Re: Why is Church's thesis a Miracle?

[Philip Thrift]

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  > 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=rep1=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 

Re: Why is Church's thesis a Miracle?

[John Clark]

On Sun, Sep 9, 2018 at 6:44 AM Bruno Marchal  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

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Re: The codical-material universe

[Philip Thrift]

On Sunday, September 9, 2018 at 5:28:25 AM UTC-5, Bruno Marchal wrote:
>
>
> On 8 Sep 2018, at 23:53, John Clark > 
> wrote:
>
>
> Bruno Marchal Wrote:
>
> *> I cannot see primary matter. In fact I am not sure what you mean by 
>> matter, or by “mathematical-material universe”. [...] I have proven (40 
>> years ago) that materialism (the belief in some primary matter, or 
>> physicalism) and Mechanism are incompatible.*
>
>
> If you don't know what "matter" means then you certainly don't know what 
> "primary matter" means, so what the hell did you prove 40 years ago?  
>
>
> That if mechanism is true, the observable has to rely on a sophisticated 
> “sum” on all computations. 
>
> Matter = observable
>
> Primary matter is the doctrine by Aristotle according to which there is a 
> primary physical universe, or a primary sort of (non mathematical) reality 
> from which those observable would have emerge. With mechanism, it can be 
> shown that the laws pertaining on the observable have to be reduced to some 
> mode of arithmetical self-reference.
>
>
>
> I'm not even going to ask what you think physicalism means because any 
> such answer has to include physics and physics has to involve matter which 
> you admit confuses you. 
>
>
> No, it does not confuse me. It is just shown inconsistent to believe that 
> we have to assume its existence. A realm is primary if it cannot be reduced 
> to some other field”. May believe that biology is not primary, because it 
> can be reduced (apparently) to chemistry and physics. Similarly, with 
> Mechanism, physics is reducible to number theory or Turing equivalent.
>
>
>
>
>
> And for the same reason I'm not going to ask about "Mechanism" , the reply 
> would only contain yet more words you can neither define nor give examples 
> of.
>
>
> Digital Mechanism  is the doctrine that there is a level of description of 
> our body such that we can survive with a (physical) digital brain or body, 
> if it faithfully represents our body’s functionality at that description 
> level.
>
> Bruno
>
>
>
I seems *possible *to me that there could be a matter 
decompiler/transporter/compiler that takes *me*, decompiles *me* into some 
code, transports that code, and compiles that code into a 
digital-technology-based "brain" in some sort of "body". And it would be *me 
2*. and "I" would exist again.

But if it never recompiled me into any kind of material output -  I don't  
think I would exist anymore.

- pt

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Re: Why is Church's thesis a Miracle?

[Bruno Marchal]

> On 9 Sep 2018, at 01:12, John Clark  wrote:
> 
> On Sun, Sep 2, 2018 at 2:19 PM Bruno Marchal  > wrote:
> 
> > A function is computable if we can explain to a dumb (but docile) human 
> > being how to compute it, on any of its argument.
> 
> And some functions (the Sine function for example)


We talk only about functions from N to N. The computable real functions 
requires a good understanding first of the computable functions from subset of 
N to N?




> can be proven to be computable and some functions (the Busy Beaver function 
> for example) can be proven to be non-computable) but there is no general way 
> to know if any given function is computable or not.


>From its code, indeed. That is Rice theorem, and I have just proven it in this 
>thread.



>  
> > Each f_n is computable (by definition!) and so each f_n(n) can be computed, 
> > and adding one is certainly computable, so, the only thing which can be NOT 
> > computable is the bijection itself. This means that the f_i, although 
> > enumerable, are not recursively enumerable.
> If a universal language exist, then it cannot compute the enumeration of all 
> computable function from N to N.
> 
> The Ackermann function is not primitive recursive  and yet it is computable, 
> like the Busy Beaver the numbers soon become huge (although finite) but 
> unlike the Busy Beaver a Turing Machine can always calculate them. 

No problem with this. I avoid using the primitive recursive functions.



