> On 22 Apr 2018, at 00:56, John Clark <johnkcl...@gmail.com> wrote: > > On Sat, Apr 21, 2018 at 5:10 PM, Telmo Menezes <te...@telmomenezes.com > <mailto:te...@telmomenezes.com>> wrote: > > > Turing machines don’t need infinite tape, they need sufficient tape, if > > you start to run out of tape then add more, > > > And for the general case there will be instances where you always need > more. > > Any calculation will ALWAYS require only a finite amount of tape, if more > tape is ALWAYS required then the problem can not be calculated. > > > Non-Turing universal machines can perform some computations. Even useful > ones, for sure. > > Well..., I admit none of the 64 possible one state Turing Machine is > universal and none of the 20,736 possible two state Turing Machines is > either, and I admit even a one state machine could perform useful > calculations, but if you know how to make a one state machine then it is a > trivial matter to make a N state machine, and that is universal. And a one > state machine is as simple as things get, anything simpler can't calculate > anything. > > > Computations realized in the physical world will always stop, > > I agree they will always stop but they will not always produce an answer.
In which case we say they do not stop. If they are stopped by an asteroid, or the Big Crunch, the first person associated to them still feel to continue, as its mind is associated with all computations in arithmetic, where the non stopping genuinely do not stop. To say all machines stop, you have to talk of very special case of machines. > > > If you apply to Turing the same demands that you apply to Bruno, you > can only conclude that Turing was a moron for > working on mathematical models that correspond to machines that cannot exist. > > The difference is a Turing Machine in the real physical world can very often > make calculations, often enough to create a trillion dollar industry, and > Turing told us exactly how to build such a device, but Bruno's "Löbian > machine" can NEVER make a calculation in the real physical world because > Bruno has no idea how to make one. See my answer in my other post of today. It is really an easy exercise to implement a Löbian machine.The combinators, like RA are Turing universal, but not Löbian. But implemented on prolog, you need only to add the induction axioms: like P(K) and P(S) and [(P(x) & P(y)) -> P((x y))] -> for all x, y P(x, y) (Induction axioms written for the combinators, for a change). > > > These machines are finite approximations of the machine that Turing > defined, > > A Turing Machine exists in the real physical world You cannot invoke god or reality, or real, or truth, in a scientific discourse. You assume a “real physical world”. I do not, and then shows that such an assumption, in company of Mechanism, leads to a contradiction. > that can calculate 2+2 and that machine has no need to be infinite and the > answer it produces is exact not approximate. But Bruno can't even tell how to > build a "finite approximation" of a Löbian machine in the real physical world. Why do you say things like that, which is utterly ridiculous (and ad hominem)?. Why not ask politely “how would you implement a Löbian machine” in the physical world (real or apparent), and that is easy to answer, and indeed is part of the easy exercise of my course. When you buy a physical computer, the hard part of Löbianity is already implemented. To make it into a set of beliefs, you need only to reimplemented in first order logic, already done if you use Prolog, and then to add the induction axioms, either as a meta-rule, or as a higher order axiom. Bruno > > John K Clark > > > > > > > -- > 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 everything-list+unsubscr...@googlegroups.com > <mailto:everything-list+unsubscr...@googlegroups.com>. > To post to this group, send email to everything-list@googlegroups.com > <mailto:everything-list@googlegroups.com>. > 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 everything-list+unsubscr...@googlegroups.com. To post to this group, send email to everything-list@googlegroups.com. Visit this group at https://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/d/optout.
