On Thu, Sep 21, 2000 at 09:46:41PM -0700, Marcus Smith wrote:
> That comment on negative numbers -- that's the way I actually do think of
> them.  Seems valid to me, since you can't have negative distances, you
> can't hold negative amounts, you can't move at negative speeds -- they are
> just some abstract place holder to show that things are not going in the
> same direction as the focus of your inquiry.

Exactly!! That's what's so revolutionary about your statement. Negativity
exists simply because numbers have a different direction than what you're
looking at. A more interesting question might be, is negativity unique?
i.e., why must it be exactly opposite of positive numbers? Why can't it be
some other angle? ...

>  And don't get me started on
> imaginary numbers!  ;-)  (Actually, I quite like them -- very fun.)

Imaginary numbers are very interesting from a mathematical point of view
as well -- they are closed under every basic mathematical operation --
addition/subtraction, multiplication/division, exponentiation/logarithm.
In a sense, you can think of imaginary (complex) numbers as the "ultimate"
closure of numbers under these operations.

> Must be why I'm a linguist rather than a mathematician.  :-)

You sound like you *should* be a mathematician. The way you interpret
things like negativity could open up a totally new way to look at math :-)