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.
The length of each lane in an Olympic swimming pool is slightly different!
Why do the lengths of lanes differ? The short answer is: physics. To begin with, a pool can only be built so precisely. There will always be natural variations in length across the width of the pool due to how perfectly (or imperfectly) it's made. Making matters more complicated is the fact that pools are filled with water, and this water weighs a lot—around 4,000 tons for an Olympic-sized pool. The weight of all this water pushes on the walls of the pool and can actually distort its shape and change the lengths of lanes by small but potentially significant amounts.
So why does this matter? How does it relate to the limited precision with which Olympic swimming events are timed? Remember, as I said earlier, it has to do with fairness to the competitors. In particular, as we calculated last time, it has to do with the fact that elite Olympic swimmers move through the water at speeds up to about 5.3 miles per hour. And thus, in 0.01 seconds (the smallest time interval measured in Olympic swimming competitions), an Olympic swimmer may swim up to around 2.4 centimeters. Which, as you've hopefully noticed, it very close to the 3 centimeter tolerance allowed for the natural variations in each lane.
Significant and Insignificant Digits
The point is that if the powers that be decided to add another significant digit and record times in Olympic swimming races down to the nearest thousandth of a second, they would be measuring differences in distances of just a few millimeters (that's how far an Olympic swimmer moves in 0.001 seconds). But the various lanes in an Olympic swimming pool can be not just a few millimeters but actually tens of millimeters different in length.
Which means that one swimmer might finish a few thousandths of a second faster than another simply because they were in a slightly shorter lane. Obviously that's not fair to the athletes. Which is precisely why Olympic swimming events are measured only to the nearest hundredth of a second. If one swimmer finishes 0.01 seconds ahead of another, that means they finished at least a few centimeters ahead of that swimmer. And, according to the tolerances allowed in building Olympic pools, that means that the winning swimmer in this case finished first because they were actually faster … not just because they were in a shorter lane. In other words, it means they won fair and square.
Okay, that's all the Olympic math we have time for today.
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Until next time, this is Jason Marshall with The Math Dude’s Quick and Dirty Tips to Make Math Easier. Thanks for reading, math fans!
Swimming pool image from Shutterstock.