Automata and Life

Translated from: А. Н. Колмогоров, Автоматы и жизнь: Kolmogorov’s preface (25 August 1961) and the popular exposition of his report prepared by N. G. Rychkova, Техника — молодёжи, nos. 10–11 (1961); and Автоматы и жизнь (тезисы доклада) (1 March 1961). Texts reproduced in the Vivos Voco dossier (2000); the theses are restored from the copy belonging to V. A. Uspensky.

Automata and Life#

Kolmogorov’s Preface#

My report “Automata and Life,” prepared for the seminar of the research staff and postgraduate students of the Faculty of Mechanics and Mathematics of Moscow State University, aroused interest among the very widest circles of listeners.

The editors of the magazine Tekhnika–Molodezhi have resolved to publish a popular exposition of the report, prepared by my colleague at the MGU Laboratory of Probabilistic and Statistical Methods, N. G. Rychkova. This exposition is correct in all its essential features, although at times the verbal shaping of the thought — and consequently some of its shades — belong to N. G. Rychkova.

Let me underline the principal ideas of the report, those of the widest interest.

I. The definition of life as “a special form of the existence of protein bodies” (Engels)Friedrich Engels, Anti-Dühring (1878): “Life is the mode of existence of protein bodies [Eiweißkörper].” Older English renderings have “albuminous bodies.” was progressive and correct so long as we had to deal only with the concrete forms of life that developed on Earth. In the age of cosmonautics there arises a real possibility of encountering “forms of the motion of matter” (see the article “Life” in the Great Soviet Encyclopedia) that possess the basic properties — practically important for us — of living and even thinking beings, but are constituted otherwise. The task of a more general definition of the concept of life thereby acquires a wholly real significance.

II. Modern electronic technology opens very wide possibilities for the modelling of life and thought. The discrete (arithmetical) character of modern computing machines and automata creates no essential limitation in this respect. Systems composed of a very large number of elements, each of which acts purely “arithmetically,” can acquire qualitatively new properties.

III. If the property of some material system of “being alive,” or of possessing the capacity to “think,” is defined in a purely functional manner (for example, any material system with which one can reasonably discuss the problems of contemporary science or literature will be acknowledged to be thinking), then one will have to acknowledge the artificial creation of living and thinking beings to be, in principle, entirely feasible.

IV. At the same time, however, one must remember that the real achievements of cybernetics and automatics along this path are considerably more modest than is sometimes depicted in popular books and articles. For example, in describing “self-teaching” automata, or automata able to “compose” music or to write verse, one sometimes proceeds from an extremely simplified notion of the actual character of man’s higher nervous activity, and, in particular, of creative activity.

V. Real advance in the direction of understanding the mechanism of higher nervous activity — including the highest manifestations of human creativity — naturally cannot detract in any way from the value and beauty of man’s creative achievements. I think this is just what the editors of the magazine Tekhnika–Molodezhi wished to say when they made the slogan “Materialism is beautiful!” one of the subheadings in the exposition of my report.

Academician A. N. Kolmogorov

25 August 1961

Popular Exposition of the Report#

“I belong,” said Kolmogorov, “to those extreme, desperate cyberneticists who see no fundamental limitations whatever in the cybernetic approach to the problem of life, and who suppose that one may analyse life in its full completeness — including human consciousness with all its complexity — by the methods of cybernetics.”

The interest attaching to the following questions is well known:

Can machines reproduce their own kind, and can there occur, in the process of self-reproduction, a progressive evolution leading to the creation of machines substantially more perfect than the original ones?

Can machines experience emotions: rejoice, grieve, be discontented with something, want something?In preparing this exposition of Kolmogorov’s report a defective copy of the “Theses…” was, unfortunately, used. In the authentic text (see below), the second of the questions reads: “Can machines think and experience emotions?” — note by N. G. Khimchenko.

Can machines, finally, set themselves tasks not set for them by their constructors?

Sometimes people try to dispose of these questions, or to justify negative answers to them, by proposing, for example, to define the concept “machine” as something artificially created by man on each occasion. Under such a definition part of the questions — say the first — automatically falls away. But one can hardly regard as reasonable a stubborn unwillingness to get to the bottom of questions that are genuinely interesting and complex, taking cover behind a forcibly narrowed understanding of the terms.

The question whether, along the path of the cybernetic approach to the analysis of vital phenomena, it is possible to create authentic, real life — life that will continue and develop of its own accord — remains a pressing problem of our time. Already now it is timely, fit for serious discussion, for the study of the analogies between artificial automata and a real living system already serves, on the one hand, as a principle for investigating the phenomena of life themselves and, on the other, as a means helping to seek out ways of creating new automata.

There is also another way of answering all these questions at once — to turn to the mathematical theory of algorithms. It is well known to mathematicians that within every formal system sufficiently rich mathematically one can formulate questions that seem substantive and meaningful and ought to presuppose the existence of a definite answer, although within the given system no such answer can be found. And it is therefore proclaimed that the development of the formal system itself is a task for the machine, whereas the thinking-out of the correct answer to the question is already a matter for man — a distinguishing property of human thought.