>  
> > Then the Löbian machine are those universal machine which knows that they 
> > are universal, and so get acquainted with the consequences (the infinite, 
> > the non provable, the non observable, …).
> 
> 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 are many definition, but they are all equivalent. Any Turing complete 
theory of any universal machine, with sufficiently strong induction axiom (like 
sigma_1 induction)  constitute a Löbian machine. Distinguished feature; their 
provability predicate verifies Löb’s formula: []([]p->p)->[]p. 

Easy exercice, show that Löbian machine obeys to Gödel’s second Gödel’s theorem 
<>t -> ~[]<>t.





> 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, or, if you 
don’t want to do philosophy of mind, just read the mathematical part. The 
notion of Löbian machine is easy to construct, and the mathematical reality is 
full of example of Löbian machine, and Löbian god (mathematical object which 
are not Turing emilable but having still a notion of belief associated with 
them which still obeys the Löb’s formula.



> Can it tell if any given function is computable?  Can it find the 8000th Busy 
> Beaver number? Can it even find the 5th?


A Lpobian machine is just a universal machine capable of proving its own 
universality. Why do you want it to be able to do what a god can do? I don’t 
like such sentence as it assumes that I would have something like that, but 
that is simply not the case. I study Mechanism. No machine can ever decide if 
any code is a code of  a total computable function, nor compute a non 
computable function.



> 
> >Here there is a second miracle, which is that the propositional part of the 
> >theology is decidable!
> 
> Homemade gibberish. 

?


> 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. Note that the theology of machine has highly undecidable at 
the first order level. G and G* are decidable, but qG (provable machine’ logic 
of belief/proof  with quantifier) is PI_2 complete (and thus highly 
undecidable), and qG* (true machine’s logic  of belief/proof* with quantifier) 
is PI_1 complete in the oracle of truth. 

Bruno





> 
> John K Clark
> 
> John K Clark
> 
>  
> 
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Re: The codical-material universe

[Bruno Marchal]

> On 8 Sep 2018, at 23:53, John Clark  wrote:
> 
> 
> Bruno Marchal Wrote:
> 
> > I cannot see primary matter. In fact I am not sure what you mean by matter, 
> > or by “mathematical-material universe”. [...] I have proven (40 years ago) 
> > that materialism (the belief in some primary matter, or physicalism) and 
> > Mechanism are incompatible.
> 
> If you don't know what "matter" means then you certainly don't know what 
> "primary matter" means, so what the hell did you prove 40 years ago? 

That if mechanism is true, the observable has to rely on a sophisticated “sum” 
on all computations. 

Matter = observable

Primary matter is the doctrine by Aristotle according to which there is a 
primary physical universe, or a primary sort of (non mathematical) reality from 
which those observable would have emerge. With mechanism, it can be shown that 
the laws pertaining on the observable have to be reduced to some mode of 
arithmetical self-reference.



> I'm not even going to ask what you think physicalism means because any such 
> answer has to include physics and physics has to involve matter which you 
> admit confuses you. 

No, it does not confuse me. It is just shown inconsistent to believe that we 
have to assume its existence. A realm is primary if it cannot be reduced to 
some other field”. May believe that biology is not primary, because it can be 
reduced (apparently) to chemistry and physics. Similarly, with Mechanism, 
physics is reducible to number theory or Turing equivalent.





> And for the same reason I'm not going to ask about "Mechanism" , the reply 
> would only contain yet more words you can neither define nor give examples of.

Digital Mechanism  is the doctrine that there is a level of description of our 
body such that we can survive with a (physical) digital brain or body, if it 
faithfully represents our body’s functionality at that description level.

Bruno



> 
> John K Clark
> 
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Re: The codical-material universe

[Bruno Marchal]

> On 8 Sep 2018, at 14:57, Philip Thrift  wrote:
> 
> 
> 
> On Saturday, September 8, 2018 at 4:00:41 AM UTC-5, Bruno Marchal wrote:
> 
>> On 7 Sep 2018, at 14:43, Philip Thrift > 
>> wrote:
>> 
>> 
>> 
>> On Friday, September 7, 2018 at 3:59:08 AM UTC-5, Bruno Marchal wrote:
>> 
>>> On 6 Sep 2018, at 21:48, Philip Thrift > wrote:
>>> 
>>> 
>>> 
>>> On Thursday, September 6, 2018 at 11:47:46 AM UTC-5, Bruno Marchal wrote:
>>> 
 On 6 Sep 2018, at 17:04, Philip Thrift > wrote:
 
