Automata and Life

Translated from: А. Н. Колмогоров, Автоматы и жизнь, together with the accompanying materials of the Vivos Voco dossier (2000), assembled by N. G. Khimchenko (Rychkova): her memoir “How It Was…”; Kolmogorov’s popular exposition of the report (Техника — молодёжи, nos. 10–11, 1961), prepared by N. G. Rychkova, with his prefatory note of 25 August 1961; the authentic theses of the report (1 March 1961), restored from the copy belonging to V. A. Uspensky; and V. M. Tikhomirov’s essay “A Few Words on ‘Kolmogorov and Cybernetics.’”

Translation note: The report “Automata and Life,” delivered at Moscow State University on 6 April 1961, is among the founding statements of the Soviet cybernetic programme — a materialist wager that life and mind, human consciousness included, are in principle modelable on discrete mechanisms, and that what matters in the analysis of life is “not the dialectics of the infinite but the dialectics of the large.” The popular exposition has appeared in English only once, in the long-out-of-print Mir Publishers anthology Cybernetics Today (trans. F. and V. Palkin); the authentic theses and the two commentaries of 2000 do not appear to have been published in English before. Emphasis in the originals — Russian letter-spacing [razryadka] and words set in capitals — is rendered as italics, except where a text remarks on the capitals themselves. Bracketed glosses give Library-of-Congress transliterations of key Russian terms; the author’s own notes are marked “[Author’s note:]”. One item listed in the dossier’s contents, V. A. Uspensky’s “From Reminiscences,” was not part of the source provided and is not included here.

How It Was…#

The beginning of the sixties coincided with the beginning of a stormy development of cybernetic ideas in our country. It had become generally accepted that research in the field of the science of the principles of control (as cybernetics was most often defined) was acutely necessary not only for the progress of technology, but might also foster success in many fields of science: in mathematics, biology, psychology… Disputes around problems of this kind did not die down, yet no universally recognised, settled answers were to be found.

Sensing this breath of the times, the editors of the well-known popular-science magazine Tekhnika–Molodezhi [Technology for the Youth] resolved to invite mathematicians, philosophers, biologists, and engineers — all who had a part in this set of problems — to speak in its pages. A discussion was opened in the magazine under the title “We Discuss the Problems of Cybernetics Today.” Within this discussion the following appeared in Tekhnika–Molodezhi: Academician I. I. Artobolevsky and Doctor of Technical Sciences A. E. Kobrinsky (“A Living Being and a Technical Device,” no. 2, 1962); Academician A. I. Berg (“Cybernetics — into the Service of Communism,” nos. 3 and 4, 1962); the Czech academician E. Kolman (“Can Machines Possess a Psyche?,” no. 1, 1962); the American mathematician Professor W. Ross Ashby (“What Is an Intelligent Machine?,” no. 6, 1962);W. Ross Ashby (1903–1972) was in fact British, though by 1962 he had moved to the University of Illinois — hence, presumably, the memoir’s “American.” the engineer P. Kuznetsov (“Chemical Cybernetics,” no. 2, 1962); the mathematician S. A. Stebakov (“One Can Derive an Equation of Health,” no. 12, 1961); Academician N. G. Bruevich (“The Automation of Mental Labour,” no. 11, 1961); Academician V. M. Glushkov (“To Make Cybernetics a Genuine Helper of Man’s Mental Activity,” no. 6, 1962); and a student from the city of Kuibyshev, A. Kondratov (“The Birth of an Idea. The Contours of a New Science — iskusstvometriya [the metric study of art],” no. 5, 1962).

But the discussion opened with the contribution of Academician Andrei Nikolaevich Kolmogorov. In issues 10 and 11 for the year 1961 there appeared the publication “Automata and Life.” I should like to tell something of the history of this publication.

