Comment to John Conway
 
Subject: Re: Reply to "Do Points Have Area?
Author: Kirby Urner <pdx4d@teleport.com>
Date: 18 Dec 97 20:07:13 -0500 (EST)
 
> = Conway
 = Urner
 
>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 Euclid's Elements are suddenly 
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.
 
Kirby

http://forum.swarthmore.edu/epigone/geometry-research/swenkhartil/ht95m5q5jlla@forum.swarthmore.edu

 

 

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