Re: ... cosmology? KNIGHT & KNAVE
Hi, At 19:47 23/07/04 +0200, I wrote: Big Problem 5: Could a native tell you "You will never know that I am knight" ? Very Big Problem 6: Could a native tell you "You will never believe that I am knight" ? It was perhaps not pedagogical to say "big" and "very big". Here John Mikes would be accurate to say those are not problems, but koans. So you can *meditate* on it ... My intent in the use of the word "big" was more to point on the fact that ,going from the preceding problems to those new one is, as you can guess, the passage from ordinary logic to modal logic, giving that "knowing" and "believing" are modalities. Still we do have intuition on what knowledge and believe can be, and we can try to get some conclusion. Let us try the problem 5. Just to be sure let me know if you agree that the proposition: You will not know that Lance Amstrong has win the "Tour de France", is false. I mean the negation of "You will not know p" is "you will know p". OK then. Suppose the native is a knave. Then it means he is lying when he say that "you will never know I am knight". But that means I will know he is a knight. But I cannot *know* he is a knight if he is a knave, so he cannot be a knave, and thus he is a knight. But having reach that conclusion I know he is a knight, but then he was lying (giving he told me I will never know that. So he is a knave, yes but we have already show he cannot be a knave. It looks like we are again in an oscillating state of mind. Is it a tourist again? No. I told you it is a native and all native are, by the definition of the KK island, either knight or knave. So what? I will give many critics later on some "less good" chapter of FU, (ex: the chapter "the heart of the matter" is too short, or when he identify a reasoner with a world in his possible world chapter, etc.) But Smullyan's discussion on the problem 5 is really quite instructive. Its attack of the problem 5 is quite alike my attack on the mind body problem, Smullyan will interview "reasoner" (actually machine) on those questions. And he goes on very meticulously by defining a hierarchy of type of reasoner, making those problem, mainly the problem 6 more and more interesting. Indeed, with the problem 5, we are quickly done, giving that the problem 5 leads toward a genuine contradiction even with the reasoner of lowest type: the one Smullyan calls the "reasoner of type 1". A reasoner, or a machine, or a system (whatever) will be said to be of type 1 if by definition the following conditions hold: 1) he believes all classical tautologies (our lowest type of reasoner is already a platonist!) 2) if the reasoner ever believes both X and X ->Y, he will believe Y. I will also say, following Smullyan and ... Theaetetus, that a reasoner know p, in the case the reasoner believes p and p is true, that is when the reasoner correctly believes p. There is nothing metaphysical in our use of the word "believe". You can substitute it by "prove" or even just "print". That would mean you are in front of a sort of theorem prover which will, for any classical tautology, print it one day or an other (condition 1), and, in case it prints X and X->Y, it will, soon or later, print Y. That is he prints a proposition if and only if he believes it. To transform the "koan 5" into a genuine problem, I must explain what it means for a reasoner to believe in the rules of the island. It means that if he met a native asserting a proposition p, then he believes the proposition "the native is a knight if and only if p is true". We will write Bp for the reasoner believes p, and Kp for the reasoner knows p. For exemple we have Kp <-> p & Bp problem 5' (ameliorated version): A visitor of type 1 meets, on the KK island, a native telling him "you will never know I am a knight". Convince yourself that this really cannot happen. Derive a contradiction. Problem 6' (new version): A visitor of type 1 meets, on the KK island, a native telling him "you will never believe I am a knight". Convince yourself that this can happen. Derive as many conclusions as you can (note that all FU will follow, and even my thesis!!! (if you are patient enough). The idea is to give more and more self-awareness to the visitor ... Curiously enough that path converges. Bruno PS Those who feels overwhelmed can wait I come back on problem 4, when I will recall a little bit more matter on propositional logic. Apology for my post to Jesse which could look a little bit "advanced" for many (it presupposes FU and a little bit more). Actually writing this stuff helps me for my paper. I thank you in advance. http://iridia.ulb.ac.be/~marchal/
Shahriar S. Afshar Quantum Rebel (2)
Comments (rants, peals of laughter)?: http://www.kathryncramer.com/wblog/archives/000674.html http://www.kathryncramer.com/wblog/archives/000530.html http://64.233.161.104/search?q=cache:AN9UxmCda50J:faculty.washington.edu/jcramer/PowerPoint/Boskone_0402.ppt++Afshar+experiment&hl=en Cheers! CMR<- insert gratuitous quotation that implies my profundity here ->
Re: Shahriar S. Afshar Quantum Rebel (2)
