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


> > 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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