Introduction to Embodiments of Mind by Warren S. McCulloch
By Seymour Papert
Embodiments of Mind was published in Cambridge, MA by the M.I.T. Press in 1965.
When McCulloch’s essays are hard to understand, the trouble lies less often in the internal logic of the individual arguments than in the perception of a unifying theme that runs, sometimes with exuberant clarity, sometimes in a tantalizingly elusive way, through the whole work. The consequent perplexity is partly intentional — McCulloch is at least as much concerned with questions as with answers — and partly the result of his way of expressing the general through the particular. But much of the difficulty exists because we come with habits based on more fashionable modes of thought, expecting philosophical questions to be discussed in the manner of the contemporary philosophers, and cybernetic questions with the same intention as they are given by other cyberneticists. On both counts we can be led seriously astray.
Embodiments of Mind must not be read as a more pleasing name for the set of puzzles sometimes called “the mind-body problem.” The radical difference is marked by the possibility of discussion about whether these puzzles are “linguistic” rather than “genuine theoretical problems.” Those that worry McCulloch are unquestionably genuinely theoretical, and linguistic only in the sense that they require as part of their solution the construction of a better theory of language than we possess today. Consider an example: A man has a mind to say something and says it. The embodiment problem is directed toward describing coherently, and relating on all levels of interpretation, the complex of events involved in such situations: the intention, the utterance, the reference of the utterance, the happenings in the man’s brain.
It would be futile to discuss whether this enterprise belongs to philosophy, to neurology, or to psychology except that each of these disciplines has established traditions and modes of thought that preclude progress by deformation of the problem. The philosopher is skilled in the fine analysis of the logical structure of concepts but spurns all consideration of mechanisms and shies away from the formulation of general laws, while the tradition of the psychology of thinking leads to the choice of such simple experimental situations and theoretical models as to miss the philosophically interesting structural features of knowledge. There are, of course, good historical reasons for this polarization. Few thinkers in the mainstream of our philosophical tradition make any sharp distinction between what would today be classified as psychological and philosophical arguments. The dialogue between British “empiricist” philosophers and Continental rationalists about the existence of innate ideas constantly combines philosophical analysis with appeals to psychological evidence. Moreover, each side postulates mechanisms to account for the facts as it conceives them. A clear case in point is the associationist theory of knowledge. On the opposite side we find Kant making statements that would not be out of place in a discussion on techniques of programming: “our representation of things, as these are given to us, does not conform to these things as they are in themselves, but… these objects, as appearances, conform to our mode of representation.” But while the embodiment of associationism poses no immediate conceptual problem, Kant’s doctrine could neither be translated into material terms nor adequately developed on a clear, logical basis without concepts of representation and computation that would not come into being until our own period. The opposition between Hume and Kant is merely one example of a general process of growth in which epistemological sophistication outpaced the development of notions of logical and material mechanisms. A split had eventually to come between psychology, which was based on mechanism but unable to reach the complex properties of thought, and philosophy, which took the properties of thought seriously but could be satisfied with no conceivable mechanism.
We need no longer be trapped in this dilemma. Nevertheless, when the development of logic in the nineteen-thirties and of cybernetics in the next decade offered a way out, the opposition had, by the operation of one of the most general laws of the dynamics of systems of ideas, become categorized and built into many structural features of our thinking. The result was that a more thoroughgoing reconstruction than most men could tolerate was needed to reverse the process on an individual basis.
Thus McCulloch is not historically isolated in his plea for a theoretical epistemology, as opposed to the set of analytical and critical techniques to which the influential modern schools of philosophy restrict the theory of knowledge. And although this places him in a minority position among his contemporaries, he is not alone.
In listing some of his allies it is fitting to begin by mentioning the proposal for philosophical reform published in 1943 by a young British psychologist who was unable to live long enough to assume the role that should have been his in the development of cybernetic epistemology. The spirit of Kenneth Craik’s thought is shown by the following quotation from his book The Nature of Explanation:
| Our question, to emphasize it once again, is not to ask what kind of thing a number is, but to think what kind of mechanism could represent so many physically possible or impossible, and yet self-consistent, processes as number does. |
By a remarkable coincidence, which shows that these ideas were well rooted in that period, two important papers written in this spirit were published in the same year in the United States. One, by Julian Bigelow, Arturo Rosenblueth, and Norbert Wiener, set out the general principles for mechanisms that would embody the concept, no less difficult philosophically than number, of purpose. The other, by Warren McCulloch and Walter Pitts, described a logical calculus and the principles of construction for a class of computing machines that would permit the embodiment of any theory of mind or behavior provided only that it satisfied some very general principles of finitude and causality. These two papers introduce so clearly the new frame of thought that their publication could well be taken as the birth of explicit cybernetics. To that matter we shall return, after mentioning a fourth, rather different but equally important, focus of the new epistemological approach.
