Kris Carlson

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von Neumann on axiomatizing the nervous system

“In comparing living organisms, and, in particular, that most complicated organism, the human central nervous system, with artificial automata, the following limitations must be kept in mind. The natural systems are of enormous complexity, and it is clearly necessary to subdivide the problem that they represent into several parts. One method of subdivision, which is particularly significant in the present context, is this: The organisms can be viewed as made up of parts which to a certain extent are independent, elementary units. We may, therefore, to this extent, view as te first part of the problem the structure and functioning of such elementary units individually. The second part of he problem consists of understanding how these elements are organized into a whole, and how the functioning of the whole is expressed in terms of these elements….
“With this attitude [of the mathematician or logician], we will be inclined to remove the first part of the problem by the process of axiomatization, and concentrate on the second one.
“The Axiomatic Procedure. Axiomatizing the behavior of the elements means this: We assume that the elements have certain well-defined, outside, functional characteristics; that is, they are to be treated as ‘black boxes.’ They are viewed as automatisms, the inner structure of which need not be disclosed, but which are assumed to react to certain unambiguously defined stimuli, by certain unambiguously defined responses.
“This being understood, we may then investigate the larger organism that can be built up from these elements, their structure, their functioning, the connections between the elements, and the general theoretical regularities that may be detectable in the complex syntheses of the organism in question.
“I need not emphasize the limitations of this procedure. Investigators of this type may furnish evidence that the system of axioms used is convenient and, at least in its effects, similar to reality. They are, however, not the ideal method, and possibly not even a very effective method, to determine the validity of the axioms. Such determinations of validity belong primarily to the first part of the problem [structure and function of the individual units]. Indeed they are essentially covered by the properly physiological (or chemical or physical-chemical) determinations of the nature and properties of the elements.”

von Neumann, “The General and Logical Theory of Automata,” in James R. Newman, The World of Mathematics, Volume 4, pp.2070-2071.

July 19, 2010 - Posted by | Uncategorized | , ,

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