RE: Re: The number 8. A TOE?
Ben Goertzel <[EMAIL PROTECTED]> wrote: >> BG: You seem to be making points about the limitations >> >of the folk-psychology notion of identity, rather than about the actual >> >nature of the universe... >> >> >> BM: Then you should disagree at some point of the reasoning, for the >> reasoning is intended, at least, to show that it follows from >> the computationalist hypothesis, that physics is a subbranch of >> (machine) psychology, and that the actual nature of the universe >> can and must be recovered by machine psychology. > >BG; I tend to think that "physics" and "machine psychology" are limiting terms >that will be thrown off within future science, in favor of a more unified >perspective. Sure, but before having that future science we must use some terms. As I said in the first UDA posting http://www.escribe.com/science/theory/m1726.html, it is really the proof that "physics is a branch of psychology" which provides the explanation of such terms. Basically machine psychology is given by all true propositions that machine or collection of machine can prove or bet about themselves. Eventually it is given by the Godel Lob logic of provability with their modal variants. I take the fact that a consistent machine cannot prove its own consistency as a psychological theorem. Consciousness can then be approximated by the unconscious (automated, instinctive) anticipation of self-consistency. >Perhaps, from this more unified perspective, a better approximation will be >to say that "physics" and "machine psychology" are subsets of each other >(perhaps formally, in the sense of hypersets, non-foundational set theory, >who knows...) Perhaps. I guess a sort of adjunction, or a Chu transform? I don't know. > > >> Physics is taken as what is invariant in all possible (consistent) >> anticipation by (enough rich) machine, and this from the point of >> view of the machines. If arithmetic was complete, we would get >> just propositional calculus. But arithmetic is incomplete. >> This introduces nuances between proof, truth, consistency, etc. >> The technical part of the thesis shows that the invariant propositions >> about their probable neighborhoods (for >> possible anticipating machines) structure themtselves into a sort >> of quantum logic accompagned by some renormalization problem (which >> could be fatal for comp (making comp popperian-falsifiable)). >> This follows from the nuances which are made necessary by the >> Godel's incompleteness theorems, but also Lob and Solovay >> fundamental generalization of it. But it's better grasping first >> the UDA before tackling the AUDA, which is "just" the translation >> of the UDA in the language of a "Lobian" machine. > >Could you point me to a formal presentation of AUDA, if one exists? >I have a math PhD and can follow formal arguments better than verbal >renditions of them sometimes... You can click on "proof of LASE" in my web page, and on Modal Logic if you need. The technical part of my thesis relies on the work of Godel, Lob, Solovay, Goldblatt, Boolos, Visser. Precise references are in my thesis (downloadable, but written in french). You can also look at the paper "Computation, Consciousness and the Quantum". When I will have more time I can provide more explanations. Let me insist that that technics makes much more sense once you get the more informal, but nevertheless rigorous, UDA argument. Regards, Bruno
RE: RE: Re: The number 8. A TOE?
> You seem to be making points about the limitations > >of the folk-psychology notion of identity, rather than about the actual > >nature of the universe... > > > Then you should disagree at some point of the reasoning, for the > reasoning is intended, at least, to show that it follows from > the computationalist hypothesis, that physics is a subbranch of > (machine) psychology, and that the actual nature of the universe > can and must be recovered by machine psychology. I tend to think that "physics" and "machine psychology" are limiting terms that will be thrown off within future science, in favor of a more unified perspective. Perhaps, from this more unified perspective, a better approximation will be to say that "physics" and "machine psychology" are subsets of each other (perhaps formally, in the sense of hypersets, non-foundational set theory, who knows...) > Physics is taken as what is invariant in all possible (consistent) > anticipation by (enough rich) machine, and this from the point of > view of the machines. If arithmetic was complete, we would get > just propositional calculus. But arithmetic is incomplete. > This introduces nuances between proof, truth, consistency, etc. > The technical part of the thesis shows that the invariant propositions > about their probable neighborhoods (for > possible anticipating machines) structure themtselves into a sort > of quantum logic accompagned by some renormalization problem (which > could be fatal for comp (making comp popperian-falsifiable)). > This follows from the nuances which are made necessary by the > Godel's incompleteness theorems, but also Lob and Solovay > fundamental generalization of it. But it's better grasping first > the UDA before tackling the AUDA, which is "just" the translation > of the UDA in the language of a "Lobian" machine. Could you point me to a formal presentation of AUDA, if one exists? I have a math PhD and can follow formal arguments better than verbal renditions of them sometimes... thanks Ben G
RE: Re: The number 8. A TOE?
