Re: [FRIAM] Complex Numbers .. the end of the line?

es > for prep and lecture time. Its a beautiful subject with a very colorful > history, and includes the quaternions, octonians, Lie algebras, Jordan > algebras, associative algebras, everything mentioned by the FRIAM > commentariat. > > ** ** > > Regards- Dean Gerbe

Re: [FRIAM] Complex Numbers .. the end of the line?

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 for interesting algebras not yet considered?" Yes

Re: [FRIAM] Complex Numbers .. the end of the line?

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 intima

Re: [FRIAM] Complex Numbers .. the end of the line?

M commentariat. Regards- Dean Gerber 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

Re: [FRIAM] Complex Numbers .. the end of the line?

This is *way *outside my area of competence -- to the extent that I still have one -- but I remember reading about Conway's Surreal numbers, which may be of interest. *-- Russ* On Tue, Jan 24, 2012 at 10:21 AM, Joshua Thorp wrote: > Thanks Roger, in

Re: [FRIAM] Complex Numbers .. the end of the line?

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: > http://geocalc.clas.asu.edu/pdf/OerstedMedalLectur

Re: [FRIAM] Complex Numbers .. the end of the line?

Complexity Coffee Group Subject: Re: [FRIAM] Complex Numbers .. the end of the line? 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

Re: [FRIAM] Complex Numbers .. the end of the line?

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 mu

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 out of steam! Roger Critchlow: > http://geocalc.clas.asu.edu/pdf/OerstedMedalLecture.pdf > Now t

Re: [FRIAM] Complex Numbers .. the end of the line?

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 Alge

Re: [FRIAM] Complex Numbers .. the end of the line?

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 unsati

Re: [FRIAM] Complex Numbers .. the end of the line?

http://geocalc.clas.asu.edu/pdf/OerstedMedalLecture.pdf -- rec -- On Mon, Jan 23, 2012 at 5:38 PM, Owen Densmore wrote: > 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.

Re: [FRIAM] Complex Numbers .. the end of the line?

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 wh

Re: [FRIAM] Complex Numbers .. the end of the line?

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 consi

[FRIAM] Complex Numbers .. the end of the line?

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 c