Re: Polysign numbers Was: Give wedge products the wedgie they deserve
- From: amy666 <tommy1729@xxxxxxxxxxx>
- Date: Sun, 10 Aug 2008 18:21:52 EDT
Edward Green wrote :
On Aug 7, 9:38 am, "Timothy Golden
BandTechnology.com"
<tttppp...@xxxxxxxxx> wrote:
http://bandtechnology.com/PolySigned
Hmm... Ok. Some interesting history:
http://en.wikipedia.org/wiki/Negative_and_non-negative
_numbers
"In Hellenistic Egypt, Diophantus in the third
century A.D. referred
to an equation that was equivalent to 4x + 20 = 0
(which has a
negative solution) in Arithmetica, saying that the
equation was
absurd."
"In the 15th century, Nicolas Chuquet, a Frenchman,
used negative
numbers as exponents and referred to them as 'absurd
numbers'. "
http://en.wikipedia.org/wiki/Imaginary_number
"Imaginary numbers were defined in 1572 by Rafael
Bombelli. At the
time, such numbers were thought not to exist, much as
zero and the
negative numbers were regarded by some as fictitious
or useless.
http://en.wikipedia.org/wiki/Quaternion
"In mathematics, quaternions are a non-commutative
extension of
complex numbers. They were first described by the
Irish mathematician
Sir William Rowan Hamilton".
http://en.wikipedia.org/wiki/Surreal_numbers
"In mathematics, surreal numbers are the elements of
a field[1]
containing the real numbers as well as infinite and
infinitesimal
numbers, respectively larger or smaller in absolute
value than any
positive real number, and therefore the surreals are
algebraically
similar to superreal numbers and hyperreal numbers".
So, once upon a time, we only had positive numbers,
and then we had
negative numbers, and then... well, the rest is
history (and
undoubtedly incomplete history in this post). Now,
you are proposing
to add to the list with "polysign" numbers, by
extending the list of
signs beyond "+" and "-". Bravo! It is the genius
-- or the
pathology -- of mathematics to look at a given
structure and ask what
would happen if we relaxed this, or added that.
Your disdain for the work of Grassmann and Clifford,
which takes
something of the same flavor as the early skepticism
for negative, and
later imaginary numbers (by the time we got the
quaternions, I guess
people were inured to the fancy of mathematicians) is
possibly ironic,
since you want to introduce yet another flavor of
number system, or
algebraic system, to the menu. :-)
for any questions about the polysigned , you may ask me.
i have had much contact with timothy golden and supported his polysigned and other projects of him / us.
( on his website you will find other thoughts apart from polysigned , which are the result of our talks on sci.math and our e-mail traffic )
note however that in a way his idea is not totally new ; although no negative exists , one could see n-signed as vectors in n-space starting at the origin ...
perhaps also intresting to you is the ' object convulation ' or ' minkowski products ' on his site , which is a consequence of me talking to him.
( i claim credit , but on the other hand minkowski was actually the first of course )
we are still looking for closed form solutions for minkowski products in P3 and P4 !!
nice to see someone intresting in polysigned again here on sci.math.
regards
tommy1729
.
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