On 09 Oct 2015, at 05:18, John Clark wrote:
On Thu, Oct 8, 2015 at 6:49 PM, Jason Resch <[email protected]>
wrote:
>> You've got it exactly precisely backwards. Our
mathematical objects are only emulating (mimicking)
computers which perform these computations. If you doubt this ask
yourself 2 questions:
1) Does the simple emulate the complex or does the complex emulate
the simple?
2) Which is more complex, a Turing Machine or a silicon processor
that obeys all the laws of physics?
> A Turing machine has unlimited memory.
That is incorrect.
I can agree with you. A Turing machine has unlimited memory, like
humans, in the sense that they might use virtual or physical
neighborhood as a memory, like a human can use paper or walls.
In Turing minds, the potentially infinite tape is just modeling the
papers and ink that a human can use when doing a computation by hand.
There is no evidence a Turing machine, or any abstract entity for
that matter, has a memory at all;
That is false. It has the tape where it can store previous calculation
result. the tape is not a physical thing though.
its memory is not infinite and it's not unlimited either but is in
fact very limited indeed, limited by zero . A Turing machine has
ZERO memory.
That is false. It has a potentially unlimited memory (but no actual
infinite memory).
> No physical computer built to date has unlimited memory,
They can use the universe, and it might be unlimited if it extends
properly.
But plenty of physical computers have enough memory to get the job
done and all physical computers have nonzero memories.
Like all non physical, purely arithmetical universal numbers.
> so our approximations of ideal mathematical objects known as
Turing machines, will remain approximations.
But no Turing machine has enough memory to get the job done. No
Turing machine has enough memory to get ANY job done. No Turing
machine has any memory at all. No Turing machine can do anything
whatsoever except to simplify things so we can understand how real
computers work.
That is simply physicalist revisionism à-la-Deutsch.
> There will be things Turing machines can compute, but our
physical approximations cannot compute
There is no evidence for and no reason to think that a Turing
machine can compute anything a physical computer can, or anything a
physical computer can't, or that a Turing machine can compute
ANYTHING. And that's a shame really because Turing machines would
be one hell of a lot easier to make than silicon microchips
You can make a physical Turing machine with toilet paper and pebble,
or ropes and strings. In arithmetic, all Turing machines are
implemented by all universal numbers, even by the Heisenberg matrix of
the Milky way. That will emulate all Turing machine in arithmetic,
soon or late in terms of UD's number of steps. Indeed, the problem of
the computationalist is in the filtering of a priori too much
computations.
Bruno
John K Clark
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