Re: Is the universe computable?
Dear Russel, The reference page is about the necessary resources for quantum computation in general. The result that our space-time structure can emerge from a computation on a Hilbert space is not complicated, we just prove that the class of all possible evolutions of QM systems includes QM computations. Then we take Deutsch's work showing how classical systems can be simulated by quantum computations and identify the subset(class) of simulations with the subset(class) of our experiences of our world and figure out how to switch from a 3rd person to a 1st person representation (something like what Bruno Marchal proposes) . The hard part is taking the idea that Hilbert space is a representation of something that has ontological reality - not just a mental construct. Kindest regards, Stephen - Original Message - From: Russell Standish [EMAIL PROTECTED] To: Stephen Paul King [EMAIL PROTECTED] Cc: [EMAIL PROTECTED]; [EMAIL PROTECTED] Sent: Sunday, February 22, 2004 6:04 PM Subject: Re: Is the universe computable? On Wed, Jan 21, 2004 at 11:46:17AM -0500, Stephen Paul King wrote: Again, that does not work because we can not take space-time (ala GR) to be big enough to allow us to fit QM into it. On the other hand, it has been shown that a QM system, considered as a quantum computational system, can simulate, with arbitrary accurasy, any classical system, given sufficient Hilbert space dimensions - which play the role of physical resources for QM systems. See: http://arxiv.org/abs/quant-ph/0204157 This leads me to the idea that maybe space-time itself is something that is secondary. It and all of its contents (including our physical bodies) might just be a simulation being generated in some sufficiently large Hilbert space. This idea, of course, requires us to give Hilbert space (and L^2 spaces in general?) the same ontological status that we usually only confer to space-time. ;-) Interesting speculation. I'm not sure that it follows from the ref you give above, however if indeed our space-time structure can emerge from a computation on a Hilbert space as you suggest, then this would be a powerful result. I have already shown (viz my Occam's Razor paper) that the Hilbert space stucture follows from Anthropic arguments on ensemble theories. Getting the space time structure is the next big task to be solved. Cheers A/Prof Russell Standish Director High Performance Computing Support Unit, Phone 9385 6967, 8308 3119 (mobile) UNSW SYDNEY 2052 Fax 9385 6965, 0425 253119 () Australia[EMAIL PROTECTED] Room 2075, Red Centrehttp://parallel.hpc.unsw.edu.au/rks International prefix +612, Interstate prefix 02
Re: Is the universe computable?
On Sun, Feb 22, 2004 at 10:33:37PM -0500, Stephen Paul King wrote: Dear Russel, The reference page is about the necessary resources for quantum computation in general. The result that our space-time structure can emerge from a computation on a Hilbert space is not complicated, we just prove that the class of all possible evolutions of QM systems includes QM computations. Then we take Deutsch's work showing how classical systems can be simulated by quantum computations and identify the subset(class) of simulations with the subset(class) of our experiences of our world and figure out how to switch from a 3rd person to a 1st person representation (something like what Bruno Marchal proposes) . Ahh, that little word can. I was taking your previous statement as stating something much more profound - that 4D space-time must emerge from a Hilbert space computation. Still - perhaps it is possible. I was at dinner a couple of weeks ago with a quantum theorist who claimed exactly that, starting from a standard QED formulation, and taking the h-0 limit. Alas, they tend not to teach QED at undergraduate level, so my ability to evaluate this claim is impoverished. The hard part is taking the idea that Hilbert space is a representation of something that has ontological reality - not just a mental construct. Its not so hard. If we accept ensembles of descriptions as having the ultimate ontological reality (similar, if not equivalent, to Bruno's arithmetic realism), then Hilbert spaces emerge as the highest measure structure under fairly mild assumptions about the nature of consciousness. (detailed in my Why Occam's Razor paper). Kindest regards, Stephen - Original Message - From: Russell Standish [EMAIL PROTECTED] To: Stephen Paul King [EMAIL PROTECTED] Cc: [EMAIL PROTECTED]; [EMAIL PROTECTED] Sent: Sunday, February 22, 2004 6:04 PM Subject: Re: Is the universe computable? On Wed, Jan 21, 2004 at 11:46:17AM -0500, Stephen Paul King wrote: Again, that does not work because we can not take space-time (ala GR) to be big enough to allow us to fit QM into it. On the other hand, it has been shown that a QM system, considered as a quantum computational system, can simulate, with arbitrary accurasy, any classical system, given sufficient Hilbert space dimensions - which play the role of physical resources for QM systems. See: http://arxiv.org/abs/quant-ph/0204157 This leads me to the idea that maybe space-time itself is something that is secondary. It and all of its contents (including our physical bodies) might just be a simulation being generated in some sufficiently large Hilbert space. This idea, of course, requires us to give Hilbert space (and L^2 spaces in general?) the same ontological status that we usually only confer to space-time. ;-) Interesting speculation. I'm not sure that it follows from the ref you give above, however if indeed our space-time structure can emerge from a computation on a Hilbert space as you suggest, then this would be a powerful result. I have already shown (viz my Occam's Razor paper) that the Hilbert space stucture follows from Anthropic arguments on ensemble theories. Getting the space time structure is the next big task to be solved. Cheers A/Prof Russell Standish Director High Performance Computing Support Unit, Phone 9385 6967, 8308 3119 (mobile) UNSW SYDNEY 2052 Fax 9385 6965, 0425 253119 () Australia[EMAIL PROTECTED] Room 2075, Red Centrehttp://parallel.hpc.unsw.edu.au/rks International prefix +612, Interstate prefix 02 -- A/Prof Russell Standish Director High Performance Computing Support Unit, Phone 9385 6967, 8308 3119 (mobile) UNSW SYDNEY 2052 Fax 9385 6965, 0425 253119 () Australia[EMAIL PROTECTED] Room 2075, Red Centrehttp://parallel.hpc.unsw.edu.au/rks International prefix +612, Interstate prefix 02 pgp0.pgp Description: PGP signature
Re: Is the universe computable?
Dear Russel, Does this quantum theorist have anything published on this that i can find online? I do need to do better than can! I need a must! ;-) Stephen - Original Message - From: Russell Standish [EMAIL PROTECTED] To: Stephen Paul King [EMAIL PROTECTED] Cc: Russell Standish [EMAIL PROTECTED]; [EMAIL PROTECTED]; [EMAIL PROTECTED] Sent: Sunday, February 22, 2004 11:22 PM Subject: Re: Is the universe computable? On Sun, Feb 22, 2004 at 10:33:37PM -0500, Stephen Paul King wrote: Dear Russel, The reference page is about the necessary resources for quantum computation in general. The result that our space-time structure can emerge from a computation on a Hilbert space is not complicated, we just prove that the class of all possible evolutions of QM systems includes QM computations. Then we take Deutsch's work showing how classical systems can be simulated by quantum computations and identify the subset(class) of simulations with the subset(class) of our experiences of our world and figure out how to switch from a 3rd person to a 1st person representation (something like what Bruno Marchal proposes) . Ahh, that little word can. I was taking your previous statement as stating something much more profound - that 4D space-time must emerge from a Hilbert space computation. Still - perhaps it is possible. I was at dinner a couple of weeks ago with a quantum theorist who claimed exactly that, starting from a standard QED formulation, and taking the h-0 limit. Alas, they tend not to teach QED at undergraduate level, so my ability to evaluate this claim is impoverished. The hard part is taking the idea that Hilbert space is a representation of something that has ontological reality - not just a mental construct. Its not so hard. If we accept ensembles of descriptions as having the ultimate ontological reality (similar, if not equivalent, to Bruno's arithmetic realism), then Hilbert spaces emerge as the highest measure structure under fairly mild assumptions about the nature of consciousness. (detailed in my Why Occam's Razor paper). Kindest regards, Stephen - Original Message - From: Russell Standish [EMAIL PROTECTED] To: Stephen Paul King [EMAIL PROTECTED] Cc: [EMAIL PROTECTED]; [EMAIL PROTECTED] Sent: Sunday, February 22, 2004 6:04 PM Subject: Re: Is the universe computable? On Wed, Jan 21, 2004 at 11:46:17AM -0500, Stephen Paul King wrote: Again, that does not work because we can not take space-time (ala GR) to be big enough to allow us to fit QM into it. On the other hand, it has been shown that a QM system, considered as a quantum computational system, can simulate, with arbitrary accurasy, any classical system, given sufficient Hilbert space dimensions - which play the role of physical resources for QM systems. See: http://arxiv.org/abs/quant-ph/0204157 This leads me to the idea that maybe space-time itself is something that is secondary. It and all of its contents (including our physical bodies) might just be a simulation being generated in some sufficiently large Hilbert space. This idea, of course, requires us to give Hilbert space (and L^2 spaces in general?) the same ontological status that we usually only confer to space-time. ;-) Interesting speculation. I'm not sure that it follows from the ref you give above, however if indeed our space-time structure can emerge from a computation on a Hilbert space as you suggest, then this would be a powerful result. I have already shown (viz my Occam's Razor paper) that the Hilbert space stucture follows from Anthropic arguments on ensemble theories. Getting the space time structure is the next big task to be solved. Cheers -- -- A/Prof Russell Standish Director High Performance Computing Support Unit, Phone 9385 6967, 8308 3119 (mobile) UNSW SYDNEY 2052 Fax 9385 6965, 0425 253119 () Australia[EMAIL PROTECTED] Room 2075, Red Centre http://parallel.hpc.unsw.edu.au/rks International prefix +612, Interstate prefix 02 -- --
Re: Is the universe computable?
Dear Russell, Let me add that I do not think that it is sufficient to embed space-time in Hilbert space, we also need some way of explaining how space-time phenomena acts on the Hilbert space's vectors. The infamous back-action... I have an idea but it is pure vapor at this point ... Kindest regards, Stephen - Original Message - From: Stephen Paul King [EMAIL PROTECTED] To: Russell Standish [EMAIL PROTECTED] Cc: [EMAIL PROTECTED]; [EMAIL PROTECTED] Sent: Sunday, February 22, 2004 11:39 PM Subject: Re: Is the universe computable? Dear Russel, Does this quantum theorist have anything published on this that i can find online? I do need to do better than can! I need a must! ;-) Stephen - Original Message - From: Russell Standish [EMAIL PROTECTED] To: Stephen Paul King [EMAIL PROTECTED] Cc: Russell Standish [EMAIL PROTECTED]; [EMAIL PROTECTED]; [EMAIL PROTECTED] Sent: Sunday, February 22, 2004 11:22 PM Subject: Re: Is the universe computable? On Sun, Feb 22, 2004 at 10:33:37PM -0500, Stephen Paul King wrote: Dear Russel, The reference page is about the necessary resources for quantum computation in general. The result that our space-time structure can emerge from a computation on a Hilbert space is not complicated, we just prove that the class of all possible evolutions of QM systems includes QM computations. Then we take Deutsch's work showing how classical systems can be simulated by quantum computations and identify the subset(class) of simulations with the subset(class) of our experiences of our world and figure out how to switch from a 3rd person to a 1st person representation (something like what Bruno Marchal proposes) . Ahh, that little word can. I was taking your previous statement as stating something much more profound - that 4D space-time must emerge from a Hilbert space computation. Still - perhaps it is possible. I was at dinner a couple of weeks ago with a quantum theorist who claimed exactly that, starting from a standard QED formulation, and taking the h-0 limit. Alas, they tend not to teach QED at undergraduate level, so my ability to evaluate this claim is impoverished. The hard part is taking the idea that Hilbert space is a representation of something that has ontological reality - not just a mental construct. Its not so hard. If we accept ensembles of descriptions as having the ultimate ontological reality (similar, if not equivalent, to Bruno's arithmetic realism), then Hilbert spaces emerge as the highest measure structure under fairly mild assumptions about the nature of consciousness. (detailed in my Why Occam's Razor paper). Kindest regards, Stephen - Original Message - From: Russell Standish [EMAIL PROTECTED] To: Stephen Paul King [EMAIL PROTECTED] Cc: [EMAIL PROTECTED]; [EMAIL PROTECTED] Sent: Sunday, February 22, 2004 6:04 PM Subject: Re: Is the universe computable? On Wed, Jan 21, 2004 at 11:46:17AM -0500, Stephen Paul King wrote: Again, that does not work because we can not take space-time (ala GR) to be big enough to allow us to fit QM into it. On the other hand, it has been shown that a QM system, considered as a quantum computational system, can simulate, with arbitrary accurasy, any classical system, given sufficient Hilbert space dimensions - which play the role of physical resources for QM systems. See: http://arxiv.org/abs/quant-ph/0204157 This leads me to the idea that maybe space-time itself is something that is secondary. It and all of its contents (including our physical bodies) might just be a simulation being generated in some sufficiently large Hilbert space. This idea, of course, requires us to give Hilbert space (and L^2 spaces in general?) the same ontological status that we usually only confer to space-time. ;-) Interesting speculation. I'm not sure that it follows from the ref you give above, however if indeed our space-time structure can emerge from a computation on a Hilbert space as you suggest, then this would be a powerful result. I have already shown (viz my Occam's Razor paper) that the Hilbert space stucture follows from Anthropic arguments on ensemble theories. Getting the space time structure is the next big task to be solved. Cheers -- -- A/Prof Russell Standish Director High Performance Computing Support Unit, Phone 9385 6967, 8308 3119 (mobile) UNSW SYDNEY 2052 Fax 9385 6965, 0425 253119 () Australia[EMAIL PROTECTED] Room 2075, Red Centre http://parallel.hpc.unsw.edu.au/rks International prefix +612, Interstate prefix 02 --
Re: [issues] Re: Is the universe computable?
Dear Russell, Don Page explored a similar idea to mine in: quant-ph/9506010 Kindest regards, Stephen - Original Message - From: Stephen Paul King [EMAIL PROTECTED] To: Russell Standish [EMAIL PROTECTED] Cc: [EMAIL PROTECTED]; [EMAIL PROTECTED] Sent: Sunday, February 22, 2004 11:45 PM Subject: [issues] Re: Is the universe computable? Dear Russell, Let me add that I do not think that it is sufficient to embed space-time in Hilbert space, we also need some way of explaining how space-time phenomena acts on the Hilbert space's vectors. The infamous back-action... I have an idea but it is pure vapor at this point ... Kindest regards, Stephen - Original Message - From: Stephen Paul King [EMAIL PROTECTED] To: Russell Standish [EMAIL PROTECTED] Cc: [EMAIL PROTECTED]; [EMAIL PROTECTED] Sent: Sunday, February 22, 2004 11:39 PM Subject: Re: Is the universe computable? Dear Russel, Does this quantum theorist have anything published on this that i can find online? I do need to do better than can! I need a must! ;-) Stephen - Original Message - From: Russell Standish [EMAIL PROTECTED] To: Stephen Paul King [EMAIL PROTECTED] Cc: Russell Standish [EMAIL PROTECTED]; [EMAIL PROTECTED]; [EMAIL PROTECTED] Sent: Sunday, February 22, 2004 11:22 PM Subject: Re: Is the universe computable? On Sun, Feb 22, 2004 at 10:33:37PM -0500, Stephen Paul King wrote: Dear Russel, The reference page is about the necessary resources for quantum computation in general. The result that our space-time structure can emerge from a computation on a Hilbert space is not complicated, we just prove that the class of all possible evolutions of QM systems includes QM computations. Then we take Deutsch's work showing how classical systems can be simulated by quantum computations and identify the subset(class) of simulations with the subset(class) of our experiences of our world and figure out how to switch from a 3rd person to a 1st person representation (something like what Bruno Marchal proposes) . Ahh, that little word can. I was taking your previous statement as stating something much more profound - that 4D space-time must emerge from a Hilbert space computation. Still - perhaps it is possible. I was at dinner a couple of weeks ago with a quantum theorist who claimed exactly that, starting from a standard QED formulation, and taking the h-0 limit. Alas, they tend not to teach QED at undergraduate level, so my ability to evaluate this claim is impoverished. The hard part is taking the idea that Hilbert space is a representation of something that has ontological reality - not just a mental construct. Its not so hard. If we accept ensembles of descriptions as having the ultimate ontological reality (similar, if not equivalent, to Bruno's arithmetic realism), then Hilbert spaces emerge as the highest measure structure under fairly mild assumptions about the nature of consciousness. (detailed in my Why Occam's Razor paper). Kindest regards, Stephen - Original Message - From: Russell Standish [EMAIL PROTECTED] To: Stephen Paul King [EMAIL PROTECTED] Cc: [EMAIL PROTECTED]; [EMAIL PROTECTED] Sent: Sunday, February 22, 2004 6:04 PM Subject: Re: Is the universe computable? On Wed, Jan 21, 2004 at 11:46:17AM -0500, Stephen Paul King wrote: Again, that does not work because we can not take space-time (ala GR) to be big enough to allow us to fit QM into it. On the other hand, it has been shown that a QM system, considered as a quantum computational system, can simulate, with arbitrary accurasy, any classical system, given sufficient Hilbert space dimensions - which play the role of physical resources for QM systems. See: http://arxiv.org/abs/quant-ph/0204157 This leads me to the idea that maybe space-time itself is something that is secondary. It and all of its contents (including our physical bodies) might just be a simulation being generated in some sufficiently large Hilbert space. This idea, of course, requires us to give Hilbert space (and L^2 spaces in general?) the same ontological status that we usually only confer to space-time. ;-) Interesting speculation. I'm not sure that it follows from the ref you give above, however if indeed our space-time structure can emerge from a computation on a Hilbert space as you suggest, then this would be a powerful result. I have already shown (viz my Occam's Razor paper) that the Hilbert space stucture follows from Anthropic arguments on ensemble theories. Getting the space time structure is the next big task to be solved. Cheers -- -- A/Prof Russell
Re: Is the universe computable
Dear Bruno, I realized something this morning, as I was ruminating over your response below, that if my thesis is true so is your take on comp! But only in one sense. ;-) Do you the Calude et al paper, discussing the idea of embedding quantum logics into classical logics and the other paper by Calude et al that discusses how an Quantum comp, with a Hamiltonian of infinite degrees of freedom, can solve the Halting problem? My realization is this, that if we consider the case of the Calude system, classical comp would be isomorphic or something similar to an infinite classical machine, such as your Universal Dovetailer. But this is where our views, I think, diverge. Your argument, to me, resembles that of Julian Barbour for the "non-existence of time" in his celebrated book and a similar one by Stuart Kauffman and Lee Smolin, as discussed here: http://www.edge.org/3rd_culture/smolin/smolin_p2.html My difficulty is that the assumption of timelessness at the level of the totality of existence does not necessitate that timelessness prevails within all aspects of existence. Prof. Hitoshi Kitada, with Lance Fletcher, wrote a paper discussing this: http://www.kitada.com/timeV.html I have found independent reasoning by Michael C. Mackey,within the study of thermodynamics, that lead to the same conclusion. So, what does this have to do with comp? Let me first quote something your wrote below: "If a machine can believe something, it will be hard for her to believe in comp and in its consequences, until she realizes that indeed if a machine can believe something, it will be hard for her to believe in comp and in its consequences, until she realizes that indeed if a machine can believe something, it will be hard for her to believe in comp and in its consequences until she realizes that indeed if " This situation is almost identical to that occurs in the "bisimulation" hypothesis that I have been working on IFF one assumes that the computational system has infinite computational resources. For example: System A can simulateA simulatingA simulatingA ... System A can simulate system B simulating A simulating B System A can simulate system B simulating system C One can easily avoid this regress by requiring that the computational resources and/or "power" of the systems be finite. What I am thinking is that your own notion of "it is hard to believein comp, until she realizes that indeed if a machine can believe something"implicitly involves a durationand/or distinction between the state of "believing" and the state of "realizing" that can not be shrunk to zeroand retain its meaningfulness. What the various forms of realisms that introduce Platonic realms to "support" their necessary structure is that they seem to want to retain the meaningfulness of numbers, AR in your case, all the while removing the necessity for distinguishing such. One can not have one's cake and eat it too! Barbour would have us believe that the computational complexity involved in his "best matching" scheme is obviated by the mere postulation that all of the possible ways that the world could be co-exist in Platonia. The experience of time is merely an illusion that follows from seeing the time capsules from the inside. The trouble is that it is inconsistent to allow forthe mere possibility of belief, or computations in general,if time is just in an illusion. As Lucas likes to say, such reasoning is Self-Stultifying!I see the same situation in your attempt to make comp "Popperian falsifiable". Your seem to try to avoid this pathology with the assumption of "digital substitutability" but I seethis as akin to allowing for the existence of perpetual motion machines, in that for a classical system to simulate faithfully my mind, it would have to also simulate every possible experience that I could have, including any experiment that I might perform involving explicitly "weird" QM behavior. Thus it must, de facto, be able to simulate a QM system and it has been shown that this is only possible in the case of systems with infinite resources. We find ourselves unable to get to an explanation of the "illusion" of time, and physicality in general! My main criticism is that this problem "goes away" if we shift from thinking of existence as a timeless and static "Being" and use, instead, a thinking of Existence as an eternal "Becoming". We can have our UDA and isomorphism between Quantum comp and Classical comp at the Totality of existence level, but this indistiguishability breaks down when we consider finite comp systems. Am I making any sense so far? Kindest regards, Stephen - Original Message - From: Bruno Marchal To: Stephen Paul King ; [EMAIL PROTECTE
Re: Is the universe computable
Dear Stephen, [SPK] No, Bruno, I like Comp, I like it a LOT! I just wish that it had a support that was stronger than the one that you propose ... [BM] Where do I give a support to comp? I don't remember. No doubt that I am fascinated by its consequences, and that I appreciate the so deep modesty and silence of the Wise Machine. But the reason why I work on comp is just that it makes mathematical logic a tool to proceed some fundamental question I'm interested in. and that in addition to your 1 and 3-determinacy that there would be a way to shift from the Dovetailer view (the from the outside view) to the inside view such that some predictiveness would obtain when we are trying to predict, say the dynamics of some physical system. Otherwise, I claim, your theory is merely an excursion into computational Scholasticism. The whole point of my work consists to show (thanks to math) that comp is indeed popper falsifiable. It is just a matter of work and time to see if the logic of observable proposition which has been derived from comp gives a genuine quantum logic and ascribes the correct probability distribution to the verifiable facts. The weakness of the approach is that it leads to hard mathematical question. I am sanguine about QM's weirdness! I see it as implying that there is much more to Existence than what we can experience with our senses. ;-) I agree with you. Now comp shows much more easily that it *must* be so. You know Bohr said that someone pretending to understand QM really does not understand it. The same with comp, it can even be justified. If a machine can believe something, it will be hard for her to believe in comp and in its consequences, until she realizes that indeed if a machine can believe something, it will be hard for her to believe in comp and in its consequences, until she realizes that indeed if a machine can believe something, it will be hard for her to believe in comp and in its consequences until she realizes that indeed if (apology for this infinite sentence). [BM] comp = 1) there is level of description of me such that I cannot be aware of functional digital substitution made at that level. [SPK] Here we differ as I do not believe that digital substitution is possible, IF such is restricted to UTMs or equivalents. No consistent machine can really believe that indeed. But this does not mean a consistent machine will believe not-comp. The point is: are you willing to accept it for the sake of the reasoning. 2) Church thesis [SPK] I have problems with Churches thesis because it, when taken to its logical conclusion, explicitly requires that all of the world to be enumerable and a priori specifiable. Peter Wegner, and others, have argued persuasively, at least for me, that this is simply is not the case. Church thesis entails that the partial (uncontrolable a priori) processes are mechanically enumerable. AND Church thesis entails that the total (controlable) processes are NOT mechanically enumerable. In each case we face either uncontrolability or non enumerability. It is Church thesis which really protects comp from reductionnism. That was the subject of one thesis I propose in the seventies. Since then Judson Webb has written a deep book on that point. (Webb 1980, ref in my thesis, url below). See my everything-list posts diagonalisation for the proof of those facts. 3) Arithmetical Realism) makes the physical science eventually secondary with respect to number theory/computer science/machine psychology/theology whatever we decide to call that fundamental field ... [SPK] I have no problem with AR, per say, but see it as insufficient, since it does not address the act of counting, it merely denotes the list of rules for doing so. Certainly not. AR is the doctrine that even in a case of absolute catastrophe killing all living form in the multiverse, the statement that there is no biggest prime will remain true. It has nothing to do with axioms and rules of formal system. Indeed by Godel's incompleteness theorem Arithmetical truth extends itself well beyond any set of theorem provable in any axiomatizable theory. Now, what do you mean by AR is insufficient? AR just say that arithmetical truth does not depend on us. It does not say that some other truth does not exist as well (although as a *consequence* of comp plus occam they do indeed vanish). Don't confuse AR with Pythagorean AR which asserts explicitely AR and no more. We got P.AR as a consequence of comp, but we do not postulate it in the comp hyp. I will go through your thesis step by step again and see if I can wrestle my prejudices down into some reasonableness. ;-) OK. Be sure to go to step n only if you manage to go to step n-1 before. Don't hesitate to ask question if something is unclear. Be sure you accept the hypotheses (if only for the sake of the argument). Best Regards, Bruno http://iridia.ulb.ac.be/~marchal/
Re: Is the universe computable
At 17:12 27/01/04 -0500, Stephen Paul King wrote: Dear Kory and Hal, Kory's idea strongly reminds me of the basic idea explored by John Cramer in his Interactional interpretation in that it takes into account both past and future states. Please see: http://www.lns.cornell.edu/spr/2000-03/msg0023110.html http://mist.npl.washington.edu/npl/int_rep/tiqm/TI_toc.html One thing you might wish to bear in mind is that David Deutsch has pointed out that Cramer's idea is equivalent to the Many worlds interpretation, but I can not find the exact quote at this time. ;-) The main problem that I have with any CA based model is that it explicity requires some from of absolute synchronicity of the shift functions of the cells. I see this as a disallowance of CA based models to guide us into our questions about the appearence of a flow of time, it assumes a form of Newton's Absolute time from the onset! Only if you think of a physical implementation of a CA, which is what people here try to avoid (I think). In addition, it has been pointed out be several CA experts that CAs are equivalent to universal Turing Machines and if UTMs are incapable of deriving QM and its phenomena then neither can CAs. Just to be clear (because your term deriving is a little ambiguous), but UTM can emulate (perfectly simulate) any quantum piece of matter including quantum computer (just dovetail on the superpositions). This entails an exponential slow down, but as we search to define time from inside this is not a problem. As I say in my other post, the real problem is the apparent computability of matter/physical processes. Newton physics would not have been falsified I would have pretend having find a refutation of comp, for comp makes reality much weirder than classical physics. bruno
Re: Is the universe computable
At 11:57 27/01/04 -0500, Stephen Paul King wrote: Thank you for this post. It gives me a chance to reintroduce one problem that I have with your model. Like you, I am very interested in comments from others, as it could very well be that I am misunderstanding some subtle detail of your thesis. You wrote: ... remembering the comp 1-indeterminacy, that is that if you are duplicate into an exemplary at Sidney and another at Pekin, your actual expectation is indeterminate and can be captured by some measure, let us say P = 1/2, and this (capital point) independently of the time chosen for any of each reconstitution (at Pekin or Sidney), giving that the delays of reconstitution cannot be perceived (recorded by the first person)). Now my problem is that IF there is any aspect of perception and/or observers that involves a quantum mechanical state there will be the need to take the no-cloning theorem into account. For example, we find in the following paper a discussion of this theorem and its consequences for teleportation: http://arxiv.org/abs/quant-ph/0012121 This is a question people ask me often. But not only the cloning theorem is not a problem with the comp hyp, but actually it is highly plausible the non-cloning theorem is a direct consequence of comp. Remember that, with comp, physicalities emerges from an average of an infinity of computationnal histories: it is a priori hard to imagine how we could clone that. This is no more amazing than the fact the white rabbit. remember that with comp, from inside things look a priori not computable. The apparant computability of the laws of physics is what is in need to be explain with comp. We should perhaps come back when you have accept all the steps in uda step by step. As a possible way to exploit a potential loop hole in this, I point you to the following: http://www.fi.muni.cz/usr/buzek/mypapers/96pra1844.pdf My main question boils down to this: Does Comp 1-determinacy require this duplication to be exact? Is it sufficient that approximately similar copies could be generated and not exact duplicates? It must be exact if the duplication is done exactly at the right level of substitution (which exits by hypothesis), and can be approximate if some lower level of duplication is chosen instead. How would this affect your ideas about measures, if at all? I understand that you are trying to derive QM from Comp and thus might not see the applicability of my question, but as a reply to this I will again point your to the various papers that have been written showing that it is impossible to embed or describe completely a QM system (and its logics) using only a classical system (and its logics), if that QM system has more that two Hilbert space dimensions associated. Start with the Kochen-Specker theorem... http://plato.stanford.edu/entries/kochen-specker/ I'm afraid you make a confusion of level here. What KS showed is that you cannot put a boolean algebra of values to quantum observable pertaining to some systems. But this is exactly what comp predict for matter and time notion. That is why we get quantum logics for the first person verifiable proposition. Nowhere I pretend to recover a classical logic in which quantum measurement value can be embedded, quite the contrary with comp classical logic is plainly false for all verifiable 1-notion right at the beginning. BTW, even if KS was a threat, your argument does not follow because KS is a theorem in quantum mechanics, and as you say, I just show that the physics is derivable from comp; if KS is false in the physics derived from comp then KS would indeed be a problem, but I insist it is not. It is only the apparent computability of the universe which still remains the miracle. My feeling Stephen is just that you don't like comp, and I have no problem with that. Some people takes my work to be a beginning of refutation of comp, and perhaps they are right. I want just illustrate that this is not obvious, and the tiny part of physics I have extracted from comp is for me just very weird (and no more so I estimate we are still far from a real reductio ad absurde of comp). The weirdness is the many world like feature of any comp reality, the non computability of the physical processes in any reality compatible with comp, and a sort of quantum logic weaker than usual quantum logic. Is that so weird? Certainly no more weird than quantum weirdness. If you are really interested in my reasoning, I would dare to insist going from step to step. If you prefer not studying the consequences of comp because you don't have the taste for it, I will not insist at all. My point is just that comp (that is 1) there is level of description of me such that I cannot be aware of functional digital substitution made at that level. 2) Church thesis 3) Arithmetical Realism) makes the physical science eventually secondary with respect to number theory/computer science/machine psychology/theology whatever we
Re: Is the universe computable
Dear Bruno, Let me put to the most salient part of your reply: My feeling Stephen is just that you don't like comp, and I have no problem with that. Some people takes my work to be a beginning of refutation of comp, and perhaps they are right. I want just illustrate that this is not obvious, and the tiny part of physics I have extracted from comp is for me just very weird (and no more so I estimate we are still far from a real reductio ad absurde of comp). [SPK] No, Bruno, I like Comp, I like it a LOT! I just wish that it had a support that was stronger than the one that you propose and that in addition to your 1 and 3-determinacy that there would be a way to shift from the Dovetailer view (the "from the outside" view) to the "inside" view such that some predictiveness would obtain when we are trying to predict, say the dynamics of some physical system. Otherwise, I claim, your theory is merely an excursion into computational Scholasticism. The weirdness is the many world like feature of any comp reality, the non computability of the physical processes in any reality compatible with comp, and a sort of quantum logic weaker than usual quantum logic. Is that so weird? Certainly no more weird than quantum weirdness. [SPK] I amsanguine about QM's "weirdness"! I see it as implying that there is much more to "Existence" than what we can experience with our senses. ;-) If you are really interested in my reasoning, I would dare to insist going from step to step. If you prefer not studying the consequences of comp because you don't have the taste for it, I will not insist at all. My point is just that comp (that is 1) there is level of description of me such that I cannot be aware of functional digital substitution made at that level. [SPK] Here we differ as I do not believe that "digital substitution" is possible, IF such is restricted to UTMs or equivalents. 2) Church thesis [SPK] I have problems with Churches thesis because it, when taken to its logical conclusion,explicitly requires that all of the world to be enumerable and a priori specifiable. Peter Wegner, and others, have argued persuasively, at least for me, that this is simply is not the case. 3) Arithmetical Realism) makes the physical science eventually secondary with respect to number theory/computer science/machine psychology/theology whatever we decide to call that fundamental field ... [SPK] I have no problem with AR, per say, but see it as insufficient, since it does not address the "act" of counting, it merely denotes the list of rules for doing so. I will go through your thesis step by step again and see if I can wrestle my prejudices down into some reasonableness. ;-) Kindest regards, Stephen Bruno - Original Message - From: Bruno Marchal To: [EMAIL PROTECTED] ; [EMAIL PROTECTED] Cc: [EMAIL PROTECTED] Sent: Wednesday, January 28, 2004 9:27 AM Subject: Re: Is the universe computable At 11:57 27/01/04 -0500, Stephen Paul King wrote: Thank you for this post. It gives me a chance to reintroduce one problem that I have with your model. Like you, I am very interested in comments from others, as it could very well be that I am misunderstanding some subtle detail of your thesis. You wrote:"... remembering the comp 1-indeterminacy, that is that if you are duplicateinto an exemplary at Sidney and another at Pekin, your actualexpectation is indeterminate and can be captured by some measure, let us say P = 1/2, and this (capital point) independently of the timechosen for any of each reconstitution (at Pekin or Sidney), giving that the delays of reconstitution cannot be perceived (recorded by the first person))." Now my problem is that IF there is any aspect of perception and/or "observers" that involves a quantum mechanical state there will be the need to take the "no-cloning" theorem into account. For example, we find in the following paper a discussion of this theorem and its consequences for teleportation:http://arxiv.org/abs/quant-ph/0012121This is a question people ask me often. But not only the cloning theorem is not a problem with the comp hyp, but actually it is highly plausible the non-cloning theorem is a direct consequence of comp. Remember that, with comp, physicalities emerges from an average of an infinity of computationnal histories: it is a priori hard to imagine how we could clone that. This is no more amazing than the fact the white rabbit. remember that with comp, from inside things look a priori not computable. The apparant computability of the laws of physics is what is in need to be explain with comp. We should perhaps come back when you have accept all the steps in uda step by step. As a possible way to exploit
