re:Re: All feedback appreciated - An introduction to Algebraic Physics
JamesTauber wrote: 1) the problem is theirs not ours vs 2) it is their problem not our problem So, if I understand well, our problems are ours, and their problems are theirs. Thanks for the teaching: I didn't dare to put a s on their, up to now, especially after a plural (but only contingently so if I can say). Semantically, I'm afraid theirs problems can be ours too, and our problems can be theirs too, by the Shit Spreading Principle ... or by the unicity of the first person ... Am I grammactically correct? Am I semantically correct? Am I politically correct? Am I self-referentially correct? :)? Bruno James (who happened to do his undergrad linguistics degree where Russell did his undergrad physics/maths) 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 [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
re:Computability and Measure
Günther Greindl wrote: Hi List, I found this: S. A. Terwijn, Computability and measure, PhD thesis, University of Amsterdam, 1998. Downloadable here: http://www.logic.at/people/terwijn/publications/thesis.pdf (I am currently attending his course, he is a very good teacher :-) Maybe of interest to the OM-measure/White Rabbit question? It is quite technical and still over my head I must admit, but maybe Bruno or some others can glean some interesting stuff from this work? Thanks Günther. This asks for some amount of work, though. They are already good measure theoretical idea in the Rogers book, but hard to use directly. It should be more easy for the ASSA people, unless some simple but still lacking idea, made it directly usable for the relative approach. Well, all this at first sight, and the thesis makes a clear and worth to read sum up of recursion theory. In the long run such works could pave a way, or play a role perhaps. Measure on RE sets? Interesting, but conditions are added so that proofs are made possible. Wanting to use such result to quickly can lead to conceptual obscurity. My mind is more problem driven, trying to clear conceptual issues before jumping to technics. This could only reflect my incompetence 'course ... Bruno --~--~-~--~~~---~--~~ You received this message because you are subscribed to the Google Groups Everything List group. To post to this group, send email to [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
re:Re: All feedback appreciated - An introduction to Algebraic Physics
Hello Günther, I have already presented an argument (an easy consequence of the Universal Dovetailer Argument, which is less easy probably) showing that: - CRH implies COMP - COMP implies the negation of CRH - Thus, with or without COMP (and with or without the MUH) the CRH does not hold. Regarding: COMP implies the negation of CRH Is this also in your Sane 2004 paper? (then I missed that point) - if not, where did you argue this? It is not in the Sane 2004 paper. I have argue that COMP imples NOT-CRH online, in reply to Schmidhuber or someone defending the idea that the universe could be the product of a computer program. Universality, Sigma_1 completeness, m-completness, creativity (in Post sense), all those equivalent notion makes sense only through complementary notion which are strictly sepaking more complex (non RE, productive, ...). The self-introspecting universal machine can hardly miss the inference of such realities, and once she distinguishes the 1, 1-plural, 3-person points of view, she has to bet on the role of the non computable realities (even too much getting not just randomness, like QM, but an hard to compute set of anomalous stories (white rabbits, coherent but inconsistent dreams). It's a bit like understanding (putting in a RE set) the (code of) the total computable functions, forces us to accept the existence of only partially computable functions, which sometimes (most of the time, see the thesis by Terwijn) have a non recursive domain. OK, the ontic part of a comp TOE can be no *more* than Sigma_1 complete, but a non self-computable part of Arithmetical truth and analytical truth, is needed to get the *internal* measure, we can't even give a name to our first person plenitude and things like that. The quantified angel guardian of a simple Lobian machine like PA, that is qG*, is itself Pi_1 in the Arithmetical Truth (see Boolos 1993 book). The God of PA (already unameable by PA) is already NOT omniscient about PA's intelligible reality, if you follow the arithmetical interpretation of Plotinus I did propose. Perhaps this is why the Intelligible has been discovered (Plato) before the ONE (Plotin). It is far bigger. With comp you can restrict the ontic to the Universal Machine (the baby ONE), but its intelligible realm is well beyond its grasp. All this is related to the fact, already understood by Judson Webb, that comp is truly a vaccine against reductionist theories of the mind. Have a good day, 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 [EMAIL PROTECTED] To unsubscribe from this group, send email to [EMAIL PROTECTED] For more options, visit this group at http://groups.google.com/group/everything-list?hl=en -~--~~~~--~~--~--~---
