By Norbert and J. P. Schade (edited by) Wiener
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Additional resources for Cybernetics of the Nervous System
Organic chemistry and physical chemistry and may in due course be greatly helped by quantum mechanics. . The second T H E PROBLEM OF O R G A N I S M I C RELIABILITY 25 part is (connected with logic) . . (We) remove the first part of the problem by the process of axiomatiration, and concentrate on the second one. The Axiomatic Procediire. Axiomatizing the behaviour of the elements means this: We assume that thc elements have certain well-defined, outside functional characteristics; that is, they are to be treated as ‘black boxes’.
E. Shannon’s noisy channel coding theorem (op. ) is then proved: THE PROBLEM OF ORGANISMIC RELIABILITY 45 Givenf-neurons which can compute any Boolian function, all with the same computation capacity Cc, for any automaton A that computes a (definite event), and any (rate of information processing, Rc < G), an arbitrarily reliable automaton A may be (constructed) that computes the event with a rate R,‘ such that R e < R,’ < Ce.
I t is important to note however, that this error probability is an average. In particular it is an average over all codes that encode only high probability message sequences from S , and since it tends to zero with increasing n, provided H ( X ) 5 C, it follows that there exists at least one code for whiclz P, + 0. e. the distortion will not in general cause confusion of signals. This is accomplished by the introduction of redundancy, not in the manner used by Von Neumann (op. ) but as follows: Messages of length k issuing from a source of information S, are coded into blocks of signal code words of length n, where k - 6 C n k i n is in fact identified with the rate of transmission of information per signal digit, through the channel.
Cybernetics of the Nervous System by Norbert and J. P. Schade (edited by) Wiener