Is there a unified theory of mathematics, theoretical physics, and theoretical computer science?
According to Steven Weinberg, "Everyone knows that electronic computers have enormously helped the work of science. Some scientists have had a grander vision of the importance of the computer. They expect that it will change our view of science itself, of what it is that scientific theories are supposed to accomplish, and of the kinds of theories that might achieve these goals. ... Wolfram goes on to make a far-reaching conjecture, that almost all automata of any sort that produce complex structures can be emulated by any one of them, so they are all equivalent in Wolfram's sense, and they are all universal. This doesn't mean that these automata are computationally equivalent (even in Wolfram's sense) to systems involving quantities that vary continuously. Only if Wolfram were right that neither space nor time nor anything else is truly continuous (which is a separate issue) would the Turing machine or the rule 110 cellular automaton be computationally equivalent to an analog computer or a quantum computer or a brain or the universe. But even without this far-reaching (and far- out) assumption, Wolfram's conjecture about the computational equivalence of automata would at least provide a starting point for a theory of any sort of complexity that can be produced by any kind of automaton. The trouble with Wolfram's conjecture is not only that it has not been proved--a deeper trouble is that it has not even been stated in a form that could be proved. What does Wolfram mean by complex? ..."
What is a precise mathematical formulation of Wolfram's concept of complexity? What might be a decisive empirical test of Wolfram's cosmological automaton? My guess is that at the Planck scale the concepts of energy and spacetime somehow fail -- the failure is either in terms of higher mathematics (i.e. mathematical symmetries of the string landscape) or in terms of lower mathematics (i.e. Wolfram's cosmological automaton). I further speculate that the string landscape depends upon generalizing Heisenberg's uncertainty principle to include alpha-prime, while Wolfram's cosmological automaton depends upon modifying Einstein's field equations to include nonzero dark-matter-compensation-constant, Koide cutoff, and Lestone cutoff. Who might be the world's greatest living theoretical physicist? The answer might be Witten. Who might be the world's greatest living mathematician? The answer might be Mochizuki.
According to David Castelvecchi, "The overarching theme of inter-universal geometry, as Fesenko describes it, is that one must look at whole numbers in a different light -- leaving addition aside and seeing the multiplication structure as something malleable and deformable. Standard multiplication would then be just one particular case of a family of structures, just as a circle is a special case of an ellipse. Fesenko says that Mochizuki compares himself to the mathematical giant Grothendieck -- and it is no immodest claim. "We had mathematics before Mochizuki's work -- and now we have mathematics after Mochizuki's work," Fesenko says."
How might the concepts of energy and spacetime be introduced into algebraic/arithmetic geometry? The answer to the preceding question might involve a unified theory of string theory and Mochizuki's IUT -- deformations of string vacua might have analogues within IUT. I have speculated that if my idea of dark-matter-compensation-constant = square-root((60±10)/4) * 10^-5 is empirically invalid, then MOND-chameleon particles might be the most likely alternative. Because individual gravitons cannot be detected, any suggested modification of Einstein's field equations might be interpreted in terms of weird particles combined with 100% truth of Einstein's field equations. I conjecture that there might be a theorem that, under plausible hypotheses, the following three assumptions imply that MOND-chameleon particles exist.
ASSUMPTION 1. Milgrom's MOND is approximately valid for a wide range of gravitational accelerations.
ASSUMPTION 2. Newton's 3 laws of motion are (non-relativistically) correct, and supersymmetry needs to be replaced by MOND-compatible-supersymmetry.
ASSUMPTION 3. String theory with MOND-compatible-supersymmetry explains the empirical successes of MOND.
Am I wrong about Fredkin-Wolfram information?
"So: Is Wolfram, as he plainly believes, the new Copernicus? Or is he merely a new Darwin or Einstein? Well, if it's comparisons you are seeking, the one that occurred to me was the astronomer in Dr. Johnson's Rasselas, who, after years of intense, solitary intellection, went quietly nuts." -- John Derbyshire
"Not Quite Copernicus", National Review, 16 September 2002
Is is true that Fredkin-Wolfram information somehow encodes quantum information?