re:Re: QM not (yet, at least) needed to explain why we can't experience other minds
Dear Stephen, When you say: [...] We might not be able to know what it is like to be a bat but surely we could know what it is like to be an ameoba! It is amusing because I describe often---for exemple my thesis or http://www.escribe.com/science/theory/m3651.html--- my whole work as an attempt to know what it is like to be an amoeba. In my thesis I express myself exactly like that. I am thinking for sure to a self-dividing amoeba, and that's what has lead me to the comp indeterminacy. Frankly if you know what it does look like to be an amoeba, even in between self-divisions, you should try to describe it! Bruno, I am still not convinced that the statements that If we are consistent machine we cannot know which machine we are and Godel's and Lob's incompleteness prevent us to identify any intuitive first person knowledge with objective third person communicable statements mutes my question since it seems that it makes my predicament much worse! It seems that your idea prevents me from knowing what it is like to be a bat by not allowing me to have any 1-person certainty at all. I don't see why. You can still have a lot of 1-person certainties. It is just that 'knowing which machine you are' is not among them. But you can keep the 1-certainty that 1+1 = 2, or that there is no integers p and q such that p/q = sqrt(2), etc. You can *bet* that you are well defined at such or such level of description, but you cannot consistently assert you can prove being well-defined at those levels. (A non-computationalist just pretend that there are no such levels, not even the quantum one because the quantum level is emulable classicaly). All what follows from Godel in this setting is that you cannot consistently ascribe univocally a well defined machine to your 1-person experience. Once you bet on a level, you can ascribe to your experience an infinite vague sets of machines, though. Those machines are going through an infinite vague set of histories. I should have said perhaps that you cannot know *precisely* which machine you are. (Z1* should provide, by construction, the geometry of that vagueness). Best Regards, Bruno
re:Fw: Humour: Santa Claus Hypothesis Debunked
Tony Hollick forwarded us an argument by Chris Tame, casting doubt about the existence of Santa Claus (See below). This is hard to swallow especially before Christmas. I hardly resist the pleasure of giving you a straight proof of the existence of Santa Claus. Consider the following sentence S If this sentence is true then Santa Claus exists. or equivalently: If S is true then Santa Claus exists. S being that very sentence. I will first prove that S is true. To prove it, let us suppose that S is true. But then S is true and If S is true then Santa Claus exists is true. But then by the usual modus ponens it follows than Santa Claus exists. So I have proved that from assuming S true it follows that Santa Claus exists. But this is exactly what S says so I have given a proof of S. Now, we know that S is true. But S says exactly that if S is true then Santa Claus exists. So by applying modus ponens again, we can conclude that Santa Claus exists. QED. I hope this settles the matter once and for all ;-) Comment: this is a version of the well known Curry Paradox which plays a proeminent role in Lob proof of its generalisation of Godel's theorem. It is a version of Epimenide paradox which does not use negation. About both Epimenide or Curry paradox, most people considers that the paradox comes from the self-referential nature of the sentence. But since Godel we know that such self-reference can be construct in the language of a consistent machine or mathematical (sufficiently rich) theory. What cannot be done, and what really prevents the paradox in the world of consistent machines, is the fact that there is no translation of the word true (about the machine) *in* the language of the machine (this is Tarski theorem). If we use provable, which *can* be translated in the machine language, instead of true, well, from Epimenide we get Godel's incompleteness, and from the proof of the existence of Santa Claus, we get Lob's theorem. Lob's theorem asserts, among other things, that sentence asserting their own provability are automatically true and provable! Isn't it nice? Some positive thought seems to work in computerland! Merry Christmas, Bruno - Original Message - From: Dr Chris R. Tame [EMAIL PROTECTED] Sent: Wednesday, December 18, 2002 12:58 AM Subject: Humour: Santa Claus Hypothesis Debunked Ok lets get serious for a moment here I've assembled a few relevant facts here to set the story straight about jolly old St Nick. There are approximately two billion children (persons under 10) in the world. However, since Santa does not visit children of Muslim, Hindu, Jewish or Buddhist (except maybe in Japan) religions, this reduces the workload for Christmas night to 15% of the total, or 378 million (according to the population reference bureau). At an average (census) rate of 3.5 childrenper household, that comes to 108 million