Torture yet again
Sorry, I can't let go of this one. I'm trying to understand it psychologically. Here's another thought experiment which is roughly equivalent to our original scenario. You are sitting in a room, with a not very nice man. He gives you two options. 1) He'll toss a coin. Heads he tortures you, tails he doesn't. 2) He's going to start torturing you a minute from now. In the meantime, he shows you a button. If you press it, you will get scanned, and a copy of you will be created in a distant town. You've got a minute to press that button as often as you can, and then you are getting tortured. What are you going to choose (Stathis and Bruno)? Are you *really* going to choose (2), and start pressing that button frantically? Do you really think it will make any difference? I'm just imagining having pressed that button a hundred times. Each time I press it, nothing seems to happen. Meanwhile, the torturer is making his knife nice and dull, and his smile grows ever wider. Cr^%^p, I'm definitely choosing (1). Ok, sure, each time I press it, I also step out of a booth in Moscow, relieved to be pain-free (shortly to be followed by a second me, then a third, each one successively more relieved.) But I'm still choosing (1). Now, the funny thing is, if you replace torture by getting shot in the head, then I will pick (2). That's interesting, isn't it? Jonathan Colvin
Re: Torture yet again
On Tue, Jun 21, 2005 at 04:05:02AM -0700, Jonathan Colvin wrote: Now, the funny thing is, if you replace torture by getting shot in the head, then I will pick (2). That's interesting, isn't it? Why is that interesting? It's indistinguishable from a teleportation scenario. -- Eugen* Leitl a href=http://leitl.org;leitl/a __ ICBM: 48.07100, 11.36820http://www.leitl.org 8B29F6BE: 099D 78BA 2FD3 B014 B08A 7779 75B0 2443 8B29 F6BE signature.asc Description: Digital signature
Re: What is an observer moment?
Le 21-juin-05, à 05:33, George Levy a écrit : x-tad-bigger An interesting thought is that a psychological first person can surf simultaneously through a large number of physical OMs /x-tad-bigger With comp, we should say that the first person MUST surf simultaneously through an INFINITY of third person OMs. (I would not use the term physical at all, because at this stage it is not defined. But with the negation of comp + assumption of slightly incorrect QM what you say seems to me plausible.) Bruno http://iridia.ulb.ac.be/~marchal/
Re: death
Bruno Marchal wrote: Then in another post you just say: It's a bit hard for me to come up with a satisfactory answer to this problem, because I don't start from the assumption of a physical universe at all--like Bruno, I'm trying to start from a measure on observer-moments and hope that somehow the appearance of a physical universe can be recovered from the subjective probabilities experienced by observers And this answers the question. That was actually me who wrote that, not Hal Finney. But in reply to that comment, Hal wrote: I have a similar perspective. However I think it will turn out that the simplest mathematical description of an observer-moment will involve a Big Bang. That is, describe a universe, describe natural laws, and let the OM evolve. This is the foundation for saying that the universe is real. Jesse
Re: death
Bruno Marchal writes: Le 20-juin-05, =E0 18:16, Hal Finney a =E9crit : That's true, from the pure OM perspective death doesn't make sense because OMs are timeless. I was trying to phrase things in terms of the observer model in my reply to Stathis. An OM wants to preserve the measure of the observer that it is part of, due to the effects of evolution. Decreases in that measure would be the meaning of death, in the context of the multiverse. I will keep reading your posts hoping to make sense of it. Still I was=20= about asking you if you were assuming the multiverse context or if=20 you were hoping to extract (like me) the multiverse itself from the=20 OMs. In which case, the current answer seems still rather hard to=20 follow. I was trying to use Stathis' terminology when I wrote about the probability of dying. Actually I am now trying to use the ASSA and I don't have a very good idea about what it means to specify a subjective next moment. I think ultimately it is up to each OM as to what it views as its predecessor moments, and perhaps which ones it might like to consider its successor moments. Among the problems: substantial, short-term mental changes might be so great that the past OM would not consider the future OM to be the same person. This sometimes even happens with our biological bodies. I can easily create thought experiments that bend the connections beyond the breaking poing. There appears to be no bright line between the degree to which a past and future OM can be said to be the same person, even if we could query the OM's in question. Another problem: increases in measure from a past OM to a future OM. We can deal with decreases in measure