reality, a non-computable fractal ?
This looks interesting. Has it been noticed here? The Invariant Set Hypothesis: A New Geometric Framework for the Foundations of Quantum Theory and the Role Played by Gravity Authors: T.N.Palmer http://arxiv.org/find/quant-ph/1/au:+Palmer_T/0/1/0/all/0/1 (Submitted on 5 Dec 2008 (v1 http://arxiv.org/abs/0812.1148v1 ), last revised 17 Feb 2009 (this version, v3)) Abstract: The Invariant Set Hypothesis proposes that states of physical reality belong to, and are governed by, a non-computable fractal subset I of state space, invariant under the action of some subordinate deterministic causal dynamics D. The Invariant Set Hypothesis is motivated by key results in nonlinear dynamical-systems theory, and black-hole thermodynamics. The elements of a reformulation of quantum theory are developed using two key properties of I: sparseness and self-similarity. Sparseness is used to relate counterfactual states to points not on I thus providing a basis for understanding the essential contextuality of quantum physics. Self similarity is used to relate the quantum state to oscillating coarse-grain probability mixtures based on fractal partitions of I, thus providing the basis for understanding the notion of quantum coherence. Combining these, an entirely analysis is given of the standard mysteries of quantum theory: superposition, nonlocality, measurement, emergence of classicality, the ontology of uncertainty and so on. It is proposed that gravity plays a key role in generating the fractal geometry of I. Since quantum theory does not itself recognise the existence of such a state-space geometry, the results here suggest that attempts to formulate unified theories of physics within a quantum theoretic framework are misguided; rather, a successful quantum theory of gravity should unify the causal non-euclidean geometry of space time with the atemporal fractal geometry of state space. http://arxiv.org/abs/0812.1148 --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Victor Korotkikh
Bruno: I will wait for your most recent UDA to be posted here. I have problems with infinite time and resources for your computations, if done in this physical Universe. Ronald On May 14, 12:22 pm, Bruno Marchal marc...@ulb.ac.be wrote: Ronald, On 14 May 2009, at 13:19, Ronald (ronaldheld) wrote: Can you explain your Physics statement in more detail, which I can understand? UDA *is* the detailed explanation of that physics statement. So it would be simpler if you could tell me at which step you have a problem of understanding, or an objection, or something. You can search UDA in the archives for older or more recent versions, or read my SANE2004 paper: http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHALAbstract... In a nutshell, the idea is the following. If we are machine we are duplicable. If we distinguish the first person by their personal memories, sufficiently introspective machine can deduce that they cannot predict with certainty they personal future in either self- duplicating experience, or in many-identical-states preparation like a concrete universal dovetailer would do all the time. So, if you are concretely in front of a concrete universal dovetailer, with the guaranty it will never stop (in some steady universe à-la Hoyle for example), you are in a high state of first person indeterminacy, given that the universal dovetailer will execute all the computations going through your actual state. Sometimes I have to remind the step 5 for helping the understanding here. In that state, from a first person perspective you don't know in which computational history you belong, but you can believe (as far as you are willing to believe in comp) that there are infinitely many of them. If you agree to identify an history by its infinite steps, or if you accept the Y = II principle (that if a story bifurcate, Y , you multiply their similar comp-past, so Y gives II), then you can understand that the cardinal (number) of your histories going through you actual state is 2^aleph_zero. It is a continuum. Of course you can first person distinguish only a enumerable quotient of it, and even just a finite part of that enumeration. Stable consciousness need deep stories (very long yet redundant stories, it is deep in Bennett sense) and a notion of linear multiplication of independent stories. Now the laws of arithmetic provides exactly this, and so you can, with OCCAM just jump to AUDA, but you have to study one or two book of mathematical logic and computer science before. (the best are Epstein Carnielli, or Boolos, Burgess and Jeffrey). Or, much easier, but not so easy, meditate on the eighth step of UDA, which shows that form their first point of view universal machine cannot distinguish real from virtual, but they cannot distinguish real from arithmetical either, so that the arithmetical realm defines the intrinsic first person indeterminacy of any universal machine. Actually the eighth step shows that comp falsifies the usual mind/physical-machine identity thesis, but it does not falsify a weaker mind/many-mathematical machines thesis. If interested I suggest you study UDA in Sane2004, and ask any questions, or find a flaw etc. (or wait for a more recent version I have yet to put on my page) Thanks for the reference to Kent's paper (it illustrates very well the knotty problems you get into when you keep Everett, materialism and the identity thesis, but I have read it only diagonally just now). Hope this helped a bit. Bruno On May 13, 11:30 am, Bruno Marchal marc...