Re: Observer-Moment Measure from Universe Measure
I wanted to add a few points to my earlier posting about how to derive OM measure in a Schmidhuberian multiverse model. The method is basically to take all the universes where the OM appears and to sum up the contribution they make to the OM measure. However, the key idea is that this contribution has two components. One is the measure of the universe. The greater the measure of the universe, the greater the contribution to OM measure. But the other is the fraction of the universe that is involved in the OM. This means that a smaller universe that contains an OM gives a greater fraction of its measure as its contribution to the OM measure. Smaller universes make more contribution than larger ones. This last step may seem ad hoc but in fact it can be seen in a very natural way. It can be thought of as a two step way to output the description of a given OM: first write a program to output a universe with the OM in it, then write a program to take that universe and output the OM. We can think of combining these two programs into one: write a program that outputs the OM. Then, the sum of the measure of all such programs is the measure of the OM. That last sentence is merely the definition of measure in a Schmidhuberian context - the measure of anything is the fraction of all programs that output that thing. It IMPLIES the formula I described for downgrading a universe's contribution to an OM by virtue of the relative size of the OM compared to the universe. It can be said that we have derived and proven that relationship by assuming this fundamental definition of measure. Note that we could also write a program to output an OM without regard to creating a universe first. However, I believe that at least for observers like us, it will always be a much simpler program to first create a universe and then find the OM in it. This lets evolution work and everything is simple. Ultimately, this allows the AUH (all universe hypothesis, ie the multiverse exists) to JUSTIFY the belief that we are not brains (or OMs) in vats, that the universe is probably real. Okay, so that's just restating what I had before in different words, explaining it from a different perspective that might be more obvious. Here are a couple of interesting additions. First, what about our universe? Why is it so damn big? If the measure of an OM is smaller in a big universe, the AUH should predict that the universe is no bigger than it needs to be. Yet, looking around, our universe looks a lot bigger than necessary. There's a lot of wasted space. I conclude that it is likely that the universe is not in fact much bigger than it needs to be. It actually needs to be as big as it is. This might imply that intelligent life is extremely rare in universes like ours. Only by creating a truly enormous universe can we have a good chance of creating observers. Let me expand on this a little. All universes exist. Some have complex laws of physics and some are simple. Some have complex initial conditions and some are simple. Physicists believe that our universe is relatively simple by both measures. The laws of physics are not completely understood but the ones we know have a very simple mathematical formulation. And the initial conditions also appear to represent a very smooth and uniform condition immediately after the Big Bang. The bottom line is that you would not have to write a very big program to simulate our universe. Yet, even with these simple laws, our universe supports life that can evolve into consciousness. That's pretty amazing, maybe. What are the odds that another universe with equally simple laws could do so? We know that our own physical laws appear to be relatively fine tuned such that even a tiny change in various properties would cause life as we know it to be impossible. That suggests that maybe it is not so easy to have life. Maybe almost no universes with laws as simple as ours create life. And, maybe life is not all that easy to create even in our universe. What if life, at least intelligent life, is overwhelmingly unlikely, even in a universe as well suited as our own? Maybe we need ten billion light years' worth of galaxies, stars and planets in order to have a decent chance of evolving life. Maybe, in short, our universe is as big as it needs to be, given our laws of physics, to allow life to evolve. There may be other sets of laws of physics that would be more fecund, where life could evolve more easily. Those might get by with smaller universes. But if so, the AUH would predict that such universes would have much more complicated laws of physics and/or initial conditions than our own. Otherwise we would live there. Given that the universe is as big as we see, and given the AUH, we can predict that it is not full of intelligent life. We can predict that there should be almost no other intelligent civilizations within the universe. This then solves the Fermi paradox - where are the
RE: Observer-Moment Measure from Universe Measure
Jonathan Colvin writes: I presume the answer is that rather than look at physical size/weight of our bodies, one must try to calculate the proportion of the universe's information content devoted to that part of our beings essential to being an observer (probably something to do with the amount of grey matter). Yes, I think that's right. Our bodies don't directly contribute to our conscious experiences. But again, this surely changes as we age. My brain (and consciousness) at age 2 was much smaller than at age 30, and will start to shrink again as I get senile. Does our measure increase with age? I think you meant decrease, at least in terms of becoming elderly. Of course we already know that measure decreases with age due to the continual risk of dying. But yes, I think this argument would suggest that there is a small decrease in measure due to brain shrinkage. It would not be a very large effect, though, I don't think. If we get brain surgery, does our measure diminish? You mean if they cut out a piece of your brain? I guess that would depend on whether it affected your consciousness. If it did you probably have bigger problems than your measure decreasing. Your consciousness would change so much that your previous self might not view you as the same person. And once the transhumanist's dream of mental augmentation is possible, will our measure increase as our consciousness increases? Yes, I think so, assuming the brains actually become bigger. Although there is a counter-effect if the brains instead become faster and smaller, as I wrote earlier. So this raises a paradox, why are we not super-brains? Perhaps this is an argument against the possibility that this will ever happen, a la the Doomsday Argument (why do we not live in the Galactic Empire with its population billions of times greater than today?). Although these conclusions may be counter-intuitive, I find it quite exciting to be able to derive any predictions at all from the AUH in the Schmidhuber model. It suggests that uploading your brain to a computer might be tantamount to taking a large chance of dying; unless you could then duplicate your uploaded brain all over the world, which would greatly increase your measure. And all this comes from the very simple assumption that the measure of something is the fraction of multiverse resources devoted to it, a simple restatement of the Schmidhuber multiverse model. Hal Finney
RE: Observer-Moment Measure from Universe Measure
Hal Finney wrote: I presume the answer is that rather than look at physical size/weight of our bodies, one must try to calculate the proportion of the universe's information content devoted to that part of our beings essential to being an observer (probably something to do with the amount of grey matter). Yes, I think that's right. Our bodies don't directly contribute to our conscious experiences. But again, this surely changes as we age. My brain (and consciousness) at age 2 was much smaller than at age 30, and will start to shrink again as I get senile. Does our measure increase with age? I think you meant decrease, at least in terms of becoming elderly. Of course we already know that measure decreases with age due to the continual risk of dying. But yes, I think this argument would suggest that there is a small decrease in measure due to brain shrinkage. It would not be a very large effect, though, I don't think. If we get brain surgery, does our measure diminish? You mean if they cut out a piece of your brain? I guess that would depend on whether it affected your consciousness. If it did you probably have bigger problems than your measure decreasing. Your consciousness would change so much that your previous self might not view you as the same person. And once the transhumanist's dream of mental augmentation is possible, will our measure increase as our consciousness increases? Yes, I think so, assuming the brains actually become bigger. Although there is a counter-effect if the brains instead become faster and smaller, as I wrote earlier. So this raises a paradox, why are we not super-brains? Perhaps this is an argument against the possibility that this will ever happen, a la the Doomsday Argument (why do we not live in the Galactic Empire with its population billions of times greater than today?). There's a simple answer to that one. Presumably, a million years from now in the Galactic Empire, the Doomsday argument is no longer controversial, and it will not be a topic for debate. The fact that we are all debating the Doomsday argument implies we are all part of the reference class: (people debating the doomsday argument), and we perforce can not be part of the Galactic Empire. Although these conclusions may be counter-intuitive, I find it quite exciting to be able to derive any predictions at all from the AUH in the Schmidhuber model. It suggests that uploading your brain to a computer might be tantamount to taking a large chance of dying; unless you could then duplicate your uploaded brain all over the world, which would greatly increase your measure. And all this comes from the very simple assumption that the measure of something is the fraction of multiverse resources devoted to it, a simple restatement of the Schmidhuber multiverse model. I find these conclusions counter-intuitive enough to suggest that deriving measure from a physical fraction of involved reasources is not the correct way to derive measure. It is not unlike trying to derive the importance of a book by weighing it. Jonathan Colvin
RE: Observer-Moment Measure from Universe Measure
Jonathan Colvin writes, regarding the Doomsday argument: There's a simple answer to that one. Presumably, a million years from now in the Galactic Empire, the Doomsday argument is no longer controversial, and it will not be a topic for debate. The fact that we are all debating the Doomsday argument implies we are all part of the reference class: (people debating the doomsday argument), and we perforce can not be part of the Galactic Empire. Well, I don't want to open up discussion of the DA. Suffice it to say that good thinkers have spent considerable amounts of time considering it and don't necessarily think that this reply puts it to bed. http://www.anthropic-principle.com has an exhaustive discussion. [Regarding measure and size] I find these conclusions counter-intuitive enough to suggest that deriving measure from a physical fraction of involved reasources is not the correct way to derive measure. It is not unlike trying to derive the importance of a book by weighing it. Don't be too eager to throw out this concept of measure. It is fundamental to the Schmidhuber and Tegmark approach to the multiverse. It allows deriving why induction works as well as Occam's razor. It explains why the universe is lawful and has a simple description. It allows us in principle to calculate how likely we are to be in The Matrix or some such simulation vs a basement-level universe. It is quite an amazing quantity of results from such a simple assumption. I don't think you will find anything else like it in philosophy. As far as the specific issue of measure and size, suppose you agree that making copies of a structure increases its measure, but you object to the idea that scaling up its size would do so. Years ago I came up with a thought experiment that adopted the position you have, that size doesn't matter. (That's what my wife kept telling me, after all...) From that I proved that copies didn't matter either, which wasn't too appealing. Today I would say that my premise was wrong. Size matters. Here is a simple example. Suppose we have a book in a computer memory. Now we make two copies of the book in memory. Perhaps you will agree that this increases its measure. Maybe the measure doubles, or maybe it doesn't go up quite that much, but it does increase. Now suppose we arrange the two copies interleaved in memory. Instead of It was the best of times, it was the worst of times... in two places, we have IItt wwaass tthhee bbeesstt ooff ttiimmeess Is this still two copies, or is it one copy with extra big data representation? The difference is not so clear. This should suggest, maybe there isn't any difference in terms of measure of the two cases. I have several other examples I have used as well. In one I have a pair of electronic computers running exactly the same program side by side, in lockstep. This is two instances and arguably the program has larger measure. Now I attach wires between the corresponding parts of the electronic circuits that make up the computers. Point A in the left computer is attached to point A in the right computer, and so on for every circuit element. These wires have variable resistance that can be smoothly changed from full conductivity to perfect insulation. When the wires are insulated, there is no interaction between the two computers and there are two copies. When the wires are conductive, the corresponding circuit elements are electrically joined so the system acts like a single computer that is twice as big. By varying the resistance we can smoothly go from one case to the other. Imagine a conscious program running on this system. When there are two computers, perhaps there are two conscious entities, each with their unique identity. When there is only one computer, there is only one consciousness. Yet we can switch smoothly between the two. We can go from two people to one and back! How much sense does that make? I wouldn't put it like that today, but if we just focus on measure, we again go from a pair of computations to a computation that is twice as big. It makes sense that the two cases would have the same measure. From these and other thought experiments I find that it is not as surprising as it seems at first to imagine that increasing size increases measure. The fact that it follows immediately from Schmidhuber's simple principle only came to me recently. I find it interesting and provocative that these two independent arguments lead to the same conclusion. Hal Finney