by the traditional method of expected probability. But increases in measure appear to require probability 1. That doesn't make sense, again causing me to question the whole idea of a subjective probability distribution over possible next moments. Then in another post you just say: It's a bit hard for me to come up with a satisfactory answer to this=20= problem, because I don't start from the assumption of a physical=20 universe at all--like Bruno, I'm trying to start from a measure on=20 observer-moments and hope that somehow the appearance of a physical=20 universe can be recovered from the subjective probabilities=20 experienced by observers Actually I didn't write this, Jesse Mazer did. But I do largely agree with this approach, and I wrote the reply: I have a similar perspective. However I think it will turn out that the simplest mathematical description of an observer-moment will involve a Big Bang. That is, describe a universe, describe natural laws, and let the OM evolve. This is the foundation for saying that the universe is real. And this answers the question. I am glad of your interest in the=20 possibility to explain the universe from OMs, but then, as I said I=20 don't understand how an OM could change its measure. What is clear for=20= me is that an OM (or preferably a 1-person, an OM being some piece of=20 the 1-person) can change its *relative* measure (by decision, choice,=20 will, etc.) of its possible next OMs. The OM can change the universe, and this will include changing the measure of many people's future OMs. Wei Dai, in whose footsteps I largely travel, finally decided that *any* philosophy for an OM was acceptable, and its only task was to optimize the multiverse to suit its preferences. This does not require that we introduce a subjective probability for measure of next OM, but it can allow OMs to think that way. If the current OM has an interest in certain OMs, the ones it chooses to call its next OMs, and it wants to adjust the relative measure of those OMs to suit its tastes, that can be accommodated in this very general model. Hal Finney
Re: Torture yet again
Jonathan Colvin writes: You are sitting in a room, with a not very nice man. He gives you two options. 1) He'll toss a coin. Heads he tortures you, tails he doesn't. 2) He's going to start torturing you a minute from now. In the meantime, he shows you a button. If you press it, you will get scanned, and a copy of you will be created in a distant town. You've got a minute to press that button as often as you can, and then you are getting tortured. I understand that you are trying to challenge this notion of subjective probability with copies. I agree that it is problematic. IMO it is different to make a copy than to flip a coin - different operationally, and different philosophically. What you need to do is to back down from subjective probabilities and just ask it like this: which do you like better, a universe where there is one of you who has a 50-50 chance of being tortured; or a universe where there are a whole lot of you and one of them will be tortured? Try not to think about which one you will be. You will be all of them. Think instead about the longer term: which universe will best serve your needs and desires? There is an inherent inconsistency in this kind of thought experiment if it implicitly assumes that copying technology is cheap, easy and widely available, and that copies have good lives. If that were the case, everyone would use it until there were so many copies that these properties would no longer be true. It is important in such experiments to set up the social background in which the copies will exist. What will their lives be like, good or bad? If copies have good lives, then copying is normally unavailable. In that case, the chance to make copies in this experiment may be a once-in-a-lifetime opportunity. That might well make you be willing to accept torture of a person you view as a future self, in exchange for the opportunity to so greatly increase your measure. OTOH if copying is common and most people don't do it because the future copies will be penniless and starve to death, then making copies in this experiment is of little value and you would not accept the greater chance of torture. This analysis is all based on the assumption that copies increase measure, and that in such a world, observers will be trained that increasing measure is good, just as our genes quickly learned that lesson in a world where they can be copied. Hal Finney
Re: another puzzzle
Stathis wrote:To summarise my position, it is this: the measure of an observer moment is relevant when a given observer is contemplating what will happen next... Now, minimising acronym use, could you explain what your understanding is of how measure changes with number of copies of an OM which are instantiated, and if it doesn't, then how does it change, and when you use it in calculating how someone's life will go from OM to OM.
