On 17 Sep 2013, at 19:39, John Clark wrote:

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On Mon, Sep 16, 2013 Bruno Marchal <marc...@ulb.ac.be> wrote:>> So you are suggesting that a thing like broken glass is made ofnumbers> ???? I was just saying that things are not made up of things. Abroken glass is NOT made of number. That has no meaning at all. Whathappens is that addition and multiplication of natural numbersemulate dreams, which might be dream of a broken glass.OK. How is that any different from saying broken glass is made ofnumbers?

`It would be like saying that the relation between matter and energy (E`

`= mc^2) is made of ink or of pixels.`

>> don't tell me there is no such thing as a thing, that's just moregibberish.> It is a matter of tedious, and not so simple, exercise to see thatthe computations exist in some definite sense when we postulatearithmetic. (This is done in good textbook, and very well done inEpstein & Carnielli, but also in Boolos & Jeffrey). Physical thingsthen appears as stable perceptAnd concerning broken glass I said in my September 11 post "It musthave stable properties of some sort or I wouldn't be able toidentify it as a thing".

`I agree. But a computation can provide stable things for another`

`computations or subcomputations.`

Then arithmetical truth is rather stable itself.

> by persons living those dreams.OK. Therefore the physical universe and the physical things in itexist.

`That makes sense. Just that such an existence is a first person plural`

`construction. This exists for all universal system which can "run"`

`different computations in parallel, and makes them interact.`

>> Make up your mind! First you say everything is the process of"natural numbers" in "relative computations" and then you say"digital machines, which are defined in term of number relations"are an exception to this because what they do "is not a process".The sum of number relations is not a process?? None of this makesany sense to me.> Some number relation defines some machines, or some programs,which are static entities.*Other number relations, involving the preceding one, definescomputations, or processes,Name a number relation that does not involve a computation or someother process!

`It is difference between a number j used as a name for a program, like`

`in the arithmetical relation phi_j(k) = r, and a number coding a`

`computation, that is some sequence like phi_j(k)^1, phi_j(k)^2,`

`phi_j(k)^3, phi_j(k)^4, phi_j(k)^5, phi_j(k)^6, phi_j(k)^7, ...`

`Here phi_i is an enumeration of the partial computable functions, k is`

`a natural number input, and "^s" means the sth step of the computation.`

> A machine, in that setting is basically one number, relative tosome universal number.Relative? A relation needs at least 2 things,

Yes. The two things are 1) the number playing the role of the machine (the j in phi_j(k)), and

`2) the universal system (seen as a number, unless we start in the`

`basic system assumed, like arithmetic, or the combinators) which`

`computes phi_j(k).`

`You can look at the Matiyasevitch book for a nice implementation of`

`arbitrary Turing machine *and* their computations (seen as something`

`very dynamic) in the terms of Diophantine equations (since as very`

`static). That can help. Providing examples is very long and technical,`

`alas, but we will come back on this most probably.`

and some sort of computation with them.

Absolutely, Bruno http://iridia.ulb.ac.be/~marchal/ -- 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 http://groups.google.com/group/everything-list. For more options, visit https://groups.google.com/groups/opt_out.