We discussed Afshar's experiment before. Kathryn Cramer, the blogger, is John Cramer's daughter. John Cramer invented the Transactional Interpretation of QM, similar in flavor to Bohm's pilot wave theory, and his daughter is pushing Afshar's results as being best understood in the context of the TI. Actually she goes further and claims that Afshar falsifies both the Many-World and the Copenhagen Interpretations. The CI is not falsifiable IMO because it is too vague and amounts to little more than a policy of not asking embarrassing questions. Physicists can get their work done and leave philosophizing to others. The problem the Transactional Intepretation has with the MWI is that worlds in the MWI never fully disengage. There is always an exponentially decreasing connection between them. This means that the quantum formalism would reflect the actions of intelligent beings in shadow worlds who are different from ourselves, if we calculated to enough precision. This is true even in the TI or in Bohm's theory. Those theories may deny the reality of other worlds, but in principle they have to take into consideration what would be happening there in order to make their calculations. This is obvious in a double slit experiment, but the phenomenon never goes away completely, no matter how far we go towards decoherence. Let Schrodinger's cat become alive or dead, but suppose there is some super-advanced technology that can reverse the process of death at the quantum level, undo the decoherence and restore a coherent state. Now, even the TI has to take into consideration the actions of those in the other world who performed that technological miracle. This may seem too far-fetched even to consider, but we are taking tiny steps today in this direction, pushing farther into the decoherence frontier. So far everything suggests that QM holds up, meaning that interference is still detectable with proper experimental setup even after substantial amounts of decoherence. All the MWI says is that this effect, which is exactly what is predicted by standard QM, will persist even as decoherence advances so far that we can no longer measure the interference. Either an interpretation has to accept the reality of parallel worlds, making it a version of the MWI; or predict that this effect will no longer occur, which will violate QM; or deny that the people in the shadow worlds are real, even though the ripples of their actions affect our own world; or it has to stick its head in the sand and deny that it matters since we can't detect those ripples anyway today, and probably will never be able to do so. I'd be curious to know which choice the Transactional Interpretation makes. Hal Finney
Re: ... cosmology? KNIGHT & KNAVE
Bruno, (and Class) We have an overwhelming ignorance about Ks and Ks. We don't know their logical built, their knowledege-base, their behavior. Is the K vs K rule a physical, or rather human statement, when - in the latter case there may be violations (punishable by jail - ha ha). Do K & K abide by 100.00% by the ONE rule we know about them, or ~99.999%, when there still may be an aberration? Are they robots or humans? Looks like machines. Are machines omniscient? To your present 2 problems: none of them CAN be a knight, because in all fairness, nobody knows what may a person 'know' or 'believe' in the future. If I go to the Office of Records, I may learn what that 'K' is. John Mikes - Original Message - From: "Bruno Marchal" <[EMAIL PROTECTED]> To: <[EMAIL PROTECTED]> Sent: Monday, July 26, 2004 12:49 PM Subject: Re: ... cosmology? KNIGHT & KNAVE > Hi, > > > At 19:47 23/07/04 +0200, I wrote: > >Big Problem 5: > > > >Could a native tell you "You will never know that I am knight" ? > > > >Very Big Problem 6: > > > >Could a native tell you "You will never believe that I am knight" ? > > > It was perhaps not pedagogical to say "big" and "very big". > Here John Mikes would be accurate to say those are not problems, > but koans. So you can *meditate* on it ... > My intent in the use of the word "big" was more to point on the fact > that ,going from the preceding problems to those new one is, > as you can guess, the passage from ordinary logic > to modal logic, giving that "knowing" and "believing" are modalities. > Still we do have intuition on what knowledge and believe can be, and > we can try to get some conclusion. > > Let us try the problem 5. Just to be sure let me know if you agree > that the proposition: > > You will not know that Lance Amstrong has win the "Tour de France", > is false. I mean the negation of "You will not know p" is "you will know p". > > OK then. Suppose the native is a knave. Then it means he is lying when > he say that "you will never know I am knight". But that means I will know > he is a knight. But I cannot *know* he is a knight if he is a knave, so he > cannot be > a knave, and thus he is a knight. But having reach that conclusion I know > he is a knight, but then he was lying (giving he told me I will never > know that. So he is a knave, yes but we have already show he cannot > be a knave. It looks like we are again in an oscillating state of mind. > Is it a tourist again? No. I told you it is a native and all native are, > by the definition of the KK island, either knight or knave. So what? > > I will give many critics later on some "less good" chapter of FU, (ex: > the chapter "the heart of the matter" is too short, or when he identify > a reasoner with a world in his possible world chapter, etc.) > But Smullyan's discussion on the problem 5 is really quite instructive. > Its attack of the problem 5 is quite alike my attack on the mind body > problem, Smullyan will interview "reasoner" (actually machine) on those > questions. And he goes on very meticulously by defining a hierarchy > of type of reasoner, making those problem, mainly the problem 6 more > and more interesting. > Indeed, with the problem 5, we are quickly done, giving that the > problem 5 leads toward a genuine contradiction even with the reasoner > of lowest type: the one Smullyan calls the "reasoner of type 1". > > A reasoner, or a machine, or a system (whatever) will be said to be > of type 1 if by definition the following conditions hold: > > 1) he believes all classical tautologies (our lowest type of reasoner > is already a platonist!) > 2) if the reasoner ever believes both X and X ->Y, he will believe Y. > > I will also say, following Smullyan and ... Theaetetus, that a reasoner > know p, in the case the reasoner believes p and p is true, that is when > the reasoner correctly believes p. > There is nothing metaphysical in our use of the