homes, presuming there is at least one good child in each. Santa has about 31 hours of Christmas to work with,thanks to the different time zones and the rotation of the earth, assuming east to west (which seems logical). This works out to 967.7 visits per second. This is to say that for each Christian household with a good child,Santa has around 1/1000th of a second to park the sleigh, hop out, jump down the chimney, fill the stocking, distribute the remaining presents under the tree, eat whatever snacks have been left for him and get back up the chimney into the sleigh and get onto the next house. Assuming that each of these 108 million stops is evenly distributed around the earth (which, of course, we know to be false, but will accept for the purposes of our calculations), we are now talking about 0.78 miles per household; a total trip of 75.5 million miles, not counting bathroom stops or breaks. This means Santa's sleigh is moving at 650 miles per second or 3,000 times the speed of sound. For purposes of comparison, the fastest man made vehicle, the Ulysses space probe, moves at a poky 27.4 miles persecond, and a conventional reindeer can run (at best) 15 miles per hour. The payload of the sleigh adds another interesting element. Assuming that each child gets nothing more than a medium sized LEGO set (two pounds), the sleigh is carrying over 500 thousand tons, not counting Santa himself. Onland, a conventional reindeer can pull no more than 300 pounds. Even granting that the flying reindeer can pull 10 times the normal amount, thejob can't be done with eight or even nine of them - Santa would need 360,000of them. This increases the payload, not counting the weight of the sleigh,another 54,000 tons, or roughly seven times the weight of the Queen Elizabeth (the ship, not the monarch). A mass of nearly 600,000 tons traveling at 650 miles per second creates enormous air resistance this would heat up the reindeer in the same fashion as a spacecraft re-entering the earth's atmosphere. The lead pair of reindeer would
Re: Quantum Probability and Decision Theory
Stephen Paul King wrote: Yes. I strongly suspect that minds are quantum mechanical. My arguement is at this point very hand waving, but it seems to me that if minds are purely classical when it would not be difficult for us to imagine, i.e. compute, what it is like to be a bat or any other classical mind. I see this as implied by the ideas involved in Turing Machines and other Universal classical computational systems. I'm afraid you have a pregodelian (or better a preEmilPostian) view of machine. If we are consistent machine we cannot know which machine we are. We cannot consistently identify formal and intuitive probability. Godel's and Lob's incompleteness prevent us to identify any intuitive first person knowledge with objective third person communicable statements. Gunderson has given also non-godelian argument, based on simple assymmetry considerations illustrating the point. Actually duplication experiments provide intuitive understanding of that phenomenon: if you are duplicated at the right level, none of you can understand what it is like to be the other. You could look at Benacerraf in the archive to see more. Note also the UD Argument works for quantum brain too. Although quantum states are not duplicable, it is still possible to prepare them in many instances, and that is what the UD does (quantum universal machine *are* emulable by classical machine). The no-cloning theorem is also a consequence of comp. Knowing that our experiential states supervene not on a physical state but on the whole set of histories going through that states, it is hard to imagine how anyone could duplicate anything below its substitution level. Bruno
re:Re: Everything need a little more than 0 information
Jesse Mazer wrote [snip] ... Doesn't the UDA argument in some sense depend on the idea of computing in the limit too? Yes. This follows from the invariance lemma, i.e. from the fact that the first persons cannot be aware of delays of reconstitution in UD* (the complete work of the UD). The domain of uncertainty can be defined by the collection of all maximal consistent extensions of our actual state/history. Those maximal extensions are not r.e. (not recursively enumerable, not algorithmically generable, not computable in some sense), but are r.e. in the limit, on which our average experiences will proceed (and this is enough for the working of the UDA). (An interesting paper from recursion theory which is relevant for *further* studies is the technical but readable paper by Posner 1980. Readable by beginners in Recursion Theory I mean. POSNER D.B. 1980, A Survey of non r.e. degrees ? O', in F.R. Drake and S.S. Wainer (eds), Recursion Theory: its generalisation and applications, Cambridge University Press.) I think that Schmidhuber has *different* motivations for the limit computable functions. There are also important in the field of inductive inference theory. Bruno
re:Re: Everything need a little more than 0 information
