388 Information Storage and Neural Control 



Finally, run a net of the form lb from C\ and Cb to fs, and derive 



.¥3(0 . ^ . .S[.Vi(Ov.V,(0] 



. ^ . .StVi(0 v.S'[GSWo(0) . ~A'2(0]1. 



These expressions for N z{t) and iV4(/) are the ones desired; and 

 the realizing net in toto is shown in Figure le. 



This illusion makes very clear the dependence of the correspond- 

 ence between perception and the "external world'' upon the 

 specific structural properties of the intervening nervous net. The 

 same illusion, of course, could also have been produced under 

 various other assumptions about the behavior of the cutaneous 

 receptors, with correspondingly different nets. 



We shall now consider some theorems of equivalence: i.e., 

 theorems which demonstrate the essential identity, save for time, 

 of various alternative laws of nervous excitation. Let us first dis- 

 cuss the case of relative inhibition. By this we mean the supposition 

 that the firing of an inhibitory synapse does not absolutely prevent 

 the firing of the neuron, but merely raises its threshold, so that 

 a greater number of excitatory synapses must fire concurrently 

 to fire it than would otherwise be needed. We may suppose, losing 

 no generality, that the increase in threshold is unity for the firing 

 of each such synapse; we then have the theorem: 



Theorem IV 



Relative and absolute inhibition are equivalent in the extended sense. 



We may write out a law of nervous excitation after the fashion 

 of (1), but employing the assumption of relative inliibition instead; 

 inspection then shows that this expression is a TPE. An example 

 of the replacement of relative inhibition by absolute is given by 

 Figure If. The reverse replacement is even easier; we give the 

 inhibitory axons afferent to c, any sufficiently large number of 

 inhibitory synapses apiece. 



Second, we consider the case of extinction. We may write this 

 in the forni of a variation in the threshold 6, after the neuron Ct 

 has fired; to the nearest integer — and only to this approximation 

 is the variation in threshold significant in natural forms of excita- 

 tion — this may be written as a sequence di + bj for j synaptic 



