Something of an aside …
On Sep 18, 2013, at 1:29 AM, Gregg Reynolds <dev@mobileink.com> wrote:
> The suggestion that a pair of mathematical entities with exactly the same extension are not equal doesn't help - it reads like an attempt to redefine mathematics.
Gregg
I think you misunderstand mathematics ...
I attach two pictures.
The first is my copy, of Jones' copy of a diagram in a book in the vatican library which is a tenth century, maybe fifth generation, copy of a diagram drawn by Pappus of Alexandria in the 4th century, which may in turn have been a (n-th generational) copy of a diagram drawn by Euclid a few hundred years earlier.
The copy in the vatican library, has, according to Jones, got a mistake in it: which he corrected, assuming it to be a copyist's error and not an error of Pappus or Euclid.
All these copies will have minor variations .. such as angles and distances and sizes being slightly different
In some sense there is one diagram, even the one with a mistake in it, which refer to the same mathematical concept. In another sense there are multiple diagrams - the one in this e-mail is even in some sense different from the one at
http://oriented.sourceforge.net/images/jones139.jpg which is bitwise identical. The intent of the two pictures is quite different - within this e-mail I am discussing the meaning of pictures, on that website I am interested mainly to compare and contrast with my own picture, the second picture here, which, I boldly assert is a picture of the same mathematical concept as Pappus' original picture. (My picture and Pappus' original form the same arrangement of pseudolines in the projective plane - concepts which had not been invented when Pappus drew his picture)
The point of all this is that even in mathematics we need to be able to talk about the very human tasks relating to copying and changing and making my own copy … where notions such as identity move from being obvious to being really very subtle.
Sandro is trying to understand the notion of identity that Pat and I see as obvious when it comes to graph naming, and by way of technical questions trying to probe the subtleties
Jeremy
