Re: The Time Deniers and the idea of time as a "dimension"
Yes, you are definitely a conventional thinker Chris. The challenging point of view I express goes beyond the obvious qualia -differences- of space relative to time, and instead identifies certain similarities, that in turn identify how quantum mechanics and classical relativity can be unified. Interestingly, even Einstein missed this key aspect - of his own mathematics. So, let me ask you the straight fundamental question that rests at the heart of the topic of time (dimensional or not dimensional). Is the universe operatively Abelian, or non-Abelian or co-Abelian? James chris peck wrote: > > Hi James; > > >You unfortunatly are making the same fatal-flaw > >mistake that all conventional thinkers > > I hope i am a 'conventional thinker'. It gives me reason to think im onto > something, that ive got something right. That seems to be how things become > conventional. > > >spatial. You and all .. conflate commutative -and- > >non-commutative standards when analyzing dimensions. > > Im not sure I do. > > '>Let me pose this simple everyday definition that is > >typically laxly understood/applied, to see what you think:' > > I can feel a dreadfully non everyday definition approaching : > > >Tenet JNR-01: every exponent is indicative of 'dimension(s)', > >not just positive integer exponents. > > You should decide whether this is conventional (everyday) or not. > > Im fairly sure you are attacking a straw man. We can just say that 'now' > races towards the future rather than the opposite without us exerting any > effort, whilst 'here' doesnt really move at all. Especially for a rock. At > least the a priori notions of each spatial dimension dont involve change of > position, but our a priori notion of time at least involves a change of > time. If time has no arrow one way or the other, if there is no succession > of events, then time stops. > > I am left wondering whether you know what I mean at all when I say that we > are embeded in time in a way we are not in space. Its more the point that > there is a direction to time rather than whether we characterise the > direction one way or the other, or whether it can be flipped, or whether > backwards in time need be or neednt be represented by positive integers. One > way or the other, time moves on. And if it doesnt, everything stops. > > regards; > > Chris. > > >From: James N Rose <[EMAIL PROTECTED]> > >To: everything-list@eskimo.com > >Subject: Re: The Time Deniers and the idea of time as a "dimension" > >Date: Wed, 13 Jul 2005 06:56:28 -0700 > > > >Chris, > > > >You unfortunatly are making the same fatal-flaw > >mistake that all conventional thinkers -even the > >outside the box inventive ones- continue to make: > > > >you cannot identify, distinguish, specify or apply - > >complete non-Abelian, non-commutative aspects to > >considerations of 'dimensions' - whether temporal or > >spatial. You and all .. conflate commutative -and- > >non-commutative standards when analyzing dimensions. > > > >You also ignore basic arithmetic definitions and > >pretend they hold no meaning, particularly when > >those definition standards arise in weakly discussed > >situations. > > > >Let me pose this simple everyday definition that is > >typically laxly understood/applied, to see what you think: > > > >Tenet JNR-01: every exponent is indicative of 'dimension(s)', > >not just positive integer exponents. > > > >James > > > >13 July 2005 > > > > > > > >chris peck wrote: > > > > > > Hi James; > > > > > > I suspected that this part of my argument to Stephen would raise > >objections > > > from other members of this board. > > > > > > '>Actually, this is not correct; but a presumption of experiential > > > pre-bias.' > > > > > > It may be. Nevertheless, without the experience to hand at all, I > >maintain > > > that the asymetry exists in the sense that my movement in spatial > >dimensions > > > is second nature, movement in time - other than the apparantly > >inevitable > > > next step forward - is theoretical at best. It is not something I can > >just > > > do, I am in the 'now' in a stronger sense than I am 'here'. > > > > > > But, say time travel is possible, we have a futher asymetry in so far as > >the > > > idea that time is a dimension in the same sense that x,y,z leads to > > > paradoxes if we attempt to move around it. Spatial movement does not > >involve > > > paradoxes. > > > > > > I think this is enough to establish an asymetry in nature rather than > >just > > > experience. > > > > > > Regards > > > > > > Chris. > > > > > > >From: James N Rose <[EMAIL PROTECTED]> > > > >To: everything-list@eskimo.com > > > >CC: Stephen Paul King <[EMAIL PROTECTED]> > > > >Subject: The Time Deniers and the idea of time as a "dimension" > > > >Date: Mon, 11 Jul 2005 07:11:55 -0700 > > > > > > > >chris peck wrote: > > > > > > > > > > Hi Stephen; > > > > > > > > > > I suppose we can think of time as a dimension. However, there are >
RE: is induction unformalizable?
I agree that " As S goes to infinity, the AI's probability would converge to 0, whereas the human's would converge to some positive constant. " but this doesn't mean induction is unformalizable, it just means that the formalization of cognitive-science induction in terms of algorithmic information theory (rather than experience-grounded semantics) is flawed... ben -Original Message-From: Wei Dai [mailto:[EMAIL PROTECTED]Sent: Thursday, July 14, 2005 1:05 AMTo: Ben Goertzel; everything-list@eskimo.comSubject: Re: is induction unformalizable? >> Correct me if wrong, but isn't the halting problem only>> undecidable when the length of the program is unbounded? Wouldn't the AI assign non-zero>> probability to a machine that solved the halting problem for>> programs up to size S? (S is the number of stars in the sky, grains of sand,>> atoms in the universe, etc...) As an aside, this would actually be my best guess as to>> what was really going on if I were presented with such a box (and I'm not>> even programmed with UD+ASSA, AFAIK). Any sufficiently advanced>> technology is indistinguishable form magic (but not actual magic) and all that ;->... Moshe The AI would assign approximately 2^-S to this probability. A human being would intuitively assign a significantly greater a priori probability, especially for larger values of S. As S goes to infinity, the AI's probability would converge to 0, whereas the human's would converge to some positive constant. Why 2^-S? Being able to solve the halting problem for programs up to size S is equivalent to knowing the first S bits of the halting probability (Chaitin's Omega). Since Omega is incompressible by a Turing machine, the length of the shortest algorithmic description of the first S bits of Omega is just S (plus a small constant). See http://www.umcs.maine.edu/~chaitin/xxx.pdf. Here's another way to see why the AI's method of induction does not capture our intuitive notion. Supposed we've determined empirically that the black box can solve the halting problem for programs up to some S. No matter how large S is, the AI would still only assign a probability of 2^-100 to the black box being able to solve halting problems for programs of size S+100.
Re: is induction unformalizable?
