Pebbles to Computers: The Thread 0195405366, 9780195405361

Citation preview

Stafford Beer Davi d Suzuki

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OMPUTERS The Thread is book is about the connexions that

k and pattern the story of humanity’s tempt to understand its experience. If

e could not organise our perceptions ) as to interpret them, then our cosmos Ould seem to be random and meaningss. The need to organise and analyse is e of the characteristics that make us man. Our responses to that need

ake up the history of thought. The story of computation, from the rliest use of pebbles to the most soisticated modern circuits, is one of the

sntral themes in the story of human deavour, but this book is more than a

story. Here the insights of the artist, e philosopher and the scientist are ought together in a unique conjuncon. Like a prismatic lens they reveal ylours and planes that are otherwise dden from sight. HANS BLOHM is an internationally reywned photographer in the forefront scientific camerawork. He has deribed the first time he photographed a icon chip through a microscope. “I It as though I stood upon a mountainp, marvelling at the beauty all around, mbled and elated at the same time.’ became so fascinated by devices for formation storage that he undertook sars Of research, travelling over the (continued on back jacket flap)

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Digitized by the Internet Archive in 2022 with funding from Kahle/Austin Foundation

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PEBBLES TO COMPUTERS

Ministre d'Etat Sciences ct Cechnologic

PAinister of Stute Science and Cechnology Canada

OTTAWA,

December 1985.

Dear Reader,

Hans Blohm’s and Stafford Beer's personal vision is a remarkable testament to the depth and richness of humanity’s technological achievements. In their book Pebbles to Computers, they present a convincing visual argument that high technology does indeed go back to the dawn of time. Canada represents an impressive part of that achievement, overcoming its great size and relatively small population through the genius of modern communications. It was the first country to launch its own domestic satellite and the third to put a satellite into orbit. There is more to come. Perhaps a later edition of the present book will feature the genius of space-age materials, lasers and fiber optics, as high technology in Canada continues to evolve.

Yours sincerely,

The

Honourable Frank Oberle, P.C., M.P.,

Minister

gf State for Science and Technology.

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PEBBLES TO COMPUTERS The [hread

Hans Blohm Stafford Beer David

Suzuki

OXFORD UNIVERSITY PRESS

Allen County Public Library Ft. Wayne, Indiana

FROM

HANS BLOHM

FROM STAFFORD

In memory of my father whose enquiring mind prepared me for this venture

To my mother with my love for all of hers

Hans-Ludwig

Tony

PEBBLES TO‘;COMPUTERS the Thread Original Idea and Photography by Hans Blohm Text and Design by Stafford Beer Special Contributions by Rudi Haas Introduction by David Suzuki © Oxford University Press (Canadian Branch) 1986 OXFORD is a trademark of Oxford University Press

© Photographs Hans-L. Blohm Produced by Fortunato Aglialoro for Boulton Publishing Services, Inc., Toronto

CANADIAN

CATALOGUING

IN PUBLICATION

DATA

Blohm, Hans Pebbles to computers ISBN 0-19-540536-6

1. Science. History.

2. Knowledge, Theory of. 3. Numeration — I. Beer, Stafford.

1936Q172.B58 1986

I]. Suzuki, David T..,

IIL. Title; 500 C86-093331-8

1234-9876 Printed in Hong Kong by Scanner Art Services, Inc., Toronto

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David T. Suzuki

uman beings are remarkable creatures. We evolved out H of nature itself and remain inextricably bound up in it but we have a sense of self-awareness that gives us the feeling of being special. We perceive ourselves as being different from all other life-forms and in many ways unique and superior. Yet we are not particularly gifted—an elephant can easily outrun us, a fierce dog can overwhelm

was a high ‘brain-to-brawn’ ratio. Information flowing from peripheral sense organs into that complex brain could be processed, the potential consequences of different responses estimated, and then a decision made. Now there was choice and a future of multiple possibilities. The brain could remember, recognize problems, solve them by abstract thought and learn from experience.

us. We can’t see in the ultraviolet or infrared, we don’t

have night vision, we can’t hear low or high frequencies, we can’t smell or taste minute concentrations of molecules,

nor detect magnetism—yet many other organisms can. So physically there is nothing that distinguishes us. But we do have a large brain, an organ that has more than compensated for our deficiencies in physical prowess. With that brain we have created technology, which has enabled us to extend with machines the range of our sensory acuity and physical strength, beyond anything known in the biological world. The survival strategy of our distant hominid ancestors

Organizing the World However long ago consciousness emerged, it was accompanied by a desire to ‘make sense’ of the world around, for the human brain has a need to create order out

of chaos. To those early men for whom there was no causal basis for daily events, life must have been chaotic; and

accompanying chaos is terror. By creating order in the surrounding environment, early man had some hope of predicting and controlling the cosmic forces impinging on his life. Those early people had to be keen observers,

because for them this meant the difference between survival and death, and they must have accumulated a large body of knowledge based on their observations and beliefs. However fantastic to us their explanations for the rise and fall of tides, the seasons, day and night, animal migrations, illness or death may seem, for them the explanations worked, providing a causal basis and a significance to all events. Even earthquakes, floods, diseases and accidents

could be explained by invoking supernatural forces. The need for order resulted in “‘worldviews’—complete explanations of the entire universe in which everything was intimately linked. Thus the occurrence of an extraordinary event, such as the birth of a severely defective child, an eclipse or an earthquake, marked a conjunction of all the cosmic forces. Such occurences then had to be seen as the consequences of past events or as portents of future ones. Worldviews provide explanations for everything (although gods usually are a big fudge factor). Mythology is the codification of that body of knowledge. Of course, mythology is an amalgam of superstition, close observation and a great deal of folk wisdom. North American Indians knew they should consume foxgloves for certain ailments, although it took scientists to characterize the active ingredient as digitalis for heart problems. South American Indians poisoned fish with extracts of plant roots that are only now known to yield curare. Ancient Chinese acupuncturists could control pain without knowing that they were stimulating the release of endorphins in the brain.

