Re: Definition of universe
David, It is the motivation of Everett to make coherent the wave equation and the idea that mind is not something substantial acting on matter (like Copenhagians are obliged to admit in a way or another). To derive the phenomenology of the collapse, he used only local interactions and local memories, that is, intuitive mechanism. Quantum indeterminacy is made first person indeterminacy (Everett uses subjective). We will never know if Everett would have said yes to a digitalist doctor of course. But the origin of the physical laws have to be independent of the choice of the computational base, so we have to explain why the appearances favor a quantum universal machine in our neighborhood. The answer is that below our substitution level the information flux relates to our stories through a sum on all computations (going through the actual states, relative). And what I say here can be translated in arithmetic. The other way round is probable too: Quantum mechanics makes the laws of physicist (but not of observation) computable, unless you introduce in physics explicit non computable Halmitonian. For example e^icH(x,t) with c Chaitin number may be an acceptable physical wave, but it is ad hoc if used to say that some non computational object exist in the physical world. e^icH(x,t) is even worst than an UFO, it justifies that we cannot recognize it. c, for us (machine) is undistinguishable from randomness. Here we meet really the question what is a computable function from R to R. Unlike for N to N, the question is not settled. Does real number exist in the physical world, etc. With comp, this can be said to be solved: real number exists epistemologically, but not ontologicallly. I recall that Physics is also epistemological: it is the map of our indeterminate histories. Bruno On 02 Mar 2010, at 17:45, David Nyman wrote: On 2 March 2010 16:13, Bruno Marchal marc...@ulb.ac.be wrote: I think that you are forgetting the 8th step of the UDA. That is the Movie Graph Argument (MGA). It shows that, assuming comp, the physical supervenience has to be abandonned, and should be substituted by the comp supervenience thesis, which is that, roughly speaking: consciousness has to be associated with computation (a purely mathematical notion), and not with anything physical. I seem to be frustratingly unable to get my point across (maybe it wasn't a very good point!) No, I clearly recall the 8th step and the MGA (although a detailed restatement of the latter on the list would be very nice). I'm sure you haven't forgotten how many discussions we've had on these topics. Consequently, whenever you make a statement clearly assuming comp, as you say above, I always have this in mind. Therefore, when I asked my question about EQM, it was because I wasn't sure on what basis you would take the view that *Everett himself assumed comp*. I wondered if it was because, as you say, it is more or less the default theory of mind amongst physicists, and that consequently you feel justified in attributing it to him. Or is there something aspect of EQM, or the SWE, that inescapably entails comp as a theory of mind, irrespective of the originators' assumptions? That's my question. Sorry about the confusion. David On 01 Mar 2010, at 11:58, David Nyman wrote: On 1 March 2010 08:26, Bruno Marchal marc...@ulb.ac.be wrote: Everett uses comp, in the usual intuitive way, because he characterizes the observer by its crisp memory, and he derives the phenomenology of the wave packet reduction, by showing it to appears through physical interaction in the memory/diary of the experimenter. He presents QM-without- collapse as being a way for not using a magical dualism between mind and matter. He does not mention Church thesis, so digitalism is implicit, but his reasoning presupposes that the observer is described by the wave itself, which is a computational object (the solution of Schroedinger equation are Turing emulable). When you say Turing emulable - i.e. literally *capable* of being emulated by a TM - it's not clear to me that this should be taken to be equivalent to actually being computed by a TM or its equivalent. In the latter case (i.e. something achieved through an actual occasion of computation) I can see that digitalism and its consequences are entailed, but in the former case, I don't see why this necessarily follows. To be merely *capable* of being computed is surely not equivalent to an actual occasion of computation? I'm obviously missing something, because you typically use the term Turing emulable as a knock-down statement to the effect that digital mechanism is to be assumed as a consequence, but I still don't see why. Do you perhaps mean it to be taken in conjunction with the assumption that digitalism is the default (and hence Everett's) explanation for mind in physics (i.e. the desire to avoid magic dualism)? In
Re: Definition of universe
On 01 Mar 2010, at 11:58, David Nyman wrote: On 1 March 2010 08:26, Bruno Marchal marc...@ulb.ac.be wrote: Everett uses comp, in the usual intuitive way, because he characterizes the observer by its crisp memory, and he derives the phenomenology of the wave packet reduction, by showing it to appears through physical interaction in the memory/diary of the experimenter. He presents QM-without- collapse as being a way for not using a magical dualism between mind and matter. He does not mention Church thesis, so digitalism is implicit, but his reasoning presupposes that the observer is described by the wave itself, which is a computational object (the solution of Schroedinger equation are Turing emulable). When you say Turing emulable - i.e. literally *capable* of being emulated by a TM - it's not clear to me that this should be taken to be equivalent to actually being computed by a TM or its equivalent. In the latter case (i.e. something achieved through an actual occasion of computation) I can see that digitalism and its consequences are entailed, but in the former case, I don't see why this necessarily follows. To be merely *capable* of being computed is surely not equivalent to an actual occasion of computation? I'm obviously missing something, because you typically use the term Turing emulable as a knock-down statement to the effect that digital mechanism is to be assumed as a consequence, but I still don't see why. Do you perhaps mean it to be taken in conjunction with the assumption that digitalism is the default (and hence Everett's) explanation for mind in physics (i.e. the desire to avoid magic dualism)? In that case computation, and hence Turing-emulability, would indeed be a prerequisite for being capable of having a mind, and I could see why your arguments would apply. If I could clear up this confusion it would help my understanding of a lot of threads in the list. I think that you are forgetting the 8th step of the UDA. That is the Movie Graph Argument (MGA). It shows that, assuming comp, the physical supervenience has to be abandonned, and should be substituted by the comp supervenience thesis, which is that, roughly speaking: consciousness has to be associated with computation (a purely mathematical notion), and not with anything physical. A nice thing when you remember that physicist have not yet succeeded in defining what is, in general, a physical computation (cf notably the implementation problem, etc.) Already in UDA-step-7, (where I recall that the protocol is that we are in a concrete physical universe executing integrally a UD), to be capable of being computed (or Turing emulated) ENTAILS being computed (by that UD, soon or later, but the first person invariance makes this soon or later irrelevant for the first person experience). But in step 8, that is by the MGA, consciousness is attached to the mathematical (and thus arithmetical) notion of computation. All actuality notions (now, here, actual, current, etc.) becomes indexical, that is relative computational (mathematical) state. If you want I will (re)send the MGA. Less people get it than the UDA- seven first steps (and even some part of the seven step is not always well understood). Only in my french papers and books the argument is developed in detail. Maudlin found (later) a very similar argument, but since the last explanation of MGA on this list, I have understood that MGA is more precise than Maudlin, and even more simple (no need to even mention the counterfactuals; yet still subtle, but then the mind body problem is subtle. Many scientist miss it entirely. Some people take a long time to understand the term 'qualia'). In my older (french) presentation of the UDA, the MGA was the first step. It is *the* argument showing that the mind body problem is not solved by mechanism per se, as many materialist believe. The MGA argument (UDA-8) is a proof by reductio ad absurdum. It shows that comp +physical supervenience entails that consciousness has to be attached to a physical movie of a corresponding physical computation in real time, which is absurd because the movie don't compute at all. The movie does describe a computation, but a description of a computation is not a computation. That last point still makes problem for some other, I think. You may search in the archive (last year notably) on MGA, MGA1, MGA2, MGA3 (but I am not entirely satisfied by MGA3: the absurdity comes before). It is really the movie graph which eliminates the possibility to invoke physicalness, if we keep comp. WE have to choose between digital mechanism, or materialism. This solves also the question what is now, what is here, etc. It reduce all this to the handling of indexicals in the manner of Kleene, Post, Gödel, etc. With comp, physics get a purely mathematical justification or (re)definition, with both the quanta and the qualia
Re: Definition of universe
