Home » Reading clubs » Classic » Summary: McCullough and Pitts (1943) A Logical Calculus of the Ideas Immanent in Nervous Activity

Summary: McCullough and Pitts (1943) A Logical Calculus of the Ideas Immanent in Nervous Activity

This a most peculiar paper that must be the initial Neural Networks paper and thus is extremely famous.

The paper is not easy to read due to a lot of terms taking from a 1938 textbook by Rudolf Carnap and I (Jotun) could well have missed some finer points, but I think I got the the basic ideas: We have discrete time, only boolean values, and the fundamental unit is the neuron and has input from many neuron and all that matters is how many 0s and 1s it receives (not their order). From this networks evaluating most logical expression can be designed. One can add extra “carrier neurons” that copies the content of a neuron and effectively allows a neuron to receive input from another neuron several time steps back. Cycles needs special treatment.

There is no Hebbian (1949) learning in this paper, so the parameters of each neuron is preset.

The paper is motivated by the brain but the M-P states that model should not be interpreted to literally as representing how the brain works. Nevertheless they end the paper with a series of very specific hopes for this model lile (131):
“To psychology, however defined, the net would contribute all that could be achieved in that field – even if the fields were pushed to ultimate psychic units or ‘psychons,’ for a psychon can be no less than the activity of a single neuron. Since that activity is inherently propositional, all psychic events have an intentional, or semiotic character. The ‘all-or-none’ character of these activities, and the conformity of their relations to those of the logic of propositions, insure that the relations of those of the logic of propositions insure thtat the relations of psychins are those of the the two-valued logic of propositions. Thus in psychology, introspective, behavioristic and physiological, the fundamental relations are those of two-value logic”

Thus M-P is quite confident that their model represent some sort physical reality of the brain. They also mention tinitus, paraesthesias, hallucinations, delusions and disorientations (p131) so they are keen to move on the applicability of their network theory.

I find it fascinating to read the papers from 30s, 40s and 50s by von Neumann, Wiener, MP and their wild ambition and optimism stemming from the belief that a biological machine, such as the brain, is just the right kind of wired system that can be exactly modelled. It has proven a lot harder and it is still an open question what a biological machine is and how detailed physics needs to be retained to for instance modeling the neurone. Ganti (1971) used the term Soft Machine that is a nice metaphor, but seems to have contributed little.

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