> On 15 Nov 2018, at 19:14, John Clark <johnkcl...@gmail.com> wrote:
> 
> On Thu, Nov 15, 2018 at 6:27 AM Bruno Marchal <marc...@ulb.ac.be 
> <mailto:marc...@ulb.ac.be>> wrote:
> 
>  >> I see precisely ZERO evidence that "phi_u(x, y)" can emulate a machine or 
> emulate anything a or in fact do anything at all because "phi_u(x, y)" never 
> changes, not in time and not in space. You wrote "phi_u(x, y)"  in the above 
> about 11 hours ago thousands of miles from me, but here I am looking at 
> "phi_u(x, y)"  and "phi_u(x, y)" is still just "phi_u(x, y)” .
>  
> > Your confusion here
> 
> I'm not the one that's totally confused by personal pronouns.
>  
> > is equivalent with confusing a far away galaxy with the telescope, or 
> > confusing a physical universe with a book on the physical universe.
> 
> You are also confused about what is modeling what. A galaxy is more complex 
> than a telescope, and the universe is more complex than a book, and a 
> physical system is ALWAYS more complex than the mathematical model that's 
> trying to simulate it, and that's why the mathematical model NEVER does a 
> perfect job. Models are ALWAYS simpler than the thing being modeled.  A 
> mathematical model of a hurricane needs to conform with the real thing to be 
> any good but the physical hurricane doesn't need to conform with the model or 
> with anything else except for the laws of physics. Physics tells mathematics 
> what to do not the other way around because physics is more fundamental .


The same is true for the mathematical reality. Theories like PA or ZF only 
scratch the “simple” arithmetical reality, and Gödel’s theorem explains the why 
here.

A practical difficulty here is that logicians used the term model like 
painters: the model is the reality intended through the theories. The model is 
the tree, the theory is the painting. Physicists use model for what logicians 
called theories, like the Bohr model of the atom.

It is the theories which is always simpler than the reality/model intended, 
like a brain is simpler than a physical universe, no doubt.

But, you are the one, it seems to me, doing that confusion in mathematics all 
the time. The arithmetical reality is bigger than PA, ZF and you and me.

We can compare realities (models in the logician sense). For all we know, the 
physical universe is far less complex than a model of ZF. Estimation are 
usually that the whole of mathematical physics (with the real and complex 
numbers) are definable in V_o, with o being some reasonable constructive 
ordinal. 

But all of finite means can only scratch all this. The Rieman hypothesis is a 
“simple” PI_1 relation, the negation of a sigma_1 sentence, but that resists, 
it is a complex and deep reality. 






>  
> > A model is complete by definition:
> 
> Hogwarts is a school of magic BY DEFINITION.  And for you "by definition" = 
> "abracadabra”. 

I alluded to the fact that you can identify (by clear definable bijection) a 
model with the set of (Gödel number) of all true sentences in (the standard 
model of) arithmetic. This is a *very* complex set, highly non computable. But 
that set, seen as a theory is complete, by definition: it proves all true 
sentences. It escapes Gödel’s theorem, but there is no mystery: it is the truth 
oracle, an arithmetical god, or oracle. It is complete but is not a theory: it 
is the model (reality disguised in a (non axiomatizable) theory.

I just train you a bit on the vocabulary of the logicians. 




> 
> > if you are OK that 2+2=4
> 
> I am.

Good.



> 
> > and similar are true independently of you and me, 
> 
> Its independent of you or me but it is NOT independent of matter that obeys 
> the laws of physics. 


How so?






> 
> > computations and their many realisation all exists, in a provable way, 
> 
> If so then INTEL has been wasting colossal amounts of money over the last 40 
> years messing around with silicon, you have the power to put them out of 
> business and  become the richest man who ever lived. What are you waiting for?


You already need 2+2=4 to make sense of matter, of “being made-of”, and of 
silicon. 

But you don’t need silicon, or “being made-of” to define the numbers. You need 
simpler principle, usually invoked by anyone when we ask them to explain matter.

If 2+2=4 depends on matter, tell me how a magnetic field, or a electromagnetic 
field, or a gravitational field, or any physical field could pertubate 2+2=4.






> 
>  > in a provable way,
> 
> What exactly have you proven to exist?


Not me. Gödel, and Turing, etc.  The notion of Turing universality, emulation, 
computations, can be defined in Peano arithmetic; and are arithmetical notion 
(definable in term of classical logic + the symbols +, *, 0, s. 
Note that the notion of “arithmetical notion” is not arithmetical.



> A mathematical proof that's all, and a mathematical proof can't change in 
> space or time so it can't compute anything. 

You confuse the notion of physical computation with the notion of computation. 
You assume a physical reality. 
Better to be agnostic when working on the mind-body problem with the scientific 
attitude. 
It is not the place to defend a philosophical opinion.









> 
> >>> A model is a model of a theory.
>  
> >>So I guess a model of a theory is a model of a model of a theory, and a 
> >>model of a model of a theory is a model of a model of a model of a theory, 
> >>and a model of….
> 
> > You might decide one day to study a bit of mathematical logic.
> 
> If you studied a bit of information theory you'd know that "a model is a 
> model" has zero informational content 
>  
> > The notion of model applies to a theory, only, or to a machine,
> 
> According to you the notion of a model also applies to a model.

No. Only according to people who extends the sense of theory to non 
axiomatizable theory. I don’t do that. I did it by “charity” only once to make 
sense of something you said. In our context, it is better to see a theory as a 
finite object, and the models/realities intended will be usually much more 
complex, as you said above.

Bruno




> 
> John K Clark
> 
> 
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