On 13 January 2012 17:24, Stephen P. King <stephe...@charter.net> wrote:

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> I submit to you that you cannot just ignore the > universals vs. nominal problem and posit by fiat that just because one can > proof the truth of some statement that that statement's existence determines > its properties. Our ability to communicate ideas follows from their > universality, that they do not require *some particular* physical > implementation, but that is not the same as requiring *no* physical > implementation. You argue that *no* physical implementation is necessary; I > disagree. Forgive me for butting in (particularly in the light of the fact that I too lack Bruno's erudition, only in spades) but I simply don't read Bruno's work in the way you are representing it. I see it like this: we have little option but to split our theories of "what there is" into two parts: the epistemological (i.e. the only form in which, and the exclusive means whereby, we have any access to information) and the ontological (i.e. some coherent theoretical framework in which to situate what that knowledge seems to reveal, and also, ideally, one that is able to account satisfactorily for how we are able to come by such knowledge in the first place). But after Kant, we can surely no longer believe that the ontological component of this dyad can possibly give us direct access to some ultimate ding and sich? Rather, what we seek in such theories is a mathematical schema in terms of which the relations between "primitive" theoretical entities, which themselves explicitly lack any further internal relations or characteristics, can be framed. Of course, this bare mathematical depiction cannot be reconciled with any aspect of experience without recombination with the epistemological component, which in most theories typically entails a sleight-of-thought that is still, to say the least, almost entirely opaque. If the foregoing is even vaguely true, then surely your debate with Bruno cannot be about whether either matter or numbers "really exist", because the very notion of "real existence" transcends anything about which we can theorise or have experience. Since mathematics delimits any possible ontological characterisation, the debate can in consequence only be about the derivation, priority and hence relative "primitiveness", of the mathematical "entities" thus characterised. In fact, this is an implicit assumption, so far as I can see, amongst physicists, who have until quite recently assumed that the mathematical structure of physics, as currently known, simply was the relevant "primitive" structure. However, attempts to reach beyond the puzzles of current theory have already led some, like Tegmark, to an explicitly mathematical characterisation of physical ontology. Bruno's work, it seems to me, is in the same spirit, with the critical distinction that he believes that, unless the epistemological component is placed at the centre of the theory, the appearances cannot ultimately be saved. Consequently, it is inaccurate to say that "physical representation" is not a core aspect of his theory - it is absolutely central, just not primitive, in the sense that the theory seeks to derive it as an aspect of a more fundamental (in fact, in Bruno's contention, the MOST fundamental) mathematical framework . David > Hi Bruno, > > > On 1/13/2012 4:38 AM, Bruno Marchal wrote: > > Hi Stephen, > > On 13 Jan 2012, at 00:58, Stephen P. King wrote: > > Hi Bruno, > > On 1/12/2012 1:01 PM, Bruno Marchal wrote: > > > On 11 Jan 2012, at 19:35, acw wrote: > > On 1/11/2012 19:22, Stephen P. King wrote: > > Hi, > > I have a question. Does not the Tennenbaum Theorem prevent the concept > of first person plural from having a coherent meaning, since it seems to > makes PA unique and singular? In other words, how can multiple copies of > PA generate a plurality of first person since they would be an > equivalence class. It seems to me that the concept of plurality of 1p > requires a 3p to be coherent, but how does a 3p exist unless it is a 1p > in the PA sense? > > Onward! > > Stephen > > > My understanding of 1p plural is merely many 1p's sharing an apparent 3p > world. That 3p world may or may not be globally coherent (it is most > certainly locally coherent), and may or may not be computable, typically I > imagine it as being locally computed by an infinity of TMs, from the 1p. At > least one coherent 3p foundation exists as the UD, but that's something very > different from the universe a structural realist would believe in (for > example, 'this universe', or the MWI multiverse). So a coherent 3p > foundation always exists, possibly an infinity of them. The parts (or even > the whole) of the 3p foundation should be found within the UD. > > As for PA's consciousness, I don't know, maybe Bruno can say a lot more > about this. My understanding of consciousness in Bruno's theory is that an > OM(Observer Moment) corresponds to a Sigma-1 sentence. > > > You can ascribe a sort of local consciousness to the person living, > relatively to you, that Sigma_1 truth, but the person itself is really > related to all the proofs (in Platonia) of that sentences (roughly > speaking). > > > OK, but that requires that