to Heidegger’s thinking: both terms “Technik” and “Technologie” exist in the German language, but only the former remains indetermined as to whether logics be subjected to mathematics, in their interplay that is constitutive for technics, or the other way around. For an english translation cf. Martin Heidegger, “The Question Concerning Technology,” in The Question Concerning Technology and other Essays, transl. by William Lovitt (New York: Garland, 1977). 27 Max Bense, Über Leibniz. Leibniz und seine Ideologie. Der geistige Mensch und die Technik (Leipzig: Karl Rauch, 1946). 28 Cf. Gilles Deleuze, Difference and Repetition (Minneapolis: University of Minnesota Press, 1986 [1968]).

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aesthetic-compositional framework of action, which provides both reliable references in the imagination of the artistic domain, as well as strategies in the real domain that are able to be fed back (instrumentally, vocally) to real positions and bodies. As media interfaces and as resonance spaces of three-dimensional acoustic vibration bodies, virtual instruments provide exactly this sort of “moving dialectic,” which also still includes the modeling of a playing body as a part of the instrumental sound generation process. VI

Real Virtuality of Digital Composition

Along with Max Mathew’s pioneering work on digital sound synthesis, Lejaren Hiller and Leonard M. Isaacson worked at the University of Illinois in the 1950s on the digital analysis methods of existing music. Statistical analyses of existing musical works were to help in making personal compositional styles and musical genres quantitatively describable, and thus able to be produced automatically as algorithmic models. The computer could then, for example, produce any number of new Mozart pieces and modulate with any other personal style or genre. The ambitious research project in Illinois foundered quickly with the technical capabilities of the time, in the face of the complexity of the statistical description of the rule systems of music theory, and its complexly-interlaced, period-specific breakings and shifts. Hiller and Isaacson reduced the complexity of the output data by attempting to describe simple, basic principles of music theory algorithmically, in the melody and harmony of triads. Their program on the tube-powered ILLIAC mainframe at the University of Illinois could correspondingly generate simple musical rule systems. Hiller and Isaacson used this for a series of tests, in which they increasingly refined and differentiated parameter in the formalized rule system, almost as if fastforwarding through history. In a technique known as score synthesis, the results of their calculations were transferred from punch cards into a score and interpreted by a string quartet of their human colleagues. The four-movement “ILLIAC Suite for String Quartet” of 1957 is the first algorithmically-generated musical composition with respect to the old, classical European music system, and accordingly, to an aesthetically long-antiquated standard. It was an important attempt at making complex relationships between many dependent and complexly-interlaced parameters (as they appear in a musical work) quantitatively describable, and hence at being able to subdue program-controlled manipulations. With the personal style of Mozart, of course, this is still quite far off—even using today’s big data. For contemporary composition and current aesthetic positions, it is the Rumanian mathematician, architect and composer, Iannis Xenakis, who generatively applies the methods of algorithmic composition with

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micro- (sound) and macro-forms (compositional structures) in equal parts. Xenakis thus stands in the tradition of Edgar Varèse, and is the first to fundamentally re-analyse the problem of symbolic formalization both with respect to its medial and aesthetic processes, and to enormously expand the range of possible operations with probability and chance operations. Not least of all, his personal experiences with mass phenomena during his time as a resistance fighter in Greece against the German occupiers left lasting impressions, for which he sought adequate representative structures in the aesthetic domain. Xenakis was mathe­ matically trained, and as an architect and composer, he had a broad, transdisciplinary approach at his disposal. Against this backdrop, it was not abnormal for him to think about sonic and structural translations of various codes in the aesthetics of differing media forms, and, indeed, in music. In his musical work, not only instrumental, electronic and computer music is to be found, but also an interesting mixture of works with traditional instruments and completely new formal structures, as a basis for theoretical, compositional modelings. “In 1954, I introduced probability theory and calculus in musical composition in order to control sound masses both in their invention and in their evolution. This inaugurated an entirely new path in music, more global than polyphony, serialism, or, in general, ‘discrete’ music. From hence came stochastic music. […] But the notion of entropy, as formulated by Boltzmann or Shannon, became fundamental. Indeed, much like a god, a composer may create the reversibility of the phenomena of masses, and apparently, invert Eddington’s ‘arrow of time.’ Today, I use probability distributions either in computer generated sound synthesis on a micro or macroscopic scale, or in instrumental composition. […]” 29 At the core of his work are expanded formulations of irreversible timestructures, and thus a mathematically-derived structural expansion of formal causality, which allowed him to find novel approaches to the “dynamization” of formal processes. The fundamental question here was whether and how it is possible to gain regulating and non-regulating structures from chaotic processes, as was generally attempted in the 1970s in making scientific phenomena from quantum physics, the state of cybernetics and modern biology, fruitful for aesthetic processes. “Can order be established from noise?” Michel Serres asks the young Xenakis in his thesis defence 30 relating to issues of thermodynamics. 29 Iannis Xenakis, Formalized Music: Thought and Mathematics in Composition (Stuyvesant, NY: Pendragon Press, 1992 [1962]). 30 Iannis Xenakis, Arts/Sciences—Alloys. The Thesis Defense of Iannis Xenakis before Olivier Messiaen, Michel Ragon, Olivier Revault d’Allonnes, Michel Serres, and Bernard Teyssèdre, Aesthetics in Music Series, No. 2 (New York: Pendragon Press, 1985), 66.

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Serres invokes aspects of repetition and arbitrary polyphonic glissandos from Xenakis music as examples illustrating the background to his question. With his mathematically-derived methods, Xenakis was able to finally leave behind “neo-serial” approaches of his time that sought inherent systematic solutions, defining his work, rooted in the principle of indeterminacy, as “Stochastic Music.” 31 Still fully in analogue, it was a matter of testing the programming and algorithmization of the aesthetic and its automation, which at the time accompanied questions of cybernetics and artificial intelligence, as they had already played a role in the computer music of Hiller and Isaacson. Even before the digital revolution, Xenakis, along with composers such as Edgar Varèse, Erik Satie, Karlheinz Stockhausen and Luigi Nono, tested in the aesthetic domain of formal compositional processes the very procedures which have become the basis today for digital music activity in our everyday interaction with our universal information machines. This includes sonic spatialization, in which the compositional, inner spaces of the formal structures are put outwardly into the real synthetic sound structures and correspondent algorithmically-modular forms in real space. Xenakis was able to tie in with the American computer music of Max Mathews, John Pierce, and Lerjaren Hiller, among others, who dealt with fundamentally aesthetic problems of knowledge, and who radically reformulated, from new structural viewpoints, the question of the nature of the digital in the tradition of mechanical music and composing devices. Aesthetic experiments in sonorous music took place, which today, even if having failed, appear nonetheless as a trial to achieve aesthetic foundations for the digital sphere. These were stimulated by the theoretical, scientific, and especially aesthetic issues of the serialists and of cybernetics, by Claude Shannon’s emerging information theory in view of the paradigm shift of the digital, and by the “objective aesthetics” of Max Bense and Heinrich Scherchen’s studio in Gravesano. Consequently, Iannis Xenakis, in his 1955 essay, “La crise de la musique sérielle,” criticises that the prevailing serial electronic music of his day operatively and aesthetically pushes the borders not just of a compositional-medial practice that is already more developed internationally. “The serial system is thrown into question on its own two bases, which embody the seed of their own destruction and inadequacy: a) the series and b) their polyphonic structure. The series (irrespective of structure) arises from a linear category of thought. It is a rosary of objects of finite numbers. There are objects, there are finite numbers, because there is the piano tuned with 12 tones (in each octave). It would be absurd to think solely in quantities of frequencies in the electronic field. Why 12, and not 13, or N tones? Why not the continuity of the entire spectrum 31 Cf. Iannis Xenakis, Arts/Science—Alloys, ibid.

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of frequencies? Or that of the sound spectrum? Or that of the spectrum of intensity, or the spectrum of durations? But let us leave the question of continuity aside. It will at some point play a crucial role in research anyway; we turn again to the irregularity in the sound spectrum as the fundamental aspect of human perception […].” 32 From a musical work as a formulated thesis, historical development leads to the work as evidence for a theory or experimental design, and finally to a working concept for the truly openly-designed experiments. In his system, this is formulated so far as a rule, that ultimately, no interpretation is needed anymore in a concrete performance, but as the medially-documented result of work coinciding with the will of the composer. The working concept itself thus begins to dissolve in favor of a medial predisposition. Aesthetic-compositional processes of formal determination become technically feasible, representing the first step towards its formal automation, which nonetheless can only be finally achieved with the program-controlled symbol processing of digital computers. At the same time, the technically-described, and thus aesthetically representation-less sound—as a freely available signifier in a structural association space—begins to emancipate itself, and even to become a starting point for formal structurings, as the serial system had already burst open in a sensitive place. Owing to these problematic parallel movements of two systems and their differing reference spaces, Stuckenschmidt comes to his strangely emphatic ”…concept of the ‘third era’ as the electro-musical stage of development, whose ‘dehumanized music’ can develop in the ‘domain of the pure spirit,’ which is why it may be said that the ‘music most alien to man’ that had hitherto been developed—namely, electronic music—‘could boast’ to have been elaborated in a ‘previously unknown dimension’ of ‘the spirit of man’ […].” 33 The “spiritual” of the methods is no longer situated in the aesthetic, but in the systemic dispositive of mathematical abstractions of number systems. It is no wonder that, through this mystification of the material concept and the abstract manipulation of symbol systems, one promised an artistic link between algorithms, charged with “pure spirit,” and their sonorous results. The diverse, failed artistic attempts succumbed to the same errors that had long been powerful in cybernetics and artificial 32 Yannis Xenakis, “La crise de la musique sèrielle,” in Heinrich Scherchen, ed., Gravesaner Blätter Nr. 1, (Gravesano: 1955), 3; German translation available in Michael Harenberg, Neue Musik durch neue Technik? (Kassel: Reihe Bärenreiter Hochschulschriften, 1989), 68. 33 Stuckenschmidt quoted after: Elena Ungeheuer, Wie die elektronische Musik “erfunden” wurde … Quellenstudie zu Werner Meyer-Epplers Entwurf zwischen 1949 und 1953 (Mainz: Schott Music, 1992), pp. 11.

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intelligence. Carl Dahlhaus and Rudolf Stephan consequently criticize and point out, at the material level, a veritable gulf between the intention of manipulations in the virtual, symbolic world, and their audible results, which materialize at the level of aesthetic reception.34 The idea of the use of operative symbols, as the peak of the formalization history, enables the separation of the manipulation of symbol series from their interpretation—the fundamental “techné,” an artifice that mediates between the symbolic and the real. At the cost of enforcing stricter linearity in symbolic representation, the spirit should be relieved of the technical rationality of algorithmic generation procedures, as machines are better equipped to perform them. The result is a calculated use of symbols as a method for creating a new class of reference objects of a formal language, like the numbers of mathematics, as a component of a symbolic reality. Such a system can, like Xenakis does, be treated as a symbolic machine, which, however, only allows statements about equally-symbolic worlds, and in no case about the real world in terms of a given, empirically aesthetic reality. The fetishization of numbers in a virtual intermediate space, as somehow alien to systems, was recognized by the 1970s as a fundamental problem by the young composer, Gottfried Michael Koenig, who worked as an assistant in the Cologne studio with many international composers, and thus obtained an intimate insight into the methods, practices and issues of his time. Koenig concluded from this that he must go deeper and more analytically into the formal procedures—e.g., to better understand the micro-design of the time relationships in sound synthesis, and to arrange according to musical aspects. “The best and most plausible concept has to thus first prove itself to the musical reality; the conclusiveness within compositional abstraction need not yield conclusive, sensible, rational music. […] In the process, the fundamental experience of all new music is forgotten after the collapse of tonality: namely, that there are no pre-musical relationships—whether historically or physically conveyed—that guarantee the consistency of a piece of music; that, rather, the context in which the piece is composed must in any case be prepared first.” 35 The solution for Koenig lies in the use of program-controlled and symbol-processing “data processing equipment,” as he uses them in the course of his “Projekt 1” and “Projekt 2,” in order to be able to make aesthetic instances artistically productive, amidst the gulf spanning between operational symbol manipulation and musical operationalization 34 Carl Dahlhaus, Rudolf Stephan, “Eine ‘dritte Epoche’ der Musik? Kritische Bemerkungen zur elektronischen Musik,” in Deutsche Universitätszeitung, H 17 (Berlin: DUZ, 1955): 14-18. 35 Ulrich Dibelius, Moderne Musik I: 1945–1965. Voraussetzungen, Verlauf, Material (München: Piper, 1966), pp. 165.

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systems.36 Along with composer Herbert Brün, he thus established a German branch of the “computer music” that cantered on American universities and research institutes, resting between digital score- and sound synthesis. It found a broad forum in the “Gravesano Review” of the great conductor, theorist and promoter Herrmann Scherchen. Thus, the discussion in the late 1950s arrived at a point where electronic and computer-aided composition techniques began to be further differen­ tiated technically and aesthetically. With the Cologne WDR studio, a new aesthetic research and testing approach existed in the field of electronic music, which developed its own dynamic around Eimert and especially, later, around Stockhausen. The importance of basic experiences with strict formalization systems demonstrates the further development, prototypically, for example, with György Ligeti. Konrad Boehmer evaluates this first phase: “As long as there will be music, the aesthetic judgment will be related to the logic and consistency of the unfolding of its sonorous manifestations—whether elaborate numerical constructions and deterministic strategies hide behind them or not. The rage of comprehensive determination, as it arose in the fifties and continues to proliferate in the minds of some composers of so-called ‘computer music,’ is quite explicable from the state of musical material at the time, which was virtually as limitless as it was amorphous. This state allured many composers to operate to some extent at the level of pure, or as Kant describes, ‘empty’ terms, in confidence that the application of the abstract construct will endow sonic reality with musical contexts automatically. Thus, many composers of the time eagerly gobbled up popular science [and media theory…, M.H.] works, like those of Norbert Wiener or Colin Cherry, on questions of cybernetics and communication research, developing into true Pythagoreans of numeric symbolism and numerology […] Compositional determination only makes sense where it breaks through the walls of established consciousness. Where it raises walls, further hardens solidified states, it is only good for bringing forth musical skeletons—it is the pretentious craft, in which every attempt at aesthetic innovation becomes entangled and suffocated.” 37 The “Pythagoreans of numeric symbolism and numerology” are outgrowths of a phase in which it was attempted for the first time to strictly formalize and, as with Hiller, to analytically and quantitatively modulate the entire number-theoretical foundation of Western music theory. 36 Wolf Frobenius, Stefan Fricke, Sigrid Konrad and Roger Pfau, eds., Gottfried Michael Koenig. Ästhetische Praxis: Texte zur Musik (Saarbrücken: Pfau, 1993). 37 Konrad Boehmer, “Das Prinzip der Determination, Teil 2,” in Vom Innen und Außen der Klänge. Die Hörgeschichte der Musik des 20. Jahrhunderts, transcript of the SWR2 broadcast from April 17th 2000, 10:05 pm to 11:00 pm.

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In the process, results emerge that are justifiably criticized, which demonstrate that here, too, the proper questions for the respective formalization process must be asked. The recognition remains that, unlike in other arts, music has a strong symbolic basis formed in number theory— which today, nonetheless, is no longer so unparalleled—and provides the foundation for our musical listening and thinking. VII Non-Linear Structures in Musical Reality Literally everything audible can be transformed as musical material. Music itself has become the starting material for music, stored and further processed again and again in global digital archives. Programcontrolled, algorithmically, playfully and intuitively, unpredictable new structures and forms arise in the overlay of multiple modulations, in the mix, reuse, remix, and mashup. Aesthetically, plagiarism is not just allowed, but a consequence of a digital media practice that experiences every artistic element at once as always already given, and as arbitrarily manipulatable. A DJ in Jochen Bonz’s book Sound Signatures 38 describes that it is not about inventing new things, but deciding what is played when. The rift between Romantic compositions and trivial selections from a vast, but finite mass of a universal digital archive of all music ever written is an epochal rift, which popularly manifests itself today primarily in the permanent self-validation of loop-oriented experimental Club Culture. And of all things, the old analogue DJ set is emerging as the ideal contemporary instrument for playings from the digital archive, and for their infinite fragmentation and recombination into new structures, overlays, sounds, loops and grooves. Techno and Hip Hop, as popular music styles and in youth movements, have become a popular embodiment of the potential of digital access to the global sound archive. At the same time, identification with the aesthetic archive is so completely and emotionally charged that, contrary to Walter Benjamin’s theory, the aura of every selecting action becomes so totalitarian that the subjects of this identification begin to “become music” in the resonance of a process-oriented synchronicity—as Theweleit fantasizes with Flusser.39 In a historical turnover into a still pre-digital musical thinking, loopbased remix strategies are also already outdated techniques that experiment now for the first time, within the historically-familiar domain of analogue techniques, with novel, digital aesthetic strategies. This involves strategies that are far ahead of their own instrumental practice: as the universal digital archive, and its musical practices, has itself become formal. This process begins to emerge as an option among current 38 Jochen Bonz, ed., Sound Signatures: Pop-Splitter (Frankfurt: Suhrkamp, 2001). 39 Cf. Klaus Theweleit, ed., Heiner Müller. Traumtext (Basel: Stroemfeld, 1996).

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technical strategies, but as an aesthetic genre, artistically formulated in detail, it has not yet been invented. The question itself is only slowly becoming able to be formulated—the new artistic strategies and the associated business models must still be developed. The strategies of the “new music” of the 20th century are already equally historical; its protagonists, witnesses of a historical debate on a different aesthetic. And yet, we can have inklings about how in the dissolution of traditional forms and completed working terms, in favor of self-overlapping, interconnected processes of a fluid musical practice, an idealized, infinite recombination of aesthetic strategies emerges, which might allow us to adequately operate artistically in digital environments. The ideal goal is a collaborative practice as interactive feedback of bodies and machines, with human creativity as a damping factor to avoid redundant feedback phenomena. It is a matter of transformation processes—de- and re-composition of a new aesthetic—which is not digital, but liberated, made conceivable and designable, by the digital. “From recording, editing, processing, and manipulating emerges what could be: invisible sonic sculptures in time, sonic modulations creating not a two-dimensional progression but a spacious materiality: almost tangible, static, and moving at the same time, fixed-fluidity expanding its own location. The recognizable is covered in synthetic sounds that question its origin and expand what it might be: connecting, reconnecting, disconnecting oddments in timespace, tinkling, clicking, and breathing existence into the unseen.” 40 The result is the processing and analysis of microscopic time structures of pulses, modulations and samples, beyond the limits of the analogue scratch and cut techniques of electronic music and musique concrète. Algorithmic strategies in the micro- and macrocosms of structures and sounds and their endless modulations—Xenakis’ motion capture. And again: everything becomes the proverbial aesthetic raw material. Everything works in the madness of the interconnectedness of machines, semantics, strategies and aesthetics. The completed work loses itself in non-Euclidean, rhizomatic interconnection. The “liquefaction” of musical structures, which are digitally coded in network music, makes any neo-Adornian discussion on material questions with respect to their materiality obsolete. Instant data processing in the big data universe points to the volatility of the results, to their multiplication in edits, re-edits, versions, variables, shifts, suspensions, modulations and resonance phenomena, etc. The sound packets resulting from these processes are temporalized; their permutation is turned over to a code that must ensure the connectivity and compatibility of operations. Meaning and sense effects 40 Salomé Voegelin, Sonic Possible Worlds (New York: Bloomsbury Academic, 2014), 72.

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proceed such types of computer music in tele-topological networks only in the form of compatibility/non-compatibility. Each isolated track is thus just a local and temporary interruption of compatibility, as a fixed, regular work. The result is a need for permanent innovation, in the form of aesthetic questioning of a track according to the possibilities of transmedial, external connections. As a system of formal relationships, music mentally directs and activates patterns with which music is perceived and external meanings are brought to it. At the same time, media systems in networks potentiate fewer sense effects, as sense disruptions, meaningless meaning carriers. Music is open to meanings. Where machines transmit messages and signals that are constantly information from other machines, the meanings are reduced to short-term, codified collections, as intervals of the information from itself. At the current position—in the interruption of acceleration of the musical reformation of musical material—it can be discussed how problematization of the physical material concept can be migrated to the problematization of the program-controlled transformation of the material. This, in order to understand program control that first and foremost generates the material in transjunction with subjective components. The live electronic works of Olga Neuwirth or Fausto Romitelli, the multimedia works of Ryoji Ikeda, the varied forms and style mixes of Stefan Prins and Jennifer Walshe, and the complex media-operas of Bernhard Lang and Bernhard Gander enable us to guess at how diversely music develops and becomes further differentiated in its medial manifestations. “In the digital age, sound finally became fully autonomous: As a pure stream of information it is now amenable to any method of synthesis, transformation, or analysis without the involvement of a sounding body in the conventional sense. […] As the apparatus of music becomes less apparent, particularly in the digital domain, so sound becomes more completely itself, the purest manifestation of a disembodied, time based art. Freed from the distraction of ranked violinists dressed in black and white sawing at their instruments, guitarists leaping around on stage, entire typing pools of keyboard players, choreographed dancers, drum risers, video walls and pyrotechnics, the intangible core of music, the part that makes some people close their eyes when they listen, is allowed its full power.” 41 Indeed, there are currents of experimental, electroacoustic music, which still carry out microscopic reductions in the search for traditional strategies of artistic complexity, and devise the smallest of patterns that can be endlessly repeated and varied. This circular minimalism is owed to the absence of linear writing in the symbolic, and proceeds the inner workings of sounds and music objects. It would be abandoned in favor 41 David Toop, Haunted Weather: Music, Silence, Memory (London: Serpent’s Tail, 2004), 14.

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of super-contextualization, in favor of newer, structure-generating processes, and the production of polyvalent and polylinear structures. This would also correspond to the formations of the medial, as, with respect to the specific mediality of the musical, form is always given in the reference horizon of other forms, and constantly updated in compatibility. On the other hand, the medium is virtually present, and may, itself, be modulated down to the level of algorithms as an aesthetic strategy.42

42 cf. Harenberg, Michael, Virtuelle Instrumente im akustischen Cyberspace. Zur musikalischen Ästhetik des digitalen Zeitalters, (Bielefeld: Transkript, 2012).

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III Media Metaphorology: Irritations in the Epistemic Field of Media Studies1 Georg Christoph Tholen  [↗ P. 100]

Georg Christoph Tholen, Prof. em. Dr. phil., has been full professor for media science, with focus on cultural philosophy, since 2010 at the University of Basle. He studied philosophy, sociology, and psychology at the universities of Bonn, Cologne, Marburg, and Hanover, completed his doctorate in 1986 and his habilitation 1995. Between 1980 and 2000 he was, among other things, manager and deputy director of the Scientific Centre for Cultural Research at the University of Kassel, and lecturer in cultural philosophy and media theory at, among others, the universities of Berlin, Bremen, Frankfurt/Main, Kassel, Klagenfurt, Lüneburg and others. 1998/99 he was interim chair of Cultural Media Theory/Theories of Comparative Figurativeness of the University of Jena. 1980–2000, he was the editor-in-chief of the periodical Fragmente. Schriftenreihe für Kultur-, Medien- und Psychoanalyse, and of the e-journal, Zäsuren. Selected publications: Die Zäsur der Medien (2002); Schnittstellen (2006, co-ed. with Sigrid Schade and Thomas Sieber); Mnêma – Derrida zum Andenken (2007, co-ed. with Hans-Joachim Lenger); Blickregime und Dispositive audiovisueller Medien (2011, co-ed. with Nadja Elia-Borer and Samuel Sieber). Since 2008, he has been the publisher of the series MedienAnalysen, transcript Publishers, Bielefeld.

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With the evolution of “new media,” the question of the specific epistemic place of the media has undeniably become more urgent for the history of the most important Cultural Studies.2 Only with the spread of computers into almost every area of society was it first possible to talk about an inclusive “universal medium” that could integrate all media in one digital code.3 And the revaluation of the “personal computer” as an interactive multimedium gave it a cultural significance that resulted in both media euphoria and media skepticism. Yet the polarization of critical and affirmative discourse is nothing new. The tendency of cultural critique to demonize technical innovation as life-threatening artificiality can be found in   

 

[↗ P. 100]

 [↗ P. 100]

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Rousseau as well as Romanticism, where it is based on assumptions of lost immediacy. Inversely, celebrating the artifacts of technology as a means of salvation also promi­ ses a paradise of transparency— without mediation and delay. But the metaphors that restrict the Ersatzwelt of technical media to bodily extension or amputation (hammer equals reinforced fist, camera equals enlarged eye, radio equals amplified ear, and so on) are now further irritated due to the unspecified and manifold capabilities of digital media beyond mechanic and organic models. The validity and limitations of any supposed similarity between 1 2 3

100

First published in “Medium Cool,” ed. A. McNamara and P. Krapp, special issue, South Atlantic Quarterly 101, no. 3. (Summer 2002): 559–672. A good overview can be found in Sybille Krämer, ed., Medien, Computer, Realität: Wirklichkeitsvorstellungen und Neue Medien (Frankfurt am Main: Suhrkamp, 1998). Martin Seel, “Medien der Realität und Realität der Medien,” in Krämer ibid., 244–68: quotation from 258. Translations, unless otherwise mentioned, are by the author.

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man and machine are no longer determined by functions of motion and intelligence, as they were introduced in artificial intelligence research, which of course never achieved complete identification of computer and brain. Today, the arbitrariness of metaphors is due to the many different uses of digital media, since their definitions are looser and more indefi­ nite than the precisely defined media of storage or transmission. This ateleologic openness of digital code—heuristically we might call it universal—applies to more than just local transformations of how we act with tools. Symbolic acts as such—including language and thought, depiction and representation—are mediatized to the extent of raising the question of Media Metaphorology: Irritations in the Epistemic Field of Media Studies

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the constitutive place of the media. The validity of media studies as an independent area of research therefore depends on coming to terms with the permissiveness of digital technology regarding its use for text, image, or sound, a fact that necessitates theoretical reflection on indifferent transmissibility as such (Übertragbarkeit).4 I would first like to demonstrate how the circumscription of this “new” epistemic field of digital media studies layers metaphoric and conceptual interpretations of what decides the mediality of media. The multiplicity of images and concepts applied to media does not only stem from theories or methodologies that situate media according to each perspective as either a means of (self-referential) communication, an instrument of information processing, or its own message. The variability of such metaphors is not limited to the respective range of signification. Rather, it is questionable whether the choice between means, instrument, or message denotes the proper core of the medium, in the Aristotelian sense of a clear and simple idea, or whether these words only represent provisional metaphoric expressions. The question is whether their “as if” status is simply the application—innovative, but soon worn out—of a meaning that itself stems from other semantic areas (for instance, that of mechanic tools) and is only borrowed for explication’s sake. A metaphorology of the conceptual history of media will be able to distinguish 4

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For a systematic and historical analysis of the technical openness of uses of transmission, see Hans-Dieter Bahr, Über den Umgang mit Maschinen (Tübingen: Konkursbuchverlag C. Gehrke, 1983). For more on to what extent the concept of style refers to semiotic reference in languages and machines, which in turn refer, in the context of uses of digital media, to the chasm between signifier and signified, see Winfried Nöth and Karin Wenz, eds., Medientheorie und die digitalen Medien (Kassel: Kassel University Press, 1998).

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the epistemic fields that remain absolutely essential for contemporary media theories.5 By the same token, there are plenty of indications that an investigation into the place of media also affects the question of the relation between concept and metaphor. In this sense, we will sketch out a metaphorology of media.6 First, it is impossible to overlook that the digitalization of media caused the proliferation of metaphoric as-if descriptions. Yet this proliferation correlates with a strange fuzziness concerning the ontological status of media “themselves”: in defining the apparent specificity of a medium in the context of its digital resolution and reproducibility, one encounters a seemingly unfettered disruption by as-if options that undermines the distinction between concept and metaphor. Furthermore, there are additional aspects, less to do with media themselves, that come to puncture and dissolve the epistemic borders of the mediality of media: with the advent of digital coding, the intermingling of singular modes of storage and transmission (associated, for example, with photography, cinema, and television) becomes technically possible. The global acceleration of digital networks makes it less plausible to describe such phenomena in spatiotemporal or sociogeographic terms. Even the common discourses of one-way and two-way media and their respective paradigms of communication that served as the basis for theories of mass media appear questionable—not only sociologically—due to the tele-technological extension of the Internet. From the telephone to the Internet, the effect of a distancing, or resolution, of bodily proximity evidently leads to the inherent aporia of communication; namely, the immediate communion suggested in face-to-face contact. The interstices of the mediated frame of communication become more apparent with the diffusion of spatial relations between proximity and distance on the Internet.7 Heterotopias between real and virtual spaces, such as virtual communities, digital cities, or interactive marketplaces, are addressed by media analyses in terms of theater or performance. The bots, artificial constructs, and personae of those environments demonstrate without a doubt that traditional ideas of identity associated with bodily presence 5 Hans Blumenberg, Paradigmen zu einer Metaphorologie (Frankfurt am Main: Suhrkamp, 1998). 6 See Hans-Dieter Bahr, “Medien und Philosophie: Eine Problemskizze in 14 Thesen,” in Konfigurationen: Zwischen Kunst und Medien, ed. Sigrid Schade and Georg Christoph Tholen (Munich: Fink, 1998), 50–68; as well as Hans-Joachim Lenger, “Lenger, Host – Point – Poll: Ist Medientheorie ‘ontologisch’?,” in ibid., 69–79; and Samuel Weber, “Virtualität der Medien,” in ibid., 35–49. 7 Wolfgang Hagen has demonstrated this self-deception for the example of empirical media sociology and its exclusion of the war horizon of media technology: Wolfgang Hagen, “Mediendialektik: Zur Archäologie eines Scheiterns,” in Medien und Öffentlichkeit: Positionierungen, Symptome, Simulationsbrüche, ed. Rudolf Maresch (Munich: Boer, 1996), 41–65. Albeit in contrast with pragmatic acceptance of technology and its massmedia effects, the “critique of the consciousness industry,” which wants to understand media only as manipulative or emancipatory, marks another blind spot in the historio­ graphy of media.

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are insufficient.8 In translating the oscillations of such role-play between presence and absence in the categories of metapsychology, we arrive at the sobering insight that intersubjectivity is always already mediated in language, and thus the supposition of a monad that would mirror the other face to face is merely due to the imaginary pull of the communication paradigm. In virtual masquerades, speaking subjects imagine a union with the ego ideal that always remains barred, as speaking subjects are constituted in reference to the other. Thus in its subjectivity, the subject is always already heterotopic, never immediately at one with itself, never completely identical to itself. Yet this diagnosis, as Sherry Turkle has emphasized, only becomes more evident when telematic interaction multiplies the imaginary figures in their intercorporal divergence.9 In this sense, the manifold concepts of self in cyberspace—in the role-play of MUD and MOO as Turkle described them—prove the non-unitary partiality of what such patterns of identification provide. The only new thing about them is that in the asynchronous and disembodied telecommunication of the Internet, they emerge as truly virtual objects instead of false real objects, and thus communicate among themselves.10 However, the inaccessible place of the other, the absent who simultaneously opens and disrupts the fictional space of imaginary unity and completion, is not in reality translatable or transferable into a fictional space where the distinction of self-reference and other-reference would be sublated: “The space where cyberspace is installed is as much or as little a cyberspace as the bed where the dreamer lies is a dreamt bed.” 11 All three traits mentioned so far—the transparency of the digital medium, the absent presence of telematic space, and the diffusion of roles in cyberspace—are part and parcel of a permissive sphere of the as-if, a pretense that warrants further discussion. This permissiveness, I will show, is owed to the play of metaphoric and conceptual distinctions in defining the mediality of media. I use only a limited number of these distinctions to demonstrate that the detour of a metaphorology of media could be worthwhile. The most general description that would be valid for all media can be summed up as follows: “Mediality expresses how our understanding of our world, and with it all our activities and experiences with access to, not merely construction of, that world are determined See Sherry Turkle, Life on the Screen (New York: Simon and Schuster, 1995); Elena Esposito, “Fiktion und Virtualität,” in Krämer, Medien, Computer, Realität, 269–96; also Slavoj Žižek, “Cyberspace: Von der Möglichkeit, die Phantasmen zu durchqueren,” in Schade and Tholen, Konfigurationen, 104–21; and Victor Burgin, “Jennis Zimmer,” in ibid., 94–103. 9 For the concept of “intercorporality” (Zwischenleiblichkeit) cf. Bernhard Waldenfels, “Experimente mit der Wirklichkeit,” in Krämer, Medien, Computer, Realität, 213–43; quotation from 213. 10 Esposito, “Fiktion und Virtualität,” 270. 11 Waldenfels, “Experimente mit der Wirklichkeit,” 239. 8

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by the possibilities of distinction that the media offer.” 12 In other words, mediality functions as a fragmentary disclosure of our world. This can be extended in allusion to the well-known axiom of Gregory Bateson: a medium is a difference that makes a difference.13 This constructivist thesis certainly has the advantage of shoring up the “ontological fuzziness” of mediated access to the world, and it comprehends the constitutive instability and variability of media presentations as a function of the proliferating differences that media initiate. Yet the question remains whether the fundamental difference of binary code that is at its core can account for the relation of intentionality and reality. In other words, if the integrated computer, for instance, is understood to merely exacerbate our troubles with self-comprehension and self-division, without itself bringing about a change in our culture and our idea of ourselves, then how does this model account for historic change, and how does it theorize intentionality? 14 In the field of systems theory and constructivism, the question of the possibility of a horizon of systemic self-reference is replaced with the assumption of a strictly causal iteration of system–context interactions, or observations of observations. Even if these (self-)observations remain fragmentary, an intentionality that is always already transparent to itself has no blind spot. It is conceived as a self-sufficient, continuous transparency of cognitive decisions. This observation enjoys the privilege of the divine eye in platonic epistemology. Thus the metaphors of systems theory are those of communication, and media are means of communication: “People cannot communicate, not even their brains can communicate, not even consciousness can communicate. Only communication can communicate.” 15 And what comes in between is, in Aristotelian teleology, a means of self-preservation above all: “A medium therefore is only a medium for one form, only as observed by one form.” 16 Likewise, the constructivist definition that follows these presuppositions preserves autopoietic, intentional, given cognition and communication and translates them into the process of social self-renewal: “We consider ‘media’ all materialities that can be used systematically for a regulated

12 Sybille Krämer, “Was haben die Medien, der Computer und die Realität miteinander zu tun?,” in Medien, Computer, Realität, 9–26; quotation from 15. 13 Seel, “Medien der Realität und Realität der Medien,” 245. 14 Regarding the inheritance of Husserl’s eidetics in systemic communication theory, see also G. C. Tholen, “Platzverweis: Unmögliche Zwischenspiele von Mensch und Maschine,” in Computer als Medium. Literatur- und Medienanalysen, ed. Norbert Bolz, Friedrich Kittler, and Georg Christoph Tholen (Munich: Fink, 1996), 11–138; esp. 23–28. 15 Niklas Luhmann, “Wie ist Bewußtsein an Kommunikation beteiligt?,” in Materialität der Kommunikation, ed. Hans Ulrich Gumbrecht (Frankfurt am Main: Suhrkamp, 1988), 884–908; quotation from 884. 16 Ibid., 891–92.

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and socially relevant semiotic (or symbolic) coupling of living systems.” 17 Just as in the theory of generalized media of communication, the metaphorics of nontransparency and transparency remains uninterrogated. Instrumental metaphors of media as means are the counterpart to anthropological metaphors, and supplement them. I will only highlight a few tropes and figures of this discourse, for two reasons: one, the following examples show that the classic metaphoric patterns of substitution and similarity remain valid for contemporary media theories; and two, trying to replace “man” with “technology,” as some expressly non-metaphoric media theories do, will always result in an involuntary continuation of the imaginary mirror symmetry and binarism of anthropological and instrumental discourses. To consider technical media replacements or extensions of organs is the metaphor of bodily projection, which rhetorically opposes natural and artificial functions. After Arnold Gehlen, it is above all Jürgen Habermas who falls for the same circular arguments in his book Technology and Science as “Ideology” (Technik und Wissenschaft als “Ideologie,” 1968), which also organizes theories of artificial intelligence. The “technical project of humanity,” defined as a “functional circle of rational acts,” is projected, over the course of time, from the body onto the world of “technical means.” Marshall McLuhan’s popular rhetorical figure of media as amputations and extensions of man, and Derrick de Kerckhove in his footsteps, repeat that same equation of brain and technology, as well as the opposition of the sensual and the abstract.18 This amalgamation results in the familiar structure of the anthropological critique of media. The rhetoric of a loss of immediacy tips into the promise of a planetary consciousness.19 The doppelgänger of such holistic organ metaphors that define humans as quasi-machines (in the anthropological discourse) is the universalization of the machine as the inhuman that will at least partially replace humans (instrumental or materialistic discourse). Even a discourseanalytical definition such as Friedrich Kittler’s, taking technical codes for bearers of media, cannot avoid metaphors of imitation and implementation, simulation and substitution (of, for instance, subjectivity and intelligence).20 The claim to replace human language, or, more precisely, to replace the metaphoric logic of substitution in language (that irritating chasm between the symbolic and the real, in the Lacanian sense), with a purported materialism of technology—this claim merely transfers the alleged immediacy of the subject onto technology. Any ontological real17 S. J. Schmidt, “Medien: Die Kopplung von Kommunikation und Kognition,” in Krämer, Medien, Computer, Realität, 55–72; quotation from 57. 18 Marshall McLuhan, Understanding Media (New York: McGraw-Hill, 1968), 63. 19 Derrick de Kerckhove, Schriftgeburten: Vom Alphabet zum Computer (Munich: Fink, 1995), 29. 20 Friedrich Kittler, Draculas Vermächtnis: Technische Schriften (Leipzig: Reclam, 1993), 8.

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ism that pretends to avoid the detours of metaphor leads to the positing of concepts as “absolute metaphors.” 21 Consequently, a “purely” technical (or even mathematical) discourse on media must consider human language, understood as merely “natural,” a dwindling moment in the materiality of communication, and thus posits something very akin to the Hegelian Geist. The comparison with Hegel’s concept of absolute knowledge not only serves as a metaphor, but also claims the same validity as the concept of spirit, while replacing it with that of the machine or of calculability. The dialectical movement of the concept and its sublation is transferred onto the movement of media and their sublation by the Turing machine: “With the Universal Discrete Machine, the media system is closed. Media of storage and transmission both dissolve into the simulation of all information machines, simply because it stores, transmits, and calculates in each and every loop of its program. A depopulated bureaucracy assumes all functions sufficient and necessary for a formal definition of intelligence.” 22 Apart from presupposing “functional” achievements of intelligence, a move that repeats the instrumental metaphors of artificial intelligence in its equation of brain and computer and overlooks human subjectivity may not be fully circumscribed by intelligence. This attempted “closure” of the genealogy of media in the code differs from Hegelian dialectics only insofar as the “idea” or the “concept” is here dressed, or camouflaged, as the Turing machine. The commingling of the diverse and differing categorical statuses of mimesis, imitation, or simulation turns the as-if of the Turing machine, as a machine of complete calculability of the calculable, into an ontological statement that would fixate the essence of man anthropologically in order to sublate it: the calculation machine is the “paper machine,” which is man. However, Turing always insisted on the metaphoric chasm without which the famous comparison of his imitation game would not be a comparison.23 And it is only when metaphors of the comparability or similarity of humans and machines are taken to be ontological determinations that one can speak of “the end of man,” which the axiom of bodily projection for the sake of completion, completeness, and closure cannot avoid doing.24 The apocalyptic figure of speech that would reveal the “essence” of man as “come to itself” in 21 For example, Bernhard Dotzler and Friedrich Kittler, eds., Alan M. Turing: Intelligence Service; Schriften (Berlin: Brinkmann and Bose, 1987), 5; also Friedrich Kittler, Grammophon, Film, Typewriter (Berlin: Brinkmann and Bose, 1986), 8. 22 Friedrich Kittler, “Die künstliche Intelligenz des Weltkriegs: Alan Turing,” in Arsenale der Seele: Literatur- und Medienanalyse seit 1870, ed. Friedrich Kittler and Georg Christoph Tholen (Munich: Fink, 1989), 187–202; quotation from 196. 23 Alan Turing, “Über berechenbare Zahlen mit einer Anwendung auf das Entscheidungsproblem,” in Dotzler and Kittler, Alan Turing, 17–60; quotation from 20; Alan Turing, “Intelligente Maschinen,” in ibid., 81–114; quotation from 86 and 91. 24 G. C. Tholen, “Ende des Menschen?,” in Lab. Jahrbuch 1995/96 für Künste und Apparate (Cologne: Verlag der Buchhandlung Walther König, 1996), 320–24.

