Re: Are we simulated by some massive computer?
Hi Stephen Sorry I was tired when I replied to you. Let me be expend on the last post and be a little more explicit. THIS IS A REPOST OF THE LAST POST TO YOU. George Stephen Paul King wrote: Dear George, Interleaving. - Original Message - From: George Levy To: Stephen Paul King Sent: Wednesday, May 12, 2004 3:00 PM Subject: Re: Are we simulated by some massive computer? Stephen, Stephen Paul King wrote: Dear George, How does indeterminacy and multiple-world-occupation follow from an inability to deduce that one is not in a simulation? The total ignorance (not his inability) of an observer of whether his world is or is not in a simulation effectively places his whole universe in a state of superposition. Equivalently, this observer occupies several worlds some of them in simulators and others not in simulators. This multiplicity of world forms an ensemble of worlds that he occupies. The elements of the ensemble belong to different levels in a simulation hierarchy. His act of performing a measurement on his world to extract the information he seeks about his world being in a simulator, results in different a outcome in each world in the ensemble. In order for the observer to remain consisten with the world he observes, his states must change accordingly. As a result the states of the observer diverge or "split." Each world in the ensemble now contains a diffeent observer. Equivalently, each of these observers occupies a much reduce ensemble. Equivalently, each of these observers do not occupy a world in superposition. [GL] It seems to me that if two worlds are indistinguishable from the point of view of an observer, then the two worlds could be switched on the observer - or conversely that the observer could be teleported from one world to the other - without him knowing it. [SPK] The 3rd person abilty to interchangeidentical worlds does notnecessitate the a priori existence of a multitute of identical worlds from a 1st person point of view, because, as you wrote they could be switched without him (the 1st person) knowing it. So why entertain their existence in the first place? The existence of multiple worlds is a consequence of the principle of sufficient reason as I have explained before. If a world is in a particular state, and there is no reason for it to be in this state, then it must also be in all possible states. By the way this principle has an echo in elementary particle physics. The 3rd person is almost not in my vocabulary except when I talk about first persons who share identical or almost identical frames of references. Therefore I do not quite understand your reference to a 3rd person ability to interchange identical worlds. It just does not make sense to me. Let us also take into account that the kind of teleportation that you bring up here is not physically possible. I do not understand how it continues to be used as apedagological device. Such teleportation would be trivial for creatures living in a simulation or even in the real world when you have a distributed computing capability like the Internet.. Applets are being teleported on the Internet every day. In the future, robots may get to have their software teleported from one machine in Paris to another one in Washington. It just so happen that carbon based creatures using wetware AI cannot be easily teleported. [GL] The existence of many such worlds give rise to Quantum indeterminacy. [SPK] I beg to differ. IIRC, David Deutsch and others have repeatedly pointed out that it is the superposition principle of Quantum Mechanics that implies the existence of "many worlds" not the prior existence of multiple identical worlds. It all depends what your starting axioms are. As I said my starting axiom is the conscious "I" capable of logic and applying the principle of sufficient reason. BOTH superposition AND the existence of "many-worlds are consequences of this principle. Unless you believe in the "I" and that you believe that you are capable of logical thinking, there is absolutely no sane reasoning that you can do. This applies to "David Deutsch and others." Their reasoning is not wrong, it just starts with one of my theorems. [GL] Measurement only restricts the size of the ensemble. [SPK] Are you assuming the "collapse of the wave-function" or some classical or "ignorance based" interpretation of probabilities here? Neither. As I have explained above, when an observer exists in two worlds, (or equivalently in a single world in two states of superposition), and this observer makes a measurement, then obviously the measurement will come out differently in each world. The observer'
Re: Are we simulated by some massive computer?
Hi Stephen Stephen Paul King wrote: Dear George, Interleaving. - Original Message - From: George Levy To: Stephen Paul King Sent: Wednesday, May 12, 2004 3:00 PM Subject: Re: Are we simulated by some massive computer? Stephen, Stephen Paul King wrote: Dear George, How does indeterminacy and multiple-world-occupation follow from an inability to deduce that one is not in a simulation? Multiple world + comp = indeterminacy [GL] It seems to me that if two worlds are indistinguishable from the point of view of an observer, then the two worlds could be switched on the observer - or conversely that the observer could be teleported from one world to the other - without him knowing it. [SPK] The 3rd person abilty to interchangeidentical worlds does notnecessitate the a priori existence of a multitute of identical worlds from a 1st person point of view, because, as you wrote they could be switched without him (the 1st person) knowing it. So why entertain their existence in the first place? The existence of multiple worlds is a consequence of the principle of sufficient reason as I have explained before. If a world is in a particular state, and there is no reason for it to be in this state, then it must also be in all possible states. Let us also take into account that the kind of teleportation that you bring up here is not physically possible. I do not understand how it continues to be used as apedagological device. Such teleportation would be trivial for creatures living in a simulation or even in the real world when you have a distributed computing capability like the Internet.. Applets are being teleported on the Internet every day. In the future, robots may get to have their software teleported from one machine in Paris to another one in Washington. [GL] The existence of many such worlds give rise to Quantum indeterminacy. [SPK] I beg to differ. IIRC, David Deutsch and others have repeatedly pointed out that it is the superposition principle of Quantum Mechanics that implies the existence of "many worlds" not the prior existence of multiple identical worlds. As I mentioned above, multiple worlds + comp = indeterminacy [GL] Measurement only restricts the size of the ensemble. [SPK] Are you assuming the "collapse of the wave-function" or some classical or "ignorance based" interpretation of probabilities here? No. When an observer exists in two worlds, (or equivalently in a single world in two states of superposition), and this observer makes a measurement, then obviously the measurement will come out differently in each world. The observer's states which must remain consistent with the world that he observes, must then diverge.) The world he now occupies is a single world (or equivalently there is no more superposition). [GL] A creature nominally living in a simulation as observed (3rd person) by an experimenter, lives from the first person point of view in multiple simulations located at multiple levels. [SPK] It seems to me that you are assuming what I define as the "voyeur's framing" when considering the notion of a simulation. That is ok, IHMO, so long as you acknowledge that such a simulation will involve less computational power that one that dissallows for the voyeur's framing. It is like observing the game "EverQuest" on your computer monitor. When you make this assumption it follows that many -even an infinity - of simulated worlds could simultaneously exits, but I am arguing that the support for the multitute of identical worlds vanishes when we consider the caseof the simulation that requires more computational power than that available to *ANY* observer that you, from within the simulation, could communicate with. To follow the EverQuest analogy, consider yourself as a NPC (non-player character) within the EverQuest "world". The maximal computational power that you would have available would be the computational power needed to generate the unfolding of events you could observe from a 1st person point of view. I argue that we have a similar situation in our "real" world. Stephen Wolfram wrote: http://www.stephenwolfram.com/publications/articles/physics/85-undecidability/2/text.html "The behavior of a physical system may always be calculated by simulating explicitly each step in its evolution. Much of theoretical physics has, however, been concerned with devising shorter methods of calculation that reproduce the outcome without tracing each step. Such shortcuts can be made if the computations used in the calculation are more sophisticated than those that the physical system can i
Re: Are we simulated by some massive computer?
Dear George, How does indeterminacy and multiple-world-occupation follow from an inability to deduce that one is not in a simulation? Also, how is multiple-world-occupation knowable 1st person unless by the means I discusses previously? Does this not violate the anthropic principle? I am missing something. :_( Stephen - Original Message - From: George Levy To: Everything List Sent: Wednesday, May 12, 2004 1:12 AM Subject: Re: Are we simulated by some massive computer? Hi StephenStephen Paul King wrote: Dear George, My take of Russell's post is: Unless the creature had some experience that was not dismissible as a hallucination (1st person) and/or was witness by others (a proxy of 3rd person?) that lead him to the conclusion that it existed within a virtual reality then it would have no ability to make such a deduction.True. But from its own point of view its world would then be indeterminate. The creature would occupy several worlds as long as this indeterminacy exists.George
Re: Are we simulated by some massive computer?
IMHO, this latter situation seem to be what D. Deutsch proposes as a test for his MWI. If we can create a physical implementation of a quantum computation that has greater computational power than that allowed by the classical (as per the Copenhagen Interpretation or other interpretations) case, then it would verify .MWI. A failure of such would be a falsification. Perhaps Stephen, but I offer that it would ultimately only lend support to the view that the classical model is incomplete. This reasoning reminds me of the anecdote about the eminent astronomer who, when his student commented on how naive it was that for so long people believed the earth to be the center of the universe , replied on the contrary, given a belief that one is stationary relative to the celestial panoply and given no additional hard evidence other than the sun, for instance, appearing in the east -arcing across the sky - then sinking out of sight in the west, it would be foolish to think otherwise. It was at the time the simplest explanation, lacking any solid additional detailed observation. And it was simply wrong. On the subject of consciousness, I wonder how fruitful it is to conduct thought experiments that infer the observer's consciousness. The reason I wonder this is (because I am? no, that's another story..) that I'm reading more and more of late about the zombie within concept where it seems that while we operate under the illusion of self control, in fact some entity that is the product of one's integrated anatomical and physiological pattern is actually acting and reacting measurably before I am aware; even when I believe I thought of and initiated the action. Whether or not one is hallucinating, we may in fact all be in the end delusional. My question is: if real, how does the above situation effect assumptions that are founded on the assumption of a single conscious observer/actor's first person experience? Perhaps all we can safely refer to is the observerand make no additional claims as to their, or even my own, conscious experience *lacking additional supportive empirical data*. Cheers CMR -- insert gratuitous quotation that implies my profundity here --
Re: Are we simulated by some massive computer?
At 15:59 11/05/04 -0700, George Levy wrote: snip I remember discussing this topic but I do not remember you calling me silly. Oh sorry you were only thinking it. Thank you :-) You are welcome. You know on these matters we can never be sure :-) Now when you say that the first person is all there is I am not sure it fits nicely with the methodology I am following. I am not sure I understand why you don't need the UD, given that the UD is just a nice third person description of the comp plenitude. [That such a thing could exist is a highly non trivial consequence of the closure of the set of programmable functions for the diagonalization: the existence of a universal machine. (The Post Turing discovery)]. Cf the diagonalization posts. You could as well just say you don't need comp. (But I use comp to just benefits from computer science and mathematical logic taking into account Post Turing Church ...Solovay). The first person essentially will be an intuitionist/constructivist machine, a self-extending entity which goes through locally anti-symmetric sequences of knowledge states. Physics seems to appears in the first person plural (where vast collection of interacting machines are multiplied), but the last discovery ---(that a quantum logic [even an infinity*] appears in the pure singular first person pov)--- surely makes me more open to the importance of the pure (intuitionist) first person. Please recall me your feelings about the comp hyp in the cognitive science/philosophy of mind, if you mind. I use comp if only because my more primary goal is to show that some hypothesis could make some theological question empirically testable. Bruno * That infinity of QL (Quantum Logic) converging toward CL (Classical logics) could be a form of *arithmetical decoherence* as experimented by all sound Universal Machine with respect to their normal neighborhoods/consistent extensions. You should study logic just to see the beauty. (Or the error! This material is new, and has not been verified by someone else. Caution.) http://iridia.ulb.ac.be/~marchal/
Re: Are we simulated by some massive computer?
Dear CMR, - Original Message - From: "CMR" [EMAIL PROTECTED] To: "Everything List" [EMAIL PROTECTED] Sent: Wednesday, May 12, 2004 10:22 AM Subject: Re: Are we simulated by some massive computer? [SPK] IMHO, this latter situation seem to be what D. Deutsch proposes as a test for his MWI. If we can create a physical implementation of a quantum computation that has greater computational power than that allowed by the classical (as per the Copenhagen Interpretation or other interpretations) case, then it would verify .MWI. A failure of such would be a falsification. [CMR] Perhaps Stephen, but I offer that it would ultimately only lend support to the view that the classical model is incomplete. This reasoning reminds me of the anecdote about the eminent astronomer who, when his student commented on how naive it was that for so long people believed the earth to be the center of the universe, replied "on the contrary, given a belief that one is stationary relative to the celestial panoply and given no additional hard evidence other than the sun, for instance, appearing in the east -arcing across the sky - then sinking out of sight in the west, it would be foolish to think otherwise". It was at the time the simplest explanation, lacking any solid additional detailed observation. And it was simply wrong. [SPK] This situation would seem to argue against Occam's Razor without further contemplations. People that I correspond with often ask me: "What is the "problem" for which your solution is offered? I respond by pointing to this notion of incompleteness that you mention as a start. As to the story of the eminent astronomer, let us recall howtend toassume as "truth"our beliefs even though they are often justified by no more than a consensus of opinion. [CMR] On the subject of consciousness, I wonder how fruitful it is to conduct thought experiments that infer the observer's consciousness. The reason I wonder this is (because I am? no, that's another story..) that I'm reading more and more of late about the "zombie within" concept where it seems that while we operate under the illusion of "self" control, in fact some entity that is the product of one's integrated anatomical and physiological pattern is actually acting and reacting measurably before "I" am aware; even when I believe I thought of and "initiated" the action. Whether or not one is hallucinating, we may in fact all be in the end delusional. [SPK] Indeed, there is some empirical evidence (discussed in Roger Penroses wonderful books) that what we consider as our 1st person experience of the world is nothing more than a construct formed fractions of a second prior to our awareness of it. What is amazing is how the generation of this construct (simulation!) is edited continuously and edited such that what is taken to be subjectively as the exact present moment is actually up to ½ of a second in the past. Could you tell us the names of some of the books and papers that you are reading about the "zombie within" concept? [CMR] My question is: if "real", how does the above situation effect assumptions that are founded on the assumption of a single conscious observer/actor's "first person" experience? Perhaps all we can safely refer to is the observer and make no additional claims as to their, or even my own, conscious experience *lacking additional supportive empirical data*. [SPK] This is exactly the kind of question that has pushed me to question the entire idea of realism as it is used in physics and mathematics. Could what we take as reality be nothing more than a collective delusion or "Maya"? I mean this in all seriousness. The question then becomes: Given that we each have a 1st person experience of a world, what is necessary and sufficient to explain how it is generated? I believe that we already have a wide variety of mathematical and conceptual tools to go through this question and to form coherent conclusions. I do not see how a mere postulation of a Platonic Plenitude, wherein my own 1st person experience is an infinitesimal fraction, is sufficient to bridge the gap to the probability 1 that I have of actually experiencing the writing of these words. We need an explanation of how the appearance of chance is necessitated. Kindest regards, Stephen
Re: Are we simulated by some massive computer?
Dear George, Interleaving. - Original Message - From: George Levy To: Stephen Paul King Sent: Wednesday, May 12, 2004 3:00 PM Subject: Re: Are we simulated by some massive computer? Stephen, Stephen Paul King wrote: Dear George, How does indeterminacy and multiple-world-occupation follow from an inability to deduce that one is not in a simulation? [CMR] It seems to me that if two worlds are indistinguishable from the point of view of an observer, then the two worlds could be switched on the observer - or conversely that the observer could be teleported from one world to the other - without him knowing it. [SPK] The 3rd person abilty to interchangeidentical worlds does notnecessitate the a priori existence of a multitute of identical worlds from a 1st person point of view, because, as you wrote they could be switched without him (the 1st person) knowing it. So why entertain their existence in the first place? If the existence of such is merely to construct a statistical ensemble, then fine, but bear in mine that such is merely a construct with its own set of assumptions and embelishments. Let us also take into account that the kind of teleportation that you bring up here is not physically possible. I do not understand how it continues to be used as apedagological device. [CMR] The existence of many such worlds give rise to Quantum indeterminacy. [SPK] I beg to differ. IIRC, David Deutsch and others have repeatedly pointed out that it is the superposition principle of Quantum Mechanics that implies the existence of "many worlds" not the prior existence of multiple identical worlds. [CMR] Measurement only restricts the size of the ensemble. [SPK] Are you assuming the "collapse of the wave-function" or some classical or "ignorance based" interpretation of probabilities here? [CMR] A creature nominally living in a simulation as observed (3rd person) by an experimenter, lives from the first person point of view in multiple simulations located at multiple levels. [SPK] It seems to me that you are assuming what I define as the "voyeur's framing" when considering the notion of a simulation. That is ok, IHMO, so long as you acknowledge that such a simulation will involve less computational power that one that dissallows for the voyeur's framing. It is like observing the game "EverQuest" on your computer monitor. When you make this assumption it follows that many -even an infinity - of simulated worlds could simultaneously exits, but I am arguing that the support for the multitute of identical worlds vanishes when we consider the caseof the simulation that requires more computational power than that available to *ANY* observer that you, from within the simulation, could communicate with. To follow the EverQuest analogy, consider yourself as a NPC (non-player character) within the EverQuest "world". The maximal computational power that you would have available would be the computational power needed to generate the unfolding of events you could observe from a 1st person point of view. I argue that we have a similar situation in our "real" world. Stephen Wolfram wrote: http://www.stephenwolfram.com/publications/articles/physics/85-undecidability/2/text.html "The behavior of a physical system may always be calculated by simulating explicitly each step in its evolution. Much of theoretical physics has, however, been concerned with devising shorter methods of calculation that reproduce the outcome without tracing each step. Such shortcuts can be made if the computations used in the calculation are more sophisticated than those that the physical system can itself perform. Any computations must, however, be carried out on a computer. But the computer is itself an example of a physical system. And it can determine the outcome of its own evolution only by explicitly following it through: No shortcut is possible. Such computational irreducibility occurs whenever a physical system can act as a computer. The behavior of the system can be found only by direct simulation or observation: No general predictive procedure is possible." I take this reasoning and invert to to argue that what we experience as "reality" is indistinguishable from a simulation of the world using the most computational power available, the latter being the world as a physical system, acting as a computer, computing its own evolution. What we take as a 1st person "reality" is nothing more than the best possible simulation. My rubric is: if we cannot 1st person distiguish between a "real" object and a simulate
Re: Are we simulated by some massive computer?
I'd love to take credit for George's arguments (he probablyknows morethan me, after all) but that wouldn't be ethical (andI don't think we want to revisit THAT thread!) cheers! Dear George, Interleaving. [CMR] It seems to me that if two worlds are indistinguishable from the point of view of an observer, then the two worlds could be switched on the observer - or conversely that the observer could be teleported from one world to the other - without him knowing it. [SPK] The 3rd person abilty to interchangeidentical worlds does notnecessitate the a priori existence of a multitute of identical worlds from a 1st person point of view, because, as you wrote they could be switched without him (the 1st person) knowing it. So why entertain their existence in the first place? If the existence of such is merely to construct a statistical ensemble, then fine, but bear in mine that such is merely a construct with its own set of assumptions and embelishments. Let us also take into account that the kind of teleportation that you bring up here is not physically possible. I do not understand how it continues to be used as apedagological device.
Re: Are we simulated by some massive computer?
