Bruno, I always anticipate your thoughtful replies. I seem to transcend my own logical capabilities each time you introduce some concept which, at first, seems paradoxical to me. Resolution of paradox (due to language ambiguity or sensory illusion) seems to me to be an essential growth mechanism. It causes the integration of some new subtle distinction/pattern into a learner's knowledge base.
I'd sometime mentioned Schmidhuber's formal theory of discovery/creativity (scientific, artistic, etc.) as subjective compression progress. This is what deep learning accomplishes- dynamically improving compression of sensory input data (e.g. http://people.idsia.ch/~juergen/compressednetworksearch.html ). I was searching for more information about Post's number when I stumbled on a report on metamathematics by Chaitin (http://arxiv.org/html/math/0203002v2) with the claim: "We need a dynamic, not a static metamathematics, one that deals with the evolution of new mathematical concepts and theories. Where do new mathematical ideas come from? Classical metamathematics with its incompleteness theorems deals with a static view of mathematics, it considers a *fixed* formal axiomatic system. But mathematics is constantly evolving and changing! Can we explain how this happens? What we really need now is a new, optimistic *dynamic* metamathematics, not the old, pessimistic *static* metamathematics." Dynamic metamathematics... is this not what Schmidhuber's compression progress (i.e., the whole endeavor of deep learning AFAIK) is essentially about- automated theory formation? A Darwinian asymptotic approach towards minimum description length? I had read some article on psychology which said that subjective time for an observer slows down whenever it is presented with "interesting" sensory data (i.e., data with patterns that are neither too random or too simple in relation to existing knowledge). [ http://mindhacks.com/2011/04/18/time-flies-when-youre-having-fun/] Perhaps it is why life seems to pass more quickly as we age: we make less compression progress (unless we continue to place ourselves in new sensory environments and try new experiences). On Tuesday, March 29, 2016 at 12:55:01 PM UTC-4, Bruno Marchal wrote: > > Hi Dan, > > > On 29 Mar 2016, at 01:36, Dan wrote: > > Bruno, I don't understand your arguments fully. Specifically, > > I don't understand how the fact that the propositional logic of true but > unprovable sentences can be structured by "modal logic G* minus G" (??) is > useful to provide distinction between qualia and quanta. > > > Because G* is decidable, so the machine looking inward, or the machine > talking about herself (and remaining silent if necessary) can (in fact > cannot not) discover truth about itself which escapes its ability to > justify rationally. > Then it is not just G* \ G, but the intensional variants (Z1* \ Z1, X1* \ > X1, and S4Grz1). So there is a simple algorithm which can be selected by > evolution, or that a machine can just discover by looking inward, which the > machine can use to "intuit" many non provable truth about itself, and then > change itself into a new machine by incorporating the new formula, or using > them in many other ways. > > > > > When you say Godel incompleteness result is "constructive" rather than the > non-constructive Chaitin "relative complexity" result, do you mean that it > provides a way for some entity to precisely identify elements from the set > of empirically evident emergent truths which it is unable to describe > formally (e.g., with finite set of differential equations or a sequence of > instructions in some universal description language)? In other words, are > you saying Godel-type incompleteness is the mechanism by which some > observer is able to recognize emergent complex phenomena (e.g., > measurements of social/economic systems characterized by scale-free > power-law distributions, generated with preferential attachment processes, > and modeled by minimization of Fisher information) even though it is beyond > ability of observer to describe deterministically using equations, > programs, etc.? If this is what you mean, I don't understand how the > Godelian result is "constructive" in this sense or why the Chaitin result > is by comparison "non-constructive." > > > Chaitin shows the existence of infinitely many sentences which are > undecidable, like this long string of symbols is incompressible, but the > machine is unable to prove them for any specific strings. In the case of > GOdel's incompleteness, the machine can find the specific undecidable > statements, and indeed a transfinite number of them. > In no case is that related to anything empirical. the empirical reality is > eventually explained in term of a statistics on all computations supporting > consistent extension of "myself". I can't explain here the details, but if > you tell me if you understand the Universal Dovetailer Argument (like in > the paper sane04, or comp-2013) we can build from that. > > I am not criticizing the Kolmogorov-Chaitin approach, just that it uses an > incompleteness which does not help to explain why we can be aware of > things that we can hardly explain or justify, like consciousness and > qualia, or the intuition of the transcendental truth, ... > > > > > > > > How are the Chaitin-type results using inequalities of algorithmic > complexities (of the observer and observed) "eventually emergent on the > Gödel-Löbian sort of limitation?" This would be an argument of ontological > primacy and so it should have no assumptions. > > > ? > > All universal numbers suffer from both limitations. We have them both, and > just as a consequence of elementary arithmetic. We don't need to assume a > primary physical universe. Actually I argue that we cannot use it to > singularize or stabilize the conscious experiences, which is why at some > point physics is reduced to computer science/arithmetic. > > > > > When we say true but unprovable, it makes me think of relative algorithmic > complexity. > > > That is correct. Chaitin does show the existence of true but non provable > sentences, (the one similar to those found by E. Post manybyears ago), but > it does not give a criteria which makes the machine able to find them and > produce them as output. That is contrary to the case of Gödel's type of > incompleteness. Both are interesting, but the second one can be used to put > light on the qualia/consciousness problem: how do we "know" non provable > sentences? The constructive aspect of Gödel's incompleteness explains why > the machine is confronted to such truth all the time, and how that enrich > its mental space, even before she bet on some world. > > > > > A "self-aware [mathematical] substructure," in Tegmark's terms, of given > Kolmogorov complexity cannot recognize patterns which have greater > Kolmogorov complexity than itself. When we say a truth (i.e., pattern in > nature) is unprovable, this claim is relative to some particular observer > and it is not an objective claim. > > > Yes, and the invocation of some Nature is not really working, for > conceptual reason explained in the UDA, especially step 7 and 8 (which are > not so easy). > > > > Indeed, deep learning techniques like neuroevolution and clustering by > compression enable an agent with different channels of perception from a > human to be able to make *decisions* by discerning patterns it observes > (intelligent decisions that will maximize entropy, future possibilities) > without any need to store any explicit analytical, symbolic, or linguistic > expression of the patterns themselves. > > > I have no problem with this. > > > > Further, these may be patterns which the machine's channels of perception > would enable it to symbolically represent, but perhaps which could not be > symbolically expressible for a human. > > > That necessarily happens. In fact consciousness happens for such a reason, > although it uses both Gödel's constructive incompleteness, and Tarski's > constructive (in a weaker sense though) inexpressibility (of truth and > semantic of oneself) theorem. > > > > > I am partial to Tegmark's terms when it comes to channels of perception: > "frog" perspective (first person, subjective), "consensus" (first person, > collective), and "bird" (third person, objective). > > > Well, I extracted those notion directly from number's self-reference > (first person is given by []p & p, first person plural from []p & <>t, > third person is just []p). But then, the splitting of G and G* splits in > two each of those points of view. Eventually I have 8 such notions, if not > 4 + 4*infinity, because the logics with "<>t" are graded, which is useful > for having some nice correspondence between the quantum and space to be > recovered in the quantum logic of the machine's observable extracted from > self-reference. Tegmark is on the right track, in a different direction (as > he comes from physics). I start directly from the mystical (eyes closed) > machine's interview. the fact that it matches is a good sign for digital > mechanism (computationalism). > > > > > Estimation theory probably has not received enough attention in the > philosophies of mind, science, and language (at least until Frieden and > Romanini > quantified the semiotic philosophy of CS Pierce using Extreme Physical > Information). > > Reviewing your paper "COMP (2013) - by Bruno Marchal", I see the > following: "An argument against the comp hypothesis has to speculate on > some unknown non-computable, and non-first person comp-recoverable (as > explained later) function in Nature, and this has never been observed." > > If so, is this following recent discovery an argument against comp? Does > first person indeterminacy come to the rescue in this case, as you showed > it does for collapse of QM wave function? http://arxiv.org/abs/1502.04573 > > > No, if they could show that the spectral gap is Turing complete (and thus > undecidable, but with a complement complete for the halting problem) then > this would more confirm comp than be a problem. A priori, comp make the > machine confronted to something too much complex, with an a priori too much > information (from white rabbits to white noise). in QM, already the 0-body > problem is Turing universal. IF QM is the "correct" comp physics, the > spectral gap result will not change many thing, on the contrary, it add > some more level of universality in physics, and provides hopes for some > more Turing complete, even quantum-Turing complete, subsystems in the > physical reality. Very interesting paper, but, well, if you think you could > refute computationalism from there give some clues. > > > > > > I have just come across and ordered your book "The Amoeba's Secret" and am > looking forward to reading it. Have you seen the Youtube playlist created > by Sante Fe Institute on Complexity? It raises questions in my mind about > validity of COMP; I mention one example in my blog which references the > following paper, where genetic algorithms are used to evolve locally > interacting agents of cellular automata to coordinate and perform some > global task: > > > But saying this means that you are using comp, especially with cellular > automata, which can be emulated with a sequential "stubborn" Turing-von > Neuman type of universal machine. Not in real time, but normally after the > UDA, you know there is no real time: just pieces of machines dreams glued > or not by universal numbers. > > > > > > (paper: http://rundle.physics.ucdavis.edu/PHYGEO30/MitchellCAsandGAs.pdf , > video: > https://www.youtube.com/watch?v=hdRTcrTYfiQ&index=99&list=PLF0b3ThojznRyDQlitfUTzXEXwLNNE-mI > ). > As I learn more about information transfer in complex systems (as in > biosemiotics), I increasingly begin to question the validity of COMP or at > least am unable to see how the hypothesis explains such > information-theoretic descriptions of nature. EDIT: Actually, it seems > quite obvious now that COMP is valid in such a case... the cellular > automata rule which evolves from the genetic algorithm is the simple > computation. > > > OK. Nice you see this now. You save my time. yes, all the Santa Fe > approach uses comp. "My" comp is the weakest comp hypothesis in the > literature, and all I want to share is that it fits much better with Plato > theology than with Aristotle theology (which assume a primary material > universe). > Note that the comp ethics does not fit well with Plato's politic, as > someone made me realize, and I see now that even Plato made the "machine's > blasphem" error, (mixing philosophy/theology with human practical affairs). > > The real recent progress (the working democracy, i.e. the voting system), > does avoid the argument by authority on the fundamental satisfying machine > (human) aspirations). The antic greeks have missed the genuine notion of > democracy, or altered it at the start. A recurrent human mistake. > > > > > From the perspective of any one agent in the cellular automata, however, > the description of the overall system behavior is beyond symbolic > expression (the system is Relatively, not Absolutely, complex because > indeed the researchers were able to codify the emergent patterns using a > "particle physics" framework). > > > Nice it is a bit like the comp explanation of free-will. the system is > globally determined, but in no way accessible to the system, yet the system > can codify emergent set of possible choice/solution, and ponder which one > will satisfy it more relatively to some short term or longer term goal. > But again, to attach a qualia to such "set of pattern", the constructive > undecidability makes this automatic: it is just true that from that > position the machine get a type of undoubtable certainty but without any > means to justify its presence rationally. > > I don't think there is any problem between the possible physical > motivation in computer science complexity theory. But for the mind and the > theological ultra-basic questioning (on the nature of reality), the > constructive incompleteness of Gödel gives all the answers (well at the > propositional logical