Abstract
If we regard social members as moving points, abstracting their personalities and environment, it may be deduced topologically that a social region which consists of n members contains always a certain number of islets, as indicated by the following formula: In=1/2(n-1)(n-2). The islets mean tabu in the juristic, moral, and religious sense. It can be said in topological aspect, (1) that sociality is a system of tabu; (2) that since both one person region and two persons region have no islet and are topologically equal to each other, society is defined as a region which consists of three members or more (Figs. 1 & 2); (3) if we set a threshold on the moving ability of members, there may occur innersaturation of tabu corresponding to the islets less than In in the region, which is remarkable in the ancient feudal societies; (4) if a region is differentiated into two segments of different qualities, there may occur over-saturation of tabu based on conflicting tabus of the same islets in the region, which is remarkable in the capitalistic societies; (5) both by separation of a region and by connection of two regions, inner-saturation is forced to occur and some members are locked out from the region; and (6) that social tension is defined as conflicting tabus of the same islets. Thus, Lewin's formula of human behavior should be modified as follows: B=f(P, S, E) where S means sociality.
It can be said in dynamic aspect, (7) that as the communication between two regions are performed by an arm of one region which is stretched to another (Figs. 3 & 4), an upper region can be defined as an locus of communication routes (i.e. arms) between them (Fig. 5); (8) that social regions communicate each other by their arms in the upperregion (i.e. outer-region) as well as personal regions do in the region (Fig. 5); and (9) that social evenis are defined as an overlapping of two arms of conflicting regions.
When two conflicting arms overlapped, there arises radiation of a great deal of social energy and a new power-field occurs at the overlapping point, which may force a similar social event to occur. The latent time-interval between the first and the next social events may be shortened by the powerfield. We can see in molar aspect from the atlas of social events (Fig. 7), (10) that the latent time-interval may be shorter at the nearer behavioral distance than at the farther one from the point. We may call this phenomenon as a temporal field in sociality.
