1The formative process is the supreme process, indeed the only one, alike in nature and art.

2Within fifty to a hundred years, a new class of organisms is likely to emerge. These organisms will be artificial in the sense that they will originally be designed by humans. However, they will reproduce, and will evolve into something other than their initial form; they will be “alive” under any reasonable definition of the word.

3In September 1987, the first workshop on Artificial Life was held at the Los Alamos National Laboratory. Jointly sponsored by the Center for Nonlinear Studies, the Santa Fe Institute, and Apple Computer Inc, the workshop brought together 160 computer scientists, biologists, physicists, anthropologists, and other assorted ‘-ists,’ all of whom shared a common interest in the simulation and synthesis of living systems. During five intense days, we saw a wide variety of models of living systems, including mathematical models for the origin of life, self-reproducing automata, computer programs using the mechanisms of Darwinian evolution to produce co-adapted ecosystems, simulations of flocking birds and schooling fish, the growth and development of artificial plants, and much, much more.

The workshop itself grew out of my frustration with the fragmented nature of the literature on biological modeling and simulation. For years I had prowled around libraries, shifted through computer-search results, and haunted bookstores, trying to get an overview of a field which I sensed existed but which did not seem to have any coherence or unity. Instead, I literally kept stumbling over interesting work almost by accident, often published in obscure journals if published at all.

4Throughout the workshop, there was a growing sense of excitement and camaraderie — even profound relief — as previously isolated research efforts were opened up to one another for the first time. It quickly became apparent that despite the isolation we had all experienced a remarkably similar set of problems, frustrations, successes, doubts, and visions. Even more exciting was that, as the workshop progressed, one could sense an emerging consensus among the participants — a slowly dawning collective realization of the “essence” of Artificial Life.

5Although I think that none of us could have put it into words at the time, I think that many of us went away from that tumultuous interchange of ideas with a very similar vision, strongly based on themes such as bottom-up rather than top-down modeling, local rather than global control, simple rather than complex specifications, emergent rather than prespecified behavior, population rather than individual simulation, and so forth.

Perhaps, however, the most fundamental idea to emerge at the workshop was the following: Artificial systems which exhibit lifelike behaviors are worthy of investigation on their own rights, whether or not we think that the processes that they mimic have played a role in the development or mechanics of life as we know it to be. Such systems can help us expand our understanding of life as it could be.

By allowing us to view the life that has evolved here on Earth in the larger context of possible life, we may begin to derive a truly general theoretical biology capable of making universal statements about life wherever it may be found and whatever it may be made of.

6Thus it was into a rich cauldron of revolutionary ideas that the announcement of a workshop on “Artificial Life” dropped in 1987. Even though I had nothing to present, I managed to scrape together enough funding to attend. The experience was eye-opening. Here was an entire burgeoning field that shared some of my misgivings about classical AI, my increasingly biological perspective on cognition, and my intuition that these ideas could be explored through computer simulation.

7exploring the wild frontier, unencumbered by staid disciplinary boundaries, more Burning Man than Royal Society

8AL attempts to look beyond the collection of naturally occurring life in order to discover things about that set that could not be discovered by studying that set alone. AL isn’t the same thing as computational biology, which primarily restricts itself to computational problems arising in the attempt to analyze biological data, such as algorithms for matching protein sequences to gene sequences, or programs to reconstruct phylogenies from comparisons of gene sequences. Artificial life reaches far beyond computational biology. For example, AL investigates evolution by studying evolving populations of computer programs — entities that aren’t even attempting to be anything like “natural” organisms.

Many biologists wouldn’t agree with that, saying that we’re only simulating evolution. But what’s the difference between the process of evolution in a computer and the process of evolution outside the computer? The entities that are being evolved are made of different stuff, but the process is identical. I’m convinced that such biologists will eventually come around to our point of view, because these abstract computer processes make it possible to pose and answer questions about evolution that are not answerable if all one has to work with is the fossil record and fruit flies.

9Physics has largely been the science of necessity, uncovering the fundamental laws of nature and what must be true given those laws. Biology, on the other hand, is the science of the possible, investigating processes that are possible, given those fundamental laws, but not necessary.

10The demonstration of a purely logical living system, existing only in an abstract mathematical world, is the goal that Chris and others are working toward. If they succeed, then we will have a new and profound understanding of life.

11A reporter once asked me how I would feel about my children living in an era in which there was a lot of artificial life. I answered, “Which children are you referring to? My biological children, or the artifactual children of my mind?” — to use Hans Moravec’s phrase. They would both be my children, in a sense.

12I believe the day must come when the biologist will—without being a mathematician—not hesitate to use mathematical analysis when he requires it.

13Must we then give up fathoming the depths of life? Must we keep to that mechanistic idea of it which the understanding will always give us—an idea necessarily artificial and symbolical, since it makes the total activity of life shrink to the form of a certain human activity which is only a partial and local manifestation of life, a result or by-product of the vital process? We should have to do so, indeed, if life had employed all the psychical potentialities it possesses in producing pure understandings—that is to say, in making geometricians. But the line of evolution that ends in man is not the only one.

14The organized elements composing the individual have themselves a certain individuality, and each will claim its vital principle if the individual pretends to have its own.

15Of phenomena in the simplest forms of life, it is hard to say whether they are still physical and chemical or whether they are already vital. Life had to enter thus into the habits of inert matter, in order to draw it little by little, magnetized, as it were, to another track. The animate forms that first appeared were therefore of extreme simplicity. They were probably tiny masses of scarcely differentiated protoplasm, outwardly resembling the amoeba observable to-day, but possessed of the tremendous internal push that was to raise them even to the highest forms of life.

16Living things are made of the same chemical elements as minerals; a living being is the arena of the same physical forces as those which affect the inorganic world.

17The passage from animate to inanimate is gradual and insensible. The step between a stalagmite and a polyp is less than that between a polyp and a man, and even the trained biologist is often at a loss to determine whether a given borderland form is the result of life, or of the inanimate forces of the mineral world.

18A living being is a transformer of matter and energy, both matter and energy being uncreateable and indestructible, i.e. invariable in quantity. A living being is only a current of matter and of energy, both of which change from moment to moment while passing through the organism.

19The essential character of the living being is its Form. This is the only characteristic which it retains during the whole of its existence, with which it is born, which causes its development, and disappears with its death. The task of synthetic biology is the recognition of those physico-chemical forces and conditions which can produce forms and structures analogous to those of living beings.

20Just as synthetic chemistry began with the artificial formation of the simplest organic products, so biological synthesis must content itself at first with the fabrication of forms resembling those of the lowest organisms.

21The synthesis of life, should it ever occur, will not be the sensational discovery which we usually associate with the idea. If we accept the theory of evolution, then the first dawn of the synthesis of life must consist in the production of forms intermediate between the inorganic and the organic world, forms which possess only some of the rudimentary attributes of life, to which other attributes will be slowly added in the course of development by the evolutionary action of the environment.

22I wrote this book in wartime, and its revision has employed me during another war. It gave me solace and occupation, when service was debarred me by my years.

23Cell and tissue, shell and bone, leaf and flower, are so many portions of matter, and it is in obedience to the laws of physics that their particles have been moved, moulded and conformed. They are no exceptions to the rule that God always geometrizes.

24To treat the living body as a mechanism was repugnant, and seemed even ludicrous, to Pascal; and Goethe, lover of nature as he was, ruled mathematics out of place in natural history. Even now the zoologist has scarce begun to dream of defining in mathematical language even the simplest organic forms. When he meets with a simple geometrical construction, for instance in the honeycomb, he would fain refer it to psychical instinct, or to skill and ingenuity, rather than to the operation of physical forces or mathematical laws; when he sees in snail, or nautilus, or tiny foraminiferal or radiolarian shell a close approach to sphere or spiral, he is prone of old habit to believe that after all it is something more than a spiral or a sphere, and that in this “something more” there lies what neither mathematics nor physics can explain. In short, he is deeply reluctant to compare the living with the dead, or to explain by geometry or by mechanics the things which have their part in the mystery of life.

25In our own day the philosopher neither minimises nor unduly magnifies the mechanical aspect of the Cosmos; nor need the naturalist either exaggerate or belittle the mechanical phenomena which are profoundly associated with Life, and inseparable from our understanding of Growth and Form.

26How far even then mathematics will suffice to describe, and physics to explain, the fabric of the body, no man can foresee. It may be that all the laws of energy, and all the properties of matter, and all the chemistry of all the colloids are as powerless to explain the body as they are impotent to comprehend the soul. For my part, I think it is not so. Of how it is that the soul informs the body, physical science teaches me nothing; and that living matter influences and is influenced by mind is a mystery without a clue. Consciousness is not explained to my comprehension by all the nerve-paths and neurones of the physiologist; nor do I ask of physics how goodness shines in one man’s face, and evil betrays itself in another. But of the construction and growth and working of the body, as of all else that is of the earth earthy, physical science is, in my humble opinion, our only teacher and guide.

27Some physicists declare, as Maxwell did, that atoms or molecules more complicated by far than the chemist’s hypotheses demand, are requisite to explain the phenomena of life. If what is implied be an explanation of psychical phenomena, let the point be granted at once; we may go yet further and decline, with Maxwell, to believe that anything of the nature of physical complexity, however exalted, could ever suffice. Other physicists, like Auerbach, or Larmor, or Joly, assure us that our laws of thermodynamics do not suffice, or are inappropriate, to explain the maintenance, or (in Joly’s phrase) the accelerative absorption, of the bodily energies, the retardation of entropy, and the long battle against the cold and darkness which is death.

28The terms Growth and Form, which make up the title of this book, are to be understood, as I need hardly say, in their relation to the study of organisms. We want to see how, in some cases at least, the forms of living things, and of the parts of living things, can be explained by physical considerations, and to realise that in general no organic forms exist save such as are in conformity with physical and mathematical laws. And while growth is a somewhat vague word for a very complex matter, which may depend on various things, from simple imbibition of water to the complicated results of the chemistry of nutrition, it deserves to be studied in relation to form: whether it proceed by simple increase of size without obvious alteration of form, or whether it so proceed as to bring about a gradual change of form and the slow development of a more or less complicated structure.

29Wherever we have a true cellular complex, an arrangement of cells in actual physical contact by means of their intervening boundary walls, we find these general principles in force; we must only bear in mind that, for their easy and perfect recognition, we must be able to view the object in a plane at right angles to the boundary walls. For instance, in any ordinary plane section of a vegetable parenchyma, we recognise the appearance of a ‘froth,’ precisely resembling that which we can construct by imprisoning a mass of soap-bubbles in a narrow vessel with flat sides of glass; in both cases we see the cell-walls everywhere meeting, by threes, at angles of 120°, irrespective of the size of the individual cells: whose relative size, on the other hand, determines the curvature of the partition-walls.

30The bee makes no claim to skill in mathematics; but the mathematician has much to learn from the bee’s honeycomb.

31The engineer, who had been busy designing a new and powerful crane, saw in a moment that the arrangement of the bony trabeculae was nothing more nor less than a diagram of the lines of stress, or directions of tension and compression, in the loaded structure: in short, that Nature was strengthening the bone in precisely the manner and direction in which strength was required; and he is said to have cried out, ‘That’s my crane!’

32An organism is so complex a thing, and growth so complex a phenomenon, that for growth to be so uniform and constant in all the parts as to keep the whole shape unchanged would indeed be a much harder thing to understand than the most widespread and remote departures from such a condition.

33For the harmony of the world is made manifest in Form and Number, and the heart and soul and all the poetry of Natural Philosophy are embodied in the concept of mathematical beauty.

34Faced with the problem of life’s origin, modern natural science is called upon to draw a correct picture of the consecutive evolution of matter which led to the appearance of the first living beings, to analyze the individual stages in the historical development of matter on the basis of scientific fact, and to lay bare the laws which consecutively appeared in the process of evolution and ushered in life.

35When I first turned to the study of the problem of life’s origin — some thirty years ago — the question of the primary formation of organic substances seemed a mystery which defied investigation and understanding. For direct observations of our natural environment showed that the vast mass of the organic substances of the animate world now originates on the Earth as a result of the vital activity of organisms. Living green plants, absorbing inorganic carbon from the air, produce from it with the use of solar energy the organic substances they require. Animals, fungi, bacteria, and other organisms which are not coloured green obtain the necessary organic substances by feeding on plants or by decomposing their bodies and remains. In this manner, the entire modern living world owes its existence to this process of photosynthesis or the analogous process of chemosynthesis. Moreover, even all the organic substances which are deposited in the bowels of the Earth in the form of peat, coal, and oil also for the most part originated as a result of the vital activity of numerous organisms that once inhabited the Earth and were later interred in the Earth’s crust.

36Early in the nineteenth century it was erroneously thought that complex organic substances which make up the bodies of plants and animals — various sugars, proteins, fats, etc. — can only be extracted from living beings, while their artificial production is entirely out of the question. A laboratory synthesis of these substances was held to be inconceivable, inasmuch as organic substances, it was believed, were formed only in living beings by a certain ‘vital force’. However, extensive investigations by organic chemists of the 19th and 20th centuries did away with this prejudice. At present, by making use of hydrocarbons and their elementary derivatives, we can obtain by chemical means substances typical of organisms, such as various sugars, fats, numerous vegetative pigments, alizarin, indigo, substances which colour flowers, fruits, and berries, substances which lend them taste and fragrance — various terpenes, tannins, alkaloids, india-rubber, etc. In recent times even such complex and biologically extremely active compounds as vitamins, antibiotics, and certain hormones, have been obtained. Thus, ‘vital force’ has been banished from scientific usage, and it has been proved beyond any shadow of doubt that all the substances which make up the bodies of plants and animals can be obtained from non-living nature, independently of life.

37From the point of view of philosophy of science the conception associated with entropy must, I think, be ranked as the great contribution of the nineteenth century to scientific thought. It marked a reaction from the view that everything to which science need pay attention is discovered by a microscopic dissection of objects.

38UNTIL about 150 years ago it was generally believed that living beings were constantly arising out of dead matter. Maggots were supposed to be generated spontaneously in decaying meat. In 1668 Redi showed that this did not happen provided insects were carefully excluded. And in 1860 Pasteur extended the proof to the bacteria which he had shown were the cause of putrefaction. It seemed fairly clear that all the living beings known to us originate from other living beings.

39“The large and important and very much discussed question is: How can the events in space and time which take place within the spatial boundary of a living organism be accounted for by physics and chemistry? The preliminary answer which this little book will endeavor to expound and establish can be summarized as follows: The obvious inability of present-day physics and chemistry to account for such events is no reason at all for doubting that they can be accounted for by those sciences.

40Thus we have come to the conclusion that an organism and all the biologically relevant processes that it experiences must have an extremely ‘many-atomic’ structure and must be safeguarded against haphazard, ‘single-atomic’ events attaining too great importance.

41The non-physicist cannot be expected even to grasp, let alone to appreciate, the relevance of the difference in ‘statistical structure’ stated in terms so abstract as I have just used. To give the statement life and colour, let me anticipate what will be explained in much more detail later, namely, that the most essential part of a living cell — the chromosome fibre — may suitably be called an aperiodic crystal. In physics we have dealt hitherto only with periodic crystals. To a humble physicist’s mind, these are very interesting and complicated objects; they constitute one of the most fascinating and complex material structures by which inanimate nature puzzles his wits. Yet, compared with the aperiodic crystal, they are rather plain and dull. The difference in structure is of the same kind as that between an ordinary wallpaper in which the same pattern is repeated again and again in regular periodicity and a masterpiece of embroidery, say a Raphael tapestry, which shows no dull repetition, but an elaborate, coherent, meaningful design traced by the great master.

42It has often been asked how this tiny speck of material, nucleus of the fertilized egg, could contain an elaborate code-script involving all the future development of the organism. A well-ordered association of atoms, endowed with sufficient resistivity to keep its order permanently, appears to be the only conceivable material structure that offers a variety of possible (‘isomeric’) arrangements, sufficiently large to embody a complicated system of ‘determinations’ within a small spatial boundary. Indeed, the number of atoms in such a structure need not be very large to produce an almost unlimited number of possible arrangements.

43The living organism seems to be a macroscopic system which in part of its behaviour approaches to that purely mechanical (as contrasted with thermodynamical) conduct to which all systems tend, as the temperature approaches absolute zero and the molecular disorder is removed.

44What is the characteristic feature of life? When is a piece of matter said to be alive? When it goes on ‘doing something’, moving, exchanging material with its environment, and so forth, and that for a much longer period than we would expect of an inanimate piece of matter to ‘keep going’ under similar circumstances. When a system that is not alive is isolated or placed in a uniform environment, all motion usually comes to a standstill very soon as a result of various kinds of friction; differences of electric or chemical potential are equalized, substances which tend to form a chemical compound do so, temperature becomes uniform by heat conduction. After that the whole system fades away into a dead, inert lump of matter. A permanent state is reached, in which no observable events occur. The physicist calls this the state of thermodynamical equilibrium, or of ‘maximum entropy’.

45It is by avoiding the rapid decay into the inert state of ‘equilibrium’ that an organism appears so enigmatic; so much so, that from the earliest times of human thought some special non-physical or supernatural force (vis viva, entelechy) was claimed to be operative in the organism, and in some quarters is still claimed. How does the living organism avoid decay? The obvious answer is: By eating, drinking, breathing and (in the case of plants) assimilating. The technical term is metabolism.

46How would we express in terms of the statistical theory the marvellous faculty of a living organism, by which it delays the decay into thermodynamical equilibrium (death)? We said before: ‘It feeds upon negative entropy’, attracting, as it were, a stream of negative entropy upon itself, to compensate the entropy increase it produces by living and thus to maintain itself on a stationary and fairly low entropy level. … Thus the device by which an organism maintains itself stationary at a fairly high level of orderliness (= fairly low level of entropy) really consists in continually sucking orderliness from its environment.

47Living matter evades the decay to equilibrium.

48These specialized fields are continually growing and invading new territory. The result is like what occurred when the Oregon country was being invaded simultaneously by the United States settlers, the British, the Mexicans, and the Russians — an inextricable tangle of exploration, nomenclature, and laws.

There are fields of scientific work, as we shall see in the body of this book, which have been explored from the different sides of pure mathematics, statistics, electrical engineering, and neurophysiology; in which every single notion receives a separate name from each group; and in which important work has been triplicated or quadruplicated; while still other important work is delayed by the unavailability in one field of results that may have already become classical in the next field.

It is these boundary regions of science which offer the richest opportunities to the qualified investigator. They are at the same time the most refractory to the accepted techniques of mass attack and the division of labor. If the difficulty of a physiological problem is mathematical in essence, ten physiologists ignorant of mathematics will get precisely as far as one physiologist ignorant of mathematics, and no further. If a physiologist, who knows no mathematics, works together with a mathematician who knows no physiology, the one will be unable to state his problem in terms that the other can manipulate, and the second will be unable to put the answers in any form that the first can understand.

49The fundamental problem of communication is that of reproducing at one point either exactly or approximately a message selected at another point. Frequently the messages have meaning; that is they refer to or are correlated according to some system with certain physical or conceptual entities. These semantic aspects of communication are irrelevant to the engineering problem.

50Information is a measure of one’s freedom of choice when one selects a message.

51This means that when we write English half of what we write is determined by the structure of the language and half is chosen freely.

52The redundancy of a language is related to the existence of crossword puzzles. If the redundancy is zero any sequence of letters is a reasonable text in the language and any two dimensional array of letters forms a crossword puzzle.

53If a source can produce only one particular message its entropy is zero, and no channel is required. A computing machine set up to calculate the successive digits of π produces a definite sequence with no chance element. No channel is required to ‘transmit’ this to another point. One could construct a second machine to compute the same sequence at the point.

54The concept of information developed in this theory at first seems disappointing and bizarre — disappointing because it has nothing to do with meaning, and bizarre because it deals not with a single message but rather with the statistical character of a whole ensemble of messages. I think, however, that these should be only temporary reactions; and that one should say, at the end, that this analysis has so penetratingly cleared the air that one is now, perhaps for the first time, ready for a real theory of meaning.

55Good problems and mushrooms of certain kinds have something in common: they grow in clusters. Having found one, you should look around; there is a good chance that there are some more quite near.

56What is the difference between the astronomical and the meteorological situation which brings about all these differences, and in particular the difference between the apparent reversibility of astronomical time and the apparent irreversibility of meteorological time? In the first place, the meteorological system is one involving a vast number of approximately equal particles, some of them very closely coupled to one another, while the astronomical system of the solar universe contains only a relatively small number of particles, greatly diverse in size, and coupled with one another in a sufficiently loose way that the second order coupling effects do not change the general aspect of the picture we observe, and the very high order coupling effects are completely negligible.

57The record of paleontology indicates a definite long-time trend, interrupted and complicated though it might be, from the simple to the complex.

58In tidal evolution as well as in the origin of species, we have a mechanism by means of which a fortuitous variability, that of the random motions of the waves in a tidal sea, and of the molecules of the water, is converted by a dynamical process into a pattern of development which reads in one direction.

59This transition from a Newtonian, reversible time to a Gibbsian, irreversible, time has had its philosophical echoes. Bergson emphasized the difference between the reversible time of physics, in which nothing new happens, and the irreversible time of evolution and biology, in which there is always something new. The realization that the Newtonian physics was not the proper frame for biology was perhaps the central point in the old controversy between vitalism and mechanism; although this was complicated by the desire to conserve in some form or other at least the shadows of the soul and of God against the inroads of materialism.

60At every stage of technique since Daedalus or Hero of Alexandria, the ability of the artificer to produce a working simulacrum of a living organism has always intrigued people. This desire to produce and to study automata has always been expressed in terms of the living technique of the age. In the days of magic, we have the bizarre and sinister concept of the Golem, that figure of clay into which the Rabbi of Prague breathed in life with the blasphemy of the Ineffable Name of God. In the time of Newton, the automaton becomes the clockwork music box, with the little effigies pirouetting stiffly on top. In the nineteenth century, the automaton is a glorified heat engine, burning some combustible fuel instead of the glycogen of the human muscles. Finally, the present automaton opens doors by means of photocells, or points guns to the place at which a radar beam picks up an airplane, or computes the solution of a differential equation.

