> On 5 Nov 2018, at 11:41, Philip Thrift <[email protected]> wrote: > > > > On Monday, November 5, 2018 at 3:36:59 AM UTC-6, Bruno Marchal wrote: > >> On 2 Nov 2018, at 15:02, Philip Thrift <[email protected] <javascript:>> >> wrote: >> >> >> >> On Friday, November 2, 2018 at 3:45:53 AM UTC-5, Bruno Marchal wrote: >> >>> On 1 Nov 2018, at 19:43, John Clark <[email protected] <>> wrote: >>> >>> >>> On Thu, Nov 1, 2018 at 2:27 PM Philip Thrift <[email protected] <>> wrote: >>> >>> > infinite time Turing machines are more powerful than ordinary Turing >>> > machines >>> >>> That is true, it is also true that if dragons existed they would be >>> dangerous and if I had some cream I could have strawberries and cream, if I >>> had some strawberries. >>> >>> > How "real" you think this is depends on whether you are a Platonist or a >>> > fictionalist. >>> >>> No, it depends on if you think logical contradictions can exist, if they >>> can then there is no point in reading any mathematical proof and logic is >>> no longer a useful tool for anything. >>> >> >> >> No Turing machine can solve the halting problem. You are right on this. But >> an oracle can, or a machine with infinite speed can. >> >> Now, such machine have only be introduced (by Turing) to show that even such >> “Turing machine with magical power making them able to solve the halting >> problem” are still limited and cannot solve, for example the totality >> problem (also an arithmetical). >> >> Turing showed that there is a hierarchy of problem in arithmetic, where >> adding magic (his “oracle”) never make any machine complete. It is a way to >> show how complex the arithmetical reality is. Adding more and more magical >> power does not lead to completeness. >> >> Post and Kleene have related such hierarchies with the number of alternating >> quantifiers used in the arithmetical expression. P is a sigma_0 = pi_0 >> formula, without quantifier. >> >> ExP(x, y). Sigma_1 (negation = AxP(x,y) = Pi_1, more complex than sigma_1, >> already not computable). >> ExAyP(x, y, z) = Sigma_2 (beyond today’s math!) (negation = Pi_2). >> Etc. >> >> More and more “infinite task” are needed. >> >> Note that such magic does not change the “theology”. It remains the same >> variants of the Gödel-Löb-Solovay self-reference logics (G and G*). >> >> Bruno >> >> >> >> >> There are other "Turing machine" models other than infinite-time ones people >> have "invented", e.g. inductive Turing machines: >> >> Algorithmic complexity as a criterion of unsolvability >> https://pdfs.semanticscholar.org/cd8f/442a9f7667891fff6f276a1bc638dd59b937.pdf >> >> <https://pdfs.semanticscholar.org/cd8f/442a9f7667891fff6f276a1bc638dd59b937.pdf> >> : >> >> Let us take an inductive Turing machine M that given a description of the >> Turing machine T and first n + 1 words x0, x1, . . . , xn from the list x0, >> x1, . . . , xn, . . ., produces the (n + 1)th partial output. This output is >> equal to 1 when the machine T halts for all words x0, x1, . . . , xn given >> as its input, and is equal to 0 when the machine T does not halt for, at >> least, one of these words. In such a way, the machine M solves the totality >> problem for Turing machines. >> >> ? >> >> >> cf. >> https://en.wikipedia.org/wiki/Super-recursive_algorithm#Inductive_Turing_machines >> >> <https://en.wikipedia.org/wiki/Super-recursive_algorithm#Inductive_Turing_machines> >> https://bitrumagora.wordpress.com/about/marl-burgin/ >> <https://bitrumagora.wordpress.com/about/marl-burgin/> >> >> >> Nothing is settled in computing. > > > But this does not clearly violate Church-Thesis. Inference inductive is not > the same as computing. We know that there are many different Turing machine, > which are not equivalent for proving or inducting, etc. All humans are like > that. We are still the same *as* Turing machine (combinators, etc.). > Universality is with respect to computing, and is false with everything else. > Now, if you add magical, or actual infinities, or oracles, or infinite speed, > then you get machine which are no more digital finite machine, and so cannot > violate the Church-Turing thesis either. > > Bruno > > > > > > From all the super-Turing math and CS news (I've followed over the years), > there seems to be a consensus forming: > > > There are no super-Turing computers! (that can be found in nature or > manufactured by us) > > > cf. > https://phys.org/news/2015-09-limit-church-turing-thesis-accounts-noisy.html > > The only ones are fictional ones (the infinite-time and super-recursive ones > above). > > So that seems to be the consensus.
Thank you for the good news, although I do not care on consensus too much, except to despair of humanity ... > > > But I claim an experience-processing computer (like our brain) is not > super-Turing, but is non-Turing: All information it can process is > Turing-computable, but it also processes experience. I think we agree on this. Experience is NOT information processing. That is provable using very standard definition (the greek one) and using mechanism. But you go out of mechanism by your use of matter in the process of those experiences. Which seems to me very weird, as it is like invoking a supernatural being (some primitive matter) which is actually part of the difficulty when solving the mind-body problem, with or even without mechanism. It would be nice if you study the first steps of the Universal Dovetailer Argument so that we might perhaps be able to isolate where we might really differ or not, beyond your apparent belief in “matter”. Cf http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHALAbstract.html Bruno > > > - pt > > > > > -- > 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 post to this group, send email to [email protected] > <mailto:[email protected]>. > Visit this group at https://groups.google.com/group/everything-list > <https://groups.google.com/group/everything-list>. > For more options, visit https://groups.google.com/d/optout > <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.
