From: Osher Doctorow, Ph.D. [EMAIL PROTECTED], Mon. Nov. 27, 2000 10:17PM As I mentioned on primes-L, my recent paper on logic-based probability (LBP) was published in the volume Quantum Gravity, Generalized Theory of Gravitation, and Superstring Theory-Based Unification, Editors B. N. Kursunoglu, S. L. Mintz, and A. Perlmutter, Kluwer Academic/Plenum: New York 2000. The paper has the title "Magnetic monopoles, massive neutrinos and gravitation via logical-expermental unification theory (LEUT) and Kursunoglu and is on pages 89-97 of the book. Mathematical physics is only one small field to which LBP applies. I am especially interested in its number theory applications, which now include quadratic fields and a whole array of primes problems. Since the paper cited above, I have expanded the theory of LBP considerably. Some of the power of LBP derives from its generalization of maximum entropy and its slight modification of elementary operations. For example, it replaces division in Bayesian probability/statistics with subtraction (plus the addition of the constant 1). Like Non-Euclidean geometry, it provides a whole different world of results, but it also provides powerful ordering principles somewhat analogous to the Principle of Equivalence in general relativity and beyond. One remarkable result is that it indicates that linear and quadratic/conic (including cross product terms like cxy in the unrotated conic) expressions rather than higher degree polynomials are key in number theory (actually across mathematics). Simple exponentials of form exp(kx) are also considered by LBP to be very important across mathematics, where k may be complex, but composite functions and inverse functions are much less important (in fact, composite functions are among the worst, which is interesting in view of the high degree of composition involved in iterated fractal/chaos expressions). Osher Doctorow Doctorow Consultants, West Los Angeles College, etc. _________________________________________________________________________ Unsubscribe & list info -- http://www.scruz.net/~luke/signup.htm Mersenne Prime FAQ -- http://www.tasam.com/~lrwiman/FAQ-mers
