Re: on formally describable universes and measures
Russell Standish wrote: Marchal wrote: Hi Juergen, I would like to nuance my last Post I send to you. First I see in other posts, written by you, that your computable real numbers are *limit* computable. It still seems to me possible to diagonalize against that, although it is probably less trivial. But I think it isn't really relevant in our present discussion, because the continuum I am talking about appears in the first person discourse of the machines, so it is better to keep discussing the main point, which is the relevance of the first person point of view, with comp, when we are searching for a TOE. It seems to me that the cardinality of UD*, or whether UD* is a continuum or not is rather irrelevant. My understanding is that the UD argument implies a first person indeterminancy, ie every first person experience will have access to a random oracle. All right. I guess you agree that such random oracle appears also with the iterative self-duplication, which is itself appearing in UD*. I think the argument goes something like this: 1) UD algorithms will have high measure in the space of all computations, much higher than a direct implementation of a conscious AI (assuming such things exist). Hopefully so. Intuitively so. Not so easy to prove. Note also that if you implement a conscious AI it will itself be embedded in UD*, from his own point of view, and it will have access also to some random oracle. 2) Therefore, it is more likely that a conscious AI will find itself imbedded in the output of a UD, with access to a random oracle That's what I was saying ! And that conscious AI will even find itself in the output of an immaterial UD in Plato heaven. (Of course my viewpoint is that consciousness _requires_ access to a random oracle, making conclusion 2 even stronger, but it is not necessary for the argument). Consciousness _requires_ access to a random oracle for having relatively stable histories. Perhaps through the phase randomisation of the white rabbits (cf my recent paper). Bruno
If I'm computable, then so is my universe.
In his IMO excellent message Algorithmic TOEs vs Nonalgorithmic TOEs, Schmidhuber states that things one cannot describe, do not exist. If I interpret correctly, Schmidhuber was aiming, in this context, at _entire_ universes one cannot describe. I agree with this, but propose to extend this reasoning to _aspects_ of universes one cannot describe: I define my universe as equal to all I know about my universe. Now suppose that I (me being my mind state at this moment in time) am computable. That means that all I know about my universe is computable too, because this knowledge is part of my mind state. Therefore, if I'm computable, then so is my universe. (Forgive me if this is stupid or old.) Michiel de Jong, http://www.cwi.nl/~mbj
Re: another anthropic reasoning paradox
Wei Dai wrote: The paradox is what happens if we run Alice and Bob's minds on different substrates, so that Bob's mind has a much higher measure than Alice's. I fail to understand the paradox. In the case where they are on the same substrate, they are more likely to push button 2. OK In the case where they run on different substrate, the decision is not any different: Bob's memory has been erased and his decision will still be to push button 2, independently of his measure. He will lose, but since he has no memory of his past, he can't even verify that he is Bob by running the same experiment 1000 times for example. Erasing their memory puts a big cabosh on the meaning of who they really are. I could argue that Bob is not really Bob and Alice is not really Alice. Their identity has been reduced to a *bare* I and they are actually identical In addition, I think the whole concept of measure is faulty. If you could measure your measure you would find the measurement always identical no matter where, when or who you are. I mentioned this in earlier posts as a kind of Cosmological principle. Substrates and measures are just red herrings. George
Re: another anthropic reasoning paradox
I don't see a paradox here. In the latter situations, the volunteers are acting in accordance with different information, ie that of their measures. If they were not aware of their measures, they would have to assume a 50/50 chance of being A or B, hence would choose button 1. Cheers Wei Dai wrote: Consider the following thought experiment. Two volunteers who don't know each other, Alice and Bob, are given temporary amnesia and placed in identical virtual environments. They are then both presented with three buttons and told the following: If you push 1, you will lose $9 If you push 2 and you are Alice, you will win $10 If you push 2 and you are Bob, you will lose $10 I'll assume that everyone agrees that both people will push button 2. The paradox is what happens if we run Alice and Bob's minds on different substrates, so that Bob's mind has a much higher measure than Alice's. If they apply anthropic reasoning they'll both think they're much more likely to be Bob than Alice, and push button 1. If you don't think this is paradoxical, suppose we repeat the choice but with the payoffs for button 2 reversed, so that Bob wins $10 instead of Alice, and we also swap the two minds so that Alice is running on the substrate that generates more measure instead of Bob. They'll again both push button 1. But notice that at the end both people would have been better off if they pushed button 2 in both rounds. Any anthropic reasoning proponents want to tackle this? Dr. Russell Standish Director High Performance Computing Support Unit, Phone 9385 6967 UNSW SYDNEY 2052 Fax 9385 6965 Australia[EMAIL PROTECTED] Room 2075, Red Centrehttp://parallel.hpc.unsw.edu.au/rks
Re: on formally describable universes and measures
The best you can achieve is an algorithm that outputs at least the computable infinite reals in the sense that it outputs their finite descriptions or programs. I am not sure I understand you here. Are you aware that the set of descriptions of computable reals is not closed for the diagonalisation procedure. That is: you cannot generate all (and only) descriptions of computable reals. The algorithm you are mentionning does not exist. You can only generate a superset of the set of all computable reals. That set (of description of all computable reals) is even constructively not *recursively enumerable* in the sense that, if you give me an algorithm generating the (description of) computable real, I can transform it for building a computable real not being generated by your algorithm. I guess you know that. That is why most formal constructivists consider their set of constructive reals as subset of the Turing computable reals. For exemple you can choose the set of reals which are provably computable in some formal system (like the system F by Girard, in which you can formalize ..., well Hilbert space and probably the whole of the *constructive* part of Tegmark mathematical ontology! That is very nice and big but not enough big for my purpose which has some necessarily non constructive feature. About natural numbers and machines I am a classical platonist. About real numbers I have no definite opinion. The describable reals are those computable in the limit by finite GTM programs. There is a program that eventually outputs all finite programs for a given GTM, by listing all possible program prefixes. Sure, in general one cannot decide whether a given prefix in the current list indeed is a complete program, or whether a given prefix will still grow longer by requesting additional input bits, or whether it will even grow forever, or whether it will really compute a real in the limit, or whether it won't because some of its output bits will flip back and forth forever: http://rapa.idsia.ch/~juergen/toesv2/node9.html But what do such undecidability results really mean? Are they relevant in any way? They do not imply that I cannot write down finite descriptions of the describable reals - they just mean that in general I cannot know at a given time which of the current list elements are indeed complete descriptions of some real, and which are not. Still, after finite time my list of symbol sequences will contain a complete description of any given computable real. Thus undecidable properties do not necessarily make things nonconstructive. Can you imagine yourself as a Platonist for a while, if only for the sake of the reasoning? I am not even sure what exactly a Platonist is. Do I need any additional preliminaries to realize why I genuinely fail to understand your invariance lemma? Sure. The delays question for exemple. Let us follow Jesse Mazer idea of torture. Suppose I duplicate you and reconstitute you, not in Washington and Moscow but in some Paradise and some Hell. Would you feel more comfortable if I tell you I will reconstitute you in paradise tomorow and in hell only in 3001 after C. ? Is that what you would choose? Choose? Do I have a choice? Which is my choice? Computationalism is more a human right than a doctrinal truth. I skipped this statement and related ones... Juergen
