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On The Legacy of W.S. Mc Culloch

Roberto Moreno-D�az1 and Arminda Moreno-D�az2

1.Institute of Cybernetics, Universidad de Las Palmas de Gran Canaria

2.Computer Science School, Technical University of Madrid

W. S. Mc Culloch (1898-1969) was a brain research scientist at Yale University, Professor of Psychiatry at the University of Illinois in Chicago, and later a scientist at the MIT Research Laboratory of Electronics, in Cambridge, MA. Together with Wiener, von Neumann, von Foerster and others, he is credited with having been one of the pillars of Cybernetics from the forties on, and one of the great thinkers of the previous century. In the search for an experimental theory of the origin, nature, methods and limits of knowledge (experimental epistemology) he went from psychology to psychiatry, and on to neurophysiology, to which he brought an array of mathematical, logical and symbolic skills.

From early times to the University of Yale

Mc Culloch had already as a young man received a multidisciplinary education. As a freshman, he took courses in theology, along with a considerable number of others in philosophy, psychology, mathematics and mathematical physics at Haverford College and later at Yale University. He had served during World War 2 as a second-class seaman engaged in �marlin-spike� seamanship and semaphore (he considered these activities to represent topology and communication respectively), and from a very early age he was attracted to the epistemic problems of mathematics. He used to recall that when asked by a College professor what he wanted to do in life, he answered that he �wanted to know what is a number that a man may know it, and a man that he may know a number � His professor made the prophetic comment, �Friend, thee will be busy as long as thee lives�. In 1961, Mc Culloch purported a tentative solution in a paper with that title.

After obtaining a B.A. (1923) he embarked upon graduate studies, gaining a Master�s degree in Psychology. Confronted with the eclecticism of the psychology of the time, consisting as it did of introspective, psychoanalytic and behaviouristic components, he became convinced that no progress was possible without assembling as much knowledge as possible of the nervous system and the brain.He thus entered medical school and received an M.D. from Columbia in 1927. Subsequently, he decided to acquaint himself with neurological disorders and became a practising physician both at Bellevue Hospital and at the Rockland State Hospital for the Insane (1927-1930). Nevertheless, he still found time to improve his abilities in the formulation of theoretical concepts by attending courses in mathematical physics at New York University.

Next, he turned to research and went to Yale to work on the structure of the brain with Dusser de Barenne, bringing with him a considerable body of knowledge of symbolic logic, mathematical theory and epistemology, as well as experience gained in neurological clinics. De Barenne was known for his ideas on the �physiological a priori�, i.e., a priori brain structures and functions to handle sensory data, which influenced Mc Culloch�s later work. He concentrated on the experimental study of the relations between the firing of cortical neurons and motor areas of the cortex, the functional organization of the sensory cortex and the interrelations of the cortical hemispheres. Most of his publications on cortex structure appeared in partnership with De Barenne.

It was at the meetings of his Yale scientific group seminars on the analysis of the theories and methods of mathematical physics and in symbolic logic that Mc Culloch first urged others and was himself urged to proceed in the direction of the symbolic logical formulation of the firing activities of the neural networks.

At the University of Chicago and the Macy Foundation Conferences

In 1941 Mc Culloch went to the University of Chicago to organize a team of specialists to form the biological basis of the Department of Psychiatry of the University of Illinois. They were to be involved in neuroanatomy, neurophysiology, physics and chemistry, excluding behavioural problems, which were dealt with elsewhere. The period from 1941 to 1943 corresponds to the genesis and publication of the paper, which is probably the most influential and often quoted work, by Mc Culloch and Walter Pitts: �A logical Calculus of the Ideas Immanent in Nervous Activity� (1943), although it has probably been frequently misunderstood. Twenty years later, Mc Culloch wrote: �In 1941 I presented my notions of the flow of information through ranks of neurons to Rashevsky�s seminar in the Committee of Mathematical Biology of the University of Chicago and met Walter Pitts… He was working on a mathematical theory of learning…He was interested in problems of circularity, how to handle regenerative nervous activity in closed loops�� �I had to suppose such loops to account for epileptic activity of surgically isolated brain and even of undercut cortex. Lorente de N� had shown their significance in vestibular nystagmus. I wanted them to account for causalgia persisting after amputation of a painful limb or even after section of the spin thalamic tract; also to account for the early stages of memory and conditioning, for compulsive behaviour, for anxiety and for the effects of shock therapy. These appear to be processes that once started seem to run on in various ways� For two years Walter and I worked on (the formal side) of these problems, which require modal mathematics � Finally we got it in proper form and we published A Logical Calculus in 1943.� �In substance what it proved via its three theorems is that a net of formal neurons can compute those and only those numbers that a Turing Machine can compute with a finite tape� �Fortunately for our calculus, von Neumann used our article in teaching the general theory of digital computers and it gave rise to the algebraic theory of finite automata. It formed the basis on which I solved the Heterarchy of Values Determined by the Topology of Nervous Nets, and, again with Walter Pitts, of How We Know Universals.�

