Re: OT: Africa needs God

On Sun, 04 Jan 2009 01:07:41 -0500, Walter Bushell wrote:

In article
<73d20577-f65e-4802-9cf0-610326c2e242@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>,
Vend <vend82@xxxxxxxxxxx> wrote:

What about imaginary numbers? They don't correspond to physical
reality,

Ask a physicist or an engineer about it :)

It will not phase them.

OTOH, you might say that about the Quaternions, for which, IIUC we have
yet to discover a use.

Fighting words.
http://en.wikipedia.org/wiki/Quaternions -
"However, quaternions have had a revival in the late 20th century,
primarily due to their utility in describing spatial rotations.
Representations of rotations by quaternions are more compact and faster
to compute than representations by matrices. For this reason, quaternions
are used in computer graphics,[1] control theory, signal processing,
attitude control, physics, bioinformatics, and orbital mechanics.
For example, it is common for spacecraft attitude-control systems to be
commanded in terms of quaternions. Quaternions have received another
boost from number theory because of their relation to quadratic forms."

http://www.amazon.com/Quaternions-Clifford-Algebras-Relativistic-Physics/dp/3764377909 -
"The use of Clifford algebras in mathematical physics and engineering
has grown rapidly in recent years. Whereas other developments have
privileged a geometric approach, the author uses an algebraic approach
which can be introduced as a tensor product of quaternion algebras and
provides a unified calculus for much of physics.
The book proposes a pedagogical introduction to this new calculus,
based on quaternions, with applications mainly in special relativity,
classical electromagnetism and general relativity.
The volume is intended for students, researchers and instructors in
physics, applied mathematics and engineering interested in this new
quaternionic Clifford calculus."

http://sigfpe.blogspot.com/2006/09/more-low-cost-geometric-algebra.html -
"Before that I should say a bit more about Clifford algebras. These
are an important tool in many branches of mathematics - algebraic
topology, K-theory, representation theory and in theoretical physics.
But one interesting aspect is that they can provide an alternative to
the usual vector language of geometry. Many people will be familiar
with the use of quaternions to represent 3D rotations. Clifford
algebras generalise this to N-dimensions."

"Have yet to discover a use", indeed.

John

.

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