The Role of Information The father of modern science, Francis Bacon, observed in

the seventeenth century that ‘knowledge is power’ and so it has been ever since human brains began to process information. Information, knowledge, experience, could

be stored in the brain as memory, retrieved at will and transmitted from individual to individual and from generation to generation. Special knowledge gave individuals like the shaman power over others, provided groups of people like priests with influence over other classes, gave One nation an advantage over another. Information has always been a vital commodity in the strategy for human survival and the existence of power élites within societies but much of it was bound up in superstition and fantasy. ‘Once there was only god, Ymir. And from his skull, the world was created. From his hair, the plants; from his tongue, the oxen; and man came forth from his CVCSs This incredible Norse creation-myth is no more remarkable than hundreds of myths from other societies. Here is another. ‘Once all matter in the entire universe was contained in a point. Matter as we know it didn’t exist, time had no meaning, nor was there space. Then, fifteen billion years ago, that point exploded and boiled out into

space as hundreds of new states of matter appeared from nothing and disappeared into nowhere. And as the universe grew, gradually clots of dust coalesced into a ball that burst into flame, lumps of matter circled such fires, and life appeared on one of them where none existed before.’ Is this ‘creation story’, told by scientists, any less fantastic than the Norse myth? Of course not. Yet this one we ‘believe’ while the others we dismiss. Why?

The Rise of Modern Science During the time of the ancient Greeks a new spirit of questioning arose, a faith in the ultimate power of the human intellect. The Greeks accepted nothing and questioned everything, laying to rest many mystical explanations of the world around them. In the process, they laid the foundations for the twentieth century. When the Renaissance breathed new life into open enquiry, the stage was ready for the explosive force of a new way of knowing—science. Science did not set as its goal a new worldview. Instead, scientists recognized that they couldn't explain such an immensely complex universe in its totality. Theirs was a far more modest task, to focus on a small part of nature, to isolate it from everything else, and to learn as much about it as possible. This meant reducing parts of nature to their smallest or simplest level. And remarkably,

this reductionist approach provided powerful new insights into those isolated parts. The great success of science was in limiting its field of vision to a narrow sphere. This knowledge provided power, power to interfere, to manipulate, and ultimately to control. Science arose within a Western worldview in which Man was seen to be the pinnacle of all life, created in the image of God. Ours was the mandate to fill the earth and dominate all of nature; and so progress came to be measured by the degree to which we controlled nature. As the power élites of religion recognized the challenge of scientific insight, they chose to fight. Galileo, Darwin, Freud and Einstein were the eventual victors over the forces of dogmatism. Having lost faith in religious doctrines, people turned increasingly to the possessors of scientific knowledge for truth. But science can never provide a worldview—by its very methodology, it is incapable of it. Limits to Science

In this century, scientists themselves began to realize an unsettling fact, that the goal of finding absolute truth was impossible. Where Isaac Newton had once viewed the universe as a gigantic clockwork mechanism, ultimately knowable through the power of science, now relativity suggests that truth may depend on our point of view. In any scientific experiment, the act of observation perturbs the observed so that we can never ‘know’ it as it is in its natural state. And even at the level of subatomic particles,

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behaviour can only be predicted as a statistical probability, not as an absolute certainty. Scientists also began to realize that it is not possible, by understanding properties of matter at one level, to predict or extrapolate to a more complex level. Thus information about subatomic particles informs us very poorly about how atoms behave. Knowledge about single atoms does not generate predictions about their activity in molecules. This is true at higher levels of complexity, from the components of cells, multicells and individuals, to groups and ecosystems. Our knowledge of how single neurons work in the brain is of little or no help in treating a psychotic person or coping with loneliness. In a world of human values, science is singularly incapable of answering the most important questions—about what is right or wrong, the differences between good and evil, the

significance of murder or love.

Technological Power Yet the output of our brains in the form of science and technology has taken us to a position of global dominance in a startingly short period of time. Indeed to some we seem like a feral species, newly introduced to an environment and out of biological control. We are now the most numerous large mammal on the planet and we are ubiquitous. Perhaps the most astonishing achievement of our species has been the invention of a technology, namely

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the computer, that has the potential to be even more creative and powerful than our own brains. To the philosopher who once suggested that the brain is too complex ever to understand itself must be added the cautionary note that it may have created something so much faster and potentially so much more powerful, that it will transcend the brain and decipher it. Today we live in a period of social change accelerated by scientific insight and invention. Where once pottery, metal, needles or dyes heralded social revolutions many centuries apart, noW multiple revolutions occur within a single lifetime. Anyone over the age of 40 has already witnessed the introduction of plastics, television, jets,

satellites, computers, lasers, tranquillizers, recombinant DNA, oral contraceptives, nuclear power and organ transplants. To-day’s youth will spend most of their adult lives in the 2/st century and will take for granted what we now regard as science fiction. The key to this revolution is, as at the dawn of human consciousness, information, and nowhere is it more

profound than in our understanding of information in genes, brains and computers. As we acquire knowledge in these areas, we will also gain in manipulative power and control. But who will have access to that knowledge, and how will it be used? Have we learned from history the limitations of scientific reductionism and the concentration of knowledge in a power élite? Can we go on applying fragmentary knowledge to affect entire groups or ecosystems?