On 2 March 2010 16:13, Bruno Marchal marc...@ulb.ac.be wrote: I think that you are forgetting the 8th step of the UDA. That is the Movie Graph Argument (MGA). It shows that, assuming comp, the physical supervenience has to be abandonned, and should be substituted by the comp supervenience thesis, which is that, roughly speaking: consciousness has to be associated with computation (a purely mathematical notion), and not with anything physical. I seem to be frustratingly unable to get my point across (maybe it wasn't a very good point!) No, I clearly recall the 8th step and the MGA (although a detailed restatement of the latter on the list would be very nice). I'm sure you haven't forgotten how many discussions we've had on these topics. Consequently, whenever you make a statement clearly assuming comp, as you say above, I always have this in mind. Therefore, when I asked my question about EQM, it was because I wasn't sure on what basis you would take the view that *Everett himself assumed comp*. I wondered if it was because, as you say, it is more or less the default theory of mind amongst physicists, and that consequently you feel justified in attributing it to him. Or is there something aspect of EQM, or the SWE, that inescapably entails comp as a theory of mind, irrespective of the originators' assumptions? That's my question. Sorry about the confusion. David On 01 Mar 2010, at 11:58, David Nyman wrote: On 1 March 2010 08:26, Bruno Marchal marc...@ulb.ac.be wrote: Everett uses comp, in the usual intuitive way, because he characterizes the observer by its crisp memory, and he derives the phenomenology of the wave packet reduction, by showing it to appears through physical interaction in the memory/diary of the experimenter. He presents QM-without-collapse as being a way for not using a magical dualism between mind and matter. He does not mention Church thesis, so digitalism is implicit, but his reasoning presupposes that the observer is described by the wave itself, which is a computational object (the solution of Schroedinger equation are Turing emulable). When you say Turing emulable - i.e. literally *capable* of being emulated by a TM - it's not clear to me that this should be taken to be equivalent to actually being computed by a TM or its equivalent. In the latter case (i.e. something achieved through an actual occasion of computation) I can see that digitalism and its consequences are entailed, but in the former case, I don't see why this necessarily follows. To be merely *capable* of being computed is surely not equivalent to an actual occasion of computation? I'm obviously missing something, because you typically use the term Turing emulable as a knock-down statement to the effect that digital mechanism is to be assumed as a consequence, but I still don't see why. Do you perhaps mean it to be taken in conjunction with the assumption that digitalism is the default (and hence Everett's) explanation for mind in physics (i.e. the desire to avoid magic dualism)? In that case computation, and hence Turing-emulability, would indeed be a prerequisite for being capable of having a mind, and I could see why your arguments would apply. If I could clear up this confusion it would help my understanding of a lot of threads in the list. I think that you are forgetting the 8th step of the UDA. That is the Movie Graph Argument (MGA). It shows that, assuming comp, the physical supervenience has to be abandonned, and should be substituted by the comp supervenience thesis, which is that, roughly speaking: consciousness has to be associated with computation (a purely mathematical notion), and not with anything physical. A nice thing when you remember that physicist have not yet succeeded in defining what is, in general, a physical computation (cf notably the implementation problem, etc.) Already in UDA-step-7, (where I recall that the protocol is that we are in a concrete physical universe executing integrally a UD), to be capable of being computed (or Turing emulated) ENTAILS being computed (by that UD, soon or later, but the first person invariance makes this soon or later irrelevant for the first person experience). But in step 8, that is by the MGA, consciousness is attached to the mathematical (and thus arithmetical) notion of computation. All actuality notions (now, here, actual, current, etc.) becomes indexical, that is relative computational (mathematical) state. If you want I will (re)send the MGA. Less people get it than the UDA-seven first steps (and even some part of the seven step is not always well understood). Only in my french papers and books the argument is developed in detail. Maudlin found (later) a very similar argument, but since the last explanation of MGA on this list, I have understood that MGA is more precise than Maudlin, and even more simple (no need to even mention the counterfactuals; yet still
Re: Definition of universe
On 28 Feb 2010, at 18:43, David Nyman wrote: On 28 February 2010 15:45, Bruno Marchal marc...@ulb.ac.be wrote: UDA shows that the wave equation (not just the collapse) has to emerge from a relative state measure on all computational histories. The schroedinger equation has to be itself the result of the abandon of the identity thesis. Bruno, I'm sorry but I think I failed to make clear what I was actually asking you. I assumed, when you made you comment about Everett Quantum Mechanics, that you didn't simply mean EQM in the context of *already assuming* the computationalist hypothesis to be true, but even in the contrary case of assuming some notion of the primitively physical to be the case. When you mention UDA as you do above, I can only assume that you intend the reader to understand your comment in the context of the comp hypothesis. Of course, I understand that in this case, EQM and physics in general would be derived from comp, and not vice versa, and hence your comment about EQM would necessarily follow. But my question was whether you were intending to say something stronger - i.e. that EQM, or the SWE itself under any interpretation, reveal the implausibility of the mind/body (or minds-bodies) identity thesis, as when you say: Everett uses comp (or one of its weakening), he has to pursue his task and derive the phenomenology of the wave (or matrix) from the collection of all computations (by UDA). What do you mean by Everett uses comp (or one of its weakening)? Do you mean that he was explicitly assuming the comp hypothesis, or that his approach implicitly presupposes it? I'm confused. Everett uses comp, in the usual intuitive way, because he characterizes the observer by its crisp memory, and he derives the phenomenology of the wave packet reduction, by showing it to appears through physical interaction in the memory/diary of the experimenter. He presents QM-without-collapse as being a way for not using a magical dualism between mind and matter. He does not mention Church thesis, so digitalism is implicit, but his reasoning presupposes that the observer is described by the wave itself, which is a computational object (the solution of Schroedinger equation are Turing emulable). This is hardly original: comp is the implicit hypothesis of all materialist or physicalist. (Thus, it is normal some takes some time to understand that comp is incompatible with (weak) materialism). On the contrary, those who believed (without evidences) that the collapse of the wave is a real phenomenon are obliged to refer to a non comp dualist theory of mind. Since Descartes, we can say that comp is the default hypothesis of all rationalist. Comp is just Mechanism made clear mathematically by the discover of Turing, Post, Church. Bruno On 27 Feb 2010, at 18:38, David Nyman wrote: On 8 Feb, 14:12, Bruno Marchal marc...@ulb.ac.be wrote: The main problem with Tegmark is that he assumes an implicit identity thesis mind/observer-state which does not work once we assume the computationalist hypothesis, (and thus cannot work with Everett Quantum Mechanics either). The weakness of such approaches is that they ignore somehow the complexity and non triviality of the mind- body or consciousness/reality problem. Bruno, I'm just trying to catch up with some older posts whilst continuing to think about your most recent comments, and I'd like to enquire why you say above and thus cannot work with Everett Quantum Mechanics either. UDA shows that the wave equation (not just the collapse) has to emerge from a relative state measure on all computational histories. The schroedinger equation has to be itself the result of the abandon of the identity thesis. You can still locally ascribe a mind to an apparent body, but you cannot ascribe a body to a mind. You can only ascribe an infinity of body, corresponding to the possible computations of your parts below your level of substitution. By the invariance delay of the first person experiences, in UD-time/step, the average first person body is a function depending on all possible universal machine/numbers. Negative interference, and indeed a quantum computer, should appear from the statistic or measure logic, with observability described by Bp Dt, for probability or credibility one (true in all accessible worlds + there is a world, p Sigma_1). It corresponds plausibly to Plotinus bastard calculus, an expression borrow to Plato, and used in their matter theory. Everett uses comp (or one of its weakening), he has to pursue his task and derive the phenomenology of the wave (or matrix) from the collection of all computations (by UDA). I think I've asked before about the distinction between can be computed and is (in fact) being computed. A can be computed if there is a UD-time-step t such that A is being computed. is being computed is an arithetical proposition which is
Re: Definition of universe
