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

Mathematical models and methods 535
predict the subsequent course of the process. The fact that the process can be
expressed by a third degree polynomial is simply accepted without attempting
to deduce it from the nature of the phenomenon.
Examples of this tradition are Gannet’s work in demography, that of Schultz
in economics, or some of Quktelet’s work in sociology. Here, as elsewhere,
demography, economics and sociology have often found guidance and inspiration
in biology where, indeed, we find a particularly rich tradition of curvefitting
to observed data, down to about the 1910-1920 decade, especially in
epidemiology. There is, for instance, the work of Evans, published in 1875, on
the smallpox epidemic of IS~I-1872, or that of Brownlee who in 1906 carried
out systematic experiments in fitting Pearson curves to epidemiological phenomena
of various kinds. From 1920 onwards, this tradition, which all in all had
not been brilliantly successful, became relatively outmoded and epidemiology
returned to the tradition of analytical models made famous by Verhulst pending
a massive switch to stochastic models.
Things followed the same course in demography, economics and sociology:
curve-fitting-had always been regarded as a make-shift which needed to be outgrown.
Be it noted, however, that it still has a r61e in sciences like economics or
demography, which use curve-fitting techniques for prediction purposes. In
many instances, when no way is known of constructing a more efficacious
theoretical model, empirical curve-fitting to a data series is the least unsatisfactory
means available for predicting the evolution of a phenomenon.
It should, however, be observed that the wide currency of this approach is
not due solely to its facility. It also comes from the influence exerted on the
human and social sciences by the triumphs of physics. Hypnotized by the pattern
of Newtonian physics, the human and social sciences long believed that in
the domain of human phenomena, as in that of physics, there were general laws
to be discovered whose formulae it was important to lay bare. In social psychology,
for instance, this is illustrated by the work of Tarde, who thought that in
‘geometrical progression’ he had the universal law of imitation phenomena. It is
also no coincidence that the first applications of mathematical methods to
psychological problems issued in a law which was thought no less universal than
the law of gravity: namely the Weber-Fechner law.
The seminal r6le of the Newtonian model can be seen in all these experiments.
In most cases, statistical regularities or regular patterns in experimental data
are analysed by methods which are imagined to be analogous to those of the
physicist: the researcher wants to reduce them to rigid laws. The attempt which
best illustrates the influence of Newtonian physics is Haret’s curious book, La
mdcanique sociale, published in Paris in 1910, which attempted nothing less
than the rigourous application of classical mechanics to the analysis of social
phenomena.
It was important to recall these three main trends into which the earliest
applications of mathematics to the human and social sciences became split,
firstly for a better appraisal of the progress made since then, and secondly because
the three trends, while losing their sharp differentiation, still persist and
are still imperfectly reconciled. Thus the sociology of the phenomena of popu-