>> Correct me if wrong, but isn't the halting problem only>> undecidable when the length of the program is unbounded? Wouldn't the AI assign non-zero>> probability to a machine that solved the halting problem for>> programs up to size S? (S is the number of stars in the sky, grains of sand,>> atoms in the universe, etc...) As an aside, this would actually be my best guess as to>> what was really going on if I were presented with such a box (and I'm not>> even programmed with UD+ASSA, AFAIK). Any sufficiently advanced>> technology is indistinguishable form magic (but not actual magic) and all that ;->... Moshe The AI would assign approximately 2^-S to this probability. A human being would intuitively assign a significantly greater a priori probability, especially for larger values of S. As S goes to infinity, the AI's probability would converge to 0, whereas the human's would converge to some positive constant. Why 2^-S? Being able to solve the halting problem for programs up to size S is equivalent to knowing the first S bits of the halting probability (Chaitin's Omega). Since Omega is incompressible by a Turing machine, the length of the shortest algorithmic description of the first S bits of Omega is just S (plus a small constant). See http://www.umcs.maine.edu/~chaitin/xxx.pdf. Here's another way to see why the AI's method of induction does not capture our intuitive notion. Supposed we've determined empirically that the black box can solve the halting problem for programs up to some S. No matter how large S is, the AI would still only assign a probability of 2^-100 to the black box being able to solve halting problems for programs of size S+100.
RE: is induction unformalizable?
Wei, I forwarded your post to a few of my colleagues, and one of them (Moshe Looks) replied with basically the same solution as I already posted here, but in different words... Here is his reply... -- Ben > Correct me if wrong, but isn't the halting problem only > undecidable when the length of the program is unbounded? Wouldn't the AI assign non-zero > probability to a machine that solved the halting problem for > programs up to size S? (S is the number of stars in the sky, grains of sand, > atoms in the universe, etc...) As an aside, this would actually be my best guess as to > what was really going on if I were presented with such a box (and I'm not > even programmed with UD+ASSA, AFAIK). Any sufficiently advanced > technology is indistinguishable form magic (but not actual magic) and all that ;->... > > Moshe -Original Message-From: Ben Goertzel [mailto:[EMAIL PROTECTED]Sent: Wednesday, July 13, 2005 11:35 PMTo: Wei Dai; everything-list@eskimo.comSubject: RE: is induction unformalizable? Wei, Isn't the moral of this story that, to any finite mind with algorithmic information I, "uncomputable" is effectively synonymous with "uncomputable within resources I"? Thus, from the perspective of a finite mind M, A = P( X is uncomputable) should be equal to B = P(X is uncomputable within resources I) since there is no evidence comprehensible by M that can distinguish A from B. Any formalization of induction that says A and B are unequal is not a correct model of induction as experienced by a finite mind. Induction is formalizable, but only using *experience-based semantics*, in which one assigns probabilities to propositions based on actual experienced pieces of evidence in favor of these propositions. Considering induction outside of the context of a particular finite system's experience leads to apparent paradoxes like the one you're suggesting. But if one construes induction experientially, one finds that these paradoxes never occur in any finite system's experience. As an example of experience-based semantics, see Pei Wang's NARS theory of AI. I don't fully accept the NARS theory, I have my own related theory that is probabilistically grounded, unlike NARS. But NARS is an example of what experience-based semantics means in concrete mathematical practice. -- Ben -Original Message-From: Wei Dai [mailto:[EMAIL PROTECTED]Sent: Wednesday, July 13, 2005 11:15 PMTo: everything-list@eskimo.comSubject: is induction unformalizable? One day, Earth is contacted by a highly advanced alien civilization, and they tell us that contrary to what most of us think is likely, not all of the fundamental physical laws of our universe are computable. Furthermore, they claim to be able to manufacture black boxes that work as oracles for the Halting Problem of Turing machines (one query per hour). They give us one free sample, and want to sell us more at a reasonable price. But of course we won't be allowed to open up the boxes and look inside to find out how they work. So our best scientists test the sample black box in every way that they can think of, but can't find any evidence that it isn't exactly what the aliens claim it is. At this point many people are ready to believe the claim and spend their hard earned money to buy these devices for their families. Fortunately, the Artificial Intelligence in charge of protecting Earth from interstellar fraud refuses to allow this. Having been programmed with UD+ASSA (see Hal Finney's 7/10/2005 post for a good explanation of what this means), it proclaims that there is zero probability that Halting Problem oracles can exist, so it must be pure chance that the sample black box has correctly answered all the queries submitted to it so far. The moral of this story is that our intuitive notion of induction is not fully captured by the formalization of UD+ASSA. Contrary to UD+ASSA, we will not actually refuse to believe in the non-existence of uncomputable phenomena no matter what evidence we see. What can we do to repair this flaw? Using a variant of UD, based on a more powerful type of computer (say an oracle TM instead of a plain TM), won't help because that just moves the problem up to a higher level of the computational hierarchy. No matter what type of computer (call it C) we base UD' on, it will always assign zero probability to the existence of even more power types of computer (e.g., ones that can solve the halting problem for C). Intuitively, this doesn't seem like a good feature. Earlier on this mailing list, I had proposed that we skip pass the entire computational hierarchy
RE: is induction unformalizable?
Wei, Isn't the moral of this story that, to any finite mind with algorithmic information I, "uncomputable" is effectively synonymous with "uncomputable within resources I"? Thus, from the perspective of a finite mind M, A = P( X is uncomputable) should be equal to B = P(X is uncomputable within resources I) since there is no evidence comprehensible by M that can distinguish A from B. Any formalization of induction that says A and B are unequal is not a correct model of induction as experienced by a finite mind. Induction is formalizable, but only using *experience-based semantics*, in which one assigns probabilities to propositions based on actual experienced pieces of evidence in favor of these propositions. Considering induction outside of the context of a particular finite system's experience leads to apparent paradoxes like the one you're suggesting. But if one construes induction experientially, one finds that these paradoxes never occur in any finite system's experience. As an example of experience-based semantics, see Pei Wang's NARS theory of AI. I don't fully accept the NARS theory, I have my own related theory that is probabilistically grounded, unlike NARS. But NARS is an example of what experience-based semantics means in concrete mathematical practice. -- Ben -Original Message-From: Wei Dai [mailto:[EMAIL PROTECTED]Sent: Wednesday, July 13, 2005 11:15 PMTo: everything-list@eskimo.comSubject: is induction unformalizable? One day, Earth is contacted by a highly advanced alien civilization, and they tell us that contrary to what most of us think is likely, not all of the fundamental physical laws of our universe are computable. Furthermore, they claim to be able to manufacture black boxes that work as oracles for the Halting Problem of Turing machines (one query per hour). They give us one free sample, and want to sell us more at a reasonable price. But of course we won't be allowed to open up the boxes and look inside to find out how they work. So our best scientists test the sample black box in every way that they can think of, but can't find any evidence that it isn't exactly what the aliens claim it is. At this point many people are ready to believe the claim and spend their hard earned money to buy these devices for their families. Fortunately, the Artificial Intelligence in charge of protecting Earth from interstellar fraud refuses to allow this. Having been programmed with UD+ASSA (see Hal Finney's 7/10/2005 post for a good explanation of what this means), it proclaims that there is zero probability that Halting Problem oracles can exist, so it must be pure chance that the sample black box has correctly answered all the queries submitted to it so far. The moral of this story is that our intuitive notion of induction is not fully captured by the formalization of UD+ASSA. Contrary to UD+ASSA, we will not actually refuse to believe in the non-existence of uncomputable phenomena no matter what evidence we see. What can we do to repair this flaw? Using a variant of UD, based on a more powerful type of computer (say an oracle TM instead of a plain TM), won't help because that just moves the problem up to a higher level of the computational hierarchy. No matter what type of computer (call it C) we base UD' on, it will always assign zero probability to the existence of even more power types of computer (e.g., ones that can solve the halting problem for C). Intuitively, this doesn't seem like a good feature. Earlier on this mailing list, I had proposed that we skip pass the entire computational hierarchy and jump to the top of the set theoretic hierarchy, by using a measure that is based a set theoretic notion of complexity instead of a computational one. In this notion, instead of defining the complexity of an object by the length of its shortest algorithmic description, we define its complexity by the length of its shortest description in the language of a formal set theory. The measure would be constructed in a manner analogous to UD, with each set theoretic description of an object contributing n^-l to the measure of the object, where n is the size of the alphabet of the set theory, and l is the length of the description. Lets call this STUM for set theoretic universal measure. STUM along with ASSA does a much better job of formalizing induction, but I recently realized that it still isn't perfect. The problem is that it still assigns zero probability to some objects that we intuitively think is very unlikely, but not completely impossible. An example would be a device that can decide the truth value of any set theoretic statement. A universe that contains such a device would exist in the set theoretic hierarchy, but would have no finite description in form
is induction unformalizable?