On 1 March 2010 08:26, Bruno Marchal marc...@ulb.ac.be wrote: Everett uses comp, in the usual intuitive way, because he characterizes the observer by its crisp memory, and he derives the phenomenology of the wave packet reduction, by showing it to appears through physical interaction in the memory/diary of the experimenter. He presents QM-without-collapse as being a way for not using a magical dualism between mind and matter. He does not mention Church thesis, so digitalism is implicit, but his reasoning presupposes that the observer is described by the wave itself, which is a computational object (the solution of Schroedinger equation are Turing emulable). When you say Turing emulable - i.e. literally *capable* of being emulated by a TM - it's not clear to me that this should be taken to be equivalent to actually being computed by a TM or its equivalent. In the latter case (i.e. something achieved through an actual occasion of computation) I can see that digitalism and its consequences are entailed, but in the former case, I don't see why this necessarily follows. To be merely *capable* of being computed is surely not equivalent to an actual occasion of computation? I'm obviously missing something, because you typically use the term Turing emulable as a knock-down statement to the effect that digital mechanism is to be assumed as a consequence, but I still don't see why. Do you perhaps mean it to be taken in conjunction with the assumption that digitalism is the default (and hence Everett's) explanation for mind in physics (i.e. the desire to avoid magic dualism)? In that case computation, and hence Turing-emulability, would indeed be a prerequisite for being capable of having a mind, and I could see why your arguments would apply. If I could clear up this confusion it would help my understanding of a lot of threads in the list. David On 28 Feb 2010, at 18:43, David Nyman wrote: On 28 February 2010 15:45, Bruno Marchal marc...@ulb.ac.be wrote: UDA shows that the wave equation (not just the collapse) has to emerge from a relative state measure on all computational histories. The schroedinger equation has to be itself the result of the abandon of the identity thesis. Bruno, I'm sorry but I think I failed to make clear what I was actually asking you. I assumed, when you made you comment about Everett Quantum Mechanics, that you didn't simply mean EQM in the context of *already assuming* the computationalist hypothesis to be true, but even in the contrary case of assuming some notion of the primitively physical to be the case. When you mention UDA as you do above, I can only assume that you intend the reader to understand your comment in the context of the comp hypothesis. Of course, I understand that in this case, EQM and physics in general would be derived from comp, and not vice versa, and hence your comment about EQM would necessarily follow. But my question was whether you were intending to say something stronger - i.e. that EQM, or the SWE itself under any interpretation, reveal the implausibility of the mind/body (or minds-bodies) identity thesis, as when you say: Everett uses comp (or one of its weakening), he has to pursue his task and derive the phenomenology of the wave (or matrix) from the collection of all computations (by UDA). What do you mean by Everett uses comp (or one of its weakening)? Do you mean that he was explicitly assuming the comp hypothesis, or that his approach implicitly presupposes it? I'm confused. Everett uses comp, in the usual intuitive way, because he characterizes the observer by its crisp memory, and he derives the phenomenology of the wave packet reduction, by showing it to appears through physical interaction in the memory/diary of the experimenter. He presents QM-without-collapse as being a way for not using a magical dualism between mind and matter. He does not mention Church thesis, so digitalism is implicit, but his reasoning presupposes that the observer is described by the wave itself, which is a computational object (the solution of Schroedinger equation are Turing emulable). This is hardly original: comp is the implicit hypothesis of all materialist or physicalist. (Thus, it is normal some takes some time to understand that comp is incompatible with (weak) materialism). On the contrary, those who believed (without evidences) that the collapse of the wave is a real phenomenon are obliged to refer to a non comp dualist theory of mind. Since Descartes, we can say that comp is the default hypothesis of all rationalist. Comp is just Mechanism made clear mathematically by the discover of Turing, Post, Church. Bruno On 27 Feb 2010, at 18:38, David Nyman wrote: On 8 Feb, 14:12, Bruno Marchal marc...@ulb.ac.be wrote: The main problem with Tegmark is that he assumes an implicit identity thesis mind/observer-state which does not work once we assume the computationalist
Re: Definition of universe
On 27 Feb 2010, at 18:38, David Nyman wrote: On 8 Feb, 14:12, Bruno Marchal marc...@ulb.ac.be wrote: The main problem with Tegmark is that he assumes an implicit identity thesis mind/observer-state which does not work once we assume the computationalist hypothesis, (and thus cannot work with Everett Quantum Mechanics either). The weakness of such approaches is that they ignore somehow the complexity and non triviality of the mind- body or consciousness/reality problem. Bruno, I'm just trying to catch up with some older posts whilst continuing to think about your most recent comments, and I'd like to enquire why you say above and thus cannot work with Everett Quantum Mechanics either. UDA shows that the wave equation (not just the collapse) has to emerge from a relative state measure on all computational histories. The schroedinger equation has to be itself the result of the abandon of the identity thesis. You can still locally ascribe a mind to an apparent body, but you cannot ascribe a body to a mind. You can only ascribe an infinity of body, corresponding to the possible computations of your parts below your level of substitution. By the invariance delay of the first person experiences, in UD-time/step, the average first person body is a function depending on all possible universal machine/numbers. Negative interference, and indeed a quantum computer, should appear from the statistic or measure logic, with observability described by Bp Dt, for probability or credibility one (true in all accessible worlds + there is a world, p Sigma_1). It corresponds plausibly to Plotinus bastard calculus, an expression borrow to Plato, and used in their matter theory. Everett uses comp (or one of its weakening), he has to pursue his task and derive the phenomenology of the wave (or matrix) from the collection of all computations (by UDA). I think I've asked before about the distinction between can be computed and is (in fact) being computed. A can be computed if there is a UD-time-step t such that A is being computed. is being computed is an arithetical proposition which is recursive (computable), Sigma_0. can be computed is recursively enumerable (semi-computable), Sigma_1. It's only in the latter case, AFAICS, that your comment would apply (i.e. if we assume that we're participants in an Everett multiverse that is in fact a computational artefact, as per the comp hypothesis). It is just that with comp, we inherite (all lobian machines inherit) a multiverse. To derive the Schroedinger (Dirac DeWitt-Wheeler etc.) equation of physics consists in showing that the sharable physical part of the lobian machines (the 3th, 4th, 5th hypostases, with p Sigma_1) is the same as the one described by the physicists. But if - as physicalists would - we take the view that what exists is primitively-physical, as opposed to computationally-generated, Careful, the primitively physical apparent in comp is NOT (never) computed nor computable. It is really the 1-p-p view. In particular it is 1-p, and 1-p is unaware of the arithmetical delay of the UD. In a sense all UD* is processed in 0 seconds, at each of its observer moments. A priori, the results of any observation for any observer moment depends on a statistic involving all universal machines and all their computations (emulated infinitely often by the UD). The mystery here is that the laws of physics seems (empirically) to be computable. No White Rabbits! But the difference of points of view (the hypostases) suggests clearly the mathematical reason why the non computable take refuge below our substitution level, giving rise to locally sharable universal structures (sharable by population of universal machines). I'm no longer sure of your reason for saying thus. It seems to me that the UD Argument explains why computationalism makes the notion 'primitively physical' meaningless, or without any explanation power for the appearance of the primitively physical. On the contrary, the appearance of the 'primitively physical' are 'completely' (= completely except for a justified gap), explained in a theory of belief (knowledge, observable, sensible, etc.) by universal machines. UDA is a reduction of the mind body problem to the body problem. Mind is whatever universal machine can experience. And eventually matter is what mind cannot determinate (in arithmetic). Is it related to what I've been saying about the non-computability of the mind from the starting-point of purely 3-p processes (thus EQM): i.e. that mind - 1- p qualitative experience - is simply inaccessible from a primitively- physical 3-p pov? I am not sure. The 1-p are inaccessible by any computation, and are even not definable in the language of a Löbian machine on which it applies. The 1-p are accessible, and even 'defined' on infinite sets in some sense. If you want a primitively
Re: Definition of universe
On 28 February 2010 15:45, Bruno Marchal marc...@ulb.ac.be wrote: UDA shows that the wave equation (not just the collapse) has to emerge from a relative state measure on all computational histories. The schroedinger equation has to be itself the result of the abandon of the identity thesis. Bruno, I'm sorry but I think I failed to make clear what I was actually asking you. I assumed, when you made you comment about Everett Quantum Mechanics, that you didn't simply mean EQM in the context of *already assuming* the computationalist hypothesis to be true, but even in the contrary case of assuming some notion of the primitively physical to be the case. When you mention UDA as you do above, I can only assume that you intend the reader to understand your comment in the context of the comp hypothesis. Of course, I understand that in this case, EQM and physics in general would be derived from comp, and not vice versa, and hence your comment about EQM would necessarily follow. But my question was whether you were intending to say something stronger - i.e. that EQM, or the SWE itself under any interpretation, reveal the implausibility of the mind/body (or minds-bodies) identity thesis, as when you say: Everett uses comp (or one of its weakening), he has to pursue his task and derive the phenomenology of the wave (or matrix) from the collection of all computations (by UDA). What do you mean by Everett uses comp (or one of its weakening)? Do you mean that he was explicitly assuming the comp hypothesis, or that his approach implicitly presupposes it? I'm confused. David On 27 Feb 2010, at 18:38, David Nyman wrote: On 8 Feb, 14:12, Bruno Marchal marc...