Jesse wrote: Well, see my last response to Hal Finney... The measure on the set of all unique observer-moments is really the fundamental thing, physical notions like "number of copies" are secondary. But I have speculated on the "anticipatory" idea where multiple copies affects your conditional probabilities to the extend that the copies are likely to diverge in the future; so in your example, as long as those 10^100 copies are running in isolated virtual environments and following completely deterministic rules, they won't diverge, so my speculation is that the absolute and relative measures would not be affected in any way by this... There is the question of what it is, exactly, that's supposed to be moving between OMs, and whether this introduces some sort of fundamental duality into my picture of reality...
Soif the copies are completely synchronized, this puzzle is a no-brainer (easy). But what about if one of the neurons in one of the copies does a little jig of its own for second?
More in general, I'm doubting the legitimacy of the puzzle in the first place: If, in your theory, measure really corresponds to the probability of having a next observer moment, and then you bring God into the picture and have him totally mess up the probabilities by doing what he wants, how are you going to conclude anything meaningful as a continuation of your definition of measure? The flip side of the coin is that apparently the probability of having a next OM is 100% ("everything exists"). In this theory, no matter what God does with 10^100 copies, there are 10^100^n other identical next OMs out there to replace them.It seems like what I've seen so far on this listis an exercise in forgetting that "everything exists" for a moment to do a thought experimentto conclude more about "everything exists".
Tom Caylor
Re: Torture yet again
Le 21-juin-05, à 13:05, Jonathan Colvin a écrit : Sorry, I can't let go of this one. I'm trying to understand it psychologically. Here's another thought experiment which is roughly equivalent to our original scenario. You are sitting in a room, with a not very nice man. He gives you two options. 1) He'll toss a coin. Heads he tortures you, tails he doesn't. 2) He's going to start torturing you a minute from now. In the meantime, he shows you a button. If you press it, you will get scanned, and a copy of you will be created in a distant town. You've got a minute to press that button as often as you can, and then you are getting tortured. What are you going to choose (Stathis and Bruno)? Are you *really* going to choose (2), and start pressing that button frantically? Do you really think it will make any difference? I will choose 2, and most probably start pressing the button frantically. Let us imagine that I press on the button 64 times. The one who will be tortured is rather unlucky, he has 1/2^64 chance to stay in front of you. He will probably even infer the falsity of comp, but then you will kill him! The 63 other brunos will infer comp is true, and send 63 more arguments for it to the list, including the argument based on having survive your experiment! OK with the number? Bruno http://iridia.ulb.ac.be/~marchal/
Re: Conscious descriptions
Le 21-juin-05, à 12:28, Russell Standish a écrit : On Mon, Jun 20, 2005 at 11:40:03AM +0200, Bruno Marchal wrote: Le 17-juin-05, ? 07:19, Russell Standish a ?crit : Hmm - this is really a definition of a universal machine. That such a machine exists is a theorem. Neither depend on the Church-Turing thesis, which says that any effective computation can be done using a Turing machine (or recursive function, or equivalent). Of course the latter statement can be considered a definition, or a formalisation, of the term effective computation. Hmm - I disagree. Once you give a definition of what a turing machine is, or of what a program fortran is, then it is a theorem that universal turing machine exists and that universal fortran program exists. To say that a universal machine exists, computing by definition *all* computable function, without any turing or fortran qualification, you need Church thesis. Bruno http://iridia.ulb.ac.be/~marchal/ From Li Vitanyi: Church's thesis: The class of algorithmically computable numerical functions (in the intuitive sense) coincides with the class of partial recursive functions OK. Turing's thesis: Any process that can be naturally called an effective procedure is realized by a Turing machine. Not OK. Please give me the page. Both of these are really a definition of what it means call an algorithm effective. By who? Effective has more than one meaning in logic. Theorem: the class of Turing machines corresponds to to the class of partial recursive functions. Consequently, both theses are equivalent. OK. Theorem: The class of Fortran machines corresponds to the class of Turing machines. OK. (I don't think this is proved in Li Vitanyi, but I'm sure it is proved somewhere. It is