Re: Mathematical Universe Hypothesis

[agrayson2000]

On Friday, November 2, 2018 at 4:48:05 PM UTC, John Clark wrote:
>
> On Fri, Nov 2, 2018 at 12:16 AM > wrote:
>
> *> You sound like a young fool who has no respect for his elders*. 
>
>
> And you sound like a old fool who has placed so much respect for his 
> elders it approaches the level of ancestor worship. But It's not just you, 
> this entire list's reverence for the ancient Greeks has reached comic 
> proportions.
>


*Hard to see what's in front of your nose, or just to understand the logic 
involved. AG *

>
>  > *Zeno pointed out something significant*
>
>
> When Zeno  pointed it out it was a significant puzzle with no obvious 
> answer, but in the last 2500 years we've learned a thing or two and an 
> answer has been found so it is no longer a paradox. 
>

*For you, presumably, the answer is that moving test particles know 
Calculus. AG *

>
> John K Clark
>
>
>
>

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Re: Mathematical Universe Hypothesis

[John Clark]

On Fri, Nov 2, 2018 at 4:45 AM Bruno Marchal  wrote:

*> No Turing machine can solve the halting problem. You are right on this.
> But an oracle can, or a machine with infinite speed can.*
>

If such a oracle could exist then logical contradictions could too and then
there would be no point in listening to your arguments or anybody's logical
argument about anything because mathematics and even logic itself would be
purest form of nonsense.

> *Note that such magic does not change the “theology”* [...]
>

Sorry, I don't know what you said after that, I fell asleep.

 John K Clark


>

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Re: Mathematical Universe Hypothesis

[John Clark]

On Fri, Nov 2, 2018 at 12:16 AM  wrote:

*> You sound like a young fool who has no respect for his elders*.


And you sound like a old fool who has placed so much respect for his elders
it approaches the level of ancestor worship. But It's not just you, this
entire list's reverence for the ancient Greeks has reached comic
proportions.

 > *Zeno pointed out something significant*


When Zeno  pointed it out it was a significant puzzle with no obvious
answer, but in the last 2500 years we've learned a thing or two and an
answer has been found so it is no longer a paradox.

John K Clark

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Re: Mathematical Universe Hypothesis

[Philip Thrift]

On Friday, November 2, 2018 at 3:45:53 AM UTC-5, Bruno Marchal wrote:
>
>
> On 1 Nov 2018, at 19:43, John Clark > 
> wrote:
>
>
> On Thu, Nov 1, 2018 at 2:27 PM Philip Thrift  > 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 
:

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://bitrumagora.wordpress.com/about/marl-burgin/


*Nothing is settled in computing.*

- pt

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Re: Mathematical Universe Hypothesis

[Bruno Marchal]

> On 1 Nov 2018, at 19:59, Philip Thrift  wrote:
> 
> 
> 
> On Thursday, November 1, 2018 at 1:44:19 PM UTC-5, John Clark wrote:
> 
> On Thu, Nov 1, 2018 at 2:27 PM Philip Thrift  > 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.
> 
> John K Clark
> 
> 
> 
> Of course logics are fiction too. (They're just languages after all.)


There is a logical language, but that is different from a logical theory. It is 
important to distinguish the languages from the theories, and the theories from 
the models/interpretations.

Bruno



> 
> - pt
> 
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Re: Mathematical Universe Hypothesis

[Bruno Marchal]

> On 1 Nov 2018, at 19:43, John Clark  wrote:
> 
> 
> On Thu, Nov 1, 2018 at 2:27 PM Philip Thrift  > 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








> John K Clark
> 
> 
> 
>  
> 
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Re: Mathematical Universe Hypothesis

[Philip Thrift]

On Thursday, November 1, 2018 at 6:33:31 PM UTC-5, Philip Thrift wrote:
>
>
>
> On Thursday, November 1, 2018 at 6:15:50 PM UTC-5, Brent wrote:
>>
>>
>>
>> On 11/1/2018 4:02 PM, Philip Thrift wrote:
>>
>>
>>
>> On Thursday, November 1, 2018 at 4:02:56 PM UTC-5, Brent wrote: 
>>>
>>>
>>>
>>> On 11/1/2018 11:59 AM, Philip Thrift wrote:
>>>
>>>
>>>
>>> On Thursday, November 1, 2018 at 1:44:19 PM UTC-5, John Clark wrote: 


 On Thu, Nov 1, 2018 at 2:27 PM Philip Thrift  
 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.

 John K Clark


>
>>> Of course logics are fiction too. (They're just languages after all.)
>>>
>>>
>>> OK.  Sentences written down are physical and not fictions.  But can they 
>>> be contradictory?  How does "This page is red." contradict "This page is 
>>> blue." unless they have some meaning as propositions.  But this must be a 
>>> relation between a proposition (an abstract thing) and a fact (the color of 
>>> this page).
>>>
>>> Brent
>>>
>>
>>
>>
>>
>> Sentences, like this one, are physical *only* in the sense that they are 
>> (in this case) made up of electronic bits displayed on a screen (as you are 
>> looking at right now, maybe on a laptop or smartphone) - or they could be 
>> made up of ink strokes on paper, etc.
>>
>>
>> One can't read anything more into them physically that that. What one 
>> reads out of them (a person looking at this sentence, or a computer 
>> scanning one) is a difference matter.
>>
>> There are no abstractions in an immaterial sense.
>>
>>
>> But there are abstractions in the sense that the same proposition is 
>> instantiated in different substrates.   So the contradiction can be between 
>> different instances, e.g. a spoken sentence can contradict a written one.
>>
>> Brent
>>
>
>
> "the same proposition is instantiated in different substrates"
>
>
> Those are in reality different propositions (sentences) materially because 
> they are made up of different particles in difference locations.
>
> There is no "proposition" existing in a Platonic realm that appears here 
> on Earth in different "fleshes".
>
> We group all these material proposition particulars together, but only 
> pragmatically, and call this grouping "a proposition".
>
> - pt
>

I remembered the case of the

*Intentionally blank page *[Wikipedia]

"Sometimes, these pages carry a notice such as "This page [is] 
intentionally left blank." Such notices typically appear in printed works, 
such as legal documents, manuals, and exam papers, in which the reader 
might otherwise suspect that the blank pages are due to a printing error 
and where missing pages might have serious consequences."

So if one sees a page in a book or document with only *This page 
intentionally left blank* printed in the middle of it, one might say "But 
it's not blank! I see *This page intentionally left blank *printed on it! 
My eyes don't lie!"

- pt



 

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