NUMERICAL RELATIONS OF SOCIAL FORMS 129
the group. In that case the size immediately determines
the form.!
Definite correlations between characteristic sociological
 formations and arithmetically definable magnitudes
appear only near the lower boundary of the numerical
series. Higher up in the scale such a definite mathematical
formulation is not possible, and the modifications must be
formulated in terms of more or less. More precisely, however,
 the situation is this. To every definite number of elements
 there correspond, in accordance with the purpose
and the spirit of their association, a specific sociological
form, a characteristic organization, and a definite degree
of firmness of texture. With every added or subtracted element
 these experience a modification, however small and
indeterminable. There are, however, no special terms for
these different sociological conditions, even in a case where
the differences can be observed. This forces us to describe
the situation as if it were a combination of two conditions
with the one more, the other less conspicuous.
The Monad

The simplest structure which may be subsumed under
the sociological category is the single individual, however
paradoxical and essentially contradictory it may seem.
The two phenomena, isolation and freedom, which appear
in relation to the individual are distinctly of a sociological
character. Not only are they characteristic of the relation
between the individual and the group, but the amount of
freedom and isolation which the group allows the individual
 elements is immediately significant for the structure of
the whole.
The mere fact that an individual maintains no reciprocal
 relationships with other individuals is. of course. not

' Soz., p. 47.