Please bare my abstract thought...If real numbers define a point, and a complex number defines a rotation about a point in 2D, and a quaternion number defines a rotation about an axis in 3D, shouldn't octonions define a rotation about a plane in 4D?

-- cenla (elachney@earthlink.net), April 05, 2004

Answers

Hello Cenla:

I have an odd view on this question because it starts with quaternions as an event in spacetime.

Snap your fingers. That happened at a particular time in 3D space. Quaternions have a real number (the one for time) and three imaginary numbers for the spatial directions. Although quaternions are used to calcualte 3D rotations, my own perspective is that quaternions should be viewed as a way to visualize animations of events.

If the real numbers are given the job of representing time, then a point in time either has an event or it does not. This will look like a flashlight turning on and off instead of the real number line.

I have made up a few animations of complex numbers and quaternions (URL at the end). Turns out these are not easy for most browsers to see. You need either Opera with a plug in or on Linux Konqueror. Someday I should make a few mpegs. Viewing numbers as the stuff of animations is fun to think about.

I have not work with onctonians yet, sorry.

doug

http://www.theworld.com/~sweetser/quaternions/qemation/Dynamic_graphs/index.html

-- Douglas Sweetser (sweetser@alum.mit.edu), June 27, 2004.