Re: Penrose and algorithms
Le 06-juil.-07, à 14:53, LauLuna a écrit : But again, for any set of such 'physiological' axioms there is a corresponding equivalent set of 'conceptual' axioms. There is all the same a logical impossibility for us to know the second set is sound. No consistent (and strong enough) system S can prove the soundness of any system S' equivalent to S: otherwise S' would prove its own soundness and would be inconsistent. And this is just what is odd. It is odd indeed. But it is. I'd say this is rather Lucas's argument. Penrose's is like this: 1. Mathematicians are not using a knowably sound algorithm to do math. 2. If they were using any algorithm whatsoever, they would be using a knowably sound one. 3. Ergo, they are not using any algorithm at all. Do you agree that from what you say above, 2. is already invalidate? Bruno http://iridia.ulb.ac.be/~marchal/ --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Penrose and algorithms
Le 06-juil.-07, à 19:43, Brent Meeker a écrit : Bruno Marchal wrote: ... Now all (sufficiently rich) theories/machine can prove their own Godel's theorem. PA can prove that if PA is consistent then PA cannot prove its consitency. A somehow weak (compared to ZF) theory like PA can even prove the corresponding theorem for the richer ZF: PA can prove that if ZF is consistent then ZF can prove its own consistency. Of course you meant ..then ZF cannot prove its own consistency. Yes. (Sorry). So, in general a machine can find its own godelian sentences, and can even infer their truth in some abductive way from very minimal inference inductive abilities, or from assumptions. No sound (or just consistent) machine can ever prove its own godelian sentences, in particular no machine can prove its own consistency, but then machine can bet on them or know them serendipitously). This is comparable with consciousness. Indeed it is easy to manufacture thought experiements illustrating that no conscious being can prove it is conscious, except that consciousness is more truth related, so that machine cannot even define their own consciousness (by Tarski undefinability of truth theorem). But this is within an axiomatic system - whose reliability already depends on knowing the truth of the axioms. ISTM that concepts of consciousness, knowledge, and truth that are relative to formal axiomatic systems are already to weak to provide fundamental explanations. With UDA (Universal Dovetailer Argument) I ask you to implicate yourself in a thought experiment. Obviously I bet, hope, pray, that you will reason reasonably and soundly. With the AUDA (the Arithmetical version of UDA, or Plotinus now) I ask the Universal Machine to implicate herself in a formal reasoning. As a mathematician, I limit myself to sound (and thus self-referentially correct) machine, for the same reason I pray you are sound. Such a restriction is provably non constructive: there is no algorithm to decide if a machine is sound or not ... But note that the comp assumption and even just the coherence of Church thesis relies on non constructive assumptions at the start. Bruno http://iridia.ulb.ac.be/~marchal/ --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Asifism revisited.
Le 05-juil.-07, à 14:19, Torgny Tholerus wrote: David Nyman skrev: You have however drawn our attention to something very interesting and important IMO. This concerns the necessary entailment of 'existence'. 1. The relation 1+1=2 is always true. It is true in all universes. Even if a universe does not contain any humans or any observers. The truth of 1+1=2 is independent of all observers. I agree with you (despite a notion as universe is not primitive in my opinion, unless you mean it a bit like the logician's notion of model perhaps). As David said, this is arithmetical realism. 2. If you have a set of rules and an initial condition, then there exist a universe with this set of rules and this initial condition. Because it is possible to compute a new situation from a situation, and from this new situation it is possible to compute another new situation, and this can be done for ever. This unlimited set of situations will be a universe that exists independent of all humans and all observers. Noone needs to make these computations, the results of the computations will exist anyhow. OK, but I would mention bifurcating computations (with respect to Oracle or just Universal machine ...) 3. All mathmatically possible universes exists, and they all exist in the same way. Our universe is one of those possible universes. Our universe exists independant of any humans or any observers. I can agree or disagree with the first sentence. It is too fuzzy. I disagree with the second sentence. I have argued that the comp assumption you should say our universes (note the s), and strictly speaking all (accessible) universes are ours. Of course universes, or better (imo) computational histories (up to some equivalence) exists independent of observers, like the fact that machine A on argument B stops or does not stops independently of me. 4. For us humans are the universes that contain observers more interesting. Oh! Surely the discovery of a baby tiny universe would be interesting, even without observers (like the moon is not so bad ...) But there is no qualitaive difference between universes with observers and universes without observers. They all exist in the same way. It really depends what you mean by universe. This cannot be an obvious notion in the comp setting. Have you read the UDA up to step 7 (at least) ? The GoL-universes (every initial condition will span a separate universe) exist in the same way as our universe. But because we are humans, we are more intrested in universes with observers, and we are specially interested in our own universe. Again what do you mean by our own universe? Are you meaning Deutsch Multiverse or the comp-many computations seen from inside ? I think that apparent universes emerge from personal gluing of histories. But otherwise there is noting special with our universe. There is nothing special about our historical geographies I would say. Bruno http://iridia.ulb.ac.be/~marchal/ --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Penrose and algorithms
On Jul 7, 12:59 pm, Bruno Marchal [EMAIL PROTECTED] wrote: Le 06-juil.-07, à 14:53, LauLuna a écrit : But again, for any set of such 'physiological' axioms there is a corresponding equivalent set of 'conceptual' axioms. There is all the same a logical impossibility for us to know the second set is sound. No consistent (and strong enough) system S can prove the soundness of any system S' equivalent to S: otherwise S' would prove its own soundness and would be inconsistent. And this is just what is odd. It is odd indeed. But it is. No, it is not necessary so; the alternative is that such algorithm does not exist. I will endorse the existence of that algorithm only when I find reason enough to do it. I haven't yet, and the oddities its existence implies count, obviously, against its existence. I'd say this is rather Lucas's argument. Penrose's is like this: 1. Mathematicians are not using a knowably sound algorithm to do math. 2. If they were using any algorithm whatsoever, they would be using a knowably sound one. 3. Ergo, they are not using any algorithm at all. Do you agree that from what you say above, 2. is already invalidate? Not at all. I still find it far likelier that if there is a sound algorithm ALG and an equivalent formal system S whose soundness we can know, then there is no logical impossibility for our knowing the soundness of ALG. What I find inconclusive in Penrose's argument is that he refers not just to actual numan intellectual behavior but to some idealized (forever sound and consistent) human intelligence. I think the existence of a such an ability has to be argued. If someone asked me: 'do you agree that Penrose's argument does not prove there are certain human behaviors which computers can't reproduce?', I'd answered: 'yes, I agree it doesn't'. But if someone asked me: 'do you agree that Penrose's argument does not prove human intelligence cannot be simulated by computers?' I'd reply: 'as far as that abstract intelligence you speak of exists at all as a real faculty, I'd say it is far more probable that computers cannot reproduce it'. I.e. some versions of computationalism assume, exactly like Penrose, the existence of that abstract human intelligence; I would say those formulations of computationalism are nearly refuted by Penrose. I hope I've made my point clear. Best --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Boltzmann brains
I have never been able to understand how a singularity can be highly ordered. Is there any room for order in such a tiny thing? Best On May 31, 1:51 pm, Russell Standish [EMAIL PROTECTED] wrote: I came across a reference to Boltzmann brains in a recent issue of New Scientist. The piece, quoted in full is: Spikes in space-time There is another way to think about why our universe began in a highly ordered or low entropy state. In 2002, a group of physicists led by Leonard Susskind at Stanford University in California proposed that entities capable of observing the universe could arise via random thermal fluctuations, as opposed to the big bang, galaxy formation and evolution. This idea has been explored by others, including Don Page at the University of Alberta in Edmonton, Canada. Some researchers argue that under certain conditions, self-aware entities in the form of disembodied spikes in space-time - Boltzmann brains - are more likely to emerge than complex life forms. Because they depend on fluctuations of particles, Boltzmann brains would be more common in regions of high entropy than low entropy. If the universe had started out in a state of high entropy, it would be more likely to be populated by Boltzmann brains than life forms like us, which suggests that the entropy of our early universe had to be low. As a low-entropy initial state is unlikely, though, this also implies that there are a huge number of other universes out there that are unsuitable for us. It seemed to me that a Boltzmann brain was none other than one of our white rabbits, or at least very closely related. Any thoughts? -- - A/Prof Russell Standish Phone 0425 253119 (mobile) Mathematics UNSW SYDNEY 2052 [EMAIL PROTECTED] Australiahttp://www.hpcoders.com.au - --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
Re: Asifism revisited.