Re: Is the universe computable
At 1/27/04, Hal Finney wrote: One way to approach an answer to the question is to ask, is there such a CA in which a universal computer can be constructed? That would be evidence for at least a major prerequisite for conscious observations. Do you have any examples like this? In my opinion, computation universality is the *only* prerequisite for the possibility of SASs, so I agree that the correct question to ask is can a CA with bi-directional time be computation universal? I think that the answer is almost certainly yes. Let me explain why. First, lets get a really clear picture of what we're talking about. I want to consider a CA with only 2 spacial dimensions, because I find it easy to picture the resulting 3D block universe. (It's too hard for me to picture the 4D block universe that results from a 3+1D CA.) Lets imagine that the spacial planes of this CA are stacked on top of each other, so that the block universe looks like a tall tower, with the time dimension being the up and down directions. Now, the state of any particular cell of this block universe is determined by the 3x3 square of cells directly below it, as well as the 3x3 square of cells above it. For the rest of this discussion, lets refer to any particular chosen cell as the center cell, and the 18 cells below and above it as the neighborhood. For every possible combination of states of those 18 cells, the rules of the CA dictate what state the center cell must be in. Now, lets imagine that the cells in this particular CA have three possible states - lets call them black (empty), blue, and red. Lets set up the rules of the CA in the following way. First of all, lets consider a center cell whose neighborhood contains nothing but blue cells and empty cells. Lets define our CA rule so that, in such a case, the state of the center cell will either be blue or black, and this will be determined only by the 3x3 square of cells below it. In fact, lets go ahead and use Conway's life rule here. So, if the lower 9 cells are all blue and the upper 9 cells are any combination of blue and black, the center cell must be black. And so on. Now lets imagine the exact same thing for the red cells, except this time the state of the center cell is determined by the 9 cells *above* the center cell. For any 18-cell neighborhood that contains *only* red cells and black cells, the center cell will either be red or black, as determined by the upper 9 cells. Basically, what we have so far is a universe which contains blue matter which moves forward in time (i.e. upwards along the tower), and red anti-matter which moves backwards in time (downwards along the tower). Each kind of matter, in isolation, will follow the old familiar rules of Conway's life. If you were to grow an instance of the universe containing only red matter or only blue matter, it would be indistinguishable from Conway's life. And of course, we know that Conway's life is computation universal. So this universe is capable of containing SASs. Now, of course, we need to define what happens when matter and anti-matter interact. In other words, for every possible combination of 18 neighbors that contains both red and blue cells, we need to specify what the state of the center cell should be. It should be clear that there is a Vast number of possibilities here, each representing a unique universe. We can consider the simplest possible rule, which is that the center cell is always empty for any neighborhood which contains both red and blue cells. Perhaps under that rule, matter and anti-matter will tend to obliterate each other. I can imagine a whole range of other possible rules, some of which cause red and blue gliders to bounce off of each other, etc. Clearly we can imagine universes which contain large, isolated chunks of blue matter or red matter, and those portions of the universe would be capable of containing SASs. We can imagine stray red gliders occasionally wandering into realms of blue space, and vice-versa, causing subtle changes, but not necessarily destroying any of the SASs there. It seems to me that this is enough to show that it must be possible for CAs with bi-directional time to contain universal computation, and therefore, potentially, SASs. After saying all of this, I'm realizing that I don't really need to consider these bi-directional CAs to make the original points I was trying to make. I can just as easily consider a normal CA like Conway's life (or some other hypothetical CA that's more conducive to life). We can still do the trick of running through all the possible block universes of a given size, and discarding all of those that don't represent a valid evolution of the rule in question. If our universes are big enough, some of the remaining ones will contain patterns that look like SASs. Are these patterns really conscious? At what point in the testing process did they become conscious? And so on. However,
Re: Is the universe computable
At 1/26/04, Stephen Paul King wrote: The modern incarnation of this is the so-called 4D cube model of the universe. Again, these ideas only work for those who are willing to completely ignore the facts of computational complexity and the Heisenberg Uncertainty principle. I think you and I are living in two completely different argument-universes here. :) I'm not arguing that our universe is computable. I'm not arguing that our universe can definitely be modeled as a 4D cube. I'm not arguing that only integers exist. The only reason why I keep using CA models is that they're extraordinarily easy to picture and understand, *and*, since I believe that SASs can exist even in very simple computable universes like CAs, it makes sense to use CA models when trying to probe certain philosophical questions about SASs, physical existence, and instantiation. Quantum physics and the Heisenberg Uncertainty principle are simply irrelevant to the particular philosophical questions that I'm concerned with. Forget about our own (potentially non-computable) universe for a second. Surely you agree that we can imagine some large-but-finite 3+1D CA (it doesn't have to be anything like our own universe) in which the state of each bit is dependent on the states of neighboring bits one tick in the future as well as one tick in the past. Surely you agree that we could search through all the possible 4D cube bit-strings, discarding those that don't follow our rule. (This would take a Vast amount of computation, but that's irrelevant to the particular questions I'm interested in.) Some of the 4D cubes that we're left with will (assuming we've chosen a good rule for our CA) contain patterns that look all the world like SASs, moving through their world, reacting to their environment, having a sense of passing time, etc. This simple thought experiment generates some fascinating philosophical questions. Are those SASs actually conscious? If so, at what point did they become conscious? Was it at the moment that our testing algorithm decided that that particular 4D block followed our specified CA rule? Or is it later, when we animate portions of the 4D block so that we can watch events unfold in realtime? These are not rhetorical questions - I'd really like to hear your answers, because it might help me get a handle on your position. (I'd like to hear other people's answers as well, because I think it's a fascinating problem.) Anyway, the point that I'm really trying to make is that, while these thought experiments have a lot of bearing on the question of mathematical existence vs. physical existence, they have nothing at all to do with quantum physics or Heisenberg uncertainty. The fact it seems so to you makes me think that we're not even talking about the same problem. -- Kory
Re: Is the universe computable
Hi Kory, Hi Stephen, Hi All, At 01:19 27/01/04 -0500, Kory Heath wrote: At 1/26/04, Stephen Paul King wrote: The modern incarnation of this is the so-called 4D cube model of the universe. Again, these ideas only work for those who are willing to completely ignore the facts of computational complexity and the Heisenberg Uncertainty principle. I think you and I are living in two completely different argument-universes here. :) I'm not arguing that our universe is computable. I'm not arguing that our universe can definitely be modeled as a 4D cube. I'm not arguing that only integers exist. The only reason why I keep using CA models is that they're extraordinarily easy to picture and understand, *and*, since I believe that SASs can exist even in very simple computable universes like CAs, it makes sense to use CA models when trying to probe certain philosophical questions about SASs, physical existence, and instantiation. Quantum physics and the Heisenberg Uncertainty principle are simply irrelevant to the particular philosophical questions that I'm concerned with. Forget about our own (potentially non-computable) universe for a second. Surely you agree that we can imagine some large-but-finite 3+1D CA (it doesn't have to be anything like our own universe) in which the state of each bit is dependent on the states of neighboring bits one tick in the future as well as one tick in the past. Surely you agree that we could search through all the possible 4D cube bit-strings, discarding those that don't follow our rule. (This would take a Vast amount of computation, but that's irrelevant to the particular questions I'm interested in.) Some of the 4D cubes that we're left with will (assuming we've chosen a good rule for our CA) contain patterns that look all the world like SASs, moving through their world, reacting to their environment, having a sense of passing time, etc. This simple thought experiment generates some fascinating philosophical questions. Are those SASs actually conscious? If so, at what point did they become conscious? Was it at the moment that our testing algorithm decided that that particular 4D block followed our specified CA rule? Or is it later, when we animate portions of the 4D block so that we can watch events unfold in realtime? These are not rhetorical questions - I'd really like to hear your answers, because it might help me get a handle on your position. (I'd like to hear other people's answers as well, because I think it's a fascinating problem.) Anyway, the point that I'm really trying to make is that, while these thought experiments have a lot of bearing on the question of mathematical existence vs. physical existence, they have nothing at all to do with quantum physics or Heisenberg uncertainty. The fact it seems so to you makes me think that we're not even talking about the same problem. -- Kory I understand Kory very well and believe he argues correctly in this post with respect to Stephen. But at the same time, I pretend that if we follow Kory's form of reasoning we are lead to expect a relation with (quantum) physics. This can seem a total miracle, ... but only for someone being both computationnalist and physicalist, and that has been showed impossible (marchal 88, Maudlin 89, ref in my thesis). Let me try to explain shortly. The reason is that if the initial CA is universal enough the (and that follows for theoretical computer science) universal CA will dovetail on an infinite number of similar computations passing through each possible SAS computational state, and then ... ... remembering the comp 1-indeterminacy, that is that if you are duplicate into an exemplary at Sidney and another at Pekin, your actual expectation is indeterminate and can be captured by some measure, let us say P = 1/2, and this (capital point) independently of the time chosen for any of each reconstitution (at Pekin or Sidney), giving that the delays of reconstitution cannot be perceived (recorded by the first person)). So if we run an universal dovetailer (implemented in CA, or FORTRAN, or even just arithmetical truth), each SAS will have an indeterminate futur and his/her/its expectation (from his 1-person pov) will be given by a measure on all its computational continuation, runned, or even just defined, in the complete procession of the universal CA. Now, that measure on those computations must fit the SAS's physical law, if not the SAS will correctly infer that comp is false, which, we know, must be true (we runned the CA, for exemple). So the physical laws must result from a relative (conditional to a state S) measure on all computations continuing S. (and actually this looks like Feynman formulation of QM). OK, I was short, please look at (where UDA = Universal Dovetailer Argument) UDA step 1 http://www.escribe.com/science/theory/m2971.html UDA step 2-6 http://www.escribe.com/science/theory/m2978.html UDA step 7 8 http://www.escribe.com/science/theory/m2992.html UDA step 9 10
Re: Is the universe computable
Dear Bruno, Thank you for this post. It gives me a chance to reintroduceone problem that I have with your model. Like you, I am very interested in comments from others, as it could very well be that I am misunderstanding some subtle detail of your thesis. You wrote: "... remembering the comp 1-indeterminacy, that is that if you are duplicateinto an exemplary at Sidney and another at Pekin, your actualexpectation is indeterminate and can be captured by some measure, let us say P = 1/2, and this (capital point) independently of the timechosen for any of each reconstitution (at Pekin or Sidney), giving that the delays ofreconstitution cannot be perceived (recorded by the first person))." Now my problem is that IF there is any aspect of perception and/or "observers" that involvesa quantum mechanical state there will be the need to take the "no-cloning" theorem into account. For example, we find in the following paper a discussion of this theorem and its consequences for teleportation: http://arxiv.org/abs/quant-ph/0012121 As a possible way to exploit a potential loop hole in this, I point you to the following: http://www.fi.muni.cz/usr/buzek/mypapers/96pra1844.pdf My main question boils down to this: Does Comp 1-determinacy require this duplication to be exact? Is it sufficient that approximately similar copies could be generated and not exact duplicates? How would this affect your ideas about measures, if at all? I understand that you are trying to derive QM from Comp and thusmight not see the applicability of my question, but as a reply to this I will again point your to the various papers that have been written showing that it is impossible to embed or describe completely a QM system (and its logics) using only a classical system (and its logics), if that QM system has more that two Hilbert space dimensions associated. Startwith the Kochen-Specker theorem... http://plato.stanford.edu/entries/kochen-specker/ I will address Kory's post latter. Kindest regards, Stephen - Original Message - From: Bruno Marchal To: [EMAIL PROTECTED] Sent: Tuesday, January 27, 2004 10:46 AM Subject: Re: Is the universe computable Hi Kory, Hi Stephen, Hi All, I understand Kory very well and believe he argues correctly in this post with respect to Stephen.But at the same time, I pretend that if we follow Kory's form of reasoning we are lead to expect a relation with (quantum) physics.This can seem a total miracle, ... but only for someone being both computationnalist and physicalist, and that has been showedimpossible (marchal 88, Maudlin 89, ref in my thesis).Let me try to explain shortly.The reason is that if the initial CA is universal enough the (and thatfollows for theoretical computer science) "universal CA" willdovetail on an infinite number of similar computations passing througheach possible SAS computational state, and then .. remembering the comp 1-indeterminacy, that is that if you are duplicateinto an exemplary at Sidney and another at Pekin, your actualexpectation is indeterminate and can be captured by some measure, let us say P = 1/2, and this (capital point) independently of the timechosen for any of each reconstitution (at Pekin or Sidney), giving that the delays ofreconstitution cannot be perceived (recorded by the first person)).So if we run an universal dovetailer (implemented in CA, or FORTRAN,or even just arithmetical truth), each SAS will have an indeterminate futurand his/her/its expectation (from his 1-person pov) will be given bya measure on all its computational continuation, runned, or even just defined,in the complete procession of the universal CA.Now, that measure on those computations must fit the SAS's physical law,if not the SAS will correctly infer that comp is false, which, we know,must be true (we runned the CA, for exemple).So the physical laws must result from a relative (conditional to a state S) measureon all computations continuing S. (and actually this looks like Feynman formulationof QM).OK, I was short, please look at (where UDA = Universal Dovetailer Argument)UDA step 1 http://www.escribe.com/science/theory/m2971.html UDA step 2-6 http://www.escribe.com/science/theory/m2978.html UDA step 7 8 http://www.escribe.com/science/theory/m2992.html UDA step 9 10 http://www.escribe.com/science/theory/m2998.html UDA last question http://www.escribe.com/science/theory/m3005.html Joel 1-2-3 http://www.escribe.com/science/theory/m3013.html Re: UDA... http://www.escribe.com/science/theory/m3019.html George'sigh http://www.escribe.com/science/theory/m3026.html Re:UDA... http://www.escribe.com/science/theory/m3035.html Joel's nagging question http://www.escribe.com/science/theory/m3038.html Re:UDA... http://www.escribe.com/science/theory/m3042.h
Re: Is the universe computable
Dear Kory and Hal, Kory's idea strongly reminds me of the basic idea explored by John Cramer in his Interactional interpretation in that it takes into account both past and future states. Please see: http://www.lns.cornell.edu/spr/2000-03/msg0023110.html http://mist.npl.washington.edu/npl/int_rep/tiqm/TI_toc.html One thing you might wish to bear in mind is that David Deutsch has pointed out that Cramer's idea is equivalent to the Many worlds interpretation, but I can not find the exact quote at this time. ;-) The main problem that I have with any CA based model is that it explicity requires some from of absolute synchronicity of the shift functions of the cells. I see this as a disallowance of CA based models to guide us into our questions about the appearence of a flow of time, it assumes a form of Newton's Absolute time from the onset! In addition, it has been pointed out be several CA experts that CAs are equivalent to universal Turing Machines and if UTMs are incapable of deriving QM and its phenomena then neither can CAs. Kindest regards, Stephen - Original Message - From: Hal Finney [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Tuesday, January 27, 2004 1:33 PM Subject: Re: Is the universe computable Kory Heath writes: Forget about our own (potentially non-computable) universe for a second. Surely you agree that we can imagine some large-but-finite 3+1D CA (it doesn't have to be anything like our own universe) in which the state of each bit is dependent on the states of neighboring bits one tick in the future as well as one tick in the past. Surely you agree that we could search through all the possible 4D cube bit-strings, discarding those that don't follow our rule. (This would take a Vast amount of computation, but that's irrelevant to the particular questions I'm interested in.) Some of the 4D cubes that we're left with will (assuming we've chosen a good rule for our CA) contain patterns that look all the world like SASs, moving through their world, reacting to their environment, having a sense of passing time, etc. That is indeed a fascinating thought experiment, and I agree with everything up to the last part. Are you sure that a CA whose state depends on the future as well as the past can have self aware subsystems? This seems different enough from our own physics that I'm not sure that we can assume that it will work like that. I'm not saying it can't happen, but I'm curious to see evidence that it can. Our own universe's microphysics appears to be basically reversible, and I remember that Wolfram's book had some CAs, I think universal ones, which could be expressed in reversible terms. A reversible CA is one where the present state can be deduced either from the future or the past. But I think you're talking about something stronger and stranger, where you'd need to know both the future and the past in order to compute the present. This puts your questions about when the consciousness exists in a much sharper light. (I do have answers to those questions which I have somewhat explained in recent postings.) One way to approach an answer to the question is to ask, is there such a CA in which a universal computer can be constructed? That would be evidence for at least a major prerequisite for conscious observations. Do you have any examples like this? Hal Finney
Re: Is the universe computable
Dear Kory, Interleaving below. - Original Message - From: Kory Heath [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Monday, January 26, 2004 2:54 AM Subject: Re: Is the universe computable At 1/24/04, Stephen Paul King wrote: I should respond to Kory's ME == PE idea. In PE we find such things as thermodynamic entropy and temporality. If we are to take Kory's idea (that Mathspace doesn't require resources) seriously, ME does not. This seems a direct contradiction! Perhaps Kory has a paper on-line that lays out his thesis of Instantiationism. No, I wish had the energy to write such an online paper. :) Anyway, please note that my own position is not Instantiationism. This was the word I used to describe the position that I *don't* accept - i.e., the idea that computations need to somehow be physically instantiated in order for them (or more importantly, the SASs within them) to be real or conscious. If I had to come up with a name for my position, I might call it Mathematical Physicalism. [SPK] I am not arguing for the necessity of physical instatiation, in the sense of a prior. I am claiming that the notion of computation itself, however one wants to represent it, implicitly requires some form of implementation, even if such is merely possible if one is going to try to build a theoretical model of the world we experience, a world where we can not predict to arbitrary accurasy what is going to happen next. The idea I have is that the computations that render our worlds of experience are implemented by the unitary evolution of quantum mechanical systems and that these computations are not reducible to Turing Machines. Notice that this idea involves a form of realism for quantum wavefunctions similar to that proposed by Bohm and others. I have to confess that I'm not sure I'm following your argument. Are you referring to the tension between the static view of Mathspace, in which there is no concept of resources and computational structures exist all at once, and the dynamic, 1st-person view that we have as creatures, where time exists and resources are limited? I'm willing to admit that there's tension there, but it seems to me that the tension exists for the Instantiationist as well as the Mathematical Physicalist. [SPK] Yes, that tension is part of what I am trying to address. There is a similar situation involved in the problem of Time. One solution has been proposed by Julian Barbour with his idea of a time capsule. I hope that you get a chance to read his book The End of Time which discusses this idea. I have serious problems with Barbour's proposal and have found that it is the same problem that I trying to point out as existing in the various computalionalist theories. His best matching scheme involves the same kind of computational intractibility that disallows it to be taken as preexisting. All I can do is trundle out the same old thought experiments that we're all familiar with. Imagine a 2D CA in which the state of each cell is determined by the state of its neighbors one tick in the future as well as one tick in the past. Such CA cannot be computed one tick of the clock at a time like a regular CA. Instead you'd have to consider the whole structure as a 3D block of bits (one of the dimensions representing time) and somehow accrete the patterns within it. Or you could do a brute-force search through every possible block of bits, discarding all those that don't follow the rules. Some of the universes that you're left with may exhibit thermodynamic entropy and temporality - we can imagine a particular block universe that contains patterns which represent observers moving around, interacting with their environment, etc. - and yet from our perspective the whole structure is entirely static. [SPK] Your 3D CA will only work IF and only IF the computational content is Turing Machine emulable and this requires that the TM is specifiable with integers (enumerable). This, to me, explains why Comp proponents only seen to want the Intergers to exist and will go to great and clever lengths to explain why only they are needed. The problem is that there is a large class of physical systems that are not computable by TMs, i.e., they are intractable. Did you read the Wolfram quote that I included in one of my posts? Please read the entire article found here: http://www.stephenwolfram.com/publications/articles/physics/85-undecidability/2/text.html Another way of thinking of this is to concider the Laplacean notion where given the specification of the initial conditions and/or final conditions of the universe that all of the kinematics and dynamics of the universe would be laid out. The modern incarnation of this is the so-called 4D cube model of the universe. Again, these ideas only work for those who are willing to completely ignore the facts of computational complexity and the Heisenberg Uncertainty principle
Re: Is the universe computable
The problem is that there is a large class of physical systems that are not computable by TMs, i.e., they are intractable. Did you read the Wolfram quote that I included in one of my posts? Please read the entire article found here: Another way of thinking of this is to concider the Laplacean notion where given the specification of the initial conditions and/or final conditions of the universe that all of the kinematics and dynamics of the universe would be laid out. The modern incarnation of this is the so-called 4D cube model of the universe. Again, these ideas only work for those who are willing to completely ignore the facts of computational complexity and the Heisenberg Uncertainty principle. Stephen, Am I correct that you're essentially saying that our universe is algorithmically incompressible? If so I would agree and, interestingly, so does my friend Jim in a parallel thread I sparked from this very thread on the infophysics list a week or so back; thought I'd post it because he represents the hard info physical view on this subject much better than I could: From: Jim Whitescarver [EMAIL PROTECTED] Subject: Re: [InfoPhysics] Fw: Is the universe computable In so far as the universe is logical it can be modeled as a logical information system. The information nature of the quantum makes such a model convenient. It seems surprising how closely nature obeys logic granting validity to science. If we suppose that it is indeed logical and has no other constraints outside that logic, we then find it is an incompressible computation, that cannot be represented with fewer states. The universe is computably as it is a computer, but only a computer larger than the universe itself could model it. In this sense, the universe is not technically computable in practical terms. Intractability, however, is not exclusive of there existing good solutions. Unknowability is inherent in complex systems and we can capitalize on the the uniformity of the unknowable in the world of the known. Consider a pure entropy source, e.g. a stationary uncharged black hole. It effective eats all the information that falls in irretrievably randomizing it into the distant future. It is not that systems falling in stop behaving determistically, it is that we no longer care what their state is effectively randomized and outside our window of observation. Nothing in our world covaries with what happens inside the black hole but we know that there would be correlations due to the determinism that exists independently on the inside and the outside. I am not saying we can compute all of this. What happens at any point is the result of the entire universe acting at that point at this instant. Clearly this is not knowable. Causes are clearly not locally deterministic. But we can represent the black hole as a single integer, its mass in Plank action equivalents. From this all it's relevant properties to our perspective are known in spite of however complex it is internally. All participants, modeled as information systems, are entropy sources like black holes, but we get samplings of their internal state suggesting a finite state nature and deterministic behavior. The distinction is whether we can determine what that deterministic systems is or not. We cannot without communicating with all the participants and that is not always possible. But given a set of perspectives, there is no limit to how closely we can model them. Where no model works randomness may be substituted and often we will get good, if not perfect, results. Even legacy quantum mechanics, misguidedly based on randomness, yields deterministic results for quantum interactions shown accurate to many dozens of decimal places. This suggests that simple deterministic models will most likely be found. Jim
Re: Is the universe computable
Dear John, If we grant your point that: So while the natural numbers and the integers have a rich internal structure (rich enough to contain the whole universe and more, according to most subscribers on this list, I suspect), the reals can be encoded in the single 'program' of tossing a coin. How do you distinguish the generation of the Reals from the 'program' of tossing a coin? Are they one and the same? If so, I can go along with that, but what about complex numbers? The main problem that I have with your reasoning is that it seems to conflate objective existence (independent of implementation or representation) with representable existence, the latter being those that can be known by finite entities, such as us humans (or Machines pretending to be humans). Your reasoning also neglects the meaningfulness of the NP-Complete problem. Kindest regards, Stephen - Original Message - From: John Collins [EMAIL PROTECTED] To: Stephen Paul King [EMAIL PROTECTED]; [EMAIL PROTECTED] Sent: Thursday, January 22, 2004 6:02 AM Subject: Re: Is the universe computable - Original Message - From: Stephen Paul King [EMAIL PROTECTED] To: [EMAIL PROTECTED] Cc: [EMAIL PROTECTED]; [EMAIL PROTECTED] Sent: Wednesday, January 21, 2004 5:39 PM Subject: Re: Is the universe computable SPK wrote: You are confussing the postential existence of a computation with its meaningfulness. But in the last time you are getting close to my thesis. We should not take the a priori existence of, for example, answers to NP-Complete problems to have more ontological weight than those that enter into what it takes for creatures like us to view the answers. This is more the realm of theology than mathematics. ;-) ..This is rather like an argument I like to put forward when I'm feeling outrageous, and one which I've eventually come to believe: That the real number line 'does not exist.' There are only countably many numbers you could give a finite description of, even with a universal computer (which the human mathematical community probably constitutes, assuming we don't die out), and in the end the rest of the real numbers result from randomly choosing binary digits to be zero or one (see eg. anything by G. Chaitin). So while the natural numbers and the integers have a rich internal structure (rich enough to contain the whole universe and more, according to most subscribers on this list, I suspect), the reals can be encoded in the single 'program' of tossing a coin. By this I mean that the only 'use' or 'meaning' you could extract from some part of the binary representation would be of the form 'is this list of 0s and 1s the same as some pre-chosen lis of 0s and 1s?', which just takes you back to the random number choosing program you used to create the reals in the first place. -- Chris Collins
Re: Is the universe computable?
Dear Jesse,
- Original Message -
From: Jesse Mazer [EMAIL PROTECTED]
To: [EMAIL PROTECTED]
Sent: Wednesday, January 07, 2004 9:45 PM
Subject: RE: Is the universe computable?
David Barrett-Lennard wrote:
Georges Quenot wrote:
Also I feel some confusion between the questions Is the universe
computable ? and Is the universe actually 'being' computed ?.
What links do the participants see between them ?
An important tool in mathematics is the idea of an isomorphism between
two sets, which allows us to say *the* integers or *the* Mandelbrot set.
This allows us to say *the* computation, and the device (if any) on
which it is run is irrelevant to the existence of the computation. This
relates to the idea of the Platonic existence of mathematical objects.
This makes the confusion between the above questions irrelevant.
I think it was John Searle (who argues that computers can't be aware)
who said A simulation of a hurricane is not a hurricane, therefore a
simulation of mind is not mind. His argument breaks down if
*everything* is a computation - because we can define an isomorphism
between a computation and the simulation of that computation.
- David
Isn't there a fundamental problem deciding what it means for a given
simulated object to implement some other computation? Philosopher David
Chalmers discusses the similar question of how to decide whether a given
physical object is implementing a particular computation in his paper
Does
a Rock Implement Every Finite-State Automaton?, available here:
http://www.u.arizona.edu/~chalmers/papers/rock.html
--Jesse Mazer
I am VERY interested in this question because it is part of a hypothesis
that I am working on as a model of interactions within Prof. Hitoshi
Kitada's theory of Local Time.
In the Chalmer's paper that you reference we find:
begin quote
***
For a Putnam-style counterexample to be possible, every component state must
be sensitive to every previous component state. The most straightforward way
to do this is as follows: build an implementation in which state [a,b,c]
with input I transits into state [abcI,abcI,abcI] (where abcI is a
concatenation of a, b, c, and I). Now, we are assured that for every
resultant component state, there is a unique candidate for the preceding
state and input. Then we can construct the natural mapping from strings abcI
(in various positions) onto substates of the CSA, without fear of troubles
with recombination. A recombined state such as [a,b',c'] will transit into a
new state with unique component states in every position, each of which can
be mapped to the appropriate CSA substate.
But this sensitivity comes at a price. A system like this will suffer from
an enormous combinatorial explosion, getting three times bigger at every
time-step. If the strings that make up each component have length L at one
point, within 100 time-steps they will have length 3^{100}L, which is about
5.10^{47} times larger. In a very short time, the system will be larger than
the known universe! CSAs that are candidates to be bases for cognition will
have many more than three components, so the situation there will only be
worse. Here, the implementing system will reach the boundaries of the
universe in number of steps corresponding to a fraction of a second in the
life of a brain. So there is no chance that any realistic system could ever
qualify as an implementation in this manner.
***
end quote
It is this combinatorial explosion that I have been addressing in
terms of NP-Completeness and has proposed that we consider the possibility
that the necessary computational power is available to QM systems and not
to classical (realistic) systems. As an example please read:
http://arxiv.org/abs/quant-ph/0304128
It has been pointed out by Feynman and Deutsch that classical systems
can be simulated with arbitrary precision by a quantum computation that has
sufficient resources, and these resources are the Hilbert space
dimensions of the QM system that is doing (via its unitary evolution?) the
computing.
http://citeseer.nj.nec.com/gramss94speed.html
http://beige.ucs.indiana.edu/B679/
My conjecture is that the Unitary evolution of an arbitrary QM system is
equivalent to the computational behavior of an quantum computer.
One idea that I have proposed informally is that an experienced object
is indistinguishable from the *best possible* simulation of the object.