61The living organism is above all a heat engine, burning glucose or glycogen or starch, fats, and proteins, into carbon dioxide, water, and urea. It is the metabolic balance which is the center of attention; and if the low working temperatures of animal muscle attract attention as opposed to the high working temperatures of a heat engine of similar efficiency, this fact is pushed into a corner and glibly explained by a contrast between the chemical energy of the living organism and the thermal energy of the heat engine.

62In short, the newer study of automata, whether in the metal or in the flesh, is a branch of communication engineering, and its cardinal notions are those of message, amount of disturbance or « noise » — a term taken over from the telephone engineer — quantity of information, coding technique, and so on.

63The machines of which we are now speaking are not the dream of the sensationalist, nor the hope of some future time. They already exist as thermostats, automatic gyro-compass ship-steering systems, self-propelled missiles — especially such as seek their target — anti-aircraft fire-control systems, automatically controlled oil-cracking stills, ultra-rapid computing machines, and the like. They had begun to be used long before the war — indeed, the very old steam-engine governor belongs among them — but the great mechanization of the second world war brought them into their own, and the need of handling the extremely dangerous energy of the atom will probably bring them to a still higher point of development. Scarcely a month passes but a new book appears on these so-called control mechanisms or servo-mechanisms, and the present age is as truly the age of servo-mechanisms as the nineteenth century was the age of the steam engine or the eighteenth century the age of the clock.

64One of the inspirations of the present symposium has been the life work of d’Arcy Wentworth Thompson, that truly remarkable man who occupied the chair of biology at St. Andrews’ University for nearly half a century. His magnum opus “Growth and Form”, which first appeared in 1917, and was revised as a second edition in 1942, remains one of the two or three most brilliant and original books in the life sciences which this century has seen or is likely to see. D’Arcy Thompson’s approach was fundamentally mathematical; he saw in the myriad manifestations of living form a wonderful opportunity for mathematical analysis. I always remember one particular demonstration of his, that the spirals in fir-cones and other plant structures involve the famous Fibonacci series (named after the 13th century Italian mathematician) which corresponds to a continued fraction and has very far-reaching implications.

D’Arcy Thompson studied, in this 1,100-page book of his, all conceivable aspects of the mathematics of living forms the shapes of cells, in isolation or association; the shapes of concretions, spicules, and skeletons; the twists of horns, teeth, and tusks; the characters of eggs and hollow structures. His final chapter deals with the interesting theory of transformations. If certain animal or plant bodies are plotted upon Cartesian coordinates, it is found that when these are systematically distorted in various ways, forms characteristic of species related to the original species plotted appear. While d’Arcy Thompson often examined the engineering problems which living organisms have had to face, his primary interest was the mathematical description of their forms.

65What is this character, which the naturally organic possesses and the artificial usually lacks? It has something, certainly, to do with growth. Organic forms develop. The flow of time is an essential component of their full nature, and the spatial objects we can hold in our hands and examine, with eyes or microscope, during a short few minutes is only a single still out of a continuous sequence of forms which continuously unfolds, sometimes quickly, sometimes more slowly, throughout the life of the organism of which it is a part. All scientific consideration of organic form must start from this point. Science is essentially concerned with causal relations; and causal relations cannot be expressed unless there is change. It is therefore in the changes of form - during individual development, during evolution, or under the influence of function - that the biologist is mainly interested.

66The developing organism is at all times a going concern, at all times a functioning whole, and not merely a set of parts being assembled. It is self-forming, and the ‘information’ which guides its development is not a blueprint external to the process but is embedded in the process itself.

67The study of form in organisms goes by the name of Morphology, a term introduced into biology by Goethe in 1827. He regarded plants as variants of an “archetypical” form, his “Urpflanze” consisting of an axial structure (the stem) bearing lateral appendages, the leaves. Development he regarded as a reiteration of successive parts, thus a “time pattern” constituting the life history of the plant, in the course of which modifications of the fundamental repetitive unit occur - essentially a “metamorphosis” of the leaf culminating in the organs of the flower, which Goethe regarded as modified leaf structures. It is not easy in post-Darwinian days to recapture the notion of the archetype in its essential simplicity; what to us appears artificial is the divorce of a pure form or shape from any functional consideration. And yet the notion of a pure morphology exerted a powerful influence over biological thought in the early part of last century. The morphological categories of leaf, stem, and root were generally accepted, and the notion of metamorphosis was transferred from the purely abstract realm to the realm of reality, in that the functional aspect of the plant organs became the dominant consideration. The categories of leaf, stem, and root of the higher plants are the seats of essential functional activities; thus the leaf synthesizes organic constituents of the plant; the stem tissues conduct the essential materials, water and nutritive elements, to the leaf and translocate the final products to the various parts of the plant, and in addition provide the mechanical support for the effective display of the leaves to light and air; the root absorbs nutrients and water from the soil and provides the necessary anchorage for the plant.

68The principal function of the higher centres, which must pilot a vulnerable animal through a changing and hostile world, a world where chaos and cosmos are interlaced and superimposed, where anything may happen, but nothing happens twice, is to deal with uncertainty.

69There is no gruesome vitalistic fascination about viruses; they have the same gruesome mechanistic fascination as nitro-glycerine or a soufflé.

70A perfect crystal is, from the point of view of growth, a dead crystal.

71All of this will lead to theories which are much less rigidly of an all-or-none nature than past and present formal logic. They will be of a much less combinatorial, and much more analytical, character. In fact, there are numerous indications to make us believe that this new system of formal logic will move closer to another discipline which has been little linked in the past with logic. This is thermodynamics, primarily in the form it was received from Boltzmann, and is that part of theoretical physics which comes nearest in some of its aspects to manipulating and measuring information. Its techniques are indeed much more analytical than combinatorial, which again illustrates the point that I have been trying to make above.

72There is a great feeling of satisfaction, that no one can deny, in being able to take a living phenomenon and apply the ruler and balance to it.

73Neither development nor crystallization are downhill processes, yet each will occur spontaneously. They are machines, as Aristotle thought of them, but unlike clocks or mechanical devices, they do not decrease their thermodynamic order, but increase it by bleeding the environment.

74Here also order seems to spring from chaos, and this is perhaps even more remarkable as the crystal has no metabolic machinery, and cannot capture and store energy.

75An interesting field of application for models consisting of an infinite number of interacting elements may exist in the recent theories of automata. A general model, considered by von Neumann and the author, would be of the following sort: Given is an infinite lattice or graph of points, each with a finite number of connections to certain of its ‘neighbors.’ Each point is capable of a finite number of ‘states.’ The states of neighbors at time Tn induce, in a specified manner, the state of the point at time Tn+1. One aim of the theory is to establish the existence of subsystems which are able to multiply, i.e., create in time other systems identical (‘congruent’) to themselves.

76It is suggested that a system of chemical substances, called morphogens, reacting together and diffusing through a tissue, is adequate to account for the main phenomena of morphogenesis. Such a system, although it may originally be quite homogeneous, may later develop a pattern or structure due to an instability of the homogeneous equilibrium, which is triggered off by random disturbances.

77Most of an organism, most of the time, is developing from one pattern into another, rather than from homogeneity into a pattern. One would like to be able to follow this more general process mathematically also. The difficulties are, however, such that one cannot hope to have any very embracing theory of such processes, beyond the statement of the equations. It might be possible, however, to treat a few particular cases in detail with the aid of a digital computer.

78It must be admitted that the biological examples which it has been possible to give in the present paper are very limited. This can be ascribed quite simply to the fact that biological phenomena are usually very complicated. Taking this in combination with the relatively elementary mathematics used in this paper one could hardly expect to find that many observed biological phenomena would be covered. It is thought, however, that the imaginary biological systems which have been treated, and the principles which have been discussed, should be of some help in interpreting real biological forms.

79Rarely does it happen in mathematics that a new discipline achieves the character of a mature and developed scientific theory in the first investigation devoted to it.

80I suspect that a deeper mathematical study of the nervous system… will affect our understanding of the aspects of mathematics itself that are involved. In fact, it may alter the way in which we look on mathematics and logics proper.

81One conversation centered on the ever accelerating progress of technology and changes in the mode of human life, which gives the appearance of approaching some essential singularity in the history of the race beyond which human affairs, as we know them, could not continue.

82Information theory is relevant to statistical inference and should be of basic interest to statisticians. Information theory provides a unification of known results, and leads to natural generalizations and the derivation of new results.

83It is a fairly widespread delusion among physicists that statistical physics is the least well-founded branch of theoretical physics. Reference is generally made to the point that some of its conclusions are not subject to rigorous mathematical proof; and it is overlooked that every other branch of theoretical physics contains just as many non-rigorous proofs, although these are not regarded as indicating an inadequate foundation for such branches.

84In principle, we can obtain complete information concerning the motion of a mechanical system by constructing and integrating the equations of motion of the system, which are equal in number to its degrees of freedom. But if we are concerned with a system which, though it obeys the laws of classical mechanics, has a very large number of degrees of freedom, the actual application of the methods of mechanics involves the necessity of setting up and solving the same number of differential equations, which in general is impracticable. It should be emphasised that, even if we could integrate these equations in a general form, it would be completely impossible to substitute in the general solution the initial conditions for the velocities and coordinates of all the particles.

At first sight we might conclude from this that, as the number of particles increases, so also must the complexity and intricacy of the properties of the mechanical system, and that no trace of regularity can be found in the behaviour of a macroscopic body. This is not so, however, and we shall see below that, when the number of particles is very large, new types of regularity appear.

85A fundamental feature of this approach is the fact that, because of the extreme complexity of the external interactions with the other parts of the system, during a sufficiently long time the subsystem considered will be many times in every possible state.

86The following circumstance is extremely important in statistical physics. The statistical distribution of a given subsystem does not depend on the initial state of any other small part of the same system, since over a sufficiently long time the effect of this initial state will be entirely outweighed by the effect of the much larger remaining parts of the system. It is also independent of the initial state of the particular small part considered, since in time this part passes through all possible states, any of which can be taken as the initial state. Without having to solve the mechanical problem for a system (taking account of initial conditions), we can therefore find the statistical distribution for small parts of the system.

The determination of the statistical distribution for any subsystem is in fact the fundamental problem of statistical physics. In speaking of ‘small parts’ of a closed system, we must bear in mind that the macroscopic bodies with which we have to deal are usually themselves such ‘small parts’ of a large closed system consisting of these bodies together with the external medium which surrounds them.

If this problem is solved and the statistical distribution for a given subsystem is known, we can calculate the probabilities of various values of any physical quantities which depend on the states of the subsystem (i.e. on the values of its coordinates q and momenta p). We can also calculate the mean value of any such quantity f(p, q), which is obtained by multiplying each of its possible values by the corresponding probability and integrating over all states.

87In practice, however, when statistical physics is applied to macroscopic bodies, its probabilistic nature is not usually apparent. The reason is that, if any macroscopic body (in external conditions independent of time) is observed over a sufficiently long period of time, it is found that all physical quantities describing the body are practically constant (and equal to their mean values) and undergo appreciable changes relatively very rarely; we mean, of course, macroscopic quantities describing the body as a whole or macroscopic parts of it, but not individual particles.

88These statistical laws resulting from the very presence of a large number of particles forming the body cannot in any way be reduced to purely mechanical laws.

89According to the results of statistics, the universe ought to be in a state of complete statistical equilibrium. Everyday experience shows us, however, that the properties of Nature bear no resemblance to those of an equilibrium system; and astronomical results show that the same is true throughout the vast region of the Universe accessible to our observation.

90It has already been mentioned in § 83 that the transition between phases of different symmetry (crystal and liquid; different crystal modifications) cannot occur in a continuous manner such as is possible for a liquid and a gas. In every state the body has either one symmetry or the other, and therefore we can always assign it to one of the two phases.

The transition between different crystal modifications is usually effected by means of a phase transition in which there is a sudden rearrangement of the crystal lattice and the state of the body changes discontinuously. As well as such discontinuous transitions, however, another type of transition involving a change of symmetry is also possible.

91The great beauty and power of a mathematical theory or model lies in the separation of the relevant from the irrelevant.

92Mathematically, white Gaussian noise is the least predictable. To a human being, however, all white Gaussian noise sounds alike.

93Vitalism amounted to the assertion that living things do not behave as though they were nothing but mechanisms constructed of mere material components; but this presupposes that one knows what mere material components are and what kind of mechanisms they can be built into.

94(1) The universe is homogeneous.

(2) Space and time take on only discrete integer values.

(3) Only local action can occur at any one time.

(4) The universe is in Euclidean N-space.

(5) The laws of behavior of the universe are deterministic.

(6) Erasing is possible.

From these six assumptions (and perhaps other hidden ones which I have not noticed) it can be concluded that Garden-of-Eden configurations exist.

95The phenotype is the product of the harmonious interaction of all genes. The genotype is a ‘physiological team’ in which a gene can make a maximum contribution to fitness by elaborating its chemical ‘gene product’ in the needed quantity and at the time when it is needed in development. There is extensive interaction not only among the alleles of a locus, but also between loci. The main locale of these epistatic interactions is the developmental pathway. Natural selection will tend to bring together those genes that constitute a balanced system. The process by which genes are accumulated in the gene pool that collaborate harmoniously is called ‘integration’ or ‘coadaptation.’ The result of this selection has been referred to as ‘internal balance.’ Each gene will favor the selection of that genetic background on which it can make its maximum contribution to fitness. The fitness of a gene thus depends on and is controlled by the totality of its genetic background.

96Intricate adaptations, involving a great complexity of genetic substitutions to render them efficient would only be established, or even maintained in the species, by the agency of selective forces, the intensity of which may be thought of broadly as proportional to their complexity.

97It always bothers me that, according to the laws as we understand them today, it takes a computing machine an infinite number of logical operations to figure out what goes on in no matter how tiny a region of space, and no matter how tiny a region of time. How can all that be going on in that tiny space? Why should it take an infinite amount of logic to figure out what one tiny piece of space/time is going to do? So I have often made the hypotheses that ultimately physics will not require a mathematical statement, that in the end the machinery will be revealed, and the laws will turn out to be simple, like the chequer board with all its apparent complexities.

98Complication, on its lower levels, is probably degenerative, that is, every automaton that can produce other automata will only be able to produce less complicated ones. There is, however, a certain minimum level where this degenerative characteristic ceases to be universal. At this point automata which can reproduce themselves, or even construct higher entities, become possible.

99It is a fundamental fact of the theory of automata that any automaton which is powerful enough to be a universal constructor must also be powerful enough to include a universal computing machine.

100Ladies and gentlemen, I wish to thank you for your very friendly welcome on my five occasions to talk to you, and I hope that I will be able to offer something for the variety of interests which are represented here. I will talk about automata-the behavior of very complicated automata and the very specific difficulties caused by high complication. I shall discuss briefly the very plausible, very obvious analogies which come to mind between artificial automata and organisms, which within a certain limit of their functioning are natural automata. We must consider the similarities, the dissimilarities, the extent to which the dissimilarities are due to our skill or clumsiness (the latter being the more normal phenomenon), and the extent to which these dissimilarities are really matters of principle.

101Unfortunately, because of his premature death, von Neumann was unable to put in final form any of the research he was doing in automata theory. In his last work on this subject he said that ‘it would be very satisfactory if one could talk about a “theory” of such automata. Regrettably, what at this moment exists … can as yet be described only as an imperfectly articulated and hardly formalized “body of experience”.’ Von Neumann’s accomplishments in this area were nevertheless substantial. He outlined the general nature of automata theory: its structure, its materials, some of its problems, some of its applications, and the form of its mathematics. He began a comparative study of artificial and natural automata. Finally, he formulated and partially answered two basic questions of automata theory: How can reliable systems be constructed from unreliable components? What kind of logical organization is sufficient for an automaton to be able to reproduce itself?

102What kind of logical organization is sufficient for an automaton to reproduce itself? This question is not precise and admits to trivial versions as well as interesting ones. Von Neumann had the familiar natural phenomenon of self-reproduction in mind when he posed it, but he was not trying to simulate the self-reproduction of a natural system at the level of genetics and biochemistry. He wished to abstract from the natural self-reproduction problem its logical form.

103von Neumann and Thatcher have shown that one may construct self-reproducing universal arrays using as basic cells finite automata with only 29 states. The simplicity of the components necessitates complex programming.

We present a self-reproducing universal array with simple programming. This is made possible by using as basic unit a finite automaton which can execute an internal program of up to 20 instructions.

104Natural and Artificial Automata. The scope of the theory of automata and its interdisciplinary character are revealed by a consideration of the two main types of automata: the artificial and the natural. Analog and digital computers are the most important kinds of artificial automata, but other man-made systems for the communication and processing of information are also included, for example, telephone and radio systems. Natural automata include nervous systems, self-reproductive and self-repairing systems, and the evolutionary and adaptive aspects of organisms.

Automata theory clearly overlaps communications and control engineering on the one hand, and biology on the other. In fact, artificial and natural automata are so broadly defined that one can legitimately wonder what keeps automata theory from embracing both these subjects. Von Neumann never discussed this question, but there are limits to automata theory implicit in what he said. Automata theory differs from both subjects in the central role played by mathematical logic and digital computers. Though it has important engineering applications, it itself is a theoretical discipline rather than a practical one. Finally, automata theory differs from the biological sciences in its concentration on problems of organization, structure, language, information, and control.

Automata theory seeks general principles of organization, structure, language, information, and control. Many of these principles are applicable to both natural and artificial systems, and so a comparative study of these two types of automata is a good starting point. Their similarities and differences should be described and explained. Mathematical principles applicable to both types of automata should be developed. Thus truth-functional logic and delay logic apply to both computer components and neurons, as does von Neumann’s probabilistic logic.

105All of this will lead to theories which are much less rigidly of an all-or-none nature than past and present formal logic. They will be of a much less combinatorial, and much more analytical, character. In fact, there are numerous indications to make us believe that this new system of formal logic will move closer to another discipline which has been little linked in the past with logic. This is thermodynamics, primarily in the form it was received from Boltzmann, and is that part of theoretical physics which comes nearest in some of its aspects to manipulating and measuring information. Its techniques are indeed much more analytical than combinatorial, which again illustrates the point that I have been trying to make above.

106By axiomatizing automata in this manner, one has thrown half of the problem out the window, and it may be the more important half. One has resigned oneself not to explain how these parts are made up of real things, specifically, how these parts are made up of actual elementary particles, or even of higher chemical molecules.

107I suspect that a deeper mathematical study of the nervous system… will affect our understanding of the aspects of mathematics itself that are involved. In fact, it may alter the way in which we look on mathematics and logics proper.

108Signal detectability is a function of both the signal-to-noise ratio and the observer’s criterion.

109The beauty of life is, therefore, geometrical beauty of a type that Plato would have much appreciated.

110I remember being struck, as was my friend C. H. Waddington in his geological studies, with the extreme persistence of complex patterns in fossils, or, like my friend Joseph Needham, with the sequential evolution in chemical processes: with the different ways that organisms, as they evolved, got rid of their nitrogen products successively as ammonia, urea and uric acid, for biological reasons that were quite clear in themselves but depended, essentially, on teleological considerations on how far the processes helped the organism in its way of life on sea or land. Underlying both these examples was the concept of biological chemical action, occurring on a different basis from that of the chemical laboratory, namely, as a reaction brought about by enzymes, at that time mysterious but tangible substances which effected chemical changes at ordinary temperatures in the absence of strong reagents.

111I had a very interesting discussion on this point with Einstein in Princeton in 1946, from which it appeared to me that the essential clue was that life involved another element, logically different from those occurring in physics at that time, by no means a mystical one, but an element of history. The phenomena of biology must be, as we say, contingent on events. In consequence, the unity of life is part of the history of life and, consequently, is involved in its origin.

My particular contribution in my 1947 lecture on this fundamental physical basis of life was specifically to the second stage of that evolution, from chemicals suspended in a primitive ocean, the so-called primary soup, to the concentrations leading to the formation of definite organisms, the ‘eobionts’ of Pirie. I suggested that the mechanism of this was essentially that of adsorption of the active chemicals on fine clay particles derived from earlier rocks and deposited in estuarine waters.

112The problem of the origin of life is apparently very easily stated: at one time there existed nothing more complex than an ordinary inorganic chemical, subject to a possible heating to several thousand degrees Centigrade; at the end there is the whole panorama of the multiplicity of living organisms covering the world and possibly spreading to other planets.

113Crystals, by definition, are evidence of precise equality in molecular reproduction, which in turn calls out for a mechanism to produce it. This is a further example of the explanation of actually microscopically visible structures, or electron microscopically visible structures, various kinds of crystals first noted in the tobacco mosaic virus particles. All the structures found in cells seem to be of this character, whether of sheets, tubules or fibres or, occasionally, three-dimensional crystals. The beauty of life is, therefore, a geometrical beauty of a type that Plato would have much appreciated: sets of identical particles which hold themselves together by the principles of self-assembly in the most elaborate structures.

114My provisional definition of life: Life is a partial, continuous, progressive, multiform and conditionally interactive self-realization of the potentialities of atomic electron states.

115Morphic Processes. Since around 1870 the branch of physics concerned with natural tendencies - i.e. processes going one way towards some characteristic terminus - has been somewhat unbalanced in its emphasis. Much attention has been paid to the tendency towards dynamical disorder (heat processes, entropy), and much less to the extensive and important class of contrary processes leading towards spatial order. Curiously enough this class has not yet a clear scientific name of its own, though it must be responsible for the existence of organisms and of organisms with minds. In my view Schrodinger insulted this pre-eminent class of processes by giving them a negative and, in certain technical respects, misleading name: negative entropy (now structural neg-entropy).

