Re: Are conscious beings always fallible?
How would they ever know that I wonder? Well let's see. I'm conscious and I'm not fallible. Therefore ;-) David Barrett-Lennard wrote: I'm wondering whether the following demonstrates that a computer that can only generate thoughts which are sentences derivable from some underlying axioms (and therefore can only generate true thoughts) is unable to think. This is based on the fact that a formal system can't understand sentences written down within that formal system (forgive me if I've worded this badly). Somehow we would need to support free parameters within quoted expressions. Eg to specify the rule It is a good idea to simplify x+0 to x It is not clear that language reflection can be supported in a completely general way. If it can, does this eliminate the need for a meta-language? How does this relate to the claim above? - David I don't see the problem with representing logical meta-language, and meta-metalanguage... etc if necessary in a computer. It's a bit tricky to get the semantics to work out correctly, I think, but there's nothing extra-computational about doing higher-order theorem proving. http://www.cl.cam.ac.uk/Research/HVG/HOL/ This is an example of an interactive (i.e. partly human-steered) higher-order thereom prover. I think with enough work someone could get one of these kind of systems doing some useful higher-order logic reasoning on its own, for certain kinds of problem domains anyway. Eric
Re: Are conscious beings always fallible?
I agree with you. Actually you can use the second recursion theorem of Kleene to collapse all the orders. This is easier in an untyped programming language like (pure) LISP than in a typed language, although some typed language have a primitive for handling untyped self-reference, like the primitive SELF in Smalltalk ... Bruno At 23:29 19/01/04 -0800, Eric Hawthorne wrote: How would they ever know that I wonder? Well let's see. I'm conscious and I'm not fallible. Therefore ;-) David Barrett-Lennard wrote: I'm wondering whether the following demonstrates that a computer that can only generate thoughts which are sentences derivable from some underlying axioms (and therefore can only generate true thoughts) is unable to think. This is based on the fact that a formal system can't understand sentences written down within that formal system (forgive me if I've worded this badly). Somehow we would need to support free parameters within quoted expressions. Eg to specify the rule It is a good idea to simplify x+0 to x It is not clear that language reflection can be supported in a completely general way. If it can, does this eliminate the need for a meta-language? How does this relate to the claim above? - David I don't see the problem with representing logical meta-language, and meta-metalanguage... etc if necessary in a computer. It's a bit tricky to get the semantics to work out correctly, I think, but there's nothing extra-computational about doing higher-order theorem proving. http://www.cl.cam.ac.uk/Research/HVG/HOL/ This is an example of an interactive (i.e. partly human-steered) higher-order thereom prover. I think with enough work someone could get one of these kind of systems doing some useful higher-order logic reasoning on its own, for certain kinds of problem domains anyway. Eric
Re: Is the universe computable
Dear Stephen, At 13:19 19/01/04 -0500, Stephen Paul King wrote: Dear Hal, and Friends, Were and when is the consideration of the physical resources required for the computation going to obtain? Is my question equivalent to the old first cause question? This is a good question for a physicalist. But if you accept the idea that the very notion of time, energy, space are secondary and logically emerges as a modality in the average memory of an average universal machine, then that question is solved (once we get the right measure of course). Now, about the measure, I am not convinced by Hal Finney's attempt to define or compute it for reason we have already discussed a lot, and which has just been recalled by George Levy in his last post. I could add this: if you take the Universal Dovetailer (UD), you must take into account the fact that he generates all version of all programs an infinite number of times. For computer science reasons it is not possible to cut out the vast redundancy of the codes in the production of the UD. Now, this does not mean that some other reasons could not be invoked for justifying the importance of little programs, though. Regards, Bruno Stephen - Original Message - From: Hal Finney [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Monday, January 19, 2004 12:23 PM Subject: RE: Is the universe computable Kory Heath wrote: At 1/18/04, Hal Finney wrote: Now consider all possible program tapes being run at the same time, perhaps on an infinite ensemble of (virtual? abstract?) machines. Of those, a fraction of 1 in 2^100 of those tapes will start with that 100 bit sequence for the program in question. [snip] Now consider another program that is larger, 120 bits. By the same reasoning, 1 in 2^120 of all possible program tapes will start with that particular 120-bit sequence. And so 1/2^120 of all the executions will be of that program. Yes, but if we're really talking about all possible finite bit strings, then the number of bit strings that begin with that 100 bit program is exactly the same as the number that begin with the 120 bit program - countably infinite. You can put them into a 1 to 1 correspondence with each other, just like you can put the integers into a 1 to 1 correspondence with the squares. The intuition that there must be more integers than squares is simply incorrect, as Galileo pointed out long ago. So shouldn't your two programs have the exact same measure? Well, I'm not a mathematician either, so I can't say for sure. And actually it's worth than this, because I spoke of infinite program tapes, so the number of programs is uncountably infinite. However, here is an alternate formulation of my argument which seems to be roughly equivalent and which avoids this objection: create a random program tape by flipping a coin for each bit. Now the probability that you created the first program above is 1/2^100, and for the second, 1/2^120, so the first program is 2^20 times more probable than the second. That seems correct, doesn't it? And it provides a similar way to justify that the universe created by the first program has 2^20 times greater measure than the second. Hal Finney
Re: Is the universe computable
Dear Bruno, Interleaving. - Original Message - From: Bruno Marchal [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Tuesday, January 20, 2004 5:55 AM Subject: Re: Is the universe computable Dear Stephen, At 13:19 19/01/04 -0500, Stephen Paul King wrote: Dear Hal, and Friends, Were and when is the consideration of the physical resources required for the computation going to obtain? Is my question equivalent to the old first cause question? This is a good question for a physicalist. But if you accept the idea that the very notion of time, energy, space are secondary and logically emerges as a modality in the average memory of an average universal machine, then that question is solved (once we get the right measure of course). [SPK] I do not accept that the very notion of time, energy, space are secondary nor do I elevate logicality above physicality; I take them as having the same ontological status, this follows from the proposed dualism of Pratt that we have discussed previously. While we can argue coherently that all of the content of experience is that which is simulated by our universal machine, we still must give some accounting for these. This is why I asked the question. Now, about the measure, I am not convinced by Hal Finney's attempt to define or compute it for reason we have already discussed a lot, and which has just been recalled by George Levy in his last post. [SPK] Could it be that the sought after measure is only a meaningful notion when given from within a world? For example, when we consider the White Rabbit problem we are taking as a base line our mutal non-experience of White Rabbits and other Harry Potter-ish phenomena. This argues along a similar line as what we find in Tipler et al's Anthropic principle, a way of thinking going back to Descartes: What I experience here and now must be given a probability of 1 since I can not question that it is being