Re: ConNumbers

Interesting!  I know that fuzzy systems mathematicians have worked out
perfectly usable systems of "fuzzy numbers," where "fuzzy one," "fuzzy
two," and "fuzzy three" and so on are actually graded categories with
peaks at the points we would call one, two, and three respectively,
and decreasing degree-of-membership curves as you move away from that.
 (For example, what we call the number "two" could be expressed in
such a system as either "fuzzy two to degree 100%" or "fuzzy one to
degree 20%" (or some similarly low number) or "fuzzy one hundred to
degree damn close to zero".

Of course, then you need standard numbers to mark the degree of
categorial membership, but you can fuzzify *those* numbers, and so on
recursively, so you *never* get nailed down to anything!

We have such numbers in our own natlang vocabulary, of course, but
they're derivative: "about four" or "four-ish" can be expressed as a
fuzzy set which has a membership curve that peaks to 100% at four, and
trails off in either direction.  The speed with which it trails off
would depend on context, of course.

So, yeah, such a system is conceivable, and kind of cool!

Ed Heil ------ edheil@postmark.net
--- http://purl.org/net/edheil ---

Chris Peters wrote:

> a la Tom Weir:
> >Here's a system I've never seen worked out, or even heard of:
> >a system based on pi, or e, or other irrational numbers like that.
> >Anyone want to take a crack at that?
>
>         It's possible, certainly, but is it practical?  I suppose
mathematically
> you could write base-pi numbers using only the digits 0, 1, 2 and 3, but
> what kind of crazy stuff would it give us?  I do see its mathematical
> application ... maybe a geometrically-inclined conculture would use it?
>         Along those lines, I recently read the book "Anvil of Stars" by
Greg Bear.
> He created an alien race he called "The Brothers" that used a really odd
> mathematical system like that.  They don't even have counting numbers like
> we do.  Instead they use "smears of probability" (to borrow Bear's phrase).
> It's certainly a good read ... Bear is quite a good author.
>
>
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