To do something to correct this unbalance, to emphasize the positive aspect of these formative processes, and to make clear how extensive and rich with consequences they are, I have given them a scientific name: morphic. This is defined to mean ‘displaying a movement toward greater three-dimensional spatial order, symmetry, or form’.

116The meaning of a message can be defined as its selective function on the range of the recipient’s states of conditional readiness.

117A noise generator can be regarded as a source of completely original but meaningless information. A logical computer per contra provides completely unoriginal but rigorously meaningful information.

118It seems important to rid ourselves of the current heresy that only what can be expressed precisely in words has precise meaning. The selective function of an utterance for an individual may obviously be perfectly well-defined, although he can say nothing well-defined about it.

119It is a fundamental question whether metabolic stability and epigenesis require the genetic regulatory circuits to be precisely constructed.

120There can be a moral element in conceptual blindness.

121The freedom we attribute to each other is not a matter of convention, but a matter of fact.

122Artificiality connotes perceptual similarity but essential difference, resemblance from without rather than within. The artificial object imitates the real by turning the same face to the outer system. … Resemblance in behavior of systems without identity of the inner systems is particularly feasible if the aspects in which we are interested arise out of the organization of the parts, independently of all but a few properties of the individual components.

123We have now identified four indicia that distinguish the artificial from the natural; hence we can set the boundaries for sciences of the artificial:

1. Artificial things are synthesized (though not always or usually with full forethought) by human beings.
2. Artificial things may imitate appearances in natural things while lacking, in one or many respects, the reality of the latter.
3. Artificial things can be characterized in terms of functions, goals, adaptation.
4. Artificial things are often discussed, particularly when they are being designed, in terms of imperatives as well as descriptives.

124We watch an ant make his laborious way across a wind- and wave-molded beach. He moves ahead, angles to the right to ease his climb up a steep dunelet, detours around a pebble, stops for a moment to exchange information with a compatriot. So as not to anthropomorphize about his purposes, I sketch the path on a piece of paper. It is a sequence of irregular, angular segments-not quite a random walk, for it has an underlying sense of direction, of aiming towards a goal. Viewed as a geometric figure, the ant’s path is irregular, complex, hard to describe. But its complexity is really a complexity in the surface of the beach, not a complexity in the ant. On that same beach another small creature with a home at the same place as the ant might well follow a very similar path. The ant, viewed as a behaving system, is quite simple. The apparent complexity of its behavior over time is largely a reflection of the complexity of the environment in which it finds itself.

125This month we consider Conway’s latest brainchild, a fantastic solitaire pastime he calls ‘life’. Because of its analogies with the rise, fall and alternations of a society of living organisms, it belongs to a growing class of what are called ‘simulation games’ — games that resemble real-life processes.

126You will find the population constantly undergoing unusual, sometimes beautiful and always unexpected change. In a few cases the society eventually dies out (all counters vanishing), although this may not happen until after a great many generations. Most starting patterns either reach stable figures — Conway calls them ‘still lifes’ — that cannot change or patterns that oscillate forever. Patterns with no initial symmetry tend to become symmetrical. Once this happens the symmetry cannot be lost, although it may increase in richness.

127It has always been clear that we were not so deeply interested in the theory of any particular biological phenomenon for its own sake, but mainly in so far as it helps to a greater comprehension of the general character of the processes that go on in living as contrasted with non-living systems.

128The existence of self-reproducing machines is only a very special case of a much wider phenomenon, the theory of which might conceivably be applied to situations of quite a different kind from those occurring in biological simulation.

129Thus we have proved that the existence of two indistinguishable configurations is a necessary as well as a sufficient condition for the existence of Garden-of-Eden configurations.

130Unrestricted adaptability requires that the adaptive system be able initially to generate any of the programs of some universal computer.

131The study of adaptation involves the study of both the adaptive system and its environment. In general terms, it is a study of how systems can generate procedures enabling them to adjust efficiently to their environments. If adaptability is not to be arbitrarily restricted at the outset, the adapting system must be able to generate any method or procedure capable of an effective definition. The intuitive idea of an effectively defined procedure has several equivalent characterizations; here, following Turing, the set of all effectively defined procedures will be identified with the set of all programs of some suitably specified universal computer. In these terms, unrestricted adaptability (assuming nothing is known of the environment) requires that the adaptive system be able initially to generate any of the programs of some universal computer. The process of adaptation can then be viewed as a modification of the generation process as information about the environment accumulates. This suggests that adaptive systems be studied in terms of associated classes of generation procedures — the associated class in each case being the repertory of the adaptive system.

132The power of an adaptive system depends critically upon its ability to exploit common factors in successful techniques. If the system has meager means for analyzing elements of its repertory, this ability will be sharply curtailed, no matter how extensive the repertory. Contrariwise, if the system has a great many different ways of describing (or representing) the same device, i.e., if it has a rich variety of ways to decompose elements of its repertory, chances of detecting common factors are greatly enhanced. Each time a device is tried, information accrues about components of each of the potential decompositions. Thus, the richer the variety of decompositions, the higher the effective sampling rate. Of course, to exploit this information about components, the adaptive system must use it to infer the performance of untried devices. And these inferences must, in turn, be used to plan which devices should be generated and tried next. At each stage, the flexibility and success of the process depends upon the flexibility and richness of the system’s analysis and synthesis procedures — qualities ultimately depending upon the definitions of structure employed by the system.

133In attempting to supply a rich set of representations (with attendant analysis and synthesis procedures), it helps to look at procedures actually exploited by successful adaptive plans. Among the most important are:

(1) Substitution — components common to several highly rated devices are substituted in other related devices.

(2) Abstraction — by a process of abstraction, highly rated devices are used to provide schemata (patterns for substitution) for the development of related devices.

(3) Refinement — now ‘cues’ for reacting to the environment are provided by refining the input alphabet or time-scale, adjusting internal processing accordingly.

(4) Modeling — the environment is approximated by some part of the internal structure with the intention of checking predictions of this model against observed outcomes and modifying it accordingly.

(5) Change of representation — new primitives and operations are introduced so that problems presented by the environment are more easily modeled and related to previous models, outcomes, or stored information.

(6) Metacontrol — rules for employing the preceding techniques are implemented in the device and they in turn are subject to the same techniques; additional levels are added as required. By searching for structural traits which will give these techniques broad scope, we obtain suggestions for requirements on the structural formalism. These requirements will be briefly described here, and then each in turn will be discussed at length.

(1) Hierarchical description. Substitution and abstraction can be greatly facilitated if the devices used by the adaptive plan have many alternative descriptions in terms of “block diagram” hierarchies. A great variety of schemata can then be formed from a single device by simply deleting the contents of one or more blocks in different ones of its hierarchical descriptions. Any device which satisfies the input-output interface of such an “empty” block becomes a candidate for substitution therein. Refinement proceeds most easily if alphabets and time-scales of blocks in the hierarchical description can be changed without requiring overall structural reorganization. The minimal constraints possible are those imposed by interfaces with other blocks and by identifications with parts of higher-level blocks.

(2) Self-Applicability. The operations for connecting blocks should themselves be defined by exactly the same hierarchical descriptions as the objects to which they are applied (permitting new operations to be introduced as needed). Operations should apply equally directly to blocks at any level in the hierarchical descriptions (permitting any block to be treated as primitive). Taken together these provisions permit the adaptive plan to add new levels of control as required.

(3) Incorporation of models. Primitives and operations should be such that models of the environment can easily be implemented, used, and altered by the overall adaptive plan. There should be a clear means of designating the control exercised by active portions (cf. active subroutines) of the model. There should also be natural structural provisions for making and recording predictions based upon the model. These provisions permit the adaptive plan to check predictions against outcome and make corresponding modifications of responsible parts of the model (a technique used to great advantage by Samuel).

134The question about the origin of life often appears as a question about ‘cause’ and effect. Physical theories of macroscopic processes usually involve answers to such questions, even if a statistical interpretation is given to the relation between ‘cause’ and ‘effect’. It is mainly due to the nature of this question that many scientists believe that our present physics does not offer any obvious explanation for the existence of life, which even in its simplest forms always appears to be associated with complex macroscopic (i.e. multimolecular) systems, such as the living cell.

135What is required in order to solve such a problem of interplay between cause and effect is a theory of selforganization which can be applied to molecular systems, or more precisely, to special molecular systems under special environmental conditions. We may envisage that such a process of molecular selforganization includes many random events which do not have any instructed functional significance. What really matters is how certain such random effects are able to feed back to their origin and thus become themselves the cause of some amplified action. Under certain external conditions such a multiple interplay between cause and effect may build up to a macroscopic functional organization, which includes selfreproduction, selection and evolution to a level of sophistication where the system can escape the prerequisites of its origin and change the environment to its own advantage.

136At the ‘beginning’ — whatever the precise meaning of this may be — there must have been molecular chaos, without any functional organization among the immense variety of chemical species. Thus, the selforganization of matter we associate with the ‘origin of life’ must have started from random events. This statement, however, does not imply that any — even primitive — organisms as we know them today can assemble in a random fashion.

137I believe it was N. Wiener who once proposed that information be regarded as a new variable in physics.

138What Properties of Matter are Required to Start Selforganization? Logically, we should distinguish several phases of evolution, which temporally are not completely separated:

1. a prebiotic ‘chemical’ phase,
2. the phase of selforganization to replicating ‘individuals’,
3. the evolution of individual species.

139Selforganization is based on certain chemical prerequisites as well as on special environmental conditions. It is not ‘just plainly’ a property of matter. The prebiotic phase is chemistry and as such is described ‘in principle’ by quantum mechanical theory. However, it has to be shown, of course, that conditions on the early earth were such as to favor the formation of the required material.

140Catalytic function in combination with various feedback mechanisms causing certain self-enhancing growth properties of the system will be shown to be one of the decisive prerequisites for selforganization.

141Under what Environmental Conditions can Selforganization Occur? One fundamental answer was given by E. Schrodinger who wrote: ‘Living matter evades the decay to equilibrium’. Equilibrium (in an isolated system) is a state of maximum entropy. If we keep the system away from equilibrium, we have to compensate steadily for the production of entropy, which means we have to ‘feed’ the system with free energy or energy-rich matter. This energy is used by the machinery to ‘drive’ certain reactions which keep the system from ‘fading away’ into the inert or ‘dead’ state of equilibrium. This statement is obviously correct and Schrodinger deserves the credit for having expressed it so clearly.

142Orderliness in a complex reaction system which involves a large variety of different chemical compounds requires the formation of a selfreproducing ‘functional code’. The word ‘functional code’ specifies two properties: one executive and one legislative. The executive property requires machinery which can control all reactions going on in the system and may be represented by an ensemble of interacting and selfregulating catalysts, preferably made of uniform material, but involving practically unrestricted functional capacity. Regardless of whether the primary structure of this executive machinery also provides the instruction for its reproduction, or whether this has to be translated from a different legislative source, selforganization and further evolution of correlated and reproducible functional behavior must start at the level of a selfreproducing molecular code.

143What the Theory Does Explain is the general principle of selection and evolution at the molecular level, based on a stability criterion of the (non-linear) thermodynamic theory of steady states. Evolution appears to be an inevitable event, given the presence of certain matter with specified autocatalytic properties and under the maintenance of the finite (free) energy flow necessary to compensate for the steady production of entropy. The theory provides a quantitative basis for the evaluation of laboratory experiments on evolution.

144It was a sort of investigation where you got a good lead, and certainly you had to pursue that; and before you reached the end of that lead up opened another, and this was if anything even more fascinating. One kept on going in several stages; one beautiful lead opening up after the other, and every one much too good to abandon.

145Reductionism, roughly speaking, is the view that everything in this world is really something else, and that the something else is always in the end unedifying. So lucidly formulated, one can see that this is a luminously true and certain idea.

146But then when we see how the branching of trees resembles the branching of arteries and the branching of rivers, how crystal grains look like soap bubbles and the plates of a tortoise’s shell, then we cannot help but wonder why nature uses only a few kindred forms in so many different contexts.

147By the time Reverend Lazarus fought his way through the maze of interlinked credit-appraisal computers and nailed the tapeworm that had just been hatched, he could well be ragged and starving.

148How can computers be programmed so that problem-solving capabilities are built up by specifying ‘what is to be done’ rather than ‘how to do it’?

There is no collective name for such problems, but whenever the term adaptation (ad + aptare, to fit to) appears it consistently singles out the problems of interest.

To what parts of its environment is the organism (system, organization) adapting?

How does the environment act upon the adapting organism (system, organization)?

What structures are undergoing adaptation?

What are the mechanisms of adaptation?

What part of the history of its interaction with the environment does the organism (system, organization) retain?

What limits are there to the adaptive process?

How are different (hypotheses about) adaptive processes to be compared?

149The first technical descriptions and definitions of adaptation come from biology. In that context adaptation designates any process whereby a structure is progressively modified to give better performance in its environment. The structures may range from a protein molecule to a horse’s foot or a human brain or, even, to an interacting group of organisms such as the wildlife of the African veldt. Defined more generally, adaptive processes have a critical role in fields as diverse as psychology (“learning”), economics (“optimal planning”), control, artificial intelligence, computational mathematics and sampling (“statistical inference”). Basically, adaptive processes are optimization processes, but it is difficult to subject them to unified study because the structures being modified are complex and their performance is uncertain. Frequently nonadditive interaction (i.e., “epistasis” or “nonlinearity”) makes it impossible to determine the performance of a structure from a study of its isolated parts. Moreover possibilities for improved performance must usually be exploited at the same time that the search for further improvements is pressed. While these difficulties pose a real problem for the analyst, we know that they are routinely handled by biological adaptive processes, qua processes. The approach of this book is to set up a mathematical framework which makes it possible to extract and generalize critical factors of the biological processes. Two of the most important generalizations are: (1) the concept of a schema as a generalization of an interacting, coadapted set of genes, and (2) the generalization of genetic operators such as crossing-over, inversion, and mutation. The schema concept makes it possible to dissect and analyze complex “nonlinear” or “epistatic” interactions, while the generalized genetic operators extend the analysis to studies of learning, optimal planning, etc. The possibility of “intrinsic parallelism” — the testing of many schemata by testing a single structure — is a direct offshoot of this approach. The book develops an extensive study of intrinsically parallel processes and illustrates their uses over the full range of adaptive processes, both as hypotheses and as algorithms.

150However, in general, the fitness of an allele depends critically upon the influence of other alleles (epistasis). The replacement of any single allele in a coadapted set may completely destroy the complex of phenotypic characteristics necessary for adaptation to a particular environmental niche. The genetic operators provide for the preservation of coadapted sets by inducing a ‘linkage’ between adjacent alleles — the closer together a set of alleles is on a chromosome, the more immune it is to separation by the genetic operators.

151An adaptive system faces its principal challenge when the set of possible structures a is very large and the performance functions μ_E involve many local maxima. It is important then for the adaptive system to provide itself with whatever insurance it can against a prolonged search. It is clear that the search of a must go on so long as significant improvements are possible (unless the system is to settle for inferior performance throughout the remainder of its history). At the same time, unless it exploits possibilities for improved performance while the search goes on, the system pays the implicit cost of a performance less even than the best among known alternatives. Moreover, unexploited possibilities may contain the key to optimal performance, dooming the system to fruitless search until they are implemented. There is only one insurance against these contingencies. The adaptive system must, as an integral part of its search of a, persistently test and incorporate structural properties associated with better performance.

Almost by definition useful properties are points of comparison between structures yielding better-than-average performance. The question then is: How are the structures in a to be compared? If the structures are built up from components, comparison in terms of common components is natural and the question becomes: How is credit for the above-average performance of a structure to be apportioned to its components?

152We will see that each structure generated and tested by a genetic plan in effect tests a multitude of schemata and that the plan actually preserves and exploits this information.

153In sum: This chapter has been concerned with removing the limitations imposed by fixed representations. To this end it is possible to devise languages — the broadcast language is an example — which use strings to rigorously define all effectively specifiable representations, models, operators, etc. Since the objects of the language are presented as strings, they can be made grist for the mill provided by genetic plans. As a consequence the advantages of compact storage of accrued information, operational simplicity, intrinsic parallelism, robustness, etc., discussed in chapters 6 and 7, extend to adaptation of representations.

154It is worthwhile to notice with Leach that “change is no longer something that is done to us by nature but something we can choose to do to nature and to ourselves.” Clearly, in this perspective one of the major objectives of science is to elucidate the dynamics of change. The methods described in this monograph might be one step in this direction.

Although much work remains to be done, it already clearly appears that self-organization is an emerging paradigm of science (Jantsch, 1975) emphasizing macroscopic coordination processes at many levels, in which nonlinear processes and nonequilibrium conditions play a significant role.

155The spectacular progress of molecular biology has been of utmost importance in the formulation of our approach to self-organization. Indeed, a preliminary condition for the study of the relation between function and structure is a detailed knowledge of the chemical mechanisms involved.

156Spandrels — the tapering triangular spaces formed by the intersection of two rounded arches at right angles (figure 1) — are necessary architectural by-products of mounting a dome on rounded arches. Each spandrel contains a design admirably fitted into its tapering space. An evangelist sits in the upper part flanked by the heavenly cities. Below, a man representing one of the four Biblical rivers (Tigris, Euphrates, Indus and Nile) pours water from a pitcher into the narrowing space below his feet.

The design is so elaborate, harmonious and purposeful that we are tempted to view it as the starting point of any analysis, as the cause in some sense of the surrounding architecture.

157We wish to question a deeply engrained habit of thinking among students of evolution. We call it the adaptationist programme, or the Panglossian paradigm. It is rooted in a notion popularized by A. R. Wallace and A. Weismann (but not, as we shall see, by Darwin) toward the end of the nineteenth century: the near omnipotence of natural selection in forging organic design and fashioning the best among possible worlds.

158Gödel showed that provability is a weaker notion than truth, no matter what axiomatic system is involved.

159It is an inherent property of intelligence that it can jump out of the task which it is performing, and survey what it has done; it is always looking for, and often finding, patterns.

160The fascinating thing is that any such system digs its own hole; the system’s own richness brings about its own downfall.

161The secret of self-reproducing programs — and, as we shall see, of self-reproducing molecules — is that one string functions in two ways: first as program, and second as data.

162I think; therefore I have no access to the level where I sum.

163The self comes into being at the moment it has the power to reflect itself.

164Every room is its own recording studio.

165It is a striking experience, especially for a nonbiologist, to attend a movie describing the development of, for example, the chicken embryo. We see the progressive organization of a biological space in which every event proceeds at a moment and in a region that make it possible for the process to be coordinated as a whole. This space is functional, not geometrical. The standard geometrical space, the Euclidean space, is invariant with respect to translations or rotations. This is not so in the biological space. In this space the events are processes localized in space and time and not merely trajectories.

166Jacques Monod has called living systems ‘these strange objects,’ and they are very strange indeed compared with the ‘nonliving’ world (Monod 1970). Thus, one of my objectives is to try to disentangle a few general features of these objects. In molecular biology there has been fundamental progress without which this discussion would not have been possible. But I wish to emphasize other aspects: namely, that living organisms are far-from-equilibrium objects separated by instabilities from the world of equilibrium and that living organisms are necessarily ‘large,’ macroscopic objects requiring a coherent state of matter in order to produce the complex biomolecules that make the perpetuation of life possible.

167It is probably not an exaggeration to say that Western civilization is time centered. Is this perhaps related to a basic characteristic of the point of view taken in both the Old and the New Testaments?

168Instead of finding stability and harmony, wherever we look, we discover evolutionary processes leading to diversification and increasing complexity. This shift in our vision of the physical world leads us to investigate branches of mathematics and theoretical physics that are likely to be of interest in the new context.

169The mere fact of adopting a certain type of modelling, e.g., choosing to describe the situation in discrete time, has already a profound influence on the outcome of the analysis.

170The two sets (periodic and aperiodic) are intimately intertwined: between any two values of μ for which the orbit is periodic, there is one for which it is aperiodic, and vice versa.

171This is a story about dynamics: about change, flow, and rhythm, mostly in things that are alive. The subject matter being dynamics, we are embarked upon a study of temporal morphology, of shapes not in space so much as in time.

172The phase singularity itself is not an instability, but just an alternative — and fatal — mode of operation in normal tissue.

173A lot of behavioral physiology is temporally organized in periodic patterns. If I had to decide what impresses me as the single most conspicuous feature of natural ecosystems, I would say that it is the daily and seasonal periodism.

174One can visualize the necessity of some such irregularity by trying to construct a smooth surface of data points over the square, subject to the constraint that along the boundary it must rise up one floor like a parking garage rampway. Think how this is arranged in the garage: It isn’t.

175The first serious proposal to use material space probes for interstellar exploration is properly credited to Bracewell. According to his calculations, if the Galaxy is heavily populated with extraterrestrial civilizations (~10 light-years average separation) then it makes sense to communicate using radio waves. If the Galaxy is only very thinly populated (~1000 light-years separation) communication is virtually impossible because of time lag and acquisition difficulties. However, if the Milky Way is populated at some intermediate level (~100 light-years separation) then the best way to explore and contact other races is by automated messenger probe.

176A sophisticated self-reproducing starprobe must be able to function in highly generalized environments. It will not be able to pick up its parts (or bits of structural information) ‘free’ from the environment, hence it must carry with it much more descriptive data than any replicating machine built to date. But there is little doubt that such a machine can, in theory, be designed.

177On a strictly material basis, the presence of a single REPRO in a star system represents a de minimis mass loss to the native inhabitants thereof. A typical jovian atmosphere will contain enough fusion fuel to fill ~10¹³ self-reproducing starships, and a single large jovian moon (100 km in diameter) may contain sufficient molybdenum to construct ~10⁵ REPRO machines. Even if 10-100 offspring are generated by each FACTORY the mass loss is negligible. Nevertheless, it is highly unlikely that humanity would take kindly to an alien starcraft landing on one of the Jovian moons Himalia or Elara and reproducing itself there without at least first asking our permission. Probably we would regard it as one of Dyson’s ‘technological cancers loose in the Galaxy’ and attempt to destroy or disable it.

