Re: Predictions duplications
Hal Finney wrote: Isn't this fixed by saying that the uniform measure is not over all universe histories, as you have it above, but over all programs that generate universes? Now we have the advantage that short programs generate more regular universes than long ones, and the WAP grows teeth. I agree with Juergen on this: there is no uniform measure over all programs (nor on all integers). But in anycase you know I argue, unlike Juergen, that the measure should be put on all (relative) consistent computational extensions appearing in UD*. This gives indeed a sort of Weak Turing-tropic Principle. In which relative *speed* is a by product, not a prior. Bruno
Re: ODP: Free will/consciousness/ineffability
rwas wrote: --- Marchal [EMAIL PROTECTED] wrote: Brent Meeker wrote: On 10-Oct-01, Marchal wrote: You talk like if you have a proof of the existence of matter. Like if it was obvious subtancia are consistent. But you know substancia only appears in Aristote mind when he misunderstood Plato doctrine on intelligible . . . You mean as is everything is material. ? Be careful. I certainly does not believe everything is computational. Quite the contrary, IF I am the result of a computation then I can expect to be confronted with many non computational things. Perhaps you were meaning everything is immaterial? That's is indeed a consequence of the computational hypothesis. Rwas wrote I am confused with this. Not to be combative but how can one know they are not in a simulator, ie., arcade game or virtual reality? Good question! In fact you are superposed in multiple environments some of them could be simulators, others very large and complex Hollywood type sets and so on. Your environment is subject to the indeterminacy principle just like anything else you may want to know. One way to find out in which environment you actually are is to make a measurement. Depending on which interpretation you prefer, your measurement collapses the wave function of your environment (Copenhagen school) or selects you and your environment from the multiverse (MWI). An interesting question that we have been discussing in many forms is what is the meaning of consciousness when you are in a superposition. Is a superposition of conscious states one single consciousness or many? Does it make sense to claim that there could be many consciousnesses when these consciousnesses themselves cannot distinguish themselves from each other? I believe not. This brings us to the perception of consciousness which I believe to be a relativistic issue. Perception of conscious self and perception of conscious others can vary in kind depending on who does the observing. Free will is also relativistic. A consciousness gives the impression of having free will if its behavior is unpredicatble (ineffable - unprovable) BY THE OBSERVER. The self gives the impression to the OBSERVING SELF of having free will because the self cannot predict what its own behavior will be. And when a measurement is performed and a branching occurs, does it make sense to say that there occur an sudden increase in the measure of the consciousness involved in this process. I do not believe so. There is a diversification of consciousness but no increase in measure. George
Re: ODP: Free will/consciousness/ineffability
Zbigniew Motyka wrote: [...] http://iridia.ulb.ac.be/~marchal It would be not polite from my side to express any opinion about UDA before I really make acquaintance with it. Thanks. I whish everyone were like you :-) For now I may only repeat: When you start from some suitable axiomatic positions, you may prove almost everything using all rules of logic. I am afraid that UDA may start from such positions from very beginning. I could aknowledge it. Most who understand the UDA just throw out comp. I just show COMP entails sort of weirdness (experimentaly verifiable) A case is made that quantum weirdness is part of comp weirdness. By comp I mean really three things: 1) There is a level of description of myself such that I can survive through a digital emulation of myself at that level. 2) Church (Kleene, Post, Turing, Markov) Thesis. 3) Arithmetical Platonism (proposition like 17 is prime of FERMAT are true independently of my or ours knowledge of them). I don't postulate there is a universe, still less a computable universe. I just don't know, but I don't need it. It could happen that a maximal universal covering for dense subset of computational histories can be eventually be isolated, it would then define a natural unique multiverse, but at first sight the arithmetical translation is not going in that direction. But then it is not yet clear (imo) that the MWI makes possible classical realism too ... But... I promised, I see. Though, my opinion should not be anything binding for you, of course. Obviously, I would be more interested if you found a serious failure :) I am just rank physicist and maybe too aventurous for this rank. The UDA needs only some imagination and passive knowledge of computer science. The translation of the UDA in arithmetic, and its use for extracting the logic of the measure 1 out of the (arithmetical) geometry of the consistent computational extensions, need familiarity with both logic and physics. (It's technical). Bruno