Re: Re-Observer-Moment Measure from Universe Measure
Le 14-juin-05, à 00:35, George Levy a écrit : Bruno Marchal wrote: Godel's theorem: ~Bf - ~B(~Bf), which is equivalent to B(Bf - f) - Bf, Just a little aside a la Descartes + Godel: (assume that think and believe are synonymous and that f = you are) All right. Of course this follows that for any p in the language of the machine, we have indeed that the machine can prove B(Bp - p) - Bp That is: the machine does prove its Lob's theorem. (in my post to Brent f was the constant FALSE). B(Bf - f) - Bf can be rendered as: If you believe that if you think that you are therefore you are, then you think you are. Nice! This makes a relation between Lob's theorem (which generalizes Godel's second incompleteness theorem) and Descartes systematic doubting procedure. The link exists already with Godel's theorem. If you look at the arithmetical placebo phenomenon (in my SANE paper), you are relating Descartes and the Placebo. Quite cute! That's what Descartes thought! I agree essentially. See Slezak for a pionering and readable paper relating Godel and Descartes: SLEZAK P., 1983, Descartes 's Diagonal Deduction, Brit. J. Phil. Sci. 34, pp. 13-36. And this is related also with the debate on Godel and Mechanism (against Penrose and Lucas), on which Slezak wrote a paper, which could be needed for the reading of its Godelian reading of Descartes. SLEZAK P., 1982, Gödel's Theorem and the Mind, Brit. J. Phil. Sci. 33, pp. 41-52. Bruno http://iridia.ulb.ac.be/~marchal/
Re: Observer-Moment Measure from Universe Measure
Hi Brent, You didn't answer my last post where I explain that Bp is different from Bp p. I hope you were not too much disturbed by my teacher's tone (which can be enervating I imagine). Or is it because you don't recognize the modal form of Godel's theorem: ~Bf - ~B(~Bf), which is equivalent to B(Bf - f) - Bf, by simple contraposition p - q is equivalent with ~p - ~q, and using also that ~p is equivalent to p - f, where f is put for false. This shows that for a consistent (~Bf) machine, although Bf - f is true, it cannot be proved by the machine. Now (Bf f) - f trivially. So Bf and Bf f are not equivalent for the machine (although they are for the guardian angel). Bruno http://iridia.ulb.ac.be/~marchal/
Re-Observer-Moment Measure from Universe Measure
Bruno Marchal wrote: Godel's theorem: ~Bf - ~B(~Bf), which is equivalent to B(Bf - f) - Bf, Just a little aside a la Descartes + Godel: (assume that think and believe are synonymous and that f = you are) B(Bf - f) - Bf can be rendered as: If you believe that if you think that you are therefore you are, then you think you are. That's what Descartes thought! :-)George
Re: Observer-Moment Measure from Universe Measure
- Original Message - From: Brent Meeker [EMAIL PROTECTED] To: Saibal Mitra [EMAIL PROTECTED] Sent: Sunday, June 12, 2005 02:43 AM Subject: RE: Observer-Moment Measure from Universe Measure -Original Message- From: Saibal Mitra [mailto:[EMAIL PROTECTED] Sent: Sunday, June 11, 2000 4:01 PM To: Brent Meeker; :everything-list@eskimo.com Subject: Re: Observer-Moment Measure from Universe Measure - Original Message - From: Brent Meeker [EMAIL PROTECTED] To: Saibal Mitra [EMAIL PROTECTED] Sent: Friday, June 10, 2005 06:41 PM Subject: RE: Observer-Moment Measure from Universe Measure -Original Message- From: Saibal Mitra [mailto:[EMAIL PROTECTED] Sent: Friday, June 10, 2005 11:39 PM To: Brent Meeker; everything Subject: Re: Observer-Moment Measure from Universe Measure - Original Message - From: Brent Meeker [EMAIL PROTECTED] To: Saibal Mitra [EMAIL PROTECTED] Sent: Wednesday, June 08, 2005 02:23 PM Subject: RE: Observer-Moment Measure from Universe Measure -Original Message- From: Saibal Mitra [mailto:[EMAIL PROTECTED] Sent: Wednesday, June 08, 2005 1:16 PM To: Patrick Leahy; Hal Finney; [EMAIL PROTECTED]; [EMAIL PROTECTED] Cc: everything-list@eskimo.com Subject: Re: Observer-Moment Measure from Universe Measure I think one should define an observer moment as the instantaneous description of the human brain. I.e. the minimum amount of information you need to simulate the brain of a observer. This description changes over time due to interactions with the environment. Even if there were no interactions with the environment the description would change, but this change is fixed by the original description. That means that, supposing the brain is a classical, the moment cannot be defined by a description of values, omitting rates; just as the path of a ballistic projectile cannot be specified by it location, omitting its velocity. But to include rates means an implicit introduction of time and continuity of OMs. This implies that OMs form causal chains and it makes no sense to talk about the same OM being in two different chains. That's true in an isolated personal universe that is not interacting with an 'outside world'. I could, e.g. take your brain and simulate that on a computer. The evolution equations for your brain are deterministic, so the simulation will describe a unique chain of causal links provided you fix the boundary conditions. If the personal universe is embedded in another universe (like in our case), then the evolution equations will be constantly perturbed. But a lot of the motivation for OMs comes from the brain *not* being classical; from the idea that the brain gets copied into Everett's multiple relative states or MWIs. Decoherence in the brain is very much faster than the neurochemical processes - that's why it's approximately classical. So what is going on when QM predicts different OMs? From Everett's point of view the brain must be treated as part of the QM system and it gets copied - but not by itself. Its description must include its entanglement with the quantum systems observed. So it seems that in either case, classical or quantum, an OM as a description of a brain state, has links outside itself. In the classical case it has casual links in time. In the QM case it has Hilbert space links to what has been observed. I agree. But the entangled state of a brain with the rest of the universe in the MWI corresponds to an ensemble of different worlds such that in each member of the ensemble the brain is in some definite state. So, I see no problem with Hal's way of thinking about OMs Observers are can be thought of as their own descriptions and thus universes in their own right. Observer moments are observers in particular states i.e. their ''personal'' universe being in a certain state. The causal relation between successive states is already defined when we specify which observer we are talking about. i.e., we have already specified the laws of physics for the personal universe of an observer which defines the observer. Specifying the initial state of the personal universes thus suffices. That would hold for a classical brain in a classical universe. But does it in a QM universe? I see a tension between the idea of personal universe and quantum entanglement. I don't see problems here. If you assume that our universe is described by some fundamental laws of physics then those laws of physics also describe our brains. The way a particular brain works is thus fixed. This then defines the personal universe. There seems to be a big jump between those last two sentences. Defining the laws
RE: Observer-Moment Measure from Universe Measure
- Original Message - From: Brent Meeker [EMAIL PROTECTED] To: Saibal Mitra [EMAIL PROTECTED] Sent: Friday, June 10, 2005 06:41 PM Subject: RE: Observer-Moment Measure from Universe Measure -Original Message- From: Saibal Mitra [mailto:[EMAIL PROTECTED] Sent: Friday, June 10, 2005 11:39 PM To: Brent Meeker; everything Subject: Re: Observer-Moment Measure from Universe Measure - Original Message - From: Brent Meeker [EMAIL PROTECTED] To: Saibal Mitra [EMAIL PROTECTED] Sent: Wednesday, June 08, 2005 02:23 PM Subject: RE: Observer-Moment Measure from Universe Measure -Original Message- From: Saibal Mitra [mailto:[EMAIL PROTECTED] Sent: Wednesday, June 08, 2005 1:16 PM To: Patrick Leahy; Hal Finney; [EMAIL PROTECTED]; [EMAIL PROTECTED] Cc: everything-list@eskimo.com Subject: Re: Observer-Moment Measure from Universe Measure I think one should define an observer moment as the instantaneous description of the human brain. I.e. the minimum amount of information you need to simulate the brain of a observer. This description changes over time due to interactions with the environment. Even if there were no interactions with the environment the description would change, but this change is fixed by the original description. That means that, supposing the brain is a classical, the moment cannot be defined by a description of values, omitting rates; just as the path of a ballistic projectile cannot be specified by it location, omitting its velocity. But to include rates means an implicit introduction of time and continuity of OMs. This implies that OMs form causal chains and it makes no sense to talk about the same OM being in two different chains. That's true in an isolated personal universe that is not interacting with an 'outside world'. I could, e.g. take your brain and simulate that on a computer. The evolution equations for your brain are deterministic, so the simulation will describe a unique chain of causal links provided you fix the boundary conditions. If the personal universe is embedded in another universe (like in our case), then the evolution equations will be constantly perturbed. But a lot of the motivation for OMs comes from the brain *not* being classical; from the idea that the brain gets copied into Everett's multiple relative states or MWIs. Decoherence in the brain is very much faster than the neurochemical processes - that's why it's approximately classical. So what is going on when QM predicts different OMs? From Everett's point of view the brain must be treated as part of the QM system and it gets copied - but not by itself. Its description must include its entanglement with the quantum systems observed. So it seems that in either case, classical or quantum, an OM as a description of a brain state, has links outside itself. In the classical case it has casual links in time. In the QM case it has Hilbert space links to what has been observed. I agree. But the entangled state of a brain with the rest of the universe in the MWI corresponds to an ensemble of different worlds such that in each member of the ensemble the brain is in some definite state. So, I see no problem with Hal's way of thinking about OMs Observers are can be thought of as their own descriptions and thus universes in their own right. Observer moments are observers in particular states i.e. their ''personal'' universe being in a certain state. The causal relation between successive states is already defined when we specify which observer we are talking about. i.e., we have already specified the laws of physics for the personal universe of an observer which defines the observer. Specifying the initial state of the personal universes thus suffices. That would hold for a classical brain in a classical universe. But does it in a QM universe? I see a tension between the idea of personal universe and quantum entanglement. I don't see problems here. If you assume that our universe is described by some fundamental laws of physics then those laws of physics also describe our brains. The way a particular brain works is thus fixed. This then defines the personal universe. There seems to be a big jump between those last two sentences. Defining the laws of physics may define the *way* a brain works - but not its content, not the specifics of its processes - and the same for a universe. Entanglement of the brain with another system can only happen if there are interactions with the outside. Sure, and there must be such interactions according to what we know of physics. Even in the classic case these intercations make the evolution of the personal universe nondeterministic. Right. But in that case on observer moment, defined as: ...one should define an observer moment as the instantaneous
RE: Observer-Moment Measure from Universe Measure
