DESIGN FOR A BRAIN 13/13 



The presence of threshold precludes the previous assumption of 

 independence in the probabilities; for now a variable's chance of 

 being at a state of equilibrium will vary in some correspondence 

 with the values of the variable's parameters. In the case of two 

 or more neurons, the correspondence will be one way if the effect 

 is excitatory, and inversely if it is inhibitory. (If there is a mixture 

 of excitatory and inhibitory modes, the outcome may be an 

 approximation to the independent form.) To follow the subject 

 further would lead us into more detail than is appropriate in 

 this survey; and at the present time little can be said on the 

 matter. 



13/13. To sum up: The polystable system, if composed of 

 parts whose states of equilibrium are distributed independently 

 of the states of their inputs, goes to a final equilibrium in a way 

 that depends much on the amount of functional connexion. 



When the connexion is rich, the line of behaviour tends to be 

 complex and, if n is large, exceedingly long; so the whole tends to 

 take an exceedingly long time to come to equilibrium. When 

 the line meets a state at which an unusually large number of the 

 variables are stable, it cannot retain the excess over the average. 



When the connexion is poor (either by few primary joins or by 

 many constancies in the parts), the line of behaviour tends to be 

 short, so that the whole arrives at a state of equilibrium soon. 

 When the line meets a state at which an unusually large number 

 of the variables are stable, it tends to retain the excess for a time, 

 and thus to progress to total equilibrium by an accumulation of 

 local equilibria. 



Dispersion 

 13/14. The polystable system shows another property that 

 deserves special notice. 



Take a portion of any line of behaviour of such a system. On 

 it we can notice, for every variable, whether it did or did not 

 change value along the given portion. Thus, in Figure 12/18/1, 

 in the portion indicated by the letters B and C both y and z 

 change but x does not. In the portion indicated by F, x and ~ 

 change but y does not. By dispersion I shall refer to the fact that 

 the active variables (y and z) in the first portion are not identical 

 with those (x and z) of the second. (In the example the portions 



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