Math & Science Tell Us

We position math and science as independent arbiters of truth. Let’s not forget who is really doing the talking.

Motherboard is a great place to get a little breather during the workday. That’s where I stumbled across an article about “A Typology of Street Patterns,” a new study published in the Interface, a journal of the Royal Society. The authors of the study propose a new quantitative method to classify cities according to their street pattern.

Rémi Louf and Marc Barthelemy developed a mathematical technique to sort street shapes into distinct patterns, in the hopes of defining the ‘fingerprint’ of each city. They used a clustering method, developing a dendrogram that shows hierarchical relationships. A dendrogram can look something like this:

A simple dendrogram applies a hierarchical structure to show continuity of information over time.

In the summary of their study, the authors say they discovered four large families of cities, and that most European cities and American cities in their sample fall into one of these families. To see images from the study and hear from Barthelemy, check out the Motherboard article: “There Are Only Four Types of City in the World, Says Math”.

Says Who?

Or maybe you just did a mental double-take at that headline and want to stick with me a little longer. Says Math? That’s right, that cutely flippant statement points out a massively popular phraseology in math and science journalism, in which math and science tell us objective facts about the world. The problem is, math and science don’t tell us anything — mathematicians and scientists do. And mathematicians and scientists aren’t objective. Nor, by the way, are economists, doctors, lawyers, or any other educated professional. Their education lends them a point of view — a valuable point of view informed by extended study of a field.

In applying quantitative methods to sort, filter, and synthesize information (i.e. math), human decisions guide the process and shape outcomes according to the views held by the author of that process.

Take, for example, the simple process of averaging numbers together. Over the summer, Thicket’s multidisciplinary team of researchers and designers where we discussed methods to average several numbers together into a single value. Here is a visual representation of four methods to average two numbers between 0 and 1.

Four ways to average numbers generate very different outcomes.

The first graph (far left), [A], represents: x*y — multiplication. [A] tends towards the low — either x or y being low pulls the combined value down as visible in the large swath of dark blue.

The second graph, [B], represents: (x+y)/2 — an arithmetic mean. [B] is perfectly linear and values both equally.

The third graph, [C], represents: √x*y — a geometric mean. In [C], very low values in either x or y still naturally pull the combined value down, but either being a high value pulls the combined value up.

The fourth graph (far right), [D], represents: x+y-x*y — addition minus overlap. [D] is a generous metric best used for finding “combined coverage” of two things that “stack” on each other.

Visual analysis is a great way to see how subjectivity is still a massive consideration even in the hardest of sciences. As our data sets get bigger and our analytics more sophisticated, never doubt that there is a human being making important choices behind those analytics, and humans will always be subjective. And subjectivity is not a bad thing.

In the case of physicists Louf and Barthelemy and their incredible work on cities, they are showing how a single study can have many applications — helping us better understand historical population flows as well as today’s urban design challenges. And they are a prime example of the power of mixing disciplines (applying statistical physics to urban design) for richer results. I hope that soon we’ll be able to see headlines like “There are Four Types of Cities in the World, say Louf and Barthelemy.” And we’ll trust the information even more, because they have earned our trust with their track records.

This article was written by Deepthi Welaratna. Visual and textual analysis of averaging methods contributed by Lukas WinklerPrins. Header image designed by Sam Hutch.