On 9 Sep 2018, at 21:51, Philip Thrift <cloudver...@gmail.com
<mailto:cloudver...@gmail.com>> wrote:
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 <mar...@ulb.ac.be
<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 manypeople
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.
/
Idon'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
