The Significance of Numbers for Social Life

Simmel's emphasis onthe structural determinants of social action is perhaps best exemplifiedin his seminal essay, "Quantitative Aspects of the Group." Here hecomes nearest to realizing his goal of writing a grammar of social lifeby considering one of the most abstract characteristics of a group: themere number of its participants. He examines forms of group process andstructural arrangement insofar as these derive from sheer quantitativerelationships.

A dyadic relationship differs qualitatively fromall other types of groups in that each of the two participants isconfronted by only one another and not by a collectivity. Because thistype of group depends only on two participants, the withdrawal of onewould destroy the whole: "A dyad depends on each of its two elementsalone--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 thatsuperpersonal life which, in all other groups, creates among its membersa sense of constraint. Yet the very lack of superpersonal structurealso entails intense absorption of the participants in their dyadicrelationship. The dependence of the whole on each partner is obvious;in all other groups duties and responsibilities can be delegated, butnot in the dyad, where each participant is immediately and directlyresponsible for any collective action. Because each partner in the dyaddeals with only one other individual, who forms a unit with him, neitherof the two can deny responsibility by shifting it to the group; neithercan hold the group responsible for what he has done or failed to do.

When a dyad is formed into a triad, the apparently insignificant factthat one member has been added actually brings about a major qualitativechange. In the triad, as in all associations involving more than twopersons, the individual participant is confronted with the possibilityof being outvoted by a majority.

The triad is the simpleststructure in which the group as a whole can achieve domination over itscomponent members; it provides a social framework that allows theconstraining of individual participants for collective purposes. Thedyad relies on immediate reciprocity, but the triad can impose its willupon one member through the formation of a coalition between the twoothers. Thus, the triad exhibits in its simplest form the sociologicaldrama that informs all social life: the dialectic of freedom andconstraint, of autonomy and heteronomy.

When a third memberenters a dyadic group, various processes become possible wherepreviously they could not take place. Simmel singled out three suchprocesses, although others have since been identified. A third membermay play the role of mediator vis-a-vis the other two, helping, throughhis own impartiality, to moderate passions that threaten to tear thegroup apart. He may, alternately, act as a tertius gaudens (thethird who rejoices), seeking to turn to his own advantage a disagreementbetween the other two. Finally, through a strategy of divide etimpera (divide and rule), he may intentionally created conflictsbetween the other two in order to attain a dominant position or othergains.

This brief outline of three types of strategy open to thethird participant can hardly exhaust the richness of Simmel's thought inthis analysis. He offers a great variety of examples, deliberatelycomparing intimate human involvements, such as the competition of twomen for one woman, with such large-scale events as the European balanceof power and the formation of coalitions among political parties. Hecompares the strategy of a mother-in-law who confronts a newly marriedcouple with the ways in which Rome, after subjugating Greece, dealt withAthens and Sparta.

It is a virtuoso performance, one of the morepersuasive demonstrations of the power of sociological analysis. Simmelreveals the sterility of total psychological reductionism bydemonstrating how the apparently peripheral fact that a third member hasbeen added to a group of two opens up possibilities for actions andprocesses that could not otherwise have come into existence. Heuncovers the new properties that emerge from the forms of associationamong individuals, properties that cannot be derived fromcharacteristics of the individuals involved. The triad provides newavenues of social action while at the same time it restricts otheropportunities, such as the expression of individuality, which wereavailable in the dyadic group.

Simmel does not restrict hisanalysis of numbers to the dyad and triad. Although it is not possibleto demonstrate that each addition of new members would produce adistinct sociological entity, he shows that there is a crucialdifference 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 mustbe mediated through formal arrangements. In order to come to grips withthe increasing complexity of relationships among large numbers ofindividuals, the group must create special organs to help the patterningof interactions among its members. Thus, no large group can functionwithout the creation of offices, the differentiation of statuspositions, and the delegation of tasks and responsibilities. This isthe reason larger groups become societies of unequals: in order tomaintain themselves, they must be structurally differentiated. But thismeans that the larger group "gains its unity, which finds expression inthe group organs and political notions and ideals, only at the price ofa great distance between all of these structures and the individual."

The smaller the group, the greater the involvement of its members, forinteraction among a few tends to be more intense than interaction amongmany, 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 theirpersonalities instead of as whole human beings. The larger groupdemands less of its members, and also creates "objective" structuresthat confront individuals with superpersonal powers: "For it is thislarge number which paralyzes the individual element and which causes thegeneral element to emerge at such a distance from it that it seems thatit could exits by itself, without any individuals, to whom in fact itoften enough is antagonistic."

Although through its formalarrangement the larger group confronts the individual with a distant andalien power, it liberates him from close control and scrutiny preciselybecause it creates greater distance among its members. In the dyad, theimmediacy of the we is not yet marred by the intrusion ofstructural constraints, and, it will be remembered, in the triad twomembers may constrain the third and force their will upon him. In thesmall group, however, the coalitions and majorities that act toconstrain individual action are mitigated by the immediacy ofparticipation. In the large group, the differentiated organs constrainthe individual through their "objective" powers, even though they allowfreedom from the group through segmental rather than total involvement.

Simmel's discussion of the differences between small and largegroups--between the intensity of involvement among individuals in theprimary group and the distance, aloofness, and segmentation ofindividuals in larger groups--reveals his general dialectical approachto the relation between individual freedom and group structure. Hisminute sociological analysis is part of his general philosophical viewof the drift of modern history. Like Durkheim, Simmel theorizes abouttypes and properties of group relations and social solidarities as partof a more general endeavor to assess and evaluate the major trends ofhistorical development and to elaborate a diagnosis of his time.

From Coser, 1977:186-189.

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