Re: Maximization the gradient of order as a generic constraint ?
Hal Finney wrote: Georges Quenot writes: Considering the kind of set of equation we figure up to now, completely specifying our universe from them seems to require two additional things: 1) The specification of boundary conditions (or any other equivalent additional constraint. 2) The selection of a set of global parameters. My suggestion is that for 1), instead of specifying initial conditions (what might be problematic for a number of reasons), one could use another form of additional high level constraint which would be that the solution universe should be as much as possible more ordered on one side than on the other. Of course, this rely on the possibility to give a sound sense to this, which implies to be able to find a canonical way to tell whether one solution of the set of equations in more more ordered on one side than on the other than another solution. I think this is a valid approach, but I would put it into a larger perspective. The program you describe, if we were to actually implement it, would have these parts: It has a certain set of laws of physics; it has a certain order-measuring function (perhaps equivalent to what we know as entropy); and it has a goal of finding conditions which maximize the difference in this function's values from one side to the other of some data structure that it is modifying or creating, and which represents the universe. That's it. I would say that this is a clever reformulation back in the context of the computational perspective. However I do not find this perpective larger. It would not be particularly difficult to implement a toy version of such a program based on some simple laws of physics, and perhaps as you suggest our own universe might be the result of an instance of such a program which is not all that much more large or complex. In the context of the All Universe Principle as interpreted by Schmidhuber, all programs exist, and all the universes that they generate exist. This program that you describe is one of them, and the universe that is thus generated is therefore part of the multiverse. So to first order, there is nothing particularly surprising or problematical in envisioning programs like this as contributing to the multiverse, along with the perhaps more naively obvious programs which perform sequential simulation from some initial conditions. All programs exist, including ones which create universes in even more strange or surprising ways than these. By the way, Wolfram's book (wolframscience.com) does consider some non-sequential simulations as models for simple 1- and 2-dimensional universes. These are what he calls Systems Based on Constraints discussed in his chapter 5. Where I think your idea is especially interesting is the possibility that the program which creates our universe via this kind of optimization technique (maximizing the difference in complexity) might be much shorter than a more conventional program which creates our universe via specifying initial conditions. Shorter programs are considered to have larger measure in the Schmidhuber model, hence it is of great importance to discover the shortest program which generates our universe, and if optimization rather than sequential simulation does lead to a much shorter program, that means our universe has much higher measure than we might have thought. In the more classical mathematical perspective, I would say that this principle could be considered as an additional axiom from which a lot could be derived, leading (possibly) to a description of universes much shorter in axiom count than many alternatives. An even more general axiom would be that if a symmetry has to be broken, it has to be broken as much as possible, things having to either as symmetrical as possible or as asymmetrical as possible. However, I don't think we can evaluate this possibility in a meaningful way until we have a better understanding of the physics of our own universe. Yes and maybe even if we finally figure which laws are to be used. I am somewhat skeptical that this particular optimization principle is going to work, because our universe's disorder gradient is dominated by the Big Bang's decay to heat death, and these cosmological phenomena don't necessarily seem to require the kinds of atomic and temporal structures that lead to observers. I know of the dominance of the near big bang decay to heat death but it might be that however small the remaining might be, it could still be enough to make a difference. Also, the remaining operates on a much longer time-scale and this could somehow balance things. It is certainly too early to decide whether this optimization principle is actually useful and whether the optimal point would actually turn out to be our type of universe. I am not so confident that it would but I don't think either that this could be ruled out yet. If you look at
Determinism
Thanks Hal (also Norman and others who answered), I will just comment on one passage you wrote as it may be of general interest. At 5:12 PM -0800 1/11/04, Hal Finney wrote: That would require that it is infinitely improbable that you could exist. But I don't think that is the case, because there are only a finite number of possible arrangements of matter of the size of a human being. (Equivalently, humans embody only a finite amount of information.) So it would seem that the probability of a human appearing in some universe must be finite and greater than zero, hence there would be an infinite number of instances across an infinity of universes. First, no what I suggested was not infinite improbability but a probability so close to zero it takes infinite chances for the event to be expected even once. What I think may be of general interest is that the discussion in the physical sciences has assumed reductionism -- that human persons are reducible to their physical bodies. However, Dennett notwithstanding, reductionism has not only not been vindicated, it remains in trouble. There is an important implication for this issue if mental states (i.e., thoughts, beliefs, emotions) cannot be reduced to physical states. The reason is that ideas (thoughts) are not only infinite but unlike universes, which are presumably discrete), ideas are uncountably infinite. Consider, for example, how you would count ideas. Unlike the real numbers, ideas cannot even be ordered into intervals. As a result, ideas may well represent a vastly greater infinity than universes. If so, even with infinite universes, you or I may never show up again. Anyway, this is what I have been thinking. And, re free will, Dennett's compatibilism ultimately remains, I think, a sleight of hand. But if reductionism fails, then so does determinism (but that is a larger, social scientific argument). Thanks again. doug -- doug porpora dept of culture and communication drexel university phila pa 19104 USA [EMAIL PROTECTED]
Re: Is the universe computable?
