> On Thu, 5 Nov 1998, 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.
>
> 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.
How could you possibly imagine I was claiming you could do relativity or
quantum mechanics with just the mathematics known to the Greeks? Did I
not SAY that things like Hilbert space was involved?
Which of my views on ethnomathematics are you referring to? I expressed
my admiration for people who achieved so much without formal proof or
axioms to state explicitly. I would appreciate it if people didn't make
unjustified inferences from my words and accuse me of attributing
everything to the Greeks. All I said was that they made a unique
contributions, surely a modest claim.
> > 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-)
Again, what are you accusing me of saying? I never denied the
contributions of non-Greek sources to modern mathematics, and I never
would. Please clear your mind of the thought that I have said radio is
the result of theory ALONE. I specifically mentioned Faraday to include
the role of non-mathematical sources and the importance of experiment.
All I said (again a modest claim) is that the invention would not have
occurred if the possibility hadn't come out of Maxwell's theoretical
summary of all these results. And if you think you can explain how any
piece of modern laboratory equipment works without theory, YOU are wrong.
Period.
Roger Cooke