178A remarkable feature of the LMTR problem, discovered by Shannon and established in great generality by further research, is a phenomenon suggesting the heuristic interpretation that information, like liquids, ‘has volume but no shape’, i.e. the amount of information is measurable by a scalar. Just as the time necessary for conveying the liquid content of a large container through a pipe (at a given flow velocity) is determined by the ratio of the volume of the liquid to the cross-sectional area of the pipe, the LMTR equals the ratio of two numbers, one depending on the source and fidelity criterion, the other depending on the channel.

179At first it might appear that the distinction between orderly and chaotic motions is merely one of the complexity of the system involved. In the parlance of dynamical systems theory, the orderly motions described above involve just one ‘degree of freedom’, whereas the chaotic fluid involves many - in conventional hydrodynamics, infinitely many - degrees of freedom. It is thus tempting to associate simple systems with order and complicated ones with chaos.

In fact, this naive association is wrong for several fundamental reasons, some obvious and some subtle. First, everyday experience tells us that complicated systems with many degrees of freedom can undergo very orderly motion. For example, a fluid in smooth (laminar) flow moves in a regular, totally predictable manner.

Second, it is less familiar but nonetheless true that very simple physical systems can exhibit chaotic behavior, with all the associated randomness and unpredictability. Numerical experiments show that the motion of a rigid plane pendulum, if damped and driven, becomes truly chaotic. This result illustrates strikingly that a completely deterministic system can produce chaos without the addition of any external random noise. In other words, one does not have to put randomness in to get it out. The existence of deterministic motions that produce chaos is a clear example of order in chaos.

Third, it is now well established that, at least in some cases, the chaos observed in very complicated systems can be understood quantitatively in terms of simple models that involve very few degrees of freedom. This profound result is of great potential significance for understanding chaotic behavior in the physical world.

180The second law of thermodynamics implies that isolated microscopically reversible physical systems tend with time to states of maximal entropy and maximal ‘disorder.’ However, ‘dissipative’ systems involving microscopic irreversibility, or those open to interactions with their environment, may evolve from ‘disordered’ to more ‘ordered’ states. The states attained often exhibit a complicated structure. Examples are outlines of snowflakes, patterns of flow in turbulent fluids, and biological systems.

181Investigations of simple ‘self-organization’ phenomena in physical and chemical systems have often been based on the Boltzmann transport differential equations (or its analogs) for the time development of macroscopic quantities. The equations are obtained by averaging over an ensemble of microscopic states and assuming that successive collisions between molecules are statistically uncorrelated. For closed systems (with reversible or at least unitary microscopic interactions) the equations lead to Boltzmann’s H theorem, which implies monotonic evolution towards the macroscopic state of maximum entropy.

182With ‘random’ initial configurations, the irreversible character of the cellular automaton evolution leads to several self-organization phenomena.

183To discover and analyze the mathematical basis for the generation of complexity, one must identify simple mathematical systems that capture the essence of the process. Cellular automata are a candidate class of such systems. This article surveys their nature and properties, concentrating on fundamental mathematical features. Cellular automata promise to provide mathematical models for a wide variety of complex phenomena, from turbulence in fluids to patterns in biological growth. The general features of their behavior discussed here should form a basis for future detailed studies of such specific systems.

184The notorious solitaire computer game ‘Life’ (qualitatively similar in some respects to the game of ‘Go’) is an example of a two-dimensional cellular automaton.

185As a consequence of their locality, cellular automaton rules define no intrinsic length scale other than the size of a single site (or of a neighborhood of three sites) and no intrinsic time scale other than the duration of a single time step.

186Finite one-dimensional cellular automata are similar to a class of feedback shift registers.

187A particular type-II two-dimensional cellular automaton whose evolution has been studied extensively is the game of ‘Life’. The local rules take a site to ‘die’ (attain value zero) unless two or three of its neighbors are ‘alive’ (have value one). If two neighbors are alive, the value of the site is left unchanged; if three are alive, the site always takes on the value one. Many configurations exhibiting particular properties have been found. The simplest isolated configurations invariant under time evolution are the ‘square’ (or ‘block’) consisting of four adjacent live sites, and the ‘hexagon’ (or ‘beehive’) containing six live sites. ‘Oscillator’ configurations which cycle through a sequence of states are also known. The simplest is the ‘blinker’ consisting of a line of three live sites, which cycles with a period of two time steps. Oscillators with periods 3, 5, and 7 are also known; other periods may be obtained by composition. So long as they are separated by four or more unfilled sites, many of these structures may exist without interference in the configurations of a cellular automaton, and their effects are localized.

188The game of ‘Life’ is an example of a special class of ‘totalistic’ cellular automata, in which the value of a site depends only on the sum of the values of its neighbors at the previous time step, and not on their individual values. Such cellular automata may arise as models of systems involving additive local quantities, such as chemical concentrations.

189A potentially important feature of cellular automata is the capability for ‘self-reproduction’ through which the evolution of a configuration yields several separated identical copies of the configuration.

190Many of the qualitative features found for elementary cellular automata appear to survive in more complicated cellular automata, although several novel phenomena may appear. For example, in one-dimensional cellular automata with three or more possible values at each site, protective membranes may be generated which shield finite regions from the effects of external noise, and allow very regular patterns to grow from small seeds.

191Cellular automata may be viewed as computers, with initial configurations considered as input programs and data processed by cellular automaton time evolution. Sufficiently complicated cellular automata are known to be universal computers, capable of computing any computable function given appropriate input. Such cellular automata may be considered as capable of the most complicated behavior conceivable and are presumably capable of simulating any physical system given a suitable input encoding and a sufficiently long running time. In addition, they may be used to simulate the evolution of any other cellular automaton. If the necessary encoding is sufficiently simple, the statistical properties of the simulated cellular automaton should follow those of the universal cellular automaton. Although not capable of universal simulation, simpler cellular automata may often simulate each other. This capability may well form a basis for the universality found in the statistical properties of various cellular automata.

192A common complaint of insomniacs is a leaking faucet. No matter how severely the tap is wrenched shut, water squeezes through, the steady, clocklike sound of the falling drops often seems just loud enough to preclude sleep. If the leak happens to be worse, the patter of the drops can be more rapid, and irregular. A dripping faucet is an example of a system capable of a chaotic transition, the same system can change from a periodic and predictable to an aperiodic, quasi-random pattern of behavior, as a single parameter (in this case, the flow rate) is varied. Such a transition can readily be seen by eye in many faucets, and is an experiment well worth performing in the privacy of one’s own kitchen. If you slowly turn up the flow rate, you can often find a regime where the drops, while still separate and distinct, fall in an irregular, never-repeating pattern. The pipe is fixed, the pressure is fixed; what is the source of the irregularity?

Only recently has it been generally realized that simple mechanical oscillators can undergo a transition from predictable to unpredictable behavior analogous to the transition from laminar to turbulent flow in a fluid.

193The world swarms with life forms, many bearing an individual neural net. Each thin web is capable of directing a complex entity, and in each is mirrored the passion of the world. Yet this ship sprang from the slime!

194The tapestry of reality flutters with moving causal structures, both preserving and generating information at all length scales. This brew of freedom and constraint generates a complexity that renders a simple faucet an enigma, let alone consciousness and evolution.

195It may also be possible to quantitatively characterize more fully developed turbulence, measuring the size of typical coherent volumes, as well as the ‘entropy per unit volume,’ or ‘degrees of freedom per unit volume,’ or ‘number of positive characteristic exponents per unit volume’ [50].

Lack of funding has precluded the early experimental test of these ideas.

196These loops are also significantly simpler than the machines of von Neumann or Codd. If we imagine a continuous scale of complexity of self-reproducing entities, with one end representing the simple, marginally self-facilitating copying processes which must have been supported by the physics and chemistry (the ‘transition rules’) of the early pre-biological ‘soup’, and the other end representing the highly complex mechanisms of molecular self-reproduction, as well as the universal constructors of von Neumann and Codd, these loops occupy a spot somewhere in the middle ground. They are sufficiently complex so as to be quite clearly self-reproductive, yet, at the same time, they are sufficiently simple so as to constitute ‘believable’ extensions of simpler copying processes.

197The theory of mutually entraining oscillators has a potential importance comparable to the theory of general cooperative phenomena which has been one of the central subjects of statistical and solid-state physics.

198Actually, even if an ingenious experimenter were to devise wholly quantum apparatus, in the end the observer himself and his observational instruments would necessarily still themselves be solid, broken-symmetry objects; otherwise, the pointers wouldn’t point, the recorders wouldn’t record, etc.

199”… basically do new science in a universe where all the smart guys haven’t already nixed you out two or three hundred years ago. It’s your life story if you’re a mathematician: every time you discover something neat, you discover that Gauss or Newton knew it in his crib. With Life you’re the first guy there, and there’s always fun stuff going on. You can do everything from recursive function theory to animal husbandry. There’s a community of people who are sharing their experiences with you. And there’s the sense of connection between you and the environment. The idea of where’s the boundary of a computer. Where does the computer leave off and the environment begin?”

200There is a fantastic computer game called Life. It is played by collegiate computer hackers, by distracted employees of companies with large computers, by filmmakers experimenting with computer animation, and by sundry others on home computers. Life was devised in 1970 by John Horton Conway, a young mathematician at Gonville and Caius College of the University of Cambridge. It was introduced to the world at large via two of Martin Gardner’s columns in Scientific American (October 1970 and February 1971). The game has had a cult following ever since. Life went through a notorious phase in which it was often played on stolen computer time. (In 1974, Time magazine complained that ‘millions of dollars in valuable computer time may have already been wasted by the game’s growing horde of fanatics.’) The advent of inexpensive home computers has opened Life to a much wider audience.

201Life is described as a game or, sometimes, a video art form. Neither label quite captures the appeal of Life. Certainly Life is nothing like familiar video games. No one ever wins or loses. Life is more like a video kaleidoscope — a way of producing abstract moving pictures on a television screen.

But it’s more than that. The Life screen, or plane, is a world unto itself. It has its own objects, phenomena, and physical laws. It is a window onto an alternate universe. Shimmering forms pulsate, grow, or flicker out of existence. ‘Gliders’ slide across the screen. Life fields tend to fragment into a ‘constellation’ of scattered geometric forms suggestive of a Miro painting.

202Much of the intrigue of Life is the suspicion that there are ‘living’ objects in the Life universe. Conway adapted Von Neumann’s reasoning to prove that there are immense Life objects that can reproduce themselves. There is reason to believe that some self-reproducing Life objects could react to their environment, evolve into more complex ‘organisms,’ and even become intelligent.

Conway further showed that the Life universe — meaning by that a hypothetical infinite Life screen — is not fundamentally less rich than our own. All the variety, complexity, and paradox of our world can be compressed into the two dimensions of the Life plane. There are Life objects that model every precisely definable aspect of the real world.

203When Life was first introduced, three of the biggest questions Life players wondered about were these: Is there any general way of telling what a pattern will do? Can any pattern grow without limit (so that the number of live cells keeps getting bigger and bigger)? Do all patterns eventually settle down into a stable object or group of objects?

Actually, Conway chose the rules of Life just so that these sorts of questions would be hard to answer. He tried many different numerical thresholds for birth and survival. He had three objectives.

First, Conway wanted to make sure that no simple pattern would obviously grow without limit. It should not be easy to prove that any simple pattern grows forever.

Second, he wanted to ensure, nonetheless, that some simple patterns do grow wildly. There should be patterns that look like they might grow forever.

Third, there should be simple patterns that evolve for a long time before stabilizing. A pattern stabilizes by either vanishing completely or producing a constellation of stable objects.

204The glider creeps something like an amoeba or hydra, changing its shape as it goes. It assumes four different phases. Two phases are the shifted mirror images of the other two. Any phase is exactly reproduced four generations later. By then, the glider has moved one cell diagonally.

205The glider is one of the commonest Life objects. When a Life screen starts with a random pattern of on and off pixels, gliders form naturally out of the chaos. Yet Conway did not ‘put’ the gliders into Life. The designers of ordinary video games have to sit down, draw the graphics, figure how to animate them, and write it all up as a complicated program. Life’s program is simple and seems to say nothing about gliders (or blinkers, blocks, beehives …). Everything you see, no matter how unexpected, is the inevitable consequence of Conway’s rules.

Simple rules can have complex consequences.

206Heisenberg once wrote of quanta, ‘I would guess that the structures with which we are confronted are beyond any objective description in imaginable terms and that they are a kind of abstract expression of the laws of nature rather than matter.’ This idea finds its apotheosis in Life. All Life objects are expressions of Conway’s rules. Even so, there is no simple way of deducing the variety of Life phenomena from a mere statement of Life’s rules. This fact likely reflects a similar difficulty of real-world physics.

207This is an exercise in fictional science, or science fiction, if you like that better. Not for amusement: science fiction in the service of science. Or just science, if you agree that fiction is part of it, always was, and always will be as long as our brains are only minuscule fragments of the universe, much too small to hold all the facts of the world but not too idle to speculate about them.

I have been dealing for many years with certain structures within animal brains that seemed to be interpretable as pieces of computing machinery because of their simplicity and/or regularity. Much of this work is only interesting if you are yourself involved in it. At times, though, in the back of my mind, while I was counting fibers in the visual ganglia of the fly or synapses in the cerebral cortex of the mouse, I felt knots untie, distinctions dissolve, difficulties disappear, difficulties I had experienced much earlier when I still held my first naive philosophical approach to the problem of the mind. This process of purification has been, over the years, a delightful experience. The text I want you to read is designed to convey some of this to you, if you are prepared to follow me not through a world of real brains but through a toy world that we will create together.

208Valentino Braitenberg is a cybernetician, a neuroanatomist, and a musician. He seeks to understand how the beautiful structures of the brain constitute a machine that can enable us to exhibit such skilled behavior as that involved in playing music. Since the early 1960s, I have turned to Valentino for detailed neuroanatomy and for lively essays that cut away the technical details to illuminate the key issues of what we may call cybernetics or artificial intelligence or cognitive science.

209At this point we are ready to make a fundamental discovery. We have gathered evidence for what I would like to call the ‘law of uphill analysis and downhill invention.’ What I mean is this. It is pleasurable and easy to create little machines that do certain tricks. It is also quite easy to observe the full repertoire of behavior of these machines - even if it goes beyond what we had originally planned, as it often does. But it is much more difficult to start from the outside and to try to guess internal structure just from the observation of behavior.

210This story is quite old and goes by the name of Darwinian evolution. Many people don’t like the idea that everything beautiful and marvelous in organic nature should be due to the simple cooperation of reproduction, errors, and selection. This is no problem for us. We have convinced ourselves that beautiful, marvelous, and shrewd machines can be made out of inorganic matter by this simple trick. Moreover, we already know that analysis is much more difficult than synthesis. Where there has been no conscious engineering at all, as in the case of our type 6 vehicles, analysis will necessarily produce the feeling of a mysterious supernatural hand guiding the creation. We can imagine that in most cases our analysis of brains in type 6 vehicles would fail altogether: the wiring that produces their behavior may be so complicated and involved that we will never be able to isolate a simple scheme. And yet it works.

211Now it is different with type 14 vehicles. They move through their world with consistent determination, always clearly after something that very often we cannot guess at the outset - something that may not even be there when the vehicle reaches the place it wants to get to. But it seems to be a good strategy, this running after a dream. Most of the time the chain of optimistic predictions that seems to guide the vehicle’s behavior proves to be correct, and Vehicle 14 achieves goals that Vehicle 13 and its predecessors ‘couldn’t even dream of.’ The point is that while the vehicle goes through its optimistic predictions, the succession of internal states implies movements and actions of the vehicle itself. While dreaming and sleepwalking, the vehicle transforms the world (and its own position in the world) in such a way that ultimately the state of the world is a more favorable one.

We observe at some stage how one of the vehicles of type 14 is waiting for another vehicle to appear. This other vehicle carries a very appealing source which Vehicle 14 intends to tap. It seems to be waiting impatiently, since every now and then it performs the motions that are associated with the tapping, as if by anticipating its own behavior in the presence of the desired event, it could accelerate the event’s occurrence. ‘This is very human,’ we say. ‘Haven’t we all felt an urge to run to the door long before the doorbell rings, when waiting impatiently for a beloved friend?’ Indeed, it is aberrant behavior dictated by a very subjective law of causality, but it does seem to reflect a basic attitude of humankind, this irrational belief in the effectiveness of one’s own actions.

212The more there is of the quality to which the sensor is tuned, the faster the motor goes.

213Kolmogorov complexity and Shannon entropy both increase monotonically with disorder, making them measures of randomness rather than complexity. When we call a random pattern ‘not complex,’ we are implicitly assigning it to an ensemble, and it is the ensemble that is simple.

214The experimental approaches to the question of the anatomical nature of the engram are all marred by a fundamental difficulty. (Engrams are the memory traces postulated many years ago by psychologists, long before there was any hope of ever finding one in the brain.) Suppose we have some idea about the anatomical changes responsible for memory and want to prove it. We present some input to one animal, but not to another animal, in order to use it as a control. It is not that the control animal has experienced nothing while the experimental animal received its input: it has had its own experiences and its own thoughts. In order to compare the traces left in the brains of the two animals by the two different inputs, we would have to know exactly where the information ended up in the two animals. In truth we don’t. Most likely, two inputs that may have entirely different meanings are represented in the brain in quite the same way, as diffuse patterns of activity in an enormous network of neurons.

Suppose the engram were embodied in changes that are very easily visible in the electron microscope, or possibly in the light microscope: a change in the thickness of axonal terminals, a change in the number of synaptic vesicles, or a change in the amount of pre- or postsynaptic thickening. No matter what kind of information we presented to the animal, in the end we would expect to see some synapses of one kind and some of the other, for information must be represented in a pattern of elements in different states, or else it wouldn’t be information at all. But different patterns can only be distinguished if they are understood in every detail. In other words, they cannot be distinguished at the present stage of our knowledge of the brain.

215“The familiar characteristic aggregates of the time evolution of 1d CA’s are reminiscent of a common form for economic data — rectangular arrays giving observations on firms (rows) over time. The resemblance is more than superficial. There are several important classes of dynamic economic models in which a firm’s expectations and actions are strongly influenced by recent actions of its economic neighbors: competing firms within an industry, suppliers, customers. In many of these models the relevant expectation information is qualitative in nature and representable by state variables: Are firms in the neighborhood now discounting a previously stable price? Do neighboring firms’ actions signal a weak, normal, or strong market?”

216“When the iterates of an integer function are tabulated in base 2, they may exhibit patterns similar to those of one-dimensional cellular automata. The bit patterns make visible important features of the evolution of these iterates.”

217“We examine the qualitative behavior of spatially-extended systems discretized in time and space with continuous local variables, called lattice dynamical systems. When these systems are approximated using a finite number of states at each site, the resulting system is a cellular automaton. The number of states per site, or resolution, can be thought of as the arithmetical precision with which a continuous-state lattice dynamical system is simulated.”

218“We present a new model for the temporal evolution of interface in two dimensions. The model interface may represent many different physical phenomena, including fluid interface dynamics (in the Hele-Shaw configuration), solidification, and diffusion limited aggregation.”

219“Most software for generating cellular automata is not ‘user-friendly’ and may require special equipment or large amounts of computer memory. I have developed new software for educational purposes, which satisfies the following criteria: Simple. Flexible. Fast. Convenient. Standard equipment. Easily modified. The Conway ‘Game of Life’ is offered, plus eight additional variants of the usual formula. Ten different colors can appear on the screen simultaneously. The field size can be varied from 9 x 9 to 39 x 39.”

220Artificial Life is the study of man-made systems that exhibit behaviors characteristic of natural living systems. It complements the traditional biological sciences concerned with the analysis of living organisms by attempting to synthesize life-like behaviors within computers and other artificial media. By extending the empirical foundation upon which biology is based beyond the carbon-chain life that has evolved on Earth, Artificial Life can contribute to theoretical biology by locating life-as-we-know-it within the larger picture of life-as-it-could-be.

221Certainly life, as a dynamic physical process, could ‘haunt’ other physical material: the material just needs to be organized in the right way. Just as certainly, the dynamic processes that constitute life — in whatever material bases they might occur — must share certain universal features — features that will allow us to recognize life by its dynamic form alone, without reference to its matter.

Since it is quite unlikely that organisms based on different physical chemistries will present themselves to us for study in the foreseeable future, our only alternative is to try to synthesize alternative life-forms ourselves: Artificial Life: life made by man rather than by nature.

222Whereas biology has largely concerned itself with the material basis of life, Artificial Life is concerned with the formal basis of life. Biology has traditionally started at the top, viewing a living organism as a complex biochemical machine, and worked analytically downwards from there — through organs, tissues, cells, organelles, membranes, and finally molecules — in its pursuit of the mechanisms of life. Artificial Life starts at the bottom, viewing an organism as a large population of simple machines, and works upwards synthetically from there — constructing large aggregates of simple, rule-governed objects which interact with one another nonlinearly in the support of life-like, global dynamics.

223The ‘key’ concept in AL is emergent behavior. Natural life emerges out of the organized interactions of a great number of nonliving molecules, with no global controller responsible for the behavior of every part. Rather, every part is a behavior itself, and life is the behavior that emerges from out of all of the local interactions among individual behaviors. It is this bottom-up, distributed, local determination of behavior that AL employs in its primary methodological approach to the generation of lifelike behaviors.

224The essential features of computer-based Artificial Life models are:

• They consist of populations of simple programs or specifications.
• There is no single program that directs all of the other programs.
• Each program details the way in which a simple entity reacts to local situations in its environment, including encounters with other entities.
• There are no rules in the system that dictate global behavior.
• Any behavior at levels higher than the individual programs is therefore emergent.