One day, Earth is contacted by a highly advanced alien civilization, and they tell us that contrary to what most of us think is likely, not all of the fundamental physical laws of our universe are computable. Furthermore, they claim to be able to manufacture black boxes that work as oracles for the Halting Problem of Turing machines (one query per hour). They give us one free sample, and want to sell us more at a reasonable price. But of course we won't be allowed to open up the boxes and look inside to find out how they work. So our best scientists test the sample black box in every way that they can think of, but can't find any evidence that it isn't exactly what the aliens claim it is. At this point many people are ready to believe the claim and spend their hard earned money to buy these devices for their families. Fortunately, the Artificial Intelligence in charge of protecting Earth from interstellar fraud refuses to allow this. Having been programmed with UD+ASSA (see Hal Finney's 7/10/2005 post for a good explanation of what this means), it proclaims that there is zero probability that Halting Problem oracles can exist, so it must be pure chance that the sample black box has correctly answered all the queries submitted to it so far. The moral of this story is that our intuitive notion of induction is not fully captured by the formalization of UD+ASSA. Contrary to UD+ASSA, we will not actually refuse to believe in the non-existence of uncomputable phenomena no matter what evidence we see. What can we do to repair this flaw? Using a variant of UD, based on a more powerful type of computer (say an oracle TM instead of a plain TM), won't help because that just moves the problem up to a higher level of the computational hierarchy. No matter what type of computer (call it C) we base UD' on, it will always assign zero probability to the existence of even more power types of computer (e.g., ones that can solve the halting problem for C). Intuitively, this doesn't seem like a good feature. Earlier on this mailing list, I had proposed that we skip pass the entire computational hierarchy and jump to the top of the set theoretic hierarchy, by using a measure that is based a set theoretic notion of complexity instead of a computational one. In this notion, instead of defining the complexity of an object by the length of its shortest algorithmic description, we define its complexity by the length of its shortest description in the language of a formal set theory. The measure would be constructed in a manner analogous to UD, with each set theoretic description of an object contributing n^-l to the measure of the object, where n is the size of the alphabet of the set theory, and l is the length of the description. Lets call this STUM for set theoretic universal measure. STUM along with ASSA does a much better job of formalizing induction, but I recently realized that it still isn't perfect. The problem is that it still assigns zero probability to some objects that we intuitively think is very unlikely, but not completely impossible. An example would be a device that can decide the truth value of any set theoretic statement. A universe that contains such a device would exist in the set theoretic hierarchy, but would have no finite description in formal set theory, and would be assigned a measure of 0 by STUM. I'm not sure where this line of thought leads. Is induction unformalizable? Have we just not found the right formalism yet? Or is our intuition on the subject flawed?
RE: The Time Deniers
Jesse Mazer writes: > I've sometimes thought that if uploads are ever created, and can be run in a > simulation with time-reversible fundamental laws, it would be very > interesting to take a snapshot at the end of a simulation and do the trick > of reversing everything, but with a tiny perturbation--the simulation might > appear to behave like a reversed version of the original run for a little > while, but then the butterfly effect would probably kick in and the upload's > psychological arrow of time would *reverse* in the middle of the simulation. > What would this feel like subjectively, from the upload's point of view? > Obviously he wouldn't have a memory of experiencing everything backwards, > but it still would be interesting to interview the upload about it > afterwards. For example, what would happen if the reversal of the upload's > psychological arrow of time happened at the same moment that the entropic > arrow of time reversed in the simulated physical world around the upload, > and at that moment pieces of a vase were rushing together to reassemble, but > instead failed to meet up exactly and just broke apart again? The upload > should have a memory of seeing the vase fall, but at the moment it landed it > might appear to behave very strangely, assuming the upload didn't just > perceive himself blacking out at that moment. That's a cool problem. I've given it some thought and here is what I came up with. The short answer is that as we are running backwards, due to the chaotic nature of the physics, the transition from an accurate backwards one to a locally disrupted one will be nearly instantaneous. The divergence from the original forwards run will grow exponentially, meaning that if you have set it so that it "kicks in" after say -5 seconds, then at -4. seconds everything would still look normal. Then, once you had divergence in a specific location, I think the effects would spread out at the speed of sound. We are relying on every atom moving the opposite of what it did before, and atoms generally move at the speed of sound, so as soon as one starts misbehaving it will kick its neighbors, which will kick their neighbors, and the disruption will spread at that speed. Once the disruption has occured then I think you are right that time will effectively start forward again, and probably take a different path than it did the first time through. This would imply then that subjectively there are two paths, the one we ran the first time, and the one which resulted from the alteration. They would subjectively diverge at the point where the butterfly effect kicked in during the reverse run. The transition would be subjectively instantaneous, with the whole brain flipping in a millisecond or less from backwards to forwards motion. >From the measure perspective, I'd say that the first half that was shared has measure 1, the second half that got run twice (once forward, once backward) had measure 2, and the alternate second half would have measure 1. > And perhaps something like this could help explain the low-entropy big bang, > which is apparently the source of the arrow of time in our universe and yet > doesn't have any agreed-upon explanation by physicists. It would certainly > be interesting if even a complete theory of quantum gravity didn't explain > it, so that the only remaining option would be either "intelligent design" > or some sort of "meta-physical" explanation in terms of a multiverse with > different types of universes having different measure. Right, that is one of the big selling points of the Tegmark and Schmidhuber concept, that the Big Bang apparently can be described in very low-information terms. Tegmark even has a paper arguing that it took "zero information" to describe it (but frankly I am getting pretty turned off on the "zero information" concept since several people here use it to describe completely different things, and if it really took zero information then there couldn't be more than one thing described, could it?). > >My feeling is that causality, like time, is in the eye of the beholder. > >It's not an inherent or fundamental property. Rather, it is a way that > >we can interpret events in some kinds of universes. Completely chaotic > >universes (where every moment is random and uncorrelated with the next) > >would not have causality in any meaningful sense. Likewise for static > >universes. > > But if such a chaotic universe is computable, then for those of us watching > the computation from the outside, the read/write head of the Turing machine > is still obeying regular laws, in terms of when it decides to flip a > particular bit or change its internal pointer-state or move from one > location on the bitstring to another...if it's possible to define a > mathematical notion of "causal structure" for any particular algorithm, I > would think it would be possible to apply it to *all* algorithms. But > perhaps no su