Such an argument, however, makes use of an idealist interpretation of the concept “thinking,” with the help of which one can easily prove that not only the machine but man himself is incapable of thought. For it is here presupposed that man can give correct answers to any questions whatever, including those posed informally, and that the human brain is capable of performing unboundedly complex formal calculations. Yet there are no grounds for imagining man in so idealised a fashion — as an organism of infinite complexity, containing an infinite quantity of truths. To attain such a condition, we may remark in jest, one would have to settle mankind throughout the starry worlds so that, making use of the infinity of the world, one might organise formal logical calculations in infinite space and even transmit them by inheritance (that is, dispose of infinite time as well). Only then could one hold that mankind is able to develop any mathematical algorithm to infinity.

But this argument can hardly have any bearing on the real state of affairs. And in any case it cannot serve as an objection to the posing of the question of the possibility of creating artificial living beings, capable of reproduction and progressive evolution, and, in their higher forms, possessed of emotions, will, and thought.

This same question is posed elegantly, though formally, by the mathematician Turing in his book Can a Machine Think?:The Russian edition of Alan Turing’s “Computing Machinery and Intelligence” (1950) appeared under the title Может ли машина мыслить? — “Can a Machine Think?” can one build a machine that could not be distinguished from a human being? Such a formulation seems no worse than ours, and is moreover simpler and shorter. In reality, however, it does not fully capture the essence of the matter. For, in essence, what is interesting is not the question whether one can create automata reproducing the properties of man already known to us — one wishes to know whether it is possible to create new life, just as highly organised, though it may be very peculiar and not at all resembling our own.

In modern science fiction one comes upon works that touch on these themes. Interesting and witty is the story “The Friend,” in Stanisław Lem’s collection Invasion from Aldebaran, about a machine that conceived a wish to rule mankind. As a rule, however, the fantasy of the novelists is not distinguished by any special inventiveness. I. A. Efremov, for example, advances the conception that everything perfect resembles everything else. Consequently a highly organised being ought, in his opinion, to have two eyes and a nose, save perhaps of somewhat altered form. In the age of cosmonautics it is no idle supposition that we may, perhaps, have to encounter other living beings, very highly organised and at the same time utterly unlike ourselves. Shall we be able to establish what the inner world of these beings is like, whether they are capable of thought, whether aesthetic experiences and ideals of beauty are proper to them or foreign, and so on? Why should a highly organised being not, for example, have the appearance of a thin film — a mould spread flat upon the stones?

The question we have posed is closely bound up with others: and what is life, what is thought, what is emotional life, aesthetic experience?

In what, let us say, does the difference consist between aesthetic experiences and simple, elementary pleasures — from a pie, for example, or something else of that kind? Speaking more seriously, it must be said: a precise definition of such concepts as will, thought, and emotion has not yet been achieved. But at the natural-scientific level of rigour such a definition is possible. If we do not acknowledge this possibility, we shall find ourselves defenceless against the arguments of solipsism.

One should like to learn, on the basis of behaviour, for example, to draw conclusions about the inner state of a living, highly organised being. Here the following paths open up: first, one may study in detail the behaviour of animals or of man; second, one may study the construction of their brain; and, finally, one may sometimes content oneself with so-called sympathetic understanding. (If, say, one simply observes a cat or a dog attentively, then, even without knowing the science of behaviour and of conditioned reflexes, one can understand perfectly what is on their mind and what they want. It is somewhat harder to attain such an understanding with birds, or, for example, with fish, but even this is hardly impossible.)

This is not a new question; in part it is already solved, in part easily soluble, and in part difficult. The experience of the inductive development of science tells us that questions which long found no solution are nonetheless gradually resolved, and there is hardly reason to think that precisely here there exist predetermined limits beyond which one cannot advance.

How is one to study higher nervous activity by means of the cybernetic approach? If we hold that the analysis of any highly organised system naturally belongs within cybernetics, we shall have to abandon the widespread opinion that the foundations of cybernetics comprise only the study of systems having predetermined goals.

Cybernetics is often defined as the science concerned with the study of control systems. It is held that all such systems possess common properties, and that property number one among them is the presence of a goal. This is true only so long as everything we single out as organised systems governing their own activity resembles ourselves. But if we wish, by the methods of cybernetics, to study the origin of such systems and their natural evolution, then such a definition becomes too narrow. It is hardly likely that cybernetics will entrust to some other science the task of clarifying how the ordinary causal connection in complex systems, by way of natural development, leads to the possibility of regarding the whole system as acting purposively.

Ordinarily the concept of “acting purposively” includes the ability to guard oneself against destructive external influences or, say, the capacity to further one’s own reproduction. The question arises: do crystals act purposively or not? If the “germ” of a crystal is placed in a non-crystalline medium, will it develop? For no separate organs can be distinguished in a crystal — it is therefore a kind of intermediate form. And the existence of such forms is inevitable.