At 15:42 09/01/04 -0500, Jesse Mazer wrote: Bruno Marchal wrote: I don't think the word universe is a basic term. It is a sort or deity for atheist. All my work can be seen as an attempt to mak it more palatable in the comp frame. Tegmark, imo, goes in the right direction, but seems unaware of the difficulties mathematicians discovered when just trying to define the or even a mathematical universe. Of course tremendous progress has been made (in set theory, in category theory) giving tools to provide some *approximation*, but the big mathematical whole seems really inaccessible. With comp it can be shown (first person) inaccessible, even unnameable ... Inaccessible in what sense? How do you use comp to show this? If this is something you've addressed in a previous post, feel free to just provide a link... This is a consequence of Tarski theorem. Do you know it? I think I have said this before but I don't find the links (I have to much mentioned the result by McKinsey and Tarski in Modal logic, so searching the archive with tarski does not help). Let me explain it briefly. With the platonist assumption being a part of the comp hyp, we can identify in some way truth and reality (in a very large sense which does not postulate that reality is necessarily physical reality). That is Reality is identified with the set of all true propositions in some rich language. Now Tarski theorem, like Godel's theorem, can be applied to any sufficiently rich theory or to any sound machine. Tarski theorem says that there is no truth predicate definable in the language of such theories/machines. Nor is knowledge definable for similar reason. So any complete platonist notion of truth or knowledge cannot be defined in any language used by the machine, strictly speaking such vast notion of truth is just inaccessible by the machine, and this despite the fact a machine can build transfinite ladder of better approximation of it. By way of contrast the notion of consistency *is* definable in the language of the machine, only themachine cannot prove its own consistency (by Godel), but the machine can express it. Now, with Tarski the machine cannot even express it. Like Godel's theorem, tarski theorem is a quasi direct consequence of the *diagonalisation lemma: For any formula A(x), there is a proposition k such that the machine will prove k - A(k).Note: A(k) is put for the longer A(code of k) In case a truth predicate V(x) could be defined in arithmetic or in the machine's tong, the machine would be able to define a falsity predicate (as -V(x) ), and by the diagonalisation lemma, the machine would be able to prove the Epimenid sentence k - -V(k), which is absurd V being a truth predicate. Truth, or any complete description of reality cannot have a definition, or a name: semantical notion like truth or knowledge are undefinable (unnameable). Actually we don't really need comp in the sense that these limitation theorem applies to much powerful theories or divine machine with oracle, ... OK? Bruno
Re: Is the universe computable?
