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| Authored by: Anonymous on Monday, June 11 2012 @ 08:46 PM EDT |
Executing software boils down to purely mental steps if you do it in your head.
(Programmers do this while debugging.)
Of course, you can do it with the aid of physical medium such as pencils and
paper. Then you don't have to remember it all in your head. But you're still
just doing math (executing a mathematical algorithm).
If a CPU executes your software, it does it with the aid of a physical medium
(tiny transistor switches and circuits that transfer electrical charges around),
but its still just doing math (executing a mathematical algorithm). In fact its
executing *a specific algorithm* which you can use to interpret a written
description of any other algorithm, and execute that algorithmic description.
But its still basically the same as running a Universal Turing machine in your
head (or with pencil and paper, etc).
Ignoring resource limitations (running time and finite memory), a human being
could compute anything which is computable, purely within their own mind.
Ignoring resource limitations (running time and finite memory), a Universal
Turing machine execute any description of a computation and thereby carry out
the described computation -- it can compute anything that is computable.
Ignoring resource limitations (running time and finite memory), an actual
physical computer CPU can execute any description of a computation (i.e. a
software program) and thereby carry out the described computation (the algorithm
embodied in that software) -- again, it can compute anything that is computable.[ Reply to This | Parent | # ]
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