Main trends of research in the social and human ... - unesdoc - Unesco

XLII Samy Friedman
era1 description of the mathematics used in the early days of the social sciences
and then on defining the most striking present-day applications. The initial
investigation is of more than merely historical interest. It shows up trends that
are still to be found in science. Game theory, for example, may go back to
Buffon’s work on moral arithmetic; Condorcet’s studies on vote-counting
forshadow modem operational research; Verhulst anticipated the theories on the
spread of epidemics; and the ‘curve-fitting’ tradition is still used for forecasting
in demography as well as in economics or sociology. The author is,
however, particularly concerned with the more up-to-date aspects of mathematics
as applied to the social sciences when he draws attention to the amazing
flood of works (Luce and Bush in psychology, Lazarsfeld and Coleman in sociology,
Alker in political science, as well as those inspired by Kemeny and Snell,
etc.) which have appeared in the scientific field since 1960, and which emphasize
the growing diversification of the uses of mathematics in the social sciences. New
fields of research, in social psychology with measurement theories, in linguistics
with Chomsky’s mathematics, in economics with game theory, in anthropology
with the analysis of kinship structures, etc., bear witness to the vitality of
these new approaches. At the same time, new mathematics are developing:
higher, especially linear, algebra, with Leontieff matrices in &onomics; the stochastic
process theory with Markov chains; Koenig and Berge’s graph theory
which is frequently applied in the analysis of social structures ; simulation
methods successfully used in demography, economics and political sociology
for dealing with the problems of election forecasting, etc. ‘Two forms of naivetd’
are thus increasingly being put aside. The first consists in the belief that, for
some obscure reason, human phenomena cannot be treated mathematically,
which may be considered in conjunction with the similar cautious attitude
towards the application of experimental methods to human phenomena, which
has for a long time held up progress. The second consists in believing that a
language devised for the natural sciences can be directly applied to the social
sciences. In fact, the social sciences require a language of their own, which is
now coming into being through the development of models and the notion of
structure. For these sciences, ‘... it is more often a matter of inventing new
mathematical methods than applying existing ones . .’.
The chapter ends with a description of the models and methods used in the
social sciences; the classification - into theoretical, descriptive and inductive
models - may perhaps be arbitrary, but there are epistemological considerations
behind it. At any rate, it has the great advantage of providing many examples
of the practical uses to which these instruments are put.
The author concludes on a fairly optimistic note. There are many factors -
not least of which is the growing interest of mathematicians in the social
sciences - conducive to the development of mathematical methodology in those
sciences. In spite of limitations which may prove difficult to overcome, mathe-
matical treatment will become increasingly common in the social sciences. There
is no certainty, however, that this will, at least in the near future, result directly
in closer relations between them, not to say uniiication, since the differences are
still so great.