ITERATED SYSTEMS 12/3 



which are adapted will increase, or may stay constant, but cannot 

 decrease (in the conditions assumed here : more complex conditions 

 are discussed later). If the number of stable systems is regarded 

 as measuring, in a sense, the degree of adaptation achieved by the 

 whole, then, in a whole which consists of iterated systems, the 

 degree of adaptation tends always to increase. The whole will 

 therefore show a progression in adaptation. 



12/3. Let us now compare the two types of system, (a) the 

 fully connected, and (b) the iterated, in the times they take, 

 on the average, to reach terminal fields, other things, including 

 the number of main variables, being equal. (The calculation 

 can only be approximate but the general conclusion is unam- 

 biguous.) 



We start with a system of N main variables and want to find, 

 approximately, how long the system will take on the average to 

 reach the condition where all N main variables belong to systems 

 with stable fields , Three arrangements will be examined ; they are 

 extreme in type, but they illustrate the possibilities. (1) All the 

 N main variables belong to one system, so that to stabilise all 

 N a field must stabilise all simultaneously. (2) Each main vari- 

 able is in a system which includes it alone, and where the systems 

 are related in such a way that only after the first is stabilised can 

 the second start to get stabilised, and so on in succession. (3) 

 Each system, also containing only one main variable, proceeds 

 independently to find its own stability. 



In order to calculate how long the three types will take, suppose 

 for simplicity that each main variable has a constant and inde- 

 pendent probability p of becoming stable in each second. 



The type in which stability can occur only when all the N 

 events are favourable simultaneously will have to wait on the 



average for a time given by 1\ = —. The type in which sta- 

 bility can occur only by the variables achieving stability in succes- 

 sion will have to wait on the average for a time given by 1\ = N/p. 

 And the type in which the variables proceed independently to 

 stability will have to wait on the average for a time which is 

 difficult to specify but which will be of the order of T 3 = 1/p. 

 These three estimates of the time taken are of interest, not for 

 their quantitative exactness, but for the fact that they tend to 



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