Apparently particular problems of this kind will, after all, be solved by the sciences directly connected with them — the experience of the individual sciences can on no account be neglected. But to exclude from the content of cybernetics the general conceptions of causal connections in purposively acting systems that set themselves goals is likewise quite impermissible — just as it is impermissible, for example, even in the imitation of life by automata, to disregard the fact that these goals themselves change in the course of evolution, and, together with this, the conception of them changes too.

When it is said that the mechanism of heredity, which allows living organisms to transmit their purposive structure to their descendants, has the goal of recreating the given species, of endowing it with definite properties, and also with the possibilities of variability and progressive evolution — then who sets this goal? Or, if we consider the system as a whole, then who, if not the system itself, sets before itself the goal of development by way of sifting out the unfit specimens and multiplying the more perfect ones?

Summing up these considerations, one may say that the study, in general form, of the emergence of systems to which the concept of purposiveness is applicable is one of the chief tasks of cybernetics. Study in general form naturally presupposes knowledge abstracted from the details of physical realisation — from energetics, chemistry, the possibilities of technology, and so forth. What interests us here is only how the possibility arises of preserving and accumulating information. So broad a posing of the problem contains within it many difficulties, but to renounce it at the present stage of the development of science is by now impossible.

If we acknowledge the importance of the task of defining, in objective, generalised terms, the essential properties of the inner life (the higher nervous activity) of some highly organised system unknown to us and unlike us, then might not the same path be proposed for application to our own system — human society? One should like to be able, in a common language, one and the same for all highly organised systems, to describe any phenomena of the life of human society as well.

Let us imagine an imaginary outside observer of our life, one who possesses neither any sympathy for us nor any ability to understand what we think and feel. He simply observes a large accumulation of organised beings and wishes to understand how it is arranged. (Exactly as, say, we observe an anthill.) After a time he will, perhaps, be able without particular difficulty to understand what role is played by the information contained, for example, in railway timetables (a man loses such a timetable and cannot catch the train he needs). The observer would, it is true, have to run up against great difficulties. How, for example, is he to make sense of the following scene: a group of people comes of an evening into a large room; several of them mount a raised platform and begin to make disorderly movements, while the rest sit quietly by, and at the end they disperse without any discussion whatever?

One of the young mathematicians, perhaps in jest, offers yet another example of inexplicable behaviour: people enter a room, there receive bottles of some liquid, and thereupon begin to gesticulate senselessly. It will be hard for the outside observer to establish what this is — merely a disorder in the machine, some failure in its continuous, meaningful working — or whether one can describe what is happening in each of these two cases and establish the difference between them.

Let us now formulate seriously the problem that arises here: to learn to carry out, in terms of behaviour, an objective description of the very mechanism conditioning that behaviour, and to be able to distinguish the several kinds of activity of a highly organised system. It was I. P. Pavlov who first, in our country, established the possibility of an objective study of the behaviour of animals and of man, and of the brain processes regulating that behaviour, without any subjective hypotheses set forth in psychological terms. The profound study of the stated problem here proposed is nothing other than the Pavlovian programme of the analysis of higher nervous activity in its further development.

The practical creation of highly organised living beings exceeds the possibilities of the technology of our day. But any restrictive tendencies, any disbelief — or even any assertion of the impossibility of attaining, along rational paths, an objective description of human consciousness in its full completeness — would now be a brake upon the development of science. The resolution of this problem is necessary, since the interpretation of the various kinds of activity may itself already serve as a spur to the development of machine technology and automatics. On the other hand, the possibilities of an objective analysis of the nervous system are now so great that one does not wish to halt in advance before tasks of any complexity whatever.

If the technical difficulties are overcome, the question of the practical expediency of carrying out the corresponding programme will remain, at the least, disputable. Within the framework of the materialist worldview, however, there exist no sound arguments of principle against an affirmative answer to our question. Moreover, this affirmative answer is the modern form of the convictions concerning the natural emergence of life and the material basis of consciousness.

In cybernetics and the theory of automata the most fully developed at present is the theory of the working of discrete devices — that is, of devices consisting of a large number of separate elements and working in separate steps. Each element can be in one of a small number of states, and the change of state of a single element depends on the previous states of a comparatively small number of elements. So the electronic machines are arranged; so, presumably, is the human brain. (It is held that the brain has some 10¹⁰ such separate elements (nerve cells), and perhaps even more! Somewhat simpler, but still more grandiose in respect of volume, is the apparatus of heredity.)

From this the conclusion suggests itself that cybernetics ought to concern itself only with discrete devices. Against such an approach two objections are not infrequently advanced.

First, real complex systems — both many machines and all living beings — do in fact also possess devices based on the principle of continuous action. As regards machines, the steering wheel of a motor car may serve as such an example. If we turn to human activity — conscious, but not subordinated to the laws of formal logic, that is, intuitive or semi-intuitive (for example, to motor reactions) — we shall find that the great perfection and finish of the mechanism of continuous movement pertain to movements of a continuously geometrical character. If a man performs a triple jump or a pole vault, or, for example, sets out on a slalom course, his movement must be mapped out in advance as continuous (for the mathematicians: the slalomist’s path turns out to be even an analytic curve). One may suppose, however, that this is no radical objection against discrete mechanisms. Most probably the intuition of a continuous line is, after all, realised in the brain on the basis of a discrete mechanism.

