By the time we are three, many of us will have learned how to count. Once we’ve learned how, it seems as if there’s nothing to stop us counting indefinitely. While infinity may seem like a perfectly innocuous idea however, keep counting and you enter a paradoxical world where nothing is quite as it seems.

Mathematicians have discovered there are infinitely many infinities, each one infinitely bigger than the last, and if the universe goes on forever, the consequences are even more bizarre. In an infinite universe, there are infinitely many copies of the Earth and infinitely many copies of you.