`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`

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