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Contributions To the Theory of Scalar Strings/Branes/DualityPosted by OsherDoctorow on April 03, 2002 at 11:54:42: Before I begin, I should mention that I have proven on geometry-research@forum.swarthmore.edu that the n-dimensional proximity function, the n-dimensional determinant, and alternating series maximize the number of sign changes. There is actually an almost one sentence proof, since if successive terms alternate in sign there cannot be more sign changes, but I decided to go into somewhat more detail. There IS NO theory of scalar strings/branes/duality (well, except for Steven Weinberg's and mine - see below), which makes it even more interesting! One is tempted to ask why not. Steven Carlip of UC Davis and Dale Woodside of MacQuarrie University Australia argued in http://www.lns.cornell.edu/spr/2000-08/msg0027650.html approved by John Baez of UC Riverside that even a scalar-tensor theory of gravity is unlikely, not to mention a scalar theory, because of such things as lack of solar ablateness and a spin zero field giving the wrong coupling to solar energy (negative contribution for the kinetic energy, no contribution of potential energy to *gravitational mass.* We must be cautious in concluding that the earth is flat or that space is Euclidean because there is little detectable so-and-so (whatever that refers to - I suppose curvature here, although before somebody came up with a theory of curvature things looked eminently bleak in that direction). This is not to insult the excellent work of Steven Carlip in particular, who is at the forefront of (2+1)-dimensional quantum gravity, although he never did quite get around to answering my email (the non-mainstream tends to be ignored by the mainstream, even those who advance the mainstream more than others). The mastery of mainstream tensors by John Baez cannot be doubted, although in the little contact that I have myself had with his large number of mainstream colleagues in forums on which he himself appeared, his silence was more noteworthy than his speech. I do not know anything about Dale Woodside, and undoubtedly I should try to find out, which I may. Australia is a mixture of the non-mainstream and the incredibly conformist. For example, anzap-l at the University of Adelaide has posted my applied probability contributions for a long time when nobody else did (an interesting mystery is why probability as opposed to statistics has so few forums in the USA - although I suspect that the answer is best left untold at present). On the other hand, several mathematics education forums and other types of forums appear to be dominated by direct descendants of the original convicts who settled Australia (the USA was partly populated by convicts, but more by victims of religious and political persecution than the hard core type of murdering-stealing convicts). I want to thank Steven Weinberg for writing Gravitation and Cosmology Principles and Applications of the General Theory of Relativity (Wiley: N.Y. 1974), since he answered the objection of Steven Carlip and the other persons-in-agreement by equation 7.1.4 page 155 which he used to obtain equation 7.1.5 (the Einstein Field Equation) of the same page. This equation says R = 8piGTu^u (first u superscript, second u subscript). So the scalar curvature is nicely related to the scalar energy-momentum tensor. In fact, there is even a unnumbered equation on the same page which ends the section and in which Einstein's cosmological constant is included together with R, Ruv, Tuv, guv, G. I want to also thank George Cantor whose Contributions to the Theory of Transcendental Numbers inspired the title of this posting. Cantor discovered the infinity of the continuum and the various other types of infinities, and was not permitted to publish until his Chair Kronecker passed away (Kronecker was a fanatic believer in finiteness who might be at home in the current computer foundations forums), after which he selected the title to recognize that the ideas of more than one person (or more than just the mainstream, I like to think) can be important.
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