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: A paper
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
Re: Constraints on everything existing
My comments at the bottom too. Jean-Michel At 08:51 AM 1/22/2003 -0800, Eric Hawthorne wrote: My comment at the bottom of the message. Eric Jean-Michel Veuillen wrote: Eric Hawthorne wrote: Unless a world (i.e. a sequence of information state changes) has produced intelligent observers though, there will be no one around in it to argue whether it exists or not. Then our universe did not exist before there were intelligent observers in it, which is not true. I think that is better to say that all self-consistent mathematical structures exist. To restrict existence to universes containing SASs (self-aware structures) is not only is very cumbersome but leads to contradictions. Perhaps we're just quibbling about terminology. My argument for a narrower definition of exists would be that if everything (or even just everything self consistent) exists, then perhaps existence in that sense is not that interesting a concept. So I posit that a better definition of exists or classically exists is: self-consistent, and metric and organized to the degree to be observable Notice that this does not require is observed. It requires would be observable if observers happened to be around. So our Earth 3 billion years ago was still observable in this sense, even though we weren't there yet. So, in otherwords, I define exists as that which is an aspect of a structure which is of the form/behaviour as to be, in principle, observable. I think we will be able to define a set of properties (stronger than just self-consitency) that will define in principle, observable. -- difficult exercise. All other self-consistent mathematical structures are, to me, just potentially or partially existent, because there is something wrong with their properties that would make them, in principle, unobservable. Vague statement building up this intuition: The operative question is whether a mathematical structure can only be abstract (without observable instantiation) or whether it can also be tract. I would argue that these other less-than-existent self-consistent mathematical structures may be part of quantum potentiality but can never be part of an existent world that exhibits classical physical properties. Eric I agree that in principle, observable is difficult to define. If, instead of looking at the Earth 3 billion years ago, you looked at our universe 1 second after the Big Bang, would you say that it was in principle, observable ? Even if you managed to show that the answer should be Yes, you would then have to show that for another universe whose parameters would differ by only the slightest amounts, the answer should be No. One of these universes would exist one second after the Big Bang, not the other one, which would be very much against intuition. And if you answer No, you have to cope with the fact the answer is now Yes, so you would have our universe which did not exist one second after the Big Bang and which exists now. Here is what I would propose: Following David Lewis and Modal Realism (http://users.ox.ac.uk/~worc0337/modal.realism.html) all possible worlds exist. Max Tegmark proposes in http://www.hep.upenn.edu/~max/toe.pdf that only worlds which have mathematical existence exists. This gives the self-consistent constraint. I agree with that. Tegmark then goes on and gives an operational definition of existence which requires SAS's. I think that this unfortunate: If we were the only SAS's in this universe and blew up the Earth, our universe would not cease to exist. If we agreed that it did and if SAS's appeared somewhere else later, would they say that they universe did not exist, then existed when it was inhabited by us, then did not exist and then existed again ? I find it absurd to make the existence of an universe depend on the fact that it contains SAS's or not. I simply propose that we say that some universes contain SAS's and some do not, without any consequence on the existence of these universes. Jürgen Schmidhuber proposes that possible universe means computable universe (without any reference to SAS's). See: http://www.idsia.ch/~juergen/everything/html.html http://www.idsia.ch/~juergen/everything/node1.html Again, I think it is simpler to say that some possible universes are computable, and that some are not, and that what Schmidhuber says in his article applies to computable universes only. Jean-Michel
Re: Constraints on everything existing
At 08:40 PM 1/17/2003 -0800, Eric Hawthorne wrote: John M wrote: Eric: do I detect in your 'circumstances' some 'anthropocentric/metric/logic' restrictions? is the multiverse exclusively built according to the system we devised on this planet as 'our physical laws'? (your 'factor' #1, although you oincluded in factor #2 the (CLASSICAL existence) modifier.) Brings to mind Mr Square's opponents in Abbott's Flatland, with the 2-D vs 3-D joke. It may seem that way (anthropocentric) but when I say intelligent observer I mean any kind of intelligent observer or couched in some more terminology any emergent system or pattern that functions as an intelligent observer. So no, I'm not talking about a human-centric anthropic principle, I'm talking about an arbitrary intelligent observer, generically defined. As you would expect, I would guess that there are some pretty tight constraints on how an intelligent observer would have to function to be considered such, but human is definitely too narrow a definition of it. I see intelligent observer production as being a threshold level of organization achieved by certain constraint regimes on all sequences of state changes. Of course, as a thought experiment, you could set a lower threshold criterion for fully existing worlds, such as the ability to be organized enough to produce some interesting (non-trivial) stable emergent systems that seem to exhibit some higher-level functions including self-preserving functions. Unless a world (i.e. a sequence of information state changes) has produced intelligent observers though, there will be no one around in it to argue whether it exists or not. Then our universe did not exist before there were intelligent observers in it, which is not true. I think that is better to say that all self-consistent mathematical structures exist. To restrict existence to universes containing SASs (self-aware structures) is not only is very cumbersome but leads to contradictions. On another subject, I read on the list that different universes cannot communicate. I see at least one possibility for communication: One scientist in our universe implements a computer simulation of an universe containing SASs. The scientist could then communicate with them. There is also of course the possibility that we ourselves live in a computer simulation Which brings us around to the conclusion that after all, the question of classical existence or not of some world is only ever a concern of intelligent observers. It is not really a concern for the non-thinking aspects of worlds or potential worlds, precisely because those parts are content to just be, or maybe be, as the case may be. Those parts are just the potential for information. Only when something comes along that cares to conceptualize about the various possibilities borne of different states of information, does there arise a question of existence, and then, it is a question of existence from the perspective of those that can observe and care about such things.
