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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