word "believe". You can > substitute it by "prove" or even just "print". That would mean you are > in front of a sort of theorem prover which will, for any classical tautology, > print it one day or an other (condition 1), and, in case it prints X and X->Y, > it will, soon or later, print Y. That is he prints a proposition if and > only if he believes it. > > To transform the "koan 5" into a genuine problem, I must explain what it > means for a reasoner to believe in the rules of the island. It means that > if he met a native asserting a proposition p, then he believes the proposition > "the native is a knight if and only if p is true". > We will write Bp for the reasoner believes p, and Kp for the reasoner > knows p. For exemple we have Kp <-> p & Bp > > problem 5' (ameliorated version): > A visitor of type 1 meets, on the KK island, a native telling him > "you will never know I am a knight". Convince yourself that this > really cannot happen. Derive a contradiction. > > Problem 6' (new version): > A visitor of type 1 meets, on the KK island
regarding QM and infinite universes
I posted this today on the Fabric of Reality Yahoo Group, but would like to get responses to it over here as well. First, regarding the idea of magical universes or quantum immortality for that matter, doesn't this assume a truly infinite number of universes? However, if you start with the idea that the reality we experience is being created by a mechanical/computational process, isn't it more likely that the number of universes is just extremely large?Why should we assume the "creator" (however you choose to define that) has access to infinite resources? Also, everything that makes up our universe appears to have finite characteristics (per QM), so it seems like every possibility within the parameters of the multiverse could be covered by an enormous, but not infinite range of possibility. My understanding of QM is that it describes possibilities (even if vanishingly small) of bizarre things occurring in our everyday world. For instance, I once read a book in which the author calculated the possibility(incredibly small obviously) that our planet would suddenly appear in orbit, fully intact, around another star. He argued that QM allows for this possibility. I think we are overlooking something here. It seems like there should be a quanta of probabilty, just as there is (apparently) with time, space, and matter. In other words, once the probability of something happening falls below a certain threshold, it is not realized. Could there be a Planck scale of probability? Does decoherence somehow keep these strange events from occurring on a macro scale? Also, it seems to me that the violation of other physical laws comes into play in preventing many scenarios from taking place. For instance, with quantum immortality, I understand the concept that if there are infinite copies of me, there will always be one more universe in which I survive another second. But the reality is that there would seem to be a rate of diminishing return here. The probability curve would have a point where it approaches zero, even as the number of alternatives approached infinity. Another way to resolve the immortality issue is to presume consciousness survives death, but I will not remark on that further. One thing that I think hurts the MWI as a theory is the misconception among many that everytime a choice is made, the entire universe splits in two, and there is a proliferation of all of these virtually identical copies of universes out there somewhere. In reality there is only one universe, and there is a proliferation of differences being created. The only thing that matters are the recorded differences, everything else remains unchanged. If you view our reality as a virtual reality it is much easier to understand this concept. For instance a program that predicts the weather doesn't have to create an entirely new simulation for each outcome it predicts- it can overlap the various possibilities in one simulation.
Does Omega point theory allow for an eternally self-creating universe?
Assuming MWI is correct, and that Tipler's Omega point theory is correct in that in at least some portion of the multiverse there will exist the physical capacity for a computer to exist with infinite computing power, even in the confines of a finite universe, does this then allow for an eternally self-recreating universe with no outside explanation necessary? Specifically, the question is whether the Omega point computer could simulate the birth of a new, fully intact multiverse and run it through to the creation of a new virtual omega point computer, that would then continue the process in an endless cycle (or chain)? Does one computer with infinite computing power (and only a millisecond to exist from an objective viewpoint) allow for this infinite layer of creation? Does it matter whether the multiverse itself is infinite or just very large?
RE: regarding QM and infinite universes
You don't need an infinite number of universes, or even an infinite number
of states in the one universe (if there is only one universe) to have
something approaching immortality. If you limit yourself to the information
theoretically containable in even something as small as a human-sized
object, it would be many orders of magnitude greater than the amount of
information processed by a human brain in a single lifetime. I think it
would be relatively straightforward to calculate how many orders of
magnitude using the Beckenstein Bound - perhaps someone could comment. If
you allow for the potential information content in the whole visible
universe, I'm sure that would be plenty of lifetimes for every human that
has ever lived. The problem is not the number of possible lifetimes squeezed
into the universe, but whether these possibilities will actually be
realised.
