Points & points
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)
On 20 Jan 1998, Jesse Yoder wrote:
> [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;
 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?
 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".
 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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