Limits to Technology The rapidity with which modern technology has developed now threatens all life on the planet. Powerful machines can ‘harvest’ natural resources like oil and gas, trees, fish, soil

and water in vast quantities; but a side effect is the industrial toxins that now poison the air, water and earth and so devastate portions of the ecosystem that they may never recover. Nuclear technology has become so powerful, accurate and fast that it lies beyond the human capacity to respond. We regard the dinosaurs as losers because they suddenly disappeared, yet they flourished for 150 million years. We haven’t been here for a million years, yet already we are changing the planet as explosively as in the period when the dinosaurs disappeared. We must resist the temptation to be mesmerized by our technological success. Where once our brains served to compensate for our lack of physical strength, that ability coupled with technology can now become counterproductive. For we continue to apply technology as if we were still under the same survival imperatives as our huntergatherer predecessors; but it is a ‘brute force’ technology that is neither subtle nor cognizant of natural boundaries established by millions of years of evolution. This struck me one summer when I spent time with the San People of the Kalahari Desert, one of the last group of huntergatherers on the planet. I appeared suddenly in their midst with all of the paraphernalia of an industrial civilization— deen eens

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planes, film, canned goods, camping gear. They had never seen television, a refrigerator or a computer, yet they are the remnants of a culture that has lived in equilibrium with the environment for tens of thousands of years. Much to their amusement I wasn’t able to crack open the mongongo nut on which they depend, nor could I read the signs that told of the kudu that had passed by a few hours before. They could survive easily with just their wits. I had the power to radically alter their surroundings, but wouldn’t last long even with my support-technology because it and I were not in harmony with that environment. Intoxicated with our achievements, have we lost sight of what it’s all for and of our own place in the natural order?

The Flaw in Science To the San People, survival depends on an understanding of nature far more sophisticated and profound than we can ever achieve with our analytic tools of science. That is because the great strength of science is also its weakness. By looking at nature in bits and pieces, our understanding of it can only be fragmentary, for nature is not the sum of its isolated parts. Components of ecosystems interact in ways not predictable by separate knowledge of each component. Too often the history of modern science has been the derivation of insights which, when applied through technology, have unexpected and often unpredictable effects. In focussing on problems amenable SSS

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to analysis and solution, we can never encompass the larger context within which that problem is important. For people living within a different worldview, with a different perspective from the scientific and technological approach of the West, the linearity of our thinking must be puzzling. To an Amazonian Indian, our system of plant classification would be as mystifying as it is useless compared to his, which is based on seasons, habitat and edibility. To the North American Indian who asks forgiveness before taking the life of an animal, the spirit world is as real as the atom is to us. In the world of science,

although its practitioners are first and foremost human, there is no equation for emotions or things spiritual, yet it may be just those aspects that are vital to prevent this great enterprise from taking us into insurmountable difficulties.

Many Realities Like all other organisms, we have the ability to receive information about the world through our sensory apparatus. That information is far from complete. We also have the ability to filter out, from among the many inputs, the signals that we deem important. The filtering mechanisms are conditioned by handwiring (inborn neural circuitry) and learning-through-experience. Thus, we create reality, and that reality is highly personal. Science only knows through a restricted set of tools that provide repeatable, verifiable observations and results; but when

reality is a construct of personal heredity and experience, there is much that cannot be validated by scientific methods. That is why scientific pronouncements often elicit a sense of discomfort, because they seem to deny a large part of our own spheres of reality.

The Search for Answers Since the earliest days of human consciousness, we have sought to know who we are, how we got here, why we’re here and where we’re going. Now science and technology add insight to the answers, helping us to eliminate superstition and misconceptions, but also giving us a picture that is uncomfortably incomplete. We have to retain a sense of mystery, wonder and awe at the forces of nature and at the enormous variety of human perceptions. Only then can we balance the illusion that our technology is so powerful that nothing lies beyond its reach, and that all of nature, including human nature, can be wrestled under our control.

Historical Puzzles

Human beings have been gifted with the ability to communicate through systems of images, from prehistoric paintings to pictographs to abstract characters of language. You are about to embark on an adventure that continues that long tradition.

This book gives us a peek at the long history of human inventiveness in print and calculation. Many of the symbols and devices shown are still opaque to our understanding. That of course is why they fascinate. What motivated people in so many cultures in the past to invest so much time, thought and effort to construct the puzzles that remain to-day? It is a tribute to the human spirit and imagination that they should leave such artifacts for us to ponder. Some, in the chauvinism of the contemporary, seem to find it impossible to accept that people in the past could have been as clever as we, and therefore postulate visitors from outer space who must have provided the intelligence. It is the height of arrogance to think that because we can’t figure out some things, people in the past couldn’t have done so either. We think of computers as recent inventions. While the silicon chip of a modern computer is certainly a recent arrival, the roots of this technology go back long before transistors and vacuum tubes, before electricity, indeed before recorded history. Now, when the scientists living

today comprise over ninety percent of all the scientists who have ever lived, there is a tendency to think that our Own generation has a virtual monopoly in the history of intelligence. In terms simply of population numbers, there may be more ‘smart people’ around today than at any time before but, in terms of creative imagination and the quality of thought, many ancient cultures were fully as perceptive as our own. Their philosophers and scientists were every bit as ‘smart’ as ours. Today there is so much information available that a budding scientist must focus early and intensely to reach the cutting edge of research. Too often that will be at the expense of a historical appreciation. This book should help to correct that deficiency, giving us an inspiring view of the vast sweep of human creativity, and putting modern science into perspective, as we consider the reach of a long and wonder-woven story. Daigs:

Pebbles... Everyone picks up and examines pebbles from time to time. Perhaps the fascination lies in the smoothness, or in beautiful markings. But there is something else about a pebble, which maybe stirs us more profoundly.

