PART THREE 



XIV 



THE BOOLEAN ALGEBRA OF NEURAL NETS 



To the extent that our neurons are representative of those stud- 

 ied by the physiologist, our quantities s and j must be interpreted as 

 time-averages. The assumptions underlying any purely formal theory 

 can be justified only to the extent that the predictions to be drawn 

 from them are borne out by experience. However, our theory is not 

 intended to be a formal one only. On the contrary, it is intended that 

 the theoretical neural structures will represent in some sense the 

 essential character of the actual anatomical structures and that the 

 postulated behavior of the constituent neurons will be representative 

 of the actual physiological activity of the neurons, or at least of re- 

 curring complexes of these, in the real organism. Hence our postu- 

 lated £ and j must be identified with physiological states or events, 

 and the postulated laws of their development, or something closely 

 approximating them, must be deduced from more fundamental prin- 

 ciples. 



In large measure this is a statement of a program for future re- 

 search. It is evident, of course, that the e and j are to be correlated 

 with the "action-spikes" of the neurons. These occurrences occupy 

 milliseconds, whereas ordinary psychological behavior is generally a 

 matter of seconds at least, which justifies a statistical averaging pro- 

 cedure. The first step in the deduction has been made by McCulloch 

 and Pitts (1943), and we now outline their picture, microscopic as 

 to time, of the neuron's behavior, a picture that rests almost immedi- 

 ately upon direct observations. Later, in the next chapter, we indi- 

 cate how, by carrying out a suggestion due to Landahl, McCulloch and 

 Pitts (1943), this deduction might be completed. But since the com- 

 plete deduction of the macroscopic picture, with which we have been 

 concerned so far, from the microscopic picture, is still wanting, these 

 chapters constitute largely a digression from the main trend of our. 

 discussions and will appear to be, in some details, even contradictory. 



The most striking feature of the nervous discharge as observed 

 in the laboratory is its all-or-none character. A change in the. physio- 

 logical state of the neuron — e.g. one due to a change in the. oxygen, 

 tension — may alter the potential of any discharge the neurpn is ca- 

 pable of making, but in any given condition either the maximal re- 

 sponse or none at all will occur. Since nearly all overt reactions 

 have gradations the complete deduction must explain in detail how 



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