- Original Message - From: Brent Meeker [EMAIL PROTECTED] To: Saibal Mitra [EMAIL PROTECTED] Sent: Wednesday, June 08, 2005 02:23 PM Subject: RE: Observer-Moment Measure from Universe Measure -Original Message- From: Saibal Mitra [mailto:[EMAIL PROTECTED] Sent: Wednesday, June 08, 2005 1:16 PM To: Patrick Leahy; Hal Finney; [EMAIL PROTECTED]; [EMAIL PROTECTED] Cc: everything-list@eskimo.com Subject: Re: Observer-Moment Measure from Universe Measure I think one should define an observer moment as the instantaneous description of the human brain. I.e. the minimum amount of information you need to simulate the brain of a observer. This description changes over time due to interactions with the environment. Even if there were no interactions with the environment the description would change, but this change is fixed by the original description. That means that, supposing the brain is a classical, the moment cannot be defined by a description of values, omitting rates; just as the path of a ballistic projectile cannot be specified by it location, omitting its velocity. But to include rates means an implicit introduction of time and continuity of OMs. This implies that OMs form causal chains and it makes no sense to talk about the same OM being in two different chains. That's true in an isolated personal universe that is not interacting with an 'outside world'. I could, e.g. take your brain and simulate that on a computer. The evolution equations for your brain are deterministic, so the simulation will describe a unique chain of causal links provided you fix the boundary conditions. If the personal universe is embedded in another universe (like in our case), then the evolution equations will be constantly perturbed. But a lot of the motivation for OMs comes from the brain *not* being classical; from the idea that the brain gets copied into Everett's multiple relative states or MWIs. Decoherence in the brain is very much faster than the neurochemical processes - that's why it's approximately classical. So what is going on when QM predicts different OMs? From Everett's point of view the brain must be treated as part of the QM system and it gets copied - but not by itself. Its description must include its entanglement with the quantum systems observed. So it seems that in either case, classical or quantum, an OM as a description of a brain state, has links outside itself. In the classical case it has casual links in time. In the QM case it has Hilbert space links to what has been observed. I agree. But the entangled state of a brain with the rest of the universe in the MWI corresponds to an ensemble of different worlds such that in each member of the ensemble the brain is in some definite state. So, I see no problem with Hal's way of thinking about OMs Observers are can be thought of as their own descriptions and thus universes in their own right. Observer moments are observers in particular states i.e. their ''personal'' universe being in a certain state. The causal relation between successive states is already defined when we specify which observer we are talking about. i.e., we have already specified the laws of physics for the personal universe of an observer which defines the observer. Specifying the initial state of the personal universes thus suffices. That would hold for a classical brain in a classical universe. But does it in a QM universe? I see a tension between the idea of personal universe and quantum entanglement. I don't see problems here. If you assume that our universe is described by some fundamental laws of physics then those laws of physics also describe our brains. The way a particular brain works is thus fixed. This then defines the personal universe. Entanglement of the brain with another system can only happen if there are interactions with the outside. Even in the classic case these intercations make the evolution of the personal universe nondeterministic. Saibal - Defeat Spammers by launching DDoS attacks on Spam-Websites: http://www.hillscapital.com/antispam/
Re: Observer-Moment Measure from Universe Measure
Le 09-juin-05, à 23:00, Jonathan Colvin a écrit : Bruno wrote: I don't believe in observers, if by observer one means to assign special ontological status to mental states over any other arrangement of matter. I don't believe in matters, if by matters one means to assign special ontological status to some substance, by which it is mean (Aristotle) anything entirely determined by its parts. Hehe, the usual response to idealism is to drop a rock onto the propounder's finger, and then ask them if they still do not believe in material objects. And the usual answer of the idealist is that they dream sometimes on rock dropped on their fingers. That proves nothing. With comp you can invoke the matrix or Galouye's Simulacron III. This is similar to the objection to the classic interpretation of QM, whereby an observation is required to collapse the WF (how do you define observer?..a rock?..a chicken?..a person?). Yes, but Everett did succeed his explanation of the apparent collapse by defining an observer by just classical memory machine. But the point is that observation is not central to Everett's theory at all; observation is wholly peripheral, and is only discussed insofar as why it *appears* that a collapse happens. I have argued at length that this is a weak point in Everett. The idea is that once you postulate comp like Everett does, then you need to explain why you take only the quantum computation into account. snip Perhaps you could try to tell me what do you mean by matter? Something that kicks back (has an effect on the universe). I don't take the word universe as granted, still less physicalist type of universe. Actually I search an explanation of just that. With comp, my point is that universe emerges from all (immaterial, mathematical) computations. Arithmetical truth alone can be shown to be a vast video game or simulacron ... Perhaps you could study a little bit of theoretical computer science. They are many conuter-intuitive results which could help to think that what I say is at least pausible. Note that this excludes epiphenomena such as qualia or some interpretions of consciousness, since it appears that the universe would keep running exactly the same way without them. All what I say is that if you are right on this point, then comp is false. (Or there is an error in my thesis, but this I am always assuming by default). Bruno http://iridia.ulb.ac.be/~marchal/
Re: Observer-Moment Measure from Universe Measure
- Original Message - From: Brent Meeker [EMAIL PROTECTED] To: Saibal Mitra [EMAIL PROTECTED] Sent: Wednesday, June 08, 2005 02:23 PM Subject: RE: Observer-Moment Measure from Universe Measure -Original Message- From: Saibal Mitra [mailto:[EMAIL PROTECTED] Sent: Wednesday, June 08, 2005 1:16 PM To: Patrick Leahy; Hal Finney; [EMAIL PROTECTED]; [EMAIL PROTECTED] Cc: everything-list@eskimo.com Subject: Re: Observer-Moment Measure from Universe Measure I think one should define an observer moment as the instantaneous description of the human brain. I.e. the minimum amount of information you need to simulate the brain of a observer. This description changes over time due to interactions with the environment. Even if there were no interactions with the environment the description would change, but this change is fixed by the original description. That means that, supposing the brain is a classical, the moment cannot be defined by a description of values, omitting rates; just as the path of a ballistic projectile cannot be specified by it location, omitting its velocity. But to include rates means an implicit introduction of time and continuity of OMs. This implies that OMs form causal chains and it makes no sense to talk about the same OM being in two different chains. That's true in an isolated personal universe that is not interacting with an 'outside world'. I could, e.g. take your brain and simulate that on a computer. The evolution equations for your brain are deterministic, so the simulation will describe a unique chain of causal links provided you fix the boundary conditions. If the personal universe is embedded in another universe (like in our case), then the evolution equations will be constantly perturbed. But a lot of the motivation for OMs comes from the brain *not* being classical; from the idea that the brain gets copied into Everett's multiple relative states or MWIs. Decoherence in the brain is very much faster than the neurochemical processes - that's why it's approximately classical. So what is going on when QM predicts different OMs? From Everett's point of view the brain must be treated as part of the QM system and it gets copied - but not by itself. Its description must include its entanglement with the quantum systems observed. So it seems that in either case, classical or quantum, an OM as a description of a brain state, has links outside itself. In the classical case it has casual links in time. In the QM case it has Hilbert space links to what has been observed. I agree. But the entangled state of a brain with the rest of the universe in the MWI corresponds to an ensemble of different worlds such that in each member of the ensemble the brain is in some definite state. So, I see no problem with Hal's way of thinking about OMs Observers are can be thought of as their own descriptions and thus universes in their own right. Observer moments are observers in particular states i.e. their ''personal'' universe being in a certain state. The causal relation between successive states is already defined when we specify which observer we are talking about. i.e., we have already specified the laws of physics for the personal universe of an observer which defines the observer. Specifying the initial state of the personal universes thus suffices. That would hold for a classical brain in a classical universe. But does it in a QM universe? I see a tension between the idea of personal universe and quantum entanglement. I don't see problems here. If you assume that our universe is described by some fundamental laws of physics then those laws of physics also describe our brains. The way a particular brain works is thus fixed. This then defines the personal universe. Entanglement of the brain with another system can only happen if there are interactions with the outside. Even in the classic case these intercations make the evolution of the personal universe nondeterministic. Saibal
Re: Observer-Moment Measure from Universe Measure
Le 09-juin-05, à 01:19, Jonathan Colvin a écrit : I don't believe in observers, if by observer one means to assign special ontological status to mental states over any other arrangement of matter. I don't believe in matters, if by matters one means to assign special ontological status to some substance, by which it is mean (Aristotle) anything entirely determined by its parts. This is similar to the objection to the classic interpretation of QM, whereby an observation is required to collapse the WF (how do you define observer?..a rock?..a chicken?..a person?). Yes, but Everett did succeed his explanation of the apparent collapse by defining an observer by just classical memory machine. But this was in response to a comment that it was time to get serious about observer-moments. An observer is such a poorly defined and nebulous thing that I don't think one can get serious about it. My definition is that an observer is a universal (Turing) machine. With Church's thesis we can drop the Turing qualification. Actually an observer is a little more. It is a sufficiently rich universal machine. To be utterly precise (like in my thesis) an observer is a lobian machine, by which I mean any machine which is able to prove ExP(x) - Provable(ExP(x)) for any decidable predicate P(x). ExP(x) means there is a natural number x such that P(x), and provable is the provability predicate studied by Godel, Lob and many others. But then I need to explain more on the provability logic to explain the nuances between the scientist machine, the knowing machine, the observing machine, etc. You can look at my sane paper for an overview. I'd note that your definition is close to being circular..an observer is something sufficiently similar to me that I might think I could have been it. But how do we decide what is sufficient? The qualities you list (consciousness, perception etc) are themselves poorly defined or undefinable. Consciousness can be considered as a first person view of the result of an automatic bet on the existence of a model (in the logician sense) of oneself. From this we can explain why consciousness is not representable in the language of a machine. And consciousness get a role: self-speeding up oneself relatively to our most probable computational histories. It should develop in all self-moving mechanical entity. I define variant of first person view by applying Theaetetus' definition of knowledge (and popperian variants) on the Godel self-referential provability predicate. Perhaps you could try to tell me what do you mean by matter? Bruno http://iridia.ulb.ac.be/~marchal/
RE: Observer-Moment Measure from Universe Measure
-Original Message- From: Jonathan Colvin [mailto:[EMAIL PROTECTED] Sent: Wednesday, June 08, 2005 5:51 AM To: everything-list@eskimo.com Subject: RE: Observer-Moment Measure from Universe Measure Hal Finney wrote: To apply Wei's method, first we need to get serious about what is an OM. We need a formal model and description of a particular OM. Consider, for example, someone's brain when he is having a particular experience. He is eating chocolate ice cream while listening to Beethoven's 5th symphony, on his 30th birthday. Imagine that we could scan his brain with advanced technology and record his neural activity. Imagine further that with the aid of an advanced brain model we are able to prune out the unnecessary information and distill this to the essence of the experience. We come up with a pattern that represents that observer moment. Any system which instantiates that pattern genuinely creates an experience of that observer moment. This pattern is something that can be specified, recorded and written down in some form. It probably involves a huge volume of data. Sorry for the delay in response, but eskimo started bouncing mail from my other smtp for some unknown reason. There's a question begging to be asked, which is (predictably I suppose, for a qualia-denyer such as myself), what makes you think there is such a thing as an essence of an experience? I'd suggest there is no such thing as an observer-moment. I'm happy with using the concept as a tag of sorts when discussing observer selection issues, but I think reifying it is likely a mistake, and goes considerably beyond Strong AI into a full Cartesian dualism. Is it generally accepted here on this list that a substrate-independent thing called an observer moment exists? Jonathan Colvin I agree. There seems to be a jump from the Strong AI idea that a brain can be instantiated in some medium other than neurons (e.g. a computer) to the idea that the brain has states that instantiate experiences. Somehow static patterns get slipped in place of processes. Brent Meeker
RE: Observer-Moment Measure from Universe Measure
Jonathan Colvin writes: There's a question begging to be asked, which is (predictably I suppose, for a qualia-denyer such as myself), what makes you think there is such a thing as an essence of an experience? I'd suggest there is no such thing as an observer-moment. I'm happy with using the concept as a tag of sorts when discussing observer selection issues, but I think reifying it is likely a mistake, and goes considerably beyond Strong AI into a full Cartesian dualism. Is it generally accepted here on this list that a substrate-independent thing called an observer moment exists? Here's how I attempted to define observer moment a few years ago: Observer - A subsystem of the multiverse with qualities sufficiently similar to those which are common among human beings that we consider it meaningful that we might have been or might be that subsystem. These qualities include consciousness, perception of a flow of time, and continuity of identity. Observer-moment - An instant of perception by an observer. An observer's sense of the flow of time allows its experience to be divided into units so small that no perceptible change in consciousness is possible in those intervals. Each such unit of time for a particular observer is an observer-moment. So if you don't believe in observer-moments, do you also not believe in observers? Or is it the -moment that causes problems? Hal Finney
