4/20 AN INTRODUCTION TO CYBERNETICS 



some coherence is introduced into the whole. Suppose then that 

 into the system's diagram of immediate effects some actions, i.e. 

 some arrows, are added, but only enough to give coherency to the 

 set of parts. The least possible number of arrows, if there are n 

 parts, is n — 1 ; but this gives only a simple long chain. A small 

 amount of coupling would occur if the number of arrows were 

 rather more than this but not so many as n^ — n (which would give 

 every part an iimnediate effect on every other part). 



Smallness of the amount of interaction may thus be due to small- 

 ness in the number of immediate effects. Another way, important 

 because of its commonness, occurs when one part or variable affects 

 another only under certain conditions, so that the immediate effect 

 is present for much of the time only in a nominal sense. Such 

 temporary and conditional couplings occur if the variable, for any 

 reason, spends an appreciable proportion of its time not varying 

 (the "part-function"). One common cause of this is the existence 

 of a threshold, so that the variable shows no change except when the 

 disturbance coming to it exceeds some definite value. Such are 

 the voltage below which an arc will not jump across a given gap, and 

 the damage that a citizen will sustain before he thinks it worth 

 while going to law. In the nervous system the phenomenon of 

 threshold is, of course, ubiquitous. 



The existence of threshold induces a state of affairs that can be 

 regarded as a cutting of the whole into temporarily isolated sub- 

 systems; for a variable, so long as it stays constant, cannot, by 

 S.4/12, have an effect on another; neither can it be affected by another. 

 In the diagram of immediate effects it will lose both the arrows that 

 go from it and those that come to it. The action is shown dia- 

 grammatically in Fig. 4/20/1. 



The left square shows a basic network, a diagram of immediate 

 effects, as it might have been produced by the method of Ex. 4/19/5. 

 The middle square shows what remains if thirty per cent of the 

 variables remain constant (by the disturbances that are coming to 

 them being below threshold). The right square shows what remains 

 if the proportion constant rises to fifty per cent. Such changes, 

 from left to right, might be induced by a rising threshold. It will 

 be seen that the reacting sub-systems tend to grow smaller and 

 smaller, the rising threshold having the effect, functionally, of cutting 

 the whole network into smaller and smaller parts. 



Thus there exist factors, such as "height of threshold" or "pro- 

 portion of variables constant", which can vary a large system con- 

 tinuously along the whole range that has at one end the totally-joined 

 form., in which every variable has an immediate effect on every other 



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