225Biologists today reject vitalism, believing rather that life as we know it will eventually be explainable completely within the context of biochemistry. Thus, most biologists would agree — in principle anyway — with the following statement: living organisms are nothing more than complex biochemical machines. However, they are different from the machines of our everyday experience. A living organism is not a single, complicated biochemical machine. Rather it must be viewed as a large population of relatively simple machines. The complexity of its behavior is due to the highly nonlinear nature of the interactions between all of the members of this polymorphic population. To animate machines, therefore, is not to ‘bring’ life to a machine; rather it is to organize a population of machines in such a way that their interactive dynamics is ‘alive.’

226The key insight into the natural method of behavior generation is gained by noting that nature is fundamentally parallel. This is reflected in the ‘architecture’ of natural living organisms, which consist of many millions of parts, each one of which has its own behavioral repertoire. Living systems are highly distributed, and quite massively parallel. If our models are to be true to life, they must also be highly distributed and quite massively parallel. Indeed, it is unlikely that any other approach will prove viable.

227Stan Ulam — one of von Neumann’s colleagues at Los Alamos who also investigated dynamic models of pattern production and competition — suggested an appropriate formalism, which has come to be known as a cellular automaton (CA).

228Von Neumann’s CA model was a constructive proof that an essential characteristic behavior of living things — self-reproduction — was achievable by machines. Furthermore, he determined that any such method must make use of the information contained in the description of the machine in two fundamentally different ways:

• INTERPRETED, as instructions to be executed in the construction of the offspring.
• UNINTERPRETED, as passive data to be duplicated to form the description given to the offspring.

Of course, when Watson and Crick unraveled the mystery of DNA, they discovered that the information contained therein was used in precisely these two ways in the processes of transcription/translation and replication.

229The term ‘cybernetics’ is derived from the Greek kybernetes — or steersman — which was used by Plato in the sense of ‘government.’ For Wiener, the word imparted a sense of goal-oriented, purposeful control of behavior.

230Von Neumann’s program of the application of discrete mathematics to the synthesis of behavior and Wiener’s program of the application of continuous mathematics to the analysis of behavior are entirely complementary endeavors, and there is quite a large area of potential overlap between them. Indeed, many of the same phenomena can be represented equally well within either of the two methodological approaches, and it was one of von Neumann’s dreams to develop a continuous version of his discrete, automaton approach.

231James Thatcher completed a simplified version of von Neumann’s self-replicating CA model. E. F. Codd developed a version using only eight states per cell. Richard Laing demonstrated a clever variation on the von Neumann plan in which a machine first constructs a description of itself by self-inspection, and then uses that description to construct a copy of itself. This latter model would be capable of passing on acquired characteristics in Lamarckian fashion, unlike von Neumann’s model. Laing also developed a system of self-reproducing artificial organisms based on what he called artificial molecular machines — dynamic ‘program tapes’ interacting within a sort of ‘soup.’ This model attempted to combine in one system the best features of von Neumann’s CA and kinematic models.

232And there may come a time when way out there, or even back here on a much-altered Earth, a group of such much-altered rogue factories will gather to discuss their ultimate nature and their origins. Some will surely take note of their own amazing complexity, their cunning design almost miraculously suited to their environmental circumstances, and conclude that only a very clever first designer, and one undoubtedly very like themselves, could account for their creation. Another faction will scoff at this and insist that their origins lie in time and chance alone. At this, some factory with a mathematical bent will quickly calculate that, given the amount of time that factories are known by archaeological evidence to have existed, it is easy to see that factories could not have arisen by mere physical jostling. ‘Why,’ this witty factory may remark, ‘it would be as absurd as supposing that one of us could be produced by a tornado howling through a junkyard.’ They do not all agree, but yet they all laugh.

233Artificial Life involves the realization of lifelike behavior on the part of man-made systems consisting of populations of semi-autonomous entities whose local interactions with one another are governed by a set of simple rules. Such systems contain no rules for the behavior of the population at the global level, and the often complex, high-level dynamics and structures observed are emergent properties, which develop over time from out of all of the local interactions among low-level primitives by a process highly reminiscent of embryological development, in which local hierarchies of higher-order structures develop and compete with one another for support among the low-level entities. These emergent structures play a vital role in organizing the behavior of the lowest-level entities by establishing the context within which those entities invoke their local rules and, as a consequence, these structures may evolve in time.

234Several people raised the question of establishing a general measure of complexity, adaptability, or progress in evolutionary processes. Such a measure — or measures — would certainly be valuable, and there have been efforts to apply Shannon’s entropy concept and Chaitin’s algorithmic complexity measures to living systems and the process of evolution — with somewhat mixed results! The field awaits an appropriate, natural measure of complexity, as do many other fields.

235There was little discussion of possible practical applications of Artificial Life.

236Nor was there much discussion of the moral or ethical issues involved in the pursuit of Artificial Life. Such issues must be discussed before we go much further down the road to creating life artificially. We are once again at a point where our technical grasp of a problem is far ahead of our moral understanding of the issues involved, or of the possible consequences of mastering the technology.

237It is, perhaps, not coincidental that the first workshop on Artificial Life was held at Los Alamos, site of the mastery of atomic fission and fusion. Both technologies have tremendous potential for benefiting life on earth, but both also have tremendous potential for abuse, whether intentional or accidental. Whereas the technology of death was developed in secret, under government mandate, and with little official attention to social and moral consequences, this first workshop on the technology of life was held in the open, by voluntary participation, and we must see to it that it is pursued with the most careful attention to social and moral consequences.

238Life is a property of form, not matter, a result of the organization of matter, rather than something that inheres in the matter itself. Neither nucleotides nor amino acids nor any other carbon-chain molecule is alive — yet put them together in the right way, and the dynamic behavior that emerges out of their interactions is what we call life. It is effects, not things, upon which life is based — life is a kind of behavior, not a kind of stuff — and as such, it is constituted of simpler behaviors, not simpler stuff.

239A cellular automata machine is a universe synthesizer.

240Cellular automata are stylized, synthetic universes defined by simple rules much like those of a board game. They have their own kind of matter which whirls around in a space and a time of their own. One can think of an astounding variety of them. One can actually construct them, and watch them evolve. As inexperienced creators, we are not likely to get a very interesting universe on our first try.

241In a cellular automaton, there are no ‘particles’ — only bits. Yet when we watch the screen, we irresistibly see objects that move, collide, bounce, and scatter. The question of what constitutes an ‘object’ in a CA, and what it means for that object to ‘move,’ is more subtle than it first appears. Identity is not given by the substrate but by the pattern.

242In principle, evolution, life, and intelligence can take place within a world governed by a very simple cellular-automaton rule.

243In a cellular automaton, objects that may be interpreted as passive data and objects that may be interpreted as computing devices are both assembled out of the same kind of structural elements and subject to the same fine-grained laws; computation and construction are just two possible modes of activity.

244Gleick’s Chaos is not only enthralling and precise, but full of beautifully strange and strangely beautiful ideas.

245When Mitchell Feigenbaum began thinking about chaos at Los Alamos, he was one of a handful of scattered scientists, mostly unknown to one another. A mathematician in Berkeley, California, had formed a small group dedicated to creating a new study of ‘dynamical systems.’ A population biologist at Princeton University was about to publish an impassioned plea that all scientists should look at the surprisingly complex behavior lurking in some simple models. A geometer working for IBM was looking for a new word to describe a family of shapes - jagged, tangled, splintered, twisted, fractured - that he considered an organizing principle in nature. A French mathematical physicist had just made the disputatious claim that turbulence in fluids might have something to do with a bizarre, infinitely tangled abstraction that he called a strange attractor.

246Chaos poses problems that defy accepted ways of working in science. It makes strong claims about the universal behavior of complexity. The first chaos theorists, the scientists who set the discipline in motion, shared certain sensibilities. They had an eye for pattern, especially pattern that appeared on different scales at the same time. They had a taste for randomness and complexity, for jagged edges and sudden leaps. Believers in chaos - and they sometimes call themselves believers, or converts, or evangelists - speculate about determinism and free will, about evolution, about the nature of conscious intelligence. They feel that they are turning back a trend in science toward reductionism, the analysis of systems in terms of their constituent parts: quarks, chromosomes, or neurons. They believe that they are looking for the whole.

247Relativity eliminated the Newtonian illusion of absolute space and time; quantum theory eliminated the Newtonian dream of a controllable measurement process; and chaos eliminates the Laplacian fantasy of deterministic predictability.

248The simplest systems are now seen to create extraordinarily difficult problems of predictability. Yet order arises spontaneously in those systems - chaos and order together. Only a new kind of science could begin to cross the great gulf between knowledge of what one thing does - one water molecule, one cell of heart tissue, one neuron - and what millions of them do.

249Sudden cardiac death is a problem in topology.

250The singularity is a state, not merely a stimulus.

251The rotor is a singularity incarnate in a physical medium.

252it is comparatively easy to make computers exhibit adult-level performance in solving problems on intelligence tests or playing checkers, and difficult or impossible to give them the skills of a one-year-old when it comes to perception and mobility.

253If we think of complexity as a physical property of an object (such as mass or entropy) then there is a puzzle. Objects can be copied. A bull is a complex object. Are seven bulls seven times as complex as one bull? Can complexity proliferate so cheaply?

254It took billions of years for the earth to evolve one bull; but one bull and a few compliant cows will produce seven bulls relatively speedily.

255The algorithmic definition of complexity is really a definition of randomness (a profound one).

256Take a glass and smash it with a hammer. Keep on smashing, and you will in short order create a mass of shards that contains an amount of mutual information greater than that between all the DNA in the human body. Since a bowl of glass dust ought not to be more complex than human genes, mutual information ought not to be considered a measure of complexity.

257The value of a message appears to reside not in its information (its absolutely unpredictable parts), nor in its obvious redundancy (verbatim repetitions, unequal digit frequencies), but rather in what might be called its buried redundancy — parts predictable only with difficulty, things the receiver could in principle have figured out without being told, but only at considerable cost in money, time, or computation.

258If a computation is encoded as an attractor of a dynamical system, then small perturbations are automatically corrected as the system relaxes back to the attractor. The system is self-repairing.

259Fractal geometry will make you see everything differently. There is danger in reading further. You risk the loss of your childhood vision of clouds, forests, flowers, galaxies, leaves, feathers, rocks, mountains, torrents of water, carpets, bricks, and much else besides.

260A cat following a bird with its eyes need not do floating-point arithmetic to know where to pounce.

261The genetic complexity of an organism is proportional to the amount of genetic information tried out and discarded by the process of natural selection on the ancestors of the organism.

262Cellular automata were invented in the late 1940s by Stanislaw Ulam (1909 - 1984) and John von Neumann (1903 - 1957). One can say that the “cellular” comes from Ulam, and the “automata” from von Neumann.

Ulam was primarily a mathematician. He invented the Monte Carlo simulation technique, the highly infinite “measurable cardinals” of set theory, and he made contributions to analysis and number theory. With Edward Teller, Ulam was the co-inventor of the hydrogen bomb. Von Neumann was a still more wide-ranging mathematician. He did work in set theory, in the foundations of quantum mechanics, in economics, and in game theory. In addition, von Neumann greatly influenced the logical architecture of the first electronic computers.

263In general, when sufficient physical insight is lacking and one makes more or less arbitrary probabilistic assumptions about the data and proceeds to make logical deductions, the results must be considered irrelevant to the task at hand, which is to learn from the data.

264Periodic behavior has low information content; purely random behavior has high information content; but both are simple. The interesting behavior lies between these extremes, where a process is an amalgam of regular and stochastic components.

265It is my experience from talks I have given on the subject that a person well indoctrinated in traditional statistical thinking may have greater difficulty in understanding the new concepts than one who is not so blessed.

266A chaotic map possesses three ingredients: unpredictability, indecomposability, and an element of regularity.

267If F has a periodic point of period 3, then F has periodic points of all periods.

268The period-doubling route to chaos is one of the most commonly observed transitions from simple to complicated behavior in parameterized families of maps. It is also universal: the same constants arise for all families.

269Broadly speaking, there are two types of problems concerning cellular automata: the forward problem and the inverse problem. The forward problem is: Given a cellular automaton rule, determine (predict) its properties. The inverse problem is: Given a description of some properties, find a rule, or set of rules, which have these properties.

270Life breaks free. Life expands to new territories. Painfully, perhaps even dangerously. But life finds a way.

271The specter of information is haunting sciences.

272It from bit. Otherwise put, every it — every particle, every field of force, even the spacetime continuum itself — derives its function, its meaning, its very existence entirely — even if in some contexts indirectly — from the apparatus-elicited answers to yes-or-no questions, binary choices, bits.

273Build physics, with its false face of continuity, on bits of information!

274That seminal workshop gave birth to the growing field of Artificial Life. Since that first workshop, a large number of people have become interested in the field and its methodological approaches and have initiated new research projects. Many of these new research projects were reported at the Second Artificial Life Workshop, held in February 1990, in Santa Fe, New Mexico. This volume constitutes the proceedings of that second workshop.

It is difficult to compare the two workshops. We will never recapture the novelty and excitement of the first workshop. It was the first time many of the participants became aware of the true depth and breadth of the questions and techniques they had been toying with until then. For many of us, it was the first confirmation that we were not crazy — that there was a solid basis for the line of inquiry we had all been pursuing in isolation: studying biological phenomena without studying biological things.

275The primary purpose of the first workshop was to find out what kinds of approaches researchers were pursuing in their attempts to simulate or even synthesize life, evolution, ecological dynamics, and so forth. Another goal was to find out what kinds of fundamental biological questions were most appropriately addressed by such techniques.

The proceedings from that first workshop constituted an overview of the possibilities. Although there were no major theoretical breakthroughs reported in any of the papers, and many of the research efforts were clearly in the very earliest stages of development, it was easy to see the power implicit in these early tentative experiments. However, it was not easy to predict the direction in which the field would progress from such a start.

These proceedings of the 1990 Artificial Life Workshop provide a second data point on the direction in which the field of Artificial Life is progressing, and I am very pleased with the trajectory that it appears to be on. Overall, there is more good science and less “gee-whiz” than in the first proceedings. This is not to put down those first Proceedings—they were exactly what they had to be. However, it is clear that the field has matured a good deal in the intervening two years, and this is a sign of more good things to come.

276To understand the breadth and scope of the field of Artificial Life, it is only necessary to note that we can replace the references to ‘self-reproduction’ above with references to many other biological phenomena, including: the origin of life, molecular self-assembly, embryogenesis (including growth, development, and differentiation), animal behavior (ethology), insect-colony dynamics, evolution, speciation, ecological dynamics, and even linguistic and socio-cultural evolution.

In addition to providing new ways to study the biological phenomena associated with life here on Earth, life-as-we-know-it, Artificial Life allows us to extend our studies to the larger domain of the ‘bio-logic’ of possible life, life-as-it-could-be, whatever it might be made of and wherever it might be found in the universe.

Thus, Artificial Life is not only about studying existing life, but also about the possibility of synthesizing new life, within computers or other ‘artificial’ media. The life that is realized in these alternative media will force us to broaden our understanding of the proper domain of biology to include self-organizing, evolving, and even ‘living’ machines, regardless of the specific physical stuff of which they are constituted, or whether or not they are based upon the same chemical and physical principles as the life that has evolved here on Earth.

277The talks at the second workshop were arranged to reflect the chronological and hierarchical ordering evident in the natural world. Thus, talks treating the origin of life came first, followed by talks on the evolutionary process, on development and differentiation, learning, computer life, ecological dynamics, and finally to discussions on the future evolution of life. Progressing through the material in this natural sequence continuously reinforces the ‘emergent’ nature of biological structures and functions, as the phenomena under discussion on one day can be seen to have emerged ‘on the shoulders,’ so to speak, of the phenomena under discussion the day before.

278Modern organisms owe their structure to the complex process of biological evolution, and it is very difficult to discern which of their properties are due to chance, and which to necessity. If biologists could ‘re-wind the tape’ of evolution and start it over, again and again, from different initial conditions, or under different regimes of external perturbations along the way, they would have a full ensemble of evolutionary pathways to generalize over. Such an ensemble would allow them to distinguish universal, necessary properties (those which were observed in all the pathways in the ensemble) from accidental, chance properties (those which were unique to individual pathways). However, biologists cannot rewind the tape of evolution, and are stuck with a single, actual evolutionary trace out of a vast, intuited ensemble of possible traces.

279We consider co-evolution occurring among species each of which is itself adapting on a rugged, multipeaked fitness landscape. But the fitness of each genotype, via the phenotype, of each species is affected by the genotypes via the phenotypes of the species with which it is coupled in the ecosystem. Adaptive moves by one co-evolutionary partner, therefore, may change the fitness and the fitness landscapes of the co-evolutionary partners. Anecdotally, development of a sticky tongue by the frog alters the fitness of the fly, and what it ought to do: it should develop slippery feet. In this framework, adaptive moves by any partner may deform the fitness landscapes of other partners.

280One interesting result is that co-evolutionary systems seem to achieve a ‘poised’ state ‘at the edge of chaos,’ lending support to an idea originally due to Norman Packard and Chris Langton, that evolutionary dynamics will bring populations to the vicinity of a phase transition between ordered and disordered behaviors.

281After hearing Kristian Lindgren’s talk at the workshop, many researchers went back to their models, took another look at the ongoing evolutionary dynamics, and discovered a similar pattern of long periods of stasis punctuated by brief periods of rapid evolutionary change. I think a lot of these researchers kicked themselves for not having noted this feature in their data earlier, a consequence of concentrating on the products of the process, rather than on the process itself.

282Evolutionary adaptation can be viewed as a kind of ‘learning’ that takes place on time scales much longer than the lifetimes of individual organisms. Traditional computational learning methods, such as back-propagation applied to neural nets, often require that each action of the learning system be evaluated by a ‘teacher’ or ‘critic,’ who ‘knows’ what the correct action should have been, and provides the learning system with an evaluation of its performance, ranging from a simple ‘yes’ or ‘no’ to providing it with the ‘correct’ answer. However, in many real learning situations, there is no ‘correct’ answer, or even if there is, it may be computationally intractable to determine what it is, so there can be no teacher that provides the system with the correct feedback. In such learning situations, neural networks perform rather poorly.

283The paper by David Ackley and Michael Littman employs an adaptation strategy they call Evolutionary Reinforcement Learning (ERL). ERL ‘combines genetic evolution with neural network learning, and an artificial life “ecosystem” called AL, within which populations of ERL-driven adaptive “agents” struggle for survival.’ During the course of their simulations, they observe that the best performance occurs when both evolutionary learning and short-term learning are employed. More importantly, however, they observe the occurrence of a number of subtle effects at the level of population genetics that appear to enhance overall learning, such as the classic ‘Baldwin effect,’ a mechanism by which changes in behavior learned over the short term can eventually be transferred to the ‘genetics’ of long-term learning.

284Multicellular organisms start life as a single cell. Through repeated cell divisions, cell movements, and cellular differentiation, the mature organism develops via the complex process known as morphogenesis. The mechanics of the process by which the growing body of cells shapes itself and produces all the right kinds of cells in all the right places is still largely a mystery. All the cells contain the same genetic program, and it is not well understood how the different types of cells diverge into different domains of genetic program space.

285Lindenmayer systems (L-systems) have found broad application within the Artificial Life community for analyzing the complex process of morphogenesis. The use of L-systems is in keeping with the overall spirit of the Artificial Life approach. L-systems abstract the ‘logical form’ of the natural problem of morphogenesis. They allow researchers to work and experiment with systems that grow, develop, and differentiate like real organisms, but which are not, themselves, real organisms. They are another instance of the general class of growing, developing, and differentiating things. Therefore, by studying them, and by comparing and contrasting them with the growth, development, and differentiation of living systems, we can learn more about the ‘real’ system by understanding the general class of systems it belongs to.

Sadly, Aristid Lindenmayer, the inventor of L-systems, recently passed away after a battle with cancer. However, he has inspired many researchers to carry on his work.

286It should be clear by this point that representation is a major issue in Artificial Life research. A representation scheme for implementing algorithms that is understandable by human beings (such as a familiar programming language like Pascal or Fortran) may not be amenable to manipulation by genetic algorithms. Thus, programmable representations may not be evolvable, and evolvable representations may not be programmable. Many of the research efforts reported in these proceedings employ representations that were chosen for their evolvability, not for their programmability.

John Koza attempts to effect a compromise between programmability and evolvability. By applying a genetic algorithm to the parse tree of a program (rather than to its linear representation as a bit-string), and by respecting syntactic categories, Koza is able to achieve evolution within the context of a programmable language. In the context of the tree representation of a program, the crossover operator of the genetic algorithm is allowed to swap subtrees between two parent programs when the roots of those subtrees belong to the same syntactic category. In Koza’s system, all subtrees are S-expressions in Lisp. Since all S-expressions belong to the same syntactic category, any subtree can be interchanged with any other. Koza has applied this system to evolve programs to solve a number of hard problems, including a number of Artificial Life problems.

287If we want to understand what makes symbols meaningful (and related phenomena such as intentionality), then AI — at least as currently pursued — will not do. If we want genuine meaning and original intentionality, then communication must have real relevance to the communicators. Furthermore, if we are to understand the pragmatic context of the communication and preserve ecological validity, then it must occur in the communicators’ natural environment, that to which they have become coupled through natural selection. Unfortunately, the natural environments of biological organisms are too complicated for carefully controlled experiments.

288Von Neumann’s studies of self-reproduction involved the construction of structures which were not at all like any known living things. Yet, through their study, he was able to determine principles which are likely to be true of any self-reproducing system, including known biological organisms. For instance, he found that the genetic description of an organism must be used in two different ways: 1) interpreted as instructions to construct its offspring, and 2) uninterpreted as data to be copied to create duplicates of the description to be passed on to its offspring. This was found to be the case for biological organisms once Watson and Crick revealed the workings of the DNA molecule.