Re: Observer-Moment Measure from Universe Measure
Le 08-juin-05, à 07:51, Jonathan Colvin a écrit : Hal Finney wrote: To apply Wei's method, first we need to get serious about what is an OM. We need a formal model and description of a particular OM. Consider, for example, someone's brain when he is having a particular experience. He is eating chocolate ice cream while listening to Beethoven's 5th symphony, on his 30th birthday. Imagine that we could scan his brain with advanced technology and record his neural activity. Imagine further that with the aid of an advanced brain model we are able to prune out the unnecessary information and distill this to the essence of the experience. We come up with a pattern that represents that observer moment. Any system which instantiates that pattern genuinely creates an experience of that observer moment. This pattern is something that can be specified, recorded and written down in some form. It probably involves a huge volume of data. Sorry for the delay in response, but eskimo started bouncing mail from my other smtp for some unknown reason. There's a question begging to be asked, which is (predictably I suppose, for a qualia-denyer such as myself), what makes you think there is such a thing as an essence of an experience? I'd suggest there is no such thing as an observer-moment. I'm happy with using the concept as a tag of sorts when discussing observer selection issues, but I think reifying it is likely a mistake, and goes considerably beyond Strong AI into a full Cartesian dualism. Not at all. You get dualism only because *you* are reifying metaphysical notion like substantial matter, time etc. Is it generally accepted here on this list that a substrate-independent thing called an observer moment exists? To be sure I have problem with the notion of observer moments, or more precisely with the idea that observer-moments can be taken as primitive. With comp (which is stronger than strong AI, strictly speaking) it has been proved that both space-time-energy-matter-sharable-measurable-quantity AND their qualitative features emerges from arithmetical truth. Comp implies a neutral monism. Bruno http://iridia.ulb.ac.be/~marchal/
RE: Observer-Moment Measure from Universe Measure
On Tue, 7 Jun 2005, Hal Finney wrote: Jonathan Colvin writes: There's a question begging to be asked, which is (predictably I suppose, for a qualia-denyer such as myself), what makes you think there is such a thing as an essence of an experience? I'd suggest there is no such thing as an observer-moment. I'm happy with using the concept as a tag of sorts when discussing observer selection issues, but I think reifying it is likely a mistake, and goes considerably beyond Strong AI into a full Cartesian dualism. Is it generally accepted here on this list that a substrate-independent thing called an observer moment exists? Here's how I attempted to define observer moment a few years ago: Observer - A subsystem of the multiverse with qualities sufficiently similar to those which are common among human beings that we consider it meaningful that we might have been or might be that subsystem. These qualities include consciousness, perception of a flow of time, and continuity of identity. Observer-moment - An instant of perception by an observer. An observer's sense of the flow of time allows its experience to be divided into units so small that no perceptible change in consciousness is possible in those intervals. Each such unit of time for a particular observer is an observer-moment. So if you don't believe in observer-moments, do you also not believe in observers? Or is it the -moment that causes problems? Obviously, its the -moment. I'm pleased to see that Jonathan and Brent have the same problem with the concept that I do. Being an observer is a process. Slicing it into moments is OK mathematically, where a moment corresponds to a calculus dt (and hence is neither a particular length of time nor an instant). But to regard the observer-state at a particular moment as an isolated entity which is self-aware makes as much sense as regarding individual horizontal slices through a brain as being self-aware. It is the causal relation between successive brain states (incorporating incoming sense data) which constitutes intelligence, and self-awareness is just an epiphenomenon on top of intelligence, i.e. I would not agree that anything can be self-aware but have no intelligence. Paddy Leahy
RE: Observer-Moment Measure from Universe Measure
Jonathan Colvin writes: There's a question begging to be asked, which is (predictably I suppose, for a qualia-denyer such as myself), what makes you think there is such a thing as an essence of an experience? I'd suggest there is no such thing as an observer-moment. I'm happy with using the concept as a tag of sorts when discussing observer selection issues, but I think reifying it is likely a mistake, and goes considerably beyond Strong AI into a full Cartesian dualism. Is it generally accepted here on this list that a substrate-independent thing called an observer moment exists? I don't see why you make a big deal out of observer moments. You observe something, so that's an observer moment; then you observe something else, and that's another observer moment; and so on. There is no implied theory about what brings about these OM's, how long a moment is, whether the OM's can in any sense have an existence separate from the substrate they are implemented on, whether a brain is necessary or a computer will do, whether two different OM's belonging to the same observer can each be implemented on different hardware, etc. These may be worthwhile questions to ask, and the OM concept may help in the process of trying to find an answer, but the concept itself does not constitute or imply a theory. --Stathis Papaioannou _ REALESTATE: biggest buy/rent/share listings http://ninemsn.realestate.com.au
Re: Observer-Moment Measure from Universe Measure
I think one should define an observer moment as the instantaneous description of the human brain. I.e. the minimum amount of information you need to simulate the brain of a observer. This description changes over time due to interactions with the environment. Even if there were no interactions with the environment the description would change, but this change is fixed by the original description. So, I see no problem with Hal's way of thinking about OMs Observers are can be thought of as their own descriptions and thus universes in their own right. Observer moments are observers in particular states i.e. their ''personal'' universe being in a certain state. The causal relation between successive states is already defined when we specify which observer we are talking about. i.e., we have already specified the laws of physics for the personal universe of an observer which defines the observer. Specifying the initial state of the personal universes thus suffices. Saibal - Original Message - From: Patrick Leahy [EMAIL PROTECTED] To: Hal Finney [EMAIL PROTECTED] Cc: everything-list@eskimo.com Sent: Wednesday, June 08, 2005 01:04 PM Subject: RE: Observer-Moment Measure from Universe Measure On Tue, 7 Jun 2005, Hal Finney wrote: Jonathan Colvin writes: There's a question begging to be asked, which is (predictably I suppose, for a qualia-denyer such as myself), what makes you think there is such a thing as an essence of an experience? I'd suggest there is no such thing as an observer-moment. I'm happy with using the concept as a tag of sorts when discussing observer selection issues, but I think reifying it is likely a mistake, and goes considerably beyond Strong AI into a full Cartesian dualism. Is it generally accepted here on this list that a substrate-independent thing called an observer moment exists? Here's how I attempted to define observer moment a few years ago: Observer - A subsystem of the multiverse with qualities sufficiently similar to those which are common among human beings that we consider it meaningful that we might have been or might be that subsystem. These qualities include consciousness, perception of a flow of time, and continuity of identity. Observer-moment - An instant of perception by an observer. An observer's sense of the flow of time allows its experience to be divided into units so small that no perceptible change in consciousness is possible in those intervals. Each such unit of time for a particular observer is an observer-moment. So if you don't believe in observer-moments, do you also not believe in observers? Or is it the -moment that causes problems? Obviously, its the -moment. I'm pleased to see that Jonathan and Brent have the same problem with the concept that I do. Being an observer is a process. Slicing it into moments is OK mathematically, where a moment corresponds to a calculus dt (and hence is neither a particular length of time nor an instant). But to regard the observer-state at a particular moment as an isolated entity which is self-aware makes as much sense as regarding individual horizontal slices through a brain as being self-aware. It is the causal relation between successive brain states (incorporating incoming sense data) which constitutes intelligence, and self-awareness is just an epiphenomenon on top of intelligence, i.e. I would not agree that anything can be self-aware but have no intelligence. Paddy Leahy
RE: Observer-Moment Measure from Universe Measure
Paddy Leahy wrote: [quoting Hal Finney] Here's how I attempted to define observer moment a few years ago: Observer - A subsystem of the multiverse with qualities sufficiently similar to those which are common among human beings that we consider it meaningful that we might have been or might be that subsystem. These qualities include consciousness, perception of a flow of time, and continuity of identity. Observer-moment - An instant of perception by an observer. An observer's sense of the flow of time allows its experience to be divided into units so small that no perceptible change in consciousness is possible in those intervals. Each such unit of time for a particular observer is an observer-moment. So if you don't believe in observer-moments, do you also not believe in observers? Or is it the -moment that causes problems? Obviously, its the -moment. I'm pleased to see that Jonathan and Brent have the same problem with the concept that I do. Being an observer is a process. Slicing it into moments is OK mathematically, where a moment corresponds to a calculus dt (and hence is neither a particular length of time nor an instant). But to regard the observer-state at a particular moment as an isolated entity which is self-aware makes as much sense as regarding individual horizontal slices through a brain as being self-aware. It is the causal relation between successive brain states (incorporating incoming sense data) which constitutes intelligence, and self-awareness is just an epiphenomenon on top of intelligence, i.e. I would not agree that anything can be self-aware but have no intelligence. You're making it far more complicated than it needs to be. An observer moment is just a period of conscious experience. Usually it is taken to be the shortest possible period, which for a human is somewhere between 100 and 500 ms, but there is no reason not to discuss observer minutes, hours or whatever seems appropriate to the context. The real entity is the observer, not the observer moment, but it sometimes helps to divide up the observer's experience into time slices just as it is helpful to divide up the day into hours, minutes and seconds. The division does not imply any theory about how the brain actually gives rise to conscious experience, any more than clocks imply any theory about how the planet rotates on its axis. --Stathis Papaioannou _ REALESTATE: biggest buy/rent/share listings http://ninemsn.realestate.com.au
RE: Observer-Moment Measure from Universe Measure
-Original Message- From: Hal Finney [mailto:[EMAIL PROTECTED] Sent: Wednesday, June 08, 2005 6:11 PM To: everything-list@eskimo.com Subject: RE: Observer-Moment Measure from Universe Measure Brent Meeker writes: But the problem I see is that we don't know with certainity the present moment either. I have thoughts and perceptions in a stream, these have finite durations (on the order of hundreds of milliseconds) that overlap one another. When you say we know a present moment you are introspecting a memory of what just happened and I think it likely that you are just confabulating that you not only read the above line but that you were *aware of reading it* at the time. So what do you know? What would you use as a starting point in a philosophical exploration? Do you assume the world is real? That it is inconceivable that you are living in a simulation? Do you assume that your memories are correct? Or would you go in the other direction and say that it is possible that you are not conscious, perhaps that you don't even exist? It seems to me that we have to choose something between assuming that all our memories are real and the world is exactly as it seems (which is too much); or assuming that we might not exist (which is too little). The OM seems to me to fit the bill as far as what is the right thing to assume. What would you suggest as an alternative? Hal Finney I suggest we take thoughts (not assuming a thinker) as evidence - but not as fundamental in the sense of incorrigble. For example, there is seeing of words on my computer screen at this time (awkward in English to avoid saying I see..). But perceptual evidence must be fitted with other evidence (necessarily from memory) to support a theory of the world, including our existence in it. In a metaphor, experiences are like the clues in a crossword puzzle - how we intepret them must fit them together to complete the puzzle. In fact I think this is where common-sense and science come from - except that evolution already provided us with some modes of perception and some categories of thought (c.f. Singer's How the Mind Works). Whatever we think we know amounts to a model or theory about reality. It seems to me that the object of these models is to explain and predict what we experience. But if we take our experiences as fundamental what are we going to do - explain reality in terms of them? I can see this as a project similar to Bruno's, Experiences-Common-sense-Science-Experiences, where each - corresponds to creating a model. Brent Meeker
