I thank my parents;

my friends;

the authors of all of the references;

my teachers in the Cartersville public schools;

Lit Meeks, who advised me to attend Princeton;

my teachers at Princeton, where I majored in mathematics and wrote my thesis under Edward Nelson;

Armand Wyler, who wrote a paper in 1971 using ratios of volumes of bounded homogeneous domains to calculate the electromagnetic fine structure constant;

Bill Saenz, who told me in 1981 that David Finkelstein was at Georgia Tech;

David Finkelstein, who had written about quaternionic structures in the 1960's, whose Georgia Tech seminars 1981-1984 with Ernesto Rodríguez, David Luedtke, Christian Holm, Sarah Flynn, and Shlomit Finkelstein taught Clifford algebras, and who refereed my first publication;

Steve Sutton and David Hunicutt, who discussed my work at Georgia Tech around 1986;

Ernesto Rodríguez, who even after leaving Clifford algebras at Georgia Tech and going to JPL to map Venus has continued to read and discuss my work;

Bob Gilmore and Xiangdong Ji of Drexel University, who reviewed my work in 1984 and encouraged me to continue;

Saul-Paul Sirag, whose unpublished paper gave me the idea to consider the importance of the Weyl group;

Carlo Rubbia, for stating at the 1984 Santa Fe meeting of the APS DPF that CERN had found the t-quark at 30-60 GeV, while I said at the same meeting that my calculated value of 130 GeV was correct;

J. S. R. Chisholm and many others at the NATO ASI on Clifford Algebras and Their Applications in Mathematical Physics in 1985 who taught me more about Clifford algebras and discussed my work;

David Hestenes and Jaime Keller, who used minimal ideals of Clifford algebras for internal symmetries;

Yuval Ne'eman, for his advice and his paper on the MacDowell- Mansouri mechanism;

Lou Clavelli, Ben Harms, Larry Carson, Ivan Leblanc, Hitoshi Konno, Jerry Busenitz, Kajia Yuan, and Al Stern in particle physics and Gene Byrd in astronomy at the University of Alabama, who have kept me up to date in particle physics and astronomy during 1990-1992;

Ed Thomas and Henry Valk at Georgia Tech for their encouragement, and for Henry Valk's interesting and entertaining talks and lectures; and

David Finkelstein, who reminded me to use both the left and right ideals of the Cl(8) Clifford algebra and told me to look more closely at Weyl group symmetric structures such as Casimir operators, and the 1991-1992 Georgia Tech physics seminar participants, including Wolfgang Mantke, Marc Kolodner, Mike Gibbs, John Wilson, Lee Harrell, Dmitrii Ivanov, Bill Kalsfell, and Ron Wachman.

Geoffrey Dixon at Brandeis and Boston Un. for very helpful comments and e-mail conversations.

Lie groups are central to much of mathematics. - Edward Nelson (advice while I was in college)

Another peculiarity of four-dimensional space is the occurrence of the 24-cell {3,4,3}, which stands quite alone, having no analogue above or below. - H. S. M. Coxeter (Regular Polytopes (Dover 1973) p. 289)

Theoretical particle physics will not be unified until a realistic generalization of the Dirac equation is found. - P. A. M. Dirac (quoted by David Finkelstein from Loyola talk)

If we had a complete renormalizable theory at high energy, we could work our way down to the effective theory appropriate at any lower energy in a totally systematic way. - Howard Georgi (Weak Interactions and Modern Particle Theory (Benjamin 1984) p. 125)

You can make a model of anything from the harmonic functions on the unit disk. - William Feller (advice while I was in college)

... Lie group theory, together with differential geometry, harmonic analysis, and some devious arguments, might be able to predict some of Nature's dimensionless numbers (a, mp/me, mµ/me, G2/hc, ...). - Bob Gilmore (Lie Groups, Lie Algebras, ... (Wiley1974) p. vii)

The whole purpose of physics is to find a number, with decimal points, etc.! Otherwise you haven't done anything. - R. P. Feynman (The Theory of Fundamental Processes (Benjamin 1961) p. 75)

... too great an emphasis on [Riemannian] geometry can only obscure the deep connections between gravitation and the rest of physics. - Steven Weinberg (Gravitation and Cosmology (Wiley 1972) p. vii

... I believe that the theory that space is continuous is wrong, because we get these infinities and other difficulties, ... the laws [of physics] will turn out to be simple, like the chequer board with all its apparent complexities. - R. P. Feynman (The Character of Physical Law (MIT 1965) pp. 166, 58)

... it is more important to have beauty in one's equations than to have them fit experiment. - P. A. M. Dirac (Scientific American, May 1963, p. 47)

How can you guess the right answer if, when you calculate the result, it disagrees with experiment? You need courage to say the experiments must be wrong. - R. P. Feynman (The Character of Physical Law (MIT 1965) p. 163)