Von Neumann’s proof of the possibility of machine self-reproduction is achieved via a book-length constructive proof. The paper by Alvy Ray Smith provides a one-page proof of the possibility of machine self-reproduction. Whereas von Neumann required both computation universality and construction universality of his self-reproducing machines, Smith shows that computational universality alone suffices. Smith’s proof relies on an elegant application of the famous Recursion Theorem of recursive function theory.

289Another class of computer life-forms is already in existence, and is, in fact, becoming quite a problem. Computer viruses have been in existence for approximately ten years now, and since the introduction of the first viruses, not a single species has been eradicated. In fact, more sophisticated computer viruses are being introduced more and more rapidly, and the problem promises to become epidemic in the near future.

Biologists argue over whether or not biological viruses can be considered to be alive. Although they reproduce, they have no metabolism of their own to produce the required parts, and must take over the metabolic and reproductive machinery of a host cell in order to produce offspring. Allowing for the different medium, computer viruses appear to be every bit as much alive as biological viruses. The paper by Eugene Spafford presents an overview of the workings of different classes of computer viruses and argues that the release of computer viruses onto a network is as morally reprehensible as would be the release of biological viruses into a public reservoir.

290The debate about the possibility of machine life will have something in common with the debate about the possibility of machine intelligence. Both AI and AL study their respective subject matter by attempting to realize it within computers. Although AI has not yet achieved anything that even its most ardent supporters would call genuine machine intelligence, AI has completely changed the way in which scientists think about what it is to be ‘intelligent,’ and has, therefore, made a major scientific contribution, even though it hasn’t achieved its overall goal.

Similarly, Artificial Life will force us to rethink what it is to be ‘alive.’ The fact is, we have no commonly agreed upon definition of ‘the living state.’ When asked for a definition, biologists will often point to a long list of characteristic behaviors and features shared by most living things (such as the list collated by Mayr) which includes things like self-reproduction, metabolic activity, mortality, complex organization and behavior, etc. However, as most such lists are constituted of strictly behavioral criteria, it is quite possible that we will soon be able to exhibit computer processes that exhibit all of the behaviors on such a list. When that happens, we will have two choices, either 1) admit that the computer process is alive, or (more likely!) 2) change the list so as to exclude the computer process from being considered alive. Part (but only part) of the failure of AI to achieve ‘intelligence’ is due to the fact that it is chasing a moving target. It used to be thought that playing chess required true intelligence. Now that computers can beat most humans at it, the ability to play chess is no longer considered an indicator of intelligence.

291There is a caution here that we all must attend to. Attempts to create Artificial Life may be pursued for the highest scientific and intellectual goals, but they may have very devastating consequences in the real world, if researchers do not take care to insure that the products of their research cannot ‘escape,’ either into computer networks or into the biosphere itself.

292What will the world be like when the means to produce self-reproducing robots is as widely available as the means to produce self-reproducing computer programs?

293The paper by Peter Cariani addresses the difficult concept of ‘emergence,’ a central, but poorly defined, concept in many fields, including Artificial Life. Cariani identifies the different senses in which the term ‘emergence’ is typically used, and argues that computers cannot exhibit ‘genuinely’ emergent processes. Rather, Cariani argues, only nature can support emergence in the most important sense of the term. Although his conclusions are in opposition to some of the beliefs held by many Artificial Life researchers, he is clearly correct that our usage of the term ‘emergence’ must be more carefully qualified, if it is to have any real meaning or utility in the theories that we ultimately construct.

294These organisms will evolve in a fundamentally different manner than contemporary biological organisms, since their reproduction will be under at least partial conscious control, giving it a Lamarckian component. The pace of evolutionary change consequently will be extremely rapid. The advent of artificial life will be the most significant historical event since the emergence of human beings. The impact on humanity and the biosphere could be enormous, larger than the industrial revolution, nuclear weapons, or environmental pollution. We must take steps now to shape the emergence of artificial organisms; they have potential to be either the ugliest terrestrial disaster, or the most beautiful creation of humanity.

295With the advent of artificial life, we may be the first species to create its own successors. What will these successors be like? If we fail in our task as creators, they may indeed be cold and malevolent. However, if we succeed, they may be glorious, enlightened creatures that far surpass us in their intelligence and wisdom. It is quite possible that, when the conscious beings of the future look back on this era, we will be most noteworthy not in and of ourselves but rather for what we gave rise to. Artificial life is potentially the most beautiful creation of humanity. To shun artificial life without deeper consideration reflects a shallow anthropocentrism.

296A simple and brief proof of the existence of nontrivial self-reproducing machines, as cellular automata (CA) configurations, is presented, which relies only on computation universality. Earlier proofs are book length and rely on “construction universality.” Furthermore, simple CA are shown to support nontrivial self-reproduction—hence, simultaneously simple and nontrivial.

297John von Neumann introduced the concept in a book which also created the field of CA theory (from a suggestion by Stanislaw Ulam). We will use the term ‘machine’ in the same sense as von Neumann — a finite collection of non-quiescent cells in a CA. Both his CA (29-state cells) and his self-reproducing configuration (40,000 or so nonquiescent cells) were complex and inspired others to simplify.

298There has been a revival in interest in CA theory since the combined advent of chaos, fractals, and interactive computer graphics in the 1980s, inspired principally by Wolfram and the other authors. There is a surprising ignorance by much of the post-revival literature of the hundreds of papers written during the preceding 20 years or so. Part of the problem is the lack of knowledge that CA had many other names then: iterative arrays, tessellation automata, cellular spaces, modular arrays, polyautomata, etc. The references herein can be used as pointers into this literature.

299The recent revival of interest in CA has concentrated on the totalistic case, where the transition function is required to be an arithmetic function of the neighborhood states. A result that has been rediscovered numerous times is that trivial self-reproduction — that is, self-replication — is possible in totalistic CA.

300My most recent work stems from my association with the Santa Fe Institute in Santa Fe, New Mexico. About five years ago the Santa Fe Institute, then newly founded, began developing a new interdisciplinary approach to the study of adaptive systems. The studies center on a class of systems, called complex adaptive systems, that have a crucial role in a wide range of human activities. Economies, ecologies, immune systems, developing embryos, and the brain are all examples of complex adaptive systems. Despite surface dissimilarities, all complex adaptive systems exhibit a common kernel of similarities and difficulties, and they all exhibit complexities that have, until now, blocked broadly based attempts at comprehension:

1. All complex adaptive systems involve large numbers of parts undergoing a kaleidoscopic array of simultaneous nonlinear interactions.

2. The impact of these systems in human affairs centers on the aggregate behavior, the behavior of the whole.

3. The interactions evolve over time, as the parts adapt in an attempt to survive in the environment provided by the other parts.

4. Complex adaptive systems anticipate.

301Computer simulation offers new ways of carrying out both realistic experiments, of flight-simulator precision, and well-defined gedanken experiments, of the kind that have played such an important role in the development of physics. For real complex adaptive systems — economies, ecologies, brains, etc. — these possibilities have been hard to come by because (1) the systems lose their major features when parts are isolated for study, (2) the systems are highly history dependent, so that it is difficult to make comparisons or tease out representative behavior, and (3) operation far from equilibrium or a global optimum is a regime not readily handled by standard methods.

302Though we readily ascribe internal models, cognitive maps, anticipation, and prediction to humans, we rarely think of them as characteristic of other systems. Still, a bacterium moves in the direction of a chemical gradient, implicitly predicting that food lies in that direction. The repertoire of the immune system constitutes its model of its world, including an identity of ‘self.’ The butterfly that mimics the foul-tasting monarch butterfly survives because it implicitly forecasts that a certain wing pattern discourages predators. A wolf bases its actions on anticipations generated by a mental map that incorporates landmarks and scents. Because so much of the behavior of a complex adaptive system stems from anticipations based on its internal models, it is important that we understand the way in which such systems build and use internal models.

A general theory of complex adaptive systems that addresses these problems will be built, I think, on a framework that centers on three mechanisms: parallelism, competition, and recombination. Parallelism lets the system use individuals (rules, agents) as building blocks, activating sets of individuals to describe and act upon changing situations. Competition allows the system to marshal its resources in realistic environments where torrents of mostly irrelevant information deluge the system. Recombination underpins the discovery process, generating plausible new rules from building blocks that form parts of tested rules.

303Scaling is the observation; the renormalisation group is the explanation.

304An ice cube floating in a glass of water, at just the melting point, poses a genuine conceptual problem in theoretical physics.

305The phenomenon of critical opalescence is one of the most visually dramatic manifestations of critical phenomena. Normally transparent fluids become milky white near the critical point, because density fluctuations occur on all length scales, including those comparable to the wavelength of visible light.

306Imagine poor Ising’s disappointment on deriving this result!

307Symmetry-breaking is a paradox only if you confuse the symmetry of the underlying laws with the symmetry of the things that those laws govern.

308Symmetry is not a number, not a shape, not a property: it is a transformation — an action — that leaves the thing apparently unchanged.

309The Geometer God constructed the universe using symmetry as a guide: then She broke it.

310Anomalous dimensions are the fingerprints of the microscopic world, persisting at macroscopic scales through the collective action of fluctuations at all intermediate scales.

311What is life? Gnarl, sex, and death.

What is artificial life? Computer programs that act that way.

How do you tweak such a program? You let it evolve.

312A simple rule of thumb for creating artificial life on the computer is that the program should produce output that looks gnarly. ‘Gnarly’ is, of course, not the word that most research scientists use. Instead, they speak of life as being chaotic or complex. Chaos as a scientific concept became popular in the 1980s. Chaos can be defined to mean complicated but not random.

The surf at the shore of an ocean beach is chaotic. The patterns of the water are clearly very complicated. But, and this is the key point, they are not random. The patterns the waves move in are, from moment to moment, predictable by the laws of fluid motion. Waves don’t just pop in and out of existence. Water moves according to well understood physical laws.

313Life is an expected, emergent, collective property of complex systems of polymer catalysts.

314Ordered systems are too frozen to coordinate complex behavior; chaotic systems are too wild to coordinate complex behavior; systems near the edge of chaos are most likely to coordinate complex behavior.

315Again, remarkably, coevolving systems may optimize their capacity to coevolve by mutually attaining the edge of chaos.

316MALCOLM

I’m a chaotician. (deprecating smile)
That’s what they call us. Mathematicians
who study chaos theory.

317Our experiment produced very different results, and we suggest that the interpretation of the original results is not correct.

318The main constructive results of our study are identifying the emergence and competition of computational strategies and analyzing the central role of symmetries in an evolutionary system. In particular, we demonstrate how symmetry breaking can impede the evolution toward higher computational capability.

319Thus for this class of computational tasks, the λ_c values associated with an ‘edge of chaos’ are not correlated with the ability of rules to perform the task.

320In addition, it is not clear that anything like a drive toward universal-computational capabilities is an important force in the evolution of biological organisms. It seems likely that substantially less computationally-capable properties play a more frequent and robust role. Thus asking under what conditions evolution will create entities (including CA) capable of universal computation may not be of great importance in understanding natural evolutionary mechanisms.

In short, it is mathematically important to know that some CA are in principle capable of universal computation. But we argue that this is by no means the most scientifically interesting property of CA. More to the point, this property does not help scientists much in understanding the emergence of complexity in nature or in harnessing the computational capabilities of CA to solve real problems.

321The great question of developmental theory is this: Do the self-organizing structures of living organisms paint themselves into three-dimensional pictures by joining together structurally, bit by bit in building-block or jigsaw-puzzle fashion, in sufficient strength to overcome the hurricane, or does development at some stage make use of the hurricane and produce order out of chaos in the Boltzmann-statistical manner?

322Anyone can feel this wind when hearing the remarkably evocative music played. Only a fully trained musician can feel it when looking silently at the printed score. When one contemplates an electron micrograph, and then a diagram of chemical changes in biochemical cycles, one should feel first the storm which raises the question and then the great determined flows through it which shape the organism.

323The terms in equations have functions in the organism, as groups of amino acids do. Here is an alpha-helix; it helps to make the protein span a membrane. Here is a cubic term; it helps the organism to make stripes.

324Scientific theory is an art in which the surface on which to elaborate the details is not available a priori, but is itself a product of the enterprise.

325From a theoretical point of view, since we are not near equilibrium there is no a priori reason to suppose that we have a Gibbs ensemble or a free energy functional whose minima yield the patterns obtained under given external conditions.

326The most interesting aspect of mollusk shell patterns is that they are generated one row at a time, during growth, so that the two-dimensional pattern on the shell surface represents a space-time record of a one-dimensional solution of the model equations.

327If we take selection as the sole source of order, it is because we have come to suppose that without selection there could be only chaos.

328In sufficiently complex systems, selection cannot avoid the order exhibited by most members of the ensemble.

329Thus I suspect that the same principles of self-organization apply to the emergence of a protometabolism. I suggest that the formation of a connected web of metabolic transformations arises almost inevitably in a sufficiently complex system of organic molecules and polymer catalysts. This view implies that, from the outset, life possessed a certain inalienable holism. It also suggests that almost any metabolic web, were life to evolve again, would have a very similar statistical structure.

330The alternative attractors in a genomic regulatory network, for example, can be interpreted as the alternative cell types in the organism.

331Real morphogenesis is due not to the unfolding of any single developmental mechanism but to the beautifully ordered unfolding in time and space of some richly integrated combination of simpler mechanisms such as cell-sorting, sheet-folding, positional discontinuities, and reaction-diffusion mechanisms.

332The usual biologists’ explanations are fundamentally hierarchical. You don’t try to get back to the boss and change his mind. The essence of a Turing model is the existence of feedback loops in which everything interacts back on everything else and there is no boss.

333In short, the capacity to evolve is itself subject to evolution and may have its own lawful properties.

334I believe this to be a genuinely fundamental restraint facing adaptive evolution. As systems with many parts increase both the number of those parts and the richness of interactions among the parts, it is typical that the number of conflicting design constraints among the parts increases rapidly. Those conflicting constraints imply that optimization can attain only ever poorer compromises. No matter how strong selection may be, adaptive processes cannot climb higher peaks than afforded by the fitness landscape. This limitation cannot be overcome by stronger selection.

335As in New England, in rugged landscapes ‘you can’t get there from here.’

336Evolution is not just ‘chance caught on the wing.’ It is not just a tinkering of the ad hoc, of bricolage, of contraption. It is emergent order honored and honed by selection.

337The fundamental order lies deeper, the routes to life are broader.

338To suppose, as I do, that such an intellectual task may one day be achieved is, among other things, to suspect with quiet passion that below the particular teeming molecular traffic in each cell lie fundamental principles of order any life would reexpress.

339Contrary to intuition, morphogenesis may be deeply robust. Organisms, rather than being tinkered-together contraptions, may exhibit a nearly inevitable and stable order.

340Genetic algorithms permit virtual entities to be created without requiring an understanding of the procedures or parameters used to generate them. The measure of success, or fitness, of each individual can be calculated automatically, or it can instead be provided interactively by a user.

341It is convenient to use the biological terms genotype and phenotype when discussing artificial evolution. A genotype is a coded representation of a possible individual or problem solution. In biological systems, a genotype is usually composed of DNA and contains the instructions for the development of an organism. Genetic algorithms typically use populations of genotypes consisting of strings of binary digits or parameters. These are read to produce phenotypes which are then evaluated according to some fitness criteria and selectively reproduced. New genotypes are generated by copying, mutating, and/or combining the genotypes of the most fit individuals, and as the cycle repeats the population should ascend to higher and higher levels of fitness.

342In the spirit of unbounded genetic languages, directed graphs are presented here as an appropriate basis for a grammar that can be used to describe both the morphology and nervous systems of virtual creatures. New features and functions can be added to creatures, or existing ones removed, so the levels of complexity can also evolve.

343A genetic language for representing virtual creatures with directed graphs of nodes and connections allows an unlimited hyperspace of possible creatures to be explored. It is believed that these methods have potential as a powerful tool for the creation of desirable complexity for use in virtual worlds and computer animation.

As computers become more powerful, the creation of virtual actors, whether animal, human, or completely unearthly, may be limited mainly by our ability to design them, rather than our ability to satisfy their computational requirements. A control system that someday actually generates ‘intelligent’ behavior might tend to be a complex mess beyond our understanding. Artificial evolution permits the generation of complicated virtual systems without requiring design, and the use of unbounded genetic languages allows evolving systems to increase in complexity beyond our understanding. Perhaps methods such as those presented here will provide a practical pathway toward the creation of intelligent behavior.

344Chris Langton is a cellular-automata engineer. He’s following in the footsteps of John von Neumann, engineering self-reproducing systems with cellular automata. Von Neumann showed that it was possible to hand-engineer a self-replicating pattern — engineer a universe — by writing down a particular cellular automaton with a certain set of rules. He was able to show that there are patterns in that universe that replicate themselves, and are both construction universal and computation-universal. What that means is that the pattern is capable of constructing any pattern, and, secondly, that it’s capable of making any computation that a computer can do.

345The Hungarian mathematician John Von Neumann had the insight that we could learn a lot even if we didn’t try to model some specific existing biological thing. He went after the logical basis, rather than the material basis, of a biological process, by attempting to abstract the logic of self-reproduction without trying to capture the mechanics of self-reproduction (which were not known in the late 1940s, when he started his investigations).

Von Neumann demonstrated that one could have a machine, in the sense of an algorithm, that would reproduce itself. Most biologists weren’t interested, because it wasn’t like any specific instance of biological self-reproduction (it wasn’t a model of chromosomes, for example). Von Neumann was able to derive some general principles for the process of self-reproduction. For instance, he determined that the information in a genetic description, whatever it was, had to be used in two different ways: (1) it had to be interpreted as instructions for constructing itself or its offspring, and (2) it had to be copied passively, without being interpreted. This turned out to be the case for the information stored in DNA when James Watson and Francis Crick determined its structure in 1953. It was a far-reaching and very prescient thing to realize that one could learn something about “real biology” by studying something that was not real biology — by trying to get at the underlying “bio-logic” of life.

346People have been working with genetic algorithms ever since, but these algorithms haven’t been very useful tools for studying biological evolution. This isn’t because there’s anything wrong with the algorithms per se, but rather because they haven’t been embedded in the proper biological context. As genetic algorithms have been traditionally implemented, they clearly involve artificial selection: some human being provides explicit, algorithmic criteria for which of the entities is to survive to mate and reproduce. The real world, however, makes use of natural selection, in which it is the “nature” of the interactions among all the organisms — both with one another and with the physical environment — that determines which entities will survive to mate and reproduce. It required a bit of experimentation to work out how to bring about natural selection within the artificial worlds we create in computers.

Over the last several years, however, we’ve learned how to do that, through the work of Danny Hillis, Tom Ray, and others. We don’t specify the selective criteria externally. Rather, we let all the “organisms” interact with one another, in the context of a dynamic environment, and the selective criteria simply emerge naturally. To any one of these organisms, “nature,” in the computer, is the collective dynamics of the rest of the computerized organisms there. When we allow this kind of interaction among the organisms — when we allow them to pose their own problems to one another — we see the emergence of a Nature with a capital “N” inside the computer, whose “nature” we can’t predict as it evolves through time.

Typically, a collection of organisms in such artificial worlds will form an ecology, which will be stable for a while but will ultimately collapse. After a chaotic transition, another stable ecology will form, and the process continues. What defines fitness — and what applies the selective pressure — is this constantly changing collective activity of the set of organisms themselves. I argue that such a virtual ecosystem — what I have termed “artificial life” — constitutes a genuine “nature under glass,” and that the study of these virtual natures within computers can be extremely useful for studying the nature of nature outside the computer.

347Stuart Kauffman is a theoretical biologist who studies the origin of life and the origins of molecular organization. Twenty-five years ago, he developed the Kauffman models, which are random networks exhibiting a kind of self-organization that he terms “order for free.” Kauffman is not easy. His models are rigorous, mathematical, and, to many of his colleagues, somewhat difficult to understand. A key to his worldview is the notion that convergent rather than divergent flow plays the deciding role in the evolution of life. With his colleague Christopher G. Langton, he believes that the complex systems best able to adapt are those poised on the border between chaos and disorder.

Kauffman asks a question that goes beyond those asked by other evolutionary theorists: if selection is operating all the time, how do we build a theory that combines self-organization (order for free) and selection? The answer lies in a “new” biology, somewhat similar to that proposed by Brian Goodwin, in which natural selection is married to structuralism.

348Chris Langton is wild, scattered, deeply intuitive, not very critical, very creative, good, good, good intuitions. His thesis about the edge of chaos, phase transitions, was a lovely thing to have done. He developed the ideas of looking at cellular automata and a phase transition, and the idea that you have to ask how complex systems can actually generate, create, and pass information around. The idea that it may happen best as a phase transition may not be correct, but it’s a lovely hypothesis.

349What kinds of complex systems can evolve by accumulation of successive useful variations? Does selection by itself achieve complex systems able to adapt? Are there lawful properties characterizing such complex systems? The overall answer may be that complex systems constructed so that they’re on the boundary between order and chaos are those best able to adapt by mutation and selection.

Chaos is a subset of complexity. It’s an analysis of the behavior of continuous dynamical systems — like hydrodynamic systems, or the weather — or discrete systems that show recurrences of features and high sensitivity to initial conditions, such that very small changes in the initial conditions can lead a system to behave in very different ways. A good example of this is the so called butterfly effect: the idea is that a butterfly in Rio can change the weather in Chicago. An infinitesimal change in initial conditions leads to divergent pathways in the evolution of the system. Those pathways are called trajectories. The enormous puzzle is the following: in order for life to have evolved, it can’t possibly be the case that trajectories are always diverging. Biological systems can’t work if divergence is all that’s going on. You have to ask what kinds of complex systems can accumulate useful variation.

We’ve discovered the fact that in the evolution of life very complex systems can have convergent flow and not divergent flow. Divergent flow is sensitivity to initial conditions. Convergent flow means that even different starting places that are far apart come closer together. That’s the fundamental principle of homeostasis, or stability to perturbation, and it’s a natural feature of many complex systems. We haven’t known that until now. That’s what I found out twenty-five years ago, looking at what are now called Kauffman models — random networks exhibiting what I call “order for free.”

