DESIGN FOR A BRAIN 



20/10 



P = 0-10) with the hypothesis that the probability for a matrix 

 of order n x n is 1/2". That this may be the correct expression 

 for this particular case is suggested partly by the fact that it 

 may be proved so when n = 1 and n = 2, and partly by the 

 fact that, for stability, the matrix has to pass all of n tests. 

 And in fact about a half of the matrices failed at each test. 

 If the signs of the determinants in Hurwitz' test are statistically 

 independent, then l/2 n would be the probability in this case. 



In these tests, the intrinsic stabilities of the variables, as 

 judged by the signs of the terms in the main diagonal, were 

 equally likely to be stable or unstable. An interesting variation, 

 therefore, is to consider the case where the variables are all 

 intrinsically stable (all terms in the main diagonal distributed 

 uniformly between and — 9). 



The effect is to increase their probability of stability. Thus 

 when n is 1 the probability is 1 (instead of J); and when n is 

 2 the probability is § (instead of J). Some empirical tests gave 

 the results of Table 20/10/2. 



Table 20/10/2. 



The probability is higher, but it still falls as n is increased. 



A similar series of tests was made with the Homeostat. Units 

 were allowed to interact with settings determined by the uni- 

 selectors, which were set at one position for one test, the usual 

 ultrastable feedback being severed. The percentage of stable 

 combinations was found when the number of units was two. 

 Then the percentage was found for the same general conditions 

 except that three units interacted; and then four. The general 

 conditions were then changed and a new triple of percentages 

 found. And this was repeated six times altogether. As the 

 general conditions sometimes encouraged, sometimes discouraged, 

 stability, some of the triples were all high, some all low; but in 

 every case the per cent stable fell as the number of interacting 



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