110 MATHEMATICAL BIOPHYSICS OF THE CENTRAL NERVOUS SYSTEM 



If Cj and c 2 each has two endfeet upon c 2 , the existential sen- 

 tence is realized: 



N*(t) . = . (Ez)t.SNi(z). 



This is a symbolic formulation of the assertion that c^ will fire at the 

 time t provided N^ has fired in some interval z prior to t . For in 

 this case the cycle formed by c 2 , being once set into activity, will 

 continue in a state of permanent activity. In either case we could 

 replace iVj (t) by any TPE, and the neuron d by the net which realizes 

 this TPE. Again, in the case of the "existential" net, if instead of 

 the single self-exciting neuron c 2 we have a cycle of n neurons, then, 

 activity being once started, each neuron of the cycle will be active 

 subsequently once every n time-intervals, and not in every time-in- 

 terval. 



It is understood, of course, that some common features of neu- 

 ronal activity are left out of the formalized picture given here. On 

 the other hand, some of these can be given a formal representation in 

 these terms, such a formal representation having by no means, how- 

 ever, the purport of factual description or explanation of the phe- 

 nomenon in question. Thus learning could be described in terms of 

 activated cycles and facilitation in terms of internuncials in the net. 

 Extinction can be described in terms of relative inhibition, and ref- 

 erence has already been made to the fact that relative inhibition can, 

 in turn, be replaced formally by total inhibition in nets of somewhat 

 different structure. 