Dear George and CMR, Whops! My apologies. But does this cancel out what I wrote? Stephen - Original Message - From: CMR To: Stephen Paul King Cc: [EMAIL PROTECTED] Sent: Wednesday, May 12, 2004 6:02 PM Subject: Re: Are we simulated by some massive computer? I'd love to take credit for George's arguments (he probablyknows morethan me, after all) but that wouldn't be ethical (andI don't think we want to revisit THAT thread!) cheers! Dear George, Interleaving. [CMR] It seems to me that if two worlds are indistinguishable from the point of view of an observer, then the two worlds could be switched on the observer - or conversely that the observer could be teleported from one world to the other - without him knowing it. [SPK] The 3rd person abilty to interchangeidentical worlds does notnecessitate the a priori existence of a multitute of identical worlds from a 1st person point of view, because, as you wrote they could be switched without him (the 1st person) knowing it. So why entertain their existence in the first place? If the existence of such is merely to construct a statistical ensemble, then fine, but bear in mine that such is merely a construct with its own set of assumptions and embelishments. Let us also take into account that the kind of teleportation that you bring up here is not physically possible. I do not understand how it continues to be used as apedagological device.
Re: Are we simulated by some massive computer?
Bruno and George, amazing how accurately you describe in math words what I wrote in 1998 and put on the WEB in 1999, based on the 1997 paper (Pre-Geometric origins) of Rainer Zimmermann - the NARRATIVE (no math) of the (no Plato-based)Plenitude - Bigbangs unlimited, including ours. No comp, no simulation, just a plain logical 'story' how bigbangs have got to emerge. I work on comp-leting (!) it ever since. In plain langauge - give it some more 2-300 years. My purpose was to "keep the Big bang-like beginning" for the convenience (after I fought against the cosmologists' follies) and describe a logical necessity for it to occur with a subsequent history it underwent in our universe (amongst innumerable others) to re-dissipate into the Plenitude. They are not any similar to ours, I can't put Tegmar's ideas into them.All occur and dissipate aspatialy-atemporally. Related stuff: on the Karl Jaspers Forum (networks 2003): http://www.douglas.qc.ca/fdg/kjf/62-TAMIK.htm- while on the (apache) "Index of jamikes" - my website - the entries following:http//pages.prodigy.net/jamikes/... ...Plenitude00.html, ..bigbang.html, ...evolJuly00.html show my approach in its forming (not even by far any similar to yours). Just FYI - I claim no part in the UD-related thoughts.G Cheers John Mikes - Original Message - From: "Bruno Marchal" [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Tuesday, May 11, 2004 9:59 AM Subject: Re: Are we simulated by some massive computer? At 15:51 10/05/04 -0700, George Levy wrote: BM: But you agree there is no plenitude without an UD. GL: No I don't agree. I don't agree that the UD is the origin of all things. But to say that there is no plenitude without an UD does not mean that the UD is the origin of all things. This is typical classical thinking. But I am a classical (boolean) thinker. (and actually it was a typical confusion between A-B and B-A, don't worry it happens all the time). To paraphrase "In the beginning there was the UD (eg. x=x+1). (Technical details: the UD is a little more than x = x+1, but OK) And the UD generated the Plenitude (eg. 0, 1, 2, 3, ...) Be careful. I thought we agreed that the Plenitude is a first person notion. the O, 1, 2, 3, could not even be used to describe a notion of 3-plenitude. The 3-plenitude is best described by the whole arithmetical truth, which has been proved to be not describable by any finite theory. It is not completely unifiable. . Out of the plenitude came out different worlds. But you *do* have understand the UDA argument (I have links!), and now you begin to talk like Schmidhuber. With the comp hyp only one physical world exists, and it is an emerging (from the 1-point of view) appearance. It emerges from all the comp histories. For exemple, although newtonian worlds are generated by the UD, no consciousness can ever stabilize on it because it is (or should be) of measure zero. Out of some of these worlds conscious creatures emerged. We are some of these creatures." And so this sentence has just no meaning with (classical) comp. This is 3rd person thinking. It leads to the mind-body problem. I resolve the mind-body problem at the outset by using the observer as a starting point. The "I" is both an observable fact and an axiom. "I" can observe that "I" am capable of logical thinking and that my thoughts are consistent. ( I will leave to you the detail regarding what kind of logic applies) My logical ability leads me to the principle of sufficient reason One way to phrase this principle is "If there is no reason for something not to be then it must be. Since I am in a particular state and there is no reason for me not to be in any other state, then I must also be in those states. This leads me to think that there are other observers beside myself, in fact, all possible observers. I can also apply this same principle to the world that I observe. If the world is in a particular state, and there are no reasons for this world to be in this particular state, then in must be in all possible states. This leads me to the plenitude. Thus the plenitude includes all possible worlds. The indistinguishability of which observer I am and (conjugately?) which world I occupy leads to first person indeterminacy. I agree with all this. my point is that this is indeed the correct (with comp) discourse of the first person. I can't say more without technics. If not recall me what you mean by the plenitude. Remember also that from a machine's point of view (1 or 3 whatever) the plenitude is given by the the UD, or more exactly its complete execution (UD*). I suppose "I" am the UD. Or maybe "I*" am the UD??? I don't know if this makes sense. I don't think so. It may be possible that the need t
Re: Are we simulated by some massive computer?
Bruno Marchal wrote: At 15:51 10/05/04 -0700, George Levy wrote: BM: But you agree there is no plenitude without an UD. GL: No I don't agree. I don't agree that the UD is the origin of all things. But to say that there is no plenitude without an UD does not mean that the UD is the origin of all things. I am being the devil's advocate. I actually agree with you, except that I don't understand the need for a UD. To paraphrase In the beginning there was the UD (eg. x=x+1). (Technical details: the UD is a little more than x = x+1, but OK) And the UD generated the Plenitude (eg. 0, 1, 2, 3, ...) Be careful. I thought we agreed that the Plenitude is a first person notion. the O, 1, 2, 3, could not even be used to describe a notion of 3-plenitude. The 3-plenitude is best described by the whole arithmetical truth, which has been proved to be not describable by any finite theory. It is not completely unifiable. . Out of the plenitude came out different worlds. But you *do* have understand the UDA argument (I have links!), and now you begin to talk like Schmidhuber. Sorry that I wasn't clearer. I was just playing the devil's advocate. I do not agree with Schmidhuber, I agree mostly with you except that I don't see the need of a UD. With the comp hyp only one physical world exists, and it is an emerging (from the 1-point of view) appearance. It emerges from all the comp histories. For exemple, although newtonian worlds are generated by the UD, no consciousness can ever stabilize on it because it is (or should be) of measure zero. Out of some of these worlds conscious creatures emerged. We are some of these creatures. And so this sentence has just no meaning with (classical) comp. I agree with you. This is 3rd person thinking. It leads to the mind-body problem. I resolve the mind-body problem at the outset by using the observer as a starting point. The I is both an observable fact and an axiom. I can observe that I am capable of logical thinking and that my thoughts are consistent. ( I will leave to you the detail regarding what kind of logic applies) My logical ability leads me to the principle of sufficient reason One way to phrase this principle is If there is no reason for something not to be then it must be. Since I am in a particular state and there is no reason for me not to be in any other state, then I must also be in those states. This leads me to think that there are other observers beside myself, in fact, all possible observers. I can also apply this same principle to the world that I observe. If the world is in a particular state, and there are no reasons for this world to be in this particular state, then in must be in all possible states. This leads me to the plenitude. Thus the plenitude includes all possible worlds. The indistinguishability of which observer I am and (conjugately?) which world I occupy leads to first person indeterminacy. I agree with all this. my point is that this is indeed the correct (with comp) discourse of the first person. I can't say more without technics. As I said I think the UD is a remnant of 3rd person thinking. I don' t understand why you dislike so much 3-person thinking (although I appreciate very much your respect for the 1-person). It is not that I dislike the 3rd person. I believe that the 1st person is all there is. The 3rd person is only an approximation that 1st persons can use to communicate when they share the same approximate frame of reference. The first person can be useful, just like Newtonian mechanics can be useful. However, in certain situations the third person point of view just breaks down. 3-person thinking is called usually science. It is communicable falsifiable (mainly) propositions and proofs. Like a proof that 17 is a prime number. I agree. But only for observers sharing the same frame of reference. It is simpler to assume the plenitude as an axiom than an arbitrary UD. At least there is nothing arbitrary about the plenitude. But the UD is just a machine-independent (and thus non arbitrary) description of the comp plenitude as it can be talked about in a 3-person way by (consistent) machines. I keep insisting that the UD is not given as an possible explanation, but it is a *necessary problem* (once we postulate comp). I don't see why the UD is necessary. Maybe I am missing something. I did prove that that necessary problem is equivalent to the extraction of the physical laws from number theory/arithmetic. Why don't you use the observer himself to do this. It may be that using the observer as starting points will force White Rabbits to be filtered out of the observable world And again I totally agree. It *is* what is proved in my thesis. I have done two things: the other (related to an error in my thesis I talked about in some previous post) is the apparition of a new quantum logic (I did not command it!) and even (I must verify) an infinity of quantum
Re: Are we simulated by some massive computer?
Russell OK. You are suffering from 3rd person thinking which leads you to these conclusions: 1) As a scientist experimenting with this simulated creature, you have absolutely no evidence that this creature is conscious. 2) You believe that the creature (conscious or unconscious) is stuck in your simulation. 3) You believe that your simulator is the world of the creature. First person thinking leads to other conclusions: 1) You perceives this creature as a different instantation of your own "I." Therefore you believe that the creature has some form of consciousness, maybe not identical to your own, but nevertheless, consciousness. 2) The world this creature exists in is to some extent indeterminate. It may be your own simulator that you purchased with some government grant, or it could be another almost identical simulator that *[EMAIL PROTECTED] run on Alpha Centauri 1,000,000 years ago. Or it could be yet another one. Only the creature itself can perform experiments to refine its perception of its world. Should you pull the plug on your simulator, the creature would continue to exist somewhere or somewhen else in the plenitude. 3) The indeterminacy and the experiment that the creature can conduct are limited by its own perception of itself, of its mind, of its body and of its world. Its own mind will shape its own world. George Russell Standish wrote: Sorry, but I fail to see it as self evident. Imagine being a creature immersed in a virtual reality setup its entire life, a virtual reality that does not include a representation (ie a body) of the creature itself. Would that creature deduce that it is in a virtual reality, and that it has a body in another (unobservable to it) reality? Or would it even be conscious? Cheers On Tue, May 11, 2004 at 04:10:15PM -0700, George Levy wrote: Russell wrote However, the mind-body problem doesn't completely disappear - rather it is transformed into "Why the Anthropic Principle?". Once you have accepted that "I" exist and that "I" am capable of logical thinking and capable of following a logical chain, then the Anthropic principle becomes trivial. What "I" am and what "I" observe becomes the initial boundary condition for a logical chain leading to the proof of the existence of the world: "I am therefore the world is." This is the Anthropic Principle. George
Re: Are we simulated by some massive computer?
Dear George, My take of Russell's post is: Unless the creature had some experience that was not dismissible as a hallucination (1st person) and/or was witness by others (a proxy of 3rd person?) that lead him to the conclusion that it existed within a virtual reality then it would have no ability to make such a deduction. Another possibility is to consider the upper bound on the computational recourses required to generate the totality of theexperience of such a creature and ask if that creature could have a 1st person experience an event that required more than that upper bound. IMHO, this latter situation seem to be what D. Deutsch proposes as a test for his MWI. If we can create a physical implementation of a quantum computation that has greater computational power than that allowed by the classical (as per the Copenhagen Interpretation or other interpretations) case, then it would verify MWI. A failure of such would be a falsification. Kindest regards, Stephen - Original Message - From: George Levy To: Everything List Sent: Tuesday, May 11, 2004 7:57 PM Subject: Re: Are we simulated by some massive computer? RussellOK. You are suffering from 3rd person thinking which leads you to these conclusions: 1) As a scientist experimenting with this simulated creature, you have absolutely no evidence that this creature is conscious. 2) You believe that the creature (conscious or unconscious) is stuck in your simulation. 3) You believe that your simulator is the world of the creature.First person thinking leads to other conclusions: 1) You perceives this creature as a different instantation of your own "I." Therefore you believe that the creature has some form of consciousness, maybe not identical to your own, but nevertheless, consciousness. 2) The world this creature exists in is to some extent indeterminate. It may be your own simulator that you purchased with some government grant, or it could be another almost identical simulator that *[EMAIL PROTECTED] run on Alpha Centauri 1,000,000 years ago. Or it could be yet another one. Only the creature itself can perform experiments to refine its perception of its world. Should you pull the plug on your simulator, the creature would continue to exist somewhere or somewhen else in the plenitude. 3) The indeterminacy and the experiment that the creature can conduct are limited by its own perception of itself, of its mind, of its body and of its world. Its own mind will shape its own world.George Russell Standish wrote: Sorry, but I fail to see it as self evident. Imagine being a creature immersed in a virtual reality setup its entire life, a virtual reality that does not include a representation (ie a body) of the creature itself. Would that creature deduce that it is in a virtual reality, and that it has a body in another (unobservable to it) reality? Or would it even be conscious? Cheers On Tue, May 11, 2004 at 04:10:15PM -0700, George Levy wrote: Russell wrote However, the mind-body problem doesn't completely disappear - rather it is transformed into "Why the Anthropic Principle?". Once you have accepted that "I" exist and that "I" am capable of logical thinking and capable of following a logical chain, then the Anthropic principle becomes trivial. What "I" am and what "I" observe becomes the initial boundary condition for a logical chain leading to the proof of the existence of the world: "I am therefore the world is." This is the Anthropic Principle. George
Re: Are we simulated by some massive computer?
Hi Stephen Stephen Paul King wrote: Dear George, My take of Russell's post is: Unless the creature had some experience that was not dismissible as a hallucination (1st person) and/or was witness by others (a proxy of 3rd person?) that lead him to the conclusion that it existed within a virtual reality then it would have no ability to make such a deduction. True. But from its own point of view its world would then be indeterminate. The creature would occupy several worlds as long as this indeterminacy exists. George
Re: Are we simulated by some massive computer?
I saw the documentary movie Tibet: Cry of the Snow Lion the other day. In one scene, a group of monks is sitting around in a circle, and the Dalai Llama is overseeing. The monks are industriously and methodically placing individual tiny coloured beads (there are maybe 4 or 5 colours) around the perimeter of an enormous circular mandala pattern (made of 10s of 1000s of beads). The pattern has grown to almost two metres in diameter, and it features an extrordinarily elaborate kaleidoscopic pattern with perfect radial symmetry, and large complex patterns built on tiny patterns. If someone places a single bead out of its proper place in the pattern, the pattern will be distorted and it will not be possible to maintain the growing recursive pattern. But if every bead is placed correctly, the perimiter can grow by one bead width maintaining the order of the pattern, and the process can repeat, growing larger and larger. OBSERVABLE REALITY IS LIKE THE MANDALA. EVERYTHING MUST BE JUST SO, TO MAINTAIN THE OBSERVABLE ORDER OVER A LARGE PERIMETER. ALMOST EVERY CHOICE (ABOUT WHERE TO PLACE BEADS) OR ABOUT PROGRAM NEXT STEPS, LEADS TO CHAOS RAPIDLY. A SELECT FEW PATHS CAN MAINTAIN THE ORDER. p.s. Later in the movie, they return to this scene, with the monks around an enormous, wondrously complex circular pattern. A monk takes a wooden yardstick, and with a few brief sweeps, obliterates the pattern, leaving chaos. The chaos; the sand of beads, is cleared to one side, and a monk places a single bead in the centre of the circle That last part is the real lesson of the mandala. Eric George Levy wrote: Bruno, Bruno Marchal wrote: And a priori the UD is a big problem because it contains too many histories/realities (the white rabbits), and a priori it does not contain obvious mean to force those aberrant histories into a destructive interference process (unlike Feynman histories). It may be that using the observer as starting points will force White Rabbits to be filtered out of the observable world George
Re: Are we simulated by some massive computer?
At 15:51 10/05/04 -0700, George Levy wrote: BM: But you agree there is no plenitude without an UD. GL: No I don't agree. I don't agree that the UD is the origin of all things. But to say that there is no plenitude without an UD does not mean that the UD is the origin of all things. This is typical classical thinking. But I am a classical (boolean) thinker. (and actually it was a typical confusion between A-B and B-A, don't worry it happens all the time). To paraphrase In the beginning there was the UD (eg. x=x+1). (Technical details: the UD is a little more than x = x+1, but OK) And the UD generated the Plenitude (eg. 0, 1, 2, 3, ...) Be careful. I thought we agreed that the Plenitude is a first person notion. the O, 1, 2, 3, could not even be used to describe a notion of 3-plenitude. The 3-plenitude is best described by the whole arithmetical truth, which has been proved to be not describable by any finite theory. It is not completely unifiable. . Out of the plenitude came out different worlds. But you *do* have understand the UDA argument (I have links!), and now you begin to talk like Schmidhuber. With the comp hyp only one physical world exists, and it is an emerging (from the 1-point of view) appearance. It emerges from all the comp histories. For exemple, although newtonian worlds are generated by the UD, no consciousness can ever stabilize on it because it is (or should be) of measure zero. Out of some of these worlds conscious creatures emerged. We are some of these creatures. And so this sentence has just no meaning with (classical) comp. This is 3rd person thinking. It leads to the mind-body problem. I resolve the mind-body problem at the outset by using the observer as a starting point. The I is both an observable fact and an axiom. I can observe that I am capable of logical thinking and that my thoughts are consistent. ( I will leave to you the detail regarding what kind of logic applies) My logical ability leads me to the principle of sufficient reason One way to phrase this principle is If there is no reason for something not to be then it must be. Since I am in a particular state and there is no reason for me not to be in any other state, then I must also be in those states. This leads me to think that there are other observers beside myself, in fact, all possible observers. I can also apply this same principle to the world that I observe. If the world is in a particular state, and there are no reasons for this world to be in this particular state, then in must be in all possible states. This leads me to the plenitude. Thus the plenitude includes all possible worlds. The indistinguishability of which observer I am and (conjugately?) which world I occupy leads to first person indeterminacy. I agree with all this. my point is that this is indeed the correct (with comp) discourse of the first person. I can't say more without technics. If not recall me what you mean by the plenitude. Remember also that from a machine's point of view (1 or 3 whatever) the plenitude is given by the the UD, or more exactly its complete execution (UD*). I suppose I am the UD. Or maybe I* am the UD??? I don't know if this makes sense. I don't think so. It may be possible that the need to invoke a UD originates from classical 3rd person (objective or absolute) thinking in which several separate physical worlds are simulated. I would be prudent before linking objective with absolute. I could argue that only the subjective is absolute (for example it is hard to relativize actual pain ...). Also, I insist (I know you did got that probably subtle point), but with comp the adjective physical cannot be applied to anything capable of being emulated (because the physical is a sum on all possible emulations at once, and that cannot be emulated). As I said I think the UD is a remnant of 3rd person thinking. I don' t understand why you dislike so much 3-person thinking (although I appreciate very much your respect for the 1-person). 3-person thinking is called usually science. It is communicable falsifiable (mainly) propositions and proofs. Like a proof that 17 is a prime number. The comp hypothesis may be better off without a UD simply because it is possible to derive the plenitude without a UD. And should you refuse to accept the observer as a starting point, you could assume the plenitude as a starting pont axiom. It is simpler to assume the plenitude as an axiom than an arbitrary UD. At least there is nothing arbitrary about the plenitude. But the UD is just a machine-independent (and thus non arbitrary) description of the comp plenitude as it can be talked about in a 3-person way by (consistent) machines. I keep insisting that the UD is not given as an possible explanation, but it is a *necessary problem* (once we postulate comp). I did prove that that necessary problem is equivalent to the extraction of the physical laws
Re: Are we simulated by some massive computer?