@ulb.ac.be wrote: Thanks Russell, I will take a look. At first sight he makes the same error with numbers that Wolfram makes with cellular automata. Those are still mathematical form of physicalism, incompatible with the mechanist thesis in the cognitive science. Of course we converge toward rather similar (recursively isomorphic or weakened) ontologies. But they seems to believe they can recover some physics from that, where, saying yes to the surgeon requires to abandon that very idea. Physics, like in Plato and Plotinus, is not a mathematical structure among others, it is a mathematical structure which relate all mathematical structures in a precise way. Physics is somehow much more fundamental than being a thing completely describable by a set of mechanical laws. Pu in another way, such theories are unaware of the mind-body problem and still use an identity relation between a mind and a implementation of a program which UDA forces to abandon, to be frank. This does not mean those works are uninteresting of course, and they may play some role in the unravelling of the Minds and Bodies problems. Sure. Bruno On 13 May 2009, at 01:15, russell standish wrote: Hi
Re: No MWI
I still do not see any arguments against what I read, that one Universe fits observations better than the MWI. Ronald On May 15, 1:01 am, daddycay...@msn.com wrote: On May 14, 9:47 pm, daddycay...@msn.com wrote: On May 14, 4:45 pm, Colin Hales c.ha...@pgrad.unimelb.edu.au wrote: At the same time position 1 completely fails to explain an observer of the kind able to do 1a. I would say that position 2 fails to explain the observer too, you have to actually explain the observer to claim that a position explains the observer. But position 2 at least provides the topology to allow doubt, so that there is room for an observer to be explained in the future. ... Yet position 1 behaviour stops you from finding position 2 ... and problems unsolved because they are only solvable by position 2 remain unsolved merely because of 1b religiosity. If what you mean by religiosity is the disallowance of doubt, then yes by definition position 1 has religiosity and position 2 does not. I agree that disallowance of doubt is not a good thing to have. I think you said that physicists would also agree, but that they don't practice that way. I think it's just a matter of frame of mind. In math we do that a lot, where we suppose that something is true and see where it leads. I guess in physics the supposing just lasts longer. And the supposing in physics is in the form of math. What other form could supposing in physics possibly take? It seems that anything you suppose true you can put in the form of a mathematics statement. I think it all boils down to the fact that we have to keep remembering that we were just supposing, and be able to step back out of it and suppose something else. I think that's where having lots of people it an advantage, some people are the really dedicated logical inference one step at a time see where the supposition leads, do many experiments, etc. Other people are the broad brush outside of the box thinkers that think up lots of different possibilites. Hmmm. Just in case there's a misunderstanding of position 2, here's their contrast rather more pointedly: Position 1 1a There's a mathematics which describes how the natural world behaves when we look. 1b Reality is literally made of the mathematics 1a. (I act as if this were the case) Position 2 1a There's a mathematics which describes how the natural world behaves when we look. 1b There's a *separate* mathematics of an underlying reality which operates to produce an observer who sees the reality behaving as per 1a maths. 1c There's the actual underlying reality, which is doubted (not claimed) to 'be' 1b or 1a. I think that your first description of position 2 seemed to necessitate some kind of basic matter that things are made of. But I think your second description of position 2 (above, by the way, 2a, 2b, 2c typo above) doesn't necessarily require that. In face your 2c above says that the underlying reality is doubted to be 1b or 1a. I think that your doubt and underlying reality could all be placed in 2b instead and you could get rid of 2c. I think that Bruno's G might correspond to 2a and G* might correspond to 2b, and viola, comp! Tom i.e. in the case where you put the doubt and underlying reality into 2b, then G* could correspond to 2b.- Hide quoted text - - Show quoted text - --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: No MWI
