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[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
[EL]
If you have studied the number theory, you would have not asked this
question.
Yes indeed, countability and divisibility extends the Euclidean
conceptions but there are other identities and transcendental numbers
that are far from classical.
The Minkowski 4D Space and the Riemann Space are both non-Euclidean and
yet are parts of the number theory on the mathematical side of the same
physical representation. To the surprise of many of the careless minds,
the theory of Chaos in its temporal form is a 4D Euclidean manifold of
deterministic, nonlinear, long-term change of states world. While it is
the Minkowski 4D manifold that is a static panorama of all spacetime at
once.
Our consciousness is under a refresh rate and we conceive the renewable
Euclidean space under change. The 4D Minkowski manifold is like a lens
wide open capturing a long interval of time and all displacements
within, but the picture is a blurry, mentally-inconceivable, stretch of
spacetime, with either same place at many times or many places at many
times, or ultimately all places at all times.
I am not extremely fond of Penrose's bizarre concepts of the unnatural
possibilities of the mind. What is the merit! We are trying very hard
to understand what nature obscures and I doubt that we should be
wasting time on figuring out what nature does not even have to obscure.
A non-standard arbitration is useless to science as much as the
multiple arbitrations of the constancy of the speed of light under
covariance of length and time dimensions per frame of reference.
EL
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