Russell Standish wrote: Hal Finney wrote: That would be true IF you include descriptions that are infinitely long. Then the set of all descriptions would be of cardinality c. If your definition of a description implies that each one must be finite, then the set of all of them would have cardinality aleph-zero. What Russell wrote was that the set of all descriptions could be computed in c time on an ordinary Universal Turing Machine. My question is, does it make sense to speak of a machine computing for c steps; it seems like asking for the cth integer. The descriptions in the Schmidhuber ensemble are infinite in length. The computations are infinite, but descriptions are supposed to be finite. At this stage, I see no problem in talking about machines computing c steps, but obviously others (such as Schmidguber) I know would disagree. And me too, here. c type of infinities appears only from first person point of views which relies on all infinite digital conputations. Its like asking for the cth real number, rather than the cth integer, if you like. I'm not sure what the connection is with this non-standard model of computation and others such as Malament-Hogarth machines (sp?) Ah. Yes, what you say make sense with non-standard notion of machines. (Well beyond comp I think). Bruno
RE: Applied vs. Theoretical
Ben Goertzel [EMAIL PROTECTED] wrote: Tim May wrote: As I hope I had made clear in some of my earlier posts on this, mostly this past summer, I'm not making any grandiose claims for category theory and topos theory as being the sine qua non for understanding the nature of reality. Rather, they are things I heard about a decade or so ago and didn't look into at the time; now that I have, I am finding them fascinating. Some engineering/programming efforts already make good use of the notions [see next paragraph] and some quantum cosmologists believe topos theory is the best framework for partial truths. The lambda calculus is identical in form to cartesian closed categories, program refinement forms a Heyting lattice and algebra, much work on the fundamentals of computation by Dana Scott, Solovay, Martin Hyland, and others is centered around this area, etc. FWIW, I studied category theory carefully years ago, and studied topos theory a little... and my view is that they are both very unlikely to do more than serve as a general conceptual guide for any useful undertaking. (Where by useful undertaking I include any practical software project, or any physics theory hoping to make empirical predictions). My complaint is that these branches of math are very, very shallow, in spite of their extreme abstractness. There are no deep theorems there. There are no surprises. There are abstract structures that may help to guide thought, but the theory doesn't tell you much besides the fact that these structures exist and have some agreeable properties. The universe is a lot deeper than that Division algebras like quaternions and octonions are not shallow in this sense; nor are the complex numbers, or linear operators on Hilbert space Anyway, I'm just giving one mathematician's intuitive reaction to these branches of math and their possible applicability in the TOE domain. They *may* be applicable but if so, only for setting the stage... and what the main actors will be, we don't have any idea... Although I would agree that there is an atom of truth in the idea that categories are shallow structures, I do think they will play a more and more important role in the math, physics and (machine) psychology of the future. 1: Shallowness is not incompatible with importance. Sets are shallow structures but are indispensable in math for example. 2: Categories are just sets, in first approximation, where morphism are taken into account, and this has lead to the capital notion of natural transformation and adjunction which are keys in universal algebra. 3: Categories are non trivial generalisation of group and lattice, so that they provide a quasi-continuum between geometry and logic. This made them very flexible tools in a lot of genuine domains. 4: Special categories are very useful for providing models in logic, like *-autonomous categories for linear logic, topoi for intuitionist logic, etc. Some special categories appear in Knot Theory, and gives light on the role of Quantum field in the study of classical geometry. Despite all this, some domain are category resistant like Recursion Theory (I read the 1987 paper by Di Paola and Heller Dominical Categories: Recursion Theory Without Element The journal of symbolic logic, 52,3, 594-635), but I still cannot digest it, and I don't know if there has been a follow-up. So my feeling is that category theory and some of its probable quantum generalisation will play a significant role in tomorow's sciences. In fact, categories by themselves are TOEs for math. Topoi are mathematical universes per se. At the same time, being problem driven, I think category theory can distract the too mermaid-sensible researcher. 'Course there is nothing wrong with hunting mermaids for mermaids sake, but then there is a risk of becoming a mathematician. Careful! ;-) Bruno
Re: The class of Boolean Algebras are a subset of the class of Turing Machines?
