> 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.
Hmmm... you can't do quantum mechanics with Greek mathematics either
because it had no negative numbers (in fact, even Aristotle argues for
quantities to represent only "real" measures). Oddly enough, it was
Indian mathematics that had the earliest written use of negative
numbers. What does this do for your views on "ethnomathematics"? There
is more to this issue than simply counting fingers and toes in different
order.
> Airplanes are perhaps too mechanical an invention to make the point.
> People have some experience of the action of wind and motion that
> makes it at least possible to build an airplane in your garage, as
> indeed the Wright brothers nearly did.
>
> A better example is radio. It could never have been invented by people
> just tinkering around. It was the experiments of Faraday, Ohm, Oersted,
> and others, put together into a theory by Maxwell, and experimentally
> tested by Hertz, that inspired Marconi and other to undertake its
> development. Say what you will, it DOES work, and it led to television
> and a whole electronics industry for which a non-scientific world-view
> has no explanation of any kind.
<sound of jaw dropping to the floor>
...and none of this work would have been possible without someone decidedly
not mathematically oriented (was his given name Benjamin by any chance?)
coming up with a useful NONMATHEMATICAL (and, no, I'm not shouting) metaphor
for electricity. If we still used Aristotelian interpretation of physics,
this discussion would not have been possible (or would have taken much
longer to exchange the clay tablets...er...scrolls :-) Look, any example
you cite along these lines will be bad. Period. It is not possible to
trace any invention to a narrow culturally-specific idea. Much of modern
mathematics is due to the merger of Indian, Babylonian and Greek ideas in
Arabic mathematics. The claim that Greek axiomatic view came to dominate
mathematics on its own sounds silly to me. There is a difference between
"dogmatic" and "axiomatic".
VS-)