Maths/Causes/Theories/Public (long and d

Wed, 3 May 1995 10:21:00 PDT

Enkerli has provided a very nice discussion of the kind of role that
mathematics can play in anthropology.

"...there is a distinction to be made between two
aspects of math in relation to research in Social Sciences. One is the
actual application of mathematical methods and the other can be thought of
more as a general viewpoint on reality, a special logical configuration
that can be influent on research... I don't think that numbers can prove
anything about society or discover anything totally new. But it can help,
sometimes, to get a new picture, to change the angle by which you view your
data.... we have...the other aspect of the relation between mathematical
methods and research in Social Sciences. And I announce: "general viewpoint
on reality".... This is not to say there's only one way to achieve the
development of a truly original way of thinking about reality or even that
there is one. But mathematical concepts can be a part of the process aiming
at this achievement."

If we look at a discipline such as physics, mathematics has gone from methods
used to model reality to being the means to express reality. That is,
mathematics has gone from being an auxiliary to theorizing to being the means
by which theorizing takes place through mathematics in certain areas being
the only means to represent reality.

Enkerli draws our attention, as have others, to the potential role that
mathematics can play in how we think and theorize about reality.
Levi-Strauss recognized this role in his structural framework and refers to
the needed integration of mathematical thinking. This second role that
Enkerli discusses is not, in my experience, a very well understood idea. In
my experience, to most people mathematics means numbers and possibly methods
(as Enkerli discusses in the first part of his memo). But this has little to
do with what mathematics is about. Mathematics is, foremost, a discipline
involved with reasoning and drawing out the logical consequences of a
hypothetical situation. To put it in more anthropological terms, if the
local "universe" defined by such and such groups' cultural constructs frames
for them how they are to understand, react to and act as individuals, what
are the implications that can be derived with regard to the logic of those
concepts? Here the logic refers not to behavior, per se, but to the logic of
the cultural universe that has been constructed. The Tiwi, for example (to
use an example from a course I teach on Hunters and Gatherers) have a very
complex (from our perspective) system of marriage, social groupings and the
like that begin to make sense when we consider the logic of their concepts
and how constructs in one area (e.g., division simultaneously into
patrilineally defined moities and matrilineally defined moities) seem to
arise out of the logic of another area (their kinship terminology).

As important as the role of mathematics as providing method may be, it is in
this second role that mathematics can play a far more significant, and far
more consequential role in our attempts to make sense of what we are about as
a species.

D. Read