We’ve been sent a copy of Matthew Lane’s Power-Up: Unlocking the Hidden Mathematics in Video Games, and despatched Aperiodical regular and video game fan Paul Taylor to review it.

Rather than a survey of mathematical research on a common topic like Hannah Fry’s The Mathematics of Love, Power Up is a look at interesting maths-y topics applied to more or less contrived situations arising from playing or thinking about various computer games. Probabilities are explained through the problem of getting the same word again and again in Draw Something! (a common frustration I imagine), while the travelling salesman problem is discussed in relation to collecting the 100 ‘data fragments’ in an Assassin’s Creed game via the shortest route possible (I haven’t played any Assassin’s Creed but I assume that nobody would have any call to actually do this).

If your field of reference overlaps with the examples in the book — lots of Mario, Threes! Rather than 2048 — there’ll probably be plenty of smiles of recognition. Lane ponders lots of topics that a reader with a mathematical mindset is likely to have considered. Why, for example, when Mario jumps from a stationary position on a moving platform in Super Mario Bros, does he spring vertically up from where he took off, rather than moving with the platform as Galilean relativity dictates? And why in Super Mario 64 and subsequent 3D games has order been restored, with Mario duly landing at the same point on the platform from which he jumped?

Lane explains some pretty technical concepts in an accessible way, from chaos and dynamical systems (relationships in The Sims and the bouncing of MarioKart green shells) to P vs NP (Tetris and Minesweeper, though I think computer scientists after a bit of easy publicity have probably proved pretty much every game is NP-hard by now). Most of the hairier explanations are quarantined in appendixes, though I admit I did skip over a few of the details of some differential equations in the main text.

There’s no overarching thread to Power Up, so you can dip into whichever of the eight main chapters you like and find something interesting. The final chapter is the author’s thesis on the value of games to teaching maths (unsurprisingly, he’s in favour of it). There is one unforgivable lapse I spotted: a graph of daily active users of Draw Something over time, used to illustrate the fall in popularity of the app attributed to the paucity of available words to draw, has its y-axis truncated to start at 9 million. An apparent complete exodus from the game over a month turns out to be merely a 35% drop, presumably not too disastrous in an environment where sudden initial surges in popularity are the norm. But unless you take a fully zero-tolerance approach to data-visualisation transgressions you shouldn’t let this put you off giving Power Up a read if you want a fun survey of interesting maths related through the lens of video games.

More information

Power-Up: Unlocking the Hidden Mathematics in Video Games at Princeton University Press

Power-Up: Unlocking the Hidden Mathematics in Video Games at Amazon