Stephen Paul King wrote: I am asking this to try to understand how Bruno has a problem with BOTH comp AND the existence of a stuffy substancial universe. It seems to me that the term machine very much requires some kind of stuffy substancial universe to exist in, even one that is in thermodynamic equilibrium. I fail to see how we can reduce physicality to psychology all the while ignoring the need to actually implement the abstract notion of Comp. I really would like to understand this! Sets of zero information fail to explain how we have actual experiences of worlds that are stuffy substancial ones. It might help if we had a COMP version of inertia! Even Descartes realised the incompatibility between Mechanism and Weak Materialism (the doctrine that Stuff exits), in his Meditation. I think Stuff has been introduced by Aristotle. Plato was aware, mainly through the dream argument, that evidence of stuff is no proof, and he conjectured that stuff was shadows of a deeper, invariant and ideal reality, which is beyond localisation in space or time. My question is why do you want postulate the existence of stuff. The only answer I can imagine is wanting that physics is fundamental. But that moves makes both physics and psychology, plus the apparent links between, quite mysterious. No doubt that Aristotle errors has accelerated the rise of experimental science and has made possible the industrial revolution. But Aristotle stuff has been only use to hide fundamental question which neither science nor technics will be able to continue to hide. Dennett argues that consciousness, for being explained at all, must be explained without postulating it. I think the same is true for matter, space, time, and any sort of stuff. But, now, with comp, what I say here becomes a consequence of the movie graph argument or of Maudlin's article computation and consciousness. See Maudlin or movie in the archive for more explanation or references. You can also dismiss the movie/Maudlin argument if both: 1) You grant me the comp apparition of physics through the proof of LASE 2) You accept some form of OCCAM razor (the concetual form used by Everett or by most 'everythingers'). Regards, Bruno
RE: Algorithmic Revolution?
Colin Hales wrote ... Not really TOE stuff, so I?ll desist for now. I remain ever hopeful that one day I?ll be able to understand Bruno?. :-) Ah! Thanks for that optimistic proposition :-) Let us forget the AUDA which needs indeed some familiarity with mathematical logic. But the UDA? It would help me to understand at which point you have a problem. For example I understand where Hall Finney stops, although I still does not understand why. I got a pretty clear idea where and why Stephen King disagrees. This can help me to ameliorate the presentation. You could also help yourself through the formulation of precise questions. Perhaps you did and I miss it? (*) Bruno (*) My computer crashed badly some weeks ago and I use the university mailing system which is not so stable. Apology for funny spellings, RE:RE:-addition in replies, lack of signature, etc.
Everything need a little more than 0 information
From: Russell Standish [EMAIL PROTECTED] There is no problem is saying that all computations exist in platonia (or the plenitude). This is a zero information set, and requires no further explanation. Stricly speaking I disagree. The expression all computations needs Church thesis for example. And Church thesis is a non trivial bag of info. But I see where is the point. The all computation set is a zero information set, but is not a zero meta-information set, should we say. Same for all numbers, all sets You still need to define axiomatically numbers or sets. There will always be some mysterious entity we need to postulate. That is why I postulate explicitely the Arithmetical Realism in comp. Too vague Everything could lead to inconsistencies. Bruno
Re: Is classical teleportation possible?