On 05/07/07, Torgny Tholerus [EMAIL PROTECTED] wrote: For us humans are the universes that contain observers more interesting. But there is no qualitaive difference between universes with observers and universes without observers. They all exist in the same way. I still disagree, but I have a slightly different formulation of my previous replies which might be more consistent with my remarks to Bruno re the 1-personal discrimination of self-relation as 'action' or 'behaviour'. Essentially, if we conceive of the plenitude of all possible universes as existing 'statically', then the recovery of 'dynamic' or temporal existence must be seen as characteristic of 1-personal self-relation: that is, 1-persons are active participants, not merely 'observers'. What I said to Bruno was that my justification was simply that such a brute claim seems to be required if dynamism is to be recovered at all from stasis. I'm less sure however that such a claim is strictly 'necessary' in the logical sense. Given this, I suppose it is possible to conceive of a B-Universe in which this brute claim is not granted. IOW no aspect of the self-relation of the B-Universe is characteristically dynamic or 1-personal. Such a universe would be static in all aspects - 'inside' and 'outside' - and consequently it would contain no active participants and consequently none of the stuff characteristic of such participative behaviour. However, such a static universe could not, by the same token, be claimed to be exactly the same as the A-Universe, precisely because nothing whatsoever could be said to 'happen' to any object it instantiates. The points I made earlier about the mutual inaccessibility of A and B-Universes still stand. Consequently we can't 'interview' B-Universe objects. In some sense 'interviews' between B-Universe structures could be said to exist, but not to 'occur'. The content of the statements of B-Universe objects about their internal states would be similarly 'justified' in terms of static self-relation as those in the A-Universe, but it wouldn't indeed be 'like anything to be' a B-Universe object. What is really interesting about this is it suggests that the notion of consciousness as equating to 'what it's like to be' something is incoherent. Rather, consciousness seems more 'what it's like to enact' something. Consequently, the 'absolute' quality of consciousness is just what its like for the One (per Plotinus) to enact particular kinds of self-relation. And such quality indeed seems 'absolute' as opposed to 'relative', because it doesn't seem logically necessary for such enaction to emerge 1-personally from static self-relation. It's just that our own case demonstrates its 'absolute' contingency in the A-Universe. So zombies may be possible, but not in the A-Universe, and consequently we needn't fear ever being fooled by one in any accessible encounter. What this amounts to is understanding 'consciousness' essentially as the recovery of dynamism from stasis, or active participation from instantiation, or time from eternity, or the A-series from the B-series. It's also treating 'dynamism' as 'experientiaI' rather than 'physical', which of course is moot. But I've never seen any really satisfactory direct treatment of dynamism with respect to static formulations of existence except as a brute assertion, or mere implication, of its being characteristic of 1-personal self-relation to appropriate structure. Perhaps Bruno could comment whether this way of looking at things is consistent with comp? For example, it might seem that 'dovetailing' carries some implication of dynamism, or at least sequentiality, with it from the outset. Alternatively, if a static background is not granted, then in such a view dynamism is already at the heart of self-relation, and with it, the necessary return of 1-personal participation. However, a fundamentally 'tensed' view of reality presents its own (particularly structural) problems, which are kettle of fish for a different discussion. David David Nyman skrev: You have however drawn our attention to something very interesting and important IMO. This concerns the necessary entailment of 'existence'. 1. The relation 1+1=2 is always true. It is true in all universes. Even if a universe does not contain any humans or any observers. The truth of 1+1=2 is independent of all observers. 2. If you have a set of rules and an initial condition, then there exist a universe with this set of rules and this initial condition. Because it is possible to compute a new situation from a situation, and from this new situation it is possible to compute another new situation, and this can be done for ever. This unlimited set of situations will be a universe that exists independent of all humans and all observers. Noone needs to make these computations, the results of the computations will exist anyhow. 3. All mathmatically possible universes exists, and
Re: Boltzmann brains
On Sat, Jul 07, 2007 at 07:56:57AM -0700, LauLuna wrote: I have never been able to understand how a singularity can be highly ordered. Is there any room for order in such a tiny thing? Best Highly ordered means small entropy. All you need is a small number of states, so small things naturally have small entropy, and large things naturally have high entropy. What's unnatural are large things with low entropy. Cheers -- A/Prof Russell Standish Phone 0425 253119 (mobile) Mathematics UNSW SYDNEY 2052 [EMAIL PROTECTED] Australiahttp://www.hpcoders.com.au --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