A pebble is an entity. It is one of the simplest, most familiar things that demonstrate a unity. After all, if we had a pebble that was rather flat or worn down at one end, it would not be tempting to say: this is really only nine-tenths of a pebble. No, a pebble marks itself off from everything else—to be ITSELF. In that case, it is remarkable that no two pebbles out of billions are alike. This apparently simplest and most familiar of things turns Out to be quite an abstract concept! The abstraction derives from ignoring the specific shape, the peculiar colouring, of any particular pebble. We pass from that physical unity, to the notion of a unit—any unit, as typified by any pebble. But that unit still constitutes a mark that makes a distinction.

All computing is based on this idea.

There was an early start to it all. For example, let’s go back to the early years of Athenian democracy. That is a journey in time of roughly two-and-a-half thousand years. The meeting of the people, the ecclesia, held ballots. As the voters passed by the tellers, each person cast a pebble into the pot that indicated his preference. So now the pebble, the mark that draws a distinction, stands for the voter’s preference itself—and the pebbles may be counted.

The ballots were called wypor, the very word for ‘pebbles. Any subsequent democratic decree drew on that root again, to be

called whdtope. Transliterating the Greek to Roman letters, we get psephoi and psephisma.Small wonder then that academic commentators who appear on television at election time to talk of ‘swings’ this way and that are called ‘psephologists’. They are students of the way the pebbles are falling. They need computers to do it.

Digging around in pots of pebbles and counting all day long: it would be a tedious way of doing arithmetic, or even of storing information... The photograph shows a reconstruction by Rudi Haas of an early pebble computer. There are only four significant pebbles on the sand, one in each of the rings. As the diagram shows, each ring represents an order of magnitude—it shifts the register, times ten. It is often said that nothing much could happen in computation until the invention of ‘places’ in a row to indicate that times-ten register. Thus we recognize that the ‘one’ in the expression ‘1776’ stands for one thousand, because it is three places in from the right. Multiplying, or even adding, MCVIII and CCCLIX would not be much fun, because Roman numerals have no system of ‘places’. But the ancient pebble computer achieves the same effect concentrically.

10 Again, it is often said that computation relies heavily on the invention of the zero—the ‘nought’ that marks the skipping of a place. Thus ‘1006’ means a thousand and six, and not sixteen. Again, Roman numerals have no zeros, since they have no ‘places’ to leave empty. But the pebble computer needs no zero. These two diagrams show why not. The act of displacement to the next higher ring knocks off a nought. Follow the examples, always clockwise.

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The Red Thread That Connects the pebble computer to this modern disc-storage device travels far through space and time—and technological distance too. Yet always we are dealing with the same fundamental ideas. If you worked at the 6x4 multiplication example, you will have realized that pebble computers did not ‘know their tables’. Was it disappointing to find that six was being added to six, four times over? It should not be—for that is exactly how your pocket calculator does the trick! The computer disc records its ‘pebbles’ in a spiral space. It reads its record by radial as well as spiral movements of its tracking arm. It has a memory made accessible in two dimensions. So has the pebble computer: you can read ‘1986’ above without counting nearly two thousand positions to see what is in each one. We continue to use the disc idea for exactly the reason that the man we imagined did not want to sift through pots of pebbles all day long. Mind you, this shining disc records the equivalent of thirty million pebbles —which is just as well.

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proposes clear links between the pebble and the computer. The pebble is a discrete unit—a self-contained entity. As soon as we begin to compute with it, the point is simply whether or not the pebble is there in a given position and, if so, how to find it. Is it in the voting pot, or not? Is it in the sand or magnetic disc, just bere, or not?

packaging: it puts connexion back—and in an overriding role— as a guide to the book itself.

But there are other links; and this thread cannot claim to be

unique. Threads connote connexion, a concept that is nearly lost to our neatly packaged existence...

There is a thread, the picture says, that links the cosmos—the whole of everything, whatever that may be—to us humans who partake of it. We ‘live’ the cosmos in various ways; surely one way is by observing it. Our observations help make the cosmos what it is: we select and direct and magnify and distort and suppress all our perceptions of it. In turn we become what it

e We have packaged physics and packaged chemistry, just as if God knows the difference between them. We have packaged health and packaged education, as if it were not the same person who is well and literate, ill and illiterate,

or any other combination between those two. e We packaged genes into well-favoured food plants, the nutrients to go with them, the pesticides to protect them...and lost sight of the multiple connexions to the rest of life. So there are dust-bowls, depleted gene-pools, and strains of pests that can survive almost anything— even to the radiation of nuclear war, the scenarios for which have lost all track of their connecting threads. For example, when the world’s leaders crawl out of their bunkers, who will they find to bury all those dead?

declares, because we have ‘observed’ the cosmos to contain, not

to exclude us. Then we may recognize the patterns, the design, that we have put there: the picture shows the double reinforcement of that basic loop. A view that once was ‘mystical’ is NOW centred in contemporary science. ¢ These ideas are firmly set in modern physics, in leading discoveries of the neurosciences, in arcane areas of

epistemological research. This basis lends high credence to the attitude to life that flows from this picture, and this account of it. Our age often complains about ‘alienation’. Workers are supposedly alienated from the

Large thoughts have soon invoked a purpose belied by so small a book. The idea of connexion is central to it, and that is

product of their labour, and children from their parents. People are alienated from the society of which they are supposedly a part. Some are audacious enough to count themselves alienated from God: the audacity springs from adding ‘if there is one’. But, says the picture, we CANNOT be alienated from the cosmos whose children we are. e Amen to that. Let’s get on with the book.