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the universal calculation machine merely dissembles and hides its own metaphor or revelation. We can also observe a tendency to anthropomorphize metaphors in the field of software history.25 The beginning of programming languages in the 1950s does not start a pure or linear story of its ideas and concepts; a Babylonian chain of interrupted developments, partial continuations, and paradigm shifts allows a history to be recorded in the sense of metaphorology or discourse analysis.26 Regardless of whether one describes programming languages according to their functional, structural, or object-oriented style and compares them with historical tendencies, or whether one situates an atopical space of different imperatives, oriented toward either the machine or communication, the dynamics of modular approaches and applications owes itself to the openness of the digital medium for different uses, even if it forgets its own origins. Especially since object-oriented computing in connection with direct manipulation of user interfaces carried the day, one should be wary of strictly contrasting the “authentic” code and its “inauthentic” metaphors. Instead, programming and its stylistic history follow procedures similar to linguistic styles. While initially the algorithms were given and programming was mainly a syntagmatic business that had to adhere to the connections of machinic logic, structural programming paradigmatically specified a complete problem space inherent to the matter at hand rather than having the programmer determine it. Objectoriented programming acknowledges that software development is mainly a syntagmatic process of moving without a holistic vision from component to component. The “objectivized” fragments then serve as metaphoric markers that help orient their metonymic combination.27 Here metaphoricity is not exhausted in a supporting role in developing concepts. Its nonconceptual character is systemic, as Hans Blumenberg demonstrated regarding the paradigm shifts of the concept of technology itself, especially from mechanistic to pragmatic metaphors.28 And it is not because of used-up metaphors, but rather because there is no simple concept of the digital to sum up software engineering as a kind of “information hiding”: each module should hide what it does.29 25 In addition to Sherry Turkle, see Wolfgang Hagen, “Computerpolitik,” in Bolz et al., Computer als Medium, 139–60, and “Der Stil der Sourcen,” in HyperKult: Geschichte, Theorie und Kontext digitaler Medien, ed. Martin Warnke, Wolfgang Coy, and Georg Christoph Tholen (Frankfurt am Main: Stroemfeld/Nexus, 1997), 33–68; Peter Schefe, “Prolegomena zu einer Agentologie,” in ibid., 411–32; Jörg Pflüger, “Über die Verschiedenheit des maschinellen Sprachbaus,” in Bolz et al., Computer als Medium, 139–60, and “Distributed Intelligence Agencies,” in Warnke et al., HyperKult, 433–60. 26 Wolfgang Hagen, “Die verlorene Schrift: Skizzen zu einer Theorie der Computer,” in Kittler and Tholen, Arsenale der Seele, 187–202. 27 Pflüger, “Distributed Intelligence Agencies,” 441. 28 Blumenberg, Paradigmen zu einer Metaphorologie, 91 29 Pflüger, “Distributed Intelligence Agencies,” 442.

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This dissimulation opens to a limitless metaphorization where a description of the interfaces of human–machine communication, and in particular the design of multimedia user interfaces, is attempted. The most common metaphors represent well-known models: dialogue, interaction, role-play, theatricality, performance. Taking computers as theater, we encounter mediators and agents as metaphors of performance. In terms of this metaphorical world theater in which we all play our roles, virtual agents may take our roles on the World Wide Web: “An agent is one who initiates and performs actions.” 30 In trying to decide whether artificial agents, softbots, or userbots on the Internet only improve the filtering of information or whether they can “replace” the intentionality and identity of the individual, the newest cyborg debates are not dissimilar from earlier literature on the automaton, and share with them certain prophesies of a cybernetic symbiosis of man and machine.31 After such a brief and incomplete overview of the metaphoric field, which lends epistemological contours to media studies and media theories, I would like to return to the question of the place of the medium. The definition of the digital medium as universal medium of transmission or simulation of signs and media generalizes the process and status of semiosis. What is the condition of such a transfer for the history of science? And how does the metaphoricity of the “as if” function as its pivot? Martin Burckhardt and others have traced its emergence in media history: if the “electromagnetic writing” of the digital code has opened the metaphoric and “trans-anthropological” horizon of media theory, then the concept of information is situated as an a priori of modernity. The computer as Turing machine relies on a historic mix of discourses and inventions, including Jacquard’s punch cards, Babbage’s analytic machine, and George Boole’s algebra. Martin Burkhardt is right to point out that Boole’s An Investigation of the Laws of Thought (1854) takes pride of place here. Once “0” and “1” no longer represent something, but become markers of a system within which something appears, the alternating oscillation of presence and absence is made possible along with “the universal medium of the electric 30 Brenda Laurel, Computers as Theatre (Reading, MA: Addison-Wesley, 1991), 47. Jörg Pflüger has precisely traced the genealogy of the metaphor of interaction: “Agents are computer programs that simulate a human relationship, by doing something that another person could otherwise do for you.” Instead of hierarchy and delegation, as Patti Maes records, we now also have the metaphor of collaboration: “The metaphor used is that of a personal assistant who is collaborating with the user in the same work environment.” Patti Maes, “Agents That Reduce Work and Information Overload,” Communications of the ACM 37, vol. 7 (July 1994): 30–40. 31 Hans-Dieter Bahr, Über den Umgang mit Maschinen (Tübingen: Konkursbuchverlag C. Gehrke, 1983); and Peter Galison, “Die Ontologie des Feindes: Norbert Wiener und die Vision der Kybernetik,” in Räume des Wissens: Repräsentation, Codierung, Spur, ed. Hans-Jörg Rheinberger, Bettina Wahrig-Schmidt, and Michael Hagner (Berlin: Akademie-Verlag, 1997), 281–324.

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current” as a carrier that stays neutral as to its message.32 This signals a transition of the understanding of metaphor from a merely figural expression to a means of transportation. But what meaning does this trace of difference of the electromagnetic binary code or “metawriting” have? Should the paradox of the nature of the electric sign be understood ontologically or metaphorically—or by another approach altogether? Burckhardt’s definition approaches the tipping point between metaphor and concept, and in the transition from the alphanumeric to the electric sign, everything is on the same level: “For the computer could care less whether it is a voice, an x-ray of a tooth, or the hyperlinked version of the Apocalypse of St. John. The message of the computer is always ‘Everything is the same’, and: ‘Nothing in the computer is what it is’.” 33 And yet, for media metaphorology in all its multiplicity, despite all the inflation and proliferation of expression, everything is not the same. What all of these different approaches have in common is that they rely on a concept of metaphor founded on a fundamental difference, namely the difference between concept and metaphor, which in turn is based on the metaphoric opposition of authentic and inauthentic meaning. Any attempt to determine metaphor without metaphors will result in the attempt to distinguish between a pure and an impure metaphor. This is not the place to rehearse the philosophical aporia from Plato and Aristotle to the present day, as Jacques Derrida demonstrated.34 Nor is the elective affinity between metaphor and technology news: but without problematizing the hierarchy of figural and proper meaning, of concept and metaphor and the like in media studies, one would be stuck repeating the same structures and considering them the proper meaning of media or man. Only the determination of metaphor as transferability as such allows a withdrawal of metaphor from itself, which allows us in turn to withdraw the mediality of the media from anthropological or instrumental interpretations. The interference between old and new media, and particularly the technically possible but aesthetically not yet fully comprehended simultaneity of heterogeneous modes of audibility, visibility, and so on, disperses not only the referential horizon of pragmatic media use, but also the space of mediality itself. The structure of digital metaphorics that can transmit different modes of transmissibility is articulated as interruption 32 Jacques Lacan, “Kybernetik und Psychoanalyse oder Von der Natur der Sprache,” in Das Ich in der Theorie Freuds [Das Seminar, Buch II], Weinheim und Berlin: 1991, originally in French: Le Seminaire, vol. 2, 1954–1955 (Paris: Seuil, 1988); Martin Burckhardt, “Unter Strom: Der Autor und die elektromagnetische Schrift,” in Krämer, Medien, Computer, Realität, 27–54, quotation from 44; see also Jens Schreiber, “Stop Making Sense,” in Bolz et al., Computer als Medium, 91–110. 33 Burckhardt, “Unter Strom,” 43–44. 34 Jacques Derrida, “The White Mythology: Metaphor in the Text of Philosophy,” New Literary History 6, vol. 1 (1974): 7–74, and “The Retrait of Metaphor,” Enclitic 2, vol. 2 (1978): 5–34. Following him is Anselm Haverkamp, ed., Theorie der Metapher (Darmstadt: Wissenschaftliche Buchgesellschaft, 1996), and Christiaan L. Hart Nibbrig, ed., Was heißt “Darstellen? (Frankfurt am Main: Suhrkamp, 1996).

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and deferral of media metaphorizations, which are equally valid and equivalent to the transmitting binary code. Even the most general, toollike definition of the computer as a universal medium of symbolic processing of data and symbolic “machines” points toward a metaphoric field that is at odds with the traditional understanding of metaphor. It not only contains the multiple uses, but also brings to the fore the metaphoricity of the metaphor in the word “as”: the computer as calculator has no different attributes from the computer as typewriter or as a means of telecommunication. In other words, the play of the “as if” is neither inherent nor external to the digital medium—rather, it marks the indifference of purely combinatory options in intermedial representation. It is possible to relate this to the disinterested technology of art, but the freedom from instrumentalizing references as they are alleged about the realm of disinterested pleasure are not simply given. At least under digital conditions it is not a matter of an aesthetic discourse of genius, creator, or author. The oscillation between presence and absence may help rearticulate the relationship between art and technology: the indifference of the digital medium to signs, sounds, images, poetics, and so forth points to a technology that is different in itself—points to its interstice, which aesthetics reconfigures anew, again and again. Now what would a metaphorological determination of the computer as medium look like? Does the computer become the integrator of all other media, and is it transferred into all other media? When something is transported by something else to another place, then we have an atopical space of transferability without which the transfer would not take place.35 But how would the nonmetaphoric transfer of the computer “as such” be distinct from the mere metaphoric transfer that proliferates in its multimedia representations? The computer as medium only exists in differing from itself—that is to say, in deferring its “authentic” meaning in all its interfaces, programmable entities, and user surfaces. The digital medium only exists in its manifold metaphoricity. And if it is not possible to deal with metaphorology unmetaphorically, then each and every concept of metaphor can itself be metaphorized. No meta-metaphor, no metaphorology will ever be shored up against the strong pull of signification; metaphors happen—by way of a reserve, a withdrawal, a turn on themselves. Metaphoricity in the determination of the computer as medium shows itself as transferability of (neither authentic nor inauthentic) metaphors without which multimedia representation would be mere apparition. Programming languages as well as the source code are representations of the processor, not the processor itself. In this sense, they are, along with the operating systems and applications they make possible, fragmentary dissimulations. The mediatic noncoincidence of 35 See Samuel Weber, “Virtualität der Medien,” in Schade and Tholen, Konfigurationen, 35–49.

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the digital medium with itself is repeated on the metaphoric levels of graphic user interfaces and their iconic appearance. And its metaphoricity increases with the digital representation of earlier storage and transmission media, because it means the simulation not only of their apparatus but also of their specific forms—which are intermingled into hybrids that, beyond mere recycling, try out new forms and techniques of perception, composition, and montage.36 Even under digital conditions, the interface between humans and media remains accessible only by way of imaginary interfacing. It would be a metaphoric short circuit to talk about a symbiosis of technology and subject, and the same goes for the apocalyptic image of humans losing themselves by removing themselves from themselves with the help of electronic media and prostheses. In the applications of new media, that is to say in the mise-en-scène of simulated surfaces, observations, and points of view, certain epic forms of closed and continuous narration are dispersed and interrupted in the disseminating performance of theater, installation, and dance, because their theatricality takes place as mediatic exposition of “inauthentic” gestures and utterances. McLuhan’s claim that what appears in media is other media can only become readable when the status of this appearing itself turns into the focus of media theory. Media metaphorology directs us to understand them as neither means nor milieu, but as partial framing and skewing of the perceptible and the communicable. If it is true that contemporary art—from early video installation to nonclassical dance performance to postdramatic montage onstage—asks the question of the place of the body anew and differently, then such practice constitutes a consciously hybrid performance and perforation of the supposed immediacy of the body. Performance here means reflection and displacement of phantasmatic self-images and human ideals, insofar as they are increasingly staged by the media as bodycentric—from the endless confessionals of the talk shows to the dream bodies in cyberspace. Performance art would be the art of breaking, ironically or grotesquely, with the traditional narration of self-identity. At the same time, the artistic experiment of shifting horizons also fragments the telematically spreading identification with globalized and globalizing norms of a homogenous culture, by reminding us of the differences they would make us forget. The transmission of this decentering intervention within the global net of communication can only be achieved in exposing the homogenizing metaphor of connected, “social” communication, and especially as the interruption of that message that would tell us that the medium itself is good tidings. 36 Case studies of this art of intermedial intersection can be found in Barbara Naumann, ed., Vom Doppelleben der Bilder (Munich: Fink, 1993); Yvonne Spielmann, Gundolf Winter, eds., Bild, Medium, Kunst (Munich: Fink: 1999); and Schade and Tholen, Zwischen Kunst und Medien.

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IV From Pebbles to Digital Signs. The Joint Origin of Signs for Numbers and for Script—Their Intercultural Standardization and Their Renewed Conjunction in the Digital Era Gert Schubring I Mesopotamia 116 — iI The Way to Effective Positional Systems 120 —  iII Introducing the Metric System - Resistance to Universalization 123 —  iV The Digital Era 125

Gert Schubring is a retired member of the Institut für Didaktik der Mathematik, a research institute at Bielefeld University, and at present is visiting professor at the Universidade Federal do Rio de Janeiro (Brazil). His research interests focus on the history of mathematics and the sciences in the eighteenth and nineteenth centuries and their systemic interrelation with social-cultural systems. One of his specializations is history of mathematics education. He has published several books, among which is Conflicts between Generalization, Rigor and Intuition: Number Concepts Underlying the Development of Analysis in 17th–19th century France and Germany (New York, 2005). He is Chief-Editor of the International Journal for the History of Mathematics Education.

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The historical development of the encoding of information, until its current, almost universal dominance, has been extraordinarily complex. Encodings began as concrete materializations and were intimately tied to specific social and cultural forms of living. Characteristic stages of encodings, from highly differentiated material sign systems to abstract and globally used symbols, will be presented and ana­ lyzed in this text. Particularly revealing for characteristic patterns of these transformations is how the two encoding systems—numbers and script, or numeracy and literacy, which developed separately over millennia—were and are related to each other. It is worth noting that the resulting processes of universalization and standardization by Media Metaphorology: Irritations in the Epistemic Field of Media Studies

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no means occurred smoothly or easily; rather, these processes were confronted with considerable resistance, due to the weight of local and regional traditions. I Mesopotamia The emergence of sign systems for script and for numbers has been especially studied for the Mesopotamian cultures, which is due to the durable material they used for writing and calculating. The first artifacts used there, since about the fifth millennium BC, were quite different from any known form of writing at the time, and were therefore not studied by archaeologists for a long time. They were seemingly strange objects, made from stone instead of clay, cut into differently shaped but non-standardized forms. The Greeks, in particular the Pythagoreans, would use them for representing figurate numbers and call them yhjoi (psephoi). The Romans standardized them for calculating and called them calculi—the origin of calculus resides in the oldest known artifacts for sign systems! The English term for them is pebbles or tokens. Fig. 1 Simple tokens. Denise SchmandtBesserat, How Writing Came About (Austin: University Press, 2008), 16.

The tokens simultaneously indicated a quantity and a quality: they signified an object (quality) and its size (quantity). They were laid on top of each container to indicate the objects in the container and their amount. From the earliest times of Mesopotamian states, before 3000 BC, the artifacts were used for administrating goods delivered by the tributaries to the temples, which were the state administrative as well as economic centers. With the evolution of administrative practice, the tokens were made more specific to indicate qualities and quantities of objects—particularly once the technique to engrave signs with clay tablets emerged—so that bookkeeping could occur away from the place where the objects were stored. Recent research has been able to establish the list of signs used for bookkeeping in Uruk, an early urbanized civilization from the third millennium BC in Mesopotamia. Here is a list of sixty signs that shows sophisticated cuneiform techniques:

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Fig. 2 The numerical signs of the protocuneiform texts from Uruk. Hans J. Nissen et al., Archaic Bookkeeping: Early Writing and Techniques of Economic Administration in the Ancient Near East (Chicago: University of Chicago Press, 1993), 26.

It must be stressed that this list was only possible due to modern computer techniques that enabled the systematic evaluation of the clay tablets preserved in various sites and museums around the world. However, even more importantly, these computer techniques were decisive in unraveling the meaning of these signs. The traditional literature contained contradictory attributions and unresolved questions of the signs’ meaning, since it was not possible to systematically evaluate all the signs in the context of how they were used on the clay tablets. A group of researchers—Peter Damerow, Robert Englund, and Hans Nissen—undertook this careful and extensive investigation, since the 1970s. Their research revealed not just one number system—the sexagesimal system, for instance, which one might expect—but several metrological systems, and each system was specific for a certain class of objects. Furthermore, numerous signs were used in multiple diverse metrological systems, and the signs had differing meanings in several of them. This result resolved the inconsistent attributions of meaning to the Uruk signs; yet it implied that the signs represented about six thousand different meanings. Here are three different metrological systems to illustrate their specificity for object classes: Fig. 3 Metrological systems, different for classes of objects. Nissen et al., Archaic Bookkeeping, 28.

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The first system counts mainly discrete objects, such as humans and animals, fish, and containers; the second counts dead animals and jars of certain liquids; and the third counts other discrete objects, such as grains and fresh fish. Even more specific are the sign systems for various grains, in particular for barley, malt, oats, and barley groats. One remarks by the frequency of ingredients the importance of brewing beer. In these early sign systems, the signs stand for classes of objects—thus, for qualities—and for their quantities. Hence, they do not signify numbers, but magnitudes. Research on the history of writing—especially the work of Denise Schmandt-Besserat 1 —and research on the history of mathematics agree that number and script originated in the same sociocultural setting. Eleanor Robson, a researcher of Mesopotamian mathematics, recently formulated the consensus of both sides: “The temple administrators of Uruk adapted token accounting to their increasingly complex needs by developing the means to record not only quantities but the objects of account as well. Thus numeracy became literate for the first time in world history.” 2 Writing and calculating was thus taught in an intertwined manner: “As the production of accounts entailed complex multi-base calculations, trainee scribes had to practice both writing and calculating, and they did so increasingly systematically.” 3 There is a noticeable steady process of standardization in these metrological systems, which also implies a greater abstraction of operations with quantities. A highly telling example is a clay tablet where various amounts of different grains are added, thus abstracting the specific type of grain. Fig. 4 Complex protoarithmetical summation involving replacement rules for symbols representing concrete units. Nissen et al., Archaic Bookkeeping, 133.

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See Denise Schmandt-Besserat, How Writing Came About (Austin: University of Texas Press, 1996). Eleanor Robson, Mathematics in Ancient Iraq (Princeton, NJ: Princeton Univ. Press, 2008), 28. Ibid., 40.

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At first, the given units of grains were indicated with the signs from the different systems for barley, barley groats, and malt—which followed an operation by which the signs for units of barley groats and malt were transformed into the signs for barley. Having homogeneous terms in just one metrological system, the differentiated units were now simplified, transforming them into the respective less differentiated, thus more general or ‘higher’ units, finally ending with the sum of all products in a simple expression—one general quality of grain. In the long run, the standardization of metrological systems and the abstraction of qualities continued universally, such that only two signs remained in the Old Babylonian civilization: no longer quantities, but now numbers—namely, the signs for 1 and for 10 (and its higher powers in the sexagesimal system): Fig. 5 The main stages of the evolution of cuneiform signs. Robson, Mathematics in Ancient Iraq, 76.

As is well known, this considerably developed number system suffered from one defect, the lack of a sign for zero, so that the place values were not unequivocally determinable. There are examples of clay tablets where Babylonian scribes had committed calculating errors because they had not considered the empty space necessary for representing an empty unit. Occurring parallel to the transformation of magnitudes into numbers, cuneiform signs were evolving for writing words, from the multitude of early icons to composite forms of the simple wedge element: Fig. 6 Evolution of signs for words, from iconic symbols to cuneiform signs. A. H. Podany and Marni McGee, The Ancient Near Eastern World (New York: Oxford University Press, 2005), 41.

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II

The Way to Effective Positional Systems

Sumerian-Babylonian script was not an alphabetic system—apparently, the first alphabetic system was Phoenician, which emerged around 1000 BC. The Phoenician alphabet became the model for the Greek alphabet, and the Greeks used it to considerably improve the number system. The number system of Miletus applies the letters of the Greek alphabet as signs for numbers, an improvement that leaves no ambiguity with regard to the values of the numbers—even without a sign for zero, numbers can be written without any doubt about their positional value. Fig. 7 The Greek numeration system of Miletus. Gottfried Friedlein, Die Zahlzeichen und das elementare Rechnen der Griechen und Römer und des christlichen Abendlandes vom 7. bis 13. Jahrhundert (Erlangen, 1869), 71.

The numbers are written by juxtaposing signs. For instance, 867 is indicated as wxz and 807 as wz. This system needed twenty-seven signs, but the Greek alphabet only had twenty-four. To remedy this, three additional signs were introduced from older script variants and from the Phoenician: the signs for 6, 90, and 900. While the Egyptian system of numeration and its Roman counterpart, which followed its structure, did not present innovations in the direction of a more general positional system, the first time a decimal positional system with a sign for zero developed was in India around AD 500. Yet the writing for this system, which was transmitted in the ninth century to the Islamic civilization and therefore became known as the HinduArabic number system, varied enormously and was, for a long time, not standardized. In particular, there were the Western Arabic and Eastern Arabic variants; it was the Western Arabic variant (no. 8 in the following table) that found reception in Europe (the Eastern Arabic one is no. 5.)

Fig. 8 The evolution of the Hindu-Arabic numeral system. Johannes Tropfke, Geschichte der ElementarMathematik. Arithmetik und Algebra (4th edition, Berlin: de Gruyter, 1980), 66.

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It is often recounted that the Hindu-Arabic numbers were not accepted immediately in (Christian) Europe during the Middle Ages: in numerous historical accounts, the Catholic Church is credited with forbidding the use of these numbers in the fourteenth century. As a detailed recent study has shown, the Church was not involved at all; there were no fundamental or ideological reasons against the use of the Hindu-Arabic numbers. Instead, it was the guild of merchants in Florence that warned against their use in 1299—the non-standardization of the numbers in written form resulted in the evident danger of fraud.4 Hesitation or resistance to the numeral system was not only restricted to Western Europe. Although our present terms “Arabic numbers” and “Hindu-Arabic numbers” suggest that they became the dominant system in the Islamic civilization, this is not actually the case. In reality, this new system was not generally accepted, and two traditional systems remained in practice until the nineteenth century (Abdeljaouad 1986): on the one hand, the sexagesimal system and, on the other, an alphabetical system that was a transposition of the Greek system of Miletus.5 Fig. 9 The alphabetic Arabic numeral system.

III

Introducing the Metric System

Although the Hindu-Arabic numbers were effectively accepted and used in Western European cultures since the introduction of the printing press—all the printed arithmetic and mathematics books used the “new” numbers—a decisive advantage of this system was not yet understood and applied: that they constituted a decimal system. The units for weights and measures did not have a decimal structure for their subunits, but instead used highly complicated systems. Think of the old subdivisions of a British pound—one pound was twenty shillings and 4 5

Heinz Lüneburg, Von Zahlen und Größen: Dritthalbtausend Jahre Theorie und Praxis (Basel: Birkhäuser, 2008), 106–9. See Mahdi Abdeljaouad, “Vers une épistémologie des décimaux,” Fragments d'histoire des mathématiques, tome 1, ed. APMEP (Paris: APMEP, 1986), 69–97.

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one shilling was twelve pence—or the subdivisions of yard into feet and inches, or of ounces, and so forth. Moreover, there was no uniformity for the absolute values of the measures—neither for the territory of a given country, nor for entire regions; rather, the values might be different from one town to the next. These incompatible weights and measures constituted major obstacles for commerce. One of the major projects of the French Revolution was to standardize and universalize weights and measures. The Republic even organized the first international congress on science, in 1798/99 in Paris, to establish the exact definitions of the new measures, the meter in particular.6 A preliminary definition of the new units of length had already been established and published in 1793. The conception for the new measures was to have them based on “natural” data; thus, the meter was defined as one-millionth of the earth’s meridian. Fig. 10 The three prototypes for the new poids et mésures: meter, kilogram, and liter. Musée des Arts et Métiers, Paris. Photo by the author.

Extensive and sophisticated astronomical observations were carried out to achieve exact values. The 1793 publication also gave the concordance of the new length units with the old units: Fig. 11 The new system of weights and measures, here showing length units, as decreed by the French parliament on August 1, 1793. Décret no. 1393 de la Convention nationale, du 17 août 1793, l'an second de la République française, une et indivisible, qui établit l’uniformité et le système général des poids et mesures (Mamers: Imprimerie de Boulanger, 1793).

6 Michael Crosland, “The Congress on Definitive Metric Standards, 1798–1799: The First International Scientific Conference?,” Isis 60, no. 2 (Summer 1969): 226–31.

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In 1793, the liter and kilogram were not yet in use; rather, pinte (pint) was the measure for volume and grave (heavy) was the measure for weight. The reformers’ intention to universalize a metric decimal system was so radical that the seven-day week was also changed to the ten-day décade, and the circle was divided in 400 degrees (each right angle had 100 degrees). While the décade did not survive very long, the 400-degree circle was implemented for quite a while, particularly in astronomy. IV

Resistance to Universalization

The destiny of the metric system, however, is telling. The French Revolution was driven by the “tiers état” (third estate)—the bourgeoisie— against the feudal powers and the clergy. The famous three keywords for the Revolution—liberté, égalité, fraternité—were originally slightly different: liberté, égalité, propriété. These expressed a clear socio-economic program: not only individual liberty, but also free economic exchanges, freedom for commerce without risks for property. For the free circulation of goods, obstacles like the abundance of local measures should be substituted by a universal standardized system of weights and measures. One of the objectives of the international Science Congress in 1798/99 was therefore to disseminate the metric system to all countries. Due to France’s conflict with Great Britain, the British neither participated nor accepted the metric system. Countries that were in some way allied with France accepted the new measures, although in general they discontinued them after the fall of the Napoleonic Empire. Despite the strong political intention to universalize the metric system, extraordinarily enough it was met with strong resistance by those who were mainly meant to apply it, particularly merchants. They had internalized the old systems that were embedded in century-long traditions, although they were impractical and unwieldy, to such an extent that simple laws prescribing the application of the metric system proved ineffective. A law from November 4, 1800, tried to urge the acceptance of the metric system by allowing the substitution of the new names by the old ones—thus pound instead of kilogram, pint instead of liter, and finger instead of centimeter. In 1812, a return to the old subdivisions was even allowed. Regarding lengths, for instance: “une toise de 2 mètres, se divisant en 6 pieds; le pied valant ainsi un tiers du mètre, se divisant en 12 pouces, le pouce en 12 lignes.” 7 This resulted in enormous confusion and a considerable amount of fraud. Nevertheless, it was a law only from 7

Dénis Fevrier, Métrologie: Histoire du mètre, at the site of the French Ministère de l’Artisanat, du Commerce et du Tourisme: http://www.entreprises.gouv.fr/metrologie/ histoire-metre (last modified November 12, 2014). See also Marquet, Louis, Albert Le Bouch, and Yves Roussel. Le système metrique, hier et aujourd'hui (Amiens: ADCS, 1997). “One toise being equivalent to two metres, to be divided in 6 feet; one foot thus having the value of one third of a metre, to be divided into 12 inches, and one inch into 12 lines”.

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July 4, 1837, that definitively applied the metric system as mandatory in France, effective beginning in 1840. In other European countries, governments were generally not active in introducing the metric system, and popular resistance endured for extended periods. Nineteenth-century Germany’s multitude of independent states is a case in point. A particularly telling example concerns the duchy of Holstein, north of Hamburg. An 1854 currency reform had measures specific for each sub-region (as shown by an arithmetic schoolbook from the period). For instance, grains had different measures in Hamburg and Dithmarschen. In Hamburg, the measures for wheat, rye, and peas, were different from those for barley and oats. The first group is measured in Last,8 which subdivides into three Wispel. For the second group, one Last divides into two Wispel. For both groups, one Wispel divides into ten Scheffel (bushel). But the Scheffel divides differently: into two Fass (barrel) for the first group and three Fass for the second. One Fass divides into two Himpten, and one Himpten into four Spint. In Dithmarschen, linseed is measured by dividing one Tonne (ton) into six Scheffel and each Scheffel into ten and two-thirds Kannen (pot).9 Regarding the measure of areas, the following extract from the schoolbook shows the enormous differentiation among even much smaller regions: between the towns of Hamburg and Glückstadt, the Ämter (administrative units) Steinburg and Wilster Marsch, and even the north and south of Dithmarschen. The principal area unit is called a Morgen (acre). Fig. 12 Metrological systems for areas in various regions of Holstein. Kroymann, Gemeinnützliches Rechenbuch, 341.

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Since all these metrological units were so highly local and unknown in other regions and countries, a translation into English can be given only when there is some resemblance to more widely used terms. The intention here is to visualise the complex structure of the metrological systems. J. Kroymann, Gemeinnützliches Rechenbuch, vierzehnte Auflage, vermehrt und verbessert von J. Alpen (Altona: Hammerich, 1854), 340.

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V

The Digital Era

While script and numbers originated together, they developed along different paths, although the Greek and the Arabic numeration systems showed affinities. Both strands converged again, however, with the rise of the digital era. The establishment of the theoretical foundations for digitalizing mathematics in its entirety can be attributed to David Hilbert. In his famous 1917 Zürich conference on axiomatic thinking, he reported on the progress of his program to arithmetizing mathematics. Satisfied, he asserted that the entire extended theory of Euclidean geometry can be constructed by means of analysis, based on the theory of real numbers. This theory, in turn, can be shown to be free of contradictions when the theory of integer numbers is free of contradictions. The only open problem is, as he pointed out, showing that the axioms of the integer numbers are free of contradictions, which should be the task of logic.10 Although this last step was not successful, due to Gödel’s incompleteness theorem of 1931, dynamic software demonstrates vigorously how mathematics can be digitalized. Regarding script, it proved to be even easier to digitalize words, to transform them into chains of the two signs “0” and “1”: words had to be dissected into their letters, the ASCII code of these letters had to be found, and then their binary codes had to be established. As these procedures evolved, words and numbers were documented to be of the same nature: certain binary codes. Fig. 13 The first PC for word processing— the Commodore 64.

As in all the historical cases so far, we can also note some resistance here against complete universalization. The digitalization of words supposes that words are constituted by means of an alphabet. Yet some languages are not based on an alphabet—and these, like Chinese and Japanese, are not 10 David Hilbert, “Axiomatisches Denken,” Mathematische Annalen 78 (1918): 406ff.

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minor languages, and are based on ideograms, tens of thousands of them! On the other hand, computers are used to compose texts in Chinese and Japanese. The ideograms cannot actually be coded directly; a relatively slow way is to write out the symbols with the mouse, so that the resulting geometrical figure will be transformed into encoded elements. Quicker ways consist so far of software programs that treat the ideograms as graphical elements. One of these software approaches for Chinese is the Cangjie input method, which corresponds to a simplified use of Chinese. Fig. 14 An example of how a Chinese term is decomposed into elements that can be coded.11

Chinese icons are composed of “radicals.” There are twenty-four such radicals; the Cangjie method is based on a geometric decomposition of the icons. The decomposition becomes specialized by seventy-six auxiliary shapes—often rotated or transposed versions of the radicals. Radicals and auxiliary shapes can be coded so that they can be entered into a computer on the standard keyboard. The use of this kind of software is not so simple. With Cangjie, for instance, you have to know the names of all the radicals and also of all their auxiliary shapes. Moreover, you have to be familiar with the decomposition rules for the icons. In the case of non-alphabetic scripts, indirect methods have to be applied that will eventually succeed in encoding their signs, too. Thus, globally, one can affirm a joint universalized encoding. In 2010, French artist Miguel Chevalier represented the existence of this code as a “binary wave”. Fig. 15 Miguel Chevalier, Binary Wave, 2010.

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V Foucault, Boole, And Our Deleuzean Century Gordon C.F. Bearn

I Limit-experiences in The Order of Things 131 — II Broaching Boole 135  — III George Boole (1815-1864) 139 · a) Purifying Language: Positivism and Formalization 140 · ­b) Interpretation 145 — IV The Hapless Task (Continental and Analytical Philosophy) 146 — V Waking Up: Our Deleuzean Century 151

Gordon C.F. Bearn is Professor of Philosophy at Lehigh University in Bethlehem, Pennsylvania (USA). He completed his PhD in philosophy at Yale University in 1985, acted as the Founding Director of the Humanities Center at Lehigh University from 2001 to 2008, and recently spent a year as a Visiting Scholar at Doshisha University, Kyoto, Japan (2014-15). He is the author of Life Drawing: A Deleuzean Aesthetics of Existence (Fordham University Press, 2013) and Waking to Wonder: Wittgenstein’s Existential Investigations (Suny Press, 1997).

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“It is this de-subjectifying undertaking, the idea of a ‘limit-experience’ that tears the subject from itself, which is the fundamental lesson that I have learned from these authors [Blanchot, Bataille, Nietzsche]. And no matter how boring and erudite my resulting books have been, this lesson has always allowed me to conceive them as direct experiences to ‘tear’ me from myself, to prevent me from always being the same.” Michel Foucault 1

It didn’t begin this way. This essay began with my surprise at stumbling across George Boole in the pages of Michel Foucault’s The Order of Things. That book, devoted to an archaeology of the Human Sciences and to a famous speculation about Foucault, Boole, And Our Deleuzean Century

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what the newspapers referred to as the End of Man, had also—en passant—sketched an archaeology of the formal sciences. This is the sentence that stopped me: “It was inevitable that a symbolic logic should come into being, with Boole, at precisely that period when languages were becoming philological objects.” 2 This paper thus began merely as an effort to moderate that surprise—not to discover whether it was true, but simply how Foucault came to write such a sentence. But as I plotted my trajectory, I found myself drawn both to the hapless task of distinguishing analytical 1

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Michel Foucault, “Remarks on Marx” [Interviews with Duccio Trombadori in 1978], (New York: Semiotext(e), 1991.), 31-32. These interviews, from 1978, give the lie to the widespread opinion that Foucault’s interest in limit-experiences subsided or disappeared from his work after about 1970. Unfortunately for me, in the same series of interviews [99-100], Foucault implies that The Order of Things is not an a experience book: “I have already spoken to you about the ‘limit-experiences’; this is really the theme that fascinates me. Madness, death, sexuality, crime: these are the things that attract my attention most. I have always considered The Order of Things a kind of formal exercise.” As I see it, the book comes into better focus as an analysis of a limit-experience. Michel Foucault, The Order of Things. (New York: Vintage Books, 1966), 297.

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from continental philosophy and to the more fortunate thought that one could find in Foucault’s 1966 book grounds for his suggestion, a scant four years later, that “perhaps one day, this century will be known as Deleuzean.” 3 I’m afraid I won’t be able to avoid that hapless task entirely, but I promise I will be setting my sights on a Deleuzeanism to come. But first, what is Foucault’s book about? Limit-experiences in The Order of Things.

I

Here is Foucault, ten paragraphs into his Preface: “The present study is an attempt to analyze that experience.” 4 What experience is he talking about? The shortest characterization is that it is the experience of violent laughter that shattered his world while reading Borges, which he describes in the very first sentence of the book: “This book first arose out of a passage in Borges, out of the laughter that shattered, as I read the passage, all the familiar landmarks of my thought–our thought, the thought that bears the stamp of our age and our geography–breaking up all the ordered surfaces and all the planes with which we are accustomed to tame the wild profusion of existing things, and continuing long afterwards to disturb and threaten with collapse our age-old distinction between the Same and the Other.” 5 3

Michel Foucault, “Theatrum Philosophicum” [a 1970 review of two books by Deleuze, Difference and Repetition (1968) and The Logic of Sense (1969)] in Aesthetics, Method, and Epistemology, Essential Works of Foucault, volume 2. (New York: The New Press, 1998), 343. 4 Foucault, Order, xxi. 5 Foucault, Order, xv.

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If metaphysics is the study of kinds of things, which things are the same and which are different, then Foucault’s laughter brought him to the threshold of a metaphysical experience, an experience of the wild profusion of being. The cause of this laughter was a classification of animals into not only unfamiliar but seemingly ridiculous categories. Foucault’s citation has made this passage famous, but perhaps it retains some of its original improbability. So here once again—newly laid out—Borges quoting a certain Chinese encyclopedia sorting all animals into the following fourteen categories: belonging to the emperor, embalmed, tame, suckling pigs, sirens, fabulous, stray dogs, included in the present classification, frenzied, innumerable, drawn with a very fine camelhair brush, et cetera, having just broken the water pitcher, that from a long way off look like flies.6 Foucault suggests that what confronts us in this classification is the limit of our system of thought; not the closure of our understanding, which continues without end, but the threshold of a beyond. In his words: “the naked [nue] impossibility of thinking that.” 7 A few pages later, he tells us that his book is an attempt to analyze an experience he describes as “the naked [nue] experience of order and of its modes of being.” 8 That is this book’s target. A bit further on, the Preface concludes by contrasting what he calls the “limit-experience” of the Other, which he had tracked in an earlier book on madness, with the present book’s focus on conceptions of 6

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Ibid. The passage from Borges appears in his 1942 essay “John Wilkins’ Analytical Language”. John Wilkins (1614-1672) was an English Bishop, an author, and one of the founders of The Royal Society. Borges’ essay is itself a criticism of the possibility, discussed by Wilkins, of there being a universal language of precisely the sort that was —according to Foucault—the Leibnizian gravitational center of the classical age (57). It ends with this lovely passage, which may also have appealed to the author of The Order of Things: “Hopes and utopias aside, perhaps the most lucid words written about language are these by Chesterton: ‘Man knows that there are in the soul tints more bewildering, more numberless, and more nameless than the colors of an autumn forest. . . . Yet he seriously believes that these things can every one of them, in all their tones and semi-tones, in all their blends and unions, be accurately represented by an arbitrary system of grunts and squeals. He believes that an ordinary civilized stockbroker can really produce out of his own inside noises which denote all the mysteries of memory and all the agonies of desire’” (Borges, “John Wilkins’ Analytical Language”, 1942, 232). Ibid., xv. Ibid., xxi.

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the Same, but I am not convinced by the contrast.9 I think that, by beginning with an order-shattering laughter, he opened a way to receive this book as addressed to a limit-experience: “the naked experience of order and its modes of being.” 10 That is the experience The Order of Things sets out to analyze.11 But it is still obscure. Foucault further characterizes this naked experience of order by way of a brief discussion of order in general. At this point, his leading example of an ordering is the fact—as we take it to be—that a dog and a cat resemble each other less than two greyhounds. We give the similarity between the two dogs more weight, even if the dog and the cat have both recently broken a water pitcher.12 Furthermore, it is, as he puts it, “immediately apparent” that the weighting of these similarities is not forced on us by either rational or empirical necessity.13 But this suggests that, even if an order convinces us it lives in the essences of things, this order could never be the whole story, because that order, however natural or involuntary it seems, is an ordering of what is—as Foucault puts it—“capable of being ordered.” 14 I am aware that it is notoriously difficult to decide how to write about what is capable of being ordered, for such capability ought to be a function of order, not prior to order. In an essay on Blanchot from the same year as our book, Foucault borrows Blanchot’s expression “things in their latent state,” and this notion of latency may help us approach the idea of being capable of being ordered. It will certainly put some of us in mind of the Deleuzean virtual.15 At this point, I simply want to draw attention to its being an issue of metaphysics. Foucault’s discussion has taken us to the door of metaphysics. But back to our Preface and its characterization of order. Here is Foucault: “Order is, at one and the same time, [1] that which is given in things as their inner law, the hidden network that determines the way they confront one another, and [2] also that which has no existence except in the grid created by a glance, an examination, a language; and it is only in the blank spaces of this grid that order manifests itself in depth as though already there, waiting in silence for the moment of its expression.” 16 The surface order of things is the grid or network that explains the behavior of things, but it is also, in depth, what becomes manifest in the bare fact that there is a grid. This order in depth has no existence except 9 Ibid., xxiv. 10 Ibid., xxi. 11 Ibid. 12 Ibid., xix. 13 Ibid., xix. 14 Ibid., xx. 15 Michel Foucault, “The Thought of the Outside”, 1966, in Foucault, Aesthetics, 155 and Gilles Deleuze, “Immanence: A Life”, 1995, in Gilles Deleuze, Pure Immanence: Essays on A Life, (New York: Zone Books, 2001), 25-33. 16 Foucault, Order, xx [numbers in brackets my own].

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in that grid, but in the blank spaces of that grid—the inaudible spaces beyond consistency and contradiction—”order manifests itself in depth as though already there, waiting in silence for the moment of its expression.” 17 Order in depth is not surface order, the grid providing the possibility of linking this to that, but neither is it surface disorder, the grid providing the possibility of confusing these with those in a great tangle. Neither order nor disorder, order in depth makes one understand the attraction of such a Joycean word as chaosmos.18 The “naked experience of order”—which our book sets out to analyze—is something like an experience of the silent depth of order.19 But Foucault’s characterization continues. The silent depth of order is introduced as the intermediary between “the fundamental codes of a culture,” codes that unreflectively show themselves in what we find remarkable—linguistically, perceptually, or otherwise remarkable—and explicit theories about that unreflective order.20 The ordinary grammar of the many dimensions of our lives set against theoretical accounts of that ordinary grammar. In between—or beneath—these domains is Foucault’s target domain, and he concedes that it is “more confused, more obscure, and probably less easy to analyze” than the other two.21 Here is a long sentence describing that obscure domain —the silent depth of order—the experience of which is the target of his analysis: “It is here that a culture, imperceptibly deviating from the empirical orders prescribed for it by its primary codes, instituting an initial separation from them, causes them to lose their original transparency, relinquishes its immediate and invisible powers, frees itself sufficiently to discover that these orders are perhaps not the only possible ones or the best ones; this culture then finds itself faced with the brute fact [devant le fait brut] that there exists, below the level of its spontaneous orders, things that are in themselves capable of being ordered, that belong to a certain mute order [ordre muet]; the fact, in short, that order exists [qu’il y a de l’ordre].” 22 17 Ibid. 18 Gilles Deleuze and Félix Guattari, What is Philosophy? (New York: Columbia University Press, 1994.), 204. 19 Foucault, Order, xxi. 20 Ibid., xx. 21 Ibid. 22 Ibid. There is a passage in Wittgenstein’s Philosophical Investigations that recalls the elements of these opening pages of The Order of Things, laughter, depth, and the ordinary grammar of our lives. Here is Wittgenstein: “The problems arising through a misinterpretation of our forms of language have the character of depth. They are deep disquietudes; they are as deeply rooted in us as the forms of our language, and their significance is as great as the importance of our language.—Let’s ask ourselves: why do we feel a grammatical joke to be deep. And that is what the depth of philosophy is.”  [Ludwig Wittgenstein. Philosophical Investigations, revised fourth edition. (Oxford: Wiley-Blackwell, 2009), §111].