The reasoning that I am using here follows a similar line as that which
Turing used in his famous Test for intelligence combined with an inversion
of Wolfram's observation that an arbitrary physical system can not be
simulated better or faster than they are actually experienced to evolve.
http://www.stephenwolfram.com/publications/articles/physics/85-undecidability/2/text.html
This paper has suggested that many physical systems are computationally
irreducible, so that their own evolution is effectively
Re: Is the universe computable
Dear Bruno, Interleaving. - Original Message - From: Bruno Marchal [EMAIL PROTECTED] To: [EMAIL PROTECTED]; [EMAIL PROTECTED] Cc: [EMAIL PROTECTED]; [EMAIL PROTECTED] Sent: Friday, January 23, 2004 9:42 AM Subject: Re: Is the universe computable Dear Stephen, At 12:39 21/01/04 -0500, Stephen Paul King wrote: Dear Bruno and Kory, Interleaving. - Original Message - From: Bruno Marchal [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Wednesday, January 21, 2004 9:21 AM Subject: Re: Is the universe computable At 02:50 21/01/04 -0500, Kory Heath wrote: At 1/19/04, Stephen Paul King wrote: Were and when is the consideration of the physical resources required for the computation going to obtain? Is my question equivalent to the old first cause question? [KH] The view that Mathematical Existence == Physical Existence implies that physical resources is a secondary concept, and that the ultimate ground of any physical universe is Mathspace, which doesn't require resources of any kind. Clearly, you don't think the idea that ME == PE makes sense. That's understandable, but here's a brief sketch of why I think it makes more sense than the alternative view (which I'll call Instantiationism): [SPK] I should respond to Kory's ME == PE idea. In PE we find such things as thermodynamic entropy and temporality. If we are to take Kory's idea (that Mathspace doesn't require resources) seriously, ME does not. This seems a direct contradiction! Perhaps Kory has a paper on-line that lays out his thesis of Instantiationism. [SPK] Again, the mere postulation of existence is insufficient: it does not thing to inform us of how it is that it is even possible for us, as mere finite humans, to have experiences that change. We have to address why it is that Time, even if it is ultimately an illusion, and the distingtion between past and future is so intimately intetwined in our world of experience. [BM] Good question. But you know I do address this question in my thesis (see url below). I cannot give you too much technical details, but here is a the main line. As you know, I showed that if we postulate the comp hyp then time, space, energy and, in fact, all physicalities---including the communicable (like 3-person results of experiments) as the uncommunicable one (like qualie or results of 1-person experiment) appears as modalities which are variant of the Godelian self-referential provability predicates. As you know Godel did succeed in defining formal provability in the language of a consistent machine and many years later Solovay succeeds in formalising all theorems of provability logic in a couple of modal logics G and G*. G formalizes the provable (by the machine) statements about its own provability ability; and G* extends G with all true statements about the machine's ability (including those the machine cannot prove). [SPK] In my thinking all 1st person experiences are best possible simulations. The problem I find is that we can not use the modern equivalent to Leibniz' preordained harmony, whether in the form of a universal prior or modelization of some modal logic, since the list of all possible interactions is not enumerable. This is the aspect that I have tried to address by referencing Wolfram on the computational intractibility of some key aspects of physicality. There is also the seperate issue of how does one aspect of a logic address some other? We have the example of a Turing Machine that considers a tape and a head: there are separate in that one can move relative to the other all the while the transitions of the state of the head and the spot on the tape change. I do not see how some form of Monism can explain this. Additionally, there is the problem of simulating QM using formal logics. I have reference the Calude et al paper on this and you have said that it is good, but you seem to not have actually read it and let its implications set in. ;-) [BM] Now, independently, temporal logicians have defined some modal systems capable of formalizing temporal statements. Also, Brouwer developed a logic of the conscious subject, which has given rise to a whole constructive philosophy of mathematics, which has been formalize by a logic known as intuitionist logic, and later, like the temporal logic, the intuitionist logic has been captured formally by an modal extension of a classical modal logic. Actually it is Godel who has seen the first that Intuitionist logic can be formalised by the modal logic S4, and Grzegorczyk makes it more precise with the extended system S4Grz. And it happens that S4Grz is by itself a very nice logic of subjective, irreversible (anti-symmetric) time, and this gives a nice account too of the relationship Brouwer described between time and consciousness. Now, if you remember, I use the thaetetus trick of defining (machine) knowledge
Re: Is the universe computable
Dear Stephen, At 12:39 21/01/04 -0500, Stephen Paul King wrote: Dear Bruno and Kory, Interleaving. - Original Message - From: Bruno Marchal [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Wednesday, January 21, 2004 9:21 AM Subject: Re: Is the universe computable At 02:50 21/01/04 -0500, Kory Heath wrote: At 1/19/04, Stephen Paul King wrote: Were and when is the consideration of the physical resources required for the computation going to obtain? Is my question equivalent to the old first cause question? [KH] The view that Mathematical Existence == Physical Existence implies that physical resources is a secondary concept, and that the ultimate ground of any physical universe is Mathspace, which doesn't require resources of any kind. Clearly, you don't think the idea that ME == PE makes sense. That's understandable, but here's a brief sketch of why I think it makes more sense than the alternative view (which I'll call Instantiationism): [SPK] Again, the mere postulation of existence is insufficient: it does not thing to inform us of how it is that it is even possible for us, as mere finite humans, to have experiences that change. We have to address why it is that Time, even if it is ultimately an illusion, and the distingtion between past and future is so intimately intetwined in our world of experience. Good question. But you know I do address this question in my thesis (see url below). I cannot give you too much technical details, but here is a the main line. As you know, I showed that if we postulate the comp hyp then time, space, energy and, in fact, all physicalities---including the communicable (like 3-person results of experiments) as the uncommunicable one (like qualie or results of 1-person experiment) appears as modalities which are variant of the Godelian self-referential provability predicates. As you know Godel did succeed in defining formal provability in the language of a consistent machine and many years later Solovay succeeds in formalising all theorems of provability logic in a couple of modal logics G and G*. G formalizes the provable (by the machine) statements about its own provability ability; and G* extends G with all true statements about the machine's ability (including those the machine cannot prove). Now, independently, temporal logicians have defined some modal systems capable of formalizing temporal statements. Also, Brouwer developed a logic of the conscious subject, which has given rise to a whole constructive philosophy of mathematics, which has been formalize by a logic known as intuitionist logic, and later, like the temporal logic, the intuitionist logic has been captured formally by an modal extension of a classical modal logic. Actually it is Godel who has seen the first that Intuitionist logic can be formalised by the modal logic S4, and Grzegorczyk makes it more precise with the extended system S4Grz. And it happens that S4Grz is by itself a very nice logic of subjective, irreversible (anti-symmetric) time, and this gives a nice account too of the relationship Brouwer described between time and consciousness. Now, if you remember, I use the thaetetus trick of defining (machine) knowledge of p by provability of p and p. Independently Boolos, Goldblatt, but also Kusnetsov and Muravitski in Russia, showed that the formalization of that form of knowledge (i.e. provability of p and p) gives exactly the system of S4Grz. That's the way subjective time arises in the discourse of the self-referentially correct machine. Physical discourses come from the modal variant of provability given by provable p and consistent p (where consistent p = not provable p): this is justified by the thought experiment and this gives the arithmetical quantum logics which capture the probability one for the probability measure on the computational histories as seen by the average consistent machine. Physical time is then captured by provable p and consistant p and p. Obviously people could think that for a consistent machine the three modal variants, i.e: provable p provable p and p provable p and consistent p and p are equivalent. Well, they are half right, in the sense that for G*, they are indeed equivalent (they all prove the same p), but G, that is the self-referential machine cannot prove those equivalences, and that's explain why, from the point of view of the machine, they give rise to so different logics. To translate the comp hyp into the language of the machine, it is necessary to restrict p to the \Sigma_1 arithmetical sentences (that is those who are accessible by the Universal Dovetailer, and that step is needed to make the physicalness described by a quantum logic). The constraints are provably (with the comp hyp) enough to defined all the probabilities on the computational histories, and that is why, if ever a quantum computer would not appear in those logics, then (assuming QM is true!) comp would definitely be refuted
RE: Is the universe computable
Yes, I agree that my definition (although well defined) doesn't have a useful interpretation given your example of perfect squares interleaved with the non perfect-squares. - David -Original Message- From: Kory Heath [mailto:[EMAIL PROTECTED] Sent: Wednesday, 21 January 2004 8:30 PM To: [EMAIL PROTECTED] Subject: RE: Is the universe computable At 1/21/04, David Barrett-Lennard wrote: Saying that the probability that a given integer is even is 0.5 seems intuitively to me and can be made precise (see my last post). We can say with precision that a certain sequence of rational numbers (generated by looking at larger and larger finite sets of integers from 0 - n) converges to 0.5. What we can't say with precision is that this result means that the probability that a given integer is even is 0.5. I don't think it's even coherent to talk about the probability of a given integer. What could that mean? Pick a random integer between 0 and infinity? As Jesse recently pointed out, it's not clear that this idea is even coherent. For me, there *is* an intuitive reason why the probability that an integer is a perfect square is zero. It simply relates to the fact that the squares become ever more sparse, and in the limit they become so sparse that the chance of finding a perfect square approaches zero. Once again, I fully agree that, given the natural ordering of the integers, the perfect squares become ever more sparse. What isn't clear to me is that this sparseness has any affect on the probability that a given integer is a perfect square. Your conclusion implies: Pick a random integer between 0 and infinity. The probability that it's a perfect square is zero. That seems flatly paradoxical to me. If the probability of choosing 25 is zero, then surely the probability of choosing 24, or any other specified integer, is also zero. A more intuitive answer would be that the probability of choosing any pre-specified integer is infinitesimal (also a notoriously knotty concept), but that's not the result your method is providing. Your method is saying that the chances of choosing *any* perfect square is exactly zero. Maybe there are other possible diagnoses for this problem, but my diagnosis is that there's something wrong with the idea of picking a random integer from the set of all possible integers. Here's another angle on it. Consider the following sequence of integers: 0, 1, 2, 4, 3, 9, 5, 16, 6, 25 ... Here we have the perfect squares interleaved with the non perfect-squares. In the limit, this represents the exact same set of integers that we've been talking about all along - every integer appears once and only once in this sequence. Yet, following your logic, we can prove that the probability that a given integer from this set is a perfect square is 0.5. Can't we? -- Kory
Re: Is the universe computable
At 1/19/04, Stephen Paul King wrote: Were and when is the consideration of the physical resources required for the computation going to obtain? Is my question equivalent to the old first cause question? The view that Mathematical Existence == Physical Existence implies that physical resources is a secondary concept, and that the ultimate ground of any physical universe is Mathspace, which doesn't require resources of any kind. Clearly, you don't think the idea that ME == PE makes sense. That's understandable, but here's a brief sketch of why I think it makes more sense than the alternative view (which I'll call Instantiationism): Here's my definition of Computational Realism, which is sort of a restricted version of Mathematical Realism. (I'm not sure if my definition is equivalent to what others call Arithmetic Realism, so I'm using a different term.) Let's say that you're about to physically implement some computation, and lets say that there are only three possible things that this computation can do: return 0, return 1, or never halt. Computational Realism is simply the belief that *there is a fact of the matter* about what this computation will do when you implement it, and that this fact is true *right now*, before you even begin the implementation. Furthermore, CR is the belief that there is fact of the matter about what the result of the computation *would be*, even if it's never actually implemented. CR implies that there is such a fact of the matter about every conceivable computation. It's from this perspective that I can begin to explain why I feel that implementation is not a fundamental concept. In my view, implementing a computation is a way of viewing a structure that already exists in Mathspace (or Platonia, or whatever you want to call it). Implementation is clearly something that occurs within computational structures - for instance, we can imagine creatures in a cellular automata implementing computations on their computers, and they will have all the same concerns about physical resources that we do - computational complexity, NP-complete problems, etc. However, the entire infinite structure of their CA world exists *right now*, in Mathspace. If we consider the rules to their CA, and consider an initial state (even an infinite one - say, the digits of pi), then there is *a fact of the matter* about what the state of the infinite lattice would be in ten ticks of the clock - or ten thousand, or ten million. And the key point is that the existence of these facts doesn't require resources - there's really no concept of resources at all at that level. Every single fact about every single possible computation is simply a fact, right now. Every conceivable NP-complete problem has an answer, and it doesn't require any computational resources for these answers to exist. But of course, computational creatures like us require computational resources to view these answers. Since our resources are severely limited, we don't have access to most of the truths in Mathspace. I don't think that this form of realism automatically leads to the conclusion that ME == PE, but it certainly points in that direction. ME == PE becomes especially appealing when we consider the infinite regress problem that the alternative position generates. You ask if your question is equivalent to the old first cause question. I propose that it is exactly equivalent, and brings with it all of the attendant paradoxes and problems. If you believe that implementation is a fundamental concept - if you believe that, somehow, our universe must be instantiated, or must have some other special quality that gives it its true reality - then you've got an infinite regress problem. Certainly, I can imagine that our universe is instantiated in some larger computation, but then that computation will have to be instantiated in something else to make *it* real... and where does it all end? Or is it turtles all the way down? Or does our universe simply have the elusive quality of physical existence, while other mathematical structures lack it? In my opinion, the idea that ME == PE points to a solution to these problems. -- Kory
Re: Is the universe computable
On Tue, Jan 20, 2004 at 10:33:57PM -0800, CMR wrote: Yes! you've captured the gist and fleshed out the raw concept that hit me whilst reading your post on weightless computation; that's potentially the value of it as an avenue to explore, I think: that there is an equivalence/symmetry/correspondence by which the universe's map to one another but it's not direct(?) is it a form of information conveyance? hmmm.. While it is not possible to infer physics of the metalayer, it is possible to infer the number of bits necessary to encode this universe. Give the visible universe's timespace complexity (assuming, it's not just an elaborate fake rendered for a few observers, which is synononymous to postulating gods or a God), the metalayer needs to store an awful lot of bits, and track them over an awful lot of iterations (or represent time implicitly). It is very, very big, judged by our standards of computational physics. As such postulating matrioshka universes implies running very large simulations is essentially free, this is not true in a darwinian context (which applies for all places supporting imperfect replication and limited amount of dimensions). Reference time... -- Eugen* Leitl a href=http://leitl.org;leitl/a __ ICBM: 48.07078, 11.61144http://www.leitl.org 8B29F6BE: 099D 78BA 2FD3 B014 B08A 7779 75B0 2443 8B29 F6BE http://moleculardevices.org http://nanomachines.net pgp0.pgp Description: PGP signature
Re: Is the universe computable
At 02:50 21/01/04 -0500, Kory Heath wrote: At 1/19/04, Stephen Paul King wrote: Were and when is the consideration of the physical resources required for the computation going to obtain? Is my question equivalent to the old first cause question? The view that Mathematical Existence == Physical Existence implies that physical resources is a secondary concept, and that the ultimate ground of any physical universe is Mathspace, which doesn't require resources of any kind. Clearly, you don't think the idea that ME == PE makes sense. That's understandable, but here's a brief sketch of why I think it makes more sense than the alternative view (which I'll call Instantiationism): Here's my definition of Computational Realism, which is sort of a restricted version of Mathematical Realism. (I'm not sure if my definition is equivalent to what others call Arithmetic Realism, so I'm using a different term.) OK. Just to cut the hair a little bit: with Church thesis computational realism is equivalent to a restricted form of arithmetical realism. Comp. realism is equivalent to Arith. realism restricted to the Sigma_1 sentences, i.e. those sentence which are provably equivalent (in Peano arithmetic, say) to sentences of the form it exists x such that p(x) with p(x) a decidable (recursive) predicate. This is equivalent to say that either a machine (on any argument) will stop or will not stop, and this independently of any actual running. Indeed, sometimes I say that (Sigma_1) arithmetical realism is equivalent to the belief in the excluded middle principe (that is A or not A) applied to (Sigma_1) arithmetical sentences. (Sigma_1 sentences plays a prominant role in the derivation of the logic of the physical propositions from the logic of the self-referential propositions). Actually the Universal Dovetailing is arithmetically equivalent with an enumeration of all true Sigma_1 sentences. The key feature of those sentences is that their truth entails their provability (unlike arbitrary sentences which can be true and not provable (by Peano arithmetic, for exemple). Let's say that you're about to physically implement some computation, and lets say that there are only three possible things that this computation can do: return 0, return 1, or never halt. Computational Realism is simply the belief that *there is a fact of the matter* about what this computation will do when you implement it, and that this fact is true *right now*, before you even begin the implementation. Furthermore, CR is the belief that there is fact of the matter about what the result of the computation *would be*, even if it's never actually implemented. CR implies that there is such a fact of the matter about every conceivable computation. It's from this perspective that I can begin to explain why I feel that implementation is not a fundamental concept. In my view, implementing a computation is a way of viewing a structure that already exists in Mathspace (or Platonia, or whatever you want to call it). Implementation is clearly something that occurs within computational structures - for instance, we can imagine creatures in a cellular automata implementing computations on their computers, and they will have all the same concerns about physical resources that we do - computational complexity, NP-complete problems, etc. However, the entire infinite structure of their CA world exists *right now*, in Mathspace. If we consider the rules to their CA, and consider an initial state (even an infinite one - say, the digits of pi), then there is *a fact of the matter* about what the state of the infinite lattice would be in ten ticks of the clock - or ten thousand, or ten million. And the key point is that the existence of these facts doesn't require resources - there's really no concept of resources at all at that level. Every single fact about every single possible computation is simply a fact, right now. Every conceivable NP-complete problem has an answer, and it doesn't require any computational resources for these answers to exist. But of course, computational creatures like us require computational resources to view these answers. Since our resources are severely limited, we don't have access to most of the truths in Mathspace. I don't think that this form of realism automatically leads to the conclusion that ME == PE, but it certainly points in that direction. ME == PE becomes especially appealing when we consider the infinite regress problem that the alternative position generates. You ask if your question is equivalent to the old first cause question. I propose that it is exactly equivalent, and brings with it all of the attendant paradoxes and problems. If you believe that implementation is a fundamental concept - if you believe that, somehow, our universe must be instantiated, or must have some other special quality that gives it its true reality - then you've got an infinite regress
Re: Is the universe computable
I think, Hal, you still used your human (anthropocentric) imagination when you wanted to show a 'free' thinking: cince they were missing from your 'eliminated' concepts: do you take space and time for granted in the 'universes' of different (physical?) principles? How about 'our' logic? causality (without time)? WHEN does such a universe exist (in our terms)? We have a hint to such impossibilities: I call it 'idation', pure thought (since we have nothing to assign instead). We muster thought beyond the restrictions of space and time, dreams etc. surpass our physical system. Such ideas are not esoteric just unusual, especially in our physical natural science - brainwashed brains. When I speculated how to arrive at a Big Bang from a plenitude that has no info for us - including 'everything' (knowable and not), in some perfect invariant symmetry of an overall exchange, I found that the symmetry-brake may be a motor. Not spatial, not timely, the total infinite symmetry of the unlimited change, of unlimited identities which break just by the unlimitedness: it must lead to asymmetical elements as well in its infinity. So there we were at Big Bangs in unlimited qualities. One of them is ours, where an INSIDE 'system' of space-time evolved in causality and which, from the inside. played off the evolutional process of complexities, all the way to the final dissipation - back into the plenitude's infinite invariant symmetry. Other universes (I did not find a better word) may be completely different, based on the participant elements constituting the occurring fulgurations of occurring asymmetrical knots . In the timeless system all occur and dissipate (immediately? it has no sense) and may or may not have any impact on each other. I was careful NOT to imply on other such occurrences 'our' inside data about our system which we don't even know well ourselves. I don't believe we may have the imagination to dream up different ones. All (sci-fi, white rabbit, comp, etc.) are variations upon our universe. I try to be consequent in my scientific agnosticism. Just FYI, I do not request acceptance. My 'narrative'. John Mikes - Original Message - From: Hal Finney [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Tuesday, January 20, 2004 1:39 PM Subject: Re: Is the universe computable At 13:19 19/01/04 -0500, Stephen Paul King wrote: Where and when is the consideration of the physical resources required for the computation going to obtain? Is my question equivalent to the old first cause question? Anything physical is by definition within a universe (by my definition, anyway!). What are the physical properties of a system in our universe? Mass, size, energy, electrical charge, partical composition, etc. If we at least hypothetically allow for the existence of other universes, wouldn't you agree that they might have completely different physical properties? That they might not have mass, or charge, or size; or that these properties would vary in some bizarre way much different from how stable they are in our universe. Consider Conway's 2-dimensional Cellular Automota universe called Life. Take a look at http://rendell.server.org.uk/gol/tm.htm, an amazing implementation of a computer, a Turing Machine, in this universe. I spent a couple of hours yesterday looking at this thing, seeing how the parts work. He did an incredible job in putting all the details together to make this contraption work. So we can have computers in the Life universe. Now consider this: what is the mass of this computer? There is no such thing as mass in Life. There are cells, so you could count the number of on cells in the system (although that varies quite a bit as it runs). There is a universal clock, so you could count the time it takes to run. Some of our familiar properties exist, and others are absent. So in general, I don't think it makes sense to assume literally that computers require physical resources. Considered as an abstraction, computation is no more physical than is mathematics or logic. A theorem doesn't weigh anything, and neither does a computation. Hal Finney
Re: Is the universe computable
Greetings Eugen While it is not possible to infer physics of the metalayer, it is possible to infer the number of bits necessary to encode this universe. I'm familiar with the concept of a metalayer in software dev as a compatibility interface between apps etc.. So, in this case the meta-layer being I assume the interface between the universes abstractly and between the simulation and the platform concretely, or is it referring to the computational device itself that the simulation is running on (per your bit storage reference below)? Give the visible universe's timespace complexity (assuming, it's not just an elaborate fake rendered for a few observers, which is synononymous to postulating gods or a God), the metalayer needs to store an awful lot of bits, and track them over an awful lot of iterations (or represent time implicitly). The visible universe meaning ours(?) I assume, and the the bit storage accounting for our 4th Dimensional progression? It is very, very big, judged by our standards of computational physics. Indeed As such postulating matrioshka universes implies running very large simulations is essentially free, this is not true in a darwinian context (which applies for all places supporting imperfect replication and limited amount of dimensions). matrioshka = nested I assume as in the dolls; I interpret this to mean that selection would favor a universal resource economy of high efficiency and so the cost of simulating a universe of at least our's complexity would be deleterious to the survival of the host universe and thus lower it's relative fitness? Or am I full of it here? Ever fearing the latter, CMR -- insert gratuitous quotation that implies my profundity here --
Re: Is the universe computable
Dear Bruno and Kory, Interleaving. - Original Message - From: Bruno Marchal [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Wednesday, January 21, 2004 9:21 AM Subject: Re: Is the universe computable At 02:50 21/01/04 -0500, Kory Heath wrote: At 1/19/04, Stephen Paul King wrote: Were and when is the consideration of the physical resources required for the computation going to obtain? Is my question equivalent to the old first cause question? [KH] The view that Mathematical Existence == Physical Existence implies that physical resources is a secondary concept, and that the ultimate ground of any physical universe is Mathspace, which doesn't require resources of any kind. Clearly, you don't think the idea that ME == PE makes sense. That's understandable, but here's a brief sketch of why I think it makes more sense than the alternative view (which I'll call Instantiationism): [SPK] Again, the mere postulation of existence is insufficient: it does not thing to inform us of how it is that it is even possible for us, as mere finite humans, to have experiences that change. We have to address why it is that Time, even if it is ultimately an illusion, and the distingtion between past and future is so intimately intetwined in our world of experience. How is it that we can think that it is reasonable to expect the physically impossible to become possible by just postulating that it be so? There ain't no such thing as a free lunch! - Robert Heinleim Here's my definition of Computational Realism, which is sort of a restricted version of Mathematical Realism. (I'm not sure if my definition is equivalent to what others call Arithmetic Realism, so I'm using a different term.) [BM] OK. Just to cut the hair a little bit: with Church thesis computational realism is equivalent to a restricted form of arithmetical realism. Comp. realism is equivalent to Arith. realism restricted to the Sigma_1 sentences, i.e. those sentence which are provably equivalent (in Peano arithmetic, say) to sentences of the form it exists x such that p(x) with p(x) a decidable (recursive) predicate. This is equivalent to say that either a machine (on any argument) will stop or will not stop, and this independently of any actual running. Indeed, sometimes I say that (Sigma_1) arithmetical realism is equivalent to the belief in the excluded middle principe (that is A or not A) applied to (Sigma_1) arithmetical sentences. (Sigma_1 sentences plays a prominant role in the derivation of the logic of the physical propositions from the logic of the self-referential propositions). Actually the Universal Dovetailing is arithmetically equivalent with an enumeration of all true Sigma_1 sentences. The key feature of those sentences is that their truth entails their provability (unlike arbitrary sentences which can be true and not provable (by Peano arithmetic, for exemple). [SPK] Bruno, I do not understand why you use so weak a support for your very clever theory! If we are to take the collection of a true Sigma_1 sentenses to have independent of implementation existence, why not all of the endless hierarchy of Cantor's Cardinals? I have never understood this Kroneckerian attitute. [KH] Let's say that you're about to physically implement some computation, and lets say that there are only three possible things that this computation can do: return 0, return 1, or never halt. Computational Realism is simply the belief that *there is a fact of the matter* about what this computation will do when you implement it, and that this fact is true *right now*, before you even begin the implementation. Furthermore, CR is the belief that there is fact of the matter about what the result of the computation *would be*, even if it's never actually implemented. CR implies that there is such a fact of the matter about every conceivable computation. [SPK] That seems to me to be equivalent to postulating the existence of a List of all possible algorithms and claiming that the postulation is sufficient to prove that the output of an arbitrary computation *exists*. This reminds me of the joke about Money growing on trees: We would still have to pay people to do the picking. My point is that while it ok to assume that what the result of the computation *would be*, even if it's never actually implemented this is not the same as eliminating the mere possibility of the implementation. This is just the usual contrafactual - what could of happended but did not - and illustrates some problems that can occur when such are considerred. [KH] It's from this perspective that I can begin to explain why I feel that implementation is not a fundamental concept. In my view, implementing a computation is a way of viewing a structure that already exists in Mathspace (or Platonia, or whatever you want to call it). Implementation is clearly something that occurs within computational
Re: Is the universe computable
On Wed, Jan 21, 2004 at 09:34:50AM -0800, CMR wrote: I'm familiar with the concept of a metalayer in software dev as a compatibility interface between apps etc.. So, in this case the meta-layer being I assume the interface between the universes abstractly and between the simulation and the platform concretely, or is it referring to the computational device itself that the simulation is running on (per your bit storage reference below)? The latter. Just ab abstraction of the physical layer embedding the simulation. The visible universe meaning ours(?) I assume, and the the bit storage Yes. accounting for our 4th Dimensional progression? That depends whether we're an object, or a process in the metalayer. matrioshka = nested I assume as in the dolls; I interpret this to mean that Yes, e.g. us implementing a virtual universe large enough to include observers. The limitations of the host substrate (relativistic universe of limited duration, constraints of computational physics -- upper limit to the bits and number of operations on these bits). selection would favor a universal resource economy of high efficiency and so the cost of simulating a universe of at least our's complexity would be deleterious to the survival of the host universe and thus lower it's relative fitness? Or am I full of it here? No, this is not selection of universes, just motivations of systems occupying an universe. Matter and energy is a scarce commodity in the current universe, so assuming an universe we're currently observing is not doesn't require trivial resources to run there's a negative pressure on the motivations to run it. -- Eugen* Leitl a href=http://leitl.org;leitl/a __ ICBM: 48.07078, 11.61144http://www.leitl.org 8B29F6BE: 099D 78BA 2FD3 B014 B08A 7779 75B0 2443 8B29 F6BE http://moleculardevices.org http://nanomachines.net pgp0.pgp Description: PGP signature
Re: Is the universe computable
Dear Stephen, At 13:19 19/01/04 -0500, Stephen Paul King wrote: Dear Hal, and Friends, Were and when is the consideration of the physical resources required for the computation going to obtain? Is my question equivalent to the old first cause question? This is a good question for a physicalist. But if you accept the idea that the very notion of time, energy, space are secondary and logically emerges as a modality in the average memory of an average universal machine, then that question is solved (once we get the right measure of course). Now, about the measure, I am not convinced by Hal Finney's attempt to define or compute it for reason we have already discussed a lot, and which has just been recalled by George Levy in his last post. I could add this: if you take the Universal Dovetailer (UD), you must take into account the fact that he generates all version of all programs an infinite number of times. For computer science reasons it is not possible to cut out the vast redundancy of the codes in the production of the UD. Now, this does not mean that some other reasons could not be invoked for justifying the importance of little programs, though. Regards, Bruno Stephen - Original Message - From: Hal Finney [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Monday, January 19, 2004 12:23 PM Subject: RE: Is the universe computable Kory Heath wrote: At 1/18/04, Hal Finney wrote: Now consider all possible program tapes being run at the same time, perhaps on an infinite ensemble of (virtual? abstract?) machines. Of those, a fraction of 1 in 2^100 of those tapes will start with that 100 bit sequence for the program in question. [snip] Now consider another program that is larger, 120 bits. By the same reasoning, 1 in 2^120 of all possible program tapes will start with that particular 120-bit sequence. And so 1/2^120 of all the executions will be of that program. Yes, but if we're really talking about all possible finite bit strings, then the number of bit strings that begin with that 100 bit program is exactly the same as the number that begin with the 120 bit program - countably infinite. You can put them into a 1 to 1 correspondence with each other, just like you can put the integers into a 1 to 1 correspondence with the squares. The intuition that there must be more integers than squares is simply incorrect, as Galileo pointed out long ago. So shouldn't your two programs have the exact same measure? Well, I'm not a mathematician either, so I can't say for sure. And actually it's worth than this, because I spoke of infinite program tapes, so the number of programs is uncountably infinite. However, here is an alternate formulation of my argument which seems to be roughly equivalent and which avoids this objection: create a random program tape by flipping a coin for each bit. Now the probability that you created the first program above is 1/2^100, and for the second, 1/2^120, so the first program is 2^20 times more probable than the second. That seems correct, doesn't it? And it provides a similar way to justify that the universe created by the first program has 2^20 times greater measure than the second. Hal Finney
Re: Is the universe computable
Dear Bruno, Interleaving. - Original Message - From: Bruno Marchal [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Tuesday, January 20, 2004 5:55 AM Subject: Re: Is the universe computable Dear Stephen, At 13:19 19/01/04 -0500, Stephen Paul King wrote: Dear Hal, and Friends, Were and when is the consideration of the physical resources required for the computation going to obtain? Is my question equivalent to the old first cause question? This is a good question for a physicalist. But if you accept the idea that the very notion of time, energy, space are secondary and logically emerges as a modality in the average memory of an average universal machine, then that question is solved (once we get the right measure of course). [SPK] I do not accept that the very notion of time, energy, space are secondary nor do I elevate logicality above physicality; I take them as having the same ontological status, this follows from the proposed dualism of Pratt that we have discussed previously. While we can argue coherently that all of the content of experience is that which is simulated by our universal machine, we still must give some accounting for these. This is why I asked the question. Now, about the measure, I am not convinced by Hal Finney's attempt to define or compute it for reason we have already discussed a lot, and which has just been recalled by George Levy in his last post. [SPK] Could it be that the sought after measure is only a meaningful notion when given from within a world? For example, when we consider the White Rabbit problem we are taking as a base line our mutal non-experience of White Rabbits and other Harry Potter-ish phenomena. This argues along a similar line as what we find in Tipler et al's Anthropic principle, a way of thinking going back to Descartes: What I experience here and now must be given a probability of 1 since I can not question that it is being experienced. The skeptic would say: But what if it is just an illusion or the machinations of an evil demon? (See the Bennaceraf, Lucas, Searle, etc. debate...) In reply I would say: Even if it is just an illusion, simulation or whatever, the fact that it is experienced and not some thing else demands that it be taken as probability one when we start considering possible worlds and other modal ideas. You have to start somewhere and the most obvious place is right where one is stating. I could add this: if you take the Universal Dovetailer (UD), you must take into account the fact that he generates all version of all programs an infinite number of times. For computer science reasons it is not possible to cut out the vast redundancy of the codes in the production of the UD. Now, this does not mean that some other reasons could not be invoked for justifying the importance of little programs, though. [SPK] UD, UTM, QComp or whatever, all of these depend existentially on some kind of physical resource, be it some portion of Platonia, infinite tape and read/write head, Hilbert space or whatever; you can not even define your precious AR without representing it somehow. It is this necessity of representation that you seem to dismiss so easily. Again: When will a consideration of physical resources obtain? Kindest regards, Stephen Regards, Bruno Stephen - Original Message - From: Hal Finney [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Monday, January 19, 2004 12:23 PM Subject: RE: Is the universe computable Kory Heath wrote: At 1/18/04, Hal Finney wrote: Now consider all possible program tapes being run at the same time, perhaps on an infinite ensemble of (virtual? abstract?) machines. Of those, a fraction of 1 in 2^100 of those tapes will start with that 100 bit sequence for the program in question. [snip] Now consider another program that is larger, 120 bits. By the same reasoning, 1 in 2^120 of all possible program tapes will start with that particular 120-bit sequence. And so 1/2^120 of all the executions will be of that program. Yes, but if we're really talking about all possible finite bit strings, then the number of bit strings that begin with that 100 bit program is exactly the same as the number that begin with the 120 bit program - countably infinite. You can put them into a 1 to 1 correspondence with each other, just like you can put the integers into a 1 to 1 correspondence with the squares. The intuition that there must be more integers than squares is simply incorrect, as Galileo pointed out long ago. So shouldn't your two programs have the exact same measure? Well, I'm not a mathematician either, so I can't say for sure. And actually it's worth than this, because I spoke of infinite program tapes, so the number of programs is uncountably infinite. However, here is an alternate formulation of my argument which seems
Re: Is the universe computable
At 13:19 19/01/04 -0500, Stephen Paul King wrote: Where and when is the consideration of the physical resources required for the computation going to obtain? Is my question equivalent to the old first cause question? Anything physical is by definition within a universe (by my definition, anyway!). What are the physical properties of a system in our universe? Mass, size, energy, electrical charge, partical composition, etc. If we at least hypothetically allow for the existence of other universes, wouldn't you agree that they might have completely different physical properties? That they might not have mass, or charge, or size; or that these properties would vary in some bizarre way much different from how stable they are in our universe. Consider Conway's 2-dimensional Cellular Automota universe called Life. Take a look at http://rendell.server.org.uk/gol/tm.htm, an amazing implementation of a computer, a Turing Machine, in this universe. I spent a couple of hours yesterday looking at this thing, seeing how the parts work. He did an incredible job in putting all the details together to make this contraption work. So we can have computers in the Life universe. Now consider this: what is the mass of this computer? There is no such thing as mass in Life. There are cells, so you could count the number of on cells in the system (although that varies quite a bit as it runs). There is a universal clock, so you could count the time it takes to run. Some of our familiar properties exist, and others are absent. So in general, I don't think it makes sense to assume literally that computers require physical resources. Considered as an abstraction, computation is no more physical than is mathematics or logic. A theorem doesn't weigh anything, and neither does a computation. Hal Finney
Re: Is the universe computable
Dear Hal, A theorem doesn't weigh anything, and neither does a computation. Nice try but that is a very smelly Red Herring. Even Conway's Life can not exist, even in the abstract sense, without some association with the possibility of being implemented and it is this Implementation that I am asking about. Let us consider Bruno's beloved Arithmetic Realism. Are we to believe that Arithmetic can be considered to exist without, even tacitly, assuming the possibility that numbers must be symbolic representable? If they can be, I strongly argue that we have merely found a very clever definition for the term meaninglessness. I beg you to go directly to Turing's original paper discussing what has become now know as a Turing Machine. You will find discussions of things like tape and read/write head. Even if these, obviously physical, entities are, as you say, by definition within a universe and that such universes can be rigorously proven to be mathematical entities, this only strengthens my case: An abstract entity must have a possibility of being physically represented, even if in a Harry Potter Universe, to be a meaningful entity. Otherwise what restrains us from endless Scholastic polemics about how many Angels can dance on the head of a Pin and other meaningless fantasies. The fact that an Algorithm is independent of any particular implementation is not reducible to the idea that Algorithms (or Numbers, or White Rabbits, etc.) can exist without some REAL resources being used in their implementation (and maybe some kind of thermodynamics). BTW, have you read Julian Barbour's The End of Time? It is my opinion that Julian's argument falls flat on its face because he is making the very same mistake: Assuming that his best-matching scheme can exists without addressing the obvious status that it is an NP-Complete problem of uncountable infinite size. It is simply logically impossible to say that the mere postulation of a Platonia allows for the a priori existence of the solution to such a computationally intractable problem. Kindest regards, Stephen - Original Message - From: Hal Finney [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Tuesday, January 20, 2004 1:39 PM Subject: Re: Is the universe computable At 13:19 19/01/04 -0500, Stephen Paul King wrote: Where and when is the consideration of the physical resources required for the computation going to obtain? Is my question equivalent to the old first cause question? Anything physical is by definition within a universe (by my definition, anyway!). What are the physical properties of a system in our universe? Mass, size, energy, electrical charge, partical composition, etc. If we at least hypothetically allow for the existence of other universes, wouldn't you agree that they might have completely different physical properties? That they might not have mass, or charge, or size; or that these properties would vary in some bizarre way much different from how stable they are in our universe. Consider Conway's 2-dimensional Cellular Automota universe called Life. Take a look at http://rendell.server.org.uk/gol/tm.htm, an amazing implementation of a computer, a Turing Machine, in this universe. I spent a couple of hours yesterday looking at this thing, seeing how the parts work. He did an incredible job in putting all the details together to make this contraption work. So we can have computers in the Life universe. Now consider this: what is the mass of this computer? There is no such thing as mass in Life. There are cells, so you could count the number of on cells in the system (although that varies quite a bit as it runs). There is a universal clock, so you could count the time it takes to run. Some of our familiar properties exist, and others are absent. So in general, I don't think it makes sense to assume literally that computers require physical resources. Considered as an abstraction, computation is no more physical than is mathematics or logic. A theorem doesn't weigh anything, and neither does a computation. Hal Finney
Re: Is the universe computable
The fact that an Algorithm is independent of any particular implementation is not reducible to the idea that Algorithms (or Numbers, or White Rabbits, etc.) can exist without some REAL resources being used in their implementation (and maybe some kind of thermodynamics). To paraphrase Bill, that depends on what the meaning of the word real is. My point being that, if one accepts, even if only hypothetically (humor me), that a (toy) universe can be modeled by a CA, then would not the self-consistent physics of the universe emerge from following the rule? Given this, then, would not the resources be mapped directly only to those physics and not directly to ours, even though the CA is implemented according to and via our physics. What I'm getting at here is that weight as a function of mass and gravitation may well have no direct correspondence in the CA's physics. If not, then it could be argued that the computation within the context of it's own universe has no weight (i.e: consumes no EXTRA-universal resources) even though the implemention of same does. Then question then becomes, I suppose, if in fact our universe is a digital one (if not strictly a CA) havng self-consistent emergent physics, then might it not follow that it is implemented (run?) via some extra-universal physical processes that only indirectly correspond to ours? (if the above is too painfully obvious (or goofy?) and/or old news then, again, do humor me..)