On 15 May 2009, at 14:27, ronaldheld wrote: I still do not see any arguments against what I read, that one Universe fits observations better than the MWI. Just comp predicts many worlds/histories and the fact they play a key role in the statistics of experiences. But with QM, many worlds seems to me to be a direct consequence of a) linearity of evolution b) linearity of the tensor product c) superposition of states d) and nothing else (that is only quantum physical histories, no Bohm potential, no classical isolated computations, etc.) In this, comp is a problem for d: the comp supervenience asks for *all* histories, and to solve the mind body problem (or just the body problem) we have to either justify completely a, b, c, and d, from a measure extracted from classical computer science, or to reject comp or QM. But nature, both the observable one, and the one which proceeds by the richness of the structure of the integers, suggests that Many is much simpler than One. The Mandelbrot set illustrates this too: a very simple iteration leads to incredibly complex; self-similar, repetitive (and probably universal) structure. Even without QM and/or mechanism, the unicity of anything is rather doubtful. This is the starting idea of the everything list. I also disagree a bit technically on some points in Kent's paper, and generally I disagree even with MWI partisan. I have never understood the Copenhagian Wave collapse. Even when you give a special dualist role of consciousness: it does not work. Once you abandon the wave collapse, or better, once you agree that physicist obeys to QM, it seems to me that the many world cannot be avoided at all. Kent criticizes it on the fact that we don't yet recover the Born rules, but in my opinion this follows from Gleason Theorem + comp indeterminacy. A very old book by Paulette Fevrier (a pioneer in quantum logic) already suggests this (without really going through Gleason-like theorem). It is the equivalent of such a Gleason's theorem that comp is still lacking, and that is why I hope the Z1* and X1* logic(s) gives the right quantum logics capable of realizing von Neumann's dream to extract the quantum proba from the quantum logic. Z1* and X1* are quite promising with that respect, but a lot of work still remains to be done. Now, I don't understand why Wallace introduces a notion of fuzzyness, and some passage of Kent's paper remains a bit obscur. Perhaps you could tell us what precisely makes you feel (in Kent's paper, or by other way) that QM is still consistent with the idea of one world without introducing a non (quantum) mechanical selection principle. Kent is the author of many paper against Everett, and none have ever convinced me. Give me time I read it less diagonally though ... Bruno On May 15, 1:01 am, daddycay...@msn.com wrote: On May 14, 9:47 pm, daddycay...@msn.com wrote: On May 14, 4:45 pm, Colin Hales c.ha...@pgrad.unimelb.edu.au wrote: At the same time position 1 completely fails to explain an observer of the kind able to do 1a. I would say that position 2 fails to explain the observer too, you have to actually explain the observer to claim that a position explains the observer. But position 2 at least provides the topology to allow doubt, so that there is room for an observer to be explained in the future. ... Yet position 1 behaviour stops you from finding position 2 ... and problems unsolved because they are only solvable by position 2 remain unsolved merely because of 1b religiosity. If what you mean by religiosity is the disallowance of doubt, then yes by definition position 1 has religiosity and position 2 does not. I agree that disallowance of doubt is not a good thing to have. I think you said that physicists would also agree, but that they don't practice that way. I think it's just a matter of frame of mind. In math we do that a lot, where we suppose that something is true and see where it leads. I guess in physics the supposing just lasts longer. And the supposing in physics is in the form of math. What other form could supposing in physics possibly take? It seems that anything you suppose true you can put in the form of a mathematics statement. I think it all boils down to the fact that we have to keep remembering that we were just supposing, and be able to step back out of it and suppose something else. I think that's where having lots of people it an advantage, some people are the really dedicated logical inference one step at a time see where the supposition leads, do many experiments, etc. Other people are the broad brush outside of the box thinkers that think up lots of different possibilites. Hmmm. Just in case there's a misunderstanding of position 2, here's their contrast rather more pointedly: Position 1 1a There's a mathematics which describes how the natural world
Re: Consciousness is information?
