Cafe Math

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.

Can folding a piece of paper 45 times get you to the moon? By seeing what happens when folding just one piece of paper, we see the unbelievable potential of exponential growth. This lesson will leave you wanting to grab a piece of paper to see how many times you can fold it!

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How do you investigate hypotheses? Do you seek to confirm your theory - looking for white swans? Or do you try to find black swans? I was startled at how hard it was for people to investigate number sets that didn't follow their hypotheses, even when their method wasn't getting them anywhere.