The second objection against the discrete approach consists in the following: it is a certainty that the human brain — and even (unfortunately, often) computing machines — by no means always act deterministically, in a fully law-governed manner. The result of their action (at a certain moment, in a certain cell) not infrequently depends on chance. In answer to this objection one may say that into automata, too, one can “introduce randomness.” It is hardly likely that the imitation of randomness (that is, the replacement of chance by some regularities having no direct relation to the given situation) can do any serious harm in the modelling of life. It is true that the “introduction of randomness” is often treated somewhat primitively: a sufficiently long tape of random numbers is prepared, which is then used to imitate chance in various problems. But with frequent use this prepared “randomness” in the end ceases to be randomness. In view of these considerations, the question of imitating chance on automata should be approached with great caution. In principle, however, it is in any case a thing that is possible.

The argument just set out leads us to the following principal conclusions:

There is no doubt that information processing and the control processes in living organisms are built upon a complex interweaving of discrete (digital) and continuous mechanisms, on the one hand, and of the deterministic and the probabilistic principles of action, on the other.

Discrete mechanisms, however, are the leading ones in the processes of information processing and control in living organisms. There exist no sound arguments in favour of a fundamental limitation of the possibilities of discrete mechanisms as compared with continuous ones.

Doubts about the possibility of modelling human consciousness on automata are often built on the ground that the number of functions of man’s higher nervous activity is immeasurably great, and that no machine could become a model of conscious human activity in its full extent. Of nerve cells alone there are, in the cerebral cortex, of the order of 10¹⁰. What, then, must be the number of elements in a machine imitating the whole complex higher nervous activity of man?

This activity, however, is bound up not with individual nerve cells but with fairly large aggregates of them. It is impossible to imagine that, say, some mathematical theorem “sits” in one single nerve cell specially prepared for it, or even in some definite number of them.

Apparently the matter stands quite otherwise. Our consciousness operates with comparatively small quantities of information. The number of units of information that a man’s consciousness takes in and processes in, say, a second is quite small. Here is one somewhat paradoxical example: a slalomist, in covering the course, takes in and processes over the span of ten seconds considerably more information than in other, seemingly more intellectual, kinds of activity (in any case, more than a mathematician passes through his head in forty seconds of intense mental work!). In general, the whole conscious activity of man is arranged in some very peculiar and complex way; but when its regularities have been studied, the modelling of this activity will require far fewer elementary cells than the modelling of the brain itself — paradoxical as this may be.

What volumes of information, then, can already create the qualitative distinctiveness of complex phenomena such as life, consciousness, and the like? To attempt to answer this question, let us turn to the notion of categories of numbers.

Numbers can be divided into small, medium, large, and super-large. (This classification is not strict; within it one will not be able to say that such-and-such a number is, for example, medium, while the one following it is already large. Numbers are divided into categories only up to order of magnitude. But greater strictness is not needed by us here.) What, then, are these categories? Let us begin with definitions for the mathematicians.

We shall call a number A small if it is practically possible to enumerate all the schemes made of A elements with two inputs and outputs (or, what is the same, to write out for them all the functions of the algebra of logic with A arguments);

We shall call a number B medium if we prove unable to enumerate in practice all the schemes made of B elements, but can enumerate only these elements themselves or (what is a shade more difficult) work out a system of notation for any system of B elements;

A number C is large if we are unable in practice to enumerate such a number of elements, but can only establish a system of notation for these elements;

And, finally, numbers are super-large if even this cannot be done in practice (these, as we shall see further on, we shall not even need).

Let us now clarify these definitions with simple examples. Suppose that to a single electric bulb three switches are connected, each of which can be in the left (L) or the right (R) position. Then, evidently, the number of possible joint positions of the three switches will be 2³ = 8. Let us list them for clarity:

The wiring to our switches can be made in such a way that in each of the positions written out the bulb may either burn or not burn. It is easy to compute that the number of distinct positions of the switches, accompanied by the marks “burns,” “does not burn,” will be 2²³, that is, 2⁸ = 256 (the reader can readily verify this for himself, supplementing the positions of the switches written out above with such marks). The fact that such an exercise is not only within the reader’s powers but will not take him too much time is precisely what convinces us that the number 3 (the number of switches) belongs among the small ones.

If there were not 3 switches but, say, 5, then one would have to write out 2²⁵ = 4,294,967,296 distinct joint positions of the switches accompanied by the marks “burns,” “does not burn.” It is hardly possible to carry all this out in practice, without losing count, in any reasonable time. The number 5, therefore, can no longer be considered small.

To make clear what a medium number is, let us give the following example: imagine that you have been brought into a room in which there are 1,000 people, and invited to shake hands with each of them. True, your hand after such exercises will feel none too well, but to carry out such an exercise in practice (as regards time) is entirely possible — to go up, without losing count, to each of the thousand and hold out your hand to him. But if there followed an invitation for the whole thousand present to exchange handshakes with one another, and moreover for each company of three within its own little circle to exchange additional handshakes, and so on, then this would prove unrealisable. The number 1,000 is precisely a medium one. One may say that we have, as the definition proposes, enumerated a thousand elements, marking each of them (by a handshake) as we did so.