Hi Jesse, On 15 May 2009, at 06:32, Jesse Mazer wrote: Maudlin shows that you can reduce almost arbitrarily the amount of physical activity for running any computation, and keep their computational genuineness through the use of inert material. So the isomorphism you introduce vanish on the original Olympia (Pre- olympia). Olympia *is* Pre-Olympia + Klara (the inert (for the computation PI) machinery needed for the counterfactuals) OK? Olympia run the computation PI. But what do you mean when you say the isomorphism vanishes? Do you mean that the causal structure of pre-Olympia would *not* be isomorphic to the causal structure of the original Turing machine that pre-Olympia was supposed to imitate (according to the definition of causal structure in terms of logical relations between propositions about the system's state at different moments)? Yes. When I assume physical supervenience, for the benefit of the refutation. Olympia, relatively to me, implements Alice (or PI), Pre- Olypia does not. I would say yes to a doctor if he gives me an Olympia brain, no if he gives me pre-Olympia! That is what I mean by the vansihing of the causal isomorphism. Of course my goal, when I say yes to the doctor, is to preserve my consciousness, and my ability to manifest it in the normal (most probable) histories. My consciousness is already in plato heaven, so what I need here are the right dispositional devices. If so, that would mean that regular Olympia (pre-Olympia + Klara) wouldn't have a causal structure isomorphic to the Turing machine either, since I was defining causal structure solely in terms of propositions about events that *do* occur in the system's history, meaning the extra counterfactual conditions provided by Klara are irrelevant to Olympia's causal structure, so Olympia's causal structure would be the same as pre-Olympia's. Right. But Maudlin manages to show that Olympia can have an empty causal structure, and that you have to say yes to the doctor when he proposes to substitute your brain by nothing. Personally I conceive propositions only in a net of related propositions by theories or models. The causal structure is mainly given by axioms and inference or computation rules, or by a (mathematical) semantics (model). You can't separate a proposition from other propositions like you can't separate a number from the other numbers. I guess you would say that the movie-graph (the movie of the filmed active boolean graph corresponding to Alice's dream) would vehiculate Alice's dream. I can agree if you call the causal structure the computation corresponding to the local events lending to that graph, but then you have abandon the real time physical supervenience thesis already (or comp). It is a very subtle and complex point here, we can go back on this later. If that's the case, why can't we postulate that consciousness supervenes on causal structure, since causal structure is after all part of the physical world? The point is that you can realize any computation with any causal structure in that sense. Maudlin's construction explains well that the Klaras, or the *material* for the counterfactuals are a read herring as far as giving a role in the logical relations describing a computation. And not just the material one! Any choice of a particular universal system cannot work, you have to take them all. You can then choose the simplest one (+ and *) to retrieve those who define observable realities from the point of view of universal machines. In fact one could say that physics is *only* concerned with causality in the sense of lawlike relations between propositions about observations, since the laws of physics tell us nothing about what particles or fields or wavefunctions really are, only about how they interact with one another and how they can be used to predict the outcomes measurements. So if we say consciousness supervenes on causal structure, then Olympia would not qualify as an instantiation of the observer-moments that the original Turing machine instantiated, in much the same way that a lookup table wouldn't qualify. I don't see that at all. Olympia is just a crazy implementation of an algorithm, but it is correct on all inputs. Its resemblance with a look-up table is local, finite, and does not change Olympia's semantics. If such a change makes a change, I would no more say yes to a doctor. My consciousness would depend on the nature of the implementation. I don't have a problem with the idea that a giant lookup table is just a sort of zombie, Look-up table contains the counterfactuals. I am not sure that a giant look-up up table can be considered as a zombie. The problem is that such a look-up table would be gigantic and hard to address. Also, its origin, relatively to me, would need a strange history.
Re: 3-PoV from 1 PoV?