RE: The Time Deniers
Hal Finney wrote: > True, it isn't always necessary to compute things in the same order--if > you're simulating a system that obeys time-symmetric laws you can always > reverse all the time-dependent quantities (like the momentum of each > particle) in the final state and use that as an initial state for a new > simulation, and the new simulation will behave like a backwards movie of the > original simulation. One problem with this in practice is that it seems that the information needed to specify the final state is far greater than the information needed to specify the original state, at least with physics like ours. In our universe, you could take a snapshot at some time that recorded all the particle motions in a brain. Then you could evolve it forward and produce the successive subjective experiences. However, I don't think the snapshot has to be completely detailed. Some sloppiness is acceptable. The brain is robust and you could change the details of thermal motions very considerably and the brain would still work fine. If you took a snapshot at the end and evolved it backward it would also work, in theory, but in practice it would not work unless every detail of every motion was precise to an incredible degree. (This is ignoring issues of QM state reduction and such, I'm basically considering a Newtonian clockwork here.) It's like, it's easy to come up with motions to scramble an egg; but to come up with motions to unscramble one will require absolute precision in every respect. The result is that the information requirements for specifying a final-state based simulation that includes an arrow of time are exponentially greater than the information needed to create a plausible initial-state simulation. I've sometimes thought that if uploads are ever created, and can be run in a simulation with time-reversible fundamental laws, it would be very interesting to take a snapshot at the end of a simulation and do the trick of reversing everything, but with a tiny perturbation--the simulation might appear to behave like a reversed version of the original run for a little while, but then the butterfly effect would probably kick in and the upload's psychological arrow of time would *reverse* in the middle of the simulation. What would this feel like subjectively, from the upload's point of view? Obviously he wouldn't have a memory of experiencing everything backwards, but it still would be interesting to interview the upload about it afterwards. For example, what would happen if the reversal of the upload's psychological arrow of time happened at the same moment that the entropic arrow of time reversed in the simulated physical world around the upload, and at that moment pieces of a vase were rushing together to reassemble, but instead failed to meet up exactly and just broke apart again? The upload should have a memory of seeing the vase fall, but at the moment it landed it might appear to behave very strangely, assuming the upload didn't just perceive himself blacking out at that moment. If we then add the concept of measure based inversely on the size of the information description, we find that almost all measure of such simulations comes from initial-state based ones rather than final-state based. And perhaps something like this could help explain the low-entropy big bang, which is apparently the source of the arrow of time in our universe and yet doesn't have any agreed-upon explanation by physicists. It would certainly be interesting if even a complete theory of quantum gravity didn't explain it, so that the only remaining option would be either "intelligent design" or some sort of "meta-physical" explanation in terms of a multiverse with different types of universes having different measure. > But since I don't have a well-defined mathematical > theory of what it means for two computations to have the same "causal > structure", I'm not sure whether the causal structure would actually be any > different if you computed a universe in reverse order. When I think of > "causal structure", I'm not really presupposing any asymmetry between > "cause" and "effect", I'm just imagining a collection of events which are > linked to each other in some way like in a graph, but the links need not > have any built-in direction--if two events are linked, that doesn't mean one > event is the cause and the other is the effect, so the pattern of links > could still be the same even if you did compute things in reverse order. > >From what I've read about loop quantum gravity, it's a theory in which space > and time emerge from a more primitive notion of linked events, but I'm > pretty sure it's not a time-asymmetric theory. My feeling is that causality, like time, is in the eye of the beholder. It's not an inherent or fundamental property. Rather, it is a way that we can interpret events in some kinds of universes. Completely chaotic universes (where every momen
Re: The Time Deniers and the idea of time as a "dimension"
chris peck wrote: Hi Jesse; we can just understand it in terms of our brains having different memories and anticipations of the future at different points along our worldline. I think that is necessary for an understanding of time, but insufficient. What governs which set of memories and anticipations is being entertained? The laws of physics, I suppose. And certainly time is not treated the same way as spatial dimensions are by the laws of physics, but all of physics can be understood in terms of the "block time" view, and relativity actually seems to favor it. Somehow, each set is individuated from the others, what process prevents the whole set from striking one all together. I guess the same thing that prevents events at different spatial locations from all happening in the same place--events just have different locations in spacetime. Do you accept the existence of timeless mathematical structures like the Mandelbrot set, with different elements of this set having different locations in the complex plane? If so, what's wrong with the idea of our universe's spacetime and the events within it just being another such timeless mathematical structure? Not that we *must* accept such a view, but I don't see any logical problems with it. Relativity poses severe problems for the idea that there is actually a single "present moment" which is constantly moving towards the future in some universal, objective sense. True. Im not unaware of that and I find it a really difficult problem. Isnt it the case that staggered 'nows' are caused by physical rather than conceptual circumstances? Actually travelling at different speeds and so on. How does this happen if 'now' is merely conceptual and completely subjective? I don't really understand your question...it's not that "now" is completely subjective, given a particular object moving inertially there is an objective truth about how simultaneity is defined in that object's rest frame. But the fact that different coordinate systems disagree about whether two events have the same t-coordinate doesn't seem fundamentally different from the idea that two spatial coordinate systems can disagree about whether two objects have the same x-coordinate. Jesse
RE: The Time Deniers