RE: Observer-Moment Measure from Universe Measure
Hal Finney wrote: Jonathan Colvin writes: There's a question begging to be asked, which is (predictably I suppose, for a qualia-denyer such as myself), what makes you think there is such a thing as an essence of an experience? I'd suggest there is no such thing as an observer-moment. I'm happy with using the concept as a tag of sorts when discussing observer selection issues, but I think reifying it is likely a mistake, and goes considerably beyond Strong AI into a full Cartesian dualism. Is it generally accepted here on this list that a substrate-independent thing called an observer moment exists? Here's how I attempted to define observer moment a few years ago: Observer - A subsystem of the multiverse with qualities sufficiently similar to those which are common among human beings that we consider it meaningful that we might have been or might be that subsystem. These qualities include consciousness, perception of a flow of time, and continuity of identity. Observer-moment - An instant of perception by an observer. An observer's sense of the flow of time allows its experience to be divided into units so small that no perceptible change in consciousness is possible in those intervals. Each such unit of time for a particular observer is an observer-moment. So if you don't believe in observer-moments, do you also not believe in observers? Or is it the -moment that causes problems? I don't believe in observers, if by observer one means to assign special ontological status to mental states over any other arrangement of matter. This is similar to the objection to the classic interpretation of QM, whereby an observation is required to collapse the WF (how do you define observer?..a rock?..a chicken?..a person?). But this was in response to a comment that it was time to get serious about observer-moments. An observer is such a poorly defined and nebulous thing that I don't think one can get serious about it. I'd note that your definition is close to being circular..an observer is something sufficiently similar to me that I might think I could have been it. But how do we decide what is sufficient? The qualities you list (consciousness, perception etc) are themselves poorly defined or undefinable. We end up with an observer is an observer if I think it is an observer; which is a bit circular IMHO. Jonathan Colvin
RE: Observer-Moment Measure from Universe Measure
-Original Message- From: Bruno Marchal [mailto:[EMAIL PROTECTED] Sent: Monday, June 06, 2005 12:36 PM To: Brent Meeker Cc: EverythingList list Subject: Re: Observer-Moment Measure from Universe Measure Le 06-juin-05, à 01:40, Brent Meeker a écrit : What do you take to be the standard definition of knows? Is it X knows Y iff X believes Y is true and Y is true? That's the one by Theaetetus. Or do you include Gettier's amendment, X knows Y iff X believes Y is true and Y is true and There is a causal chain between the fact that makes Y true and X's belief that Y? It could depend of the axiom chosen to describe belief. For knowability I take the S4 axioms and rules: 1) axioms: all classical tautologies BX - X BX - BBX B(X-Y) - (BX - BY) 2) Rule: X X - Y X --- - (Modus ponens, necessitation) YBX But in the interview of the Lobian machine I recover the S4 axioms + Grz, from defining knowing X by proving X formally and X true (I apply the Theaetetus on formal provability). I cannot use Gettier's given that I have no notion of causality to start with. (Recall I don't have any physical notion to start with). Bruno In that case, how does true differ from provable? If it is simply a formal system, with no facts which can make a proposition true by reference, then it seems that there is no separate notion of true apart from provable. Brent Meeker
Re: Observer-Moment Measure from Universe Measure
Le 07-juin-05, à 00:31, Brent Meeker a écrit : BM: For knowability I take the S4 axioms and rules: 1) axioms: all classical tautologies> BX -> X BX -> BBX B(X->Y) -> (BX -> BY) 2) Rule: X X -> Y X --- - (Modus ponens, necessitation) YBX But in the interview of the Lobian machine I recover the S4 axioms + Grz, from defining knowing X by proving X formally and X true (I apply the Theaetetus on formal provability). I cannot use Gettier's given that I have no notion of causality to start with. (Recall I don't have any physical notion to start with). Bruno In that case, how does true differ from provable? If it is simply a formal system, with no facts which can make a proposition true by reference, then it seems that there is no separate notion of true apart from provable. I know you are honest, so I knew you would ask, and I am very glad because you are putting your finger on the most utterly important (admittedly subtle) point which gives sense to the interview of the lobian machine, and which is really no less than Godel incompleteness theorem (or better LOB's theorem, see below). If B represents provability in sound (correct) formal system it is just plainly true that BX -> X In particular if F represents a falsity (your favorite contradiction, P NOT P, for instance), then it is again plainly true that BF -> F BUT BF -> F is equivalent with NOT BF (P -> F has the same truth table as NOT P). So BF -> F is NOT BF, and this is a consistency statement: the false is not provable. So, given that we are talking about a sound formal system, we know that BF->F is true, but as a consistency statement, we know also, by Godel's second incompleteness theorem, that the system cannot prove its own consistency: BF->F is true but not provable Put in another way BF->F is true, but B(BF->F) is false. In particular you see that B cannot behave like a knowledge modal operator In particular again BF F is truly equivalent to BF, but the machine cannot prove that equivalence. And so what logic does B obeys to? Given the apparition of a gap between truth and provability we get two logics, one for what the machine is able to prove about its own B, and one for what is true about that B. The first is G, and the second is G*. Note that the machine is sound, which means all what the machine proves is correct, so that G is included in G*. But G* is much larger than G. For example G* proves that the machine is consistent -BF. G* proves that the machine cannot prove its own consistency -B(-BF). G* prove that BP -> (BP P), but the machine cannot prove it. So it makes sense to define knowledge, for the machine, by a new modal operator Cp (say) defined by Cp = Bp p. (Theaetetus) It can be shown that it obeys the S4 axioms, and one more which is the grz formula (the Grzegorczyk formula) which is rather ugly, it is: B(B(p -> Bp) -> p)-> p Perhaps ugly, but it should make Stephen happy, because it introduces an irreversible temporality in the possible evolution of the machine knowledge. To show this we should need the Kripke semantics stuff. But my main point here is that by Godel incompleteness Bp -> p although always true, is not always provable. LOB theorem says exactly when Bp->p is provable, it is provable only when p is provable! The machine M is closed for the rule: if M proves Bp -> p then M proves p. M can prove it!M proves B(Bp -> p) -> Bp And Solovay will prove that this Lob's formula is enough, along with B(p->q)->(Bp->Bq) to derive the whole discourse of the machine with the modus ponens and the necessitation rule. (that's G). G* has as axioms all the theorems of G, + Bp -> p, and is closed for the modus ponens rule BUT NOT FOR THE NECESSITATION rule Exercise 1: show that G* would be inconsistent if you add the necessitation rule. Exercise 2: what was precisely wrong in your comment? Bruno appendice: Taken from my post: http://www.escribe.com/science/theory/m2855.html with [] = B here. x-tad-biggerI recall that a formal presentation of G is: AXIOMS[](p -> q) -> ([]p -> []q) K []([]p -> p) -> []p L RULES p p -> qp Modus Ponens --- Necessitation q []p and G* is AXIOMSAny theorem of G []p -> p RULES p p -> q Modus Ponens(only! No Necessitation rule!!!) q (Plus some obvious but tedious substitution rules)/x-tad-bigger http://iridia.ulb.ac.be/~marchal/
RE: Observer-Moment Measure from Universe Measure
Hal Finney wrote: To apply Wei's method, first we need to get serious about what is an OM. We need a formal model and description of a particular OM. Consider, for example, someone's brain when he is having a particular experience. He is eating chocolate ice cream while listening to Beethoven's 5th symphony, on his 30th birthday. Imagine that we could scan his brain with advanced technology and record his neural activity. Imagine further that with the aid of an advanced brain model we are able to prune out the unnecessary information and distill this to the essence of the experience. We come up with a pattern that represents that observer moment. Any system which instantiates that pattern genuinely creates an experience of that observer moment. This pattern is something that can be specified, recorded and written down in some form. It probably involves a huge volume of data. Sorry for the delay in response, but eskimo started bouncing mail from my other smtp for some unknown reason. There's a question begging to be asked, which is (predictably I suppose, for a qualia-denyer such as myself), what makes you think there is such a thing as an essence of an experience? I'd suggest there is no such thing as an observer-moment. I'm happy with using the concept as a tag of sorts when discussing observer selection issues, but I think reifying it is likely a mistake, and goes considerably beyond Strong AI into a full Cartesian dualism. Is it generally accepted here on this list that a substrate-independent thing called an observer moment exists? Jonathan Colvin
Re: Observer-Moment Measure from Universe Measure
Hi Brent, Le 05-juin-05, à 13:21, Brent Meeker a écrit : -Original Message- From: Bruno Marchal [mailto:[EMAIL PROTECTED] Sent: Sunday, June 05, 2005 7:02 AM To: Hal Finney Cc: everything-list@eskimo.com Subject: Re: Observer-Moment Measure from Universe Measure Le 05-juin-05, à 05:53, Hal Finney a écrit : Lee Corbin writes: But in general, what do observer-moments explain? Or what does the hypothesis concerning them explain? I just don't get a good feel that there are any higher level phenomena which might be reduced to observer-moments (I am still very skeptical that all of physics or math or something could be reduced to them---but if that is what is meant, I stand corrected). Rather, it always seems like a number of (other) people are trying to explain observer-moments as arising from the activity of a Universal Dovetailer, or a Platonic ensemble of bit strings, or something. I would say that observer-moments are what need explaining, rather than things that do the explaining. Or you could say that in a sense they explain our experiences, although I think of them more as *being* our experiences, moment by moment. As we agreed: An observer-moment is really all we have as our primary experience of the world. The world around us may be fake; we may be in the Matrix or a brain in a vat. Even our memories may be fake. But the fact that we are having particular experiences at a particular moment cannot be faked. Nothing could be truer. All right. So you both (Hal Finney and Lee Corbin) with the first axiom defining a knower. It is the incorrigibility axiom: let us write Cp for to know p (or to be aware of p, or to be conscious of p). incorrigibility can be stated by: Cp - p Meaning that for any proposition p we have that Cp - p is true. The implication arrow - is just the classical implication. It has nothing to do with notions of causality, or deduction or whatever ... We can define A - B by ((not A) or B) or (not (A and not B)) as this can be verified by truth-table. I recall: A - B 1 1 1 1 0 0 0 1 1 0 1 0 OK? No. To be conscious of p, where p is some proposition, doesn't imply that p is true - one is often mistaken. You are right. (i *was* supposing p true!) It seems to me that the incorrigibility of experience is just CCp-Cp, i.e. propositions that you seem to perceive p may be incorrigble. Cp-p only works where p isimplicitly is of the form Cq. OK, but this is Loeb theorem and I will use the B instead of C. I continue to accept Cp - p for standard knowledge. We don't say say John knew that (a+b)^2 = a^2 + b^2, but he was false we say John believed that (a+b)^2 = a^2 + b^2, but he was false . By definition we cannot know something false. It is the standard definition. But you are right I should not have used the term conscious nor aware here! Thanks for the correction, Bruno http://iridia.ulb.ac.be/~marchal/
Re: Observer-Moment Measure from Universe Measure
Le 05-juin-05, à 17:30, Stephen Paul King a écrit :
FAR AWAY IN THE HEAVENLY ABODE OF THE GREAT GOD INDRA, THERE IS A
WONDERFUL NET WHICH HAS BEEN HUNG BY SOME CUNNING ARTIFICER IN SUCH A
MANNER THAT IT STRETCHES OUT INDEFINITELY IN ALL DIRECTIONS. IN
ACCORDANCE WITH THE EXTRAVAGANT TASTES OF DEITIES, THE ARTIFICER HAS
HUNG A SINGLE GLITTERING JEWEL AT THE NET'S EVERY NODE, AND SINCE THE
NET ITSELF IS INFINITE IN DIMENSION, THE JEWELS ARE INFINITE IN
NUMBER. THERE HANG THE JEWELS, GLITTERING LIKE STARS OF THE FIRST
MAGNITUDE, A WONDERFUL SIGHT TO BEHOLD. IF WE NOW ARBITRARILY SELECT
ONE OF THESE JEWELS FOR INSPECTION AND LOOK CLOSELY AT IT, WE WILL
DISCOVER THAT IN ITS POLISHED SURFACE THERE ARE REFLECTED ALL THE
OTHER JEWELS IN THE NET, INFINITE IN NUMBER. NOT ONLY THAT, BUT EACH
OF THE JEWELS REFLECTED IN THIS ONE JEWEL IS ALSO REFLECTING ALL THE
OTHER JEWELS, SO THAT THE PROCESS OF REFLECTION IS INFINITE
THE AVATAMSAKA SUTRA
FRANCIS H. COOK: HUA-YEN BUDDHISM : THE JEWEL NET OF INDRA 1977
***
I am suggesting that these jewels give us an excellent way to
think of OMs. If we are to allow for a value K {ranging from 0 to 1}
to represent the degree to which one jewel reflects or is similar
to or implies, it seems that we get a very neat way to span a whole
lot of logics and math with a simple picture. And, to top it off, we
have a way to deal with infinite regress and circularity without
paradox. (BTW, this is what Non-Well founded set theory is trying to
explain!)
