What good are applications?

What We're Doing Wrong: Programming in Theory Classes, from Michael Mitzenmacher's blog My Biased Coin. Mitzenmacher claims that the standard introductory classes in algorithms don't include programming assignments; furthermore, he thinks this is bad for theoretical computer science, because non-theoretical computer scientists get the idea that theory isn't actually good for anything.

I think the theoretical computer scientists are doing it right! But I think this from a selfish point of view -- I'm taking an algorithms class that nominally requires that I have certain classes which involve programming as a prerequisite, and I don't feel lost for not having had those classes. From a less facetious point of view, I agree with Mitzenmacher, even though it would hurt me. If someone learning something new has no idea how it connects to anything they've ever learned, it's not going to stick in their brain. The human brain is not a computer -- and even if it were, that doesn't mean that throwing a bunch of random facts in it is the best way to do things.

The same statement holds, I would think, for any course in any field that covers the "theory" behind some other material. Within mathematics, for example, it's possible to teach people what a category is without giving examples of all the familiar structures they know that are in fact categories; it's possible to teach real analysis without pointing out the connections to the calculus students already know; it's possible to teach rigorous measure-theoretic probability without appealing to (often flawed, but still useful) intuition that people have about flipping coins and rolling dice and distributing objects among boxes. I'm sure my readers can provide other examples.