Academician A. N. Kolmogorov’s report under this title took place on 6 April 1961 at Moscow State University. Prepared for the methodological seminar of the research staff and postgraduate students of the Faculty of Mechanics and Mathematics, this report aroused such unprecedented interest and such an unheard-of influx of listeners that it had to be moved from the already enormous lecture hall 02 to the hall of the MGU Palace of Culture.

Andrei Nikolaevich had prepared theses for this report in advance (the date given is 1 March 1961); they were reproduced on a hectograph, and one could consult them in the Faculty library (as well as in all the departments). I know of only one of the surviving copies of the theses typed by A. N. Kolmogorov’s own hand on a plain typewriter and bearing corrections entered in his hand — this copy belongs to V. A. Uspensky. Hectograph copies are not hard to find, and over the intervening years they have been reprinted many times in various editions — but together with the vexing misprints that crept in when the original text was prepared for reproduction.

Kolmogorov’s theses for the report “Automata and Life” are published below, and one may trace what has happened to the text over its long life.

The original version, of fifteen theses, was divided into two parts: the first part contained eight points, and the following seven were assigned to the second (the numbering of the points, however, was kept continuous). At the report itself there was, so far as I recall, no interval, nor any other marking of the separation of the one part from the other. And, above all, one can hardly say that the report followed its theses at all. Those who knew A. N. Kolmogorov closely, who worked with him and studied under him, will most likely not be surprised by such a turn. Andrei Nikolaevich found it tedious, in general, to “repeat one and the same thing.” When he found a receptive listener and wished to be understood, he experienced such an emotional elevation that he could hardly follow a plan thought out in advance.

On the setting in which this report and several of A. N. Kolmogorov’s subsequent “large” public appearances took place, it is interesting to read V. A. Uspensky’s essay in the collection Kolmogorov in Reminiscences (editor-compiler A. N. Shiryaev, Moscow, Nauka, 1993), or his essays in the recently published Essays on the History of Informatics in Russia (Novosibirsk, Scientific-Publishing Centre OIGGM SO RAN, 1998).

Let us return, however, to the history of the report’s publication in the magazine Tekhnika–Molodezhi. By what means rumours of the extraordinary success of this appearance reached its editor-in-chief Vasily Dmitrievich Zakharchenko has remained unknown to us. Yet soon after the report, somewhere in April or May, the head of the science section of Tekhnika–Molodezhi, V. D. Pekelis, approached Andrei Nikolaevich with a request to set out the report for the magazine. Needless to say, such work held no interest for Kolmogorov, and he declined it. Then Viktor Davydovich proposed simply to work up for print the stenographic record of the report (in those days such large public appearances by scholars were taken down in shorthand) — this proposal met with even less interest. But Pekelis continued to insist, and then Andrei Nikolaevich charged me (at that time a junior research fellow of the Chair of Probability Theory of Moscow University, which he headed) with working over the stenogram and, if it should prove possible, preparing it for print.

This task I carried out as conscientiously as I could; I showed the resulting text to Andrei Nikolaevich and, having received his approval, took it to the editorial office. In the magazine’s opinion, however, the text had turned out “too serious” and “inaccessible to the comprehension of the average reader.” The editors demanded that it be simplified, whereas I did not feel that I had such authority. The editors found a way out without my participation: the text was broken up into small pieces, to which simple (and sometimes frivolous) subheadings were given, and the artist G. Kychakov furnished it with cheerful drawings (hardly reflecting the essence of the matter). In this form it reached Andrei Nikolaevich for approval.

I do not know what conversation then took place between V. D. Pekelis and A. N. Kolmogorov, but a compromise was found: the text remained in the form dissected by the editors and with the pictures, but before it, in a separate column, was placed a short introduction by A. N. Kolmogorov, in which he sharpened the questions raised in the report without the excessive over-simplification (against which he had spoken in the report itself).

