In summary, the original metrizable topological space was decomposed into an orthogonal Euclidean space times[21] a denumerable random cartesian product of irreducible (wrt direct product) denumerable groups. Thus, since any individual component of a random cartesian product may be studied independently of the others, all that one needs to study is: (1) a Gaussian distribution on a single real axis and (2) the irreducible denumerable groups. [21] Random cartesian product. Finally, it should be emphasized that there are only these two ways of decomposing a metrizable topology; (1) if a (statistical) basis is given, use the diagonalization of a symmetric matrix algorithm described earlier (and given in detail in the three channels in cascade problem), and (2) otherwise use a suitable network of the NPO’s with n₀=1. Of course, any hybrid of these two methods may be employed as well. On Functional Neuron Modeling C. E. HENDRIX _Space-General Corporation_ _El Monte, California_ There are two very compelling reasons why mathematical and physical models of the neuron should be built. Model building, while widely used in the physical sciences, has been largely neglected in biology. However, there can be little doubt that building neuron models will increase our understanding of the function of real neurons, if experience in the physical sciences is any guide. Secondly, neuron models are extremely interesting in their own right as new technological devices. Hence, the interest in, and the reason for symposia on self-organizing systems. We should turn our attention to the properties of real neurons, and see which of them are the most important ones for us to imitate. Obviously, we cannot hope to imitate _all_ the properties of a living neuron, since that would require a complete simulation of a living, metabolizing cell, and a highly specialized one at that; but we can select those functional properties which we feel are the most important, and then try to simulate those. The most dramatic aspect of neuron function is, of course, the axon discharge. It is this which gives the neuron its “all-or-nothing” character, and it is this which provides it with a means for propagating its output pulses over a distance. Hodgkin and Huxley (1) have developed a very complete description of this action. Their model is certainly without peer in describing the nature of the real neuron. On the technological side, Cranes’ “neuristors” (2) represent a class of devices which imitate the axonal discharge in a gross sort of way, without all the subtle nuances of the Hodgkin-Huxley model. Crane has shown that neuristors can be combined to yield the various Boolean functions needed in a computer.