clearly not a consequence of the Church-Turing thesis). It depends of the context, but you can prove it without Church's thesis. Theorem: There exist formalisable processes that aren't simulable by Turing machines. Such processes are called hypermachines. See Toby Ord, math.LO/0209332 It is an obvious consequence of Church's thesis. See the diagonalisation posts in my url. Conjecture: All physical processes can be simulated by a Turing machine. I suspect this is false, and point to beta decay as a possible counter example. OK. I even pretend it is provably false with comp. You cannot simulate a priori all 1-person continuations generated by the UD in one stroke, as the first person lives it from his point of view given that the first person is unaware of the number of steps the UD computes to get at it, in its dovetailing way. Conjecture: All harnessable physical processes can be simulated by a Turing machine. By harnessable, we mean exploited for performing some computation. I suspect this is true. I don't understand. Machines with random oracles with computable means only compute the same class of functions as do Turing machines. (classic result by de Leeuw et al. in 1956) OK. Without computable means: random oracle makes them more powerfull. (Kurtz and Smith). So, no I don't think the Turing thesis is needed for a universal machine. I still disagree. I will say more but I have a meeting now. Bruno http://iridia.ulb.ac.be/~marchal/
Re: Dualism and the DA
On Jun 20, 2005, at 10:44 AM, Hal Finney wrote:Pete Carlton writes: snip-- we don't need to posit any kind of dualism to paper over it, we just have to revise our concept of "I". Hal Finney wrote:Copies seem a little more problematic. We're pretty cavalier aboutcreating and destroying them in our thought experiments, but the socialimplications of copies are enormous and I suspect that people's viewsabout the nature of copying would not be as simple as we sometimes assume.I doubt that many people would be indifferent between the choice ofhaving a 50-50 chance of being teleported to Moscow or Washington, vshaving copies made which wake up in both cities. The practical effectswould be enormously different. And as I wrote before, I suspect thatthese practical differences are not to be swept under the rug, but pointto fundamental metaphysical differences between the two situations.I think the practical differences are large, as you say, but I disagree that it points to a fundamental metaphysical difference. I think what appears to be a metaphysical difference is just the breakdown of our folk concept of "I". Imagine a primitive person who didn't understand the physics of fire, seeing two candles lit from a single one, then the first one extinguished - they may be tempted to conclude that the first flame has now become two flames. Well, this is no problem because flames never say things like "I would like to keep burning" or "I wonder what my next experience would be". We, however, do say these things. But does this bit of behavior (including the neural activity that causes it) make us different in a relevant way? And if so, how?This breakdown of "I" is very interesting. Since there's lots of talk about torture here, let's take this extremely simple example: Smith is going to torture someone, one hour from now. You may try to take steps to prevent it. How much effort you are willing to put in depends, among other things, on the identity of the person Smith is going to torture. In particular, you will be very highly motivated if that person is you; or rather, the person you will be one hour from now. The reason for the high motivation is that you have strong desires for that person to continue their life unabated, and those desires hinge on the outcome of the torture. But my point is that your strong desires for your own survival are just a special case of desires for a given person's survival - in other words, you are already taking a third-person point of view to your (future) self. You know that if the person is killed during torture, they will not continue their life; if they survive it, their life will still be negatively impacted, and your desires for the person's future are thwarted.Now, if you introduce copies to this scenario, it does not seem to me that anything changes fundamentally. Your choice on what kind of scenario to accept will still hinge on your desires for the future of any persons involved. The desires themselves may be very complicated, and in fact will depend on lots of hitherto unspecified details such as the legal status, ownership rights, etc., of copies. Of course one copy will say "I pushed the button and then I got tortured", and the other copy will say "I pushed the button and woke up on the beach" - which is exactly what we would expect these two people to say. And they're both right, insofar as they're giving an accurate report of their memories. What is the metaphysical issue here?
