Traffic Colors 🚦

"¿Que le dijo un semáforo al otro?

'No me veas, me estoy cambiando.'"

— chiste de mi amigo chileno

Back when I was fifteen in driver's ed, I remember our teacher asked a cool irl mathematical question. We were covering stoplights, and the teacher asked which color was most common. My first knee-jerk thought was that they'd be about equal. I knew more about geometry than driving at the time :( .

Then I forced myself to think the problem through. You're trying to guarantee people on perpedicular paths of an intersection don't kill each other. So I came up with some thoughts:

• green and green can never happen on either side of the stoplight.
• yellow is effectively just green but warning that red is close at hand.
• that way, red must be at least a as much as the other half's g+y color-time proportion.
• red and red is expected with imperfect humans.

I came up with this vague sketch in my head:

So answering the instructor's question, red is the most common traffic color. green second, yellow the remnant third. This is a very symmetric diagram. It assumes both roads are equally "green". But the main point is that if you add up both lights' colors-seconds per cycle, red has to be half of the color-time at a minimum, but usually the majority¹ outright.

And what is color-time? I mention it above a few times, but since this is such a cyclical model, color-time is just the proportion of each color's light in a complete traffic light period.

I made up a cooler diagram of two "gears" of stoplight colors with angles representing the color-time versus the boring line segments above:

A cool thought I wanted to share that I've remembered many times during long, boring red lights on the road.