Ever notice when you’re behind two cars that have their turn signals on and while they’re currently blinking at alternating intervals, they always seem to sync up and blink at the same time before going back to alternating blinks. How?
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I think it’s because they are milliseconds off from each other, so at times they seem in sync until those milliseconds add up and they go off sync before back again.
Any two series that don’t have the same period or multiple of the same period will eventually synchronize.
For example suppose we chart their blinks on a number line, one with a period of 7 and other with a period of 3. The slower one blinks at 0, 7, 14, **21**, 28, 35, etc. The faster one blinks on 0, 3, 6, 9, 12, 15, 18, **21**, etc.
Notice how they both blinked on 21, but also consider the lead up to that point. On the faster one’s third blink it is at 6, only 1 unit behind the slower one at 7, but because its period isn’t an even multiple of 7 there will be some remainder that will gradually shift the blink into synchronization.
We can easily figure out where this point is by multiplying the period of one series by the other, in this case 3 x 7 = 21.
It’s because they aren’t actually synced. In order for them to be (really) synced, these things would have to be true:
1. Both drivers activated their turn signals at the exact same instant
2. All the parts of the turn signal system would have to work exactly alike: they’d have to start lighting up the lamps the exact same amount of time after the driver flicked the lever, and they’d have to make the lamps go *on* for the exact same amount of time, *stay* on for the exact same amount of time, go *off* for the exact same amount of time, and *stay* off for the exact same amount of time
Usually neither of these two conditions are met. But when two cars are *close* to synchronized, then you can get the illusion that they *are* synchronized. Here’s how it works: one car’s signals are lit up for a slightly longer or shorter time than the other car’s signals, and/or the on/off flash rate on one car is slightly faster or slower, and so as you watch both cars’ signals flashing on and off over time, you see the difference between them in the form of a sort of ‘movement’ relative to each other. Think of it like two cars going the same direction, with one car passing the other car very slowly (that is, both cars are going *almost* the same speed, but not quite): there will be a period during which it looks like they’re going the exact same speed, because they are exactly side-by-side. But before and after that side-by-side period, the slightly faster car will first be behind the slightly slower car, then ahead of it.
Think of a pattern going …O…O…O…O…O…O
And another going. ..O..O..O..O..O..O..O..O
…O…O…s…O…O…s
..O..O..O..s..O..O..O..s
They eventually sync at common multiples
When blink duration differs, the time difference between them accumulates every cycle. When the accumulated difference approaches roughly the average cycle duration between each car, the lights are in sync again.
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