At 13:36 09/01/04 +0100, Georges Quenot wrote: Bruno Marchal wrote: It seems, but it isn't. Well, actually I have known *one* mathematician, (a russian logician) who indeed makes a serious try to develop some mathematics without that infinite act of faith (I don't recall its name for the moment). Such attempt are known as ultrafinitism. Of course a lot of people (especially during the week-end) *pretend* not doing that infinite act of faith, but do it all the time implicitly. This is not what I meant. I did not refer to people not willing to accept that natural numbers exist at all but to people not wlling to accept that natural numbers exist *by themselves*. Rather, they want to see them either as only a production of human (or human-like) people or only a production of a God. What I mean is that their arithmetical property are independent of us. Do you think those people believe that the proposition 17 is prime is meaningless without a human in the neighborhood? Giving that I hope getting some understanding of the complex human from something simpler (number property) the approach of those people will never work, for me. Also, I would take (without added explanations) an expression like numbers are a production of God as equivalent to arithmetical realism. Of course if you add that God is a mathematical-conventionalist and that God could have chose that only even numbers exist, then I would disagree. (Despite my training in believing at least five impossible proposition each day before breakfast ;-) And I said unfortunately because some not only do not want to see natural numbers as existing by themselves but they do not want the idea to be simply presented as logically possible and even see/designate evil in people working at popularizing it. OK, but then some want you being dead because of the color of the skin, or the length of your nose, ... I am not sure it is not premature wanting to enlighten everyone at once ... I guess you were only talking about those hard-aristotelians who like to dismiss Plato's questions as childish. Evil ? Perhaps could you be more precise on those people. I have not met people seeing evil in arithmetical platonism, have you? Bruno
Re: Is the universe computable?
On Mon, Jan 12, 2004 at 03:50:42PM +0100, Bruno Marchal wrote: What I mean is that their arithmetical property are independent of us. Do you think those people believe that the proposition 17 is prime is meaningless without a human in the neighborhood? Of course it is meaningless. Natural numbers are representation clusters by infoprocessing systems: currently machines or animals. Pebbles can't count themselves, obviously. No realization without representation. I have no trouble seeing the universe as artifact from some production system (but that metalayer be transcendent by definition), but assuming universe exists because numbers exist does strike me as a yet another faith. -- Eugen* Leitl a href=http://leitl.org;leitl/a __ ICBM: 48.07078, 11.61144http://www.leitl.org 8B29F6BE: 099D 78BA 2FD3 B014 B08A 7779 75B0 2443 8B29 F6BE http://moleculardevices.org http://nanomachines.net pgp0.pgp Description: PGP signature
Re: Is the universe computable?
At 16:02 12/01/04 +0100, Eugen Leitl wrote: On Mon, Jan 12, 2004 at 03:50:42PM +0100, Bruno Marchal wrote: What I mean is that their arithmetical property are independent of us. Do you think those people believe that the proposition 17 is prime is meaningless without a human in the neighborhood? Of course it is meaningless. Natural numbers are representation clusters by infoprocessing systems: currently machines or animals. Pebbles can't count themselves, obviously. Natural numbers are not representation. They are the one represented, for exemples by infosystems, or pebbles, animals etc. It seems to me you confuse the thing abstract immaterial numbers, and the things which represent them. Pebbles can't count themselves, obviously. But it is not because pebbles can't count that two pebbles give an even number of pebbles. Electron cannot solve schroedinger equation (only a physicist can do that), nevertheless electron cannot not follow it (supposing QM). No realization without representation. It depends of the level of description. It depends of your favorite primitive act of faith. I have no trouble seeing the universe as artifact from some production system (but that metalayer be transcendent by definition), but assuming universe exists because numbers exist does strike me as a yet another faith. That numbers exists independently of us is based on a act of faith I agree. But all theories are based on some act of faith. That the universes follows from numbers is not an act of faith, but a consequence of comp. See my thesis for that, or links to explanations in this list: all that in my url below. Bruno PS there is a missing word in my answer to Jesse. Just to be clearer: Godel's theorem: self-consistency is not provable by consistent machine Tarski's theorem: truth (and knowledge) is not even expressible by the consistent machine. http://iridia.ulb.ac.be/~marchal/
Re: Is the universe computable?
On Mon, Jan 12, 2004 at 04:18:56PM +0100, Bruno Marchal wrote: Natural numbers are not representation. They are the one represented, for exemples by infosystems, or pebbles, animals etc. They are the one represented is a yet another assertion. I would be more inclined to listen, if you'd show how a group of pebbles can conduct a measurement. (Counting is a measurement). It seems to me you confuse the thing abstract immaterial numbers, and the things which represent them. If I'd kill you, you'd have no chance of thinking that thought. If I killed all animals capable of counting, abstract immaterial numbers would become exactly that: immaterial. Pebbles can't count themselves, obviously. But it is not because pebbles can't count that two pebbles give an even number of pebbles. Electron cannot solve schroedinger equation (only a physicist can do that), nevertheless electron cannot not follow it (supposing QM). The universe does what it does, it certainly doesn't solve equations. People solve equations, when approximating what universe does. As such, QM is a fair approximation; it has no further reality beyond that. H\psi=E\psi in absence of context is just as meaningless as 2+2=4. -- Eugen* Leitl a href=http://leitl.org;leitl/a __ ICBM: 48.07078, 11.61144http://www.leitl.org 8B29F6BE: 099D 78BA 2FD3 B014 B08A 7779 75B0 2443 8B29 F6BE http://moleculardevices.org http://nanomachines.net pgp0.pgp Description: PGP signature
Re: Is the universe computable?