 
 
 On Thursday, September 6, 2018 at 4:23:23 AM UTC-5, Bruno Marchal wrote:
 
> On 5 Sep 2018, at 18:58, Philip Thrift > wrote:
> 
> 
> 
> On Wednesday, September 5, 2018 at 9:12:49 AM UTC-5, Bruno Marchal wrote:
> 
>> On 5 Sep 2018, at 11:54, Philip Thrift > wrote:
>> 
>> 
>> 
>> On Wednesday, September 5, 2018 at 2:28:39 AM UTC-5, Bruno Marchal wrote:
>> 
>>> On 2 Sep 2018, at 21:32, Philip Thrift > wrote:
>>> 
>>> 
>>> 
>>> On Sunday, September 2, 2018 at 8:15:01 AM UTC-5, Bruno Marchal wrote:
>>> 
 On 30 Aug 2018, at 01:04, Philip Thrift > wrote:
 
 
 
 On Wednesday, August 29, 2018 at 4:55:12 PM UTC-5, Brent wrote:
 Do you have some evidence for doubting CT?  It seems that it's 
 essentially a definition of digital computation.  So you could offer 
 some other definition, but it would need to be realisable. 
 
 Brent 
 
 On 8/29/2018 12:12 PM, Philip Thrift wrote: 
 > also thought by some in what I call the UCNC gang 
 
 Also thought WHAT? 
  
 
 
 
 In terms of theory, Joel David  Hamkins  @JDHamkins 
    (the set-theorist now at Oxford) 
 considers infinite-time TMs to be a part of "computation":
 
 http://jdh.hamkins.org/ittms/ 
 
 
 If computation is the fundamental "substrate" of nature, and  ITTMs 
 are "natural" extensions of TMs, there is no reason to exclude ITTMs.
 
>>> I have explained in this list, and in my papers, that Church’s thesis 
>>> (with Mechanism) entails that matter and nature are non computable. 
>>> Elementary arithmetic realise/emulate all computations, and physics is 
>>> reduced into a statistic on all computations, which is not something a 
>>> priori computable. If mechanism is refuted some day, it will be by 
>>> showing that nature is “too much computable”, not by showing that 
>>> nature is not computable. Mechanism in cognitive science is 
>>> incompatible with Mechanism in physics. Now, it could be that the only 
>>> not computable things is just a random oracle, but this does not change 
>>> the class of computable function. It would change the class of 
>>> polynomial-time computable function, as we suspect nature do, but that 
>>> confirms mechanism which predicts this.
>>> 
>>> 
>>> 
>>> 
 
 But what does the presence of ITTMs  mean for the CT thesis? Whether 
 ITTMs are "realizable" remains to be seen.
 
>>> 
>>> The CT thesis identifies human intuitively computable functions with 
>>> functions programmable on a computer. It is a priori neutral on what 
>>> the physical reality can compute. With mechanism, CT entails the 
>>> existence of non emulable phenomena by computer “in real time”.
>>> 
>>> 
>>> 
 
 In terms of practice, UCNC people think that computers made with 
 non-standard materials, e.g. "live" bioware produced by synthetic 
 biology, could have novel computational (behavioural) abilities not 
 equivalently replicable in a simulation.
 
 
>>> 
>>> Quantum computer can emulate some piece of matter more quickly than a 
>>> classical computer. But that was a prediction of mechanism. You can 
>>> read the basic explanation in my paper here if interested. 
>>> 
>>> 
>>> B. Marchal. The Origin of Physical Laws and Sensations. In 4th 
>>> International System Administration and Network Engineering Conference, 
>>> SANE 2004, Amsterdam, 2004.
>>> http://iridia.ulb.ac.be/~marchal/publications/SANE2004MARCHALAbstract.html
>>>  
>>> 
>>>  (sane04)
>>> 
>>> 
>>> The key notion if the “first person indeterminacy” which is just the 
>>> fact that if we are machine, we are duplicable, and duplicated in 
>>> arithmetic, and whatever we predict about our first person experience 
>>> is indeterminate on the set of all computations (in arithmetic) which 
>>> go through our local and actual state of mind (that is: an infinity). 
>>> Physicalism is refuted