@ulb.ac.be wrote: The main problem with Tegmark is that he assumes an implicit identity thesis mind/observer-state which does not work once we assume the computationalist hypothesis, (and thus cannot work with Everett Quantum Mechanics either). The weakness of such approaches is that they ignore somehow the complexity and non triviality of the mind-body or consciousness/reality problem. Bruno, I'm just trying to catch up with some older posts whilst continuing to think about your most recent comments, and I'd like to enquire why you say above and thus cannot work with Everett Quantum Mechanics either. UDA shows that the wave equation (not just the collapse) has to emerge from a relative state measure on all computational histories. The schroedinger equation has to be itself the result of the abandon of the identity thesis. You can still locally ascribe a mind to an apparent body, but you cannot ascribe a body to a mind. You can only ascribe an infinity of body, corresponding to the possible computations of your parts below your level of substitution. By the invariance delay of the first person experiences, in UD-time/step, the average first person body is a function depending on all possible universal machine/numbers. Negative interference, and indeed a quantum computer, should appear from the statistic or measure logic, with observability described by Bp Dt, for probability or credibility one (true in all accessible worlds + there is a world, p Sigma_1). It corresponds plausibly to Plotinus bastard calculus, an expression borrow to Plato, and used in their matter theory. Everett uses comp (or one of its weakening), he has to pursue his task and derive the phenomenology of the wave (or matrix) from the collection of all computations (by UDA). I think I've asked before about the distinction between can be computed and is (in fact) being computed. A can be computed if there is a UD-time-step t such that A is being computed. is being computed is an arithetical proposition which is recursive (computable), Sigma_0. can be computed is recursively enumerable (semi-computable), Sigma_1. It's only in the latter case, AFAICS, that your comment would apply (i.e. if we assume that we're participants in an Everett multiverse that is in fact a computational artefact, as per the comp hypothesis). It is just that with comp, we inherite (all lobian machines inherit) a multiverse. To derive the Schroedinger (Dirac DeWitt-Wheeler etc.) equation of physics consists in showing that the sharable physical part of the lobian machines (the 3th, 4th, 5th hypostases, with p Sigma_1) is the same as the one described by the physicists. But if - as physicalists would - we take the view that what exists is primitively-physical, as opposed to computationally-generated, Careful, the primitively physical apparent in comp is NOT (never) computed nor computable. It is really the 1-p-p view. In particular it is 1-p, and 1-p is unaware of the arithmetical delay of the UD. In a sense all UD* is processed in 0 seconds, at each of its observer moments. A priori, the results of any observation for any observer moment depends on a statistic involving all universal machines and all their computations (emulated
Re: Definition of universe
On 8 Feb, 14:12, Bruno Marchal marc...@ulb.ac.be wrote: The main problem with Tegmark is that he assumes an implicit identity thesis mind/observer-state which does not work once we assume the computationalist hypothesis, (and thus cannot work with Everett Quantum Mechanics either). The weakness of such approaches is that they ignore somehow the complexity and non triviality of the mind-body or consciousness/reality problem. Bruno, I'm just trying to catch up with some older posts whilst continuing to think about your most recent comments, and I'd like to enquire why you say above and thus cannot work with Everett Quantum Mechanics either. I think I've asked before about the distinction between can be computed and is (in fact) being computed. It's only in the latter case, AFAICS, that your comment would apply (i.e. if we assume that we're participants in an Everett multiverse that is in fact a computational artefact, as per the comp hypothesis). But if - as physicalists would - we take the view that what exists is primitively-physical, as opposed to computationally-generated, I'm no longer sure of your reason for saying thus. Is it related to what I've been saying about the non-computability of the mind from the starting-point of purely 3-p processes (thus EQM): i.e. that mind - 1- p qualitative experience - is simply inaccessible from a primitively- physical 3-p pov? David Actually we have already discussed this a lot, and the work I explain here (uda, auda) can be considered as an answer to Tegmark (or Schmidhuber), except that it has been published many years before, and relies on philosophy of mind/computer science or machine's theology. The main problem with Tegmark is that he assumes an implicit identity thesis mind/observer-state which does not work once we assume the computationalist hypothesis, (and thus cannot work with Everett Quantum Mechanics either). The weakness of such approaches is that they ignore somehow the complexity and non triviality of the mind-body or consciousness/reality problem. This is relevant for the (very hard) question what is a (physical) universe?. This is a notion more or less taken for granted by the physicalists, but which can no more taken as such by the computationalist cognitive scientist. Indeed machine dreams becomes prevalent, and the question of universe becomes equivalent with the question of how does the dreams glue together. It is the problem of passing from first person to first person plural, and this needs a notion of entanglement of computation. If you define a universe by the coherent structure corresponding to all what is observable, the question becomes: is there a unique coherent structure accounting for all observations? What is its internal and external logic? Today, if we accept (Everett) QM, we may say that such a coherent structure exists, has Boolean (classical) logic as external logic, and some quantum logic as internal logic. Indeed, it is the major interest of Everett QM that it reintroduces booleanity at the basic third person description level. Such a logical completion of the quantum observation leads to the multiverse, and it can be seen a unique coherent (super) universe (nut multi-cosmos, multi-histories). But Everett uses comp, and comp per se leads to an explosion of realties (first person and first person plural), and it is just an open problem to really count the number of complete boolean structures capable of attributing values to anything observable. This should be clear for the reader of the UD argument. I mean those few who get the whole thing clearly in their mind (I am aware of some subtleties not yet well understood: like what is a (mathematical) computation. The fact that we have empirical data giving evidences that we share the quantum indeterminacy suggests that we all share some computation: this really means that we (human population) are multiplied by the indeterminacy below our level of substitution. Such happenings makes difficult to even define precisely what is a universe, and if that really exists beyond its local appearances. This why I prefer to use the expression many-dreams or many--histories instead of many worlds or many-universes. Universe becomes defined by the complete boolean extension of sharable dreams/histories (computations as seen from a first person perspective). All this looks probably like utter nonsense for those who miss the seven first steps of the universal dovetailer argument. Bruno On 07 Feb 2010, at 21:07, Brian Tenneson wrote: Assuming a 4-level hierarchy of universe as posited by Tegmark here... http://arxiv.org/abs/0905.1283v1 Then the universe would be an aggregate of all mathematical structures. On Tue, Dec 29, 2009 at 6:07 AM, Mindey min...@gmail.com wrote: Hello, I was just wondering, we are talking
Re: Definition of universe
Actually we have already discussed this a lot, and the work I explain here (uda, auda) can be considered as an answer to Tegmark (or Schmidhuber), except that it has been published many years before, and relies on philosophy of mind/computer science or machine's theology. The main problem with Tegmark is that he assumes an implicit identity thesis mind/observer-state which does not work once we assume the computationalist hypothesis, (and thus cannot work with Everett Quantum Mechanics either). The weakness of such approaches is that they ignore somehow the complexity and non triviality of the mind-body or consciousness/reality problem. This is relevant for the (very hard) question what is a (physical) universe?. This is a notion more or less taken for granted by the physicalists, but which can no more taken as such by the computationalist cognitive scientist. Indeed machine dreams becomes prevalent, and the question of universe becomes equivalent with the question of how does the dreams glue together. It is the problem of passing from first person to first person plural, and this needs a notion of entanglement of computation. If you define a universe by the coherent structure corresponding to all what is observable, the question becomes: is there a unique coherent structure accounting for all observations? What is its internal and external logic? Today, if we accept (Everett) QM, we may say that such a coherent structure exists, has Boolean (classical) logic as external logic, and some quantum logic as internal logic. Indeed, it is the major interest of Everett QM that it reintroduces booleanity at the basic third person description level. Such a logical completion of the quantum observation leads to the multiverse, and it can be seen a unique coherent (super) universe (nut multi-cosmos, multi-histories). But Everett uses comp, and comp per se leads to an explosion of realties (first person and first person plural), and it is just an open problem to really count the number of complete boolean structures capable of attributing values to anything observable. This should be clear for the reader of the UD argument. I mean those few who get the whole thing clearly in their mind (I am aware of some subtleties not yet well understood: like what is a (mathematical) computation. The fact that we have empirical data giving evidences that we share the quantum indeterminacy suggests that we all share some computation: this really means that we (human population) are multiplied by the indeterminacy below our level of substitution. Such happenings makes difficult to even define precisely what is a universe, and if that really exists beyond its local appearances. This why I prefer to use the expression many-dreams or many--histories instead of many worlds or many-universes. Universe becomes defined by the complete boolean extension of sharable dreams/histories (computations as seen from a first person perspective). All this looks probably like utter nonsense for those who miss the seven first steps of the universal dovetailer argument. Bruno On 07 Feb 2010, at 21:07, Brian Tenneson wrote: Assuming a 4-level hierarchy of universe as posited by Tegmark here... http://arxiv.org/abs/0905.1283v1 Then the universe would be an aggregate of all mathematical structures. On Tue, Dec 29, 2009 at 6:07 AM, Mindey min...@gmail.com wrote: Hello, I was just wondering, we are talking so much about universes, but how do we define universe? Sorry if that question was answered somewhere, but after a quick search I didn't find it. Inyuki http://www.universians.org -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-l...@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com . For more options, visit this group at http://groups.google.com/group/everything-list?hl=en . -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-l...@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com . For more options, visit this group at http://groups.google.com/group/everything-list?hl=en . http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-l...@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: Definition of universe
