### Re: Are we simulated by some massive computer?

At 13:08 13/04/04 -0700, George Levy wrote: Put in another way, *either* the massive computer simulates the exact laws of physics (exact with comp = the laws extractible from the measure on all 1-computations) in which case we belong to it but in that case we belong also to all its copy in Platonia, and our prediction or physics relies on all those copies (so that to say we belong to the massive computer has no real meaning: if it stops, nothing can happen to us for example); *or* the massive computer simulates only an approximation of those laws (like a brain during the night), and then we can in principle make the comparison, and find the discrepancies, and conclude we inhabit a fake reality ... OK? Bruno This is a very interesting method of testing what I thought was untestable. However, I see some problems. The number of simulations within Platonia is likely to be infinite. In addition, you may be simulated at more than one level, possibly at an infinite number of levels, including at the base level in Platonia if there is such a thing. OK. Although I am not sure by what you mean by base in Platonia. While the number of instances of you in the computer may be limited, the number of computers in Platonia may be infinite. In addition, the number of real you in Platonia is also likely to be infinite. Yes. Plausibly 2^aleph_0 (the power of the continuum). Your existence at the base level in Platonia is much more likely than the existence of a simulation computer (because the computer is presumably much more complex than you) and therefore, your measure in Platonia will swamp out your measure in the computers. OK. Your proposed test idea is interesting but it should be designed to cancel out these infinities. If that is possible. The translation of the reasoning in arithmetic leads me to think that these infinities are not cancellable. Comp would predict that the toe cannot be renormalizable. It is too early to make definite conclusion however. Bruno http://iridia.ulb.ac.be/~marchal/

### Re: Computational irreducibility and the simulability of worlds

Dear Stephen, snip [BM] Giving that I *assume* that arithmetical truth is independent of me, you and the whole physical reality (if that exists), I do have infinite resources in that Platonia. Remember that from the first person point of view it does not matter where and how, in Platonia, my computational states are represented. Brett Hall just states that the proposition we are living in a massive computer is undecidable (and he adds wrongly (I think) that it makes it uninteresting), but actually with my hypotheses physics is a sum of all those undecidable propositions ...(Look again my UDA proof if you are not yet convinced, but keep in mind that I assume the whole (un-axiomatizable by Godel) arithmetical truth, which I think you don't. [SPK] This is very unsettling for me as it seems to claim that we can merely postulate into existence whatever we need to make up for deficiencies in our theories. This can not be any kind of science. But Mendeelev discovered new atoms by that method. I am not sure what you mean. But I can put that complaint aside. It is what is missing in this Platonia that bothers me: how does it necessitate an experienciable world. It necessitates the experienciable truth, and worlds emerge from that. The fact that I experience a world must be explained, even if it is merely an illusion. It must be necessitated by our theories of Everything. Sure. I tend to think of the truth in Arithmetic Truth (and any other formal system) to be more of a notion that is derived from game theoretics (http://www.csc.liv.ac.uk/~pauly/Submissions/mcburney.ps and http://staff.science.uva.nl/%7Ejohan/H-H.pdf) than from hypostatization. arithmetical truth is not (by Godel, Tarski, ...) formally definable in any formal arithmetic. This, of course, degenerates the notion of objective truth, but I have come to the belief that this notion is, at best self-stultifying. What sense does it make to claim that some statement X is True or that some Y exists independent of me, you and the whole of physical reality when X and Y are only meaningful to me, you, etc.? I know you dislike arithmetical realism, but it is hard for me to believe that the primality of 317 is contingent, or even remotely linked to us. We can claim that anything at all is True, so long as it is not detectable. This entire argument of independence teeters on the edge of indetectability. I don't understand. You should put your cart on the table. What are your presupposition? [SPK] I agree with most of your premises and conclusions but I do not understand how it is that we can coherently get to the case where a classical computer can generate the simulation of a finite world that implies QM aspects (or an ensemble of such), for more than one observer including you and I, without at least accounting for the appearance of implementation. But I do. See the ref to the everything-list in my url. [BM] A non genuine answer would be the following: because the solutions of Schroedinger equations (or Dirac's one, ...) are Turing-emulable. This does not help because a priori we must take into account all computation (once we accept we are turing-emulable), not only the quantum one (cf UDA). [SPK] A priori existing UDA, Platonia, whatever, how is this more than mere hypostatization? Because those are well defined arithmetical object. UD is a well defined program. Again I am reminded of Julian Barbour's notion of best matching. He himself discussed the difficulty of running the computations to find best matchings among a small (finite!) number of possibilities, and yet, when faced with an infinity of possibilities the complexity is hand waved away by an appeal to Platonia! Even if we assume that Platonia has infinite Resources, the kind of computation that you must run takes an Eternity to solve. Yes, but our first person experiences rely on that infinity just because we cannot be aware of any delay in the UD processing, so that we must take into account the infinite union of all initial segment of the whole processing of the UD. It is like a Perfectly Fair game: it takes forever to verify its fairness and, once that infinity has passed, it is a game that never ends. Is our 1 person experience a trace of this game? Not exactly. It is less false to consider it as a partial view on an infinity of traces, giving that we cannot distinguish the infinity of version of that trace. [BM] A priori comp entails piece of non-computable stuff in the neighborhood, but no more than what can be produced by an (abstract) computer duplicating or differentiating all computational histories. [SPK] Surely, but all computational histories requires at least one step to be produced. In Platonia, there is not Time, there is not any way to take that one step. There is merely a Timeless Existence. That is true for any block universe. In general relativity time is also a

