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: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: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: Quantum Probability and Decision Theory
Dear Stephen,
>[SPK]
>
>When what is [relevant]?
>
>> Quantum computer can be emulated by classical computer (see below).
>
>[SPK]
>
>Please point me to some paper, other than yours, that gives something
>better than a hand-waving argument of this statement.
See Deutsch 1985. (precise ref in my thesis)
>
>> Quantum computer does not violate Church thesis. The set of
>> quantum computable functions is the same as the set of classically
>> computable functions.
>
>[SPK]
>
>This is one statement that I found:
>
>http://www.netaxs.com/people/nerp/automata/church8.html
>"Church's thesis. All the models of computation yet developed, and all those
>that may be developed in the future, are equivalent in power. We will not
>ever find a more powerful model."
>
>
>Statements of this kind are found in religious dogma and are not
>acceptable in mathematical and logical circles unless they have adjoining
>caveats and attempted proofs. No where do I find this. It reminds me of
>Kronecker's statement "God made the integers; all else is the work of man."
Church thesis is indeed a non trivial hypothesis in the foundation
of computer science. The main conceptual argument is the closure of the
set of partial recursive functions for the diagonalisation procedure.
An empirical argument is that all attempt to define the set of computable
functions leads to the same class of functions. A relevant book is Webb 1980.
>
>I do not intend to be impolite here, Bruno, but, Please, give me some
>reference that discusses how it is that "The set of
>quantum computable functions is the same as the set of classically
>computable functions."
It is perhaps up to you to show me a quantum computable function not
being classicaly computable. But if you succeed you will give me
something like an unitary transformation, and then I will show
you how to write a classical program emulating this unitary transformation.
See Pour El and Richard's book on how to conceive differential equations
with non computable solutions (but still locally generable by the UD though),
but anyway, linear quantum waves are classicaly emulable. It is a tedious
but conceptually not so hard exercise.
>
>I can not see how this is possible given that (as Svozil et at state in
>http://tph.tuwien.ac.at/~svozil/publ/embed.htm )
>"for quantum systems representable by Hilbert spaces of dimension higher
>than two, there does not exist any such valuation s: L® {0,1} ... there
>exist different quantum propositions which cannot be distinguished by any
>classical truth assignment."
>
>If there does not exist a unique Boolean valuation for QM systems that
>can be taken to exist a priori and given that UTMs, including UD, demand the
>existence of such for their definition, how is it that you can continue to
>make this statement?
Because the physical world is a first person modality. The accessible
probable worlds can not *appear* in a boolean way from inside. Apparantly
it appears in some quantum logical way. The physical world is not
include in the UD; it emerges from the inside modal first person
statistics from the machines point of view. Those modalities are made
non trivial by the constraints of theoretical computer science and
logic of provability.
>[SPK]
>
>Can UD run them all simultaneously or in some concurrent way that would
>give us some way of finding solutions to the "foliation of space-like
>hypersurfaces" problem of GR? Also, what are the "physical resource"
>requirements of UD? What consitutes it's "memory" and its "read/write head"?
Good question. I hope so :)
>Also, what are the "physical resource"
>requirements of UD? What consitutes it's "memory" and its
>"read/write head"?
I do not need the hypothesis of the existence of "physical resource".
The UD has no other requirement than arithmetical truth. You know,
infinity of primes, and other chinese theorems ...
>I like this part of your thesis and my interest in it makes me ask these
>very pointed questions. Additionally, I hope you would agree that there may
>be an additional problem of how the "Principle of Least action" of physics
>come about. Could it be considered, within your thesis, as just another
>1-person aspect?
Absolutely. Unless comp is false, and that's what makes comp testable.
>Appeals to polls and beliefs should not be made. It would be more
>helpfull if we considered such things as G. Chaitin's Omega when discussing
>random sequences. Can UD compute Omega?
No. But it trivially generates it. Uninterestingly, 'cause we cannot
recognize it. If you dont't like polls you can use the betting manner
of defining probabilities by iterating duplication of population of
machines.
>> Now, the simple reason why the quantum is turing-emulable is that the
>> solutions of Schroedinger or Dirac Wave Equation(s) are computable.
>
>[SPK]
>
>Where is this explained? Please, some papers that you did not write...