Assuming a 4-level hierarchy of universe as posited by Tegmark here... http://arxiv.org/abs/0905.1283v1 Then the universe would be an aggregate of all mathematical structures. On Tue, Dec 29, 2009 at 6:07 AM, Mindey min...@gmail.com wrote: Hello, I was just wondering, we are talking so much about universes, but how do we define universe? Sorry if that question was answered somewhere, but after a quick search I didn't find it. Inyuki http://www.universians.org -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-l...@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.comeverything-list%2bunsubscr...@googlegroups.com . For more options, visit this group at http://groups.google.com/group/everything-list?hl=en. -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-l...@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: Definition of universe
Bruno: is there a free version of Theoretical computer science and the natural sciences? Ronald On Feb 4, 2:45 pm, Bruno Marchal marc...@ulb.ac.be wrote: On 04 Feb 2010, at 15:28, Jason Resch wrote: On Wed, Feb 3, 2010 at 1:47 PM, Bruno Marchal marc...@ulb.ac.be wrote: On 03 Feb 2010, at 15:49, Jason Resch wrote: On Wed, Feb 3, 2010 at 3:14 AM, Bruno Marchal marc...@ulb.ac.be wrote: On 03 Feb 2010, at 03:00, Jason Resch wrote: Is your point that with addition, multiplication, and an infinite number of successive symbols, any computable function can be constructed? You can say so. You could also have said that with addition + multiplication axioms + logic, any computable function can be proved to exist. So I suppose that is what I was wondering, given at minimum, those, how is the existence of a computable function proved to exist? Could you provide an example of how a simple function, like f(x) = x*2 exists, or is it a very tedious proof? I guess you ask: how is the existence of a computable function proved to exist in a theory T. Usually logicians use the notion of representability. The one variable function f(x) is said to be representable in the theory T, if there is a formula F(x, y) such that when f(n) = m, the theory T proves F(n, m), and usually (although not needed) that T proves Ax (F(n,x) - x = m). Here you will represent the function f(x) = x*2 by the formula F(x, y) : y = x*2. Depending on your theory the proof of the true formula F(n, m) will be tedious or not. For example F(2, 1) is s(s(0)) = s(0) * s(s(0), and you need a theory having at least logic + equality rules, and the axioms 1) x * 0 = 0 2) x* s(y) = x * y + x 3) x + 0 = 0 4) x + s(y) = s(x + y) I let you prove that s(s(0)) = s(0) * s(s(0) from those axioms (using the usual axiom for egality). s(0) * s(s(0)) = s(0) *s(0) + s(0) By axiom 2 with x = s(0) and y = s(0) s(0) *s(0) + s(0) = s(s(0) + 0) By axiom 4 with x = s(0) *s(0) and y = 0 s(s(0) + 0) = s(s(0)) By substitution of identical (logic + equality rules) s(0) * s(s(0)) = s(s(0)) Transitivity of equality (logic + equality rules) s(s(0)) = s(0) * s(s(0)) equality rule (x = y - y = x) And this is F(2, 1), together with its proof. Not very tedious, but F(2010, 1005) would be much more tedious! Note that from this we can also deduce the existential sentence ExF(x, 1), a typical sigma_1 sentence. Or do the relations imposed by addition and multiplication somehow create functions/machines? You can say so but you need logic. Not just in the (meta) background, but made explicit in the axiom of the theory, or the program of the machine (theorem prover). Thanks, You are welcome. Such questions help to see where the difficulties remain. Keep asking if anything is unclear. Thanks again, things are becoming a little more clear for me. My background is in computer science, in case that applies and helps in writing an explanation for my question above. The nice thing is that a function is partial recursive (programmable) if an only if it is representable in a Sigma_1 complete theory. A sigma_1 complete theory is a theory capable of proving all the true sentences equivalent with ExP(x) with P decidable. In particular the theory above (with some more axioms like s(x) = s(y) - x = y, ..) is Sigma_1 complete, and thus Turing universal. All computable functions can be represented in that theory, and all computations can be represented as a proof of a Sigma_1 sentence like above. To show that such a weak theory is Sigma_1 complete is actually long and not so easy. But then, to prove that the game of life is turing universal is rather long also. For weak system, such proof asks for some machine language programming, and the meticulous verification that everything works well. Always tedious, and there are some subtle points. It is well done in the book by Epstein and Carnielli, or Boolos, Burgess and Jeffrey. Here is another very short Turing universal theory (a purely equational logic-free theory!) : ((K x) y) = x (((S x) y) z) = ((x z)(y z)) (x = x) (x = y) == (y = x) (x = y) ; (y = z) === (x = z) (x = y) === ((x z) = (y z)) (x = y) === ((z x) = (z y)) === is informal deduction, and ; is the informal and. You may look at my paper Theoretical computer science and the natural sciences for more on this theory, and its probable importance in deriving the shape of physics from numbers. http://www.sciencedirect.com/science?_ob=ArticleURL_udi=B75DC-4GX6J4... Hmm... It is 32 $ ... You may look at my older posts on the combinators (Smullyan's
Re: Definition of universe
On 05 Feb 2010, at 13:13, ronaldheld wrote: Bruno: is there a free version of Theoretical computer science and the natural sciences? I have still many preprints. People interested can send me their addresses out of line. Oops! I just see the axiom 3) below is not correct. Please replace x + 0 = 0 (which says that if you add nothing in your bank account, you make it empty!), by x + 0 = x (which says that if you add nothing to your bank account then it remains the same). I hope everyone agree with this major change in the axiom 3) :) Bruno I guess you ask: how is the existence of a computable function proved to exist in a theory T. Usually logicians use the notion of representability. The one variable function f(x) is said to be representable in the theory T, if there is a formula F(x, y) such that when f(n) = m, the theory T proves F(n, m), and usually (although not needed) that T proves Ax (F(n,x) - x = m). Here you will represent the function f(x) = x*2 by the formula F(x, y) : y = x*2. Depending on your theory the proof of the true formula F(n, m) will be tedious or not. For example F(2, 1) is s(s(0)) = s(0) * s(s(0), and you need a theory having at least logic + equality rules, and the axioms 1) x * 0 = 0 2) x* s(y) = x * y + x 3) x + 0 = 0 4) x + s(y) = s(x + y) I let you prove that s(s(0)) = s(0) * s(s(0) from those axioms (using the usual axiom for egality). s(0) * s(s(0)) = s(0) *s(0) + s(0)By axiom 2 with x = s(0) and y = s(0) s(0) *s(0) + s(0) = s(s(0) + 0)By axiom 4 with x = s(0) *s(0) and y = 0 s(s(0) + 0) = s(s(0)) By substitution of identical (logic + equality rules) s(0) * s(s(0)) = s(s(0)) Transitivity of equality (logic + equality rules) s(s(0)) = s(0) * s(s(0)) equality rule (x = y - y = x) http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-l...@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: Definition of universe
On Wed, Feb 3, 2010 at 1:47 PM, Bruno Marchal marc...@ulb.ac.be wrote: On 03 Feb 2010, at 15:49, Jason Resch wrote: On Wed, Feb 3, 2010 at 3:14 AM, Bruno Marchal marc...