Comment to John Conway
Subject: Re: Reply to "Do Points Have Area?
Author: Kirby Urner <email@example.com>
Date: 18 Dec 97 20:07:13 -0500 (EST)
>meaningless. To learn the appropriate questions to ask about
>real physical space, you first have to learn a lot of physics.
>Euclidean 3-space is only an approximation that's valid when no
>dimensions are two large or too small.
Re: "Euclidean 3-space" I find it confusing when people into
the standard academic notions of dimensionality and real numbers
appropriate the adjective "Euclidean" for their exclusive use.
As I've posted above (or below, as the case may be), I don't
see how serious students of
's Elements are suddenly Euclid
less serious if they don't buy that volume is "three
dimensional" for example. Nowhere in The Elements is
volume so defined.
I say the linear algebra conventions which treat "positive" and
"negative" spokes of the Cartesian six-spoked "jack" asymmetrically,
calling only the former "basis vectors" and the latter not,
because the result of an operation (direction reversal by
means of multiplication by -1) is all conceptual apparatus
which we might want to take with a grain of salt. And
Euclid should not be saddled with necessarily arguing on
behalf of such conventions.
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