THE GENERAL NEURAL NET 



If the response of the organism can be expressed as some func- 

 tion of the stimulus, this function must depend upon whatever para- 

 meters are required for describing the structure of the nervous sys- 

 tem. The psychologists can tell us much about the empirical charac- 

 ter of this function but nothing about the parameters. The anat- 

 omists and physiologists can tell us many things about the para- 

 meters. Our hope is for a synthesis of the results of both lines of 

 endeavor. 



If we knew all about the structure, we might hope to devise meth- 

 ods for deducing the function. Actually, with complex structures, 

 this becomes exceedingly difficult, though we have done this for struc- 

 tures of some very simple types. If we knew all about the function, 

 empirically, we might hope to deduce some of the characteristics of 

 the structure. However, there is never a single, unique structure, but 

 many possible ones, all leading to a function of the same empirical 

 characteristics. And, of course, we do not know all about either the 

 structure or the function, but only some things about each. 



Certainly the structure of the complete nervous system can be 

 no less complex than the behavior which is an expression of it, and 

 any Golgi preparation of a section from the retina or the cortex abun- 

 dantly exhibits such complexity. We have already mentioned one of 

 two general principles concerning this structure first stated by Lo- 

 rente de No in a paper which appeared in the Archives of Neurology 

 and Psychiatry, Vol. 30 (1933), pp. 245 ff. His statement of these 

 is as follows: 



"Law of Plurality of Connections. — If the cells in the spinal or 

 cranial ganglia are called cells of the 'first order' and the following 

 ones in the transmission system cells of the second, third to ••• nth. 

 order, it can be said that each nucleus in the nervous system always 

 receives fibers of at least n and n + 1 order, and often of n , n + 1 

 and n + 2 order." 



"Law of Reciprocity of Connections.— If cell complex A sends 

 fibers to cell or cell complex B , B also sends fibers to A , either direct 

 or by means of one internuncial neuron." 



In chapter ii we assumed the function <f> or y> for each neuron to 

 be linear with S between the threshold and a certain maximal value 

 characteristic of the neuron, and elsewhere constant. The coefficient 



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