I have a justification for a belief in Platonia. > The closest that I can get to Platonia is something like the class of all > verified proofs (which supervenes on some form of physical process.) > > > You need just to believe that in the standard model of PA a sentence is true > or false. I have not yet seen any book in math mentioning anything physical > to define what that means. > *All* math papers you cited assume no less. > > > I cannot understand how such an obvious concept is not understood, even > the notion of universality assumes it. The point is that mathematical > statements require some form of physicality to be known and communicated, it > just is the case that the sentence, model, recursive algorithm, whatever > concept, etc. is independent of any particular form of physical > implementation but is not independent of all physical representations. We > cannot completely abstract away the role played by the physical world. > > > > I simply cannot see how Sigma_1 sentences can interface with each other such > that one can "know" anything about another absent some form of physicality. > > > The "interfaces" and the relative implementations are defined using addition > and multiplication only, like in Gödel's original paper. Then UDA shows why > physicality is an emergent pattern in the mind of number, and why it has to > be like that if comp is true. AUDA shows how to make the derivation. > > > No, you have only proven that the idea that the physicalist idea that > "mind is an epiphenomena" is false, i.e. that material monism is false. A > proof that I understand and agree with. Your arguments and discussions in > support of ideal monism and, like Berkeley's, still fail because while the > physical is not primitive, it is not merely the epiphenomena of the mind > either. You are perhaps confused by the fact that unlike the physical, ideas > can represent themselves. > > > > > > If I take away all forms of physical means of communicating ideas, no > chalkboards, paper, computer screens, etc., how can ideas be possibly > communicated? > > > Because arithmetical truth contains all machine 'dreams", including dreams > of chalkboards, papers, screens, etc. UDA has shown that a "real paper", or > & "real screen" is an emergent stable pattern supervening on infinities of > computation, through a competition between all universal numbers occurring > below our substitution level. You might try to tell me where in the proof > you lost the arguement. > > > When these "infinities of computations" are taken to have specific > properties merely because of their existence. You are conflating existence > with property definiteness. Most people have this problem. > > > > > Mere existence does not specify properties. > > > That's not correct. We can explain the property "being prime" from the mere > existence of 0, s(0), s(s(0)), ... and the recursive laws of addition and > multiplication. > > > No, existence does not specify anything, much less that "0, s(0), > s(s(0)), ..." is distinct from any other string, nor does it specify the > laws of addition or multiplication. Existence is not a property that an > object has. You need to study the "problem of universals" in philosophy, it > is well known and has been debated for even thousands of years. For example > see 1 or 2. > > > > I go so far as considering that the wavefunction and its unitary evolution > exists and it is a sufficiently universal "physical" process to implement > the UD, but the UD as just the equivalent to Integers, nay, that I cannot > believe in. “One cannot speak about whatever one cannot talk.” ~ Maturana > (1978, p. 49) > > > I think Maturana was alluding to Wittgenstein, and that sentence is almost > as ridiculous as Damascius saying "one sentence about the ineffable is one > sentence too much". But it is a deep meta-truth playing some role in > number's theology. > > > OK, I deeply appreciate your erudition, you are much more educated than > I am, but nevertheless, I submit to you that you cannot just ignore the > universals vs. nominal problem and posit by fiat that just because one can > proof the truth of some statement that that statement's existence determines > its properties. Our ability to communicate ideas follows from their > universality, that they do not require *some particular* physical > implementation, but that is not the same as requiring *no* physical > implementation. You argue that *no* physical implementation is necessary; I > disagree. > > > But I think that you cannot define the universal wave without postulating > arithmetical realism. In fact real number+trigonometrical function is a > stronger form of realism than arithmetical realism. Adding "physical" in > front of it adds nothing but a magical notion of primary substance. > Epistemologically it is a form of treachery, by UDA, it singles out a > universal number and postulate it is real, when comp explains precisely that > such a move cannot work. > > > I am allowing for realism, it is a belief that may be true, but it is > not a unique singleton in the universe of models. I am arguing against the > idea that the physical is primitive, against substantivalism especially as > it is occurring in physics, for example see: > www.dur.ac.uk/nick.zangwill/Haeccieties.doc or 4. > In physics there is a huge debate over the haecceity of space-time and > your result is important in this, but your attempt to argue from the other > side is as treacherous because it ignores the necessity of the physical. > Material monism would have us believe that the physical is necessary and > sufficient for existence. You seem to argue that idealism is necessary and > sufficient. I argue that both the physical and the ideal are necessary but > not sufficient. My argument is a form of inversion of Bertrand Russell's > argument for neutral monism, but I fear that my lack of erudition hides the > concept that I am trying to communicate. > I can only hope that some person that is better at communicating ideas > will some day publish the paper that makes this idea clear to any that are > interested. > > Onward! > > Stephen > > > > Bruno > > > > Bruno > > > I think you might be confusing structures/relations which can be contained > within PA with PA itself. > > On 1/11/2012 12:07 PM, acw wrote: > > On 1/10/2012 17:48, Bruno Marchal wrote: > > > On 10 Jan 2012, at 12:58, acw wrote: > > On 1/10/2012 12:03, Bruno Marchal wrote: > > > On 09 Jan 2012, at 19:36, acw wrote: > > > > To put it more simply: if Church Turing Thesis(CTT) is correct, > mathematics is the same for any system or being you can imagine. > > > I am not sure why. "Sigma_1 arithmetic" would be the same; but higher > mathematics (set theory, analysis) might still be different. > > > > > If it's wrong, maybe stuff like concrete infinities, hypercomputation > and infinite minds could exist and that would falsify COMP, however > there is zero evidence for any of that being possible. > > > Not sure, if CT is wrong, there would be finite machines, working in > finite time, with well defined instructions, which would be NOT Turing > emulable. Hypercomputation and infinite (human) minds would contradict > comp, not CT. On the contrary, they need CT to claim that they compute > more than any programmable machines. CT is part of comp, but comp > is not > part of CT. > Beyond this, I agree with your reply to Craig. > > > In that response I was using CT in the more unrestricted form: all > effectively computable functions are Turing-computable. > > > I understand, but that is confusing. David Deutsch and many physicists > are a bit responsible of that confusion, by attempting to have a notion > of "effectivity" relying on physics. The original statement of Church, > Turing, Markov, Post, ... concerns only the intuitively human computable > functions, or the functions computable by finitary means. It asserts > that the class of such intuitively computable functions is the same as > the class of functions computable by some Turing machine (or by the > unique universal Turing machine). Such a notion is a priori completely > independent of the notion of computable by physical means. > > Yes, with the usual notion of Turing-computable, you don't really need > more than arithmetic. > > It might be a bit stronger than the usual equivalency proofs between a > very wide range of models of computation (Turing machines, Abacus/PA > machines, (primitive) recursive functions (+minimization), all kinds > of more "current" models of computation, languages and so on). > > > Yes. I even suspect that CT makes the class of functions computable by > physics greater than the class of Church. > > > That could be possible, but more evidence is needed for this(beyond > the random oracle). I also wonder 2 other things: 1) would we be able > to really know if we find ourselves in such a world (I'm leaning > toward unlikely, but I'm agnostic about this) 2) would someone > performing my experiment(described in another message), lose the > ability to find himself in such a world (I'm leaning toward 'no, if > it's possible now, it should still be possible'). > > If hypercomputation was actually possible that would mean that strong > variant of CT would be false, because there would be something > effectively computable that wasn't computable by a Turing machine. > > > OK. > > > > In a way, that strong form of CT might already be false with comp, > only in the 1p sense as you get a free random oracle as well as always > staying consistent(and 'alive'), but it's not false in the 3p view... > > > Yes. Comp makes physics a first person plural reality, and a priori we > might be able to exploit the first plural indeterminacy to compute more > function, like we know already that we have more "processes", like that > free random oracle. The empirical fact that quantum computer does not > violate CT can make us doubt about this. > > > > In the third person, there's no need to consider more than UD, which > seems to place some limits on what is possible, but in the first > person, the possibilities are more plentiful (if COMP). > > Also, I do wonder if the same universality that is present in the > current CT would be present in hypercomputation (if one were to assume > it would be possible) > > > Yes, at least for many type of hypercomputation, notably of the form of > computability with some oracle. > > > - would it even retain CT's current "immunity" from diagonalization? > > > Yes. Actually the immunity of the class of computable functions