experienced. The skeptic would say: But what if it is just an illusion or the machinations of an evil demon? (See the Bennaceraf, Lucas, Searle, etc. debate...) In reply I would say: Even if it is just an illusion, simulation or whatever, the fact that it is experienced and not some thing else demands that it be taken as probability one when we start considering possible worlds and other modal ideas. You have to start somewhere and the most obvious place is right where one is stating. I could add this: if you take the Universal Dovetailer (UD), you must take into account the fact that he generates all version of all programs an infinite number of times. For computer science reasons it is not possible to cut out the vast redundancy of the codes in the production of the UD. Now, this does not mean that some other reasons could not be invoked for justifying the importance of little programs, though. [SPK] UD, UTM, QComp or whatever, all of these depend existentially on some kind of physical resource, be it some portion of Platonia, infinite tape and read/write head, Hilbert space or whatever; you can not even define your precious AR without representing it somehow. It is this necessity of representation that you seem to dismiss so easily. Again: When will a consideration of physical resources obtain? Kindest regards, Stephen Regards, Bruno Stephen - Original Message - From: Hal Finney [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Monday, January 19, 2004 12:23 PM Subject: RE: Is the universe computable Kory Heath wrote: At 1/18/04, Hal Finney wrote: Now consider all possible program tapes being run at the same time, perhaps on an infinite ensemble of (virtual? abstract?) machines. Of those, a fraction of 1 in 2^100 of those tapes will start with that 100 bit sequence for the program in question. [snip] Now consider another program that is larger, 120 bits. By the same reasoning, 1 in 2^120 of all possible program tapes will start with that particular 120-bit sequence. And so 1/2^120 of all the executions will be of that program. Yes, but if we're really talking about all possible finite bit strings, then the number of bit strings that begin with that 100 bit program is exactly the same as the number that begin with the 120 bit program - countably infinite. You can put them into a 1 to 1 correspondence with each other, just like you can put the integers into a 1 to 1 correspondence with the squares. The intuition that there must be more integers than squares is simply incorrect, as Galileo pointed out long ago. So shouldn't your two programs have the exact same measure? Well, I'm not a mathematician either, so I can't say for sure. And actually it's worth than this, because I spoke of infinite program tapes, so the number of programs is uncountably infinite. However, here is an alternate formulation of my argument which seems to be
Re: Is the universe computable
At 13:19 19/01/04 -0500, Stephen Paul King wrote: Where and when is the consideration of the physical resources required for the computation going to obtain? Is my question equivalent to the old first cause question? Anything physical is by definition within a universe (by my definition, anyway!). What are the physical properties of a system in our universe? Mass, size, energy, electrical charge, partical composition, etc. If we at least hypothetically allow for the existence of other universes, wouldn't you agree that they might have completely different physical properties? That they might not have mass, or charge, or size; or that these properties would vary in some bizarre way much different from how stable they are in our universe. Consider Conway's 2-dimensional Cellular Automota universe called Life. Take a look at http://rendell.server.org.uk/gol/tm.htm, an amazing implementation of a computer, a Turing Machine, in this universe. I spent a couple of hours yesterday looking at this thing, seeing how the parts work. He did an incredible job in putting all the details together to make this contraption work. So we can have computers in the Life universe. Now consider this: what is the mass of this computer? There is no such thing as mass in Life. There are cells, so you could count the number of on cells in the system (although that varies quite a bit as it runs). There is a universal clock, so you could count the time it takes to run. Some of our familiar properties exist, and others are absent. So in general, I don't think it makes sense to assume literally that computers require physical resources. Considered as an abstraction, computation is no more physical than is mathematics or logic. A theorem doesn't weigh anything, and neither does a computation. Hal Finney
Re: Is the universe computable
Dear Hal, A theorem doesn't weigh anything, and neither does a computation. Nice try but that is a very smelly Red Herring. Even Conway's Life can not exist, even in the abstract sense, without some association with the possibility of being implemented and it is this Implementation that I am asking about. Let us consider Bruno's beloved Arithmetic Realism. Are we to believe that Arithmetic can be considered to exist without, even tacitly, assuming the possibility that numbers must be symbolic representable? If they can be, I strongly argue that we have merely found a very clever definition for the term meaninglessness. I beg you to go directly to Turing's original paper discussing what has become now know as a Turing Machine. You will find discussions of things like tape and read/write head. Even if these, obviously physical, entities are, as you say, by definition within a universe and that such universes can be rigorously proven to be mathematical entities, this only strengthens my case: An abstract entity must have a possibility of being physically represented, even if in a Harry Potter Universe, to be a meaningful entity. Otherwise what restrains us from endless Scholastic polemics about how many Angels can dance on the head of a Pin and other meaningless fantasies. The fact that an Algorithm is independent of any particular implementation is not reducible to the idea that Algorithms (or Numbers, or White Rabbits, etc.) can exist without some REAL resources being used in their implementation (and maybe some kind of thermodynamics). BTW, have you read Julian Barbour's The End of Time? It is my opinion that Julian's argument falls flat on its face because he is making the very same mistake: Assuming that his best-matching scheme can exists without addressing the obvious status that it is an NP-Complete problem of uncountable infinite size. It is simply logically impossible to say that the mere postulation of a Platonia allows for the a priori existence of the solution to such a computationally intractable problem. Kindest regards, Stephen - Original Message - From: Hal Finney [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Tuesday, January 20, 2004 1:39 PM Subject: Re: Is the universe computable At 13:19 19/01/04 -0500, Stephen Paul King wrote: Where and when is the consideration of the physical resources required for the computation going to obtain? Is my question equivalent to the old first cause question? Anything physical is by definition within a universe (by my definition, anyway!). What are the physical properties of a system in our universe? Mass, size, energy, electrical charge, partical composition, etc. If we at least hypothetically allow for the existence of other universes, wouldn't you agree that they might have completely different physical properties? That they might not have mass, or charge, or size; or that these properties would vary in some bizarre way much different from how stable they are in our universe. Consider Conway's 2-dimensional Cellular Automota universe called Life. Take a look at http://rendell.server.org.uk/gol/tm.htm, an amazing implementation of a computer, a Turing Machine, in this universe. I spent a couple of hours yesterday looking at this thing, seeing how the parts work. He did an incredible job in putting all the details together to make this contraption work. So we can have computers in the Life universe. Now consider this: what is the mass of this computer? There is no such thing as mass in Life. There are cells, so you could count the number of on cells in the system (although that varies quite a bit as it runs). There is a universal clock, so you could count the time it takes to run. Some of our familiar properties exist, and others are absent. So in general, I don't think it makes sense to assume literally that computers require physical resources. Considered as an abstraction, computation is no more physical than is mathematics or logic. A theorem doesn't weigh anything, and neither does a computation. Hal Finney
