DESIGN FOR A BRAIN 12/15 



one of equilibrium; and constancy in the presence of small impul- 

 sive disturbances implies stability. 



The converse is also > true. If a subsystem is at a state of 

 equilibrium, then it will stay at that state, i.e. hold a constant 

 value (so long as its parameters do not change value). 



Constancy, equilibrium, and stability are thus closely related. 



12/15. Are such variables (or subsystems) common? Later 

 (S. 15/2) it will be suggested that they are extremely common, 

 and examples will be given. Here we can notice two types that 

 are specially worth notice. 



One form, uncommon perhaps in the real world but of basic 

 importance as a type-form in the strategy of S. 2/17, is that in 

 which the subsystem has a definite probability p that any particu- 

 lar state, selected at random, is equilibrial. We shall be con- 

 cerned with this form in S. 13/2. (In explanation, it should be 

 mentioned that the sample space for the probabilities is that given 

 by a set of subsystems, each a machine with input and therefore 

 determinate in whether a given state, with given input-value, is 

 or is not equilibrial.) The case would arise when the observer 

 faced a subsystem that was known (or might reasonably be 

 assumed) to be a determinate machine with input, but did not 

 know which subsystem, out of a possible set, was before him ; the 

 sample space being provided by the set suitably weighted, the 

 observer could legitimately speak of the probability that this 

 system, at this state, and with this input, should be in equilibrium. 



The other form, very much commoner, is that which shows 

 8 threshold ', so that all states are equilibrial when some para- 

 metric function is less than a certain value, and few or none are 

 equilibrial when it exceeds that value. Well-known examples are 

 that a weight on the ground will not rise until the lifting force 

 exceeds a certain value, and a nerve will not respond with an 

 impulse until the electric intensity, in some form, rises above a 

 certain value. 



What is important for us here is to notice that threshold, by 

 readily giving constancy, can readily give what is necessary for 

 the connexions between variable and variable to be temporary. 

 Thus the changes in the diagram of Figure 12/12/1 could readily 

 be produced by parts showing the phenomenon of threshold. 



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