> True, it isn't always necessary to compute things in the same order--if > you're simulating a system that obeys time-symmetric laws you can always > reverse all the time-dependent quantities (like the momentum of each > particle) in the final state and use that as an initial state for a new > simulation, and the new simulation will behave like a backwards movie of the > original simulation. One problem with this in practice is that it seems that the information needed to specify the final state is far greater than the information needed to specify the original state, at least with physics like ours. In our universe, you could take a snapshot at some time that recorded all the particle motions in a brain. Then you could evolve it forward and produce the successive subjective experiences. However, I don't think the snapshot has to be completely detailed. Some sloppiness is acceptable. The brain is robust and you could change the details of thermal motions very considerably and the brain would still work fine. If you took a snapshot at the end and evolved it backward it would also work, in theory, but in practice it would not work unless every detail of every motion was precise to an incredible degree. (This is ignoring issues of QM state reduction and such, I'm basically considering a Newtonian clockwork here.) It's like, it's easy to come up with motions to scramble an egg; but to come up with motions to unscramble one will require absolute precision in every respect. The result is that the information requirements for specifying a final-state based simulation that includes an arrow of time are exponentially greater than the information needed to create a plausible initial-state simulation. If we then add the concept of measure based inversely on the size of the information description, we find that almost all measure of such simulations comes from initial-state based ones rather than final-state based. > But since I don't have a well-defined mathematical > theory of what it means for two computations to have the same "causal > structure", I'm not sure whether the causal structure would actually be any > different if you computed a universe in reverse order. When I think of > "causal structure", I'm not really presupposing any asymmetry between > "cause" and "effect", I'm just imagining a collection of events which are > linked to each other in some way like in a graph, but the links need not > have any built-in direction--if two events are linked, that doesn't mean one > event is the cause and the other is the effect, so the pattern of links > could still be the same even if you did compute things in reverse order. > >From what I've read about loop quantum gravity, it's a theory in which space > and time emerge from a more primitive notion of linked events, but I'm > pretty sure it's not a time-asymmetric theory. My feeling is that causality, like time, is in the eye of the beholder. It's not an inherent or fundamental property. Rather, it is a way that we can interpret events in some kinds of universes. Completely chaotic universes (where every moment is random and uncorrelated with the next) would not have causality in any meaningful sense. Likewise for static universes. In fact I would suggest that causality only exists in our universe in areas where there is an arrow of time; that is, in areas which are far from equlibrium and where entropy is unusually low. The problem in equilibrium regions is that you can always look at things two ways. Suppose particle A collides with B and changes its course so that B collides with C. We can express this as that A causes B to hit C. But all the physics works just as well in the reverse direction, in equilibrium, so we could just as easily say that C caused B to hit A. Scerir has also posted some interesting paradoxes along these lines relating to QM. Suppose we have a photon that passes through a polarizer oriented at 20 degrees from vertical, then through one oriented at 40 degrees, and makes it through both. At the end we would say its polarization was 40 degrees. But what was it between the two polarizers? Conventionally we would say that the first polarizer made its polarization become 20 degrees and the second polarizer then changed the polarization to 40 degrees. But actually you can just as easily argue that the photon polarization was 40 degrees between the two polarizers. That interpretation works just as well, a sort of retroactive causality. As with time, my guess is that if we restrict our attention to observers like us, of a type we can comprehend, then automatically we are going to pick out information systems that have a notion of time, an arrow of time, and hence a sense of causality. Not all systems have these properties, but some do, and all the ones that we would identify as observers fall into that category. Hal Finney
Re: The Time Deniers and the idea of time as a "dimension"
chris peck wrote: Im fairly sure you are attacking a straw man. We can just say that 'now' races towards the future rather than the opposite without us exerting any effort, whilst 'here' doesnt really move at all. Especially for a rock. At least the a priori notions of each spatial dimension dont involve change of position, but our a priori notion of time at least involves a change of time. If time has no arrow one way or the other, if there is no succession of events, then time stops. I am left wondering whether you know what I mean at all when I say that we are embeded in time in a way we are not in space. Its more the point that there is a direction to time rather than whether we characterise the direction one way or the other, or whether it can be flipped, or whether backwards in time need be or neednt be represented by positive integers. One way or the other, time moves on. And if it doesnt, everything stops. But there's no need to understand this in terms of time "moving", we can just understand it in terms of our brains having different memories and anticipations of the future at different points along our worldline. Relativity poses severe problems for the idea that there is actually a single "present moment" which is constantly moving towards the future in some universal, objective sense. In relativity, simultaneity is relative, meaning that two events which happen at the same time-coordinate in one reference frame will happen at different time-coordinates in another reference frame, and relativity says that no reference frame is physically preferred over any other. I suppose you could still imagine that one reference frame is "metaphysically preferred" and thus has the "true" definition of simultaneity, even though there is no experiment you can do to find out which reference frame this is, but this view seems rather inelegant. For more on relativity and why it tends to favor the "block time" view over the "moving present" view, see this article by Paul Davies: http://tinyurl.com/dlo3v Jesse
RE: The Time Deniers
Hal Finney wrote: Jesse Mazer writes: > Hal Finney wrote: > >I imagine that multiple universes could exist, a la Schmidhuber's ensemble > >or Tegmark's level 4 multiverse. Time does not play a special role in > >the descriptions of these universes. > > Doesn't Schmidhuber consider only universes that are the results of > computations? Can't we consider any computation as having an intrinsic > "causal structure"? How would it be possible to write an algorithm that > describes a "Life" universe where there's no time, where the t-axis is > replaced by a z-axis, for example? Well, you could just replace the letter t with the letter z, but of course that wouldn't change the underlying nature of things. You might well say that there was still a time axis, just that it had a different name. But the bigger question is whether the order in which a universe is computed must match the concept of "time" within that universe. True, it isn't always necessary to compute things in the same order--if you're simulating a system that obeys time-symmetric laws you can always reverse all the time-dependent quantities (like the momentum of each particle) in the final state and use that as an initial state for a new simulation, and the new simulation will behave like a backwards movie of the original simulation. But since I don't have a well-defined mathematical theory of what it means for two computations to have the same "causal structure", I'm not sure whether the causal structure would actually be any different if you computed a universe in reverse order. When I think of "causal structure", I'm not really presupposing any asymmetry between "cause" and "effect", I'm just imagining a collection of events which are linked to each other in some way like in a graph, but the links need not have any built-in direction--if two events are linked, that doesn't mean one event is the