Re: Measure, Doomsday argument
Le Lundi 20 Juin 2005 23:12, Hal Finney a écrit : The empirical question presents itself like this. Very simple universes (such as empty universes, or ones made up of simple repeating patterns) would have no life at all. Perhaps sufficiently complex ones would be full of life. So as we move up the scale from simple to complex, at some point we reach universes that just barely allow for advanced life to evolve, and even then it doesn't last very long. The question is, as we move through this transition region from nonliving universes, to just-barely-living ones, to highly-living ones, how long is the transition region? That is, how much more complex is a universe that will be full of life, compared to one which just barely allows for life? We don't know the answer to that, but in principle it can be learned, through study and perhaps experimental simulations. If it takes only a bit more complexity to go from a just-barely-living universe to a highly-living one, then we have a puzzle. Why aren't we in one of the super-living universes, when their complexity penalty is so low? Beside this. I just think about this : Why aren't we blind ? :-) If the measure of an OM come from the information complexity of it, it seems that an OM of a blind person need less information content because there is no complex description of the outside world available to the blind observer. So as they are less complex, they must have an higher measure ... but I'm not blind, so as a lot of people on earth... Quentin
Re: Conscious descriptions
On Tue, Jun 21, 2005 at 07:43:49PM +0200, Bruno Marchal wrote: Turing's thesis: Any process that can be naturally called an effective procedure is realized by a Turing machine. Not OK. Please give me the page. 2nd edition, page 24, about 1/3 of the way down the page. Both of these are really a definition of what it means call an algorithm effective. By who? Effective has more than one meaning in logic. I think it was by Turing actually. Its been a while since I read the original article though, so I'm not certain. Conjecture: All harnessable physical processes can be simulated by a Turing machine. By harnessable, we mean exploited for performing some computation. I suspect this is true. I don't understand. Again these are intuitive concepts. I would interpret this as saying that we can perform the same computation as any physical process, even if we cannot simulate the process itself (ie the process may do something more than computation). Machines with random oracles with computable means only compute the same class of functions as do Turing machines. (classic result by de Leeuw et al. in 1956) OK. Without computable means: random oracle makes them more powerfull. (Kurtz and Smith). Do you have a reference? Li Vitanyi appear to be unaware of this result. So, no I don't think the Turing thesis is needed for a universal machine. I still disagree. I will say more but I have a meeting now. I look forward to that. Bruno http://iridia.ulb.ac.be/~marchal/ -- *PS: A number of people ask me about the attachment to my email, which is of type application/pgp-signature. Don't worry, it is not a virus. It is an electronic signature, that may be used to verify this email came from me if you have PGP or GPG installed. Otherwise, you may safely ignore this attachment. A/Prof Russell Standish Phone 8308 3119 (mobile) Mathematics0425 253119 () UNSW SYDNEY 2052 [EMAIL PROTECTED] Australiahttp://parallel.hpc.unsw.edu.au/rks International prefix +612, Interstate prefix 02 pgpzjyqsPxc9i.pgp Description: PGP signature
Re: Doomsday and computational irreducibility
On Tue, Jun 21, 2005 at 03:25:21AM -0700, Jonathan Colvin wrote: A new (at least I think it is new) objection to the DA just occurred to me (googling computational + irreducibility +doomsday came up blank). This objection (unfortunately) requires a few assumptions: 1) No block universe (ie. the universe is a process). 2) Wolframian computational irreducibility ((2) may be a consequence of (1) under certain other assumptions) Actually, I think that 2) is incompatible with 1). A computational process is deterministic, therefore can be replaced by a block representation. 3) No backwards causation. The key argument is that by 1) and 2), at time T, the state of the universe at time T+x is in principle un-knowable, even to the universe itself. Thus, at this time T (now), nothing, even the universe itself, can know whether the human race will stop tomorrow, or continue for another billion years. In any case, computational irreducibility does not imply that the the state of the universe at T+x is unknowable. In loose terms, computational irreducibility say that no matter what model of the universe you have that is simpler to compute than the real thing, your predictions will ultimately fail to track the universe's behaviour after a finite amount of time. Of course up until that finite time, the universe is highly predictable :) The question is, can we patch up this criticism? What if the universe were completely indeterministic, with no causal dependence from one time step to the next? I think this will expose a few hidden assumptions in the DA: 1) I think the DA requires that the population curve is continuous in some sense (given that it is a function from R-N, it cannot be strictly continuous). Perhaps the notion of bounded variation does the trick. My knowledge is bit patchy here, as I never studied Lebesgue integration, but I think bounded variation is sufficient to guarantee existence of the integral of the population curve. 