Jean Piaget, by origin a zoologist, set out to elucidate the mechanisms of knowledge by studying their development in small children. The advantages of this “genetic” approach are obvious. The structure of thinking in children is simple enough for ingenious experiments to lay bare its epistemological architectonics and show in operation processes similar in nature to those postulated by philosophers. One sees very clearly, for example, the way in which reality conforms to modes of representation characteristic of various stages of development. In a certain sense this confirms the correctness and utility of the Kantian principle cited earlier. On the other hand, the dynamic development of the modes of representation shows that Kant’s theory must and can be refined and corrected in detail: the intuitions are not innate and unchangeable but can themselves be explained in terms of more fundamental processes. In his attempt to do so, Piaget is guided by his observation of children to formulate more precise theoretical tools for the conceptualization of the mechanisms of knowing than any classical epistemologist ever possessed.
The common feature of these proposals is their recognition that the laws governing the embodiment of mind should be sought among the laws governing information rather than energy or matter. This is clearest in the Bigelow-Rosenblueth-Wiener paper, but only because the situation they study is simpler than the others in its informational aspects. The principal conceptual step was the recognition that a host of physically different situations involving the teleonomic regulation of behavior in mechanical electrical, biological, and even social systems should be understood as manifestations of one basic phenomenon: the return of information to form a closed control loop. It is perhaps slightly less evident that the key insight of the McCulloch and Pitts paper is essentially the same. A brief glance at the history of some aspects of the embodiment problem may make this clearer.
The theory of perception has been plagued by the idea the there must be in the brain some sort of geometrically faithful representation of the outside world. An early incident centered about this issue is the discussion of the problem of the inverted retinal image which seems to have perplexed a number of clear thinkers including Leonardo da Vinci. The puzzle is essentially resolved in the hands of Descartes, who anticipates modern cybernetic ideas in his representation of the situation as a coding problem: there is no puzzle because no information is lost by the inversion. But if Descartes is able to think clearly about the transmission of information, in both senses, between the periphery and the brain, he is unable, for lack of a notion of computation, to say enough about intervening operations on it to provide a useful or intellectually satisfying model. This deficiency continues, to make itself felt even in the first half of the twentieth century in the context of the perception of form. For although the infiltration of words like “isomorphism” and “topological” had eliminated the more elementary paradoxes, the only neurophysiological hypotheses about perception to be described in any detail during this period were those involving some sort of quasi-spatial model in the brain. The notion that the events in the brain could in every physical sense be arbitrarily unlike the perceived world had, of course, been considered; but no one had been able to develop it on a technical level into a sufficiently elaborated model to exert a competitive influence. McCulloch and Pitts were associated with two decisive acts that penetrated this barrier: their own 1943 paper which provides for the first time a set of mathematical instruments sufficiently powerful for the conceptual description of such hypotheses; and the investigation of the frog’s visual system that culminated in the brilliant experiments carried out by their friends J.Y. Lettvin and H.R. Maturana and in the paper “What the Frog’s Eye Tells the Frog’s Brain.”
The liberating effect of the mode of thinking characteristic of the McCulloch and Pitts theory can be felt on two levels. On the global level it permits the formulation of a vastly greater class of hypotheses about brain mechanisms. On the local level it eliminates all consideration of the detailed biology of the individual cells from the problem of understanding the integrative behavior of the nervous system. This is done by postulating a hypothetical species of neuron defined entirely by the computation of an output as a logical function of a restricted set of input neurons. The construction of neural circuits using schematic neurons specified by their conditions of firing was not in itself either original or profound; these had often been used diagrammatically to illustrate such simple things as reflex arcs. The step that needed boldness of conception and mathematical acumen was the realization that one could formalize the relations between neurons well enough to allow general statements about the global behavior of arbitrarily large and only partly specified nets to be deduced from assumptions about the form and connectivity of their components.
