82 MATHEMATICAL BIOPHYSICS OF THE CENTRAL NERVOUS SYSTEM 



stant a increases with both S u and S and depends on the time between 

 repetitions and the time of stimulation at each repetition. This, too, is 

 in qualitative agreement with results of experiments on conditioning. 



This conditioning mechanism requires the continued activity of 

 some circuits and the objection could be raised that the great sta- 

 bility of well-established memory-patterns, which resist disruption 

 by either such major disturbances as shock and narcosis or by the 

 cumulative effect of countless minor vicissitudes over a period of time, 

 is inconceivable in terms of so vulnerable a structure. To this ob- 

 jection at least two replies are possible. One is that a quantitative 

 theory is useful in proportion to the extent of the phenomena for 

 which it can account, and it is not less useful for failing to account 

 for others, However, the objection can be met in a more positive way 

 by supposing that the relatively rapid changes permitted by the above 

 mechanism lead in some fashion to more permanent structural 

 changes. It is quite possible that the usual intermittent rise and fall 

 of e and j at a given synapse would have no physiological effect be- 

 yond the exciting and inhibiting effects which we have postulated, 

 whereas the maintenance at some sufficiently high value of either or 

 both would cause permanent changes involving, among other things, 

 a modification of threshold (cf. Douglas, 1932). The theory of the 

 process of conditioning would then hold as outlined, but would re- 

 quire a supplement to account in detail for the observed stability. 



But regardless of the mechanism, the facts of conditioning re- 

 quire some change in e with successive trials, leading to a change in 

 response. The simplest assumption possible is that s is proportional 

 to the number of trials, at least when the number of trials is small, 

 and this is the essential content of equation (4), with Aa the constant 



Figure 2 



