A Logical Calculus of the Ideas Immanent in Nervous Activity 389 



delays after firing, where bj = for / large enough, say 7 = M or 

 greater. We may then state 



Theorem V 



Extinction is equivalent to absolute inhibition. 



For, assuming relative inhibition to hold for the moment, we 

 need merely run M circuits U\, U'2, . . . 'hi containing respectively 

 1, 2, ... , A/ neurons, such that the firing of each link in any is 

 sufficient to fire the next, from the neuron c, back to it, where 

 the end of the circuit Wj has just b,- inhibitory synapses upon c,. 

 It is evident that this will produce the desired results. The reverse 

 substitution may be accomplished by the diagram of Figure Ig. 

 From the transitivity of replacement, we infer the theorem. To 

 this group of theorems also belongs the well-known 



Theorem VI 



Facilitation and temporal summation may be replaced by spatial sum- 

 mation. 



This is obvious: one need merely introduce a suitable secjuence 

 of delaying chains, of increasing numbers of synapses, between the 

 exciting cell and the neuron whereon temporal summation is 

 desired to hold. The assumption of spatial summation will then 

 give the required results. See e.g. Figure Ih. This procedure had 

 application in showing that the observed temporal summation in 

 gross nets does not imply such a mechanism in the interaction of 

 individual neurons. 



The phenomena of learning, which arc of a character persisting 

 over most physiological changes in nervous activity, seem to re- 

 quire the possibility of permanent alterations in the structure of 

 nets. The simplest such alteration is the formation of new synapses 

 or equivalent local depressions of threshold. We suppose that some 

 axonal terminations cannot at first excite the succeeding neuron; 

 but if at any time the neuron fires, and the axonal terminations 

 are simultaneously excited, they become synapses of the ordinary 

 kind, henceforth capable of exciting the neuron. The loss of an 

 inhibitory synapse gives an entirely equivalent result. We shall 

 then have 