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The idea seems to be that the ordinary grammar of our lives is mostly invisible because we look right through it. However, sometimes it changes, and then, even if the changes are at first imperceptible, they can become perceptible when the first waves of novelty interfere with the familiar undulating waves of the old. Through the diffraction between old and new, the grammar of our lives becomes visible. And thus to experience the grammar of our lives is simultaneously to experience the intermediate domain beyond any specific reflective or unreflective ordering, that is, the “raw being of order [l’être brut de l’ordre].” 23 And this raw being of order is “…the most fundamental of all: anterior to words, perceptions, and gestures, which are then taken to be more or less exact, more or less happy expressions of it (which is why this experience of order in its thick primary being [être massif et premier] always plays a critical role)…”.24 The Order of Things is devoted to an analysis of this limit-experience, a metaphysical experience: anterior to words, perceptions, and gestures, the naked experience of order in its mute raw being. A history of opinions about life, labor, and language would inevitably repress this naked experience of order; it would silence that experience, and thus, like The History of Madness before it, The Order of Things is not a history of opinions but an archaeology of silence.25 II

Broaching Boole

And now reread that sentence about Boole: “It was inevitable that a symbolic logic should come into being, with Boole, at pre­cisely that period when languages were becoming philological objects.” 26 Foucault is assuming a break around 1800 between the way language was written about in the Classical and Modern formations, and his claim of course is that there is something about early 19th Century symbolic logic that is congruent with the changes that gave us philology. So how does Foucault characterize the changes that turned language into a philological object? As Foucault tells it, from roughly 1600 to 1800, which he calls the Classical age, to speak was not to express oneself but to represent, to find a place where it would be possible to represent something with a name.27 Language was not expressive, it was representational—representational down to its very toes. The wild boy of Aveyron could 23 Ibid., xxi. 24 Ibid. 25 Michel Foucault, History of Madness, 1961, edited by Jean Khalfa. (London: Routledge, 2006), xxviii. 26 Foucault, Order, 297. 27 Ibid., 92, 117.

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vocalize, but until his sounds became representational, they could only be noises.28 Moreover, every part of the word or utterance was representational. Nothing was opaque; every vowel and every consonant was representational.29 “Within sentences, in that very depth where signification seems to be relying upon the mute support of insignificant syllables, there is always a dormant nomination, a form that holds imprisoned within its vocal walls the reflection of an invisible and yet indelible representation.” 30 Intrinsically representational, language was not, as we now think of it, “an exterior effect of thought,” standing in need of some theory of meaning. It had become “thought itself.” 31 The privileged status of language projected the dream of providing for each domain of knowledge an analysis of complexes into their simplest bits, and an invented language that would have one name for each of the simples and that would permit their combination in all ways, and only the ways, in which they actually combine. In other words, “…if all names were exact, if the analysis upon which they are based had been perfectly thought out, if the language in question had been ‘well made’, then there would be no difficulty in pronouncing true judgments, and error, should it occur, would be as easy to uncover and as evident as in a calculation in algebra.” 32 Foucault’s characterization of the Classical age features this project in the strongest terms. He writes: “Analysis was quickly to acquire the value of a universal method; and the Leibnizian project of establishing a mathematics of qualitative orders is situated at the very heart of Classical thought; its gravitational center.” 33 All of that was to change. Foucault’s account of how the study of language changes around 1800 features the philologist Bopp rather than Hamann and Herder and Humboldt whom, following Berlin, I will call expressivists.34 Foucault may have been indulging a desire to make historians of philosophy look narrow; after making his case, he throws out one of his testiest sentences: “Only those who cannot read will be surprised that I have learned 28 29 30 31

Ibid., 92. Ibid., 102-3. Ibid., 103. Ibid., 78. See also: Ian Hacking, Why does language matter to philosophy? (Cambridge: Cambridge University Press, 1978), 52. 32 Foucault, Order, 116. 33 Ibid., 57. 34 Isiah Berlin, Vico and Herder (1960) and The Magus of the North—J.G. Hamann and the Origins of Modern Irrationalism (1993), both now in Three Critics of the Enlightenment, (Princeton: Princeton University Press, 2000), 1-361; see also: Charles Taylor, “Language and Human Nature”, (1980), and “Theories of Meaning”, (1980), in Human Agency and Language, Philosophical Papers, volume 1, (Cambridge: Cambridge University Press, 1998), 215-292 as well as Ian Hacking, “How, Why, When, and Where Did Language Go Public,” (1992), in Historical Ontology, (Cambridge: Harvard University Press, 2002), 121-139.

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such a thing more clearly from Cuvier, Bopp, and Ricardo than from Kant or Hegel.” 35 But there is no need to choose sides—precise dating is not the issue, and the philologists and the expressivists were made for each other. After all, even though Foucault hides it in a parenthesis, he reports that “(Humboldt is not merely Bopp’s contemporary; he knew his work, and in detail).” 36 Let’s see. In the Classical era, things were made for representations. The modern era arrives with the resistance of things to representations. 37 Here is Foucault, characterizing the change: “Representation is in the process of losing its power to define the mode of being common to things and to knowledge. The very being of that which is represented is going to fall outside representation itself.” 38 Philosophers will be quick to agree with Foucault that “Kantian doctrine is the first statement” of being’s new opacity,39 but around 1800 the power of the sub-representational to organize representations also appears in the study of labor, life, and language. For example, beneath the visible characters tabled in the manner of Linnaeus, comparative anatomy discovered that “life in its non-perceptible, purely functional aspect…provides the basis for the exterior possibility of a classification.” 40 And beneath the Classical table of representational words, the philologist Bopp discovered an inflectional system guiding, from the darkness beneath, the forms and history of language. As Foucault puts it, these “formal elements, grouped into a system…impose upon the sounds, syllables, and roots an organization that is not that of representation.” 41 Language was “ceasing to be transparent to its representations, because it [was]…thickening and taking on a peculiar heaviness.42” It was becoming just another object of knowledge. You will guess from the power thus granted to the sub-representational that what is downgraded in this philological opening is meaning. In the Classical era, it was the unchanging root meaning that provided the constant thread through linguistic history; in the philological era this was reversed,43 with the meanings changing and the 35 Foucault, Order, 307. 36 Ibid., 290. 37 Ibid., 238-239. 38 Ibid., 240. 39 Ibid., 245. 40 Ibid., 268. 41 Ibid., 235, my italics. Hacking also finds language’s nonrepresentational status in the expressivist work of Hamann: “In short, language for Hamann is profoundly nonrepresentative. It is the exact opposite to what was claimed by the linguistic theories of the Enlightenment.” Hacking, “How, Why, When, and Where Did Language Go Public,” (1992), in Historical Ontology, (Cambridge: Harvard University Press, 2002), 121-139. 42 Ibid., 282. 43 Foucault, Order, 109

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non-representational inflections being preserved. 44 The individual inflectional structures are not transparent to representation, for this is an inflectional ordering of material sounds, not representational units. This privileging of sound divides language in its essence from the written word and brings it closer to speech, which, Foucault suggests, is why there is such an interest in “non-written literature, in folk tales, in spoken dialects.” 45 Separated from the dead 46 letter of the written word, language discovers its essence closer to music: “The poetic flash that disappears without a trace, leaving nothing behind it but the vibration suspended in the air for one brief moment.”  47 Philology’s expressivist sound. The way languages are individuated now changes, too. The Classical era individuated languages along a number of dimensions, all of which concern the representational form of the language. 48 Foucault: “…at that time, it was accepted that there were some languages that were more important than others, because they were able to analyze representations more precisely or more delicately. From now on, all languages have an equal value: they simply have different internal structures.” 49 Hence that curiosity for rare, little spoken, poorly “civilized” languages, of which Rask gave an example with his great voyage of inquiry through Scandinavia, Russia, the Caucasus, Persia, and India.50 Hacking underlines the togetherness of philology and expressivism by observing that Humboldt had used Bopp’s techniques to analyze some Polynesian languages, and that after Humboldt’s death, Bopp himself continued the study of Polynesian and Malayan languages.51 And as the Classical era was an age of the noun, the Modern era was an age of the (inflected or non-inflected) verb, an age of action and will. Here is Foucault: “Language is ‘rooted’ not in the things perceived, but in the active subject. And perhaps, in that case, it is a product of will and energy, rather than the memory that duplicates representation. We speak because we act, and not because recognition is a means 44 Ibid., 234. 45 Ibid., 286. 46 Berlin on Herder: “At any rate, the art of writing, the incorporation of thought in permanent forms, while it creates the possibility of a continuity of self-awareness, and makes accessible his own and other words to an individual, also arrests and kills” Berlin, Vico, 194. 47 Foucault, Order, 286. 48 Ibid., 282. 49 For expressivists, this equality of languages becomes the plurality of incommensurable values. Berlin quotes Herder maliciously setting himself against Kant’s racism: “‘there must be no order of rank…The Negro is as much entitled to think the white man degenerate…as the white man is to think of the Negro as a black beast’.” Berlin, Vico, 186 50 Foucault, Order, 285; R. C. Rask (1787-1832), a Danish philologist, began these expeditions in 1816 and returned in 1823. 51 Ian Hacking, “Night Thoughts on Philology” (1988) in Historical Ontology (Cambridge: Harvard University Press, 2002), 142.

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of cognition. Like action, language expresses a profound will to something.” 52 Language thus takes on an “irreducible expressive value,” “it manifests and translates the fundamental will of those who speak it.” 53 Such is the equally expressivist and philological conception of language of the Modern era. Foucault tells us that in a certain sense, in the Classical age, language did not exist.54 By that he meant that language was so intimately folded into representations that it had no independent, non-representational, being.55 It had unity as transparent discourse, but it was not an object of knowledge. Now language has become opaque, it exists, it does have an independent non-representational being, but it has been demoted to just another object of study. No longer the privileged medium for the tabular presentation of empirical knowledge, language has become an object like any other: dense and thick. Nevertheless, Foucault understands the Modern age as compensating for the diminished status of language in three ways: formalization, interpretation, and literature.56 Each of these compensations responds to the central feature of language in the Modern age, namely, that linguistic representation is the expression of a number of obscure sub-representational powers: powers of syntax, culture, race, class, sex, psyche, and more. I will discuss each of the three compensations, but now at last you may be hearing someone in the hall. Here comes Boole. III George Boole (1815–1864) Boole’s role in Foucault’s story is as someone seeking to purify the linguistic inflectional syntax of any specific linguistic density, not in order to let out the sub-representational will or people in our expressions, but rather to invent a syntax which, as far as possible, would not be the expression of sub-representational powers. This is in direct contrast to the role that Freud plays, which is to let dreams and slips so rattle the ordinary syntax of our language that space is made for a more authentic expression of the sub-representational powers struggling to be heard in proper speech. Foucault therefore announces: “This certainly explains the nineteenth century’s double advance, on the one hand towards formalism in thought, and on the other towards the discovery of the unconscious – towards Russell and 52 Foucault, Order, 290. 53 Ibid. 54 In this book, Foucault enjoys announcing the non-existence of what we were sure existed. During the classical age, we are not only told that language did not exist, but that life did not exist, production did not exist, and man did not exist. Ibid., 79, 128, 166, 308. 55 Ibid., 78. 56 Ibid., 296-300.

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Freud.” 57 It is really quite a remarkable sentence, even if, technically, Löwenheim might have been a better choice than Russell.58 After discussing Boole, I will tag Freud, and start heading home. A) Purifying Language: Positivism and Formalization. Foucault distinguishes two ways language was purified; purified to compensate, for instance, for the racially or nationalistically inflected sub-representational powers hidden in any language. The first method of purification he associates with “the positivist dream of language keeping strictly to the level of what is known.” 59 Positivism responded to the darker forces organizing representation by developing a language that was agnostic about the very existence of those forces. This was an aspect of the discovery in the physical sciences, and elsewhere, of “…a whole layer of phenomena given to experience whose rationality and interconnection rest upon an objective foundation which it is not possible to bring to light; it is possible to know phenomena, but not substances; laws, but not essences; regularities, but not the beings that obey them.” 60 If we think of this positivist purification as a purification of what grammatical propositions of science are about, then the second Boolean purification will be a purification of the scientific grammar itself. Here, at some length, is Foucault: “The other concern – entirely different from the first, even though in correlation with it – was the search for a logic independent of grammars, vocabularies, synthetic forms, and words: a logic that could clarify and utilize the universal implications of thought while protecting them from the singularities of a constituted language in which they might be obscured. [(And, now, here comes our sentence.)] It was inevitable that a symbolic logic should come into being, with Boole, at precisely that period when languages were becoming philological objects…”.61 An attractive thought might be to bring these two forms of purification together, a kind of Leibnizian marriage of merely observational concepts with the machinery of a logical calculus, a kind of “Logical Positivism”. But on to Boole. Boole was part of an English algebraic 57 Ibid., 299. 58 See: Jean van Heijenoort, “Logic as Calculus and Logic as Language,” Synthese, 17.3 (1967), 324-330 and Warren Goldfarb, “Logic in the Twenties: The Nature of the Quantifier,” Journal of Symbolic Logic, 44.3 (1979), 351-368. 59 Foucault, Order, 296. 60 Ibid., 245; My colleague Steve Goldman helped me to see that it is possible to read the whole of 19th Century physical theory this way: Maxwell, for example, confident of the equations characterizing electromagnetic fields but agnostic about the metaphysical nature of those fields. 61 Ibid, 297.

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tradition initiated in the 1830’s by George Peacock.62 The first sentences of Boole’s 1847 book The Mathematical Analysis of Logic, Being an Essay Towards a Calculus of Deductive Reasoning lay out what the next page calls “the true principle of the Algebra of Symbols.” 63 The sentences are these: “Those who are acquainted with the present state of the theory of Symbolical Algebra, are aware, that the validity of the processes of analysis does not depend upon the interpretation of the symbols that are employed, but solely upon the laws of their combination. Every system of interpretation that does not affect the truth of the relations supposed is equally admissible, and it is thus that the same process may, under one scheme of interpretation, represent the solution of a question on the properties of numbers, under another, that of a geometrical problem, and under a third, that of a problem of dynamics or optics.” 64 This may seem familiar, an instance of what Foucault called the Leibnizian “gravitational center” of the Classical age, the dream of a complete analysis of things so worded and regimented that, as I have already cited, “error, should it occur, would be as easy to uncover and as evident as in a calculation in algebra.” 65 But in the very passage in which he introduces Boole, Foucault makes a point of denying just that connection. That sentence again: “It was inevitable that a symbolic logic should come into being, with Boole, at precisely that period when languages were becoming philological objects: for, despite some superficial resemblances and a few technical analogies, it was not a question, as it had been for the Classical age, of constituting a universal language, but of representing the forms and connections of thought outside all language.” 66 The Classical dream requires an understanding not only of the complete Linnaean table of natural history, but of all the tables of all the empirical sciences, with each of the universal language’s simple symbols representing one of the ontological simples of the universe. Foucault’s sentence implies that he takes Boole to be doing something 62 In 1833, Peacock divided from Arithmetical Algebra something he called “Symbolical Algebra,” which was “essentially a science of symbols and their combinations, constructed upon its own rules, which may be applied to arithmetic and to all the other sciences by interpretation: by this means, interpretation will follow, and not precede, the operations of algebra and their results.” Peacock, 1833, in William Ewald, From Kant to Hilbert: A Source Book in the Foundations of Mathematics, (Oxford: Clarendon Press, 1996), 319. 63 George Boole, The Mathematical Analysis of Logic, Being an Essay Towards a Calculus of Deductive Reasoning, (New York: Philosophical Library, 1948), 4. 64 Boole, Mathematical Analysis, 3. 65 Foucault, Order, 116. 66 Ibid., 297.

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completely different; his use of arithmetical symbols to model the complexities of class membership did not presuppose an analysis of any particular domain into its simples. Boole’s algebra resonates not with Leibniz, but with Bopp. We have seen that, in a philological light, the important features of language are not the meanings but the inflectional system constituted by the interrelations of non-representational sounds. The true principle of the Algebra of Symbols can be construed as having two aspects in common with the philological formation. The first is that the mechanical power of the arithmetical operators themselves—the operators impressed by Boole into an algebra of deductive reasoning—does not depend on their individual meanings, only on their systematic relations.67 Even if Boole hopes those systematic relations will embody “the mathematics of the human intellect,” it is the relations among the algebraic operators that do the work, not the meaning of the operators themselves.68 Taking his notational system simply as a notational system, Boole was content to cite Mill: “’Whenever the nature of the subject permits the reasoning process to be without danger carried on mechanically, the language should be constructed on as mechanical principles as possible’.” 69 The other aspect of the true principle of algebra is that the elements on which Boole’s algebraic operators operate can be given any interpretation, or any interpretation “which does not affect the truth of the relations.” 70 In Foucault’s words, this would strip the singularity from any domain-specific language. Pace the mathematics of the human intellect, Boole’s algebra was mechanical all the way down. But the story of logic’s arithmetization in the 19th Century is not that simple. In 1879, Frege published what he called a Begriffschrift.71 It was also modeled on arithmetic; however, it did not share Boole’s philological spirit. It’s very name—Concept Writing—trumpeted its 67 Floyd argues that Wittgenstein’s Tractatus is an attempt to “resuscitate” this algebraic tradition: When he remarks that the essence of mathematics is work with equations according to “the method of substitution” by way of “calculation” (6.23-6.24), and when he calls the same method in logic a “mechanical expedient” (6.1262), he is resuscitating traditional algebraic terminology in order to undercut not Frege and Russell’s mathematical logic per se, but their claims for its contentfulness and success in simultaneously analyzing both logic and mathematics.” Juliet Floyd, “Number and Ascriptions of Number in Wittgenstein’s Tractatus” (2001) in Juliet Floyd and Sanford Shieh, Future Pasts: The Analytic Tradition in Twentieth-Century Philosophy (Oxford: Oxford University Press, 2001), 153, my italics. Floyd also reports, without endorsement, Dreben’s hunch that Whitehead’s early algebraic writings may have been explicitly cited in Wittgenstein’s pre-Tractatus notebooks on June 22, 1915. In Floyd, Ascriptions, 186. 68 Boole, Mathematical Analysis, 7. 69 Ibid., 2; here Boole cites: Mill, System of Logic, Ratiocinative and Inductive, vol. II, 292. 70 Boole, Mathematical Analysis, 3. 71 Floyd, Ascriptions, 150: “Indeed for Wittgenstein—unlike for Frege and Russell—a pure logic, a Begriffsschrift, is a mere Schrift, a mere script of signs used to keep track of wholly formal operations.”

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disavowal of the philological importance of non-representational inflections. Indeed, although it was never fully published, Frege became involved in a dispute with Schröder over the relation between Boole’s invention and Frege’s own: Schröder criticized Frege for only producing a Calculus not an Analysis, and Frege, confusingly, made the same charge against Boole.72 Sluga tells us that the heart of this dispute is Frege’s commitment to a principle of the priority of judgments over concepts, and that Frege himself was convinced that it was this principle that drew him to a function-argument analysis of judgments. 73 As Sluga tells the story, it was that very function-argument analysis which Frege thought freed his Begriffschrift from the charge of being merely a Calculus. In Frege’s own Leibnizian terms, it was “a universal characteristic.” 74 Frege explains: “Arithmetical, geometrical and chemical symbols can be regarded as realizations of the Leibnizian conception in particular fields. The Begriffschrift offered here adds a new one to these—indeed, the one located in the middle, adjoining the others.” 75 Just as chemical symbols have labeled and organized chemistry into inflectional 76 families, Frege has analyzed a different field, the field of truth.77 Moreover, judgments or thoughts, which according to Frege are prior to concepts, are the only things for which the question of truth or falsity can arise.78 And there you have it—by giving a function-argument analysis of judgment or thought, Frege was addressing himself to logic’s special domain: truth. That’s why Frege was convinced that the mere invention of his Begriffschrift has advanced logic, simply by virtue of the analysis it required.79 For Frege, there was more to logic than algebraic calculation; logic presupposed an analysis of a universal domain, the domain of truth, outside of which there was nothing. Foucault might therefore have distinguished Frege’s Leibnizian Classicism from Boole’s Philological Modernism, and then his account 72 Hans Sluga, “Frege Against the Booleans,” Notre Dame Journal of Formal Logic, 28.1 (1987), 80-98. If the new interpretation of function in 19th century mathematics parallels the rising importance of organic function in comparative anatomy, then it would be Frege’s interpretation of his Begriffschrift that recalled Leibniz’ Classicism, while the functional calculus itself advanced with Bopp’s Modernity. (For some of the mathematical history, see: Jamie Tappenden, “Mathematical and Logical Background to Analytic Philosophy,” in Michael Beaney, The Oxford Handbook of the History of Analytic Philosophy (Oxford: Oxford University Press, 2013), 318-354. 73 Sluga, Frege, 88. 74 Gottlob Frege, Begriffschrift: A Formula Language of Pure Thought Modeled on Arithmetic (selections) (1879) in Michael Beaney, The Frege Reader (Oxford: Blackwell Publishing, 1997), 50. 75 Frege, Begriffschrift, 50. 76 The periodic table of the elements shares in the Modern age’s reliance on opaque forces to organize families, families of inflection, families of valence; thus chemistry may be less Leibnizian than Frege assumed. 77 Gottlob Frege, “Thought” (1918) in Beaney, Frege, 325. 78 Frege, Thought, 327-328. 79 Sluga, Frege, 84 and Frege, Begriffschrift, 51.

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of the genealogy of the Formal Sciences in the 19th Century would reso­nate with a Foucauldian history of mathematical logic that we owe to a paper by van Heijenoort (published, as it happens, one year after The Order of Things).80 In Foucauldian fashion, van Heijenoort thea­tricalizes his idea by pointing out that a question that in 1930 was thought to have been immediately raised by Principia Mathematica had been invisible to the actual authors of that book in 1910. Here is van Heijenoort introducing a quotation from Gödel: “At the beginning of his 1930 paper on the completeness of quantification theory, Gödel describes the axioms and the rules of inference of Principia Mathematica and then adds: ‘Of course, when such a procedure is followed, the question at once arises whether the system of axioms and principles of inference initially postulated is complete, that is, whether it really suffices for the derivation of every true logico-mathematical proposition or whether, perhaps, true propositions (which may even be provable by other principles) are conceivable that cannot be derived in the system under consideration.’” 81 Van Heijenoort wanted an explanation for the invisibility of metasystematic questions to Frege and to Russell (and Whitehead, but that’s a different story 82). Without mentioning either Bopp or Foucault, he answered his own question by distinguishing the algebraic tradition of logic, which he described as treating language as a calculus, from the Fregean tradition of logic, which he described as treating logic as a language. Taking logic in this algebraic way, makes it possible to metasystematically compare the strengths of specific algebras. In contrast, when Frege treats logic as the language in which we do all our thinking, it is simply not possible to get outside of logic and ask whether it is complete or not, because to think is to think logically, and to think outside of logic is simply not to think at all.83 When logic is treated as a language, then metasystematic questions are not even invisible, they are unthinkable. 80 van Heijenoort, Logic. 81 van Heijenoort, Logic, 326-327, van Heijenoort’s italics. 82 Whitehead was primarily associated with Frege only in the book he co-authored with Russell, Principia (1910). We know from a footnote in Process and Reality (1929) that in the first edition of Principia, Russell took more or less complete control of the philosophical parts, and that in the second edition, there was no more or less about it. When Whitehead provided his own theory of logical symbolism in his own voice, as in the first sections of A Treatise on Universal Algebra (1898) or in first pages of Symbolism, Its Meaning and Effect (1927), he wrote purely as an algebraist. In Modes of Thought (1938, pp. 2-3), reflecting on Gödel’s recent results, Whitehead wrote as if – like Brouwer – he had had philosophical reasons for agreeing with those results long before Gödel actually achieved them. Wang reports that in a 1961 visit to Brouwer, and while speaking of Gödel’s incompleteness results, Brower “expressed his astonishment that so much had been made of them, saying that the conclusions had been evident to him for a long time before 1931.” H Wang, Reflections on Kurt Gödel (Cambridge MA: MIT Press, 1987), 57. 83 See: Ludwig Wittgenstein, Tractatus Logico-Philosophicus, trans. Pears and McGuinness (London: Routledge and Kegan Paul, 1961), proposition number 5.61).

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The convergence of Foucault and van Heijenoort gives substance to Foucault’s brief sentences about the formal sciences and provides some justification for treating the Boolean tradition, rather than the Fregean one, as closest to the gravitational center of the Modern episteme. But this convergence will immediately raise questions about the role of logic in 20th Century analytical philosophy.84 For as mathematicians have become almost entirely algebraic, philosophers have remained entrenched in a Fregean universalism. This philosophical commitment to Fregeanism is what explains the exegetical struggle against van Heijenoort’s insistence that there are two traditions of logic, whereby van Heijenoort silently implies that, because it was unable even to raise metasystematic questions, it is the Fregean tradition that has been surpassed. Consequently, in philosophy, a number of voices argue, against van Heijenoort, either that Frege and Russell had the resources to raise such questions or that they, in fact, did raise them.85 It is such a simple question: is logic an optional calculus or the only language in which thought is possible? It is so simple a question that I sometimes try to force myself to give an answer. I am tempted by the thought that logic is a calculus, and that if anything was a universal language, it would be the language as we in fact speak it. It resonates with the Philosophical Investigations, but even that doesn’t feel completely true. To insist that logic is a universal language—outside of which there is nothing—is simply part of the imperialism of logic. On the other hand, to insist that everyday language, rather than logic, is a universal language – outside of which there is nothing – would simply be part of the imperialism of everyday language. Perhaps, in the end, logic is a calculus and nothing is a universal language. And what is outside everyday language? Perhaps, after all, it is the naked experience of order in its brute being, a limit-experience. But I promised to tag Freud. Against the Classical insistence that B) Interpretation language was representational through and through, down to individual vowels, the philological Moderns insisted on the representational 84 See von Wright’s “Logic and Philosophy in the 20th Century,” (1991) in his The Tree of Knowledge, and other essays. (Leiden: E.J. Brill, 1993), 7-24. 85 For an excellent account of the literature for and against van Heijenoort, see Juliet Floyd in Anat Biletzki and Anat Matar, The Story of Analytic Philosophy: Plot and Heroes (New York: Routledge, 1998), 141-151. Floyd, following Dreben, is sensitive to the difficulty of refuting van Heijenoort simply by finding counterexamples. It is always a matter of how the putative counterexamples surface in the texts under discussion. In his 2005 essay, Kripke entered the debate on the side of Frege and Russell. He cites a counterexample to the van Heijenoort interpretation, remarking as he does that there are “many others” and that he “hopes to write on the general topic of metatheorems and metatheoretical ideas in Principia elsewhere.” Saul Kripke, “Russell’s Notion of Scope” in Saul Kripke, Philosophical Troubles: Collected Papers Volume 1 (New York: Oxford University Press, 2011), 232-3.

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opacity of syntax. In Foucault’s terms, Boole “compensated” for this by inventing a purer syntax, hoping to make expression possible without opacity. Freud was part of a different response, one that lives on in our sense that the genuine or authentic requires infor­mality, if not outright impropriety.86 In order to release what was hidden in our proper ordinary speech, the Interpretation compensation breaks the rules of proper syntax. In Foucault’s words, it tries “to shatter tyrannical modes of speech, to turn words around in order to perceive all that is being said through them and despite them.” 87 It is not just Freud who Foucault puts here. Marx broke the bourgeois syntax of our talk of value in order to reveal both alienation and exploitation at the intersection of commodity and value. In both cases, syntax is shattered to release the authentic voice of what is hidden in proper speech. Nietzsche shows up on the same shelf because of his genealogical question: Who is speaking?88 Nietzsche refuses to ask what is good, or in virtue of what the good is good; instead, he asks for whom the good is good. And that question immediately uncovers the hidden work that our moral language has been doing underneath our pressed shirts, often enough the work of revenge or ressentiment. Nietzsche may be Foucault’s best example of treating these Modern methods of exegesis and interpretation as a response to the growth of philology, not only because Foucault can quote him as saying “‘I fear indeed that we shall never rid ourselves of God, since we still believe in grammar,’” but also because, as Hacking reminds us, Nietzsche was “the most famous person ever to hold a chair of philology.” 89 I will return to Nietzsche, but first let’s take on that hapless task. IV

The Hapless Task (Continental and Analytical Philosophy)

With Boole on one side and Nietzsche, Freud, and Marx on the other, it may have seemed that what we call Continental and Analytical philosophy would shape up to be continuations of these two compensations or responses to the Modern influence of philology. Foucault may even seem to support such a reading. He tells us that these two sides—formalization and interpretation—are the “two great forms of analysis of our time—in fact, we know no others.” 90 86 Roland Barthes, Empire of Signs, (New York: Noonday Press, 1982), 63. 87 Foucault, Order, 298; Foucault abbreviates: “The first book of Das Kapital is an exegesis of ‘value’; all Nietzsche is is an exegesis of a few Greek words; Freud, the exegesis of all those unspoken phrases that support and at the same time undermine our apparent discourse, our fantasies, our dreams, our bodies.” 88 Ibid., 305. 89 Hacking, Night Thoughts, 151, Foucault cites Nietzsche at Order, 298. 90 Foucault, Order, 299.

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It is not that this story is false; there are these two forms of analysis or reflection, and Foucault insists on their philosophical importance: “The most fundamental question that can present itself to philosophy, then, concerns the relation between these two forms of reflection.” 91 But, for Foucault, simply to accept these two forms of reflection as our starting point is not enough. The distinction between formalization and interpretation “is not rigorous enough: the fork it forms has not been driven far enough down into our culture, its two branches are too contemporaneous for us to be able to say even that it is prescribing a simple option… In fact, it is a matter of two correlative techniques whose common ground of possibility is formed by the being of language, as it was constituted on the threshold of the modern age.” 92 This is a start, but Foucault gives me more help with the hapless question when he writes of sleep. He helps me to the thought that both continental and analytical philosophy are two ways of sleeping. It sounds silly, but bear with me. Kant himself thanks Hume for waking him from his dogmatic slumbers, waking him from Dogmatism to the tasks of his Critical philosophy. Foucault has made famous the fact that, towards the end of the Critical philosophy, Kant adds to his habitual list of philosophical questions about what we can know or should do or may hope a fourth question, a new one: What is man? 93 And Foucault comments: “This question, as we have seen, runs through thought from the early nineteenth century: this is because it produces, surreptitiously and in advance, the confusion of the empirical and the transcendental, even though Kant had demonstrated the division between them. By means of this question, a form of reflection was constituted which is mixed in its levels and characteristic of modern philosophy.” 94 The levels being mixed are the revealed pattern of representations and their concealed conditions, which Kant taught us to call the empirical and the transcendental, respectively. When we pursue philosophy anthropologically, we use an empirical investigation of human beings to reveal the necessary non-empirical

91 Ibid., 207. 92 Ibid., 299. 93 Ibid., 341; The three questions are said to unite all the interests of reason in both the 1781 and 1787 editions of the Critique of Pure Reason (Kant 1781/1787, A804-5/B8323). Foucault quotes the new question—What is man?—from the Jäsche Logic, published at Kant’s request in 1800 (Kant 1800, 538). Foucault remarks in another place that the new question does not appear in Kant’s Anthropology as we have it today (see: Michel Foucault, Introduction to Kant’s Anthropology (Los Angeles: Semiotext(e), 2008), 76. 94 Foucault, Order, 341.

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foundation of human being. 95 Man therefore becomes “a strange empirico-transcendental doublet, since he is a being such that knowledge will be attained in him of what renders all knowledge possible.” 96 The anthropological character of modern philosophy concerns “an empirico-critical reduplication by means of which an attempt is made to make the man of nature, of exchange, or of discourse, serve as the foundation of his own finitude.” 97 The various empirical articulations of human being simply reappear a second time, now presenting themselves as the transcendental conditions of any possible experience. And so, Foucault concludes, “we find philosophy falling asleep once more…this time not the sleep of Dogmatism but of Anthropology.” 98 Continental and Analytical philosophy are both asleep. The challenge they pose to us is not to choose one side or the other, but whether, by choosing either, you will choose to continue sleeping or, by choosing neither, you can quicken thought again.99 Anthropological sleep might seem irrelevant to much analytical philosophy; although Quine, for example, was moved by behaviorism, and there is naturalism aplenty, the mainstream of analytical philosophy moves by the logical analysis of propositions rather than the empirical analysis of human beings. Modern philosophy is therefore not well-characterized as anthropological, because that would leave out too much of the Frege-Russell tradition. We need to extend Foucault’s analysis in as straightforward a way as possible. Suppose the target is the transcendental, the concealed conditions of the world. Then there are two ways of falling asleep. One way would be by using empirical investigations as your clue to the transcendental; that is the pillow Foucault described. Another way would be by using logical, or better algebraic, investigations as a clue to the transcendental. That is a second pillow. They are both ways of falling asleep by confusing what Kant tried to keep separate. But we need a general name including both kinds of sleep, and for now let’s simply hyphenate what we can call anthropo-algebraic sleep. .

95 Deleuze implies that transcendental philosophy is essentially anthropological, that is, that it essentially confuses the empirical and the transcendental, when he writes: …Kant even invented two new forms of possibility, the transcendental and the moral. But by whatever manner one defines form, it is an odd procedure since it involves rising from the conditioned to the condition, in order to think the condition as the simple possibility of the conditioned. Here one rises to a foundation, but that which is founded remains what it was, independently of the operation which founded it… (Gilles Deleuze, Logic of Sense (New York: Columbia University Press, 1990), 18) If the hidden conditions of the conditioned are indeed hidden, then our only access to those hidden conditions is by what they have conditioned, and there you have it: the conditioned simply changes costume and becomes its own hidden conditions. In this light, there is little surprise in the discovery that Kant provided transcendental conditions for the (Newtonian) science and (Eurocentric) morality of his own time. Transcendental philosophy is essentially conformist. 96 Foucault, Order, 318. 97 Ibid., 341. 98 Ibid. 99 Ibid.

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(a) Take algebraic sleep first, and let’s content ourselves with a forest view. Some analytical philosophers treat with suspicion any range of propositions that cannot be translated into the logic of their choice. But when logic is construed algebraically, this failure of translation only gives us news about our favorite logic, namely, that it is not adequate to that range of propositions. So construed, this failure of translation is no reason to be suspicious of that range of propositions. Therefore, on those grounds, to give up thinking about that range would be to fall into algebraic sleep. It is a sign of algebraic sleep that disputes about the suspiciousness of some range of propositions can be conducted by means of disputes about extensions of the favored logic that would be adequate to the suspicious range. It is in this way that the invention of a tidy formal semantics by Tarski changed the shape of analytical philosophy, or at least took “syntax” out of the titles of Carnap’s books and substituted “semantics”. Anxious suspicions about modality disappearing in the face of an accepted modal semantics would be another example. If logic is treated as an algebraic calculus, these disputes and discoveries could have no foundational philosophical value. But of course it is precisely analytical philosophers who have clung to the Fregean treatment of logic as a language of all possible thinking. And if logic is a language of thought, and its limits are the limits of thinking, period, then not being able to be translated into logic is worse than a reason to be suspicious: it is a proof that the range of propositions is utterly unthinkable. Although its methods were algebraic, working out the limits of thinking from the inside, the Tractatus is a model of integrity in trying not to step outside of logic to say that it is impossible to step outside of logic.100 The absence of such Tractarian tangles from the writing of other analytical philosophers is a measure of their inconsistent commitment to logic as a language of thought. Their internal practice is to treat logic as an algebra, extending it in various ways to model different ranges of propositions, but their external practice, their foreign relations, still insists that the limits of logic are the limits of thought and that if a range of propositions cannot be translated into the logic of their choice, then it deserves every suspicion. They want it both ways, and that inconsistent philosophical practice is algebraic sleep. 100 For an algebraic reading of the Tractatus, see Floyd, Ascriptions. I am tempted by the thought that the Tractatus worked out the essential—non-representational—algebra of any possible thought from within, by means of the distinction between saying and showing. (Such a reading would put the Tractatus squarely in the tradition of artistic modernism as it has been differently articulated by Clement Greenberg and Michael Fried, a tradition strikingly congruent with Foucault’s modernism.) The question for such a project—whether or not it is Tractarian—is whether the empirical discovery that some form of signs is gibberish can be reframed—however silently—as showing the logical structure of the world, without thereby mixing the empirical and the transcendental in just the way Foucault warned against. Analogous questions would arise for the author of Philosophical Investigations.

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(b) Anthropological Sleep. Unlike algebraic sleep, which I just invented, humanistic scholarship is everywhere characterized by the pursuit of the transcendental by empirical means. Phenomenology took its Husserlian form in order to avoid that form of anthropologism known as psychologism. Unlike Frege, in the 1890’s Husserl was committed to an algebraic treatment of logical calculi, so in order to reveal the substantive logic of thinking, he could not rely on any particular calculus of formal logic; he had to turn elsewhere.101 He turned to a non-empirical intuition made possible by way of investigating empirical experience while bracketing its empiricity. In the progression of phenomenology, as critical attention increasingly turned to the possibility of a bracketing, Heidegger retained Husserl’s anti-psychologism, but his existential analytic of Dasein is a paradigmatic example of anthropological thinking. An account of the empirical features of human experience is lifted up—generalized and renamed—and turned into the existential conditions of any human experience at all. If this is right, then existential phenomenology—even in Sartre’s or Merleau-Ponty’s form—would be plunged into an anthropological sleep. But anthropological sleep comes in as many flavors as there are flavors of empirical investigations that are reduplicated as transcendental conditions, and anthropological sleep therefore cuts across the familiar analytical/continental divide. Existential phenomenology takes its cue from the pre-conceptual dimensions of our corporeal movements. Others take their cue from the physical sciences, using them as a clue to the necessary shape of reality. Whether this is defended as simply taking science seriously or trumpeted as the discovery of the necessary a posteriori, it sleeps either way. Others take their cue from cognitive science and tell us—in excited magazine tones—that at last we have answered the philosophical questions about the nature of belief, or love, or jealousy, or really almost anything: we now know that the concept in question is a certain regular cerebral arrangement and our sleep is undisturbed. The social scientific survey can also be used to determine the limits of human experience, for example to determine the distinctive moral standpoint of this or that sub-population of humanity. The essentially different moral stances of men and women were once said to be discovered in this way. But the anthropological version of moral philosophy is no more secure when, rather than determining essential differences between subpopulations of humans, it seeks universalism. In the wider realm of public discourse, racism of all sorts can be defended by the same sleepwalking 101 For Husserl’s commitment to an algebraic conception of logical calculi, see D. Willard, “Husserl’s Critique of Extensionalist Logic.” Idealistic Studies 9.2, 1979, 143-164 and Mirja Hartimo, “Husserl and the Algebra of Logic: Husserl’s 1896 Lectures,” Axiomathes 22.1 (March), 2012, 121-133.

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investigations, such as tests thought to prove the essentially inferior intelligence of those of African descent. In this case, so strong is the spell under which anthropology puts us, that even when good-hearted people thought these putative discoveries about African inferiority were problematic, they thought the problem was not with the procedure as a whole, but with the testing instruments—we should measure more accurately. Can nothing disturb our refusal to think? Sometimes, pulling their necks in, humanists don’t even make the jump from the empirical to the transcendental; they remain at the level of the empirical. Instead of using the reading of a text or empirical research to reveal the concealed conditions of experience, we can simply stop at the empirical level describing the response a book received or what people say when you ask them questions. Experimental philosophy may be the only one with a name, but whether digital or textual, the merely experimental humanities are flourishing. Although Foucault never, to my knowledge, indicated it, two of his own well-known topics, prisons and sexuality, can be described as revealing further forms of anthropological sleep. The prison-industrial complex does this when it treats those who break (certain) laws as revealing an essentially criminal character. And in the same way, it is often thought that if a boy enjoys kissing boys, then he has revealed his essential sexual nature, yet the glorious flexibility of human erotic enjoyments creates more and more putatively essential sexual natures, and as the essen­ tially different types of sexuality multiply and procreate, the whole process comes to seem strained and forced. Will we never wake? The hapless question now finds its hapless answer. The distinction between analytical and continental philosophy never sat very well. There may be resentments between re-identifiable groups of philosophers, but it is very hard to find a principled difference that models those resentments. Therefore, the fact that the difference between algebraic and anthropological philosophy cuts across that distinction may, all by itself, be a good thing. The distinction between algebraic and anthropological forms of modern philosophy—and of sleep—may carve this distinction closer to the bone. Between anthropological and algebraic sleep there is nothing to choose. We need to wake up. But how? V

Waking Up: Our Deleuzean Century

After telling us that there is no way to wake from our philosophical slumbers except “to destroy” the anthropological (or anthropo-algebraic) obstacle at its very foundations, Foucault makes a distinction that will carry us to our Deleuzean century.102 The distinction is made in this sentence about the anthropological obstacle: 102 Foucault, Order, 341-342.