2) The usual DA requires that the integral of the population curve from -\infty to \infty be finite. I believe this can be extended to certain case where the integral is infinite, however I haven't really given this too much thought. But I don't think anyone else has either... 3) I have reason to believe (hinted at in my Why Occam's razor paper) that the measure for the population curve is actually complex when you take the full Multiverse into account. If you thought the DA on unbounded populations was bad - just wait for the complex case. My brain has already short-circuited at the prospect :) In any case, whatever the conditions really turn out to be, there has to be some causal structure linking now with the future. Consequently, this argument would appear to fail. (But interesting argument anyway, if it helps to clarify the assumptions of the DA). -- *PS: A number of people ask me about the attachment to my email, which is of type application/pgp-signature. Don't worry, it is not a virus. It is an electronic signature, that may be used to verify this email came from me if you have PGP or GPG installed. Otherwise, you may safely ignore this attachment. A/Prof Russell Standish Phone 8308 3119 (mobile) Mathematics0425 253119 () UNSW SYDNEY 2052 [EMAIL PROTECTED] Australiahttp://parallel.hpc.unsw.edu.au/rks International prefix +612, Interstate prefix 02 pgp3uz9vGiA4N.pgp Description: PGP signature
Re: Measure, Doomsday argument
The answer is probably something along the lines of: OM with lots of sighted observers (as well as the odd blind one) will have lower complexity than OMs containing only blind observers (since the latter do not seem all that probable from an evolutionary point of view). Given there are so many sighted observers around, then it is not surprising if we're sighted. This argument is a variation of the argument for why we find so many observers in our world, rather than being alone in the universe, and is similar to why we expect the universe to be so big and old. Of course this argument contains a whole raft of ill-formed assumptions, so I'm expecting Jonathin Colvin to be warming up his keyboard for a critical response! Cheers. On Tue, Jun 21, 2005 at 10:56:48PM +0200, Quentin Anciaux wrote: Beside this. I just think about this : Why aren't we blind ? :-) If the measure of an OM come from the information complexity of it, it seems that an OM of a blind person need less information content because there is no complex description of the outside world available to the blind observer. So as they are less complex, they must have an higher measure ... but I'm not blind, so as a lot of people on earth... Quentin -- *PS: A number of people ask me about the attachment to my email, which is of type application/pgp-signature. Don't worry, it is not a virus. It is an electronic signature, that may be used to verify this email came from me if you have PGP or GPG installed. Otherwise, you may safely ignore this attachment. A/Prof Russell Standish Phone 8308 3119 (mobile) Mathematics0425 253119 () UNSW SYDNEY 2052 [EMAIL PROTECTED] Australiahttp://parallel.hpc.unsw.edu.au/rks International prefix +612, Interstate prefix 02 pgpPnVEqKU4qp.pgp Description: PGP signature
Re: Measure, Doomsday argument
Quentin Anciaux writes: Why aren't we blind ? :-) If the measure of an OM come from the information complexity of it, it seems that an OM of a blind person need less information content because there is no complex description of the outside world available to the blind observer. So as they are less complex, they must have an higher measure ... but I'm not blind, so as a lot of people on earth... There may be something of a puzzle there... Although I think specifically that blind people don't necessarily have a lower information content in their mental states. It is said that blind people have their other sense become more acute to take over the unused brain capacity (at least people blind from birth). So their mental states may take just as much information as sighted people. Beyond that, the puzzle remains as to why we are as complex as we are, why we are not simpler beings. It would seem that one could imagine conscious beings who would count as observers, as people we might have been, but who would have simpler minds and senses than ours. Certainly the higher animals show signs of consciousness, and their brains are generally smaller than humans, especially the cortex, hence probably with lower information content. Of course there are a lot more people than other reasonably large-brained animals, so perhaps our sheer numbers cancel any penalty due to our larger and more-complex brains. Hal Finney
Re: Measure, Doomsday argument
