From Osher Doctorow Ph.D.
I have been developing an expanded theory called Geometric Physics which may lead to a TOE (Theory of Everything). I discussed fractals in connection with this on geometry-research@forum.swarthmore.edu (which can also be reached by accessing http://www.mathforum.org) on 28 Aug. 03 at 19:35:07. The good news is that Geometric Physics has a good possibility of moving Fractals to center stage in mathematics, physics, engineering, and Life Sciences (biology, botany, etc.). The bad news is that I don't have the influence to do it. I am a college mathematics teacher/researcher at one or more of California State Universities and Community Colleges, which are way underfunded compared to Research Universities like UCLA or Berkeley, which in turn are underfunded. Hopefully, some members of FractInt will be interested in Geometric Physics and have more influence than me. Geometric Physics is motivated by the paradoxes, anomalies, infinities, and in fact the general lack of interdisciplinary work and open-mindedness to new ideas in physics, engineering, and to a lesser but still real degree mathematics. Basically, I decided to start physics from almost scratch. The one thing I did was concentrate on ideas related to Cosmology and Astrophysics, where the latter is probably the most tolerant of new ideas of any science. Geometric Physics defines the Universe as containing 11 Fundamental Elements: Expansion (E), Contraction (C), Rare or Rarity as in Rare Events/Processes (R), Non-Rarity (N), Knowledge as Semantics or Meaning (K), Information as Syntactics or Form of Messages (I), transmission (T), inside (i), outside (o), potential (p), actual (a). The 11 Fundamental Elements form a language via concatenation, and they can be taken as elements of Fuzzy Multivalued Lukaciewicz or Rational Pavelka Logic with logical implication (x-->y) = 1 + y - x where x, y are elements of the language in quantified form, that is to say with truth values not just 0 or 1 for true or false respectively but any real numbers between 0 and 1 inclusive, and where 0 < = y < = x < = 1 for the non-trivial cases. Michael Barnsley's contraction maps can be used to generate fractals by iterated function systems. By allowing both Expansion and Contraction, including to different degrees or distances and with different speeds in different directions at different times, one can also generate arbitrary curvature of the Universe and hence geometry and General Relativity. Quantum Theory turns out to be contractive and much less restricted than in the Mainstream. Statistical Thermodynamics including in black holes is recovered by laws of both increasing Information and increasing Knowledge with time. Temperature is derived from speeds and velocities averaged in specific circumstances. Not everybody likes the results. I have posted them recently to Researchmathematics@yahoogroups.com, http://www.superstringtheory.com/forum, and a few other forums. Loop Theory of Lee Smolin and Abhay Ashtekar and Carlo Rovelli is not in the "cards" with Geometric Physics, but superstringtheory is including M Theory and brane theory and duality theory. General relativity is in the cards, possibly with modifications, but both Quantum Mechanics (QM) and Quantum Field Theory (QFT) undergo many theoretical modifications. This doesn't make many QM and QFT people very happy when they learn about it, especially ones who are committed to Mainstream theories. Osher Doctorow Ph.D.