On 01 Jul 2012, at 09:41, meekerdb wrote:

On 7/1/2012 12:17 AM, Bruno Marchal wrote:

On 30 Jun 2012, at 22:31, meekerdb wrote:

On 6/30/2012 12:20 PM, Bruno Marchal wrote:

On 30 Jun 2012, at 18:44, Evgenii Rudnyi wrote:


I think that you have mentioned that mechanism is incompatible with materialism. How this follows then?

Because concerning computation and emulation (exact simulation) all universal system are equivalent.

Turing machine and Fortran programs are completely equivalent, you can emulate any Turing machine by a fortran program, and you can emulate any fortran program by a Turing machine.

More, you can write a fortran program emulating a universal Turing machine, and you can find a Turing machine running a Fortran universal interpreter (or compiler). This means that not only those system compute the same functions from N to N, but also that they can compute those function in the same manner of the other machine.

But the question is whether they 'compute' anything outside the context of a physical realization?

Which is addressed in the remaining of the post to Evgenii. Exactly like you can emulate fortran with Turing, a little part of arithmetic emulate already all program fortran, Turing, etc. (see the post for more).

Except neither fortran nor Turing machines exist apart from physical realizations.

Of course they do. Turing machine and fortran program are mathematical, arithmetical actually, object. They exist in the same sense that the number 17 exists. We can implement them in physical system, but this does not make them physical.



They are abstractions.

If you want. This changes nothing.




There is no need of step 8, here. It is just a mathematical fact that arithmetic emulates all programs, in the mathematical sense of "emulate".

That's a metaphorical sense.

Not at all.


"Arithmetic" doesn't act or perform anything,


Acting and performing are the metaphor here. Computation is a purely mathematical notion discovered before the building of physical computer. Some could even argue that the physical reality can only approximate them. And with comp we have to define eventually notion like acting and performing from the relation between numbers, and this is rather easy to do. What is difficult is to get the right measure on the computations, not to define action and performance. I am explaining what is a computation on the FOAR list, but you can find it also in any textbook on theoretical computer science. No notion of physics are involved at all in the definition.



it's concept and a static, timeless one at that.

Like all arithmetical truth. Time is a view from inside. That is the case in some physical based theories (for example in all theories admitting block universe).

Bruno

http://iridia.ulb.ac.be/~marchal/



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