On Tue, Jun 21, 2005 at 06:13:53PM -0700, Hal Finney wrote: Quentin Anciaux writes: Why aren't we blind ? :-) If the measure of an OM come from the information complexity of it, it seems that an OM of a blind person need less information content because there is no complex description of the outside world available to the blind observer. So as they are less complex, they must have an higher measure ... but I'm not blind, so as a lot of people on earth... There may be something of a puzzle there... Although I think specifically that blind people don't necessarily have a lower information content in their mental states. It is said that blind people have their other sense become more acute to take over the unused brain capacity (at least people blind from birth). So their mental states may take just as much information as sighted people. Beyond that, the puzzle remains as to why we are as complex as we are, why we are not simpler beings. It would seem that one could imagine conscious beings who would count as observers, as people we might have been, but who would have simpler minds and senses than ours. Certainly the higher animals show signs of consciousness, and their brains are generally smaller than humans, especially the cortex, hence probably with lower information content. Of course there are a lot more people than other reasonably large-brained animals, so perhaps our sheer numbers cancel any penalty due to our larger and more-complex brains. Hal Finney I take from this argument that the Anthropic Principle is a necessary requirement on conscious experience. In other words - self-awareness is a requirement. I cannot say why this should be so, as we do not have an acceptable theory of consciousnes, only that it must be so, otherwise we would expect to live in a too simple environment. And this is an interesting constraint on acceptable theories of consciousness. Cheers PS: only a few species have been shown to be self-aware: Homo Sapiens (older than 18 months), both Chimpanzees, one of the Gibbons (IIRC) and some species of Dolphin. Naturally, I'd expect a few more to come to light, but self-awareness does appear to be rare in the animal kingdom. Of course homo sapiens outnumbers all these species by many orders of magnitude. -- *PS: A number of people ask me about the attachment to my email, which is of type application/pgp-signature. Don't worry, it is not a virus. It is an electronic signature, that may be used to verify this email came from me if you have PGP or GPG installed. Otherwise, you may safely ignore this attachment. A/Prof Russell Standish Phone 8308 3119 (mobile) Mathematics0425 253119 () UNSW SYDNEY 2052 [EMAIL PROTECTED] Australiahttp://parallel.hpc.unsw.edu.au/rks International prefix +612, Interstate prefix 02 pgp3mLF0FpoKW.pgp Description: PGP signature
RE: Doomsday and computational irreducibility
Russell Standish wrote: A new (at least I think it is new) objection to the DA just occurred to me (googling computational + irreducibility +doomsday came up blank). This objection (unfortunately) requires a few assumptions: 1) No block universe (ie. the universe is a process). 2) Wolframian computational irreducibility ((2) may be a consequence of (1) under certain other assumptions) Actually, I think that 2) is incompatible with 1). A computational process is deterministic, therefore can be replaced by a block representation. Are you familiar with Wolframian CI systems? The idea of CI is that while the system evolves deterministically, it is impossible (even in principle) to determine or predict the outcome without actually performing the iterations. I'm not at all sure that the idea of block representation works in this case. 3) No backwards causation. The key argument is that by 1) and 2), at time T, the state of the universe at time T+x is in principle un-knowable, even to the universe itself. Thus, at this time T (now), nothing, even the universe itself, can know whether the human race will stop tomorrow, or continue for another billion years. In any case, computational irreducibility does not imply that the the state of the universe at T+x is unknowable. In loose terms, computational irreducibility say that no matter what model of the universe you have that is simpler to compute than the real thing, your predictions will ultimately fail to track the universe's behaviour after a finite amount of time. Of course up until that finite time, the universe is highly predictable :) I'm thinking of Wolframian CI. There seem to be no short-cuts under that assumption (ie. No simpler model possible). The question is, can we patch up this criticism? What if the universe were completely indeterministic, with no causal dependence from one time step to the next? I think this will expose a few hidden assumptions in the DA: 1) I think the DA requires that the population curve is continuous in some sense (given that it is a function from R-N, it cannot be strictly continuous). Perhaps the notion of bounded variation does the trick. My knowledge is bit patchy here, as I never studied Lebesgue integration, but I think bounded variation is sufficient to guarantee existence of the integral of the population curve. 2) The usual DA requires that the integral of the population curve from -\infty to \infty be finite. I believe this can be extended to certain case where the integral is infinite, however I haven't really given this too much thought. But I don't think anyone else has either... 