Comment to John Conway
Subject: Re: Reply to "Re: Reply to "Do Points Have Area?"
Author: Candice Hebden <email@example.com>
Date: 16 Jan 98 15:21:02 -0500 (EST)
sorry I haven't written in a while. On December 16, you said
(referring to me and Jesse Yoder)
"These discussions all seem very confused to me. Neither of the
participants seems to "believe" in Euclidean geometry. That's fine,
but they don't say what they MEAN by such statements as "circles
don't really exist they are just polygons with many sides" or "points
really have area".
What ARE these "circles", "polygons", and "points" being spoken of?
Are we talking about points in real physical space, or in some purely
conceptual one? All the statements are nonsense for real physical
space, which behaves very strangely indeed when dimensions get small,
and is, in particular, so unlike Euclidean 3-dimensional space that
all these terms are utterly 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."
You're right to an extent. I don't believe that the Euclidean world
exists in the real world. But I do believe that it exists in a like
"Parallel" world. I've been talking about the real world; trying to
relate it to the Euclidean one. When I say that circles do not exist,
I mean that in both the Euclidean world and the real world. Holding
the same definitions as Euclidean named, things in the real world are
closly related to polygons, but there is nothing in the real world
that resembles a circle (closer than it does a polygon).
I hope this clarifies things,