Hi Bruno, - Original Message - From: Bruno Marchal To: everything-list@googlegroups.com Sent: Thursday, May 14, 2009 10:35 AM Subject: Re: 3-PoV from 1 PoV? Hi Stephen, On 13 May 2009, at 22:20, Stephen Paul King wrote: snip By relagating the notion of implementation, to Robinson Arithmatic, etc., one only moves the problem further away from the focus of how even the appearence of change, dynamics, etc. obtain. The basic idea that you propose, while wonderfully sophisticated and nuanced, is in essense no different from that of Bishop Berkeley or Plato; it simply does not answer the basic question: Where does the appearence of change obtain from primitives that by definition do not allow for its existence? [BM] Because you can define in arithmetic, using only addition and multiplication symbols, and logic, the notion of computation, or of pieces of computation, like you can define provability (by PA, by ZF, or by any effective theory) already in the very weak (yet Turing universal) Robinson Arithmetic. [SPK] Ok, Robinson Arithmatic is ... or Q, is a finitely axiomatized fragment of Peano arithmetic (PA). ...Q is essentially PA without the axiom schema of induction. Even though Q is much weaker than PA, it is still incomplete in the sense of Gödel. http://en.wikipedia.org/wiki/Robinson_arithmetic_Q It does not tell me where the assumption of implementation of the addition and multiplication obtain. Just because one can define X does not mean that one has produced X; unless we are assuming that the act of defining a representational system is co-creative of its objects. Are we to consider that an object, physical or platonic, is one and the same as its representations? Oh, I forgot, it has been proposed that a book containing a symbolic representation of Einstein's Brain is equal/equivalent to Einstein's Mind. OK! ... Moving on. [BM] You can entirely define in arithmetic statements of the kind The machine x on input y has not yet stop after z steps. The notion of time used here through the notion of computational steps can be deined entirely from the notion of natural numbers successor (which can be taken as primitive or defined through addition and multiplication). [SPK] Ok, time (pun intended!) for a thought experiment. I go the Library of Babel and pull out the Einstein's Brain and bring it home with me. I sit down and ask it: what are your latest thoughts on the nature of Unified Fields?. How long am I going to wait before I realize that I will never get an answer? You might say:Stephen, you are going about it all wrong! You have to first create a well-formed question in the language of Eintein's Brain and then look up the appropriate responce inthe book. I answer, Ah, So Einstein's Brain can answer my question after all; it can only sit there on the table until I opening and use my own computational implementation to get my answer. So where is Einstein's Mind? Nowhere... What is it that distinguishes a random sequence of scratches on a plane of sand from the sequence of symbols of the equation representing the Grand Unified Theory of Everything? Well, one person might say: I can read the one that is an equation... Meaningfullness necessitates a subject to whom meaning obtains. Computational states, symbolic scratches or patterns of concurrent neuron firings or distributions of voltage potentials, mean something because their existance is such that situations would be different otherwise for some system other than that of the states, scratches, patterns, etc.. Remember the notion of Causation? X is the Cause of Y if and only if X would not occur without the occurence of Y. David Deutsch defines it more pointedly: ...an event X causes an event Y in our universe if both X and Y occur in our universe, but in most variants of our universe in which X does not happen, Y does not happen either. The trouble is that unless there exists a unique measure on the space where in events are coded in the Universe of possible statements or sentences of Robinson Arithmatic, it is undecidable if X happens or Y happens because one can not distinguish between actual computational steps that would generate a means to distinguish X from Y or strings that code some other computational string. Remember how Goedel numbering works... Only if the number of possible statements that can be coded with the same string are computationally isomorphic (generate the same output per input) can one obtain a means to distinguish X from Y, but if we require this it will be no longer possible to code any variants of our universe. Variants would not be allowed. Without the possibility of variants, how does one obtain a notion of contrafactuality? To claim that the ordering of natural numbers from the notion of succession allow for us to
Re: No MWI