And Lee wrote in the same vain:
As for circular, too bad your theories aren't circular! They'd
explain more.
My theories are full of circular constructions! But as it is well
known circular construction can lead to paradoxes or even to frank
contradictions. Recursion theory, and then theoretical computer science
have provided founded semantics for most unfounded mathematical
structure appearing in computer science.
Don't forget I postulate comp which does give some importance to the
founded notion of bits and numbers. The magic is that bits and numbers
leads automatically and naturally to non-founded (circular) structure
with respect to universal machine/environment.
This is illustrated by the last post on combinators, which I have
introduced in part as an introduction to computer-theoretical circular
structure. I don't want to use Non-Well-founded set theory (nor any set
theory), nor category theory because the minimum of logic I use is
considered as already too abstruse to many. But those are very
interesting of course.
Note that John Case, one of the master of computer self-reference,
refers to the INDRA NET to introduce its generalization of Kleene fixed
point theorem. My whole approach is based on similar circular
self-reference, but, being programs or sets, mathematicians can use
them only when they have founded model of it. Look at the combinators:
it is only when Dana Scott provide founded models that the work on the
circular combinatory structures explodes in the literature.
Bruno
PS Lee, I will take some time to comment your posts. Thanks for your
patience.
http://iridia.ulb.ac.be/~marchal/
RE: Observer-Moment Measure from Universe Measure
Stathis Papaioannou writes: Hal Finney writes: There are a few unintuitive consequences, though, such as that large instantiations of OMs will have more measure than small ones, and likewise slow ones will have more measure than fast ones. This is because in each case the interpretation program can be smaller if it is easier to find the OM in the vastness of a universe, and the slower and bigger an OM is the easier it is to find. I am inclined to tentatively accept these results. It does imply that the extreme future vision of some transhumanists, to upload themselves to super-fast, super-small computers, may greatly reduce their measure, which would mean that it would be like taking a large chance of dying. Could someone please explain what will happen to the hapless transhumanists in their computer when their measure falls to alarmingly low levels? Will they develop severe headaches, turn transparent like ghosts, or what? This is a kind of transformation that hasn't been possible in the world before, so no normal phenomenon will exactly capture what happens. To a first approximation, if their measure were reduced by 90%, what would happen subjectively would be the same as if they took steps that had a 90% chance of killing them, in this model. Now, objectively this is different because it would require other people to deal with their deaths. But subjectively it would be pretty much the same. Perhaps a closer approximation could be achieved if they were not only killed, but somehow everyone else's memory was changed so that no one remembered them or noticed that they were gone. Imagine instead the question, what would it be like, subjectively, to die instantly and without warning? It's a hard question to answer. But it is related to the question, what would it be it like to have your measure suddenly reduced? You could imagine your larger before-measure as being represented by your mind being instantiated as many copies. Then a certain percentage of those copies are instantly killed. What is it like subjectively? To the copies which remain, there is no subjective change. To the copies which were killed, perhaps it is like nothing subjectively, because there is no longer any subject there. But it is still a change. I think a reduction of measure would be like a certain percentage of my instances being instantly killed. When I imagine what it is like, I picture myself being one of the unlucky instances. I stop and never know I stopped, while other copies go on. The other night I had a strange dream. I came into a room and met someone whom I came to understand was myself. I was a copy who had been created a few moments earlier, and he was the original. There was a switch on the wall which would instantly destroy the copy, and I was supposed to push it. But I hesitated. My own consciousness would be destroyed. On the other hand I was supposedly a copy made just moments earlier, so only a few seconds of memories would be lost, hardly consequential. Still I had to face that dilemma: what would it feel like to just stop, instantly? Nervously, I went ahead and pushed the button, squeezing my eyes shut and making a kind of mental flinch or jerk. To my surprise, I was still there, and when I opened my eyes, the other person was gone. It turned out that he was the copy and I was the original. Imagine facing your copy, perhaps an exact copy whose mind is synchronized with yours, and seeing a coin flip which will determine which one is destroyed. Your measure will be halved. In a sense it will have no subjective effect, your thoughts and memories will be preserved in one of you. But in another sense you face a 50-50 chance of experiencing that mysterous effect of instant death. I think it would be scary. Logically, similar reductions of measure should be viewed in the same light. Hal Finney
Re: Observer-Moment Measure from Universe Measure
Le 06-juin-05, à 01:40, Brent Meeker a écrit : What do you take to be the standard definition of knows? Is it X knows Y iff X believes Y is true and Y is true? That's the one by Theaetetus. Or do you include Gettier's amendment, X knows Y iff X believes Y is true and Y is true and There is a causal chain between the fact that makes Y true and X's belief that Y? It could depend of the axiom chosen to describe belief. For knowability I take the S4 axioms and rules: 1) axioms: all classical tautologies BX - X BX - BBX B(X-Y) - (BX - BY) 2) Rule: X X - Y X --- - (Modus ponens, necessitation) YBX But in the interview of the Lobian machine I recover the S4 axioms + Grz, from defining knowing X by proving X formally and X true (I apply the Theaetetus on formal provability). I cannot use Gettier's given that I have no notion of causality to start with. (Recall I don't have any physical notion to start with). Bruno http://iridia.ulb.ac.be/~marchal/
RE: Observer-Moment Measure from Universe Measure
Hal Finney writes: Stathis Papaioannou writes: Hal Finney writes: There are a few unintuitive consequences, though, such as that large instantiations of OMs will have more measure than small ones, and likewise slow ones will have more measure than fast ones. This is because in each case the interpretation program can be smaller if it is easier to find the OM in the vastness of a universe, and the slower and bigger an OM is the easier it is to find. I am inclined to tentatively accept these results. It does imply that the extreme future vision of some transhumanists, to upload themselves to super-fast, super-small computers, may greatly reduce their measure, which would mean that it would be like taking a large chance of dying. Could someone please explain what will happen to the hapless transhumanists in their computer when their measure falls to alarmingly low levels? Will they develop severe headaches, turn transparent like ghosts, or what? This is a kind of transformation that hasn't been possible in the world before, so no normal phenomenon will exactly capture what happens. To a first approximation, if their measure were reduced by 90%, what would happen subjectively would be the same as if they took steps that had a 90% chance of killing them, in this model. Now, objectively this is different because it would require other people to deal with their deaths. But subjectively it would be pretty much the same. Perhaps a closer approximation could be achieved if they were not only killed, but somehow everyone else's memory was changed so that no one remembered them or noticed that they were gone. Imagine instead the question, what would it be like, subjectively, to die instantly and without warning? It's a hard question to answer. But it is related to the question, what would it be it like to have your measure suddenly reduced? You could imagine your larger before-measure as being represented by your mind being instantiated as many copies. Then a certain percentage of those copies are instantly killed. What is it like subjectively? To the copies which remain, there is no subjective change. To the copies which were killed, perhaps it is like nothing subjectively, because there is no longer any subject there. But it is still a change. I think a reduction of measure would be like a certain percentage of my instances being instantly killed. When I imagine what it is like, I picture myself being one of the unlucky instances. I stop and never know I stopped, while other copies go on. The other night I had a strange dream. I came into a room and met someone whom I came to understand was myself. I was a copy who had been created a few moments earlier, and he was the original. There was a switch on the wall which would instantly destroy the copy, and I was supposed to push it. But I hesitated. My own consciousness would be destroyed. On the other hand I was supposedly a copy made just moments earlier, so only a few seconds of memories would be lost, hardly consequential. Still I had to face that dilemma: what would it feel like to just stop, instantly? Nervously, I went ahead and pushed the button, squeezing my eyes shut and making a kind of mental flinch or jerk. To my surprise, I was still there, and when I opened my eyes, the other person was gone. It turned out that he was the copy and I was the original. Imagine facing your copy, perhaps an exact copy whose mind is synchronized with yours, and seeing a coin flip which will determine which one is destroyed. Your measure will be halved. In a sense it will have no subjective effect, your thoughts and memories will be preserved in one of you. But in another sense you face a 50-50 chance of experiencing that mysterous effect of instant death. I think it would be scary. Logically, similar reductions of measure should be viewed in the same light. Hal, What I think you're describing is akin to the traditional view of personal identity as something firmly attached to a particular animal, computer or whatever. The most important insight the observer moment concept offers, to my mind, is that the observer effectively dies every moment, and the illusion of an individual persisting through time is created by the stringing together of appropriately related OM's. I wouldn't even call this a theory; I think it is true ipso facto. Consider an observer experiencing a series of conscious moments OM1, OM2, OM3... etc. Just as OM3 is about to start, he is vapourised by a nuclear explosion. Assuming for simplicity there are no parallel universes, the observer has died. What does dying mean in this context? It means that his last conscious moment was OM2, and there will be no more. Notice that nothing special has happened to OM2; it is the same as if he had continued living, and it is unaffected by what may or may not follow. Death consists in the absence of successors to OM2. Therefore, provisionally, as