### RE: Are we simulated by some massive computer?

At 09:58 13/04/04 -0400, Ben Goertzel wrote: 6) This shows that if we are in a massive computer running in a universe, then (supposing we know it or believe it) to predict the future of any experiment we decide to carry one (for example testing A or B) we need to take into account all reconstitutions at any time of the computer (in the relevant state) in that universe, and actually also in any other universes (from our first person perspective we could not be aware of the difference of universes from inside the computer). Yes, but this is just a fancy version of the good old-fashioned Humean problem of induction, isn't it? That would be the case if there were no measure on the computations. Indeed, predicting the future on a sound a priori basis is not possible. One must make arbitrary assumptions in order to guide predictions. This is a limitation, not of the comp hypothesis specifically, but of the notion of prediction itself. You cannot solve the problem of induction with or without comp, so I don't think you should use problem-of-induction related difficulties as an argument against comp. I was not arguing against comp! (nor for). In fact, comp comes with a kind of workaround to the problem of induction, which is: To justify induction, make an arbitrary assumption of a certain universal computer, use this to gauge simplicity, and then judge predictions based on their simplicity (to use a verbal shorthand for a lot of math a la Solomonoff, Levin, Hutter, etc.). This is not a solution to the problem of induction (which is that one must make arbitrary assumptions to do induction), just an elegant way of introducing the arbitrary assumptions. This can help for explaining what intelligence is, but cannot help for the mind body problem where *all* computations must be taken into account. So, in my view, we are faced with a couple different ways of introducing the arbitrary assumptions needed to justify induction: 1) make an arbitrary assumption that the apparently real physical universe is real 2) make an arbitrary assumption that simpler hypotheses are better, where simplicity is judged by some fixed universal computing system There is no scientific (i.e. inductive or deductive) way to choose between these. From a human perspective, the choice lies outside the domain of science and math; it's a metaphysical or even ethical choice. I am not convinced. I don't really understand 1), and the interest of 2) relies, I think, in the fact that simplicity should not (and does not, I'm sure Schmidhuber would agree) on the choice of the universal computing system. Bruno http://iridia.ulb.ac.be/~marchal/

### Re: Computational irreducibility and the simulability of worlds

Hi Stephen: What I am basically saying is that you can not define a thing without simultaneously defining another thing that consists of all that is left over in the ensemble of building blocks. I suspect that usually the left over thing is of little practical use. However, this duality also applies to the Nothing and its left over which is the Everything. A look at this pair allows the derivation that the boundary between them [the definition pair] can be represented as a normal real and can not be a constant if zero info is to be maintained. Thus, given the dynamic, this boundary's representation as I said in the last post can be modeled as the output of a computer with an infinite number of asynchronous multiprocessors. A cellular automaton with asynchronous cells. Universes are interpretations of this output. Sort of a left wing proof that we are in a massive computer. The Hintikka material you pointed me to is far too imbedded in mathematical language symbols for me to understand. Yours Hal At 12:03 AM 4/13/2004, you wrote: Dear Hal, I will have to think about this for a while. Very interesting. Meanwhile I ask that you take a look at the game theoretic semantic idea by Hintikka. Kindest regards, Stephen