Re: Overcoming Incompleteness
Stephen Paul King wrote: Dear Jesse, Hasn't Stephen Wolfram proven that it is impossible to shortcut predictions for arbitrary behaviours of sufficienty complex systems? http://www.stephenwolfram.com/publications/articles/physics/85-undecidability/ Stephen The paper itself doesn't seem to prove it--he uses a lot of tentative language about how certain problems may be computational irreducible or are expected to be, as in this paragraph: Many complex or chaotic dynamical systems are expected to be computationally irreducible, and their behavior effectively found only by explicit simulation. Just as it is undecidable whether a particular initial state in a CA leads to unbounded growth, to self-replication, or has some other outcome, so it may be undecidable whether a particular solution to a differential equation (studied say with symbolic dynamics) even enters a certain region of phase space, and whether, say, a certain -body system is ultimately stable. Similarly, the existence of an attractor, say, with a dimension above some value, may be undecidable. Still, I think it's plausible that he's correct, and that there are indeed computations for which there is no shortcut to finding the program's state after N steps except actually running it for N steps. Jesse _ Catch suspicious messages before you open them--with Windows Live Hotmail. http://imagine-windowslive.com/hotmail/?locale=en-usocid=TXT_TAGHM_migration_HM_mini_protection_0507 --~--~-~--~~~---~--~~ 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 -~--~~~~--~~--~--~---
Re: Overcoming Incompleteness
*Russell,* *Sounds plausible that self-aware systems can manage this. I'd like to see this done as a formal system though, as I have a natural mistrust of handwaving arguments! * I like it too :). I think the computational view would help in construction. *Jesse, I definitely don't think the two systems could be complete, since (handwavey argument follows) if you have two theorem-proving algorithms A and B, it's trivial to just create a new algorithm that prints out the theorems that either A or B could print out, and incompleteness should apply to this too* ** They're not independent systems.putting that aside, I can't find the correspondence to my argument. It would be nice if you could clarify your point.* * * * *Brent,* *But doesn't that depend on having adopted rules of inference and values, i.e. the sentence is either true or false. Why shouldn't we suppose that self-referential sentences can have other values or that your informal reasoning above is a proof and hence there is contradiction* Actually this is the main advantage of making such loop. you're right only when we're talking about ONE system and that system has concluded the truth of such statement. But it can be avoided by two or more systems. They are reliable in each other's view, and have statements for that. maybe that is the only (symmetric!) difference of those systems. Except for that, both(all) are the same. Mohsen Ravanbakhsh --~--~-~--~~~---~--~~ 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 -~--~~~~--~~--~--~---
Re: Attempt toward a systematic description
Bruno, I have a criticism to your argument for teleportation. in the third step, Before the teleportation to cities A and B, you're assuming an uncertainty of first person in appearing in one of those cities. Suppose it to be A. *Where does this asymmetry come from?* I as the first person have been asymmetrically transported to A and not to B. Why? parallel universes again? I thing it wont be creditable, because we have (as far as we know) no quantum collapse. A mere information transfer does not need branching :) ! Does it mean comp is wrong? -- Mohsen Ravanbakhsh, --~--~-~--~~~---~--~~ 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 -~--~~~~--~~--~--~---
Re: Overcoming Incompleteness
Le 24-mai-07, à 19:32, Mohsen Ravanbakhsh a écrit : Thanks for your patience! , I know that my arguments are somehow raw and immature in your view, but I'm just at the beginning. S1 can simulate S2, but S1 has no reason to believe whatever S2 says. There is no problem. Hofstadter strange loop are more related to arithmetical self-reference or general fixed point of recursive operator OK then it, becomes my own idea! Suppose S1 and S2 are the same systems, and both KNOW that the other one is a similar system. They cannot *know* that. The first person associated to each system is different of the other. Unless you mean something *very* general by similar. Then both have the reason to believe in each others statements, with the improvement that the new system is COMPLETE. Why? Only if S2 is much more simple than S1, can S1 be complete on S2. No system can be complete on itself or on anything similar to itself. We've not exploited any more powerful system to overcome the incompleteness in our system. I think this is a great achievement! It's actually like this: YOU believe in ME. THEY give you a godelian statement (You theoretically can not prove this statement) you give it to