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“We know, in any case, that all efforts to think afresh are in fact directed at that obstacle: whether [1] it is a matter of crossing the anthropological field, tearing ourselves free from it with the help of what it expresses, and rediscovering a purified ontology or radical thought of being; or whether [2], rejecting not only psychologism and historicism, but all concrete forms of the anthropological prejudice, we attempt to question afresh the limits of thought, and to renew contact in this way with the project of a general critique of reason.” 103 This sentence distinguishes two different efforts to bring philosophy back from its anthropo-algebraic sleep to waking life: the second sounds like Foucault himself, the first sounds like the Deleuze Foucault was to review in 1970. Let’s take the second one first. Foucault rejects psychologism, historicism, and all forms of the anthropological prejudice; not only our book but the work he later conducted as a Professor of the “history and systems of thought” could be described as “an attempt to question afresh the limits of thought, and to renew contact in this way with the project of a general critique of knowledge.” 104 It is also striking that this description would put its exemplars in the lineage of Foucault’s advisor, the historian of biology and medicine, Georges Canguilhem.105 In the opening of this paper, we found Foucault telling us that the project of The Order of Things was an attempt to analyze the “naked experience of order and its modes of being.” 106 In these terms, our book is an attempt, by the diffraction between epistemological formations, to bring us an experience of being, raw. And in a passage already cited, Foucault describes this raw being as “anterior to words, perceptions, and gestures, which are then taken to be more or less exact, more or less happy expressions of it (which is why this experience of order in its pure primary being always plays a critical role).” 107 That “critical” is precisely the critique to which our current passage refers as the general critique of reason. By revealing the fact that we think and act the way we do, we can experience the opportunity to think and act otherwise. But for Foucault, to reveal this fact means more than simply showing that, for example, this was written or launched in response to that. That is why his archaeological investigations can look so foreign to some kinds of intellectual history. Introducing the English translation of The Order of Things, he writes: “In this book, I have tried to determine the basis or archaeological system common to a whole series of scientific ‘representations’ or ‘products’ dispersed throughout the 103 Ibid., 342, my numbers in brackets. 104 Ibid. 105 Canguilhem had been Foucault’s advisor while he was writing the big book on madness, and the idea for The Order of Things was hatched during discussions with Canguilhem about the general lessons Foucault felt able to draw from his two more or less medically oriented archaeologies (see: Foucault, Remarks, 99). 106 Foucault, Order, xxi. 107 Ibid.

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natural history, economics, and philosophy of the Classical Period.” 108 At that level, he does not purport to reveal the difference between theories of the Classical and theories of the Modern period, but to help to an experience of the difference between the way the “space of knowledge” was “arranged” in the two eras.109 The Order of Things is the analysis of a limit-experience that will renew the general critique of reason. This early book, therefore, anticipates Foucault’s late essay on the Kantian question: “What is Enlightenment?” In that essay, we can see Foucault still distancing himself from anthropological sleep when he writes that “this critique will be genealogical in the sense that it will not deduce from the form of what we are what it is impossible for us to do and to know…”.110 To deduce from the contingent empirical form of what we are, the non-contingent impossibility of transgressing the limits of that form, would be a form of anthropological sleep. And Foucault tells us that this is precisely what the general critique of reason would not be. Foucault’s genealogical critique “will separate out, from the contingency that has made us what we are, the possibility of no longer being, doing, or thinking what we are, do, or think. It is not seeking to make possible a metaphysics that has finally become a science; it is seeking to give new impetus, as far and wide as possible, to the undefined work of freedom.” 111 Again: “The point, in brief, is to transform the critique conducted in the form of necessary limitation into a practical critique that takes the form of a possible transgression.” 112 This is interesting enough from the point of view of Foucault’s oeuvre, but to us it is mostly exciting as a way of catching a glimpse of thinking that has escaped the recitation of empirical discoveries or algebraic inventions as if they were transcendental requirements, and that has therefore escaped anthropo-algebraic sleep. If Foucault’s books look in on this limit-experience from the side of the diffraction that makes them visible, then Deleuze plunges right into the experience of being, raw. That’s why Foucault’s characterization of a first way to destroy the anthropological obstacle sounds like Deleuze: ”…it is a matter of crossing the anthropological field, tearing ourselves free from it 108 Foucault, Foreword to the English edition of Order, xi-xii; at this time, Foucault thinks of such an archaeological system in terms of rules, and Sluga, by way of criticism of Foucault, has observed that there are Wittgensteinian reasons against articulating such a system in terms of rules (Sluga, Frege, 210). I suspect this is not a lethal objection to the notion of an “archaeological system.” 109 Foucault, Foreword, xi. That Foucault finds himself speaking obscurely of such an experience is a sign that, here, Foucault’s trajectory has intersected with Wittgenstein’s struggle with the experience of aspect-seeing in the Investigations. 110 Foucault, “What is Enlightenment?” in The Foucault Reader, ed. Paul Rabinow (New York: Pantheon Books, 1984), 46. 111 Foucault, Enlightenment, 46. 112 Ibid., 45.

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with the help of what it expresses, and rediscovering a purified ontology or radical thought of being.” 113 Deleuze can seem to carry forward the metaphysical trajectory of The Order of Things. He makes his move beyond anthropo-algebraic thinking, and its sleep, by taking a cue from Bergson, who wrote—hopefully enough—in his 1896 Matter and Memory: “But there is a last enterprise that might be undertaken. It would be to seek experience at its source, or rather above that decisive turn where, taking a bias in the direction of our utility, it becomes properly human experience.” 114 Like the ontological project of Bergson’s great admirer, William James, it sounds like “a world of pure experience.” 115 Before experience becomes useful to humans, this world is where we must seek a purified ontology, one no longer shackled to human being. But how? Throughout The Order of Things, Foucault lofts arrows at something he calls literature. He tells us it is a third way of compensating for or responding to the philological opacity of syntax.116 “At the beginning of the nineteenth century, at a time when language was burying itself within its own density as an object and allowing itself to be traversed, through and through, by knowledge, it was also reconstituting itself elsewhere, in an independent form, difficult of access, folded back upon the enigma of its own origin and existing wholly in reference to the pure act of writing. Literature is the contestation of philology (of which it is nevertheless the twin figure): it leads language back from grammar to the naked power of speech, and there encounters the untamed imperious being of words.” 117 In addition to the Boolean formalism that purifies natural syntax to make it safe for no matter what content, and in addition to the Freud-MarxNietzsche rattling of that natural syntax to release the sounds of that content that hides in polite speech, there is a third response: literature. And literature no longer seeks the authentic expression of anything, at all. If we must speak of the expression of content, then Foucault suggests that literature “could have no other content than the expression of its own form.” 118 In what Foucault calls literature, what is expressed is the expression doing the expressing, or in words Deleuze put together at the very start of his career: “the expressed is the expressing.” 119 113 Foucault, Order, 342. 114 Henri Bergson, Matter and Memory (New York: Zone Books, 1988), 184. 115 William James, “A World of Pure Experience” (1904), republished in William James, Essays in Radical Empiricism (Mineola, NY: Dover Publications, 2003), 21-47. 116 Foucault, Order, 299-300. 117 Ibid., 300. 118 Ibid. 119 Gilles Deleuze, “Description of Woman” (1945) republished in English in Angelaki 7:3 (2002), 18.

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Literature doesn’t accept ordinary grammar (Bopp), it doesn’t purify it (Boole), it doesn’t rattle it to release a hidden expression (Nietzsche, Freud, Marx), it “leads language back from grammar to the naked power of speech, and there it encounters the untamed [sauvage] imperious being of words.” 120 Leaving representation behind, Foucault tells us that, in literature, “speech develops from itself, forming a network in which each point is distinct, distant from even its closest neighbors, and has a position in relation to every other point in space that simultaneously holds and separates them all.” 121 At such times he often speaks of Mallarmé, and here Foucault seems almost to be citing this well-known passage: “The pure work implies the disappearance of the poet speaking, who yields the initiative to words [qui cède l’initiative aux mots], through the clash of their ordered inequalities; they light each other up through reciprocal reflections like a virtual swooping of fire across precious stones…”.122 Literature destroys grammar, not to clear a path for expression of any subject, personal or supra-personal, but to clear a path for experience without an experiencing subject.123 To clear a path not for a whom but for a what: the word.124 The power of literature is the power of words, not as types having their separate tokens, but the power of singularity, the power of this singular shape of sound, here in this room, of that singular shape of ink, there on that page. Agrammaticality. It may remind some as much of Mallarmé as of Stein’s writing, Cage’s performances, and Armstrong’s scat. Nietzsche, that old philologist, was here before us. In an early essay on words and concepts, he insists that concepts and their grammar work by ignoring the singularity of things and our experiences. Silently invoking a Leibnizian example, Nietzsche insists that no leaf is the same as any other; the concept “leaf” is formed by “arbitrarily discarding these individual differences and by forgetting the distinguishing aspects.” 125 We forget because forgetting is good for the utility of the “herd.” 126 Struggling in the herd, Nietzsche says that to free the intellect, to enjoy singularity, we must spurn utility and “smash this framework to pieces,” leaving concepts behind in order to feast on singular intuitions.127 Perhaps this is the way to a Bergsonian ontology no longer designed for human consumption. Listen to our old philologist: 120 Foucault, Order, 300. 121 Michel Foucault, “The Thought of the Outside” (1966) in Foucault, Aesthetics, 149 122 Stéphane Mallarmé, “Crisis of Verse” in Stéphane Mallarmé, Divagations trans. Barbara Johnson (Cambridge; Belknap Press, 2007), 208; see Foucault, Order, 306. 123 This idea of experience without an experiencing subject is an aspect of what Deleuze, gesturing to the radical empiricism of William James, but using Sartrean terminology, called a transcendental field. (Deleuze, Immanence: A Life, 25-27). 124 Foucault, Order, 382. 125 Nietzsche (1873, p. 83). Friedrich Nietzsche, “On Truth and Lies in a Nonmoral Sense” (1873) in Daniel Breazeale, Philosophy and Truth, selections from Nietzsche’s Notebooks of the early 1870’s (New Jersey: Highlands Press, 1979), 79-97. 126 Ibid., 81. 127 Ibid., 90.

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“There exists no word for these intuitions; when man sees them he grows dumb, or else he speaks only in forbidden metaphors and in unheard-of combinations of concepts. He does this so that by shattering and mocking the old conceptual barriers, he may at least correspond creatively to the impression of the powerful present intuition.” 128 The destruction of syntax in order to experience singularities is an assault on syntax parallel to the assault on comparative anatomy embodied in the very idea of a body without organs. It is a matter of “rediscovering a purified ontology or a radical thought of being.” 129 In Difference and Repetition, Deleuze writes: “There is an experience of difference and a corresponding experiment: every time we find ourselves confronted or bound by a limitation or an opposition, we should ask what such a situation presupposes.” 130 With that experience of difference, Deleuze might have been describing the opening experience of Borgesian laughter that shattered all the familiar landmarks of Foucault’s thought and brought him face to face with the limit of his own, but that would only be Foucault’s awakening to the history of systems of thought and the renewal of a general critique of reason, it would not be Deleuze’s ontological awakening. In the next sentence Deleuze tells us what – ontologically – the experience of limitation presupposes: “It presupposes a swarm of differences, a pluralism of free, wild or untamed differences; a properly differential and original space and time; all of which persist alongside the simplifications of limitation and opposition… Oppositions are roughly cut from a delicate milieu of overlapping perspectives, of communicating distances, divergences, and disparities, of heterogeneous potentials and intensities. Nor is it a question of dissolving tensions in the identical, but rather of distributing the disparities in a multiplicity.” 131 This is the source of the purified ontology that Foucault discovered for the first time in Deleuze’s Difference and Repetition (1968). Is it any wonder, then, that when reviewing Deleuze’s book, Foucault discerned “a lightning storm…which will bear the name of Deleuze: new thought is possible; thought is again possible.” 132 “Perhaps one day, this century will be known as Deleuzean.” 133

128 Ibid. 129 Foucault, Order, 342. 130 Gilles Deleuze, Difference and Repetition, (London: Athlone Press, 1994), 50. 131 Deleuze, Differemce, 50. 132 Foucault, Theatrum, 387. 133 Ibid., 343; but for the interest of George Mote, this paper would never have been written. An earlier version was first presented at the Second Annual Lehigh University Philosophy Conference, October 2014. This version benefited from the advice and encouragement of George Mote, Juliet Floyd, Vera Bühlmann, Keith Robinson, Alex Haitos, Daniel W. Smith, and the Lehigh Philosophy Faculty Seminar Fall 2015.

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VI A Mathematical Drama: Articulating a Thing Entirely in its Own Terms Vera Bühlmann 1 A Spectrograph 163— II The Spectrometer 163 — III The Generic 164 · Grammatizing symbolic domains 165 · An abstract object’s integrity: Political subjectivization 167 · Beyond urban comfort, in a state of expulsion  173  · Generic as an adverb, the liveliness of nature  174  · Bodies-to-think-in live in algebraic universality 176 — IV Characterizations of The Generic 178  · Characterization on a grammatical level 178 · The man without qualities (Robert Musil) 179 · The city without identity (Rem Koolhaas) 179 — v Falling in Love With the In-Sinuousness Proper to an Economy of Entropy 181  · Primary abundance 181— vi The Master 184 · Toward an informationbased architectonics 184 · Within the Generic City: Master, yet in “whose” house? 187 — viI Characterizations of The Master 189 · Attracted by the volatility of a flirtation between the philosophical stances of “critical rationalism” and “speculative realism” 189 · Cosmic untendedness, prosaicness in verse 193 · Cosmo-politics, or putting to work a symbolist meter 199  · Cosmo-literacy, or the alphabetization of the nature of number 200 —  viIi Acquiring a Body-to-Think-In 203 · The most common representation of the nature of numbers … 203 · … and how it got into trouble still not resolved today 204 · Algebraic operations, or how the nature of numbers can be brought to work 205 — ix Masterpieces, and Why There Are so Few of Them 208

Vera Bühlmann is founder and head of the Laboratory for Applied Virtuality at the Chair for Computer Aided Architectural Design (CAAD), Swiss Federal Institute of Technology (ETH) in Zurich. She studied English language and literature and philosophy at the University of Zurich, and holds a PhD from the Institute for Media Sciences, University of Basel. Her work focuses on the double-articulation of semiotics and (mathematical) communication, especially on how an algebraic understanding of code and programming languages enable us to consider computability within a general literacy of architectonic articulations. She has edited several books in this field, has published many essays and is author of Die Nachricht, ein Medium : Annäherungen an Herkünfte und Topoi städtischer Architektonik (ambra, 2014). www.­monasandnomos.org

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“The very possibility of the science of mathematics seems an insoluble contradiction. If this science is deductive only in appearance, whence does it derive that perfect rigor no one dreams of doubting? If, on the contrary, all the propo­sitions it enunciates can be deduced one from another by the rules of formal logic, why is not mathematics reduced to an immense tautology? The syllogism can teach us nothing essentially new, and, if everything is to spring from the principle of identity, everything should be capable of being reduced to it. Shall we then admit that the enunciations of all those theorems which fill so many volumes are nothing but devious ways of saying A is A! …Does the mathematical method proceed A Mathematical Drama: Articulating a Thing Entirely in its Own Terms

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from particular to the general, and, if so, how can it be called deductive?” Henry Poincaré 1 This text gives an account of a drama I have been witnessing ever since I began to be interested in computation and programming: two conceptual persona (masks), The Generic and The Master, both compete in how to address the authority of Sovereign Knowledge. In my account they are treated as masks in the sense of technical spectra, which render apparent through partition schemes, as different articulations (frequency domains) of one and the same activity (radiation), how matter come to matter. Masks in this sense do not capture acts of deception and concealment, even though 1

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Henry Poincaré, Science and Hypothesis (New York: Dover, 2011 [1902]): 1.

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they are what they are because they encrypt what they encrypt. The account of this drama here introduces these conceptual persona in a zone of intellectual intimacy, where the particular spectralities of both are mingled, interfere, resonate, and trigger diffractive patterns of an immanence (The Authority of Sovereign Knowledge). The masks saturate this immanence with indexes of the apparentness they render present. The character of this immanence ultimately remains elusive, it appears and takes shape only through the distinctiveness that the two conceptual perso­ na are capable of articulating. The account given in this text treats the stage on which the witnessed drama happens as a zone of intellectual intimacy—a zone that is A Mathematical Drama: Articulating a Thing Entirely in its Own Terms

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playful rather than sacred, but creative rather than representational. The concern of this text is in how to conceive a notion of organized formality (which I call a body-tothink-in) that were capable of inducing, from within such a zone, a shared experience of Common Sense. The plot depicted here displays how such a zone of intellectual intimacy, between The Generic and The Master, is capable of animating with liveliness a sovereignty of knowledge that grows stale and lifeless, despotic and tyrannical, whenever its demand to settle from its active and naturally confuse, entropic restlessness into an all-too formal manner of conduct is no longer challenged; or put otherwise, when it demands to be addressed as a canonical corpus. 162

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I

The Spectrograph

This text dramatizes the role of knowledge in a manner that seeks its politicization. It is a politicization whose economy is entropic, circuitious, and whose stocks are those accumulated, from an infinite welling (the nature of the universe), through intellection, understanding, embodied knowing that and knowing how. The cities of such a politicization are cosmic once more, yet real rather than ideal. The orders of the cosmos themselves (the galaxies) are considered to be born and vulnerable (every galaxy has once been “born” and eventually “dies“), a nature that evolves, so the common sense narrative within which my account is rooted, from a dynamics whose principle unity is, paradoxically, one of partition (the universe expands). This principle is itself subject to two forces: live and death, conservation and dissipation, the first law of thermodynamics and the second one. What the common sense narrative does not capture, is how information, in its quasi-thermodynamic physicality, thwarts the interplay of these two “forces”. This is the drama addressed here as a mathematical drama. Ii

The Spectrometer

My account here has been written down four years ago. Here are some indications of what I would foreground and sharpen if I were to rewrite it today. The assumptions that seem mandatory to me are: 1) objectivity is real even though it is engendered by abstraction; 2) subjectivity is real even though objectivity determines it in manifold manners, respective to the literacies at work in abstraction; 3) the universal is real: it is the totality of the universe’s entropic disposition whose disorder is the indefiniteness of its own any-order, a sum of the possible that can only be totalized with respect to the ciphers that underlie its encryption; 4) such totality is one that can be counted only symbolically, in a manner that is subject to the laws of great numbers (numbers that are considered as indefinitely large, rather than as finite or infinite); 5) for large numbers it is constitutive that the magnitude counted by them is magnificent (its greatness, lat. magnus, is made, lat. factitious); 6) such magnitude is organized in bodies-to-think-in; 7) they are the organons in which the sovereignty of knowledge rules, through acquiring and inhabiting a particular body-to-think-in, a body that is not proper (one’s own) but a symbolic corporeality (distributed and collective); 8) each one of those bodies is at once universal and lively, animate, mortal and finite; 9) there is a generational dynamics between bodies-to-think-in; 10) the governance in which the sovereignty of knowledge enacts its ruling in such bodies-tothink-in is organized infra- as well as intra-specularly; 11) all populations of bodies-to-think-in are subject to one universal principle: that of finite synthesis, enacted in the law of large numbers (improbability is their

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shared origin, and they are subject to chance); 12) bodies-to-think-in are inhabited and animated by anyone who devotes herself to truly learning what she is, socially, supposed to know, and thus aspires to familiarize all expertise into common sense; 13) the universal principle of finite synthesis is all the more powerful (or powerless) the more (or less) complexly articulate and proprioceptive the bodies-to-think-in have grown, through the manner in which they are being inhabited. Iii

The Generic

Most anyone interested in computational design today shares a tremendous fascination with the somewhat dubious notion of “the generic” and its promise of the “one-of-a-kind particularity” of instances that can be computed.2 Much of the widespread attractiveness of this promise is owed to the idea that such one-of-a-kind particularity be neither example nor prototype, that its organization be not governed by a logic of rigid classification. Every generic instance counts as “typical” (not needing any surplus qualities to be specified) even though it may well be “singular,” the only one of its “kind.” In programming, the notion of the generic means to formulate functions that are of highest possible generality such that they apply to no specific structures of data, but to (virtually) any structure of data. More straightforwardly: in programming, the notion of a generic object suggests that its instances are a this, without being a such. Their one-of-a-kind particularity can only be indexed, pointed to; it is a particularity that never manifests as corresponding to a certain genus, but only in terms of indefinite adequation within a scope of genericness that aspires to be universal (not classificatory), and that is being articulated by each particular manifestation of such an instance. The extraordinary—if not straightforwardly salvational—implication thereby is that with generic objects, articulation engenders universality. Generic objects promise, as objects with a nontransparent and apparently singular autonomy, to be shielded off from any attempt at appropriation by individually vested will, desire, interest, or meaning. Instances that are realized from such a generic object appear in a peculiarly innocent sense “genuine.” The great fascination for such genuineness today, as I understand it, is driven by a certain subversive pleasure geared against the exhaustive and demanding “political dynamics” of what is often referred to as an economy 2

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Here, “tremendous fascination” is deliberately “exported” from religious vocabulary, where mysterium tremendum et fascinosum is used to attribute holiness to God. It is an ambiguous expression that acknowledges the finitude of man’s capacities to understand. It makes reference to something that is fascinating and yet at the same time profoundly unsettling, because it promises a kind of automatic comfort, belonging, and beauty, in which everyone is welcome, while also confronting us with man’s helplessness and insignificance in the face of divine inviolability.

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of recognition.3 It sets the political confines for most of the twentiethcentury structuralist and post-structuralist discourses around a necessity to give difference and self-reference a primacy with regard to identity and representation. In all brevity, central for an economy of recognition is that anything that can participate in and profit from it—anything that can find accommodation within the “modern” nomos (political as opposed to cosmological law) of a “modern” oikos that is “mastered” collectively (house-as-state)—needs to be mediated through language and concepts. Such “mediation” involves all the complex cultural issues related to questions such as, what is actually the “object” described by linguistics? Does language, if we could find its pure form, describe natural kinds? Is there a pure form to language at all, or is language in its everyday use a “natural” language—and if yes, are there many natures of language, and what does such an assumption entail? Should we regard language as a system, a structure, or something else? Is it possible at all to generalize from the diversity of languages actually spoken and written, and what does it entail to do so? To make a long story (very) short, a peculiar inseparability between interpretation and formalization has haunted notions of theory, objectivity, and subjectivity throughout the twentieth century. The respective discourses have grown quite removed, in all “critical” negotiation, from what is perceived by many as the “real issues at stake” (to improve and optimize global living conditions), and the voices raised are inevitably, it seems, also always acting tactically. But most of all, the idea of a position that could clarify permanently the confusions that spring and proliferate from linguistic attempts at clarification, appears to many, meanwhile, as raising the issues in inadequate terms.4 Our relation to language simply remains as intimate as our relation to breathing. Grammatizing symbolic domains Now this is exactly what computational linguists like Noam Chomsky began to readily affirm: yes, he holds, language is so intimate to all of us that it makes sense to imagine it as a kind of a cultural “genome” we are born with, just like we are born with a biological genome. Such a radical move, whose affirmation must count as a veritable philosophical capitulation, was actually capable of moving beyond the preoccupation of “critical” philosophy with the (politically all but innocent!) foundational issues about the nature and role of language for thought, specifically (ethnic and racial discrimination), 3 4

Louis Althusser may be considered as the most important theoretician here, yet the same symmetrical relation—albeit in significantly diverse manners—is also constitutively present in the work of Jacques Lacan and, arguably, that of Alain Badiou. Especially the diverse attempts of a post-critical return to philosophy as a rational and metaphysical enterprise, which are referred to as marking a “speculative turn” in recent philosophy, associated with philosophers such as Quentin Meillassoux, Ray Brassier, and Graham Harman.

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generally (socialism), or individually (capitalism). Instead, it was capable of modernizing the interest in language itself by postulating a categorical break with the mimesis tradition altogether. No longer focusing on mimesis and its questions of interpretation, truth, and the definition of meaning, the interest now shifted to the pragmatism of sheer transformability. The so-called transformational or context-free “grammars” and “vocabulary” with which programming “languages” work do not even claim to be “natural”; they are, to put it a bit provocatively, genuinely engendered. Let us look briefly at the development of two very strong paradigms in programming throughout the last decades. Early languages such as Fortan, Ada, or C started out with a procedural paradigm. The main interest was to make available for easy application, as a kind of toolbox of “instruments” in coded “form,” the precise way of how a certain organizational procedure needs to be set up in order to function well. Every step of decision can thereby be “dispersed” into constitutive procedures, and hence, an infinitesimal limberness can be introduced into organizational forms. The paradigm subsequent to this pursued a much less directly hands-on approach, and instead became more didactical. With languages like smalltalk, Java, and C++, an object-oriented paradigm followed the procedural one, and it strictly kept apart the levels of what (described by procedures) and how (the specification of this what). Through this distinction, negotiation began to be supplied by “computational augmentation” about what is to be reached, and about how systems can be devised that allow the instantiation of procedures (whats) in much wider variations. Objectoriented programming allows devising entire “libraries” of “abstract objects” that depend on no statically specified order or classification system. Yet such abstract objects are not really “objects,” they incorporate entire “objectivities”—they allow for one-of-a-kind particulars to “concretize” singularly, and optimally be fitted according to the requirements of a task. This is what we are talking about with the generic in computation: the ambition of programmers to develop informational “coatings” as a kind of abstract packaging, as “symbolic cases” that preserve and protect the “abstract object’s integrity.” All the potential functionalities offered by it ought to be provided in a most robust and compact “manner,” and for a largest possible variety of instances. Equipped with the technological power of such “languages,” the subversive pleasure that seems to accompany the wide interest in generic design today lives on the one hand from a radical affirmation of those liberating and disciplining constraints within an economy of recognition, which dictates that the nature of a thing is to be considered in the (politically sanctioned) terms in which it is actually addressed; yet it also lives from responding to this dictate by what I would call an “expansion in dimensionality” by investing its energies into the “substantiation” of speculative notions of reality: it sets up, by means of such genuinely engendered “languages,” symbolic domains that can accommodate the objects under investigation in the terms sanctioned for

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describing them, but that open up further possible spaces as well—which are governed “infra- as well as intra-specularly,” within an imaginary locus proper to particular objectivities (or any combination of elements of combined objectivities).   An abstract object’s integrity: Political subjectivization But what kind of integrity are we talking about here, when referring to an abstract object’s integrity? What kind of integrity is proper to symbolic domains that are governed by many infra-specularities? Much of what this text will be dealing with concerns this question. Far from desiring to disenchant the fascination that surrounds emerging notions of the generic, this text will suggest radicalizing this fascination. Yet to radicalize here, we will see, doesn’t mean to “sharpen,” as if a weapon, or to specifically devise an instrument that could be put to a worthwhile cause. To radicalize a fascination is to radicalize what charms us, the “spells” that take hold of us, and it is meant here as it literally applies to certain ideas about the nature of numbers, which I will come back to later. In essence, it is about mathematical adjunction in field theory, which emerged out of algebraic considerations regarding the solvability of equations. For now we can say that to radicalize the notion of the generic involves affirming the symbolic nature of numbers.5 And this entails, literally, regarding numbers in terms of finite, yet infinitely extendable “corporeality.” 6 With the rise of abstract algebra in the nineteenth century, people were also speaking of providing domains of rationality for a certain (numerical) solution space (instead of taking universal conditions of rationality for granted, as is the habit in a nonsymbolic understanding of numbers).7 Put in general terms, corpus theory is central for establishing domains of unique factorization—that is, numerical domains where the arithmetic operations are well defined for all elements of a corpus (i.e., not in general, but specifically). Thereby, arithmetics ceases to be, in a unproblematic manner, universally applicable. We regard this as central to a different 5 6 7

An example of such extensions of numerical corporeality is complex numbers, which are composed by adding the imaginary unit √ -1 to real numbers. Field theory is more adequately, albeit less often in English, called the theory of numerical corpus. This is consistent with the French expression for field, which is corps, as well as the German Körper. To provide domains of rationality for a certain (numerical) solution space, makes sure that the roots of a polynomial with coefficients raised to the nth power can be expressed in terms of radicals according to an integral domain governed by the principle of unique factorization. Leopold Kronecker especially preferred to speak of domains of rationality, in distinction to the main inventor of corpus theory, Richard Dedekind. Instead of domains of rationality, Dedekind thought about the possibility to extend a numerical corpus in terms of prime ideals. The two stances can be seen to represent two epistemological vectors of induction (primary in Kronecker’s empirically grounded approach), and the strange mixture that Charles Sanders Peirce—another key figure in the rise of universal algebra in the latter half of the nineteenth century—attempted to define as abduction that establishes the conditions of deduction (Dedekind’s approach grounded in abstraction).

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paradigm of programming—not a procedural or object-oriented one, but one that might be called pre-specific.8 This has several consequences for how we think about computability. Calculations cannot only be right or wrong, but they can also be set up in an adequate or inadequate manner. The solution spaces that are provided for calculations have different capacities. To put it quite provocatively: computing turns into an art (again), just like mechanics used to be an art (and not a science) before industrialization. Even the expression “to be industrious” once meant to be apt and diligent, in terms of personal qualities one has acquired—very different from the meaning of industriousness as an alienating submission to an orchestration that is strictly clocked by a responsibility external to oneself, which has become the predominant understanding today. The entailments for revitalizing this legacy of computing as an art are ambiguous, and they seem twofold: on the one hand, its promise is to gain the possibility for a new criticality, yet on the other hand, this new criticality is rooted in a kind of local universality. When suggesting to speak of an abstract object’s integrity, this relates to the particular capacities provided by the solution space that is constituted by such an abstract object. But let us not discuss this further here in the rather technical terms of mathematics,9 and instead refer to the same issue—criticality in relation to a certain capacity and ability that is involved in partitioning, identifying parts and wholes and their interdependencies—in the context of contemporary political theory. Within the modern oikos, sheltered by a modern nomos (a political, not anymore divine, nomos), each “theme” has to be treated as a “subject” in order to find a platform for public address (newspaper, education, etc.): what once enjoyed generosity in how it was treated (or the silencing violence, or the doctrinary appropriation) attributable to common places (a theme as a “topos”), now has to be accommodated within an overall organization, and that means its treatment (discourse) has to be surveilled and negotiated. Such a “subject,” in a purely passive and nonpolitical way, is an “object” in the sense of the grammatical case of the accusative—the case of that which is “caused,” that which is “called to account” and needs to be “accommodated in its proper place,” 8

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For a discussion of the Dedekind approach to ground corpus theory in acts of abstraction in relation to an understanding of computation and calculability, see Vera Bühlmann, “Continuing the Dedekind Legacy Today, Some Ideas Towards Architectonic Computability,” (lecture, Turing 2012 Conference, Manila, Philippines, March 2012), http://www.monasandnomos.org/2012/12/05/computing-within-the-open-totalityof-anything-that-can-be-the-object-of-thought-continuing-the-dedekind-legacy/. Cf. also: Vera Bühlmann, Ludger Hovestadt, Vahid Moosavi, eds., Coding as Literacy, Metalithikum V (Basel: Birkhäuser, 2015). For those interested in following this line of thought toward a criticality that is local and universal, see the superb book Jules Vuillemin, La philosophie de l’algèbre (Paris: PUF, 1962), especially chap. 4, “La théorie de Galois,” 222–300, in relation to adjacency in mathematics, its relation to the notion of groups, and its overall entailments for Kantian and post-Kantian notions of criticality.

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i.e., categorized.10 A theme as a subject in that sense, as one that is to be categorized,11 is what is put before public assembly, because its predication is yet to be clarified. If we are to consider the integrity of those abstract objects that constitute the solution spaces in generic computations within a scale of adequacy, every commonplace interest (theme) turns into a “subject-with-dispositions-and-capacities.” The new criticality at stake, a criticality of finite synthesis, concerns the symbolic constitutions—and through that, the capacities of abstract objects—that are orientating power (public address and its surveillance) in discourse. This same abstract issue—the partitioning, the identification of parts and wholes and their interdependencies as problematic—features centrally, for example, in Jacques Rancière’s contributions to contemporary political theory.12 His notion of political subjectivation, which he developed in a 2004 essay entitled “Who Is the Subject of the Rights of Man?,” is very helpful for developing an idea about what such criticality entails. “Political subjects are surplus names,” he holds, “names that set out a question or a dispute (in French, litige) about who is included in their count.” 13 For Rancière, the name of such a political subject cannot be a proper name, nor the name of a general class (a noun). It is whatever and however may qualify such a noun: the adjective of the general class of humans. Thus, the name of such political subjects can only be “generic,” and as such it is, for him, the name of the demos.14 Thus he refers to the demos in an adjectival sense, from the Latin adjectivum, “that which is added to (the noun).” It is in this adjectival sense that political subjects are surplus subjects for Rancière, 10 The accusative is the grammatical case whose primary function is to express destination or goal of motion, from the Latin (casus) accusativus, “(case) of accusing,” from accusatus, past participle of accusare. The Latin accusare means “to call to account,” from ad-, “against,” + causari, “give as a cause or motive,” from causa, “reason.” Online Etymology Dictionary, s.v. “accusative,” http://www.etymonline.com/index. php?term=accusative&allowed_in_frame=0. 11 From the Greek kategoria, “accusation, prediction, category,” verbal noun from kategorein, “to speak against; to accuse, assert, predicate.” Online Etymology Dictionary, s.v. “category,” http://www.etymonline.com/index.php?term=category&allowed_in_frame=0. 12 The way Rancière approaches and unfolds his political arguments, which center around a foundation of politics in aesthetic judgments, involves following him on an unusually high and demanding level of abstraction. Indeed, this is often one of the key points for which he is criticized—it raises people’s suspicion because it is not easy to follow (in understanding, not in action!). Contrary to this view, his engagement with abstraction is precisely what exposes him within the current landscape of political theory and philosophy—which is to a large amount straightforwardly programmatic, if not outright polemic, by not demanding the reader to understand the abstractions at work in it. This is unfortunate because it cannot facilitate a problematic engagement with the proposed arguments, but rather demands devoted followership—the creation of “movements,” by being promised (by the authority of expertise that is declared too difficult for the common person to understand, and hence needs to be presented in trivialized and infantilized manners) to “stand on the right side of history.” See for example Slavoj Žižek, Die bösen Geister des himmlischen Bereichs. Der linke Kampf um das 21. Jahrhundert (Frankfurt am Main: S. Fischer, 2011). 13 Jacques Rancière, “Who Is the Subject of the Rights of Man?,” South Atlantic Quarterly 103, nos. 2/3 (Spring/Summer 2004): 303. 14 Ibid., 306.

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a view that grants that giving a definition of the noun (humanity, in this case) is not necessary—it is barred from articulation and being spelled out and must be taken as a premise and treated approximately, just like the continuities of movements are treated in modern differential calculus.15 Here is not the place to discuss Rancière’s position in any adequate detail, yet it needs to be pointed out that our own proposition turns away from Rancière’s at a certain point. By raising the issue of an abstract object’s integrity, I propose to treat his notion of political subjects not in classificatory terms altogether, but in categorial terms. This means that I opt for regarding political subjects, subjects named generically, as universal and adverbial (not as adjectival).16 We will come back to what this entails in more detail; 15 Leibniz’s dictum was, famously, that nature makes no jumps—the assumption of uniform continuity in natural processes has been central for applying the then-new infinitesimal methods in modern science. It is needed to support all epistemological positions that consider themselves analytical-empirical. It seems to us that Rancière is opting for a similar framework as this one between movement-continuity (infinitesimal calculus in science) for his context, that of political-acting-human (aesthetic judgments in politics). 16 If you are slightly irritated by this counter-positioning and ask yourself why “universal” should not also be an adjective—an adjective of all that is—you are hitting the crucial point: by seeing it that way, as an adjective, you would consider all that is in terms of a given set, class, kind, or representable rather than instantiatable totality. With due respect to the distinctions between these terms, in all cases the notion of the universal would be a descriptive notion. And all conceptual dynamics involving an idea of “surplus” need to be treated in the stigmatizing terms of accumulation on one side, correlated with deprivation and exploitation on the other. This all is well known. Our interest in Rancière’s notion of political subjects as surplus subjects comes from his rebuttal of such a notion of surplus. By taking recourse to aesthetics as that which he holds capable of “rooting” a political subject, he proposes to ground politics in a manner that involves rationality and the sublime in which the latter is not treated as a finite stock and resource, but as an infinite source of dignity. Such a notion of surplus shifts the problematics from issues of just distribution and optimal rationalization of stocks to the more abstract issues of partitioning and manners of counting that depend upon the decisions involved in partitioning, prior to the finitude of anything materially manifest and given. So in his case, reading demos as an adjective for the human, he turns demos into something like a political soul, a divine reality that lives in the people, and is only derivatively there for an individual to participate in—never to own or have. For him, demos comprehends the totality of a “universal” authority proper to all those who strive to act responsibly in a sense that is not based on qualifications that cannot be listed as sources of legitimate authority. I describe it tentatively as a “soul” because he decidedly demarcates his notion of the demos against that of “bare life” (Agamben), and also against one that comprehends by it generally “the lower classes.” Opting in favor of a categorial approach against a classificatory one, even a generative one in the manner of Rancière, means to invert the outlook he presents: it is not by barring “the noun” from being articulated and spelled out that we can avoid the deadening reification of settling with representations of identities—but by excessive articulation and spelling out of “the noun in its actions,” this inverted view holds. To our mind, the activity of the political subject depends upon a categorial view that bears in mind that categories are operative and abstract, in infinite mode, one that never arrests and mistakes them for describing general states. It means, in short, to treat it as adverbial, not as adjectival. Or to put it in metaphorical terms, Being friendly is not easy, and, annoyingly so, It gets more difficult the more clarified and defined our understanding of “friendliness” is. Clarification depends upon schemata, and directly opposes richness and wealth of understanding when the levels of abstraction, on which the schemata are operative in providing clarification, are conflated into the representational plane of a general concept. Abstract concepts are actualized within the bounds of finite corporeality; hence what qualifies them seems best to be treated adverbially, as adverbs describe the circumstances of activities, events, happenings, enacted properties, and relations.

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for now let me simply point you to Michel Serres, who has most forcefully articulated such a perspective in his 1990 book The Natural Contract: “My book argues that this Declaration [the Declaration of the Rights of Man and the Citizen from the French Revolution, and its update by the declaration published by UNESCO after the Second World War] is not yet universal as long as it does not determine that all living beings and all inert objects, in short, all of Nature have in turn become legal subjects.” 17 Let’s remember, our interest is in a notion of criticality that need not sacrifice the infinite, into which thought plunges, in order to gain a notion of consistency. This means to be looking for a notion of criticality that is not grounded in a general principle of sufficient reason, but one, we might say, that is governed in the way it is foundational for discourse, by a universal principle that is creative: one of abundant reason and finite synthesis.18 How can we picture such governance? The topicality of a theme that comes to be of general interest cannot be treated as an “objective fact”—precisely because as an “objective fact,” it is called into account. What I would like to suggest to see in action, in the expansion of the generic whose instances are viewed as pre-specific, is a universal corpo-reality, a corpo-reality of symbolic nature. Thanks to its symbolic nature, such corporeality is not “the one body of the collective,” as the political-state form may be interpreted, and it is not “the one soul of the people,” as Rancière’s notion of the demos seems to maintain. Nevertheless, it is political. It binds, as symbolic corporeality, in lofty and contingent manner, what Rancière conceives as dissensus: “This is what I call a dissensus: putting two worlds in one and the same world. A political subject, as I understand it, is a capacity for staging such scenes of dissensus.” 19 A dissensus for Rancière, as for me, is not a conflict of interests, opinions, or values; it is, as he puts it, “a division put in the ‘common sense’: a dispute about what is given, about the frame within which we see something as given.” 20 What names political subjectivity understood as such must be generic, we can agree with Rancière. But if we understand it as categorial, as an adverb of universality and not as an adjective of a particular natural class, it does not name mankind in terms of demos, it names nature itself. The change is profound: both approaches opt for confounding the distinction between politics and nature, but Rancière’s classificatory treatment of the generic name places us within a naturalness of politics, while the categorial treatment of it confronts us with a politicality of nature. Everything 17 Michel Serres, “Revisiting The Natural Contract,” trans. Anne-Marie Feenberg-Dibon (lecture, Institute of the Humanities, Simon Fraser University, Vancouver, May 4, 2006), http://www.ctheory.net/articles.aspx?id=515. 18 For a contemporary contextualization of this idea see Sjoerd van Tuinen, “Difference and Speculation: Heidegger, Meillassoux and Deleuze on Sufficient Reason,” in Deleuze and Metaphysics, eds. Alain Beaulieu, Edward Kazarian, and Julia Sushytska (Lanham, MD: Lexington Books, forthcoming/2013). 19 Rancière, “Who Is the Subject of the Rights of Man?,” 304. 20 Ibid.

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among which we live—facts and laws, artifacts and things, elements and climate, codes and rules— appear under their proper natality aspect. Such a politicality of nature puts a dimensionality of genuineness in the place of points of origin and hereditary lineage. More precisely, it suggests treating questions of origin and lineage by recourse to distributiveness. Such a dimensionality of distributed politicality adds the modality of probability to those of possibility and necessity, which govern in rationalist philosophy anything that extends in space and in time. Hence the political is not a sphere, both our views agree; rather, it separates, as Rancière puts it, “the whole of the community from itself.” 21 The political, for both views, shapes the gap between abstract literalness and the conditionality of possible verification of what is meant by abstract literalness. Such a politics of difference is acted out, according to Rancière, by distinguishing two “counts of counting” the community: “You can count the community as the sum of its parts—of its groups and of the qualifications that each of them bears.” This way of counting is entirely rule based and uninvolved, and it results in cold observation and surveillance according to a logics of classification (Rancière calls it “police”). He puts a second way of counting as follows: “You can count a supplement to the sum, a part of those who have no part, which separates the community from its parts, places, functions, and qualifications.” 22 To Rancière, only this second “counts of counting” is politics, and such counting is not uninvolved, it is acted out by political subjects, and it does not submit to rules in any mechanical manner.23 Its procedures are infinitary, as opposed to the finitary way of counting by summation (that of his notion of “police”). His usage of “counting” consciously evokes that mathematical practice in its irreducibly intertwined double sense of accounting and governing. Such politicized counting, which affirms to count in infinitary values as supplements to each totalizing “sum,” follows in Rancière what might be called a materialist aesthetics of classification (not a formalist logics of classification). We can see now where the naturalization of politics happens in Rancière’s position: his politics of difference is acted out in a twofold manner, by the police and by political subjects. Thereby, responsibility is delegated to one side only—that of political subjects, while the police is treated almost like we treat the weather: as the quasi-material incarnation of necessities whose constraints are determined on a more abstract level (climate), but that we have to deal with for bringing both rhythm and chaos, fertility and destruction, homogeneous and disrupted growth, prosperity and corruption. 21 Ibid., 305. 22 Ibid. 23 See footnote 10. This is what distinguishes Rancière’s approach from those that demand followership by faithful devotion (of the illiterate) rather than critical subscription (by the literate), with the effect that his arguments hardly lend themselves to creating a movement that will realize a political program.