A quite simple example of a large number is the number of visible stars in the firmament. Everyone knows that it is impossible to count the stars off on one’s fingers, and yet there exists a catalogue of the starry sky (that is, a system of notation has been worked out), by means of which we can at any moment obtain information about the star that interests us.

Naturally a computing machine can, first, work without losing count longer than a man, and, second, it composes the various schemes many times faster. Therefore, in each category the corresponding numbers for the machine will be larger than for a man.

From this table two essential conclusions follow:

— although the corresponding numbers (within one category) for the machine are far larger than for a man, they remain on the same level;

— between the numbers of different categories, however, there exists an impassable boundary: numbers that are medium for a man do not become small for a machine, just as numbers that are large for a man do not become medium for a machine (10³ is incomparably greater than 10, and 10¹⁰⁰ is hopelessly greater than 10¹⁰).

Let us note that the memory capacity of a living being (and even of a machine) is characterised by medium numbers, whereas many problems solved by way of so-called simple enumeration are characterised by large ones. Thus we at once pass beyond the limits of what can be compared by way of simple enumeration.

Problems that cannot be solved without large-scale enumeration will remain beyond the possibilities of the machine at however high a stage of the development of technology and culture. We have arrived at this conclusion without having recourse to the concept of infinity. We had no need of it, and are hardly likely to need it, in solving the real problems that arise along the path of the cybernetic analysis of life.

On the other hand, another question becomes important: do there exist problems that are posed and solved without the necessity of large-scale enumeration? Such problems ought to interest the cyberneticists first of all, for they are really soluble. The fundamental possibility of creating full-fledged living beings, built entirely upon discrete (digital) mechanisms of information processing and control, does not contradict the principles of materialist dialectics. The opposite opinion can arise only because some are accustomed to seeing dialectics only where infinity appears. In the analysis of the phenomena of life, however, what is essential is not the dialectics of the infinite but the dialectics of the large number.

At the present time it is, perhaps, more important for cybernetics than for any other science what is written about it. A. N. Kolmogorov defined his attitude to the cybernetic literature thus: “I do not belong among the great enthusiasts of all that cybernetic literature which is now published so widely, and I see in it a great deal, on the one hand, of exaggeration and, on the other, of over-simplification.”

One cannot, of course, say that this literature asserts what is in fact unattainable, but one often comes upon rapturous articles in it whose very titles already cry out about successes in the modelling of various complex kinds of human activity which in reality are as yet modelled very poorly indeed.

For example, in the American literature on cybernetics (and in ours too, at times even in wholly serious scientific journals) one may come upon works on the so-called machine composition of music. By this is usually meant the following (this does not apply to the works of R. Kh. Zaripov): into the machine’s memory is “laid” the musical notation of a considerable number (say, 70) of cowboy songs or, for example, church hymns. Then, from the first four notes of one of these songs, the machine seeks out all the other songs in which these four notes occur in the same order, and, having chosen one of these songs at random, takes from it the next, the fifth, note. Now before the machine there are again four notes (the 2nd, 3rd, 4th, and 5th), and it once more, by the same method, carries out its search and choice. Thus the machine, as if by touch, “creates” a certain new melody. And it is asserted that if there were cowboy songs in the machine’s memory, then in its creation too something “freedom-loving” is to be heard, whereas if they were church hymns — then something “divine.”

The question arises: what will happen if the machine conducts its search not by four but by seven consecutive notes? Since in reality one hardly ever meets two compositions containing seven identical notes in succession, then, evidently, having “struck up” seven notes from some song, the machine will be forced to sing it through to the end. If, on the contrary, one sets the machine only two notes for its creative work (and of compositions with two identical notes there are any number), then here so wide a choice would present itself that instead of a melody there would arise a cacophony of sounds.

This uncomplicated scheme is what is presented in the literature as “the machine composition of music,” and it is asserted in all seriousness that, as the number of notes needed “to strike up” is increased, the machine begins to create music of a more serious, classical character, while as this number is decreased it passes over to the modern, the jazz kind.

As of today we are still very far from carrying out the analysis and description of the higher forms of human activity. We have not even yet learned to give, in objective terms, definitions of many of the categories and concepts required here, to say nothing of modelling such complex kinds of this activity as the creation of music. If we are unable to understand what distinguishes living beings that have need of music from beings that have no need of it, then, in setting about the machine composition of music straightaway, we shall find ourselves in a position to model only purely external factors.

“The machine composition of music” is only an example of the simplified approach to the problems of cybernetics. Another widespread shortcoming consists in this, that the adherents of cybernetics have been so carried away by the possibilities of the cybernetic approach to the solution of any of the most complex tasks that they permit themselves to neglect the experience accumulated by other sciences over the long centuries of their existence. It is often forgotten that the analysis of the higher forms of human activity was begun long ago and has advanced rather far. And although it is conducted in other, non-cybernetic terms, it is in essence objective, and it must be seriously studied and made use of. Whereas what the cyberneticists have managed to do “with their bare hands,” and around which they raise such a clamour, frequently does not go beyond the investigation of the most primitive phenomena.