Re: Is the universe computable
The fact that an Algorithm is independent of any particular implementation is not reducible to the idea that Algorithms (or Numbers, or White Rabbits, etc.) can exist without some REAL resources being used in their implementation (and maybe some kind of thermodynamics). To paraphrase Bill, that depends on what the meaning of the word real is. My point being that, if one accepts, even if only hypothetically (humor me), that a (toy) universe can be modeled by a CA, then would not the self-consistent physics of the universe emerge from following the rule? Given this, then, would not the resources be mapped directly only to those physics and not directly to ours, even though the CA is implemented according to and via our physics. What I'm getting at here is that weight as a function of mass and gravitation may well have no direct correspondence in the CA's physics. If not, then it could be argued that the computation within the context of it's own universe has no weight (i.e: consumes no EXTRA-universal resources) even though the implemention of same does. Then question then becomes, I suppose, if in fact our universe is a digital one (if not strictly a CA) havng self-consistent emergent physics, then might it not follow that it is implemented (run?) via some extra-universal physical processes that only indirectly correspond to ours? (if the above is too painfully obvious (or goofy?) and/or old news then, again, do humor me..)
Re: Is the universe computable?
Dear CMR, - Original Message - From: CMR [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Tuesday, January 20, 2004 5:19 PM Subject: Re: Is the universe computable [SPK previous] The fact that an Algorithm is independent of any particular implementation is not reducible to the idea that Algorithms (or Numbers, or White Rabbits, etc.) can exist without some REAL resources being used in their implementation (and maybe some kind of thermodynamics). [CMR] To paraphrase Bill, that depends on what the meaning of the word real is. [SPK] Ok, how about: Reality is that which is unimpeachable. ;-) [CMR] My point being that, if one accepts, even if only hypothetically (humor me), that a (toy) universe can be modeled by a CA, then would not the self-consistent physics of the universe emerge from following the rule? [SPK] Ok, I will bite. ;-) [CMR] Given this, then, would not the resources be mapped directly only to those physics and not directly to ours, even though the CA is implemented according to and via our physics. What I'm getting at here is that weight as a function of mass and gravitation may well have no direct correspondence in the CA's physics. If not, then it could be argued that the computation within the context of it's own universe has no weight (i.e: consumes no EXTRA-universal resources) even though the implemention of same does. Then question then becomes, I suppose, if in fact our universe is a digital one (if not strictly a CA) havng self-consistent emergent physics, then might it not follow that it is implemented (run?) via some extra-universal physical processes that only indirectly correspond to ours? [SPK] Again, shifting the resources problem via a mapping to alternative worlds is the logical equivalent of sweeping the dirt under the rug. It still exists! This reminds me of how an ameoba (the twin of Bruno's) that lives in the bottom drawer of my refrigerator has the belief that his universe (the inside of the refrigerator) has a thermodynamic arrow that is anti-parallel (goes in the opposite direction) to the one outside when ever the light goes out... BTW, have you ever read about the Maxwell Demon? [CMR] (if the above is too painfully obvious (or goofy?) and/or old news then, again, do humor me..) [SPK] It was a good try! ;-) Stephen
Re: Is the universe computable
Pete Carlton writes: Imagine a Life universe that contains, among other things, two SASes talking to each other (and showing each other pictures, and in general having a very lucid, conscious, conversation.) Imagine that instead of being implemented on a computer, it's implemented by a large 2d array of coins: heads represents live, and tails represents dead. Each timestep, the coins are flipped over in concordance with the Life rules. Does this setup implement a universe? Let's say it does. If you say it does, how about the next step: Instead of doing flipping operations on one set of coins, each new generation is laid down in the proper configuration on top of the preceding one with a new set of coins. Does this process of laying down coins also implement a universe? Yes, it would seem that laying down coins isn't conceptually different from flipping them, from the point of view of performing a calculation. If you say it does, then what about the stack itself? (One can imagine pointing to each layer in succession, saying This is the current step, Now this is the current step, etc..) Does the stack's bare existence suffice for the implementation of a universe? The problem with this example is that you can't create the stacks without laying them down first. So there has definitely been an implementation during the lay-down phase. What you have to be asking is, in some sense, is the implementation still going on? This assumes a certain time-bound nature to the concept of implementation which may not be valid. You are assuming that the region of our universe where the implementation occurs can be bounded in time, and asking if the boundary only encloses the active lay-down phase, or also encloses the passive stack phase. You get the same problems if you try to describe the exact physical boundaries of the implementation in space. Does the implementation encompass the spaces between the coins, for example? Assuming you also need some small calculator to compute how to flip each coin (a simple lookup table for the 512 possibilities of 9 coins in a square), is that part of the implementation? What about the space between the coins and the calculator? Or perhaps the coins themselves don't have well-defined boundaries, etc. These questions suggest that it is difficult to consider whether a particular implementation is going on to be a yes-or-no question that can be asked at each point-event in space-time. So it may not be meaningful to ask whether the stack is also an implementation. Having said that, I'll give two contradictory answers: If not, then can you say what it is about the active process of flipping or laying down that counts as computation but does not count when the stack is a static block? In the philosophical literature on implementation (a good jumping-off point is David Chalmers paper at http://www.u.arizona.edu/~chalmers/papers/rock.html) it is considered that a mere trace of a program execution does not count as an implementation, for two reasons: first, there are no causal connections between the layers, they're just sitting there; and second, the trace does not represent counterfactuals, i.e. if you were to change a cell's value, what would happen is not clear from the trace. If you think the static block counts as the implementation of a universe, then I think you can go all the way to abstract Platonism. Because since the stack's just sitting there, why not knock it down? Or melt it into a big ball? Or throw it into a black hole...the two SASes won't care (will they?) On the other hand, if I apply what I have been calling the Wei Dai heuristic (about which I wrote a few messages in the past few days; BTW Wei suggested the idea but it's not necessarily something he advocates), I'd say that the presence of the stack does increase the measure of the simulated universe, because it increases the percentage of our universe's resources which are used by the simulation. More precisely, its presence would allow a shorter program to locate the implementation among all the vastness of our universe. However, in that case, knocking down or destroying the stack would eliminate this property; the stack would no longer contain the information which would allow shortening the program which would localize the implementation. Hal Finney
Re: Is the universe computable?