At 16:13 07/05/04 -0700, George Levy wrote: Bruno, Bruno Marchal wrote: My view is that the observer-experience simply consists in the (virtual) transitions from one observer-moment to another where the transition is filtered by having to be consistent with the observer-state. Note how the observer bootstraps himself into consciousness out of the plenitude. So maybe my UD is the nul UD : it is the maximally dumb UD. A maximally dumb UD? I am not sure I understand. This may be the crux of our misunderstanding. I think that an observer can emerge out of the penitude without a UD. The maximally dumb UD is the Null-UD. But you agree there is no plenitude without an UD. If not recall me what you mean by the plenitude. Remember also that from a machine's point of view (1 or 3 whatever) the plenitude is given by the the UD, or more exactly its complete execution (UD*). First person (relative or relativistic) experience is the only one that matters. The world(s) he perceives is the portion of the plenitude consistent with himself. (The body must be consistent with the mind) I agree. It may be possible that the need to invoke a UD originates from classical 3rd person (objective or absolute) thinking in which several separate physical worlds are simulated. I disagree, or I don't understand. I don't think there is a *need* to *invoke* a UD. It is just that the UD is there, and we cannot make it disappears by simple wish (without abandoning the comp hyp). And a priori the UD is a big problem because it contains too many histories/realities (the white rabbits), and a priori it does not contain obvious mean to force those aberrant histories into a destructive interference process (unlike Feynman histories). And so apparently comp is false, and then my work points on the fact that we cannot yet conclude to the falsity of comp because, by interviewing self-referentially correct machines on the 1-possible histories, the machine does propose a highly non trivial quantum geometry so that destructive interference of too complex histories remains possible (without a priori priors). Bruno http://iridia.ulb.ac.be/~marchal/
Re: Are we simulated by some massive computer?
Bruno, Bruno Marchal wrote: At 16:13 07/05/04 -0700, George Levy wrote: Bruno, Bruno Marchal wrote: My view is that the observer-experience simply consists in the (virtual) transitions from one observer-moment to another where the transition is filtered by having to be consistent with the observer-state. Note how the observer bootstraps himself into consciousness out of the plenitude. So maybe my UD is the nul UD : it is the maximally dumb UD. A maximally dumb UD? I am not sure I understand. This may be the crux of our misunderstanding. I think that an observer can emerge out of the penitude without a UD. The maximally dumb UD is the Null-UD. But you agree there is no plenitude without an UD. No I don't agree. I don't agree that the UD is the origin of all things. This is typical classical thinking. To paraphrase: In the beginning there was the UD (eg. x=x+1). And the UD generated the Plenitude (eg. 0, 1, 2, 3, ...). Out of the plenitude came out different worlds. Out of some of these worlds conscious creatures emerged. We are some of these creatures. This is 3rd person thinking. It leads to the mind-body problem. I resolve the mind-body problem at the outset by using the observer as a starting point. The I is both an observable fact and an axiom. I can observe that I am capable of logical thinking and that my thoughts are consistent. ( I will leave to you the detail regarding what kind of logic applies) My logical ability leads me to the principle of sufficient reason One way to phrase this principle is If there is no reason for something not to be then it must be. Since I am in a particular state and there is no reason for me not to be in any other state, then I must also be in those states. This leads me to think that there are other observers beside myself, in fact, all possible observers. I can also apply this same principle to the world that I observe. If the world is in a particular state, and there are no reasons for this world to be in this particular state, then in must be in all possible states. This leads me to the plenitude. Thus the plenitude includes all possible worlds. The indistinguishability of which observer I am and (conjugately?) which world I occupy leads to first person indeterminacy. If not recall me what you mean by the plenitude. Remember also that from a machine's point of view (1 or 3 whatever) the plenitude is given by the the UD, or more exactly its complete execution (UD*). I suppose I am the UD. Or maybe I* am the UD??? I don't know if this makes sense. First person (relative or relativistic) experience is the only one that matters. The world(s) he perceives is the portion of the plenitude consistent with himself. (The body must be consistent with the mind) I agree. It may be possible that the need to invoke a UD originates from classical 3rd person (objective or absolute) thinking in which several separate physical worlds are simulated. I disagree, or I don't understand. I don't think there is a *need* to *invoke* a UD. It is just that the UD is there, and we cannot make it disappears by simple wish (without abandoning the comp hyp). As I said I think the UD is a remnant of 3rd person thinking. The comp hypothesis may be better off without a UD simply because it is possible to derive the plenitude without a UD. And should you refuse to accept the observer as a starting point, you could assume the plenitude as a starting pont axiom. It is simpler to assume the plenitude as an axiom than an arbitrary UD. At least there is nothing arbitrary about the plenitude. And a priori the UD is a big problem because it contains too many histories/realities (the white rabbits), and a priori it does not contain obvious mean to force those aberrant histories into a destructive interference process (unlike Feynman histories). It may be that using the observer as starting points will force White Rabbits to be filtered out of the observable world George
Re: Are we simulated by some massive computer?
On Mon, May 10, 2004 at 03:51:34PM -0700, George Levy wrote: But you agree there is no plenitude without an UD. No I don't agree. I don't agree that the UD is the origin of all things. This is typical classical thinking. To paraphrase: In the beginning there was the UD (eg. x=x+1). And the UD generated the Plenitude (eg. 0, 1, 2, 3, ...). Out of the plenitude came out different worlds. Out of some of these worlds conscious creatures emerged. We are some of these creatures. This is 3rd person thinking. It leads to the mind-body problem. I resolve the mind-body problem at the outset by using the observer as a starting point. The I is both an observable fact and an axiom. I can observe that I am capable of logical thinking and that my thoughts are consistent. ( I will leave to you the detail regarding what kind of logic applies) My logical ability leads me to the principle of sufficient reason One way to phrase this principle is If there is no reason for something not to be then it must be. Since I am in a particular state and there is no reason for me not to be in any other state, then I must also be in those states. This leads me to think that there are other observers beside myself, in fact, all possible observers. ... It may be that using the observer as starting points will force White Rabbits to be filtered out of the observable world George I think this email is quite profound. I find myself in agreement with George's statement, and I basically say the same thing (in a more clumsy way) in Why Occam's Razor. However, the mind-body problem doesn't completely disappear - rather it is transformed into Why the Anthropic Principle?. See Bruno's critique of my paper, circa early 2000. The AP demands that our observed universe contains an instantiation of our consciousness. This is needed, as otherwise we will only see trivial worlds, contrary to observation. My guess is that the AP is a reflection of some deep principle of consciousness that we haven't unravelled - something necessarily self-reflexive. Cheers A/Prof Russell Standish Director High Performance Computing Support Unit, Phone 9385 6967, 8308 3119 (mobile) UNSW SYDNEY 2052 Fax 9385 6965, 0425 253119 () Australia[EMAIL PROTECTED] Room 2075, Red Centrehttp://parallel.hpc.unsw.edu.au/rks International prefix +612, Interstate prefix 02 pgp0.pgp Description: PGP signature
Re: Are we simulated by some massive computer?
Bruno Marchal wrote: I agree with George, but note that I arrive at an equivalent assertion without using that lower levels have lower complexity and therefore higher measure. That is possible, but the problem is that it is a priori hard to estimate the dumbness of the universal dovetailer which is quite capable to entangle high complexity programs with low complexity programs, so that the multiplication related to low-complexity can be inherited to high-complexity (due to dovetailing). But you may be right, I have not proved that a UD could be that dumb! Gosh, Bruno, I don't understand what you are saying. Maybe I am too naive! Or maybe our background conceptions are too different so even if the language is the same it does not make sense. For one I don't see how a first person experience needs to depend on a UD. My view is that the observer-experience simply consists in the (virtual) transitions from one observer-moment to another where the transition is filtered by having to be consistent with the observer-state. Note how the observer bootstraps himself into consciousness out of the plenitude. So maybe my UD is the nul UD : it is the maximally dumb UD. George From a suggestion of Jacques Bailhache (an old everythinger) I have try to build an explicit UD which makes the measure on computations arbitrary, but I have not succeed, in the limit (on which bears the first points of view), the right measure seems to self-correct by itself. It is that self-measure I study with provability logic. Another problem with the idea of low level, or of simple program is that even a program with 2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^64 as minimal bit-length is quite little in comparison of almost all number in Plato Heaven. Bruno At 15:56 05/05/04 -0700, George Levy wrote: This has been an interesting thread. Unfortunately I was too busy to contribute much. However, here is a thought regarding simulation versus first and third person points of view. It does make sense to talk about a 3rd person point of view about simulation of a conscious entity on a computer. However, I don't think it applies to a first person point of view. In the plenitude we'll have an infinite number of levels of simulation as well as an infinite number of simulations per level (2^aleph_0 as suggested by Bruno in a previous post, or higher) From a first person point of view any observer moment in any simulation and at any level can transit to another observer moment in a different simulation at a different level provided the transition is consistent with the observer. Therefore from the first person point of view there is no such a thing as living in a simulator. As first persons we live in all simulators and at all levels. In addition, since lower levels have lower complexity and therefore higher measure, the number of simulations is higher at lower levels. Therefore we are more likely to occupy ensembles of simulations located at the lower levels. Is there a lowest level in the level hierarchy, that is a level below which there is no simulation, just the plenitude? Possibly. If so, we are most likely to exist most of the time at that base level, but we cannot exclude that some of the time we may be in a higher level. h. This argument points to the fact that most of the time we do not live in a simulator! George http://iridia.ulb.ac.be/~marchal/
Re: Are we simulated by some massive computer?
At 23:02 06/05/04 -0700, George Levy wrote: Bruno Marchal wrote: I agree with George, but note that I arrive at an equivalent assertion without using that lower levels have lower complexity and therefore higher measure. That is possible, but the problem is that it is a priori hard to estimate the dumbness of the universal dovetailer which is quite capable to entangle high complexity programs with low complexity programs, so that the multiplication related to low-complexity can be inherited to high-complexity (due to dovetailing). But you may be right, I have not proved that a UD could be that dumb! Gosh, Bruno, I don't understand what you are saying. Maybe I am too naive! Or maybe our background conceptions are too different so even if the language is the same it does not make sense. For one I don't see how a first person experience needs to depend on a UD. My view is that the observer-experience simply consists in the (virtual) transitions from one observer-moment to another where the transition is filtered by having to be consistent with the observer-state. Note how the observer bootstraps himself into consciousness out of the plenitude. So maybe my UD is the nul UD : it is the maximally dumb UD. But then why are you sure that lower complexity have higher measure? I understand intuitively but how would you prove that without introducing a special UD? A maximally dumb UD? I am not sure I understand. Bruno http://iridia.ulb.ac.be/~marchal/
Re: Are we simulated by some massive computer?
I agree with George, but note that I arrive at an equivalent assertion without using that lower levels have lower complexity and therefore higher measure. That is possible, but the problem is that it is a priori hard to estimate the dumbness of the universal dovetailer which is quite capable to entangle high complexity programs with low complexity programs, so that the multiplication related to low-complexity can be inherited to high-complexity (due to dovetailing). But you may be right, I have not proved that a UD could be that dumb! From a suggestion of Jacques Bailhache (an old everythinger) I have try to build an explicit UD which makes the measure on computations arbitrary, but I have not succeed, in the limit (on which bears the first points of view), the right measure seems to self-correct by itself. It is that self-measure I study with provability logic. Another problem with the idea of low level, or of simple program is that even a program with 2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^2^64 as minimal bit-length is quite little in comparison of almost all number in Plato Heaven. Bruno At 15:56 05/05/04 -0700, George Levy wrote: This has been an interesting thread. Unfortunately I was too busy to contribute much. However, here is a thought regarding simulation versus first and third person points of view. It does make sense to talk about a 3rd person point of view about simulation of a conscious entity on a computer. However, I don't think it applies to a first person point of view. In the plenitude we'll have an infinite number of levels of simulation as well as an infinite number of simulations per level (2^aleph_0 as suggested by Bruno in a previous post, or higher) From a first person point of view any observer moment in any simulation and at any level can transit to another observer moment in a different simulation at a different level provided the transition is consistent with the observer. Therefore from the first person point of view there is no such a thing as living in a simulator. As first persons we live in all simulators and at all levels. In addition, since lower levels have lower complexity and therefore higher measure, the number of simulations is higher at lower levels. Therefore we are more likely to occupy ensembles of simulations located at the lower levels. Is there a lowest level in the level hierarchy, that is a level below which there is no simulation, just the plenitude? Possibly. If so, we are most likely to exist most of the time at that base level, but we cannot exclude that some of the time we may be in a higher level. h. This argument points to the fact that most of the time we do not live in a simulator! George http://iridia.ulb.ac.be/~marchal/
Re: Are we simulated by some massive computer?
The following is a combination of several of my previous ideas which forces me to raise a question re measure in this thread. 1) The first step is to examine the act of definition. In this case the definition of a Nothing. Any definition process simultaneously defines two entities. The definition is a boundary between an entity of interest and the leftover building blocks. In the special case of a Nothing the left over is an Everything. Thus the two are dependent partners. Since the Everything contains all information the definition pair must itself specify all information and can be represented by a normal real. 2) A Nothing has an interesting logical problem: It can not answer any meaningful question about itself. Assuming there is a relevant meaningful question a Nothing would be incomplete. An inescapable meaningful question is its own stability. This is not only meaningful it is impossible to avoid answering. 3) To attempt to answer this question a Nothing randomly and spontaneously decays towards an Everything to resolve its incompleteness. But this is not sustainable since an Everything is not independent of a Nothing. Therefore a Nothing rebounds from the decay. 4) Thus the definition pair or boundary between the Nothing and Everything partners is randomly dynamic - equivalent to a random sequence of normal reals. 5) A universal dovetailer computer [the computer plus its collective dynamic input and output] is a good way to model a selector of a random sequence of normal reals. 6) Notice that the Everything also has a logical problem. Looking at the same meaningful question of its own stability it contains all possible answers. Just one would constitute a selection i.e. net internal information which is not an aspect of the Everything. Thus the Everything is inconsistent. 7) Thus the entire system while being - apparently - the only game in town is also both incomplete and inconsistent. 8) Universes are interpretations of sections of the normal real string. 9) Now a question is how many of these interpretations have internal rules that allow input from an external random oracle? If we are to maintain a zero information system then the answer must be a randomly changing percentage. So all interpretations must be able change character i.e. be subject to an external random oracle the internal rules of the particular interpretation notwithstanding. 10) What this means is that there remains some information in the system - the computer itself is incorrectly defined - to get rid of this problem the computer has to function like any computer I ever used - it must make random errors. I do not see how one can extract from this any measure re anything which to me seems reasonable since there should be no information in there anyway. Hal Hal
Re: Are we simulated by some massive computer?
Hi Kory, Are you still there? I got funny responses from the webposter, it looks there is a problem with your mail address. Hoping to hear about you soon, Bruno http://iridia.ulb.ac.be/~marchal/
Re: Are we simulated by some massive computer?
At 16:14 30/04/04 -0400, John M wrote: How about: self? is it a good enoug 1st person soul? Here you put your finger on something quite important but rather hard to explain without saying more on the incompleteness phenomenon. We will certainly come back on this more than once. The idea is that there are many notion of selves for the sound machine. (I recall I am always talking about a machine which proves theorem of arithmetic, and by definition a machine is sound if she proves true theorems). Then the third person self is defined by a correct functional description of the machine at the right level (which exist for us by comp, and which can be made explicit for simple machine like Peano-Arithmetic, ...). It is a third person self, a little like when you say I have a mouth ... I remember now that I did use the term soul for this notion of *third* person (or self) in the provocative view of comp: comp means you can save your soul on a disket. Stathis made me think that the word soul is perhaps better used for the first person self. In a nutshell, the third person self is the one which will be described by the Godelian beweisbar provability predicate Bew(x), (and then by the modal logical systems G and G* (for those who remember, I will re-explain later)). The first person self will be defined by applying the Theaetetus trick on the third person self, that is on bew. So the first person will be defined by a new predicate saying Bew(x) and True(x). But the predicate Truth(x), by Tarski theorem, cannot be defined in the language of the machine. Still, by using G (and G*) we can defined such a box (but detail will be given at time). Now the machine is sound, which means the machine proves only true proposition of arithmetic. So, obviously the first and third person are equivalent. But the incompleteness theorems will entail that neither the 3-machine self, nor 1-machine self can *prove* that equivalence. Such subtle nuances will be made cristal transparent by the explicit use of G and G*. I recall that G is a formal theory complete for the provable discours,by the machine, on the propositional provability logic of itself (the machine itself). G* is a formal theory complete for the true discours,by the machine, on the propositional provability logic of itself (the machine itself). That is: G* contains the true but unprovable sentences on and by the machine. What appears here, with the box [0] for the 3-person and [1] for the 1-person: G* proves [0] = [1], but G does not prove it. Well I guess this was difficult for those who doesn't know enough logic and my intend was to explain more before. So don't worry if you don't understand. Remember that the popular book by Smullyan Forever Undecided has been reedited, and is a not too bad introduction to the modal logic G. It could help. Old (in this list) definition of G and G* can be found here http://www.escribe.com/science/theory/m1417.html and in the neighborhood. Bruno John M - Original Message - From: Bruno Marchal [EMAIL PROTECTED] To: Stathis Papaioannou [EMAIL PROTECTED]; [EMAIL PROTECTED] Sent: Friday, April 30, 2004 9:37 AM Subject: Re: Are we simulated by some massive computer? Ok Stathis, thanks for the precision. Anyway you give me the temptation to identify the soul by the first person. We will be able to prove (with the comp hyp) that not only the soul exists but (I forget to say) also that from the *correct* soul point of view, the soul is NOT a machine. But perhaps the word soul is to charged with emotion, and perhaps we should stick on the expression first person. 'course, it is just a matter of vocabulary. (But then humans are able to fight themselves during centuries for matter of vocabulary ... :( Bruno At 22:23 30/04/04 +1000, Stathis Papaioannou wrote: On 29 April 2004 Bruno Marchal wrote: At 23:16 28/04/04 +1000, Stathis Papaioannou wrote: There is a single idea underlying much of the confusion in discussions of personal identity: the belief in a soul. Indeed. I use this term for a quality or substance which resides in a person throughout his life and is somehow responsible for his identity, and which (here is the problem) is not captured by a complete description of the person's physical and psychological state. Often, it is a hidden assumption. That's a nice definition of the soul, quite similar to the provable properties of the first person, once we will define it precisely (in the Thaetetus way). And comp will entails, *as a theorem*, the existence of the soul, then! Actually, I didn't mean to use soul as a synonym for consciousness or subjective experience, which is why I said it was something not captured by a complete description of a person's physical *or psychological* state. Subjective experience differs from other empirical data in that it can only be fully understood in a first person context, but I do not see why this should disqaulify it from being a fit
Re: Are we simulated by some massive computer?
