> Roger Cooke wrote:
>
> > I don't see how we
> > would ever have arrived at non-Euclidean geometry from any other point
> > of view.
>
> I would say only that we _didn't_ arrive at non-Euclidean geometry from
> any other point of view.
>
I thought the point of the discussion was to see whether axiomatization
contributed anything to the understanding of the world, something not
present in intuition alone. If we are going to refer vaguely to
possibilities without any specifics and use that as a reason for not
drawing any conclusion, well, fine. No point in discussing anything in
that case.
> Apart from the possibility of other routes or destinations, though, I want
> to simply ask whether it is legitimate or fruitful (or fair) to privilege
> those traditions that look like our own as though they were somehow
> 'superior' to traditions which don't look like ours. It _is_ true that
> you can't do quantum mechanics with ethnomathematics. But you can't weave
> a decent basket with quantum mechanics either.
>
> I wonder which is more useful in my day to day life...
>
> -Daryn
>
That's right. All the most important things needed for human survival
are low-tech things that don't require any particular intelligence. The
human race would never have survived if they weren't. The purpose of
exercising the rational faculties is not to keep people amused or make
their lives easier. It is to feed the understanding. I'm sure most of
the great mathematicians of this century would have been terrible bus
drivers, too....