Two things are infinite: the universe and human stupidity; and I’m not sure about the universe.

~ALBERT EINSTEIN

Infinity is the darling of cutting edge research, the measuring stick used by physicists, cosmologists, and mathematicians to determine the accuracy of their theories.

In The Infinite Book: A Short Guide to the Boundless, Timeless and Endless, Cambridge professor John Barrow takes us on a grand tour of this most elusive of ideas and describes with clarifying subtlety how this subject has shaped, and continues to shape, our very sense of the world in which we live.

But let’s take a look at The Infinite Hotel, a thought experiment created by German mathematician David Hilbert, is a hotel with an infinite number of rooms. Easy to comprehend, right?

Wrong. What if it’s completely booked but one person wants to check in? What about 40? Or an infinitely full bus of people?

Jeff Dekofsky solves these heady lodging issues using Hilbert’s paradox.