At 09:25 29/04/04 -0400, John M wrote: Bruno, I am sorry if my poorly chosen words irritated you, that was the farthest from my intentions. I can see, they did. Yes but that's ok. Thanks for caring. You give me the opportunity to take a new look to the Bochenski book. I did search that book for a long time and a friend who was working at Los Alamos brought me back a withdrawn exemplary from the Los Alamos library! It confirms my feeling that fundamental questions are multi-cultural in essence. We should come back on this but I prefer to try to explain a little bit the technical part of my work before. Please don't hesitate to intervene with question, remarks, or any skeptical critics. Bruno http://iridia.ulb.ac.be/~marchal/
Re: Are we simulated by some massive computer?
On 29 April 2004 Bruno Marchal wrote: At 23:16 28/04/04 +1000, Stathis Papaioannou wrote: There is a single idea underlying much of the confusion in discussions of personal identity: the belief in a soul. Indeed. I use this term for a quality or substance which resides in a person throughout his life and is somehow responsible for his identity, and which (here is the problem) is not captured by a complete description of the person's physical and psychological state. Often, it is a hidden assumption. That's a nice definition of the soul, quite similar to the provable properties of the first person, once we will define it precisely (in the Thaetetus way). And comp will entails, *as a theorem*, the existence of the soul, then! Actually, I didn't mean to use soul as a synonym for consciousness or subjective experience, which is why I said it was something not captured by a complete description of a person's physical *or psychological* state. Subjective experience differs from other empirical data in that it can only be fully understood in a first person context, but I do not see why this should disqaulify it from being a fit subject for scientific study. Cognitive psychologists write rigorous scientific papers of which they are very proud, and they seem to have replaced the behaviourists (who thought consciousness was at best unimportant and at worst non-existent) in most academic psychology departments. What I meant by soul was something beyond reason or empirical fact, whether of the first or the third person variety; something magical or supernatural, in other words. Stathis Papaioannou _ Find love today with ninemsn personals. Click here: http://ninemsn.match.com?referrer=hotmailtagline
Re: Are we simulated by some massive computer?
Dear Stephen, At 13:44 29/04/04 -0400, Stephen Paul King wrote: But there is no such thing as a delay in Platonia, but that is not my point. It is good it is not your point because there are delay in Platonia, at least in the sense I was using the word. A delay relative to a computational state is the minimal number of step for the UD to come back on that state or its continuations (roughly speaking). By the compiler theorem this make sense, and it is just a (computable) number. It has nothing to to with the subjective time we will be able to axiomatize once we define the first person, and it has nothing to do with the physical time which we will or will not recover from the quantum logics (given by interviewing the sound universal machine). I am trying to see how you deal with the problem of intractible computations - as implementable given infinite resources - and how it may be possible for measures to be defined using them. I had not considered this application but it is intriguing. You touch on this below. If complexity play a role it must be derived along with the measure on the comp histories. [SPK] Yes, but is this derivation on that can be taken to exist independent of the first person aspect of comp histories? This may be one of my key difficulties. On one hand, I do not have a problem with the idea of Platonic existence, re AR, of mathematical objects but I do have a problem with the seeming lack of a clear explanation of how the flow of temporality arises in the first person aspect. But we have not yet arrive at this point. Wait for S4Grz. You *will* be delighted :)(We will see ...). It seems to me that what ever our theory of Everything is, it must explain how it is not just possible to have a flow of temporality a priori; it must have a non-measure zero sampling in the class of all possible relationships between numbers - or whatever notion of Ur-object that one uses. I personaly eschew the notion of fundamental objects and use the Heraclitian notion of Process and fundamental, thus I see mathematical objects - numbers, etc. - as derivative of this notion of Process. I see Hintikka's idea of proofs as game theoretical constructs as strongly hinting at this idea... It is really a matter of convenience, to take numbers, sets, or games. But in general game theories, or set theories are richer and less simple than elementary arithmetic. I don't think those dictinction are quite relevant. You will tell me ... after I make enough precise the result I got and the propositions I conjecture. Do you know Conway game theory? Where games are jkust a slight generalisation of his concept of number? In Conscience Mecanisme I do make a case that Bennett notion of depth could play a role in order to derive the cosmological aspect of physics. Even prior a-la-Schmidhuber could play a role. But the methodology I advocate although it could justify the prior if needed, cannot rely on it at the start. [SPK] I agree. We have to have the methodology itself as an a priori existent. It is co-present in Platonia in your thinking, it seems to me. ;-) This is a little bit too vague for me I'm afraid. I do not see how the mere a priori existence of solutions (Integers) and the relationships between them (also Integers), as a priori existing numbers is sufficient. We will discuss that after I succeed in explaining how the whole things work. All Right? [SPK] Sure! ;-) BM: The comp reason why the soul or the first person is never captured by any complete third person description is akin to the reason truth and knowledge are not arithmetizable (as opposed to provable and consistent). Godel's theorem Co. makes universal machine a highly non trivial type of being. [SPK] Does not this statement, that truth and knowledge are not arithmetizable, imply that the postulation of AR is insufficient? [BM] No. And giving that Godel's incompleteness is true for much more general things than machine, we can say not only that arithmetical truth is not arithmetizable, but mathematical truth is not mathematicalizable, physical truth is not physicalizable, and more generally [whatever]-truth is not [whatver]izable. So strictly speaking AR could be sufficient (the Pythagorean version of my thesis). For reason of simplicity I do not use it. [SPK] Wait a minute! It is one thing to say that [whatever]-truth is not [whatver]izable and it is another to say that [whatever]-truth is finitely constructible or approximatable. The former deals with its existential aspects and the latter deals with its meaningfulness and expressiveness. We do not require absoluteness (truth, decidability or otherwise) in our interactions to be able to have meaningfulness. But this is not problematic to me; I am interested in how physicality MUST obtain, even if only in the first person sense. In fact, in my work I anly assume first person
Re: Are we simulated by some massive computer?
Ok Stathis, thanks for the precision. Anyway you give me the temptation to identify the soul by the first person. We will be able to prove (with the comp hyp) that not only the soul exists but (I forget to say) also that from the *correct* soul point of view, the soul is NOT a machine. But perhaps the word soul is to charged with emotion, and perhaps we should stick on the expression first person. 'course, it is just a matter of vocabulary. (But then humans are able to fight themselves during centuries for matter of vocabulary ... :( Bruno At 22:23 30/04/04 +1000, Stathis Papaioannou wrote: On 29 April 2004 Bruno Marchal wrote: At 23:16 28/04/04 +1000, Stathis Papaioannou wrote: There is a single idea underlying much of the confusion in discussions of personal identity: the belief in a soul. Indeed. I use this term for a quality or substance which resides in a person throughout his life and is somehow responsible for his identity, and which (here is the problem) is not captured by a complete description of the person's physical and psychological state. Often, it is a hidden assumption. That's a nice definition of the soul, quite similar to the provable properties of the first person, once we will define it precisely (in the Thaetetus way). And comp will entails, *as a theorem*, the existence of the soul, then! Actually, I didn't mean to use soul as a synonym for consciousness or subjective experience, which is why I said it was something not captured by a complete description of a person's physical *or psychological* state. Subjective experience differs from other empirical data in that it can only be fully understood in a first person context, but I do not see why this should disqaulify it from being a fit subject for scientific study. Cognitive psychologists write rigorous scientific papers of which they are very proud, and they seem to have replaced the behaviourists (who thought consciousness was at best unimportant and at worst non-existent) in most academic psychology departments. What I meant by soul was something beyond reason or empirical fact, whether of the first or the third person variety; something magical or supernatural, in other words. Stathis Papaioannou _ Find love today with ninemsn personals. Click here: http://ninemsn.match.com?referrer=hotmailtagline http://iridia.ulb.ac.be/~marchal/
Re: Are we simulated by some massive computer?
How about: self? is it a good enoug 1st person soul? John M - Original Message - From: Bruno Marchal [EMAIL PROTECTED] To: Stathis Papaioannou [EMAIL PROTECTED]; [EMAIL PROTECTED] Sent: Friday, April 30, 2004 9:37 AM Subject: Re: Are we simulated by some massive computer? Ok Stathis, thanks for the precision. Anyway you give me the temptation to identify the soul by the first person. We will be able to prove (with the comp hyp) that not only the soul exists but (I forget to say) also that from the *correct* soul point of view, the soul is NOT a machine. But perhaps the word soul is to charged with emotion, and perhaps we should stick on the expression first person. 'course, it is just a matter of vocabulary. (But then humans are able to fight themselves during centuries for matter of vocabulary ... :( Bruno At 22:23 30/04/04 +1000, Stathis Papaioannou wrote: On 29 April 2004 Bruno Marchal wrote: At 23:16 28/04/04 +1000, Stathis Papaioannou wrote: There is a single idea underlying much of the confusion in discussions of personal identity: the belief in a soul. Indeed. I use this term for a quality or substance which resides in a person throughout his life and is somehow responsible for his identity, and which (here is the problem) is not captured by a complete description of the person's physical and psychological state. Often, it is a hidden assumption. That's a nice definition of the soul, quite similar to the provable properties of the first person, once we will define it precisely (in the Thaetetus way). And comp will entails, *as a theorem*, the existence of the soul, then! Actually, I didn't mean to use soul as a synonym for consciousness or subjective experience, which is why I said it was something not captured by a complete description of a person's physical *or psychological* state. Subjective experience differs from other empirical data in that it can only be fully understood in a first person context, but I do not see why this should disqaulify it from being a fit subject for scientific study. Cognitive psychologists write rigorous scientific papers of which they are very proud, and they seem to have replaced the behaviourists (who thought consciousness was at best unimportant and at worst non-existent) in most academic psychology departments. What I meant by soul was something beyond reason or empirical fact, whether of the first or the third person variety; something magical or supernatural, in other words. Stathis Papaioannou _ Find love today with ninemsn personals. Click here: http://ninemsn.match.com?referrer=hotmailtagline http://iridia.ulb.ac.be/~marchal/
Re: Are we simulated by some massive computer?
Dear Bruno, I would like to focus on one thing, but will interleave comments on the rest.. - Original Message - From: Bruno Marchal [EMAIL PROTECTED] To: Stephen Paul King [EMAIL PROTECTED] Cc: [EMAIL PROTECTED] Sent: Friday, April 30, 2004 10:05 AM Subject: Re: Are we simulated by some massive computer? Dear Stephen, At 13:44 29/04/04 -0400, Stephen Paul King wrote: But there is no such thing as a delay in Platonia, but that is not my point. It is good it is not your point because there are delay in Platonia, at least in the sense I was using the word. A delay relative to a computational state is the minimal number of step for the UD to come back on that state or its continuations (roughly speaking). By the compiler theorem this make sense, and it is just a (computable) number. It has nothing to to with the subjective time we will be able to axiomatize once we define the first person, and it has nothing to do with the physical time which we will or will not recover from the quantum logics (given by interviewing the sound universal machine). [SPK] Now this statement has me very puzzled! Platonia must include all possible computational steps and even if we only consider computations as N to N maps we will find that there exist minimal recursions (like Poincare recursions where the computation returns to its initial state) that will be infinitely long. These are the type of computations that I am troubled by, computations that are attempts to solve NP-Complete problems. What kind of a delay is it when we have infinitely many steps? You seem to have ignored what I wrote below. I am distinguishing subjective time from this delay! But I wonder if you are not forgetting that Platonia is, by definition, timeless. Platonia is given, to abuse words, all at once. It is eternal and without beginning or end to its existence. Given this, it must be Complete and all inclusive. Do you not agree? [SPK] **I am trying to see how you deal with the problem of intractible computations - as implementable given infinite resources - and how it may be possible for measures to be defined using them. I had not considered this application but it is intriguing. *** snip [SPK] Yes, but is this derivation on that can be taken to exist independent of the first person aspect of comp histories? This may be one of my key difficulties. On one hand, I do not have a problem with the idea of Platonic existence, re AR, of mathematical objects but I do have a problem with the seeming lack of a clear explanation of how the flow of temporality arises in the first person aspect. [BM] But we have not yet arrive at this point. Wait for S4Grz. You *will* be delighted :)(We will see ...). [SPK] I am very interested in studying S4Grz! [SPK] It seems to me that what ever our theory of Everything is, it must explain how it is not just possible to have a flow of temporality a priori; it must have a non-measure zero sampling in the class of all possible relationships between numbers - or whatever notion of Ur-object that one uses. I personaly eschew the notion of fundamental objects and use the Heraclitian notion of Process and fundamental, thus I see mathematical objects - numbers, etc. - as derivative of this notion of Process. I see Hintikka's idea of proofs as game theoretical constructs as strongly hinting at this idea... [BM] It is really a matter of convenience, to take numbers, sets, or games. But in general game theories, or set theories are richer and less simple than elementary arithmetic. I don't think those dictinction are quite relevant. You will tell me ... after I make enough precise the result I got and the propositions I conjecture. Do you know Conway game theory? Where games are just a slight generalisation of his concept of number? [SPK] Yes, but it has been some time ago that I studied Conway's idea. I do recall that it intrigued me a great deal. What is your take on it? snip [SPK] I have been following your discussion with Kory (and all others) closely. In an attempt to put all my cards on the table I will state that my idea is a kind of process based mind-body dualism (based on Vaughan Pratt's work http://citeseer.ist.psu.edu/pratt95rational.html), but one that becomes very similar to Russell's neutral monism in the limit of the Totality of Existence, which I believe is the same as your Platonia, e.g. an asymptotically vanishing dualism. I do not see Platonia as being mental or mind, ala a new form of Berkeliean Idealism. [BM] We can guess similarities indeed. But (I told you this before) Pratt's paper are hard, and the relation with mind and bodies is implicit, nowhere does him really tackle the m/b problem. Pratt explains his idea in great detail in the above referenced paper and in several other places on his website. But it seems that his idea
Re: Are we simulated by some massive computer?
The following is a combination of two of my previous ideas which together simplify my attempt to prove that a computer is a good model of the substrate of a multi universe venue for our apparent sequence of states. 1) The first step is to examine the act of definition. In this case the definition of a Nothing. Any definition process simultaneously defines two entities. The definition is a boundary between an entity of interest and the leftover building blocks. In the special case of a Nothing the left over is an Everything. Thus the two are dependent partners. Since the Everything contains all information the definition pair must itself specify all information and can be represented by a normal real. 2) A Nothing has an interesting logical problem: It can not answer any meaningful question about itself. Assuming there is a relevant meaningful question a Nothing would be incomplete. An inescapable meaningful question is its own stability. This is not only meaningful it is impossible to avoid answering. 3) To attempt to answer this question a Nothing randomly and spontaneously decays towards an Everything to resolve its incompleteness. But this is not sustainable since an Everything is not independent of a Nothing. Therefore a Nothing rebounds from the decay. 4) Thus the definition or boundary between the Nothing and Everything pair is randomly dynamic equivalent to a random sequence of normal reals. 5) A universal computer is a good way to model a selector of a random sequence of normal reals. Hal
Re: Are we simulated by some massive computer?
wow.. 2) A Nothing has an interesting logical problem: It can not answer any meaningful question about itself. Assuming there is a relevant meaningful question a Nothing would be incomplete. An inescapable meaningful question is its own stability. This is not only meaningful it is impossible to avoid answering. 3) To attempt to answer this question a Nothing randomly and spontaneously decays towards an Everything to resolve its incompleteness. But this is not sustainable since an Everything is not independent of a Nothing. Therefore a Nothing rebounds from the decay. 4) Thus the definition or boundary between the Nothing and Everything pair is randomly dynamic equivalent to a random sequence of normal reals. 5) A universal computer is a good way to model a selector of a random sequence of normal reals. Hal
Re: Are we simulated by some massive computer?
Hi Kory,
So we met two important theories or machines:
Classical Logic CL and Peano Arithmetic PA.
As collection of theorems, the first is a subset of
the second:
PA
|
|
|
CL
Now I have chosen PA to set the things. Any theory or
machine rich enough to prove elementary theorems about
numbers will do.
What will be important is that anybody (including possible
machines) should be able to verify mechanically if a given
proof is a proof, at least in principle (in case a given proof
is 2^64 steps long).
We will interview PA about its possible (consistent) extensions.
It is Godel who showed how to make such an interview,
by showing how to translate the meta-predicate of provability
into an arithmetical sentence.
Let me be a little more specific. Don't hesitate to tell me you know
all this, but it could help some others, and it could help
in front of futur misunderstandings.
PA has a language. Here it is:
L_PA = {v, , -, not, t, f, A, E, =, +, *,
SUC, 0, (, ), x,y,z,x1, y1, z1, x2, y2, ...}
We could code those symbol by the odd integer above 1. So
the Godel number of v is 3, and this I abbreviate by ng(v)=3.
So ng()=5, ng(-)=7, ng(not)=9, ng(t)=11, ..., ng(x)=33, ng(y)=35, etc.
So exactly in the sense that you can define the divisability predicate
Div(x,y) (which is true when x divide y) only with the available symbol
as in
Div(x,y) = Ez(x*z = y) (there exist a number z such that
x multiplied by z gives y)
you can define the meta-predicate IS-A-VARIABLE(x), which is
true when x is a number representing a variable, as Godel number.
Actually, with the code we have chosen:
IS-A-VARIABLE(x) = ODD(x) BIGGER-OR-EQUAL(x,3)
= Ey(x=2y+1) Ez(x = z+33)
Now we want to talk about formula also with PA. I recall
that there are precise formula formation rule like
if A is a formula then (not A) is a formula
if A and B are formula then (A B) is a formula,
etc.
To code a formula by a number, a traditional way relies
on the well known fundamental theorem of arithmetic
saying that all number have a unique decomposition
in product of prime numbers.
So the formula Ez(x*z = y) will be coded by the number
2^(ng(E))*3^(ng(z))*5^(ng(())*7^ng(x)*11^(ng(*))*13^(ng(z))* ...
(I let you continue)
(I have also avoid the quotation mark for not wasting ink,
but ng('(') is more readable than ng((), mmhh..
Now, a proof in, or by, PA [in if you think as PA
being a theory; by if you think as PA as a machine
(a theorem prover)] is just a sequence of formula
such that they are either axioms or has been obtained
from the axioms by a finite number of application of
the inference rule.
So, although it could be hard to *find* a proof (as
unpedagogical exercice try to prove the formula (A - A)
in the systeme send yesterday), it is easy to verify
a proof once the proof is given.
