Re: Examining Mathematical Approaches
From: Leo Sorenson (sornleo_at_yahoo.com)
Date: 10/20/04
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Date: Wed, 20 Oct 2004 01:30:34 -0500
and arrogance is a guarantee of what?
"robert j. kolker" wrote:
> Gnivilq wrote:
>
> > Examining Mathematical Approaches
> >
> > I have received communications from a mathematician who asserted that my
> > statements about the validity of non-Euclidean Geometry were erroneous. He
> > apparently objected to the assertion that the definition of a straight line was
> > faulty for all geometries and that any non-Euclidean Geometry of N dimensions
> > could be contained in a Euclidean geometry of N+1 dimensions.
>
> That is not true. The two dimensional Klein Bottle requires a four
> dismensional space for an embedding. Hassler Whitney proved that an
> n-dimensional manifold can be embedded in a 2n dimensionsal euclidean
> space and no smaller number is generally sufficient, although in some
> cases a smaller dimension might suffice. What this means is there exist
> n dimensional manifolds which -require- 2n dimensions for an embedding.
>
> Once again you exhibit your ignorance and even your stupidity. We are
> all born ignorant but that can be remedied. Stupidity is the refusal to
> cure one's ignorance when the means to do so exist.
>
> Bob Kolker
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