The hilarious and bizarre Mitch Hedberg once said “Every time I go and shave I assume there’s someone else on the planet shaving, so I say ‘I’m gonna go shave, too.'” Because I am an obsessive fool who can’t leave anything alone, I started wondering if you could actually reasonably say that. I mean, there are a lot of people in the world, and a lot of people who shave, so it’s entirely possible that there’s someone shaving every second of the day.

This is a perfect place for Fermi estimation, or, if you prefer, back-of-the-envelope calculation. It’s a great method for getting a quick idea of the scope of a problem.

There are about 7 billion people on Earth. In many cultures, only the men shave. Let’s assume that half of the people in the world are men. That gives us 3.5 billion potential shavers. But, except in rare cases, men don’t start shaving until their beards begin growing at puberty. Let’s say beard growth starts at age 15. A randomly-chosen person could be pretty much any age, let’s say from 0 to 70. Only that percentage of men between 15 and 70 shave, which comes out to 79%, or 2.756 billion.

It takes me about 15 minutes to shave. Let’s assume that all the men in the world shave every day at a random time of day (this ain’t a realistic asumption, lemme tell you, but it’ll help compensate for the fact that most of the men in the world are in a different timezone than me, and for other weird factors like that.) There are 96 15-minute blocks in a 24-hour day. The probability of a man picking a particular 15-minute block to shave is 0.01. Therefore, the probability of a man *not* picking a block to shave is 0.99. The probability of every shaving-age man not picking the block in which I’m shaving is 0.99^(2,756,000,000), or 2.045e-12029404. When you see a negative exponent that large, your number is, by any sensible definition, zero.

Mitch had it right. So, from now on, when I shave, I’ll say “I’m gonna shave, too.”

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Great post !I just love things like this.

You’re right 2.045e-12029404 is a pretty small number !

The Science Geek

http://thesciencegeek01.wordpress.com/

I believe that’s actually the smallest number I’ve ever encountered in my own calculations.

As a matter of fact, I looked it up, and it’s smaller than the probability of a monkey typing Hamlet on the first try.