The point is that we can translate a proof into a number
by relying a second time on the fundamental theorem
of arithmetic. A proof is just a finite sequence of
formula F1 F2 F3 F4 F5 ... FN (actually it will be proof
of FN if F1, F2, ... are axioms or comes from axioms
and preeceeding formula by application of the inference
rule). Its (Godel) number will be
2^ng(F1)*3^ng(F2)*5^ng(F3)
Now, like we have define in PA language IS-A-VARIABLE(x)
we can translate meta-predicates like IS-AN-AXIOME(x),
HAS-BEEN-DERIVED-FROM-MODUS-PONENS(x,y,z), meaning
z is derivable from x and y by modus ponens.
Etc. Etc. So that we can defined in PA arithmetical language
IS-A-PROOF-OF(x,y) saying that y is a translation (a godel
number of) of a proof of formula (with Godel number) x.
This was the B(x,y) of yesterday.
And then the Godel formula BEW(x), that is PROVABLE(x),
is just EyB(x,y) i.e. it exist a number y such that y is a proof
of x, to make it short.
Now, a machine will be said to be consistent,if the machine
does not prove f.f is a symbol with the intended meaning of
an absurdity, or a contradiction. in arithmetic f could be defined
by the formula (1 = 0), well actually (SUC(0) = 0).
So the consistency of the machine, or of the theory, or
of PA (here) can be defined by the formula (not BEW(f)).
Godel second incompleteness theorem is that
if a machine is consistent then the machine cannot prove
she is consistent. Now I will explain in which sense we can
say that to be consistent is the same has having a consistent
extension, so you see that Godel second incompleteness
explain why, as I said to John, when we ask the machine
if she *do* have at least one consistent extension, she
remains silent.
Well that is a little bit discouraging isn' it? How could we
hope the machine to be able to give us the geometry
of its consistent extensions when she remain silent on
the very question of having consistent extensions at all?
But if you are patient enough with PA, she will justify
her silence by proving
Re: Are we simulated by some massive computer?
Dear Bruno, We are getting more coherent and on point in our understanding of each other. ;-) Interleaving. - Original Message - From: Bruno Marchal [EMAIL PROTECTED] To: Stephen Paul King [EMAIL PROTECTED] Cc: [EMAIL PROTECTED] Sent: Thursday, April 29, 2004 9:09 AM Subject: Re: Are we simulated by some massive computer? Hi Stephen, At 12:15 28/04/04 -0400, Stephen Paul King wrote: I struggle to find the right words to express the difficulty that I see. My problem is that your work ignores the computational complexity (NP-Completeness) of grading (defining measures) the relationships. This is due to the fact that from a first person point of view any delay will not been perceived. I do not pretend that complexity should always been ignored, but to introduce it at the start would be ad hoc. [SPK] But there is no such thing as a delay in Platonia, but that is not my point. I am trying to see how you deal with the problem of intractible computations - as implementable given infinite resources - and how it may be possible for measures to be defined using them. I had not considered this application but it is intriguing. You touch on this below. If complexity play a role it must be derived along with the measure on the comp histories. [SPK] Yes, but is this derivation on that can be taken to exist independent of the first person aspect of comp histories? This may be one of my key difficulties. On one hand, I do not have a problem with the idea of Platonic existence, re AR, of mathematical objects but I do have a problem with the seeming lack of a clear explanation of how the flow of temporality arises in the first person aspect. It seems to me that what ever our theory of Everything is, it must explain how it is not just possible to have a flow of temporality a priori; it must have a non-measure zero sampling in the class of all possible relationships between numbers - or whatever notion of Ur-object that one uses. I personaly eschew the notion of fundamental objects and use the Heraclitian notion of Process and fundamental, thus I see mathematical objects - numbers, etc. - as derivative of this notion of Process. I see Hintikka's idea of proofs as game theoretical constructs as strongly hinting at this idea... In Conscience Mecanisme I do make a case that Bennett notion of depth could play a role in order to derive the cosmological aspect of physics. Even prior a-la-Schmidhuber could play a role. But the methodology I advocate although it could justify the prior if needed, cannot rely on it at the start. [SPK] I agree. We have to have the methodology itself as an a priori existent. It is co-present in Platonia in your thinking, it seems to me. ;-) I do not see how the mere a priori existence of solutions (Integers) and the relationships between them (also Integers), as a priori existing numbers is sufficient. We will discuss that after I succeed in explaining how the whole things work. All Right? [SPK] Sure! ;-) BM: The comp reason why the soul or the first person is never captured by any complete third person description is akin to the reason truth and knowledge are not arithmetizable (as opposed to provable and consistent). Godel's theorem Co. makes universal machine a highly non trivial type of being. [SPK] Does not this statement, that truth and knowledge are not arithmetizable, imply that the postulation of AR is insufficient? [BM] No. And giving that Godel's incompleteness is true for much more general things than machine, we can say not only that arithmetical truth is not arithmetizable, but mathematical truth is not mathematicalizable, physical truth is not physicalizable, and more generally [whatever]-truth is not [whatver]izable. So strictly speaking AR could be sufficient (the Pythagorean version of my thesis). For reason of simplicity I do not use it. [SPK] Wait a minute! It is one thing to say that [whatever]-truth is not [whatver]izable and it is another to say that [whatever]-truth is finitely constructible or approximatable. The former deals with its existential aspects and the latter deals with its meaningfulness and expressiveness. We do not require absoluteness (truth, decidability or otherwise) in our interactions to be able to have meaningfulness. But this is not problematic to me; I am interested in how physicality MUST obtain, even if only in the first person sense. In fact, in my work I anly assume first person physicality - there is no such thing as third person or objective physicality. This is where our idea overlap strongly.;-) Let me state this in a different way. How does Digital Substitution ( yes, Doctor ) get coded into numbers without involving physical implementation? [BM] But that's the point of the whole work. Now, if you have follow a little bit the literature on the mind body problem you surely know that nobody has
Re: Are we simulated by some massive computer?
On 27 April 2004 Bruno Marchal wrote: But you will be dead in the same sense that you will be dead in the next instant, at least with what I understand when you quote Parfit. In THAT case you shouldn't care at all in the presence of any possible threats, no? Yes, you could say that we die every moment and are replaced by near-exact replicas. You could imagine a situation where this is made more explicit: alien scientists stop the world every second, make copies of everyone, kill all the originals, put the copies in their place, and repeat the procedure in another second. They could have been doing this for years, without anyone suspecting anything unusual was going on. If you are suddenly given this information, and you know that the aliens are going to continue doing this indefinitely (and there is nothing anyone can do to stop them or escape), would you suddenly stop caring about anything that happens in the future, because you'll be dead in one second anyway, and so will everyone you have ever known? There is a single idea underlying much of the confusion in discussions of personal identity: the belief in a soul. I use this term for a quality or substance which resides in a person throughout his life and is somehow responsible for his identity, and which (here is the problem) is not captured by a complete description of the person's physical and psychological state. Often, it is a hidden assumption. --Stathis Papaioannou _ Watch LIVE baseball games on your computer with MLB.TV, included with MSN Premium! http://join.msn.com/?page=features/mlbpgmarket=en-us/go/onm00200439ave/direct/01/
Re: Are we simulated by some massive computer?
At 11:03 27/04/04 -0400, John M wrote: Bruno: I really TRY to catch up with the discussions - Thanks for telling. however I can't help feeling that what's going on is a physicalistic (?) I guess you are trying to provoke me here, isn't it? (I mean you are aware that I pretend (at least) that physics could be reducible to machine's psychology/theology/biology/ number theory, etc. This is hardly physicalistic). *translation* of Judeo-Christian theology: whe we die, we (soul?) transfer to the Dear Good Lord's Heaven/Paradise (= called1000 different planets) - sometimes expressed as quantum imortality...(of the soul?) Then again, just like in the Christian myth, in heaven everybody (including God) speaks the one human language we know (or not). You mean classical logic? I don't think so. You could read the nice book by I. M. Bochenski (translated in english in 1961, University of Notre Dame Press): A History of Formal Logic. It contains a large chapter on the logics, epistemology and metaphysics of India,before and after Chr. It could change your mind on this point. Also quite astonishing in that regard is the book by Th. Stcherbatsky: Buddhist Logic. Comp itself (arguably) has appeared in the east a very long time before Plato, as most analysis of the heaven and hell concepts. (Reference in Conscience Mecanisme). Remember also Giordiano Bruno who has been burned by the Church for his questions and imaginations; (he was an explicit many worlder in the form of other planet with life form). You raise interesting question but I thing it would be premature to really tackle that now. Everything is in the pattern of our terrestrial physical taste and comp imagination. Maybe we get to hell: the mathematically illiterate planet? At least I put the carts on the table: Church Turing Post Markov ... thesis, + a minimal amount of arithmetical realism, + that special act on faith in front of a medical operation. And the game is just to see where all that could lead with respect to some unsolved fundamental question. Can't we do better? ... and then I point on the fact, about which I have probably underestimated the startlingness, that, thanks to some works done by ... Godel, ..., Solovay, we can quasi-literally ask the opinion of *the* sound classical universal machines on that question. In some sense I eliminate the act of faith by just interviewing the machine. What are you asking for? Look, I promise to Kory a hopefully readable account of what I see as an obvious (but necessarily a little bit technical) mathematical/physical confirmation of comp. It is a modest confirmation in the sense that it leads quickly to many open mathematical problems, a sequence of conjectures but also a real path from bit to qubit, should comp be true. I finish by a question. Because we are about to interview the UM on a possible measure existing on its (closer) consistent extensions, it is natural to ask her if she *do* have a consistent extension. Now on *that* question, the UM remains silent, always. Is it a western or eastern type of behavior ? ;-) Is is not a little bit like the thundering silence of Vimalakirti? ;-) Bruno http://iridia.ulb.ac.be/~marchal/
Re: Are we simulated by some massive computer?
At 23:16 28/04/04 +1000, Stathis Papaioannou wrote: There is a single idea underlying much of the confusion in discussions of personal identity: the belief in a soul. Indeed. I use this term for a quality or substance which resides in a person throughout his life and is somehow responsible for his identity, and which (here is the problem) is not captured by a complete description of the person's physical and psychological state. Often, it is a hidden assumption. That's a nice definition of the soul, quite similar to the provable properties of the first person, once we will define it precisely (in the Thaetetus way). And comp will entails, *as a theorem*, the existence of the soul, then! The comp reason why the soul or the first person is never captured by any complete third person description is akin to the reason truth and knowledge are not arithmetizable (as opposed to provable and consistent). Godel's theorem Co. makes universal machine a highly non trivial type of being. Bruno http://iridia.ulb.ac.be/~marchal/
Re: Are we simulated by some massive computer?
Hi Kori,
At 10:55 27/04/04 -0400, Kory Heath wrote:
At 10:17 AM 4/27/04, Bruno Marchal
wrote:
Don't worry, I will try NOT to give
a 120h course in
mathematical logic which is just impossible without chalk
black board. But I will try to give some insights. I must think
how to do it. It will help me, btw, to prepare my talk in Paris
and Amsterdam so that any critics is welcome.
Ok! I'm very interested to hear it, and I'll let you know where I'm
confused, and where I'm bored. :)
Yes but I must go now. Mmmh... I should definitely connect myself at
home.
I will do asap.
Here is a beginning.
1)we will interview a simple machine which has very basic beliefs in
number theory.
The most well know Escherichia Coli-machine of that
sort is know as PEANO ARITHMETIC PA.
It is an extension of classical logic CL. Originally Godel worked
with
the PRINCIPIA MATHEMATICA machine instead, but the proof will work
for a *very vast* class of machines (and even more).
2) Godel showed how to translate metaproposition (talk on proposition)
into
the language of arithmetic used by PA (talk on numbers), and this
by
coding the alphabet by numbers, formula by suitable sequence of
numbers,
proof by sequences of sequences of numbers.
He got an arithmetical formula B(x,y) such that PA proves B(n,m) if
and
only if m is a code of a proof of a formula coded by n.
And so he got easily from that a formula Bew(x) (for beweisbar =
provable
in German), which means intuitively that x represents a provable
formula.
Obviously (?) Bew(x) can be defined by EyB(y,x). OK?
Note that B(x,y) is decidable. Do you understand that any one
patient
enough can verify if B(n, m) is the case or not, in finite time.
Do you intuit this is no more obvious for Bew(n)?
I surely should say a little more about what is a proof in or by PA,
and
more about what is PA for those who never did heard about her
before.
Here is an attemp of a cut and paste from chapter 2 of Conscience
et
Mecanisme (+ minor translation in english...)
http://iridia.ulb.ac.be/~marchal/bxlthesis/Volume1CC/4z1_2sansp.pdf
giving you an explicit presentation of PA.
Axioms
1) A-(B-A) (a posteriori principle)
2) (A-B)-((A-(B-C))-(A-C))
3) A-(B-AB)
4) (A-C)-((B-C)-(AvB-C))
5) A-AvB
6) B-AvB
7) AB-A
8) AB-B
9) (A-B)-((A- B)- A)
10) Av A (exclude middle principe)
Inference Rules:
MP) A, A-B = B (I will say more about
that)
Quantifiers rules:
QE1)
A(t)-.xA(x)
QE2) A(x)-B =
.xA(x)-B
QU1)
.xA(x)-A(t)
QU2) B-A(x) =
B-.xA(x)
PA non logical axiom:
1) (0 = SUC(x))
2) (SUC(x) = SUC(y)) - x = y
3) x+0 = x
4) x+SUC(y) = SUC(x+y) ; recursive definition of
addition
5) xx0 = 0
6) xxSUC(y) =
(xxy) +
x ; recursive definition of
multiplication
And the the following infinite set of induction formula (one
for each formula A you can express in PA language).
A(0)
.x{A(x)
- A(SUC(x))} -
.xA(x)
Comments? Questions? I surely need to explain
what is an inference rule for the non logician.
-Bruno
http://iridia.ulb.ac.be/~marchal/
Re: Are we simulated by some massive computer?
Dear Bruno, This touches on a main portion of my difficulty with the notion that a Platonia based theory can be sufficient. - Original Message - From: Bruno Marchal [EMAIL PROTECTED] To: [EMAIL PROTECTED] Sent: Wednesday, April 28, 2004 11:12 AM Subject: Re: Are we simulated by some massive computer? At 23:16 28/04/04 +1000, Stathis Papaioannou wrote: There is a single idea underlying much of the confusion in discussions of personal identity: the belief in a soul. Indeed. [SPK] This seems to be related to the homunculus problem: http://www.ecs.soton.ac.uk/~harnad/Hypermail/Explaining.Mind96/0258.html The homunculus problem is basically Do we need a homunculus for understanding imagery? A homunculus is the idea of a little man in our heads which sees the images (and words) we see and understands these words and images for us. This, of course, implies an infinite regress of homunculi... http://www.ecs.soton.ac.uk/~harnad/Hypermail/Explaining.Mind97/0103.html But it seems that the same problem obtains if we replace the anthropomorphic homunculus with a machine and ignore the limits placed by quantum gravity (QC) on physical size. I use this term for a quality or substance which resides in a person throughout his life and is somehow responsible for his identity, and which (here is the problem) is not captured by a complete description of the person's physical and psychological state. Often, it is a hidden assumption. That's a nice definition of the soul, quite similar to the provable properties of the first person, once we will define it precisely (in the Thaetetus way). And comp will entails, *as a theorem*, the existence of the soul, then! [SPK] Your idea, Bruno, is VERY interesting to me as it would completely sidestep this problem (and other problems of QC such as the problem of time and space) by making all notions of 1st person phenomena, which includes everything related to physicality, QC included) reducible to modal logical aspects of eternally existing relationships among eternally existing Numbers. I struggle to find the right words to express the difficulty that I see. My problem is that your work ignores the computational complexity (NP-Completeness) of grading (defining measures) the relationships. Your thesis seems to have the same problem as Julian Barbour's thesis. He assumes that we can ignore the requirement that a computation takes at least a polynomial number of steps to perform a computation by appealing to the priori existence of solution of the computation in Platonia. I do not see how the mere a priori existence of solutions (Integers) and the relationships between them (also Integers), as a priori existing numbers is sufficient. The comp reason why the soul or the first person is never captured by any complete third person description is akin to the reason truth and knowledge are not arithmetizable (as opposed to provable and consistent). Godel's theorem Co. makes universal machine a highly non trivial type of being. [SPK] Does not this statement, that truth and knowledge are not arithmetizable, imply that the postulation of AR is insufficient? Let me state this in a different way. How does Digital Substitution ( yes, Doctor ) get coded into numbers without involving physical implementation? Kindest regards, Stephen Bruno http://iridia.ulb.ac.be/~marchal/
Re: Are we simulated by some massive computer?
At 13:55 27/04/04 +1000, Stathis Papaioannou wrote: Ok, one last stab. You are going to be copied and teleported to 1000 different planets. Only your body and your brain will be copied. On 999 of these planets, everyone speaks Spanish, and on one planet, everyone speaks French. You don't know either language, and you are only allowed to learn one of them before your departure. From my perspective, learning Spanish is the correct choice. From your perspective, there's no reason to chose one over the other. Is there? -- Kory I would learn Spanish before teleportation, in order to give my descendants the best chance of success; but going on what I said above, I shouldn't care at all, because I'll be dead and someone else (or 1000 others) will take my place! But you will be dead in the same sense that you will be dead in the next instant, at least with what I understand when you quote Parfit. In THAT case you shouldn't care at all in the presence of any possible threats, no? (BTW, concerning Parfit, he still believe (in his book Reasons and Persons) that we are token. I have already argued that with the comp hyp we can only be type. That means we cannot been made singular. The only argument Parfit gives for our token self-identity is that we would be immortal if we were type. That's not so easy, but even if it were I don't think it is a convincing argument.) I don't think we need a sophisticate theory of personal identity for understanding the consequence of comp. We need just not to confuse the first person, which are not duplicable, from their body (third person describable) which are duplicable. Your comments and answers to Kory seems rather unclear to me. What do you mean by I'll be dead giving that the comp hyp makes you dead in that sense (annihilated and then reconstituted) at each conceivable instant? Actually you do the 1/3 distinction when you say someone else (or 1000 others) will take my place. it is someone else from the 1-view, and 1000 others from the 3 view. Now we must derive physics from the 1-view of 3-splitted-differentiating machines in platonia. OK? Bruno http://iridia.ulb.ac.be/~marchal/
Re: Are we simulated by some massive computer?
