104 MATHEMATICAL BIOPHYSICS OF THE CENTRAL NERVOUS SYSTEM 



the two facts are to be reconciled and the greater part of this mono- 

 graph has been devoted to a discussion of these gradations. For the 

 present, however, let us consider some of the formal aspects of the 

 all-or-none feature alone. 



An afferent neuron may form any number of synaptic connec- 

 tions with an efferent neuron and the firing of one afferent alone may 

 or may not be sufficient to elicit a discharge in the efferent neuron. 

 In order for a discharge to be elicited, it is necessary that there be a 

 sufficient number of endfeet of discharging afferents all located with- 

 in a sufficiently small region of the stimulated neuron. The discharges 

 of the afferent neurons must, moreover, all occar within a sufficiently 

 small time-interval. The minimal number of endfeet of discharging 

 afferents required for eliciting a discharge in any neuron is what we 

 now call the threshold, 8 , of the neuron ; the endfeet may or may not 

 all come from the same afferent, but for simplicity we suppose them 

 all equal in their effectiveness. The maximal time-interval within 

 which the summation can occur is about a quarter of a millisecond. 

 There is a delay of about half a millisecond between the arrival of 

 the impulses upon a neuron and the initiation of its own discharge. 

 Compared to this synaptic delay, the time required for the conduc- 

 tion from origin to terminus is quite short. 



In some instances the arrival of a nervous discharge upon a neu- 

 ron will have the effect, not of initiating a discharge in it, but of pre- 

 venting a discharge that would otherwise occur. No explanation of 

 this phenomenon of inhibition has won general acceptance; neither 

 is it known whether the inhibition is complete or only partial. But 

 the fact of its occurrence is beyond question, and only the details of 

 the schematic structure will be affected by the assumption of partial 

 rather than complete inhibition (McCulloch and Pitts, 1943). To be 

 definite we make the arbitrary assumption that inhibition when it 

 occurs is complete. 



The McCulloch-Pitts picture involves a formal representation of 

 neural nets in terms of Boolean algebra as follows: Let the life-span 

 of the organism be divided into elementary time-intervals of common 

 length equal to the period of synaptic delay and introduce this inter- 

 val as the time-unit. Since each nerve-impulse is followed by a refrac- 

 tory period of about half a millisecond during which the neuron is 

 incapable of further activity, no neuron can fire twice within any unit 

 interval, and moreover, from the very definition of the unit of time, 

 the firing of a neuron within a given unit interval can cause the fir- 

 ing of any efferent neuron only during the next unit interval, if at all. 

 Summation or inhibition, if either occurs, is only effective in case the 

 summating or inhibiting neurons fire within the same unit interval. 