Re: Is the universe computable?
Dear CMR, - Original Message - From: CMR [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Tuesday, January 20, 2004 5:19 PM Subject: Re: Is the universe computable [SPK previous] The fact that an Algorithm is independent of any particular implementation is not reducible to the idea that Algorithms (or Numbers, or White Rabbits, etc.) can exist without some REAL resources being used in their implementation (and maybe some kind of thermodynamics). [CMR] To paraphrase Bill, that depends on what the meaning of the word real is. [SPK] Ok, how about: Reality is that which is unimpeachable. ;-) [CMR] My point being that, if one accepts, even if only hypothetically (humor me), that a (toy) universe can be modeled by a CA, then would not the self-consistent physics of the universe emerge from following the rule? [SPK] Ok, I will bite. ;-) [CMR] Given this, then, would not the resources be mapped directly only to those physics and not directly to ours, even though the CA is implemented according to and via our physics. What I'm getting at here is that weight as a function of mass and gravitation may well have no direct correspondence in the CA's physics. If not, then it could be argued that the computation within the context of it's own universe has no weight (i.e: consumes no EXTRA-universal resources) even though the implemention of same does. Then question then becomes, I suppose, if in fact our universe is a digital one (if not strictly a CA) havng self-consistent emergent physics, then might it not follow that it is implemented (run?) via some extra-universal physical processes that only indirectly correspond to ours? [SPK] Again, shifting the resources problem via a mapping to alternative worlds is the logical equivalent of sweeping the dirt under the rug. It still exists! This reminds me of how an ameoba (the twin of Bruno's) that lives in the bottom drawer of my refrigerator has the belief that his universe (the inside of the refrigerator) has a thermodynamic arrow that is anti-parallel (goes in the opposite direction) to the one outside when ever the light goes out... BTW, have you ever read about the Maxwell Demon? [CMR] (if the above is too painfully obvious (or goofy?) and/or old news then, again, do humor me..) [SPK] It was a good try! ;-) Stephen
Re: Is the universe computable
Pete Carlton writes: Imagine a Life universe that contains, among other things, two SASes talking to each other (and showing each other pictures, and in general having a very lucid, conscious, conversation.) Imagine that instead of being implemented on a computer, it's implemented by a large 2d array of coins: heads represents live, and tails represents dead. Each timestep, the coins are flipped over in concordance with the Life rules. Does this setup implement a universe? Let's say it does. If you say it does, how about the next step: Instead of doing flipping operations on one set of coins, each new generation is laid down in the proper configuration on top of the preceding one with a new set of coins. Does this process of laying down coins also implement a universe? Yes, it would seem that laying down coins isn't conceptually different from flipping them, from the point of view of performing a calculation. If you say it does, then what about the stack itself? (One can imagine pointing to each layer in succession, saying This is the current step, Now this is the current step, etc..) Does the stack's bare existence suffice for the implementation of a universe? The problem with this example is that you can't create the stacks without laying them down first. So there has definitely been an implementation during the lay-down phase. What you have to be asking is, in some sense, is the implementation still going on? This assumes a certain time-bound nature to the concept of implementation which may not be valid. You are assuming that the region of our universe where the implementation occurs can be bounded in time, and asking if the boundary only encloses the active lay-down phase, or also encloses the passive stack phase. You get the same problems if you try to describe the exact physical boundaries of the implementation in space. Does the implementation encompass the spaces between the coins, for example? Assuming you also need some small calculator to compute how to flip each coin (a simple lookup table for the 512 possibilities of 9 coins in a square), is that part of the implementation? What about the space between the coins and the calculator? Or perhaps the coins themselves don't have well-defined boundaries, etc. These questions suggest that it is difficult to consider whether a particular implementation is going on to be a yes-or-no question that can be asked at each point-event in space-time. So it may not be meaningful to ask whether the stack is also an implementation. Having said that, I'll give two contradictory answers: If not, then can you say what it is about the active process of flipping or laying down that counts as computation but does not count when the stack is a static block? In the philosophical literature on implementation (a good jumping-off point is David Chalmers paper at http://www.u.arizona.edu/~chalmers/papers/rock.html) it is considered that a mere trace of a program execution does not count as an implementation, for two reasons: first, there are no causal connections between the layers, they're just sitting there; and second, the trace does not represent counterfactuals, i.e. if you were to change a cell's value, what would happen is not clear from the trace. If you think the static block counts as the implementation of a universe, then I think you can go all the way to abstract Platonism. Because since the stack's just sitting there, why not knock it down? Or melt it into a big ball? Or throw it into a black hole...the two SASes won't care (will they?) On the other hand, if I apply what I have been calling the Wei Dai heuristic (about which I wrote a few messages in the past few days; BTW Wei suggested the idea but it's not necessarily something he advocates), I'd say that the presence of the stack does increase the measure of the simulated universe, because it increases the percentage of our universe's resources which are used by the simulation. More precisely, its presence would allow a shorter program to locate the implementation among all the vastness of our universe. However, in that case, knocking down or destroying the stack would eliminate this property; the stack would no longer contain the information which would allow shortening the program which would localize the implementation. Hal Finney
Re: Is the universe computable?
Greetings Stephen, BTW, have you ever read about the Maxwell Demon? Being partial to the information physical view; not only have I read it, I also account for it by viewing a system's information as physical. So by inference should then I be viewing the mapping of the intra and extra universal resources as informational in nature? In that the implementation informs (and thus constrins?) the evolution of our toy universe?
Re: Is the universe computable
Greetings Pete, If not, then can you say what it is about the active process of flipping or laying down that counts as computation but does not count when the stack is a static block? I suppose I'm ultimately in the hard info physics camp, in that the pattern's the thing; given the 2ds and the binary content, then the stacks would map to a time dimension I suppose; were they to be unstacked and recorded we'd have a history (were they unstacked , some flipped then read.. revisionist history?) If you think the static block counts as the implementation of a universe, then I think you can go all the way to abstract Platonism. Because since the stack's just sitting there, why not knock it down? Or melt it into a big ball? Or throw it into a black hole...the two SASes won't care (will they?) No, in this scenario I see the unverse as a function of the coins (or computer, or space-time, or matter energy and information). Toss a stack into a black whole (whether of not we get it back via hawkings radiation) and the information capacity of the universe is affected. But note here I say this scenario. So I think the anti-Platonist must answer why exactly the coins need to be actively flipped or laid down to really implement a Life universe -- and by extension, why any universe needs to be actively implemented. Because it's not there? Kidding. To elaborate on my statement above. I definitely see time, energy, matter.. as emergent phenomena of an underlying informational and probably discrete process. But they emerged from a pattern(order? information? logos?) and that pattern was informed upon( the, a, some?) void (noise, chaos, the one? the one of many?). Per my just prior post, I may in fact now see the extra-universal implementation as informational. So am I not a Platonist (or not? or am?)
Re: Is the universe computable
CMR writes: Then question then becomes, I suppose, if in fact our universe is a digital one (if not strictly a CA) havng self-consistent emergent physics, then might it not follow that it is implemented (run?) via some extra-universal physical processes that only indirectly correspond to ours? This is a good point, and in fact we could sharpen the situation as follows. Suppose multiverse theory is bunk and none of Tegmark's four levels work. The universe isn't infinite in size; there is no inflation; the MWI is false; and all that stuff about Platonic existence is so much hot air. There is, in fact, only one universe. However, that universe isn't ours. It's a specific version of Conway's 2D Life universe, large but finite in size, with periodic edge conditions. Against all odds, life has evolved in Life and produced Self Aware Subsystems, i.e. observers. These beings have developed a civilization and built computers. See the link I supplied earlier, http://rendell.server.org.uk/gol/tm.htm for a sample of such a computer. On their computers they run simulations of other universes, and one of the universes they have simulated is our own. Due to a triumph of advanced mathematics, they have invented a set of physical laws of tremendous complexity compared to their own, and these laws allow for atoms, chemistry, biology and life of a form very different from theirs. They follow our universe's evolution from Big Bang to Heat Death with fascination. Unbeknown to us, this is the basis for our existence. We are a simulation being run in a 2D CA universe with Conway's Life rules. Now, is this story inconceivable? Logically contradictory? I don't see how. The idea that only one real universe might exist, but that it could create any number of simulated ones, is pretty common. Of course it's more common to suppose that it's our universe which is the real one, but that's just parochialism. And what does it say about the physical properties which are necessary for computation? We have energy; Life has blinkiness (the degree to which cells are blinking on and off within a structure); neither property has a good analog in the other universe. Does the real universe win, in terms of deciding what properties are really needed for computation? I don't think so, because we could reverse the roles of the two universes and it wouldn't make any fundamental difference. Hal
Re: Is the universe computable
Dear Hal, Consider the last two paragraphs from one of Stephen Wolfram's papers: http://www.stephenwolfram.com/publications/articles/physics/85-undecidability/2/text.html *** Quantum and statistical mechanics involve sums over possibly infinite sets of configurations in systems. To derive finite formulas one must use finite specifications for these sets. But it may be undecidable whether two finite specifications yield equivalent configurations. So, for example, it is undecidable whether two finitely specified four-manifolds or solutions to the Einstein equations are equivalent (under coordinate reparametrization).[24] A theoretical model may be considered as a finite specification of the possible behavior of a system. One may ask for example whether the consequences of two models are identical in all circumstances, so that the models are equivalent. If the models involve computations more complicated than those that can be carried out by a computer with a fixed finite number of states (regular language), this question is in general undecidable. Similarly, it is undecidable what is the simplest such model that describes a given set of empirical data.[25] This paper has suggested that many physical systems are computationally irreducible, so that their own evolution is effectively the most efficient procedure for determining their future. As a consequence, many questions about these systems can be answered only by very lengthy or potentially infinite computations. But some questions answerable by simpler computations may still be formulated. *** It has been pointed out, by Roger Penrose himself (!), that the decidability problem for Einstein's equations is equivalent to Halting Problem of Turing Machines (pg. 337 of Shadows of the Mind). When we put these two arguments together, what do we get? See: http://arxiv.org/abs/quant-ph/0304128 ;-) Stephen - Original Message - From: Hal Finney [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Tuesday, January 20, 2004 7:18 PM Subject: Re: Is the universe computable CMR writes: Then question then becomes, I suppose, if in fact our universe is a digital one (if not strictly a CA) havng self-consistent emergent physics, then might it not follow that it is implemented (run?) via some extra-universal physical processes that only indirectly correspond to ours? This is a good point, and in fact we could sharpen the situation as follows. Suppose multiverse theory is bunk and none of Tegmark's four levels work. The universe isn't infinite in size; there is no inflation; the MWI is false; and all that stuff about Platonic existence is so much hot air. There is, in fact, only one universe. However, that universe isn't ours. It's a specific version of Conway's 2D Life universe, large but finite in size, with periodic edge conditions. Against all odds, life has evolved in Life and produced Self Aware Subsystems, i.e. observers. These beings have developed a civilization and built computers. See the link I supplied earlier, http://rendell.server.org.uk/gol/tm.htm for a sample of such a computer. On their computers they run simulations of other universes, and one of the universes they have simulated is our own. Due to a triumph of advanced mathematics, they have invented a set of physical laws of tremendous complexity compared to their own, and these laws allow for atoms, chemistry, biology and life of a form very different from theirs. They follow our universe's evolution from Big Bang to Heat Death with fascination. Unbeknown to us, this is the basis for our existence. We are a simulation being run in a 2D CA universe with Conway's Life rules. Now, is this story inconceivable? Logically contradictory? I don't see how. The idea that only one real universe might exist, but that it could create any number of simulated ones, is pretty common. Of course it's more common to suppose that it's our universe which is the real one, but that's just parochialism. And what does it say about the physical properties which are necessary for computation? We have energy; Life has blinkiness (the degree to which cells are blinking on and off within a structure); neither property has a good analog in the other universe. Does the real universe win, in terms of deciding what properties are really needed for computation? I don't think so, because we could reverse the roles of the two universes and it wouldn't make any fundamental difference. Hal
RE: Is the universe computable
At 1/19/04, Hal Finney wrote: However, here is an alternate formulation of my argument which seems to be roughly equivalent and which avoids this objection: create a random program tape by flipping a coin for each bit. Now the probability that you created the first program above is 1/2^100, and for the second, 1/2^120, so the first program is 2^20 times more probable than the second. That's an interesting idea, but I don't know what to make of it. All it does is create a conflict of intuition which I don't know how to resolve. On the one hand, the following argument seems to make sense: consider an infinite sequence of random bits. The probability that the sequence begins with 1 is .5. The probability that it begins with 01 is .25. Therefore, in the uncountably infinite set of all possible infinite bit-strings, those that begin with 1 are twice as common as those that begin with 01. However, this is in direct conflict with the intuition which says that, since there are uncountably many infinite bit-strings that begin with 1, and uncountably many that begin with 01, the two types of strings are equally as common. How can we resolve this conflict? -- Kory
RE: Is the universe computable
Kory Heath wrote: At 1/19/04, Hal Finney wrote: However, here is an alternate formulation of my argument which seems to be roughly equivalent and which avoids this objection: create a random program tape by flipping a coin for each bit. Now the probability that you created the first program above is 1/2^100, and for the second, 1/2^120, so the first program is 2^20 times more probable than the second. That's an interesting idea, but I don't know what to make of it. All it does is create a conflict of intuition which I don't know how to resolve. On the one hand, the following argument seems to make sense: consider an infinite sequence of random bits. The probability that the sequence begins with 1 is .5. The probability that it begins with 01 is .25. Therefore, in the uncountably infinite set of all possible infinite bit-strings, those that begin with 1 are twice as common as those that begin with 01. However, this is in direct conflict with the intuition which says that, since there are uncountably many infinite bit-strings that begin with 1, and uncountably many that begin with 01, the two types of strings are equally as common. How can we resolve this conflict? -- Kory I haven't studied measure theory, but from reading definitions and seeing discussions my understanding is that it's about functions that assign real numbers to collections of subsets (defined by 'sigma algebras') of infinite sets. As applied to probability theory, it allows you to define a notion of probability on a set with an infinite number of members. Again, this would involve assigning probabilities to *subsets* of this infinite set, not to every member of the infinite set--for example, if you are dealing with the set of real numbers between 0 and 1, then although each individual real number could not have a finite probability (since this would not be compatible with the idea that the total probability must be 1), perhaps each finite nonzero interval (say, 0.5 - 0.8) would have a finite probability. In a similar way, if you were looking at the set of all possible infinite bit-strings, although each individual string might not get a probability, you might have a measure that can tell you the probability of getting a member of the subset strings beginning with 1 vs. the probability of getting a member of the subset strings beginning with 01. Some references on measure theory that may be helpful: http://en2.wikipedia.org/wiki/Measure_theory http://en2.wikipedia.org/wiki/Sigma_algebra http://en2.wikipedia.org/wiki/Probability_axioms http://mathworld.wolfram.com/Measure.html http://mathworld.wolfram.com/ProbabilityMeasure.html Jesse Mazer _ Learn how to choose, serve, and enjoy wine at Wine @ MSN. http://wine.msn.com/
RE: Is the universe computable
Kory said... At 1/21/04, David Barrett-Lennard wrote: This allows us to say the probability that an integer is even is 0.5, or the probability that an integer is a perfect square is 0. But can't you use this same logic to show that the cardinality of the even integers is half that of the cardinality of the total set of integers? Or to show that there are twice as many odd integers as there are integers evenly divisible by four? In other words, how can we talk about probability without implicitly talking about the cardinality of a subset relative to the cardinality of one of its supersets? Saying that the probability that a given integer is even is 0.5 seems intuitively to me and can be made precise (see my last post). Clearly there is a weak relationship between cardinality and probability measures. Why does that matter? Why do you assume infinity / infinity = 1 , when the two infinities have the same cardinality? Division is only well defined on finite numbers. I'm not denying that your procedure works, in the sense of actually generating some number that a sequence of probabilities converges to. The question is, what does this number actually mean? I'm suspicious of the idea that the resulting number actually represents the probability we're looking for. Indeed, what possible sense can it make to say that the probability that an integer is a perfect square is *zero*? -- Kory For me, there *is* an intuitive reason why the probability that an integer is a perfect square is zero. It simply relates to the fact that the squares become ever more sparse, and in the limit they become so sparse that the chance of finding a perfect square approaches zero. - David
Re: [issues] Re: Is the universe computable
Calm, Steve, calm. :-) Remember my comment the other evening: It is the appropriate moment in human thought to change the definitions of 'objective' and 'subjective'. Implementation is the 'subjective'. Relationship need not be. In fact, relationship is necessarily -intangible-, but -is- the object of any search for 'the objective'. That 'relationship' is made explicit via implementation does not detract from its purity of specification .. its 'objectivity'. Nor is the objectivity of a 'relationship' diminished by the fact that relationship can only be explore, examined, or empirically specified, except via subjective 'instantiation'. These simultaneous aspects of reality/being are superposed with one another. Both present even as they are mutually distinguishable. This takes 'objectivity' to an independent level of identification, beyond any potential for anomaly, for variation; immune to perturbation and noise. It finally allows us to consiliently accomodate 'subjective' truths with objective basese. Objectivity is the intangible and uncorruptable 'relations', rules, and laws, of being and performance. Subjectivity is all the necessary examples and instantiations -by which- we can and do 'know' the 'relations', rules, and laws, of being and performance. Jamie Rose MetaScience Academy. Japan. Ceptual Institute. USA. Stephen Paul King wrote: Dear Hal, A theorem doesn't weigh anything, and neither does a computation. Nice try but that is a very smelly Red Herring. Even Conway's Life can not exist, even in the abstract sense, without some association with the possibility of being implemented and it is this Implementation that I am asking about. Let us consider Bruno's beloved Arithmetic Realism. Are we to believe that Arithmetic can be considered to exist without, even tacitly, assuming the possibility that numbers must be symbolic representable? If they can be, I strongly argue that we have merely found a very clever definition for the term meaninglessness. I beg you to go directly to Turing's original paper discussing what has become now know as a Turing Machine. You will find discussions of things like tape and read/write head. Even if these, obviously physical, entities are, as you say, by definition within a universe and that such universes can be rigorously proven to be mathematical entities, this only strengthens my case: An abstract entity must have a possibility of being physically represented, even if in a Harry Potter Universe, to be a meaningful entity. Otherwise what restrains us from endless Scholastic polemics about how many Angels can dance on the head of a Pin and other meaningless fantasies. The fact that an Algorithm is independent of any particular implementation is not reducible to the idea that Algorithms (or Numbers, or White Rabbits, etc.) can exist without some REAL resources being used in their implementation (and maybe some kind of thermodynamics). BTW, have you read Julian Barbour's The End of Time? It is my opinion that Julian's argument falls flat on its face because he is making the very same mistake: Assuming that his best-matching scheme can exists without addressing the obvious status that it is an NP-Complete problem of uncountable infinite size. It is simply logically impossible to say that the mere postulation of a Platonia allows for the a priori existence of the solution to such a computationally intractable problem. Kindest regards, Stephen - Original Message - From: Hal Finney [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Tuesday, January 20, 2004 1:39 PM Subject: Re: Is the universe computable At 13:19 19/01/04 -0500, Stephen Paul King wrote: Where and when is the consideration of the physical resources required for the computation going to obtain? Is my question equivalent to the old first cause question? Anything physical is by definition within a universe (by my definition, anyway!). What are the physical properties of a system in our universe? Mass, size, energy, electrical charge, partical composition, etc. If we at least hypothetically allow for the existence of other universes, wouldn't you agree that they might have completely different physical properties? That they might not have mass, or charge, or size; or that these properties would vary in some bizarre way much different from how stable they are in our universe. Consider Conway's 2-dimensional Cellular Automota universe called Life. Take a look at http://rendell.server.org.uk/gol/tm.htm, an amazing implementation of a computer, a Turing Machine, in this universe. I spent a couple of hours yesterday looking at this thing, seeing how the parts work. He did an incredible job in putting all the details together to make this contraption work. So we can have computers in the Life universe. Now consider this: what is the mass of this computer
Re: Is the universe computable?
Think of it this way, what is the cardinality of the equivalence class of representations R of, say, a 1972 Jaguar XKE, varying over *all possible languages* and *symbol systems*? I think it is at least equal to the Reals. Is this correct? If R has more than one member, how can we coherently argue that information is physical in the material monist sense? Assuming you mean R is countably infinite(?), then a solution would be a finite universe of underlying discrete structure, ala Fredkin, I imagine. What if the informing and constraining (?) is done, inter alia, by the systems that use up the universal resources? What if, instead of thinking in terms of a priori existing solutions, ala Platonia, if we entertain the idea that the *solutions are being computation in an ongoing way* and that what we experience is just one (of many)stream(s) of this computation. Such a computation would require potentially infinite physical resources... Would it be to much to assume that all we need to assume is that the resources (for Qcomputations, these are Hilbert space dimensions) are all that we have to assume exists a priori? Does not Quantum Mechanics already have such build in? Yes, this would indeed follow. But what of a view of QM itself emerging form qubits? as, for instance, expressed in the so-called Bekenstein bound: the entropy of any region of space cannot exceed a fixed constant times the surface area of the region. This suggests that the complete state space of any spatially finite quantum system is finite, so that it would contain only a finite number of independent qubits.
Re: Is the universe computable
And what does it say about the physical properties which are necessary for computation? We have energy; Life has blinkiness (the degree to which cells are blinking on and off within a structure); neither property has a good analog in the other universe. Does the real universe win, in terms of deciding what properties are really needed for computation? I don't think so, because we could reverse the roles of the two universes and it wouldn't make any fundamental difference. Yes! you've captured the gist and fleshed out the raw concept that hit me whilst reading your post on weightless computation; that's potentially the value of it as an avenue to explore, I think: that there is an equivalence/symmetry/correspondence by which the universe's map to one another but it's not direct(?) is it a form of information conveyance? hmmm.. Reference time...