Hi Bruno, At 06:46 AM 4/26/04, Bruno Marchal wrote: The important point is that once we keep up comp through the eight points, we see that the laws of physics, whatever they are, must be given by the invariant in the comp-accessible worlds. I'm pretty sure I now understand points 1-8, but let me confirm something: the conclusion of points 1-8 is *not* that comp is true. The conclusion is that *if* comp is true, then the invariant predicted by that model will ultimately match the laws of physics that we have discovered empirically. One could accept points 1-8, but still remain agnostic about whether or not the invariant actually does match the empirical laws of physics - that is, agnostic about whether or not comp is actually true. Correct? The task of point 9 is to start showing mathematically what the invariant actually looks like. You make the tantalizing claim that the invariant actually looks like quantum physics, but for the moment I have to remain agnostic, because I don't know enough about the mathematics of provability, nor do I know enough about quantum physics. From your perspective, are your results strong enough to make you suspect that comp is true? That would make a great part of quantum physics into physical laws in the sense of comp. It would be a pleasure to explain this with more details. Are you willing to hear a little bit about Godel's theorem and some of its generalisation by Lob and Solovay? I am certainly willing to hear about it - I know more about Godel's Theorem and the theory of computation than I do about quantum physics - but I doubt I know enough to make much sense of your explanations, so it might be a waste of your time. Perhaps all I can pick up right now is the flavor of your results. For instance, does your position entail that the weirdness of quantum physics is deeply connected to the weirdness of provability theory? -- Kory
Re: Are we simulated by some massive computer?
At 06:08 AM 4/27/04, Bruno Marchal wrote: (BTW, concerning Parfit, he still believe (in his book Reasons and Persons) that we are token. I have already argued that with the comp hyp we can only be type. That means we cannot been made singular. The only argument Parfit gives for our token self-identity is that we would be immortal if we were type. That's not so easy, but even if it were I don't think it is a convincing argument.) I agree that it's not a convincing argument, but it does seem like an easy statement. If comp is true, aren't we immortal? If not, why not? -- Kory
Re: Are we simulated by some massive computer?
At 08:23 27/04/04 -0400, Kory Heath wrote: Hi Bruno, At 06:46 AM 4/26/04, Bruno Marchal wrote: The important point is that once we keep up comp through the eight points, we see that the laws of physics, whatever they are, must be given by the invariant in the comp-accessible worlds. I'm pretty sure I now understand points 1-8, but let me confirm something: the conclusion of points 1-8 is *not* that comp is true. The conclusion is that *if* comp is true, then the invariant predicted by that model will ultimately match the laws of physics that we have discovered empirically. One could accept points 1-8, but still remain agnostic about whether or not the invariant actually does match the empirical laws of physics - that is, agnostic about whether or not comp is actually true. Correct? Correct. The task of point 9 is to start showing mathematically what the invariant actually looks like. You make the tantalizing claim that the invariant actually looks like quantum physics, but for the moment I have to remain agnostic, because I don't know enough about the mathematics of provability, nor do I know enough about quantum physics. From your perspective, are your results strong enough to make you suspect that comp is true? It makes me suspect indeed that comp is plausible, at least. Actually that plausibility comes both for the 1-8 reasoning which forces us to believe in some many world, so the fact that some physicists begin to think seriously about the possibility of many-things is by itself a sort of confirmation. Interviewing the machines should give more quantitative information about the interference between the possibilities. Here too I want to say I got a confirmation, but, as I will try to explain, I got something weaker than quantum logic, and I am afraid only the future will decide. The problem is that 1) physicists propose not *one* quantum logic, but a labyrinth of QL (to quote van Fraassen), and my interview gives rise also to different sorts of QL. But forget all that, I will really try to give (new) flavors of the mathematical confirmation of comp. That would make a great part of quantum physics into physical laws in the sense of comp. It would be a pleasure to explain this with more details. Are you willing to hear a little bit about Godel's theorem and some of its generalisation by Lob and Solovay? I am certainly willing to hear about it - I know more about Godel's Theorem and the theory of computation than I do about quantum physics - but I doubt I know enough to make much sense of your explanations, so it might be a waste of your time. We will see. Don't hesitate to tell me you don't understand, or that you are bored. Strictly speaking the math are much more simple than people imagine, at least for a passive understanding. But you should be frustated at the end, because we will arrive at my incompetence point, that is, a set of open questions. Perhaps all I can pick up right now is the flavor of your results. For instance, does your position entail that the weirdness of quantum physics is deeply connected to the weirdness of provability theory? Yes. The flavor is that eventually physics is equal to a sort of integral on machine's self-ignorance, that is on machine's incompleteness. But today I still don't have, for example, a proof of something as simple as the violation of Bell's inequality, although I can argue it would be a miracle if they are not violated (in the comp physics I mean) due to the high non booleanity of the Arithmetical QL we obtain. Don't worry, I will try NOT to give a 120h course in mathematical logic which is just impossible without chalk black board. But I will try to give some insights. I must think how to do it. It will help me, btw, to prepare my talk in Paris and Amsterdam so that any critics is welcome. Bruno http://iridia.ulb.ac.be/~marchal/
Re: Are we simulated by some massive computer?
At 08:34 27/04/04 -0400, Kory Heath wrote: At 06:08 AM 4/27/04, Bruno Marchal wrote: (BTW, concerning Parfit, he still believe (in his book Reasons and Persons) that we are token. I have already argued that with the comp hyp we can only be type. That means we cannot been made singular. The only argument Parfit gives for our token self-identity is that we would be immortal if we were type. That's not so easy, but even if it were I don't think it is a convincing argument.) I agree that it's not a convincing argument, but it does seem like an easy statement. If comp is true, aren't we immortal? If not, why not? I do thing that comp (and/or Everett QM) leads to a form, perhaps more than one form actually, of immortality. But the very meaning of such statement will remain very ambiguous without digging deeper in the personal identity issue (which, despite Stathis Papaioannou's remark, is not necessary for getting the physics/psycho reversal). It is perhaps less misleading to say that what comp shows is that mortality is no more obvious. It is less misleading because comp will appear to have a necessary interrogative status: no sound machine can ever entirely be convinced of the truth of comp; a comp-practitioner should infer it again and again. (I think the brain does just that in the form of an instinctive dialog between the cerebral stem and the cortex). Look perhaps at some of James Higgo immortality posts for previous discussions on that not so obvious thread. Jacques Mallah gave interesting rebuttal ... Bruno http://iridia.ulb.ac.be/~marchal/
Re: Are we simulated by some massive computer?
At 10:17 AM 4/27/04, Bruno Marchal wrote: Don't worry, I will try NOT to give a 120h course in mathematical logic which is just impossible without chalk black board. But I will try to give some insights. I must think how to do it. It will help me, btw, to prepare my talk in Paris and Amsterdam so that any critics is welcome. Ok! I'm very interested to hear it, and I'll let you know where I'm confused, and where I'm bored. :) -- Kory
Re: Are we simulated by some massive computer?
Bruno: I really TRY to catch up with the discussions - however I can't help feeling that what's going on is a physicalistic (?) *translation* of Judeo-Christian theology: whe we die, we (soul?) transfer to the Dear Good Lord's Heaven/Paradise (= called1000 different planets) - sometimes expressed as quantum imortality...(of the soul?) Then again, just like in the Christian myth, in heaven everybody (including God) speaks the one human language we know (or not). Everything is in the pattern of our terrestrial physical taste and comp imagination. Maybe we get to hell: the mathematically illiterate planet? Can't we do better? John Mikes - Original Message - From: Bruno Marchal [EMAIL PROTECTED] To: Stathis Papaioannou [EMAIL PROTECTED]; [EMAIL PROTECTED] Sent: Tuesday, April 27, 2004 6:08 AM Subject: Re: Are we simulated by some massive computer? At 13:55 27/04/04 +1000, Stathis Papaioannou wrote: Ok, one last stab. You are going to be copied and teleported to 1000 different planets. Only your body and your brain will be copied. On 999 of these planets, everyone speaks Spanish, and on one planet, everyone speaks French. You don't know either language, and you are only allowed to learn one of them before your departure. From my perspective, learning Spanish is the correct choice. From your perspective, there's no reason to chose one over the other. Is there? -- Kory I would learn Spanish before teleportation, in order to give my descendants the best chance of success; but going on what I said above, I shouldn't care at all, because I'll be dead and someone else (or 1000 others) will take my place! But you will be dead in the same sense that you will be dead in the next instant, at least with what I understand when you quote Parfit. In THAT case you shouldn't care at all in the presence of any possible threats, no? (BTW, concerning Parfit, he still believe (in his book Reasons and Persons) that we are token. I have already argued that with the comp hyp we can only be type. That means we cannot been made singular. The only argument Parfit gives for our token self-identity is that we would be immortal if we were type. That's not so easy, but even if it were I don't think it is a convincing argument.) I don't think we need a sophisticate theory of personal identity for understanding the consequence of comp. We need just not to confuse the first person, which are not duplicable, from their body (third person describable) which are duplicable. Your comments and answers to Kory seems rather unclear to me. What do you mean by I'll be dead giving that the comp hyp makes you dead in that sense (annihilated and then reconstituted) at each conceivable instant? Actually you do the 1/3 distinction when you say someone else (or 1000 others) will take my place. it is someone else from the 1-view, and 1000 others from the 3 view. Now we must derive physics from the 1-view of 3-splitted-differentiating machines in platonia. OK? Bruno http://iridia.ulb.ac.be/~marchal/
RE: Fwd: Re: Are we simulated by some massive computer?
Stathis Papaioannou wrote: Lets go over this again. There is a 100% chance that some copy of Kory Heath will find himself in the non-bizarre world, even though there will be one billion copies which find themselves in the bizarre worlds. If that single, lucky copy is not *you*, then who is he? Or rather, I should ask, if you are not *you*, then who are you? Force of habit makes us think that only one copy can be the real you, which is what you are assuming when you say that the chances are very low - one in a billion - that *I* will be that copy. If all these copies exist, then each is equally entitled to claim to be the real you, and each will probably stamp his foot and insist that he (and he alone) *is* the real you. This is what I tried to show with my teleportation vacation thought experiment. The stay-home copy believes he has been cheated because he (the real he, in his opinion) missed out on seeing the planets, whereas in fact two thousand copies with equal claim to being the real person did find themselves off Earth. I suppose our minds really are not designed to deal with the concept of multiple copies of ourselves. We insist that there can only be one copy extant at a time, and reason as if this is the case. It becomes less problematic if we talk only about third person probabilities. Your argument assumes a certain metaphysical view about consciousness--namely, that all truths about reality can be described in third-person terms, that there are no first-person truths (like truths about 'qualia', such as Nagel's question 'what is it like to be a bat' -- see http://members.aol.com/NeoNoetics/Nagel_Bat.html ) which are not just ways of restating third-person facts. From a third-person point of view, it's certainly true that it would be meaningless for me to wonder which of two copies I am about to experience becoming, but for those who see consciousness as something more than just a certain type of behavior, the question could be meaningful, and a mathematical theory of consciousness (perhaps along the lines of David Chalmers' 'psychophysical laws') might tell you the probabilities that your next experience would be that of one copy vs. another. Jesse _ FREE pop-up blocking with the new MSN Toolbar get it now! http://toolbar.msn.com/go/onm00200415ave/direct/01/
Re: Are we simulated by some massive computer?
Hi Kory, (Recall: the 1-9 points we mention can be find by clicking on http://www.escribe.com/science/theory/m5384.html ) At 00:04 24/04/04 -0400, Kory Heath wrote: Thanks very much for your clarifications. I clearly misunderstood the intent of your point 8. I thought you were arguing that, if we analyze the structure of all possible 1st-person histories of all possible self-aware-subsystems in Platonia, we would find that histories that exhibit the basic elements of what we commonly think of as our laws of physics - say, light, gravity, etc. - have a greater measure than those histories that contain (say) srats and gilixas, and that therefore our local laws are the most common ones in Platonia. I find this position highly dubious, but I no longer think that's what you were saying. Nice. My new interpretation of what you're saying (and correct me if I'm wrong again) is that if you were to examine the entire ensemble of next-possible-states of *me* (Kory Heath) at this moment, you would find that (as a mathematical fact, part of the basic structure of Platonia) most of them contain galaxies and stars, etc. Therefore, the regularities I see around me are simply the emergent effect of my first person indeterminacy domain. Yes. K: If we imagine some other computational state that represents a SAS with a personality, memories of growing up in a world that contains srats and gilixas, etc., most of that SAS's next-possible-states would contain srats and gilixas, so a very different set of stable local laws would emerge from that SAS's first person indeterminacy domain. Well, we should expect that what makes stable those different geographical data (galaxies and gilixas) are semblable. The physical laws should be what makes both galaxies and gilixas stable. The laws of physics will be the same, but they can be implemented in highly different geographical manners. (We can imagine that the resulting regularities resemble a 4+1D cellular automata, which contains nothing like our gravity, light, etc.). Actually (but this is a premature technical point) 4+1D classical cellular automata will not work. Let us come back to this point later. (You can remember me). It *is* a probable non trivial consequence of 9. I'm still confused by some parts of your post. I don't see why the assumption that most of my next-possible-states do in fact contain stars and galaxies necessarily follows from points 1-7. Well, it follows from comp and the data stars and galaxies, and the belief that stars and galaxies are not complete illusion. It is clear that at some point it will be necessary to be a little more specific about the distinction geography/physics. Grosso modo laws should be necessary, unlike geographical data which are contingent but should be consistent with the physical laws. Up to this point (the whole 1-8) it is natural to expect that physical laws could be trivial (equivalent to the classical tautologies for example): in that case, comp would entails that there is no physical laws (at least in the strong sense I use implicitly until now). Everything would be geographical! But I will give below reason to believe that comp does not make physics so trivial. The basic reason comes from Godel's theorem. Here's a very rough sketch of what I think points 1-7 *do* imply: Platonia contains every possible computational state that represents a self-aware structure, and for each such state there are X number of next-possible-states, which also exist in Platonia. The chances of one self-aware state jumping (I know my terminology is dangerously loose here) to any particular next state is 1 / X, where X is the total number of next-possible-states for the state in question. Any regularities which emerge out of this indeterminate traversal from state to state will be perceived as local laws of physics. I mainly agree. The differences are those I usually make. Indeed a machine can have only a finite number of possible states, but the DU (comp platonia) will go through those states infinitely often and the probability will be defined on the set of complete histories (those distinguishable in principle). A priori there are 2^aleph_0 histories. Your last sentence is a little bit ambiguous (probably because we have not yet decide a criteria for the geography/physics distinction). It is really the invariant we observe out of this indeterminate traversal from state to state which will play the role of laws of physics, and those will be global. Now those laws will be among those things which make galaxies stable, but I would not put the existence of galaxies in the local physical laws, only what makes those galaxies stable. So that laws will be global (by mere definition). I have mention that up to this point the laws could be trivial, but of course they could also be non trivial; so much that the existence of galaxies would be a law. I doubt it but the whole point of 1-8 is to show that
Re: Are we simulated by some massive computer?
I remember discussing this with you a few months ago. I am still not convinced though :-) - Oorspronkelijk bericht - Van: Jesse Mazer [EMAIL PROTECTED] Aan: [EMAIL PROTECTED] Verzonden: Sunday, April 25, 2004 06:19 PM Onderwerp: Re: Are we simulated by some massive computer? Saibal Mitra wrote: This is the ''white rabbit'' problem which was discussed on this list a few years ago. This can be solved by assuming that there exists a measure over the set of al universes, favoring simpler ones. Also, note that there is no such thing as ''next possible'' states. Once you consider the whole of Platonia all you have is a probability distribution over the set of all possible states you can be in (because you can't define time in a normal way anymore). There is no conditional probability for your next experience given what you have experienced now. A valid question is: What is the probability that you will be in a state P that contains the memory that you have been in a state P'. It's not necessarily true that the all-universe idea rules out conditional probabilities for experiences. If you had a mathematical theory of consciousness, it might very well define a notion of subjective time and give you something like transition probabilities between observer-moments--the probability that my next experience will be B, given that my current experience is A. Jesse _ Watch LIVE baseball games on your computer with MLB.TV, included with MSN Premium! http://join.msn.com/?page=features/mlbpgmarket=en-us/go/onm00200439ave/dire ct/01/
Re: Are we simulated by some massive computer?
- Oorspronkelijk bericht -
Van: Kory Heath [EMAIL PROTECTED]
Aan: [EMAIL PROTECTED]
Verzonden: Monday, April 26, 2004 03:00 AM
Onderwerp: Re: Are we simulated by some massive computer?
At 10:48 AM 4/25/04, Saibal Mitra wrote:
This is the ''white rabbit'' problem which was discussed on this list a
few
years ago. This can be solved by assuming that there exists a measure
over
the set of al universes, favoring simpler ones.
I don't believe there are any grounds for assuming that, so the problem
isn't solved for me.
This can be motivated in a number of ways. I think Hall Finney made this
argument some time ago, and it is my favorite argument. Suppose you identify
a universe with the program specifying it. The probability that you find
yourself in a universe X will be proportional to the priori probability of X
multiplied by the number of times you will be computed in X. It is possible
to define universes Y_{n} that are defined by executing X n times. The
probability that you find yourself in Y_{n} is thus proportional to the
prior probability of Y_{n} times n. To have a well normalizable probability
distribution Y_{n} has to go to zero faster than 1/n. Now, the size of
program Y_{n} depends linearly on Log(n) (because you have to specify the
number n in the program). So, asuming that the prior probability only
depends on program size, it must decay (at least) exponentially as a
function of program size.
Once you
consider the whole of Platonia all you have is a probability distribution
over the set of all possible states you can be in (because you can't
define
time in a normal way anymore).
I don't agree with this. I can imagine an infinite 2D lattice of cells,
seeded with the binary digits of pi, and ask the following question: if
the
rules of Conway's Life were applied to this lattice, what would it look
like after a million ticks of the clock? There's an objective answer to
this question, and that answer exists in Platonia. I believe that this
implies that the universe I just described (and all other possible CA
universes, and much more) exists in Platonia. I define time as the
ticking of the clock in such computational worlds, so I believe time
exists in Platonia. (Of course, in another sense, Platonia exists in a
timeless all at once. This is similar to the way that time exists in the
block universe of relativity theory.)
I agree. I was refering to the whole of Platonia which is timeless.
There is no conditional probability for your
next experience given what you have experienced now. A valid question is:
What is the probability that you will be in a state P that contains the
memory that you have been in a state P'.
I find this way of looking at things very confusing. What do you mean by
you in this formulation? Is you a thing that jumps from state to
state?
If so, then we have some form of time. If not, what is this you?
Obviously it is something that can be said to be in a state P
(otherwise,
you wouldn't consider your above question valid). But what does it mean
for
you to be in a state P? If it's true that you are in a state P, are
you
just timelessly in state P, or what? How can you even talk about something
being without talking about time?
It's confusing, but it has a big advantage over the more intuitive point of
view. This is how I see it (I know that others on thius list disagee with
me):
Clearly there exists a program that represents me. If you know exactly how
my brain works, you can run me on a computer. I thus have to identify myself
with that program. Note that if you run this program it will change itself
(I would have a notion of time even if simulated without any external
environment). So, by program I mean the program plus the exact computational
state it is in.
Then, I like to get rid of the concept of personal identity. The idea that
Saibal yesterday is the same as Saibal today cannot be made precise. You can
try to identify programs p and p' by saying that they represent the same
person if by running p you eventually obtain p'. But what about external
influences changing a person? There are other reasons too (see my input in
the the quantum suicide debate).
