Except in my case, it really is a digital twin. It looks like an EKG, going tch, tch, tch, and it’s developed based on the data I’ve captured about an athlete’s movements. I can model how they will race under different conditions. Over the last seven or eight years, I’ve collected thousands of swims from over 100 top athletes. So I can race your digital twin against the database, make adjustments, and assemble the optimal formula you should use for your race — how many kicks do you take off the dive, where do you place your hands coming into a turn, how many breaths do you take and in what pattern. It’s curated per athlete, per inch. We can say: If you swim using this formula, you’re going to do the 100-yard backstroke in under 48 seconds.

These simulated races between digital twins might show a competitor 2 or 3 feet ahead of you at a particular point in time — but I don’t want you to worry about that, because you’ll see that in leg 3, they’re going to slow down, and you’ll catch up.

If you watch footage of NCAA races, you’ll probably get a sense that the UVA athletes seem to have this extra swagger, like they cannot lose. And there is of course truth to that, because they are winning all the time. But one of the unexpected benefits of our work is, in their mind, they think, if I swim that formula, I win the race.

What challenges have you had to overcome while doing these analyses?

There are several. For example, the question of orientation in three-dimensional space is critical. Your body is constantly in motion. So how do we decide when the force is actually going in the direction of the swim? It’s not that easy. We had to make sure that we were basing our analyses on the right orientations.

Accelerometer data is very noisy. Accelerometers are very sensitive. So some of the mathematics that’s deeply theoretical involves how you smooth the data to dampen out the noise. I need to know when a peak is meaningful. I have to be able to look at a stream of accelerometer data and say: This is where you’re breathing to the right, but you lifted your head up a little too much; or this is how much force you generated in the instant you moved off the wall, before you started decelerating. I need that level of sensitivity. I need to have confidence that the numbers I get mean what I think they mean.

Figuring out the correct method to smooth out this noisy data was probably the most sophisticated type of mathematics that we had to do, and that’s very secret.

What have you taken away from this experience?

We haven’t discovered or invented any new math. We’re not doing rocket science here. What I think this proves is that the attention to detail that comes from thinking analytically has merit. I want to find the stuff no one else has, and use Newton’s laws, together with experimentation and some linear algebra, to help craft the best performances for the athletes we work with.

There are still coaches that don’t take us seriously. But that’s not my job. My job is to help these athletes improve as swimmers, and to help get as many of them on the Olympic team as we can.

I’m a pure mathematician by training. That can be rather lonely. So this is perhaps the one time in my life where my training as a mathematical scientist seems to matter to a large group of people. It has been a dream ride.