> See my web page for links to papers, and archive addresses with > more explanations, including the basic results of my thesis. > (Mainly the Universal Dovetailer Argument UDA and its Arithmetical > version AUDA). I read your argument for the UDA, and there's nothing there that particularly worries me. You seem to be making points about the limitations of the folk-psychology notion of identity, rather than about the actual nature of the universe... > >When you say "sum over all computational histories", what if we > just fix a > >bound N, and then say "sum over all computational histories of > algorithmic > >info. content <= N." Finite-information-content-universe, no Godel > >problems. So what's the issue? > > The main reason is that, once we postulate that we are turing emulable, > (i.e. the computationalist hypothesis comp), then there is a form > of indeterminacy which occurs and which force us to take into account the > incompleteness phenomenon. ?? I'm sorry, but I don't get it. Could you please elaborate? thanks Ben
RE: Re: The number 8. A TOE?
Ben Goertzel wrote: >Bruno wrote: >*** > Let me insist because some people seem not yet grasping >fully that idea. >In fact that 1/3-distinction makes COMP incompatible with >the thesis that the universe is a machine. If I am a machine then >the universe cannot be a machine. No machine can simulate the >comp first person indeterminacy. This shows that the >Wolfram-Petrov-Suze-... thesis is just inconsistent. If the universe >is a (digital) machine then there is level of description of myself >such that I am a machine (= I am turing-emulable, = comp), but then >my most probable neighborhood is given by a sum over all >computational histories going through my possible states, and by >godel (but see also the thought experiments) that leads to extract >the probable neighborhood from a non computable domain, in a >non computable way. In short WOLFRAM implies COMP, but COMP >implies NOT WOLFRAM(*). So WOLFRAM implies NOT WOLFRAM, so NOT WOLFRAM. >Eventually physics will be reduced into machine's machine >psychology. If octonion play a fundamental role in physics, >it means, with comp, that octonions will play a fundamental role >in psychology. >*** > >Unfortunately, I do not follow your argument in spite of some significant >effort. See my web page for links to papers, and archive addresses with more explanations, including the basic results of my thesis. (Mainly the Universal Dovetailer Argument UDA and its Arithmetical version AUDA). >When you say "sum over all computational histories", what if we just fix a >bound N, and then say "sum over all computational histories of algorithmic >info. content <= N." Finite-information-content-universe, no Godel >problems. So what's the issue? The main reason is that, once we postulate that we are turing emulable, (i.e. the computationalist hypothesis comp), then there is a form of indeterminacy which occurs and which force us to take into account the incompleteness phenomenon. Godel is not a problem. It is really Godel's incompleteness which makes comp, including the Church thesis, consistent. (Judson Webb wrote a book on that theme in 1980 " Finitism, mentalism and metamathematics, my work considerably developpes such type of reflexion). >I'll address this in a later post, unfortunately I have to catch a plane and >don't have time at the moment Thanks. I look forward to it. Take your time. I'm also very busy. Bruno
RE: Re: The number 8. A TOE?
