I’ve been looking forward to this one: cities in the mathematical domain. This is the kind of applied maths I can really get behind.

Samuel starts with Mike Batty of University College, London’s Centre for Advanced Spatial Analysis discussing how cities grow and organise themselves. The structure is frequently fractal; how does one calculate the dimension of a city?

From a top-level view of cities, he moves on to a low-level description of one of the biggest problem in cities: traffic (another thing that fascinates me). We get a glimpse of traffic waves, and the unfairness that the person responsible for the average jam doesn’t suffer from the effects. And we learn that Gábor Orosz (University of Michigan) tests his hypotheses using robots as well as simulations.

The third segment focusses on Thomas Woolley of St John’s College, Oxford, who is a guide for Maths In The City, a series of walking tours around Oxford and London. Woolley gives an overview of the stories he and his colleague tell about, for instance, why bees do it (build hexagons, obviously) and the science behind Christopher Wren’s genius.

Segment four features Lisa Schweitzer of USC Price, who uses maths and statistics to tackle the social aspects of urban planning. My take-away was her line about using maths where appropriate — if it’s the correct tool to make a point, then she’ll use it, and if not, not. Oh, and some nice little dig at physicists, and justifications for pure maths (as if justification were needed).

Last up is a fun one: Samuel Arbesman, author, complexity scientist, and SimCity superfan. It’s a nice link back to the first story talking about the fractal dimension of a city; Arbesman suggests that one way to measure the complexity of a city — or at least, a SimCity — is to use the size of a saved game as a proxy. It’s roughly linear in population. It ends, as all SimCity segments should, with a monster being unleashed on a city.

As with pretty much every episode this series, the content is excellent but perhaps a little over-Samueled; a handful of places where the host explained things that might have been better explained by guests and at least one where the explanation was immediately paraphrased by the expert. A two-host show (for example, RadioLab) can get away with this by having one host explain to the other; it can also get away with dissing its writer’s poor jokes in a way that Samuel tries to.

These are relatively minor quibbles, though: one of the key measures of mathematical media for me — podcasts or articles or talks, or anything — is that it makes me want to play with the problems. Obviously, this episode cheated slightly by picking a topic I was interested with to start with, but it still left me wondering how I’d model traffic flow around my area and use it to avoid jams.

### More information

**Listen** to Relatively Prime: Principia Metropolica at relprime.com. While you’re there, catch up on Season 1.

*Colin was given early access to Season 2 of Relatively Prime, in return for writing reviews of each episode. Furthermore, Samuel is Aperiodipal numero uno and most of us chipped some money into the Relatively Prime Kickstarter, too. Just so you know.*