Re: Numbers and math

On Thu, Sep 21, 2000 at 11:17:17PM -0400, Yoon Ha Lee wrote:
[snip]
> <puzzled look>  A flock of geese, a herd of horses, a murder of crows...I
> suspect it isn't *that* revolutionary, though it is in some sense neat.
> You could consider things like "flocks" and "herds" isomorphic to
> integral, independent vector subspaces.
Well, I was more referring to the example of owning negative X bowls
meaning *owing* somebody X bowls. Using a physical analogy, negative X
steps forward = X steps backwards. This is where directions come in:
"negative X" can be understood to be the same as X but in a different
direction. But since our universe isn't 1-dimensional, there are many
other possible directions.

So, now if you grammaticize the two pieces of information (X,direction),
then you have a vector-based number system. The native speakers may not
grasp the concept of negativity, but they would be able to grasp the
concept of numbers in different directions.

Now, take this one step further -- combining these directional numbers
(integral vectors, if you will) with each other, perhaps in simple
combinations like Pythagorean triangles, and you have a culture that
understands vectors but not negative numbers. Hmmm.... :-)

> In your example, any vector space isomorphic to the complex plane, like
> Euclidean two-space, would do just fine.  :-p
Yep. That's right. I used complex numbers 'cos it sounds more impressive
:-P

> And what does it mean to "understand" negative numbers?  Or to
> "understand" complex numbers?  This isn't a trivial question!  <G>
Perhaps claiming that they "understand" complex numbers is a bit
far-fetched. But if a culture has different words for numbers depending on
their direction -- e.g. 2-north is represented by a different word from
2-west, and so on for each integer number -- then one might ask, "so what
is 1-north plus 4-east?" This could lead to the development of directional
quantities (vectors) *before* the development of negative numbers and the
like.

Hmm, should be an interesting concultural issue to consider... :-)
But the idea of using different words for quantities in different
directions just appeal to me... perhaps that's what I should do in my
conlang! :-)

> And in physics, negative acceleration = deceleration.
Exactly.

> YHL the math major, alas
Alas??? I find math to be very enlightening in learning different ways to
think about things. I especially appreciate the courses I took on number
theory and set theory.

Set theory is really neat because you get right down to the roots of it
all, and have to deal with very fundamental issues such as vacuously true
predicates, existence, incompleteness, etc.. In more "practical" math,
such issues are often swept under the rug ("Assuming that X exists, the
theorem says Y is true"). But in set theory, there is no rug to sweep
things under -- you gotta deal with many apparently obvious statements and
make sure there are no holes in your arguments.

Anyway, I really should try to keep off-topic stuff off-list now, so I
better stop here :-)


T