To see how it works (in principle) consider Saibal doing an experiment. Let
S1 denote the program specifying me just before I start the experiment and
S2 the program after I observe the result (taking seriously what I wrote
above, I couldn't write the sentence like this...). Suppose that there are
many possible outcomes, and I want to know the probability that I will
observe a particular outcome. According to the intuitive view there exists a
conditional probability that you are in state S2 given that you were in
state S1, and that is what you should try to compute using some theory.
However, since S2 and S1 are strictly speaking different persons this is
difficult, as I wrote above. Instead, one should compute quantities that
refer to single persons (programs) only
Re: Are we simulated by some massive computer?
On 26 April 2004 Kory Heath wrote: I am definitely not claiming that only one of the copies is the real me. Every copy is the real me from its own perspective. But to each one of those copies, all the other copies are *different people*. This is true from any perspective, including the third-person one. I didn't mean to suggest that you actually believe only one of the copies can be the real you, but rather that the way we use language forces us into this way of thinking, as you aknowledge. You know, I have a horrible feeling that this subject has been argued to death 1000 times already on various newsgroups - with 1000 people taking your position, and 1000 people taking mine. Yes, you're right about this, which is why I was shying away from explicitly addressing the problem of personal identity. But since you brought it up (and Saibal Mitra in another recent post also addresses this question), I think that the only position which does not lead to confusion and paradox is to say that there is no such thing as personal identity in the way we normally use the term, i.e., as a special quality different to mere similarity between two putatively identical individuals. This is an extension of neo-Lockean theory expounded, for example, by Derek Parfit in his 1984 book Reasons and Persons. It is equivalent to saying that we effectively die every moment, to be replaced by near-replicas who share our memories, and usually (but not necessarily) our bodies. We entertain the fiction of continuity of identity because that is how our minds have evolved: an organism would not get very far if it had no concern for what was going to happen to it in the next millisecond because that would be someone else's problem. The fact that it IS a fiction would be immediately evident if we could meet our past and future selves, and if mind/body duplication with or without teleportion were a common event. With this position, it would be obvious that questions about whether the copy really is you are meaningless. The copy has most of your memories and thinks he is you; what else can you say beyond this? Ok, one last stab. You are going to be copied and teleported to 1000 different planets. Only your body and your brain will be copied. On 999 of these planets, everyone speaks Spanish, and on one planet, everyone speaks French. You don't know either language, and you are only allowed to learn one of them before your departure. From my perspective, learning Spanish is the correct choice. From your perspective, there's no reason to chose one over the other. Is there? -- Kory I would learn Spanish before teleportation, in order to give my descendants the best chance of success; but going on what I said above, I shouldn't care at all, because I'll be dead and someone else (or 1000 others) will take my place! --Stathis Papaioannou _ Get Extra Storage in 10MB, 25MB, 50MB and 100MB options now! Go to http://join.msn.com/?pgmarket=en-aupage=hotmail/es2
Re: Are we simulated by some massive computer?
At 10:36 AM 4/24/04, Stathis Papaioannou wrote: Does the fact that we never find ourselves in one of the bizarre, inconsistent worlds that are postulated to exist in Platonia cast doubt on the reality of these worlds and the validity of the underlying theory? Not yet. We know that the bizarre, inconsistent worlds must exist if the Platonia idea is correct, but we (or at least I) don't currently know how likely they are. In Platonia, there are X number of possible-next-states from my current state. (For simplicity's sake, lets even say that X is a very very large finite number.) If a vast majority of these states show me sitting in my chair typing, with my computer not turning into a kangaroo, etc., then no, the fact that my world so far has not been bizarre and inconsistent does *not* cast doubt on the validity of the Platonia theory. In fact, if we can show logically, mathematically, or computationally (for me these are all ultimately the same thing) that a vast majority of my next-possible-states do in fact show me sitting in my chair typing, with very few computers turning into kangaroos, this would be an extremely strong reason to believe that the Platonia theory is correct, because it's survived a rather stringent falsification test. Note that the tests we need to perform - tests like how many of my next possible states show me still sitting in my chair? How many of my next possible states show my computer turning into a kangaroo? - are logical / mathematical / computational ones, not empirical ones. We already have the empirical data, which we call the laws of physics. We need to know what the Platonia theory actually predicts, and compare it to the empirical data. For my part, I don't actually know what the Platonia theory predicts, because I have no idea how to go about addressing the question mathematically. Bruno Marchal says we need to create a better model of what counts as a platonistic observer, and interview it about its relative consistent extensions (what I've been calling next-possible-states), and find out what regularities it would see. To me, that's just another statement of the problem. I don't have a very good model of what counts as a platonistic observer, and I don't know how to determine the structure of its next-possible-states, etc. If we make progress on this issue, and we come to the mathematical conclusion that the probabilities we're looking for *don't* exist in Platonia - that is, if we determine that (say) my next-possible-states in which my computer turns into a kangaroo are just as common as those in which it remains a computer - then I think that that does cast doubt on the validity of the Platonia theory. For your vacation, you buy a ticket that allows you to be destructively scanned and teleported to one thousand fabulous destinations around the solar system. The machine also sends a copy of you to a receiving station next door, on Earth (it's the rules). You enter the sending station, press the red button, and a second later find yourself in slightly altered surroundings. When you get out of the machine, you realise that you are still on Earth. Disappointed, you buy another ticket on the spot and go through the same procedure again, hoping for a better result. Again, however, you walk out and see that you are still on Earth. This time, you are angry. The probability that you finish up the stay-home copy twice is less than one in one million! You suspect on this basis that the company running the teleporter has cheated you, and did not send copies to the holiday destinations at all. Your vacation-company thought-experiment brings up interesting issues about falsifiability. If I buy two tickets in a row, and I reappear on Earth both times, I'm tempted to suspect that I've been cheated. On the other hand, I know that the chances were 100% that this was going to happen to *some* copy. So maybe I'm just that unlucky copy? Unfortunately, if you continue to think in this way, you give up the idea of falsifiability completely. No matter how many times you buy a ticket and reappear on Earth, you can always argue that the chances were 100% that this would happen to some copy. No amount of empirical data can ever convince you that the company is cheating you. This is fine if you have some independent reason for trusting the company with 100% confidence, but without such an independent reason, you should suspect foul-play. -- Kory
Re: Are we simulated by some massive computer?
On 25 April 2004 Kory Heath wrote: QUOTE- Not yet. We know that the bizarre, inconsistent worlds must exist if the Platonia idea is correct, but we (or at least I) don't currently know how likely they are. In Platonia, there are X number of possible-next-states from my current state. (For simplicity's sake, lets even say that X is a very very large finite number.) If a vast majority of these states show me sitting in my chair typing, with my computer not turning into a kangaroo, etc., then no, the fact that my world so far has not been bizarre and inconsistent does *not* cast doubt on the validity of the Platonia theory. In fact, if we can show logically, mathematically, or computationally (for me these are all ultimately the same thing) that a vast majority of my next-possible-states do in fact show me sitting in my chair typing, with very few computers turning into kangaroos, this would be an extremely strong reason to believe that the Platonia theory is correct, because it's survived a rather stringent falsification test. -ENDQUOTE This analysis is sound only in the common sense single world situation. You get into trouble if you try to use conventional probabilities if multiple histories/worlds/copies are allowed, as I tried to show with the teleportation example. Suppose that the overwhelming majority of your next-possible-states are totally bizarre, according to the theory we are testing. If only one copy of you can exist at any one time, then the theory predicts that there is a billion to one probability that in the next second you will find yourself in a bizarre universe. As a matter of fact, as you read these words, you do not find that the world around you suddenly becomes bizarre. Therefore, the theory is most likely wrong. Consider now a similar theory, but multiple copies of you are allowed. The theory predicts that there will be one billion branchings of the world in the next second, with each branch containing a person who shares all your memories up to that point. The theory also predicts, as above, that all but one of these worlds will be obviously bizarre. As a matter of fact, as you read these words, you do not experience the world around you suddenly becoming bizarre. But unlike the previous example, this is entirely consistent with the theory, which predicted that one version of you would continue in the world as per usual. --Stathis Papaioannou _ Get Extra Storage in 10MB, 25MB, 50MB and 100MB options now! Go to http://join.msn.com/?pgmarket=en-aupage=hotmail/es2
Re: Are we simulated by some massive computer?
This is the ''white rabbit'' problem which was discussed on this list a few years ago. This can be solved by assuming that there exists a measure over the set of al universes, favoring simpler ones. Also, note that there is no such thing as ''next possible'' states. Once you consider the whole of Platonia all you have is a probability distribution over the set of all possible states you can be in (because you can't define time in a normal way anymore). There is no conditional probability for your next experience given what you have experienced now. A valid question is: What is the probability that you will be in a state P that contains the memory that you have been in a state P'. Quoting Stathis Papaioannou [EMAIL PROTECTED]: On 25 April 2004 Kory Heath wrote: QUOTE- Not yet. We know that the bizarre, inconsistent worlds must exist if the Platonia idea is correct, but we (or at least I) don't currently know how likely they are. In Platonia, there are X number of possible-next-states from my current state. (For simplicity's sake, lets even say that X is a very very large finite number.) If a vast majority of these states show me sitting in my chair typing, with my computer not turning into a kangaroo, etc., then no, the fact that my world so far has not been bizarre and inconsistent does *not* cast doubt on the validity of the Platonia theory. In fact, if we can show logically, mathematically, or computationally (for me these are all ultimately the same thing) that a vast majority of my next-possible-states do in fact show me sitting in my chair typing, with very few computers turning into kangaroos, this would be an extremely strong reason to believe that the Platonia theory is correct, because it's survived a rather stringent falsification test. -ENDQUOTE This analysis is sound only in the common sense single world situation. You get into trouble if you try to use conventional probabilities if multiple histories/worlds/copies are allowed, as I tried to show with the teleportation example. Suppose that the overwhelming majority of your next- possible-states are totally bizarre, according to the theory we are testing. If only one copy of you can exist at any one time, then the theory predicts that there is a billion to one probability that in the next second you will find yourself in a bizarre universe. As a matter of fact, as you read these words, you do not find that the world around you suddenly becomes bizarre. Therefore, the theory is most likely wrong. Consider now a similar theory, but multiple copies of you are allowed. The theory predicts that there will be one billion branchings of the world in the next second, with each branch containing a person who shares all your memories up to that point. The theory also predicts, as above, that all but one of these worlds will be obviously bizarre. As a matter of fact, as you read these words, you do not experience the world around you suddenly becoming bizarre. But unlike the previous example, this is entirely consistent with the theory, which predicted that one version of you would continue in the world as per usual. --Stathis Papaioannou _ Get Extra Storage in 10MB, 25MB, 50MB and 100MB options now! Go to http://join.msn.com/?pgmarket=en-aupage=hotmail/es2 -- _ Zon Gratis ADSL. De voordelen van gratis internet met de snelheid van ADSL. Zonder abonnementskosten en zonder vast contract. Je betaalt alleen voor de tijd online. Nu zonder aansluitkosten en met gratis modem. Bestel snel op zonnet.nl.
Re: Are we simulated by some massive computer?
Saibal Mitra wrote: This is the ''white rabbit'' problem which was discussed on this list a few years ago. This can be solved by assuming that there exists a measure over the set of al universes, favoring simpler ones. Also, note that there is no such thing as ''next possible'' states. Once you consider the whole of Platonia all you have is a probability distribution over the set of all possible states you can be in (because you can't define time in a normal way anymore). There is no conditional probability for your next experience given what you have experienced now. A valid question is: What is the probability that you will be in a state P that contains the memory that you have been in a state P'. It's not necessarily true that the all-universe idea rules out conditional probabilities for experiences. If you had a mathematical theory of consciousness, it might very well define a notion of subjective time and give you something like transition probabilities between observer-moments--the probability that my next experience will be B, given that my current experience is A. Jesse _ Watch LIVE baseball games on your computer with MLB.TV, included with MSN Premium! http://join.msn.com/?page=features/mlbpgmarket=en-us/go/onm00200439ave/direct/01/
Re: Are we simulated by some massive computer?
- Original Message - From: Kory Heath [EMAIL PROTECTED] To: Sent: Sunday, April 25, 2004 2:45 AM Subject: Re: Are we simulated by some massive computer? At 10:36 AM 4/24/04, Stathis Papaioannou wrote: Does the fact that we never find ourselves in one of the bizarre, inconsistent worlds that are postulated to exist in Platonia cast doubt on the reality of these worlds and the validity of the underlying theory? Not yet. We know that the bizarre, inconsistent worlds must exist if the Platonia idea is correct, but we (or at least I) don't currently know how likely they are. In Platonia, there are X number of possible-next-states from my current state. (For simplicity's sake, lets even say that X is a very very large finite number.) If a vast majority of these states show me sitting in my chair typing, with my computer not turning into a kangaroo, etc., then no, the fact that my world so far has not been bizarre and inconsistent does *not* cast doubt on the validity of the Platonia theory. In fact, if we can show logically, mathematically, or computationally (for me these are all ultimately the same thing) that a vast majority of my next-possible-states do in fact show me sitting in my chair typing, with very few computers turning into kangaroos, this would be an extremely strong reason to believe that the Platonia theory is correct, because it's survived a rather stringent falsification test. I submit that this neither supports or refutes the validity of platonia. It ultimately only suggests that the past and current states of our world have been consistent with the laws (theories) of physics and aristotilean logic, so a far as we can accurately determine same, and suggests somewhat less convincingly that the future states will continue to be so. Cheers, CMR -- insert gratuitous quotation that implies my profundity here --
Re: Are we simulated by some massive computer?
A little earlier I posted what I called a left wing proof that an ongoing computer output of a random succession of normal reals is a reasonable model for the dynamic boundary between the definitional pair Nothing and Everything. [I got left wing proof from an article by Keith Devlin on page 36 of the January 2004 Discover Magazine.] No particular kind of computer is involved, just an infinite number of randomly configured computers [including universal dovetailers] randomly distributed along the string, using it as input [or not] and doing their thing and the output of each becomes a replacement section of the string. Universes are interpretations of sections of the string. Now a question is how many of these interpretations have internal rules that allow input from an external random oracle? If we are to maintain a zero information system then the answer must be a randomly changing percentage. So all interpretations must be able change character i.e. be subject to an external random oracle the rules of the particular interpretation notwithstanding. Hal
Re: Are we simulated by some massive computer?
At 10:16 AM 4/25/04, Stathis Papaioannou wrote: Consider now a similar theory, but multiple copies of you are allowed. The theory predicts that there will be one billion branchings of the world in the next second, with each branch containing a person who shares all your memories up to that point. The theory also predicts, as above, that all but one of these worlds will be obviously bizarre. As a matter of fact, as you read these words, you do not experience the world around you suddenly becoming bizarre. But unlike the previous example, this is entirely consistent with the theory, which predicted that one version of you would continue in the world as per usual. Yes, your theory states that the chances are 100% that some copy will find itself in the non-bizarre world. But the theory also states that the chances are very low - one in a billion - that *I* will be that copy. Why isn't this second probability important? It seems to me that you only care about the first probability, and disregard the second as irrelevant. I'm assuming that the hypothetical person in these thought experiments is not certain that the copying theory is actually correct, and is trying to figure out whether or not to believe it. In such a case, the one-in-a-billion probability is relevant. If the theory states that a billion copies of me are going to be made, and only one of those copies will find itself in a non-bizarre world, and then I find myself in the non-bizarre world, this should change my assessment of the likelihood of the copying theory - it should make me a billion times more suspicious! Whether or not this causes me to reject the copying theory depends on how much credence I gave that theory before the alleged copying took place. If I thought that the copying theory was almost definitely true - say, a trillion times more likely to be true than false - then I should continue to believe it after finding myself in the (very unlikely) non-bizarre world. If I thought that the theory was only a thousand times more likely of being true than false before the alleged copying, then I should strongly doubt the theory after I find myself in the non-bizarre world. If we accept your logic, the Platonia idea is unfalsifiable. One could, I suppose, still believe it on strictly a priori logical grounds. Is that your position? -- Kory
Re: Are we simulated by some massive computer?
At 10:48 AM 4/25/04, Saibal Mitra wrote: This is the ''white rabbit'' problem which was discussed on this list a few years ago. This can be solved by assuming that there exists a measure over the set of al universes, favoring simpler ones. I don't believe there are any grounds for assuming that, so the problem isn't solved for me. Once you consider the whole of Platonia all you have is a probability distribution over the set of all possible states you can be in (because you can't define time in a normal way anymore). I don't agree with this. I can imagine an infinite 2D lattice of cells, seeded with the binary digits of pi, and ask the following question: if the rules of Conway's Life were applied to this lattice, what would it look like after a million ticks of the clock? There's an objective answer to this question, and that answer exists in Platonia. I believe that this implies that the universe I just described (and all other possible CA universes, and much more) exists in Platonia. I define time as the ticking of the clock in such computational worlds, so I believe time exists in Platonia. (Of course, in another sense, Platonia exists in a timeless all at once. This is similar to the way that time exists in the block universe of relativity theory.) There is no conditional probability for your next experience given what you have experienced now. A valid question is: What is the probability that you will be in a state P that contains the memory that you have been in a state P'. I find this way of looking at things very confusing. What do you mean by you in this formulation? Is you a thing that jumps from state to state? If so, then we have some form of time. If not, what is this you? Obviously it is something that can be said to be in a state P (otherwise, you wouldn't consider your above question valid). But what does it mean for you to be in a state P? If it's true that you are in a state P, are you just timelessly in state P, or what? How can you even talk about something being without talking about time? -- Kory
Fwd: Re: Are we simulated by some massive computer?
Forwarded at the request of the author: From: Stathis Papaioannou [EMAIL PROTECTED] On 25 April 2004 Kory Heath wrote: QUOTE- Yes, your theory states that the chances are 100% that some copy will find itself in the non-bizarre world. But the theory also states that the chances are very low - one in a billion - that *I* will be that copy. Why isn't this second probability important? It seems to me that you only care about the first probability, and disregard the second as irrelevant. -ENDQUOTE Lets go over this again. There is a 100% chance that some copy of Kory Heath will find himself in the non-bizarre world, even though there will be one billion copies which find themselves in the bizarre worlds. If that single, lucky copy is not *you*, then who is he? Or rather, I should ask, if you are not *you*, then who are you? Force of habit makes us think that only one copy can be the real you, which is what you are assuming when you say that the chances are very low - one in a billion - that *I* will be that copy. If all these copies exist, then each is equally entitled to claim to be the real you, and each will probably stamp his foot and insist that he (and he alone) *is* the real you. This is what I tried to show with my teleportation vacation thought experiment. The stay-home copy believes he has been cheated because he (the real he, in his opinion) missed out on seeing the planets, whereas in fact two thousand copies with equal claim to being the real person did find themselves off Earth. I suppose our minds really are not designed to deal with the concept of multiple copies of ourselves. We insist that there can only be one copy extant at a time, and reason as if this is the case. It becomes less problematic if we talk only about third person probabilities. Incidentally, this point applies to any many worlds theory, not just the Platonia idea. --Stathis Papaioannou
Re: Are we simulated by some massive computer?