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Beyond urban comfort, in a state of expulsion In order to see more clearly what is at stake with a categorial treatment of what names political subjects, in distinction to a classificatory one, let us briefly consider what seems to be an important motive for Rancière and his classificatory treatment. Toward the end of his text he clearly states that he sees a certain contemporary tendency intervening toward the “erasure of the political in the couple of consensual policy and humanitarian police,” 24 a tendency he sees threatening to turn what used to be political activity into “an anthropological or ontological destiny.” 25 Political correctness, administrated by discourse, perfidiously urges us to be “passive” if we want to be politically “active.” His aesthetics of classification is geared against such false “political correctness,” which in effect hands over the legacy of political thought and action to some larger power that predicates us as Subjects of Rights. This “larger power,” obviously, manifests in the process of progressive rising levels of welfare, which unfolds on a global scale, albeit in unequal manners and paces. Rancière seems to ask, what if we dared to turn our backs to this urbanity that is spreading globally, propelled by its promise of quasi-salvational comforts, and that tends to erase all politics in the manner mentioned? He does not seem to seek to somehow “overturn” the system, nor to fight for more global justice; rather he seems to ask, can there be an exodus, can we not learn to cultivate differently the grounds on which we would happen to find ourselves, if we affirmed to live in a state of expulsion? Can we not begin to oppose the auto-logy of such destiny by producing the means we need, in order to remain active political subjects, through a kind of “farming” that learns to root that for whose growth it cares, in—to use his own formulation of how political subjects “count”—the infinity of a sublime object, the object of aesthetic judgment, which virtually supplements each sum? Rancière suggests a kind of aesthetic calculus rather than a logical one. It is aesthetic because its functions map procedures in a twofold manner: by numbers that label the sums of infinite terms, yet these labels are merely indexes, pointers.26 Such an aesthetic calculus is “genetic,” its functions are productive; they do not merely represent a process, they initiate its enactment. Such is the involvement and activity that Rancière holds neces­sary for counting as political subjects. It is not an activity that fights what is counted in a police manner, but one that has decoupled from such counting and instead regards it as a quasi-weather, as temporary states 24 Ibid., 309. 25 Ibid. 26 It is important to see the difference of an aesthetic calculus to phenomenology and semiology—both of these attempt to supplement calculus with either a general theory of signs, or with perception. An aesthetic calculus, on the other hand, does not keep a notion of calculus as distinct from one such supposedly more general theory. It stresses that the notion of calculus cannot remain untouched if we want to avoid sacrificing the openness of the infinite. Thus, I describe its labels in the conventions of symbolisms as indexes and pointers (codes), and not as signs, etc.

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that are imposing certain conditions with which we have to deal, if we were to hold that it is not entirely unthinkable to begin again: by affirming to live in a state of expulsion from the secular urbanization of modernity, which used to be like a promised land but turned out to sentence its “subjects” to the status of “consumers,” allowed to “do politics” in terms of a “correctness” that is policed by a kind of counting that builds on a logic of classification that deprives the individual of holding her aesthetic judgments as “naturally legitimate.” Generic as an adverb, the liveliness of nature In all of this our own views would agree. But what is entailed now with opting for a categorial rather than a classificatory approach? How can we picture what a philosophical stance of “critical rationality” would entail, a rationalism that is coupled with a notion of critique-ability, a notion of critique in the terms of an ability that revolves around a symbolic understanding of numbers? What would it entail to stick with Rancière’s operative distinction of two “counts of counting,” while transposing them onto a stage set such that the generic name acts as a universal name, adverbial not adjectival, a stage on which it articulates and spells out the liveliness of nature? In all figurative brevity, it does not characterize life in such a state of expulsion as the life of farmers, but as that of gardeners. It is not the material grounds of a new existence, generic and singular (politics anchored in aesthetics) instead of comfortable and general (global urbanity), that need to be cultivated, but the intellectual grounds of heterotopia, common places (topoi) that are nowhere there, but nevertheless real. Heterotopias are the kind of sites that have consistency not despite but because they are distributed, they are “continents, cities, planets, universes,” as Michel Foucault imagines, that are engendered “in the heads of people from the in-between of their words, from within the deep layers of their stories and also from the place-less site of their dreams, the void in their hearts.” 27 If heterotopias are nowhere there, which we take from Foucault’s idea, it is because they are always already here. As utopian in the literal sense, a place that has no place, heterotopias spring forth from the non-places of the immediacy of a present we live through our bodies.28 Thus I would suggest that the universality named by Rancière’s notion of the political subject, once thinking about its generic name as adverbial rather than adjectival, instantiates as bodies-to-think-in. A particular body-to-think-in is one of a kind, and its kind is what I mean with symbolic corporeality. We can look at the universal as the liveliness of nature, contracted in the household of energy from which it lives. Hence it is true that 27 Michel Foucault, “Les hétérotopies,” Radio France, December 7, 1966; here cited and translated from Foucault, Die Heterotopien. Der utopische Körper (Frankfurt am Main: Suhrkamp, 2013), 39. 28 See Michel Foucault, “Le corps utopique,” Radio France, December 21, 1966; here cited and translated from ibid., 55–65.

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the symbolic is vested toward establishing consensus—for Rancière the negative of dissensus, and according to his dialectical thought, the death of politics—but it does this as a means to make room for staging scenes of dissensus. The symbolic is neither political nor doctrinaire, it is contractual, operative, and only in a derivative sense is it functional. It is “at work” indefinitely, never as a process that begins and ends. It creates the capacities proper to generic conditions of transformability, and it insists that these conditions be universal while at the same time having actuality only as local instantiations. We can see formulas or equations as the symbolic “form” such adverbial contracts take. What I would like to suggest is that they open up and cultivate an interval for the political subjectivization of any identity, just as Rancière claims for what-is-being-namedby-the-demos (he speaks only of political names and political subjects, not of political identities). Nature’s politicality dimension constitutes, in its principle expropriation of particulars from their individual genuineness (generic means to expropriate all individuality from specificity), the non-possessable disposition for staging scenes of dissensus. Things have a genuineness, they have a nature, but it is symbolically masked and roots in an elementary distributedness rather than in an individuality. The unsettling aspect about understanding the symbolic in such terms is, of course, that it may be instrumentalized in both directions—politics and/or doctrine. There can almost be no better characterization than Rancière’s own of what kind of subject is named thereby 29—cases whose kinship is unsettled: “Political names are litigious names,” he writes, “names whose extension and comprehension are uncertain and which open for that reason the space of a test or verification.” 30 For him, political names name political subjects in such a manner, and this is how they are capable of reorganizing “the frame within which we see something as given.” 31 I am aware that suggesting to see identity that can be expressed by a formula or equation in the same terms that Rancière finds for political subjects might strike one as a gross misunderstanding—isn’t the solution space for a symbolic form determined in absolutely certain ways, not in uncertain ways? On which grounds can we speak of such a politicality that belongs to nature, and of which we claim a universality that allows to characterize the abstract objects of symbolic computation in terms of their particular integrity? I briefly pointed to the importance of how we think about solution spaces when I introduced the notion of adjacency in mathe­matical corpus theory. Let us see in more detail how this is exactly what was at 29 Although he would, by what I can understand from his own programmatically political commitments—which he keeps respectfully separate from his philosophically political commitments, as I have argued before (see footnote 10)—not at all agree with my proposed application of his concept in the context proposed here. 30 Rancière, “Who Is the Subject of the Rights of Man?,” 304. 31 Ibid.

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stake with the emergence of universal algebra throughout the nineteenth century, and how we are confronted today with its entailments. Bodies-to-think-in live in algebraic universality “Let us to try to make sense of the sentence—or develop the equation.” (Jacques Rancière) Computing with the symbolic means of algebra has added a new dimension to mathematics: the input of certain values in a formula may not only turn out to be unsolvable, it may also yield a solution space that is so vast in options that none of the possible solutions seem more necessary than any other. This was indeed the key critique of George Boole’s Algebra of Logics, which is illustratively expressed in an open letter by one of his contemporaries: “The disadvantage of Professor Boole’s method is […] he takes a general indeterminate problem, applies to it particular assumptions not definitely stated in his book, but which may be shown, as I have done, to be implied in his method, and with these assumptions solves it; that is to say, he solves a particular determinate case of an indeterminate problem, while his book may mislead the reader by making him suppose that it is the general problem which is being treated of. The question arises, is the particular case thus solved a peculiarly valuable one, or one more worthy than any other of being solved? It is clearly not an assumption that must in all cases be true; nor is it one which, without knowing the connexion among the simple events, we can suppose more likely than any other to represent that connexion.” 32 Boole’s methods were not shown to be faulty or inconsistent—the reason why they had been disliked or even spurned by so many was the immense depth of horizon they had opened up. Indeed, Theodore Hailperin has, in a relatively recent paper, explained how Boole’s ideas make sense only if we read them in relation to algebraic concepts like ring, module, and domains, concepts that had, in his time, been far from digested and settled, not even on a methodological level, and certainly not on a philosophical level. I will come back to this in a later part of the paper. These preliminary indications are merely meant to induce some confidence in my postulation of the generic as constituting a kind of symbolic corporeality whose singular 32 Letter by Henry Wilbraham, published in the supplement to The Philosophical Magazine 7 (June 1854); emphasis mine. Cited in Rod Grow, “George Boole and the Development of Probability Theory,” http://mathsci.ucd.ie/~rodgow/boole1.pdf. See also Theodore Hailperin, “Boolean Algebra is Not Boole’s Algebra,” Mathematics Magazine 54, no. 4 (September 1981): 172–84; Walter Carnielli, “Polynomizing: Logic Inference in Polynomial Format and the Legacy of Boole,” http://www.cle.unicamp.br/principal/ grupoglta/Thematic-Consrel-FAPESP/Report-02-2007/C07.pdf; and Stanley Burris, “The Laws of Boole’s Thought,” http://www.math.uwaterloo.ca/~snburris/htdocs/ MYWORKS/PREPRINTS/aboole.pdf.

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instances manifest as particular bodies-to-think-in, and my speculation about what such a postulate might entail for thinking about computability. The most important aspect is that such bodies-to-think-in are collectively constituted—before they can be acquired individually. Yet this collective constitution is realized only through the individual acquisition of the bodies-to-think-in. The agility they are capable of relies upon individuals who learn to inhabit what has been collectively achieved; they turn lonely and clunky otherwise. We can think of such bodies-to-thinkin perhaps best as literacies: we can see the canonical corpus of authoritative knowledge turning into bodies-to-think-in, animated and vibrantly present in a manifold manner, according to the breadth and articulacy in which these corpora are inhabited. Does such inhabitation not point us toward the possibility of affirming mastery in a different manner than that of domination, dependency, and exploitation? Does it not announce a revival of other aspects proper to mastership, like generosity, care, and commitment? To inhabit politically such a canonical corpus requires the act of acquisition as we know it from learning-to-become-literate: not only in the sense of writing and reading correct sentences, but finding apt forms for one’s words, and apt expressions for one’s thoughts. Let us return from these preliminary remarks, and from viewing computability within the paradigms of programming, back to computational design more strictly. Here we can see in architecture, for example, how the first wave of this fascination with the generic raised an interest in form finding as opposed to giving form, or deciding about form. By now, this first wave has given way to an interest in developing the parametric conditions from which such forms can be found. Yet along with this comes a certain complication with regard to seeing in the generic a kind of genuineness that would liberate us from troubles associated with individual authorship and mastership. In the light of parametricism as a new paradigm in computational modeling, it becomes much more transparent that, indeed, the one-of-a-kind particularity attributed to instances of such abstract objects is neither example nor prototype, but that there is a “suchness” to the “thisness” of their instantiations nevertheless, and that despite the engendering of its hylomorphic identity (its form and content) through mere tentativeness (purely indexical, without a decision of how to interlink the dots into a figure), these instances are conditioned. Technically speaking, they are conditioned by a master model whose instance they are. Theoretically speaking, the form of organization and government proper to a master model (you can think of the specularly governed domains mentioned earlier in relation to the integrity of abstract objects) may well be singular, yet they are not absolute—simply for the reason that there is an open range of manners in which each and every one of them could be set up. Or to put it differently: we may well be dealing with absolutes when we deal with such abstract objects, yet they are absolutes whose symbolic nature tells us that there always are alternatives to be considered.

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Iv

Characterizations of The Generic

Characterization on a grammatical level Against our suggestion to read the generic in an adverbial sense, the “grammatical common sense” (if indeed there is such a thing) today maintains that the generic be the adjectival form for referring to a genus that can be represented by the formal notion of a class. There are many ways of how this could be explained,33 but the most important one seems to involve a strange “metaphysical competitiveness” between the notions of genericness and universality. Traditionally, any one genus could never count as universal, because its role is descriptive and representational in relation to concrete things that in reality are always individual, and whose collective nature the genus is to determine. Universality, on the other hand, has traditionally been attributed to categorial determination, of which it is clear that it is a genuine abstraction (however we might think about the nature of abstraction). No one would seek a “position in space” or “quality (per se)” as a concrete instance of it existing! 34 Categories were held to be universal, and they were what concrete things would instantiate. This is how the universal comprehends, literally, that which is the property of all things. It seems hardly an exaggeration to see in the conflation of this distinction, between classes and categories, the key aspiration for modernist political philosophy. In its striving to rid philosophy and science from metaphysics and theology, it sought to overcome orders of supposedly natural kinds 33 There is, for example, an extremely interesting history regarding the status of grammatical cases. All throughout the centuries, the disputes of the grammarians centered around how cases can be accounted for: cases express all kinds of relations—there are languages still today that have more than twenty distinct cases that differentiate the most common ones: nominative, dative, genitive, and accusative—and the question of how we can account for them involves assumptions about causality. There are two main positions for which different schools have opted: a casus is “what has fallen off” something, literally; that’s how it is caused. The common understanding today seems to hold that the case of the nominative is somehow different from all the other cases, and that the latter are indeed what falls off from the nominative—a view that puts the noun in a grammatically central position. Yet since the earliest grammarians, another view holds that the nominative case is like all the others, and that it marks the imprints of activities that are happening with some degree of regularity—activities that happen in repetitive manners. According to this view, verbs in infinitive form are marked out as central for identifying syntactic units in language, not nouns. It is easily transparent how two views entail profound metaphysical implications. See the classic 1874 book by Heinrich Hübschmann, Zur Casuslehre; and Louis Hjelmslev, La catégorie des cas (Munich: Wilhelm Fink Verlag, 1972). 34 This is of course not really true; in fact, what characterizes late scholastic philosophy is precisely a forceful dispute around the claim, raised by some scholars, that we ought to assume a reality distinct from that of concrete particular or individual things, and proper purely to the universal. It was called the problem of universals, and to liberate thought from the kind of dogmatism that could be attached to such a notion of reality was surely one of the great moving forces behind the break of the Renaissance. Universals constitute every notion of “pure reason”—against which Descartes brought forward a new analytical method linked to an attitude of “fundamental skepticism,” and with which Kant, a bit later on, sought to reconcile a certain legitimacy for speculation with the Cartesian “method of doubt” in his Critique of Pure Reason (1781).

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and their rigid class distinctions. The challenge was, and still is today, to find a way of “attaching” the universality proper to categories of abstract criteria to the notion of class that can be formed according to concrete marks of distinction. The quest for a universal subject, a universal object, or even a notion of universal reality, must try—if it wants to be critical and not dogmatic—to identify a notion of universal class. A universal class would be a class that acts genuinely without self-interest, and in the interest of all. Or to put it differently, more adequately but also more difficultly: the universal class would be the class where self-interested action coincides with the needs of humanity as a whole.35 The man without qualities (Robert Musil) Robert Musil famously wrote a novel of a man whom he portrayed in the light of such an essential abstinence from desiring individual property, as the man who aspires to be, tautologically, nothing but a man (Der Mann ohne Eigenschaften, 1930–32). The novel accounts the struggles its protagonist has to take upon himself: as a character with a life of his own, Ulrich is faced with this task as a sheer impossibility. He tries to find meaning for his life under the condition of resigning from any possibilities offered to him by the particular class to which he happens to belong—in his case as an intellectual, a mathematician by education, that of the bourgeoisie. In vain attempts to reconcile “soul and exactitude,” his vocation and his profession, he searches for a place and role purely within the “universal class of mankind”—that is, by refusing to accept any privileges that might be granted to him on the basis of his particular individuality-within-theactuality-of-the-social. Musil’s novel is appreciated widely for its capacity to express and thematize in most subtle and differentiated ways a widely shared mood of the zeitgeist of his time, and counts today as one of the most influential books of the twentieth century. The city without identity (Rem Koolhaas) More recently, the architect Rem Koolhaas has taken up this Musilian theme, yet now in relation to cities instead of an individual person. The Generic 35 What haunts modernity, and thereby hinders it to continue with itself on its own terms, is the idea of a natural reality, one capable of hosting a notion of universal commonality. Still today we can read much of contemporary political philosophy through the lens of how a universal subjectivity might be conceived—from this point of view, even very contemporary contributions to political discourse root back rather directly to Hegel’s suggestion of understanding bureaucracy as such a universal class that serves all, without self-interest, and to the Marxian totalization of this idea by seeing in the universal class the proletariat: from Laclau and Mouffe’s dialectical affirmation of the political as a condition of competing hegemony to Hardt and Negri’s Multitude as the political subject of the New World Order they postulate, Badiou’s and Žižek’s ideas about how to conceive, in secular terms, of an abstract persona whose voice is to matter most (Žižek’s Lacanian-Hegelian master discourse, and in the case of Badiou, his set-theoretically constituted mathematical ontology) to Agamben and Virno’s interest in personifying abstractly the (Marxian) concept of a general intellect.

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City gives the portrait of a city in the light of having done away with all that Musil’s protagonist still tried, in vain, to reconcile himself with—in short, identity, property, history, the entire inheritance from a premodern era with which an individual has been equipped “to-begin-and-continue-with-itself”; in short, to lead a proper life, a life of one’s own (to pick up a wording coined by Virginia Woolf in her seminal 1924 essay “A Room of One’s Own”). The Generic City confronts us with an account of the peculiar realism of the generic; there is neither identity nor history nor property in the Generic City. Consequentially, the Generic City establishes its order in purely infrastructural, systematic, and continuous terms. There is singularity in the Generic City as he portrays it, yet it is a singularity that is liberated from the standardized. Rather than incorporating a cosmic, cosmological, or otherwise transcendent order, the Generic City provides settlement within what Koolhaas in all consequentiality calls Junkspace: preempted from ever manifesting something of substance—something that would have to be conceived of in how it maintains its own finite continuation—such space is only there to ultimately be disposed of. All reason for categorization is annihilated in it. In Junkspace, order must not be wrested from chaos. Instead, oneof-a-kind particularity (which he calls “the picturesque”) is wrested from the homogenized. Unsurprisingly, the reception of Koolhaas’s portrait of the Generic City is quite different from that of Musil’s theme-opening novel. Bluntly speaking, it tends to be perceived as a bothering impertinence. Its clinical viewpoint and the somewhat drastic (and also, arguably, resigned and sarcastic) tonality is often taken for the cynicism of a global architect who portrays, with a certain braveness, it must be admitted, a threatening development that he contributes to and lives from: the drastic homoge­ nization of our living environments. For many people it seems clear that the homogenization he portrays is an effect of the global expansion of the capitalist economy and a respectively Darwinian survival-of-thefittest dynamics that go along with such expansion. To this understanding, Koolhaas’ suggestion of relating these effects of homogeneity to the strengthening expansion of the generic must appear monstrous. Large portions of the aggression Koolhaas attracts is surely because he seems to ridicule hopes that feed from the belief that there must be a way to purify the generic of the exploitative dynamics of capitalism, and to find in it, finally, a long-sought means to realize the core values of socialist and modern politics. But where am I speaking from, when daring to refer so distantly and seemingly uninvolved to this thematic locus of vibrant emotion (and activism)? Before turning to my staging of that conceptual persona that, as I would like to convince you, ought to complement that of the generic, namely the concept of the master, it seems adequate to make a few short statements about this.

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v Falling in love with the in-sinuousness proper to an entropic economy Primary abundance I am speaking from a point of view that credits a development with principle importance in a manner not usually shared today, even though as a phenomenon, it is almost permanently in the media—yet as an observation only, without instigating the least dissensus so far. The phenomenon I mean is this: our planet is literally bathing in the solar stream, with ten thousand times as much energy to be potentially harvested from its light particles as all of humanity is currently using worldwide, each day, streaming by continuously. For the first time ever, we can encapsulate and integrate, within the planet’s ecosphere, energy that is additional to that which is already stored in its manifest natural body—the weather, plants and animals, stone and earth. It may sound strange and somewhat amazing to view photovoltaics like this, but as a phenomenon it doesn’t seem to be disputable. Yet weighing this phenomenon as being of principle importance for how we think about our habitat and anything that derives from such thinking—economy, politics, how we make sense of what we experience and engage in—this is much more critical. Because it means to attempt “generalizations” that were based on what this “phenomenon” implies. What would that mean in the first place, attempting to generalize on the grounds of regarding the planet’s location in the universe not in terms of its position within the interplay of cosmic forces, as in astronomy and geometry, but in terms of the planet’s active energetization? I put “generalize” and “phenomenon” in quotation marks. Why? Because this “fact” is an “artifact.” It didn’t come about (in a naive sense) naturally, it became a fact only on the decisive grounds of human intellectuality. Photovoltaics is technics at its most sophisticated level (yet). And to generalize usually means to delineate classes such that they are capable of representing as adequately as possible, in mimetic terms, a certain common nature among different things as they are given. Yet in the case of the Earth, viewed in such terms, we have a singular situation. Attending to how we might “address” the planet’s situation in the universe in terms of its energetization inverses our well-tested and refined language games around localizability. The principle of locality in time and space—the principle that each thing has its place—needs to be replaced with a principle of circumlocution. The point is that which is being given, not that from which we can induce (extrapolate) givenness in an immediate (unconditioned) sense. It is not enough to consider circum-stances as characterizing location; more radically: we owe our location to the circum-giving (das Umgeben, in German) of rambling tails (the wave ranges of cosmic streams) that are rendered apparent by technical spectra (masking radiation). Under such conditions—let us call them adverbial—quantization precedes localization, just like the case in quantum electrodynamics, which also views light

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as particles.36 In all consequence, attempting to generalize from the implications of photovoltaics irrevocably urges us to distinguish between “generalization” and “abstraction” much more strictly. The implications of such generalization are abstract at first, they affect our notions of universality, but they also reach back to what we hold as general, the empirically based and classified descriptions of things. Attempting to generalize from the planet’s situation within the solar stream comes close to a modulation of cosmologic stability. To put it as pragmatically as possible: it suggests that we should count on a primary abundance of (clean) energy, and with that, an abundance of water and food; furthermore, bringing all materials that are rare and scarce into a regenerative cycle would not be a paramount problem anymore, because the main obstacle to recycling is energy-budget calculations, which depend upon the principle scarcity of resources. In less pragmatic and more theoretical terms: such an inversion turns the Earth not only into an object, but also into a subject. This falling together inevitably collapses the critical distance that is so necessary for thinking considerately—which literally means through observing the stars, from com- (with) + sidus (genitive sideris, constellation)—and not furiously and impetuously. This was the key motive for Gilles Deleuze, with his difficult attempt at inverting, philosophically, the entire legacy of Platonism, which he stated in strikingly clear terms: “It is not the slumber of reason that engenders monsters, but vigilant and insomniac rationality.” 37 If it didn’t sound so dramatic, it would seem adequate to say, instead of speaking about the possibility to “generalize” from this “phenomenon,” that to assume the very possibility to do so entails assuming the possibility of engendering the Earth in its kind. This is a hyperbolic way to put it, and I am aware of its polemical nature. To contextualize this, I would like to come back now to what the perspective of universalizing the Subjects of Human Rights entails in more detail. Let’s attend more closely to the position of Michel Serres already mentioned earlier. To illustrate more concretely what motivates such overstatement—that we are engendering the Earth in its kind— we can take up helpful terms he has coined. He names “collectivity” as the new object-subject distribution, and places in its range of responsibility what he calls world-objects: “By world-objects I mean tools with a dimension that is commensurable with one of the dimensions of the world. A satellite for speed, an atomic bomb for energy, the Internet for space, and nuclear waste for time […] these are four examples of world-objects.” The turn in the language game of localizability for him means that “we become the victims of our victories, the passivity of our 36 See Richard Feynman, QED: The Strange Theory of Light and Matter (Princeton, NJ: Princeton University Press, 1985). 37 Gilles Deleuze and Félix Guattari, Anti-Oedipus: Capitalism and Schizophrenia, trans. Robert Hurley, Mark Seem, and Helen R. Lane (London: Continuum, 2003), 112.

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activities. The global object becomes subject because it reacts to our actions like a partner.” 38 Hence, attempting to generalize from the planet’s situation within the solar stream in terms of its energetization and circumgivenness (instead of position and locality) comes close to a modulation of cosmologic stability, and this, perhaps, with a momentum no less severe than that of the secularization of cosmology that accompanied modernity. There is little reason to doubt that we can continue to count on what we believe to “know”—all the technical and scientific artifacts certainly bear witness to that—yet we might have to reconsider how we can account for the stability that is captured in what counts as knowledge. If our thinking about the Earth means to engender it in its kind, the Earth—of which we are, intimately, a constitutive part—is the “whole” that comprehends all that can be articulated, and all that can be substantiated in formally corporeal terms (symbolic artifacts) as well as in materially corporeal terms (manifest artifacts). Taking the implications of mastering photovoltaics seriously means to articulate the “identity” of the Earth not in its general or correct terms, but in any terms that can be substantiated. And it also means that all the terms that can be substantiated are terms that properly characterize its kind. Modern science has assumed a natural homogeneity as characterizing all things natural, in terms of which it attempted to classify scientifically all things on an equal basis, dynamic yet universally coordinated, within dimensions whose interplay applies uniformly and globally. Serres has named them as the “dimensions of the world”—energy, space, time, and its derivatives like speed. The principle that modernity found for identifying the individuality of all things in this manner, as constituted not by natural kinds but by a universal nature, was “work”: transforming energy from one form into another. The architectonics of such systematicity rests on the assumption that the total amount of energy within the cosmos is finite. Only on the basis of this assumption can we learn to understand forms of individual becoming purely on the basis of what a thing is doing, literally, through understanding the transformations of energy and matter. What I see questioned with the principle of primary abundance is not this axiom, but the adequacy of the modern (thermodynamic) stance to treat world and universe alike. I can think of no reason to reconsider the assumption that the total amount of energy within the universe be stable, and that energy is what can neither be produced nor decay. It is the equivalence between globe and universe that appears as inadequate from the energy perspective of primary abundance. In concrete terms: the total amount may well be finite and stable within the universe, yet that which is integrated and encapsulated within the ecosphere of the planet 38 Serres, “Revisiting The Natural Contract.” See also Michel Serres, Le contrat naturel (Paris: Bourin, 1990).

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Earth is not. The criticality I am looking for, one not based on a principle of sufficient reason but on one of abundant reason and finite synthesis, needs to live up this change in perspective. vI

The Master

Toward an information-based architectonics Michel Serres has recently suggested not only that but also how the two physical categories of mass and energy—those that are derived from the principle of work—could be complemented with a third component that is orthogonal to the latter two: information.39 “I do not know any living being, cell, tissue, organ, individual, or perhaps even species, of which we cannot say that they store information, that they treat (or process) information, that they emit it and they receive information. […] I know of no object in the world, atom, crystal, mountain, planet, star, galaxy, of which one could not say again that it stores information, it treats (or processes) information, it emits and it receives information. So there’s this quadruple characteristic in common between all the objects of the world, living or inert.” 40 Between all things in the world, he suggests, what is common is a fourfold activity—to store, to treat, to emit, and to receive information. While work, the transformations between energy and matter, was the emancipatory principle that allowed the overcoming of premodern doctrines of natural order by demarcating a strict separation between culture and nature, mind and matter, and spiritua­ lity and reason, the introduction of information severely complicates things. While work as a category operates on the level of representing a generality (the class of all things insofar as they are natural—or technical, in the sense of scientifically natural, as they do work), the fourfold activities operate on the level of actualizing abstractions. The cosmos (world, manifestations of things) does not represent a universal order (forms, templates, types, etc.). In fact, the universal cannot be represented because it is pure and infinite activity: storing, treating, emitting, receiving. The so-induced notion of universality cannot be represented by concepts; it acts. Concepts mask this activity, like technical spectrum masks do. Within the quantum clouds of probability distributions, it keeps predicating potentially, and can only be actualized when 39 The aspect that there is a third component is a key motive of cybernetics, and has perhaps most prominently been articulated by Norbert Wiener—“Information is not energy nor matter”—without being able to suggest a different architectonics that could accommodate all three of them. Serres’s approach here is the first that aspires to do so. 40 Michel Serres, “Les nouvelles technologies: Révolution culturelle et cognitive,” lecture held on the occasion of the 40th anniversary of INRIA, a public institution for research devoted to the sciences of computation (les sciences du numérique) in France, December 11, 2007; https://interstices.info/jcms/c_33030/les-nouvelles-technologiesrevolution-culturelle-et-cognitive?hlText=michel+serres. Thanks to Diana AlvarezMarin for translating from the original French.

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articulated (factorized and complemented with coefficients) within a formula, and expressed as a case of the symbolically established solution space. Information (what is distributed and integrated in this acting) is like the photons from the solar stream: an elementarity abounding and discrete packages of powerful indefiniteness. Articulating it, in the metaphorical terms of how an alphabet articulates the stream of breath, excites its indefiniteness to take on the characteristics of what we might call an imaginary magnitude, corresponding to how the number that counts (and through that, governs and accounts) the possibility space is indexed, and indexically labeled. Such indexing raises the indefiniteness of information into lofty probability distributions of local density (amplitudes) and local plenty (probability amplitudes). As long as information is not thus excited and raised, it is indefinite just like the photons of solar radiation are indefinite as long as they don’t incite, through interaction, state changes within the relative stability of chemical bonds. In all consequence, the relation that can be maintained to the universal, so conceived, varies locally and depends upon the capacities and abilities that can be mobilized for articulating the terms of a formula that render solvable functional mappings. As long as the virtuality of the universal is not actualized, it remains pure indefinite elementarity, an elementarity we could call ideal because it is entropic, of indefinite substance. Such virtuality of the universal is a kind of ideal that is generic to all things. In order to acquire their properly individual, specific, general (not their universal) substantiality, this universal virtual generic­ ness depends upon being actualized, and such actualization, I would suggest, is achievable in acts of acquiring understanding. Learning, literally, is an act of acquisition: it means mastering a subject matter, and it is through such mastering that the virtual can be actualized and rendered manifest. It is not the formulas that incorporate the universal in any schematic sense; the formulas, in their apparent schematism, depend upon animation through the learnedness according to which the partitioning differentiation of the activity a formula constitutes, as a matheme, is modulated. To conceive of formulas as mathemes, from the Greek mathema for “that which is learned,” has been the custom for many philosophers throughout antiquity to the Enlightenment, and has been revived very prominently in the twentieth century by Martin Heidegger in Die Frage nach dem Ding (1950), and also by Jacques Lacan or Gilles Deleuze, among others. From our point of view with regard to primary abundance, what all of these recent revivals of the matheme as a key concept in philosophy are concerned with (in very different ways!) is that the universal—if it is in act (ontologies of the event)—is literally entropic, from the Greek term entropia, en for “in” and trope for “a turning, a figure of speech.” The universal is that which keeps turning within figures of speech.

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With this, we can now summarize our proposition of an entropic economy: It is not against entropy but thanks to it that we can maintain a locally variable relation to the universal, and substantiate figures of speech by treating them as abstractions, not immediately as generalizations, and by striving to formalize them into the constitution of a possible matheme. From the point of view of mathemes, the relation we can maintain to the universal is locally variable, and it is subject to an “economy” that is both collectively and individually based, and whose “stocks” are those accumulated through the acquisition of insight and understanding, and whose exchanges are rated by the socially taxed appreciation of mastership. In all dramatic exaggeration: surplus names can be rated in terms of any scale, from completely worthless to sublime dearness. The subjects that are mastered, by learning, are political subjects in Rancière’s sense, which I introduced earlier. They are subjects whose names do not represent definite collectivities. It is in this sense that their names are abstract, not general. They are “surplus names, names that set out a question or a dispute about what is included in their count.” The predicates whose activity is being governed by such counting are, due to the virtuality of their universality, open predicates: they do reign by (arithmetic) means of summation, division, etc., yet what they sum up is symbolically constituted, and because of that, can never be exhaustively totalized as a finite sum. They are predicates that incorporate, in the activity they mask when performing (for these concepts don’t work, they mask), an opening up of a dispute about what they exactly entail and whom they concern in which cases. They are capable of introducing an interval that makes possible political subjectivization into any status quo. Let’s remember: “Political names are litigious names,” Rancière points out, “names whose extension and comprehension are uncertain and which open for that reason the space of a test or verification. Political subjects build such cases of verification. They put to test the power of political names, their extension and comprehension.” 41 It is such a putting to the test that formulas, conceived as mathemes that are allowed to calculate with what has been learned, are engaged in. What has been learned can also be taught. If we cease to represent the universal, and instead relate to it by means of actualization, what opens up is the perspective of an economy in which all acts of acquisition are contributing to—not depriving—the prosperity of universality. What comes within reach to be thought is an economy where privation (acquisition of understanding and insight) increases the wealth of that which belongs to all (the communication of understanding in knowledge). If an individual learns to know, through acquiring mastership, developing it as a proper ability and demonstrating that and how it can virtually be learned by anyone, it differentiates and proliferates the richness of the universal. 41 Rancière, “Who Is the Subject of the Rights of Man?,” 304.

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From the adverbial and categorial point of view to universality, the commonness of the common nature of things is the result of inception, rather than the result of conception. With regard to political subjects (in the extended sense proposed in this text, not in Rancière’s original sense), abstraction precedes the concrete existence of that which presents itself to us in regularities. That which appears recurrently as cases follows a categorial order before it can be tested inductively, empirically. Abstractions are for learning, generalizations are for testing and settling the learned such that it can be treated as a case, as a “such” and not only as a “this.” Contrary to pursuing a prosaic disenchantment of the fascination with the generic, I hope to have been able to express why I think it only now begins to get truly interesting: the generic introduces a possible understanding of mastership that, seemingly paradoxically, builds on the premise of expropriation. It introduces an understanding of mastership where the -ship, the affix demarcating a “state, condition of being” is primary to the individuality that actualizes and acquires this state— the masters. Within the Generic City: Master, yet in “whose” house? By coining the striking word of mankind as having to come to terms with “not being the master in his own house,” psychoanalysis has suggested that we ought to understand ourselves through roots within the unconscious as a peculiarly expropriated groundedness of what can be understood and known. Psychoanalysis has rendered explicit a veritable negative form of architectonic thought that operates by working through an element of collectivity that remains unavailable for all attempts at taking control. Jean-François Lyotard has modulated this language game by making the point that notions of humanity need to be rooted in an element of what he calls “the inhuman,” a constitutive part of us that we do not control—which may be birth, infancy, the law, God, or the unconscious. Rancière has taken up this consideration in his reflections about who is the subject of the rights of man, to which I have made reference several times: “Absolute evil begins with the attempt to tame the Untamable, to deny the situation of the hostage, to dismiss our dependency on the power of the Inhuman, in order to build a world that we could master entirely,” he writes, and continues: “Such a dream of absolute freedom would have been the dream of the Enlightenment and of Revolutionary emancipation. It would still be at work in contemporary dreams of perfect communication and transparency.” 42 Important is that such inhumanity is the irreducible otherness, the part of the untamable of which human being is both host and hostage, Gastgeber and Gast, as a relation we might perhaps call “coexistence” or “genuine 42 Ibid., 307.

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mutuality.” 43 Along the lines introduced in this text, I would say it is the infinite surplus that needs to be taken into account wherever we are working with summations, checks, and balances. The grand project of an architectonics of reason, whether in positive or in negative terms, even if it were to inverse the problematics of mastership into non-mastership—purely into activity that doesn’t require mastership at all, but that unfolds auto-logically and automatically—meets its limits and turns stale and oppressive in the reduction of its own categories to representable schematisms. A schematism cannot engage critically with its own constitution infra-specularly. Our interest in a next paradigm for programming languages, a pre-specific one after the procedural and the object-oriented ones, derives from the unease in observing that these limits are indeed being met today.44 Programming languages, as I have argued earlier on, have entirely broken with the mimetic paradigm of language (at least in the representational understanding of this paradigm)—their grammars are engendered, their structures are governed self-reliantly, symbolically, within the confines of certain arbitrarily set determinations of usefulness. Without an understanding of mastership, all engagement with specularity would mean to subject one’s own critical engagement to the governance of these arbitrary determinations. In other words, if the generic makes a worthwhile point in suggesting to trust in a “groundedness” of knowledge that roots within an elementarity of distributedness, where all particular instances are expropriated from their individual specificity, such trust would mean—in programming more generally—to subject readily to the abstractly synthesized and arbitrary master language, or to master models in object-oriented computing more specifically. The problem thereby is not that these synthesized masters are synthesized; and neither that their “nature” is induced according to the orientation of a certain ambition. The problem is that the synthesized masters tend to appear as quasi-naturalized, while in fact they are synthesized by acts of learning and on the basis of acquired mastership. The problem, hence, is that they ought to be esteemed and treated accordingly—that is, the categories with which they operate ought to be understood as characterizing “political subjects,” not the subjects of “natural kinds.” The criticality with which they need to be met is not one principled by criteria indicating when reason is sufficient, but by criteria that index the capacities that constitute acts of finite synthesis. Thus, instead of referring to this dimension of expropriation as an expansion of the Unconscious, the Law, Provenance, or Divine Chance 43 Hans-Dieter Bahr has developed this theme toward a veritable reconception of philosophy, which he calls Xenosophie. See Hans-Dieter Bahr, Die Anwesenheit des Gastes: Entwurf einer Xenosophie (Nordhausen: Bautz Verlag, 2012). 44 Vera Bühlmann, Ludger Hovestadt, Vahid Moosavi, eds., Coding as Literacy, Metalithicum V (Basel: Birkhäuser, 2015).

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into and within the scope of what can be computed, I prefer to call literacy this abstract “where,” where “what can be engendered through learning” is rooted and grounded. We need not make any appropriative claims about the untamable nature and insistence that animates literacy, if we relate to it as a kind of body-to-think-in that indeed is generic, and hosts us all generically before it can be inhabited individually, while its existence depends, at the same time, on actually being acquired and inhabited by individuals. We can now see, in literacies, that which incorporates “loftily” what I have earlier suggested to understand as the politicality aspect of nature. I have characterized it as a dimensionality constituted purely by distributiveness, and as complementing the modalities of the necessary and the possible with a further aspect, that of the probable. Expropriation and mastership maintain a kinship relation that might appear surprising.45 Yet at the same time we all well know how, in order to communicate—whether in spoken words (speech), written phrases (discourse), or symbolic terms (algebraic code in IT and IT-based CT)—we depend on means and constraints from which we may well choose, but to which we first have to submit, in order to be able to elect. As long as we don’t master articulation and expression, argumentation and composition, signal interpretation and interface decodings, the less schematic and more interesting ones of them appear to us not as wrong, but as empty, superfluous, often confusing, insufficient, not entirely adequate, etc. It sounds quite paradoxical, but we feel comfortable, individually, within this generic dimensionality (our literacies) proportional to how well we are able to “master,” individually, these collectively constituted and governed capacities.46 viI

Characterizations of the master

Attracted by the volatility of a flirtation between the philosophical stances of “critical rationalism” and “speculative realism” So let us get back then to characterizations of the second conceptual persona that features centrally in this text, next to that of the generic: the master. While many contemporary intellectuals seem prepared to submit, with all due acrimoniousness, the rich legacy in architectonic inception to forms of often all too 45 A recent discourse where thought is devoted to this kinship between expropriation and mastership, via the question of whether and how sexuality can be understood as the being of symbolic relations—i.e., the being of relation-in-general—was published in two booklets, one by Jean-Luc Nancy, L’“il y a” du rapport sexuel (Paris: Éditions Galilée, 2001), and one by Alain Badiou and Barbara Cassin, Il n’y a pas de rapport sexuel: Deux leçons sur “L’Étourdit” de Lacan (Paris: Fayard, 2010). 46 Judith Butler makes a similar argument about language as the dimension in which we are all equally dispossessed, in her essay “Giving an Account of Oneself,” Diacritics 31, no. 4 (Winter 2001): 22–40. Her argument, I would suggest, can be expanded and generalized along the lines I propose here.