exemplified by a Thread. And since there is not one thread, but a thousand, some choices have to be made. The book’s coherence its thread that connects, derives from the selection of

photographs and the relationships recognized between them. These in their turn are no more than exemplifications of the hidden thread drawn forth in the facing picture. The picture is meant as some kind of antidote to the dis-ease resulting from

19

COURTESY

NRAO/AUI Observers: Richard A. Perley and Anthony G. Willis

this is SPACE RADIATION— power exploding in distant darkness No optical telescope ever saw this image. The photons that generated it had to be collected by radio telescope, the measurements obtained being enhanced and composed into a picture by computer. Photons are small particles of energy, travelling with the speed of light. But they are measured as waves, and these are perhaps three centimeters long. They take some catching! The wavelength does not belong in the visible spectrum, and it is much shorter than most of the wavelengths belonging to the radio frequencies that broadcast to our homes. But the radio telescope can operate all the time, not just at night.

...everything begins with transmissions of Energy...

And this? Some might agree to call it GODHEAD RADIATION— power transmitted in creating man. Whether for you it represents myth or reality, this mighty image is well-known. It shows God and Adam, painted on the vault of the Sistine Chapel in Rome. Michelangelo was a sculptor first, perhaps, so that his paintings look as though they were wrought by chisels: monumental.

In any case, the resemblance to the facing page is there; resembles too HEALING RADIATION— power transmitted by LOVE. —whether we think of miracles or medicine, nurture or nursing, the touch of loving hands—

or of Steven Spielberg’s Extra-Terrestrial E.T. the fascinating ‘alien’ with the healing touch whom children will remember. And now this...

Courtesy Canadian National Research Council

CANADARM RADIATION— power transmitted in nearer space. This is a photograph of a painting depicting the manipulative system made in Canada for the U.S. Space Shuttle. The ‘radiation’ in this case is the artist’s way of showing how the joints move— to handle satellites for instance in and out of the shuttle’s cargo bay: a transmission of energy indeed. There are four ‘spaces’ indicated on these pages... and always one outstanding image.

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For those who find computer-composed images somewhat unreal, here is a ‘proper’ photograph! It was taken from an optical telescope at the Mauna Kea observatory in the clear thin air of an Hawaiian mountain top—exposure time: one whole hour. This shows the famous spiral galaxy M51, called ‘The Whirlpool’ Here is the debris of a mighty celestial explosion—bridged by the interaction of their gravitational fields to another, attendant,

galaxy. Despite the immense distance involved, it is possible to see this galaxy with field-glasses. The red spots in the spiral arms are emission nebulae; the blue spots are clusters of brilliant blue stars. Spiral patterns such as this are everywhere in nature— down to snails and fircones and the molecules of DNA

that carry our genetic codes. Just now we spoke of radio telescopes, however. We noted that they work around the clock ‘catching photons’ from the wavelengths that the eye cannot see...

adian National Research Council e/Hawaii telescope on Mauna Kea, Hawaii

d Thompson, Univ. of Hawaii

thus we find ourselves 22

by a Thread

Here is the Algonquin radio-telescope at Lake Traverse, Ontario, that does just that. The film exposure this time was short enough, but it took all day to capture the image of these spiral arms. The spirals here are absolutely NOT visual images of the galaxy! They are artefacts caused by the shape of the dish aerial, reflecting local light. So why are these reflections also spiral?

The reason is that the dish’s shape is paraboloid—quite like an average bowl, and the ‘arms’ we see are therefore parabolas. It is easy enough to understand the nature and purpose of the paraboloid.... The telescope’s job is to collect photons, and they are arriving in parallel streams. Then they have to be concentrated on a single point. Think of these particles as tennis balls. Those hitting the dish at the bottom will bounce straight upward; those hitting the side will bounce into the centre at an increasing angle. The paraboloid is the curve on the bowl for which this is [fue

to the Cosmos

which displays energy flow—

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the Thread follows a coincidence of images...

the Algonquin telescope undergoes the metamorphosis of night

...and the thrust of both energy and information into and out of the sky

pause for reflection...

With what temerity did the previous page aver: the Thread follows a coincidence of images. What does ‘coincidence’ really mean? Literally it means ‘happening together.’ Well, obviously the pictures do that much, because they are printed adjacently— as a result (we said it before) of deliberate selection. But when we say ‘coincidence’ we usually mean that something strange seems to lie behind the literal happenstance. How strange does such a WOW’ coincidence have to be? The ancient computer distributed its pebbles over a disc of sand, just as the modern computer stores its bits over a magnetic disc, where ‘just as’ means that information retrieval is made easier. So there is ‘an explanation’. Next we saw energy being transmitted through a pivotal point: but is it so surprising that this happens in four kinds of space? Two of these are distance-spaces. We made the hundred miles or so orbit of the shuttle seem relatively near by speaking first of galactic distance, and reinforcing that immensity with the image of the spiral nebula. The inner spaces of identity, in creation, and of love, in healing, are perhaps fancifully portrayed as matching arms and pivots. But if these are ‘merely’ fanciful, why do they so commonly occur? The example of energy flow is surely the easiest to handle.

The Fraser River flows downhill, following the path of least resistance. Although men built the Alaska Pipeline, they were not so stupid as to do anything else. Thus we had the pleasing mirror-image of the two on the preceding page. Was thata WOW/ coincidence or not? Does the explanation eliminate the WOW’ or not? It does not seem to be a matter of what can be explained away, which is the usual treatment for disposing of coincidences. Perhaps it 7s a matter of what can be explained: the magic may evaporate from the WOW! somewhat, but the explanation always points to the coherence of the cosmos itself—and that is magical in its turn. The status of an explanation is therefore more mysterious than we usually think. Whether the coincidences found in the images of this book are WOW’ coincidences is dependent on the reader’s imagination—but whether the explanations explain or explain away is a matter for deep thought. When we cannot see any explanation at all, the statement in the centre of this page may yield some fruit.