Stephen Paul King wrote: I found these statements: http://www.imaph.tu-bs.de/qi/concepts.html#TP Teleportation with purely classical means is impossible, which is precisely the observation making the theory of Quantum Information a new branch of Information Theory. This is correct. What the authors mean is that Quantum teleportation is impossible to do by purely classical means. They are not saying that classical teleportation is impossible. They say that because some quantum algorithm has been shown runnable by purely classical gates (but even this can be ambiguous, so be careful taking the context of the paper into account). Regards, Bruno
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: 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: Re: The number 8. A TOE?
Ben Goertzel writes: I read your argument for the UDA, and there's nothing there that particularly worries me. Good. I don't like to worry people. (Only those attached dogmatically to BOTH comp AND the existence of a stuffy substancial universe should perhaps be worried). 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 do use some minimal Folk Psychology in UDA, and that can be considered as a weakness, and that is one of the motivation--- for eliminating the need---to substitute it (folk psychology) by machine self-referential discourses in the Arithmetical-UDA). 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? 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. Bruno
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?
Tim May wrote (I was struck by the point that the sequence 1, 2, 4, 8 is the only sequence satisfying certain properties--the only scalars, vectors, quaternions, octonions there can be--and that the sequence 3, 4, 6, 10, just 2 higher than the first sequence, is closely related to allowable solutions in some superstring theories, and that these facts are related.) That's indeed what amazes me the more. I always thought that the dimension justification in string theories was unconvincing, but with the octonion apparition there, I must revised my opinion. Needless to say I hope octonions will appear in the Z1* semantics! (so we could extract string theory from comp directly). Do you know that Majid found a monoidal category in which the octonions would naturally live, even (quasi)-associatively, apparently. I think the sedenions (16 dim) could play a role too, even if they do not make a division algebra. cf the (not really easy) 1998 paper by Helena Albuquerque and Shahn Majid quasialgebra structure of the octonions. For the paper and some other see http://arXiv.org/find/math/1/ti:+octonions/0/1/0/1998/0/1 All that gives hope for finding the generalized statistics we need on the (relative) consistent histories or observer-moments (i.e, with AUDA, a Z1* semantics). Well... let us dream a bit... ;-) Bruno
re:Digital Physics web site mailing list
Hi Plamen, Thanks for the info. Actually we knew about your site since your friend Joel Dobrzelewski pointed us to it. You can search the everything-list archives with the keyword cellular automata to see what some among us think about the use of CA for developping a TOE. See my web page http://iridia.ulb.ac.be/~marchal/ for links to an argument showing that if we are turing-emulable, then physical appearances cannot be turing-emulable, in general. In that sense the quantum indeterminacy confirms the machanist hypothesis. In a nutshell, if we are machines we cannot know which machine we are, and we cannot know which computationnal histories we are living, and the detailled description of our anticipable environment relies on the infinity of computations going through our actual states. So if we are turing-emulable then the physical world cannot be turing-emulable. Physical appearance emerges from an relativized average on all computations. Of course CA are very interesting per se, but misleading for a TOE. There is a need to distinguish internal first person appearances and external possible description. In this list most people believe that we cannot single out and focuse on one system, even if it is universal, but that every-system must be taken into account. If one system emerges from that, then we will have a serious justification for it (but only then). The evidences, both theoretical and empirical, are that such a universal system, if it exists, cannot have a local realist description. That is, IF the big all is a CA, it should be a quantum CA(*). I have read, admittedly in a quick way, your CA explanation of EPR sort of phenomena. Er... I am quite skeptical to be honest. An equivalent explanation for general form of entanglement would give sort of conspiracy variable theory ... Have you try to CA simulate GHZ entanglement? (Greenberger, Horn, Zeilinger) (*) cf Wim van Dam thesis Quantum Cellular Automata, available at http://citeseer.nj.nec.com/vandam96quantum.html Bruno Original message by Plamen Petrov Dear all: I am reading this list since May, 2002, but only now I decided to post... This is to invite kindly all