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The Infinite Hotel Paradox: A Brilliant Animated Thought Experiment to Help You Grasp the Mind-Bending Concept of Infinity

What a hospitable night manager can do for our finite human minds.

“Infinity is a demented concept,” astrophysicist Janna Levin, who studies the finitude of the universe, wrote in her spectacular diary-turned-book about the universe. Infinity is also a dementing concept. Most of us find it oddly hard, impossible even, to actually wrap our minds around it and envisage a thing — for it can’t really be a number, can it? — to which we can’t simply add something else to produce infinity-plus-one, instantly rendering “infinity” finite.

To help ordinary humans tussle with this extraordinary concept, German mathematician David Hilbert conceived of what is now known as the Infinite Hotel Paradox — a brilliant and mind-bending specimen of that neat intersection of science and philosophy: the thought experiment. Hilbert came up with the Infinite Hotel Paradox in 1924, but it was popularized only after his death by Russian-American theoretical physicist George Gamow’s 1947 book One Two Three… Infinity: Facts and Speculations of Science (public library).

This illuminating short animation from TED-Ed, written by Jeff Dekofsky, brings the famous thought experiment to life — fasten your neurons:

For other stimulating TED-Ed animations, see how a dog actually “sees” the world through smell, why music benefits your brain more than any other activity, how to spot liars, and why bees build perfect hexagons.

Published February 19, 2015




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