Greetings Stephen, BTW, have you ever read about the Maxwell Demon? Being partial to the information physical view; not only have I read it, I also account for it by viewing a system's information as physical. So by inference should then I be viewing the mapping of the intra and extra universal resources as informational in nature? In that the implementation informs (and thus constrins?) the evolution of our toy universe?
Re: Is the universe computable
Greetings Pete, If not, then can you say what it is about the active process of flipping or laying down that counts as computation but does not count when the stack is a static block? I suppose I'm ultimately in the hard info physics camp, in that the pattern's the thing; given the 2ds and the binary content, then the stacks would map to a time dimension I suppose; were they to be unstacked and recorded we'd have a history (were they unstacked , some flipped then read.. revisionist history?) If you think the static block counts as the implementation of a universe, then I think you can go all the way to abstract Platonism. Because since the stack's just sitting there, why not knock it down? Or melt it into a big ball? Or throw it into a black hole...the two SASes won't care (will they?) No, in this scenario I see the unverse as a function of the coins (or computer, or space-time, or matter energy and information). Toss a stack into a black whole (whether of not we get it back via hawkings radiation) and the information capacity of the universe is affected. But note here I say this scenario. So I think the anti-Platonist must answer why exactly the coins need to be actively flipped or laid down to really implement a Life universe -- and by extension, why any universe needs to be actively implemented. Because it's not there? Kidding. To elaborate on my statement above. I definitely see time, energy, matter.. as emergent phenomena of an underlying informational and probably discrete process. But they emerged from a pattern(order? information? logos?) and that pattern was informed upon( the, a, some?) void (noise, chaos, the one? the one of many?). Per my just prior post, I may in fact now see the extra-universal implementation as informational. So am I not a Platonist (or not? or am?)
Re: Is the universe computable
CMR writes: Then question then becomes, I suppose, if in fact our universe is a digital one (if not strictly a CA) havng self-consistent emergent physics, then might it not follow that it is implemented (run?) via some extra-universal physical processes that only indirectly correspond to ours? This is a good point, and in fact we could sharpen the situation as follows. Suppose multiverse theory is bunk and none of Tegmark's four levels work. The universe isn't infinite in size; there is no inflation; the MWI is false; and all that stuff about Platonic existence is so much hot air. There is, in fact, only one universe. However, that universe isn't ours. It's a specific version of Conway's 2D Life universe, large but finite in size, with periodic edge conditions. Against all odds, life has evolved in Life and produced Self Aware Subsystems, i.e. observers. These beings have developed a civilization and built computers. See the link I supplied earlier, http://rendell.server.org.uk/gol/tm.htm for a sample of such a computer. On their computers they run simulations of other universes, and one of the universes they have simulated is our own. Due to a triumph of advanced mathematics, they have invented a set of physical laws of tremendous complexity compared to their own, and these laws allow for atoms, chemistry, biology and life of a form very different from theirs. They follow our universe's evolution from Big Bang to Heat Death with fascination. Unbeknown to us, this is the basis for our existence. We are a simulation being run in a 2D CA universe with Conway's Life rules. Now, is this story inconceivable? Logically contradictory? I don't see how. The idea that only one real universe might exist, but that it could create any number of simulated ones, is pretty common. Of course it's more common to suppose that it's our universe which is the real one, but that's just parochialism. And what does it say about the physical properties which are necessary for computation? We have energy; Life has blinkiness (the degree to which cells are blinking on and off within a structure); neither property has a good analog in the other universe. Does the real universe win, in terms of deciding what properties are really needed for computation? I don't think so, because we could reverse the roles of the two universes and it wouldn't make any fundamental difference. Hal
Re: Is the universe computable
Dear Hal, Consider the last two paragraphs from one of Stephen Wolfram's papers: http://www.stephenwolfram.com/publications/articles/physics/85-undecidability/2/text.html *** Quantum and statistical mechanics involve sums over possibly infinite sets of configurations in systems. To derive finite formulas one must use finite specifications for these sets. But it may be undecidable whether two finite specifications yield equivalent configurations. So, for example, it is undecidable whether two finitely specified four-manifolds or solutions to the Einstein equations are equivalent (under coordinate reparametrization).[24] A theoretical model may be considered as a finite specification of the possible behavior of a system. One may ask for example whether the consequences of two models are identical in all circumstances, so that the models are equivalent. If the models involve computations more complicated than those that can be carried out by a computer with a fixed finite number of states (regular language), this question is in general undecidable. Similarly, it is undecidable what is the simplest such model that describes a given set of empirical data.[25] This paper has suggested that many physical systems are computationally irreducible, so that their own evolution is effectively the most efficient procedure for determining their future. As a consequence, many questions about these systems can be answered only by very lengthy or potentially infinite computations. But some questions answerable by simpler computations may still be formulated. *** It has been pointed out, by Roger Penrose himself (!), that the decidability problem for Einstein's equations is equivalent to Halting Problem of Turing Machines (pg. 337 of Shadows of the Mind). When we put these two arguments together, what do we get? See: http://arxiv.org/abs/quant-ph/0304128 ;-) Stephen - Original Message - From: Hal Finney [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Tuesday, January 20, 2004 7:18 PM Subject: Re: Is the universe computable CMR writes: Then question then becomes, I suppose, if in fact our universe is a digital one (if not strictly a CA) havng self-consistent emergent physics, then might it not follow that it is implemented (run?) via some extra-universal physical processes that only indirectly correspond to ours? This is a good point, and in fact we could sharpen the situation as follows. Suppose multiverse theory is bunk and none of Tegmark's four levels work. The universe isn't infinite in size; there is no inflation; the MWI is false; and all that stuff about Platonic existence is so much hot air. There is, in fact, only one universe. However, that universe isn't ours. It's a specific version of Conway's 2D Life universe, large but finite in size, with periodic edge conditions. Against all odds, life has evolved in Life and produced Self Aware Subsystems, i.e. observers. These beings have developed a civilization and built computers. See the link I supplied