Computer Gaming and Fencing: the Transfinite Blade

One neat sub-branch of mathematics is Cantorian set theory. Cantor took one sly strategy, now sometimes called Cantor diagonalization, and applied it over and over again (in the same way Beethoven takes a single theme and develops it into a complete symphony) to develop the basis for an algebraic structure of infinities. Infinities?

Yes, there’s more than one if by chance you didn’t know. To be precise, there are a countable but infinite number of infinities. You can ask and answer questions like if I have two sets of two different infinite sizes and I put them together what is the infinite size of the result. Actually, that isn’t as interesting a question as it first sounds. It's more interesting to ask what is the particular infinite cardinality of interesting sets, say the Imaginary Numbers. And infinities can be ordered: one is strictly larger than another.

At this point I should mention that I have the highest regard for games, particularly those requiring strategy and analysis. Ever since 8 hours of Bridge with some particularly enjoyable partners turned a miserable, interminable wait in the Iquitos, Peru airport for a vintage airplane to take Lynn and I over the Andes into a pleasant day, I’ve had faith in the transcendent and transformative powers of games. And, obviously, games themselves can be art, just as playing them can be as shown by Ricky Jay, Bobby Fischer et al.

So I’ve just downloaded a wicked cool new game, an app for the IPAD, “Infinity Blade,” which, for once, lives up to the high praise it’s received. In spite of the limitations of the IPAD graphics engine, the game delivers dynamic real time graphics in a class with the best MMOs. But what I find particularly interesting is the game play itself, particularly the user interaction. For once, medieval combat is not trivially reduced to pushing a handful of virtual buttons. Instead, the touch screen swipe action is mapped to sword movement. Now, at any given instant you have to make the choice of whether to block or to attack and you have an infinite number of choices of how to sweep the blade, which yield greatly varying results. Combat requires continual focus, some precise hand muscle motor skills, even a little strategy. (Sound familiar?) In the parlance of the computer gaming development community, that makes the game deeply “emergent,” a very good thing.

Which leads me, naturally, to fencing. Among many other things it’s a game, too, in the strictest sense. However, I will spare you the formal, but trivial, argument showing that the infinity of potential actions in fencing is strictly larger than those in Infinity Blade. Further, stepping up into the meta-game, there are an infinite number of strategies within which are an infinite number of tactics which can lead to those actions. And it requires precise control and coordination of large and small muscles across the entire body.

So, from a certain point of view, fencing can be viewed as the equivalent of extreme computer gaming, even though a computer isn’t required.