The paper �How we know Universals: The Perception of Visual and Auditory Forms� is the second notable contribution of Pitts and Mc Culloch (1947) which strongly influenced the trend in pattern recognition and pattern perception. They proposed two mechanisms which combined to produce invariances under dilatations and two dimensional translations.The first subjected the cortical image of any stimulus pattern to a group of dilatations and then averaged over the group,while the second centered the image in its center of gravity. An important point which is still today of interest is their insistence that �the group-invariant spatio-temporal distribution of excitations which represents a figure need not resemble in any simple way the initial image… This point is specially to be taken against the Gestalt psychologists, who will not conceive a figure being known save by depicting it topographically on neuronal mosaics, and against the neurologists of the school of Huglings Jackson, who must have it fed to some specialized neuron whose business is, say, the reading of squares�.

In 1942 Mc Culloch met Norbert Wiener in the company of their mutual friend Arturo Rosenblueth. The crucial paper for the emergence of Cybernetics was presented at the first Macy Foundation meeting in New York City: “Behaviour, Purpose and Teleology”, published the following year by Norbert Wiener, Arturo Rosenblueth and Julian Bigelow.

With the establishment of the Josiah Macy Foundation, Rosenblueth and Mc Culloch had reached an important agreement to organize a yearly interdisciplinary meeting. Before they started, there was late in 1942 a meeting of engineers, physiologists and mathematicians at Princeton, referred to by Wiener in the Introduction of his book of 1948 Cybernetics. It was there, Mc Culloch says, that he met John von Neumann.

The Macy Foundation Conferences started under the name �Conferences on Circular, Causal and Feedback Mechanisms in Biological and Social Systems�, which was changed to �Conferences on Cybernetics� in 1949. This series of stimulating and constructive conferences ran until 1953. They established a new conception of living and non-living machines, which, with its successes, failures and redefinitions endured into our own days. It is fruitful to delve into that remarkable archive of ideas and inspiration. The records had been out of print for a long time, but were re-edited by Claus Pias in 2003. As Von Foerster said �The Conferences have became an oral tradition, a myth�. Today, the consequences of that myth can be found in Mc Culloch�s and other participants� essays. Many of those attending the Conferences may be considered the real founders of Cybernetics. Some names one may mention are those of W. Ross Ashby, Y. Bar-Hillel, Julian Bigelow, Jan Droogleever-Fortuyn, W. Grey Walter, Rafael Lorente de N�, Donald Mac Kay, Warren Mc Culloch (Chairman of the Conferences), J.M. Nielsen, F.S.C. Northrop, Linus Pauling, Antoine Remond, Arturo Rosenblueth, Claude Shannon, Heinz Von Foerster, John Von Neumann, Norbert Wiener. From that time on , Mc Culloch was an adviser and friend of the operational research pioneer Stafford Beer.

At the Research Laboratory of Electronics, MIT

In 1952 Mc Culloch moved to M.I.T, where Norbert Wiener was already installed. He continued neurophysiologic, logical and epistemological work, and writing essays on it, with his Chicago collaborators Jerry Lettvin, Walter Pitts and Patrick Wall. Meanwhile, a young anatomist from Chile, Humberto Maturana, had joined the group. In 1959 they produced an epoch-making work in epistemic science, this time in the field of epistemological neurophysiology: �What the Frog�s Eye tells the Frog�s Brain� by J. Lettvin, H. Maturana, W.S. Mc Culloch and W. Pitts, published in the Proceedings of the IRE-Institute of Radio Engineers. In this paper, they introduced the concept of feature detectors in neurophysiology, besides finding the �orderly mapping� of the terminations of the optic nerve in the tectum. Their description of the behaviour of the Group 2 ganglion cells is an experimental revelation of a �physiological a priori�. Reminiscences of �How we Know Universals� can be found here. The �Synthetic a priori� reappears in Mc Culloch�s �What is a number��, 1961.