earlier, http://rendell.server.org.uk/gol/tm.htm for a sample of such a computer. On their computers they run simulations of other universes, and one of the universes they have simulated is our own. Due to a triumph of advanced mathematics, they have invented a set of physical laws of tremendous complexity compared to their own, and these laws allow for atoms, chemistry, biology and life of a form very different from theirs. They follow our universe's evolution from Big Bang to Heat Death with fascination. Unbeknown to us, this is the basis for our existence. We are a simulation being run in a 2D CA universe with Conway's Life rules. Now, is this story inconceivable? Logically contradictory? I don't see how. The idea that only one real universe might exist, but that it could create any number of simulated ones, is pretty common. Of course it's more common to suppose that it's our universe which is the real one, but that's just parochialism. And what does it say about the physical properties which are necessary for computation? We have energy; Life has blinkiness (the degree to which cells are blinking on and off within a structure); neither property has a good analog in the other universe. Does the real universe win, in terms of deciding what properties are really needed for computation? I don't think so, because we could reverse the roles of the two universes and it wouldn't make any fundamental difference. Hal
RE: Are conscious beings always fallible?
Even if we utilize a language with reflection capability, do we still have an underlying problem with different levels of mathematical truth as indicated by the question of whether 3+4 equals 7? When an expression contains a sub-expression, don't we expect to be able to replace that sub-expression by an equivalent one? But deciding whether two expressions are equivalent depends on a particular perspective of mathematical truth. Btw I thought Smalltalk was weakly typed (can throw a message at any object regardless of type) - David -Original Message- From: Bruno Marchal [mailto:[EMAIL PROTECTED] Sent: Tuesday, 20 January 2004 6:44 PM To: [EMAIL PROTECTED] Subject: Re: Are conscious beings always fallible? I agree with you. Actually you can use the second recursion theorem of Kleene to collapse all the orders. This is easier in an untyped programming language like (pure) LISP than in a typed language, although some typed language have a primitive for handling untyped self-reference, like the primitive SELF in Smalltalk ... Bruno At 23:29 19/01/04 -0800, Eric Hawthorne wrote: How would they ever know that I wonder? Well let's see. I'm conscious and I'm not fallible. Therefore ;-) David Barrett-Lennard wrote: I'm wondering whether the following demonstrates that a computer that can only generate thoughts which are sentences derivable from some underlying axioms (and therefore can only generate true thoughts) is unable to think. This is based on the fact that a formal system can't understand sentences written down within that formal system (forgive me if I've worded this badly). Somehow we would need to support free parameters within quoted expressions. Eg to specify the rule It is a good idea to simplify x+0 to x It is not clear that language reflection can be supported in a completely general way. If it can, does this eliminate the need for a meta- language? How does this relate to the claim above? - David I don't see the problem with representing logical meta-language, and meta-metalanguage... etc if necessary in a computer. It's a bit tricky to get the semantics to work out correctly, I think, but there's nothing extra-computational about doing higher-order theorem proving. http://www.cl.cam.ac.uk/Research/HVG/HOL/ This is an example of an interactive (i.e. partly human-steered) higher-order thereom prover. I think with enough work someone could get one of these kind of systems doing some useful higher-order logic reasoning on its own, for certain kinds of problem domains anyway. Eric
Modern Physical theory as a basis for Ethical and Existential Nihilism
I am writing my high school senior project term paper on defending ethical and existential nihilism based on quantum and multiverse theory. I was looking for any comments on the subject. Here I place my outline for said paper: --- A Scientific Basis for Ethical and Existential Nihilism I. Introduction A. Societal habit of classification of moral disciplines B. Difference of anyone to a possibly fitting classification makes such divvying impossible C. One must evaluate the individual sets of moral principles to establish their validity II. What is ethical?Establishing a Basis for Reference A. Definition of ethic/moral 1. Participation/contribution 2. Action 3. Earning B. Earning as an ethical point for reference 1. Earning governed by psychological history 2. Psychology influenced by the physical 3. The physical is governed by causality C. Ethic is debunked by the causal nature of space-time and quantum superpositioning III. Space-Time and Quantum Physics form a basis for inevitability A. The So-Called Relativity Theory Perspective 1. The space-time manifold is a substrate upon which things exist 2. The future condition of events or anything can be determined using equations to model energy and position over time 3. All things have a definite past, present, and future, ontologically 4. Limited by information acquisition a) speed of light b) infinitesimal spaces governed by quantum theory B. Quantum Physics Perspective 1. Heisenbergs Uncertainty Principle a) impossible to know ones future b) definite past 2. Schrödingers wave function a) Schrödingers Cat Paradox b) superposition of waves c) collapse of the wave function d) Copenhagen Interpretation (CHI) e) Hugh Everett IIIs theory that all possible resultant collapses can be defined by a superposition in Hilbert Space C. Multiverse TheoryMultiple Universes in which all possibilities are played out 1. There is a total number of possible arrangements of matter based on the limits of the entropy of space-time, where the total is equal to the permutation of particles and energies and dependent on the total number of particles 2. All these possibilities are superimposed upon one another to form an infinite-dimensional Hilbert Space in which the wave function resides, evolving over time a) Each universe is a subset, a space-time system in which one arrangement of matter exists b) One space-time event sequence is merely the use of time and physical law/rules to determine a valid progression of one universal space to another c) This creates multiple space-time pathways, each of which encompasses a version of the past, present, and future d) Each point has a past with possible futures to be determined upon collapse of the wave function e) Our own physical, present reality, interpreted as a resulting situation of the collapse, is one point in space-time with a sequence of probability states with the same past configuration f) This course of action leading to each possible reality yields multiple pathways from the beginning to the end of time g) Each point in time has nearly infinite future possibilities, but each path contains only itselfone path with two endpointsessentially arriving from the restraints of causality on the topological set IV. Philosophical Implications A. Every person has a definite past 1. Every person is the result of the path of space-time upon which its universes energy has traveled 2. Because of causality and entropy bounds, one has no control over the past 3. A future is simply the result of influences of the wave function and its probabilities on space-time B. A persons future is inevitable 1. No matter what decision one chooses, the psyches action is defined and controlled by the wave function in its space 2. All decisions, choices, and outcomes are predefined, if only in a superposition of probabilities 3. This leads to a lack of personal contribution on the part of the person. C. A person is not to be held accountable for what he/she cannot control 1. If a person cannot control the set of probabilities of the outcome, then are they really making a decision? a) Yes, they do define a pathway, b) But, there is no preference of one over the other physically, except what is determined by the probabilities defined by the wave function c) No one outcome is more likely then another with respect to its