@ulb.ac.be wrote: On 03 Feb 2010, at 03:00, Jason Resch wrote: Is your point that with addition, multiplication, and an infinite number of successive symbols, any computable function can be constructed? You can say so. You could also have said that with addition + multiplication *axioms* + * logic*, any computable function can be proved to exist. So I suppose that is what I was wondering, given at minimum, those, how is the existence of a computable function proved to exist? Could you provide an example of how a simple function, like f(x) = x*2 exists, or is it a very tedious proof? I guess you ask: how is the existence of a computable function proved to exist in a theory T. Usually logicians use the notion of representability. The one variable function f(x) is said to be representable in the theory T, if there is a formula F(x, y) such that when f(n) = m, the theory T proves F(n, m), and usually (although not needed) that T proves Ax (F(n,x) - x = m). Here you will represent the function f(x) = x*2 by the formula F(x, y) : y = x*2. Depending on your theory the proof of the true formula F(n, m) will be tedious or not. For example F(2, 1) is s(s(0)) = s(0) * s(s(0), and you need a theory having at least logic + equality rules, and the axioms 1) x * 0 = 0 2) x* s(y) = x * y + x 3) x + 0 = 0 4) x + s(y) = s(x + y) I let you prove that s(s(0)) = s(0) * s(s(0) from those axioms (using the usual axiom for egality). s(0) * s(s(0)) = s(0) *s(0) + s(0)By axiom 2 with x = s(0) and y = s(0) s(0) *s(0) + s(0) = s(s(0) + 0)By axiom 4 with x = s(0) *s(0) and y = 0 s(s(0) + 0) = s(s(0)) By substitution of identical (logic + equality rules) s(0) * s(s(0)) = s(s(0)) Transitivity of equality (logic + equality rules) s(s(0)) = s(0) * s(s(0)) equality rule (x = y - y = x) And this is F(2, 1), together with its proof. Not very tedious, but F(2010, 1005) would be much more tedious! Note that from this we can also deduce the existential sentence ExF(x, 1), a typical sigma_1 sentence. Or do the relations imposed by addition and multiplication somehow create functions/machines? You can say so but you need logic. Not just in the (meta) background, but made explicit in the axiom of the theory, or the program of the machine (theorem prover). Thanks, You are welcome. Such questions help to see where the difficulties remain. Keep asking if anything is unclear. Thanks again, things are becoming a little more clear for me. My background is in computer science, in case that applies and helps in writing an explanation for my question above. The nice thing is that a function is partial recursive (programmable) if an only if it is representable in a Sigma_1 complete theory. A sigma_1 complete theory is a theory capable of proving all the true sentences equivalent with ExP(x) with P decidable. In particular the theory above (with some more axioms like s(x) = s(y) - x = y, ..) is Sigma_1 complete, and thus Turing universal. All computable functions can be represented in that theory, and all computations can be represented as a proof of a Sigma_1 sentence like above. To show that such a weak theory is Sigma_1 complete is actually long and not so easy. But then, to prove that the game of life is turing universal is rather long also. For weak system, such proof asks for some machine language programming, and the meticulous verification that everything works well. Always tedious, and there are some subtle points. It is well done in the book by Epstein and Carnielli, or Boolos, Burgess and Jeffrey. Here is another very short Turing universal theory (a purely equational logic-free theory!) : ((K x) y) = x (((S x) y) z) = ((x z)(y z)) (x = x) (x = y) == (y = x) (x = y) ; (y = z) === (x = z) (x = y) === ((x z) = (y z)) (x = y) === ((z x) = (z y)) === is informal deduction, and ; is the informal and. You may look at my paper Theoretical computer science and the natural sciences for more on this theory, and its probable importance in deriving the shape of physics from numbers. http://www.sciencedirect.com/science?_ob=ArticleURL_udi=B75DC-4GX6J45-1_user=532047_coverDate=12%2F31%2F2005_rdoc=1_fmt=_orig=search_sort=dview=c_acct=C26678_version=1_urlVersion=0_userid=532047md5=e087a268f1a31acd7cd9ef629e6dc543 Hmm... It is 32 $ ... You may look at my older posts on the combinators (Smullyan's birds!). It is not important, I wanted just to show you another example. Bruno http://iridia.ulb.ac.be/~marchal/ So then it seems the integers, addition, and multiplication (plus some logic) are the minimum axioms needed to represent and prove
Re: Definition of universe
On 04 Feb 2010, at 15:28, Jason Resch wrote: On Wed, Feb 3, 2010 at 1:47 PM, Bruno Marchal marc...@ulb.ac.be wrote: On 03 Feb 2010, at 15:49, Jason Resch wrote: On Wed, Feb 3, 2010 at 3:14 AM, Bruno Marchal marc...@ulb.ac.be wrote: On 03 Feb 2010, at 03:00, Jason Resch wrote: Is your point that with addition, multiplication, and an infinite number of successive symbols, any computable function can be constructed? You can say so. You could also have said that with addition + multiplication axioms + logic, any computable function can be proved to exist. So I suppose that is what I was wondering, given at minimum, those, how is the existence of a computable function proved to exist? Could you provide an example of how a simple function, like f(x) = x*2 exists, or is it a very tedious proof? I guess you ask: how is the existence of a computable function proved to exist in a theory T. Usually logicians use the notion of representability. The one variable function f(x) is said to be representable in the theory T, if there is a formula F(x, y) such that when f(n) = m, the theory T proves F(n, m), and usually (although not needed) that T proves Ax (F(n,x) - x = m). Here you will represent the function f(x) = x*2 by the formula F(x, y) : y = x*2. Depending on your theory the proof of the true formula F(n, m) will be tedious or not. For example F(2, 1) is s(s(0)) = s(0) * s(s(0), and you need a theory having at least logic + equality rules, and the axioms 1) x * 0 = 0 2) x* s(y) = x * y + x 3) x + 0 = 0 4) x + s(y) = s(x + y) I let you prove that s(s(0)) = s(0) * s(s(0) from those axioms (using the usual axiom for egality). s(0) * s(s(0)) = s(0) *s(0) + s(0)By axiom 2 with x = s(0) and y = s(0) s(0) *s(0) + s(0) = s(s(0) + 0)By axiom 4 with x = s(0) *s(0) and y = 0 s(s(0) + 0) = s(s(0)) By substitution of identical (logic + equality rules) s(0) * s(s(0)) = s(s(0)) Transitivity of equality (logic + equality rules) s(s(0)) = s(0) * s(s(0)) equality rule (x = y - y = x) And this is F(2, 1), together with its proof. Not very tedious, but F(2010, 1005) would be much more tedious! Note that from this we can also deduce the existential sentence ExF(x, 1), a typical sigma_1 sentence. Or do the relations imposed by addition and multiplication somehow create functions/machines? You can say so but you need logic. Not just in the (meta) background, but made explicit in the axiom of the theory, or the program of the machine (theorem prover). Thanks, You are welcome. Such questions help to see where the difficulties remain. Keep asking if anything is unclear. Thanks again, things are becoming a little more clear for me. My background is in computer science, in case that applies and helps in writing an explanation for my question above. The nice thing is that a function is partial recursive (programmable) if an only if it is representable in a Sigma_1 complete theory. A sigma_1 complete theory is a theory capable of proving all the true sentences equivalent with ExP(x) with P decidable. In particular the theory above (with some more axioms like s(x) = s(y) - x = y, ..) is Sigma_1 complete, and thus Turing universal. All computable functions can be represented in that theory, and all computations can be represented as a proof of a Sigma_1 sentence like above. To show that such a weak theory is Sigma_1 complete is actually long and not so easy. But then, to prove that the game of life is turing universal is rather long also. For weak system, such proof asks for some machine language programming, and the meticulous verification that everything works well. Always tedious, and there are some subtle points. It is well done in the book by Epstein and Carnielli, or Boolos, Burgess and Jeffrey. Here is another very short Turing universal theory (a purely equational logic-free theory!) : ((K x) y) = x (((S x) y) z) = ((x z)(y z)) (x = x) (x = y) == (y = x) (x = y) ; (y = z) === (x = z) (x = y) === ((x z) = (y z)) (x = y) === ((z x) = (z y)) === is informal deduction, and ; is the informal and. You may look at my paper Theoretical computer science and the natural sciences for more on this theory, and its probable importance in deriving the shape of physics from numbers. http://www.sciencedirect.com/science?_ob=ArticleURL_udi=B75DC-4GX6J45-1_user=532047_coverDate=12%2F31%2F2005_rdoc=1_fmt=_orig=search_sort=dview=c_acct=C26678_version=1_urlVersion=0_userid=532047md5=e087a268f1a31acd7cd9ef629e6dc543 Hmm... It is 32 $ ... You may look at my older posts on the combinators (Smullyan's birds!). It is not important, I wanted just to show you another example. Bruno http://iridia.ulb.ac.be/~marchal/ So then it seems the integers, addition, and
Re: Definition of universe
On 03 Feb 2010, at 03:00, Jason Resch wrote:
On Thu, Dec 31, 2009 at 12:38 PM, Bruno Marchal marc...@ulb.ac.be
wrote:
UDA = Universal Dovetailer Argument. It is an argument which is
supposed to show that if we take seriously the idea that we are
digitally emulable, then we have to take seriously the idea that
physics is a branch of number theory. Intensional number theory
(number can serves as code for other numbers and functions: it is
theoretical computer science, also).
Bruno, when you say code here, you are referring to code as in
programming code, correct? I understand how a number can function
as code for a function or a machine, but how can a number be code
for another number?
Consider the first order arithmetic language in which the number 2 is
denoted by s(s(0)). Now s(s(0)) is itself a string, and when we
translate meta-arithmetic in arithmetic (like Gödel) that string will
be represented by some number like
2^'s' * 3^'(' * 5^'s' * 7^'0' * 11^')' * 13^')'
(Using some Gödel numbering). Then you can consider the function which
send a number on its Gödel number. In this case it is more a cipher
which is coded than a number per se (OK).
More simply a listing of telephone numbers. Each number entry of the
listing can code a phone number.
If you represent number by operator, like it is done with the
combinators (where Church codes number n by the operator which
iterates n times the input operator: [n(f)](x) =
f(f(f(f(f(f ...f(x) n times. In that case number coding those
operator will be code for the number represented by the operator.
Code, or index, program, machine are naturally defined by the phi_i,
where i is the code of phi_i.
But I agree that coding number by number is not a good pedagogical
idea. My idea was to remind that number can code anything capable of
being described in a finite way like (partial) computable functions,
and ... numbers.
You've said many times that all it takes for everything we see to
exist are the natural numbers, addition and multiplication,
to exist in the sense of being apparent to us, not necessarily in
the first order sense of existing, although we can collapse some form
of existence through coding.
For example, a finite piece of computation is an abstract object. But
to give you an example of finite piece of computation, I will have to
describe it by some finite object. But such a finite object should not
be confused with the computation, even if it happens that we have, in
that case (of finite piece of computations):
It exist a finite piece of computation going from state A to state B
if and only if it exist a number coding that finite piece of
computation.