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unimaginative and uninspired scientism,47 a young French philosopher is currently raising hopes for the possibility of philosophy to actually continue its legacy of architectonic inception. Quentin Meillassoux is central to an emerging school called “speculative realism,” or sometimes “speculative materialism,” a vibrant field of intellectual thought and debate characterized through its reactivation of metaphysical and ontological themes, while at the same time being very active in strictly programmatic and political terms as well. Furthermore, the people associated with this community are closely watching recent technological changes, and they often take certain aspects of what they observe as their starting point. All of this is interesting enough for our context of computability, information, and architecture. Yet what I would like to focus on here, in order to bring out as clearly as I can the distinction between what I suggest to call “critical rationalism” and “speculative realism,” is not this larger context around Meillassoux in general, but a particular book he recently wrote on Stéphane Mallarmé’s poem “Un coup de dés jamais n’abolira le hazard” (“The Throw of the Dice,” 1897). This 2011 book, entitled Le nombre et la sirène, is equally brilliant as it is unsettling with regard to our interest in computability. The main protagonist in the poem is the Master, in the double sense of a particular authority and yet also (as is the case with most fictional characters) in a generic sense. We encounter the Master on a boat in the midst of a stormy and wild sea, holding dice in his fist and pointing his hand into the air. The poem never resolves what the Master actually does or intends to do with the dice, whether he wants to throw them in order to learn about his near destiny, whether he believes that he can intervene in the “fulfillment” of what appears to be his “predicament.” Are the dice a sign of the Master’s despondence, his impotence to continue being what he is, a master, vis-à-vis the powers of cosmic chance that science has just begun to affirm in the stochastic methods introduced by Laplace and others? Does the calculation with probability mark the ultimate end to any form of mastership, and instead enforce a more humble stance for man in a cosmos whose nature is determined indirectly, on the level of a second derivative, as a paradoxical determination of being undetermined? Most of the interpretations somehow unfold along these lines.48 The brilliance of Meillassoux’s reading lies in opening up, quite inversely to these readings, a novel possibility of how the poem can be interpreted 47 For any esteem of intellectuality as something that has been achieved by civilization, it is, for example, a sheer disaster that so much of research all across the social science and engineering disciplines today is evaluated, funded, and discussed along the simple and reductive line of carbon dioxide reduction. 48 The “death of the author,” which was proclaimed by Roland Barthes, Maurice Blanchot, and Jacques Derrida, among others, was decidedly rooted in particular readings of Mallarmé’s great character of our poem, the Master.

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as presenting an instance of actual, successful mastership. Meillassoux presents nothing less than an understanding of the Master in an entirely original way, which relies neither on annihilating chance nor on desiring to control it, and the calculations that are possible with it, objectively. We could easily call what Meillassoux reveals in Mallarmé’s poem a symbolist way of engaging with the theme of mastership—yet this, at first sight at least, comes close to saying nothing very surprising. And yet, the theme of symbolism as Mallarmé renders it present in the poem, and that is worked out by Meillassoux, not only affects severely what is more commonly associated with symbolism in art, it also affects the notion of symbolisms in mathematics—the entire legacy of developing, trusting, and departing from what can be learned through working out resolutions to formulas. The clue in Meillassoux’s reading—as I would put it—is to have Mallarmé engender a one-of-a-kind corpus of numbers whose “nature” is universal, while at the same time being singular. Meillassoux speaks differently about this; he does not mention the context of corpus theory in mathematics at all, for him it is all about the unique event of depositing the number that can be no other (on the side of Mallarmé) and someone (him, Quentin Meillassoux) finding it. Already before Meillassoux, many interpreters have sought to find a clue, and to be able to prove the hermetic nature of the poem as a treasure that was capable of conserving something inarticulate yet essential, by seeking to demonstrate how their clue fits the structure of the poem like a key fits the keyhole. What distinguishes Meillassoux’s reading from any such attempt is that he finds the clue he needs not in something exterior to the poem, but only because he engenders it himself, immanently, by working through and en-familiarizing with the materiality of the text, intimately and from within the poem, literally by not much else than counting, speculating reasoning, and by providing the grounds for his reasoning in clear and distinct form. And yet it would be mistaken to assume that at stake in Meillassoux’s reading is a notion of mastership that relates to a Cartesian subject, that knows how to master an object in all critical distance and pious devotion (after all, for Descartes it is God gifting us individually with ideas).49 Rather, at stake in Meillassoux’s reading is a notion of mastership based on what I would call insistentially shared intellectual intimacy. The mastership that Meillassoux portrays in Mallarmé’s poem, I would like to suggest, is mastership in succeeding to invoke acts of learning against the sheer improbability that characterizes learning. In such a situation, all clearly set identity distinctions between author, reader, and the protagonist are raised into a lofty cloud where the outcome, after settling back to “commonness” again (which we could call existential extimacy) after such exposure into the insistential intimacy 49 See Vuillemin, La philosophie de l’algèbre, especially the concluding chapter, “La mathématique universelle,” 465–518.

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of such learning, is profoundly uncertain. This is ever more remarkable, I think, if we consider that our present, in the beginning of the twentyfirst century, marks a moment when all hopes that count as reasonable with regard to the relation between chance and calculation go toward controlling chance through calculus, under the positivist restraint that such calculation needs to be combined with the provisional empirical precision and explication that characterizes the least degree of speculation. Against this critical divide between induction (empirical) and legitimate generalization (formal and deductive), Meillassoux affirms the move to symbolically encapsulate both, and work empirically within the abstract “indexicality” of the poem’s “material.” 50 I call it indexicality and materiality of the text because the stance of such “encapsulation” means to depart not from clearly bound dimensions, but from a state of mixture involving the semantics, the harmonic and graphical meter, the broader historical-political-cultural context as well as the history of the legacy he continues (poetry), and all hermeneutic aspects one can think of; having all the distinctions that grow out of these classical dimensions, he takes the liberty of putting them into a cloud of probabilistic relationality from which he then sets out to extract his own reading, where all classical stances that could be taken as a “ground” end up being slightly shifted, revolved, and rearranged in a manner that is consistent within itself, yet that lacks objective necessity in the consistency it arranges. Indeed the main hypothesis he puts forward is that Mallarmé’s project was not to represent the divine, but to dissolve it through his own poetic oeuvre.51 It is this contingent character of his reading, coupled with fine exactness and formal rigor, that sets up what I would call “the improbability of learning” that I see staged in Meillassoux’s reading. Every act of learning, I would like to argue, confronts us with just such a “confused” and “oversaturated” situation. To deal with such confusion through trust, until one has developed a “stable ground” or “consistency” that one can master in 50 In his earlier book After Finitude: An Essay on the Necessity of Contingency (London: Continuum, 2008; published in French as Après la finitude in 2006), Meillassoux reflected on what such an “encapsulating move” entails in relation to the philosophical tradition, and introduced the notion of “correlationalism” for referring to all stances that embrace a transcendental position. He suggested calling “realism” any stance that negates correlationalism. With due distance to the euphoric reception of this proposal (but also with some sympathy), Alberto Toscano has discussed the (also politically) problematic aspects about such an ambiguously “generous” generalization, in his essay “Gegen Spekulation oder eine Kritik der Kritik der Kritik,” in Realismus Jetzt, ed. Armen Avanessian (Berlin: Merve, 2013), 57–75. 51 “We have abstractly developed the hypothesis, which seemed to us to correspond in ‘The Throw of the Dice’ to Mallarmé’s draft since 1895—the one of a diffusion, rather than a representation, of the divine within the Oeuvre.” Thanks to Diana AlvarezMarin for translating this and the subsequent quotes from the original French: “Nous avons développé abstraitement l’hypothèse qui nous a paru correspondre, dans le ‘Coup de dés,’ au projet de Mallarmé depuis 1895 – celui d’une diffusion, plutôt que d’une représentation, du divin par l’Oeuvre.” Quentin Meillassoux, Le nombre et la sirène: Un déchiffrage du “Coup de dés” de Mallarmé (Paris: Fayard, 2011), 89.

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a relaxed (not in any particular and strict way dependent) manner, is the “spiritual” character of learning—in all the ambiguity this entails. I must say that this emphasis on seeing a notion of mastership introduced through Meillassoux’s reading of Mallarmé’s poem, which sets upon the fundamental improbability of learning, is not (not directly, at least) the way Meillassoux himself wants to guide the outlook that stems from his reading. For him, this point of view would be much too prosaic. In his eyes, the genius of Mallarmé (and that of himself) is—explicitly and literally so—programmatically spiritual in nature, not technically spiritual as I would prefer to have it with my emphasis on learning and literacy. The great passion that I wish to point to as being involved in any act of teaching/learning plays a crucial role for Meillassoux as well—he is very attentive to it—yet to him it does not characterize learning in general; he sees in it a singular moment that grows so powerful in this focalization as a singular moment that he recognizes in it an act of divine nature. I will not attend much here to the aspects of Meillassoux’s book where he draws quite daring consequences from this, suggesting to see in the poem a veritable liturgy that is capable of hosting and bringing comfort and orientation to a community-to-come, open to anyone who is willing to participate in performing the sacred rituals of what he calls “Mallarmé’s secular religion.” 52 Cosmic untendedness, prosaicness in verse But let me sketch a bit the larger context within which Meillassoux is inspired to such ideas. For it is a context that bears close familiarity to the contemporary situation in architecture, vis-à-vis the power of computing. So what was at stake more generally with the question of meter in poetry, and the rise of free verse? 52 “Modernity had therefore triumphed, and we did not know. The passion put, throughout the nineteenth century, to snatch the messianism from its Christian condition, to reinvent a civic religion freed from dogma, an emancipative politics exterior to the former Salvation. […] Mallarmé would have taught us that modernity had in fact produced a prophet, but erased; a messiah, but by hypothesis; a Christ, but constellatory. He would have architected a fabulous crystal of inconsistence containing in its heart, visible by transparence, the mermaid gesture, impossible and vivid, which had engendered it, and still engenders it. And the poet would thereby have broadcasted the ‘sacred’ of his own Fiction with each reader accepting to nourish herself on the mental wafer of its fragmented Pages. The whole in accordance with an accurate atheism, to which the divine is nothing beyond the Self articulating itself to the very Chance.” (From the original French: “La modernité avait donc triomphé, et nous ne le savions pas. La passion mise, tout au long du XIXème siècle, à arracher le messianisme de sa condition chrétienne, à réinventer une religion civique délivrée du dogme, une politique émancipatrice extérieure à l’ancien Salut. […] Mallarmé nous aurait appris que la modernité avait en effet produit un prophète, mais effacé ; un messie, mais par hypothèse ; un Christ, mais constellatoire. Il aurait architecturé un fabuleux cristal d’inconsistance contenant en son cœur, visible par transparence, le geste de sirène, impossible et vif, qui l’avait engendré, et l’engendre toujours. Et le poète aurait ainsi diffusé le « sacre » de sa propre Fiction auprès de chaque lecteur acceptant de se nourrir de 1’hostie mentale de ses Pages fragmentées. Le tout selon un athéisme exact, pour lequel le divin n’est rien au-delà du Soi s’articulant au Hasard même.”) Ibid., 128; see also ibid., 78.

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Since antiquity, poetry has always been credited with a certain dignity, as rightfully deserving a peculiar kind of spiritual trust. Different from other manners of expression through language, a poet did not lecture a doctrine, and did not speak in the name of an authority. And yet, there was a peculiar necessity attached to poetry, because any appreciation of excellence, as a poet, was tied to the poet’s strict subjection to a metrical law that was larger and more binding than his will: a poet strictly had to subject his verses to the conservative constraints of poetic meter.53 If a poet could lend his voice to evoke a thing with elegance, and without doing it violence—that is, through masterfully playing within these constraints—there could be attached, to that which is voiced poetically, a certain divine autonomy or gift. Like this, whatever was articulated poetically could be articulated only indirectly, and thus remain divine in nature. The oeuvre of a poet was to express this divine insight. As such, it was not appropriated by the verse that composes it, and what is more, the meter that renders the verse enunciable allows the listeners/readers to participate in the appreciation of such divine nature. There was in this sense, of a peculiarly poetic and strangely singular kind, a necessity involved in the creative vocations of addressing that which cannot be voiced directly. Due to this necessity, poets were held to deserve a particular kind of spiritual trust. Before the background of this legacy, the rise of so-called free verse in nineteenth-century poetry mirrored a profound crisis of cosmic untendedness that had its roots in a larger context, and that resulted from the strict separation of science from religion during the Enlightenment.54 For poetry, the indirect manners of linking the sounds not only in a grammatically correct way, but also figuratively coherent through rhythm, rhyme, alliteration patterns, and the like on a structural level, began to turn prosaic as the custom of fixed meter became secularized. Allegorically speaking, within the Cartesian coordinated space of representation, connecting points to the continuity of a line can count as no more but a simulated continuity. It is in a similar sense that also the poetic line (verse) literally began to turn prosaic.55 It is difficult to thematize this today, but the secularization that took possession of the ancient 53 The role of meter in poetry can be paralleled with the role of modularity in the architectural order of columns. 54 This same crisis famously provoked Kant to face the problem of philosophy being left with grounding reason within the sole alternative of either skepticism or dogmatism, an alternative that he sought to overcome with his notion of critique as a means to dethrone the centrality of whatever notion of “pure reason.” For a broader discussion see again Vuillemin, La philosophie de l’algèbre. 55 In the same manner, it is this cosmic untendedness that liberated architecture to concentrate on the vectors of how to build institutions as a form of political “tendedness” on the one hand, and on that of radically subjecting the building practices to procedures of technological industrialization—a vector that itself found an institutional form in the polytechnical universities that were founded in the late eighteenth century and all throughout the nineteenth century. The secularization movement in post-revolutionary Europe was carried by this momentum of modernization, and it affected also the fine arts. The mechanists were considered artists before this, as the French expression of industry as arts et métiers still illustrates.

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legacy of creative speech was of such awkwardness! Its old and trusted sense of necessity was threatened, naturally, by the arbitrary decisions that ordered the lines of free verse. At the time when Mallarmé was writing, that very spirit of modern prosaicness had set out to modernize even poetry, while nevertheless remaining keen on attempting to maintain a distinction between poetry and prose. Like the other symbolist poets, Mallarmé was outraged by the entailments of this development.56 Yet different from other poets, Mallarmé never seems to have released his outrage by taking sides programmatically, either for the conservatives or the modernizers. This is precisely why his poems have been interpreted in the twentieth century mainly along the lines of necessary acceptance of the impossibility of mastership (and authorship) in the exposure to stormy cosmic untendedness. His character of the Master is read with admiration as bearing up bravely in a spirit of affirmed vanity against his own awareness of his ultimate impotence. It is before this background that the recent reading of Mallarmé by Meillassoux touches such a sensitive zone. It opens up the perspective that the symbolist answer to these developments might not merely be read in terms of a bourgeois sublimation as a proclaimed continuation of the spirit of fine arts—bourgeois because in poetry, separated from its dignity, there is nothing really at stake anymore, except the gain in private pleasure. Symbolization appears, with Meillassoux’s reading, as something more than merely the crafty and artsy coating in codes and educatory puzzling of a truth that is as inevitable as it is bare of offering true delight. Let us attend now more closely to how symbolism is being substantiated by Meillassoux’s reading. His claim is to see in Mallarmé a true symbolist master, because he sees him as having engendered his own numerical corpus—i.e., a symbolic nature of numbers, from “placing” in the manner of a distribution (hidden in the seemingly arbitrary meter of the poem) the one number that cannot be another: 707.57 The entire analysis of Meillassoux revolves around determining the “identity” of this number—as the being of chance (l‘être du hasard) that consists in making itself infinite.58 Meillassoux’s thesis is that from this one number, the sum of all the words in the poem, Mallarmé has extracted the meter in which he wrote the poem—and that Meillassoux explicates as “the clue” he 56 See Jacques Rancière, Mallarmé: The Politics of the Siren, trans. Steven Corcoran (London: Continuum, 2011); original French version published in 1996. 57 The whole argument is summarized in the chapter entitled “Sommes” (Summations) in Meillassoux, Le nombre et la sirène, 47. 58 Significantly, in the subtitle of the German translation of Meillassoux’s book, déchiffrage is translated as Verrätselung, not as Entzifferung, as with the English translation (decipherment). In English, Verrätselung could perhaps best be expressed as “disciphering.” It strikingly makes Meillassoux’s point explicit: that Mallarmé’s oeuvre seeks to dissolve, rather than to represent or even resolve, the nature of the divine. See footnote 51.

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finds from the experience of what I have called the insistential intimacy “within” the poem’s proper interiority, by working through its material. The meter Meillassoux hence postulates is not, like the arbitrary structures of prose and free verse, fully contingent without any “generically necessary” motivation. Why? Because rooted within the necessities constitutive of a symbolic corpus is an entire algebraically constrained scope of articulate-ability.59 This scope of articulateability is capable of rooting, within his engendered numerical corpus, a metric of poetical structure under the strict governance of what counts how: it is a metric that is both open for some interpretative instantiation, but that also embodies as a certain transpersonal, not strictly willfully postulated, necessity. For Meillassoux, it is the being of chance. So let’s see how the meter that Meillassoux extracts from the sum of the poem’s words is not simply a representation of the meter Mallarmé has worked in, but truly a speculative extraction (inception); that is, the result of an algebraic-symbolic procedure. And let us see what is meant by this “numerical corpus.” Because his procedure is itself masterfully artistic, and it would be silly to summarize it here, it must be sufficient to indicate in inverse terms how Meillassoux proceeds: he looks for the summation of the numbers cast by the dice throw, based on Mallarmé’s line that says “Toute Pensée émet un Coup de Dés” (Every Thought engenders a Dice Throw). If the clue to the poem lies in identifying the number that could not be any other, so Meillassoux, then its “meaning” must be to achieve the inevitable engendering of this number (in German I would say, ins Werk setzen, tentatively translated as “to put into place and action”) a thought of such nature, and this in a manner such that it unfolds by necessity when being read within the oeuvre. Hence, the identity of this number that Meillassoux is looking for cannot be given as a representation, it must be “placed” operatively. As he puts it: “There is a trivial way, but by the same token accurate, of understanding this sentence. Instead of saying that this statement is about affirming, in a quite vague and rather mundane way, that every thought is a gamble, we can interpret it this way: every thought, insofar as it is formulated in a language, produces a series of random numbers related to language components necessary to formulate it. Our concluding sentence contains in fact, as any sentence, a certain number of letters, syllables, words, nouns, etc. These numbers are “engendered” by the thought 59 It needs to be pointed out again that Meillassoux himself is not speaking with reference to the mathematical theory of numerical corpus; interested as he is in dis-ciphering (see footnote 56) the notion of numbers, in order to dissolve what it renders present, he speaks of the identity of his number 707, of the particular being of this number (which he identifies as the incarnation of an altogether new notion of numbers, namely number-as-chance).

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that finds itself formulated in it​​, but they do not have in themselves any meaning—and particularly no meaning related to the thought at stake.” 60 In short, Meillassoux substantiates his hypothesis such that the final code consists of the ciphers 7 - 0 - 7, and he legitimates the entire argumentative path that leads him to this number by showing that —if written as 707—it is indeed the number that counts all the words in the poem. So if we explicate this procedure inversely, it strikingly resembles what any statistician does on an ordinary basis: he determines the “indexical magnitude” (often called random- or chance variable) of which the possibility space “consists.” All he needs for that is a code—e.g., the alphabetical code, or the Morse code, or any physically metrical measure expressed in digital code.61 The creativity of Meillassoux lies, among many other aspects, in looking out for what might count as such a code for “probabilizing” Mallarmé’s poem. More concretely, Meillassoux experiments with adjoining (metaphorical, nonmathematical) “domains of rationality” as such a code—for example, the musical scale of C major in order to determine which number is labeled by the expression car si (which returns in certain patterns throughout the poem). Such labeling numbers again indicates particular constellations that ask for further codes to decipher labels as pointers to the next steps in substantiating his hypothesis.62 For example, he ascribes a specific importance to the numbers 5 and 7, and links those to the stellar constellation of which Mallarmé says, in one line, that the final sum of the number-that-cannot-be-another is expressed in it. An excerpt of how he renders this plausible: “Yet we know […] the author of “The Throw of the Dice” took the stars in their pure dissemination for a celestial symbol of Chance. To cut by the gaze a constellation in this meaningless splendor is to perform an act totally analogous to the poetic act according to Mallarmé. For this poet is committed to making the 60 “Il y a une façon triviale, mais par là même précise, de comprendre cette phrase. Au lieu de dire qu’il s’agit dans cet énoncé d’affirmer, de façon assez vague et plutôt banale, que toute pensée est un pari, nous pouvons l’interpréter ainsi : toute pensée, dans la mesure où elle est fomulée dans un langage, produit une série de nombres aléatoires liés aux composantes de langage nécessaires pour la formuler. Notre phrase conclusive contient en effet, comme toute phrase, un certain nombre de lettres, de syllabes, de mots, de substantifs, etc. Ces nombres sont « engendrés » par la pensée qui s’y trouve formulée, mais ils n’ont par eux-mêmes aucun sens—et en particulier aucun sens lié à la pensée enjeu.” Meillassoux, Le nombre et la sirène, 32. 61 Those interested in the background of communicational coding theory, and the role of entropy measure and chance variables therein, are recommended to look at the classic paper for communication theory by Claude E. Shannon, “The Mathematical Theory of Communication” (1948), where he describes the two modes of coding that are still central today, in the distinction they have introduced, the so-called channel coding and source coding. 62 See Meillassoux, Le nombre et la sirène, 54–59.

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words sparkle, forged and disseminated by the randomness of language, by the use of a confusing syntax in which each term appears isolated by the ‘absence’ of all the others, as though decontextualized: allowing it to shine with a light we had never known it capable of.” 63 Although he does not mention it, Meillassoux is pondering one of the favorite themes in thinking about proportionality—the golden ratio. Two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to their maximum—this is exactly what Meillassoux’s reading will postulate (without stating it explicitly).64 The golden ratio has inspired people throughout many centuries precisely because it provides maximum stability for maximally different “components” within a strictly proportional framework. This is why Le Corbusier famously integrated the golden ratio into his architectural measuring system that he called “The Modulor,” and that he “rooted” in a certain partitioning scheme of the human body. However, unlike Le Corbusier, Meillassoux suggests rooting his “poetic modulor” not in the profane human body but in the numerical corpus of divine chance. As such, Meillassoux takes the noninitiated reader through a fabulous and awe-inspiring journey to how he ends up with the number 707, which—in the finale of this speculative trip through possible codes—turns out to be, and I am sorry for the prosaicness in putting it this way, the chance variable we know from ordinary statistics, the sum of all the counted words. The numberthat-cannot-be-another facilitates to carry out probabilistic analysis on Mallarmé’s text. Even in statistics, a random variable is not a variable strictly speaking, for it has no fixed value. In other words, it is not a magnitude of which we could ask metrical questions like how much? What it does is label a number that counts a magnitude that is unknown. As such, a chance number (I would prefer to call it an “indexical magnitude”) can incorporate a possibility space, and allow to experiment with it in probabilistic terms, by partitioning it into a set of events that can be combined in their interplay. Thus we can see how Meillassoux experiments with adjoining (metaphorical, nonmathematical) “domains of rationality” for his hypotheses. From the hypothetically postulated distributions, patterns, and regularities he seeks to extract a certain meter—and this means, in his case, nothing less than a proportionality of numerical infinity. 63 “Or nous savons […] que l’auteur du « Coup de dés » tenait les étoiles en leur dissémination pure comme un symbole céleste du Hasard. Découper par le regard une constellation dans cette splendeur dépourvue de sens, c’est accomplir un acte tout à fait analogue à l’acte poétique selon Mallarmé. Car ce poète s’attache à faire scintiller les mots, forgés et disséminés par le hasard de la langue, par l’usage d’une syntaxe déroutante en laquelle chaque vocable semble isolé par une « lacune » de tous les autres, comme décontextualisé: ce qui lui permet de rayonner d’une lumière qu’on ne lui avait jamais connut.” Ibid., 30. 64 In the second part of the book, entitled “Fixer l’infini,” pp. 61.

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We can put this aspired context of an agnostic-spirituality-turned-into-a-civic-religion to the side, and consider simply in terms of method how Meillassoux proceeds in order to determine the unknown indexical magnitude (chance variable). His procedure might best be called “hypothetico-inductive,” and because of its performed creativity, it can surely count as truly instructive for anyone working with statistical procedures. How Meillassoux proceeds is extremely interesting, which is only more impressive if we consider that on the formal level, it corresponds to ordinary standards in how probabilistic analysis works. Except that in scientific contexts, speculation and creativity in the determination of the chance variable is, of course, much less desired and appreciated. But there, as in the case of Meillassoux, the metrics (proportionality) “induced” can be tested “empirically” on the formal level (in the case of Meillassoux that of the poem), until a model is found that doesn’t leave any inconsistencies that could not be integrated meaningfully into that model. With this model, he then works hermeneutically to make sense of it, providing its legitimation on a numerical basis. This is how the role of the meter with which he works is not entirely arbitrary, but also not in any coercive way necessary. There might be other models of meter for measuring another chance variable on the basis of which one could carry out numerical analysis, and that would very likely be capable of “substantiating” very different overall readings. This does not weaken the brilliance of Meillassoux’s own reading, in my opinion. But it does introduce complications for the performative-lithurgic role he attaches to his reading. While I obviously do not share this programmatic stance, I very much share the interest in seeing a novel understanding of mastership, rooted in symbolization within domains of probability. Cosmo-politics, or putting to work a symbolist meter This novel understanding of mastership is rooted in a slight shift in perspective, which allows Meillassoux to look at Mallarmé’s poem in this way: he does not read the poem in terms of how it articulates the nature of chance directly, but in terms of how it articulates the nature of chance through articulating the nature of numbers. Rhetorically, this is how he can begin his book with a powerful statement like “Let’s get to the point directly” (page 9). The point he wants to get at directly is the nature of numbers. Yet, we must remember, according to Meillassoux this nature is engendered in the poem. So there can be no mentioning of “directness” in any strict sense. Directness—this is what we can pursue if we presume a nature of numbers, not if we attempt to evoke such nature in a poetically particular manner. The power of the opening of Meillassoux’s book is a rhetorical trick that envelops in a veiling manner all implications that point in this direction. For him, as he makes clear later on, Mallarmé’s act of articulating poetically the nature of numbers is an absolute and singular act—this is what moves him to see in the poet-author a figure

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no less eminent than that of Jesus Christ. The way he sees it, Mallarmé literally incorporates, in his oeuvre, the possibility of a new poetic meter to come. According to Meillassoux, Mallarmé is a figure as eminent as Christ because as the latter sacrifices his body, Mallarmé sacrifices the Corpus of his Oeuvre—the living “substance” of what makes him a master, by giving over the reception of it to the unlikeliness that is proper to anything that is governed by chance. This is how Meillassoux wants to read this engagement with the “indexical magnitude” of a “chance variable” within the Christian theme of transubstantiation. Within this Eucharist tradition, the sacrifice of Jesus Christ’s body was “necessary” to evoke the unity of a community to come—anyone who believes in the actuality and truth of this happening was welcome within the community, whose unity is grounded on no other inclusion/ exclusion criteria but the appreciation of this “act” and its particular theological interpretation. Reenacting it brought absolution and purification of the members from their sins, and from their distinctions among each other, and constitutes the “force” capable of strengthening the Holy Communion. Meillassoux reads Mallarmé’s act (of sacrificing the corpus of his oeuvre to the unlikely reception in the unlikely event that someone actually bears witness to his act, and proclaims its significance widely) in strict parallel to this tradition. He imagines also a people to come, to be united through reenacting the liturgy of Mallarmé’s poetic oeuvre as a means to strengthen such a coming sense of community. Such union Meillassoux imagines as a truly postmodern communion; that is, a people who complement a secularized politics with a poetic religion. The daring cultural-historical symmetry evoked thereby is that of modernity in the position of the Old Testament, and the problem of how to continue modernity (which is our problem today) in the position of the New Testament. In his poetically grounded cosmo-politics, Mallarmé is stigmatized by Meillassoux as the only one and true master who has managed to gain victory over chance (which reigns within science and thereby unsettles the very values that are foundational of modernity; e.g., individual identity, self-governing subjects, scientific progress through steady refinements in approaching the realization of an ideal and universal [all-inclusive] order, etc.). Meillassoux, in his reading, reveals his own communal identity as that of those who know how to bear testimony to Mallarmé’s symbolist and graceful gift to humanity—the act of his sacrifice. Cosmo-literacy, or the alphabetization of the nature of numbers If we relate this interpretation to its recent reception, it may on the one hand strike one as unbearably uncomfortable, to the degree that one feels tempted to call it silly. Yet on the other hand, one cannot help but admire the conclusiveness in actually working with the text material as it is there, in the verses of the poem and the reality of the contextual questions raised, and this makes it equally an irresistible

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attraction. Indeed, it has been a while since a voice in philosophy has dared articulate such claims on such speculative yet precise grounds! But then again, such intimacy of philosophical thought with what one might call religious energies is straightforwardly inevitable if one seeks to resist the submission of philosophy under the ultimate governance of scientifically declared legitimization—that is, to free it from all forms of inspiration and spirituality. What Meillassoux does, and what can be decoupled from his mission, I think, is to expose a notion of method that proceeds by scientific standards, yet hands it over to the field of aesthetics and art. From this perspective, and in order to appreciate the originality of Meillassoux’s reading, one does not have to follow him in the mission he attaches to it. Mallarmé’s poetic articulation of the nature of number, if we read it not as a poetic dedication in the form of a song of praise or an ode to this nature, but along with Meillassoux in a quantitatively symbolist manner, points the way to how we might consider symbolization as a means for learning how to articulate numbers and develop mastership in dealing with the indexically and symbolically given “magnitudes.” Such mastership is grounded in learning how chance variables can be counted, literally in the sense of ordered enumeration (discretizing and grammatizing), but also more comprehensively in the sense of governing. If we affirm that modernity has disenthralled us from all hopes in Aristotelian-minded symbolization, as the articulation of the voice of being,65 we might also affirm in Mallarmé’s poetic articulation of the nature of numbers a continuation in the spirit of Aristotle. Since Pythagoras, and especially since Plato’s Timeaus, the widespread idea about the nature of numbers is that the very “framework” of a cosmos that we can hope to understand by reason, consists in numbers. The numbers are the soul of the cosmos, which the Platonic Demiurge has mingled and mixed, cut into two to connect end to end, such that an inner circle comprehends all sensible becoming, while an outer circle comprehends all intelligible being. Numbers make up the auxiliary structure for a cosmo-logy, they are the necessary coefficients in any formal term. Numbers are what is capable of holding, literally, a logical cosmos in order—we come back to this in more detail in the following paragraphs. Suffice it to say that from such a perspective, Meillassoux’s reading of Mallarmé’s poem would suggest nothing less than that the nature of numbers at stake is one that can now be alphabetized. If the natural numbers are what is capable of holding, literally, a logical cosmos in a universal order, by deriving criteria for 65 Univocity is the crucial assumption in Aristotelian metaphysics. It demarcates where Aristotle departs from his teacher Plato, for whom the cosmic assumption (especially in the Timeaus) is a principle of analogy and proportionality. The book that Alain Badiou (as whose faithful disciple Meillassoux identifies himself) wrote on Gilles Deleuze, entitled The Clamour of Being, clearly itemizes these sentiments in a straightforward polemic (Minneapolis: University of Minnesota Press, 1999; originally in French in 1996).

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consistency from the assumption of primary “fullness” or “perfection,” the symbolic nature(s) of numbers need to find criteria for consistency by dealing with “primary abundance.” Dealing with primary abundance would mean that no order of consistency (logical order), no such and such “fullness,” can ever comprehend all that might, virtually, be possible. Is not this a reading whose relations to poetry feel almost banal? While ancient meter was capable of liberating logics from directly stating truth and thus made room for poetic articulation, which may count as divine because it is neither comprehensively necessary nor arbitrarily contingent, the meter engendered by Mallarmé (and any meter that can be engendered in the same manner) makes room for cosmo-literal articulations of ideas that might characterize a world to come. But, we might ask, does the assumption of such a quantitatively symbolist manner of poetic articulation not indeed confront us, as Meillassoux seems to hold, with a sheer impassability (in German, Ungangbarkeit)? To count as poetic (and not political) articulation, it would be essential for such a symbolist manner not to treat this nature that it articulates (that of number) violently. It must affirm this nature’s dignity—i.e., as inexhaustible by the reasoning of finite synthesis or speculation—while nevertheless setting out to articulate it as a means to communicate that which does not avail to appropriation by reason. In short, it must respect its “integrity” and “identity” neither on the transcendent grounds of sufficient reason, nor on the symbolist grounds of infinite speculation (as Meillassoux proposes), but on symbolic grounds of abundant reason masked by finite synthesis. Such respect would be the core aspect of a truth notion that is worthy to be called that of a critical rationalism. viiI Acquiring a body-to-think-in One of the arguably most influential documents of the history of Western Culture—Plato’s dialogue Timaeus—tells, in the form of a myth, the coming into being of the cosmos such that we can conceive of it logically. The cosmos turns into the subject of knowledge in Timeaus’s account, and he conceives of it as a symbolic body—the cosmic animal—whose corporeality he conceived, somewhat surprisingly perhaps, already 2,500 years ago as being constituted by numbers. In Plato’s cosmic animal, there is but one nature of numbers. Today, with universal algebra, we have as many natures of numbers as we can symbolize consistently into structures. We call them by the names of rings, fields (Zahlenkörper), modules, and the like. They work with matrices and “animate” relations—animate because vectors are lines that embody direction, they have a “motive force” or “cause” immanently to the relation they incorporate. We call algebraic structures universals, in the plural, and each of them has “oneof-a-kind” scopes of how their organization may be articulated. Much of our technics today is ordinarily dealing with such abstract structures. At

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the same time, philosophers and mathematicians are initiating veritable battles around how these structures are to be rooted and identified (the so-called Foundational Crisis, and more recently, the struggle between set theory and category theory for primacy in settling, as in the former, or overcoming, for the latter, the issue of foundations). Let me perhaps indicate initially where I intend to lead this line of thought. What I would like to consider is viewing what we readily call “a symbolic corpus” outside the confines of representational speculation, reflection, and mimesis, and instead in terms of indexical speculation, reflection, and mimesis. Such an indexical turn would entail relating to the symbolical corpora of mathematics not as we relate to a constellational order of the heavens, but as we relate to our bodies. Our bodies, too, do not fully avail to reason, and they constrain our sensual and motor capacities. Might not the notion of “a body” be a better word than the notion of “a house” for picturing what the philosophical tradition has strived to conceive as the architectonics of reason? A body-to-think-in, with proper constraints of intellectually sensual (intuitive) and intellectually motor (literate) capacities? Is it possible that we are so much accustomed to an understanding of numbers as giving us the one and only framework within which things can be rationalized and appear consistent, that the assumption of treating them as bodies-to-think-in sounds too frighteningly strange? Even if one might feel spontaneously compelled to agree, the question that motivates such a daring shift in perspective has been up and on the table for more than a century: How might we come to terms with universal algebra, its symbolic corporeality by probabilistic methods, and the generic instances that are articulated out of it? The most common representation of the nature of numbers … To put it in words we all remember from our school days: we take the positive integers as the proper class of natural numbers; 66 we know we can symmetrically mirror them to negativity—for the sake of speculative analysis; and we remember that the boundedness among the integers can be “spelled out” into ratios (the rational numbers)—if only we put the integers into mutual relations. Of course we also don’t forget the irrationals, those numbers that yield an indefinite value when they are put into a “ratio.” Despite their name, they are not too troubling anymore. There are sophisticated limiting and bounding processes with logarithms and series such that the counting in of irrationality seems like a reasonable and respectful tribute to be paid to the vastness of real numerical nature. An illustrative picture for this concatenated and comprehensive nature of 66 Starting from two. Even within a nature of numbers so conceived, the integration of the zero for nothing and the one for entity remains a crucial obstacle for any exhaustively explanatory consensus.

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numbers is the continuous number line. With its totality, including rationals and irrationals alike, we associate today the domain of real numbers. To put it straightforwardly: the real numbers contain all that can possibly be marked out by reason, as rational or irrational, and hence understood about numbers’ nature. … and how it got into trouble still not resolved today This was still the firm belief of one of the founding fathers of a logical calculus, Gottlob Frege (1848–1925), when he assumed—not unlike a prosaic double of Plato—the existence of a transcendent realm where the class of natural numbers rests as “objects,” eternally and ideally, and given directly to human reason without requiring mediation through the senses.67 With his text The Foundations of Arithmetics: A Logico-Mathematical Enquiry Into the Concept of Number (1884), we have another strong story about the nature of numbers by one of Mallarmé’s (1842–98) own contemporaries. While Mallarmé (according to our discussion above) has taken the Platonic numerical ideality and turned it into a probabilistic one, Frege took it and turned it into a logical one. Only three years after Frege, Edmund Husserl also wrote a treaty entitled The Concept of Number (1887). He published his own book entitled Philosophy of Arithmetics (1891) only four years later. While Frege meant to engage strictly logical issues in such elementary consideration with the intent to purify reasoning, at least ideally, Husserl instead meant to complement logical issues with psychological issues—which he hoped to be capable of treating with equal rigor as is possible for logical issues. I cannot go into this theme in much breadth here, but let me briefly recapitulate the larger context and how it relates to our two conceptual persona, the generic and the master, and the possibility to see, in what they open up in their interplay, the birth of bodies-to-think-in that are collective before they can be acquired individually, and whose nature is engendered together with the symbolic corpus of numbers according to which they are organized. First, let us take this background as an indication that indeed something larger than a poet’s personal resignation vis-à-vis the rise of free verse must have been at stake in the nineteenth century. This seems all the more justified if we remember that the mathematician George Boole (1815–64), whom I have already mentioned earlier for having been accused of proceeding in a strikingly similar manner as Meillassoux does in his reading of Mallarmé—namely of “bringing forward definite solutions from treating 67 For him, the explanation why humans have been capable of “inventing” mathematics as the core power of reason, is that these idealized natural numbers are “reason’s nearest kin.” “Frege’s central claim in the Grundlagen was that in arithmetics we are not concerned with objects which we come to know as something alien from without through the medium of the senses,” writes Michael D. Potter, “but with objects given directly to our reason and, as its nearest kin, utterly transparent to it.” Reason’s Nearest Kin: Philosophies of Arithmetics from Kant to Carnap (Oxford: Oxford University Press, 1996), 79.

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indefinite problems symbolically” 68—preceded all of these investigations on the nature of numbers by a few decades. His main work was entitled in all due provocation, An Investigation of the Laws of Thought on Which Are Founded the Mathematical Theories of Logic and Probabilities (1854). To view Mallarmé in this context adds a lot of plausibility to Meillassoux’s shift in perspective, namely that the poem is not directly about the nature of chance, but about that of numbers. But not only this. It also tells us something important about our context and interest in computability, design, and the generic today—it allows us to see the force of what Rancière calls dissensus at work in all that can be computed. Let’s recapitulate again: dissensus is “not a conflict of interests, opinions, or values” but “a division put in the ‘common sense’: a dispute about what is given, about the frame within which we see something as given.” 69 While on the level of generic instances, those one-of-a-kind particulars that can be instantiated and modulated within the framework of a master model, we might only negotiate “conflicts of interests, opinions, or values”; what is at stake with a criticality on the level of the master models is indeed dissensus as “a division put in the ‘common sense’: a dispute about what is given, about the frame within which we see something as given.” This is why we ought to treat the instances of generic computing as pre-specific rather than as typical (which would be to view them as generic in an adjectival, not in an adverbial, sense), and the respective master models as what they are: models that owe everything to mastership, and not to some generic “nature.” But let’s look more closely at how this background in number theory relates to computation. Algebraic operations, or how the nature of numbers can be brought to work As sketched above, the understanding of the nature of numbers has indeed been bracketed and marked as “something to be put in question” throughout the nineteenth century. Yet this was not a result of pure intellectual curiosity and ideological speculation, but of the facticity of technical eminence: The taming of electricity equally rests upon calculating with a domain of numbers that does not fit within the continuity (represented as the real number line) within which all that can be called natural about numbers ought to be accommodated. Calculations that regarded waves and currents had to be rooted in a numerical domain that is organized by a peculiar unit, of which it is indeterminate what magnitude (which physical quantity) it allows to measure. Descartes had suggested calling this unit “imaginary,” only to discard it as irrelevant and purely speculative—the imaginary unit is that of the square root of minus one. The “impossibility” it manifests is obvious: surely everyone remembers from somewhere that arithmetically, 68 See in this article page 176. 69 Rancière, “Who Is the Subject of the Rights of Man?,” 304.

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the multiplication of a negative number with itself must yield a positive result. Hence, it ought be categorically impossible, or at least sophistically meaningless—i.e., without any real consequences—to extract a root from a negative quantity. And yet, it does yield consequences, and not only that, it yields consequences in a reliable and modular manner: as Israel Kleiner accounts, in his book A History of Abstract Algebra, mathematicians have “given meaning to the ‘meaningless’ by thinking the ‘unthinkable,’ namely that square roots of negative numbers could be manipulated in a meaningful way to yield significant results.” 70 All electronic technics including information technology and quantum mechanics, rests on the application of this particular numerical domain—whose magnitudinal referent is symbolically determinable, while remaining physically (and philosophically) “unthinkable,” “meaningless.” To put it more simply, it remains unclear of what such a “how much” can be determined. The imaginary unit allows measuring whatever is indexed within the systematicity of a symbolism, and this makes it so peculiarly “unnatural.” Unnatural, that is, unless one were to assume a nature of such a symbolism whose magnitude is only indexically given. And this is exactly what was at stake throughout the nineteenth century as the development of abstract algebra prospered more and more. The disputes indeed centered around whether we ought to assume different natures of numbers— a variety of different numerical genera—and if yes, how many. The nature of number might not be one: Alfred North Whitehead attempted to gather all these developments in a first systematic study under the troubling caption of Universal Algebra in 1899. It was a work that cleared the view on these developments and stated as straightforwardly as it was groundbreaking: 71 the problem at stake is the relation between mathematics and logics. To be clear on what we are talking about—why was this groundbreaking? While logics promises to give adequate classification of the nature of things (or in the modern paradigm: the determination of objectivity), such adequacy has rested for Plato (as well as again later, for the moderns) on the assumption of finitude on the empirical side of science. If we start out from things as they are manifest corporeally, in terms of magnitudes that can be measured, we can depart from very basic (and through that very secure) assumptions, and reach gradually more and more abstract heights through speculative generalizations. Such is the trust in scientific method by the moderns in a kind of science that lets itself be guided by the logics of finitude, as opposed to spiritual doctrines that all involve infinity. It rests on the assumption that the nature 70 Israel Kleiner, A History of Abstract Algebra (Basel: Birkhäuser, 2007, 8). 71 It is clear that Frege’s suggestion regarding the transcendent one nature of numbers, as well as that of Husserl regarding a psychologically differentiated one nature of numbers, both aspire to ward off what Whitehead faced boldly—the universality of algebra (not of arithmetics), and with that, the nature of numbers as subject to categorial determinability.