Once, at an evening in the Moscow House of Writers, one of those present held forth from the platform to the effect that our age was bound to create — and had already created (!) — a new medicine. This new medicine is the province and object of study not of physicians but of specialists in the theory of automatic regulation! The most important thing in medicine, in the speaker’s opinion, is the cyclic processes taking place in the human organism. And such processes are precisely what is described by the differential equations studied in the theory of automatic regulation. So that to study medicine in medical institutes is now, as it were, out of date — it should be handed over to the charge of the technical colleges and the mathematics faculties. It may well be true that specialists in the theory of automatic regulation can have their say in the resolution of particular problems confronting medicine. But if they should seriously wish to take part in this work, they would first of all require a colossal requalification, for the experience accumulated by medicine, that oldest of sciences, is enormous, and in order to do anything serious in it one must first master this experience.

In general, the analysis of higher nervous activity in cybernetics is concentrated for the time being on two extreme poles.

On the one hand, the cyberneticists are actively engaged in the study of conditioned reflexes — that is, of the simplest type of higher nervous activity. (Everyone, probably, knows what a conditioned reflex is. If any two stimuli are repeatedly reproduced simultaneously with one another (for example, a bell is sounded at the same time as food is presented), then after a certain time one of these stimuli alone (the bell) evokes the organism’s responding reaction (salivation) to the other stimulus (the presentation of food). This coupling is temporary and, if it is not reinforced, gradually disappears.) A considerable part of the cybernetic problems now known under the name of the mathematical theory of learning embraces such very simple schemes, which do not exhaust even a small fraction of the whole complex higher nervous activity of man and which, even in the analysis of conditioned-reflex activity itself, represent only an initial step.

The other pole is the theory of formal-logical decisions. This side of man’s higher nervous activity lends itself well to study by mathematical methods, and with the creation of computing technology and computational mathematics, research of this kind has rapidly moved forward. Here, too, the cyberneticists have succeeded in much.

But the whole vast space between these two poles — the most primitive and the most complex kinds of mental activity (even simple forms of synthetic activity, such as, say, the mechanism of precisely calculated geometrical movement spoken of above, as yet lend themselves poorly to cybernetic analysis) — is studied exceedingly little, not to say: is not studied at all!

A special position is now occupied by mathematical linguistics. This science is only just now being created and is developing in step with the accumulation of cybernetic problems connected with language. It has to do with the analysis of the higher forms of human activity of a character rather intuitive than formal-logical, and this intuitive activity lends itself poorly to precise description. Everyone knows what a competently constructed phrase, a correct agreement of words, and so on, are, but as yet one does not succeed in conveying this knowledge adequately to the machine. A precise machine translation, logically and grammatically impeccable, would now be possible, perhaps, only from Latin and into Latin, whose grammatical rules are sufficiently complete and unambiguous. The grammatical rules of the new, living languages are, apparently, as yet insufficient for carrying out machine translation with their help. The analysis needed here has been undertaken for a long time now, and at the present time machine translation has become the object of a broadly and seriously mounted activity. One may, perhaps, say that it is precisely on this that the principal attention of the mathematical linguists is now concentrated.

However, in the theoretical works on mathematical linguistics little account is taken of the fact that language arose considerably earlier than formal-logical thought. Perhaps for theoretical science one of the most interesting investigations (one in which the ideas of cybernetics, a new mathematical apparatus, and modern logic might be naturally combined) would be an investigation of the process of the formation of words as a second signal system. Originally, when concepts were still altogether lacking, words act in the role of signals evoking a definite reaction. The emergence of the science of logic is usually assigned to a comparatively recent time: apparently it was only in ancient Greece that it was clearly grasped and formulated that words are not simply designations of certain immediate representations and images, but that from the word a concept can be separated off. Before genuine, formal-logical thinking, thoughts arose not formalised into concepts but as a combining of words that draw other words after them, as attempts to fix directly the stream of images passing before our consciousness, and so on. To trace this mechanism of the crystallising-out of words as signals bearing within themselves a complex of images, and of the creation on this basis of an early logic, is an exceedingly rewarding field of investigation (for the mathematician, in particular) — which, incidentally, has been noted more than once in the cybernetic literature.

The following question, too, may appear interesting: to investigate how logical thought is formed in man. Let us try to trace the stages of this process by the example of a mathematician’s work on some problem. First, apparently, there arises a desire to investigate this or that question. Then some approximate conception, arisen from who knows where, of what we hope to obtain as the result of our searches and by what paths we may, perhaps, succeed in attaining it. And only at the next stage do we set in motion our inner “arithmometer” of formal-logical reasoning.An arifmometr was a hand-cranked mechanical calculating machine, in common use in the USSR at the time — hence Kolmogorov’s figure for the mind’s formal-computational faculty. Such, apparently, is the path of the formation of logical thought, the scheme of the creative process.

