## Uncertainty Intervals and the Olympics

If I had to pick one topic or way of thinking that engineers and scientists have developed but other folks are often entirely unfamiliar with, I might pick the related ideas of error, uncertainty, and significance.  A good science or engineering education will spend a lot of time on assessing the error bars for any measurement, understanding how those errors propagate through a calculation, and determining which digits of an answer are significant and which ones are, as the British might say, just wanking.

It is quite usual to see examples of the media getting notions of error and significance wrong.  But yesterday I saw a story where someone actually dusted these tools off and explained why the Olympics don't time events to the millionths of a second, despite clocks that are supposedly that accurate:

Modern timing systems are capable of measuring down to the millionth of a second—so why doesn’t FINA, the world swimming governing body, increase its timing precision by adding thousandths-of-seconds?

As it turns out, FINA used to. In 1972, Sweden’s Gunnar Larsson beat American Tim McKee in the 400m individual medley by 0.002 seconds. That finish led the governing body to eliminate timing by a significant digit. But why?

In a 50 meter Olympic pool, at the current men’s world record 50m pace, a thousandth-of-a-second constitutes 2.39 millimeters of travel. FINA pool dimension regulations allow a tolerance of 3 centimeters in each lane, more than ten times that amount. Could you time swimmers to a thousandth-of-a-second? Sure, but you couldn’t guarantee the winning swimmer didn’t have a thousandth-of-a-second-shorter course to swim. (Attempting to construct a concrete pool to any tighter a tolerance is nearly impossible; the effective length of a pool can change depending on the ambient temperature, the water temperature, and even whether or not there are people in the pool itself.)

By this, even timing to the hundredth of a second is not significant.  And all this is even before talk of currents in the Olympic pool distorting times.

1. #### CC:

There is a class action out there about Starbucks not filling their cups all the way. This not only ignores the impossibility of pouring perfectly, but ignores that many people put lots of cream in their coffee and they need to leave room for that. Same with the Subway footlong. Yeah, yeah, it is really 11 inches--you can see it for yourself, and go elsewhere if it seems too short.

2. #### SamWah:

Fill the cup right to the top...and pick it up. Spillage happens.

3. #### Matthew Slyfield:

Dangerous burning hot spillage.

4. #### Theyouk:

This is shocking, and in no way makes me question how reliable our measurements of average global temperature are (within 0.01 degrees C) and those of global sea levels (within 0.01mm..... ) (sarc, in case ANYONE didn't see that coming....)

5. #### Not Sure:

"There is a class action out there..."

Addressing the issue when receiving your beverage is out of the question, then, I suppose?

6. #### DaveK:

The funny thing about the "Subway-Shorts" is that you don't get any more filling in the sandwich by stretching it out to the full 12 inches. The meats and cheeses are already pre-portioned, and the worker just slaps those onto the bread. The full 12 just gets you an extra inch of dough.

7. #### DaveK:

The "photo-finish" is how you would usually sort it out (and that happens to be a pretty amazing bit of fairly old and clever technology). Of course it's a little harder in a swimming pool, so there you might have to default to using a touch-pad at the finish, and ignore the 3rd decimal place.

8. #### marque2:

Not even that. The problem was some chains were not letting g the dough rise long enough. Same amount of dough, more air.

9. #### LoneSnark:

Given that lawsuits award far more than actual damages, not having me burn myself with my coffee causes significant financial damages.

10. #### MM:

This leaves one wondering about the accuracy of the dry land events, like

400m run. How accurate are those "staggers" that are meant to correct for the lanes going around the curves?

11. #### David in Michigan:

I would go you one more decimal place to the left. One tenth of a second (0.1 seconds) is a perfectly reasonable significant figure in human sports competition. In human terms, it's a mighty short interval. I ask you, is there really a difference in performance at 0.01 of a second? At that point other factors, such as athlete size, reach, starting point, equipment, et al, become significant and not controllable. There is nothing wrong with saying the event resulted in a tie. Olympic competition is about humans not machines. It's simply stupid to pretend otherwise.

12. #### GoneWithTheWind:

Reminds me of the discussion I had with the city surveyors who were very proud of their GPS location device. It could tell you where you were on the earths surface with an accuracy of 0.01 feet. However it gave you the coordinates to 8 decimal places. We were creating a computer database for this and I cautioned that it might be wise to keep the data to 2 or 3 decimal places. I pointed out it would possibly create mathematical errors (when computers compute results between very large and very small numbers) AND that having 8 decimal places tends to make people think that the data is accurate out to 8 decimal places. They would not relent. The device gave them 8 decimal places and 8 decimal places is what they wanted on the computer. Period !

13. #### Dan Wendlick:

IIRC, these are correct to about 1-3 cm, about the same variance in where the athletes will place their hands in the starting blocks. The interesting thing is that the radius of the turn necessarily varies across lanes, leading to an advantage for taller runners in the outside lanes and shorter runners on the inside, generally. You may also notice that each of the starting blocks has a speaker attached. This is so that runners further from the starter's location hear the start signal at the same time as those closer in. Finish lines are literally laser-straight, and do not necessarily correspond to the painted markings on the track.

14. #### Dan Wendlick:

All you need to do is average the finishing times of all the runners in the race, compare it to what the models show the actual finishing times should have been based on a regression of the past 25 Olympiads, and then "correct" the times to the more "accurate" values.