1. The Social Use of Space 3 



assembly of such particles inhabiting a particular environment, taxonomic 

 categories, such as species and genera, represent general classes of particles. 

 Although several classes may share certain characteristics, each possesses 

 characteristics peculiar to itself, which on the average differentiate it from 

 all other classes. Furthermore, the properties of any particular particle 

 may change through time as a function of maturation and experience. 

 Such changes are reflected in the individual's internal milieu. Only at this 

 level are we concerned with physiology in its classical sense. 



A social system consists of particles moving through space and time. In 

 the course of evolution and maturation, such particles may develop en- 

 hanced capacities for affecting others and, in turn, for being more affected 

 by them. This inquiry seeks that essential nature of these particles which 

 influences the course of social evolution. It concludes that each category of 

 particles which we designate as a species must develop a basic group size, 

 designated as its basic number, Nb. Then, assuming the validity of the 

 concept of an Nb, the inquiry is extended to encompass the following 

 questions : 



1. How do changes in TV from Nb alter the social system? 



2. Given a species, whose groups are of the optimum Nb type, how do 

 changes in the environment or in the nature of the particles affect 

 the social system? 



3. What are the basic organizational and interactional properties of the 

 group? 



I found very few prior studies in the literature suitable for guiding me 

 in developing formulations adequate to satisfy these objectives. Therefore, 

 this discourse will be neither a review of the literature nor even an adequate 

 presentation of empirical data. Instead, the major theme concerns develop- 

 ment of a logically sound, theoretical framework of processes underlying 

 social phenomena. 



In the course of this development some empirical data will be presented. 

 These data are not meant to prove the correctness of the formulations. 

 They are presented simply as background for the origin of ideas or to show 

 that there at least exist some data which are harmonious with the developed 

 concepts. Much of such data is presented here for the first time. I am in- 

 debted to many persons for their permission to cite such original data. 



I have attempted to place many of the concepts in sufficiently precise 

 mathematical form to permit a better understanding of the dynamics in- 

 volved. My inadequacy in the field of mathematics has been buffered by 

 the advice of several competent mathematicians : James U. Casby, Murray 

 Eden, Samuel W. Greenhouse, Seymour Geisser, Clifford Patlak, and 



