Did you notice all the ties in the swimming events of this year's Olympics? Did you wonder why they didn't (or maybe couldn't) simply use more precise timing to break the ties? Not surprisingly, the answer is math. Read on to find out why.
Like many people, I was a bit caught off guard when the woman's 100 meter freestyle swimming event at this year's Olympics resulted in a two-way tie for the gold medal. And I was even more surprised when the following night it happened again—this time the men's 100 meter butterfly ended in a three-way tie for silver.
How is this sort of ambiguity possible in the modern high-tech world? After all, we humans have developed truly astonishing technologies for calculating teeny-tiny intervals of time, so it seems like we should be able to simply use more precise timers and add significant digits to each swimmer's time to break ties. While the math behind this line of reasoning is sound, problems like this in the real world don't always cooperate in making themselves neat and tidy and easy to solve.
This leads us to today's big question: Why is it that these ties in swimming persist? Clearly, there's no way that two swimmers who "tie" actually tie to an infinite degree of precision—certainly one person must win at least by an itsty-bitsy bit. So why is it that we can't simply increase the number of significant figures and break ties? Let's find out.
How Precisely Can We Measure Time?
Before we get to the specifics of Olympic swimming, let's talk a bit about the numbers and concepts behind measuring intervals of time. As I mentioned earlier, humans have the ability to measure time incredibly precisely. In fact, physicists have developed a clock, which "ticks" upwards of 1 quadrillion times per second—that's a million billion times every second! In principle, this means we can measure time intervals down to the nearest quadrillionth of a second—aka the nearest femtosecond.
In practice, we don't yet have practical timers deployed in the wild that can reach this level of precision, but it's relatively easy to find a timer that can measure time intervals down to the nearest millionth of a second. While that's way less precise than the femtosecond timer, it's way more precise than the timers used in Olympic swimming which measure only to the nearest hundredth of a second. But before you conclude that Olympic officials are simply behind the times and unaware of the existence of these new and improved timers, you should know that there's a very good reason they've chosen to limit precision: fairness.
Why Are There Ties In Olympic Swimming?
The logic behind why it's more fair to measure time less precisely in Olympic swimming is fairly straight-forward. To begin with, swimming pools are not idealized mathematical objects—they are actual objects in the real world that are engineered and built by humans. As such, they are not perfect. In fact, if you look closely at the official rules and regulations of how Olympic swimming pools must be built, you'll find that each lane must be 50.00 meters in length with a tolerance of 0.03 meters. Since 0.03 meters is the same as 3 centimeters, this says that each lane must measure exactly 50 meters plus or minus up to 3 centimeters (which is just a little over 1 inch). Which means that the length of each lane in an Olympic pool—and thus the distance each swimmer swims—is slightly different!