On Thu, Sep 21, 2000 at 09:46:41PM -0700, Marcus Smith wrote: [snip] > 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. :-) [snip] 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 :-) T