Complex systems have evolved which may have learned to balance divergence and convergence, so that they’re poised between chaos and order. Chris Langton has made this point, too. It’s precisely those systems that can simultaneously perform the most complex tasks and evolve, in the sense that they can accumulate successive useful variations. The very ability to adapt is itself, I believe, the consequence of evolution. You have to be a certain kind of complex system to adapt, and you have to be a certain kind of complex system to coevolve with other complex systems. We have to understand what it means for complex systems to come to know one another — in the sense that when complex systems coevolve, each sets the conditions of success for the others. I suspect that there are emergent laws about how such complex systems work, so that, in a global, Gaia-like way, complex coevolving systems mutually get themselves to the edge of chaos, where they’re poised in a balanced state. It’s a very pretty idea. It may be right, too.

350By spontaneous order, or order for free, I mean this penchant that complex systems have for exhibiting convergent rather than divergent flow, so that they show an inherent homeostasis, and then, too, the possibility that natural selection can mold the structure of systems so that they’re poised between these two flows, poised between order and chaos. It’s precisely systems of this kind that will provide us with a macroscopic law that defines ecosystems, and I suspect it may define economic systems as well.

351The origin of life might be another example of order for free. If you have complex-enough systems of polymers capable of catalytic action, they’ll self-organize into an autocatalytic system and, essentially, simply be alive. Life may not be as hard to come by as we think it is.

352He’s trying to understand what aspects of organic order follow from the physical principles of matter, and the mathematical structure of nature, and need not be seen as Darwinian optimalities produced by natural selection.

He’s following in the structuralist tradition, which should not be seen as contrary to Darwin but as helpful to Darwin. Structural principles set constraints, and natural selection must work within them. His “order for free” is an outcome of sets of constraints; it shows that a great deal of order can be produced just from the physical attributes of matter and the structural principles of organization. You don’t need a special Darwinian argument; that’s what he means by “order for free.” It’s a very good phrase, because a strict Darwinian thinks that all sensible order has to come from natural selection. That’s not true.

353The standard way of looking at evolution is that evolution is a matter of transforming the physical properties of organisms. Stuart’s got models jumping around from adaptive peak to adaptive peak, to explain the early Cambrian explosion.

354I have a little harder time with his last book. The monster, The Origins of Order. Although many of the pieces in there have a flavor of something quite interesting, it doesn’t seem to me that the book hangs together as a whole. There’s too much of “Let’s assume this, and let’s assume that, and if this were right, then…” But the basic idea is that we’re back to the notion of evolution having intrinsic factors, and in this regard it has to be right.

355Francisco Varela is amazingly inventive, freewheeling, and creative. There’s a lot of depth in what he and Humberto Maturana have said. Conversely, from the point of view of a tied-down molecular biologist, this is all airy-fairy, flaky stuff. Thus there’s the mixed response. That part of me that’s tough-minded and critical is questioning, but the other part of me has cottoned on to the recent stuff he’s doing on self-representation in immune networks. I love it.

356I guess I’ve had only one question all my life. Why do emergent selves, virtual identities, pop up all over the place creating worlds, whether at the mind/body level, the cellular level, or the transorganism level? This phenomenon is something so productive that it doesn’t cease creating entirely new realms: life, mind, and societies. Yet these emergent selves are based on processes so shifty, so ungrounded, that we have an apparent paradox between the solidity of what appears to show up and its groundlessness. That, to me, is a key and eternal question.

357Regarding the subject of biological identity, the main point is that there is an explicit transition from local interactions to the emergence of the ‘global’ property — that is, the virtual self of the cellular whole, in the case of autopoiesis. It’s clear that molecules interact in very specific ways, giving rise to a unity that is the initiation of the self. There is also the transition from nonlife to life. The nervous system operates in a similar way. Neurons have specific interactions through a loop of sensory surfaces and motor surfaces. This dynamic network is the defining state of a cognitive perception domain. I claim that one could apply the same epistemology to thinking about cognitive phenomena and about the immune system and the body: an underlying circular process gives rise to an emergent coherence, and this emergent coherence is what constitutes the self at that level. In my epistemology, the virtual self is evident because it provides a surface for interaction, but it’s not evident if you try to locate it. It’s completely delocalized.

358My autopoiesis work was my first step into these domains: defining what is the minimal living organization, and conceiving of cellular-automata models for it. I did this in the early 1970s, way before the artificial-life wave hit the beach. This work was picked up by Lynn Margulis, in her research and writings on the origins of life, the evolution of cellular life, and, with James Lovelock, the Gaia hypothesis. Humberto Maturana and I invented the idea of autopoiesis in 1970. We worked together in Santiago, during the Socialist years. The idea was the result of suspecting that biological cognition in general was not to be understood as a representation of the world out there but rather as an ongoing bringing-forth of a world, through the very process of living itself.

359Stuart Kauffman and his colleague Brian Goodwin are particularly eager to discredit the powerful image first made popular by the great French biologists Jacques Monod and François Jacob — the image of Mother Nature as a tinkerer engaged in the opportunistic handiwork that the French call bricolage. Kauffman wants to stress that the biological world is much more a world of Newtonian discoveries than of Shakespearean creations. He’s certainly found some excellent demonstrations to back up this claim. Kauffman is a meta-engineer. I fear that his attack on the metaphor of the tinkerer feeds the yearning of those who don’t appreciate Darwin’s dangerous idea. It gives them a false hope that they’re seeing not the forced hand of the tinkerer but the divine hand of God in the workings of nature. Kauffman gets that from Brian Goodwin. John Maynard Smith has been pulling Kauffman in the other direction — very wisely so, in my opinion.

360There is no progress in evolution. The fact of evolutionary change through time doesn’t represent progress as we know it. Progress is not inevitable. Much of evolution is downward in terms of morphological complexity, rather than upward. We’re not marching toward some greater thing. The actual history of life is awfully damn curious in the light of our usual expectation that there’s some predictable drive toward a generally increasing complexity in time. If that’s so, life certainly took its time about it: five-sixths of the history of life is the story of single-celled creatures only.

361I would like to propose that the modal complexity of life has never changed and it never will, that right from the beginning of life’s history it has been what it is; and that our view of complexity is shaped by our warped decision to focus on only one small aspect of life’s history; and that the small bit of the history of life that we can legitimately see as involved in progress arises for an odd structural reason and has nothing to do with any predictable drive toward it.

362Symbiosis is a physical association between organisms, the living together of organisms of different species in the same place at the same time. My work in symbiosis comes out of cytoplasmic genetic systems. We were all taught that the genes were in the nucleus and that the nucleus is the central control of the cell. Early in my study of genetics, I became aware that other genetic systems with different inheritance patterns exist.

From the beginning, I was curious about these unruly genes that weren’t in the nucleus. The most famous of them was a cytoplasmic gene called “killer,” which, in the protist Paramecium aurelia, followed certain rules of inheritance. The killer gene, after twenty years of intense work and shifting paradigmatic ideas, turns out to be in a virus inside a symbiotic bacterium. Nearly all extranuclear genes are derived from bacteria or other sorts of microbes.

In the search for what genes outside the nucleus really are, I became more and more aware that they’re cohabiting entities, live beings. Live small cells reside inside the larger cells. Understanding that led me and others to study modern symbioses.

Symbiosis has nothing to do with cost or benefit. The benefit/cost people have perverted the science with invidious economic analogies. The contention is not over modern symbioses, simply the living together of unlike organisms, but over whether “symbiogenesis” — long-term symbioses that lead to new forms of life — has occurred and is still occurring. The importance of symbiogenesis as a major source of evolutionary change is what is debated.

I contend that symbiogenesis is the result of long-term living together — staying together, especially involving microbes — and that it’s the major evolutionary innovator in all lineages of larger nonbacterial organisms.

363For more than a billion years, the only life on this planet consisted of bacterial cells, which, lacking nuclei, are called prokaryotes, or prokaryotic cells. They looked very much alike, and from the human-centered vantage point seem boring. However, bacteria are the source of reproduction, photosynthesis, movement — indeed, all interesting features of life except perhaps speech! They’re still with us in large diversity and numbers. They still rule Earth.

At some point, a new more complex kind of cell appeared on the scene, the eukaryotic cell, of which plant and animal bodies are composed. These cells contain certain organelles, including nuclei. Eukaryotic cells with an individuated nucleus are the building blocks of all familiar large forms of life. How did that evolution revolution occur? How did the eukaryotic cell appear? Probably it was an invasion of predators, at the outset.

It may have started when one sort of squirming bacterium invaded another — seeking food, of course. But certain invasions evolved into truces; associations once ferocious became benign. When swimming bacterial would-be invaders took up residence inside their sluggish hosts, this joining of forces created a new whole that was, in effect, far greater than the sum of its parts: faster swimmers capable of moving large numbers of genes evolved. Some of these newcomers were uniquely competent in the evolutionary struggle. Further bacterial associations were added on, as the modern cell evolved.

364In the early seventies, I was trying to align bacteria by their metabolic pathways. I noticed that all kinds of bacteria produced gases. Oxygen, hydrogen sulfide, carbon dioxide, nitrogen, ammonia — more than thirty different gases are given off by the bacteria whose evolutionary history I was keen to reconstruct. Why did every scientist I asked believe that atmospheric oxygen was a biological product but the other atmospheric gases — nitrogen, methane, sulfur, and so on — were not? “Go talk to Lovelock,” at least four different scientists suggested. Lovelock believed that the gases in the atmosphere were biological. He had, by this time, a very good idea of which live organisms were probably “breathing out” the gases in question. These gases were far too abundant in the atmosphere to be formed by chemical and physical processes alone. He argued that the atmosphere was a physiological and not just a chemical system.

The Gaia hypothesis states that the temperature of the planet, the oxidation state and other chemistry of all of the gases of the lower atmosphere (except helium, argon, and other nonreactive ones) are produced and maintained by the sum of life. We explored how this could be. How could the temperature of the planet be regulated by living beings? How could the atmospheric gas composition — the 20-percent oxygen and the one to two parts per million methane, for example — be actively maintained by living matter?

365Gaia is a tough bitch — a system that has worked for over three billion years without people. This planet’s surface and its atmosphere and environment will continue to evolve long after people and prejudice are gone.

366Homeochaos provides a dynamic stability sustained by high-dimensional weak chaos.

367No matter how impressive the products of an algorithm, the underlying process always consists of nothing but a set of individually mindless steps succeeding each other without the help of any intelligent supervision.

368The actual is, as a matter of brute historical fact, a Vanishingly small subset of the possible.

369Searching through the Library of Mendel for the best genomes is rather like searching for a particular book in the Library of Babel, but with one important difference: there is a non-miraculous, indeed algorithmic, process that has been running for billions of years.

370In the early days of artificial intelligence, researchers assumed that the most important thing about the brain, for the purposes of understanding intelligence, was that it was a universal computer. Its parallel, distributed architecture was thought to be merely a consequence of the bizarre path that nature had to take to evolve a universal computer. Since we know that all universal computers are equivalent in principle in their computational power, it was thought that we could effectively ignore the architecture of the brain and get intelligent software running on our newly engineered universal computers, which had very different architectures. However, I think that the difference in architecture is crucial. Our engineered computers involve a central controller working from a top down set of rules, while the brain has no such central controller and works in a very distributed, parallel manner, from the bottom up. What’s natural and spontaneous for this latter architecture can be achieved by the former only by using our standard serial computers to simulate parallel, distributed systems. There’s something in the dynamics of parallel, distributed, highly nonlinear systems which lies at the roots of intelligence and consciousness — something that nature was able to discover and take advantage of.

371Think of an ant colony — a beautiful example of a massively parallel, distributed system. There’s no one ant that’s calling the shots, picking from among all the other ants which one is going to get to do its thing. Rather, each ant has a very restricted set of behaviors, but all the ants are executing their behaviors all the time, mediated by the behaviors of the ants they interact with and the state of the local environment. When one takes these behaviors on aggregate, the whole collection of ants exhibits a behavior, at the level of the colony itself, which is close to being intelligent. But it’s not because there’s an intelligent individual telling all the others what to do. A collective pattern, a dynamical pattern, takes over the population, endowing the whole with modes of behavior far beyond the simple sum of the behaviors of its constituent individuals. This is almost vitalistic, but not quite, because the collective pattern has its roots firmly in the behavior of the individual ants.

This example shows how one can be both a vitalist and a mechanist at the same time.

372In the late nineteenth century, the Austrian physicist Ludwig Boltzmann showed that one could account for many of the thermodynamic properties of macroscopic systems in terms of the collective activity of their constituent atoms. Boltzmann’s most famous contribution to our understanding of the relationship between the microcosm of atoms and the macroscopic world of our experience was his definition of entropy: S = k log W. In the 1950s, the computer scientist Claude Shannon generalized Boltzmann’s formula, lifting the concept of entropy from the thermodynamic setting in which it was discovered to the more general level of probability theory, providing a precise, quantitative meaning for the term “information.”

373As Doyne Farmer has pointed out, our current understanding of complex systems is very much in the same state as our understanding of thermodynamics was in the mid-1800s, when people were screwing around with the basic concepts but didn’t yet know which were the right quantities to measure. Until you know which are the relevant quantities to measure, you can’t come up with quantitative expressions relating those quantities to one another.

374Meanwhile, Chris has gone on to stir up interest in what he calls artificial life. I myself don’t use that way of slicing things. I believe we can learn most by considering natural and artificial complex adaptive systems together — in my view, they form a single subject. Moreover, I don’t myself subscribe to the idea that it’s valuable to separate out those artificial systems that imitate organisms or biological evolution in certain respects and put them in a separate category from those that imitate other natural complex adaptive systems, such as human societies. However, Chris’s category has caught on in a remarkable way, and the term “artificial life” is now widely used. Chris has managed in that way to attract a great deal of attention to the field of plectics and to draw a lot of people into it.

375A physical system undergoes a phase transition when its state changes — for instance, when water freezes into ice. I’ve found that during phase transitions physical systems often exhibit their most complex behavior. I’ve also found that it’s during phase transitions that information processes can appear spontaneously in physical systems and play an important role in the determination of the systems’ behavior. One might even say that systems at phase transitions are caught up in complex computations to determine their own physical state. My belief is that the dynamics of phase transitions are the point at which information processing can gain a foothold in physical systems, gaining the upper hand over energy in the determination of the systems’ behavior. It has long been a goal of science to discover where and how information theory and physics fit into each other; it’s become something of a Holy Grail. I can’t say I’ve found the Grail, but I do think I’ve found the mountain range it’s located in.

376After working for a long time creating these artificial universes, wondering about getting life going in them, and wondering if such life would ever wonder about its own existence and origins, I find myself looking over my shoulder and wondering if there isn’t another level on top of ours, with something wondering about me in the same way. It’s a spooky feeling to be caught in the middle of such an ontological recursion. This is Edward Fredkin’s view: the universe as we know it is an artifact in a computer in a more “real” universe.

377Collapse the distinction between learning and reward by making the reward signal identical to the rate of learning itself.

378If I were to give an award for the single best idea anyone has ever had, I’d give it to Darwin, ahead of Newton and Einstein and everyone else. In a single stroke, the idea of evolution by natural selection unifies the realm of life, meaning, and purpose with the realm of space and time, cause and effect, mechanism and physical law.

379Should it be that much harder for an algorithmic process to write an ode to a nightingale or a poem as lovely as a tree? Surely Orgel’s Second Rule is correct: Evolution is cleverer than you are.

380A scholar is just a library’s way of making another library.

381The mind is the effect, not the cause, of the brain’s being the way it is.

382The goals of creating artificial intelligence and artificial life can be traced back to the very beginnings of the computer age. The earliest computer scientists — Alan Turing, John von Neumann, Norbert Wiener, and others — were motivated in large part by visions of imbuing computer programs with intelligence, with the life-like ability to self-replicate, and with the adaptive capability to learn and to control their environments. These early pioneers of computer science were as much interested in biology and psychology as in electronics, and they looked to natural systems as guiding metaphors for how to achieve their visions. It should be no surprise, then, that from the earliest days computers were applied not only to calculating missile trajectories and deciphering military codes but also to modeling the brain, mimicking human learning, and simulating biological evolution. These biologically motivated computing activities have waxed and waned over the years, but since the early 1980s they have all undergone a resurgence in the computation research community. The first has grown into the field of neural networks, the second into machine learning, and the third into what is now called evolutionary computation, of which genetic algorithms are the most prominent example.

383Some of the most commonplace items in our world are also paradoxically the most improbable and wonderful: the physical properties of water, the existence of sex, the fact that the millions of animal species have only thirty-five basic body plans, the fact of evolutionary transformation through time. The latter two items, the objects of this book, are related in a seemingly antithetical way. The basic animal body plans are half a billion years old. Arthropods, chordates, mollusks, echinoderms, and others can all be recognized from the first appearance of the animal fossil record. Even so, the striking diversity of living animals shows that dramatic evolutionary transformations have taken place within these ancient patterns. Body form evolves through geologic time, but it also arises in each generation through development. The time frames and apparent processes couldn’t be more different, but explanations of the evolution of form have to consider how form is generated, and they must account for both underlying stability and immense change in design.

My awakening to the scope and significance of the relationship between development and evolution came during my first year as a graduate student at Duke University, when I read de Beer’s book, Embryos and Ancestors. I no longer remember how I found out about the book, but I got hold of a copy and set out to study it. This was not as simple a task as vacation novel reading. I was engaged in my first year of heavy coursework in biochemistry and was expected to read the Journal of Biological Chemistry in my spare time. Consequently, on Saturday mornings I sat with de Beer in the laundromat across the street from an old Durham eatery, the Little Pigs Barbecue, while I added coins to the dryers and waited for the endless drying cycles to finish. At that time I knew nothing about embryology, and so the terminology was simply mind-boggling; germ layers, neural plates, and archenterons swam before my mystified eyes until I got it all straight. But it was a stimulating experience. Until that time, my views of evolutionary change were largely of transformations between features of adult body plans. I had never considered the embryological roots of those transformations. Embryos and Ancestors provided the connection between the construction of an individual animal and the course of its evolutionary history. De Beer also presented a mechanistic explanation by which changes in the timing of developmental events in the descendant as contrasted with the ancestor could yield evolutionary novelties by changing the relations of developmental features. This phenomenon, heterochrony, has motivated most thought on the evolution of development. De Beer offered fascinating scenarios to demonstrate how animal groups, including the vertebrates, could potentially have originated by heterochronic changes. What de Beer didn’t do was consider the roles of genes in development, nor did he discuss any experimental approaches. He provided a paradigm for the evolution of morphology, but his approach lacked any means by which one might investigate the hypotheses presented. On reflection, it’s hard to blame him. It certainly took me a long time before I was able to design for myself an experimental approach to some problems in this still largely theoretical and anecdotal discipline.

384Of necessity, an understanding of the relationship between development and evolution requires synthesizing two great and traditionally separate disciplines in biology, developmental biology and evolutionary biology. The relationship between the two disciplines has always been an enterprise in creative inference making. The recognition that an appreciation of embryonic development would be important in understanding evolution appears in The Origin of Species. Darwin suggested that we could use embryos to trace evolutionary relationships because ‘the embryo is the animal in its less modified state; and in so far it reveals the structure of its progenitor.’ Darwin certainly had a concrete example before him, having earlier carried out a long study of barnacles. Barnacles were long thought to be mollusks, but once discovered, their larvae quickly gave them away as related to shrimp and other crustaceans.

From the 1860s to the end of the nineteenth century, the German evolutionary biologist Ernst Haeckel built a hypothesis as to how ontogeny and phylogeny should interact, and founded a research program that featured the large-scale application of data from embryology to working out phylogenies. Early in the twentieth century, embryologists became interested in how embryos worked rather than how they evolved, abandoned Haeckel’s program, and turned to experimental studies of development itself. The current study of the relationship between evolution and development has grown from a rebirth of interest in the subject as well as from the invention of new tools in genetics and molecular biology.

385Another element unavailable ten years ago is an understanding of the molecular machinery underlying development. During the past decade, developmental genetics has become one of the liveliest disciplines of biology. Its enormous success has come from the realization on the part of developmental biologists that genes underlie developmental processes and even serve as switches that determine the course of differentiation of cells within the embryo. During the same period, powerful tools became available to dissect developmental processes at the molecular level. The most striking part of that success has come from the joint application of genetics and molecular biology to identifying and isolating the genes that control development. The genetic analysis of development was under way a decade ago, and we could point to the roles of homeotic genes in the evolution of segmental features in insects. But there were major limitations. At that time, none of the genes involved had been cloned, and the functions of their products were not known. Without gene sequence information, gene homology could not be established. Once that information became available, it became possible to trace patterns of gene utilization in development across phylogenetic lines. The discovery during the past decade that insects and vertebrates use homologous homeobox-containing genes in their development has revealed a deep genetic relationship underlying the development of the two phyla. More than any other single discovery, this finding of a deep commonality of the genetic controls for establishing components of axial polarity in animal development has helped to fix the focus of developmental biologists on how evolutionary data can contribute to our understanding of developmental mechanisms.

386The fossil record of events around the Cambrian boundary is important in framing our questions about the mechanisms by which development affects patterns of macroevolution.

387In many cases, we can recognize constraining factors in evolution. For instance, why there are no animals with wheels is easily explained. It is not possible to connect nerves and circulatory systems to the tissue of a free-turning wheel.

388The phenotypes we observe in nature should reflect some balance between internal constraints and external selection. The empty phenotypic space houses Platonic shadow phenotypes that might be attainable under other rules than those that have operated in metazoans since the Cambrian radiation.

389Replication is an ontogenetic, that is, developmental process, involving no genetic operators, resulting in an exact duplicate of the parent organism. Reproduction, on the other hand, is a phylogenetic, that is, evolutionary process, involving genetic operators such as crossover and mutation, thereby giving rise to variety and ultimately to evolution.