It may, probably, prove interesting not only to investigate the first, the intuitive, stage of this process, but also to set oneself the goal of creating a machine able to help man in the process of creation at the stage of giving shape to a thought (the mathematician, for example, at the stage of computation): to charge such a machine, say, with understanding and fixing in complete form certain vague, auxiliary sketches of diagrams and formulae which every mathematician draws on paper in the process of his creative searches. Or, for example, with recreating from sketches the images of figures in multidimensional spaces, and so forth. In other words, it is interesting to reflect on the creation of machines which, without replacing man, would already now help him in the complex processes of creation. As yet it is difficult even to imagine in what way and along what paths such a machine might be realised. But although this task is as yet far from its resolution, talk of all such questions has already arisen in the cybernetic literature, and this, apparently, can only be welcomed.

As one can already see from the several examples adduced here, the various problems connected with understanding the objective structure of the subtlest divisions of man’s higher nervous activity are very many. And they all deserve the proper attention of the cyberneticists.

In conclusion, one should dwell on the questions touching the ethical side of the ideas of cybernetics. The denial and rejection of these ideas that one often meets with proceed from an unwillingness to acknowledge that man is indeed a complex material system — but a system of finite complexity and of very limited perfection, and therefore accessible to imitation. This circumstance seems to many humiliating and frightful. Even when they take in this idea, people do not wish to be reconciled to it: such a picture of an all-embracing penetration into the mysteries of man, up to the very possibility of even “encoding” him and “transmitting him by telegraph” to another place, seems to them repellent and alarming.

Apprehensions of another kind, too, are met with: does our inner constitution admit, in general, of an exhaustive objective description? Above, for example, it was proposed to set cybernetics the task of learning to distinguish, by objective signs, beings that have need of programmatic music from beings that have no need of it.“Programmatic music” [siuzhetnaia muzyka, literally “music with a subject”] — music understood as expressing or narrating something, as against mere combinations of sound. And what if we analyse and analyse — and it turns out that there really is no reasonable ground for singling out such music as noble in comparison with other combinations of sounds?

“It seems to me important,” said A. N. Kolmogorov, “to understand that there is nothing humiliating or frightful in the striving to comprehend oneself to the very end. Such moods can arise only out of half-knowledge: a real understanding of the whole grandeur of our possibilities, a sense of the presence of the age-old human culture that will come to our aid, ought to produce an enormous impression, ought to call forth admiration!

“Our own inner constitution can, in principle, be understood; but it is understood, too, that this constitution contains within itself colossal possibilities, limited by nothing. In truth, one must strive to replace this foolish and senseless fear of the automata that imitate us with an enormous satisfaction in the fact that such complex and beautiful things can be created by man — who, only very recently, found in simple arithmetic something incomprehensible and exalted.”

Automata and Life (Theses of a Report)#

Part One#

1. The interest attaching to the following questions is well known:

Can machines reproduce their own kind, and can there occur, in the process of such self-reproduction, a progressive evolution leading to the creation of machines substantially more perfect than the original ones?

Can machines think and experience emotions?

Can machines want something, and themselves set before themselves new tasks not set for them by their constructors?

Sometimes an attempt is made to justify a negative answer to such questions by means of

(a) a restrictive definition of the concept “machine”;

(b) an idealist interpretation of the concept “thinking,” under which the incapacity for thought is easily proved not only of machines but of man as well.[Author’s note:] The “Mathematical objection,” in A. Turing’s classification, in the booklet Can a Machine Think? [the Russian edition of “Computing Machinery and Intelligence,” 1950].

2. There exists a more traditional and simpler form of this question:

Is the creation possible of artificial living beings, capable of reproduction and progressive evolution, and, in their higher forms, possessed of emotions, will, and thought, down to its very subtlest varieties?

3. A precise definition of all the concepts entering into the question just posed is not entirely trivial. At the natural-scientific level of rigour, however, such a definition is possible. Persons who deny such a possibility are inevitably led to solipsism.

4. The creation of highly organised living beings exceeds the possibilities of the technology of the present day. If the technical difficulties are overcome, then the question of the practical expediency of carrying out the corresponding programme of work will still be, at the least, disputable.

5. It is important, however, to understand clearly that within the framework of the materialist worldview there exist no sound arguments of principle against an affirmative answer to our question. This affirmative answer is the modern form of the propositions concerning the natural emergence of life and the material nature of consciousness.

6. There is no doubt that information processing and the control processes in living organisms are built upon a complex interweaving of

(a) discrete (digital) and continuous mechanisms;

(b) the deterministic and the probabilistic principles of action.

7. Discrete mechanisms, however, are the leading ones in the processes of information processing and control in living organisms. There exist no sound arguments in favour of a fundamental limitation of the possibilities of discrete mechanisms as compared with continuous ones.

8. The fundamental possibility of full-fledged living beings, built entirely upon discrete (digital) mechanisms of information processing and control, does not contradict the principles of materialist dialectics. The opposite opinion can arise among specialists in the philosophy of mathematics only because they are accustomed to seeing dialectics solely where the infinite appears. In the analysis of the phenomena of life, what is essential is not the dialectics of the infinite but the dialectics of the large (a purely arithmetical combination of a large number of elements will create both continuity and new qualities!).

