A Logical Calculus of the Ideas Immanent in Nervous Activity 387 



(Si . So ... . S„0 . ~ {Sm+xV S,n + lV . . . .V S„), 



which is clearly a TPE. 



The method of the last theorems does in fact provide a very 

 convenient and workable procedure for constructing nervous nets 

 to order, for those cases where there is no reference to events 

 indefinitely far in the past in the specification of the conditions. 

 By way of example, we may consider the case of heat produced 

 by a transient cooling. 



If a cold object is held to the skin for a moment and removed, 

 a sensation of heat will be felt; if it is applied for a longer time, the 

 sensation will be only of cold, with no preliminary warmth, how- 

 ever transient. It is known that one cutaneous receptor is affected 

 by heat, and another by cold. If we let Ni and A^2 be the actions 

 of the respective receptors and N?. and A^4 of neurons whose 

 activity implies a sensation of heat and cold, our requirements 

 may be written as 



N^{t) : = : A'i(/-1) . v . N^.{t-^) . ^N~,{t-2) 



Ndt) . = .No(t-2) .No(t-l) 



where we suppose for simplicity that the required persistence in 

 the sensation of cold is, say, two synaptic delays, compared with 

 one for that of heat. These conditions clearly fall under Theorem 

 III. A net may consequently be constructed to realize them, by 

 the method of Theorem II. We begin by writing them in a fashion 

 which exhibits them as built out of their constituents by the 

 operations realized in Figures la, b, c, d: i.e., in the form 



N^(t) . ^ . S{A\it) V S[{SN,{t)) >'^N,(t)]} 

 N,(t) . ^ . S{[SN,{t)] .N,{t)]. 



First we construct a net for the function enclosed in the greatest 

 number of brackets and proceed outward; in this case we run a 

 net of the form shown in Figure la from Co to some neuron r„, say, 

 so that 



Nait) . = . SN,(t). 

 Next introduce two nets of the forms Ic and Id, both running 

 from Ca and c^, and ending respectively at Ci and say Cb. Then 



A^4(0 . = . S[NAt) . N,it)] . ^ . S[(SN2(t)) . N,(t)]. 