RE: Is the universe computable
David Barrett-Lennard writes: Why is it assumed that a multiple runs makes any difference to the measure? One reason I like this assumption is that it provides a natural reason for simpler universes to have greater measure than more complex ones. Imagine a Turing machine with an infinite program tape. But suppose the actual program we are running is finite size, say 100 bits. The program head will move back and forth over the tape but never go beyond the first 100 bits. Now consider all possible program tapes being run at the same time, perhaps on an infinite ensemble of (virtual? abstract?) machines. Of those, a fraction of 1 in 2^100 of those tapes will start with that 100 bit sequence for the program in question. And since the TM never goes beyond those 100 bits, all such tapes will run the same program. Therefore, 1/2^100 of all the executions of all possible program tapes will be of that program. Now consider another program that is larger, 120 bits. By the same reasoning, 1 in 2^120 of all possible program tapes will start with that particular 120-bit sequence. And so 1/2^120 of all the executions will be of that program. Therefore runs of the first program will be 2^20 times more numerous than runs of the second. If we use the assumption that each of these multiple executions or runs contributes to the measure, we therefore can conclude that the measure of the universe generated by the first program is 2^20 times greater than the measure of the universe generated by the second. And more generally, the measure of a universe is inversely related to the size of the program which creates it. Therefore, QED, universes with simple programs have a higher measure than universes with more complex programs. This conclusion then allows us to further conclude that observers are likely to evolve in lawful universes, that is, universes without flying rabbits, i.e. rare, magical exceptions to otherwise universal laws. And we can conclude that the physical laws are likely to be stable or at least predictable over time. All of these are very properties of the universe which are otherwise difficult or impossible to explain. The fact that the multiverse hypothesis can provide some grounds for explaining them is one of the main sources of its attractiveness, at least for me. However, all this is predicated on the assumption that multiple runs of the same program all contribute to the measure. If that is not true, then it would be harder to explain why simple programs are of higher measure than more complex ones. If the computation is reversible we could run the simulation backwards - even though the initial state make seem contrived because it leads to a low entropy at the end of the computation. Given that the simulated beings don't know the difference (their subjective time runs in the direction of increasing entropy) the fact that the simulation is done in reverse is irrelevant to them. Would a simulation done in reverse contribute to the measure? When I think of the abstract notion of a universal TM that runs all possible programs at once, I don't necessarily picture an explict time element being present. I think of it more as a mapping: TM + program == universe. The more programs which create a given universe, the higher the measure of that universe. However, I don't think I can escape from your question so easily. We could alternately imagine an actual, physical computer, sitting in our universe somewhere, simulating another universe. And that should contribute to that other universe's measure. In that case we should have some rule that would answer questions about how much reversible and reversed simulations contribute. I would consider applying Wei Dai's heuristic, which I discussed the other day. It says that the measure of an object is larger if the object is easier to find in the universe that holds it. I gave some rough justifications for this, such as the fact that a simple counting program eventually outputs every million bit number, but no one would say that this means that the complexity of a given million bit number is as small as the size of that program. In this context, the heuristic would say that the contribution of a physical computer simulating another universe to the measure of that simulated universe should be based on how easy it is to find the computation occuring in our own universe. Computations which occur multiple times would be easier to find, so by Wei's heuristic would have higher measure. This is another path to justify the assumption that multiple simulations should contribute more to measure. I'd say that a computation running backwards contributes as well, by making it easier to locate. Now take a complex case, where a computation ran forwards for a while, then backwards, then forwards. I'd say that this heuristic suggests that the portion of the simulated universe which was repeated 3 times (forwards, backwards, forwards) would have
RE: Is the universe computable
At 1/18/04, Hal Finney wrote: Now consider all possible program tapes being run at the same time, perhaps on an infinite ensemble of (virtual? abstract?) machines. Of those, a fraction of 1 in 2^100 of those tapes will start with that 100 bit sequence for the program in question. [snip] Now consider another program that is larger, 120 bits. By the same reasoning, 1 in 2^120 of all possible program tapes will start with that particular 120-bit sequence. And so 1/2^120 of all the executions will be of that program. Yes, but if we're really talking about all possible finite bit strings, then the number of bit strings that begin with that 100 bit program is exactly the same as the number that begin with the 120 bit program - countably infinite. You can put them into a 1 to 1 correspondence with each other, just like you can put the integers into a 1 to 1 correspondence with the squares. The intuition that there must be more integers than squares is simply incorrect, as Galileo pointed out long ago. So shouldn't your two programs have the exact same measure? I don't mean to sound so critical - I'm genuinely asking for information. I know virtually nothing about measure theory. Is there some well-defined way of getting different measures for countably infinite sub-sets of a countably infinite ensemble? -- Kory
Re: Is the universe computable
At 17:36 16/01/04 +0100, Eugen Leitl wrote: On Fri, Jan 16, 2004 at 02:28:27PM +0100, Bruno Marchal wrote: of brain and the like. I of course respect completely that opinion; but I point on the fact that once you make the computationnalist hypothesis then it is the reverse which becomes true: even if locally pi is a production of the human brain, globally the laws of physics logically develop on the set of all possible beliefs of all possible universal and immaterial (mathematical) machines embedded in all possible computations (computationnal histories). I respect that opinion, Actually it is more a theorem than an opinion. But I don't want to insist on this at this stage, I guess it would be premature. I'm just interested in theories which are instrumental in solving this universe's problems. You know, trivial stuff: wars, famines and death. A TOE which says: universe is information, every possible pattern exists, observers which can observe themselves will, is a bit sterile in that respect. That's my point: the comp hyp is popper falsifiable, because it put very strong constraint on any possible measure on the set of all computational histories (as seen from any possible sound first person). Unfortunately the notion of first person is hard to make precise without going into the modal logics. There's a little problem with some practical relevance I don't have an answer, though, which I'd like to have your opinion on. We have a finite system, iteratively evolving along a trajectory in state space. We have observers within that system, subjectively experiencing a flow of time. I have trouble alternating between the internal and the external observer view. So we have a machine crunching bits, sequentially falling from state to state. This spans a continous trajectory. We can make a full record of that trajectory, eliminating a time axis. When does the subjective observation of existence assemble into place? The first time the computation was made? The type of approach advocated in this list makes indeed possible to answer such a question. Of course I will ask you, if only for the sake of the argument, to accept that idea that all arithmetical true propositions are true in a atemporal way (and a-spatial way too btw). Now a computation can be described as a purely arithmetical object (to make this precise you need Church thesis aswell). Such computation are never run, they exist like the decimals of PI once and forall (by Arithmetical realism of course). The subjective observation as such will then also exists out of space and time, and will be felt as a time ordered, or as a space-time structured scenario only from the point of view of the observer which is related to that computation. If you want, from each instant an observer can think, that instant is now. In philosophy such a treatment of subjective time is called an indexical. This is counterintuitive because people (including many defender of comp) are used to believe in the following psycho-physical relation: (the sensation of pain/pleasure) at space-time point (x,t) is associated with the physical state of some device at space-time (x,t) But comp precludes this and forces instead: the sensation of (pain/pleasure at space-time point (x,t)) is associated with a (infinite set of equivalent) relative computational state(s). That is the space-time qualia is completely part of the sensation. I have trouble seeing my subjective observer experience as a sequence of frames, already computed. No problem. It is totally unbelievable. As it should be in case it is true. *that* can be proved. Such unbelievable but true proposition belongs to the family of undecidable but true arithmetical propositions. Is the first run magical, and the static record dead meat? I'm confused. The static record (here it is the set of all true arithmetical proposition) is similar to any block universe view in which time is internal. Note that this is the case for quantum cosmology where time disappears from the fundamental equation without precluding internal time to be defined. Remember the DeWitt Wheeler equation H = 0. With comp, space itself is illusion, although that word is misleading in the sense that comp justify the solidity and stability of such illusion. Actually this has not yet be shown, but It has been shown how to translate that problem into a mathematical question. In case the math leads to not enough stability, that will give a falsification of comp. Let's bring a little dust into the run. Let's say we use a HashLife approach, which assembles the flow from lightcone hashes. Does this screw up the subjective experience? If yes, how? I don't think this will screw up the subjective experience. The illusion of time makes part of the relativeness of the computational states. What about computing a record of all possible trajectories? Is enumerating all possible states sufficient to create an observer
Re: Is the universe computable?
At 15:05 16/01/04 +0100, Georges Quenot wrote: Possibly making you not better than them. But this not that simple. They do not disagree with dialog and argumentation. Rather they argue in different ways and/or with different premises. OK, so I perhaps did not understand you fully. I thought they did not even accept AR, or 2+2=4 for the sake of the argument. If they finally have to abandon these positions due to the amount of evidence in favor of it, the last line of defence for their conception of a personal God and for a significant role for Him could be at the level of artihmetical realism. Artihmetical realism by itself (not from a distinct personal God) is therefore seen as evil by them. As I mentionned, they usually do not put it that way. Rather they argue that such a view would prevent the foundation of human dignity and the like. They make probably the same confusion of those who believe that determinism is in contradiction with free will. I would say that one of the concern they have behind this is the question of free will versus determinism (and/or randomness). You and others might see this as making the same confusion of those who believe that determinism is in contradiction with free will. But there might also be more than one conception of free will and we could also consider that what they are doing is trying to defend another conception of free will that the one which is not in contradiction with determinism (and/or randomness). Look, I have no problem at all with any people open to defend they point, I am always prepared to make evolve my own position. But I really don't appreciate those who wants to impose any position (even mine). By its very nature free-will is hard to define and I quite believe there is as many conception of free-will than there are free-person. Though we may or may not share this conception, I don't think that we can dismiss it. The only thing we can say is that they cannot convince us of it or possibly even of its meaningfulness but in the same way we have no ground to prove them they are wrong. No problem as long as they don't use authoritative argument. Basically, they want to believe that we humans are not reducible to numbers and I think that such a reductibility cannot be proved either way. Er... No scientific proposition can *ever* be proved. Only refuted, or confirm. Except perhaps a tiny part of intuistionist mathematics. Also I understand that one could feel offended by the idea that he could be reduced to mere numbers (not more but not less he would feel offended by the idea it could be reduced to a set of interacting molecules) even if these ideas are considered as just hypotheses. They want to believe (and they want to be generally believed) that there is (much) more than this in human beings (and incidently in themselves). It is ok, in principle. It all depend on the way they will make us to believe their proposition. I am used to met people who are shocked by the idea of being a machine. I think those people ahave just a lack of trust in themselves. If I like myself and if I learn that I am a machine, then I will say formidable, some machine can be nice like me. If I dislike myself, and I learn that I am a machine, then I will say I knew I was just a stupid machine. Just to say that if someone has the faith (or some deep faith) he/she will not be afraid by *and* hypothesis. Those who are afraid by hypotheses are really afraid of the fragility of their own ideas or of their own faith. Actually I tend to think that Godel's and other incompleteness result makes comp a sort of vaccine against reductionist view of self and reality (and arithmetic). This is not obvious to me. Maybe what reductionist actually means needs to be clarified. Sure. It is a very big thread by itself. You know reason works only through doubt, and through the ability to listen to different opinions. I tend to agree but it does not seem enough just to say it. I guess it is not enough. As I said it is linked to trusting oneself. This trust is given, I think, by appropriate love and education from generation through generation. That is, a very long work. may be some shortcut exists, but there is probably no universal simple recipe. Now with Godel we can say more, which is that good faith never fears reason and rationality. Sincere Faith can only extend Ratio, and is always open to dialog. It seems that there exists other conceptions of what good faith and/or Sincere Faith should be. Idem for Ratio. Which one? Bruno
Re: Is the universe computable
I find it hard to believe that the measure of a
program/book/movie/experience is proportional to the number it is
executed/read/seen/lived, independently of everything else.
I have an alternative proposition:
Measure is a function of how accessible a particular
program/book/movie/experience is from a given observer moment.
More formally we can say that the measure of observer-moment B with
respect observer-moment A is the probability that observer moment B
occurs following observer moment A. Measure is simply a conditional
probability.
Thus, it is the probability of transition to the
program/book/movie that defines the measure. The actual number of
copies is meaningless.
This definition of measure has the advantage of conforming with
everyday experience. In addition, it is a relative quantity
because it requires the specification of an observer moment from which
the transition can be accomplished.
For example the measure of the book Digital Fortress is much
higher for someone who has read The Da Vinci Code than for
someone who hasn't, independently of how many copies of Digital
Fortress has actually been printed, or read and not understood, or
read and understood. (These books have the same author).
If one insists in using the context of program to define measure, than
one could define measure as the probability that program B be called as
a subroutine from another given program A, or more generally, from a
set of program A{}. The actual number of copies of the subroutine B is
meaningless. It is the number of calls to B from A{}that matters.
George Levy
Hal Finney wrote:
David Barrett-Lennard writes:
Why is it assumed that a multiple "runs" makes any difference to the
measure?
One reason I like this assumption is that it provides a natural reason
for simpler universes to have greater measure than more complex ones.
Imagine a Turing machine with an infinite program tape. But suppose the
actual program we are running is finite size, say 100 bits. The program
head will move back and forth over the tape but never go beyond the
first 100 bits.
Now consider all possible program tapes being run at the same time,
perhaps on an infinite ensemble of (virtual? abstract?) machines.
Of those, a fraction of 1 in 2^100 of those tapes will start with that
100 bit sequence for the program in question. And since the TM never
goes beyond those 100 bits, all such tapes will run the same program.
Therefore, 1/2^100 of all the executions of all possible program tapes
will be of that program.
Now consider another program that is larger, 120 bits. By the same
reasoning, 1 in 2^120 of all possible program tapes will start with that
particular 120-bit sequence. And so 1/2^120 of all the executions will
be of that program.
Therefore runs of the first program will be 2^20 times more numerous
than runs of the second.
RE: Is the universe computable?
Eugen said... I was using a specific natural number (a 512 bit integer) as an example for creation and destruction of a specific integer (an instance of a class of integers). No more, no less. That's plenty to bring out our difference of opinion. cf creation and destruction of a specific integer Existence of a specific integer has nothing to do with existence of a production system for a class of integers. The recipe for a series is not the dish itself. That recipe is also just information, requiring encoding in a material carrier. It would have taken considerably more work to eradicate the entire production system, as it is a bit more widespread, and has a lot more vested interest than conservation of a specific, random integer, destilled from turbulent gas flow. You say a class of integers. Does this mean you don't believe the integers are unique? I guess this is consistent with a non-platonist. However, from the Peano axioms it can be shown that the integers are unique up to isomorphism. Does the concept of uniqueness up to isomorphism seem useful or important to you? The representation (hex, need to be told that above hex string represents an integer (ignoring underlying representations as two's complements, potentials, charge buckets and magnetic domains for the moment) indicates that even that simple information transfer was encrusted with lots of implicit context people take for granted. Roll back to Sumer, and hand out little clay tablets with that hex string. What does it mean? Nothing. Not even the alphabet to parse this exists. Animals evolve representations for quantities, because resource management is a critical survival skill. After a few iterations you get consensual encodings for interactive transfer, then noninteractive consensual encodings. I used patterns of luminous pixels (translated into Braille dots, for all what I know) instead of scratches on a bone fragent, because that encoding is more familiar, and easier to transmit. Wavefront reemitted from pebbles hitting retina, being processed on the fly, tranformed into a spatiotemporal electrochemical activity pattern is an instance of a measurement of a property. It takes a specific class of detectors to do. You cannot conduct that measurement in their absence. The platonist interpretation of the above is simply that context is needed to relate a given sentence (of symbols) back to the Platonic realm. Note that the Platonic realm is *not* itself merely a bunch of sentences. It comes with semantics! You say the given integer exists because it is it is physically realizable *in principle*. That sounds like the platonic view to me - To me, this sounds like a confusion between a specific integer, and a recipe for such. It is quite difficult to feed a wedding throng with pages from a cookbook. I can't work out what you are saying! You use terms like specific integer and I've got no idea what you mean because you don't believe concepts exist independently of their production systems. The integers are an example of a concept that is *decoupled* from specific instances - by definition. A great deal of our thinking and language involves generalisation. For example the word chair is associated with a class of objects. You use generalisation in your sentences as much as anyone else. Your lines of reasoning treat these abstractions as things that can be manipulated - such as when I say the boy kicked the ball and you form an image in your mind - even though the sentence involves generalisations such as boy and ball. I presume your refutation (as a non-platonist) is that concepts only exist while someone (or something) is there to think them. The problem with that view is that many useful lines of reasoning involve the question Does there exist a concept x such that p(x) without instantiating x. In other words, it seems to be useful to conceptualise over the space of all possible concepts. This is exactly what happens when we generalise specific integers to the infinite set of all integers. I don't see how the non-platonist can accept any lines of reasoning that involve the set of integers because it is impossible to conceptualise every member of the set which (to them) would imply that the set doesn't exist. You agreed before with the hypothesis that a computer could exhibit awareness. Suppose we have (say on optical disk) a program and we have a computer on which we can run the program, but we haven't run the program yet. We can a-priori ask the question On the computer monitor, will we see a simulated person laugh?. Do you believe this a-priori question has an a-priori answer? After all, there is nothing mystical in a deterministic computation. If so doesn't that mean that the simulated person exists independently of running the actual simulation? In fact, if we postulate that our universe is computable, then the question Does there exist a person who laughs on
Re: Is the universe computable?
At 17:13 14/01/04 +, Giu1i0 Pri5c0 wrote: Please correct me if I am wrong: Bruno believes that information, for example mathematical concepts and theorems, exist independently of their encoding in some physicsl systems (arithmetic realism); in other words, that the number 4 esists independently of the presence in the physical world of sets of 4 separate objects, or that 2+2=4 is true independently of the possibility to physically verify this with 4 bottlecaps. Eugen believes that mathematics is the physics of bottlecaps, and that information cannot be said to exist if it is not carried by a physical system in the actual world. Are we sure that both mean the same thing by existence? I guess it is clear that in the following sentences pi exists and the moon exists the meaning of exists is different. But the point was the question of knowing or betting which existence is more fundamental. We differ on which one is reducible to the other. Eugen seems to pretend that it is obvious that physical existence is more fundamental than mathematical existence, and I guess he was meaning that the existence of pi is a sort of psychological existence, that is pi exists in the brain of the mathematician, so that the existence of pi could be reduce to the physical existence of brain and the like. I of course respect completely that opinion; but I point on the fact that once you make the computationnalist hypothesis then it is the reverse which becomes true: even if locally pi is a production of the human brain, globally the laws of physics logically develop on the set of all possible beliefs of all possible universal and immaterial (mathematical) machines embedded in all possible computations (computationnal histories). That's all my thesis is about. I don't pretend it is obvious, for sure. By the way I am reading Bruno's thesis, the few pages that I have read are very interesting. Thanks for saying, don't hesitate to ask questions. Bruno
Re: Is the universe computable?
On Fri, Jan 16, 2004 at 10:27:49AM +0800, David Barrett-Lennard wrote: I agree with everything you say, but did you really think I was making a point because Eugen happened to use hex?! I've fallen behind on answering my email, so sorry if this is brief and a bit out of context. This post is not talking about the universe metalayer at all. I was using a specific natural number (a 512 bit integer) as an example for creation and destruction of a specific integer (an instance of a class of integers). No more, no less. Existence of a specific integer has nothing to do with existence of a production system for a class of integers. The recipe for a series is not the dish itself. That recipe is also just information, requiring encoding in a material carrier. It would have taken considerably more work to eradicate the entire production system, as it is a bit more widespread, and has a lot more vested interest than conservation of a specific, random integer, destilled from turbulent gas flow. The representation (hex, need to be told that above hex string represents an integer (ignoring underlying representations as two's complements, potentials, charge buckets and magnetic domains for the moment) indicates that even that simple information transfer was encrusted with lots of implicit context people take for granted. Roll back to Sumer, and hand out little clay tablets with that hex string. What does it mean? Nothing. Not even the alphabet to parse this exists. Animals evolve representations for quantities, because resource management is a critical survival skill. After a few iterations you get consensual encodings for interactive transfer, then noninteractive consensual encodings. I used patterns of luminous pixels (translated into Braille dots, for all what I know) instead of scratches on a bone fragent, because that encoding is more familiar, and easier to transmit. Wavefront reemitted from pebbles hitting retina, being processed on the fly, tranformed into a spatiotemporal electrochemical activity pattern is an instance of a measurement of a property. It takes a specific class of detectors to do. You cannot conduct that measurement in their absence. You say the given integer exists because it is it is physically realizable *in principle*. That sounds like the platonic view to me - To me, this sounds like a confusion between a specific integer, and a recipe for such. It is quite difficult to feed a wedding throng with pages from a cookbook. because the number is *not* actually physically realized and yet the number is purported to have an independent existence. Are you saying otherwise? I think any form of symbolic manipulation of numbers is implicitly using the platonic view. To say they spring into existence as they are written down (which in any case only means they are realizable in Numbers don't write down themselves. Systems generate them, translate them into specific encodings, to be parsed by other instances of systems of the same class. Use a system of a different class, and you'll only parse garbage. ATGATAGTGGCCGTCCAACGGTAGACTCTAC might be a number, it might also be a shorthand for a linear biopolymer (5'-3'? there's some implicit context for you). principle) just seems silly to me. A cookbook is a promise of a meal, not the meal itself. The Platonic view just says that every mathematical system free from contradiction exists. Ie if it can exist then it does exist. There is Exists where? Two production systems of the same kind generate the same output. Surely, the output is contained within them? In there, somewhere? Mathematicians are production systems. Input is coffee, output is theorem. no need to talk about different types of reality. -- Eugen* Leitl a href=http://leitl.org;leitl/a __ ICBM: 48.07078, 11.61144http://www.leitl.org 8B29F6BE: 099D 78BA 2FD3 B014 B08A 7779 75B0 2443 8B29 F6BE http://moleculardevices.org http://nanomachines.net pgp0.pgp Description: PGP signature
Re: Is the universe computable?
Bruno Marchal wrote: At 10:14 13/01/04 +0100, Georges Quenot wrote: Some people do argue that there is no arithmetical property independent of us because there is no thing on which they would apply independentkly of us. What we would call their arithmetical properties is simply a set of tautologies that do come with them when they are considered but exist no more than them when they are not considered. But then what would be an undecidable proposition? This is how Russell's and Whitehead logicism has break down. There is a ladder of arithmetical propositions which ask for more and more ingenuity to be proved. Actually arithmetical truth extend far beyond the reach of any consistent machine (and consistent human with comp). There is an infinity of surprise in there. I guess you know that there is no natural number p and q such that (p/q)(p/q) is equal to 2. If mathematical truth were conventionnal, why did the pythagoreans *hide* this fact for so long? So those propositions are neither tautologies, nor conventions. David Deutsch, following Johnson's criteria of reality, would say that such propositions kick back. You know, about arithmetic, and about machines btw, a lot of people defends idea which are just no more plausible since Godel has proved its incompleteness theorems. Arithmetical proposition are just not tautologies. There are three classes of (arithmetical) propositions: those who are tautologies (no matter how clever one has to be to figure that, they say nothing which is not already in the axioms), those whose negation are tautologies, and those whose neither themselves nor their negation are tautologies. It might be that we don't know which is which but it should be so in principle. Giving that I hope getting some understanding of the complex human from something simpler (number property) the approach of those people will never work, for me. And certainly vice versa. Though it is difficult to have them saying it explicitely I have the feeling that the reason why they do not want the natural numbers to be out there and even as not possibly being considered as out there is that they do not accept that the complex human be understood from something simpler (number property). They do not even accept the idea being considered, were it as a mere conjecture or working hypothesis. Their more official argument is that such a view would prevent the foundation of human dignity. Damned!!! If there is one thing which could prevent the foundation of human dignity, it is certainly that totalitarian idea following which some ideas can not even be considered as an hypothesis or conjecture. This is indeed a problem. There could be more than one conception of human dignity. But that happens all the time. There has been days you could be burned even just because you ask yourself if by chance it was not the sun but the earth which was moving. Unfortunately (again), yes. Are you defending those guys? No. I am just explaining (or trying to explain) their position. Are you asking me how to reply to those guy? I am interested in anybody's opinion on that problem. My suggestion: if many people thinks like that around you, just leave them. Like Valery said, those who are not willing to use logic with you (that is to argument) are in war with you. Run or kill them! This is a safe way to have soon everybody killing everybody. It is not enough they have good intention, if they do not want arguments, they are dangerous for all humans. I like to insist, in Valery spirit, that logic is not a question of truth, but of politeness. I like the analogy. The fact is that there might be several (and possibly incompatible) protocols of politeness. I have not met any of them physically but I had discussion with some of them via Internet. There might not be so many of them but there are. You will find, at least in the US, a lot of people considering the views of evolution and/or of the big-bang as evil. Then what? If they disagree with dialog and argumentation, *I* will consider them as evil. Possibly making you not better than them. But this not that simple. They do not disagree with dialog and argumentation. Rather they argue in different ways and/or with different premises. If they finally have to abandon these positions due to the amount of evidence in favor of it, the last line of defence for their conception of a personal God and for a significant role for Him could be at the level of artihmetical realism. Artihmetical realism by itself (not from a distinct personal God) is therefore seen as evil by them. As I mentionned, they usually do not put it that way. Rather they argue that such a view would prevent the foundation of human dignity and the like. They make probably the same confusion of those who believe that determinism is in contradiction with free will. I would say that one of the concern they have behind this is the
Re: Re:Is the universe computable?
- Original Message - From: David Barrett-Lennard [EMAIL PROTECTED] 0xf2f75022aa10b5ef6c69f2f59f34b03e26cb5bdb467eec82780 didn't exist in this universe (with a very high probability, it being a 512 bit number, generated from physical system noise) before I've generated it. Now it exists (currently, as a hex string (not necessarily ASCII) on many systems (...) You admit a base 16 notation for numbers - which means you allow numbers to be written down that aren't physically realized by the corresponding number of pebbles etc. So much for talking about pebbles in your previous emails! I think that it doesn't matter what base you choose to write down the number. It is an integer, therefore it is physically realizable *in principle*. If you write '1aa3' in base 16, it means '6893' in base 10, which corresponds to a given number of pebbles. We may think that there is somehow more reality in 6893 in comparison to 1aa3, but they are both in the same footing, except that we are more used to the first representation. Why would one claim that the corresponding decimal representation of Eugen's 512-bit number has any more reality that the hexadecimal one? This shows well how we take for granted the connection between a number's representation in digits and the physical representation in pebbles. But to take from any representation to any other, some operation is necessary. What 6893 means is take 3 pebbles, sum those with 9x10 pebbles, then sum 8x100, then 6x1000 and you will have the number of pebbles represented by 6893 This operation uses implicitly the concepts of sum and multiplication, and of the physical representation of the first 10 digits (or maybe we could argue that even those are actually the representation of successive sums of units). It tooks us years in primary school to master these concepts and operations until we thought they are natural. An interesting fact is that it is very easy to represent integer numbers that cannot be physically realizable in pebbles or in atoms, not even using all of the atoms in the universe. 10^(56^579), for example. I believe that this representation is as good as the corresponding decimal or hexadecimal one, since any of them requires some operation to be converted in pebbles. But before one argues that this is an argument for arithmetical realism, it is not *necessarily* the case that 10^(56^579) exists independently of *this* representation either. I have no formed opinion on arithmetical realism, even though I tend to accept that there is some external reality to the integers. But is the reality that is assigned to numbers of the same kind that is assigned to their physical representation? Are we not discussing just words without any meaning? -Eric.
RE: Is the universe computable?
Hi Eric, 0xf2f75022aa10b5ef6c69f2f59f34b03e26cb5bdb467eec82780 didn't exist in this universe (with a very high probability, it being a 512 bit number, generated from physical system noise) before I've generated it. Now it exists (currently, as a hex string (not necessarily ASCII) on many systems (...) You admit a base 16 notation for numbers - which means you allow numbers to be written down that aren't physically realized by the corresponding number of pebbles etc. So much for talking about pebbles in your previous emails! I think that it doesn't matter what base you choose to write down the number. It is an integer, therefore it is physically realizable *in principle*. If you write '1aa3' in base 16, it means '6893' in base 10, which corresponds to a given number of pebbles. We may think that there is somehow more reality in 6893 in comparison to 1aa3, but they are both in the same footing, except that we are more used to the first representation. Why would one claim that the corresponding decimal representation of Eugen's 512-bit number has any more reality that the hexadecimal one? I agree with everything you say, but did you really think I was making a point because Eugen happened to use hex?! You say the given integer exists because it is it is physically realizable *in principle*. That sounds like the platonic view to me - because the number is *not* actually physically realized and yet the number is purported to have an independent existence. Are you saying otherwise? I think any form of symbolic manipulation of numbers is implicitly using the platonic view. To say they spring into existence as they are written down (which in any case only means they are realizable in principle) just seems silly to me. I have no formed opinion on arithmetical realism, even though I tend to accept that there is some external reality to the integers. But is the reality that is assigned to numbers of the same kind that is assigned to their physical representation? Are we not discussing just words without any meaning? The Platonic view just says that every mathematical system free from contradiction exists. Ie if it can exist then it does exist. There is no need to talk about different types of reality. - David
Re: Is the universe computable?
On Wed, Jan 14, 2004 at 10:38:51AM +0800, David Barrett-Lennard wrote: You seem to be getting a little hot under the collar! Nope, just a bit polemic. I was getting tired of glib assertions, and needed to poke a stick, to find out what's underneath. Here is a justification of why I think arithmetical realism is at least very plausible... I'm all ears. Let's suppose that a computer simulation can (in principle) exhibit awareness. I don't know whether you dispute this hypothesis, but let's assume it and see where it leads. With you so far. We already have simulated critters with behaviour, and awareness of their environment. Computational neuroscience even attempts to do it with a high degree of biological realism. Let's suppose in fact that you Eugin, were able to watch a computer simulation run, and on the screen you could see people laughing, talking - perhaps even discussing ideas like whether *their* physical existence needs to be postulated, or else they are merely part of a platonic multiverse. A simulated person may stamp his fist on a simulated coffee table and say Surely this coffee table is real - how could it possibly be numbers - I've never heard of anything so That wouldn't be abstract numbers. You'd have a system with a state, evolving along a trajectory. In your case, that system state is being rendered (in realtime, I presume) for external observers. You'd be a bit pressed to enumerate all possible system trajectories, though. You'd run out of time and space even for very, very small assemblies. ludicrous!. Now Eugin, you may argue that the existence of this universe depends on the fact that it was simulated by a computer in our universe. I find Exactly. No implementation, no state, no trajectory. Information doesn't exist without systems encoding it. (This applies to this universe being the metalayer for a simulated system; I don't make any assumptions about our own metalayer, which is pretty meaningless, since unknowable unless). this a little hard to fathom - because computer simulations are deterministic and they give the same results whether they are run once or a thousand times. I find it hard to imagine that they leap into Absolutely. Provided, they're run. (In practice, you'll see system running floats are not as deterministic as you think). existence when they are run the first time. I'm particularly motivated by the universal dove-tailing program - which eventually generates the trace of all possible programs. I don't deny that this universe exists. I do deny that the metalayers is knowable in principle, provided that metalayers is not operated by cooperating beings (which is a very purple requirement). What I *am* interested in is a simple TOE, or a set of simple equivalent TOEs, which has enough predictive power to be usable with some finite amount of computation. Do you say that most of the integers don't exist because nobody has written them down? Yeah. I'm saying that, say, 0xf2f75022aa10b5ef6c69f2f59f34b03e26cb5bdb467eec82780c2ccdf0c8e100d38f20d9f3064aea3fba00e723a5c7392fba0ac0c538a2c43706fdb7f7e58259 didn't exist in this universe (with a very high probability, it being a 512 bit number, generated from physical system noise) before I've generated it. Now it exists (currently, as a hex string (not necessarily ASCII) on many systems around the world, rendered in diverse fonts), as soon as I remove all its encodings it's gone again. P00f! Ditto applies to generator systems -- they're a bit more widespread within a lightday from here (though most of them are concentrated within a fraction of a lightsecond), but you take them out -- all of them -- numbers cease to exist. They're gone, until something else comes along, and reinvents them. I can see your point when you say that 2+2=4 is meaningless without the physical objects to which it relates. However this is irrelevant No, they're meaningful without observers with world models. The physical objects (unless they're infoprocessing systems) can't observe themselves. because you are thinking of too simplistic a mathematical system! The only mathematical systems that are relevant to the everything-list are those that have conscious inhabitants within them. Within this self I don't know what conscious means, but machine vision systems and animals can sure count. No need to use vis vitalis for that. contained mathematical world we *do* have the context for numbers. It's a bit like the chicken and egg problem. (egg = number theory, chicken = objects and observers). Both come together and can't be pulled apart. You're anthopomorphising awfully. It sure nice to be a conscious observers, but most parts of this universe have been doing fine without, and given that multiverse exists, most of those seem to do without as well. -- Eugen* Leitl a href=http://leitl.org;leitl/a __ ICBM: 48.07078,
Re: Is the universe computable?
I agree with you Ben, you make a point. My objection admits indeed your wonderful generalization. Thanks. Bruno At 11:07 13/01/04 -0500, Benjamin Udell wrote: [Georges Quenot]Some people do argue that there is no arithmetical property independent of us because there is no thing on which they would apply independentkly of us. What we would call their arithmetical properties is simply a set of tautologies that do come with them when they are considered but exist no more than them when they are not considered. [Bruno Marchal]But then what would be an undecidable proposition? You know, about arithmetic, and about machines btw, a lot of people defends idea which are just no more plausible since Godel has proved its incompleteness theorems. Arithmetical proposition are just not tautologies. This is how Russell's and Whitehead logicism has break down. There is a ladder of arithmetical propositions which ask for more and more ingenuity to be proved. Actually arithmetical truth extend far beyond the reach of any consistent machine (and consistent human with comp). There is an infinity of surprise in there. I guess you know that there is no natural number p and q such that (p/q)(p/q) is equal to 2. If mathematical truth were conventionnal, why did the pythagoreans *hide* this fact for so long? So those propositions are neither tautologies, nor conventions.David Deutsch, following Johnson's criteria of reality, would say that such propositions kick back. Since Georges Quenot's objection claims that nothing exists when unconsidered, be it a mathematical structure or concrete singular objects to which it applies, isn't the objection too broad to be singling out any particular physics-based cosmology as objectionable? The objection seems too powerful broad, seems to apply with equal force to all subject matters of mathematics empirical research, from pointset topology to Egyptology. I wouldn't demand that a philosophical objection, in order to be valid at all, offer a direction for specific research, but I'd ask how it would at least help research keep from going wrong, I don't see how the present objection would help keep any kind of research, mathematical or empirical, from getting onto excessively thin ice, except perhaps by inspiring a general atmosphere of skepticism in response to which people pay more attention to proofs, confirmations, corroborations, etc. -- not that any such thing could actually overcome such a ! radical objection. And the objection is stated with such generality, that I don't see how it escapes being applied to itself, since, after all, it is about things relations. If there's nobody to consider concrete things or mathematicals, then there's nobody to consider the objection to considering any unconsidered things to exist. The objection seems to undercut itself in the scenario in which it is meant to have force. Unless, of course, I've misunderstood the argument, which is certainly possible. Best, Ben Udell
Re: Is the universe computable?
