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On Sat, 30 Jul 2005 04:08:16 -0700, gsax wrote:
> Hi
>
> I read in Penrose's "Emperor's new Mind ", that Euclidean geometry is
> actually a Physical theory derived from our sense-experiences of the
> world around us.
>
> That is why its axioms seemed so obviously true..
>
> Hence Non-Euclidean geometries took time to be accepted as vaild.
>
> Is it possible that even our concept of numbers is similarly inspired.
>
> And so Number theory is as much a Physical theory as Euclidean
> geometry.
>
> If this is true , then what would be the analog of Non-euclidiean
> geometries, to out 'conventional' number theory..
>
> thanks
> Gsax
I don't view it as an analog of non-euclidean geometry but ring
theory is a well studied algebraic abstraction (generalization)
of the concept of integers. If a, b are memebers of a ring R, then
a+b = b+a is in R as are a*b and one has a*(b+c) = a*b+a*c. Often
a*b != b*a and one has a non-commutative ring. In QM operators
acting on a hilbert space of states form non-commutative rings.
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