Logical neurons: the enigmatic legacy of Warren McCulloch

Donald H. Perkel A great deal of attention has been paid recently to a field variously known as 'connectionism', 'neural networks', and 'parallel distributed processing 'I-4. It is based on the properties of layered networks of non-linear units, which in turn are drastically simpli- fied versions of biological neurons. Simplified neur- ons of this sort were originally introduced in 1943 by Warren S. McCulloch and Walter H. Pitts 5, both as models of biological neurons and as conceptual components for circuits that could perform 'cogni- tive' computational tasks. Both in spirit and in technical detail, the current connectionist efforts have direct roots in the formal McCulloch-Pitts neurons and in the imaginative body of work of McCulloch. It seems instructive to examine the intellectual legacy of McCulloch today, in the light of the current recrudescence of his ideas and programs. McCulloch's compendium of his chief contribu- tions, Embodiments of Mind 6 , bears on its cover the author's dramatic portrait, staring piercingly in stark black-and-white contrast. With its creased brow, high-lighted cheekbones, penetrating eyes, and white beard, the face recalls a scriptual prophet whose urgent message demands expression. The volume contains the essential corpus of McCulloch's teachings, and its titles and content are consonant with the compelling image on its cover. At the lectern as in his writings, McCulloch wholeheartedly filled the role of prophet. In his day, he attracted a wide and loyal following. The sweep of his interests and pronouncements is indicated by the titles: 'What is number, that man may know it, and a man, that he may know a number?', 'Why the mind is in the head', 'Mysterium iniquitatis of sinful man aspiring into the place of God', 'Where is fancy bred?', and 'Physiological processes underlying psychoneuroses', among others. Combining phy- siological and anatomical observations with daunt- ing mathematical symbolism, he expressed his views making full use of his vast erudition. He evidently valued concision and elegance of statement over transparency and ease of access, again consistent with the prophetic style. Nearly two decades after his death, in 1969, what has survived of his teachings? As prophecy or brain science, what has been the lasting influence of his work? In my view, the answers are as enigmatic and paradoxical as the man himself: certain branches of his work have flourished mightily, but others have withered. The most lasting consequences of McCul- loch's work may have been those he would have anticipated the least. Logical neurons and immanent ideas The most influential of McCulloch's papers is the earliest in the compendium 5. In 1943, in collabora- tion with Walter H. Pitts, he laid out a proof stating, in essence, that a network made of circuit elements following a simple threshold rule for producing a binary output signal could be devised to realize any set of prescribed input-output relations. The circuit elements resembled nerve cells, as viewed in 1943, in that they 'summed' input impulses, produced an all-or-none output impulse if and only if a threshold value of input excitation was attained, and were subject to a veto by inhibitory input. By assuming that the time to integrate the incoming impulse, to produce an output (a response or the absence of a response), and to transmit the output signal to its target unit was a constant for all units or cells, the rules for processing signals in a network of intercon- nected elements were shown to reduce to logical functions. The lasting importance of the McCulloch and Pitts result was largely due to the demonstration that such networks have universal power to .realize logical rules; the hope of the authors, however, was to show a strong connection with nervous systems. As implied in its title, 'The logical calculus of the ideas immanent in nervous activity', this seminal paper explicitly identified the non-linear circuit elements with neurons, the processing of binary signals with neural activity, and the import of the signal processing with ideas. In that era, it was by no means taken for granted that scientific investigation of the cellular constituents of nervous systems could ever solve the mystery of 'higher thought proces- ses'i or even shed a great deal of light on animal behavior. Outside a coterie of optimists, including some clinicians, it was believed that the inscrutable nature of instincts and the originality of human cultural productions, including language, consti- tuted insuperable obstacles to a mechanistic, quanti- tative theory of higher brain function. This pessi- mism, or caution, was not merely a relic of vitalism or an article of religious faith, but represented a conservative approach to the explanatory power of the biology of that time. The effect of the 'immanent ideas' paper was immediately to sweep aside these objections to the possibility of a true science of the brain. If nerve cells were equivalent to the formal neurons of McCulloch and Pitts and if circuits of such elements could be made arbitrarily complicated, then any kind of animal behavior, however marvelously complicated or however intricately linked to sensory input, could be reproduced, and hence understood, in terms of these circuits. This was an intoxicating idea, and represented the culmination of the positivist move- ment that had flourished since the 1920s 7'8, en- joying its greatest successes in the physical sciences but aspiring to conquer the psychological and related sciences as the next, perhaps inevitable step. Donald H. Perkel is at