It is easy to fall into the error of reading “A Logical Calculus of Ideas Immanent in Nervous Activity” as a document of purely historical interest where contents have become obvious and commonplace. That this is true on a certain level of interpretation is proof of the results of the revolution in thought that has taken place since Rashevsky’s valiant Bulletin of Mathematical Biophysics first presented the paper, twenty-one years ago, to a hostile or indifferent world. But if one looks behind the technical assertion at the style of thought and the intention of its authors, one soon discerns features that separate it sharply from typical current cybernetic writing. Of these the chief is its rationalist quest for necessity and comprehension as opposed to the merely pragmatic tests that so often satisfy those who build “models” of neural activities on psychological processes. The distinction is felt in the opening part of the paper. The authors will, as everyone knows, build their nets out of their now famous threshold neurons. But in doing so their first care is to make it clear that nothing of what they say is to be contingent on theoretically arbitrary choices of particular kinds of formal neuron; their first theorems assert the invariance of their basic definition with respect to a number of such choices; and if they restrict themselves to special cases, this is a matter of individual style and the lack of mathematical tools. When we reach the end of the paper, we are rewarded for the effort of struggling through its unfortunate logical notation by seeing the first birth of a true mathematical idea: Between the class of trivial combinational functions computable by simple Boolean logic and the too general class of functions computable by Turing machines, there are intermediate classes of computability determined by the most universal and natural mathematical feature of the net — its finiteness. This is pure mathematics. The theoretical assertion of the paper is that the behavior of any brain must be characterized by the computation of functions of one of these classes.
The point might be made more clearly by contrasting this statement with a widespread misinterpretation of this paper. It is often said that McCulloch and Pitts prove (critics say “only prove”) some such proposition as: Whatever can be completely described can be realized by a net of neurons. This is misleading or false. For if the “description” is by complete explicit listing, then much simpler nets (without circles) would be sufficient; but if arbitrary constructive mathematical means maybe used in the “description,” one might need a Turing machine to realize the computation, and McCulloch and Pitts know perfectly well that their net cannot compute all the functions computable by Turing machines. Any such attempt at simple statement misses the fundamental point that this paper introduces a new concept, for which we now have many formal definitions, but which can be related to simple intuitive concepts only in the sense that “force” as defined by physics is related to intuitive notions of force. The same issue arises, in material form, when it is said or denied that McCulloch and Pitts prove that the brain is a machine. A better formulation is to say that they provide a definition of “computing machine” that enables us to think of the brain as a “machine” in a much more precise sense than we could before. The advance is conceptual. From this step follows the possibility of formulating more precise particular hypotheses (as McCulloch and Pitts do themselves in “How We Know Universals” and many others have done since) about the specific structure of the net. From this also follows the familiar flood of attempts to dissolve away the problem of knowledge into simple processes of cybernetic fiddling with thresholds or random program generators. Perhaps this is the place to emphasize that McCulloch is not to blame for this. Indeed, he insists that to understand such complex things as numbers we must know how to embody them in nets of simple neurons. But he would add that we cannot pretend to understand these nets of simple neurons until we know — which we do not except for an existence proof — how they embody such complex things as numbers. We must, so to speak, maintain a dialectical balance between evading the problem of knowledge by declaring that it is “nothing but” an affair of simple neurons, without postulating “anything but” neurons in the brain. The point is, if I understand him well, that the “something but” we need is not of the brain but of our minds: namely, a mathematical theory of complex relations powerful enough to bridge the gap between the level of neurons and the level of knowledge in a far more detailed way than can any we now possess.
It would be very wrong to conclude that this mathematical deficiency in itself is any cause for skepticism about the value of the cybernetic method. On the contrary, the most convincing argument for its validity would be a demonstration that the problems and difficulties which have always faced men concerned with the nature of their own thinking — whether they are philosophers concerned with the presuppositions of knowledge, poets concerned with the mastery through simple words of man’s complex relations, or architects concerned with the embodiment in matter of the abstract forms of the mind — come up in equivalent form in the new context. However, no demonstration of this sort could be completely formal and rigorous. Nor could it be produced by a rapid analysis of a small number of examples. It could come about only by insightful rethinking of old problems in the new terms, and to this, no less than to the initial tasks of forging fundamental concepts, Warren McCulloch has made an eminent contribution with a very personal flavor. In the nature of the case it is impossible to summarize or to generalize the conclusions to be drawn from such work — and it should be particularly noted that McCulloch himself scrupulously avoids forcing his ideas into prematurely categorical form. Like some of the Greeks he knows so well, and like Wittgenstein, whom he does not know, he is a master of the technique of speaking in such a way as to set the mind of the cooperative and active auditor into that motion which will lead him to insight. To members of his audience who are led to miss the point by their habit of expecting predigested conclusions, he is fond of saying: “Don’t bite my finger, look where I am pointing.”