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

Mathematical models and methods 531
recourse by economists to algebraic methods, mostly elementary, as in the work
of Canard in France or Whewell in England.' However Cournot's example long
remained unfollowed and criticized, and accordingly it is perhaps more prudent
to date the birth of mathematical economics from the work of the Lausanne
School of the 1870s which is associated with the name of Walras and Pareto.
With these two and Marshall in England we get the start of a tradition which was
indeed to be widely criticized until a recent date but was to prove viable.
It is perhaps even more difficult to date the emergence of a mathematical
methodology in demography, inasmuch as this discipline, since its beginnings,
has run in double harness with biology. In point of fact the work of men like
Verhulst, who formulated the logistic law, Poisson, who gave his name to a
law basic to the analysis of rare events (like accidental death), Bortkiewicz,
QuCtelet, Lexis and others, most often stemmed from consideration of the
statistical data supplied by demography. But it is more correct to say that since
the work of Laplace there has been a tradition of research into typical statistical
distributions, and that its pabulum has been statistical data drawn, indeed,
from demography, but also from biology and sociology. For the work of these
savants brings in not only vital and accident,but also epidemiological and crime
statistics.
What is certain is that demography and economics were the first of the human
sciences to use mathematical methods in a systematic way.
They were followed by psychology. Although in fact there was some use of
mathematical methods in this discipline as early as the last years of the nine-
teenth century, the instances are few, and the mathematics rudimentary:
Weber-Fechner's law is perhaps the only example worth remembering in the
nineteenth century. It should indeed be conceded that this law can be regarded
as the first instance of a scientific tradition with which the names of Spearman and
Thurstone are associated. In fact the first problem sector which elicited a corpus
of cumulative mathematical researches was the mensurational, beginning with
psycho-physical measurement and going on to psychological measurement
thereafter. In this sense, Fechner and Spearman, who wrote his fundamental
article in 1904," may be considered to be the precursors of the mathematical
theory of measurement in psychology. This theory may be regarded as finally
established from the time of Thurstone's work on these problems between 1920
and 1930, and the foundation of the Psychometric Society in 1935.
As the theory of economic equilibrium long dominated mathematical eco-
nomics, so the theory of tests and psychometrics long remained the only branch
of psychology where mathematical research really took hold. Thus it was not
fortuitous that most work in mathematical psychology was until recently pub-
lished in the review Psychornetuika, the journal of the Psychometric Society.
Sociology is undoubtedly the discipline which w2s most grudging in accepting
the use of mathematical methods. But here as in other disciplines, we have a
multitude of studies dating back to the nineteenth and even the eighteenth cen-
tury. Buffon's moral arithmetic and Condorcet's research on vote-counting
operations have already been mentioned. There are also Laplace's researches on
the applications of probability calculus to the decisions of legislative assemblies