Re: Observer-Moment Measure from Universe Measure
Johnathan Corgan writes: As I'm sure many on the list are familiar, David Brin's Kiln People is an interesting science fiction treatment of similar issues. It is an interesting story which helps to make some of our philosophical thought experiments more concrete. Making copies, destroying them, the nondeterministic experience of wondering whether you will become the copy or the original, all are addressed. However I found much to dislike in the way Brin answers these questions. I wrote a review at http://www.transhumanism.org/index.php/th/more/285/ . An excerpt: I was shocked and disgusted to see that [Brin] presents the golems as having no human rights whatsoever. They are property, nothing more. They have to step to the back of the bus, get out of the way of the white, excuse me, human massas, put up with whatever humans want to do to them. This shocking recreation of the worst abuses of the slavery era is presented without much explanation by Brin, or much sensitivity to the horrific history he is echoing... Hal Finney
Re: Observer-Moment Measure from Universe Measure
Le 05-juin-05, à 05:53, Hal Finney a écrit : Lee Corbin writes: But in general, what do observer-moments explain? Or what does the hypothesis concerning them explain? I just don't get a good feel that there are any higher level phenomena which might be reduced to observer-moments (I am still very skeptical that all of physics or math or something could be reduced to them---but if that is what is meant, I stand corrected). Rather, it always seems like a number of (other) people are trying to explain observer-moments as arising from the activity of a Universal Dovetailer, or a Platonic ensemble of bit strings, or something. I would say that observer-moments are what need explaining, rather than things that do the explaining. Or you could say that in a sense they explain our experiences, although I think of them more as *being* our experiences, moment by moment. As we agreed: An observer-moment is really all we have as our primary experience of the world. The world around us may be fake; we may be in the Matrix or a brain in a vat. Even our memories may be fake. But the fact that we are having particular experiences at a particular moment cannot be faked. Nothing could be truer. All right. So you both (Hal Finney and Lee Corbin) with the first axiom defining a knower. It is the incorrigibility axiom: let us write Cp for to know p (or to be aware of p, or to be conscious of p). incorrigibility can be stated by: Cp - p Meaning that for any proposition p we have that Cp - p is true. The implication arrow - is just the classical implication. It has nothing to do with notions of causality, or deduction or whatever ... We can define A - B by ((not A) or B) or (not (A and not B)) as this can be verified by truth-table. I recall: A - B 1 1 1 1 0 0 0 1 1 0 1 0 OK? That is the sense in which I say that observer-moments are primary; they are the most fundamental experience we have of the world. Everything else is only a theory which is built upon the raw existence of observer-moments. All right. I guess you agree that this is compatible with the fact that such a theory, built upon the raw existence of OMs, could infer the existence of more primitive objects, could explain how the raw existence of OM emerges from those more primitive objects and explain also how the theory of those more primitive objects emerge from the (only apparently raw, now) observer moments. All this without being circular. OK? Bruno http://iridia.ulb.ac.be/~marchal/
Re: Observer-Moment Measure from Universe Measure
- Original Message - From: Hal Finney [EMAIL PROTECTED] To: everything-list@eskimo.com Sent: Friday, June 03, 2005 08:10 PM Subject: Observer-Moment Measure from Universe Measure To apply Wei's method, first we need to get serious about what is an OM. We need a formal model and description of a particular OM. Consider, for example, someone's brain when he is having a particular experience. He is eating chocolate ice cream while listening to Beethoven's 5th symphony, on his 30th birthday. Imagine that we could scan his brain with advanced technology and record his neural activity. Imagine further that with the aid of an advanced brain model we are able to prune out the unnecessary information and distill this to the essence of the experience. We come up with a pattern that represents that observer moment. Any system which instantiates that pattern genuinely creates an experience of that observer moment. This pattern is something that can be specified, recorded and written down in some form. It probably involves a huge volume of data. So, now that we have a handle on what a particular OM is, we can more reasonably ask whether a universe instantiates it. Wouldn't it be better to think of OMs as programs just like we think of universes? If you only look at patterns then you get the problem which you later mention like crystals that can represent an OM of a person etc. The patterns one is looking for should be capable of doing computations If I define OMs as a programs (in a particular computational state), then that is the same as saying that OMs are universes in particular states. One can then argue that these universes are very complex and have high measures and are thus likely to be found embedded in simple, low measure, universes. Then one can also address the problem of what qualia actually are. They are 'events' that occur in an OM's universe. In case of persons one can think of the neural network formed by the brain. The events that take place in the universe defined by the neural network are the qualia we experience. So, I think that Wei's interpretation program has to do more than just spot certain patterns localized in time. Similarly if I simulate the solar system on a pc, then this defines a universe in which an event could be that jupiter is at a certain position at a certain time. To 'see' this in terms of the electrons moving through the transistors one has to first 'see' the program. Seeing the program requires one to study the way the object interacts with its environment which means that you have to take it out of the universe and study how it behaves when you expose it to alternative inputs. Saibal
Re: Observer-Moment Measure from Universe Measure
Dear Hal and Bruno,
- Original Message -
From: Bruno Marchal [EMAIL PROTECTED]
To: Hal Finney [EMAIL PROTECTED]
Cc: everything-list@eskimo.com
Sent: Sunday, June 05, 2005 3:02 AM
Subject: Re: Observer-Moment Measure from Universe Measure
Le 05-juin-05, à 05:53, Hal Finney a écrit :
snip
That is the sense in which I say that observer-moments are primary;
they are the most fundamental experience we have of the world.
Everything else is only a theory which is built upon the raw existence
of observer-moments.
[BM]
All right. I guess you agree that this is compatible with the fact that
such a theory, built upon the raw existence of OMs, could infer the
existence of more primitive objects, could explain how the raw existence
of OM emerges from those more primitive objects and explain also how the
theory of those more primitive objects emerge from the (only apparently
raw, now) observer moments. All this without being circular. OK?
Could you explain to us how it is necessary that sets of Observer
Moments must be well founded such that properties like such a theory,
built upon the raw existence of OMs, could infer the existence of more
primitive objects and All this without being circular.?
Why do we insist on having an indivisible Atom from which All is
constructable? Is it not possible that the distinctions (read properties!)
between one OM and another are merely those that they do not have in common?
Instead of the idea of an Atom floating in the Void, let us consider the
idea of Indra's Net:
http://www.heartspace.org/misc/IndraNet.html
***
FAR AWAY IN THE HEAVENLY ABODE OF THE GREAT GOD INDRA, THERE IS A WONDERFUL
NET WHICH HAS BEEN HUNG BY SOME CUNNING ARTIFICER IN SUCH A MANNER THAT IT
STRETCHES OUT INDEFINITELY IN ALL DIRECTIONS. IN ACCORDANCE WITH THE
EXTRAVAGANT TASTES OF DEITIES, THE ARTIFICER HAS HUNG A SINGLE GLITTERING
JEWEL AT THE NET'S EVERY NODE, AND SINCE THE NET ITSELF IS INFINITE IN
DIMENSION, THE JEWELS ARE INFINITE IN NUMBER. THERE HANG THE JEWELS,
GLITTERING LIKE STARS OF THE FIRST MAGNITUDE, A WONDERFUL SIGHT TO BEHOLD.
IF WE NOW ARBITRARILY SELECT ONE OF THESE JEWELS FOR INSPECTION AND LOOK
CLOSELY AT IT, WE WILL DISCOVER THAT IN ITS POLISHED SURFACE THERE ARE
REFLECTED ALL THE OTHER JEWELS IN THE NET, INFINITE IN NUMBER. NOT ONLY
THAT, BUT EACH OF THE JEWELS REFLECTED IN THIS ONE JEWEL IS ALSO REFLECTING
ALL THE OTHER JEWELS, SO THAT THE PROCESS OF REFLECTION IS INFINITE
THE AVATAMSAKA SUTRA
FRANCIS H. COOK: HUA-YEN BUDDHISM : THE JEWEL NET OF INDRA 1977
***
I am suggesting that these jewels give us an excellent way to think of
OMs. If we are to allow for a value K {ranging from 0 to 1} to represent the
degree to which one jewel reflects or is similar to or implies, it
seems that we get a very neat way to span a whole lot of logics and math
with a simple picture. And, to top it off, we have a way to deal with
infinite regress and circularity without paradox. (BTW, this is what
Non-Well founded set theory is trying to explain!)