level) through the intensional nuances (whose > existence and non triviality is given by the incompleteness) of machine's > provability. It is a super-ideal case. real life, and applied physics uses > more our non-monotonic paraconsistent super-layer of Belief revision > system, natural languages, ... but this, I assume, play no part in the > origin of the physical laws (that would be like assuming an incompetent > God, or a toxic Glass-of-Milk at the start. Like assuming miracle, this > does not help to solve the fundamental problem, but it can provide jobs and > money, which is part of the game. > > Algorithmic complexity is a very interesting subject. I do not exclude > that it will play some role in the derivation of the physics from > arithmetic, that we have to do if we assume digital mechanism. But to > express first and solve genuinely if sketchy the psycho and theo logics > part of the problem, the royal road is the Gödel one, especially after > Solovay offered the arithmetically sound and complete formalization (at the > propositional level) of many entities self-reference logics G and G*. > > We get a logic of observable from some of its intensional variants, and > the complexity is more related to the hamiltonian(s), and to the depth of > the infinitely many computations which support us "here and now". I can > guess the hamiltonian is something highly symmetrical and plausibly linear, > but not much more. > But my goal is not solving a problem in physics, but in "theology" or > "philosophy of mind", when assuming a precise quite general version of > (digital) mechanism, i.e. without hiding the consciousness aspect under the > rug. > > Have you read Everett? Tegmark starts from Everett, but has clearly not > see the importance of the first person indeterminacy in the computer > science frame, and is not really aware of the importance of the universal > (in the sense of Church-Turing) machine. At least Chaitin exploits this. > Both are unaware that Everett's move needs to be extended in elementary > arithmetic, and the wave itself must be accounted phenomenologically. > > ... > > I don't find a good reference of a paper by Calude which shows almost > directly why algorithmic randomness hides a bit of the "meaning" in the > Post "information" number, or in Gödel's provability predicate. > For exemple the ith decimal of "Post number" is 0 or 1 if phi_i stops or > not, with phi_i an enumeartion of the program without input. (It is a view > of the Halting Oracle). That sequence is more or less random, but with some > extreme redundancy that the Chaitin omega number completely abstracts > itself from. But Calude's point was deeper than this, ... I will tell you > when I found this back. > > Bruno > > > > > On Thursday, March 24, 2016 at 12:56:01 PM UTC-4, Bruno Marchal wrote: >> >> >> On 24 Mar 2016, at 05:15, Dan wrote: >> >> Paper discussing exact mapping between renormalization group and deep >> learning: http://arxiv.org/abs/1410.3831 >> >> >> >> It seems interesting, thanks. >> >> >> >> Another paper relating Kolmogorov complexity to geometry, with focus on >> spacetime / causality: http://arxiv.org/abs/1206.2893 >> >> >> I will dig on this more when I have more time, but I am less convinced at >> first sight. >> >> Have you read my arguments? You would better see if some ideas there >> could help or not to extract physics from arithmetic through machine's >> self-reference. Some caution have to be taken to get the distinction quanta >> and qualia properly. >> >> In this list most people defend ensemble of universe or dreams type of >> theories, which generalize Everett conceptually, and which maintain 3p >> determinacy and 3p locality. We can exploit the fact that machine have the >> means to grasp that the truth about them extends properly what they can >> justify rationally, yet such truth is still very well structured, and >> incompleteness forces it to obey different logics for each mode. You might >> appreciate, given that you seem to appreciate Chaitin's work, which also >> relies mainly on the recursion theorem in computer science. The learning >> theory of Gold, Blum, Case and Smith, Osherson, Stob, Weinstein (to name a >> few) is also very interesting (and non constructive like Chaitin). >> The usual "Godel" result is constructive and this is what I exploit to >> put some light on the "body" problem that the mechanist philosopher is >> confronted too. >> >> Bruno >> >> >> >> >> >> >> On Monday, March 21, 2016 at 9:12:33 AM UTC-4, Bruno Marchal wrote: >> >>> >>> On 17 Mar 2016, at 16:26, spudboy100 via Everything List wrote: >>> >>> >>> Wolfram would agree with this paper in some ways. >>> https://www.youtube.com/watch?v=Re9eB_j6m-0 >>> >>> The main content gets very interesting, for me, at 1hr 8 minutes in, and >>> 1 hr 12 minutes in to Wolfram's SETI lecture. >>> >>> -----Original Message----- >>> From: Dan <[email protected]> >>> To: Everything List <[email protected]> >>> Sent: Wed, Mar 16, 2016 11:13 pm >>> Subject: Can Space-Time Be Based on Logic and Computation? >>> >>> Paper: >>> http://arxiv.org/abs/1602.06987 >>> >>> Comments: >>> Lossless compression of an image or audio file approximates its >>> Kolmogorov complexity and reveals its "compressibility," or >>> "interestingness." If it's not at all compressible it is too random to be >>> aesthetic or enjoyable, whereas too much compressibility is associated with >>> oversimplicity. Many classical works have been analyzed in this way and >>> show to be in the middle. Schmidhuber mentions a theory of creativity, fun, >>> motivation based on compression progress. Compression progress seems to be >>> essential to theory of general AI- I refer to neuroevolution techniques, >>> Cilibrasi and Vitanyi's paper Clustering by Compression for inference, as >>> well as Wissner-Gross's simulations showing tool-usage behavior upon >>> entropy maximization. Was a paper recently giving exact mapping between >>> renomalization group and deep learning. >>> >>> >>> Do you have the reference of that paper? >>> >>> >>> >>> Paper I link to above takes idea of data compression / Kolmogorov >>> complexity even beyond a relationship to statistical mechanics or deep >>> learning to explain the causal appearance of spacetime itself. I want to >>> understand how Extreme Physical Information fits in to all of this.. it >>> provides observer dependence and derivation of so many physical and >>> nonphysical laws. It also encapsulates limits of knowledge using any >>> particular channel of perception. >>> >>> >>> Of course the Gödel type of limitation (as opposed to Kolmogorov or >>> Chaitin type of limitation) is independent of even the existence of a >>> channel of perception (which are eventually emergent on the Gödel-Löbian >>> sort of limitation). A big difference between both is that the algorithmic >>> information limitation is non constructive: you get an infinity of >>> undecidable sentences, but no means to individually recognize them. On the >>> contrary, the Gödel-Löbian limitations is constructive, and gives the means >>> to the machine to build the undecidable sentences, and perhaps to extends >>> itself from them. Indeed the whole (propositional) logic of the true but >>> non provable sentences is structured by the modal logic G* minus G and its >>> intensional variants. This is useful to get the qualia and the general >>> qualitative feature associate to consciousness. >>> >>> Bruno >>> >>> >>> >>> >>> >>> -- >>> You received this message because you are subscribed to the Google >>> Groups "Everything List" group. >>> To unsubscribe from this group and stop receiving emails from it, send >>> an email to [email protected]. >>> To post to this group, send email to [email protected]. >>> Visit this group at https://groups.google.com/group/everything-list. >>> For more options, visit https://groups.google.com/d/optout. >>> >>> -- >>> You received this message because you are subscribed to the Google >>> Groups "Everything List" group. >>> To unsubscribe from this group and stop receiving emails from it, send >>> an email to [email protected]. >>> To post to this group, send email to [email protected]. >>> Visit this group at https://groups.google.com/group/everything-list. >>> For more options, visit https://groups.google.com/d/optout. >>> >>> >>> http://iridia.ulb.ac.be/~marchal/ >>> >>> >>> >>> >> -- >> You received this message because you are subscribed to the Google Groups >> "Everything List" group. >> To unsubscribe from this group and stop receiving emails from it, send an >> email to [email protected]. >> To post to this group, send email to [email protected]. >> Visit this group at https://groups.google.com/group/everything-list. >> For more options, visit https://groups.google.com/d/optout. >> >> >> http://iridia.ulb.ac.be/~marchal/ >> >> >> >> > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To unsubscribe from this group and stop receiving emails from it, send an > email to [email protected] <javascript:>. > To post to this group, send email to [email protected] > <javascript:>. > Visit this group at https://groups.google.com/group/everything-list. > For more options, visit https://groups.google.com/d/optout. > > > http://iridia.ulb.ac.be/~marchal/ > > > > -- You received this message because you are subscribed to the Google Groups "Everything List" group. 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