RE: Is the universe computable
At 1/19/04, Hal Finney wrote: However, here is an alternate formulation of my argument which seems to be roughly equivalent and which avoids this objection: create a random program tape by flipping a coin for each bit. Now the probability that you created the first program above is 1/2^100, and for the second, 1/2^120, so the first program is 2^20 times more probable than the second. That's an interesting idea, but I don't know what to make of it. All it does is create a conflict of intuition which I don't know how to resolve. On the one hand, the following argument seems to make sense: consider an infinite sequence of random bits. The probability that the sequence begins with 1 is .5. The probability that it begins with 01 is .25. Therefore, in the uncountably infinite set of all possible infinite bit-strings, those that begin with 1 are twice as common as those that begin with 01. However, this is in direct conflict with the intuition which says that, since there are uncountably many infinite bit-strings that begin with 1, and uncountably many that begin with 01, the two types of strings are equally as common. How can we resolve this conflict? -- Kory
RE: Is the universe computable
Kory Heath wrote: At 1/19/04, Hal Finney wrote: However, here is an alternate formulation of my argument which seems to be roughly equivalent and which avoids this objection: create a random program tape by flipping a coin for each bit. Now the probability that you created the first program above is 1/2^100, and for the second, 1/2^120, so the first program is 2^20 times more probable than the second. That's an interesting idea, but I don't know what to make of it. All it does is create a conflict of intuition which I don't know how to resolve. On the one hand, the following argument seems to make sense: consider an infinite sequence of random bits. The probability that the sequence begins with 1 is .5. The probability that it begins with 01 is .25. Therefore, in the uncountably infinite set of all possible infinite bit-strings, those that begin with 1 are twice as common as those that begin with 01. However, this is in direct conflict with the intuition which says that, since there are uncountably many infinite bit-strings that begin with 1, and uncountably many that begin with 01, the two types of strings are equally as common. How can we resolve this conflict? -- Kory I haven't studied measure theory, but from reading definitions and seeing discussions my understanding is that it's about functions that assign real numbers to collections of subsets (defined by 'sigma algebras') of infinite sets. As applied to probability theory, it allows you to define a notion of probability on a set with an infinite number of members. Again, this would involve assigning probabilities to *subsets* of this infinite set, not to every member of the infinite set--for example, if you are dealing with the set of real numbers between 0 and 1, then although each individual real number could not have a finite probability (since this would not be compatible with the idea that the total probability must be 1), perhaps each finite nonzero interval (say, 0.5 - 0.8) would have a finite probability. In a similar way, if you were looking at the set of all possible infinite bit-strings, although each individual string might not get a probability, you might have a measure that can tell you the probability of getting a member of the subset strings beginning with 1 vs. the probability of getting a member of the subset strings beginning with 01. Some references on measure theory that may be helpful: http://en2.wikipedia.org/wiki/Measure_theory http://en2.wikipedia.org/wiki/Sigma_algebra http://en2.wikipedia.org/wiki/Probability_axioms http://mathworld.wolfram.com/Measure.html http://mathworld.wolfram.com/ProbabilityMeasure.html Jesse Mazer _ Learn how to choose, serve, and enjoy wine at Wine @ MSN. http://wine.msn.com/
Re: Modern Physical theory as a basis for Ethical and Existential Nihilism
Sorry. Can't help myself : Is there any point in completing that term paper really? On a few points. I don't believe in the point of view of nihilism because everything will happen in the multiverse, anyway, regardless of what I do.. My reasons are a little vague, but here's a stab at it: 1. I look at us group of human observer SAS's as results of and guardians of emerged complex order in our universe. In fact I believe our universe (its temporal arrow etc) is only observable because it is the set of paths through the multiverse that has all this emerged complex order in it.I believe these potentially observable sets of paths through the multiverse's general disorder are rare (of small measure.) 2. Somehow, all of us human observers are clearly in or observing the SAME set of paths through the multiverse. Now that is significant. It tells us that in the emergent-order paths of multiverse info-state evolution, that those paths are observable consistently to ANY observer that emerges as part of the emerged complex order present in those paths. 3. I see humans (or other intelligent lifeforms) as in some strange ways the smart-lookahead guardians of the particular piece of emergent-order their most a part of (their planet, their ecosystems, their societies, themselves).The reason we emerged (or are still here) is because we have helped make our emergent complex system successful (robust). 4. For some strange reason, I value the most complex yet elegant and robust emergent order (for itself). This is why for example, I'm an environmental activist in my spare (hah!) time. 5. I think if one values elegant, robust complex order, and if one is an active part of the elegant, robust, complex order, who emerged precisely so that a SAS of the emerged system could sense and make sense of the surroundings, and could model and influence the future, and guard the SAS's own existence and that of the whole emerged system of which it is a part, then guard away I say, actively, not nihilistically. Model your world. Predict its different possible futures, and use your emerged (and cultivated, same thing) wisdom to steer yourself, and your society, and your ecosystem, and your planet, away from harm and too-soon reduction to entropy. In the very, very end, it is said, entropy wins (like the house wins in Vegas.) But why not have as good a game as possible before it ends in a billion or trillions of years. 6. Of course, it doesn't make sense to try to protect (and advance in elegance) an emergent order that is indeed truly robust, does it? But my point back there was that we are supposed to be part of the emergent system's self-defense mechanism, because we can think and plan, and change things in our universe. 