5/12 AN INTRODUCTION TO CYBERNETICS 



kind as freely as are the less intelligent, the Intelligence Quotient 

 of the community will fall. Clearly it cannot fall very low, because 

 the feebleminded can reproduce better than the idiot. So if these 

 were the only factors in the situation, the I.Q. would be stable at 

 about 90. Stability at this figure would be regarded by most people 

 as undesirable. 



An interesting example of stability occurs in the condition known 

 as "causalgia", in which severe pain, without visible cause, occurs 

 in a nerve which has previously been partly divided. Granit has 

 shown that it is almost certainly due to conduction, at the site of 

 injury, of impulses from the motor (outgoing) to the sensory (in- 

 coming) nerves, allowing the formation of a regenerative circuit via 

 the reflex centres in the spinal cord. Such a circuit has two states 

 of equilibrium, each stable: conducting few impulses or conducting 

 the maximal number. It is like a top-heavy see-saw, that will rest 

 in either of two extreme conditions but will not rest in between. 

 The patient is well aware that "stability" can be either good or bad, 

 for of the two stable states one is comfortable and the other extremely 

 painful. 



EQUILIBRIUM IN PART AND WHOLE 



5/12. We can now notice a relation between couphng and equilib- 

 rium that will be wanted later (S.12/14 and 13/19), for it has import- 

 ant applications. 



Suppose some whole system is composed of two parts A and B, 

 which have been coupled together: 



B 



and suppose the whole is at a state of equilibrium. 



This means that the whole's state is unchanging in time. But 

 the whole's state is a vector with two components: that of y4's state 

 and that of 5's. It follows that A, regarded as a sub-system, is also 

 unchanging; and so is B. 



Not only is A''s state unchanging but so is the value of ^'s input; 

 for this value is determined by B's state (S.4/7), which is unchanging. 

 Thus ^ is at a state of equilibrium in the conditions provided by B. 

 (Cf. Ex. 5/3/11.) The similar property holds for B. Thus, if the 

 whole is at a state of equilibrium, each part must be in a state of 

 equilibrium in the conditions provided by the other. 



The argument can also be reversed. Suppose A and B are at 

 states of equilibrium, and that each state provides, for the other 



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