ME and then see that I can neither prove it n or disprove it, so you tell THEM that their statement is true. If that is a proof, then you are inconsistent. If it is an intuition, or a prayer, a hope, a bet, or anything like that, then it is ok, but you don't need to system for that. S1 can use the very similar system S1 itself. The apparent infinite regression is soleved by the traditional diagonalisation technics. Look in the archive for both diagonalisation and diagonalization in the archive. Or ask (and be patient :) But the wonder is in what we do just by ourselves. We have a THEORY OF MIND. You actually do not need to ask me about the truth of that statement, you just simulate me and that's why I can see the a godelian statement is at last true. But a simulation is not a proof, especially if the simulation doesn't halt. But in the logical sense ONE system wont be able to overcome the incomp leteness, so I might conclude: I'M NOT ONE LOGICAL SYSTEM! This is how we might rich a theory of self. A loopy(!) and multi(!) self. Here I do agree (but from a different reasoning). See later, or, meanwhile, search for Plotinus or guardian angel or hypostases. Very shortly, the lobian-godelian incompleteness forces the distinction between: p Bp Bp p Bp Dt (Bp p) Dt which makes a total of eight notions of self (8, not 5, because 3 of them splits in two different logic due to incompleteness. B is for beweisbar and correspond to Goel arithmetical provability predicate. You can read them as truth provability knowability observability sensibility or, with Plotinus (300 AD): ONE INTELLECT SOUL INTELLIGIBLE MATTER SENSIBLE MATTER With the provable versus true distinction (the [ ] / [ ]* distinction), the hypostases are: one discursive Intellectdivine Intellect soul intell. matter intell. matter sensible mat. sensible mat AND THEN, éadding the comp assumption leads to the comp physics, for the soul and both matter hypostases, and it is enough to cmpare the comp-physics with the empirical physics to evaluate the degree of plausibility of comp. And that's my point. Bruno http://iridia.ulb.ac.be/~marchal/ --~--~-~--~~~---~--~~ 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 -~--~~~~--~~--~--~---
Re: Attempt toward a systematic description
Le 24-mai-07, à 19:48, Mohsen Ravanbakhsh a écrit : Hi Bruno, Thank you for the information. I understand these parts for the others it seems I need to search in archives of the list for some keywords that I do not understand. I'm not an old member. No problem. You can always ask. A mailing list is done for that. In the worst case where you ask for some explanation which I have already given ten thousand times, I will either provide links, or ... ask you to wait for the ten thousand and one explanation. I just wanted to say, most of links in your page lead to nowhere!(Error), It would be nice if you fix them. I should have updated it since a long time. My old software doesn't work since macOS-10, and I'm tired to buy always the same soft. Also I have to remind my password. I was hoping to change my web-page before' goinf to Siena, but June is the exam period and I am not sure I will be able to do that. Sorry. Bruno Mohsen Ravanbakhsh On 5/23/07, Bruno Marchal [EMAIL PROTECTED] wrote: Hi Mohsen, Le 22-mai-07, à 12:20, Mohsen Ravanbakhsh a écrit : Hi Bruno, My sixth sens says you're talking about something important :) but I don't get it. Note that it could help me if you could be a little more specific. OK I see another post of you. It could have been of much more interest, if you could elaborate, or provide us with some references for each part of your So you are able to make sense of the fact that [LOGIC+ADDITION+MULTIPLICATION] gives already a Universal Turing Machine. This is no more astosnishing than the fact that the K and S combinators provides already turing-universality, or that the Conway Game of Life is already turing universal. The advantage of [LOGIC+ADDITION+MULTIPLICATION] is that (universal) computability is seen as a particular case of provability. What is more long to explain in details is that [LOGIC+ADDITION+MULTIPLICATION + INDUCTION] is already lobian. But I will first look to your other post which title refer to incompleteness. argument.(Beginning from the 'OBVIOUS IMPORTANT QUESTION' it becomesvague for me) The key point consists in understanding the difference between computability/simulability and provability. I will come back on this, but the idea is that, assuming comp, I can simulate Einstein's brain exactly, and still not share his beliefs. Similarly the very non powerful Little-Robinson-arithmetic can simulate rich theories like PEANO or ZF, but cannot prove the theorem of PA or ZF. For example PA can prove that ZF can prove the consistency of PA, yet, PA cannot prove the consistency of PA. Bruno http://iridia.ulb.ac.be/~marchal/ -- Mohsen Ravanbakhsh, Sharif University of Technology, Tehran. http://iridia.ulb.ac.be/~marchal/ --~--~-~--~~~---~--~~ 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 -~--~~~~--~~--~--~---
