Warren McCullochWarren McCulloch spent most of his life arguing that neurons in the brain are logic gates like those in digital computers, and that the brain can be understood as a Turing machine (a universal digital computer). McCulloch and Pitts were thus the originators of today's widely supported "computational model of the mind." Their work inspired theories of "cellular automata," in which individual cells live or die according to inputs from their surrounding cells. See John Conway's "Game of Life." In their 1943 paper, "A Logical Calculus of the Ideas Immanent in Nervous Activity," McCulloch and his younger colleague Walter Pitts wrote
Because of the “all-or-none” character of nervous activity, neural events and the relations among them can be treated by means of propositional logic. It is found that the behavior of every net can be described in these terms, with the addition of more complicated logical means for nets containing circles; and that for any logical expression satisfying certain conditions, one can find a net behaving in the fashion it describes. It is shown that many particular choices among possible neurophysiological assumptions are equivalent, in the sense that for every net behaving under one assumption, there exists another net which behaves under the other and gives the same results, although perhaps not in the same time. Various applications of the calculus are discussed.McCulloch says his ideas that neural networks are similar to arguments in propositional logic and thus to computer networks dates back many years.
Many years ago one of us, by considerations impertinent to this argument, was led to conceive of the response of any neuron as factually equivalent to a proposition which proposed its adequate stimulus. He therefore attempted to record the behavior of complicated nets in the notation of the symbolic logic of propositions. The “all-or-none” law of nervous activity is sufficient to insure that the activity of any neuron may be represented as a proposition. Physiological relations existing among nervous activities correspond, of course, to relations among the propositions; and the utility of the representation depends upon the identity of these relations with those of the logic of propositions. To each reaction of any neuron there is a corresponding assertion of a simple proposition. This, in turn, implies either some other simple proposition or the disjunction of the conjunction, with or without negation, of similar propositions, according to the configuration of the synapses upon and the threshold of the neuron in question.In the 1930's McCulloch had studied logic at Yale in Frederic Fitch's course on propositional logic, based on the great Principia Mathematica of Bertrand Russell and Alfred North Whitehead. Fitch also was the thesis adviser for Ruth Barcan Marcus, whose work on the "necessity of identity" influenced Saul Kripke. Despite the fact that information flows along neurons in the brain, the neural network is not a computer network, brain processes are not algorithms, there is no central processing unit (CPU) or even distributed parallel processing. Very simply, man is not a machine and the brain is not a computer. Nevertheless, we can regard McCulloch as the first thinker to offer a solution to the mind-body problem that "embodies" an immaterial logical software mind in a material mechanical hardware computer, as the title of his 1965 book, "Embodiments of Mind, suggests.
The Macy ConferencesMcCulloch was a central organizer and frequently the chair of the Macy Conferences on Cybernetics held in the late 1940's an early 1950's. Their initial title was "Feedback Mechanisms and Circular Causal Systems in Biological and Social Systems." At the first conference in 1946 McCulloch gave a presentation on how simulated neural networks can emulate the calculus of propositional logic. He also drew attention to communication as a descriptive metaphor and noted the differences between descriptions of messages' mechanics and message content or meaning. He suggests memory may be a function of continuous cyclical impulses in a neural network. He described causal "circles" in neural networks as continuous loops that could reverberate indefinitely and be a possible location for memories. At the third conference (1947) McCulloch began collating and distributing a summary report on the conference. Earlier conferences had not been adequately documented. McCulloch attempted to summarize the key points of the first 3 conferences following the third event, then distributed this to the attendees. With the exception of Margaret Mead's shorthand notes (indecipherable owing to her personal shorthand coding) and the fragmentary results of the earlier crude recording / transcription efforts, McCulloch's retrospective remains the main documentation for the first 3 conferences. At the final 10th conference McCulloch presented his work with Walter Pitts on how neural mechanisms can recognize shapes and musical chords. He cites strong arguments from others rebutting this work, and ends with a good-natured concession that his and Pitts' efforts have been in the fine tradition of scientific refutability. (This incident is a poignant event, in that at the time it seemed to indicate one of the project streams feeding the Macy Conferences had in fact turned out to be a dead end.) McCulloch was tasked to write a final summarization of the consensus achieved during the 10 Macy Conferences. This proved difficult, because by this time it's clear that the cybernetics group is moving (and has always moved) in several different directions. McCulloch writes in part: "Our most notable agreement is that we have learned to know one another a bit better, and to fight fair in our shirt sleeves." (Transactions, p. 69) As chairperson for all 10 Macy Conferences, McCulloch no doubt desired to portray the series as having produced something. His concession of what can only be called a social networking outcome illustrates how the Macy Conferences could not even then be construed as having produced a unified theory or meta-discipline. In 1959, McCulloch and Pitts collaborated with Jerome Lettvin and Humberto Maturana to write the classic paper "What the Frog's Eye Tells the Frog's Brain," which was reprinted in McCulloch' classic "Embodiments of Mind" in 1965. This work was a great disappointment for McCulloch, perhaps more for Pitts, because the actions of the frog were dependent on the patterns of light falling on the frog's retina, long before any digital or logical information processing could occur in the brain behind the eye.
What are the consequences of this work? Fundamentally, it shows that the eye speaks to the brain in a language already highly organized and interpreted, instead of transmitting some more or less accurate copy of the distribution of light on the receptorsAlthough these operations have been encoded genetically in the frog as a species, it is an example of successful experiences with bugs in the frog's ancestors being recorded in the brain, and the reproduction of the successful actions (tongue reaching out toward a bug) when a sufficiently similar visual experience presents itself. See our Experience Recorder and Reproducer
The operations thus have much more the flavor of perception than of sensation if that distinction has any meaning now. That is to say that the language in which they are best described is the language of complex abstractions from the visual image. We have been tempted, for example, to call the convexity detectors "bug perceivers." Such a fiber responds best when a dark object, smaller than a receptive field, enters that field, stops, and moves about intermittently thereafter. The response is not affected if the lighting changes or if the background (say a picture of grass and flowers) is moving, and is not there if only the background, moving or still, is in the field. Could one better describe a system for detecting an accessible bug?
ReferencesA Logical Calculus of the Ideas Immanent in Nervous Activity, Bulletin of Mathematical Biophysics, Vol.5, 1943, pp.115-133 What the Frog's Eye Tells the Frog's Brain, Proceedings of the IRE, 1959, p.1940
The Man Who Tried to Redeem the World with Logic, by Amanda Gefter.Normal | Teacher | Scholar