It is easy to understand that the magazine’s editors wished to open a discussion of the problems of cybernetics in their pages with an article by the most eminent mathematician of the age — A. N. Kolmogorov — and not by his “junior research fellow,” and, now without any consultation with Andrei Nikolaevich at all, they placed the text under his name and with his portrait, although the first and last utterances in the exposition are accompanied by the words “said A. N. Kolmogorov” — which, you will agree, looks somewhat unusual when applied to oneself…

Thereafter this publication had the widest resonance and was reprinted many times in various editions, some more and some less serious. In the end the text from the Kvant Library (issue 64, Nauka Publishers, Moscow, 1988) came to be regarded as the standard, on the grounds that it was there that “A. N. Kolmogorov’s own corrections” had been entered into the text. The copy of Tekhnika–Molodezhi with Andrei Nikolaevich’s pencil markings belongs to V. A. Uspensky.

When, in preparing the present edition, I approached Vladimir Andreevich with a request to let me examine these corrections, it turned out that A. N. Kolmogorov had made a small correction to the text of his introduction (and it was a plain misprint that was corrected), while the text of the exposition of the report he did not touch at all (he could hardly have thought it worth spending his time on that). Those small — yet sometimes, nonetheless, substantial — changes that did after all appear in this “standard” text as compared with the original, from Tekhnika–Molodezhi of 1961, belong, apparently, to the editors of Kvant. If one looks closely at this variant, which has ever since been reprinted as the principal one, one will notice that at the end of his introduction A. N. Kolmogorov mentions the subheadings from the magazine Tekhnika–Molodezhi, but in what connection remains unclear to the reader — from the first paragraph, which explained the matter, this mention has for some reason dropped out. The text published below has been cleansed of the subheadings and the other “over-simplifications” once introduced by the editors of Tekhnika–Molodezhi.

An amusing picture results: the report was Kolmogorov’s, Rychkova wrote it, Kvant published it, and Tekhnika–Molodezhi supplied the subheadings! And, if one gets to the bottom of it, that, on the whole, is just how it was…

N. G. Khimchenko (Rychkova)

11 March 2000

Automata and Life#

The article as published in Tekhnika–Molodezhi (nos. 10–11, 1961): a prefatory note in Kolmogorov’s own hand, followed by N. G. Rychkova’s popular exposition of the report.

Kolmogorov’s Preface#

Written by Kolmogorov to introduce the published article; dated 25 August 1961.

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#

What follows is N. G. Rychkova’s popular exposition of the report, prepared from a stenogram (see the memoir above). Its opening and closing passages give Kolmogorov’s own words, marked “said Kolmogorov”; the connecting account is Rychkova’s rendering of what he said.

“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)#

The theses Kolmogorov prepared and circulated for the report — the authentic, terse original underlying the exposition above, restored from the copy belonging to V. A. Uspensky. Dated 1 March 1961. The four numbered notes are Kolmogorov’s own.

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

A Few Words on the Theme: “A. N. Kolmogorov and Cybernetics”#

Many years have passed since then — some forty — and much has changed…

Will it not seem astonishing to you that Academician Andrei Nikolaevich Kolmogorov, having received at his lecture in the Polytechnic Museum a note from a listener — from which it emerged only that he was one of the authors of a comic poem about the student life of the MGU MekhmatMekhmat — the colloquial name of the Faculty of Mechanics and Mathematics of Moscow State University (MGU). at the end of the thirties (the poem was called “Evgeny Neglinkin” and was written, in imitation of A. S. Pushkin, in the “Onegin stanza”) — sent him in reply a long epistle (not knowing the name of his addressee, Kolmogorov begins with the salutation “Most esteemed poet of the Mekhmat!”) about the intimate problems, so troubling to him, of the essence of human life and culture?

In this letter A. N. Kolmogorov expresses, in particular, his faith that

…some portion of [his] listeners catch the worldview of HUMANISM, which knows the abiding value of human culture and knows that this value has no need of the props of belief in immortality, in the ‘immateriality’ of the soul, the fundamental irrationality of creative work, and so on.

