The unreasonable effectiveness of mathematics

My family and I are on vacation in Maui. There was a contest on the flight here from SFO a couple of days ago: Guess the exact time (to the nearest second) at which the plane would reach the halfway point of the trip. The crew gave out a lot of information about airspeed, distance, and headwind, but my guess was based on just two things: the time we took off and the time we were expected to land.

I don’t recall the times, but whatever they were, I punched them into PCalc on my iPhone, converted the minutes to decimal hours, used a 24-hour basis for the hours, and averaged the two. The answer I came up with was 13.6833, which translates to 1:41:00 PM.

When we landed, the crew announced the actual halfway point as 1:40:48, just 12 seconds earlier than my calculation. This was, I thought, amazingly close for such a quick and crude estimate. I prepared myself for the announcement that I was the winner.

I didn’t win. A guy three rows behind me guessed 1:40:40, just 8 seconds off the actual time. I don’t know how he did it—maybe he did the same calculation I did and then jiggered the number a little bit. Or maybe he just guessed. Whatever the reason, he took the prize: a CD of Hawaiian songs.

I’m thinking I came out ahead in the deal.