David Deutsch gives this convincing argument against a single world: that one can't explain how quantum computers work without postulating other universes. The evidence for the multiverse, according to Deutsch, is equally overwhelming. Admittedly, it's indirect, he says. But then, we can detect pterodactyls and quarks only indirectly too. The evidence that other universes exist is at least as strong as the evidence for pterodactyls or quarks. Perhaps the sceptics will be convinced by a practical demonstration of the multiverse. And Deutsch thinks he knows how. By building a quantum computer, he says, we can reach out and mould the multiverse. One day, a quantum computer will be built which does more simultaneous calculations than there are particles in the Universe, says Deutsch. Since the Universe as we see it lacks the computational resources to do the calculations, where are they being done? It can only be in other universes, he says. Quantum computers share information with huge numbers of versions of themselves throughout the multiverse. Imagine that you have a quantum PC and you set it a problem. What happens is that a huge number of versions of your PC split off from this Universe into their own separate, local universes, and work on parallel strands of the problem. A split second later, the pocket universes recombine into one, and those strands are pulled together to provide the answer that pops up on your screen. Quantum computers are the first machines humans have ever built to exploit the multiverse directly, says Deutsch. At the moment, even the biggest quantum computers can only work their magic on about 6 bits of information, which in Deutsch's view means they exploit copies of themselves in 26 universes-that's just 64 of them. Because the computational feats of such computers are puny, people can choose to ignore the multiverse. But something will happen when the number of parallel calculations becomes very large, says Deutsch. If the number is 64, people can shut their eyes but if it's 1064, they will no longer be able to pretend. Jason On Fri, May 15, 2009 at 10:50 AM, Bruno Marchal marc...@ulb.ac.be wrote: On 15 May 2009, at 14:27, ronaldheld wrote: I still do not see any arguments against what I read, that one Universe fits observations better than the MWI. Just comp predicts many worlds/histories and the fact they play a key role in the statistics of experiences. But with QM, many worlds seems to me to be a direct consequence of a) linearity of evolution b) linearity of the tensor product c) superposition of states d) and nothing else (that is only quantum physical histories, no Bohm potential, no classical isolated computations, etc.) In this, comp is a problem for d: the comp supervenience asks for *all* histories, and to solve the mind body problem (or just the body problem) we have to either justify completely a, b, c, and d, from a measure extracted from classical computer science, or to reject comp or QM. But nature, both the observable one, and the one which proceeds by the richness of the structure of the integers, suggests that Many is much simpler than One. The Mandelbrot set illustrates this too: a very simple iteration leads to incredibly complex; self-similar, repetitive (and probably universal) structure. Even without QM and/or mechanism, the unicity of anything is rather doubtful. This is the starting idea of the everything list. I also disagree a bit technically on some points in Kent's paper, and generally I disagree even with MWI partisan. I have never understood the Copenhagian Wave collapse. Even when you give a special dualist role of consciousness: it does not work. Once you abandon the wave collapse, or better, once you agree that physicist obeys to QM, it seems to me that the many world cannot be avoided at all. Kent criticizes it on the fact that we don't yet recover the Born rules, but in my opinion this follows from Gleason Theorem + comp indeterminacy. A very old book by Paulette Fevrier (a pioneer in quantum logic) already suggests this (without really going through Gleason-like theorem). It is the equivalent of such a Gleason's theorem that comp is still lacking, and that is why I hope the Z1* and X1* logic(s) gives the right quantum logics capable of realizing von Neumann's dream to extract the quantum proba from the quantum logic. Z1* and X1* are quite promising with that respect, but a lot of work still remains to be done. Now, I don't understand why Wallace introduces a notion of fuzzyness, and some passage of Kent's paper remains a bit obscur. Perhaps you could tell us what precisely makes you feel (in Kent's paper, or by other way) that QM is still consistent with the idea of one world without introducing a non (quantum) mechanical selection principle. Kent is the author of many paper against Everett, and none have ever convinced me. Give me time I read it less diagonally though
Re: No MWI
On Fri, May 15, 2009 at 05:40:09PM -0500, Jason Resch wrote: Deutsch. If the number is 64, people can shut their eyes but if it's 1064, they will no longer be able to pretend. Jason Hopefully you meant 10^64, not 1064, which is not all that startling. -- Prof Russell Standish Phone 0425 253119 (mobile) Mathematics UNSW SYDNEY 2052 hpco...@hpcoders.com.au Australiahttp://www.hpcoders.com.au --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-list@googlegroups.com To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