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of number is one and that number is universal. From this nature, hence, it ought to be possible that one can extract universal principles that are capable of treating all things equally, and therefore justly. Such universality was seen by Frege and Husserl, and many others at the time (and still today), in arithmetics. The suggestion of Boole, on the other hand, was to ascribe the status of universality to algebra instead of arithmetics. This opens up the notion of the universal to infinitary modes of its determination. Algebra has been understood, always, as the art of determining unknown quantities through procedures of articulating the proportionate terms that in their interplay make up a formula; with the elevation of its status beyond its merely representational character (what Meillassoux calls “the correlational” 72), the meaning of “unknown” opens up the modern tradition of keeping the scientific and the artistic, in its entanglement with some sort of spirituality, strictly apart. It releases instead a nature of the technical—the means for artifice—in an unbounded condition between mastership and schematic repetition, in which all questions of legitimacy are once again unsettled. The consequences of affirming the infinitary methods are such that we can no longer maintain in an unproblematic manner that universality— that which is to be regarded as the property of all things—accommodates naturally the categories we apply, even in the natural sciences, as they too, meanwhile, fall within the domain of technology. Affirming to work with infinitary methods entails dealing with an inverse situation: the cate­ gories we apply, in science as elsewhere, determine what can be treated as universal. In all radicality, this amounts to saying that universality appears as a kind of wealth, it means that the universal can prosper or decay. It means that there is an economical play constitutive for what counts as universal; it means that that which can be the property of all things can be more or less prosperous and that this prosperity depends upon the capacities of intellectuality.73 This might seem a little like sophistry, admittedly so. And indeed, this criticism has accompanied the disputes around the nature of number from early on. Rafael Bombelli, who contributed much to the development of a calculus of this peculiarly imaginary numerical domain (constituted by the imaginary unit), wrote already in the sixteenth century that the development of such a calculus “was a wild thought in the judgment of many; and I too was for a long time of the same opinion. The whole matter seemed to rest on sophistry rather than on truth. Yet I sought so long until I actually proved this to be the case.” 74 The calculus he developed worked with articulated formulations of the One according to rules such 72 See Meillassoux, After Finitude. 73 cf. Michel Serres, “Verrat: die Thanatokratie” in Hermes III, Übersetzung (Berlin: Merve, 1992 [1974]). 74 Quoted in Kleiner, A History of Abstract Algebra, 8.

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as (+√−1)(+√−1) = −1 and (+√−1)(−√−1) = 1. These rules allow to define, mathematically, addition and multiplication; yet these definitions do not apply to all numbers in general, but only to numbers that are members of numerical domains that form corpora, and which are specified according to their immanent partitionability and organization. This is the level of abstraction proper to algebraic number theory and all mathematics and logics that work algebraically; today this entails nearly all of applied mathematics. The philosophical problems entailed thereby had been systematically put into its proper relations by Alfred North Whitehead in the abovementioned book Universal Algebra.75 Let me add, perhaps, that the relevance for keeping track of developments on such an abstract level, which urges us to assume a symbolically (not naturally) determinate “nature” of numbers is crucial for developing an understanding of what we are actually doing when we work with universal code in computation. Anything that we regard on the level of its electric materiality must count as a manifestation of such symbolically engendered nature.76 Its nature can be determined based on probabilistic measurements—measurements that we carry out today, usually without much consideration, in terms of information. It is before this background that Michel Serres urged intellectuals across all disciplines, in his lecture from 2007, to engage with the fact that the storage, treating (processing), emission, and reception of information is the “quadruple characteristic in common between all the objects of the world, living or inert.” 77 Ix Masterpieces, and Why There Are so Few of Them So we can see how much this peculiar procedure that Meillassoux “detected” in Mallarmé’s poem is indeed a procedure that is affine to what preoccupied anyone who followed the development and the rise of universal algebra. Mallarmé, with his desire to link abstraction directly to poetic texture, and his poetic interest in ex-citing through words rather than describing with words (which became famous as the mark of symbolism in art) certainly was following all of this. It seems more than likely that with his fascination for “absolute truth” he attempted to draw the consequences from what he saw happening to the idea of the universal. 75 A book that he wrote before he set out, together with Bertrand Russell, to once and for all clarify the troubles in their seminal work Principia Mathematica (1910–13). Whitehead’s subsequent turn away, after the acknowledged failure of the approach proposed in Principia, from analytical philosophy and toward a new kind of metaphysics in Process and Reality (1929), must surely be understood in terms of his awareness of the profundity of the problems involved. 76 I think it is hardly an exaggeration to say that this lies at the heart of the new attention philosophy started to attribute to a primacy of difference beneath all possible notions of identity, from Kirkegaard and Hegel via Nietzsche to Heidegger, Derrida, Deleuze, and Lacan. 77 Serres, “Revisiting The Natural Contract.”

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He hoped to be able to continue the cultural legacy he was ambitious to contribute to, poetic verse and the dignity it had always been attributed, by reconsidering, poetically, all these issues around the nature(s) of numbers, the nature(s) of counting, and the modalities of mastership in relation to both. Meillassoux’s reading is original in the way he found to quantitatively engage with the symbolist tradition in poetry. It stresses the interest in attending to the powers of symbolization in terms that are not strictly “linguistic,” thereby reducing reality to language and relations of reference and interpretation. Instead, he draws our attention to terms in algebra that are best called “formulaic.” What it stresses is not only the “nature of numbers” as problematic, as something that needs reconception, but also the “nature of formulas.” It is in this vein that another document from the early twentieth century is important to consider: Gertrude Stein’s 1936 lecture, “What Are Masterpieces and Why Are There So Few of Them.” In an inverse manner to what we have discussed so far, she does not so much attend to clarifying the “belonging” or “authorization” of the voice with which the figure of the master articulates her evocations. Instead she draws attention to the articulated evocations themselves. Stein insists on the reality of masterpieces, in all their problematics. For her, a masterpiece bears testimony to the fact of acts of engendering. She sees them motivated out of a principle unsettledness of any identity issue, the identity of the master as well as the identity of the subject matter a master masters. “It is not extremely difficult not to have identity,” she says, “but it is extremely difficult the knowing not having identity. One might say it is impossible but that it is not impossible is proved by the existence of masterpieces which are just that. They are knowing that there is no identity and producing while identity is not. That is what a masterpiece is.” 78 Like Stein, I want to hold onto the idea that articulations of things entirely in their own terms is neither absurd nor a formal and logical impossi­ bility, although it certainly seems a paradoxically tautological idea. Yet this is one of the core interests behind the interest in a literacy that arises out of such an algebraic, formulaic, and apparently tautological notion of identity, a literacy that cultivates the indefinite articulate-ability of the One (identity). If we affirm infinitary methods in computation, while subjecting them to the principle of universality of finite synthesis on the probabilistic grounds of abundant reason, the terms that express an identity are not nominal terms, but polynominal terms. And polynomial terms, unlike nominal terms, are capable of settling their clauses in amphibolic multiplicitous structures. Every polynomial term involves variable values and constant values, of which the latter can be “spelled” by attaching them to constellations of coefficients that can be designated 78 Gertrude Stein, “What Are Masterpieces and Why Are There So Few of Them?” (Los Angeles: Conference Press, 1940), http://gaslight.mtroyal.ca/masterpieces.htm.

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and balanced. In other words, they share in to a quantity that is yet to be determined. Polynomials so conceived name terms whose literalness needs to be charac­terized. They are quantitative, yet the quantity they comprehend is not a fixed value, but a genuinely relational value. They comprehend ever so much as the term is rendered capable of bounding within the constellation of amphibolic multiplicities that makes up the system of formulas in which polynomial terms feature. Properly speaking, the determinability of this ever so much is adjoined to the terms. It is in this manner that we can speak of articulating a thing entirely in its own terms. In qualitative terms, however, such articulation of course depends upon how developed and differentiated the literacy and mastership is of the person who articulates.

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VII ‘On the Baroque Line: the MindBody Problem’ and the Art of Cryptography Gregg Lambert

Gregg Lambert is Dean’s Professor of Humanities at the College of Arts and Sciences, Syracuse University, New York. Between 2008-2014, he was the founding director of the Syracuse University Humanities Center and is currently the Director of the Central New York Humanities Corridor, established by the Andrew W. Mellon Foundation. He is the author of numerous books on continental philosophy and criticism, most recently Return Statements: The Return of Religion in Contemporary Philosophy (Edinburgh University Press, 2016), Philosophy After Friendship: Gilles Deleuze’s Conceptual Personae (University of Minnesota Press, 2016), and In Search of a New Image of Thought: Gilles Deleuze and Philosophical Expressionism, also published by the University of Minnesota Press.

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Ecrire et dessiner sont identiques en leur fond—Paul Klee1   [↗ P. 214]

In The Fold (1984), the French philosopher Gilles Deleuze presents a new materialist method, partly derived from the philosophy of Leibniz, for addressing the formal difference between matter and expression. This method is defined in part as a species of “cryptography,” that is to say, “an art that can at once account for nature and decipher the soul.” It is around the notion of the cryptographic sign that we can dis­cover the allegorical significance of Baroque architecture for Deleuze, which takes the crypt as its foundation and prima principia of construction and gives a different notation to the function of ‘On the Baroque Line: the Mind-Body Problem’ and the Art of Cryptography

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a ‘key,’ or cipher. In other words, Deleuze approaches the historical concept of ‘the Baroque’ in the same way that he might approach a problem in architecture; that is, as one where the formal possibilities of the design are inseparable from the possibilities (and ‘incompossibilities’) enfolded within each material component. Accordingly, the problem of design issues from the existence of two distinct kinds of infinities that make up the universe, which Deleuze describes as two heterogeneous and irreducible types of folds that run through the Baroque construction. In turn, this problem is further complicated by the presence of a third term that exhibits a tendency to “fold between these two folds” (“entre 1

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Paul Klee, Pedagogical Sketchbook, (NewYork: Praeger Publishers 1963).

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les plis et les replies”), a tendency that Deleuze identifies with the Leibnizian concept of the monad. What occurs under the term ‘Baroque,’ therefore, no longer refers in its essence to a historical and epochal concept, but rather to a process (operatio): to something that expresses this proclivity to fold and unfold, or that “endlessly creates folds.” Obviously, the highest, if not the final, aim of philosophy is absolute knowledge. Yet, this meant something very different in its Platonic, Epicurean, and its Hegelian ages. After Descartes, at least, a certain tradition of contemporary philosophy has understood ‘absolute knowledge’ as the subject of ‘representation’ (Vorstellung), although this only fulfills and exacerbates a certain Platonism and perverts the very sense of knowledge by misrepresenting its essence as adequatio (truth as certitude, rectification with ‘a state of things or affairs’). In taking up the critique of Western philosophy after Descartes, Deleuze is not that removed from Derrida, although each expresses the critique of representation in radically different terms. For Deleuze, any critique of negativity (for example, ‘deconstruction’) still approaches the question of knowledge from an extrinsic and, therefore, representational perspective. Instead, absolute knowledge—if it is to become adequate as a knowledge of the process of creation—must be understood from a crea­tor’s point of view. (This marks the strange alliance between Leibniz and Nietzsche.) According to this view, the final goal of knowledge is the discernment of the principle by which ‘life’ is implicated with matter; knowledge is the discernment of the method by which the soul is folded with an animal’s body. Thus, the fields of embryology and cryptography may

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offer a better image of the Leibnizian philosopher’s logos than mathematics. Moreover, this principle of discernment has a practical and ethical outcome as well, since all knowledge must have a practical application in that it guides us in discerning the best principles for determining ‘how one can live.’ In The Fold (1984), this method is presented as ‘cryptography.’ Deleuze writes: “A ‘cryptographer’ is needed, that is, someone who can at once account for nature and decipher the soul, who can peer into the crannies of matter and read into the folds of the soul.” 2 Here we might discover the allegorical significance of Baroque architecture for Deleuze, which takes the crypt as its foundation and prima principia of construction and gives a different notation to the function of a ‘key,’ which I will address below. Deleuze presents the concept of ‘the Baroque’ in the same way that he might present a problem in architecture; that is, where the formal possibilities of the design are inseparable from the possibilities (and ‘incompossibilities’) enfolded within each material component. Specifically, the problem of design issues from the existence of two distinct kinds of infinities that make up the universe, which Deleuze describes as two heterogeneous and irreducible types of folds (“entre les plis et les replies”) that run through the Baroque construction. In turn, this problem is further complicated by the presence of a third term, which exhibits a tendency to ‘fold between these two folds,’ a tendency that Deleuze identifies with the Leibnizian concept of the monad. What occurs under the term ‘Baroque,’ therefore, no longer refers in its essence to a historical and epochal concept, but rather to a process (operatio): to something that expresses this proclivity to fold and unfold, or to ‘endlessly create folds.’ In so far as cryptography is ‘the art of inventing the key to an enclosed thing,’ Deleuze refers to the Baroque line as both the problem of what is called a ‘crypt,’ as well as to the proliferation of its random combinations that are like the twisted coils of matter surrounding the living beings that are caught in blocks of matter. However, if the crypt holds the key to deciphering both Leibniz and the Baroque, it cannot be understood as a content, or essence, but rather as a dynamic instability produced by the scission that runs between mind and body, “a scission that causes each of the two split terms to be set off anew.” 3 This entails a notion of the fold that runs between the mind and the body that can no longer be figured in terms of opposition and, thus, is much more complex than that of Descartes. As Deleuze argues, Descartes was unable to reconcile the body and the soul because he was unaware of the body’s own inclination and “tried to find content’s secret running along straight lines 2 3

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Gilles Deleuze, The Fold: Leibniz and the Baroque (Minneapolis: University of Minnesota Press, 1993), 3. Gilles Deleuze, Le Pli: Leibniz et le baroque (Paris: les Editions de Minuit, 1988), 5.

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and liberty’s secret in the uprightness of the soul.” 4 Deleuze locates the principle of this scission in the monad itself, and the problem of architecture refers to complete construction of the concept from its initial premise, with ‘no doors or windows.’ This unfolds the autonomy of ‘an interior without exterior,’ which can no longer be figured as the result of a simple opposition, but as the distinct product of the two infinities that run through the living being and that separate the absolute interiority of the monad from the infinite exteriority of matter. (This division also results in the creation of the two facades of Leibniz’ philosophical system, which comprise, independently of one another, the metaphysical principle of life and the physical law of phenomena.) In other words, this forms a ‘distinction in kind,’ following Bergson’s phrasing of the distinction between matter and memory, a distinction that figures prominently in Deleuze’s reading of Leibniz. And it is by means of this distinction that Deleuze locates in both Leibniz and ‘the Baroque’ a nearly schizophrenic tension between open facade and closed chamber; specifically, the absolute scission caused by the incommensurability and incommunicability of two kinds of folds that require, in order ‘to trace the thread through the labyrinth,’ a more distinctive order of procedure (or operatio) than has been represented either by mathematical clarity, or by the distinctness of the object as it appears to the senses. On the conceptual plane shared between philosophy and mathematics, this solution will require a new division of labor than the one, still present in Kant (at least, the Kant of The Critique of Pure Reason), which relegates to philosophy the use of concepts and their regulation through a process of jurisprudence, even though reason draws the construction of concepts from mathematical knowledge.5 Although the concept of the fold in some ways resembles the problem of inflection in mathe­matics, it cannot be reduced to a mathematical problem, since it concerns many other fields as well, including biology, economy, language, and the arts (hence, Deleuze’s kinship with the problem faced by Leibniz concerning the new ground of philosophical concepts, the ground of 4 Deleuze, Le Pli, 5. According to the French sociologist Gabriel Tarde, opposition should not to be conceived as a maximum of difference; rather, it is a very singular species of repetition in which two doubles enter into the destruction of each other by virtue of their very resemblance. See, Gabriele Tarde, Les Lois Sociales : Esquisse d’une Sociologie, 8th ed. (Paris: Libraire Felix Arcan, 1921), 70. Deleuze describes Tarde, from as early as Difference and Repetition, as “next to Leibniz, one of the last great philosophers of Nature.” In fact, it is Deleuze’s early reading of Tarde’s ‘Microsociology’ that prepares for the evaluation of Foucault’s later works. With regard to the question of opposition above, I cite a footnote on Tarde from Difference and Repetition: “Opposition, far from autonomous, far from being a maximum of difference, is a repetition minima in relation to difference itself.” Gilles Deleuze, Difference and Repetition (London: The Athlone Press, 1994), 264. 5 See Kant’s statement in the ‘Transcendental Doctrine of Method,’ in Critique of Pure Reason, chapter one, section one. Also see Heidegger’s explication in ‘Leibniz’ Doctrine of Judgment,’ The Metaphysical Foundations of Logic, trans. Michael Heim (Bloomington: University of Indiana, 1984), 78.

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‘non-philosophy’).6 As a result of this diversity in relation to the genesis of ideas, Deleuze claims an “entirely new regime of light” 7 is needed, that is, a philosophical constructivism that is drawn from the possibility of its own art of creating concepts, using whatever light that can be fabricated without reference to any objective facade, or the profile of a contour.8 Here, the notion of the problem that Deleuze employs in order to read this central proposition of Leibniz also finds an analogy to a problem of contemporary music in its search for new harmonies by means of an extended range of dissonance. It was Leibniz, according to Deleuze, who “makes Harmony a basic concept” of philosophy.9 We might immediately add, however, that harmony can only be understood as a solution to the problem of multiplicity, or in Leibnizian fashion, the problem of multiple and potentially ‘incompossible worlds.’ The thematic of dissonance is treated in The Fold as indicating the horizons of incompatible worlds encrypted within the monad; thus, Deleuze imports its concept from the domain of musicology in order to account for the use of the crypt within a Baroque architecture and to decipher the problem introduced by the Leibnizian notion of ‘incompossibility.’ There is a cryptic dissonance within the monad, caused by the horizons of ‘incompossible worlds,’ which could allow Deleuze to problematize the notion of harmony within a Leibnizian construction that is founded on the propositional identity. Instead, Deleuze employs a more modern conception of harmony that is present in certain modern writers, “like one finds with Joyce, or even with Maurice Leblanc, Borges or Gombrowicz,” 10 in which several divergent series, or incompossibilities, can be traced within the same virtual ‘chaosmos,’ rather than excluded to entirely different worlds. As a result, the Leibnizian notion of a central harmony (or principle of sufficient reason) undergoes a fundamental change that is best exemplified in the domain of modern literature: instead of the subject as the identity of the proposition, we have the subject as an envelope of the ‘Finnegan’ (Joyce) or ‘Fang’ (Borges) type. In place of the predicate as attribute, we have the event: to wake, to attend one’s own funeral, to mourn and be mourned, to shed a river of tears, to sing a lullaby, ‘to have a secret,’ or ‘to kill or not to kill the stranger.’ This will become an important consideration when we later analyze the role 6

This diversity forms a constant preoccupation through all of Deleuze’s work and can be traced to his early description of the role of ideas within phenomena in Difference and Repetition (figured under the notation of ‘an object=x’ which is drawn from several diverse fields: biology, economy, literature), as well as in Foucault, which takes as its central project a cartography of the different historical (or epochal) formations of the couple savior/pouvoir. 7 Deleuze, Le Pli, 44. 8 Leibniz, Philosophical Papers and Letters, v. 2 (Boston: Reidel Publishing Co., 1969), 433. 9 Gilles Deleuze, Negotiations (New York: Columbia University Press, 1995), 163. 10 Deleuze, Le Pli, 111.

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that Leibniz assigns to the concept of God within an absolute order of inclusion (or compossibility). According to both notations of the problem outlined above, the Leibnizian proposition of ‘no doors or windows’ functions as a central contradiction in a philosophical system whose newly invented task will no longer be the suppression of the dissonance it produces (as, for example, happens in Aristotle, who reduces it to a species of contradiction, or Hegel to the negative), but rather the multiplication of its principle. According to Deleuze, this proposition will also function as a ‘wild card’ that Leibniz draws from his sleeve in order to effect a complete change in the rules of the game. This is what Deleuze refers to as the Leibnizian revolution, which is the transformation of the concept of Right into a universal jurisprudence, whereby principles are given a reflective usage, and the philosopher will have to invent the principle that rules a given case.11 This accords to the philosopher a new distinction, never known before Leibniz, from which he derives his concepts by a method of inventio rather than adequatio. It is at this point that one understands the importance of this transformation for the new role of philosophy defined as ‘the artful creation of concepts’; after Leibniz, the philosopher must invent the ‘best conditions’ to justify any presentation of truth. Since principles are no longer given, nor do they fall ready-made from the sky; they must be created, which is to say they must be fashioned by hand. Returning to our discussion of the Baroque Leibniz, in response to the question, ‘What are crypts for?’ (moreover, against the usual notion that crypts are used for hiding, for repression, or exclusion), Deleuze refers to the crypt to designate a special type of reading that takes place within the monad. The crypt designates both the place of reading in the monad (the reading room sealed up in light, or the book) and an operatio, that is, the ‘act’ of reading itself (the art of cryptography). In short, it is at once crypt and cipher, secret passage and ‘the shortest path through the labyrinth.’ This movement creates what poet Yves Bonnefoy once described as the integral ‘movement of interiority’ within the Baroque, and signals a point of light that is both infinitely divided shadow and light rising up from an obscure background within the monad itself, a light defined by its damp luminosity, like the glow of large animal hides or the skins that drape the walls of the crypt and provide whatever light there is for reading. At the same time, we should recall that the crypt accounts for the creation of the concept in Leibniz’ philosophy as an extreme movement of scission by which he encrypts all perception, that is, the force engendering the subject of perception along with the unity of the perceived, within the monad in order to follow its principle ‘fold after fold, fold upon fold.’ According 11 Ibid., 91.

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to Leibniz, because they are finite, all monads must unfold their own predicates according to a prior order laid down by God’s point of view (Augenblick). However, Deleuze often employs the poetic statement ‘fold upon fold, fold after fold’ to show what happens when the vertical series of folds stacked on top of one another, representing the scholastic conception of God (Scientia Dei), fall back upon (“se rabat sur”) the horizontal series formed by the monads—like “a dance of particles folding back on themselves”.12 By constructing the relation between these two series via the concept of the fold, Deleuze improves upon the Leibnizian construction by effectively creating a ‘diagonal line’ in order to avoid the vertical line of transcendence. (In short, Deleuze renovates ‘la maison baroque’ in order to make it follow more modern principles, even tastes, which would include the rejection of the transcendent as a dominant factor.) As for the vertical line, it is curved to echo the ‘the pleats of matter.’ Thus, what Deleuze refers to as a ‘cryptography,’ and Leibniz simply as ‘the act of Reading,’ is a new method invented to discern the process by which life is enfolded/unfolded within the body of the monad, thus forming an analogy to the tensions that make up the scission between exterior and interior, between perception in matter and reading in the soul. As an aside, Deleuze gives the relevance of this method of ‘reading’ for our contemporary situation in Negotiations, where he says the following: “The move toward replacing the system of a window and a world outside with one of a computer screen in a closed room is taking place in our social life: we read the world more than we see it.” 13 Figure 1: diagram of the interior and exterior.

In order to better comprehend what Leibniz understands by an ‘act of reading in the monad,’ and Deleuze by ‘cryptography,’ it will be necessary to follow the various diagrams that Deleuze develops to theorize 12 Deleuze, Negotiations, 157. 13 Ibid., 157-158.

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the Baroque construction of the conceptual reading-seeing pair. The first diagram offered by Deleuze, ‘la maison baroque’ (an allegory of the monad), presents us with a building comprised of two levels: “above, a closed private room, draped with cloth ‘diversified by folds’ lit from below, where we find a common room that receives light ‘from a few small openings’ that designate the five senses”.14 Figure 2: ‘The Baroque House (allegory)’.

The problem of the upper room, in which all luminosity has been sealed in, can be posed in terms of the classical relation between natural perception and the source of light, to which Plato responded with his doctrine of the Ideas. Here, there is no such continuity and the direction has been reversed. It is no longer a matter of forming a continuity between perception and the ideational, since there is no relation between the two; neither is it a question of light raised to the level of the idea, nor of the idea descending to a level of a common perception, or doxa.15 Consequently, there is no mere difference in degree between the two lights, nor even an opposition, but rather “a whole new regime of light.” As Deleuze recounts, the second figure (or diagram) created to explore the interiors of the Baroque is the chambre obscure, which functions like the small chamber in the apparatus of a camera, and is linked in the 14 Deleuze, Le Pli, 7. 15 This is the metaphor of light that Derrida postulates both in ‘The White Mythology’ and in ‘The Double Session,’ where the act of reading in philosophy constitutes itself by a catachresis in order to establish itself as a higher order of perception. This allows for the eye to be usurped by the ‘point of light’ placed at the level of the idea in Platonic philosophy, which causes the series formed by perception, echoing the position of a ‘common sense,’ to defer to a latent series traced by the conceptual path of the philosopher who represents an anamnesis of the Idea. Hence, Derrida shows that the movement of logo-centrism is inseparable from the establishment of a ‘vulgar series’ in the social field, which entails both the production of clichés as well as the social and conceptual personages to embody them. See Jacque Derrida, ‘The White Mythology,’ Margins of Philosophy, trans. Alan Bass (Chicago: University of Chicago Press, 1982), 207-273; ‘The Double Session,’ Disseminations, trans. Barbara Johnson (Chicago: University of Chicago Press, 1981), 173-227.

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process of photography to the dark room where an image is developed.16 At first, the dark room has only a small, high opening through which light enters, passing through two mirrors, the second of which is tilted to follow the page upon which light will project the unseen objects that are to be drawn. And yet, as Deleuze argues, this schema will not prove adequate for an explication of the Baroque line, which, first of all, necessitates the separation of the line of light from an optical diagram. Leibniz, according to Deleuze, is the first to liberate the fold as a pure formal element: “a fold that unfolds all the way to infinity”.17 Perception is grasped from a point where it is no longer dependent upon the metaphor of light, which effaces the importance of contour. The point of light will no longer be situated as the cause of perception, and the monad is not to be confused with a surface onto which an object projects its shadow, nor somewhere beneath this first surface, with the shadow of an internal space for mental representation. Concerning these shadows, Michel Serres writes, “My knowledge is limited to these two shadows; it is only a shadow of knowledge. But there is a third shadow of which the two others only provide an image, or a projection, and which is the secret buried deep within the volume. Now it is probable that true knowledge of the things of this world lies in the solid’s essential shadow, in its opaque and black density, locked behind the multiple doors of its edges, besieged only by practice and theory. A wedge can sunder the stones, geometry can divide or duplicate cubes, and the story will, inevitably, begin again; the solid, whose surfaces cannot be exhausted by analysis, always conserves a kernel of shadow hidden in the shade of its edges.” 18 Contrary to this infinite analysis of shadow and the kernel of shadow, the superficial shadow (or edge) and the shadow of depth (interior of a solid), in the case of Leibniz the subtraction of the ‘point of light’ from the external world of objects, corresponds to the new determination of the realitus objectiva (or ob-jectum, in the sense of what stands opposite, or against, as pure possibility) that, for Leibniz, is merely passive. In Theodicy, Leibniz writes: “It is true that Form or the Soul has this advantage over Matter, that it is the source of action, having within itself the principle of motion or of change, in a word, ta autokinaton, as Plato calls it; whereas matter is simply passive, and has need of being impelled to act, agitur, ut agat. But if the soul is active of itself (as indeed 16 Sarah Koffman, ‘L’Usage de la chambre obscure at Gravesande,’ Camera Obscura (Paris: Galilee, 1973), 79-97. 17 Deleuze, Le Pli, 5. 18 Michel Serres, “What Thales Saw at the Foot of the Pyramid,” in Josue V. Harari & David F. Bell, eds., Hermes: Literature, Science, Philosophy (Baltimore: the Johns Hopkins University Press, 1982): 84-97, here 93-94.

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it is), for that very reason it is not itself absolutely indifferent to action, like matter, and must find in itself a ground of determination. According to the system of Pre-Established Harmony, the soul finds in itself, and in its ideal nature anterior to existence, the reason for its determinations, adjusted to all that shall surround it. That way it was determined from all eternity in its state of mere possibility to act freely, as it does, when it attains existence.” 19 What is important to note from the above passage is that Leibniz makes the distinction of possibility-actuality derivative of what he calls vis activa (power), which designates the pure capacity of the soul for some act, as well as its capacity to undergo becoming, or to allow something to be made out of itself. The vis activa thus corresponds to what Deleuze will later define as ‘the virtuality of the idea’ (inclination), that is, the power that belongs to the soul and is expressed by its tendency to action and by the act itself as the ultimate actualization of the action.20 As Leibniz writes: “Aside from this interior principle of change within the monad, there must also be a particular trait of what is changing, which produces, so to speak, the specification and variety of monads… and within each monad, a plurality of affections and relations, [even] though it has no parts.” 21 Leibniz’s statement that monads are simple, meaning, they have no parts, implies that the part-whole relation cannot be predicated to them, since predication entails the possession of an attribute. Yet, because monads possess no parts, they cannot enter into aggregation or composites as parts, or be determined from the perspective of a whole as a portion that is interior to the whole. Hence, “there is nothing that might be transposed, nor can there be any internal movement which could be excited, commanded, or diminished between monads.” 22 But how, then, do monads communicate with one another? This imme­diately poses the critical problem of the communication between monads in terms of the movement between apartments, or the passage between the compossible and incompossible worlds that each monad includes at its base. According to Deleuze, the passage between monads can only be deciphered by the operations of allegory and by the forms of secrecy particular to the Baroque artifice. Both the allegory and the secret are founded upon the condition that no direct communication is possible. It is precisely in response to this 19 Gottfried Wilhelm Leibniz, Theodicy (Chicago: Open Court, 1985), § 323. 20 Inclination, from the Greek clinamen, is used throughout the Theodicy to denote the determinateness of the will within a free act and is set against a condition that Leibniz refers to as “mere possibility.” See Leibniz, Theodicy, §§ 324-27. 21 Gottfried Wilhelm Leibniz, Monadology (Indianapolis: Bobbs-Merrill Co, 1965), §§ 11-13. 22 Leibniz, Monadology, §7.

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incommunicability (which Leibniz calls ‘incompossibility’) that allegory and secrecy attain communication by an indirect means. Allegory is constituted on the principle that there can be no direct presentation, or transposition, of the perceptual; therefore, perception itself must become a sign, and the sign must become a text that must be read, deciphered. The secret is constituted on the condition that no direct discourse is possible, and so communication must take place in relation to a certain “absence of a Third,” which—as linguist Emile Benveniste reminds us—founds the distinction between language and code that determines the particularity of human language as “free indirect discourse.” 23 But something quite striking occurs in this composite of the allegory and the secret, which corresponds to the formation of the crypt in architecture and the cipher in language, that is, the composite of écriredessiner (writing-designing) in the Baroque artifice. In the absence of light, perception takes its place in the design, and must be constructed, piece by piece, apartment by apartment. This allegory of perception corresponds to the function of the crypt as a topological region within the monad and is defined by the activity of reading. The monad is a book or a reading room. But the visible and the legible, the exterior and the interior, the facade and the room, are not two different worlds, because “the visible has its own way of being read (like the newspaper for Mallarmé), and the legible has its own kind of theatre (its theatre of reading). Thus, the combinations of the visible and the legible constitute the emblems or the allegories that were dear to the Baroque…and we are always being led back to a new correspondence or mutual expression, ‘inter-expression,’ ‘fold following fold.’” 24 Therefore, if we find that the secret indicates the situation of light as a ‘problem’ within the monadological construction, it is precisely the sense of a crypt placed in perception and of a type of incorporation (or inclusion) that is not as much an enclosure of the thing, but rather a process that turns perception itself into an allegory.25 23 Emile Benveniste, Problemes de linguistique generale, vol. 1 (Paris: Gallimard, 1966), 258-266. I cannot pursue this further here than to indicate the striking resemblance between some formations of the secret and those of indirect discourse. Both indicate a transcendental status of human speech by introducing the possibility of a reference to a third term that is both inter-subjective and temporal. 24 Deleuze, Le Pli, 44. 25 It may be important to clarify terms, specifically around the resemblance of the secret to the problematic first introduced by the psychoanalytic perspective. Here, the secret could correspond to what Guy Rosolato has called the “object of perspective,” which emerges in the Freudian theories of infantile sexuality in the constitution of the Phallus: the capability of the infant to compose an unreal object in place of a void, and equally the capability to negate this object in favour of its substitutes, which will have a central function in the imaginary as the objects corresponding to the partial drives. See, Guy Rosolato, ‘L’Objet de perspective dans ses assises visuelles,’ in Le Champ Visuel, (Nouvelle Revue de Psychanalyse, no. 35 / Spring 1987), 143-164.

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At this point, however, there is a danger of both perceiving too little and too much from this state of affairs. For instance, there is a danger of reducing the allegory to the composites made up of the emblems and small interior decorations that are fabricated to replace an external view. This is the case with the newspaper, in which the interval between perception and memory is founded on the analogy with perception in just one of its aspects: brevity. On the contrary, in its very act of encryption, the secret indicates a point of perception that is not continuous with its ‘figure,’ and a limit that cannot be resolved by perception (or the understanding associated with it), but rather by a formal power to extend itself infinitely. It is for this reason that perception is incapable of deciphering (unfolding) a secret, and it is pure prejudice that the understanding takes the secret to be content corresponding to its own formal limitation. In turn, this immediately leads us to a second danger, referred to above under the function of doxa (the origin of common sense and opinion) that makes the secret an expression of ideology (an allegory of power). However, this conception of power would violate the sanctity of the crypt, which cannot be thought of on the basis of the inclusion of a foreign idea or perception, since the monad contains the whole world immanently, and since Leibniz outlawed that anything could pass between monads in the form of influence (Einfluss). This is explicitly stated in the following propositions: “It is impossible also to explain how a monad can be altered, that is, internally changed, by any other creature. For there is nothing in it which might be transposed, nor can there be conceived in it any internal movement which could be excited, directed, or diminished. In composites this is possible, since the parts can interchange place, but monads have no windows through which anything could come in or go out. […] In consequence of what has been said, the natural changes of the monads must result from an internal principle, since no external cause could influence their interior.” 26 Here, the notion of the crypt evoked above cannot be reduced to an already constituted notion of the Unconscious: as a closed and sealed off room, or a variable key invented by an alien occupant. In place of this, Leibniz constructs a topography where room and occupant, world and monad, would be entirely inside, and the door would be on the outside, and would shut only from the outside. In other words, the Leibnizian crypt is utterly, one might even say infinitely, open. Thus, it follows that there is no need for doors that lock or invite, for windows that shut out or illuminate. But how can we account for this apparently bizarre and ludicrous description, this topography for lunatics—all background, as if forming a 26 Leibniz, Monadology, § 7 & 11.

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there without a corresponding here, a front without a back? This would be a necessary deduction from the statement, ‘no doors or window.’ In effect, this would entail a conception of the monad as a cryptic enclosure, the crypt being both the supreme ‘contradiction’ and the founding principle of the Monadology, because it produces the very form of the scission referred to above. Consequently, it is not a matter of representation, because the monad can never come to its own limit, but falls from level to level, by occupying a present that consists of a contracted point and an infinitely dilated bottom section, or a basement “hollowed by other basements.” 27 What is missing is precisely the foreground, the object of consciousness. The monad never becomes an object unto itself, and does not represent itself objectively, but rather becomes an objectile, the material support or canvass. In this way, the body serves as the base for drawing up the shadows that emerge with greater intensity from an even more obscure background, since whatever light there is plunges ceaselessly into shadow. Returning to Deleuze’s diagram of the monad (or ‘Baroque House’), the lower levels are “pierced with windows” or small openings, while the upper level is “sealed and sightless.” At the same time, the upper room is described as being “resonant,” a sounding box that will “render audible the visible movements coming from below.” 28 The attribute of the crypt belongs only to the upper level, “sealed in whiteness,” while the lower level remains infinitely open, both divided and infinitely divisible. The monad is that infinitely contracted point that is differentiated from an infinitely divided space. Hence, the concept of closure must be revised. We cannot say, for example, that the upper level is closed off from the other, since the attributes of closure (“door and windows”) are said to be completely lacking within the monad. Thus, Leibniz’ concept of an interior can neither find analogy with a content of perception (or a psychological datum), nor can it be based upon the composition of geometrical solids in which content is also what lies behind the representation of three facing sides, as the fourth side can only be extrapolated as a geometrical solution of the first three. Therefore, what I referred to above as ‘shadow’ is neither composed of light nor of darkness, but rather by the movements of the visible that oscillate or vibrate from the matter below; thus, it is by a process of resonance in the monad that the visible movements in matter become audible. This is why there is no analogy of perception between the soul and matter, since there are two very different kinds of receptivity involved: the receptivity of matter to the visible movements created by the light streaming in from small openings, producing movements that spiral upwards, becoming audible, resonating within a new series that has its own material consistency. 27 Deleuze, Le Pli, 6. 28 Ibid., 7.

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What is perceptible on one level becomes legible on another through a mélange of different materials and it is only by an essential ‘graphism,’ or a diagram of light that is made completely from movement, that there can be anything like communication between the two levels. Figure 3: Resonance in the Monad.

The crypt functions as the echo chamber by which the visible movements in matter are converted into an audible series without any notion of projection or any continuity established between the two levels. Any communication between interior and exterior must pass through the crypt, which resonates with the visible movements that take place below in matter. The crypt remains a breach, or scission, nonetheless, and there can be no isomorphism established between what is visible in matter and what is readable in the soul. It is important to see the combination of two different factors in the process of perception illustrated in the diagram above: at one end, that of blurred vision caused by movement, sometimes creating a series of images, like the movement of an athlete in slow motion; at the other end, the point where a clear sound trails off and is obscured by dissonance, or emerges from a background of noise. Light is not a cause of perception, because perception is essentially constituted by the fuzzy, the opaque, the indeterminate, or the blurred motion occurring in matter. Neither is it the question of a clear and distinct note in the soul that would produce an echo, because the monad can already be described as a chamber full of echoes, and it is from this cacophony of echoes that the possibility of a single note first arises. (This is because a single note never occurs without the series that conditions it.) Both factors, lacking in the distinct clarities of the visual and the audible field, seem to blend and indicate how there is communication between the two levels of the monadological construction through a process of reverberation. I already commented above on the construction of perception in the Baroque as profoundly allegorical. Suffice it to say that the figure of the crypt that Deleuze detects in the Monadology allows him to enlist the Leibnizian philosophy within a certain logic of sense inspired entirely from the domain of empiricism, “which knows how to transcend the

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experiential dimensions of the visible without resorting to ideas.” 29 Consequently, Deleuze sees in Leibniz’s philosophy the ontogenesis of ideas by means of the function of allegory, ideas being only the macrohallucinations produced and animated by the micro-movements that occur below in matter. This does not suggest that the visible movements in matter are the cause, since reverberation describes more the proclivity of the interior to resonate with itself, that is, its capacity (potentia activa) to fold, refold, manifold. Therefore, ideas can only be shaped from the resonance of a thousand tiny perceptions, and it is because of this that its contours appear fuzzy or vague, or that it can be described as without contour, since it is entirely without an object, but instead is only composed of smaller folds, ‘right down to the miniscule folds of the atom.’

29 Gilles Deleuze, Logic of Sense (New York: Columbia University Press, 1990), 32.

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VIII Nudged Viands David Schildberger

I The Cosmos 236 — Ii The Realm 236 — Iii The Machine 236 — IV The Ecology 238 — v The Obstacle 240 — vI The Antenatal Prolific Mixture 242 — viI The Discovery of a Castoff Viand 246 — viiI The Quasi-Amalgamation of a Mob 252

David Schildberger is a PhD candidate at the ETH Zürich (Chair for Computer Aided Architectural Design) and the ZHAW Wädenswil (Centre for Ingredient and Beverage Research). His research is on artificial food production in relation to land- and cityscapes. David holds degrees in Interior Design and Architecture from the Hochschule Rosenheim, Germany, and the University of Innsbruck, Austria, as well a specialization in Computer Aided Architectural Design from the ETH Zürich, Switzerland.

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“Nothing distinguishes me ontologically from a crystal, a plant, an animal, or the order of the world; we are drifting together toward the noise and the black depths of the universe, and our diverse sys­temic complexions are flowing up the entropic stream, toward the solar origin, itself adrift. Knowledge is at most the reversal of drifting, that strange conversion of times, always paid for by additional drift; but this is complexity itself, which was once called being. Virtually stable turbulence within the flow. To be or to know from now on will be translated by: see the islands, rare or fortunate, the work of chance or of necessity.” Michel Serres1

  

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the lap of luxury. We grounded ourselves and assented to only having one nature to live in. Now we feel obliged to take care of this nature, as its resources are finite, and any escape from it seems not even worth considering yet. That was the beginning, and a myth has taken its course: a machine dealing with the foundations, orders and architectonics of values, substantialized in matter, energy and information. Expressed and formalized in an urbanized landand cityscape relation; abstracted in economical theories as consistent models within an episteme. Frameworks for the characterization of a congregation of the civic and the rural. An umbilical cord, 1 Michel Serres, “The Origin of Language: Biology, Information Theory & Thermodynamics,” in Josué V. Harari and David F. Bell, ed., Hermes: Literature, Science, Philosophy (The John Hopkins University Press: Baltimore,1982, 71-83): 83.