This probably explains the confusion between computations and
description of computation.
In step 8, it is important to understand that a movie of a computation
is not a computation, but a description of a computation.
but where/how do functions and machines enter in to the picture? It
is clear to me how once we get to the objective existence of
functions,
... of computable functions. (Not all functions, unless we talk with a
set theoretical Löbian machine like ZF).
we get the UDA, but I think I am missing some step.
It is nice you are aware of that. Keep hope, I have still to continue
the seventh step serie. I am a bit stuck on how to explain the
confusion mentioned above (between computation and description of
computation, or even between number and description of number). It is
a key for both the seven and the eight step.
Is your point that with addition, multiplication, and an infinite
number of successive symbols, any computable function can be
constructed?
You can say so.
You could also have said that with addition + multiplication axioms +
logic, any computable function can be proved to exist.
Or do the relations imposed by addition and multiplication somehow
create functions/machines?
You can say so but you need logic. Not just in the (meta) background,
but made explicit in the axiom of the theory, or the program of the
machine (theorem prover).
Thanks,
You are welcome. Such questions help to see where the difficulties
remain. Keep asking if anything is unclear.
Bruno
http://iridia.ulb.ac.be/~marchal/
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Re: Definition of universe
On 03 Feb 2010, at 15:49, Jason Resch wrote: On Wed, Feb 3, 2010 at 3:14 AM, Bruno Marchal marc...@ulb.ac.be wrote: On 03 Feb 2010, at 03:00, Jason Resch wrote: Is your point that with addition, multiplication, and an infinite number of successive symbols, any computable function can be constructed? You can say so. You could also have said that with addition + multiplication axioms + logic, any computable function can be proved to exist. So I suppose that is what I was wondering, given at minimum, those, how is the existence of a computable function proved to exist? Could you provide an example of how a simple function, like f(x) = x*2 exists, or is it a very tedious proof? I guess you ask: how is the existence of a computable function proved to exist in a theory T. Usually logicians use the notion of representability. The one variable function f(x) is said to be representable in the theory T, if there is a formula F(x, y) such that when f(n) = m, the theory T proves F(n, m), and usually (although not needed) that T proves Ax (F(n,x) - x = m). Here you will represent the function f(x) = x*2 by the formula F(x, y) : y = x*2. Depending on your theory the proof of the true formula F(n, m) will be tedious or not. For example F(2, 1) is s(s(0)) = s(0) * s(s(0), and you need a theory having at least logic + equality rules, and the axioms 1) x * 0 = 0 2) x* s(y) = x * y + x 3) x + 0 = 0 4) x + s(y) = s(x + y) I let you prove that s(s(0)) = s(0) * s(s(0) from those axioms (using the usual axiom for egality). s(0) * s(s(0)) = s(0) *s(0) + s(0)By axiom 2 with x = s(0) and y = s(0) s(0) *s(0) + s(0) = s(s(0) + 0)By axiom 4 with x = s(0) *s(0) and y = 0 s(s(0) + 0) = s(s(0)) By substitution of identical (logic + equality rules) s(0) * s(s(0)) = s(s(0)) Transitivity of equality (logic + equality rules) s(s(0)) = s(0) * s(s(0)) equality rule (x = y - y = x) And this is F(2, 1), together with its proof. Not very tedious, but F(2010, 1005) would be much more tedious! Note that from this we can also deduce the existential sentence ExF(x, 1), a typical sigma_1 sentence. Or do the relations imposed by addition and multiplication somehow create functions/machines? You can say so but you need logic. Not just in the (meta) background, but made explicit in the axiom of the theory, or the program of the machine (theorem prover). Thanks, You are welcome. Such questions help to see where the difficulties remain. Keep asking if anything is unclear. Thanks again, things are becoming a little more clear for me. My background is in computer science, in case that applies and helps in writing an explanation for my question above. The nice thing is that a function is partial recursive (programmable) if an only if it is representable in a Sigma_1 complete theory. A sigma_1 complete theory is a theory capable of proving all the true sentences equivalent with ExP(x) with P decidable. In particular the theory above (with some more axioms like s(x) = s(y) - x = y, ..) is Sigma_1 complete, and thus Turing universal. All computable functions can be represented in that theory, and all computations can be represented as a proof of a Sigma_1 sentence like above. To show that such a weak theory is Sigma_1 complete is actually long and not so easy. But then, to prove that the game of life is turing universal is rather long also. For weak system, such proof asks for some machine language programming, and the meticulous verification that everything works well. Always tedious, and there are some subtle points. It is well done in the book by Epstein and Carnielli, or Boolos, Burgess and Jeffrey. Here is another very short Turing universal theory (a purely equational logic-free theory!) : ((K x) y) = x (((S x) y) z) = ((x z)(y z)) (x = x) (x = y) == (y = x) (x = y) ; (y = z) === (x = z) (x = y) === ((x z) = (y z)) (x = y) === ((z x) = (z y)) === is informal deduction, and ; is the informal and. You may look at my paper Theoretical computer science and the natural sciences for more on this theory, and its probable importance in deriving the shape of physics from numbers. http://www.sciencedirect.com/science?_ob=ArticleURL_udi=B75DC-4GX6J45-1_user=532047_coverDate=12%2F31%2F2005_rdoc=1_fmt=_orig=search_sort=dview=c_acct=C26678_version=1_urlVersion=0_userid=532047md5=e087a268f1a31acd7cd9ef629e6dc543 Hmm... It is 32 $ ... You may look at my older posts on the combinators (Smullyan's birds!). It is not important, I wanted just to show you another example. Bruno http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-l...@googlegroups.com. To
Re: Definition of universe
On Thu, Dec 31, 2009 at 12:38 PM, Bruno Marchal marc...@ulb.ac.be wrote: UDA = Universal Dovetailer Argument. It is an argument which is supposed to show that if we take seriously the idea that we are digitally emulable, then we have to take seriously the idea that physics is a branch of number theory. Intensional number theory (number can serves as code for other numbers and functions: it is theoretical computer science, also). Bruno, when you say code here, you are referring to code as in programming code, correct? I understand how a number can function as code for a function or a machine, but how can a number be code for another number? You've said many times that all it takes for everything we see to exist are the natural numbers, addition and multiplication, but where/how do functions and machines enter in to the picture? It is clear to me how once we get to the objective existence of functions, we get the UDA, but I think I am missing some step. Is your point that with addition, multiplication, and an infinite number of successive symbols, any computable function can be constructed? Or do the relations imposed by addition and multiplication somehow create functions/machines? Thanks, Jason -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-l...@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: Definition of universe
Bruno, thanks for the answer. What do you mean by universe? Do you mean, like many, the physical universe (or multiverse), or do you mean the ultimate basic reality (the third person everything)? By universe I mean what we call a universe when we talk about universes on this list, generally. By saying universes in plural in the same sentence, I mean not *the *ultimate basic reality. Inyuki http://www.universians.org -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-l...@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: Definition of universe
On 30 Dec 2009, at 17:39, John Mikes wrote: Bruno, I still wait for the reasoning of the 'primitive' in your: ...if this physical universe can be captured by a program (a number) or even by a mathematical structure. It is not a primitive structure. It has a reason linked to a statistics on computations.-... What primitive(?) structure serves the computation? The additive and multiplicative structure of the positive integers. This defines a canonical universal dovetailing, describing all the computations. But there is no reason a priori why a physical universe would be computable, or generated by the UD, because we are multiplied infinititely many times, and the results of that infinite multiplication this is not a priori computably generable. (Statistics is a nono for me: the choice of identification (exactly what definition of elements to pick) and of the domain-boundaries (what to include into our 'picking' territory) make the 'statistical results' arbitrary). I may have missed your explanation on that, when the question came up. Church thesis defines the domain of indeterminacy all the you* accessed by the UD. You are not aware of the number of steps made by the UD, and your indeterminacy is on an infinite set. And: where do you take the 'mechanism' FROM, if you consider the numbers primitive? From addition and mulitiplication. It is not so easy to show that, but it is more long and tedious, than conceptually difficult. Does your parenthesis (above) mean that a number is a program? With respect to the choice of a phi_i or of a universal machine or language (like arithmetic, comobinator, java,n c++, etc.). I assume you mean the very long number (with their mathematical structure?) to express anything - being considerable like a program, but do you indeed mean it that way? Not to express anything. Only the expressible things, by machines. Also the mathematical alteration of the numbers bothers me: if addition, etc. are included, why not express just the final number? - It is too long anyway, so it is a thought-experiment at best. Because universal machine can also search for a number having some property (always defined by addition and multiplication), sometimes such a search can not stop, and we never know some final number. By church thesis some computable function are undefined, and tha machine computing them does not stop, and nobody can infer from the structure of the machine if it will stop or not. Is such an unexpectably long number more understandable than a semanic meaning? It may be, if you mean understandable by some universal machine. Even this very post will be translated into a long number before your computer interpret it, for you, as a electronic mail. Granted, it is not easy to 'manipulate' semantic meanings, but with a better computing (e.g. fully analogue) it is imaginable, (an analogue mechanism) - maybe more so than a number-substitute (oops: the other way around: the analog meaning expression substituting for the (primitive?) number-based expression). May be. But analogue machine knows today are Turing emulable, or does not compute anything, but one phenomenon. If they use all the digits of real number in actual time, then we are no more in the digital (comp) theory. No problem. I asked earlier, but the response did not make me wiser: is there a place where I could read a (not more than a short paragraph-long) identification for UD(A) and AUDA? The texts that appeared are too long for my limited capabilites. UDA = Universal Dovetailer Argument. It is an argument which is supposed to show that if we take seriously the idea that we are digitally emulable, then we have to take seriously the idea that physics is a branch of number theory. Intensional number theory (number can serves as code for other numbers and functions: it is theoretical computer science, also). AUDA = Arithmetical UDA. Instead of asking humans, I ask universal machine, or the Peano Arithmetic machine. It is the Escherichia Coli of the self-referentially correct (Löbian) machine. Happy New Year (I will try to be smarter in 2010). Happy New Year, Bruno On Wed, Dec 30, 2009 at 10:59 AM, Bruno Marchal marc...