Re: ODP: Free will/consciousness/ineffability
Brent Meeker wrote: On 10-Oct-01, Marchal wrote: You talk like if you have a proof of the existence of matter. Like if it was obvious subtancia are consistent. But you know substancia only appears in Aristote mind when he misunderstood Plato doctrine on intelligible ideas. (My opinion!). Despite the formidable success of physics, the main problems are not solved: neither qualitative appearance, nor (the new problem which appears through the comp hypothesis), the problem of the qualitative *appearance* of matter and quantities. I don't see this as an either-or question. But it was a neither-nor affirmation. I'm just saying that with comp you need to explain *both* mind and matter. With (naive) materialism you need to explain only mind, for matter is taken as granted (more or less at some level). That everything is computational is an hypothesis and is everything is material. You mean as is everything is material. ? Be careful. I certainly does not believe everything is computational. Quite the contrary, IF I am the result of a computation then I can expect to be confronted with many non computational things. Perhaps you were meaning everything is immaterial? That's is indeed a consequence of the computational hypothesis. We should pursue every hypothesis as far as we can and see what we get. Right. David Deutsch insists on that idea too. Note that we choose the hypotheses which seduces us in a way or another ... Some will be proven wrong - Newtonian mechanics. Some will be found vacuous - God did it. But the rest we should pursue. Some may work out and they may even prove to be all different versions of the same thing. OK. Bruno
Re: Predictions duplications
Hal - that is not a uniform measure! [EMAIL PROTECTED] wrote: Juergen Schmidhuber writes: But there is no uniform prior over all programs! Just like there is no uniform prior over the integers. To see this, just try to write one down. I think there is. Given a program of length l, the prior probability is 2^(-l). (That is 2 to the power of negative l.) The length of a program is defined by interpreting it using self-delimiting rules as is customary in the AIT analysis of Greg Chaitin. Hal Finney Dr. 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: Predictions duplications
Hal Finney wrote: Juergen Schmidhuber writes: But there is no uniform prior over all programs! Just like there is no uniform prior over the integers. To see this, just try to write one down. I think there is. Given a program of length l, the prior probability is 2^(-l). (That is 2 to the power of negative l.) The length of a program is defined by interpreting it using self-delimiting rules as is customary in the AIT analysis of Greg Chaitin. This doesn't seem to be very uniform to me. Maybe you mean that with the above prior the probability for a bit, drawn randomly from the set of all programs, to be 1 is 1/2 ? Saibal Saibal
Re: Random, was Predictions duplications
According to whim or taste implies a conscious entity performing choices according to a free will. This need not be the case. In my mind, random means selected without cause (or without procedure/algorithm). Russell picked my example from a language which has no equivalent to the word random . Besides: I deny free will, except for the Creator Almighty when the world was drawn up. G Since then all free will is subject to I/O circumstances, prior art, experience, whatever (un?)conscious consideration one may include. A lot has been written on randomness, and its problematic nature. I don't for one minute suggest I have anything new to say on the matter. Maybe some choice anong controversial versions? I find Bruno's choice remarkable about the incompressibility. Will think about it, thanks, Bruno. JM
Definition of measure
To try and settle this debate on uniform measures, the best definition of measure I could find was at http://www.probability.net/. Unfortunately, this site is rather difficult to get into. However, a measure is a function m defined over the subsets of the set O in question (eg O=Z in the case of integers). It has the following two properties: m(\empty) = 0 for all A\subsetO, A_n\subsetO such that A=\union_n=1^\infty A_n and A_i \intersect A_j =\empty \forall i,j = m(A)=\sum_n=1^\infty A_n. (called the countably additive property). In less formal terms, it means you get the same number for your measure, no matter how you slice the set into disjoint subsets. Furthermore, if m(A)\in[0,\infty], the measure is called a positive measure. It can be readily seen that the cardinality function over the powerset of the integers satisfies these properties, and hence is a measure. Furthermore, it is correctly a uniform measure, as each set element contributes equal weight to the set's measure. I still think the problem has to do with confusing measure with probability distribution, which must additionally be normalisable (ie m(A)\in[0,1]). There is clearly no uniform probability distribution over the integers, or any set that is not compact for that matter. Cheers Dr. 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
