Peter Krautzberger · on the web

kids, exponential growth and 42

Last week, I was lucky enough to attend the W3C workshop on ebooks in NYC. This allowed me to visit some old and very dear friends. In a conversation with one of their kids, I pulled out a classic that I like very much.

Today, I did some fact checking and -- lo and behold -- the answer was not 52 but 42! That is, of course, fantastic.

Anyway, the question I asked was: how thick is an piece of regular office paper if you fold it 52 42 times?

The answer is: it would reach all the way to the moon!

That usually surprises kids (and non-kids) and is a nice example for the surprises of exponential growth. In fact, it also surprises me and I'm always somewhat nervous when a kid takes me up on the offer of checking that the number is actually correct.

For this you first have to decide what paper you're looking at. A piece of A4 paper (I'm German after all) is on average 0.1 mm. That's actually hard to estimate but it's what I eventually found on the interwebs; if you have the time, I invite you to delve into the art of density and calipers.

When you fold it 42 times, it's as if you stacked test \(2^{42}\) pieces of paper on top of each other. So the thickness is \(2^{42}\) x 0.1mm, which is ~439,804 km (and a kilometer is 1,000,000 milimeter).

The moon is on average 384,400km from earth, and 405,410km at its farthest -- so we'll get there no matter what day. If, that is, we could fold a piece of paper 42 times.

For what it's worth, the world record for folding paper is 13 times -- achieved by high schoolers on MIT's campus in 2011.