Roger Cooke wrote:
> In my view, the Greeks added something that no one else did, not just
> deduction, but...
> I have the highest admiration for those who achieved so much with
> intuition alone. But, fascinating as "ethnomathematics" is, you can't
> do quantum mechanics or relativity with it.
and Ralph A. Raimi wrote
>Now: What do you say to those who say quantum mechanics and
>relativity are themselves culturally determined constructs, no more valid
>for Haitians than Voodoo for New Yorkers? (Cf. Gross and Levitt, *Higher
>Superstition*).
This sort of idea, which I believe falls under the heading of Cultural
Relativism, has many proponents, but is, in my view, nonsense.
A television (whose design relies on the theory of quantum mechanics)
works. It works for someone from Haiti (whether or not they watch it) as
much as for someone from New York. It works in the sense that it does the
job it was designed to do, and this is independent of the culture in which
it is used. Similarly, to repeat an example frequently used by Richard
Dawkins, even people who support the thesis that modern scientific theories
are culturally determined fly on aeroplanes, machines that are a product of
precisely those theories. Aeroplanes work, period.
Now as far as mathematics is concerned, things are less clear cut.
Nevertheless it is true that modern mathematics does a remarkably good job
of providing answers to questions about the world around us, and it is for
precisely this reason that mathematics has developed as it has. Individuals
may work in mathematics for a wide variety of reasons, but the driving
force behind the creation of what we now recognize as mathematics has
always been its success in providing answers to questions about the world
around us.
The reason that Greek mathematics has been so influential in shaping modern
mathematics is that when it came along, the power of mathematics to answer
questions about the world we live in greatly increased. So I would argue
that the mathematics we use today works, just like an aeroplane or a TV. It
does the job it was designed to do. (And we are forever trying to refine it
so that it does the job that little bit better.)
It is true that a mathematics that developed differently might be able to
answer the same questions, but mathematics didn't develop differently and
this is the strongest evidence there is for our sort of mathematics being
the *real* thing. This may seem scant evidence to some, but there is no
evidence at all for the existence of an alternative, equally successful,
mathematics.
Chris Linton
****************************************************************
* Chris Linton * Tel: 01509-223482 *
* Department of Mathematical Sciences * Fax: 01509-223969 *
* Loughborough University * E-mail: *
* Leicestershire LE11 3TU * C.M.Linton@lboro.ac.uk *
****************************************************************
* WWW --> http://macml-mac.lboro.ac.uk/CML.html *
****************************************************************