Vi Hart is probably the best

Vi Hart (who you may recall, I think is amazing) originally became known (to me) by her "doodling in math class" series of short films.

These started as innocuous doodles which accidentally ended up showing the beauty and fascination in mathematics, but eventually became more elaborate and specific.

Things like this:

In this series she describes hexaflexagons. Watch 'em.

Magic the gathering is Turing-complete

I just mentioned Conway's Game of Life as an example of a Turing-complete system.

Though it's called the "Game" of Life, and some people describe it as a zero-player game, it's not really a game in the traditional sense of the word.

For an unexpected example of an unambiguous game which is also Turing-complete, check out Magic: The Gathering. It has been shown that a Universal Turing machine can be constructed inside Magic, and hence that it is Turing-complete.

I played a lot of Magic in high school, though it's too expensive of a habit to keep up for long. If, like me, you remember Magic fondly, but don't play it so much any more, might I recommend Mark Rosewater's Drive to Work podcast?

Life in Life

Conway's Game of Life is a well-known cellular automaton in which, every tick, the state of each of the cells on a giant grid is determined only by the states of its immediate neighbours in the previous tick. Despite its extremely simple definition, it is famously Turing-complete, which is roughly to say that it can compute any computable function.

And so, of course, someone has written a Life emulator, in Life.

Perhaps it's Life all the way down...


Schedule composition diagram

Here's what I'm doing this week: the 28th annual Mathematical Foundations of Programming Semantics conference.  I am presenting a paper there, "A graphical foundation for schedules", joint work with my PhD supervisors Guy McCusker and John Power.  There's a preliminary version of the paper which will eventually appear in ENTCS.  The talk had slides, though they contained unnecessary illustrative animations which are not there on the pdf.

"Designing to reveal the nature of the universe" — Jonathan Blow and Marc ten Bosch at IndieCade 2011

I watched this interesting talk on game design by Jonathan "Braid" Blow and Marc "Miegakure" ten Bosch. They espouse and explore a particular design aesthetic where the designer essentially plays the role of a mathematician.  "Good design" then becomes a selection of orthogonal mechanisms (axioms), and an exhaustive-yet-minimal mapping-out of what's derivable (theorems), and then demarcation of the boundary. Since it needs to be fun, the real art has to come from crafting surprise and tweaking axioms to capture exactly what you want. They both make some very interesting points, and I thought this comparison with mathematics was a particularly cool and apt way to frame the ideas.

This aesthetic is particularly apparent in the examples they use in the talk, including Braid, VVVVVV, Ikaruga and the as-yet-unreleased Miegakure.

Watch it here:

And find other videos on the IndieCade 2011 site.