On 05 Jun 2015, at 07:33, John Clark wrote:
Bruno Marchal <marc...@ulb.ac.be> wrote:
>> The physical device is far more complex than the algorithm,
astronomically more complex, so you tell me which is a simplified
approximation of which.
> The physical device is no more relevant to the algorithm than any
other universal system.
Yes, an algorithm is a simplified approximation of the way a real
computer works, and in general good simplified approximations work
with a large number of real world situations.
And so can be indeopendent of them, and belong to another realm, like
logic and arithmetic. But, actually, you are wrong. Computations have
been discovered by mathematicians (who were unaware of Babbage), and
computer have been constructed after.
> You can implement the factorial in fortran, and you can implement
fortran in lisp, and you can implement lisp
Correct again, but whatever language you implement your algorithm in
it must be implemented in matter that obeys the laws of physics
because you can't make a calculation with software alone.
But the goal of making real-life computations is not our goal. Your
remark remains non relevant.
Eventually we will have to explain "real-life appearances" by an
internal statistics on the computations existing in arithmetic.
> The level of complexity is not relevant here.
It's very relevant if you want to know what is a simplified
approximation of what. And we both agree that a electronic computer
is vastly more complex than it's logical schematic, so why can we
make a working model of the complex thing but not make a working
model of the simple thing when usually it's easier to make a simple
thing than a complex thing? The only answer that comes to mind is
that particular simplified approximation is just too simplified and
just too approximate to actually do anything. That simplification
must be missing something important, matter that obeys the laws of
physics.
If you agree that the math notion of computation miss something
(matter), then you agree that they are mathematical. Now, when a the
Milky Way is emulated by arithmetic below our substitution level,
explain me how the simulated humans can guess that matter is missing.
Do you agree that the simulated "john Clark" will still complain that
matter is missing in computation, despite we know that he refers to
number relations, without knowing it?
Bruno
John K Clark
John K Clark
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