Bruno, in the line you touched with 'numbers: I was arguing on another list 'pro' D.Bohm's there are no numbers in nature position when a listmember asked: aren't you part of nature? then why are you saying that numbers - existing in your mind - are not 'part of nature'? Since then I formulate it something like: numbers came into existence as products of 'our' thinking. (Maybe better worded). You wrote: What I mean is that their arithmetical property are independent of us. .. That may branch into the question how much of 'societal' knowledge is part of an individual belief - rejectable or intrinsically adherent? (Some may call this a fundamental domain of memes). With the 'invention' of numbers (arithmetical, that is) human mentality turned into a computing animal - as a species-characteristic. I separate this from the assignment of quantities to well chosen units in numbers. Quantities may have their natural role in natural processes - unconted in our units, just mass-wise, and we, later on - in physical laws - applied the arithmetical ordering to the observations in the quantized natural events. Such quantizing (restricted to models of already discovered elements) renders some processes 'chaotic' or even paradoxical, while nature processes them without any problem in her unrestricted (total) interconnectedness (not included - even known ALL in our quantized working models). Sorry for the physicistically unorthodox idea. Best regards John Mikes - Original Message - From: Bruno Marchal [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Monday, January 12, 2004 9:50 AM Subject: Re: Is the universe computable? At 13:36 09/01/04 +0100, Georges Quenot wrote: Bruno Marchal wrote: It seems, but it isn't. Well, actually I have known *one* mathematician, (a russian logician) who indeed makes a serious try to develop some mathematics without that infinite act of faith (I don't recall its name for the moment). Such attempt are known as ultrafinitism. Of course a lot of people (especially during the week-end) *pretend* not doing that infinite act of faith, but do it all the time implicitly. This is not what I meant. I did not refer to people not willing to accept that natural numbers exist at all but to people not wlling to accept that natural numbers exist *by themselves*. Rather, they want to see them either as only a production of human (or human-like) people or only a production of a God. What I mean is that their arithmetical property are independent of us. Do you think those people believe that the proposition 17 is prime is meaningless without a human in the neighborhood? Giving that I hope getting some understanding of the complex human from something simpler (number property) the approach of those people will never work, for me. Also, I would take (without added explanations) an expression like numbers are a production of God as equivalent to arithmetical realism. Of course if you add that God is a mathematical-conventionalist and that God could have chose that only even numbers exist, then I would disagree. (Despite my training in believing at least five impossible proposition each day before breakfast ;-) And I said unfortunately because some not only do not want to see natural numbers as existing by themselves but they do not want the idea to be simply presented as logically possible and even see/designate evil in people working at popularizing it. OK, but then some want you being dead because of the color of the skin, or the length of your nose, ... I am not sure it is not premature wanting to enlighten everyone at once ... I guess you were only talking about those hard-aristotelians who like to dismiss Plato's questions as childish. Evil ? Perhaps could you be more precise on those people. I have not met people seeing evil in arithmetical platonism, have you? Bruno
Re: Peculiarities of our universe
Hal, thanks for this comprehensive view about universes. This state of the Art essay is worth reading whether one concurs or discords. I concur with some tiny remarks (could it be otherwise???) The position that we don't 'see' other universes is correct, missing, however, the possibility of OTHER universes seeing US. Even interfere(?). Non essential style-wise - (you wrote): This observation points to the fact that with our laws of physics, the evolution of intelligent life is extremely unlikely. ... I would name our universe-system rather than the laws we abstracted from our (limited?) observations in our system-studies. Further: Presumably, there are universes whose laws make life essentially impossible. Characteristics (unobserved, in lifeless or intelligence-less universes: Yes. Laws? in different systems from any what we cannot even contemplate? No. I consider your measures in the widest (most general) sense as circumstances including features unknown to us as well. Since we cannot see other universes, I do not speculate about their particulars. Even possibilities of potentials are restricted to our experience and mindset. Our sci-fi is limited. Sorry for the hair-splitting and thank you for a good post John Mikes - Original Message - From: Hal Finney [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Sunday, January 11, 2004 12:57 PM Subject: Re: Peculiarities of our universe There has been a huge amount written about the Fermi Paradox (why are there no aliens). SNIP Hal Finney
