Numbers, maps, and me
Number: Stop rewriting history! Losers don’t get to do that.
Me: um… err… what did I do
Number: Don’t act naïve. How would you feel if I called you a monkey?
Number: We are not talking about polytheism and you are not funny. I am not going to sit silent while you badmouth me—what were you saying the other day:
Me: An endomap • –> •
Number: Whatever! We the numbers own this place—been here from the very beginning and you make it seem like we are bad guys who colonized pristine space. But for our quantitative culture… what have you gotten with all your thinking about quality???
Me: What if I say: In the beginning there was number.
Number: That’s little better, but you must practice
Me: Thank you! Let’s start with two numbers
where to next (watching our steps every step of the way)…
You: We can readily notice that
0 < 1
Me: Yes, yes there is a category which has
as objects and the relation
0 < 1
as a map.
You: I need, before I can think of 0 as an object, to know what you have in mind for the identity map from 0 to 0.
Me: How about
0 = 0
You: Why not just one ‘less than or equal to’ instead of the two: <, =
Me: That sounds like a good idea to me. So we have two objects
their identity maps
0 < 0
1 < 1
and a map from 0 to 1
0 < 1
You: There is no map from 1 to 0 since 1 is not ‘less than or equal to’ 0. It looks like there is at most one map between the two objects 0 and 1 in each one of the four pairings [(0, 0); (0, 1); (1, 0); (1, 1)].