Warren S. McCulloch, M.D. Illinois Neuropsychiatric Institute, 912 South Wood Street Chicago, Illinois June 20, 1945


Since you received the article on the above topic (Bull. Math. Biophysics, Vol. 7, No. 2), questions have arisen concerning the dependence of the anomaly on the topology of nets. It would be helpful if you could publish the following note:

Given three dromes, each of which goes over one synaptic connection which is singly insufficient to fire its subsequent neuron but which may be reinforced from one other drome, an organism which fails to respond appetitively to any one of three sensory queues singly may respond to two by what appears to be a preference for one; and three such specious choices may exhibit the circularity of the value anomaly.

Consider three dromesA, B, and Cso connected that no one sustains activity without summation from the afferent component of one other drome and let the net be such that B (and only B) necessarily contributes to A; similarly, C (and only C) to B, and A (and only A) to C. Presented with a stimulus a, b, or c separately, there will be no response; but given any pair, a and b, or b and c, or c and a, the organism will appropriate a, b, or c, respectively; and given a, b, and c, the organism will appropriate all three. Obviously the net resembles Figure 4 of the article in question except that the threshold of the afferent neurons is now such as to require impulses from the terminations of two axons, and that the heterodromic actions are summative instead of inhibitory. The same topological considerations apply. The preference, whether or not it be a true choice, is determined by a diadrome, which is no less a diadrome because its heterodromic connections are summative instead of inhibitory.


For further research:

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Keywords: Nets, Note, Anomaly, Looms, Neurons, Biophysics, Component, Choice, Organism

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1 Reprinted from the Bulletin of Mathematical Biophysics. Volume 7,1945