Hi Georges, I got that mail before. And I did answer it. Are you sure you send the right mail? see http://www.escribe.com/science/theory/m5026.html Bruno At 10:14 13/01/04 +0100, Georges Quenot wrote: Bruno Marchal wrote: At 13:36 09/01/04 +0100, Georges Quenot wrote: Bruno Marchal wrote: It seems, but it isn't. Well, actually I have known *one* mathematician, (a russian logician) who indeed makes a serious try to develop some mathematics without that infinite act of faith (I don't recall its name for the moment). Such attempt are known as ultrafinitism. Of course a lot of people (especially during the week-end) *pretend* not doing that infinite act of faith, but do it all the time implicitly. This is not what I meant. I did not refer to people not willing to accept that natural numbers exist at all but to people not wlling to accept that natural numbers exist *by themselves*. Rather, they want to see them either as only a production of human (or human-like) people or only a production of a God. What I mean is that their arithmetical property are independent of us. I don't think this is very different. I could argue that even if natural numbers were not out there, as soon as anybody consider them, their properties automatically come with and impose themselves. Even this seemingly weaker statement can be contested and it is not actually weaker but equivalent since there might be no other way than this one for natural numbers to be out there. Some people do argue that there is no arithmetical property independent of us because there is no thing on which they would apply independentkly of us. What we would call their arithmetical properties is simply a set of tautologies that do come with them when they are considered but exist no more than them when they are not considered. Do you think those people believe that the proposition 17 is prime is meaningless without a human in the neighborhood? 17 is prime is meaningless without a human in the neighborhood is exactly the kind of claim these people make (possibly generalizing the concept of human to aliens and Gods). After discussing with some of them I think they actually believe what they claim. I am not sure however that we always fully understand each other and that you or I would exactly understand such a claim in the same way as they do. Giving that I hope getting some understanding of the complex human from something simpler (number property) the approach of those people will never work, for me. And certainly vice versa. Though it is difficult to have them saying it explicitely I have the feeling that the reason why they do not want the natural numbers to be out there and even as not possibly being considered as out there is that they do not accept that the complex human be understood from something simpler (number property). They do not even accept the idea being considered, were it as a mere conjecture or working hypothesis. Their more official argument is that such a view would prevent the foundation of human dignity. Also, I would take (without added explanations) an expression like numbers are a production of God as equivalent to arithmetical realism. Yes and there are several ways to understand this. And I said unfortunately because some not only do not want to see natural numbers as existing by themselves but they do not want the idea to be simply presented as logically possible and even see/designate evil in people working at popularizing it. OK, but then some want you being dead because of the color of the skin, or the length of your nose, ... I am not sure it is not premature wanting to enlighten everyone at once ... I guess you were only talking about those hard-aristotelians who like to dismiss Plato's questions as childish. Evil ? Perhaps could you be more precise on those people. I have not met people seeing evil in arithmetical platonism, have you? I have not met any of them physically but I had discussion with some of them via Internet. There might not be so many of them but there are. You will find, at least in the US, a lot of people considering the views of evolution and/or of the big-bang as evil. If they finally have to abandon these positions due to the amount of evidence in favor of it, the last line of defence for their conception of a personal God and for a significant role for Him could be at the level of artihmetical realism. Artihmetical realism by itself (not from a distinct personal God) is therefore seen as evil by them. As I mentionned, they usually do not put it that way. Rather they argue that such a view would prevent the foundation of human dignity and the like. Georges Quénot.
Re: Is the universe computable?
On Wed, Jan 14, 2004 at 12:22:13PM +0100, Bruno Marchal wrote:
Indeed I wasn't. In general I don't like to much argue on hypotheses.
I just say lots of stuff. I don't mean it. Please attach no significance to
what I say; it's just hot air.
Also, I don't like to repeat to much arguments, so, if you want to argue
You're too dumb to get it, and I won't waste time explaining it to you.
Now I might be mistaken, but these are not nice attitudes. Expecially, if
taken together.
please look at the links to the UDA (Universal Dovetailer Argument) in my
web page (url below). Those are links to this very list.
I went there, and looked. First impression: lots of opaque lingo. This isn't
not necessarily bad in itself, but usually only mature fields develop
specialist languages. Quacks and kooks are known to use pseudospecialist
language, too.
I'll come back to you after I've actually tied to understand what it says.
I'm not sure it's worth my time, but I respect many people on this list, who
haven't come down on your argumentation, so maybe I'm wrong.
('course, in case you know french you can read my thesis).
Once, upon a time, the language of science was Latin. Then, it used to be
French.
Now, it is usually a very good idea to formulate your ideas in English, because it's
what any literate person in the world can be expected to understand,
currently.
Now I am not sure you will be interested because I *assume* Arithmetical
Realism AR (I put it in the definition of the computationalist hyp.) and it
seems
you consider that hypothesis as a glib (whatever that means: it is not in
my dictionary but I can infer the sense.).
http://dictionary.reference.com/search?q=glib
7 entries found for glib.
glib( P ) Pronunciation Key (glb)
adj. glib·ber, glib·best
1.
1. Performed with a natural, offhand ease: glib conversation.
2. Showing little thought, preparation, or concern: a glib response
to a complex question.
2. Marked by ease and fluency of speech or writing that often suggests or
stems from insincerity, superficiality, or deceitfulness.
[Possibly of Low German origin. See ghel-2 in Indo-European Roots.]glibly
adv.
glibness n.
Synonyms: glib, slick, smooth-tongued
These adjectives mean being, marked by, or engaging in ready but often
insincere or superficial discourse: a glib denial; a slick commercial; a
smooth-tongued hypocrite.
[Buy it]
Source: The American Heritage® Dictionary of the English Language, Fourth
Edition
Copyright © 2000 by Houghton Mifflin Company.
Published by Houghton Mifflin Company. All rights reserved.
glib
\Glib\, v. t. [Cf. O. Prov. E. lib to castrate, geld, Prov. Dan. live, LG.
OD. lubben.] To castrate; to geld; to emasculate. [Obs.] --Shak.
Source: Webster's Revised Unabridged Dictionary, © 1996, 1998 MICRA, Inc.
glib
\Glib\, a. [Compar. Glibber; superl. Glibbest.] [Prob. fr. D. glibberen,
glippen, to slide, glibberig, glipperig, glib, slippery.] 1. Smooth;
slippery; as, ice is glib. [Obs.]
2. Speaking or spoken smoothly and with flippant rapidity; fluent; voluble;
as, a glib tongue; a glib speech.
I want that glib and oily art, To speak and purpose not. --Shak.
Syn: Slippery; smooth; fluent; voluble; flippant.
Source: Webster's Revised Unabridged Dictionary, © 1996, 1998 MICRA, Inc.
glib
\Glib\, v. t. To make glib. [Obs.] --Bp. Hall.
Source: Webster's Revised Unabridged Dictionary, © 1996, 1998 MICRA, Inc.
glib
\Glib\, n. [Ir. Gael. glib a lock of hair.] A thick lock of hair, hanging
over the eyes. [Obs.]
The Irish have, from the Scythians, mantles and long glibs, which is a thick
curied bush of hair hanging down over their eyes, and monstrously disguising
them. --Spenser.
Their wild costume of the glib and mantle. --Southey.
Source: Webster's Revised Unabridged Dictionary, © 1996, 1998 MICRA, Inc.
glib
adj 1: marked by lack of intellectual depth; glib generalizations; a glib
response to a complex question 2: having only superficial plausibility;
glib promises; a slick commercial [syn: pat, slick] 3: artfully
persuasive in speech; a glib tongue; a smooth-tongued hypocrite [syn:
glib-tongued, smooth-tongued]
Btw I have not perceived your argument against AR. You just keep repeating
that something abstract can exist only if some piece of matter apply it.
Yeah, information doesn't exist without a material carrier. If you claim to
do computation, please stick to constraints of computational physics.
Universe may very well consist of information; show why you claim to have
insight in the architecture of the metalayer.
Giving that I don't take matter as granted (it's exactly what I try to
explain) and
Are you trying to do science, or religion?
giving that the word apply could only be used in an analogical, fuzzy or
anthropomorphical way, it is hard to figure out where your argument relies.
To be honest I don't like at all your tone which only witnesses the fact
that you
have decided in advance what
Re: Is the universe computable?
Please correct me if I am wrong: Bruno believes that information, for example mathematical concepts and theorems, exist independently of their encoding in some physicsl systems (arithmetic realism); in other words, that the number 4 esists independently of the presence in the physical world of sets of 4 separate objects, or that 2+2=4 is true independently of the possibility to physically verify this with 4 bottlecaps. Eugen believes that mathematics is the physics of bottlecaps, and that information cannot be said to exist if it is not carried by a physical system in the actual world. Are we sure that both mean the same thing by existence? By the way I am reading Bruno's thesis, the few pages that I have read are very interesting.
Re:Is the universe computable?
Hi Eugen, Yeah. I'm saying that, say, 0xf2f75022aa10b5ef6c69f2f59f34b03e26cb5bdb467eec82780c2ccdf0c8e100d38f20 d9 f3064aea3fba00e723a5c7392fba0ac0c538a2c43706fdb7f7e58259 didn't exist in this universe (with a very high probability, it being a 512 bit number, generated from physical system noise) before I've generated it. Now it exists (currently, as a hex string (not necessarily ASCII) on many systems around the world, rendered in diverse fonts), as soon as I remove all its encodings it's gone again. P00f! I can't identity with your conception of numbers but I guess you're entitled to it! You admit a base 16 notation for numbers - which means you allow numbers to be written down that aren't physically realized by the corresponding number of pebbles etc. So much for talking about pebbles in your previous emails! In statements of the form There exists integer x such that p(x) do you say this is vacuous because x hasn't been specified yet, or is it sufficient to merely name an unspecified integer to allow it to exist? Many proofs make these sorts of statements, and no where is the named integer given a specific value (even though its purported existence is crucial to the proof). Do you say these proofs are vacuous? If I write the statement for all integer x, x+1 x, does this make all the integers come into existence? Or is this another vacuous statement? - David
Re: Is the universe computable?
Eugen Leitl wrote: David Barrett-Lennard wrote: Here is a justification of why I think arithmetical realism is at least very plausible... I'm all ears. Let's suppose that a computer simulation can (in principle) exhibit awareness. I don't know whether you dispute this hypothesis, but let's assume it and see where it leads. With you so far. We already have simulated critters with behaviour, and awareness of their environment. Computational neuroscience even attempts to do it with a high degree of biological realism. Let's suppose in fact that you Eugin, were able to watch a computer simulation run, and on the screen you could see people laughing, talking - perhaps even discussing ideas like whether *their* physical existence needs to be postulated, or else they are merely part of a platonic multiverse. A simulated person may stamp his fist on a simulated coffee table and say Surely this coffee table is real - how could it possibly be numbers - I've never heard of anything so That wouldn't be abstract numbers. You'd have a system with a state, evolving along a trajectory. In your case, that system state is being rendered (in realtime, I presume) for external observers. ...but suppose we implement the same abstract program on several computers of totally different construction, like a regular computer using electronic impulses vs. a quantum computer or a gigantic babbage machine that uses only rotating gears. For the critters inside the simulation, wouldn't all these cases appear subjectively identical to them? If so, it seems the only common denominator is that all the computers were doing the same abstract computation, the physical details are apparently irrelevant in determining the experience of the simulated beings. Doesn't this lend intuitive support to the Platonic view that our own physical universe is itself just a particular abstract computation? Isn't your own belief that there is something more to our own universe, something more physical I guess, nothing more than faith in a certain metaphysical view of reality, with no more evidence (and considerably less parsimony, IMO) to justify it than the Platonic view? Jesse Mazer _ Scope out the new MSN Plus Internet Software optimizes dial-up to the max! http://join.msn.com/?pgmarket=en-uspage=byoa/plusST=1
Re: Is the universe computable?
Hi John, At 10:39 12/01/04 -0500, John M wrote: Bruno, in the line you touched with 'numbers: I was arguing on another list 'pro' D.Bohm's there are no numbers in nature position ... But what is nature ? I have never said that numbers exist in nature. The word nature or the word universe are sort of deities for atheist or naturalist (as I said in the FOR list recently). Such concept, it seems to me, explain nothing, and I have not yet see definitive evidence for those things to exist. Now, when I say that number property exist independently of me, just mean that 2+2 = 4 wil remain true even if Eugen kill me. The concept of life-insurance would not have meaning without such an act of faith. To believe that 2+2=4 would be meaningless aafter a meteor strikes earth seems to me a very large anthropomorphism. ... when a listmember asked: aren't you part of nature? then why are you saying that numbers - existing in your mind - are not 'part of nature'? Since then I formulate it something like: numbers came into existence as products of 'our' thinking. (Maybe better worded). OK John, you are not the only one, but you know I try to explain thinking in term of turing programs which relies on number properties. Also I believe that 317 is a prime number, even when no one thinks about it. That the AR (Arithmetical Realism) part of comp, which I *postulate*. You wrote: What I mean is that their arithmetical property are independent of us. .. That may branch into the question how much of 'societal' knowledge is part of an individual belief - rejectable or intrinsically adherent? (Some may call this a fundamental domain of memes). With the 'invention' of numbers (arithmetical, that is) human mentality turned into a computing animal - as a species-characteristic. I separate this from the assignment of quantities to well chosen units in numbers. Quantities may have their natural role in natural processes - unconted in our units, just mass-wise, and we, later on - in physical laws - applied the arithmetical ordering to the observations in the quantized natural events. But I do not the nature postulate at all. I follow Plato, not Aristotle. Such quantizing (restricted to models of already discovered elements) renders some processes 'chaotic' or even paradoxical, while nature processes them without any problem in her unrestricted (total) interconnectedness (not included - even known ALL in our quantized working models). Sorry for the physicistically unorthodox idea. It seems to me physicalism is quite orthodox these days, honestly. Best Regards, Bruno
Re: Is the universe computable?
On Tue, Jan 13, 2004 at 12:24:07PM +0100, Bruno Marchal wrote: If I'd kill you, you'd have no chance of thinking that thought. Actually this is pure wishful thinking, unless you mean succeeding I was referring to a gedanken experiment, of course. to kill me and my counterparts in some absolute way, but how would There are several ways imaginable, I'll point you to http://www.foresight.org/NanoRev/Ecophagy.html I don't see how the manner of destruction of the local pocket of biological life (which seems to be the only one in the visible universe) has anything to do with the validity of the argument. It's just implementation details. you be able to do a thing like that. I will not insist on this startling consequence of COMP or QM, giving that you postulate physicalism at the start. See my thesis for a proof that physicalism is incompatible with comp. We have discuss the immortality question a lot in this list. Do we have an experimental procedure to validate these fanciful scenarios? Multiverses are nice and all; so what flavour of kool aid do you prefer? If I killed all animals capable of counting, abstract immaterial numbers would become exactly that: immaterial. OK. But immaterial does not mean not existing. Even a physicalist can accept that. Only very reductionist forms of physicalism reject that. If you insist to label me thusly. But, really, instead of glib assertions and pointers to your thesis (what has formal logic to do with reality?) you are not being very convincing so far. The universe does what it does, it certainly doesn't solve equations. So we agree. (but note that anything does what it does, so what is your point). My point is that formal systems are a very powerful tool with very small reach, unfortunately. People solve equations, when approximating what universe does. As such, QM is a fair approximation; it has no further reality beyond that. That is your opinion, which is not really relevant for the question we are talking about. Because we know that QM is not a TOE. You haven't heard? We don't have a TOE. If there's such a thing as a TOE, there might be several equivalent. I would really like to see an algorithm, showing that any TOEs are equivalent. H\psi=E\psi in absence of context is just as meaningless as 2+2=4. I can understand that point and respect that opinion, but what makes you so sure. Could you give me a context in which H\psiis not equal to E\psi ? Could you give me a context in which 2+2 is not equal to 4, and where 2, +, 4, = have their usual standard meaning? This is ridiculous. You're referring to a specific notation, which needs systems to produce and to parse. Remove all instances of such systems, and everything is instanstly meaningless. Perhaps we should put our hypothesis on the table. Mine is comp by which I mean arithmetical realism, Church thesis, and the yes doctor hypothesis, that is the hypothesis that there is a level of description of myself such that I don't detect any differences in case my parts are functionaly substituted by digitalizable device. Do you think those postulates are inconsistent? I do not see how arithmetic realism (a special case of Platonic realism, is that correct?) is an axiom. I agree with the rest of your list. -- Eugen* Leitl a href=http://leitl.org;leitl/a __ ICBM: 48.07078, 11.61144http://www.leitl.org 8B29F6BE: 099D 78BA 2FD3 B014 B08A 7779 75B0 2443 8B29 F6BE http://moleculardevices.org http://nanomachines.net pgp0.pgp Description: PGP signature
Re: Is the universe computable?
At 14:08 13/01/04 +0100, Eugen Leitl wrote: you be able to do a thing like that. I will not insist on this startling consequence of COMP or QM, giving that you postulate physicalism at the start. See my thesis for a proof that physicalism is incompatible with comp. We have discuss the immortality question a lot in this list. Do we have an experimental procedure to validate these fanciful scenarios? What is the point? Do we have experimental procedure to validate the opposite of the fanciful scenario? Giving that we were talking about first person scenario, in any case it is senseless to ask for experimental procedure. (experience = first person view; experiment = third person view). If you insist to label me thusly. But, really, instead of glib assertions and pointers to your thesis (what has formal logic to do with reality?) you are not being very convincing so far. Don't tell me you were believing I was arguing. About logic, it is a branch of mathematics. Like topology, algebra, analysis it can be *applied* to some problem, which, through some hypothesis, can bear on some problem. With the comp hyp mathematical logic makes it possible to derive what consistent and platonist machine can prove about themselves and their consistent extension. My point is that formal systems are a very powerful tool with very small reach, unfortunately. But I never use formal system. I modelise a particular sort of machine by formal system, so I prove things *about* machines, by using works *about* formal system. I don't use formal systems. I prove things in informal ways like all mathematicians. Because we know that QM is not a TOE. You haven't heard? How could be *know* QM is not a TOE? (I ask this independently of the fact that I find plausible QM is not a *primitive* TOE). This is ridiculous. You're referring to a specific notation, which needs systems to produce and to parse. Remove all instances of such systems, and everything is instanstly meaningless. You believe that the theorem there is an infinity of primes is a human invention? (as opposed to a human discovery). Perhaps we should put our hypothesis on the table. Mine is comp by which I mean arithmetical realism, Church thesis, and the yes doctor hypothesis, that is the hypothesis that there is a level of description of myself such that I don't detect any differences in case my parts are functionaly substituted by digitalizable device. Do you think those postulates are inconsistent? I do not see how arithmetic realism (a special case of Platonic realism, is that correct?) is an axiom. I agree with the rest of your list. Perhaps I have been unclear. By Arithmetic Realism I mean that Arithmetical Truth is independent of me, you, and the rest of humanity. There exist weaker form of that axiom and stronger form. Tegmark for instance defends a much larger mathematical realism (so large that I am not sure what it could mean). As I said some ultrafinitist defends strictly weaker form of mathematical realism. The more quoted argument in favour of arithmetical realism is the one based on Godel's theorem, and presented by him too) which is that any formal systems (and so any ideally consistent machines) can prove, even in principle, that is with infinite time and space, all the true proposition of arithmetic. But look also to the site of Watkins http://www.maths.ex.ac.uk/~mwatkins/zeta/index.htm for a lot of evidence for it (evidence which are a priori not related to my more theoretical computer science approach). Now my goal (here) is not really to defend AR as true, but as sufficiently plausible that it is interesting to look at the consequences. You can read some main post I send to this list where I present the argument according to which if we take comp seriously (comp = AR + TC + yes doctor) then physics is eventually a branch of machine's psychology (itself a branch of computer science itself a branch of number theory. If you find an error, or an imprecision, please show them. Or, if there is a point you don't understand, it will be a pleasure for me to provide more explanations. Also, I thought you were postulating an universe, aren't you? (I just try to figure out your philosophical basic hypothesis). Regards, Bruno
Re: Is the universe computable?
At 10:14 13/01/04 +0100, Georges Quenot wrote: Some people do argue that there is no arithmetical property independent of us because there is no thing on which they would apply independentkly of us. What we would call their arithmetical properties is simply a set of tautologies that do come with them when they are considered but exist no more than them when they are not considered. But then what would be an undecidable proposition? You know, about arithmetic, and about machines btw, a lot of people defends idea which are just no more plausible since Godel has proved its incompleteness theorems. Arithmetical proposition are just not tautologies. This is how Russell's and Whitehead logicism has break down. There is a ladder of arithmetical propositions which ask for more and more ingenuity to be proved. Actually arithmetical truth extend far beyond the reach of any consistent machine (and consistent human with comp). There is an infinity of surprise in there. I guess you know that there is no natural number p and q such that (p/q)(p/q) is equal to 2. If mathematical truth were conventionnal, why did the pythagoreans *hide* this fact for so long? So those propositions are neither tautologies, nor conventions. David Deutsch, following Johnson's criteria of reality, would say that such propositions kick back. Giving that I hope getting some understanding of the complex human from something simpler (number property) the approach of those people will never work, for me. And certainly vice versa. Though it is difficult to have them saying it explicitely I have the feeling that the reason why they do not want the natural numbers to be out there and even as not possibly being considered as out there is that they do not accept that the complex human be understood from something simpler (number property). They do not even accept the idea being considered, were it as a mere conjecture or working hypothesis. Their more official argument is that such a view would prevent the foundation of human dignity. Damned!!! If there is one thing which could prevent the foundation of human dignity, it is certainly that totalitarian idea following which some ideas can not even be considered as an hypothesis or conjecture. But that happens all the time. There has been days you could be burned even just because you ask yourself if by chance it was not the sun but the earth which was moving. Are you defending those guys? Are you asking me how to reply to those guy? My suggestion: if many people things like that around you, just leave them. Like Valery said, those who are not willing to use logic with you (that is to argument) are in war with you. Run or kill them! It is not enough they have good intention, if they does not want arguments, they are dangerous for all humans. I like to insist, in Valery spirit, that logic is not a question of truth, but of politeness. I have not met any of them physically but I had discussion with some of them via Internet. There might not be so many of them but there are. You will find, at least in the US, a lot of people considering the views of evolution and/or of the big-bang as evil. Then what? If they disagree with dialog and argumentation, *I* will consider them as evil. (btw I think there are much more people like that in France and in Belgium, especially in Belgium, but that's another story). If they finally have to abandon these positions due to the amount of evidence in favor of it, the last line of defence for their conception of a personal God and for a significant role for Him could be at the level of artihmetical realism. Artihmetical realism by itself (not from a distinct personal God) is therefore seen as evil by them. As I mentionned, they usually do not put it that way. Rather they argue that such a view would prevent the foundation of human dignity and the like. They make probably the same confusion of those who believe that determinism is in contradiction with free will. Actually I tend to think that Godel's and other incompleteness result makes comp a sort of vaccine against reductionist view of self and reality (and arithmetic). You know reason works only through doubt, and through the ability to listen to different opinions. Now with Godel we can say more, which is that good faith never fears reason and rationality. Sincere Faith can only extend Ratio, and is always open to dialog. Bruno
Re: Is the universe computable?
[Georges Quenot]Some people do argue that there is no arithmetical property independent of us because there is no thing on which they would apply independentkly of us. What we would call their arithmetical properties is simply a set of tautologies that do come with them when they are considered but exist no more than them when they are not considered. [Bruno Marchal]But then what would be an undecidable proposition? You know, about arithmetic, and about machines btw, a lot of people defends idea which are just no more plausible since Godel has proved its incompleteness theorems. Arithmetical proposition are just not tautologies. This is how Russell's and Whitehead logicism has break down. There is a ladder of arithmetical propositions which ask for more and more ingenuity to be proved. Actually arithmetical truth extend far beyond the reach of any consistent machine (and consistent human with comp). There is an infinity of surprise in there. I guess you know that there is no natural number p and q such that (p/q)(p/q) is equal to 2. If mathematical truth were conventionnal, why did the pythagoreans *hide* this fact for so long? So those propositions are neither tautologies, nor conventions.David Deutsch, following Johnson's criteria of reality, would say that such propositions kick back. Since Georges Quenot's objection claims that nothing exists when unconsidered, be it a mathematical structure or concrete singular objects to which it applies, isn't the objection too broad to be singling out any particular physics-based cosmology as objectionable? The objection seems too powerful broad, seems to apply with equal force to all subject matters of mathematics empirical research, from pointset topology to Egyptology. I wouldn't demand that a philosophical objection, in order to be valid at all, offer a direction for specific research, but I'd ask how it would at least help research keep from going wrong, I don't see how the present objection would help keep any kind of research, mathematical or empirical, from getting onto excessively thin ice, except perhaps by inspiring a general atmosphere of skepticism in response to which people pay more attention to proofs, confirmations, corroborations, etc. -- not that any such thing could actually overcome such a ! radical objection. And the objection is stated with such generality, that I don't see how it escapes being applied to itself, since, after all, it is about things relations. If there's nobody to consider concrete things or mathematicals, then there's nobody to consider the objection to considering any unconsidered things to exist. The objection seems to undercut itself in the scenario in which it is meant to have force. Unless, of course, I've misunderstood the argument, which is certainly possible. Best, Ben Udell
Re: Is the universe computable?
On Tue, Jan 13, 2004 at 03:03:38PM +0100, Bruno Marchal wrote: What is the point? Do we have experimental procedure to validate the opposite of the fanciful scenario? Giving that we were talking about I see, we're at the prove that the Moon is not made from green cheese when nobody is looking stage. I thought this list wasn't about ghosties'n'goblins. Allright, I seem to have been mistaken about that. first person scenario, in any case it is senseless to ask for experimental procedure. (experience = first person view; experiment = third person view). So the multiverse is not a falsifyable theory? Don't tell me you were believing I was arguing. You were asserting a lot of stuff. That's commonly considered arguing, except you weren't providing any evidence so far. So, maybe you weren't. About logic, it is a branch of mathematics. Like topology, algebra, analysis it can be *applied* to some problem, which, through some hypothesis, can bear on some problem. With the comp hyp mathematical logic makes it possible to derive what consistent and platonist machine can prove about themselves and their consistent extension. Except that machine doesn't exist in absence of implementations, be it people, machines, or aliens. My point is that formal systems are a very powerful tool with very small reach, unfortunately. But I never use formal system. I modelise a particular sort of machine by formal system, so I prove things *about* machines, by using works *about* formal system. I don't use formal systems. I prove things in informal ways like all mathematicians. Above passage is 100% content-free. Because we know that QM is not a TOE. You haven't heard? How could be *know* QM is not a TOE? (I ask this independently of the fact that I find plausible QM is not a *primitive* TOE). Because general relativity and quantum theory are mutually incompatible. So both TOE aren't. We have several TOE candidates, and an increased number of blips heralding new physics, but no heir apparent yet. You believe that the theorem there is an infinity of primes is a human invention? (as opposed to a human discovery). Of course. Not necessarily human; there might be other production systems which invented them. Then, maybe there aren't. Infinity is something unphysical, btw. You can't represent arbitrary values within a finite physical system -- all infoprocessing systems are that. You'll also notice that imperfect theories are riddled with infinities; they tend to go away with the next design iteration. So infinities is something even more primatish than enumerable natural numbers. I do not see how arithmetic realism (a special case of Platonic realism, is that correct?) is an axiom. I agree with the rest of your list. Perhaps I have been unclear. By Arithmetic Realism I mean that Arithmetical Truth is independent of me, you, and the rest of humanity. There exist Oh, I disagree with that allright. Nonliving systems don't have an evolutionary pressure to develop enumerable quantities representation. weaker form of that axiom and stronger form. Tegmark for instance defends a much larger mathematical realism (so large that I am not sure what it could mean). As I said some ultrafinitist defends strictly weaker form of mathematical realism. The more quoted argument in favour of arithmetical realism is the one based on Godel's theorem, and presented by him too) which is that any formal systems (and so any ideally consistent machines) can prove, even in principle, that is with infinite time and space, all the true proposition of arithmetic. Sure. Notice that infinite time and space is unphysical, and of course a machine which doesn't exist doesn't produce anything. I was hoping for a falsifyable argument, showing that this spacetime is an operation artifact of some finite production system. But look also to the site of Watkins http://www.maths.ex.ac.uk/~mwatkins/zeta/index.htm Oh, basically you're arguing that the unreasonable applicability of mathematics in physics is anything but unreasonable, and that a TOE arisen from a formal system is in fact the universe itself? for a lot of evidence for it (evidence which are a priori not related to my more theoretical computer science approach). Now my goal (here) is not really to defend AR as true, but as sufficiently plausible that it is interesting to look at the consequences. You can read some I do not deny that a TOE can be immensely useful (but not necessarily so, higher levels of theory tend to require increasing amounts of crunch to predict anything useful), but that TOE has anything to do with the metalayer, or that in fact that distinction is meaningful. You don't seem to disagree, so we're not actually arguing. main post I send to this list where I present the argument according to which if we take comp seriously (comp = AR + TC + yes doctor) then physics is eventually a branch of machine's psychology
Re: Is the universe computable?