See ref above. Deutsch 1985. Or Deutsc
Re: Quantum Probability and Decision Theory
Stephen Paul King wrote: >There do exist strong arguments that the "macroscopic state" of neurons >is not completely classical and thus some degree of QM entanglement is >involved. But hand waving arguments aside, I would really like to understand >how you and Bruno (and others), given the proof and explanations contained >in these above mentioned papers and others, maintain the idea that "any >quantum computer or physical system can be simulated by a classical >computer." I agree with almost all the quotations you gave in your post http://www.escribe.com/science/theory/m4254.html But they are not relevant for our issue. Quantum computer can be emulated by classical computer (see below). Quantum computer does not violate Church thesis. The set of quantum computable functions is the same as the set of classically computable functions. The difference are the following points 1) and 2): 1) A classical computer cannot emulate a quantum computer in "real time", nor 2) can a classical computer provide a pure 3-person emulation of some quantum *processes* like the generation of truly random numbers. But this is not relevant concerning our fundamental issue. Concerning 1) the only thing which matters is that the classical UD runs all programs including quantum one. THEN, by UDA reasoning, it is shown that "real time" is a 1-person (plural) emerging notion. Even if the UD need many googol-years to compute each "quantum step", from the inside 1-person point of view, that delays are not observable. CF the "invariance lemma" in UDA. Concerning 2): idem! We cannot generate truly random sequences, but we can easily (with the comp hyp!!!) generate histories in which most average observers will correctly believe in truly random sequences. It is enough for that purpose to iterate the Washington-Moscow self-duplication experiment. If you iterate this 64 times, most of the 1.85 10^19 version of you will conclude (correctly with comp) that they are unable to predict their next self-output (W or M) and that their histories, in this context are truly random. Now, the simple reason why the quantum is turing-emulable is that the solutions of Schroedinger or Dirac Wave Equation(s) are computable. If you simulate such a wave you will realise that it simulates the many-world or many-dreams, even in such a way of making extravaguant histories much more rare than normal (lawfull) histories. This is not yet obvious with pure comp, where non quantum histories must yet be proved measure-negligeable (but see my thesis and posts to get a feeling why with comp it should be so, and why indeed it seems to be so). Bruno
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: 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: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 r
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: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 "c"th 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 "c"th real number, rather than the >"c"th 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: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
Quantum Probability and Decision Theory
Hi Wei Dai, Have you read the "revisited" paper by Wallace on Everett/decision theory? Quite interesting imo, and relevant for some discussion, about MWI and decision theory we have had on this list. http://philsci-archive.pitt.edu/documents/disk0/00/00/08/85/index.html 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
"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?
Dear Stephen, You wrote: >I followed the UDA link and read the post and fell flat on my face when >I read the term "classical teleportation". I would like to know what is the >theoretical basis of a belief that "classical teleportation" is even >possible? Classical information, in the "physical" traditionnal sense has always been considered as possible. Classical information is teleported at evry moment through phones, nets, TV-channel, etc. In Science-Fiction book, it has often been called simply "teleportation". Only with the advent of "quantum teleportation" sometimes I feel the need to add "classical" for preventing possible confusion. >I can accept TM emulability for the sake of the argument, but the >notion of classical teleportation is something that is equivalent to >perpetual motion machines in my thinking. I don't understand. If someone is Turing-emulable at level L, and if by chance he/she bet on that level for comp practice, then he/she can send his/her digital description made at that level through any classical information channel. Of course if the level is very low, for example if there is a need to encode the quantum state of the whole cosmos, then it is not possible to do it in practice. But the reasoning still follows. So if you accept Turing-emulablity at a level (even if only for the sake of the argument), then I don't see how you could deny the possibility of classical teleportation at that level (even if only for the sake of the argument). >PS. How far have you considered Chu transforms? Still not very far. Thanks for pointing me to Vaughan Pratt paper btw. The paper proves also that it is possible to be a logician and at the same time be aware of the mind-body problem (reconforting idea). But Pratt's conception of mind is to narrow for my purpose. Nor can I take his dualism as an ontological dualism, so his stuff is no really stuff, and his approach is best seen as a sort of still purely mathematical monisme, even if his use of the Chu transform give a nice dualist panorama. We will see. Today, among the logicians, I would say the Blute-Girard linear functors seems more rich, respectively to the goal of finding intermediate structures between Z1* (the comp physics) and Quantum Mechanics. Best 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.
re:Re: The universe consists of patterns of arrangement of 0's and 1's?
Stephen Paul King <[EMAIL PROTECTED]> wrote: >I agree completely with that aspect of Bruno's thesis. ;-) It is the >assumption that the 0's and 1's can exist without some substrate that >bothers me. If we insist on making such an assuption, how can we even have a >notion of distinguishability between a 0 and a 1?. >To me, its analogous to claiming that Mody Dick "exists" but there does >not exists any copies of it. If we are going to claim that "all possible >computations" exists, then why is it problematic to imagine that "all >possible implementations of computations" exists as well. But then you need to explain what "implemention" are. Computer scientist have no problem with this. There are nice mathematical formulation of it. Tim would say that an implementation is basically a functor between categories. You seen to want a material preeminent level, but this is more a source of difficulty than an explanation. What is that level? >Hardware is not an >"epiphenomena" of software nor software an "epiphenomena" of hardware, they >are very different and yet interdependent entities. That is dualism. No problem, but incompatible with comp. If you want comp, tell me where you stop in the UDA. >Additionally, the 1-uncertainty notion seems to require a neglect of the >no-cloning theorem of QM or, equivalently, that its ok for TMs to construct >(via UDA) QM theories of themselves and yet not be subject to the rules of >the theory. No problem with the no-cloning theorem. Even if Hameroff is right, and brain are quantum computer will the uda go through. Indeed the ud emulates all quantum digital machine in many copies, and the laws of physics will still be derivable by an average on many computations. In fact the comp interpretation of the no-cloning theorem is that our neighborhoods relies on all computations. to duplicate exactly a part of that neighborhoods, we really have to duplicate the whole set of "all-computations", which is certainly impossible from inside. >Could we not recover 1-uncertainty from the Kochen-Specker >theorem of QM itself? Probably so. 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: 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?
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: >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?
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: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! 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) histories or observer-moments (i.e, with AUDA, 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
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?
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
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. 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".