cause and the other is the effect, so the pattern of links could still be the same even if you did compute things in reverse order. From what I've read about loop quantum gravity, it's a theory in which space and time emerge from a more primitive notion of linked events, but I'm pretty sure it's not a time-asymmetric theory. Further, in our own universe there appears to be quite a bit of ambiguity about time ordering, and many different computational strategies will work equally well. Relativity theory shows that events either have a timelike separation, in which case it is clear which one is in the past, or a spacelike separation, which makes it ambiguous which one is farther in the past. True, but the only way for two events to be causally linked in relativity is if there is a timelike separation between them, and in that case all reference frames will agree about the order of the events. It was suggested here a while back that a Life universe could be computed using an algorithm which ran around somewhat randomly and made localized changes to cells in order to make them match the Life rules. Eventually this would converge to a stable and consistent Life universe. Any observers living in that universe would have a perceived direction of time that was very different from the actual order in which it was computed. Another way to do this might just be to have a computer generate *all* possible sequences of cell-changes over some finite number of steps and using a finite-sized board, and then check each one to see if it is obeying the rules of "Life" at each step, and throw out all those that don't. Is it possible that the "causal structure" of a program checking every cell at every step of a valid Life sequence is the same as the causal structure of actually computing that sequence from its initial conditions? Or that even if they're different, one causal structure "contains" the other, like a graph that contains another one as a subset? Again, without a well-defined notion of the causal structure of a given computation it's hard to be sure. Jesse
Re: The Time Deniers and the idea of time as a "dimension"
Hi James; You unfortunatly are making the same fatal-flaw mistake that all conventional thinkers I hope i am a 'conventional thinker'. It gives me reason to think im onto something, that ive got something right. That seems to be how things become conventional. spatial. You and all .. conflate commutative -and- non-commutative standards when analyzing dimensions. Im not sure I do. '>Let me pose this simple everyday definition that is typically laxly understood/applied, to see what you think:' I can feel a dreadfully non everyday definition approaching : Tenet JNR-01: every exponent is indicative of 'dimension(s)', not just positive integer exponents. You should decide whether this is conventional (everyday) or not. Im fairly sure you are attacking a straw man. We can just say that 'now' races towards the future rather than the opposite without us exerting any effort, whilst 'here' doesnt really move at all. Especially for a rock. At least the a priori notions of each spatial dimension dont involve change of position, but our a priori notion of time at least involves a change of time. If time has no arrow one way or the other, if there is no succession of events, then time stops. I am left wondering whether you know what I mean at all when I say that we are embeded in time in a way we are not in space. Its more the point that there is a direction to time rather than whether we characterise the direction one way or the other, or whether it can be flipped, or whether backwards in time need be or neednt be represented by positive integers. One way or the other, time moves on. And if it doesnt, everything stops. regards; Chris. From: James N Rose <[EMAIL PROTECTED]> To: everything-list@eskimo.com Subject: Re: The Time Deniers and the idea of time as a "dimension" Date: Wed, 13 Jul 2005 06:56:28 -0700 Chris, You unfortunatly are making the same fatal-flaw mistake that all conventional thinkers -even the outside the box inventive ones- continue to make: you cannot identify, distinguish, specify or apply - complete non-Abelian, non-commutative aspects to considerations of 'dimensions' - whether temporal or spatial. You and all .. conflate commutative -and- non-commutative standards when analyzing dimensions. You also ignore basic arithmetic definitions and pretend they hold no meaning, particularly when those definition standards arise in weakly discussed situations. Let me pose this simple everyday definition that is typically laxly understood/applied, to see what you think: Tenet JNR-01: every exponent is indicative of 'dimension(s)', not just positive integer exponents. James 13 July 2005 chris peck wrote: > > Hi James; > > I suspected that this part of my argument to Stephen would raise objections > from other members of this board. > > '>Actually, this is not correct; but a presumption of experiential > pre-bias.' > > It may be. Nevertheless, without the experience to hand at all, I maintain > that the asymetry exists in the sense that my movement in spatial dimensions > is second nature, movement in time - other than the apparantly inevitable > next step forward - is theoretical at best. It is not something I can just > do, I am in the 'now' in a stronger sense than I am 'here'. > > But, say time travel is possible, we have a futher asymetry in so far as the > idea that time is a dimension in the same sense that x,y,z leads to > paradoxes if we attempt to move around it. Spatial movement does not involve > paradoxes. > > I think this is enough to establish an asymetry in nature rather than just > experience. > > Regards > > Chris. > > >From: James N Rose <[EMAIL PROTECTED]> > >To: everything-list@eskimo.com > >CC: Stephen Paul King <[EMAIL PROTECTED]> > >Subject: The Time Deniers and the idea of time as a "dimension" > >Date: Mon, 11 Jul 2005 07:11:55 -0700 > > > >chris peck wrote: > > > > > > Hi Stephen; > > > > > > I suppose we can think of time as a dimension. However, there are > >provisos. > > > Time is not like x, y, or z in so far as we have no ability to freely > > > navigate the axis in any direction we choose. We are embedded in time > >and it > > > moves onwards in a single direction without anyones consent. > >Furthermore, > > > where it possible to move around in time all sorts of paradoxes would > >appear > > > to ensue that just dont when I traverse the spatial dimensions. Id > >appeal > > > to an asymmetry between time and space, it is a dimension of sorts, but > >not > > > one that can conceptually swapped with a spatial dimension easily. I > >dont > > > think the a priori requirements for space will be necessarily the same > >as > > > those for time. > > > > > > > >Actually, this is not correct; but a presumption of experiential pre-bias. > >While it is true that we can calculate negative spatial values and not > >identify negative temporal values easily - or at all in some cases
Re: The Time Deniers and the idea of time as a "dimension"