Part Two#

9. Notwithstanding what has been said in the first part, there is also a healthy side to the widespread movement against the “exaggerations of cybernetics.” The real and widespread shortcomings of the generalising literature and of individual scientific works on cybernetics are:

(a) a simplified notion of the mechanisms of information processing and control in living organisms and, especially, in the domain of man’s higher nervous activity;

(b) a neglect of the experience in the study of these mechanisms accumulated before the emergence of cybernetics as a separate science.

10. Whereas the first of these shortcomings “corrects itself in passing” (in the course of the work the untenability of the simplified notions comes to light), the second shortcoming demands a systematic struggle against it — in particular, in the planning of the training of young specialists in cybernetics and its applications.

11. In the domain of man’s higher nervous activity cybernetics has so far mastered only:

(a) the mechanism of conditioned reflexes in its simplest form (see the works on the “mathematical theory of learning”);

(b) the mechanism of formal logical thinking.

But conditioned reflexes are proper to all vertebrates, whereas logical thinking arose only at the very last stage of mankind’s development. All the kinds of synthetic activity of human consciousness that precede formal logical thinking and that go beyond the simplest conditioned reflexes have not, as yet, been described in the language of cybernetics.

12. In the developed consciousness of modern man the apparatus of formal thinking does not occupy a central position. It is, rather, a kind of “auxiliary computing device,” set going as the need arises. Since, on the other hand, the usual schemes of the theory of conditioned reflexes yield very little for the understanding of the higher divisions of man’s emotional life or, say, of a scientist’s creative intuition, it must be acknowledged that the cybernetic analysis of the working of developed human consciousness in its interaction with the subconscious sphere has as yet scarcely been begun.

13. The examples of artistic creation and perception, and of their modelling on machines, that are considered in cybernetic works (the compiling of musical melodies out of fragments of four or five notes taken from several dozen earlier melodies fed into the machine, and the like) astonish by their primitiveness, whereas in the “non-cybernetic” scientific literature the formal analysis of artistic creation has long since attained a high level. This is but one example of the primitive level of the cyberneticists’ humanistic interests — the raising of which is necessary if one is to take up in earnest the task of understanding, from the standpoint of cybernetics, the real complexity of man’s psychical life.

14. The objective study, in the terms of cybernetics, of certain of the subtlest kinds of man’s creative activity may, in the very near future, acquire great practical significance.

Here is an example closest to mathematicians. It is well known that pencil and paper are indispensable to the mathematician in the process of his intuitive creative searches. Instead of fully written-out formulae, there sometimes appear on the paper their conjectural schemes with unfilled places; a few lines and dots depict figures in a multidimensional or infinite-dimensional space; sometimes the course of the enumeration of variants is designated by signs, the variants grouped according to principles that are rebuilt in the course of the enumeration, and so on. It is entirely possible that computing machines with a suitable arrangement for the input and output of data might be of use already at this stage of scientific work.

Naturally, the working-out of a methodology for such a use of machines presupposes a preliminary objective study of the process of a scientist’s creative searches.

15. Certain other directions of the objective study of the mechanism of man’s creative activity may well not receive practical applications in the near future.[Author’s note:] In any case, my personal experiments in bringing the ideas of cybernetics into the study of verse [stikhovedenie] have no aim of helping poets to write verse.

Yet a serious objective study of man’s higher nervous activity in its full completeness appears to me a necessary link in the affirmation of materialist humanism. The development of science has many times led to the destruction of illusions habitual to man, beginning with the consoling belief in personal immortality. At the stage of half-knowledge and half-understanding these destructive conclusions of science become arguments against science itself, in favour of irrationalism and idealism. Darwin’s theory of the origin of species and Pavlov’s objective study of higher nervous activity have repeatedly been portrayed as belittling man’s higher strivings toward the creation of moral and aesthetic ideals. Similarly, in our time the fear that man might turn out to be no better than “soulless” automata is made into a psychological argument in favour of vitalism and irrationalism.[Author’s note:] The ostrich argument (the “Heads in the Sand” objection) in Turing’s terminology.

A full understanding of the mechanism of man’s higher nervous activity must, in my conviction, destroy the very source of the fear, replacing it with wonder before the results of the already-mentioned dialectics of the large.[Author’s note:] A poet can invest in a “message” of 400 printed letters (a message of a purely “digital” nature, formally carrying on the order of 10³ “bits” — a quantity, that is, negligible from the standpoint of modern technology) a whole world of feelings, which is justly acknowledged not to lend itself to “formalisation” in concepts, and can create, with such modest means, a “channel of communication” of immediate emotional intercourse with his contemporaries and descendants — a channel that reveals, breaking through the limitations of space and time, his unrepeatable individuality. I would remark that the opinion as to “unrepeatability” does not contradict arithmetic. The number of possible Russian poems of 400 letters is of the order of 10¹⁰⁰.

A. Kolmogorov

1 March 1961