Do Points Have Area?
Subject: Re: Points with no area
Author: John Conway <conway@math.Princeton.EDU>
Date: Tue, 18 Nov 1997 12:36:20 -0500 (EST)
On 10 Nov 1997, Jesse Yoder wrote:
> Candice -
> Your posting comes like a breath of fresh air. Could it be that, in
> reality, the emperor has no clothes? Certain ideas, such as those in
> mathematics that attempt to create a mathematics out of fictional
> arealess points, have become so deeply entrenched that it is difficult
> to even find an appropriate language to challenge them. How could it,
> after all, even be possible that all those calculus professors with
> tenure could be teaching a false philosophy?
> I am glad to hear that you are willing to say that these mathematical
> constructs such as arealess points and infinity make no sense, despite
> the centuries that "learned scholars" have spent repeating them and
> drilling them into students.
Even not-particularly-learned scholars have long been aware that
Euclidean geometry is merely an idealized version of the geometry
of real space. We go on teaching it because it's the simplest kind of
geometry there is, and because it's really a very good fit, and has
enormous practical value, and is very interesting.
In other words, the emperor HAS very elegant clothes that fit him
very well indeed, and are nicer to wear than skin-tight ones would be.