(Originally published on October 9, 2009)

How your blinkers never blink with the same frequency as those of the car in front of you

If you’re a driver, you no doubt spend a nontrivial amount of time waiting at an intersection, another car in front of you, you both wanting to turn left. You probably noticed that the turn signal of the car in front of you doesn’t blink with quite the same frequency as one in your car.

In fact, I have a strong suspicion that no two cars have the same frequency–at least that’s what it seems to me since I can never find turn signals to be in phase.

And so here I am, waiting for the light to turn green, with two blinkers flashing with different frequencies. I don’t like to do nothing, so I often figure out what this difference in frequencies is. It’s not as hard as it may seem–and it involves no measuring devices! It’s a pretty cool trick that takes advantage of the fact that while it’s hard to measure or compare quantities (such as speed, frequency), it’s relatively easy to detect synchronicity. First, figure out which blinker is faster. Then wait for both blinkers to be momentarily synchronized (i.e. for both to flash at the same time). Count how many times the faster blinker flashed before both are synchronized again (make sure you don’t “skip” a cycle). If the faster one blinked n times, and you captured the cycle correctly, the slower one blinked n-1 times so the faster one is n/(n-1) times faster. I like to go a step further and memorize what fractions of the form n/(n-1) come out to be as percentages to impress people with some percentage estimates while sitting in the car, with no calculator. For example, if the slow one blinks 9 times and the fast one blinks 10 times, the fast one is 11% faster.

This trick works for car blinkers in part because most cars’ blinkers flash with similar but not the same frequency (if the ratio of frequencies is fairly large, you will find it hard to not skip steps–that is, the blinkers will not synchronize fast enough). I also like to go to the gym, get on the treadmill and figure out how fast the person next to me is running by observing the synchronicity of the markings on the treadmill (treadmills have their brand names displayed on the belts)–the trick works because most people run at similar speeds (between 6.5 and 8.5 mph) and, moreover, because people tend to run at quantized speeds, I am often able to figure out the speed precisely.