Wei Dai wrote: On Tue, Jan 06, 2004 at 05:32:05PM +0100, Georges Quenot wrote: Many other way of simulating the universe could be considered like for instance a 4D mesh (if we simplify by considering only general relativity; there is no reason for the approach not being possible in an even more general way) representing a universe taken as a whole in its spatio-temporal aspect. The mesh would be refined at each iteration. The relation between the time in the computer and the time in the universe would not be a synchrony but a refinement of the resolution of the time (and space) in the simulated universe as the time in the computer increases. Alternatively (though both views are not necessarily exclusive), one could use a variational formulation instead of a partial derivative formulation in order to describe/build the universe leading again to a construction in which the time in the computer is not related at all to the time in the simulated universe. Do you have references for these two ideas? No. They actually came to me while I was figuring some other ways of simulating a universe than the sequential one that seemed to give rise to many problems to me. The second one is influenced by the prossibility to consider the whole universe within a variational formulation as suggested by Hawking in A brief history of time where he also considered the possibility of a boundaryless universe (that makes much sense to me) that would make difficult the use of any (initial or other) boundary condition. Among other problems are the one of defining a global time within a universe ruled by general relativity and including time singularities within black holes for instance. Last but not least is the problem of the emergence of the flow of time itself from the gradient of order within the universe. There might be references which I do not know of and I would say probably for the case of simple physics (possibly fluid dynamics or heat transfer for instance) phenomena which could be simulated in a 3+1 (or 2+1 or 1+1) dimensional meshes as wholes. I think the refining mesh could be practically experimented in a 1D+1D and possibly up to 2D+1D for heat conduction within a solid object with various boundary conditions. While it could much less efficient (but is it even so obvious ?) than a sequential approach, implementing a finite element mesh including the time dimension and solving the partial derivative heat diffusion equations by standard linear algebra on the whole spatio-temporal domain seems perfectly feasable to me (at least for small amounts of time). I'm wondering, suppose the universe you're trying to simulate contains a computer that is running a factoring algorithm on a large number, in order to cryptanalyze somebody's RSA public key. How could you possibly simulate this universe without starting from the beginning and working forward in time? Whatever simulation method you use, if somebody was watching the simulation run, they'd see the input to the factoring algorithm appear before the output, right? I would say there is a strong anthropomorphic bias in this view. I suggest you to read my other posts in which I comment a bit about this kind of things. Indeed, the practical implementation of the simulation of the whole universe including the considered computer would be very heavy if a variational formulation and/or a 4D iteratively refining mesh had to be used. But I do not see why it should fail to simulate the computer calculation. What is very difficult is to guarantee that all interactions propagate at the appropriate level of accuracy through all of the 4D mesh and/or through all of the action paths which can be very large and interconnected. No doubt that close (up to an unimaginable level) to singular matrices will be encountered. But is this very different if one is to simulate the universe from the big bang up to this computer calculation with the appropriate accuracy needed to ensure that from the big bang initial conditions through stellar formation and human evolution this computer would be built and would run this particular calculation ? I am not so sure. I do not believe in either case that a simulation with this level of detail can be conducted on any computer that can be built in our universe (I mean a computer able to simulate a universe containing a smaller computer doing the calculation you considered with a level of accuracy sufficient to ensure that the simulation of the behavior of the smaller computer would be meaningful). This is only a theoretical speculation. Georges Quénot.
Re: Is the universe computable?
On Tue, Jan 13, 2004 at 05:30:10PM +0100, Georges Quenot wrote: No. They actually came to me while I was figuring some other ways of simulating a universe than the sequential one that seemed to give rise to many problems to me. The second one is influenced What's your take on how subjective timeflow looks like in a HashLife universe? http://www.ericweisstein.com/encyclopedias/life/HashLife.html -- Eugen* Leitl a href=http://leitl.org;leitl/a __ ICBM: 48.07078, 11.61144http://www.leitl.org 8B29F6BE: 099D 78BA 2FD3 B014 B08A 7779 75B0 2443 8B29 F6BE http://moleculardevices.org http://nanomachines.net pgp0.pgp Description: PGP signature
Re: Is the universe computable?
Georges Quenot writes: I do not believe in either case that a simulation with this level of detail can be conducted on any computer that can be built in our universe (I mean a computer able to simulate a universe containing a smaller computer doing the calculation you considered with a level of accuracy sufficient to ensure that the simulation of the behavior of the smaller computer would be meaningful). This is only a theoretical speculation. What about the idea of simulating a universe with simpler laws using such a technique? For example, consider a 2-D or 1-D cellular automaton (CA) system like Conway's Life or the various systems considered by Wolfram. Suppose we sought to construct a consistent history of such a CA system by first starting with purely random values at each point in space and time. Now, obviously this arrangement will not satisfy the CA rules. But then we go through and start modifying things locally so as to satisfy the rules. We move around through the mesh in some pattern, repeatedly making small modifications so as to provide local obedience to the rules. Eventually, if we take enough time, we ought to reach a point where the entire system satisfies the specified rules. Now, I'm not sure how to combine this process with Georges' proposal to maximize some criterion such as the gradient of orderliness. I suppose you could simply repeat this process many times, saving or remembering the best solution found so far. But it would be nice if you could combine the two steps somehow, looking for valid solutions which also scored highly in the desired optimization property. Among simple CA models are ones which have been shown to be universal, meaning that you can set up systems which do computation within the CA universe, and those systems could do various sorts of sequential calculations. Let's suppose, as Georges' ideas might suggest, that some optimization principle can implicitly promote the formation of such sequential computational systems within the simulated universe. To get back to Wei's question, it would seem that when we do manage to create such a universe using non-sequential optimization as described above, there would be no particular need for the early steps of the simulated computation to be stabilized before the later steps. The order in which stabilization occurs in any given run could be essentially arbitrary or random. Hal
Re: Is the universe computable?
Bruno Marchal wrote: At 13:36 09/01/04 +0100, Georges Quenot wrote: Bruno Marchal wrote: It seems, but it isn't. Well, actually I have known *one* mathematician, (a russian logician) who indeed makes a serious try to develop some mathematics without that infinite act of faith (I don't recall its name for the moment). Such attempt are known as ultrafinitism. Of course a lot of people (especially during the week-end) *pretend* not doing that infinite act of faith, but do it all the time implicitly. This is not what I meant. I did not refer to people not willing to accept that natural numbers exist at all but to people not wlling to accept that natural numbers exist *by themselves*. Rather, they want to see them either as only a production of human (or human-like) people or only a production of a God. What I mean is that their arithmetical property are independent of us. I don't think this is very different. I could argue that even if natural numbers were not out there, as soon as anybody consider them, their properties automatically come with and impose themselves. Even this seemingly weaker statement can be contested and it is not actually weaker but equivalent since there might be no other way than this one for natural numbers to be out there. Some people do argue that there is no arithmetical property independent of us because there is no thing on which they would apply independentkly of us. What we would call their arithmetical properties is simply a set of tautologies that do come with them when they are considered but exist no more than them when they are not considered. Do you think those people believe that the proposition 17 is prime is meaningless without a human in the neighborhood? 17 is prime is meaningless without a human in the neighborhood is exactly the kind of claim these people make (possibly generalizing the concept of human to aliens and Gods). After discussing with some of them I think they actually believe what they claim. I am not sure however that we always fully understand each other and that you or I would exactly understand such a claim in the same way as they do. Giving that I hope getting some understanding of the complex human from something simpler (number property) the approach of those people will never work, for me. And certainly vice versa. Though it is difficult to have them saying it explicitely I have the feeling that the reason why they do not want the natural numbers to be out there and even as not possibly being considered as out there is that they do not accept that the complex human be understood from something simpler (number property). They do not even accept the idea being considered, were it as a mere conjecture or working hypothesis. Their more official argument is that such a view would prevent the foundation of human dignity. Also, I would take (without added explanations) an expression like numbers are a production of God as equivalent to arithmetical realism. Yes and there are several ways to understand this. And I said unfortunately because some not only do not want to see natural numbers as existing by themselves but they do not want the idea to be simply presented as logically possible and even see/designate evil in people working at popularizing it. OK, but then some want you being dead because of the color of the skin, or the length of your nose, ... I am not sure it is not premature wanting to enlighten everyone at once ... I guess you were only talking about those hard-aristotelians who like to dismiss Plato's questions as childish. Evil ? Perhaps could you be more precise on those people. I have not met people seeing evil in arithmetical platonism, have you? I have not met any of them physically but I had discussion with some of them via Internet. There might not be so many of them but there are. You will find, at least in the US, a lot of people considering the views of evolution and/or of the big-bang as evil. If they finally have to abandon these positions due to the amount of evidence in favor of it, the last line of defence for their conception of a personal God and for a significant role for Him could be at the level of artihmetical realism. Artihmetical realism by itself (not from a distinct personal God) is therefore seen as evil by them. As I mentionned, they usually do not put it that way. Rather they argue that such a view would prevent the foundation of human dignity and the like. Georges Quénot.
Re: Is the universe computable?
Hal Finney wrote: Suppose we sought to construct a consistent history of such a CA system by first starting with purely random values at each point in space and time. Now, obviously this arrangement will not satisfy the CA rules. But then we go through and start modifying things locally so as to satisfy the rules. We move around through the mesh in some pattern, repeatedly making small modifications so as to provide local obedience to the rules. Eventually, if we take enough time, we ought to reach a point where the entire system satisfies the specified rules. Would this be guaranteed to work? You might get local regions of space and time that internally follow the rules but that are incompatible at their boundaries, like domains in a magnet. The algorithm would keep trying to modify things to make them globally consistent of course, but isn't it possible it'd get stuck in a loop? Now, I'm not sure how to combine this process with Georges' proposal to maximize some criterion such as the gradient of orderliness. I suppose you could simply repeat this process many times, saving or remembering the best solution found so far. As long as everything that happens in the universe's history can be represented by a finite string, this brute-force method is one that's guaranteed to work...the ultimate version of this would just be to generate all possible strings of that length, then throw out all the ones that don't match the laws/boundary conditions you've chosen. This method could also be used to generate histories satisfying global constraints that could be hard to simulate in a sequential way, like a universe where backwards time travel is possible but history must be completely self-consistent, where it is possible to influence the past but not to change it. Jesse Mazer _ Find out everything you need to know about Las Vegas here for that getaway. http://special.msn.com/msnbc/vivalasvegas.armx
Re: Is the universe computable?
Jesse Mazer wrote: Hal Finney wrote: Suppose we sought to construct a consistent history of such a CA system by first starting with purely random values at each point in space and time. Now, obviously this arrangement will not satisfy the CA rules. But then we go through and start modifying things locally so as to satisfy the rules. We move around through the mesh in some pattern, repeatedly making small modifications so as to provide local obedience to the rules. Eventually, if we take enough time, we ought to reach a point where the entire system satisfies the specified rules. Would this be guaranteed to work? You might get local regions of space and time that internally follow the rules but that are incompatible at their boundaries, like domains in a magnet. The algorithm would keep trying to modify things to make them globally consistent of course, but isn't it possible it'd get stuck in a loop? Yes, you might have to do it carefully in order to avoid that. I think that if you had a stochastic (random) element to the algorithm then it would avoid loops. And you'd also have to be prepared to change your boundary conditions so that you weren't trying to solve an impossible state. (I think this part is implicit in Georges' idea of maximizing some criterion rather than using fixed boundary conditions.) Wolfram observationally divided CA universes (and more general computational systems) into four categories: static, cyclic, random and structured. Only the last class would allow for computation. I suspect that those universes capable of computation would be among the hardest ones to solve in this non-sequential way, that they would have the most global dependencies. Universes which were restricted to regular patterns would be easy. (Maybe the random ones would be hard, too, since they tend to be chaotic.) Now, I'm not sure how to combine this process with Georges' proposal to maximize some criterion such as the gradient of orderliness. I suppose you could simply repeat this process many times, saving or remembering the best solution found so far. As long as everything that happens in the universe's history can be represented by a finite string, this brute-force method is one that's guaranteed to work...the ultimate version of this would just be to generate all possible strings of that length, then throw out all the ones that don't match the laws/boundary conditions you've chosen. This method could also be used to generate histories satisfying global constraints that could be hard to simulate in a sequential way, like a universe where backwards time travel is possible but history must be completely self-consistent, where it is possible to influence the past but not to change it. Yes, that's a good idea, and it would probably be a shorter and simpler program than my suggestion. I like your idea of time travel universes; this is a mechanism for generating them that shows that they are not logically impossible or contradictory. Several science fiction writers have explored this concept, that time travel is possible and paradoxes will not occur, no matter how unlikely are the events which conspire to keep things consistent. I'm not sure how to estimate the measure of time travel universes. The program to generate them is not necessarily large, but there would be many fewer consistent solutions to the equations than in universes without time travel. So perhaps there would be fewer observers in time travel universes compared even to ones that might have ad hoc rules forbidding time travel. Such rules might make non time travel universes' programs more complex and the universes of lower measure, but this might be more than compensated for by the greater numbers of observers in universes that forbid time travel. Hal Finney
Re: Is the universe computable?
Dear Wei, Georges, et al, Where does the notion of computational resources factor in this? Stephen - Original Message - From: Wei Dai [EMAIL PROTECTED] To: Georges Quenot [EMAIL PROTECTED] Cc: [EMAIL PROTECTED] Sent: Monday, January 12, 2004 8:50 PM Subject: Re: Is the universe computable? On Tue, Jan 06, 2004 at 05:32:05PM +0100, Georges Quenot wrote: Many other way of simulating the universe could be considered like for instance a 4D mesh (if we simplify by considering only general relativity; there is no reason for the approach not being possible in an even more general way) representing a universe taken as a whole in its spatio-temporal aspect. The mesh would be refined at each iteration. The relation between the time in the computer and the time in the universe would not be a synchrony but a refinement of the resolution of the time (and space) in the simulated universe as the time in the computer increases. Alternatively (though both views are not necessarily exclusive), one could use a variational formulation instead of a partial derivative formulation in order to describe/build the universe leading again to a construction in which the time in the computer is not related at all to the time in the simulated universe. Do you have references for these two ideas? I'm wondering, suppose the universe you're trying to simulate contains a computer that is running a factoring algorithm on a large number, in order to cryptanalyze somebody's RSA public key. How could you possibly simulate this universe without starting from the beginning and working forward in time? Whatever simulation method you use, if somebody was watching the simulation run, they'd see the input to the factoring algorithm appear before the output, right?
RE: Is the universe computable?
Hi Eugin, I see, we're at the prove that the Moon is not made from green cheese when nobody is looking stage. I thought this list wasn't about ghosties'n'goblins. Allright, I seem to have been mistaken about that. You seem to be getting a little hot under the collar! Here is a justification of why I think arithmetical realism is at least very plausible... Let's suppose that a computer simulation can (in principle) exhibit awareness. I don't know whether you dispute this hypothesis, but let's assume it and see where it leads. Let's suppose in fact that you Eugin, were able to watch a computer simulation run, and on the screen you could see people laughing, talking - perhaps even discussing ideas like whether *their* physical existence needs to be postulated, or else they are merely part of a platonic multiverse. A simulated person may stamp his fist on a simulated coffee table and say Surely this coffee table is real - how could it possibly be numbers - I've never heard of anything so ludicrous!. Now Eugin, you may argue that the existence of this universe depends on the fact that it was simulated by a computer in our universe. I find this a little hard to fathom - because computer simulations are deterministic and they give the same results whether they are run once or a thousand times. I find it hard to imagine that they leap into existence when they are run the first time. I'm particularly motivated by the universal dove-tailing program - which eventually generates the trace of all possible programs. Do you say that most of the integers don't exist because nobody has written them down? I can see your point when you say that 2+2=4 is meaningless without the physical objects to which it relates. However this is irrelevant because you are thinking of too simplistic a mathematical system! The only mathematical systems that are relevant to the everything-list are those that have conscious inhabitants within them. Within this self contained mathematical world we *do* have the context for numbers. It's a bit like the chicken and egg problem. (egg = number theory, chicken = objects and observers). Both come together and can't be pulled apart. - David -Original Message- From: Eugen Leitl [mailto:[EMAIL PROTECTED] Sent: Wednesday, 14 January 2004 1:32 AM To: [EMAIL PROTECTED] Subject: Re: Is the universe computable? On Tue, Jan 13, 2004 at 03:03:38PM +0100, Bruno Marchal wrote: What is the point? Do we have experimental procedure to validate the opposite of the fanciful scenario? Giving that we were talking about I see, we're at the prove that the Moon is not made from green cheese when nobody is looking stage. I thought this list wasn't about ghosties'n'goblins. Allright, I seem to have been mistaken about that. first person scenario, in any case it is senseless to ask for experimental procedure. (experience = first person view; experiment = third person view). So the multiverse is not a falsifyable theory? Don't tell me you were believing I was arguing. You were asserting a lot of stuff. That's commonly considered arguing, except you weren't providing any evidence so far. So, maybe you weren't. About logic, it is a branch of mathematics. Like topology, algebra, analysis it can be *applied* to some problem, which, through some hypothesis, can bear on some problem. With the comp hyp mathematical logic makes it possible to derive what consistent and platonist machine can prove about themselves and their consistent extension. Except that machine doesn't exist in absence of implementations, be it people, machines, or aliens. My point is that formal systems are a very powerful tool with very small reach, unfortunately. But I never use formal system. I modelise a particular sort of machine by formal system, so I prove things *about* machines, by using works *about* formal system. I don't use formal systems. I prove things in informal ways like all mathematicians. Above passage is 100% content-free. Because we know that QM is not a TOE. You haven't heard? How could be *know* QM is not a TOE? (I ask this independently of the fact that I find plausible QM is not a *primitive* TOE). Because general relativity and quantum theory are mutually incompatible. So both TOE aren't. We have several TOE candidates, and an increased number of blips heralding new physics, but no heir apparent yet. You believe that the theorem there is an infinity of primes is a human invention? (as opposed to a human discovery). Of course. Not necessarily human; there might be other production systems which invented them. Then, maybe there aren't. Infinity is something unphysical, btw. You can't represent arbitrary values within a finite physical system -- all infoprocessing systems are that. You'll also notice that imperfect theories are riddled with infinities; they tend to go away
Re: Is the universe computable?
At 15:42 09/01/04 -0500, Jesse Mazer wrote: Bruno Marchal wrote: I don't think the word universe is a basic term. It is a sort or deity for atheist. All my work can be seen as an attempt to mak it more palatable in the comp frame. Tegmark, imo, goes in the right direction, but seems unaware of the difficulties mathematicians discovered when just trying to define the or even a mathematical universe. Of course tremendous progress has been made (in set theory, in category theory) giving tools to provide some *approximation*, but the big mathematical whole seems really inaccessible. With comp it can be shown (first person) inaccessible, even unnameable ... Inaccessible in what sense? How do you use comp to show this? If this is something you've addressed in a previous post, feel free to just provide a link... This is a consequence of Tarski theorem. Do you know it? I think I have said this before but I don't find the links (I have to much mentioned the result by McKinsey and Tarski in Modal logic, so searching the archive with tarski does not help). Let me explain it briefly. With the platonist assumption being a part of the comp hyp, we can identify in some way truth and reality (in a very large sense which does not postulate that reality is necessarily physical reality). That is Reality is identified with the set of all true propositions in some rich language. Now Tarski theorem, like Godel's theorem, can be applied to any sufficiently rich theory or to any sound machine. Tarski theorem says that there is no truth predicate definable in the language of such theories/machines. Nor is knowledge definable for similar reason. So any complete platonist notion of truth or knowledge cannot be defined in any language used by the machine, strictly speaking such vast notion of truth is just inaccessible by the machine, and this despite the fact a machine can build transfinite ladder of better approximation of it. By way of contrast the notion of consistency *is* definable in the language of the machine, only themachine cannot prove its own consistency (by Godel), but the machine can express it. Now, with Tarski the machine cannot even express it. Like Godel's theorem, tarski theorem is a quasi direct consequence of the *diagonalisation lemma: For any formula A(x), there is a proposition k such that the machine will prove k - A(k).Note: A(k) is put for the longer A(code of k) In case a truth predicate V(x) could be defined in arithmetic or in the machine's tong, the machine would be able to define a falsity predicate (as -V(x) ), and by the diagonalisation lemma, the machine would be able to prove the Epimenid sentence k - -V(k), which is absurd V being a truth predicate. Truth, or any complete description of reality cannot have a definition, or a name: semantical notion like truth or knowledge are undefinable (unnameable). Actually we don't really need comp in the sense that these limitation theorem applies to much powerful theories or divine machine with oracle, ... OK? Bruno
Re: Is the universe computable?
At 13:36 09/01/04 +0100, Georges Quenot wrote: Bruno Marchal wrote: It seems, but it isn't. Well, actually I have known *one* mathematician, (a russian logician) who indeed makes a serious try to develop some mathematics without that infinite act of faith (I don't recall its name for the moment). Such attempt are known as ultrafinitism. Of course a lot of people (especially during the week-end) *pretend* not doing that infinite act of faith, but do it all the time implicitly. This is not what I meant. I did not refer to people not willing to accept that natural numbers exist at all but to people not wlling to accept that natural numbers exist *by themselves*. Rather, they want to see them either as only a production of human (or human-like) people or only a production of a God. What I mean is that their arithmetical property are independent of us. Do you think those people believe that the proposition 17 is prime is meaningless without a human in the neighborhood? Giving that I hope getting some understanding of the complex human from something simpler (number property) the approach of those people will never work, for me. Also, I would take (without added explanations) an expression like numbers are a production of God as equivalent to arithmetical realism. Of course if you add that God is a mathematical-conventionalist and that God could have chose that only even numbers exist, then I would disagree. (Despite my training in believing at least five impossible proposition each day before breakfast ;-) And I said unfortunately because some not only do not want to see natural numbers as existing by themselves but they do not want the idea to be simply presented as logically possible and even see/designate evil in people working at popularizing it. OK, but then some want you being dead because of the color of the skin, or the length of your nose, ... I am not sure it is not premature wanting to enlighten everyone at once ... I guess you were only talking about those hard-aristotelians who like to dismiss Plato's questions as childish. Evil ? Perhaps could you be more precise on those people. I have not met people seeing evil in arithmetical platonism, have you? Bruno
Re: Is the universe computable?
On Mon, Jan 12, 2004 at 03:50:42PM +0100, Bruno Marchal wrote: What I mean is that their arithmetical property are independent of us. Do you think those people believe that the proposition 17 is prime is meaningless without a human in the neighborhood? Of course it is meaningless. Natural numbers are representation clusters by infoprocessing systems: currently machines or animals. Pebbles can't count themselves, obviously. No realization without representation. I have no trouble seeing the universe as artifact from some production system (but that metalayer be transcendent by definition), but assuming universe exists because numbers exist does strike me as a yet another faith. -- Eugen* Leitl a href=http://leitl.org;leitl/a __ ICBM: 48.07078, 11.61144http://www.leitl.org 8B29F6BE: 099D 78BA 2FD3 B014 B08A 7779 75B0 2443 8B29 F6BE http://moleculardevices.org http://nanomachines.net pgp0.pgp Description: PGP signature
Re: Is the universe computable?
At 16:02 12/01/04 +0100, Eugen Leitl wrote: On Mon, Jan 12, 2004 at 03:50:42PM +0100, Bruno Marchal wrote: What I mean is that their arithmetical property are independent of us. Do you think those people believe that the proposition 17 is prime is meaningless without a human in the neighborhood? Of course it is meaningless. Natural numbers are representation clusters by infoprocessing systems: currently machines or animals. Pebbles can't count themselves, obviously. Natural numbers are not representation. They are the one represented, for exemples by infosystems, or pebbles, animals etc. It seems to me you confuse the thing abstract immaterial numbers, and the things which represent them. Pebbles can't count themselves, obviously. But it is not because pebbles can't count that two pebbles give an even number of pebbles. Electron cannot solve schroedinger equation (only a physicist can do that), nevertheless electron cannot not follow it (supposing QM). No realization without representation. It depends of the level of description. It depends of your favorite primitive act of faith. I have no trouble seeing the universe as artifact from some production system (but that metalayer be transcendent by definition), but assuming universe exists because numbers exist does strike me as a yet another faith. That numbers exists independently of us is based on a act of faith I agree. But all theories are based on some act of faith. That the universes follows from numbers is not an act of faith, but a consequence of comp. See my thesis for that, or links to explanations in this list: all that in my url below. Bruno PS there is a missing word in my answer to Jesse. Just to be clearer: Godel's theorem: self-consistency is not provable by consistent machine Tarski's theorem: truth (and knowledge) is not even expressible by the consistent machine. http://iridia.ulb.ac.be/~marchal/
Re: Is the universe computable?
On Mon, Jan 12, 2004 at 04:18:56PM +0100, Bruno Marchal wrote: Natural numbers are not representation. They are the one represented, for exemples by infosystems, or pebbles, animals etc. They are the one represented is a yet another assertion. I would be more inclined to listen, if you'd show how a group of pebbles can conduct a measurement. (Counting is a measurement). It seems to me you confuse the thing abstract immaterial numbers, and the things which represent them. If I'd kill you, you'd have no chance of thinking that thought. If I killed all animals capable of counting, abstract immaterial numbers would become exactly that: immaterial. Pebbles can't count themselves, obviously. But it is not because pebbles can't count that two pebbles give an even number of pebbles. Electron cannot solve schroedinger equation (only a physicist can do that), nevertheless electron cannot not follow it (supposing QM). The universe does what it does, it certainly doesn't solve equations. People solve equations, when approximating what universe does. As such, QM is a fair approximation; it has no further reality beyond that. H\psi=E\psi in absence of context is just as meaningless as 2+2=4. -- Eugen* Leitl a href=http://leitl.org;leitl/a __ ICBM: 48.07078, 11.61144http://www.leitl.org 8B29F6BE: 099D 78BA 2FD3 B014 B08A 7779 75B0 2443 8B29 F6BE http://moleculardevices.org http://nanomachines.net pgp0.pgp Description: PGP signature
Re: Is the universe computable?
Bruno, in the line you touched with 'numbers: I was arguing on another list 'pro' D.Bohm's there are no numbers in nature position when a listmember asked: aren't you part of nature? then why are you saying that numbers - existing in your mind - are not 'part of nature'? Since then I formulate it something like: numbers came into existence as products of 'our' thinking. (Maybe better worded). You wrote: What I mean is that their arithmetical property are independent of us. .. That may branch into the question how much of 'societal' knowledge is part of an individual belief - rejectable or intrinsically adherent? (Some may call this a fundamental domain of memes). With the 'invention' of numbers (arithmetical, that is) human mentality turned into a computing animal - as a species-characteristic. I separate this from the assignment of quantities to well chosen units in numbers. Quantities may have their natural role in natural processes - unconted in our units, just mass-wise, and we, later on - in physical laws - applied the arithmetical ordering to the observations in the quantized natural events. Such quantizing (restricted to models of already discovered elements) renders some processes 'chaotic' or even paradoxical, while nature processes them without any problem in her unrestricted (total) interconnectedness (not included - even known ALL in our quantized working models). Sorry for the physicistically unorthodox idea. Best regards John Mikes - Original Message - From: Bruno Marchal [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Monday, January 12, 2004 9:50 AM Subject: Re: Is the universe computable? At 13:36 09/01/04 +0100, Georges Quenot wrote: Bruno Marchal wrote: It seems, but it isn't. Well, actually I have known *one* mathematician, (a russian logician) who indeed makes a serious try to develop some mathematics without that infinite act of faith (I don't recall its name for the moment). Such attempt are known as ultrafinitism. Of course a lot of people (especially during the week-end) *pretend* not doing that infinite act of faith, but do it all the time implicitly. This is not what I meant. I did not refer to people not willing to accept that natural numbers exist at all but to people not wlling to accept that natural numbers exist *by themselves*. Rather, they want to see them either as only a production of human (or human-like) people or only a production of a God. What I mean is that their arithmetical property are independent of us. Do you think those people believe that the proposition 17 is prime is meaningless without a human in the neighborhood? Giving that I hope getting some understanding of the complex human from something simpler (number property) the approach of those people will never work, for me. Also, I would take (without added explanations) an expression like numbers are a production of God as equivalent to arithmetical realism. Of course if you add that God is a mathematical-conventionalist and that God could have chose that only even numbers exist, then I would disagree. (Despite my training in believing at least five impossible proposition each day before breakfast ;-) And I said unfortunately because some not only do not want to see natural numbers as existing by themselves but they do not want the idea to be simply presented as logically possible and even see/designate evil in people working at popularizing it. OK, but then some want you being dead because of the color of the skin, or the length of your nose, ... I am not sure it is not premature wanting to enlighten everyone at once ... I guess you were only talking about those hard-aristotelians who like to dismiss Plato's questions as childish. Evil ? Perhaps could you be more precise on those people. I have not met people seeing evil in arithmetical platonism, have you? Bruno
Re: Is the universe computable?
On Tue, Jan 06, 2004 at 05:32:05PM +0100, Georges Quenot wrote: Many other way of simulating the universe could be considered like for instance a 4D mesh (if we simplify by considering only general relativity; there is no reason for the approach not being possible in an even more general way) representing a universe taken as a whole in its spatio-temporal aspect. The mesh would be refined at each iteration. The relation between the time in the computer and the time in the universe would not be a synchrony but a refinement of the resolution of the time (and space) in the simulated universe as the time in the computer increases. Alternatively (though both views are not necessarily exclusive), one could use a variational formulation instead of a partial derivative formulation in order to describe/build the universe leading again to a construction in which the time in the computer is not related at all to the time in the simulated universe. Do you have references for these two ideas? I'm wondering, suppose the universe you're trying to simulate contains a computer that is running a factoring algorithm on a large number, in order to cryptanalyze somebody's RSA public key. How could you possibly simulate this universe without starting from the beginning and working forward in time? Whatever simulation method you use, if somebody was watching the simulation run, they'd see the input to the factoring algorithm appear before the output, right?
Re: Is the universe computable?
Erick,thanks for your comments on my exchange with GeorgeQ. Although I do not claim to have understood (digested?) all of your post, I feel it may be in my line of thinking (pardon me the offense). I just use less connotations to 'time' related phrases, as may be obvious from below. Over the years I tried in several attempts to voice on this (and other) lists that all our phys-math considerations are secondary, coming from (and by) human understanding of something with/by human logic. I see no evidence that the existence (nature? everything) would follow our approval - 'our' as part/product of it. Physical law is a model of our thinking (I may be crucified for this) and fetishizing our understanding is IMO narrow. Even the 'elephant/rabbit' excursions start from some 'random' arrangement of photons, which are 'our' interpretation about sthing which may be interpreted quite differently by different mindsets. This is the reason - I think - why GeorgeQ found my ideas mystical. In my vocabulary mystical is what has not (yet?) been explained. I work with all unknown/unknowables, trying to make sense of the so far 'undiscovered' within the 'boundaries' of our mind. I call it my scientific agnosticism. Time and space are our crutches (boundaries? see below). Russell St. scolded me several times for my 'non-mathematical' stance as improper, vague, undefinable etc. - he is right, I don't 'force' my (our) understanding onto things beyond it. Equationally or not. I appreciate your remark: as later will be mentioned, boviously perception play a big role in this value, is your definition of the univers from the perspective of a human being, being that self within it's self, as projected outwards from a finite continuum into a supposedly infinite continuum? (whether 'boviously' is a typo for obviously, or a hint to the early style on this list calling adverse ideas bovine excrement). Somebody speculated on the way of 'thinking' on Venus where the clouds prevent any info about the extravenereal world (cosmology, philosophy, etc.). We are sitting closed in by a mental cloud of our understanding, ie boundaries of our mindset (epistemically steadily widening, however). I believe 'computation' here goes beyond the 'binary calculations' as well as (maybe) temporal considerations. Life I consider differently, IMO it is some natural function we overappreciate because we do it (cf the biology etc. in our reductionistic science system). 'Consciousness' I call the acknowledgement (by anything) and response to (incl, storage) of information - absolutely not restricted to functions we would deem 'life'. So I have no problem with 'universes' (not?) containing 'live' products. We muster a reductionistic way of our mindset: using limited models of observables, cut into (select) boundaries in a world of (wholistically) interconnected interaction of things way beyond our cognitive inventory. Regards John Mikes - Original Message - From: Erick Krist [EMAIL PROTECTED] To: [EMAIL PROTECTED]; John M [EMAIL PROTECTED] Sent: Tuesday, January 06, 2004 7:33 PM Subject: Re: Is the universe computable? to your series of questions I would like to add one as first: What do you call universe? i think this question is most temporally cognitively perceptual in nature. as explained: as long as we do not make this identification, it is futile to speculate about its computability/computed sate. as later will be mentioned, boviously perception play a big role in this value, is your definition of the univers from the perspective of a human being, being that self within it's self, as projected outwards from a finite continuum into a supposedly infinite continuum? or are you looking at the univers from the point of view of a rock which site blindly in time without temporant perceptual motion? obviously there are many different perceptual universes, and any of them could be philosphically percieved by the mind, therefor any of them would be physically coorect on a perceptual model of a temporant cyclical universe. we have to keep in mind, the time itself may only be a function of the combined perceptual receptions of our own internally functioning senses biologically simultaneously now. I see not too much value in assuming infinite memories and infinite time of computation, that may lead to a game and i may i beg to ask is a computer supposed to under any assumption compute a continuous value of infinite using binary logic as it's base computational rate? -calling computation the object to be computed. this is quite naturally the function of time works in the first place. time is the measure of the systematic computational functions of an internal system as measured by the temporant singularity of the external structures of that internal system as an alternatively functional singular temporant system of it's own. .: the nature of a coputationally temporant universe involves the notion
Re: Is the universe computable?