7. So can we change the multiverse as a whole? Probably not. But all that observers can ever co-observe is a single self-consistent universe in the multiverse. Look at earth and earthlife like a surfboard and surfer surfing this big coherent wave of informationally self-consistent order that is our universe. What we as the surfer can do is look ahead, and steer the board, and prolong the ride, and make it as amazing as possible before it tumbles into the vortex. That's enough control to say let's delay nihilism til the very last possible moment at least, shall we. Let's see where we might wash up if we keep riding well. Enough. Enough. This tortured analogy is killing me. 8. You may say that there's all these other virtual doppelganger surfers and surfboards (even on our same order-wave universe) so why bother steering anyway? One of us will make it. Yeah well I don't think so. I think all the emergent systems kind of compete with each other to organize things, and there's winners and losers, and the losers are all just info-noise. 8. I guess the above is premised on the supposition that we CAN steer. That we have any say over when and how our part of our universe degrades into entrop (info-noise.) This is really vague but I have some strange sense that what observing AGENT (actor) systems such as ourselves are doing is choosing (or having a part in choosing) the way in which their quantum world becomes their classical world. I think there's the possibility of free will there. It's like their steering the NOW wavefront itself (in their shared universe). If the possibly ordered paths through multiverse infospace near these observers are more than one possible path, maybe its the observers, by the sum total of their collective actions, that micro-manage the choice of future info-paths that will still be consistent with the path(s) their all on. Maybe the set of possible consistent and ordered paths is narrower and narrower as time goes on for them, but I think there are still choices to be made. It's possible that that's an illusion, but choice being an illusion is a concept for the theoretical meta-level, for OUTSIDE our universe path. Inside our path(s), our paths and the
Re: Modern Physical theory as a basis for Ethical and Existential Nihilism
Your conclusion that there is no scientific justification for morals of any sort, only that in the Darwinistic sense depends on the definition of scientific. Without morals an argument could be made that mankind would not exist - it would have self-destructed. Perhaps that is scientific justification for morals, at least as far as mankind is concerned. And perhaps our lack of morals will yet wipe us out through WMD, or other evil. Norman - Original Message - From: [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Tuesday, January 20, 2004 6:04 PM Subject: Modern Physical theory as a basis for Ethical and Existential Nihilism I am writing my high school senior project term paper on defending ethical and existential nihilism based on quantum and multiverse theory. I was looking for any comments on the subject. Here I place my outline for said paper: --- A Scientific Basis for Ethical and Existential Nihilism I. Introduction A. Societal habit of classification of moral disciplines B. Difference of anyone to a possibly fitting classification makes such divvying impossible C. One must evaluate the individual sets of moral principles to establish their validity II. What is ethical?-Establishing a Basis for Reference A. Definition of ethic/moral 1. Participation/contribution 2. Action 3. Earning B. Earning as an ethical point for reference 1. Earning governed by psychological history 2. Psychology influenced by the physical 3. The physical is governed by causality C. Ethic is debunked by the causal nature of space-time and quantum superpositioning III. Space-Time and Quantum Physics form a basis for inevitability A. The So-Called Relativity Theory Perspective 1. The space-time manifold is a substrate upon which things exist 2. The future condition of events or anything can be determined using equations to model energy and position over time 3. All things have a definite past, present, and future, ontologically 4. Limited by information acquisition a) speed of light b) infinitesimal spaces governed by quantum theory B. Quantum Physics Perspective 1. Heisenberg's Uncertainty Principle a) impossible to know one's future b) definite past 2. Schrödinger's wave function a) Schrödinger's Cat Paradox b) superposition of waves c) collapse of the wave function d) Copenhagen Interpretation (CHI) e) Hugh Everett III's theory that all possible resultant collapses can be defined by a superposition in Hilbert Space C. Multiverse Theory-Multiple Universes in which all possibilities are played out 1. There is a total number of possible arrangements of matter based on the limits of the entropy of space-time, where the total is equal to the permutation of particles and energies and dependent on the total number of particles 2. All these possibilities are superimposed upon one another to form an infinite-dimensional Hilbert Space in which the wave function resides, evolving over time a) Each universe is a subset, a space-time system in which one arrangement of matter exists b) One space-time event sequence is merely the use of time and physical law/rules to determine a valid progression of one universal space to another c) This creates multiple space-time pathways, each of which encompasses a version of the past, present, and future d) Each point has a past with possible futures to be determined upon collapse of the wave function e) Our own physical, present reality, interpreted as a resulting situation of the collapse, is one point in space-time with a sequence of probability states with the same past configuration f) This course of action leading to each possible reality yields multiple pathways from the beginning to the end of time g) Each point in time has nearly infinite future possibilities, but each path contains only itself-one path with two endpoints-essentially arriving from the restraints of causality on the topological set IV. Philosophical Implications A. Every person has a definite past 1. Every person is the result of the path of space-time upon which its universe's energy has traveled 2. Because of causality and entropy bounds, one has no control over the past 3. A future is simply the result of influences of the wave function and its probabilities on space-time B. A person's future is inevitable 1. No matter what decision one chooses, the psyche's action is defined and controlled by the wave function in its space 2. All
RE: Is the universe computable
Kory said... At 1/21/04, David Barrett-Lennard wrote: This allows us to say the probability that an integer is even is 0.5, or the probability that an integer is a perfect square is 0. But can't you use this same logic to show that the cardinality of the even integers is half that of the cardinality of the total set of integers? Or to show that there are twice as many odd integers as there are integers evenly divisible by four? In other words, how can we talk about probability without implicitly talking about the cardinality of a subset relative to the cardinality of one of its supersets? Saying that the probability that a given integer is even is 0.5 seems intuitively to me and can be made precise (see my last post). Clearly there is a weak relationship between cardinality and probability measures. Why does that matter? Why do you assume infinity / infinity = 1 , when the two infinities have the same cardinality? Division is only well defined on finite numbers. I'm not denying that your procedure works, in the sense of actually generating some number that a sequence of probabilities converges to. The question is, what does this number actually mean? I'm suspicious of the idea that the resulting number actually represents the probability we're looking for. Indeed, what possible sense can it make to say that the probability that an integer is a perfect square is *zero*? -- Kory For me, there *is* an intuitive reason why the probability that an integer is a perfect square is zero. It simply relates to the fact that the squares become ever more sparse, and in the limit they become so sparse that the chance of finding a perfect square approaches zero. - David
