Georg Simmel: The Significance of Numbers for Social Life
Simmel's emphasis on the structural determinants of social action is perhaps best exemplified in his seminal essay, "Quantitative Aspects of the Group." Here he comes nearest to realizing his goal of writing a grammar of social life by considering one of the most abstract characteristics of a group: the mere number of its participants. He examines forms of group process and structural arrangement insofar as these derive from sheer quantitative relationships.
A dyadic relationship differs qualitatively from all other types of groups in that each of the two participants is confronted by only one another and not by a collectivity. Because this type of group depends only on two participants, the withdrawal of one would destroy the whole: "A dyad depends on each of its two elements alone--in its death though not in its life: for its life it needs both, but for its death, only one."
Hence the dyad does not attain that superpersonal life which, in all other groups, creates among its members a sense of constraint. Yet the very lack of superpersonal structure also entails intense absorption of the participants in their dyadic relationship. The dependence of the whole on each partner is obvious; in all other groups duties and responsibilities can be delegated, but not in the dyad, where each participant is immediately and directly responsible for any collective action. Because each partner in the dyad deals with only one other individual, who forms a unit with him, neither of the two can deny responsibility by shifting it to the group; neither can hold the group responsible for what he has done or failed to do.
When a dyad is formed into a triad, the apparently insignificant fact that one member has been added actually brings about a major qualitative change. In the triad, as in all associations involving more than two persons, the individual participant is confronted with the possibility of being outvoted by a majority.
The triad is the simplest structure in which the group as a whole can achieve domination over its component members; it provides a social framework that allows the constraining of individual participants for collective purposes. The dyad relies on immediate reciprocity, but the triad can impose its will upon one member through the formation of a coalition between the two others. Thus, the triad exhibits in its simplest form the sociological drama that informs all social life: the dialectic of freedom and constraint, of autonomy and heteronomy.
When a third member enters a dyadic group, various processes become possible where previously they could not take place. Simmel singled out three such processes, although others have since been identified. A third member may play the role of mediator vis-a-vis the other two, helping, through his own impartiality, to moderate passions that threaten to tear the group apart. He may, alternately, act as a tertius gaudens (the third who rejoices), seeking to turn to his own advantage a disagreement between the other two. Finally, through a strategy of divide et impera (divide and rule), he may intentionally created conflicts between the other two in order to attain a dominant position or other gains.
This brief outline of three types of strategy open to the third participant can hardly exhaust the richness of Simmel's thought in this analysis. He offers a great variety of examples, deliberately comparing intimate human involvements, such as the competition of two men for one woman, with such large-scale events as the European balance of power and the formation of coalitions among political parties. He compares the strategy of a mother-in-law who confronts a newly married couple with the ways in which Rome, after subjugating Greece, dealt with Athens and Sparta.
It is a virtuoso performance, one of the more persuasive demonstrations of the power of sociological analysis. Simmel reveals the sterility of total psychological reductionism by demonstrating how the apparently peripheral fact that a third member has been added to a group of two opens up possibilities for actions and processes that could not otherwise have come into existence. He uncovers the new properties that emerge from the forms of association among individuals, properties that cannot be derived from characteristics of the individuals involved. The triad provides new avenues of social action while at the same time it restricts other opportunities, such as the expression of individuality, which were available in the dyadic group.
Simmel does not restrict his analysis of numbers to the dyad and triad. Although it is not possible to demonstrate that each addition of new members would produce a distinct sociological entity, he shows that there is a crucial difference between small groups and larger ones.
In small groups, members typically have a chance to interact directly with one another; once the group exceeds a relatively limited size, such interaction must be mediated through formal arrangements. In order to come to grips with the increasing complexity of relationships among large numbers of individuals, the group must create special organs to help the patterning of interactions among its members. Thus, no large group can function without the creation of offices, the differentiation of status positions, and the delegation of tasks and responsibilities. This is the reason larger groups become societies of unequals: in order to maintain themselves, they must be structurally differentiated. But this means that the larger group "gains its unity, which finds expression in the group organs and political notions and ideals, only at the price of a great distance between all of these structures and the individual."
The smaller the group, the greater the involvement of its members, for interaction among a few tends to be more intense than interaction among many, if only because of the greater frequency of contact. Inversely, the larger the group, the weaker the participation of its members; chances are high that they will be involved with only a segment of their personalities instead of as whole human beings. The larger group demands less of its members, and also creates "objective" structures that confront individuals with superpersonal powers: "For it is this large number which paralyzes the individual element and which causes the general element to emerge at such a distance from it that it seems that it could exits by itself, without any individuals, to whom in fact it often enough is antagonistic."
Although through its formal arrangement the larger group confronts the individual with a distant and alien power, it liberates him from close control and scrutiny precisely because it creates greater distance among its members. In the dyad, the immediacy of the we is not yet marred by the intrusion of structural constraints, and, it will be remembered, in the triad two members may constrain the third and force their will upon him. In the small group, however, the coalitions and majorities that act to constrain individual action are mitigated by the immediacy of participation. In the large group, the differentiated organs constrain the individual through their "objective" powers, even though they allow freedom from the group through segmental rather than total involvement.
Simmel's discussion of the differences between small and large groups--between the intensity of involvement among individuals in the primary group and the distance, aloofness, and segmentation of individuals in larger groups--reveals his general dialectical approach to the relation between individual freedom and group structure. His minute sociological analysis is part of his general philosophical view of the drift of modern history. Like Durkheim, Simmel theorizes about types and properties of group relations and social solidarities as part of a more general endeavor to assess and evaluate the major trends of historical development and to elaborate a diagnosis of his time.
From Coser, 1977:186-189.