Esteemed Prof. Standish, Thank you for that correction. ;-) But you are missing the point that I am trying to make here! :_( - Original Message - From: "Russell Standish" <[EMAIL PROTECTED]> To: "Stephen Paul King" <[EMAIL PROTECTED]> Cc: ; "Lee Corbin" <[EMAIL PROTECTED]> Sent: Wednesday, July 13, 2005 12:02 AM Subject: Re: The Time Deniers and the idea of time as a "dimension" On Tue, Jul 12, 2005 at 09:54:55AM -0400, Stephen Paul King wrote: How familiar are you with the details of quantum mechanics? Did you happen to know that the notion of an observable in QM has a complex value and that a real value only obtains after the multiplication of an observable with its complex conjugate? This operation of conjugation must involve the selection of some basis.. This makes the problem of a pre-existing Real value time to be, at least, doubly difficult. Complex numbers have no natural ordering, as opposed to the Reals, which do, because in general, complex numbers do not commute with each other. Only the very special subset of observables can be said to commute and thus can be mapped to some notion of a "dimension" that one can have translational transforms as functions. [RS] Tosh! I'm sorry, but you are demonstrating enormous ignorance of QM with these statements. 1) Observables are Hermitian operators. This means that their eigenvalues (which are the observed outcomes) are real valued (not complex valued as you seem to think), and so ordering of observed values is _not_ the problem you think it is. [SPK] Please notice the words "observed outcome"! This is my point! I am not talking about "after the fact of an observational event" - which is the intended application of Hermiticity -, I am talking about observables prior to the specification of the observational context of the particular observables. There is a big difference between how properties are defined in QM before and after the specification of a context within which a measurement and/or observation is made. BTW, this the what the whole controversy reqarding the "collapse of the wavefunction"! Prior to the measurement even, the possible properties of an object of observation are given by a superposition. After the fact, one obtains a single Boolean representable set of properties. When we are talking about the notion of Time, we must take this distiction into account! [RS] 2) Complex numbers indeed do not have an ordering (being basically points on a plane), however they do commute. For any two complex numbers x and y, xy=yx. [SPK] Well, it is the point that complex numbers do not have an ordering that is my point. I forgot my complex number algebra. ;-) I will let Wikipedia make my point: http://en.wikipedia.org/wiki/Quantum_superposition *** Quantum superposition is the application of the superposition principle to quantum mechanics. The superposition principle is addition of the amplitudes of waves from interference. In quantum mechanics it is the amplitudes of wavefunctions, or state vectors, that add. It occurs when an object simultaneously "possesses" two or more values for an observable quantity (e.g. the position or energy of a particle). More specifically, in quantum mechanics, any observable quantity corresponds to an eigenstate of a Hermitian linear operator. The linear combination of two or more eigenstates results in quantum superposition of two or more values of the quantity. If the quantity is measured, the projection postulate states that the state will be randomly collapsed onto one of the values in the superposition (with a probability proportional to the amplitude of that eigenstate in the linear combination). The question naturally arose as to why "real" (macroscopic, Newtonian) objects and events do not seem to display quantum mechanical features such as superposition. In 1935, Erwin Schrödinger devised a well-known thought experiment, now known as Schrödinger's cat, which highlighted the dissonance between quantum mechanics and Newtonian physics. In fact, quantum superposition does result in many directly observable effects, such as interference peaks from an electron wave in a double-slit experiment. If two observables correspond to non-commuting operators, they obey an uncertainty principle and a distinct state of one observable corresponds to a superposition of many states for the other observable. *** Kindest regards, Stephen
Stathis, Lee and the "NEAR DEATH LOGIC"
Hi, In this post I will try to make clearer my argument with Lee by using a minimal amount of modal logic (and so it's good "revision" ;) Then I will explain how Stathis seems to have (re)discovered, in its "DEATH" thread, what I call sometime "The Smallest Theory of Life and Death", or "Near Death Logic", or just C. I have never abandon C, but the interview of the Lobian machine will give C again, but through some of its most notable extensions which are G and G*. To prevent falling in the 1004-fallacy, I will use (at least temporarily) the words "state", "world", "situation", "observer-moment", "OM", etc. as synonymous. I will use "world" (if you don't mind), and I will designate individual world by w, w1, w2, w3, w4, etc. Like Stathis (and Kripke!), I will accept that some world can have *successor* world (successor OMs in Stathis terminology). More generally we suppose a relation of accessibility among worlds (that's Kripke's idea how to enrich Leibniz). I will be interested in the discourse which are true at each world, and I will assume that classical logic holds at each world. p, q, r, ... denotes propositions. And a "semantics" is given when it is said which one of p, q, r ... are true or false in each world. I suppose you know some classical logic: (p & q) is true if both p and q is true, else it is false (p v q) is true if at least one among p, q is true, else it is false (~p) is true if and only if p is false (p -> q) is true if p is false or q is true (to be sure this last one is tricky. "->" has nothing to do with causality: the following is a tautology (((p & q) -> r) -> ((p -> r) v (q -> r))) although it is false with "->" interpreted as "causality", (wet & cold) -> ice would imply ((wet -> ice) or (cold -> ice)). Someday I will show you that the material implication "->" (as Bertrand Russell called it) is arguably the "IF ... THEN ..." of the mathematician working in Platonia. (p <-> q) is true if (p->q) is true and (q->p) is true. I could have said (p <-> q) is true if p and q have the same truth value. The truth value are true and false, and I will write them t and f. You can see t as a fixed tautology like (p -> p), and f as a fixed contradiction like (p & (~p)), or add t and f in the proposition symbols and stipulate that f is always false t is always true That classical logic holds in the worlds means the "usual things", for example that - if p holds at w, and if q holds at w, then (p & q) holds at w, - if p holds at w, then p v q (read p or q) holds at w, - if p holds at w and p -> q holds at w, then q holds at w. - t holds in all world - f does not hold in any world - etc. Etc. All "tautologies" will be true in all world (p -> p), (p -> (q -> p)), ((p & q) -> p), etc. (whatever the truth value of p, q, r, ... in the worlds). I hope most of you knows the "truth table method" to verify if a proposition is a tautology or not. But I can explain or give reference or you could google. Remark. Note that if the excluded middle principle (p v (~p))is a classical tautology, it is not an intuitionist logic, and (much later) we will met this logic. We live the modern time where even the classical (Platonic) logician must aknowledge the importance of the many many many many possible logics. For example in Quantum Logic and in the Relevant Logics, the classical tautology which is "guilty" is the "a fortiori principle": (p -> (q -> p)) One of the main utility of modal logic, imo, is to give a tool to "modelize" non-classical logics in a classical setting. But this we don't need to know now. KRIPKE: Now, and this is the important line, with Kripke, some worlds can be reachable from others; and I will say that the modal proposition Bp, also often written []p or \Box p (in LATEX), is true at some world w if and only if p is true in each world which are successor of w. I say it again: KRIPKE IMPORTANT LINE: Bp is true in w if for all world x such that wRx we have that p is true in x. You can read wRx as the world w reaches the world x, or x is accessible from w. For example, with a drawing, where the (broken) line represents the oriented accessibility relations (please add an arrow so you see that it is the worlds on the top which are accessible from the world at the bottom: p p \/ \/ \/ Bp Let us consider that "multiverse" M with only three worlds: w, w0, w1, and with "successor" or "accessibility relation" R given by wRw0, and wRw1. Meaning obviously that w0 and w1 are accessible from w, and that's all. Now what I was trying to say to Lee was just that if p is true in w0, and if q is true in w1, then, B(p v q) is true in w0. p q \/ \/ \/ B(p v q) And if the world represents subjective observer moment a-la Bostrom, and if the accessibility relation represents scanning-annihilation followed by reconstitutions, the diagram w
Re: The Time Deniers and the idea of time as a "dimension"
