Great Moments in History: My Drive to the Barber

According to Google Maps, it takes 9-10 minutes to drive from our apartment to Cameron Village, where I went to get my hair cut. But Google Maps doesn't take road-miracles into account. I made the trip in four minutes and thirty seconds. 4:30!

Here is a map of the route I took. Green circles indicate times when I came to a stoplight or traffic circle (there were ten lights and three circles) and did not have to stop. The red circles represent times that I needed to stop - which as you'll notice, was only once I got to a parking space.

For any of you who are inclined towards mathematics, you might realize that the probability of making 10 consecutive green lights is not tremendously high. If we assign each light a 50% chance of being green at any given time, then the probability of making 10 consecutive lights is 0.5^10, which comes out to 0.00098, or, in other words there is a 0.098% chance of making all ten lights.

The truth is slightly more complicated, though. First, the probability of any given light being green is much less than 0.5. For some lights (like left turn arrows) the probability is probably very small - in the 0.1 range, while others (like most of the straight ahead and right turn lights that I caught) are more likely to fall somewhere in the 0.4 range. As a rough estimate, I will say that the probability of making any given green light without having to stop is somewhere in the ballpark of 0.3. At a probability of 0.3 per light, the probability becomes much lower (0.3^10 = 5.9 x 10^-6, which works out to a 0.0006% chance).

On the other hand, the status of the traffic lights is not determined randomly. Presumably, some traffic engineer had to make some decisions about how to time the lights so that traffic can move as efficiently as possible. So, let's assume that for the first light of my trip, I experienced a normal 0.3 probability of getting a green light, but, due to the dilligence of the traffic engineers, all subsequent green lights (on the same road) have a probability of 0.7. Also, the seventh light in my route is almost always green, so I will assign it a probability of 0.9. This would make my probability of getting there without a red light:
0.3 x 0.7 x 0.7 x 0.7 x 0.7 x 0.7 x 0.9 x 0.3 x 0.7 x 0.7. This comes out to a probability of 0.0067, or a 0.67% chance.

The philosopher David Hume once commented that a miracle is simply an event with a very low likelihood of occuring (I'm paraphrasing). The rationale is that if something is impossible, it cannot occur (by definition). If it could occur, then it is not impossible. The less likely the event, the more miraculous it is if that event occurs. So, in this sense, I am going to claim that my green lights, with a probability of 0.0067, constitute a minor Humean miracle.

Questions For Discussion:

1. What is your greatest driving achievement of all time?
2. What is the top speed you have ever driven (as the driver, not a passenger)? I think my top speed is probably a dowdy 85 or 90 mph.
3. Yellow light. Do you brake or speed up?