Re: on quaternions and octonions

From: John Baez (baez_at_galaxy.ucr.edu)
Date: 08/06/04 

Date: Fri, 6 Aug 2004 11:10:41 +0000 (UTC)

In article <40f95438.442470@news.ecn.ab.ca>,
John Savard <jsavard@excxn.aNOSPAMb.cdn.invalid> wrote:

>What I want to know is: when did mathematicians start getting away
>with calling Cayley's octaves "octonions", when that name had already
>been taken (preventing Cayley from using it)?

What are you claiming that name been taken for? Whatever it
was, it couldn't be nearly as important. :-)

By the way, Cayley wasn't the first to invent the octonions:
John Graves sent a letter to his friend Hamilton describing
them on December 26, 1843 - the same year Hamilton had discovered
the quaternions. He called them the "octaves" in this letter.
Hamilton promised to publish something about them in the journal
he ran, but he was distracted by working on the quaternions, and
he never got around to it until after Cayley had rediscovered them
and published a note about them as an appendix to a paper in the
Philosophical Magazine in March of 1845.

But anyway, I don't know when mathematicians started calling
them the octonions, or who started it - but I think it's a good
idea, even if it meant something else first. The word "quaternions"
already appears in the King James Bible, but that didn't stop Hamilton!

For more details try this:

http://math.ucr.edu/home/baez/Octonions/node1.html

and also check out my new webpage with photos of a pilgrimage
to Brougham Bridge - the bridge where Hamilton carved his equations
defining multiplication in the quaternions:

http://math.ucr.edu/home/baez/dublin/index.html#hamilton

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