entails > the immunity of the class of computable functions with oracle. So the > consistency of CT entails the consistency of some super-CT for larger > class. But I doubt that there is a super-CT for the class of functions > computable by physical means. I am a bit agnostic on that. > > OK, although this doesn't seem trivial to me. > > > As for the mathematical truth part, I mostly meant that from the > perspective of a computable machine talking about axiomatic systems - > as it is computable, the same machine (theorem prover) would always > yield the same results in all possible worlds(or shared dreams). > > > I see here why you have some problem with AUDA (and logic). CT = the > notion of computability is absolute. But provability is not absolute at > all. Even with CT, different machine talking or using different > axiomatic system will obtain different theorems. > In fact this is even an easy (one diagonalization) consequence of CT, > although Gödel's original proof does not use CT. provability, nor > definability is not immune for diagonalization. Different machines > proves different theorems. > > > > If questions(axiomatic system being looked into) are different, > results can be different too, but if the questions (and inference > steps) are the same, shouldn't the result always be the same? This > would follow from CTT implementing a theorem prover. > > > Although with my incomplete understanding of the AUDA, and I may be > wrong about this, it appeared to me that it might be possible for a > machine to get more and more of the truth given the consistency > constraint. > > > That's right both PA + con(PA) and PA + ~con(PA) proves more true > arithmetical theorems than PA. > And PA + con(PA + con(PA + con (PA + con PA)) will proves even more > theorems. The same with the negation of those consistency. > > > I do wonder what kind of interesting theorems would result from those. > > Note that the theory PA* = PA* + con(PA*), which can be defined finitely > by the use of the Kleene recursion fixed point proves ALL the true > propositions of arithmetic!!! Unfortunately it proves also all false > propositions of arithmetic. This follows easily by the second theorem of > Gödel, because such a theory can prove its own consistency given that > (con "itself") is an axiom, and by Gödel II, it is inconsistent. > > > PA* is the one which claims its on consistency as a theorem? It would > be inconsistent in that case, and unfortunately, even if it shows some > new truths, we lose the ability of telling true from false, making it > a bit useless once one starts making inferences from false statements. > > But, yes, once you have a consistent machine, you can extend its > provability ability on the whole constructive transfinite. > > How come? PA being able to encode a theorem prover for ZFC, wouldn't > mean PA believes in the truth of ZFC(or some other set theory)? Or did > I misunderstand something here. Maybe you should recommend me some > book or paper to read that would explain this to me. > > > > As for higher math, such as set theories: do they have a model and are > they consistent? (that's an open question) If some forms close to > Cantor's paradise are accepted in the ontology, wouldn't that risk > potentially falsifying COMP? > > > Trivially. You can refute comp in the theory ZF + ~comp (accepting some > formalization of comp in set theory). > > > With that question I was more concerned about the number of entities > appearing in the theory and that the possibility of concrete > infinities appearing in the physics and thus leading to possible > worlds where brains implementations have with concrete infinities = > lack of substitution level. > > Remember that, like consistency, (~ probable comp) is consistent with > comp. If comp is true, like consistency, it is not provable, and so you > can add (~ provable comp), or (con ~comp) to the comp theory of > everything (arithmetic) without getting an inconsistency with comp. Of > course you should not add ~comp to comp at the same (meta)level. You > will get a contradiction. > > > I've always wondered about one thing: if there are solid evidences for > COMP being true(in the sense of no evidence about it being false being > found, its predictions confirmed by observation and so on), wouldn't > that warrant a belief in it? It would be religious belief in a way, > like belief in the consistency of PA or some others belief in God or > primitive matter or reality or particular physical laws or whatever > (some may be true, other may be false, but one must have some > assumptions if they have to bet on something). > > In another way, a conscious machine can always doubt that it's a > machine and this doubt would not make it inconsistent. > > Likewise, as above, the theory PA + (PA is inconsistent) is consistent. > You can prove, in it, that the false is provable, but you cannot prove, > in it, the false. Bf -> f is not a theorem (Bf -> f) = ~Bf = > consistency. > > > I always found that as a non-intuitive consequence of Godel's theorems. > PA doesn't contains a proof of its own consistency, if it's consistent > (it is inconsistent if it does contain it). > On the other hand, in a stronger theory, which shows PA consistency > (for example