3) I have reason to believe (hinted at in my Why Occam's razor paper) that the measure for the population curve is actually complex when you take the full Multiverse into account. If you thought the DA on unbounded populations was bad - just wait for the complex case. My brain has already short-circuited at the prospect :) In any case, whatever the conditions really turn out to be, there has to be some causal structure linking now with the future. Consequently, this argument would appear to fail. (But interesting argument anyway, if it helps to clarify the assumptions of the DA). I don't see that causal structure is key. My understanding of the standard DA is that the system (universe) itself has knowledge of its future that the observer lacks (sort of bird's eye vs. frog's eye situation), which avoids the reverse -causation problem. Wolframian CI seems like it might be problematic for that account. Jonathan Colvin
RE: Measure, Doomsday argument
Russell Standish wrote: This argument is a variation of the argument for why we find so many observers in our world, rather than being alone in the universe, and is similar to why we expect the universe to be so big and old. Of course this argument contains a whole raft of ill-formed assumptions, so I'm expecting Jonathin Colvin to be warming up his keyboard for a critical response! Ok, if you insist :) I think the above are two disparate arguments. It is simpler by Occam to assume that there should be many observers rather than only one (similar argument to favouring the multiverse over only one big-bang). Once you admit the possibility of one observer, it takes extra argument to say why there should be *only* one. But we expect the universe to be old for cosmological reasons (takes stars a long time to cook up the needed elements, observer take a long time to evolve). Simplicity does not seem to be a factor here. A big universe does not seem much simpler either. Jonathan Colvin
Re: Doomsday and computational irreducibility
On Tue, Jun 21, 2005 at 09:06:22PM -0700, Jonathan Colvin wrote: Russell Standish wrote: Are you familiar with Wolframian CI systems? Yes of course. Wolfram did not invent the term. The idea of CI is that while the system evolves deterministically, it is impossible (even in principle) to determine or predict the outcome without actually performing the iterations. I'm not at all sure that the idea of block representation works in this case. Easy. Run your computer simulation for an infinite time, and save the output. There is your block representation. Computational irreducibility has nothing to do with whether the block representation is possible - only indeterminism. And even then, if you include all the counterfactuals, a block representation is possible too. In any case, computational irreducibility does not imply that the the state of the universe at T+x is unknowable. In loose terms, computational irreducibility say that no matter what model of the universe you have that is simpler to compute than the real thing, your predictions will ultimately fail to track the universe's behaviour after a finite amount of time. Of course up until that finite time, the universe is highly predictable :) I'm thinking of Wolframian CI. There seem to be no short-cuts under that assumption (ie. No simpler model possible). There are always simpler models. CI implies that no simpler model remains accurate in the long run. But in the short term it is entirely possible. An example: Conways Game of Life is a computationally irreducible system. Yet you can predict the motion of a glider most accurately while it is in free space. Only when it runs into some other configuration of blocks does it become unpredictable. In any case, whatever the conditions really turn out to be, there has to be some causal structure linking now with the future. Consequently, this argument would appear to fail. (But interesting argument anyway, if it helps to clarify the assumptions of the DA). I don't see that causal structure is key. My understanding of the standard DA is that the system (universe) itself has knowledge of its future that the observer lacks (sort of bird's eye vs. frog's eye situation), which avoids the reverse -causation problem. I've never thought of the DA in that way, but it might be valid. Analytic functions have the property that all information about what that function does everywhere is contained within the derivatives all evaluated at one point. Whilst I don't expect population curves to be analytic, I am saying the DA probably implicitly assumes some constraints, which act as information storage about the future in the here and now. Wolframian CI seems like it might be problematic for that account. Jonathan Colvin Even a computationally irreducible system contains information about the future. Its just that much of it is inaccessible. -- *PS: A number of people ask me about the attachment to my email, which is of type application/pgp-signature. Don't worry, it is not a virus. It is an electronic signature, that may be used to verify this email came from me if you have PGP or GPG installed. Otherwise, you may safely ignore this attachment. A/Prof Russell Standish Phone 8308 3119 (mobile) Mathematics0425 253119 () UNSW SYDNEY 2052 [EMAIL PROTECTED] Australiahttp://parallel.hpc.unsw.edu.au/rks International prefix +612, Interstate prefix 02 pgpoJjQ6IXmYZ.pgp Description: PGP signature