Re: Overcoming Incompleteness
Mohsen Ravanbakhsh *Jesse, I definitely don't think the two systems could be complete, since (handwavey argument follows) if you have two theorem-proving algorithms A and B, it's trivial to just create a new algorithm that prints out the theorems that either A or B could print out, and incompleteness should apply to this too* ** They're not independent systems.putting that aside, I can't find the correspondence to my argument. It would be nice if you could clarify your point. I didn't say they were independent--but each has a well-defined set of theorems that they will judge to be true, no? My point was just that they could not together be complete as you say, since the combination of the two can always be treated as a *single* axiomatic system or theorem-proving algorithm which proves every theorem in the union of the two sets A and B prove individually, and this must necessarily be incomplete--there must be true theorems of arithmetic which this single system cannot prove (meaning that they don't belong to the set A can prove or the set B can prove). Jesse _ More photos, more messages, more storage--get 2GB with Windows Live Hotmail. http://imagine-windowslive.com/hotmail/?locale=en-usocid=TXT_TAGHM_migration_HM_mini_2G_0507 --~--~-~--~~~---~--~~ 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 -~--~~~~--~~--~--~---
Re: Overcoming Incompleteness
Bruno, et al., There is a CRITICAL FUNDAMENTAL ERROR in Godel's papers and concept. If a simpler 'less complete' system - which -includes- its statements, attempts to make -presumptive statements- about a 'more complete' corresponding system ... and its relationship to the simpler 'base of statements' system, then a conclusion is: a system CANNOT accurately 'self assess' but can accurately 'other assess' information which may not in fact be present for assessment. Generalized conclusion: It is not possible to assess known information whereas it is possible to assess unknown information. James Rose --~--~-~--~~~---~--~~ 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 -~--~~~~--~~--~--~---
Re: Overcoming Incompleteness
Le 25-mai-07, à 04:12, Russell Standish a écrit : I don't think anyone yet has managed a self aware formal system, I would say all my work is about that. You can interpret Godel's theorem, or more exactly the fact that machine can prove their own provability logic, and even guess correctly the true but non provable part, as a general statement of self-awareness. Sometimes, self-awareness is defined more precisely by the 4 modal formula: Bp - BBp. This is a theorem for PA, but not for LRA. When LRA proves p, then soon or later, if not already, LRA will prove Bp (that is LRA will prove that she prove p). So Bp - BBp is true for LRA, but only PA can prove such a proposition on itself. although self-reproducing systems have been known since the 1950s, and are popularly encountered in the form of computer viruses. The principle is really the same. That is what I show in my paper amoeba, planaria, and dreaming machine. self-reproduction and self-awareness are a consequence of the closure of the set of partial computable function for the daigonalization procedure. bruno http://iridia.ulb.ac.be/~marchal/ --~--~-~--~~~---~--~~ 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 -~--~~~~--~~--~--~---
Re: Attempt toward a systematic description
Le 25-mai-07, à 02:39, Tom Caylor a écrit : On May 16, 8:17 am, Bruno Marchal [EMAIL PROTECTED] wrote: Hi, I take the opportunity that the list is calm to send a first approximation of a possibly extendable post which addresses the beginning of the background needed for the interview of the universal machine on the physical laws. It also addresses some point relevant for discussing the link formal system == Computation as in Tegmark diagram page 18 of his paper the mathematical universe (cf a post by Mark Geddes). Although schematic, it could already help me if you can list the points for which you would like examples or more technical details, or just explanations. You can also ask for *less* technical details like an explanation in (pure) english, perhaps. I am building again from Robinson Arithmetic, but I could have use the combinators or any logical description of what a universal machine (a computer) can do. The adavantage of using Robinson Arithmetic (or its little variant) is that provability in Robinson Arithmetic corresponds to universal computability, but not of universal provability (which does not exist). I am perhaps on the verge of not being able to explain the sequel in informal term, but I keep hope that non expert, but computer-open minded people, can learn and help me to be clearer or more pedagogical, without having us to study thoroughly mathematical logic. Tell me perhaps if you don't understand what I call Searle's error in the comp setting below. *** 0) historical background ARISTOTLE: reality = what you see PLATO: what you see = shadows of shadows of shadows of shadows of what perhaps could be. And would that be? nobody can say, but