Hal Finney wrote: >Bruno Marchal writes: >> Methodologically your ON theory suffers (at first sight)the same >> problem as Wolfram, or Schmidhuber's approaches. The problem consists in >> failing to realise the fact that if we are turing-emulable, then >> the association between mind-dynamics and matter-dynamics cannot be >> one-one. You can still attach a mind to the appearance of a >> machine, but you cannot attach a machine to the appearance of a >> mind, you can only attach an infinity of machines, and histories, >> to the appearance of a mind. > >I think what you are saying is that if a mind can be implemented by more >than one machine, there is first-person indeterminacy about which >machine is immplementing it. Yes. >However, wouldn't it still be the case that to the extent that the mind >can look out and see the machine, learn about the machine and its rules, >that it will still find only a unique answer? There would be a subjective >"split" similar to the MWI splits. For all possible observations in a >given experiment to learn the natural laws of the universe/machine that >was running the mind, the mind will split into subsets that observe each >possible result. Yes. >So it is still possible to make progress on the question of the nature of >the machine that is the universe, just as you can make progress on any >other observational question, right? Almost right. We can make progress on the question of the nature of the average machine that is the average "universe" (computational history) which defined our most probable neighborhood. >Also, isn't it possible that, once enough observations have been made, >there is essentially only one answer to the question about what this >machine is like? Just as there will often be only one answer to any >other factual question? Only if you observe yourself above your level of substitution. Below that level, repeated observations should give you trace of the comp indeterminacy. Like in QM. For example, you will discover that precise position of some of your particles are undefined. Below the level of substitution the statistics will be non classical for they must take into account our inability to distinguish the computational histories. >Of course, it's always possible that the machine is itself being emulated >by another machine, since one computer can emulate another. But we could >still at least say that the observed laws of physics correspond to a >particular computer program which could be most naturally implemented on a >particular architecture. I don't think that that could be the case. It could only be an approximation. Below the level of substitution we must find a sort of vagueness related to our incapacity to distinguish one computation from the many others which are possible. With comp the laws of physics must emerge from that average. You are coherent because this follows from the UDA part which you admittedly have still some problem with. cf: http://www.escribe.com/science/theory/m3817.html A little "TOE-program" is still possible, but then it must be extracted from that average---in fact it must run the definition of that average, in the case such a computational definition exists, and that is doubtful. But even if that was the case, that definition must be derived from that comp average. That's why I suspect a quantum universal dovetailer is still a possible candidate of our uni/multiverse. >We can never be sure that the universe machine >isn't sitting in someone's basement in a super-universe with totally >different laws of physics, but we can at least define the laws of physics >of our own universe, in terms of a computer program or mathematical model. I don't think so. We belong to an infinity of computational histories from which the (beliefs of the) laws of physics emerge, from which the appearance of "a universe" emerges too. "our universe" is a not well defined expression (provably so with the comp hyp). Bruno
RE: Re: The number 8. A TOE?
Bruno wrote: *** Let me insist because some people seem not yet grasping fully that idea. In fact that 1/3-distinction makes COMP incompatible with the thesis that the universe is a machine. If I am a machine then the universe cannot be a machine. No machine can simulate the comp first person indeterminacy. This shows that the Wolfram-Petrov-Suze-... thesis is just inconsistent. If the universe is a (digital) machine then there is level of description of myself such that I am a machine (= I am turing-emulable, = comp), but then my most probable neighborhood is given by a sum over all computational histories going through my possible states, and by godel (but see also the thought experiments) that leads to extract the probable neighborhood from a non computable domain, in a non computable way. In short WOLFRAM implies COMP, but COMP implies NOT WOLFRAM(*). So WOLFRAM implies NOT WOLFRAM, so NOT WOLFRAM. Eventually physics will be reduced into machine's machine psychology. If octonion play a fundamental role in physics, it means, with comp, that octonions will play a fundamental role in psychology. *** Unfortunately, I do not follow your argument in spite of some significant effort. When you say "sum over all computational histories", what if we just fix a bound N, and then say "sum over all computational histories of algorithmic info. content <= N." Finite-information-content-universe, no Godel problems. So what's the issue? *** And, dear Ben, I should still read how you link octonions and the "deep aspect", as you say, of the mind. BTW, I would be also glad if you could explain or give a rough idea how quaternions play a role in the mondane aspect of the mind, as you pretend in one of your paper, if you have the time. *** I'll address this in a later post, unfortunately I have to catch a plane and don't have time at the moment ben
RE: Re: The number 8. A TOE?
Bruno Marchal writes: > Methodologically your ON theory suffers (at first sight)the same > problem as Wolfram, or Schmidhuber's approaches. The problem consists in > failing to realise the fact that if we are turing-emulable, then > the association between mind-dynamics and matter-dynamics cannot be > one-one. You can still attach a mind to the appearance of a > machine, but you cannot attach a machine to the appearance of a > mind, you can only attach an infinity of machines, and histories, > to the appearance of a mind. I think what you are saying is that if a mind can be implemented by more than one machine, there is first-person indeterminacy about which machine is immplementing it. However, wouldn't it still be the case that to the extent that the mind can look out and see the machine, learn about the machine and its rules, that it will still find only a unique answer? There would be a subjective "split" similar to the MWI splits. For all possible observations in a given experiment to learn the natural laws of the universe/machine that was running the mind, the mind will split into subsets that observe each possible result. So it is still possible to make progress on the question of the nature of the machine that is the universe, just as you can make progress on any other observational question, right? Also, isn't it possible that, once enough observations have been made, there is essentially only one answer to the question about what this machine is like? Just as there will often be only one answer to any other factual question? Of course, it's always possible that the machine is itself being emulated by another machine, since one computer can emulate another. But we could still at least say that the observed laws of physics correspond to a particular computer program which could be most naturally implemented on a particular architecture. We can never be sure that the universe machine isn't sitting in someone's basement in a super-universe with totally different laws of physics, but we can at least define the laws of physics of our own universe, in terms of a computer program or mathematical model. Hal Finney
RE: Re: The number 8. A TOE?
