On Thu, Oct 8, 2015 at 12:37 PM, John Clark <[email protected]> wrote:

> On Wed, Oct 7, 2015  Jason Resch <[email protected]> wrote:
>
>
>> ​> ​
>> Our computers are only emulating (mimicking) mathematical objects which
>> perform these computations.
>
>
> ​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. No physical computer built to date
has unlimited memory, so our approximations of ideal mathematical objects
known as Turing machines, will remain approximations. There will be things
Turing machines can compute, but our physical approximations cannot compute
due to limited memory or time.

Jason

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