Stephen
PS, for more info on Indra''s net see:
http://ccbs.ntu.edu.tw/FULLTEXT/JR-PHIL/ew25326.htm
and on its relation to NWF sets:
http://dialog.net:85/homepage/autobook.5/refautol.pdf
RE: Observer-Moment Measure from Universe Measure
Bruno writes All right. So you both (Hal Finney and Lee Corbin) with the first axiom Arghh! My new revelation says that axioms are fine if you are doing math. But some of us are doing something here that is entirely separate: philosophy. I love math; it is my hobby. But axioms and all that shit are not pertinent to my quests! Good luck with yours! That may be the reason I can't read any of your papers? defining a knower. It is the incorrigibility axiom: let us write Cp for more about defining and axioms ARGH! [Hal writes] That is the sense in which I say that observer-moments are primary; they are the most fundamental experience we have of the world. Everything else is only a theory which is built upon the raw existence of observer-moments. All right. I guess you agree that this is compatible with the fact that such a theory, built upon the raw existence of OMs, could infer the existence of more primitive objects, could explain how the raw existence of OM emerges from those more primitive objects and explain also how the theory of those more primitive objects emerge from the (only apparently raw, now) observer moments. All this without being circular. OK? Built? Emerge? Bah, humbug. As for circular, too bad your theories aren't circular! They'd explain more. Lee
RE: (offlist) RE: Observer-Moment Measure from Universe Measure
OOPS! I meant to post it to the list. I'll now just post this. Brent -Original Message- From: Lee Corbin [mailto:[EMAIL PROTECTED] Sent: Sunday, June 05, 2005 4:52 PM To: Brent Meeker Subject: (offlist) RE: Observer-Moment Measure from Universe Measure Hi Brent, Of course science arose out of explaining subjective experiences. The basic theory of science (and common sense) is that there is some mind-indpendent reality out there. When I see green grass and an object that is similar to me and that object says, I see green grass. then I take that as evidence that the object is person with experiences like me and that there really is green grass. May I quote you on-list? I agree with this *almost* entirely, (and don't want to waste in a personal communication an essay I want to write aimed at Hal, you, and Stephen Paul King.) Thanks very much, if this would be all right. Brent Meeker Science is just common-sense writ large. How *very* true. It is by summoning almost incredible self-restraint (upon reading those words) that I don't launch into a long denunciation rant diatribe against the doctrine of the scientific method!! Lee I'm not sure what you mean by the scientific method - the hypothetico-deductive method? So far as I know all the methods of science are just common sense applied carefully and thoroughly. Brent Meeker
RE: Observer-Moment Measure from Universe Measure
Hal Finney writes: There are a few unintuitive consequences, though, such as that large instantiations of OMs will have more measure than small ones, and likewise slow ones will have more measure than fast ones. This is because in each case the interpretation program can be smaller if it is easier to find the OM in the vastness of a universe, and the slower and bigger an OM is the easier it is to find. I am inclined to tentatively accept these results. It does imply that the extreme future vision of some transhumanists, to upload themselves to super-fast, super-small computers, may greatly reduce their measure, which would mean that it would be like taking a large chance of dying. Could someone please explain what will happen to the hapless transhumanists in their computer when their measure falls to alarmingly low levels? Will they develop severe headaches, turn transparent like ghosts, or what? --Stathis Papaioannou _ SEEK: Over 80,000 jobs across all industries at Australia's #1 job site. http://ninemsn.seek.com.au?hotmail
RE: Observer-Moment Measure from Universe Measure
Hal Finney has provided some intriguing notions and possibly some very useful explanations. But I would like help in clarifying even the first several paragraphs, in order to maximize my investment in the remainder. But first a few comments; these may be premature, but if so, the comments should be ignored. Some time back Lee Corbin posed the question of which was more fundamental: observer-moments or universes? I would say, with more thought, that observer-moments are more fundamental in terms of explaining the subjective appearance of what we see, and what we can expect. But in general, what do observer-moments explain? Or what does the hypothesis concerning them explain? I just don't get a good feel that there are any higher level phenomena which might be reduced to observer-moments (I am still very skeptical that all of physics or math or something could be reduced to them---but if that is what is meant, I stand corrected). Rather, it always seems like a number of (other) people are trying to explain observer-moments as arising from the activity of a Universal Dovetailer, or a Platonic ensemble of bit strings, or something. An observer-moment is really all we have as our primary experience of the world. The world around us may be fake; we may be in the Matrix or a brain in a vat. Even our memories may be fake. But the fact that we are having particular experiences at a particular moment cannot be faked. Nothing could be truer. But the universe is fundamental, in my view, in terms of the ontology, the physical reality of the world. Universes create and contain observers who experience observer-moments. This is the Schmidhuber/Tegmark model... Yes, but now arises my need for clarification: In terms of measure, Schmidhuber (and possibly Tegmark) provides a means to estimate the measure of a universe. Consider the fraction of all bit strings that create that universe as its measure. I think that perhaps I know exactly what is meant; but I'm unwilling to take the chance. Let's say that we have a universe U, and now we want to find its measure (its share of the mega-multi-Everything resources). So, as you write, we consider all the bit strings that create U. Let's say for concreteness that only five bit strings really exist in some deep sense: 010101110100101010011101010110001010110101... 10110111010001010111001011010110100101... 0010101001110101001110100010011010... 1101110100010011010l11011101010011... 1100101110101011101000110100101001... and then it just so happens that only 2 out of these five actually make the universe U manifest. That is, in the innards of 2 of these, one finds all the structures that U contains. Am I following so far? In practice this is roughly 1/2^n where n is the size of the shortest program that outputs that universe. So each of these universes (each of the five, in my toy example) has a certain Kolmogorov complexity? Each of the five can be output by some program? But is that program infinite or finite? Argument for finite: normally we want to speak of *short* programs and so that seems to indicate the program has a limited size. Argument for infinite: dramatically *few* bit strings that are infinite in length have just a finite amount of information. Our infinite level-one Tegmark universe, for example, probably is tiled by Hubble volumes in a non-repeating irregular way so that no program could output it. Thanks, Lee The Tegmark model may allow for similar reasoning, applied to mathematical structures rather than computer programs. Now, how to get from universe measure to observer-moment (OM) measure? This is what I want to write about
RE: Observer-Moment Measure from Universe Measure
Lee Corbin writes: But in general, what do observer-moments explain? Or what does the hypothesis concerning them explain? I just don't get a good feel that there are any higher level phenomena which might be reduced to observer-moments (I am still very skeptical that all of physics or math or something could be reduced to them---but if that is what is meant, I stand corrected). Rather, it always seems like a number of (other) people are trying to explain observer-moments as arising from the activity of a Universal Dovetailer, or a Platonic ensemble of bit strings, or something. I would say that observer-moments are what need explaining, rather than things that do the explaining. Or you could say that in a sense they explain our experiences, although I think of them more as *being* our experiences, moment by moment. As we agreed: An observer-moment is really all we have as our primary experience of the world. The world around us may be fake; we may be in the Matrix or a brain in a vat. Even our memories may be fake. But the fact that we are having particular experiences at a particular moment cannot be faked. Nothing could be truer. That is the sense in which I say that observer-moments are primary; they are the most fundamental experience we have of the world. Everything else is only a theory which is built upon the raw existence of observer-moments. In terms of measure, Schmidhuber (and possibly Tegmark) provides a means to estimate the measure of a universe. Consider the fraction of all bit strings that create that universe as its measure. I think that perhaps I know exactly what is meant; but I'm unwilling to take the chance. Let's say that we have a universe U, and now we want to find its measure (its share of the mega-multi-Everything resources). So, as you write, we consider all the bit strings that create U. Let's say for concreteness that only five bit strings really exist in some deep sense: 010101110100101010011101010110001010110101... 10110111010001010111001011010110100101... 0010101001110101001110100010011010... 1101110100010011010l11011101010011... 1100101110101011101000110100101001... and then it just so happens that only 2 out of these five actually make the universe U manifest. That is, in the innards of 2 of these, one finds all the structures that U contains. Am I following so far? In the Schmidhuber picture, it's not that the strings contain U, rather the strings are programs which when run on some UTM produce U as the output. This corresponds to the concept you mention below, the Kolmogorov complexity. KC is based on the length of programs that output the objects (strings, or universes, or any other information based entity). Measure as I am using it is 1/2^KC where KC is the Kolmogorov complexity of an object. In practice this is roughly 1/2^n where n is the size of the shortest program that outputs that universe. So each of these universes (each of the five, in my toy example) has a certain Kolmogorov complexity? Each of the five can be output by some program? Yes, I think this is equivalent to my conception, although when I spoke of bit strings I was thinking of the inputs to the UTM while you are talking about the outputs. But the basic idea is the same. But is that program infinite or finite? Argument for finite: normally we want to speak of *short* programs and so that seems to indicate the program has a limited size. Argument for infinite: dramatically *few* bit strings that are infinite in length have just a finite amount of information. Our infinite level-one Tegmark universe, for example, probably is tiled by Hubble volumes in a non-repeating irregular way so that no program could output it. Now I think we are both talking about the inputs to the UTM. Should we consider infinite length inputs? I don't think it is necessary, for three reasons. First, due to the way TM's work, in practice a random tape will only have some specific number of input bits that ever get used. The chance of an infinite number of bits being used is zero. Second, you could construct tapes which used an infinite number of bits, but they would be of measure zero and hence would make no detectable contribution to the actual numeric predictions of the theory. Third, there are variants on UTMs which only accept self-delimiting input tapes that have, in effect, lengths that are easily determined. Greg Chaitin's work focuses on the use of self-delimiting programs to achieve a more precise picture of algorithmic complexity (which is equivalent to KC). The lengths of such programs are inherently finite. These UTMs are equivalent to all others. Note that you could, I think, create an infinite universe even using a finite tape. I believe that our universe, even if infinite in Tegmark's level-one sense, could be output by a finite program, at least in an MWI model. The amount of
Observer-Moment Measure from Universe Measure
Some time back Lee Corbin posed the question of which was more fundamental: observer-moments or universes? I would say, with more thought, that observer-moments are more fundamental in terms of explaining the subjective appearance of what we see, and what we can expect. An observer-moment is really all we have as our primary experience of the world. The world around us may be fake; we may be in the Matrix or a brain in a vat. Even our memories may be fake. But the fact that we are having particular experiences at a particular moment cannot be faked. But the universe is fundamental, in my view, in terms of the ontology, the physical reality of the world. Universes create and contain observers who experience observer-moments. This is the Schmidhuber/Tegmark model. (I think Bruno Marchal may invert this relationship.) In terms of measure, Schmidhuber (and possibly Tegmark) provides a means to estimate the measure of a universe. Consider the fraction of all bit strings that create that universe as its measure. In practice this is roughly 1/2^n where n is the size of the shortest program that outputs that universe. The Tegmark model may allow for similar reasoning, applied to mathematical structures rather than computer programs. Now, how to get from universe measure to observer-moment (OM) measure? This is what I want to write about. First, the measure of an OM should be the sum of contributions from each of the universes that instantiate that OM. Generally there are many possible universes that may create or contain a particular OM. Some are variants of our own, where things are different that we have not yet observed. For example, a universe which is like ours except for some minor change in a galaxy billions of light years away could contain a copy of us experiencing the same OMs. Even bigger changes may not matter; for example if you flip a coin but haven't yet looked at the result, this may not change your OM. Then there are even more drastic universes, like The Matrix where we are living in a simulation created in some kind of future or alien world. Perhaps the most extreme case is a universe which only creates that OM. Think of it as a universe which only exists for a brief moment and which only contains a brain, or a computer or some such system, which contains the state associated with that OM. This is the brain in a vat model taken to the most extreme, where there isn't anything else, and there isn't even a vat, there is just a brain. We would hope, if our multiverse models are going to amount to anything, that such universes would only contribute a small measure to each of our OMs. Otherwise the AUH can't explain what we see. But all of these universes contribute to the measure of our OMs. We are living in all of them. The measure of the OM is the sum of the contribution from each universe. However, and here is the key point, the contribution to an OM from a universe cannot just be taken as equal to the measure of that universe. Otherwise we reach some paradoxical conclusions. For one thing, a universe may instantiate a particular OM more than once. What do we do in that case? For another, intuitively it might seem that the contribution of a universe to an OM should depend to some extent on how much of the universe's resources are devoted to that OM. An enormous universe which managed to instantiate a particular OM in some little corner might be said to contribute less of its measure to that OM than if a smaller universe instantiates the same OM. The most extreme case is a trivial universe (equivalently, a program, in Schmidhuber terms) which simply counts. It outputs 1, 2, 3, 4, ... forever. This is a small program and has large measure. At some point it will output a number corresponding to any given OM. Should we count the entire measure of this small program (one of the smallest programs that can exist) to this OM? If so, it will seem that for every OM we should assume that we exist as part of such a counting program, which is another variant on the brain-in-a-vat scenario. This destroys the AUH as a predictive model. Years ago Wei Dai on this list suggested a better approach. He proposed a formula for determining how much of a universe's measure contributes to an OM that it instantiates. It is very specific and also illustrates some problems in the rather loose discussion so far. For example, what does it really mean to instantiate an OM? How would we know if a universe is really instantiating a particular OM? Aren't there fuzzy cases where a universe is only sort of instantiating one? What about the longstanding problem that you can look at the atomic vibrations in a crystal, select a subset of them to pay attention to, and have that pattern match the pattern of any given OM? Does this mean that every crystal instantiates every OM? (Hans Moravec sometimes seems to say yes!) To apply Wei's method, first we need to get serious about what is an OM. We
