12/4 DESIGN FOR A BRAIN 



have widely different values. Some numerical values will be 



calculated in order to demonstrate the differences. The values 



have not been specially selected, and if the reader will substitute 



some values of his own he will probably find that his values lead 



to essentially the same conclusions as are reached here. 



Suppose that the chance of any one variable becoming stable 



in a given second is a half. If we are testing a system with a 



thousand variables, then N = 1000 



and J\ = 2 1000 sees. 



rr 100 ° 



1 2 = — £- sees. 



T 3 = about \ sec. 

 When these are converted to more ordinary numbers, we find that 

 the three quantities differ widely. T z is about a half-second, T 2 

 is about 8 minutes, and 1\ is about 3 X 10 291 centuries. The 

 last number, if written in full, would consist of a 3 followed by 

 about five lines of zeros. 1\ and T 2 are moderate, but T 1 is so 

 vast as to be outside even astronomical duration. 



This example is typical. What it means in general is that 

 when N is large, it is not possible to get stability if all N must 

 find some favourable feature simultaneously. The calculation 

 confirms the statement of S. 11/7 that it is not reasonable to 

 assume that 10 10 neurons have formed a stable field by waiting 

 for the fortuitous occurrence of one field which stabilises all. 



12/4. The argument may also be viewed from a different angle. 

 When the system of a thousand variables could achieve stability 

 only by the occurrence of a field which was favourable to all at 

 once, it had to wait, on the average, through 3 X 10 291 centuries. 

 But if its conditions were changed so that the variables could 

 become stable in succession or independently, then the time taken 

 dropped to a few minutes or less. In other words, what was, for 

 all practical purposes, an impossibility under the first condition 

 became, under the second and third conditions, a ready possibility. 

 It is difficult to find a real example which shows in one system 

 the three ways of progression to stability, for few systems are 

 constructed so flexibly. It is, however, possible to construct, by 

 the theory of probability, examples which show the differences 

 referred to. Thus suppose that, as the traffic passes, we note the 

 final digit on each car's number-plate, and decide that we want 



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