members of Everything-list to visit our Digital Physics site at: http://digitalphysics.org and (eventually) to consider subscribing to our mailing list as well (see below). Some short introductory text follows: Digital Physics is a relatively new scientific field somewhere on the edge between theoretical physics and theoretical computer science. The pivotal idea is that our Universe is a cellular automaton (CA), or to be more precise: the Universe is something that is isomorphous to a CA. This proposition is known as Fredkin's thesis, or (as Juergen Schmidhuber will insist!) :-) Zuse's thesis, or Zuse-Fredkin thesis, if you like. Although this idea has been around since mid 1950s, only now it got a boost thanks to a recently published book by Wolfram -- A New Kind of Science (NKS). However, please note that our Digital Physics project is an independent research that has nothing to do with Wolfram's NKS, Fredkin's Digital Mechanics (DM) or Zuse's Rechnender Raum (Calculating Spaces). This is to invite also all members of Everything-list to consider subscribing to our Digital Physics mailing list as well: http://groups.yahoo.com/group/digitalphysics Our mailing list is the oldest discussion group explicitly devoted to the Universe as a CA idea; we have been there since 1997 (even before Yahoo groups). To check out our old archives, look here: http://digitalphysics.org/Mail To subscribe to our discussion list, send message to: [EMAIL PROTECTED] You can always unsubscribe later by posting to: [EMAIL PROTECTED] With best regards, P.P. --- Plamen Petrov http://digitalphysics.org
The number 8. A TOE?
Hi, I hope you have not missed Ian Steward's paper on the number 8, considered as a TOE in the last new scientist. It mentions a paper by John Baez on the octonions. The octonions seems to be a key ingredient for the quantization of general relativity. http://math.ucr.edu/home/baez/Octonions/ I am too buzy now to make comments but it seems *very* interesting, if not convincing. You can find many discussions on the net about Baez's paper. For example, one by Osher Doctorow http://superstringtheory.com/forum/superboard/messages/114.html Bruno
re:Zuse's thesis web site
I agree with Hal. CA models doesn't explain quantum non-locality. More deeply perhaps is the fact that from Kochen Specker theorem there is no boolean map on quantum reality, but a CA model always has a boolean map. When Hal says: As far as the claim that we already know the algorithm that runs our universe, and it is the UD: I think this is amusing but ultimately misleading. It's true that a dovetailer which runs all programs will indeed run our own universe's program (assuming it has one), but I think it is a misuse of terminology to say that the UD is the algorithm that is running our universe. I agree. Note that my arguments (uda, auda, etc.) shows only that IF I am Turing emulable THEN the structure of the multiverse emerges from all computations at once, as seen and anticipated by internal observers, i.e. from the first plural person point of view of consistent machines. The UD is not the explanation, it is the problem! In fact with comp no classical program can explain, per se, the universe. And even if a quantum machine can explain the universe, with comp we have to explain how that quantum machine arise, in our mind, by relative averaging on all computationnal histories. Zuse's thesis is without doubt a step in the comp direction, but without distinguishing different sort of internal points of view Zuse cannot foreseen the quantum dreamlike feature of everything, still less the physico/psycho reversal. Bruno Hal Finney wrote: Juergen Schmidhuber writes: I welcome feedback on a little web page on Zuse's 1967 thesis (which states that the universe is being computed on a cellular automaton): http://www.idsia.ch/~juergen/digitalphysics.html That's very interesting; I was not aware of Zuse. Unfortunately I don't know German so I can't read his paper. Regarding the question of the compatibility of CA models with relativity and QM, Wolfram looks into this in some detail. He essentially abandons a simple CA model in favor of a more complex network of interacting nodes, which has some features similar to the Lorentz transformation of relativity. Then to address the EPR style long-distance correlations of QM, he proposes that while the network is mostly local, it has occasional nodes which get stretched apart and are connected to distant nodes. These are rare but allow for the type of information flow necessary to reproduce long-distance QM correlations. All in all it is a pretty ad hoc and unconvincing model. I tried to read the t'Hooft paper referenced here but it was over my head. It also struck me though as not really addressing the discrepancy between long-distance correlations and local CA models. It seems very much an open and difficult question to me to show how a local CA model can reproduce relativity and QM. One issue which CA models tend to ignore is the MWI. Most CA models are built as hidden