Since 1948, Von Neumann and Mc Culloch had already been trying to find ways to build up systems which, like the nervous system, did reliable work with unreliable computing units. Von Neumann produced his channel redundancy and majority organ solution, but Mc Culloch was in pursuit of a distributed solution, closer to neurophysiology, with no dependence on majority organs. In 1959 he produced his �Toward a Probabilistic Logic�, and later in the sixties Manuel Blum and Leo Verbeek worked on a form of logic whereby not only the arguments but also the functions were subject to failure. This was concluded by Winograd and Cowan, with the use of redundancy in what Mc Culloch calls anastomotic nets (like the veins in a leaf).

Already in 1952 Mc Culloch was concerned with abductive reasoning and machinery, as distinct from deduction (nets of formal neurons) and induction (learning nets). As he expressed it �rule, fact, therefore case under rule�. He assigned this type of function to the reticular formation of the vertebrates� nervous system, �the abductive organ that commits the entire animal to one rather than to any other of a small number of incompatible modes of behaviour�. He had the anatomical and physiological basis, and with William Kilmer, from 1964, tried to find a solution to the so-called �command and control� problem. Mc Culloch used the metaphor of a network as a fleet in which the ship (module) that has the information leads. He and Kilmer realized that neither the theory of coupled oscillators nor the theory of iterated nets could help in solving the problem, and they therefore turned to computer simulations.

Mc Culloch then thought that the problem could be attacked with the tools he and Roberto Moreno-D�az had developed for the universal neural nets, which are universal in the sense that, by encoding the inputs, any possible net with loops can be realized by the net. These nets embody all modes of oscillation in closed loops, a subject which he had been occupied with since the forties.

Together with J.L. da Fonseca he confronted the problems of oscillations in non-linear shift-register-like neural nets to embody dynamic memory, by using Massey�s linearization algorithm. Next, they again broached the enduring problem of abduction and the theory of intension, this last explicated in the comment of 1964 by Mc Culloch on the republication of von Domarus� thesis. Following Charles S. Pierce theory of relations, Mc Culloch thought that it was necessary to overcome logic in a �true theory of relations�, as opposed to Russell�s and Whitehead�s theory based on �relata� (pairs, triplets, etc. lists in extenso). With Moreno-D�az he tried a first approach extending Pierce�s ideas into a Theory of Triadic Relations, where the operations were defined on the relations per se, not on the relata (individuals being related).

It must be recognized, however, that the problems of control and command in reticular formation-like networks are, strictly speaking, not yet solved. Also, the appropriate formulations of the concepts behind Mc Culloch�s ideas on intensional relations are still pending, in spite of Mc Culloch�s attempt with da Fonseca and Mira in his last epoch.

In November 1995 an International Conference was held to commemorate the personality and contributions of W.S. Mc Culloch, 25 years after his death. The Conference took place in Las Palmas de Gran Canaria, Canary Islands, Spain. It was attended by friends, family, former collaborators and scientists, with approximately one hundred contributions (cf. Moreno-D�az/Mira-Mira 1996). Special lectures were given by von Foerster, Lettvin, Arbib and Gestelland. The general conclusion was that most of Mc Culloch writings are still greatly inspiring, stimulating and provoking in fields that range from epistemology to neurophysiology, brain theory, neural simulation and computation, artificial sensory perception, artificial intelligence and robotics. We should return to his works and essays, since they still provide an extraordinary means of generating new ideas in the inexhaustible theme which Mc Culloch set himself to work on: the “Embodiments of Mind�.


�Warren S. Mc Culloch. Collected Works�; Rook Mc Culloch editor. 4 Vols. With a preface of H. von Foerster. Intersystems Publications, Salinas CA. (1989)

Mc Culloch, W.S. �Embodiments of Mind: a Collection of Papers�. The M.I.T. Press, Cambridge MA (1965)

Moreno-D�az, R. & Mira-Mira, J., editors. �Brain Processes, Theories and Models: An International Conference in Honor of W.S. Mc Culloch�. The M.I.T. Press, Cambridge MA (1996)

Pias, C., editor. “Cybernetics - Kybernetik. The Macy-Conferences 1946-1953. Transactions”. Diaphanes, Z�rich-Berlin (2003)

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