‘coincidence’ may be the inability to see what really matters

Meanwhile, here is a picture of a river delta, taken from a satellite; or perhaps it is a hair follicle; it

could be a micrograph of a polished section of nickel ore; or how about a nerve process at a synapse? Let us not take our coincidences too lightly... In fact, it is number three.

Ly

images of Energy and Information... aspects of the same thing...

That pause for reflection may have been worthwhile. Because what comes now is surely a WOW! coincidence.

The Thread of energy transmission and flow that we have been following leads straight into the world of computation through the connexion of information. This is because energy and information are aspects of the same thing—the name of which is entropy. One way of expressing the shared law of entropy mathematically is this: H = —2pllog,p,.

Light reflecting from the turbine blades that transmit the immense power of the jet engine.

There goes the only mathematical statement in this book. It is given simply to show that the law is quite precise and succinct. The residual value of H measures the energy that is available to achieve work in a given system. Its negative is exactly the amount of information that this same system contains. This is notoriously difficult to understand—and therefore worth the effort!

Information

Take energy first. The formula prescribes a way of calculating the probability (those P,’s) that a total system (that’s the 2) is in the state that it is. The cosmic system itself, and all the systems it contains, are recognizable because their elements are in some special order. The Whirlpool galaxy and the Crab nebula look different because they are ordered differently. The same goes for an oak leaf and a sycamore leaf; that sort of order is called ‘shape.’ A cup of hot coffee and a bow! of ice-cream are differently ordered in terms of their heat. But the orderliness of each example tends to disappear. The galaxies are exploding—one day their debris will be spread out evenly everywhere, and there will be no galaxy left to recognize. Both leaves will rot, and become indistinguishable in the compost. The coffee will go cold, and the ice-cream will melt. All this is because the amount of energy available to keep the orderliness is being gradually used up in so doing. The warmth we put into the coffee and the cold into the ice-cream were both forms of energy (we got it from the electricity supply) which inevitably dissipates into the surrounding atmosphere, until there is no more energy left to maintain the order that characterizes the system. The galaxies have vanished; the coffee is cold; the icecream is runny; the system is dead.

Light reflecting from the tiny microchips of a silicon wafer, which comprise the integrated circuits that transmit vast amounts of information inside the modern computer.

Information flows

To reach the twin topic of information, we sum up first on energy like this: Entropy H expresses the amount of energy still available in the system by saying how much has been used up. Eventually, that figure becomes one: 100% entropy is the death of the system. Well, the orderliness that the energy has been needed to maintain is the mark of whatever is distinctive about a system. The oak and the sycamore leaves are different because of their ‘shape’, we said. To know the shape is to enjoy the information it embodies. When the entropy is low, and energy is therefore available, the leaves remain distinctive. Descriptive information is high. But when the leaves are brown and decaying for lack of energy, their shapes become ambiguous—soon to be indistinguishable. Lukewarm ‘hot’ coffee and ‘ice’ cream are losing the information that identifies them. It turns out like this: processes gaining in entropy are losing information, and vice versa. To maintain high definition of differences, we need a great deal of information. Therefore the entropy must be low—meaning that energy available to maintain orderliness must be high. And this is not just a general outcome. It is as precise as the H formula shows it to be.

So the ‘log,’ element of the H expression has, unsurprisingly, an informational meaning. It is a measure of the number of ‘bits’ (the pebbles!) required to specify the distinctive pattern of the system in question. Information informs us; it in-forms the cosmos we know.

at Frobisher Bay, on Baffin Island, in the

Canadian Arctic, a satellite-signal receives and relays

messages...

using Energy

bringing close loved voices or the news of war

spelling out financial gain and loss from distant markets

telling the lives of people laughing... ... dying in coded streams of neutral data from the dark side

of the Earth

--- MESSaGeS...

carved

... tO be recorded

in stone

and computed with...

Here are our circular storage patterns once again. The stone one is just over five hundred years old, and weighs twenty-four tons. The other is only a tenth of an inch thick, and four inches across—see the facing page.

The Stone of the Sun, now in the Anthropological Museum in Mexico City, records the creation and destruction of four worlds—or earlier eras, called ‘suns’—and both celebrates and

determines the current era, or Fifth Sun, due for destruction by earthquake. Or so it was when dedicated as a sacrificial stone by Axayacatl, ruler of the Aztecs, in the Mexico of the late fifteenth

century. Here is a representation of the cosmos, and of the battle between good and evil; a record of the perceived history of the world, and a prophecy of final disaster. The face of the Sun God Tonatiuh, with his open mouth, is

carved in the centre. His voracious appetite for human hearts would keep him burning to the end. Such seems to have been the fatalistic philosophy of the Aztecs—one necessarily embraced by many thousands of their prisoners of war: Tonatiuh has the tongue of a voluptuary...

or silicon

Everyone by now has surely heard of ‘chips,’ the circuit boards that run modern computers. Well, ‘boards’ is too large a sounding term. A chip is about the size of a little-toe nail. It is almost impossible to believe that a chip may contain thousands of electrical circuits—even a whole micro-computer. So how is it done? Manufacture starts from a very small and pure crystal of silicon. The commonest form of silicon is the stuff on the seashore that we know as sand. Very pure silicon is a very poor conductor of electricity. A good start, you might think! Conductivity is introduced by the imposition of impurities. How big they are determines their electrical function—to be resistors or capacitors or whatever. Micro-electronics this may be: but no one could get a computer circuit onto a grain of sand. The pure crystal is processed at very high temperatures to grow—quite large. Then its rough edges are smoothed. We end up with a cylinder, some four inches in diameter, that can be sliced up like a salami. The slices are called wafers, and those are the four-inch circles on the right.

