% Convergence (draft)
% Michael Stone
% March 29, 2011

## Forms, Maps, and Convergent Sequences

Despite the surface tension between their positions, [Prof. Harper's][harper]
description of the "[computational trinity][trinity]" and [Prof. Wand's][wand]
reply that "[the map is not the territory][map]" are both accurate. Indeed,
taken together, they reveal an important fact about knowing which is that, when
discussing complicated things, we tend to "say what things are" by sketching
sequences of descriptions that (hopefully!) converge on the boundaries of the
thing in question.

## tbd.

compact vs. "effectively computable" concepts...

One of my favorite mathematical concepts is the concept of a *compact set*.

A compact set is a set for which *every* open cover $U$ has a finite sub-cover.

[trinity]: http://existentialtype.wordpress.com/2011/03/27/the-holy-trinity/
[map]: http://existentialtype.wordpress.com/2011/03/27/the-holy-trinity/#comment-203
[harper]: http://www.cs.cmu.edu/~rwh/
[wand]: http://www.ccs.neu.edu/home/wand/
[ozick]: http://www.amazon.com/Heir-Glimmering-World-Cynthia-Ozick/dp/0618618805