Reading the Comics, May 25, 2021: Hilbert’s Hotel Edition


I have only a couple strips this time, and from this week. I’m not sure when I’ll return to full-time comics reading, but I do want to share strips that inspire something.

Carol Lay’s Lay Lines for the 24th of May riffs on Hilbert’s Hotel. This is a metaphor often used in pop mathematics treatments of infinity. So often, in fact, a friend snarked that he wished for any YouTube mathematics channel that didn’t do the same three math theorems. Hilbert’s Hotel was among them. I think I’ve never written a piece specifically about Hilbert’s Hotel. In part because every pop mathematics blog has one, so there are better expositions available. I have a similar restraint against a detailed exploration of the different sizes of infinity, or of the Monty Hall Problem.

Narration, with illustrations to match: 'Hilbert's Hotel: The infinite hotel was always filled to capacity. Yet if a new guest arrived, she was always given a room. After all, there were an infinite number of rooms. This paradox assumed that management could always add one or more to infinity. The brain-bruising hotel attracted a lot of mathematicians and philosophers. They liked to argue into the wee hours abou the nature of infinity. Unfortunately, they were a bunch of slobs. Management had to hire a new maid to keep up with the mess. Daunted by the number of rooms to clean... the maid set fire to the joint. The philosophers escaped ... but the hotel burned forever.'
Carol Lay’s Lay Lines for the 24th of May, 2021. This and a couple other essays inspired by something in Lay Lines are at this link. This comic is, per the copyright notice, from 2002. I don’t know anything of its publication history past that.

Hilbert’s Hotel is named for David Hilbert, of Hilbert problems fame. It’s a thought experiment to explore weird consequences of our modern understanding of infinite sets. It presents various cases about matching elements of a set to the whole numbers, by making it about guests in hotel rooms. And then translates things we accept in set theory, like combining two infinitely large sets, into material terms. In material terms, the operations seem ridiculous. So the set of thought experiments get labelled “paradoxes”. This is not in the logician sense of being things both true and false, but in the ordinary sense that we are asked to reconcile our logic with our intuition.

So the Hotel serves a curious role. It doesn’t make a complex idea understandable, the way many demonstrations do. It instead draws attention to the weirdness in something a mathematics student might otherwise nod through. It does serve some role, or it wouldn’t be so popular now.

It hasn’t always been popular, though. Hilbert introduced the idea in 1924, though per a paper by Helge Kragh, only to address one question. A modern pop mathematician would have a half-dozen problems. George Gamow’s 1947 book One Two Three … Infinity brought it up again, but it didn’t stay in the public eye. It wasn’t until the 1980s that it got a secure place in pop mathematics culture, and that by way of philosophers and theologians. If you aren’t up to reading the whole of Kragh’s paper, I did summarize it a bit more completely in this 2018 Reading the Comics essay.

Anyway, Carol Lay does an great job making a story of it.

Two people stand in front of a chalkboard which contains a gibberish equation: 'sqrt(PB+J(ax pi)^2) * Z/y { = D/8 + H} - 17^4 x G + z x 2 / 129 \div +/o + exp(null set mickey-mouse-ears), et cetera. One person says: 'Oh, it definitely proves something, all right ... when it comes to actual equations, at least one cartoonist doesn't know squat.'
Leigh Rubin’s Rubes for the 25th of May, 2021. This and other essays mentioning Rubes are at this link. I’m not sure whether that symbol at the end of the second line is meant to be Mickey Mouse ears, or a Venn diagram, or a symbol that I’m not recognizing.

Leigh Rubin’s Rubes for the 25th of May I’ll toss in here too. It’s a riff on the art convention of a blackboard equation being meaningless. Normally, of course, the content of the equation doesn’t matter. So it gets simplified and abstracted, for the same reason one draws a brick wall as four separate patches of two or three bricks together. It sometimes happens that a cartoonist makes the equation meaningful. That’s because they’re a recovering physics major like Bill Amend of FoxTrot. Or it’s because the content of the blackboard supports the joke. Which, in this case, it does.

The essays I write about comic strips I tag so they appear at this link. You may enjoy some more pieces there.

Author: Joseph Nebus

I was born 198 years to the day after Johnny Appleseed. The differences between us do not end there. He/him.

3 thoughts on “Reading the Comics, May 25, 2021: Hilbert’s Hotel Edition”

    1. It is, yeah, but the maid has too start somewhere. And the cartoonist has to fit the labels inside the panels.

      But yeah, one practical problem with the Hilbert Hotel is that almost all the rooms are going to have numbers too large for humans to ever recognize.

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