Chris, You unfortunatly are making the same fatal-flaw mistake that all conventional thinkers -even the outside the box inventive ones- continue to make: you cannot identify, distinguish, specify or apply - complete non-Abelian, non-commutative aspects to considerations of 'dimensions' - whether temporal or spatial. You and all .. conflate commutative -and- non-commutative standards when analyzing dimensions. You also ignore basic arithmetic definitions and pretend they hold no meaning, particularly when those definition standards arise in weakly discussed situations. Let me pose this simple everyday definition that is typically laxly understood/applied, to see what you think: Tenet JNR-01: every exponent is indicative of 'dimension(s)', not just positive integer exponents. James 13 July 2005 chris peck wrote: > > Hi James; > > I suspected that this part of my argument to Stephen would raise objections > from other members of this board. > > '>Actually, this is not correct; but a presumption of experiential > pre-bias.' > > It may be. Nevertheless, without the experience to hand at all, I maintain > that the asymetry exists in the sense that my movement in spatial dimensions > is second nature, movement in time - other than the apparantly inevitable > next step forward - is theoretical at best. It is not something I can just > do, I am in the 'now' in a stronger sense than I am 'here'. > > But, say time travel is possible, we have a futher asymetry in so far as the > idea that time is a dimension in the same sense that x,y,z leads to > paradoxes if we attempt to move around it. Spatial movement does not involve > paradoxes. > > I think this is enough to establish an asymetry in nature rather than just > experience. > > Regards > > Chris. > > >From: James N Rose <[EMAIL PROTECTED]> > >To: everything-list@eskimo.com > >CC: Stephen Paul King <[EMAIL PROTECTED]> > >Subject: The Time Deniers and the idea of time as a "dimension" > >Date: Mon, 11 Jul 2005 07:11:55 -0700 > > > >chris peck wrote: > > > > > > Hi Stephen; > > > > > > I suppose we can think of time as a dimension. However, there are > >provisos. > > > Time is not like x, y, or z in so far as we have no ability to freely > > > navigate the axis in any direction we choose. We are embedded in time > >and it > > > moves onwards in a single direction without anyones consent. > >Furthermore, > > > where it possible to move around in time all sorts of paradoxes would > >appear > > > to ensue that just dont when I traverse the spatial dimensions. Id > >appeal > > > to an asymmetry between time and space, it is a dimension of sorts, but > >not > > > one that can conceptually swapped with a spatial dimension easily. I > >dont > > > think the a priori requirements for space will be necessarily the same > >as > > > those for time. > > > > > > > >Actually, this is not correct; but a presumption of experiential pre-bias. > >While it is true that we can calculate negative spatial values and not > >identify negative temporal values easily - or at all in some cases - let > >me describe motion in this alternative way for you: > > > >1. All action/motion is never a single dimension but instead, a net-vector. > >(be it spatially evaluated or temporally or both). > > > >therefore, it is quite possible to say that the impression of time > >as a positive single vector is masking its composite dimensional structure > >which it is really made of. > > > >2. Negative spatial distances are calculation illusions, usable only > >because > >we can visually identify a sequence reversal and label the suquences > >alternatively - even though - in a relativistic universe, ALL actions and > >traversals of 'distance' are and can only be done ... positively. > >"Negative" dimension values are conditional computational handwavings. > > > >And again, even spatial traversals are net-vectors. A body in true motion > >through space is ALWAYS in a positive net-vector; the same as > >presumptively ascribed only to time. > > > >Therefore, Time can and undoubtably does have, internal dimesional > >structuring; contrary to the conventional view of it not. > > > >James Rose > >ref: > >"Understanding the Integral Universe" (1972;1992;1995) > > > > _ > Want to block unwanted pop-ups? Download the free MSN Toolbar now! > http://toolbar.msn.co.uk/
Re: Quantum Suicide Bombing
Le 13-juil.-05, à 01:01, Charles Goodwin a écrit : From: [EMAIL PROTECTED] [mailto:Fabric-of- [EMAIL PROTECTED] On Behalf Of Lee Corbin I don't know what you even *mean* by "QS does not reduce the number of worlds you experience", unless you mean that nothing that I can do affects the number of worlds I can experience. (And I will not discuss free will vs. determinism.) I *think* what this means is based on the QTI rule (or theorem or whatever) that *all* observer-moments have continuers. But I could be wrong. It *is* a delicate matter. Recently Stathis Papaioannou, on the everything-list, has made a theory where "to be in an alive state" is represented by an observer-moment having at least one continuer (or successor as he called them). "to be (absolutely) dead" is represented by an observer-moment having no successor (so that: to be dead = not to be alive, which is rather natural for a platonist). And at some point in a reasoning Stathis said that we die at each instant. This gives a theory where all transient (alive) observer moments have a cul-de-sac successor. Of course an observer moment could have more than one successor and some successor can be transient. In Stathis theory, at first sight, to be immortal would consist in being forever in the state of being able to die! Now the problem with such a theory where there are cul-de-sac worlds "everywhere" (I mean "accessible from all transient worlds") is that it can be shown that there is no available notion of (relative) probability bearing on accessible observer moments. Probabilities reappears when we explicitly make abstraction of the cul-de-sac worlds or observer-moments. It is the implicit default assumption of probability: if you throw a dice you will not say the probability of getting 6 is 1/7 giving that the possible results would be getting 1, getting 2, getting 3, ... , getting 6, and dying! Doing that abstraction changes the logic, and changes the possible structure on the set of OMs. With comp such a change logic can be justified logically once we distinguish provability and truth, that is by taking into account explicitly the incompleteness phenomenon. It is hard to say more without being a tiny bit more technical. I will explain more on the everything list. The point is that quantum immortality or the more general (and older) comp-immortality is *provably* a personal opinion bearing on first person notions. But that is the case with any assertion that some theory are *true*. Bruno http://iridia.ulb.ac.be/~marchal/
Re: The Time Deniers and the idea of time as a "dimension"
Le 13-juil.-05, à 06:02, Russell Standish a écrit : Complex numbers indeed do not have an ordering (being basically points on a plane) So you pretend the axiom of choice is false. It is easy to build an ordering of the complex numbers through it. There is no ordering *which satisfies some algebraic desiderata*. But as a set, you can always ordered it (given that the axiom of choice is consistent with ZF). Bruno http://iridia.ulb.ac.be/~marchal/
Re: Quantum Suicide Bombing
Le 09-juil.-05, à 16:09, David Deutsch a écrit : On 8 Jul 2005, at 11:25am, <[EMAIL PROTECTED]> <[EMAIL PROTECTED]> wrote: Now - what should be done about the presentation of this concep of "Quantum Suicide Bombing"? By the way: The discussion is *not* about the validity of many worlds interpretation. In order to do a quantum suicide attack, one only has to *believe* in many world interpretation. In my opinion, not *only*: one also has to have some misconceptions about probability and decisions (and about morality too). *The Beginning of Infinity* is going to contain a critique of the "quantum suicide" argument and what I consider to be other misuses of the concept of probability such as the "simulation argument". Which misuses? Which misconceptions? Schmidhuber, Bostrom, or ... Bruno http://iridia.ulb.ac.be/~marchal/
