On Sunday, September 9, 2018 at 10:04:20 AM UTC-5, John Clark wrote: > > On Sun, Sep 9, 2018 at 6:44 AM Bruno Marchal <[email protected] > <javascript:>> wrote: > > >>Nobody on this planet uses the term "Löbian machine" except you. >> >> > > >*It is just a more precise version of what popular books described by >> “sufficiently rich theory”.* >> > > There is nothing precise about homemade slang used by nobody but you. > > *> There are many definition, but they are all equivalent.* >> > > And there is nothing profound about a definition, it's easy to define a > perpetual motion machine but that doesn't mean they exist, I can define a > Clark Machine as a machine that can solve the halting problem but that > doesn't mean I have the any idea how to make one or can even show that such > a thing could in principle exist. > > >> *>Any Turing complete theory of any universal machine, with sufficiently >> strong induction axiom (like sigma_1 induction) constitute a Löbian >> machine. * >> > > In the physical world induction is just a rule of thumb that usually works > pretty well most of the time, but it seldom works perfectly and never works > continuously, eventually it always fails. > > >>Turing explained exactly precisely how to build one of his machines but >>> you have never given the slightest hint of how to build a "Löbian machine" >>> or even clearly explained what it can compute that a Turing Machine can’t. >> >> >> >*?* >> > ! > > >*That means just that you need to go being step 3 in my thesis,* >> > > Step 3? Ah yes I remember now, that's the one with wall to wall personal > pronouns without a single clear referent in the entire bunch. > > >> > *The notion of Löbian machine is easy to construct,* >> > > The notion of a Perpetual Motion machine is also easy to construct as is > the Clark Machine that can solve the Halting Problem, but Turing did far > more than dream up a magical universal calculating machine, he showed > exactly how to make one. But we're not as smart as Turing, I can't do that > with my Clark Machine and you can't do that with your Löbian machine. > > >> * > and the mathematical reality is full of example of Löbian machine, >> and Löbian god* >> > > Löbian machine, Löbian god, the propositional part of the theology .... > tell me, have you ever wondered why so many people fail to take you > seriously? > > >> *>A Lpobian machine is just a universal machine capable of proving its >> own universality.* >> > > I have no trouble believing a universal machine is universal, but no > Turing Machine can in general prove it will halt and but no machine of any > sort, or anything else for that matter, can prove its own > consistency unless it is inconsistent. > > > Why do you want it to be able to do what a god can do? >> > > Odd question, who wouldn't want to do what a God can do? But if God can > solve the Halting Problem then He can also make a rock so heavy He can't > lift it. > > >>How would things be different if "the propositional part of the >>> theology" were not decidable? >> >> >> > >> *Solovay theorem would be false, and the subject of machine theology >> would be far more complex. * >> > > I don't know if that's true or not because "machine theology" is more of > your homemade gibberish, just like "the propositional part of the > theology". > > > *Note that the theology of machine has highly undecidable at the first >> order level.* >> > > And I don't know if that is true or not either because "the theology of > machine" is yet more of your patented homemade baby talk. > > John K Clark >
The only relevant "physical" theory I know about and is discussed widely is in terms of *relativistic computers* (which probably most think are forever merely fictional). Relativistic computers and the Turing barrier https://www.sciencedirect.com/science/article/abs/pii/S0096300305008398 http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.150.783&rep=rep1&type=pdf *We examine the current status of the physical version of the Church-Turing Thesis (PhCT for short) in view of latest developments in spacetime theory. This also amounts to investigating the status of hypercomputation in view of latest results on spacetime. We agree with [D. Deutsch, A. Ekert, R. Lupacchini, Machines, logic and quantum physics, Bulletin of Symbolic Logic 6 (3) (2000) 265–283] that PhCT is not only a conjecture of mathematics but rather a conjecture of a combination of theoretical physics, mathematics and, in some sense, cosmology. Since the idea of computability is intimately connected with the nature of time, relevance of spacetime theory seems to be unquestionable. We will see that recent developments in spacetime theory show that temporal developments may exhibit features that traditionally seemed impossible or absurd. We will see that recent results point in the direction that the possibility of artificial systems computing non-Turing computable functions may be consistent with spacetime theory. All these trigger new open questions and new research directions for spacetime theory, cosmology, and computability.* - 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]. 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.
