14/5 REPETITIVE STIMULI AND HABITUATION 



of the cycle bears some exact simple relation to that of the applica- 

 tions of S (an event of zero probability if they can vary con- 

 tinuously), the representative point will in fact leave X and 

 eventually be trapped at E. (The cycle around P, Q, R adds 

 complications that can be dealt with in a more detailed discussion.) 



14/5. The description given is not rigorous, but can easily be 

 made so. It is intended only to illustrate the thesis that under 

 repetitive applications of a stimulus (with sufficient delay between 

 the applications for the system to come to equilibrium) the 

 polystable system is selective, for it sticks sooner or later at a state 

 from whose confluent the stimulus cannot shift it. And, if there is a 

 metric and continuity over the phase space, this distance that the 

 stimulus S finally moves the point will be less than the average 

 distance, for short arrows are favoured. Thus the amounts of 

 change caused by the successive applications of S change from 

 average to less than average. 



We need not attempt here to formulate calculations about the 

 exact amount: they can be left to those specially interested. 

 What we should notice is that the outcome of the process is not 

 symmetric. When we think of a randomly assembled system of 

 random parts we are apt to deduce that its response to repeti- 

 tive stimulation will be equally likely to decrease or to increase. 

 The argument shows that this is not so: there is a fundamental 

 tendency for the response to get smaller. 



There is a line of argument, much weaker, which may help to 

 make the conclusion more evident. We may take it as axiomatic 

 that large responses tend to cause more change (or are associated 

 with more change) within the system than small. If the responses 

 have any action back on their own causes, then large responses 

 tend to cause a large change in what made them large; but the 

 small only act to small degree on the factors that made them 

 small. Thus factors making for smallness have a fundamentally 

 better chance of surviving than those that make for largeness. 

 Hence the tendency to smallness. 



(If the point requires illustration, we could consider the question : 

 Of two boys making their own fireworks, who has the better 

 chance of survival ? — the boy who is trying to produce the biggest 

 firework ever, or the boy who is trying to produce the tiniest !) 



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