> On 9 Mar 2020, at 12:00, Philip Thrift <[email protected]> wrote: > > > > On Monday, March 9, 2020 at 4:57:24 AM UTC-5, Bruno Marchal wrote: > >> On 5 Mar 2020, at 12:42, ronaldheld <[email protected] <javascript:>> wrote: >> >> Any comments, especially from Bruno, and the Physicalists? >> >> -- >> 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 view this discussion on the web visit >> https://groups.google.com/d/msgid/everything-list/ff950ee5-b253-464e-b0aa-9eca73399b9c%40googlegroups.com >> >> <https://groups.google.com/d/msgid/everything-list/ff950ee5-b253-464e-b0aa-9eca73399b9c%40googlegroups.com?utm_medium=email&utm_source=footer>. >> <2003.01807.pdf> > > > The paper is quite interesting, but I will have to deepen my understanding of > Black Hole (and GR) to better appreciate it. > > There are some preliminary point were “I disagree” (or the universal machine > disagree) but they might not be relevant, with respect to the paper, but > relevant to the plausible link you make between the paper and physicalism. > > Typically, the first sentence of the paper is “physicalist”, which is not > astonishing in this context. Susskind says that the original Church-Turing > thesis may be regarded as a principle of physics (which it is not). > > This can be shown inconsistant with the mechanist assumption in Cognitive > Science (not in physics). Indeed, with mechanism, a priori, the physical > reality should be able to compute more than a Turing machine. The physical > reality can simulate “real” random oracle, for examples, and any physical > object requires the entire universal dovetailing to be determined. That > entails non cloning, and a priori much more computability abilities (random > oracle, “white rabbits”, infinite sum on infinitely histoiries, the full set > of true sigma_1 sentences, but also non computable Pi_1 truth pertaining to > the distribution of accessible states, etc. > That is so true, that Mechanism must explain the apparent computability of > nature from non computable subset of the arithmetical truth. So, here, > implicitly the paper relies on physicalism, without the awareness that > eventually the physical appearances have to be explained by the statistics on > all computations in arithmetic, not just the “quantum one”, and the quantum > must be extracted from the machine’s theory of consciousness (as I did). So, > normally, it can be expected that the (original) Church-Turing thesis (which > is one half of Mechanism) might imply the falsity of the quantum > Church-Turing thesis (due to Deutch, and I have to think how much that is > related to Susskind quantum-extended Church thesis). > > This concerns only the original Church Thesis and its impact on the possible > physics available to arithmetical machine, and as physics is not yet entirely > derived neither from Arithmetic, nor from observation (cf the GR + QM > problems), it is hard at this stage to see how much mechanism will assess or > diminish the validity of Susskind’s idea on the extended Quantum and physical > version of CT. > Yet, unlike the typical use of quantum mechanics to prevent an infinite > computation to be realised in the physical universe, which would need digital > state encodable below the Planck Era (and thus hardly usable by any concrete > observer), the idea of Susskind is more subtle, and involves a notion of > “complexity” related to the interior of Black-Hole. I would need here to > revise (to say the least) Finkelstein derivation of GR from a finitist or > discrete approach to Quantum Mechanics, which is still above my head … (I > mentioned the interesting book by Selesnick on it sometimes ago). > > So, just to be clear: > > CT = anything computable is computable by a Turing machine (or by a > combinator, or by Robinson Arithmetic, or by LISP, etc.). This has a priori > nothing to do with physics. > > I will note s-CT for Susskind Physicalist version of CT: any thing physically > computable is computable by a Turing machine. (The physical reality does not > compute more). This is an open problem to me. It is not excluded that the > physical reality which emerges from all computations in arithmetic might have > non Turing computable components. > > Then s-ECT is the thesis that anything computable *efficiently* (i.e. in > polynomial time) physically, by nature, is computable in polynomial time by a > Turing machine. This thesis is usually believed to be wrong, as Susskind > says, and indeed, if that was not wrong, we would not invest in quantum > computing. Most people today believes that factoring (large) number cannot be > done in polynomial time by a Turing machine. > > qECT (Susskind notation) is the (extended) thesis that says that if nature > can compute efficiently something then a quantum computer can compute it > efficiently. That is mainly what I call the Deustch Thesis. And as <I said, I > do think that CT (+ YD, i.e. mechanism) entails its plausible falsity. > > And Susskind abounds in that direction, and this without Mechanism, which > would make this into a yet another confirmation of Mechanism. > > With Mechanism, and assuming the existence of Black Hole, it should be > obvious that whatever happens in a black hole will not play a role in the > working of your brain. A good thing, as you will not have to ask to the > Doctor to emulate the interior of a black hole. But with mechanism, this > means that a black hole is full of "crazy virtual particles" doing