Wednesday, March 21, 2018

Principlelhole Pigeon

The pigeonhole principle is the principal that states that if you play eight games of chess, two must be played on the same day of the week. If this isn't obvious think of which days you want to put the first seven games on. You'll be out of possible days to put the eighth game.

A classic demonstration of this is to show that two people have the same number of hairs. The argument goes like this:

1. No one has more than one million hairs (apparently the human average is around 150,000). This isn't a provable fact in the mathematical sense but we know it in the same way we know no one is 5 meters tall.

2. There are over seven billion people in the world.

3. Apply the pigeonhole principle.

Now this actually means that the average person is sharing the number of hairs they possess with something well north of seven thousand people.

An interesting discussion I remember having with a prof in grad school inspired by this was weather anyone is the only human in the world with k hairs, for some k? After all most people are clearly sharing a hair number with thousands, on the other hand someone has the most hairs and like most things the tails of the distribution are likely... well tails. Would we have a unique "winner" if we ranked people by most hairs? I don't know and my mind has gone back and forth a few times.

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