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| 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.
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