382 Information Storage and Neural Control 



adequate. But for nets undergoing both alterations, we can sub- 

 stitute equivalent fictitious nets composed of neurons whose con- 

 nections and thresholds are unaltered. But one point must be 

 made clear: neither of us conceives the formal equivalence to be 

 a factual explanation. Per contra! — we regard facilitation and 

 extinction as dependent upon continuous changes in threshold 

 related to electrical and chemical variables, such as after-potentials 

 and ionic concentrations; and learning as an enduring change 

 which can survive sleep, anaesthesia, convulsions and coma. The 

 importance of the formal equivalence lies in this: that the altera- 

 tions actually underlying facilitation, extinction and learning in 

 no way affect the conclusions which follow from the formal treat- 

 ment of the activity of nervous nets, and the relations of the 

 corresponding propositions remain those of the logic of propositions. 

 The nervous system contains many circular paths, whose ac- 

 tivity so regenerates the excitation of any participant neuron that 

 reference to time past becomes indefinite, although it still implies 

 that afferent activity has realized one of a certain class of con- 

 figurations over time. Precise specification of these implications 

 by means of recursive functions, and determination of those that 

 can be embodied in the activity of nervous nets, completes the 

 theory. 



THE THEORY: NETS WITHOUT CIRCLES 



We shall make the following physical assumptions for our cal- 

 culus. 



1. The activity of the neuron is an ^'all-or-none" process. 



2. A certain fixed number of synapses must be excited within 

 the period of latent addition in order to excite a neuron at any 

 time, and this number is independent of previous activity and 

 position on the neuron. 



3. The only significant delay within the nervous system is syn- 

 aptic delay. 



4. The activity of any inhibitory synapse absolutely prevents 

 excitation of the neuron at that time. 



5. The structure of the net does not change with time. 



