Hilbert's Grand Hotel

 

Hilbert's Grand Hotel, 8" x 10", linocut by Ele Willoughby, 2021

My latest linocut print illustrates the paradox of Hilbert's Grand Hotel, a thought experiment conceived by the great mathematician David Hilbert (1862-1943) in 1924 to show the paradox of infinite sets. If you imagine a regular hotel with a finite number of rooms, if they are all filled you can't add more guests. In an imaginary infinite hotel however, guests are always welcome! Even if all the (conveniently numbered 1, 2, 3, ...) rooms are filled, you simply shuffle all the guests over one room and make room for the next guest. You can repeat this argument for one more guest, two more guests, three more guests, ...infinity more guest... infinity groups of infinite guests, etcetera!

The print shows a grand hotel on a steep angle (with a vanishing point at infinity of course), labelled "Hilbert's Grand Hotel" below a cameo of Hilbert himself, and the slogan "No vancancy. Check in now!" Above the hotel is a glowing infinity symbol. The size of countably infinite sets, like all natural numbers {1,2,3, .... ∞ } is denoted by Aleph Nought ℵ0 shown on the two flags.