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Colin Hales wrote: > Hi Brian, > I was wondering if you could connect (in the paper) the maths with our > universe? As an example. What set operations or structures correspond to > the standard particle model entities, what constitutes a chemical > reaction or energy, what space is made of... that kind of thing. Maybe > this is supposed to be obvious... if it is then sorry... but you've lost > (as an audience) the entire world above mathematical > physics...especially biofolks. > I think this is what usual theoretical physics is trying to do. As an example, Torgny mentioned R^4 as being a relevant structure in General Relativity. In string theory, the relevant structure is, as far as I've read in the lay literature, some 11 (give or take) dimensional manifold. As such, connecting the ultimate context structure I am working towards to specific structures that represent things like particle interaction would constitute a complete theory of physics and, therefore, I myself am unable to see how this would be done. It perhaps can be done but I lack the knowledge to do so. Perhaps one thing to keep in mind is that this is a step towards a mathematical representation of the so called -level 4- multiverse, by which I'm referencing material here: http://space.mit.edu/home/tegmark/multiverse.html In Tegmark's "ultimate ensemble" paper, there is a diagram of physics and maths structures, part of which is here: http://space.mit.edu/home/tegmark/toe.gif All structures, including those in the top row, which are the ones I think you're asking about Colin, would have the property of being elementarily embeddable within the ultimate structure I'm investigating. (Keep in mind the deficency I mentioned in my previous post.) Roughly speaking, to quote a wiki article, "In model theory <http://en.wikipedia.org/wiki/Model_theory>, an *elementary embedding* is a special case of an embedding <http://en.wikipedia.org/wiki/Embedding#Model_theory> that preserves all first-order formulas." In short, the sub-structures, so to speak, of the ultimate structure I am working towards that are relevant to Quantum Field Theory or General Relativity (such as R^4) are covered in other texts. This paper I am working on is to provide an answer to the question which is the subject of this thread, raised my Tegmark. I'm afraid I don't know enough about mathematical physics to be more explicit. > I am a quintessentially visual/spatial thinker.. math does not speak > very well to me unless I can 'see' the operations happening. in my mind. > I don;t manipulate symbols. I manipulate 'stuff' and then retrofit symbols. > > I would also like to see how an observer with qualia might be > constructed of it. In other words...how a universe thus constructed > might create its own scientist describing it in the way you do....Having > looked at the paper I hold some hope that it might contain a formalism I > can use to construct the set theoretic basis of my own model... it might > be within yours....maybe... not sure. > > This is an excellent line of questioning and one I have high hopes to one day seeing answered. In Tegmark's first of two papers along the lines of a Mathematical Universe, he mentions what he calls Self Aware Structures (SAS's). I have spent a lot of time wondering what type of mathematical structures would have self-awareness. Two candidates that might be just fumbling in the dark are these: David Wolpert of NASA has written some interesting articles on what he calls devices. These devices are mathematical models of scientists plus investigative tools of scientists. In this mathematical device (not completely unlike a Turing machine), it starts with a question and ends with an answer; his papers form a theory of how devices operate. One of his papers is entitled "the physical limits of inference." Anyway, he talks at some point about self aware devices, and my understanding is that these devices X are ones who correctly answer the question "is X a device?" That is at least some form of self awareness. For a pseudo-second example of mathematical self awareness, I was thinking of self-referential first order logical formulas that, in essence, say "I have property P," but let P be the property "X is a 1st order formula" so these special self-referential 1st order formulas would essentially be equivalent to "I am this 1st order formula." To simplify, that is like the sentence "I am this sentence." The open question is what is the nature of SAS's that corresponds to human self-awareness. I think constructing an observer with qualia mathematically would be a most excellent step and a necessary one to solve that open problem raised in Tegmark's first MUH paper. --~--~---------~--~----~------------~-------~--~----~ You received this message because you are subscribed to the Google Groups "Everything List" group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~----------~----~----~----~------~----~------~--~---