Ben Goertzel wrote: >Regarding octonions, sedenions and physics >Tony Smith has a huge amount of pertinent ideas on his website, e.g. > >http://www.innerx.net/personal/tsmith/QOphys.html >http://www.innerx.net/personal/tsmith/d4d5e6hist.html > >His ideas are colorful and speculative, but also deep and interesting. >One could spend a very long time soaking up all the ideas on the site. >By the way, Tony is a very nice guy, who did a postdoc under Finkelstein (of >quantum set theory fame) and earns his living as a criminal-law attorney. Yes. It is hard not to cross Tony Smith's pages, or your own, when walking on the net with keyword like field, clifford, or ... octonions. Yet, until now I was less than convinced, and I was considering Smith and Smith-like colorful ideas as produced by to much attention to mathematical mermaids. Some papers by Baez, after my reading of Kauffman's book on knots changed my mind. This does not mean I am convinced, but only that I am open to the idea that such approaches could lead to the or one "right" TOE. In any case, my own approach gives *by construction* the right TOE, in the case if COMP is true. So if COMP is true, and if you or Tony (or Witten or Grothendieck ...) are correct, then we must meet. Or comp is false, or you are false. Methodologically your ON theory suffers (at first sight)the same problem as Wolfram, or Schmidhuber's approaches. The problem consists in failing to realise the fact that if we are turing-emulable, then the association between mind-dynamics and matter-dynamics cannot be one-one. You can still attach a mind to the appearance of a machine, but you cannot attach a machine to the appearance of a mind, you can only attach an infinity of machines, and histories, to the appearance of a mind. For a proof of this see http://www.escribe.com/science/theory/m1726.html Note that the shadows of this appears in your ON paper aswell when you talk of the many-universes, but you don't make the link with the first and third person distinction (or the endo-exo distinction with Rossler's vocabulary). With comp we cannot avoid that distinction. Let me insist because some people seem not yet grasping fully that idea. In fact that 1/3-distinction makes COMP incompatible with the thesis that the universe is a machine. If I am a machine then the universe cannot be a machine. No machine can simulate the comp first person indeterminacy. This shows that the Wolfram-Petrov-Suze-... thesis is just inconsistent. If the universe is a (digital) machine then there is level of description of myself such that I am a machine (= I am turing-emulable, = comp), but then my most probable neighborhood is given by a sum over all computational histories going through my possible states, and by godel (but see also the thought experiments) that leads to extract the probable neighborhood from a non computable domain, in a non computable way. In short WOLFRAM implies COMP, but COMP implies NOT WOLFRAM(*). So WOLFRAM implies NOT WOLFRAM, so NOT WOLFRAM. Eventually physics will be reduced into machine's machine psychology. If octonion play a fundamental role in physics, it means, with comp, that octonions will play a fundamental role in psychology. And, dear Ben, I should still read how you link octonions and the "deep aspect", as you say, of the mind. BTW, I would be also glad if you could explain or give a rough idea how quaternions play a role in the mondane aspect of the mind, as you pretend in one of your paper, if you have the time. Bruno (*) In the *best* case, comp could imply a QUANTUM-WOLFRAM.
RE: Re: The number 8. A TOE?
Regarding octonions, sedenions and physics Tony Smith has a huge amount of pertinent ideas on his website, e.g. http://www.innerx.net/personal/tsmith/QOphys.html http://www.innerx.net/personal/tsmith/d4d5e6hist.html His ideas are colorful and speculative, but also deep and interesting. One could spend a very long time soaking up all the ideas on the site. By the way, Tony is a very nice guy, who did a postdoc under Finkelstein (of quantum set theory fame) and earns his living as a criminal-law attorney. I spent some time a few years back trying to create a novel physics theory based on discrete Clifford algebras, which relate closely to quaternions and octonions. My effort was unfinished, and I turned my attention to other types of science, but some of my notes are at: http://www.goertzel.org/papers/main.htm (scroll to the bottom to see a list of documents under the heading "Some Incomplete Speculations on the Foundations of Physics" -- Ben Goertzel