infinitely > complex task, just because your state of mind is totally independent of > the”content of the black hole (without its boundary)". > > At first sight, Susskind seems convincing on this, but again, to be able to > asses this would require that I study much more the QM and GR of the black > hole. To compare with Mechanism, we have the rather complex task to derive GR > from QM and QM from arithmetic before, so this is a bit premature (I still > work hard to have a notion of space, although its shadow is there, but > requires the existence of large cardinal in set theory. (As I said, with > Mechanism, the ontology is extremely simple (Robinson arithmetic), but the > phenomenology is of unbounded complexity. > > So, very interesting but complex idea by Susskind, but it touches on problem > which are far from being treated with the mechanist hypothesis. If I progress > in my understating of Finkelstein, I might say more later. The paper confirms > that there is something in the holographic idea, and when you compactify a > universal dovetailing, you get a sort of similar principle, given that the > first person experience are determined only on its “boundary”. > > Bruno > > > > In the (subject of) programming in infinite domains > > https://en.wikipedia.org/wiki/B%C3%B6hm_tree > <https://en.wikipedia.org/wiki/B%C3%B6hm_tree> > > A Böhm tree is a (potentially infinite) tree-like mathematical object that > can be used to provide denotational semantics > <https://en.wikipedia.org/wiki/Denotational_semantics> (the "meaning") for > terms of the lambda calculus <https://en.wikipedia.org/wiki/Lambda_calculus> > (and programming languages in general by using translations to lambda > calculus). It is named after Corrado Böhm > <https://en.wikipedia.org/wiki/Corrado_B%C3%B6hm>. > > A simple way to read the meaning of a computation is to consider it as a > mechanical procedure consisting of a finite number of steps that, when > completed, yields a result. This interpretation is inadequate, however, for > procedures that do not terminate after a finite number of steps, but > nonetheless have an intuitive meaning. Consider, for example, a procedure for > computing the decimal expansion ofπ <https://en.wikipedia.org/wiki/Pi>; if > implemented appropriately, it can provide partial output as it "runs", and > this ongoing output is a natural way to assign meaning to the computation. > This is in contrast to, say, a program that loops infinitely without ever > providing output. These two procedures have very different intuitive meanings. > > Since a computation described using lambda calculus is the process of > reducing a lambda term to its normal form, this normal form itself is the > result of the computation, and the entire process may be considered as > "evaluating" the original term. For this reason Church's > <https://en.wikipedia.org/wiki/Alonzo_Church> original suggestion was that > the meaning of the computation (described by) a lambda term should be the > normal form it reduces to, and that terms which do not have a normal form are > meaningless.[1] <https://en.wikipedia.org/wiki/B%C3%B6hm_tree#cite_note-1> > This suffers exactly the inadequacy described above. Extending the π analogy, > however, if "trying" to reduce a term to its normal form would give "in the > limit" an infinitely long lambda term (if such a thing existed), that object > could be considered this result. > > > > No such term exists in the lambda calculus, of course, and so Böhm trees are > the objects used in this place. > >
You can do that. But it is simpler and more general to define a computation by what a universal do, when given an input, or not. If P_i, represent the ith program in an complete enumeration of all programs in some Turing-universal system, and phi_i is the corresponding partial recursive function, or partial computable function, the computation can be described by the succession of steps brought by the universal machine which is able to run those programs. It is describable by phi_i(j)^s, where s number the steps. This works both for halting and non halting computations, and is not so far from the Bohm tree (which requires lambda calculus or the combinators). Church, like many logicians and mathematicians, was still too much focusing on extensional function, and not on the very process which compute them. This does not concern so much the measure problem (on all computations), because no machine can recognise if a computation run “its first person experience”, and that is why we need a more abstract approach, to get the measure by the probability logic, restricted to the computational state, weighted by the histories going through that state, without ever precising which state in particular is obtained. This works, as we get both the many-histories and the quantum logics on them. Bruno > > > @philipthrift > > -- > 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] > <mailto:[email protected]>. > To view this discussion on the web visit > https://groups.google.com/d/msgid/everything-list/543a9058-de71-4097-acdc-26abcf8ee078%40googlegroups.com > > <https://groups.google.com/d/msgid/everything-list/543a9058-de71-4097-acdc-26abcf8ee078%40googlegroups.com?utm_medium=email&utm_source=footer>. -- 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 view this discussion on the web visit https://groups.google.com/d/msgid/everything-list/C5808489-2A86-4567-8BAF-A0F96C5CB873%40ulb.ac.be.
