Walter Pitts

What the Frog's Eye Tells the Frog's Brain

In this paper, we analyze the activity of single fibers in the optic nerve of a frog. Our method is to find what sort of stimulus causes the largest activity in one nerve fiber and then what is the exciting aspect of that stimulus such that variations in everything else cause little change in the response. It has been known for the past 20 years that each fiber is connected not to a few rods and cones in the retina but to very many over a fair area. Our results show that for the most part within that area, it is not the light intensity itself but rather the pattern of local variation of intensity that is the exciting factor. There are four types of fibers, each type concerned with a different sort of pattern. Each type is uniformly distributed over the whole retina of the frog. Thus, there are four distinct parallel distributed channels whereby the frogs eye informs his brain about the visual image in terms of local pattern independent of average illumination. We describe the patterns and show the functional and anatomical separation of the channels. This work has been done on the frog, and our interpretation applies only to the frog.

How we know universals: the perception of auditory and visual forms

Two neural mechanisms are described which exhibit recognition of forms. Both are independent of small perturbations at synapses of excitation, threshold, and synchrony, and are referred to partiular appropriate regions of the nervous system, thus suggesting experimental verification. The first mechanism averages an apparition over a group, and in the treatment of this mechanism it is suggested that scansion plays a significant part. The second mechanism reduces an apparition to a standard selected from among its many legitimate presentations. The former mechanism is exemplified by the recognition of chords regardless of pitch and shapes regardless of size. The latter is exemplified here only in the reflexive mechanism translating apparitions to the fovea. Both are extensions to contemporaneous functions of the knowing of universals heretofore treated by the authors only with respect to sequence in time.

A logical calculus of the ideas immanent in nervous activity

Because of the “all-or-none” character of nervous activity, neural events and the relations among them can be treated by means of propositional logic. It is found that the behavior of every net can be described in these terms, with the addition of more complicated logical means for nets containing circles; and that for any logical expression satisfying certain conditions, one can find a net behaving in the fashion it describes. It is shown that many particular choices among possible neurophysiological assumptions are equivalent, in the sense that for every net behaving under one assumption, there exists another net which behaves under the other and gives the same results, although perhaps not in the same time. Various applications of the calculus are discussed.

A Statistical Consequence of the Logical Calculus of Nervous Nets

A formal method is derived for converting logical relations among the actions of neurons in a net into statistical relations among the frequencies of their impulses.

The linear theory of neuron networks: The dynamic problem

The development of a general theory of neuron-networks is here extended to cases of non-steady state activity. Conditions for stability and neutrality of an equilibrium point are set up, and the possible functions representing the variation of excitation over time are enumerated. The inverse network problem is considered—which is, given a preassigned pattern of activity over time, to construct when possible a neuron-network having this pattern. Finally, a canonical form for neuron networks is derived, in the sense of a network of a certain special topological structure which is equivalent in activity characteristics to any given network.

Some observations on the simple neuron circuit

A new point of view in the theory of neuron networks is here adumbrated in its relation to the simple circuit: it is shown how these methods enable us to extend considerably and unify previous results for this case in a much simpler way.

A general theory of learning and conditioning: Part I

In the first of two parts in which a general mathematical theory of non-symbolic learning and conditioning is constructed, the sections of the theory dealing with non-symbolic learning and conditioning are presented, and a number of its qualitative implications are compared with available experimental results. In general, the agreement is found to be rather close.

A mathematical theory of the affective psychoses

The theory introduces two variables ϕ and ψ. The first represents the intensity of emotion, the second measures the intensity of activity. A set of integrodifferential equations is assumed to govern the variation of ϕ and ψ with respect to time. Since for increasing values of ϕ the conduct of the organism varies from great impassivity through a normal level of feeling to extremes of a circular depression or catatonic excitement; whereas an increase of ψ results in a transition from stupor to manic excitement, the solutions of the equations represent quatitative specifications of different psychotic states.