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supplied, in general, by photosynthesis. Nature in action, maintaining life. This is a fact. A function. Yet bursting with things that are more or less probable. As a chemi­ cal process, photosynthesis is in principle electrical: flows of energy, affections of photons and electrons ordered and bonded via information. Catalysts that allow the hacking of a noisy ground and doping of existing orders.They work on all kinds of atomic substrates, forming molecular compounds. “Living beings live in deviation from equilibrium” (Michel Serres).—In peculiar mediation of the real: intellectual ability as a nature’s fundamental source. Let us multiply this beginning: as if finding our position in a game where many balls are being played, Nudged Viands

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by many teams, all at once. A site of action, indefinite in time and space. This game explores ways towards novel natures by indexing concepts in a cataract of thoughts. A text acting as a scaffold for the staging of potential characters. Their appearance is improbable: a preferably balanced validity, exhaustively symmetrical. A nudged architectonics, “…yet which preserves its form for a time in and through the flow that destroys it … the process is life itself” (Michel Serres).—Castoff viands opening up digestible worlds: starters that make us eager to do more, from necessity to luxury. Play around. Discover. Taste. Appeal to our senses…

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Fig. 1 Divine Gift Fig. 2 Proportional Tilling

Fig. 3 Field Law Fig. 4 Customized Sovereign

Fig. 5 Duration Limit

Fig. 6 Machinic Ground Fig. 7 Functionalized Chains

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I

The Cosmos

The necessary preparation of the soil that follows on from the paradigm of the hunter-gatherer. Palladius recognizes in his Opus Agriculturae (fourth century) the fundamentals of choosing land for cultivation in earth, water and air. The richness of these basics relies on nature and application: it depends on capacity and will, introducing cycles of selection. Planting and breeding happen around a divine centre of reasoning. The choosing and clearing of open land leads to the given earth being treated as an economically handled household: a source guided by our immediate habits, like the myths of the cosmic cycles of sun, moon, weather and soil; in search of an equilibrium between god, man, world and nature. Creating a growth proportional to the surplus rooted in the soil: a natural intrinsic value, extracted through the domestication of the wild. Ii

The Realm

The clearing of earth and its tilling to fields: as supply for food, and as an economic necessity for the city. Thus Vitruvius in his Ten Books on Architecture (first century). With a surplus derived from work, as part of a rent system arranged around serfs and a landowning aristocracy; these are the key characteristics of feudalism. The development of agronomy as a result of changing technical practices on a physical level, such as enclosure, mechanization, four-field crop rotation and selective breeding. It enables unprecedented growth in populations that spread out in communes and colonies and appropriate more ground by setting up an infrastructure linked to the city. Andrea Palladio’s agricultural villa for an aristocracy interested in agriculture and land is still founded on a divine law. Also, feudalism organizes itself around a notion of necessity, but with an earthly concentration of control and power. This eventually finds its critique in Thomas More’s Utopia (1516). After that: mercantilism, with its emphasis on the ruler’s wealth, the accumulation of gold, and the balance of trade. It shifts focus onto collecting money that can be controlled by circulation regulations. The principles and methods of commerce rooted in the trade between towns and colonies: it centers around the construction of the state household. IIi

The Machine

Adam Smith describes the wealth of nations as the result of excellence in agriculture. This excellence subsequently causes a metabolic rift from which springs a surplus, which, as Karl Marx recognizes eventually, can be harvested and accumulated as labour. This gaping chasm creates a dependency in which landscape and city are tightly locked together, as well as the interdependency of production and consumption.

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Fig. 8 Common Wealth

Fig. 9 Commodity

Fig. 10 Properties Fig. 11 Geometric Growth

Fig. 12 Enclosure Fig. 13 Knowledge in Circulation

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This function is now controlled by capital: agronomy turns into industrial agriculture. Capital becomes the ground for vast urbanization. Myth gives way to fiction; a release to a real fiction. The 20th century begins to symbolize this turn. Le Corbusier develops the Ville Radieuse (1924), and the Ferme Radieuse (1940). ‘The function’ of the city is now conceived as a machine for living in, sourced by agriculture. Frank Lloyd Wright elaborates on a natural architecture in Broadacre City (1932), embedded in a decentralized agriculture. Ebenezer Howard, in the Garden Cities of Tomorrow (1902), connects civic elements grounded in an endless green; and Ludwig Hilberseimer, in the New City (1944), embeds agriculture by expanding the functionality of the city towards a whole system: from region to world, globe and sphere. Versions of belief; in groundings on the support granted by an analytical and scientific understanding of nature and its elements, together with the transformation of aristocratic power that leads to the expositions of functionalized mechanic orders of relations and ratios by the analysis of properties in terms of their variable values, in the upcoming political economy. A kind of engineering initially applied not to the city, but to the territory of the countryside, as Pier Vittorio Aureli elaborates in The Possibility of an Absolute Architecture (2011). Measurements at specific points make up a linear model, a chain of imaginary and normative causes and effects. Iv

The Ecology

Ernst Haeckel introduces the concept of ‘ecology’ in Generelle Morphologie der Organismen (1866), adjoining the Greek oikos, for house, to logos, knowledge. It names the science that is to treat the relationships of organisms to their environments within the surrounding world, including all its existent conditions. Patrick Geddes, at the turn of the twentieth century, relates environments and organisms as a single process acting within nature and tries to reformulate the relationship between city and countryside through a system of functions, an ecology. John McHale expands this approach in The Ecological Context (1970), where man is seen within a biosphere, a system where the whole human enterprise is interlocked in a large-scale man-made ecosystem. This leads to Buckminster Fuller’s Operating Manual for Spaceship Earth (1968), a cybernetic approach conceiving of operations and processes as parts of a holistic system, in dialogue between micro and macro scales; connecting everything that can be rationalized and parametrized by technics within an ecological urbanism, as the integration of everything into a system. Controlled flows alongside a geometric infrastructure within certain causalities. From then onwards, efficiency seemingly becomes humanity, as Mark Wigley puts it in Recycling Recycling (1999). The macro-scale of monetary economical theories of Friedrich Hayek and Milton Friedman, too, observe a global scale, by which the tyranny of government control over economics, and

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Fig. 14 Control of Parameters Fig. 15 Enactment all-inclusive Fig. 16 Just in Time

Fig. 17 Welfare Capitalism Fig. 18 Global Village Fig. 19 Flow Downstream

Fig. 20 Foundations

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its central planning, is supposed to be handed over to individual subjects, each acting within a liberal system, thereby gaining more of a general freedom. ‘Rules instead of authorities’: financial economics, in which money of one type or another likely appears on both sides of a trade. This provokes numerous critiques. Michael Hardt und Antonio Negri describe an Empire (2000), which is characterized fundamentally by its lack of boundaries. The Empire’s reach has no limits. It acts globally and rules over the entire civilized world. Its performance is controlled anonymously, in the amount of money distributed by institutions called central banks: a space of flows, so Manuel Castells (2004), within an urban network of financial centers. All within a Global City (1991), formulated by Saskia Sassen. Just-in-time logistics built upon a generic infrastructure; the abstract model made to work as a mechanic chain, expanding to a network. Pitching up holistic ecologies; administering everything by knowledge, within a system of functions of a globalized metropolitan logistics of processes and dynamic flows of energy and matter, on a globalized urban ground. V

The Obstacle

All this, still founded in a nature that is forced to be productive, realized on this urban ground. A cascade allowing frictionless flows of matter, energy and information. Debates on ecological and landscape urbanism try to grasp this nature by expanding the range of their analytics. The growth of data availability. New value models from the source side in agriculture, via the production line up to the consumer. And all this also in the spell of continuous optimization, leading to a naturalization of data. The argumentation being that seemingly smarter solutions integrate better into systems of a global scale. They continuously maximize the force for global impact on earth. A set of processes struggles with the constant law of growth, imposed on it and taken for granted. An agitation upwards searching for equilibrium. But this quest paradoxically originates in a parasitical relationship with nature, asking for credit from earth while exploiting surplus, and not always on an equitable scale. As Deleuze and Guattari claim: capitalists may be the masters of surplus value and its distribution, but they do not dominate the flows from which surplus value derives. A critique that problematizes old habits and their founding of the household we try to master: the city apparently just takes and does not give back. It acts as the administrator of its own ground of properties. Man is demanding. Radical exclusion and expulsion, and the treatment of all other species as fair game. Extirpation, suppression, banishment and destruction as an attempt at swimming upstream. With a sacrificial blade. First the splits, then everything included via an economized attempt at naturalization, treated further as if teleonomically controlled: a goal-driven mechanical apparatus of production, distribution and consumption, related by exchange and circulation, with price as its ultimate measure. The limits

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Fig. 21 Father of Tragedy Fig. 22 Still Life

Fig. 23 Mobile Fig. 24 Capital Fig. 25 Fuzzy Edges Fig. 26 Master

Fig. 27 Peak Out

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are evidently inherent in the infinite chain. They immanently make up its grounding in capital accumulated from labour and resources, blocked and secured by a kind of modeling that implies an economy built upon exchange, which administers at a fake equilibrium. Material and labour as rifts at the fault line, exploited by the words of the intellectual. Accumulated earth as a salad, to which the object keeps giving and from which the subject takes, having spat into it. Look at Michel Serres, Le Mal propre: Polluer pour s’approprier ? (2011). An inferior object appropriated by the supreme subject: a condition generalized, but still in the representation of the same city-countryside relationship. The subject on the city (human) side, and the object on the country (earth) side, from Enlightenment via modernism to today. The earth as host and victim: the relationship one of abuse. The master of the plot possesses the object world as cleared re-geometrised land; locally by cord, unit, measure, writing. Prestige by means of flattened regular sections as rational representations of a rich volumetrics. The farmer, the priest and the geometer: they are measuring fields, temples and space in a twinning act of exchange, at fake equality of domination and hierarchy. Either shrewd, or victim; one is always killing the other. Quantified, qualified, naturalized and re-appropriated for civilization; modes of a numb ecology of static equilibriums, trapped in a cyclical time downstream. Following the erosion of the second law of thermodynamics: real equilibrium. Death. Suspend the naturalized umbilical cord between humans and earth: a shift towards energy and information, relieving the exchange of material and calo­ries from their role as the quintessence of being. Erwin Schrödinger states that organisms decline and die even while remaining in environments that contain sufficient nutrients to sustain their life. Living organisms restrain a certain kind of organization temporally, while falling towards everincreasing entropy, the maximum of which we call death. Léon Brillouin suggests complementing an ‘energetic food’ value (energetic negentropy) with an ‘informational food’ value (informational negentropy), enhancing organic metabolism towards an idea of the metabolizable sensible and intelligible. A non-consumable form of life and of knowledge to the uncountable stock of a universal invariant amount of energy and information. So far, so descriptive. In order to master this inversion, we swell together in a continuous stream of indexes, derived from the rich body of writings by Michel Serres. Serres attempts to mirror the real through tentative balances in an equipollent identity: the equation as a contract, to be negotiated and signed within the operative paradigm of information and information technologies. Adhesive sites of the next level of abstraction: this is where we turn to its noisy manifestations. vi

The Antenatal Prolific Mixture

Michel Serres names two capitals: the sun, including fire and energy, as a productive source, and signals, relating to information as

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Fig. 28 With Pleasure

Fig. 29 Cord Fig. 30 Disgust Fig. 31 Sun from Mars

Fig. 32 Communication

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a translative source of permutation. The sun, as the ultimate capital, puts all other time-functions into the position of its own sub-capitals. Only the sun creates. Not as energy source but as time-function. Braving entropy with swimmies for the turbulent counter flow upstream. Our inventions always imitate the sun, even materialism as a sub-cult, since matter is energy and its form is informational. The first, the energy of matter, is constant and conforms to the first law of thermodynamics, the law of the conservation of energy: each specific nature consumes the universal nature, and vice versa. The second, the form of matter, is invariant. It is accounted for in the data banks of the universe; in DNA, as the stock of stocks. It is uncountable and inexhaustible. A white that entails every color, holding all the potentials inherent in its spectral ichnography. A reservoir of signals where history in its totality is being conserved in the memory bank of life itself. Primary to space and time, based on the law of chance: a replicative structure where noise is preserved along with the sound of music, as a coupling of information, a function of the ratio of the number of possible answers, and the absence of answers, called entropy. Allowing future reproduction without a master, still undetermined and retaining its imperfections: a reservoir and potential ready to be encoded and decoded for replication, transcription and translation; carried over and copied as conserved invariance in variation. All brought to one language as generic infrastructure, placing novelty adjacent to conservation and articulation. Thus we should not ask ‘what can we do?’, but pose a more political question: ‘what should we do with…?’—with all these reservoirs, capitals, stores of writings, memory banks, libraries, lists, pockets of time, cities, classes, groups, nations, banks of givens and earth—all these data banks containing collections of sub-suns and sub-banks—in order to form a non-founded city in a founded one, as sites on generic ground. Capable of growing in all kinds of directions. These capitals of surplus code are generous: debts can be derived indexically, as if from a bank account of an abundant past, rather than from an open future. This allows us to think of an exo-Darwinism of rich promises, by listening to the beauty in noise. The ‘Real Age’, as the non-integrable total of all durations of all times, bonds the economy to life as a time-function. It reopens the concept of sustainability as a promise, which is to be paid back later. Whether we do so remains a moral question and is up for discussion within the universal nature of an economy whose architectonics is parasitic, as in ‘para’, beside, a site; as the rectifier of relations: affecting object and world as well as subject and humanity, with bonds of a collectivity in an object-subject distribution, to be para-sited by an instructed third, formalized as the empty body of a neutral joker; filled by a viable stream. Not on a plot of earth, not in a specific case, not empirical, but as an identity equipollent to the real. As a basket of times founded in the flow of multiple dimensions, all ultimately drifting in one direction. Not linear, but mingled and merged, via quasi-objects as bonds to a ground;

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Fig. 33 Code Fig. 34 Couple Fig. 35 Potential

Fig. 36 Bank Account

Fig. 37 Promise Fig. 38 Periphery

Fig. 39 Vessel Fig. 40 Source

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shifting from the earth to the universe. There are no fixed assumptions of a point zero or an origin. There is a risk, but at an ecstatic point, removed from place: an origin always looking for another origin, up to a ground zero. The origin in stochastical distribution: a reiterated origin, multiplying its images towards an inaccessible vanishing point. From there, rendered original copies of non-standardised multiplicities can pass the point of identity. Obtained via a hyperbolically open, branched and expanding relationship of symmetrical representation, dealing within the desired equipollence of the real and the rational; using sections through a stereometric space of sterochemical affinity. Within the structure of the code, an ichnography as an intrinsic beyond, carrying magnificent extravagances: from plane to volume by means of an experimental representation, synthesizing the multiple with an indexical architectonics, which bridges rational islands on site. Not as tragedy, but as a comical bond of an irrational mixture, dividable but still ‘viand’. An exo-Darwinism that renders, restores, yields, unlocks and deciphers probability figures as a kind of all-that-could-have-been. In all times. Articulations out of masked instances of a spectrality rendered into the empirical and sensible. A terroir as a crystallization of an invariance, spaced out through variation into a solid symbolic character that articulates. Let it talk, circulate, communicate and exchange between ‘I’ and ‘We’. A thing that as Michel Serres states, emits, receives, stores and processes information. On every scale secrets, traces and temporary equilibriums can be found. In a nascent way, within the universal law of chance, rather than bonded to the political of human collectivities. And the rules of contracts, stories, brands and communities, looking for a new habitus in the city: the structure where all this can happen. Irrational but still polite, in-between free and human. Rich in characters staged as terroirs of the observable, cast off their natural earthly grounding as possible worlds that draft possible narratives into a scenography. A Sisyphean predicament to climb towards the source. Towards black boxes, in order to invent. Potential islands of negative entropy fall towards the equilibrial sea. Everything falls to zero: the nullity of information. Awaited by re-use-eaters placing themselves below each other to be fed unimpeded. Further downstream there is the one who eats, in an updated downgraded welfare state below the institutionalized infrastructures of wealth, so as to exploit the masters and get fed by the fruits of luxuriation. So think universal, render local and integrate global. Use energy plus information. Turn off the light to see the abundance upon black boxes. Within this body, a viand departs locally. A concept, not stable but gaseous. A probabilistic setup of a stochastic cloud. VIi

The Discovery of a Castoff Viand

It is not a product. It is neither stable, nor global nor generalized. It is potentially something else. A capital for a rebirth. The next parturition after so many deaths of raped ingredients, as cleared ground with the

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Fig. 41 Section Fig. 42 Love

Fig. 43 Symbolic

Fig. 44 Exchange Fig. 45 Stage

Fig. 46 Spiral Fig. 47 Well fed

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noise of top-down processes in its aroma. An endeavor to mingle with the banks of nature and reason, within the habitual banks of humanity, in departure from the rational islands of physics, chemistry, biology, analytics and procedures. All these are denounced spaces, denuding the ground. Far from equilibrium; engaged in an effort at climbing the pyramid, instead of trying to get to the bottom where the feast is rich and where you are fed by the host, with no need for homogenizing all the jokers, as there is in agriculture—the old primary parasitism. Eliminated by the parasites of the megalopolis. But way below, closer to the sea of entropy, where there is a higher degree of complexity, where generic infrastructures necessitate political decisions based on chance. A parasite initiates the last cut that slices everything into three. Inside the sacred and outside the profane. In-between, another parasite as impostor. Kind, so as to reach the richness of cases. Circulating an equivalence of signs as substitute for having to identify a victim. Way richer in information than in abuse. The parasite as interruptor of circumstances constitutes his own sites where he can take hold of milk and honey once again, by coupling information and noise. Sets as bonds of landscapes, full of information within entropic countrysides. Affiliated in the being of a cell. The cell, an initial host for a generic site, whose channels get parasited on the way towards the architectonics of a viand. Initiated in an in-vitro setup of sender and receiver: a couple that is connected through a channel, chasing out all other parasites that are not part of the communication scheme. Keeping it sterile to the outside, inside, the cell is subject to the same fate. Like Russian matryoshka dolls at play: inside is always an outside to the other direction; a kind of point of view: touch and being touched. As sender and receiver, as being ordered and defying disorder. To the inside the directed vectors express, to the outside there is covering up. The outside looms as a black box. On the surface, some potential ratios of information and noise. Thus, the structure of the subject is always imposed on the object. At each level, an essential attempt to make sense by listening to the black box. The higher level tries to decode and decipher. The outsider has to ask the appropriate question to reach the surplus of code, to realize its yield by coupling information and noise. The information that’s eventually mobilized gets filtered, integrated, transformed, fixed, displaced and interlaced. The interactions happening within are not mechanical, they happen by chance within a sequentiality of rectifiers and converters of time. The body elects, like a crystal, and starts growing through reproduction and transmission of information corresponding to the internal structure. The transmission between sender and receiver produces noise. This is where the parasite excites the system and hacks the homeorhetic flow of circulating relations. Dealing with the subject from the periphery, transcribing in-situ, and by this, balancing the changes of relations. A continuous play with temporally obtained equilibria. Not yet fixed in their identity, indeterminate. Cast by chance. As variations of the

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Fig. 48 Foam Party Fig. 49 Mingle

Fig. 50 Probability Fig. 51 Interruption

Fig. 52 Channel Fig. 53 Cell

Fig. 54 Black Box

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invariant, within an irreversibility. The aggregated structure will change, at best, towards order up the stream. While the universal temporality keeps falling, the local gets differentiated by individual times—a viand. A circumstance out of chance. Not added and accumulated, but transcribed and then translated. Towards a fully rendered bricolage. In a rendered bouquet of times, a duration has begun. Within the cell milieu an initial set of signals spreads: related to each species, encoded in a channel upon a medium. In a liquid of instructed chemical reactions; a suspension being held in an unrooted abeyance. Just temporarily halting, because constantly interrupted by deprivation and exclusion from any privilege. The cell gets apprised by an enzyme in the medium, which operates an ordercreating function. The cell has the capacity to form, with other molecules, stereospecific and non-covalent complexes. These proteins are exorcised by a demoniacal function. Relating signals, desires, warnings, pleasures, pains and information coupled with noise. In the channel, a listening instrument of internal sensations; inducing keys to decipher the signals in the communication medium that circulates the substrate, which is the material upon which an enzyme acts. Binding a thing, not by function but with a language. Mediating in-between, like a membrane towards an inhibit mode of circulating information, activated by chemical potentials relaying the transformation of signals at the border. The enzyme as joker and transmitter pitches a stereometrical space with undetermined receptors. With every fluctuation and every transformation it changes name. With every reaction, it changes formula. Like a word that pitches a solution space for meaning: multiple voices conglobated. Complexions with degrees of probability, as aggregation of rational islands in an ocean of entropy. Towards an energetics for information, with a catalyst agent as its condition. An excluded memory activates a stock of time to unfold, allowing ages without time to escape through formed folds. Singular times written by gestures of the included and enfolded in a practice of repetition. Applied memory nudges amnesic natures of irreversible objective beings, as the conjunction of bonds inheres memory outside of the linearity of the fall. Lively beings are conceived and discovered in deviation from equilibrium, explicit in the division of cells and growth, in a state of constant ordering and disordering. Life is the exception. And by this, it disrupts the laws of nature. Except that of chance. A declination evokes a coded sequence as a memory and preservation of conditions: everything exists in the form of writing and code, from being to existence to world. The code as an empty vessel to swim upstream for time memorial. Reversible in large circles. Globally not the same river, but a mixture of the other and the same. A chance in time. Unfolded in an experiment on a local level. Addressed via code. Beyond that we are lost, as the path from local to global is not predictable and not integrable by reason. From a global perspective appear pockets of local order in a rising entropy. Under constant flux and flow, eroding the surrounding banks in

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Fig. 55 Diner

Fig. 56 Growth Fig. 57 Acceleration Fig. 58 Maverick

Fig. 59 Enzyme Fig. 60 Catalyse

Fig. 61 Aggregation

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stable turbulences. The parasited channel, as glue of rationalities, binds bouquets of times out of the medium. A metabolism as release from all the entropy produced while alive. Tender information to gather bond-free energy. In debt to nature. Life outdaring death by negentropy: born old, dying infantile. The cell as subject can make sense of the corrected information; it can filter, digest and order, until a viand falls back into a world as an instance of a population: an identity as an original copy is born. vIii

The Quasi-Amalgamation of a Mob

What follows is a venture of cells and a fuzzy We. Species and humanity relate via contracts, comprising promises and obligations between them. The cell once more becomes the subject, trying to equate the scale of exchanges. Same or different. Energy for information, and vice versa. Giving energy to the cells and getting paid with information. Let them talk. Then, change subject and object again, and the direction of the channel. A translation in which the body mingles with the world, within the frame of content and expression, as well as form and substance, in an inaugurated ball game. Stumbling into a comic scene, evocating and constructing collectivity. Everybody could have a turn and be the subject. Yet, the ball circulates. One or another possesses, for a short moment, the essence of social relations. He is only one factor in it, and he possesses the whole. The final receiver is he who utters language, the one who asks the right question. The one who signs as the architect of a kind of garden, which is bound together as a fully elaborated architectonics. A firme on a dedifferentiated neutral site. The masking of viandness in colorful greyscales. The public adjusts the concept, the story and the brand through circulation. An invocation. To like the passed-on, not yet fully determined, as it is. The subject of the object is always multiple: the cells talking to the world. A quasi-object stabilizes time with a joker, metabolized in a communion. Dialogues of characters, grounded in libraries and collections of data banks of the ancients, engendered in the rebirths of a viand, out of the abundance of a viandness. Articulating itself as a sensory concept: a multiplicity of values and potentials oscillating between an I and a We. And by this, becoming increasingly specific. Again transfer and translation by a parasite. Again bridging, glueing and mediating. Again a matryoshka game with sender and receiver and object and subject. The subject isn’t at the foundation of the object. Nor is the transcendental. There is no object without a collective. There is no human collective without an object. Knowledge is founded in this practice, a fusion founded on what flows. These relations constitute the object. The object, passed on in a multiplicity, establishes the relations and constitutes the group. An attempt to look for the alliance of the exact and the social sciences. Objects and relations, and nature and history. A passage of a nascent fetish. A third

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Fig. 62 Existence Fig. 63 Surge

Fig. 64 Parturition

Fig. 65 Playing Together Fig. 66 Hunt the Slipper Fig. 67 Garden Architecture Fig. 68 Desire

Fig. 69 Articulation

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copula. In-between encoding and decoding, valid only throughout the ball game. A viand becoming branded. The centric quasi-object as totality, without addition. Not a global added to the local, nor a simulacra of locals leading to an ideal global. No rest that is bound to remain, when setting out to reach the global via the local. No “accursed share” (George Bataille, 1949), as if it worked, although it does not actually do so. No economy of thwarted excesses, making sure that it won’t work, because it works too well. The surplus needs disposition, instead of being stocked through the exchange of symbols. Balance, but do not accumulate: get rid of it. Distribute it. Bring it into the game. Surplus expelled, rather than kept, chased instead of maintained. Otherwise it will rot while changing state, for parasites will come. Instead of locking it away, reward it with more significance. To stabilize the unstable. A conservation of the same invariant power, as equipollence between the real and the rational. The quasi-object acts as an integrator and as a differentiator. It marks the relations to the real, where the rational can’t go: where only the rite and the fetish can go, and without which the surplus would vanish and disappear. The fetish as necessity to encode and decode ciphered information, in the communication that makes a community. An intersubjective remedy commutating a quasi-object. Up to its firming as a particularly stratified object. A statue. Here death temporarily reappears in a cyclical eternal return on the linear natural path, with an angle of contingency hollowing out predetermined directionality. Intrinsic in the DNA, as its void. Evoking a spiral. With a generic trajectory, absent from the common nature. Yet the casting off from it knows no end. In doing so one finds glues for the universal. Make it unknown, foreign; discover and bring it back. Upstream, where birth never halts. More generalized— becoming the mother of an old, and dying, mother. See this as an obligation, a contract towards a categorical imperative. In a sheaf of times, allowing sets of temporalities to meet in a knot. Outdaring death. To be reborn as a new specimen on the high seas, where strangeness surrounds space. Subsequently, head towards world objects: objects which share a dimension with the world. A thing we can live in. A new species, which reproduces as long as globality does not settle with a particular remainder or waste. Adequalising the natural with what so far is called artificial. Rendering natures equivalent to the earth, by casting off indexical architectonics. Start with the information and entropy couple. Render it back onto the stage as a rich viand, a nature that talks: the birth of a delicate symbolic existence, approaching the empirical as further digestibility: ‘Mmmh—this viand really tastes delicious’. That is luxury.

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Fig. 70 Bridge Fig. 71 A new Constitution Fig. 72 Marathon Fig. 73 Like

Fig. 74 Centered Void Fig. 75 Natural Contract Fig. 76 Cityness

Fig. 77 Delicatesse

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image references All websites were last accessed on March 20, 2016. We have taken great care to identify all rights owners. In the unlikely event that someone has been overlooked, we would kindly ask that person to contact the publisher. A SCHEME FOR A FANTASTIC GENEALOGY OF THE ARTICULABLE, BY LUDGER HOVESTADT – FIG. 1: Oskar Schlemmer, The Triadic Ballet, 1916. Image source: http://publicationes.de/verschiedenes/ holzwelten/139-triadisches-ballett.html . FIG. 2: Busby Berkeley, Footlight Parade, 1933. Image source: https://musicadecomedia.wordpress.com/2014/10/24/busby-berkeley-coreografo-yii/ . FIG. 3: Jaques Tati, Playtime, 1967. . FIG. 4: Quentin Tarantino, Pulp Fiction, 1994. . FIG. 5: James Cameron, Avatar, 2009. FROM PEBBLES TO DIGITAL SIGNS, BY GERT SCHUBRING – FIG. 1: Simple tokens. Denise SchmandtBesserat, How Writing Came About (Austin: University Press, 2008), 16. . FIG. 2: The numerical signs of the proto-cuneiform texts from Uruk. Hans J. Nissen et al., Archaic Bookkeeping: Early Writing and Techniques of Economic Administration in the Ancient Near East (Chicago: University of Chicago Press, 1993), 26. . FIG. 3: Metrological systems, different for classes of objects. Nissen et al., Archaic Bookkeeping, 28. . FIG.  4: Complex proto-arithmetical summation involving replacement rules for symbols represent- ing concrete units. Nissen et al., Archaic Bookkeeping, 133. . FIG. 5: The main stages of the evolution of cuneiform signs. Robson, Mathematics in Ancient Iraq, 76. . FIG.  6: Evolution of signs for words, from iconic symbols to cuneiform signs. A. H. Podany and Marni McGee, The Ancient Near Eastern World (New York: Oxford University Press, 2005), 41. . FIG. 7: The Greek numeration system of Miletus. Gottfried Friedlein, Die Zahlzeichen und das elementare Rechnen der Griechen und Römer und des christlichen Abendlandes vom 7. bis 13. Jahrhundert (Erlangen, 1869), 71. . FIG. 8: The evolution of the Hindu-Arabic numeral system. Johannes Tropfke, Geschichte der Elementar-Mathematik. Arithmetik und Algebra (4th edition, Berlin: de Gruyter, 1980), 66. . FIG. 9: The alphabetic Arabic numeral system. . FIG. 10: The three prototypes for the new poids et mésures: meter, kilogram, and liter. Musée des Arts et Métiers, Paris. Photo by the author. . FIG. 11: The new system of weights and measures, here showing length units, as decreed by the French parliament on August 1, 1793. Décret no. 1393 de la Convention nationale, du 17 août 1793, l’ an second de la République française, une et indivisible, qui établit l’uniformité et le système général des poids et mesures (Mamers: Imprimerie de Boulanger, 1793). . FIG.  12: Metrological systems for areas in various regions of Holstein. Kroymann, Gemeinnützliches Rechenbuch, 341. . FIG. 13: The first PC for word processing—the Commodore 64. . FIG. 14: An example of how a Chinese term is decomposed into elements that can be coded. Image source: http://en.wikipedia.org/wiki/Cangjie_input_method. . FIG. 15: Miguel Chevalier, Binary Wave, 2010. ‘ON THE BAROQUE LINE: THE MIND-BODY PROBLEM’ AND THE ART OF CRYPTOGRAPHY, BY GREGG LAMBERT – FIG. 1: ‘Diagram of interior and exterior’ (author’s sketch). . FIG. 2: ‘The baroque house (allegory),’ from Gilles Deleuze, Le pli, 7. . FIG. 3: ‘Resonance in the monad’ (author’s sketch). NUDGED VIANDS, BY DAVID SCHILDBERGER – FIG.1: Divine Gift / Psalter world map, around 1260. Image source: https://en.wikipedia.org/wiki/Psalter_world_map#/media/File:Psalter_ World_Map,_c.1265.jpg . FIG. 2: Proportional Tilling. Image source: http://www.wikiwand.com/ en/Economics_of_English_agriculture_in_the_Middle_Ages . FIG.  3: Field Law / Alexandre Calame, Swiss Landscape, 1830. . FIG. 4: Customized Sovereign / Palladio, Villa Rotonda, 156670, in James Ackerman: The Villa: Form and Ideology of Country Houses. Image source: http:// corporate-eden.weebly.com/corporate-villas.html . FIG.  5: Duration Limit / Thomas More, Utopia, 1516. Image source: https://upload.wikimedia.org/wikipedia/commons/2/28/Insel_Utopia. png . FIG.  6: Machinic Ground. Image source: https://static-secure.guim.co.uk/sys-images/ Guardian/Pix/pictures/2013/11/22/1385133220926/c2345d7f-2911-4da8-af26-38521c4c940d2060x1236.jpeg . FIG. 7: Functionalized Chains / Le Corbusier, Ville Radieuse (Conceptual Plan), 1924. Image source: https://thinkseecreate.files.wordpress.com/2013/09/plan.jpg . FIG. 8: Common Wealth / Bone/Levine Architects, Water-Works, the Architecture and Engineering of the New York City Water Supply. Image source: http://www.bonelevine.net/water-works/ . FIG. 9: Commodity / Jørgen Leth, 66 Scenes from America, Andy Warhol eating a hamburger, 1982. . FIG. 10: Properties / Ludwig Hilberseimer, The New City–The City in the Landscape, 1944

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FIG. 11: Geometric Growth / Tizian, Das Venusfest, 1518. . FIG. 12: Enclosure / Ernst Haeckel, Sea Anemones (Actiniae), 1904. . FIG.  13: Knowledge in Circulation / R. Buckminster Fuller, Operating Manual for Spaceship Earth, 1968. Image source: http://renespitz.de/fileadmin/img/ Designtheorie/Publ330_130315_ReneSpitz_Designtheorie_BuckminsterFuller_SpaceshipEarth. jpg . FIG.  14: Control of Parameters. Image source: https://theviewfromtheterrace.files.wordpress.com/2015/02/international_congress_on_hail_shooting.jpg?w=3000&h=2143 . FIG.  15: Enactment all-inclusive. Image source: https://i.ytimg.com/vi/cMsehPa2AfA/maxresdefault. jpg . FIG. 16: Just in Time. Image source: https://culturexchange1.files.wordpress.com/2013/01/ rungis.jpg . FIG. 17: Welfare Capitalism / Nestle Logo, 1868. Image source: http://www.watson. ch/Wirtschaft/Essen/710582911-Wissen-Sie--woher-der-Name-Nestlé-kommt--SchauenSie-einfach-das-Logo-an . FIG.  18: Global Village / Lars von Trier, Dogville, 2003. . FIG.  19: Flow Downstream / Joseph Mallord William Turner, Staffa, Fingal’s Cave, 1832. . FIG.  20: Foundations / Giovanni Battista Piranesi, The Roman Antiquities, t. 4, Plate VI. Construction details of the Mausoleum of Hadrian and d`Elio Bridge St. Angelo and their foundations. Image source: http://www.wikiart.org/pt/giovanni-battista-piranesi/the-roman-antiquitiest-4-plate-vi-construction-details-of-the-mausoleum-of-hadrian-and-d-elio#supersizedartistPaintings-262362 . FIG.  21: Father of Tragedy. Image source: http://www.truthbeknown. com/images/persephonehades.jpg . FIG.  22: Still Life / Juan Sánchez Cotán, Quince, Cabbage, Melon and Cucumber, 1602. . FIG.  23: Mobile. Image source: http://freie-energie-projekt.de/ wp-content/uploads/2013/05/bessler-rad.jpg . FIG.  24: Capital / Jean-François Millet, The Gleaners, 1857. . FIG. 25: Fuzzy Edges / Sandro Botticelli, Primavera, 1477-1482. . FIG. 26: Master. Image source: http://img15.nnm.ru/5/e/1/8/1/6d69f6da78980f7c09b6c07b0dc.jpg . FIG.  27: Peak Out. Image source: http://www.codex99.com/cartography/images/everest/everest_imhof_lg.jpg . FIG.  28: With Pleasure / Marco Ferreri, La Grande Bouffe, 1973. . FIG.  29: Cord / Andrei Arsenjewitsch Tarkowski, Stalker, 1979. . FIG. 30: Disgust / Arakawa & Gins, Bioscleave House, 2004. Image source: http://the-archipelago.net/wp-content/uploads/2013/10/IMGP8216. jpg . FIG. 31: Sun from Mars. Image source: http://www.jpl.nasa.gov/spaceimages/images/wallpaper/PIA07997-1920x1200.jpg . FIG. 32: Communication / Peter Paul Rubens, Musizierende Engel, 1625-1626. . FIG. 33: Code / Image source: http://www.topbritishinnovations.org/~/media/Voting/ Images/DNA%20sequencing_detail.jpg . FIG.  34: Couple / NASA MODIS Web, Cloud Streets in the Labrador Sea. Image source: http://images.spaceref.com/modis/image02152013_500m. jpg . FIG.  35: Potential. Image source: https://sumofus-production-media.s3.amazonaws.com/a/ img/bd75bb1a-acbb-4de0-af6f-7e3135b36ab5.jpg . FIG.  36: Bank Account / David Tenniers the Younger, The Gallery Of Archduke Leopold In Brussels, 1640. . FIG. 37: Promise. Image source: http://www.downies.com/aca/auction308/aca/images/lots/308/3191.jpg . FIG.  38: Periphery / Image source: https://en.wikipedia.org/wiki/Journalist#/media/File:Reporter.jpg . FIG. 39: Vessel / John Landis, Michael Jackson, Thriller, 1983. . FIG. 40: Source / Sandrine Alouf, Perrier France. Image source: http://www.nestle-waters.com/content/documents/css/images/media/imagebank/ oth_nw_perrier_spring__fact_hr.jpg . FIG. 41: Section / John Soane, Bank of England, Plan 1833. Image source: http://41.media.tumblr.com/tumblr_lhv4f3Yt6j1qztueno1_1280.jpg . FIG. 42: Love / Andrei Arsenjewitsch Tarkowski, Ivan’s Childhood, 1962. . FIG. 43: Symbolic / Klaus Pichler, Just the Two of Us. Image source: http://kpic.at/images/2631 . FIG. 44: Exchange. Image source: https:// lh5.googleusercontent.com/-BV8cTKQm6I8/UxRK2SWv-dI/AAAAAAAACRc/YdSl0rYiVDM/ w2048-h1152/All-ONS_1719520allOnS_0XPOSURE_ellen_selfie.jpg . FIG.  45: Stage. Image source: http://www.lettadiary.co/wp-content/uploads/2015/11/kitchen-show-modern-concept1-1024x575.jpg . FIG. 46: Spiral / Werner Herzog, Fitzcarraldo, 1982. . FIG. 47: Well-fed / Francis Ford Coppola, The Godfather, 1972. . FIG. 48: Foam Party. Image source: https://scontent.cdninstagram.com/hphotos-xfp1/t51.2885-15/s640x640/sh0.08/e35/12331915_216168955380811_338875 747_n.jpg . FIG. 49: Mingle / Henk Wildschut, Food. Image source: http://graphics8.nytimes.com/ images/2013/10/01/world/europe/food15-slide-XRLI/food15-slide-XRLI-jumbo.jpg . FIG.  50: Probability / Gerhard Richter, Apples [DESTROYED], 1984. . FIG. 51: Interruption. Image source: http://www.xenophonstrategies.com/main/wp-content/uploads/2013/08/20090409_090404 c-0101.jpg . FIG. 52: Channel. Image source: http://www.smp.no/incoming/article11902239.ece/ ntpglm/ALTERNATES/w980-default/tabfd196.jpg . FIG. 53: Cell. Image source: http://41.media. tumblr.com/tumblr_lqftagAg5H1qg1up7o1_1280.jpg . FIG.  54: Black Box / NASA, M. Estacion (STScI). Image source: http://i.ytimg.com/vi/N5uZyW9-wms/maxresdefault.jpg . FIG. 55: Diner / Barry Levinson, Diner, 1982. . FIG. 56: Growth. Image source: https://upload.wikimedia.org/wikipedia/commons/1/18/Callus1.jpg . FIG. 57: Acceleration. Image source: http://techanddesign.ca/ hamilton-tech-networking/ . FIG. 58: Maverick / Brad Elterman, Bowie walks, 1975. Image source: http://www.bradelterman.com/story.php?s=10 . FIG. 59: Enzyme. Image source: http://www.desy. de/infos__services/presse/pressemeldungen/2012/pm_290112/index_ger.html . FIG. 60: Catalyse. Image source: https://da.wikipedia.org/wiki/Brændværdi . FIG. 61: Aggregation / Benoit Vollmer, Image source: http://www.lumieredencre.fr/wp-content/uploads/2009/05/benoit-vollmer1.jpg

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Symbolizing existence — Metalithikum III

FIG. 62: Existence / John Hejduk, Victims. Image source: http://socks-studio.com/img/blog/ Victims-John-Hejduk-09.jpg . FIG.  63: Surge. Image source: http://www.caad.arch.ethz.ch/ blog/wp-content/uploads/2014/09/Digital-Baroque-Island_reference.jpg . FIG.  64: Parturition / Bob Dylan, Subterranean Homesick Blues, Sony WEB. Image source: http://www.fact.co.uk/ media/5734193/BobDylan-Subterranean%20Homesick%20Blues(C)Sony%20WEB.jpg . FIG. 65: Playing Together. Image source: https://www.sartorius.de/de/mab/upstream/ . FIG. 66: Hunt the Slipper / Hunt the Slipper, Antique Pring. Image source: http://www.atticpaper.com/prodimages/london/huntslipper.jpg . FIG.  67: Garden Architecture. Image source: https://www.dsmz. de/uploads/pics/Cell-cluster-2_04.jpg . FIG.  68: Desire / Sergio Leone, Once Upon a Time in America, 1984. . FIG. 69: Articulation / Red Bull Stratos. Image source: http://sqmagazine.co.uk/ wp-content/uploads/2012/10/skydiving-from-the-edge-of-space-news.jpg . FIG.  70: Bridge / Leonardo da Vinci, The Last Supper, 1494-1499. . FIG. 71: A new Constitution / Monty Phyton. Image source: http://s.newsweek.com/sites/www.newsweek.com/files/styles/embed-lg/pub lic/2014/06/16/6.20fe0125montypython04.jpg . FIG.  72: Chased. Image source: http://www. theprivateguides.com/wp-content/uploads/2015/02/2012-honda-la-marathon-9.jpg . FIG.  73: Like. Image source: http://2.bp.blogspot.com/-5d74J1w6zQo/VO5TGHu0KOI/AAAAAAAADy0/ MaRRwk2Bsjc/s1600/MFW-Street-Day5-26.jpg . FIG. 74: Centered Void / David Jacques-Louis, The Intervention of the Sabine Women, 1799 . FIG. 75: Natural Contract. Image source: https:// en.wikipedia.org/wiki/Economy_of_Switzerland#/media/File:Swiss_landscape_with_cows. JPG . FIG.  76: Cityness / Vivienne Gucwa. Image source: https://www.flickr.com/photos/ vivnsect/5689022042 . FIG. 77: Delicatesse / Reuters, Toby Melville, Image source: https://www. theguardian.com/science/2013/aug/05/synthetic-meat-burger-stem-cells

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