ZFC), wouldn't PA + (PA is inconsistent) be inconsistent? > Or to put it different, wouldn't it lack a model (because 'PA is > inconsistent' would be false, despite not being provable within PA > itself)? > Maybe it could even be generalized to adding a sentence which could be > false, but from which nothing false could be proven within some > axiomatic system. > > I hope that some of these ideas will be clearer to me after I'm done > reading those books on logic and provability. > > I can see many reasons why a particular machine/system would want to > talk about such higher math, but I'm not sure how it could end up with > different discourses/truths if the machine('s body) is computable. > > > Here there is a difficulty, and many people get it wrong. There is a > frequent error in logic which mirrors very well Searles error in his > chinese room argument. With comp I can certainly simulate Einstein's > brain, but that fact does not transform me into Einstein. If someone > asks me a complex question about relativity, I might be able to answer > by simulating what Einstein would respond, but I might still not have a > clue about what the meaning of Einstein's answer. In fact I would just > make it possible for Einstein to answer the question. Not me. > Like wise, a quasi debilitating arithmetical theorem system like > Robinson Arithmetic, which cannot prove x+y = y+x, for example, is still > Turing universal, and as such can imitate PA perfectly through its > provability abilities. That is, RA is able to prove that PA can prove > x+y=y+x. But RA has not the power to be convinced by that PA's proof, > like I can simulate Einstein without having the gift to understand any > words by him. > > RA can simulate PA and ZF, and even ZF+k (which can prove the > consistency of ZF), but this does not give to RA the *provability* power > of PA, ZF or ZF+k. > > PA can prove that ZF can prove the consistency of PA, but PA can still > not prove the consistency of PA. > > > > I don't think I said that PA can take other system's truths as their > own, even if it can simulate other systems, it cannot believe they are > true, and if it could, it no longer would be PA, but some other system. > What I was talking about was a bit different, formal systems can be > simulated by some UTM, thus while the UTM wouldn't "be" the system (in > the same way that in COMP, a brain could allow a mind to manifest > relatively to some other observers, but it wouldn't be that mind), > given the same questions asked to some particular Turing-emulable > system, the answers will always be the same. That of course doesn't > mean that PA can take ZFC truths as its own - they are not provable in > PA. > > In another way, the totality of possible discourses should be present > within PA, but that doesn't mean PA can take them as its truths. > There's another problem here: not all formal systems will be > consistent or have models, but unless we have proofs of their > inconsistency, we will never know. > > Some of this confusion might be because, we as humans, sometimes take > other people or system's beliefs as our own, even if doing so is not > always rational, but despite that this increases the risk of being > wrong, it also lets us get to a lot more truth. > > I can see it discovering the independence of certain axioms (for > example the axiom of choice or the continuum hypothesis), but wouldn't > all the math that it can /talk/ about be the same? The machine would > have to assume some axioms and reason from there. > > > Yes. And with different axioms you get different provability aptitudes. > Once a machine can prove all true arithmetical sigma_1 sentences (with > the shape ExP(x) with P decidable) she is universal, with respect to > *computability. You can add as many axioms you want, the machine will > not *compute* more functions. But adding axioms will always lead the > machine into proving more *theorems*. > > In AUDA, "belief" is modeled by provability (not computability), and > then knowledge is defined in the usual classical (Theaetetus) ways. All > beliefs of the correct machines will obeys to the same self-referential > logic, but all belief-content will differ from a machine to a different > machine. PA and ZF have the same self-referential logics, but they have > quite different belief, even restricted on the numbers. > For example ZF proves more arithmetical truth than PA. ZFC and ZF+(~C) > proves exactly the same theorem in arithmetic, despite they proves quite > different theorem about sets (so arithmetic is deeply independent of the > axiom of choice). ZF+k (= ZF + it exists an inaccessible cardinal) > proves *much more* arithmetical theorem than ZF. > > To sum up: > Computability is an absolute notion. > Provability is a relative notion. > > > > I think we're mostly in agreement here, beliefs (what's provable) will > differ per machine, and with adding more axioms, more beliefs are > possible. > > There can be many 'believers'(axiomatic systems), but all of them can > be implemented by the same base(their "body", some theorem prover > implemented by some UTM). > > However, I would like to know what the many more arithmetical theorems > ZF(and some of its extensions) that proves are. The only ones I'm > familiar