@ulb.ac.be wrote: Hi Mindey, On 29 Dec 2009, at 15:07, Mindey wrote: I was just wondering, we are talking so much about universes, but how do we define universe? Sorry if that question was answered somewhere, but after a quick search I didn't find it. What do you mean by universe? Do you mean, like many, the physical universe (or multiverse), or do you mean the ultimate basic reality (the third person everything)? I think that if we assume mechanism, then it is absolutely undecidable if there is anything more than positive integers + addition and multiplication. Ontologically, if you want. All the rest belongs to
Re: Definition of universe
Hi Mindey, On 29 Dec 2009, at 15:07, Mindey wrote: I was just wondering, we are talking so much about universes, but how do we define universe? Sorry if that question was answered somewhere, but after a quick search I didn't find it. What do you mean by universe? Do you mean, like many, the physical universe (or multiverse), or do you mean the ultimate basic reality (the third person everything)? I think that if we assume mechanism, then it is absolutely undecidable if there is anything more than positive integers + addition and multiplication. Ontologically, if you want. All the rest belongs to the epistemology of numbers, or, put it differently, of the inside views of arithmetic. The physical universe becomes the sharable (first person plural) ignorance of the universal numbers. It is an open question if this physical universe can be captured by a program (a number) or even by a mathematical structure. It is not a primitive structure. It has a reason linked to a statistics on computations. Matter is sort of derivative of the (machine's) mind. Cf the UDA reasoning, if you have followed. There is a Skolem like paradox. Arithmetic, from outside, is infinite, but it is a relatively small and simple mathematical structure. Yet, as seen from inside, it escapes the whole of mathematics, because it looks *very* big for inside. So big that such a bigness is not even nameable by any of the creatures which live there. There is a need of some amount of mathematical logic and computer science to give sense on all this. Especially for expression like as seen from inside, etc. Bruno Marchal http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-l...@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: Definition of universe
Bruno,* * I still wait for the reasoning of the 'primitive' in your: *...if this physical universe can be captured by a program (a number) or even by a mathematical structure. It is not a primitive structure. It has a reason linked to a statistics on computations.-...* What primitive(?) structure serves the *computation*? (Statistics is a nono for me: the choice of identification (exactly what definition of elements to pick) and of the domain-boundaries (what to include into our 'picking' territory) make the 'statistical results' arbitrary). I may have missed your explanation on that, when the question came up. And: where do you take the 'mechanism' FROM, if you consider the numbers * primitive*? Does your parenthesis (above) mean that a number is a program? I assume you mean the very long number (with their mathematical structure?) to *express anything* - being considerable like a program, but do you indeed mean it that way? Also the mathematical alteration of the numbers bothers me: if addition, etc. are included, why not express just the final number? - It is too long anyway, so it is a thought-experiment at best. Is such an unexpectably long number more understandable than a semanic meaning? Granted, it is not easy to 'manipulate' semantic meanings, but with a better computing (e.g. *fully analogue*) it is imaginable, (*an analogue mechanism*) - maybe more so than a number-substitute (oops: the other way around: the analog meaning expression substituting for the (primitive?) number-based expression). I asked earlier, but the response did not make me wiser: is there a place where I could read a (not more than a short paragraph-long) identification for UD(A) and AUDA? The texts that appeared are too long for my limited capabilites. Happy New Year (I will try to be smarter in 2010). John Mikes On Wed, Dec 30, 2009 at 10:59 AM, Bruno Marchal marc...@ulb.ac.be wrote: Hi Mindey, On 29 Dec 2009, at 15:07, Mindey wrote: I was just wondering, we are talking so much about universes, but how do we define universe? Sorry if that question was answered somewhere, but after a quick search I didn't find it. What do you mean by universe? Do you mean, like many, the physical universe (or multiverse), or do you mean the ultimate basic reality (the third person everything)? I think that if we assume mechanism, then it is absolutely undecidable if there is anything more than positive integers + addition and multiplication. Ontologically, if you want. All the rest belongs to the epistemology of numbers, or, put it differently, of the inside views of arithmetic. The physical universe becomes the sharable (first person plural) ignorance of the universal numbers. It is an open question if this physical universe can be captured by a program (a number) or even by a mathematical structure. It is not a primitive structure. It has a reason linked to a statistics on computations. Matter is sort of derivative of the (machine's) mind. Cf the UDA reasoning, if you have followed. There is a Skolem like paradox. Arithmetic, from outside, is infinite, but it is a relatively small and simple mathematical structure. Yet, as seen from inside, it escapes the whole of mathematics, because it looks *very* big for inside. So big that such a bigness is not even nameable by any of the creatures which live there. There is a need of some amount of mathematical logic and computer science to give sense on all this. Especially for expression like as seen from inside, etc. Bruno Marchal http://iridia.ulb.ac.be/~marchal/ -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-l...@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.comeverything-list%2bunsubscr...@googlegroups.com . For more options, visit this group at http://groups.google.com/group/everything-list?hl=en. -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-l...@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Definition of universe
Hello, I was just wondering, we are talking so much about universes, but how do we define universe? Sorry if that question was answered somewhere, but after a quick search I didn't find it. Inyuki http://www.universians.org -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-l...@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: Definition of universe
Mindey, I hurry to reply before some smarter guys do so on this list, so here is MY opinion: I consider this OUR universe a part of the Multiverse (unknown, unknowable, but assumed) with its 'physical' (so far discovered!) built (similarly assumed) and described as (our) so called 'physical world' in (our) conventional sciences. I wrote a 'narrative' in 2000 (partly obsolete in my today's views) which is best findable in my Karl Jaspers Forum publication ( www.kjf.ca look up TA-62 - Networks-2003 under [A4] - ) which contains my assumptions, not agreeable to the topics on most of this list. It outlines a view about (our and other) universes in a not-so-scientific manner. Good luck to it and to other views John Mikes On Tue, Dec 29, 2009 at 9:07 AM, Mindey min...@gmail.com wrote: Hello, I was just wondering, we are talking so much about universes, but how do we define universe? Sorry if that question was answered somewhere, but after a quick search I didn't find it. Inyuki http://www.universians.org -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-l...@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.comeverything-list%2bunsubscr...@googlegroups.com . For more options, visit this group at http://groups.google.com/group/everything-list?hl=en. -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-l...@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: Definition of universe
On Wed, Dec 30, 2009 at 1:07 AM, Mindey min...@gmail.com wrote: Hello, I was just wondering, we are talking so much about universes, but how do we define universe? Sorry if that question was answered somewhere, but after a quick search I didn't find it. To me it would be that which is contained when you specify a number of dimensions. 2d? The universe can be a piece of paper. Inyuki http://www.universians.org -- -- silky http://www.mirios.com.au/ http://island.mirios.com.au/t/rigby+random+20 drape experimentation COLDBLOODED, verisimilitude: fragment-mum gloriously? CONTRACTOR prickl... -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-l...@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
Re: Definition of universe
To me it would be that which is contained when you specify a number of dimensions. 2d? The universe can be a piece of paper. But that implies that dimensionality is a fundamental property of reality. It is conceivable that dimensionality is not fundamental, but rather emergent. -- You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to everything-l...@googlegroups.com. To unsubscribe from this group, send email to everything-list+unsubscr...@googlegroups.com. For more options, visit this group at http://groups.google.com/group/everything-list?hl=en.