In a many worlds interpretation of QM, all possibilities WILL be realised in
some universe. If the universe is unique but infinite in extent (and hence
contains an infinite amount of information), all possibilities will be
realised provided that it is homogeneous but non-repeating. If all possible
computations are implemented by virtue of their platonic existence, without
the need for a "real" physical universe at all, then again all possibilities
will be realised and we are immortal in this virtual heaven. If the universe
collapses in such a way as to allow an infinite number of computations in a
finite amount of time, as per Tipler, then potentially we will experience
immortality, although I have not been able to understand how the
quantisation of time would allow such a thing.
In a recent post ("All possible worlds in a single world cosmology?") I
wondered about this question in a more pessimistic situation: one universe,
containing a finite amount of matter/energy/information, expanding and
cooling forever. As discussed above, even this model contains the
possibility of near-immortality; certainly the possibility of at least every
possible future our current limited minds could conceive. As you suggested,
even single word interpretations of QM allow for extremely improbable
events, such as the Earth quantum tunnelling to another star. I don't accept
your notion of a minimal quantum of probability; there seems no reason to
postulate such a thing. Given infinite time, such improbable events MUST
occur - provided that the probability statys constant or increases per unit
time. But if the probability decreases with time, then, even given eternity,
it is NOT certain that the given improbable-but-not-impossible event will
occur, so that immortality is not guaranteed. Bummer!
So far, no-one has been able to tell me what happens to the probability of
bizarre quantum events occurring as t->infinity in a finite, eternally
expanding universe, which incidentally seems more likely than the Tipler
scenario.
Stathis Papaioannou
From: Danny Mayes <[EMAIL PROTECTED]>
To: [EMAIL PROTECTED]
Subject: regarding QM and infinite universes
Date: Mon, 26 Jul 2004 20:54:33 -0400
I posted this today on the Fabric of Reality Yahoo Group, but would like to
get responses to it over here as well.
First, regarding the idea of magical universes or quantum immortality
for that matter, doesn't this assume a truly infinite number of
universes? However, if you start with the idea that the reality we
experience is being created by a mechanical/computational process,
isn't it more likely that the number of universes is just extremely
large?Why should we assume the "creator" (however you choose to
define that) has access to infinite resources? Also, everything that
makes up our universe appears to have finite characteristics (per QM),
so it seems like every possibility within the parameters of the
multiverse could be covered by an enormous, but not infinite range of
possibility.
My understanding of QM is that it describes possibilities (even if
vanishingly small) of bizarre things occurring in our everyday world.
For instance, I once read a book in which the author calculated the
possibility(incredibly small obviously) that our planet would suddenly
appear in orbit, fully intact, around another star. He argued that QM
allows for this possibility.
I think we are overlooking something here. It seems like there should
be a quanta of probabilty, just as there is (apparently) with time,
space, and matter. In other words, once the probability of something
happening falls below a certain threshold, it is not realized. Could
there be a Planck scale of probability? Does decoherence somehow keep
these strange events from occurring on a macro scale?
Also, it seems to me that the violation of other physical laws comes
into play in preventing many scenarios from taking place. For
instance, with quantum immortality, I understand the concept that if
there are infinite copies of me, there will always be one more
universe in which I survive an
Re: regarding QM and infinite universes
So far, no-one has been able to tell me what happens to the probability of bizarre quantum events occurring as t->infinity in a finite, eternally expanding universe, which incidentally seems more likely than the Tipler scenario. Stathis Papaioannou I think there are many things that never happen in even an infinite universe, for reasons that are hard to put into words, and certainly not expressable in terms of math. For instance, I do not believe there will ever exist, anywhere in the multiverse, a reality in which Osama Bin Laden is elected president of the United States in 2004, and is carried into the White House on the shoulders of a boisterous, enthusiatic public. QM does not overtake other physical laws, including difficult to define laws of psychology. A computer could simulate such an event without granting the actors in the simulation consciousness, but for it to actually happen in a universe in which the participants were conscious actors on the stage of reality, such an event would require countless millions of people to not only do something totally illogical, but vehemently against everything they would wish for or desire. I assume if the probability of bizarre quantum events descreases at all over time, then these events may never occur even given infinity? Why should the probability of these events change? Is it based on a theory that the laws of physics are not constant, or they are only local? Also, I assume that if you accept the MWI, regardless of whether "our universe" is expanding forever, you accept there are countless universes (or better described as countless permutations of "our universe") that appear identical to us right now, that will actually contract into a big crunch, making the issue of whether any one particular universe is going to expand forever or collapse pointless? Danny Mayes