390It took until 1990 for the first conclusive experimental evidence of Turing patterns to appear.

391When two waves in an excitable medium collide, they annihilate one another, because each wave leaves behind it a refractory region in which the system cannot be excited. This behavior is exactly the opposite of what occurs with linear waves such as sound or light, which pass through one another.

392The term ‘complexity’ has been used without qualification by so many authors, both scientific and nonscientific, that it has been almost stripped of its meaning.

393The physics lies in the fluctuations.

394‘Know thyself’ seems to be an impossible command for a computer program. If a model of computation is so weak that it cannot ask questions about programs, then it will skirt the abyss, but at the cost of being too stupid to solve interesting problems.

395Between any two entrained regions, no matter how close together in frequency ratio, there is always another entrained region — a chemical analog of the number-theoretic result that between any two rational numbers there is always another rational.

396The BZ reaction in a Petri dish provides some of the most beautiful and instructive demonstrations in all of chemistry.

397Would it not be extraordinary, however, if these laws could by themselves contrive to generate rich and beautiful patterns?

398Dissipative dynamics, symmetry breaking, phase transitions, bifurcations, and pattern formation, acting over different temporal and spatial scales, at different levels and on different substrates, are presumably responsible for assembling and freezing in the wide diversity of structures observed in the natural world. Each of these processes has its more-or-less well-developed foundations. But where are the principles that define and describe their products? What is structure itself?

399You put in featureless, indiscriminate energy, and the out-of-equilibrium system uses it to organize itself into patterns that can astonish.

400Patterns live on the edge, in a fertile borderland between these extremes, where small changes can have large effects. Pattern appears when competing forces banish uniformity but cannot quite induce chaos. It sounds like a dangerous place to be, but it is where we have always lived.

401The choice of macroscopic states is not a detail — it is the entire problem.

402As on the sea’s wrinkled surface, it is the pattern that remains, not its individual components.

403If life were started from scratch a thousand times over, it would every time alight on these fundamental structures eventually.

404Competition lies at the heart of beauty and complexity in pattern formation. If the competition is too one-sided, all form disappears, and one gets either unstructured, shifting randomness or featureless homogeneity — bland, in either event. Patterns live on the edge, in a fertile borderland between these extremes, where small changes can have large effects.

405The symmetry of a pattern formed by a symmetry-breaking force does not always reflect the symmetry of that force. If you heat a shallow pan of oil, it will develop roughly hexagonal circulation cells. The system was initially uniform, and the symmetry-breaking force was also applied uniformly — yet suddenly this uniformity is lost. Where has this sixfold pattern come from?

406The diverse range of pelt patterns and markings can be explained with the same basic mechanism. William of Ockham would have reminded us that if we can account not only for the leopard’s spots but also for the zebra’s stripes and the giraffe’s dapples with the same theoretical model, that is surely more satisfactory.

407There is no way we could detect the ‘presence’ of this geometric principle by decoding the genetic information in the bee’s DNA. We could see that they make use of it only by watching the organism as a whole go about her job.

408It is as though individuals in a jabbering crowd were able to converse with one another from opposite sides of a room.

409Equilibrium is a dull place to be. Nothing happens there. If the Universe were itself at thermodynamic equilibrium, it would be a lifeless place pervaded by a uniform, dim glow of just a few degrees above absolute zero. Just about every phenomenon that interests us is an out-of-equilibrium process — life, to mention one.

410One is ‘swimming around in Occam’s pool’ of possible state representations, and epsilon-machines sit at the shallowest point.

411Quite apart from the fact that percolation theory has its origin in an honest applied problem, it is a source of fascinating problems of the best kind for which a mathematician can wish: problems which are easy to state with a minimum of preparation, but whose solutions are apparently difficult and require new methods.

412I’m Artificial Life aficionado from way back. Called “Alife” for short, this field studies how to create computer simulations of things that behave like living creatures. In a thorough-going Alife simulation, the creatures will even breed and evolve. Alife was big in the 1980s, but it’s kind of died out. Like Artificial Intelligence, Alife failed to deliver on its initial wild-eyed promises. Simulations don’t in fact evolve into cool things very fast. If you regard Earth as a large, specialized computer, you’ll observe that it’s been running for billions of years, parallel processing itself at every point of space, pumping along at an update speed limited only by things like Planck’s constant and the speed of light. Kind of hard to match that on your desk-top machine.

So I’m excited to see that the conference has a tutorial on Artificial Life in Games. The game community still hasn’t really picked up on Alife. The tendency is to have games that behave in predictable, replicable ways — unlike living things. It would be great if Alife could rise out of academia and break into the lively, moneyed world of videogames. Finally an application!

413One day when I was trying for the nth time to get Richard to understand why a Cellular Automaton was an interesting model for discrete physics, I finally got through to him. He suddenly became very serious and pensive. It was a tremendous moment for me because it was now a good dozen years since I started trying to get him to understand my point of view. Up until then he had always listened, asked questions only to understand what I was getting at, tried to understand what I was thinking, and then always pointed out that my ideas were off the wall. What happened next just blew me away.

Then, Richard quietly said something that struck me like a thunderbolt out of the blue. What he said was, from Richard Feynman, the greatest possible validation of what I had been trying to get him to understand over and over since I had first met him. What Richard said, with annoyance and a little bit of anger in his voice was: ‘You know, I’m sure I’ve already thought about the idea that some kind of Cellular Automata is probably the fundamental process in physics…’ which I had been trying to convince him for more than a decade. He continued; ’… and I know I said something about it somewhere…’ Richard Feynman was claiming priority for my idea, which I had been pestering him about for 12 years!!! What greater endorsement was possible? Nothing. Nothing at all.

414Biological life is in control of its own means of reproduction, and this autonomy of design and manufacture is a key element which has not yet been understood or reproduced artificially.

415The field of Artificial Life examines “life as it could be” based on understanding the principles and simulating the mechanisms of real biological forms. Just as airplanes use the same principles as birds, but have fixed wings, artificial lifeforms may share the same principles, but not the same implementation in chemistry. Every feature of living systems seems wondrous until it is understood: Stored energy, autonomous movement, and even animal communication are no longer miracles, as they are replicated in toys using batteries, motors, and computer chips.

416Our approach is based on use of only elementary building blocks and operators in both the design and fabrication process. As building blocks are more elementary, any inductive bias associated with them is minimized, and at the same time architectural flexibility is maximized. Similarly, use of elementary building blocks in the fabrication process allows it to be more systematic and versatile. As a theoretic extreme, if we could use only atoms as building blocks, laws of physics as constraints and nano-manipulation for fabrication, the versatility of the design space would be maximized. Earlier reported work used higher-level components and limited architectures (like only tree structures) resulted in expedited convergence to acceptable solutions, but at the expense of truncating the design space. Furthermore, these design spaces did not consider manufacturability.

417Although the underlying dynamics describing this system is very simple, and entirely deterministic, there is an enormous variety, and complexity, of emergent particle-particle interactions. Such simple systems are powerful reminders that complex higher-level dynamics need not have a complex underlying origin. Indeed, suppose that we had been shown such a space-time pattern but were told nothing whatsoever about its origin. How would we make sense of its dynamics? … It would take a tremendous leap of intuition to fathom the utter simplicity of the real dynamics.

418What we are thus seeing … is rather dramatic (albeit crude) evidence of the phenomenon of self-organization, in which an initially random state evolves to a state exhibiting long-range correlations and whose overall space-time patterns contain manifestly nonlocal structure.

419Such systems provide evidence that an apparent global ordered collective dynamics need not stem from an intrinsically global cooperative dynamics, but may instead be nothing more than an emergent high-level (phenotype) construct stemming from an essentially non-cooperative low-level (genotype) dynamics.

420Complexity generically increases with randomness up until a phase transition is reached, beyond which further increases in randomness decrease complexity.

421Life — like all computationally universal systems — defines the most efficient simulation of its own behavior.

422Inside any sufficiently large random broth, we expect just by chance, there will be some of these self-replicating creatures.

423We conclude from this fact that undecidability and computational irreducibility are not good measures for physical complexity.

424Diffusion is usually considered a stabilising process which is why this was such a novel concept.

425Perhaps we should turn the pattern formation question around and ask: ‘What patterns cannot be formed by such simple mechanisms?’

426The fundamental importance of pattern and form in biology is self-evident. Whatever pattern we observe in the animal world, it is almost certain that the process that produced it is still unknown. The genes themselves cannot create the pattern.

427Computational mechanics — in its focus on letting the process speak for itself through (possibly impoverished) measurements — follows the spirit that motivated one approach to experimentally testing dynamical systems theory.

428The right strategy is to formalize pattern, then define complexity as the amount of pattern, then define organization as the growth of complexity, and finally define self-organization as self-generated growth of complexity.

429An epsilon-machine reconstruction algorithm takes in data and gives back a representation of causal patterns, suitable for use in prediction or intervention, ‘untouched by human hands.’ Such an algorithm is a phenomenological engine.

430Statistical mechanics handles randomness and disorder well, but it lacks a coherent, principled way to describe, quantify, and detect the many kinds of structure nature exhibits.

431Epsilon-machines are simultaneously maximally predictive, minimally complex, unique, and minimally stochastic.

432Complexity, on this view, must be a function of the process that generates configurations; we need movies, not snapshots. But this should not be distressing to physicists: we, of all people, should be very suspicious if pattern appeared without a causal history to back it up.

433‘Organized’ does not equal ‘ordered’ — order means low entropy, while organization lies between order and randomness.

434To call something emergent is therefore not to say anything about the property at all, but merely to make a confession of scientific and mathematical incompetence.

435Set a child alone with a heap of Legos, and in an hour the Legos are probably a lot more ordered than they were at the start. Their organization has increased, but in a pretty unmysterious and, to us, uninteresting way: the kid organized them. On the other hand, there are some things which will organize without this kind of outside intervention, which self-organize.

436We are not trying to explain everything we can measure; we are trying to find what’s intrinsically important in our measurements. Emergence is anti-regression.

437No unbiased estimator for entropy or mutual information exists.

438Unfortunately, this is a statement that is ‘obviously true’ but turns out to be false.

439The fitness-based approach is no better than random search, demonstrating that the objective function, rather than helping, has actually been misleading search away from the true answer.

440When I first read a biology textbook, it was like reading a thriller. Every page brought a new shock. As a physicist, I was used to studying matter that obeys precise mathematical laws. But cells are matter that dances.

441Although cells evolved to function and did not evolve to be comprehensible, simplifying principles make biological design understandable to us.

442Evolution converges again and again to the same network motifs in transcription networks. This suggests that motifs are selected because they confer an advantage relative to other circuit designs.

443Development is the remarkable process in which a single cell, an egg, becomes a multicellular organism. During development, cells must assume different fates in a spatially organized manner.

444Apparent randomness can arise from very simple deterministic systems.

445The presence of chaos in a system implies that perfect prediction is impossible not only in practice but also in principle, since we can never know x(0) to infinitely many decimal places.

446The creation of this book and the science it describes has been a vast personal undertaking, spanning the better part of half my life so far. And for it to all have been even remotely possible has required a series of particular personal circumstances. Foremost among them is that I have lived at the moment in history when technology has first made it possible to do the kinds of things I have done. But also crucial has been that my early successes in science and business have for more than twenty years allowed me to be free to pursue the personal intellectual objectives I have chosen.

447I did what is in a sense one of the most elementary imaginable computer experiments: I took a sequence of simple programs and then systematically ran them to see how they behaved. And what I found — to my great surprise — was that despite the simplicity of their rules, the behavior of the programs was often far from simple. Indeed, even some of the very simplest programs that I looked at had behavior that was as complex as anything I had ever seen.

448Griffeath and Hickerson construct a finite Game of Life initial seed — exactly 2,392 cells — whose growing crystal has an asymptotic density of (3 − √5)/90, an irrational number.

449The word complex comes from the Latin root plectere: to weave, entwine.

450It is conceivable that there are processes which organize themselves into conditions so complex that no human being can grasp them. They would be so organized, in other words, that they would look very like noise.

451Curiosity reward should be proportional to predictor improvement, not predictor error.

452Animals prove that this kind of learning is possible, and set a lower bound on how well it can be achieved: anything a sea slug, a lorikeet, or a tenured professor can do, a learning algorithm can do.

453I am happy to still have a sense of wonder when reading the chapters. The wonder comes because networks of thousands of interacting components are generally incomprehensible, yet simplifying principles can still be found.

454Instability is not merely the breakdown of order — it is the mechanism by which nature spontaneously generates spatial structure.

455The Nagel-Schreckenberg traffic model: the addition of a single stochastic step to deterministic acceleration and deceleration rules produces spontaneous traffic jam formation from homogeneous initial conditions.

456No river, regardless of size, runs straight for more than about ten times its average width.

457Of all regular tessellations that tile the plane, hexagons enclose the most area for a given perimeter — a fact bees have exploited for millions of years, and that Thomas Hales proved rigorously only in 1999.

458The deep ideas of computation are intimately related to the deep ideas of life and intelligence.

459It’s always seemed like a big mystery how nature, seemingly so effortlessly, manages to produce so much that seems to us so complex. Well, I think we found its secret. It’s just sampling what’s out there in the computational universe.

460Any system is a channel that communicates its past to its future through its present.

461A completely ordered universe, however, would be dead. Chaos is necessary for life.

462Determinism and randomness are not opposites but essential and unavoidable twins.

463The crucial lesson: maximal randomness (fair coin) has zero structural complexity, and perfect periodicity has zero randomness but nonzero structural complexity. The two quantities are genuinely independent.

464The most characteristic feature of a critical point turns out to be the divergence of the correlation length that renders microscopic details oblivious.

465The line between an explanation and a description of SOC is blurred; an explanation usually contains a description but whether it should contain a prescription is a contentious epistemological question.

466The most important lesson SOC has taught is that it exists as a robust phenomenon. The two models just mentioned are perfect candidates to put to the test any future theory of emergence, which complexity is waiting for. No complete theory of SOC exists.

467We provide the first quantitative evidence, via the local information dynamics framework, for the long-held conjecture that in cellular automata, domains are information storage, particles are information transfer, and particle collisions are information modification.

468Classification schemes are the holy grail in the theory of cellular automata.

469There is no general method to directly link the definition of a cellular automaton with its global, long-term behavior.

470A central problem in the subject is computation of the entropy rate (sometimes known simply as entropy) of an HMP.

471There is a very simple closed-form formula for the entropy rate of a finite-state Markov chain, but there is no such simple formula for entropy rate of HMPs except in very special cases. However, more than fifty years ago Blackwell discovered an expression for the entropy rate of an HMP as the integral of a very simple integrand with respect to a typically very complicated measure on a simplex.

472Ockham’s razor is a consequence, not an assumption.

473The beautiful fractal patterns of rules like 60, 90, and 150 are infinitely fragile. They exist only at a measure-zero point in parameter space and have no robustness whatsoever to stochastic perturbations.

474Rather than measuring novelty explicitly, nature is guided by a single, fundamental constraint: survive long enough to reproduce. Surprisingly, this simple constraint produces both complexity and diversity in a continual process unparalleled by any algorithm to date.

475Lenia: a continuous generalization of cellular automata in which space, time, and state are all made continuous. A handful of parameters — a kernel peaks vector, a growth center, a growth width — generate over 400 species organized into 18 families. The parameter space maps exactly to Wolfram’s four classes: desert, savannah, forest, and river — where the river is where the lifeforms swim.

476The critical state is a global attractor of the dynamics.

477The ‘law of series’ refers to a popular, intuitively felt tendency of rare events to occur in clusters rather than being spread uniformly in time. While it has been commonly dismissed as a purely psychological effect of selective attention, in many cases it has a sound mathematical basis rooted in the ergodic theory of dynamical systems.

478Universality lurks just below the surface of almost any system complex enough to be interesting.

479Whatever policy learned inside of this generated environment will achieve a perfect score most of the time, but will obviously fail when unleashed into the harsh reality of the actual world, underperforming even a random policy.

480We believe that the boundary between easy and hard problems, between the computable and the uncomputable, is not an artifact of a particular mathematical formalism. We believe it is carved into the fabric of the universe.

481If P = NP, then the world would be a profoundly different place than we usually assume it to be. There would be no special value in ‘creative leaps,’ no fundamental gap between solving a problem and recognizing the solution once it’s found. Everyone who could appreciate a symphony would be Mozart; everyone who could follow a step-by-step argument would be Gauss.

482The Church-Turing thesis is one of the most remarkable convergences in the history of ideas. A dozen different formalisms were proposed for capturing the notion of ‘effective computation.’ Every single one turned out to define exactly the same class of computable functions.

483The universality of NP-completeness is one of the most remarkable phenomena in all of mathematics. Thousands of problems, arising from the most diverse corners of science, engineering, and mathematics, turn out to be equivalent to each other.

484Zero-knowledge proofs are among the most paradoxical objects in all of mathematics. They allow you to convince someone that a statement is true without conveying any information beyond the truth of the statement itself.

485IP = PSPACE tells us that conversation is extraordinarily powerful: a single conversation with an untrusted genius is as powerful as an exponential amount of trusted computation.

486Randomness and hardness are two sides of the same coin: the existence of hard problems lets us generate pseudorandomness, and pseudorandomness lets us remove the need for true randomness.

487The geometry of the solution space of a random formula undergoes a series of remarkable transitions as the density of clauses increases. At low densities, the solutions form a single giant connected cluster. At higher densities, this cluster shatters into an exponential number of smaller clusters.

488In the frozen phase, the landscape of solutions is like an archipelago of tiny islands in an exponentially vast ocean, and no local algorithm can island-hop its way to satisfaction.

489The theory of computation is not just about computers — it is about the nature of the physical universe, and what it allows us to know.

490The year 2024 marks the 30th anniversary of the formation of the Artificial Life journal by Chris Langton in 1993. It is also the 37th anniversary of the very first Artificial Life conference organized by Chris Langton at Los Alamos National Labs in 1987.

491In 1985, a philosophy professor, David Helman, gave me a preprint of a penetrating critique of classical AI by Terry Winograd and Fernando Flores. Chapter 4 of that book introduced the ideas of the Chilean biologists Humberto Maturana and Francisco Varela, which provided a road map for an entirely different way of thinking about cognition that was inextricably grounded in its biological underpinnings. This chapter was to have a profound influence on the subsequent direction of my research. I immediately set about reading every book and paper of Maturana and Varela’s that I could find and organizing a small reading group in which I tried to come to grips with the dense, unfamiliar ideas that went against almost everything I had been taught in computer science and AI.

A number of other very important things were also happening in the influential years 1985–1987. The roboticist Rodney Brooks (1986) began a line of work that emphasized the fundamental importance of physical embodiment to intelligent behavior. In parallel, and from the unlikely direction of anthropology and human–computer interaction, came a line of work emphasizing the fundamental situatedness of intelligent systems and the importance of that environmental context to their actions. Additionally, these years saw the beginning of the second neural network revolution, following the original excitement around perceptrons in the 1950s and preceding the current enthusiasm for deep learning.

492Within a typical ALife conference proceedings or volume of Artificial Life, one might find work on oil droplets, large language models, chemical and DNA computing, neural network architectures and learning algorithms, evolutionary algorithms, education, robotics, economics, affective computing, cellular automata, reinforcement learning, ethics, reservoir computing, ecology, evolvable hardware, cooperative behavior, artificial chemistry, neuroscience, sociology, computer music and art, cognitive science, information theory, and culture. The point is not that some aspects of these many topics do not belong in Artificial Life. But Artificial Life cannot just be about neural networks, or evolutionary algorithms, or reinforcement learning, or dynamical systems theory, or information theory. These are merely methods, many of which already have their own communities, conferences, and journals. Likewise, Artificial Life cannot be AI, or robotics, or neuroscience, or chemistry, or biology, or ecology, or sociology, or economics; these already exist as independent scientific fields, with histories much longer than Artificial Life’s. And while the intersection of all these activities threatens to be empty, their union is nothing less than the totality of science and engineering.

493I have been reviewing papers for 35 years, in fields ranging from neuroscience to software engineering, from robotics to cognitive science, from philosophy to mathematics, and the inconsistency of reviews in Artificial Life is among the worst I have seen.

494The vast majority of research projects in ALife are one-offs. They tackle a particular problem of interest to the authors, with an idiosyncratic combination of methods and at best a shallow analysis of results, and then they are dropped. This has the consequence that the literature is filled with many minor but incommensurable variations on a theme.

495We prove a strict hierarchy: globally universal CA form a strict subset of universally self-replicating CA, which form a strict subset of locally universal CA.

496Quantitative theories of physics are possible because macroscale phenomena are often independent of microscopic details.

497A shockingly wide variety of physical systems — from ordinary physical objects to biological cells to brains to the universe as a whole — have come to be regarded by researchers and scholars in multiple disciplines as ‘computational.’ The notion of computation may seem to have lost its distinctiveness.

498For any given sequence of physical microstates visited in the arbitrary time evolution of any sufficiently complex system (e.g., a rock), there exists an assignment of physical microstates to computational states such that the time evolution of the microstates is consistent with the system having performed the computation f. This is not very impressive.

499Shift spaces are to symbolic dynamics what shapes like polygons and curves are to geometry.

500Promptbreeder is not just improving task-prompts, but it is also improving the mutation-prompts that improve these task-prompts.

501Even without any background mutation, this state transition occurs with roughly the same frequency. It is not simply random bit-flipping that causes self-replicators to arise.

502The pansculpturalist would declare that a block of marble is every sculpture that could be chiseled from it because they can interpret the block that way, denying any real distinction between an imagined surface within the block of marble and a real physical surface rendered from the chiseling of the block to expose it.

503It would be absurd to maintain that all there is to sunshine, rain, snow, or hail is that it is the output of a computation. Computational outputs may be taken to represent sunshine, rain, snow, or hail, but they make nothing illuminated, wet, or cold.

504what
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