`Points & points`
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`Subject:      Re: Reply to Do Points Have Area?`
`Author:       John Conway <conway@math.Princeton.EDU>`
`Date:         Wed, 21 Jan 1998 16:31:01 -0500 (EST)`
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`On 20 Jan 1998, Jesse Yoder wrote:`
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`> [John Conway]`
`> >"If we're just talking about some purely conceptual space then the`
`> assertions are meaningless until that space is somehow defined.  `
`> Jesse speaks of "circular geometry", in which a "point" is the`
`> smallest unit area, and in other statements he's made it clear`
`> that he thinks of these "points" as little circles and lines`
`> as like strings of beads:  oooooooooooooooooo, in which `
`> any two adjacent ones touch each other at a point."`
`> `
`> [Jesse]`
`> "Response: You seem to understand pretty well what I mean. Here is how`
`> a plane would look, with lots of points;`
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`   It still surprises me that you didn't even notice the double`
`use of the word "point" in the sentence I obliquely quoted from you!`
`How can two points touch at a point?`
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`   Of course, you've now agreed to distinguish between "Points"`
`and "points", but it really seems to me that in a fundamental`
`sense this vitiates your system, because it bases it on the`
`traditional notions.  Surely you should be able to describe`
`the structure and arrangement of your Points without using`
`Euclid's points?  If not, it can hardly be true that "a Point`
`is the smallest allowable unit of area".`
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`   I have difficulty in following your comments about switching to`
`new frames of reference.  Do you think this is legal, or were you`
`really saying it was impossible?  It seems to me that it's obviously`
`impossible in your system.  If a Point is really the smallest`
`allowable unit of area, then no kind of changing frames of`
`reference can possibly produce a smaller Point.`
` `
`     John Conway`

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