Re: [issues] Re: Is the universe computable
Calm, Steve, calm. :-) Remember my comment the other evening: It is the appropriate moment in human thought to change the definitions of 'objective' and 'subjective'. Implementation is the 'subjective'. Relationship need not be. In fact, relationship is necessarily -intangible-, but -is- the object of any search for 'the objective'. That 'relationship' is made explicit via implementation does not detract from its purity of specification .. its 'objectivity'. Nor is the objectivity of a 'relationship' diminished by the fact that relationship can only be explore, examined, or empirically specified, except via subjective 'instantiation'. These simultaneous aspects of reality/being are superposed with one another. Both present even as they are mutually distinguishable. This takes 'objectivity' to an independent level of identification, beyond any potential for anomaly, for variation; immune to perturbation and noise. It finally allows us to consiliently accomodate 'subjective' truths with objective basese. Objectivity is the intangible and uncorruptable 'relations', rules, and laws, of being and performance. Subjectivity is all the necessary examples and instantiations -by which- we can and do 'know' the 'relations', rules, and laws, of being and performance. Jamie Rose MetaScience Academy. Japan. Ceptual Institute. USA. Stephen Paul King wrote: Dear Hal, A theorem doesn't weigh anything, and neither does a computation. Nice try but that is a very smelly Red Herring. Even Conway's Life can not exist, even in the abstract sense, without some association with the possibility of being implemented and it is this Implementation that I am asking about. Let us consider Bruno's beloved Arithmetic Realism. Are we to believe that Arithmetic can be considered to exist without, even tacitly, assuming the possibility that numbers must be symbolic representable? If they can be, I strongly argue that we have merely found a very clever definition for the term meaninglessness. I beg you to go directly to Turing's original paper discussing what has become now know as a Turing Machine. You will find discussions of things like tape and read/write head. Even if these, obviously physical, entities are, as you say, by definition within a universe and that such universes can be rigorously proven to be mathematical entities, this only strengthens my case: An abstract entity must have a possibility of being physically represented, even if in a Harry Potter Universe, to be a meaningful entity. Otherwise what restrains us from endless Scholastic polemics about how many Angels can dance on the head of a Pin and other meaningless fantasies. The fact that an Algorithm is independent of any particular implementation is not reducible to the idea that Algorithms (or Numbers, or White Rabbits, etc.) can exist without some REAL resources being used in their implementation (and maybe some kind of thermodynamics). BTW, have you read Julian Barbour's The End of Time? It is my opinion that Julian's argument falls flat on its face because he is making the very same mistake: Assuming that his best-matching scheme can exists without addressing the obvious status that it is an NP-Complete problem of uncountable infinite size. It is simply logically impossible to say that the mere postulation of a Platonia allows for the a priori existence of the solution to such a computationally intractable problem. Kindest regards, Stephen - Original Message - From: Hal Finney [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Tuesday, January 20, 2004 1:39 PM Subject: Re: Is the universe computable At 13:19 19/01/04 -0500, Stephen Paul King wrote: Where and when is the consideration of the physical resources required for the computation going to obtain? Is my question equivalent to the old first cause question? Anything physical is by definition within a universe (by my definition, anyway!). What are the physical properties of a system in our universe? Mass, size, energy, electrical charge, partical composition, etc. If we at least hypothetically allow for the existence of other universes, wouldn't you agree that they might have completely different physical properties? That they might not have mass, or charge, or size; or that these properties would vary in some bizarre way much different from how stable they are in our universe. Consider Conway's 2-dimensional Cellular Automota universe called Life. Take a look at http://rendell.server.org.uk/gol/tm.htm, an amazing implementation of a computer, a Turing Machine, in this universe. I spent a couple of hours yesterday looking at this thing, seeing how the parts work. He did an incredible job in putting all the details together to make this contraption work. So we can have computers in the Life universe. Now consider this: what is the mass of this computer?
Re: Is the universe computable?
Think of it this way, what is the cardinality of the equivalence class of representations R of, say, a 1972 Jaguar XKE, varying over *all possible languages* and *symbol systems*? I think it is at least equal to the Reals. Is this correct? If R has more than one member, how can we coherently argue that information is physical in the material monist sense? Assuming you mean R is countably infinite(?), then a solution would be a finite universe of underlying discrete structure, ala Fredkin, I imagine. What if the informing and constraining (?) is done, inter alia, by the systems that use up the universal resources? What if, instead of thinking in terms of a priori existing solutions, ala Platonia, if we entertain the idea that the *solutions are being computation in an ongoing way* and that what we experience is just one (of many)stream(s) of this computation. Such a computation would require potentially infinite physical resources... Would it be to much to assume that all we need to assume is that the resources (for Qcomputations, these are Hilbert space dimensions) are all that we have to assume exists a priori? Does not Quantum Mechanics already have such build in? Yes, this would indeed follow. But what of a view of QM itself emerging form qubits? as, for instance, expressed in the so-called Bekenstein bound: the entropy of any region of space cannot exceed a fixed constant times the surface area of the region. This suggests that the complete state space of any spatially finite quantum system is finite, so that it would contain only a finite number of independent qubits.
Re: Is the universe computable
And what does it say about the physical properties which are necessary for computation? We have energy; Life has blinkiness (the degree to which cells are blinking on and off within a structure); neither property has a good analog in the other universe. Does the real universe win, in terms of deciding what properties are really needed for computation? I don't think so, because we could reverse the roles of the two universes and it wouldn't make any fundamental difference. Yes! you've captured the gist and fleshed out the raw concept that hit me whilst reading your post on weightless computation; that's potentially the value of it as an avenue to explore, I think: that there is an equivalence/symmetry/correspondence by which the universe's map to one another but it's not direct(?) is it a form of information conveyance? hmmm.. Reference time...
