XV 



A STATISTICAL INTERPRETATION 



The time-units in the Boolean formulation are of the order of 

 milliseconds, the approximate minimal separation between consecu- 

 tive impulses in any neuron being, in fact, about half this unit. Hence, 

 for even the briefest of overt responses, which require generally a 

 duration of seconds or longer, there is time for the occurrence of 

 hundreds or even thousands of individual impulses on the part of 

 any one of the participating neurons. It is legitimate, therefore, and 

 necessary, to develop a statistical theory of the temporal distribution 

 of these impulses for application to the temporally macroscopic psy- 

 chological processes. 



Whether this statistical development will lead immediately to 

 quantities that can be interpreted as being the postulated e and j of 

 the Rashevsky theory is still to be seen. It is quite possible, indeed, 

 that £ and j must rather be regarded as the statistical effects of im- 

 pulses in certain groups of neurons, rather than individual neurons. 

 As Rashevsky (1940, chap, viii) has emphasized, while the postulated 

 development of e and j is suggested by direct observation of the ac- 

 tion of individual neurons, it is necessary to suppose only that there 

 are neural units or groups of some kind whose activity follows the 

 postulated pattern, and the interpretation in terms of groups is 

 strongly suggested by the paucity of hypothetical neurons required 

 to account for many of the psychological processes discussed in earlier 

 chapters of this monograph. Moreover, the predictive success of the 

 theory provides strong presumptive evidence in favor of the supposi- 

 tion that the development of e and j as postulated does correspond to 

 some basic physiological processes, whatever these may be. 



As a step toward the deduction of the macroscopic from the mi- 

 croscopic theory, Landahl, McCulloch, and Pitts (1943) have shown 

 how the propositional equivalences can be transformed immediately, 

 by well-defined formal replacements, into statistical relations. To 

 obtain the rule for making these replacements, we now let d repre- 

 sent the period of latent addition, the interval within which the mini- 

 mal number of converging impulses must occur in order to result in 

 a stimulation. If v } is the mean frequency of the impulses in the neu- 

 ron Cj afferent to the neuron Ci , then Vjd is the probability that an 

 impulse will occur in c, during any particular interval 6 , and 1 — v } d 

 is the probability that an impulse will not occur in c k . If the im- 

 pulses in the various neurons c ; concurrent upon d are statistically in- 

 Ill 



