Abstract

Our topic comes out of a juxtaposition of two classic papers: the 1943 paper A logical calculus of the ideas immanent in nervous activity by McCulloch and Pitts and the 1959 paper What the frog's eye tells the frog's brain by Lettvin, Maturana, McCulloch, and Pitts. The nervous system is made up of individual signaling elements, the neurons. McCulloch and Pitts proposed a simplified model of this system. There every neuron receives a number of signals, which are nonnegative real numbers, at time t ; if a weighted sum of these signals exceeds a prescribed threshold, then the neuron sends signal 1 to other neurons at time t + 1; else it sends signal 0. Lettvin et al. discovered that the frog's optical nerve transmits to the brain information obtained by preprocessing the data in the retina by four separate operations: sustained contrast detection, net convexity detection, moving edge detection, and net dimming detection. We speculate about McCulloch-Pitts networks that could implement the fourth of these operations, the detection of sudden dimming. To be biologically plausible, such networks must conform to what is known about frog's anatomy: its retina consists one million photoreceptors, three to four million other neurons, every neuron receives signals from fewer than 100,000 neurons, and it sends signals to fewer than 10,000 neurons. We construct such networks that, within a narrow margin of error, detect dimming from time t to t + 1 and respond at time t + 4.