, 2012 9:34 AM
*To:* Complexity Coffee Group
*Subject:* Re: [FRIAM] Complex Numbers .. the end of the line?
Arlo:
...Would it not be better to say, are there number(data?)-structures
that provide for interesting algebras not yet considered?
Yes indeed. I was fumbling for a way to say that but ran
-boun...@redfish.com] *On
Behalf Of *Owen Densmore
*Sent:* Tuesday, January 24, 2012 9:34 AM
*To:* Complexity Coffee Group
*Subject:* Re: [FRIAM] Complex Numbers .. the end of the line?
** **
Arlo:
...Would it not be better to say, are there number(data?)-structures that
provide
On Jan 23, 2012, at 5:38 PM, Owen Densmore wrote:
The obvious question is what next? I.e. if we look at complex numbers at
2-tuples with a peculiar algebra, shouldn't we expect 3-tuples and more that
are needed for operations beyond polynomial equations?
The Fundamental Theorem of Algebra
Arlo:
...Would it not be better to say, are there number(data?)-structures that
provide for interesting algebras not yet considered?
Yes indeed. I was fumbling for a way to say that but ran out of steam!
Roger Critchlow:
http://geocalc.clas.asu.edu/pdf/OerstedMedalLecture.pdf
Now that is
This link to an Oersted Medal talk is indeed of great interest. The
author, the theoretical physicist David Hestenes, built on the
foundation laid by mathematicians in the 19th century and in an
important sense completed their work on what is called Geometric
Algebra, a framework which unifies
Thanks Roger, interesting paper.
I have always been fascinated at the relationship between the language of a
mathematics and corresponding science that can be described with it.
--joshua
On Jan 23, 2012, at 11:43 PM, Roger Critchlow wrote:
This is *way *outside my area of competence -- to the extent that I still
have one -- but I remember reading about Conway's Surreal
numbershttp://en.wikipedia.org/wiki/Surreal_number,
which may be of interest.
*-- Russ*
On Tue, Jan 24, 2012 at 10:21 AM, Joshua Thorp jth...@redfish.com wrote:
From: friam-boun...@redfish.com [mailto:friam-boun...@redfish.com] On Behalf
Of Owen Densmore
Sent: Tuesday, January 24, 2012 9:34 AM
To: Complexity Coffee Group
Subject: Re: [FRIAM] Complex Numbers .. the end of the line?
Arlo:
...Would it not be better to say, are there number(data
With only an intuitive, skating on soap bubble films, grasp, I still
enjoyed reading all these posts -- look forward to some kind of
computer interactive game learning process to convey the widest most
comprehensive framework to unify all these partial frameworks -- I
suspect it will have to
Integers, Rationals, Reals .. these scalars seemed to be enough for quite a
while. Addition, subtraction, multiplication, division all seemed to do
well in that domain.
But then came the embarrassing questions that involved the square root of
negative quantities and the brilliant invention of
Sadly, I am not going to answer your question, because I am still focussing
in my current education on vanilla complex number geometries anyway.
Instead, I am going to comment on are there higher order numbers beyond
complex needed for algebraic operations by emphasizing 'needed' - I always
Consider Baez on Octonions - talks about what the issues are. Beyond me
for now. Suspect you are about to pop out of algebra and end up
someplace else as interesting.
Carl
On 1/23/12 5:38 PM, Owen Densmore wrote:
Integers, Rationals, Reals .. these scalars seemed to be enough for
quite a
http://geocalc.clas.asu.edu/pdf/OerstedMedalLecture.pdf
-- rec --
On Mon, Jan 23, 2012 at 5:38 PM, Owen Densmore o...@backspaces.net wrote:
Integers, Rationals, Reals .. these scalars seemed to be enough for quite
a while. Addition, subtraction, multiplication, division all seemed to do
Actually, I can think of one application for which quaternions and such are
not enough: 3D fractals. I will have to find the thread on fractalforums.com,
but it describes the creation of the MandelBox and MandelBulb in accessible
language but technical detail, as the story of an artist being
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