NUMBER AS DETERMINIMG FORM OF GROUP 45
manifoldly two combined individuals accomplish more than two that are isolated, yet the decisive factor in this case is that each must actually perform something, and that, when he refuses to do this, only the other remains, without any superindividual energy such as, even in the case of a combination of only three, is in some measure present. The significance of this detail resides, however, by no means merely in the negative, in that which it excludes ; from it grows rather a close and special modu- lation of the union of two. Precisely the fact that each knows he can depend only upon the other, and upon nobody else, gives to such a combination for example, marriage, friendship, and even more external combinations up to political adjustment of two groups a special consecration ; each element in them is, in respect to its sociological destiny and everything dependent upon this, much more frequently made to confront the alterna- tive of all or nothing than in other associations. This peculiar intimacy appears most simply in the contrast between it and combinations of three. In such a case each individual element operates as a court of appeal between the two others, and exhibits the double function of such an organ. It operates both in combining and separating. Where three elements, A, B, C, constitute a community, there is added to the immediate rela- tionship which exists, for example, between A and B, the imme- diate relationship which they gain by their common relation to C. This is unquestionably a sociological enrichment, apart from the bond by the straight and shortest line ; each pair of elements are now joined by a broken line. Points upon which the pair could find no immediate contact are put in reciprocal relation- ship by the third element, which offers to each another side, and joins these, nevertheless, in the unity of its personality. Separa- tions which the parties could not of themselves reconcile are accommodated by the third, or by their being included in a com- prehensive whole. On the other hand, the direct union is not merely strengthened by the indirect, but it may also be destroyed. There is no relationship so complete between three that each individual may not, under certain circumstances, be regarded by the other two as an intruder, even if it is only to the extent of
