From Osher Doctorow
Category Theory uses composition of morphisms as its main operation, while Rare Event Theory (RET) uses addition-subtraction as its main operation although multiplication-division are shown to be secondary. See my postings at http://www.mathforum.org/math-history-list. This does not mean that composition does not exist in RET, but it does mean that when examining an iterated function in fractals it is enough in the RET representation to examine the original function ordinarily. If a pathology is found in the original function, that is usually enough, and vice versa. I will simply add here that in my opinion an enormous weight of evidence indicates that RET plays the key role in GROWTH (expansion- contraction) processes in the mathematical and physical universes, and the superstringtheory.com site as well as my paper in B. N. Kursunuglu et al. (Eds.) "Quantum Gravity, Generalized Theory of Gravitation, and Superstring Theory-Based Unification," Kluwer: N.Y. 2000 89-97 should be looked at for this. Radiation from a source is also a growth process, by the way. I respect opposite or different views and encourage competition between them, since in my opinion there are many pictures and many theories that lead to knowledge, and competition is extremely valuable for quantitative sciences/mathematics and philosophy and engineering and medicine. Osher Doctorow