On Entropy and Radius of Gyration

In our dashboard, we focused on two metrics that are extremely useful, driven by human mobility, and, for most people who don’t live and breathe this stuff, wonderfully obscure. Let’s try to make them a bit more understandable.

Let’s start with radius of gyration. One colleague said that, when hearing that term, that he couldn’t stop thinking about hula hoops, which is a great visual, but not exactly right. When we’re thinking about how people move, there’s an instinct to just measure the furthest people move. But, if someone is spending the vast majority of time in a small area, but has one short trip far away and back, just measuring the furthest point does not really reflect that that single trip was not really a normal part of the person’s movement. Radius of gyration allows us to take different patterns of movement, simplify them mathematically so they all “act like” circles, and really get a sense of patterns of movement. 

Entropy is about unpredictability. You can stay in a small area but be moving unpredictably or traverse a large area very predictably. The example I’ve been using is one in which someone is in their neighborhood, but is helping out their neighbors by moving to different homes, depending on need, and dropping off food. It won’t be obvious where that person is going to go because how often they visit any one place is not going to be obvious. (The less charitable version of this is someone staying in their neighborhood but bar hopping.) Someone just staying at home, or just going to work from home, is extremely predictable (though they may be traveling far from home).

In the case of COVID-19, a doctor wouldn’t be interested in an individual’s radius of gyration and entropy. In that case, it’s much more important to figure out the contacts that a person had with others. But, if you want to study populations, which is what epidemiologists need to do, a group’s mean and median radius of gyration and entropy matters a lot. It can speak to how much people are staying at home and keeping to rigorous social distancing guidelines. 

These are not the only ways to measure human movement – and especially not the only correct ways. But, using these, epidemiologists and specialists in human mobility can truly understand how large groups of people travel and how effective our social distancing interventions truly are.

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