110 John B. Calhoun 



amount of time is spent in frustrating refractory periods. 

 Here 



e'r' = af:i-' (65) 



And from Eqs. (63), (64), and (65) it is obvious that 



qCw) _ n(m) 



(66) 



Since Nb is a special, and the most important, case of Nm, Eq. (66) 

 represents a significant consequence of evolution, as well as adjustment to 

 current group size different from Nb. It means that when members of a 

 group attempt to maximize satisfaction from social interaction, they will 

 of necessity spend an equivalent amount of time experiencing frustration 

 from social interaction. Evolution having transpired in such a system of 

 social physics, physiology must be in harmony with this normal degree of 

 frustration. Likewise, any marked decrease or increase of /„p from /^p"'^ 

 should prove stressful. 



From Eqs. (51), (59), and (61), when mm' and a remain appropriate 

 to Nb but A'' fluctuates, it follows that 



^ MN - ly- 



As N approaches zero, /„p approaches zero. As N approaches infinity, 

 lap approaches the fc characteristic of Nb, that is when/^ = Nb — I = l/ab. 

 Yet at the same time (see discussion following Eq. (52)) /„„ approaches 

 zero as N approaches infinity with reference to its divergence from Nb- 

 At N's much larger than Nb the frequency of contacts resulting in refrac- 

 tory periods (i.e., faa and f^p) comes to approximate the total contacts 

 transpiring in Nb] however, practically all of such contacts are of the type 

 frustrating to individuals having returned to the responsive state. 



1. Terms and Equations 



The following assembly of definitions will facilitate understanding later 

 discussions. Insofar as possible the N animals in the group will serve as the 

 basis of the definitions. Some terms utilized in later sections will also be 

 included here. 



N = Total niunber of individuals in the group. In the strictest sense, 

 a group is defined by habitation of an exclusive area in which 

 each resident member has a good chance of contacting all others. 

 d = Target diameter of an individual. In the simplest sense, d 

 specifies the actual physical diameter with the "animal" having 

 no more d properties than a billiard ball. Included under d are 