(Andrei Nikolaevich himself sets off the word “humanism” on a separate line and writes it in capital letters; the letter is published in the journal Novoe Literaturnoe Obozrenie [New Literary Review], no. 6 (1994), pp. 183–187.)

This lofty theme Kolmogorov touched upon in moments of emotional elevation, before people by whom he wished to be understood, without even counting on their agreement. (The unknown author Kolmogorov calls in the letter “a conventional stand-in for the general image of a young man of the mid-twentieth century.”)

Or here is another example: in 1963, having received in Rome the Balzan Prize (with this prize, conceived on the level of the Nobel, Kolmogorov was honoured together with the composer Hindemith, the biologist Frisch, the historian Morison, and the head of the Roman Catholic Church, Pope John XXIII), Andrei Nikolaevich, returning to Moscow, found himself in the same compartment as the Polish cardinal Wyszyński. And, as he himself says, he “somehow got drawn into proving to him that belief in immortality is not at all necessary for a positive human philosophy…”

These were the years that rounded off the golden period in A. N. Kolmogorov’s work, begun in 1953, when, in his own words (spoken to V. I. Arnold), hope appeared and he felt some extraordinary elevation. In those years, when a wind of freedom had begun to blow, it was Kolmogorov’s destiny to solve several great mathematical problems, to take part in many socially important undertakings, and to know the joy of wide public recognition.

In these years his humanistic interests were fertilised by the ideas of cybernetics. These ideas proved unusually consonant with his sense of the world. There occurred what, in Pushkin’s Egyptian Nights, the poet (Charsky) describes upon hearing the improviser:

Another’s thought had barely touched your hearing and had already become your own property, as though you had been carrying it about, cherishing it, developing it unceasingly.

Somewhere in the middle of the fifties the first echoes of Wiener’s cybernetics reached us. It was the time of the very beginning of the creation of “electronic computing machines,” clumsy and cumbersome, and the sole means of “individual printing” was the typewriter. But scarcely had Wiener’s thought “touched the hearing” of the great scholar than, to the 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?” he gives an unconditionally affirmative answer. And from this he is, of necessity, compelled to rest upon the “abiding value of human culture,” without the “props of belief in immortality.” To those who do not agree that man is a special mechanism created by Nature, he proposes to set up an experiment: to create the Universe anew, to light the stars, to set the planets spinning, and to wait several billion years, until a new Mankind is born.

In his report “Automata and Life” A. N. Kolmogorov calls himself an “extreme, desperate cyberneticist” — it seemed to him then that the central ideas of cybernetics might become a support for HUMANISM, and that this, in its turn, might become a support for the ideology of the future.

But mankind proved unready to receive this ideology — and one can hardly say whether for a time or forever… Cybernetics, and science in general, are not at all what most of all agitates present-day mankind. But in the coming millennium there awaits it once again an attempt — one that had not hitherto seemed real — to resolve the problem of its own survival: the survival of Mankind as a single whole, the survival of the whole human race, of people belonging to different races, nations, and countries. And it appears inevitable that one day the ideas of a “single positive human philosophy” will be grasped — a philosophy shared (whether from one’s own convictions or by force of stern necessity) by all (or “almost all”) the individuals living on Earth.

And it is difficult to imagine that this philosophy will not be filled with the “worldview of HUMANISM, which knows the abiding value of human culture.” And, perhaps, then the thoughts of Andrei Nikolaevich Kolmogorov, uttered by him at the dawn of the birth of cybernetics, will once again become timely.

V. M. Tikhomirov

7 March 2000

The materials of this dossier were kindly provided for publication in Vivos Voco! by Natalya Grigorievna Khimchenko (Rychkova); the editors thanked Yakov Ilyich Fet for his assistance and remarks. From the A. N. Kolmogorov page of Vivos Voco! (“I call the living!”), September 2000.