Re: Peculiarities of our universe
On Sun, Jan 11, 2004 at 09:57:18AM -0800, Hal Finney wrote: [...] That is (turning to the Schmidhuber interpretation) it must be much simpler to write a program that just barely allows for the possibility of life than to write one which makes it easy. This is a prediction of the AUH, and evidence against it would be evidence against the AUH. evidence against it would be evidence against the AUH is similar to the Doomsday Argument. Let's assume that in fact universes with lots of intelligent life don't all have much lower measure than our own. Then AUH implies the typical observer should see many nearby intelligent life. Your argument is that since we don't see many nearby intelligent life, AUH is probably false. In the Doomsday Argument, the non-doomsday hypothesis implies the typical observer should have a high birth rank, and the argument is that since we have a low birth rank, the non-doomsday hypothesis is probably false. I want to point this out because many people do not think the DA is valid and some have produced counterarguments. Some of those counterarugments may work against Hal's argument as well.
Re: Is the universe computable?
On Tue, Jan 06, 2004 at 05:32:05PM +0100, Georges Quenot wrote: Many other way of simulating the universe could be considered like for instance a 4D mesh (if we simplify by considering only general relativity; there is no reason for the approach not being possible in an even more general way) representing a universe taken as a whole in its spatio-temporal aspect. The mesh would be refined at each iteration. The relation between the time in the computer and the time in the universe would not be a synchrony but a refinement of the resolution of the time (and space) in the simulated universe as the time in the computer increases. Alternatively (though both views are not necessarily exclusive), one could use a variational formulation instead of a partial derivative formulation in order to describe/build the universe leading again to a construction in which the time in the computer is not related at all to the time in the simulated universe. Do you have references for these two ideas? I'm wondering, suppose the universe you're trying to simulate contains a computer that is running a factoring algorithm on a large number, in order to cryptanalyze somebody's RSA public key. How could you possibly simulate this universe without starting from the beginning and working forward in time? Whatever simulation method you use, if somebody was watching the simulation run, they'd see the input to the factoring algorithm appear before the output, right?
RE: Peculiarities of our universe
Let X be some predicate condition on the universes in the multiverse. I think Hal is assuming that if all the following are true 1. X can be described in a compact form (ie it doesn't fill up a book with detailed data) 2. X is true for our universe 3. AUH = P(X)=0 then we deduce that AUH is (probably) false. Are you saying Wei, that there is a flaw in this logic? - David -Original Message- From: Wei Dai [mailto:[EMAIL PROTECTED] Sent: Tuesday, 13 January 2004 9:22 AM To: Hal Finney Cc: [EMAIL PROTECTED] Subject: Re: Peculiarities of our universe On Sun, Jan 11, 2004 at 09:57:18AM -0800, Hal Finney wrote: [...] That is (turning to the Schmidhuber interpretation) it must be much simpler to write a program that just barely allows for the possibility of life than to write one which makes it easy. This is a prediction of the AUH, and evidence against it would be evidence against the AUH. evidence against it would be evidence against the AUH is similar to the Doomsday Argument. Let's assume that in fact universes with lots of intelligent life don't all have much lower measure than our own. Then AUH implies the typical observer should see many nearby intelligent life. Your argument is that since we don't see many nearby intelligent life, AUH is probably false. In the Doomsday Argument, the non-doomsday hypothesis implies the typical observer should have a high birth rank, and the argument is that since we have a low birth rank, the non-doomsday hypothesis is probably false. I want to point this out because many people do not think the DA is valid and some have produced counterarguments. Some of those counterarugments may work against Hal's argument as well.
