By Keith Douglas 
To recap from last time, Democritus’ cone, as it is called, can be used (as have many of the conundrums) to reflect on idealizations, the relationship between math and the world, etc. I especially like it for the latter, because it shows actually that much of what we learned in math classes (particularly quantitative geometry and trigonometry) was actually protophysics.
Something new, then.
Hilbert’s Hotel
Many summers I like to take trips to this conference or that, to talk to people working on familiar yet different problems and interests, to see the sights and enjoy some new foods. This summer, since I’m not likely to go very far for the reasons you might sadly realize, I’m thinking of a certain special hotelier who has been important to me in the past, a Mr. D. Hilbert.
It turns out he was once trying to accommodate a large number of guests in his wondrous facility (try the vegetable stew!). Normally he puts guests sequentially into available rooms as they arrive: the first in the first room, the second in the second, and so on. But once, so many guests arrived that the line at the desk was ended by a guy whose ticker-tape serve number read “omega + 1.”
Nevertheless, Mr. Hilbert wanted the business of all these people. Since there were so many, he offered a massive discount to all. He put them all into rooms, even offering a spare room between each pair of guests, and charged them the reciprocal of their room number in dollars per night.
Hilbert’s hotel has rooms starting at 1 and going up from there. Ever since that wonderful night of backgammon, chess, and those little crackers with salmon (not to mention Twister), Mr. Hilbert has been a very rich man indeed. I understand he’s looking to retire and put his sizable fortune into musical performances, focusing on symmetry of exposition and pieces which require diophantine analysis to play. My favourite musicians could use the money! I hope a good amount goes to them! (But can one play a diophantine piece on the cello? Hmmmm!)
(Your mission is to comment on my admittedly fanciful tale of Mr. Hilbert, including to guess his given name, which oddly I am not sure I remember.)
What a selfish guy, that hotelier. Almost as bad as Mass Murderer donald. He should have charged them, in $CDN of course, the sum of 1 over the squares of their room numbers.
Peter