On 24 April 2004 Kory Heath wrote (in response to Bruno Marchal's post of 13 April 2004): QUOTE- Platonia contains every possible computational state that represents a self-aware structure, and for each such state there are X number of next-possible-states, which also exist in Platonia. The chances of one self-aware state jumping (I know my terminology is dangerously loose here) to any particular next state is 1 / X, where X is the total number of next-possible-states for the state in question. Any regularities which emerge out of this indeterminate traversal from state to state will be perceived as local laws of physics...The real question is, what reason do we have to believe that any regularities actually emerge? In other words, how do we *know* that most of my next-possible-states do in fact contain stars and galaxies? -ENDQUOTE Does the fact that we never find ourselves in one of the bizarre, inconsistent worlds that are postulated to exist in Platonia cast doubt on the reality of these worlds and the validity of the underlying theory? Consider this thought experiment: You are living in a time when humanity has colonised other planets in the solar system and teleportation is commonplace. For your vacation, you buy a ticket that allows you to be destructively scanned and teleported to one thousand fabulous destinations around the solar system. The machine also sends a copy of you to a receiving station next door, on Earth (it's the rules). You enter the sending station, press the red button, and a second later find yourself in slightly altered surroundings. When you get out of the machine, you realise that you are still on Earth. Disappointed, you buy another ticket on the spot and go through the same procedure again, hoping for a better result. Again, however, you walk out and see that you are still on Earth. This time, you are angry. The probability that you finish up the stay-home copy twice is less than one in one million! You suspect on this basis that the company running the teleporter has cheated you, and did not send copies to the holiday destinations at all. You demand a refund. The confusion here arises from using the pronoun you in the traditional way: as if there can only be one you in existence at any one time. Stay-home-you imagines he has missed out on seeing Jupiter from its moons, because, obviously, he is here and not there. This is valid reasoning when a person cannot be in two places at once, but in this case we are starting with the premise that a person can be in at least 1001 places at once! In a similar vein, if the existence of multiple versions of me branching out from the present moment in Platonia/Multiverse is allowed, the fact that I-typing do not experience, say, my laptop computer turning into a kangaroo and hopping away does not mean that it doesn't happen. (The above discussion brings up the old arguments about personal identity, but I will refrain from starting a thread on that topic unless others are interested.) Stathis Papaioannou. _ Find love today with ninemsn personals. Click here: http://ninemsn.match.com?referrer=hotmailtagline
Re: Are we simulated by some massive computer?
Bruno - Thanks very much for your clarifications. I clearly misunderstood the intent of your point 8. I thought you were arguing that, if we analyze the structure of all possible 1st-person histories of all possible self-aware-subsystems in Platonia, we would find that histories that exhibit the basic elements of what we commonly think of as our laws of physics - say, light, gravity, etc. - have a greater measure than those histories that contain (say) srats and gilixas, and that therefore our local laws are the most common ones in Platonia. I find this position highly dubious, but I no longer think that's what you were saying. My new interpretation of what you're saying (and correct me if I'm wrong again) is that if you were to examine the entire ensemble of next-possible-states of *me* (Kory Heath) at this moment, you would find that (as a mathematical fact, part of the basic structure of Platonia) most of them contain galaxies and stars, etc. Therefore, the regularities I see around me are simply the emergent effect of my first person indeterminacy domain. If we imagine some other computational state that represents a SAS with a personality, memories of growing up in a world that contains srats and gilixas, etc., most of that SAS's next-possible-states would contain srats and gilixas, so a very different set of stable local laws would emerge from that SAS's first person indeterminacy domain. (We can imagine that the resulting regularities resemble a 4+1D cellular automata, which contains nothing like our gravity, light, etc.). I'm still confused by some parts of your post. I don't see why the assumption that most of my next-possible-states do in fact contain stars and galaxies necessarily follows from points 1-7. Here's a very rough sketch of what I think points 1-7 *do* imply: Platonia contains every possible computational state that represents a self-aware structure, and for each such state there are X number of next-possible-states, which also exist in Platonia. The chances of one self-aware state jumping (I know my terminology is dangerously loose here) to any particular next state is 1 / X, where X is the total number of next-possible-states for the state in question. Any regularities which emerge out of this indeterminate traversal from state to state will be perceived as local laws of physics. Now, you say: Let us (re)define the laws of physics as the laws we can always predict and verify consistently (if any!). Now, having accepted the 1-7 points, the occurrence of such laws must have a measure 1, so the laws of physics must be derivable from what has measure 1 relatively to the measure on the computational histories. I agree with this, but to me it seems like a simple tautology - another statement of my above paragraph. It sounds to me like you're saying that the (local) laws of physics are whatever regularities emerge when we examine the entire ensemble of next-possible-states from my current state (and the ensemble of all the next-possible-states from each of those possible-states, and so on). This is tautologically true - whatever emerges, emerges. The real question is, what reason do we have to believe that any regularities actually emerge? In other words, how do we *know* that most of my next-possible-states do in fact contain stars and galaxies? This idea doesn't necessarily follow from anything in points 1-7. Perhaps you're arguing the following: we do in fact perceive a world filled with regularities, which we have codified into our local laws of physics. Therefore, *if* points 1-7 are true - that is, if comp is true - then it must be the case that most of my next-possible-states do in fact contain stars and galaxies and gravity and light. If I were (somehow) able to completely mathematically analyze one of my computational states and all of its next-possible-states, and if I then determined that the probabilities in this ensemble of next-possible-states *didn't* match the regularities I actually perceive, then I should conclude that comp is false. If this is your argument, then it might be helpful to add another point - lets call it Point 7.5 - which states that we do in fact perceive regularities that we codify into (local) laws of physics. Then your argument can run: if points 1-7.5 are all true, then it must be true that most of my next-possible-states contain stars and galaxies. This argument implies a constraint on comp - which is good, because it means that comp is falsifiable - but it doesn't give me any clue how to show mathematically that most of Kory Heath's next-possible-states actually do contain stars and galaxies - i.e. that most of Kory Heath's next-possible-states match the laws of physics, or at least exhibit some kind of probabilistic bias that would result in perceived regularities. I suppose that this is what you mean when you say that we need to modelize or better identify a platonistic
Re: Are we simulated by some massive computer?
At 05:27 21/04/04 -0400, Kory Heath wrote: Bruno Marchal wrote a 10-point argument about determining whether or not we are simulated by some massive computer. Here is point 9 from that post: 9) Now, from computer science and logic, startlingly enough perhaps, we can isolate a measure on the 1-person comp histories, and this give us the laws of physics (this is too technical to be put here, and actually I have derived only the logical structure of the probability one, but I got something non trivial and very close to a quantum logic (which can be seen as the logic of the quantum probability one, as von Neumann has shown). Bruno, I agree with everything in points 1-7 of the post I'm referring to. Cool. (Kory is referring to my post http://www.escribe.com/science/theory/m5384.html ) I think I understand the main thrust of points 8 and 10, but they both depend on the truth of the quoted point 9. Not at all. The point 8 follows only from the points 1-7. Actually the points 1 to 8 sum up the main result of my thesis, that is the reversal physics/machine's psychology (once we assume comp). This made the point 9 just a mathematical confirmation. I will try to explain, but actually it is me who does not understand why you don't see that the point 8 follows from the point 1-7. The proof really stop at 8. 9 is a mathematical confirmation with observer modelized (or even identify) with equivalence class of states of sound universal Turing machines. I find this point [9] highly dubious, and I'm interested to hear more about why you believe it (or whether I'm actually interpreting it correctly). OK. I promise I will try to make it clear, but that will be possible only if you realize that 8 follows from 1-7. Keeping we assume comp all through. I will first continue to comment your post, as a sort of preparation. Is it your contention that if we start only with the idea of Platonia (which contains all possible computational structures and events), and we analyze the structure of all possible 1st-person histories weaving their way through this Platonia, we would see that a majority of them find themselves in universes like the one we currently inhabit, with stars, galaxies, relativity, quantum physics, etc.? No. Such a contention is not mine. What you say here does not follow from neither 1-8, nor 9. Only the laws of physics follows, but the existence of the moon or of galaxies are not necessarily laws of physics, but are quite possibly geographical laws (like being in Moscow instead of Washington). Now the stability of the appearance of matter is related to the laws of physics, and so, if (to talk like you) we analyze the structure of all possible 1st-person histories going trough your actual Kory-Heath state (including your memory of stars and galaxies) then the measure of your computational continuations in Platonia without stars and galaxies will (or should) be negligible. The disappearance of galaxies could be seen as a talking white rabbit event. So, only worlds with entities very similar to Kory Heath should contains galaxies. If this was false (in Platonia) then comp would be false (and refutable). I find that extremely hard to believe; there are an infinite number of multi-dimensional cellular-automata worlds that contain nothing like stars, galaxies, or the familiar physics we know, But then they don't contain entities sufficiently close to Kory Heath, (they don't go through Kory-Heath comp states) and those world/stories don't belong to your actual first person indeterminacy domain. and I don't see any reason to believe that all the 1st-person histories weaving their way through these computational structures (which surely exist in Platonia) have less measure than those that weave through the structures more resembling our own universe. You are right. No doubt there are worlds without stars and galaxies, but having srats and gilixas instead, and some Burno arguing to some Kyro about the geographical nature of those objects. Nothing in 1-8 prevents this. I find it much easier to believe - in fact, it seems almost necessarily true - that, when we analyze the structure of all the 1st-person histories weaving their way through Platonia, we see that virtually all observers observe indeterminacy. This in itself seems like a non-trivial finding. It would be even more non-trivial if one could analyze the structure of the indeterminacy that virtually all 1st-person observers must observe, and find that it is very much like quantum logic. This seems to be one of your claims, and it certainly seems possible (though I don't know enough yet to judge the issue for myself). However, it's a much further leap to conclude that we can go on to derive the laws of physics from the analysis of 1st-person histories weaving their way through Platonia. In the quote above, you acknowledge that you haven't actually done this - actually I have derived only the logical structure of
Re: Are we simulated by some massive computer?
Bruno Marchal wrote a 10-point argument about determining whether or not we are simulated by some massive computer. Here is point 9 from that post: 9) Now, from computer science and logic, startlingly enough perhaps, we can isolate a measure on the 1-person comp histories, and this give us the laws of physics (this is too technical to be put here, and actually I have derived only the logical structure of the probability one, but I got something non trivial and very close to a quantum logic (which can be seen as the logic of the quantum probability one, as von Neumann has shown). Bruno, I agree with everything in points 1-7 of the post I'm referring to. I think I understand the main thrust of points 8 and 10, but they both depend on the truth of the quoted point 9. I find this point highly dubious, and I'm interested to hear more about why you believe it (or whether I'm actually interpreting it correctly). Is it your contention that if we start only with the idea of Platonia (which contains all possible computational structures and events), and we analyze the structure of all possible 1st-person histories weaving their way through this Platonia, we would see that a majority of them find themselves in universes like the one we currently inhabit, with stars, galaxies, relativity, quantum physics, etc.? I find that extremely hard to believe; there are an infinite number of multi-dimensional cellular-automata worlds that contain nothing like stars, galaxies, or the familiar physics we know, and I don't see any reason to believe that all the 1st-person histories weaving their way through these computational structures (which surely exist in Platonia) have less measure than those that weave through the structures more resembling our own universe. I find it much easier to believe - in fact, it seems almost necessarily true - that, when we analyze the structure of all the 1st-person histories weaving their way through Platonia, we see that virtually all observers observe indeterminacy. This in itself seems like a non-trivial finding. It would be even more non-trivial if one could analyze the structure of the indeterminacy that virtually all 1st-person observers must observe, and find that it is very much like quantum logic. This seems to be one of your claims, and it certainly seems possible (though I don't know enough yet to judge the issue for myself). However, it's a much further leap to conclude that we can go on to derive the laws of physics from the analysis of 1st-person histories weaving their way through Platonia. In the quote above, you acknowledge that you haven't actually done this - actually I have derived only the logical structure of the probability one, but I got something non trivial and very close to a quantum logic - but you seem to believe that it can be done. Why? -- Kory
Re: Are we simulated by some massive computer?
At 13:08 13/04/04 -0700, George Levy wrote: Put in another way, *either* the massive computer simulates the exact laws of physics (exact with comp = the laws extractible from the measure on all 1-computations) in which case we belong to it but in that case we belong also to all its copy in Platonia, and our prediction or physics relies on all those copies (so that to say we belong to the massive computer has no real meaning: if it stops, nothing can happen to us for example); *or* the massive computer simulates only an approximation of those laws (like a brain during the night), and then we can in principle make the comparison, and find the discrepancies, and conclude we inhabit a fake reality ... OK? Bruno This is a very interesting method of testing what I thought was untestable. However, I see some problems. The number of simulations within Platonia is likely to be infinite. In addition, you may be simulated at more than one level, possibly at an infinite number of levels, including at the base level in Platonia if there is such a thing. OK. Although I am not sure by what you mean by base in Platonia. While the number of instances of you in the computer may be limited, the number of computers in Platonia may be infinite. In addition, the number of real you in Platonia is also likely to be infinite. Yes. Plausibly 2^aleph_0 (the power of the continuum). Your existence at the base level in Platonia is much more likely than the existence of a simulation computer (because the computer is presumably much more complex than you) and therefore, your measure in Platonia will swamp out your measure in the computers. OK. Your proposed test idea is interesting but it should be designed to cancel out these infinities. If that is possible. The translation of the reasoning in arithmetic leads me to think that these infinities are not cancellable. Comp would predict that the toe cannot be renormalizable. It is too early to make definite conclusion however. Bruno http://iridia.ulb.ac.be/~marchal/
RE: Are we simulated by some massive computer?
At 09:58 13/04/04 -0400, Ben Goertzel wrote: 6) This shows that if we are in a massive computer running in a universe, then (supposing we know it or believe it) to predict the future of any experiment we decide to carry one (for example testing A or B) we need to take into account all reconstitutions at any time of the computer (in the relevant state) in that universe, and actually also in any other universes (from our first person perspective we could not be aware of the difference of universes from inside the computer). Yes, but this is just a fancy version of the good old-fashioned Humean problem of induction, isn't it? That would be the case if there were no measure on the computations. Indeed, predicting the future on a sound a priori basis is not possible. One must make arbitrary assumptions in order to guide predictions. This is a limitation, not of the comp hypothesis specifically, but of the notion of prediction itself. You cannot solve the problem of induction with or without comp, so I don't think you should use problem-of-induction related difficulties as an argument against comp. I was not arguing against comp! (nor for). In fact, comp comes with a kind of workaround to the problem of induction, which is: To justify induction, make an arbitrary assumption of a certain universal computer, use this to gauge simplicity, and then judge predictions based on their simplicity (to use a verbal shorthand for a lot of math a la Solomonoff, Levin, Hutter, etc.). This is not a solution to the problem of induction (which is that one must make arbitrary assumptions to do induction), just an elegant way of introducing the arbitrary assumptions. This can help for explaining what intelligence is, but cannot help for the mind body problem where *all* computations must be taken into account. So, in my view, we are faced with a couple different ways of introducing the arbitrary assumptions needed to justify induction: 1) make an arbitrary assumption that the apparently real physical universe is real 2) make an arbitrary assumption that simpler hypotheses are better, where simplicity is judged by some fixed universal computing system There is no scientific (i.e. inductive or deductive) way to choose between these. From a human perspective, the choice lies outside the domain of science and math; it's a metaphysical or even ethical choice. I am not convinced. I don't really understand 1), and the interest of 2) relies, I think, in the fact that simplicity should not (and does not, I'm sure Schmidhuber would agree) on the choice of the universal computing system. Bruno http://iridia.ulb.ac.be/~marchal/
RE: Are we simulated by some massive computer?
6) This shows that if we are in a massive computer running in a universe, then (supposing we know it or believe it) to predict the future of any experiment we decide to carry one (for example testing A or B) we need to take into account all reconstitutions at any time of the computer (in the relevant state) in that universe, and actually also in any other universes (from our first person perspective we could not be aware of the difference of universes from inside the computer). Yes, but this is just a fancy version of the good old-fashioned Humean problem of induction, isn't it? Indeed, predicting the future on a sound a priori basis is not possible. One must make arbitrary assumptions in order to guide predictions. This is a limitation, not of the comp hypothesis specifically, but of the notion of prediction itself. You cannot solve the problem of induction with or without comp, so I don't think you should use problem-of-induction related difficulties as an argument against comp. In fact, comp comes with a kind of workaround to the problem of induction, which is: To justify induction, make an arbitrary assumption of a certain universal computer, use this to gauge simplicity, and then judge predictions based on their simplicity (to use a verbal shorthand for a lot of math a la Solomonoff, Levin, Hutter, etc.). This is not a solution to the problem of induction (which is that one must make arbitrary assumptions to do induction), just an elegant way of introducing the arbitrary assumptions. So, in my view, we are faced with a couple different ways of introducing the arbitrary assumptions needed to justify induction: 1) make an arbitrary assumption that the apparently real physical universe is real 2) make an arbitrary assumption that simpler hypotheses are better, where simplicity is judged by some fixed universal computing system There is no scientific (i.e. inductive or deductive) way to choose between these. From a human perspective, the choice lies outside the domain of science and math; it's a metaphysical or even ethical choice. -- Ben Goertzel
RE: Are we simulated by some massive computer?
Ben Goertzel writes: So, in my view, we are faced with a couple different ways of introducing the arbitrary assumptions needed to justify induction: 1) make an arbitrary assumption that the apparently real physical universe is real 2) make an arbitrary assumption that simpler hypotheses are better, where simplicity is judged by some fixed universal computing system There is no scientific (i.e. inductive or deductive) way to choose between these. From a human perspective, the choice lies outside the domain of science and math; it's a metaphysical or even ethical choice. But is there a way to test these? Could we make different predictions on the basis of these assumptions, and then reject one or the other based on our observations? Hal Finney
Re: Are we simulated by some massive computer?
Bruno Marchal wrote: Put in another way, *either* the massive computer simulates the exact laws of physics (exact with comp = the laws extractible from the measure on all 1-computations) in which case we belong to it but in that case we belong also to all its copy in Platonia, and our prediction or physics relies on all those copies (so that to say we belong to the massive computer has no real meaning: if it stops, nothing can happen to us for example); *or* the massive computer simulates only an approximation of those laws (like a brain during the night), and then we can in principle make the comparison, and find the discrepancies, and conclude we inhabit a fake reality ... OK? Bruno This is a very interesting method of testing what I thought was untestable. However, I see some problems. The number of simulations within Platonia is likely to be infinite. In addition, you may be simulated at more than one level, possibly at an infinite number of levels, including at the base level in Platonia if there is such a thing. While the number of instances of you in the computer may be limited, the number of computers in Platonia may be infinite. In addition, the number of real you in Platonia is also likely to be infinite. Your existence at the base level in Platonia is much more likely than the existence of a simulation computer (because the computer is presumably much more complex than you) and therefore, your measure in Platonia will swamp out your measure in the computers. Your proposed test idea is interesting but it should be designed to cancel out these infinities. George
