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From: liberte@uiucdcs.UUCP (liberte )
Newsgroups: net.math
Subject: Re: i**i, foundations and philosophy - (nf)
Message-ID: <6029@uiucdcs.UUCP>
Date: Mon, 5-Mar-84 22:27:57 EST
Article-I.D.: uiucdcs.6029
Posted: Mon Mar  5 22:27:57 1984
Date-Received: Wed, 7-Mar-84 05:10:36 EST
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#R:houem:-23000:uiucdcs:28200031:000:744
uiucdcs!liberte    Mar  5 21:46:00 1984

There is more to it than quaternions.  Charles Muses has come up with
(what he claims is) a complete hierarchy of "Hypernumbers" of which the
complex and quaternion numbers are only on the first two levels.  I know
very little about this myself, but can give references.

All the hypernumbers can be represented as n-dimensional arrays, but it
turns out to be simpler to deal with them as abstract symbols with certain
algebraic properties.

What are they good for?  I'm sure alot, once we develop the physics to need
them.  After all, complex numbers (not quite accepted because of their
imaginary stigma) are still finding new applications in electronics and
optics.  We know so little about the world.  Keep an open mind.

Daniel LaLiberte