Norman Samish : Max Tegmark, at http://207.70.190.98/toe.pdf, published in Annals of Physics, 270, 1-51 (1998), postulates that all structures that exist mathematically exist also physically. Max Tegmark postulated or conjectured even more in that paper: that the distinction between mathematical existence and physical existence is meaningless, at least from a scientific point of view. I also had this idea about two years ago: if (this is not a small if but this is the assupmtion here) the universe is isomorphic to a mathematical (presumably arithmetic) object, it must be this very object since all isomorphic objects are the same object. In other words (probably inaccurately but ine can grasp the idea anyway): no matter what substance particles are made of as long as they obey a given set of equations/rules, everything that does happen as we perceive it depends only of this given set of equations/rules, and not at all of any hypothetical substance the particles would be made of. If the substance of particle does not matter, it doesn't even matter that they have any substance at all and every question (nature, existence, ...) about such hypothetical substance is purely metaphysical. There are however several assumptions behind this idea, at least the one mentionned above and another one about arithmetical realism. Incidently, I found this mailing list (and soon after Tegmark's paper) by trying to figure how original that idea might be and how seriously it could be taken (I just entered the question Do natural numbers exist by themselves ? or possibly a variant of it like Who supports the idea that natural numbers exist by themselves ? in the general purpose question answering system: http://www.languagecomputer.com/demos/question_answering/internet_demo/index.html). Georges Quénot.
Re: Is the universe computable?
Bruno Marchal wrote: At 11:34 08/01/04 +0100, Georges Quenot wrote: I am very willing (maybe too much, that's part of the problem) to accept a Platonic existence for *the* integers. I am far from sure however that this does not involve a significant amount of faith. Indeed. It needs an infinite act of faith. But I have no problem with that ... Unfortunately, it seems that some people do. I am not sure how much I share that faith. As I mentionned, I am willing to but since I could not find some ground to support that willingness, I might be a bit agnostic too. There are some objections to it and I am not sure that none of them make sense. Also, as someone said (if anybody has the original reference, in am interested): the desire to believe is a reason to doubt. I think that, even if it is true, arithmetic realism needs to be postulated (or conjectured) since I can't figure how it could be established. All right. That's why I explicitly put the AR in the definition of computationalism. About your question is the universe computable? the problem depends on what you mean by universe. The definition you gave recently are based on some first person point of view, and even that answer does not makes things sufficiently less ambiguous to answer. Don't hesitate to try again. I have no problem with definitions that inculde some first person point of view. I do not find them so first person point of view since I believe that every person I can talk with, using the same first person point of view, would see the same universe. We could at least say the universe in a consistent way among us. I might try again but I would like first to see what others have to say on the subject (to get an idea of in what direction I would need to make things clearer). You can also read my thesis which bears on that subject (in french). Yes. I have found the reference too. One of my next readings I think (though I have a pipe quite full...). You may be interested in learning that at least the *physical* universe cannot be computable once we postulate the comp hypothesis (that is mainly the thesis that I or You are computable; + Church thesis + AR). The reason is that with comp, as with Everett (and despite minor errors in Everett on that point), the traditional psycho-parallelism cannot be maintained. See my URL below for more. Why there is no FAQ? Because we are still discussing the meaning of a lot of terms I saw some posts on tentative glossaries of acronyms. Maybe before complex terms, we should focus on basic ones like universe. I would not be upset to encounter definitions for several possible senses of that word. Welcome, Thanks. Georges.
Re: Is the universe computable?
At 09:45 09/01/04 +0100, Georges Quenot wrote:
Bruno Marchal wrote:
At 11:34 08/01/04 +0100, Georges Quenot wrote:
I am very willing (maybe too much, that's part of the
problem) to accept a Platonic existence for *the* integers.
I am far from sure however that this does not involve a
significant amount of faith.
Indeed. It needs an infinite act of faith. But I have no problem
with that ...
Unfortunately, it seems that some people do.
It seems, but it isn't. Well, actually I have known *one* mathematician,
(a russian logician) who indeed makes a serious try to develop
some mathematics without that infinite act of faith (I don't recall
its name for the moment). Such attempt are known as ultrafinitism.
Of course a lot of people (especially during the week-end) *pretend*
not doing that infinite act of faith, but do it all the time implicitly. You
know an ultrafinitist cannot assert that he is an ultrafinitist without
going beyong ultrafinitism. So perhaps only animals do not do that
infinite act of faith, but IMO, most mammals does it in a sort of
passive and implicit way. If you pretend to understand a statement
like:
N ={1, 2, 3 ...}, or N = {l, ll, lll, ,
l, ll, lll, ...},
then you do it. Words like never, always, more, until, while, etc.
have intuitive meaning relying on it. I have worked with highly mentally
disabled people, and only with a few of them I have concluded that there
was perhaps some evidence in their *non grasping* of the simple
potential infinite. All finitist and all intuitionnist accept it. Second order
logic and any piece of mathematics rely on it.
Some people would like to doubt it but I think they confuse Arithmetical
Realism with some substancialist view of number which of course I reject.
(I reject substancialism even in physics, actually I showed it logically
incompatible with the comp hyp).
Fearing the death in the long run (as opposed of fearing some near catastroph)
also rely on that faith in the infinite, at least implicitly.
Some people believe that human are religious because they fear death, but
it is the reverse which seems to me much more plausible: it is because
we are religious (i.e. we believe in some infinite) that we are fearing death.
I am not sure how much I share that faith. As I mentionned,
I am willing to but since I could not find some ground to
support that willingness, I might be a bit agnostic too.
No problem. The point is that it is a nice and deep hypothesis
which makes comp fun and extremely powerful. It is definitely
among my working hypotheses.
snip
Why there is no FAQ? Because we are still discussing the meaning of
a lot of terms
I saw some posts on tentative glossaries of acronyms. Maybe
before complex terms, we should focus on basic ones like
universe. I would not be upset to encounter definitions
for several possible senses of that word.
I don't think the word universe is a basic term. It is a sort
or deity for atheist. All my work can be seen as an attempt to mak
it more palatable in the comp frame.
Tegmark, imo, goes in the right direction, but seems unaware
of the difficulties mathematicians discovered when just trying to
define the or even a mathematical universe. Of course tremendous
progress has been made (in set theory, in category theory) giving
tools to provide some *approximation*, but the big mathematical
whole seems really inaccessible. With comp it can be shown
(first person) inaccessible, even unnameable ...
Bon week-end,
Bruno
Re: Is the universe computable?
Bruno Marchal wrote:
At 09:45 09/01/04 +0100, Georges Quenot wrote:
Bruno Marchal wrote:
At 11:34 08/01/04 +0100, Georges Quenot wrote:
I am very willing (maybe too much, that's part of the
problem) to accept a Platonic existence for *the* integers.
I am far from sure however that this does not involve a
significant amount of faith.
Indeed. It needs an infinite act of faith. But I have no problem
with that ...
Unfortunately, it seems that some people do.
It seems, but it isn't. Well, actually I have known *one* mathematician,
(a russian logician) who indeed makes a serious try to develop
some mathematics without that infinite act of faith (I don't recall
its name for the moment). Such attempt are known as ultrafinitism.
Of course a lot of people (especially during the week-end) *pretend*
not doing that infinite act of faith, but do it all the time implicitly.
This is not what I meant. I did not refer to people not willing
to accept that natural numbers exist at all but to people not
wlling to accept that natural numbers exist *by themselves*.
Rather, they want to see them either as only a production of
human (or human-like) people or only a production of a God.
And I said unfortunately because some not only do not want to
see natural numbers as existing by themselves but they do not
want the idea to be simply presented as logically possible and
even see/designate evil in people working at popularizing it.
You know an ultrafinitist cannot assert that he is an ultrafinitist
without going beyong ultrafinitism. So perhaps only animals do not do
that infinite act of faith, but IMO, most mammals does it in a sort of
passive and implicit way. If you pretend to understand a statement
like:
N ={1, 2, 3 ...}, or N = {l, ll, lll, ,
l, ll, lll, ...},
then you do it. Words like never, always, more, until, while, etc.
have intuitive meaning relying on it. I have worked with highly mentally
disabled people, and only with a few of them I have concluded that there
was perhaps some evidence in their *non grasping* of the simple
potential infinite. All finitist and all intuitionnist accept it. Second order
logic and any piece of mathematics rely on it.
Some people would like to doubt it but I think they confuse Arithmetical
Realism with some substancialist view of number which of course I reject.
(I reject substancialism even in physics, actually I showed it logically
incompatible with the comp hyp).
I would not say infinite act of faith but rather act of faith
in infinity. I don't know the work of the mathematician you think
of neither of any other such kind of work but I flatly consider
that we only manipulate infinity formally within obviously finite
formalisms. I am not sure that it is necessary that any infinite
exists (let's say by itself in some platonic sense) for that
everything that we are talking abour within this kind of finite
formalism makes sense (and exists in some platonic sense).
Fearing the death in the long run (as opposed of fearing some near catastroph)
also rely on that faith in the infinite, at least implicitly.
Some people believe that human are religious because they fear death, but
it is the reverse which seems to me much more plausible: it is because
we are religious (i.e. we believe in some infinite) that we are fearing death.
I do not share all of Dawkins' views (especially from the social
point of view) but I have a Dawkins' view of religion. I would
say that human are religious simply because this induces among
themselves a behavior that increases their fitness (at the level
of communities). The corresponding set of memes interact in various
ways with other aspects like fear of death in complex networks
from which it might be vain to try to isolate simple one-way causal
relations.
I am not sure how much I share that faith. As I mentionned,
I am willing to but since I could not find some ground to
support that willingness, I might be a bit agnostic too.
No problem. The point is that it is a nice and deep hypothesis
which makes comp fun and extremely powerful. It is definitely
among my working hypotheses.
I think I can consider both this one and some alternatives
(not simulatneously, of course). However I do not find the
alternatives very fecund currently (and I am even more
agnostic about them).
Why there is no FAQ? Because we are still discussing the meaning of
a lot of terms
I saw some posts on tentative glossaries of acronyms. Maybe
before complex terms, we should focus on basic ones like
universe. I would not be upset to encounter definitions
for several possible senses of that word.
I don't think the word universe is a basic term. It is a sort
of deity for atheist.
I guess this would be called pantheism (the difference might
lie in the level of worship involved rather than in the level
of faith).
All my work can be seen as an attempt
Re: Is the universe computable?
Bruno Marchal wrote: I don't think the word universe is a basic term. It is a sort or deity for atheist. All my work can be seen as an attempt to mak it more palatable in the comp frame. Tegmark, imo, goes in the right direction, but seems unaware of the difficulties mathematicians discovered when just trying to define the or even a mathematical universe. Of course tremendous progress has been made (in set theory, in category theory) giving tools to provide some *approximation*, but the big mathematical whole seems really inaccessible. With comp it can be shown (first person) inaccessible, even unnameable ... Inaccessible in what sense? How do you use comp to show this? If this is something you've addressed in a previous post, feel free to just provide a link... Jesse _ Worried about inbox overload? Get MSN Extra Storage now! http://join.msn.com/?PAGE=features/es
Re: Is the universe computable?
John M wrote: George Q wrote (among many others, full post see below): A.the universe in which I live according to the current intuition I have of it and B: the possibility to simulate the universe at any level of accuracy. First I wanted to ask what is intuition, but let us stay with common sense (however divergent that may be). I don't have your intuition and you don't have mine. There is an assumption here which is that however divergent these intuition or common sense views of it might be, there exist (in some sense) something that we can refer to as the universe. By the way, this is not the first series of post with that title and though I am not sure I went through all of them this is the first time I see this issue discussed here. This is indeed a good question but why me ? And how do other participants define what the universe could be ? Now if A is true, I wonder upon WHAT can you simulate? I don't understand the question. Your reply points to first person processes. Yes but this is onky in one sense. There might exist a lot of other universes. Among all possible universes, I mean I am talking about the one I feel I live in. This is just a way to designate one specific universe (not to mean that I am not interested in the computability of others but I have a special interest in that one). I like better a 'mixed' way: MY 'interpretation' of something to which I have access only through such interpretation - but there must be a basis for the inter[retation both as my way of doing it, but more importantly the 'thing' to interpret. The (common sense) intuition comes into the 'my way'. Do we really disagree ont that ? C. (universe:)the smallest independent piece that does include myself First I object to independent which would lead to a multiple existence of parallel natures (all of them singularities for the others) and we cannot gain information from them - which would connect in some ways. Existence as we can reasonably speak about it, is interconnected - nothing independent. I think we agree here. I gave indication of what I meant by dependence (and therefore by independence) as: space-time continuity, particle interaction and this kind of things and I feel that everything in the universe is interconnected in that way (this makes my definition of universe a tautology but it can be linked in some way to the common sense) even when considering causally isolated regions of space-time (because these would be connected in some future and they cannot be considered as isolated from that future). If you make concessions to that and accept 'relative' independence, then the smallest 'unit' including you is you. I don't think you want to go solipsistic. I don't believe I can isolate something like 'me'. If you expand further - well, I did not find a limit. I am not sure of that. If many universes do exist, they might well be considered independent of each other (because of lack of spatio-temporal continuity or particle interaction or the like). This is why I concocted a narrative about a 'plenitude' (undefined, not Plato's concept) FROM which distinct 'universes' occur (in timeless and countless fulgurations, callable BigBangs) with some INTERNAL history - in 'ours' including space and time. So I have a 'universe to talk about' - within my intuition G. And many more 'universes', obscured by ignorance (no info) - not excluded. I don't restrict 'them' to our logic, math, system, not even causality. This sounds very speculative (not to say mystical) to me. I like your metaphor of the dominos. It pertains to a view we may have in our (exclusively possible) reductionist ways about the world: THIS ONE is the cause of an event (one side of the domino) while the rest of the system (all of it) is also influencing - whether we consider it in our limited model (within our chosen boundaries) or not. I have two views of causality. In the first one, causality is a local and macroscopic (and mesoscopic) emergent property linked to the fact that the universe would be more ordered on one side that on the other. In the second, events continuously trigger other events. The second view seems to be some kind of idealisation of the first one that will always be no more than a convenient simplification/approximation. Considering that everything occurs or must occur according to the second view sounds like an error to me. This error tends to make the universe viewed as somthing evolving through time while it should be viewed as a static (intemporal) object within which (the flow of) time emerges from its structure as a local property. This is also why views in which universes continously fork as events occur in one way or the other does not make much sense for me. This list goes many times beyond the reductionist ways of thinking. I don't think that the first view is beyond the reductionist ways of thinking. Both views are compatible with a completely mathematic
Re: Is the universe computable?
Dear Jesse, A very good question, containing its own answer! You wrote: Why, out of all possible experiences compatible with my existence, do I only observe the ones that don't violate the assumption that the laws of physics work the same way in all places and at all times? Have you taken into account the idea that observers can communicate their finding to each other and that, maybe - just maybe - this plays into the wave function's behavior? David Deutsch has just posted a paper discussing a related subject (http://xxx.lanl.gov/abs/quant-ph/0401024). Let us take some time to read it and then pick this discussion back up. ;-) Kindest regards, Stephen - Original Message - From: Jesse Mazer [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Thursday, January 08, 2004 1:17 AM Subject: Re: Is the universe computable? Stephen Paul King wrote: Dear Jesse, Would it be sufficient to have some kind of finite or approximate measure even if it can not be taken to infinite limits (is degenerative?) in order to disallow for white rabbits? A very simple and very weak version of the anthropic principle works for me: Any observation by an observer must not contradict the existence of that observer. But there are plenty of observations that would not result in my destruction, like seeing a talking white rabbit run by me, anxiously checking its pocket watch. To pick a less fantastical example, it would also not be incompatible with my existence to observe a completely wrong distribution of photons hitting the screen in the double-slit experiment. Why, out of all possible experiences compatible with my existence, do I only observe the ones that don't violate the assumption that the laws of physics work the same way in all places and at all times? I disagree with David's claim that The universe doesn't depend on the rock for its existence... since the notion of quantum entanglement, even when considering decoherence, implies that the mere presense of a rock has contrapositive effects on the whole of the universe. The various discussions of null measurements by Penrose and others given a good elaboration on this. I think you're talking about a different issue than David was. You're talking about a rock that's a component of our physical universe, while I think David was responding to Chalmers' question about whether random thermal vibrations in a rock instantiate all possible computer simulations, including a complete simulation of the entire universe (complete with all the rocks inside it). To me the computational question boils down to the question of how does Nature solve NP-Hard (or even NP-Complete) problems, such as those involved with protein folding, in *what appears to be* polynomial time. What do you mean by the computational question? Are you addressing the same question I was, namely how to decide whether some computer simulation is instantiating a copy of some other program? If we imagine something like a detailed physical simulation of some computer circuits running program X, it seems intuitive that this simulation instantiates a copy of program X, but Chalmers' paper suggests we don't have a general rule for deciding whether one program is instantiating any other given program. And as I said, this is relevant to the question of measure, and a measure on observer-moments is probably key to solving the white rabbit problem. --Jesse _ Get reliable dial-up Internet access now with our limited-time introductory offer. http://join.msn.com/?page=dept/dialup
Re: Is the universe computable?
At 11:34 08/01/04 +0100, Georges Quenot wrote: I am very willing (maybe too much, that's part of the problem) to accept a Platonic existence for *the* integers. I am far from sure however that this does not involve a significant amount of faith. Indeed. It needs an infinite act of faith. But I have no problem with that ... There are some objections to it and I am not sure that none of them make sense. Also, as someone said (if anybody has the original reference, in am interested): the desire to believe is a reason to doubt. I think that, even if it is true, arithmetic realism needs to be postulated (or conjectured) since I can't figure how it could be established. All right. That's why I explicitly put the AR in the definition of computationalism. About your question is the universe computable? the problem depends on what you mean by universe. The definition you gave recently are based on some first person point of view, and even that answer does not makes things sufficiently less ambiguous to answer. Don't hesitate to try again. You can also read my thesis which bears on that subject (in french). You may be interested in learning that at least the *physical* universe cannot be computable once we postulate the comp hypothesis (that is mainly the thesis that I or You are computable; + Church thesis + AR). The reason is that with comp, as with Everett (and despite minor errors in Everett on that point), the traditional psycho-parallelism cannot be maintained. See my URL below for more. Why there is no FAQ? Because we are still discussing the meaning of a lot of terms I agree with you in your critics of Searle. I agree with most critics of Chalmers too, also. Welcome, Bruno http://iridia.ulb.ac.be/~marchal/
Re: Is the universe computable?
Possibly relevant to this thread: NYTimes: January 8, 2004 New-Found Old Galaxies Upsetting Astronomers' Long-Held Theories on the Big Bang By KENNETH CHANG ATLANTA, Jan. 7 Gazing deep into space and far into the past, astronomers have found that the early universe, a couple of billion years after the Big Bang, looks remarkably like the present-day universe. Astronomers said here on Monday at a meeting of the American Astronomical Society that they had found huge elliptical galaxies that formed within one billion to two billion years after the Big Bang, perhaps a couple of billion years earlier than expected. A few days earlier, researchers had announced that the Hubble Space Telescope had spotted a gathering cloud of perhaps 100 galaxies from the same epoch, an early appearance of such galactic clusters. On Wednesday, astronomers at the meeting said that three billion years after the Big Bang, one of the largest structures in the universe, a string of galaxies 300 million light-years long and 50 million light-years wide, had already formed. A light-year is the distance that light travels in one year, or almost six trillion miles. That means the string is nearly 2,000 billion billion miles long. Some astronomers said the discoveries could challenge a widely accepted picture of the evolution of the universe, that galaxies, clusters and the galactic strings formed in a bottom-up fashion, that the universe's small objects formed first and then clumped together into larger structures over time. The universe is growing up a little faster than we had thought, said Dr. Povilas Palunas of the University of Texas, one of the astronomers who found the string of galaxies. We're seeing a much larger structure than any of the models predict. So that's surprising. In the prevailing understanding of the universe, astronomers believe that slight clumpiness in the distribution of dark matter, the 90 percent of matter that pervades the universe but still has not been identified, drew in clumps of hydrogen gas that then collapsed into stars and galaxies, the first stars forming about a half billion years after the Big Bang. The galaxies then gathered in clusters, and the clusters gathered in long strings with humongous, almost empty, voids in between. The first such string, named the Great Wall, was discovered in 1989 about 250 million light-years away. The newly discovered string lies in a southern constellation, Grus, at 10.8 billion light-years away, and represents what the universe looked like 10.8 billion years ago, or three billion years after the Big Bang. The international team of researchers identified 37 very bright galaxies in that region of space and found that they were not randomly distributed, as would be expected, but instead appeared to line up along the string. Such structures are rarely seen in computer simulations of the early universe, said Dr. Bruce E. Woodgate of the NASA Goddard Space Flight Center, a member of the team. We think it disagrees with the theoretical predictions in that we see filaments and voids larger than predicted, Dr. Woodgate said. Dr. Robert P. Kirshner of the Harvard-Smithsonian Center for Astrophysics said the findings were interesting, but that it was too early to eliminate any theories. What is probably needed was a better understanding how of a clump of dark matter leads to the formation of stars. What we're seeing here, Dr. Kirshner said, is the beginning of the investigation how structure grows. At the astronomy meeting on Monday, another team of researchers reported finding a large number of large elliptical galaxies. As part of an investigation known as the Gemini Deep Deep Survey, the astronomers explored 300 faint galaxies dating from when the universe was three billion and six billion years old. The large elliptical galaxies are supposedly a merged product of smaller spiral galaxies. Yet not only did they exist that early in the universe, but the stars within these galaxies also appeared a couple of billion years old already, implying that they had formed as early as a billion and a half years after the Big Bang. Massive galaxies seem to be forming surprisingly early after the Big Bang, said Dr. Roberto Abraham of the University of Toronto and a co-principal investigator on the team. It is supposed to take time. It seems to be happening right away. The data actually fit better with the views that astronomers held before the rise of the current dark-matter models, when they theorized that the largest galaxies formed first. If we presented this to astronomers 25 years ago, Dr. Abraham said, they wouldn't have been surprised. A third team of astronomers found two clusters of galaxies that also point to a precocious universe. Using the Hubble telescope, the astronomers spotted a cluster of at least 30 galaxies dating from when the universe was younger than two billion years old and extending three million light-years across. Which is similar in size to what
Re: Is the universe computable?
Georges Quenot writes: I would be interested in reading the opinions of the participants about that point and about the sense that could be given to the question of what happens (in the simulated universe) in any non- synchronous simulation when the simulation diverges ? I'll make two points. First, you're right that there are other ways of computing a universe than simply starting with some initial conditions and evolving time forward step by step, computing the state of the universe at each subsequent instant. You list several ways this might happen and I agree that this concept makes sense. We might call this non-sequential or non-temporal simulation. But, given the specific temporal structures that exist in our universe, there are limitations to how this computation can be done. Specifically, we are able to construct physical computers in this universe which perform complex calculations. And among these calculations are those which are believed to be inherently sequential and lengthy, calculations for which the answer cannot be computed without spending a great deal of time from the initial values. Given that our universe contains systems like this, it constrains the amount of computation which must be done in any kind of non-sequential simulation. Specifically, the non-sequential simulation must do at least as much computation in order to produce our universe as the more traditional kind of sequential simulation. This demonstrates a limit on the power of non-sequential simulation. My second point is with regard to your specific question, what would happen if we tried to simulate a universe which diverged in some space-time region from the conventional physical laws? This is our often-discussed flying rabbit paradox (we have other names as well), where it seems that if all universes exist, we might as well be living in a universe which was lawful everywhere except in some small region, or up until a certain time, as in one where the laws are truly universal. Your question is whether this concept makes sense in a non-sequential simulation, or whether it assumes sequential simulation. I think it makes just as much sense in the context of non-sequential simulation. The non-sequential simulator is trying to find or create a universe which satisfies certain physical laws. It may be iteratively solving a differential equation or using some other non-temporal method, but that is its goal, its mechanism. The case at hand is simply a matter of defining the physical laws to be different in different regions of space-time. We could define the physical laws which the non-sequential simulator is trying to solve in some such terms. We'd say, observe these laws in this region, but these other laws in that region. For example, we might say to observe the true laws of our universe (whatever they turn out to be) up to simulated time T, and then to observe other laws after time T. Or similarly we could have one set of laws up to spatial coordiate X, and another set of laws on the other side of X. The non-sequential simulator would have no more difficulty in creating a universe which satisfied such non-uniform physical laws than in one where the laws were the same everywhere. So I'd say that the issue of sequential vs non-sequential simulation is irrelevant to the question of the existence of flying rabbit universes and does not shed light on the issue. Hal Finney
Re: Is the universe computable?
You asked what I meant: (- Original Message - From: Georges Quenot To: John M Cc: [EMAIL PROTECTED] Sent: Thursday, January 08, 2004 3:50 AM) ( John M wrote: [earlier excerpts from GQ's post]: A.the universe in which I live according to the current intuition I have of it and B: the possibility to simulate the universe at any level of accuracy. Snip, and later: Now if A is true, I wonder upon WHAT can you simulate?) [GQ remark]: I don't understand the question. [JM]: Your reply points to first person processes. If you consider (the) (your) universe, something according to YOUR current intuition what YOU have of it, then there is nothing else upon which you can simulate it. You definitely need something ELSE on which a simluation can be based. More than just your intuition-based universe. (I didn't say: 'outside reality'!). My (rethorical) question pointed to this dichotomy. It may be wrong, but probably understandable now. Further on : [GQ]: I don't believe I can isolate something like 'me'. Full agreement here. However: If you expand further - well, I did not find a limit. [GQ]: I am not sure of that. If many universes do exist, they might well be considered independent of each other (because of lack of spatio-temporal continuity or particle interaction or the like). [JM]: I don't restrict my views to spatio-temporal continuity, or to the 'particle-interaction' views of reductionistic human science. We MAY not know everything by today (ha ha). I leave open my 'scientific agnosticism' - the potential answer: I dunno. So you mat find a limit what I didn't. No argument here. To your remark on my narrative (watch the name I use): This sounds very speculative (not to say mystical) to me. Not more than the white or pink elephants/rabbits. Or some computation that takes infinite time and infinite virtual memory . Finally I like to use instead of triggers (in causality #2) 'facilitates' and must occur - may occur, leaving open changing circumstances to alter what we may postulate upon our closed model. With best regards John Mikes SNIP the rest
Re: Is the universe computable?
Georges Quenot wrote: [...] I would be interested in reading the opinions of the participants about that point and about the sense that could be given to the question of what happens (in the simulated universe) in any non- synchronous simulation when the simulation diverges ? Thanks for the replies. Until now I feel a bit confuse with them, possibly because I do not have an appropriate idea of what is meant exactly by computable and/or by what accounts for a simulation of the universe. I probably have some naive intuition about them. So maybe it would help to clarify some points: By computable, is by default assumed something like physically computable using current or future technologies or only formally computable (possibly considering virtual computers containing very much more memory locations than there are particles in the visible universe and for computation times very much longer than the actual age of the universe) ? In the latter case, does the memory of the computer need to be finite or can it be considered as unlimited ? Do the simulation has to end within a finite time or can the simulated universe be something like an asymptotic state of its description in a given formalism ? Alternatively or in other words, could the simulated universe be in some way the limit of a series of approximations computed with increasing available memories and computation times ? Is computable relative to the universe as a (spatio-temporal) whole or only to given supbarts of it ? Also I feel some confusion between the questions Is the universe computable ? and Is the universe actually 'being' computed ?. What links do the participants see between them ? Finally, what link is there between the computability of the universe and the possibility of its exact description in the context of arithmetic ? Maybe too many questions for a single post. I didn't go through the whole archive and there might well be already answers to most of these so I welcome any reference to appropriate previous posts. By the way, are there some FAQs about these questions ? Georges.
Re: Is the universe computable?
Dear George, to your series of questions I would like to add one as first: What do you call universe? as long as we do not make this identification, it is futile to speculate about its computability/computed sate. I see not too much value in assuming infinite memories and infinite time of computation, that may lead to a game of words, calling computation the object to be computed. Is 'Multiverse' part of your universe, or vice versa? Regards John Mikes - Original Message - From: Georges Quenot [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Wednesday, January 07, 2004 4:44 AM Subject: Re: Is the universe computable? Georges Quenot wrote: [...] I would be interested in reading the opinions of the participants about that point and about the sense that could be given to the question of what happens (in the simulated universe) in any non- synchronous simulation when the simulation diverges ? Thanks for the replies. Until now I feel a bit confuse with them, possibly because I do not have an appropriate idea of what is meant exactly by computable and/or by what accounts for a simulation of the universe. I probably have some naive intuition about them. So maybe it would help to clarify some points: By computable, is by default assumed something like physically computable using current or future technologies or only formally computable (possibly considering virtual computers containing very much more memory locations than there are particles in the visible universe and for computation times very much longer than the actual age of the universe) ? In the latter case, does the memory of the computer need to be finite or can it be considered as unlimited ? Do the simulation has to end within a finite time or can the simulated universe be something like an asymptotic state of its description in a given formalism ? Alternatively or in other words, could the simulated universe be in some way the limit of a series of approximations computed with increasing available memories and computation times ? Is computable relative to the universe as a (spatio-temporal) whole or only to given supbarts of it ? Also I feel some confusion between the questions Is the universe computable ? and Is the universe actually 'being' computed ?. What links do the participants see between them ? Finally, what link is there between the computability of the universe and the possibility of its exact description in the context of arithmetic ? Maybe too many questions for a single post. I didn't go through the whole archive and there might well be already answers to most of these so I welcome any reference to appropriate previous posts. By the way, are there some FAQs about these questions ? Georges.
Re: Is the universe computable?
John M wrote: Dear Georges, to your series of questions I would like to add one as first: What do you call universe? I would naively answer: the universe in which I live according to the current intuition I have of it. I am not sure this makes sense and I also understand that others may have different intuitions of it. Maybe a bit more formally I would refer to the smallest independent piece that does include myself (in case there is anything else and hoping that we can get a common intuition of that; dependence is relative to space-time continuity, particle interaction and this kind of things). as long as we do not make this identification, it is futile to speculate about its computability/computed sate. Maybe this is an opportunity to clarify the concept and to see up to which point it is shared among us. I am not sure we can easily go much farther than intuition we have of it and to isolate the possible differences we have. I see not too much value in assuming infinite memories and infinite time of computation, that may lead to a game of words, calling computation the object to be computed. Maybe I was just not clear enough. I was just thinking of the possibility to simulate the universe at any level of accuracy. However small but non zero the accuracy, there would exist a simulation of finite but possibly very large size and time that meets it. Infinite memory and running time would be necessary only to run an infinite sequence of simulations with an accuracy going asymtotically close to zero. Is 'Multiverse' part of your universe, or vice versa? I am not sure I understand the concept(s) of multiverse enough to make a reasonable answer to this question. For what I understand of it (them), it is (they are) not consistent with the view I have of causality (which is more related to the fact that the universe is more ordered on one side that on the other than to dominos pushing each other). Regards. Georges Quénot.
