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Division Algebras: - Octonions Quaternions Complex Numbers and the Algebraic Design of Physics (Paperback, Softcover reprint of hardcover 1st ed. 1994)
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Division Algebras: - Octonions Quaternions Complex Numbers and the Algebraic Design of Physics (Paperback, Softcover reprint of hardcover 1st ed. 1994)
Series: Mathematics and Its Applications, 290
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I don't know who Gigerenzer is, but he wrote something very clever
that I saw quoted in a popular glossy magazine: "Evolution has
tuned the way we think to frequencies of co-occurances, as with the
hunter who remembers the area where he has had the most success
killing game." This sanguine thought explains my obsession with the
division algebras. Every effort I have ever made to connect them to
physics - to the design of reality - has succeeded, with my
expectations often surpassed. Doubtless this strong statement is
colored by a selective memory, but the kind of game I sought, and
still seek, seems to frowst about this particular watering hole in
droves. I settled down there some years ago and have never feIt
like Ieaving. This book is about the beasts I selected for
attention (if you will, to ren der this metaphor politically
correct, let's say I was a nature photographer), and the kind of
tools I had to develop to get the kind of shots Iwanted (the tools
that I found there were for my taste overly abstract and
theoretical). Half of thisbook is about these tools, and some
applications thereof that should demonstrate their power. The rest
is devoted to a demonstration of the intimate connection between
the mathematics of the division algebras and the Standard Model of
quarks and leptons with U(l) x SU(2) x SU(3) gauge fields, and the
connection of this model to lO-dimensional spacetime implied by the
mathematics.
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