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

Mathematical models and methods 573
(with grammatical theory). However, the reader will note the importance of the
renewal in economic theory brought about by the development of the theories
of games and of decision-making, by cybernetics, by simulation, etc. Recourse
to these new instruments has forced the economist to think out ph,enomena in
terms of parameters and systems of variables. The result has been a formulation
of economic theory which makes it better fitted-for collation with the factual
realities.
In sociology inductive methods are mathematically less developed than in
econometrics, and, above all, less unified, but research in: the field is ‘live’
and abundant. Three categories of research can be distinguished of which the
first deals with the general methods applicable to the analysis of sociological
surveys. On certain points these methods are absolutely similar to those of eco-
nometrics on the one hand and of psychometrics on the other.46
However the fact that the sociologist for the most part collects his basic data
though surveys rather than from among administrative statistics, gives him
greater freedom than the economist to ‘tailor’ his data-collection to fit the
problem. Thus, it is no coincidence that the development of mathematical meth-
ods in sociology accompanied that of complex forms of survey, like contextual
surveys (those assuming several stages of sampling, for instance a sample of
secondary education institutions, of classes in these institutions and of students
in these classes) or panel surveys (those carried out several times on the same
sample).
The third point to stress is the increasing interest of sociologists in simulation
methods enabling models to be constructed to represent hypotheses which are
relatively complex and hence difficult to analyse by deductive methods.
IV. THE FUTURE
Obviously it is not possible to give a clear picture of what the applications of
mathematical methods wil be in the social sciences in twenty or even ten years
time: the recent history of such applications shows several examples of relatively
brusque breakthroughs. Now, the final factors in determining the development
of an effective methodology are above all the relatively unforeseeable discoveries
which have radically changed the course of research in this or that domain,
whether it be the work of Cournot, Walras and Pareto in economics, or of LBvi-
Strauss in ethnology, of Chomsky in linguistics, or of Estes or Piaget in psychol-
ogy, to give but a few examples. The most that can be forecast is the growth and
acuity of certain needs; thus one can foresee the urgency of developing the ap-
plications of stochastic process theory to social phenomena.
Nevertheless, certain factors whose action can be expected to persist and
increase in the years to come, give an indication of the lines of force operative
in the development of a mathematical methodology in the sciences of man.
These factors are:
I. A gaggle of technological inducements (whether translating machines, com-
puters, or the technical development of actual mathematics);