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"Edward Green" <spamspamspam3@xxxxxxxxxxx> writes:
>Lefty wrote:
>
>> Einstein's Relativity is interesting because it uses independent frames of
>> reference w/respect to motion. How can you do this with numbers ? How to
>> think of a space which has no geometric origin, but still has all the nice
>> properties of R(n) ?
>
>Euclidean space?
>
>Unless I am mistaken, Euclidean space has no preferred origin.
You are not mistaken, but many people are, and persistently make
the error of taste and judgment of identifying the vectorspace
R^n (or R(n) as Lefty writes it) with the affine space E_n, which
they then call Euclidean space. Of course Euclid's lines, planes,
and space only become affine spaces (of dimensions 1, 2, and 3,
respectively) upon interpretation--but they can only become
vectorspaces upon *mis*interpretation.
Followups removed from sci.physics.
Lee Rudolph
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