About two hundred and fifty chips are imprinted on each wafer. ‘Imprinted’ is a good word, because the thousands of circuits are photographed onto the crystal—using chemicals, and masks, and ultraviolet light. The chemicals maintain the non-conductivity of the silicon where it is needed, for layer upon layer of circuits imposed.

the Thread meanders...

... then makes thts basic mark to recognize flat space: the up-and-down slashed by the across Until we met the ‘chip’ on the previous page, our Thread was moving in a linear way: that is to say, like a line. It achieved area—two dimensionality—essentially by continuing the line asa spiral. Although we saw concentric rings, we made little leaps to get onto the next circle: and there was the linear spiral once again.

The chip uncompromisingly slashed up the area, two ways: a mathematician would say ‘orthogonally’, meaning ‘at right angles’. This concept is enormously important in approaching our universe, our cosmos. With orthogonal dimensions, you may proceed in one direction, without moving in another dimension at all.

For example, take a high-rise office block: beautifully described in this night-image as the jewelry it looks less like by day. Step into an elevator; ascend for thirty floors. You will step out, and you have prefigured the floor plan in your mind because the building has orthogonal design.

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What any self-respecting Thread-watcher would like to know is this. How is it that the Thread can move about orthogonally in space—across any one of three dimensions, in fact, without

invading either of the other two—but must in the process necessarily take up time? This fourth dimension seems not to be orthogonal at all. The elevator needs time to go directly up. These are tricky but not irrelevant thoughts. Look first above, at the wiring of an early computer. It reduplicates the dancing, slashing Thread. Those shining copper wires are connected in highly complicated but orthogonal ways. And if anything went wrong with the circuitry, it sometimes took days to disentangle the knitting. Now to the chip again: on the right, a micro-circuit magnified five hundred times. The orthogonality is still in evidence—the jewelry too, perhaps, to the eye of our ‘coincidence’.

But whereas the unit of non-orthogonal time in that early computer was a millisecond, we work in terms of nanoseconds,

at the most, today. Well, in 1950 a millisecond, as a thousandth

of a second, seemed a fast response. But a nanosecond is a thousand millionth—a billionth—of a second. If that is the measure, what can we do ‘in time’? The consequences of all this are astonishing: turn the page...

oy)

the last page says: a nanosecond ts a thousand millionth

of a second

Why should anyone bother about so inaccessible a concept? There are serious reasons.

Nothing can travel faster than light. At the very moment when a particle of matter attains that speed, it turns into light. That’s what happens in the cosmos as understood by Albert Einstein. The speed of light is a limiting factor in that universe. Consider then:

e ina nanosecond light itself moves less than a single foot; ® today we compute in fractions of nanoseconds. So that is exactly why microprocessors became inevitable. Were they not minuscule, light could not traverse the chip ‘in time’. Chips will necessarily grow smaller yet.

another chip...

This in turn explains why, as long ago as thirty years ago, some scientists began to think that biological computers might be constructed to outpace even electronic achievement. At that time it was not clear that transistors themselves would become reliable! Attempts were made to implicate living cells—microorganisms—in computations. In England in the fifties, one such computer solved an equation in four hours that a bright school girl or boy could solve in (maximum) four minutes. Its time had not yet come! Today, biotechnology is taking us into the ultimately small in computation. Called genetic engineering, it recombines long

molecules that constitute the stuff of life. And frightening it is.

Here is another ‘coincidence’ of form, the sides of which are not r TS)

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chip-sized as a toenail. The sides are probably two hundred and fifty metres long. As to the incursion of this spatial array into time: what is left of this construction is about four thousand years old...

This is the plan of a temple labyrinth at Lake Moeris in Egypt that was built by King Amenemhet III (1842-1797 B.C.). The plan was drawn in 1840 by the Italian archaeologist Camina. He based it on descriptions left to us by the Greek historian Herodotus, who went to see it in the fifth century BC, and by others— including the Roman Pliny, who got there five hundred years later. Nearly fifty years after the plan was drawn, the British archaeologist Flinders Petrie discovered and disclosed the actual

site. We see twelve courts, and the designations of three thousand rooms—half of which were above and half below the ground. The tombs of kings were here, and sacred crocodiles...

not another chip, atall...

But there are drawings similar to this, never transformed to massive architecture. In India there are mandalas—pictures conveying sacred insights not expressed in words. Our modern chips may not be sacramentals, but they use no form of words. Come now (someone might protest), we know what the chip does, the functions it performs. So (it should be replied) did the yogis of India, the lamas of Tibet, also understand their own mandalas.

Then what did Amenemhet himself understand by his labyrinthine temple? Surely it was not made like this just to confuse Herodotus and Pliny, late-comers as they were. That would be like saying that chips are really made to fool archaeologists two thousand years from now into thinking that we wore such things as costume jewelry...

the Thread explores a little... The simplest version of the up-down-andacross investigation of flat space is the cross itself, which marks out two

dimensions.

The pattern on the left suggests why the mathematical consequences of exploring a flat space by making crosses tend to create ‘courts’ and ‘squares’—as we saw in palaces and chips, and see in towns.

The Cross, and variants upon it such as the Swastika, were powerful symbols of antiquity—long before they acquired the particular potency that each holds for contemporary culture. There is another way of cutting space in two, of demarcating the up-down-andacross, whereby the across becomes a lintel upheld by two supports—just like a doorway.

