Re: Infinite computing
I was wondering, if it's true that Hawking radiation always causes a black hole to evaporate after some finite time, wouldn't that mean that any observer travelling into one will see it evaporate before he crosses the event horizon? Is it possible that quantum gravity could do away with the notion of seeing the entire infinite history of the universe by travelling into a black hole? Jesse Mazer _ MSN 8 helps eliminate e-mail viruses. Get 2 months FREE*. http://join.msn.com/?page=features/virus
Re: Infinite computing: A paper
At 03:21 PM 2/10/2003 -0500, Stephen Paul King wrote: Dear Jean-Michel and Hal, All good humor aside, Hal makes a good point! The conditions that would exist as one approaches the event horizon seem to be such that any signal would be randomized such that the end result would be that Nature prevents infinite information (or conclusions requiring infinite computational power) from reaching any finite part of itself. Interestingly this seems to be the same situation as what forms an event horizon (around a space-time singularity) in the first place. Could it be that this is an active example of the so-called anthropic principle? It also reminds me of a solution to the Quantum Suicide problem! Kindest regards, Stephen Thank you to all of you for your ideas. Let us say that my suggestion was merely provocative. It seems to be that hypercomputers are logically possible, but that it is still speculative whether they are physically possible or not. This is Toby Ord's view in http://arxiv.org/pdf/math.LO/0209332. I find his survey very good. In particular, it contains a reference to Does General relativity Allow an Observer to View an Eternity in a Finite Time ? by Mark L. Hogarth, and to Non-Turing computations via Malament-Hogarth space-times, by Etesi and Németi, http://www.math-inst.hu/pub/algebraic-logic/turing.ps, which will be of interest to many, and especially to Jesse Mazer, as it discusses his question. All the best. Jean-Michel - Original Message - From: Hal Finney [EMAIL PROTECTED] To: [EMAIL PROTECTED]; [EMAIL PROTECTED] Sent: Monday, February 10, 2003 12:19 PM Jean-Michel Veuillen writes: There are other possibilities to obtain hypercomputers or Infinite Time Turing Machines: For instance, from general relativity: put a computer in orbit around a black hole, start an infinite computation on it, arrange that the results are sent to you by radio, and jump into the black hole: when you reach the horizon, you get the result of the infinite computation (and witness the end of the rest of the universe). For a survey: arxiv.org/pdf/math.LO/0209332 ...and burn to death as infinite amounts of radiation fall on you in a finite time? Maybe the universe is like a character from a spy novel: it could tell us what it knows (solving the halting problem, etc.), but then it has to kill us. Hal F.
Re: Infinite computing
Dear George, As I read your post I was struck by the necessary assumptions that you noted: 1) that the black hole is large enough that the tidal forces do not rip apart the observer falling into it2) death occurs in one branch of the multiverse but not in another. What if we considered the case where we used the size (mass) of the black as a parameter to evaluate the communicability of our hypothetical infinite computer? What would be the analogue in the multiverse? I have been re-reading my copy of Bohm and Hiley's The Undivided Universe and in particular the discussion of Gell_Mann and Hartle's consistent histories interpretation and comparison with MWI. It occurs to me that the size of the black hole (a function of its mass) and the differences between a pair of branches of the multiverse (a function of the non-commutability of their associated operators?) both seem to be 3-person notions (borrowing Bruno Marchal's term) while the idea of infinite computing that we are discussing seems to be a 1-person notion. The relation that Hawking et al have written about between a black hole's mass and its entropy seem to be 3-person notions and we seem to be in need of a 1-person analogue. Could it be that the notion of decoherence could be this 1-person analogue? I will be reading the papers that Jean-Michel referenced and dreaming up a thought experiment. Do you have any ideas at this time? Kindest regards, Stephen - Original Message - From: George Levy To: [EMAIL PROTECTED] Sent: Tuesday, February 11, 2003 1:23 AM Subject: Re: Infinite computing Stephen,Amazingly, I had kind-of the same thought. From the point of view of information flow, there seems to be an analogy between 1) falling down into a black hole and 2) "dying." Both events results in the cessation of information flow between two observers. In both cases one of the observers appears to "die"from a third person point of view, but stays alive from a first person point of view. In the first case the cessation of information flow is due to a relativistic effect. In the second case, the continuing of the information flow is due to a quantum effect. The following must be assumed: 1) that the black hole is large enough that the tidal forces do not rip apart the observer falling into it2) death occurs in one branch of the multiverse but not in another.There is definitely a relationship between entropy and black holes as Hawkings has shown and there is a relationship between entropy and information. This topic is ripe for a nice thought experiment.GeorgeStephen Paul King wrote: Dear Jean-Michel and Hal, All good humor aside, Hal makes a good point! The conditions that would exist as one approaches the event horizon seem to be such that any signal would be randomized such that the end result would be that Nature prevents infinite information (or conclusions requiring infinite computational power) from reaching any finite part of itself. Interestingly this seems to be the same situation as what forms an event horizon (around a space-time singularity) in the first place. Could it be that this is an active example of the so-called anthropic principle? It also reminds me of a solution to the Quantum Suicide problem! Kindest regards, Stephen SNIP
Infinite computing;self-organization
Here is a line of reasoning that is a frontal assault on extant (inadequate) AI paradigms conjoined with the question of 'self-organization' AND shining a light of awareness on -the important- Turing/computation question that .. comes AFTER .. the Halting Problem: Self-organization .. which themata includes inside-to-out emergent productivity .. AND COVALENTLY .. sensitive adaptability to/with any/all external effective information and energy .. is one on one isomorphic with the one important behavior that comes after any resolution of a 'halting problem' - and therefore supercedes it: Can a (computational) system which 'halts' [for any reason whatsoever] .. restart or re-initiate itself? Even if to deal with or process an entirely different question or computation. There is no self-organization if there is an absense of capacity to function sans external inputs. The Halting Problem is a minor issue compared with ReActivation Capacity?. But interestingly, because the question of ReActivation Capacity subsumes a greater scope of event space (information) than any given instantiation of the Halting Problem, there are more informational resources that can be brought to bear on 'the question', so essentially, the ReActivation Capacity issue is easier to answer - in the general, if not in the particular. Another way of juxtaposing the above questions is to bring in the relationship: relevance (opportunistic pertinence). If a computation would take longer than the age of the universe .. why would it/anyone bother instantiating the computation? It wouldn't just be a waste of energy, it would be an abuse of it. And any self-relevant system worth its own respect wouldn't engage in the effort. Self-organization - as a global themata - has to include additionally any and all co-habitation of any possible emergents coming out of self-organizing events (at and among any and all tiers of activities). And such products must be prior, current and forward, relatable .. in order for 'self-organization' to be a wholly self-consistent phenomenon. Therefore, Halting may or may not occur in given local event spaces, but, Activation/ReActivation -will- occur as long as relation and relational relevance is an a priori priority to 'existence'. Jamie Rose Ceptual Institute Feb 10, 2003
