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

Mathematical models and methods 543
problems of group dynamics, and in a more general way for the analysis of
organizations' and of the processes of social diffusion and migration. One of
the most highly mathematicized fields in these disciplines is that of small-
group research, on which there have been several joint publicationss in recent
years. There is also mathematical research into the development of sociological
survey data.Q
In linguistics, the development of mathematical methods is of particular
importance. Initially the dominant branch of structural linguistics was structural
phonology. Here, the shift towards a mathematical methodology has only
developed quite recently and the methods used by researchers like Trubetzkoy,
Roman Jakobson or Andre Martinet are not properly mathematical. The
notable development of mathematical methods in linguistics dates mainly from
Chomsky's research on the theory of grammars. This theory which began as an
outcome of reflexions on the grammatical structure of natural languages, later
engendered a theory of grammars of a more general type, which is, in effect, a
full fledged branch of mathematics.
The mathematical interest of the theory of grammars is all the greater for its
being susceptible of translation into the language of the mathematical theory of
abstract automata, so that well-determined classes of grammars can be repre-
sented by well-defined automata. As a result the situation of the two theories
today is one of interdependence and fecund interaction.
But grammar is not the only field in linguistics where recourse to a
mathematical methodology has increased considerably. Phonological problems
are also beginning lo be handled mathematically.
It should be noted that the considerable development of mathematical lin-
guistics is largely due to the growth of interest in mechanical translation: an
ideal translating machine - at present non-existent - would be one capable of
getting behind the varieties of an utterance's formulation to lay bare its struc-
ture.I0
In anthropology, one field, that of kinship structure analysis already men-
tioned in the preceding section, now largely depends on a mathematical method-
ology. Here the initial stimulation comes from the work of Lkvi-Strauss which
has inspired a whole series of mathematical models, notably by Andre Weil,
Robert S. Bush and Harrison Whyte."
Outside these research fields associated with specific disciplines, there are
other groups of problems notable for a considerable extension of the use of
mathematical methods and models. The most important of these groups is un-
doubtedly that of the decision-making and action problems where game theory
has been a potent revitalizing factor. The discoveries of game theory although
- at present - they seem primarily applicable to economic problems, obviously
provide a common capital available to all the sciences which analyse human
action and decision in competitive situations.
Along with game theory, there is the considerable development of statistical
methods. While this arises from the growing requirements primarily of econo-
metrics, and secondarily of psychometrics, it is, of course, a gain for the totality
of the social and human sciences.