Instead of staying with the minimum division of space by two components, we now acknowledge three. This one is a trilithon, meaning (from Greek) ‘threestones’. This element too had potency—and retains it too. For here, on a lonely moor in Western England, folk arrive each year to celebrate

five thousand years of lonely mystery and people-populated magic...

...Of course it is Stonehenge

Older than Amenemhet’s temple by a thousand years, and much more visible today, Stonehenge receives the better part of a million tourists a year. As a result, it is widely known that the axis of Stonehenge pointed to the rising sun on the horizon at the summer solstice—which is the furthest sunrise to the North. ‘The Druids’, so people vaguely think, worshipped this phenomenon. Certainly, moderns clad in white robes, together with many strangers who are mystically inclined, attend Stonehenge (police permitting) on the 21st day of June each year. However, the historical Druids were actually Celts, who did not

appear on the scene for two-and-a-half thousand years after the first circles (starting with a ditch and bank) were begun. The fact seems to be that Stonehenge was both a solar and a lunar observatory. Wonderful scientific work has been carried out, not only by archaeologists but by mathematicians too, onthese megalithic remains. It took some calculating to prove that when the sun rose over the Heel Stone four thousand years ago, exactly half the solar disc would be visible! Professor Thom demonstrated this, and also that four (of five) sets of the trilithons are precisely contained within two significant ellipses. There is an error of only an inch or two after all these years...

When the whole geometry was in position, covering not only the trilithons but the major ring, the only stones that did not fit perfectly were those that had been ‘straightened’ in the last hundred years or so. Taking both age and complexity into account, Stonehenge is probably the most venerable computer still extant. It is difficult to contemplate, surely—everything is so stolid and so static. The ‘pebbles’ of this computer are massive: the trilithon supports weigh fifty tons apiece!

Stonehenge... Computer ‘pebbles’ weighing fifty tons apiece... Let’s think, though, why this should be strange. They do not move. Yet neither does the chip have moving parts. This has become a tale of Relativity. Clocks, and music boxes, and the early kinds of computing machines, have moving parts. They are seen to be ‘computing’. The chip has moving parts we do not see. They are called electrons. These fundamental particles are moving like mad (as we Saw, it’s at the speed of light) to change negative flows to positive and back again—thereby churning out the logic they sustain. This is the micro computer, after all. So what moves at Stonehenge? Ah— Stonehenge is a macro computer. What is moving relatively is the sky. That much is understood. But computers are supposed [ODE ACCUrAaLe 2.7 The answer is exciting. The critical faces of those gigantic stones, the megaliths, were precisely finished. They were polished. Then, from an exact spot, one

might align two polished surfaces across the ring. The sun, when it arose would flash across a tiny chink—at a moment to be recorded with great accuracy. More: the ‘ray’ of the sun that registered this moment would cross the land that stretches to the horizon. This ray would ‘graze’ a mound or hillock on the way. Thom calls these markers ‘foresights’ and ‘backsights’: he has identified points in front and to the rear that might have served. The farthest is nine miles away.

—it can hardly be left at that... Hence one may think of Stonehenge as a computer, maybe twenty miles across— On its major axis. This computer is fixed against the Earth. But it is moved in relation to the sky like a giant telescope—steered by the Earth’s rotation. Some contemporary radiotelescopes work just like this: they have an array of fixed aerials, spread across some miles of terrain.

An image of Stonehenge according to this understanding, seen from the air, would look much like the picture on this page. The central portion with the dark surround stands for the monument we know. Foresights and backsights, and sidewayson-sights (measured from the surrounding ditch and bank) would align features on the local landscape, and on the horizon,

with the sun’s rays at Critical times. You will know well enough by now that this is not an artist’s impression of Stonehenge. It is a photograph of an integrated circuit—a chip—with attachments leading to its carrier frame.

|

At Nazca in Peru gigantic birds and beasts are marked into the ground: they cover more than one hundred square miles. No one can be sure what they mean; but it is

not inconceivable that they also constituted a celestial computer.

If so,

then they record stellar events older than the two-thousand-year-old ceramic relics found in that place. Incredibly, the ancient lines are so straight that even modern air-survey techniques cannot detect deviations—which are no more than two metres in each kilometre.

Below is a section of a standard photograph of one of the Nazca birds, colour enhanced by Hans Blohm—while on the right is a massive enlargement of the integrated circuit’s carrier frame... Et

eee.

evidently

there are other kinds

of THREESOME...

This is Stonehenge’s larger ring, outside the trilithons, part of awhole circle. It is a foursome—because lintels are missing from the adjacent stones. The ones we see in place are held together by mortice and tenon joints—still, to this day, bracketing arcs of the compass, telling the time (and how much more?) within this celestial computer. There were thirty uprights and thirty lintels, in a ring of a hundred-foot diameter. It made an immensely strong structure.

The breaking-up of spaces for engineering use thus becomes the problem of

we started with a single line— threading, spiralling...

func tonal

then we came to

design

two-fold space thence

to trilithons, arrow-heads— now FOURS,

and...

Why foursomes? Each design has its own rationality behind its own aesthetic. Trilithons share the lintel’s weight between two supports. Four props will nearly halve its weight (nearly, because of course there are now three lintel stones instead of two) on each. The gardener below distributes his foot’s thrust over four tines: perhaps he finds this the most effective way of breaking up the soil. Who guessed the chip-carrier frame on the right? (And who said: ‘Chips with Everything’?!) This is the carrier frame.

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There is nothing magical about this number four—beyond the magic that we may discern in any number whatsoever... Humankind has always delighted in the properties of number. If it were not so, we should never have done much with quantities

at all—as we shall shortly see. Meantime, let’s take another pause to spend a final moment at Stonehenge...

STONEHENGE 1973

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