everybody can get glimpses by looking inward, even (universal) machines. Twentieth century: two creative bombs: - The Universal Machine (talks bits): UM (Babbage, Post, Turing, Church, Suze, von Neumann, ...) - The other universal machine (talks qubit): QUM (Feynman, Deutsch, Kitaev, Freedman, ...) Could you please expand on how these 20th century ideas extended Aristotle and Plato? Aristotle is (partially?) responsible to the come back to the naive idea that matter exist primitively, and this leads quickly to the idea that science = mainly empirical science. Plato's intuition is that the empirical world is but one aspect of a bigger reality, and that intuition comes from self-introspection. The Universal Machine can illustrate that indeed when she introspects herself, she can discover her own limitation (Godel and Lob theorem are provable by the machines on themselves: a point frequently missed by those who try to use Godel against Mechanism). Of course the quantum part is an extension, but what about the universal part? As you may suspect, I am questioning as usual the even-more- fundamental assumptions which might be underneath this. Sorry I don't really have any time lately either, so I understand if you just want to get on with your description based on your assumptions. OK. Never forget I have never defend the comp hyp. I have (less modestly) prove that it is impossible to believe in both the comp hyp, and the weak materialist thesis (the thesis that there exist primary matter having a relation with the physical knowledge). With comp matter emerges from mind which emerges from numbers. Comp = Milinda-Descartes Mechanism in a digital version. = (also) YES DOCTOR + CHURCH'S THESIS. (I suppress the arithmetical realism, because it is implicit in CHURCH'S THESIS). UDA: a reasoning which shows that if comp is correct then the physical laws have to be derived by a measure on states (the measure being made up through their computational histories). Subgoal: extract QUM from UM's self-observation. Link with everything-list: search for the observer moments and the relevant structure operating on them (not yet solved). *** 1) The ontic theory of everything: LRA (Little Robinson Arithmetic), CLASSICAL LOGIC (first order predicate logic axioms and inference rules) AXIOMS OF SUCCESSION AXIOMS OF ADDITION AXIOMS OF MULTIPLICATION That's all. It is the Schroedinger equation of the comp-everything! The reason is that LRA is already as powerful as a universal machine. LRA proves all verifiable sentences with the shape ExP(x), with P(x) decidable. It is equivalent with the universal dovetailer. Now we have to do with LRA what Everett has done with QM. Embed the observer in the ontic reality. For this we have to modelize the observer/knower/thinker. *** 2) The epistemic theory, or the generic observer theory: PA (the lobian machine I will interview). CLASSICAL LOGIC (first order predicate logic axioms and inference rules)
Re: Overcoming Incompleteness
Hi Russell, - Original Message - From: Russell Standish [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Friday, May 25, 2007 12:14 AM Subject: Re: Overcoming Incompleteness On Thu, May 24, 2007 at 11:53:59PM -0400, Stephen Paul King wrote: For me the question has always been how does one overcome Incompleteness when it is impossible for a simulated system to be identical to its simulator unless the two are one and the same. Is it though? If the simulated system is different from the original, then indeed I would agree with you. [SPK] It was the difference that i was trying to focus on... Bisimulation is, after all, a form of identity if exact. In the case of human self-awareness, I thought it was implemented not by simulation as such, but by decoupling the actual inputs and outputs from the real world, and then feeding the scenario input into the actual brain circuit, and examine the output _without_ actually moving a muscle. It has something to do with the mirror neurons, and it really is quite a neat trick (at least Dennett thinks so, and I tend to agree). [SPK] Ok, but that is it that is generating and examining the inputs and outputs? I am trying to frame this in software terms... Not being into supernatural explanations, I think a perfectly mechanical, or formal model should be able to capture this ability. But how to do it without running into infinite regress is the challenge. And if and when we have this formal model, we can then see whether this idea of solving incompleteness has any merit. I'm as sceptical as anyone, but I do believe the case is more subtle than to be destroyed by a couple of lines of handwaving argument :). [SPK] We avoid infinite regress by having only finite computational resourses. X can only generate a simulation of itself with a resolution whose upper bound is determined by the resourses that X has available within the span of of the simulation of X. Remember, X is not a static entity... Kindest regards, Stephen --~--~-~--~~~---~--~~ 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 -~--~~~~--~~--~--~---
