On Sat, Feb 9, 2013 at 2:16 PM, Craig Weinberg <whatsons...@gmail.com>wrote:

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>
>
> > They [mathematicians] are just elaborating existing concepts of
> geometry, not creating it from mathematical scratch.
>
But all those concepts of geometry, like the trigonometric functions, can
be derived from one dimensional numerical sequences with no pictures or
diagrams involved and if told that a particle with N degrees of freedom
changes in a certain way and then changed again in a different way but one
that is still consistent with those functions a one dimensional geometer
could still specify what the coordinates of that particle will now have in
N space.
> It doesn't matter how many dimensions you make the machine, the tape is
> still one dimensional
Yes but it can make calculations in N dimensional space, and a Turing
Machine might not even know that it is one dimensional, or even that it is
a Turing Machine.
John K Clark
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