Sunday, May 15, 2011

Computation & Cardinality

So about a month ago I spoke at code'n'splode, a women-focused tech group. Yes, women-focused as in "primarily for women" but men can attend when given the capability. Of course, like any proper capability system revocation is supported.

My goal was to start with the cardinality of sets and get through Church encodings of common data types in the untyped lambda calculus.

I think the talk was, for the most part, a success. I think I lost about half the room by the end, but given that I didn't get to give a practice talk and that my dying laptop prevented me from using the interpreters I wrote for examples I think it went fairly well.

One of the main things I hope everyone understood right from the beginning is that the "set" of all mathematical functions is absurdly, ridiculously, mind-bogglingly bigger than the set of computable functions. There are only countable computable functions, but the set of all functions from the naturals to the naturals is already the size of the real numbers.

In that light, computer science seems like an awesome - in the old sense of the word - pursuit!

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