variable theories which define a single universe. Some multiverse models have that structure as well. But it seems to me that this is an entirely unnecessary restriction. If a CA can model a universe, it can model a multiverse, and likewise with any other computing model like TMs. The MWI is fully deterministic, which may make it a more attractive target for modelling with a deterministic computational theory than attempting to reproduce the statistical phenomena of QM, essentially via hidden variables. Any hidden variable theory, CA based or not, has two strikes against it from the beginning due to the the many well known difficulties of Bell inequalities and EPR correlations. Regarding entropy, it is pointed out that entropy does not grow in a CA model. Wolfram discusses this as well. While entropy technically does not grow, you can get phenomena that look very much like entropy growth in a CA model. Eventually you will get a Poincare recurrence if the universe is finite. But if you start in a sufficiently simple state, there are many CA models which will mimic entropy growth into a more complex state. And this may be close enough to explain our universe. Alternatively, of course the MWI as a deterministic theory also does not have entropy growth. As mentioned above, computational models of our universe might well do better to aim towards an MWI world. As far as the claim that we already know the algorithm that runs our universe, and it is the UD: I think this is amusing but ultimately misleading. It's true that a dovetailer which runs all programs will indeed run our own universe's program (assuming it has one), but I think it is a misuse of terminology to say that the UD is the algorithm that is running our universe. I would reserve that phrase to refer to the specific program that generates our universe and no others. It will be a tremendous accomplishment of physics and philosophy when that program is discovered, but it is misleading to give the impression that we already know what it is. I think a better terminology here would be something like, we don't
Anyonic quantum machine cannot violate Church Thesis
I do no more believe that Freedman P/NP paper shows that some Quantum Universal machine can compute more than Deutsch QUM, or, consequently, more than any Turing Universal Machine. (Nor do Freedman himself, see http://arxiv.org/abs/quant-ph/?0001071 ) About Calude attempts to go beyond the Turing barrier, I should reread his paper, but from quant-ph/?0001071, it seems that Calude machine cannot be implemented with an anyonic quantum machine, making hard to believe Calude machine can exist in some concrete way. But this deserves more thinking. Note that this *is* good for the conceptual classical Church thesis (if something like that was needed!) Bruno
re:Re: Many Fermis Interpretation Paradox -- So why aren't they here?
Saibal Mitra wrote: Bruno wrote: At 16:25 +0200 11/10/1996, Saibal Mitra wrote: You can still have realism, but it must be the case that at least some of the things we think of as ``real physical objects´´ like e.g. electrons are not real. What would that mean? What would be real? Even in my thesis, electrons are supposed to have some degree of reality like relative stability as mind pattern in normal machine dreams (1-person plural histories) for example. Well, his theory is rather complicated, but he starts from a deterministic theory formulated in terms of primordial variables, that do represent ``real things´´. Although I don't think that his ideas are necessarily correct, it does give food for thought. snip By Bell and Kochen Specker theorems those primordial variable should be non local and contextual, or 't Hooft should be clear about the different (from QM) experimental predictions his theory gives. Perhaps I miss something. Of course you know I believe indeterminism is a consequence of Mechanism, so 't Hooft move seems to me without clear purpose. I mean even without QM, I expect verifiable non-locality and contextuality, or Many-Worlds.
re:Re: Many Fermis Interpretation Paradox -- So why aren't they here?
Gordon wrote: But you have an inconsistent idea in that on the one hand a theory which say that they are physical object that becoame no physical and then just comp pure comp.Now although I dont thing it that narrow just like the old Clock work view, I do think that your theory can be simpler in that you dont need to call eletron real or not that dont matter.Just has everything as it is but araise from Comp.It the same theory just dont have to bother with QM directly? I don't understand. I am saying that physics is a branch of psychology, (where physics becomes the study of a relative measure on sharable computationnal histories). Now we can compare that physics with empirical physics, if not just to confirm or refute comp. But then we have to bother with QM, isn'it? (Note that I do not extract the measure from comp but I do extract the logic of yes-no experiments, which can be compare with some quantum logics or algebras). Bruno