with are the type of PA's consistency and Goodstein's theorem > as well as similar results about the fact that some sequences > terminate/halt. > > > > > BTW, acw, you might try to write a shorter and clearer version of your > joining post argument. It is hard to follow. If not, I might take much > more time. > > Bruno > > > > I think I talked about too many different things in that post, not all > directly relevant to the argument (although relevant when trying to > consider as many consequences as possible of that experiment). If some > parts are unclear, feel free to ask in that thread. The general > outline of what I talked about in the part you have yet to comment on: > a generalized form of the experiment the main character from > "Permutation City" novel performed is described in detail(assuming > COMP), a possible explanation for why it might not actually be useless > to perform such an experiment and why it might be a good practical > test for verifying the consequences described in the UDA, various > variations/factors/practicalities of that experiment are discussed > (with goals such as reducing white rabbits, among a few others), some > not directly relevant to the argument and at the end I tried to see if > the notion of observer can be better defined and tried to show that > the notion of "generalized brain" might not always be an appropriate > way to talk about an observer. That post was mostly meant to be > exploratory and I hoped the ensuing discussion would lead to 2 things: > 1) assessing the viability of that experiment if COMP is assumed AND > 2) reaching a better definition of the notion of observer. > > > OK. This I think I understood this, but your style is not easy, and it > might be useful, even within your goal, to work on a clearer and shorter > version, with shorter sentences, without any digression, with clear > section and subsection, so as to invite most people (including me) to > grasp it, or to find a flaw, and this in reasonable time. In particular > I fail to see the point of discussing the use of different universal > systems like you did with the Cellular Automata (CA). > > Bruno > > > http://iridia.ulb.ac.be/~marchal/ > > > > > I will consider rewriting it if the time allows. The original idea as > presented in that book, had a CA as their "primary physics", so I > tried to show the difference between my experiment and the experiment > in the book. > > If one assumes COMP, there is no longer a need for choosing any > particular physical system, such as a CA. I then went on to say that > if a 'physical CA' is chosen, there are many practical problems that > could occur, both a decrease in stability(white rabbits, jumpyness), > as well as many problems for those living with the system > (speed-of-light limit and most social problems present in our physical > world). > > I think it could only be 100% stable if the (mind's) substitution > level is exactly at the CA level, which was not the case in the book. > > Instead of such a "primary physics", I just choose an easy to > design/program Turing-equivalent machine (such as something based on a > PA machine), which implements a message-passing operating > system/scheduler on top of it. I argue that the careful use of a > random oracle should reduce the chance of white-rabbits and increase > the overall world's stability(1p experiences not being too jumpy), but > I still don't know to what degree this would be sufficient (oracle > implemented by dovetailing or leaving "undefined"). I tried to > consider how the choice of OS and observer's implementation could > affect the world's stability(1p). > > As a thought experiment, I could have stopped there, but I decided to > consider more practical details as well, because if one day there will > be a computationalist doctor to say yes to and one wants to perform > such an experiment, they better have all their details right, > otherwise after performing the experiment, their future 1p experiences > might not be very pleasant. > > > > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To post to this group, send email to everything-list@googlegroups.com. > To unsubscribe from this group, send email to > everything-list+unsubscr...@googlegroups.com. > For more options, visit this group at > http://groups.google.com/group/everything-list?hl=en. > > > http://iridia.ulb.ac.be/~marchal/ > > > > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To post to this group, send email to everything-list@googlegroups.com. > To unsubscribe from this group, send email to > everything-list+unsubscr...@googlegroups.com. > For more options, visit this group at > http://groups.google.com/group/everything-list?hl=en. > > > http://iridia.ulb.ac.be/~marchal/ > > > > > -- > You received this message because you are subscribed to the Google Groups > "Everything List" group. > To post to this group, send email to everything-list@googlegroups.com. > To unsubscribe from this group, send email to > everything-list+unsubscr...@googlegroups.com. > For more options, visit this group at > http://groups.google.com/group/everything-list?hl=en. -- You received this message because you are subscribed to the Google Groups "Everything List" group. 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