Another gem I found while cleaning out my office over Christmas – from an old Humanistic Mathematics Journal (Issue #24). Here’s the song, Hotel Infinity, sung to the tune of the Eagles Hotel California, except that this is about the Hotel Hilbert. The lyrics were written by Lawrence Mark Lesser.

“Hotel Infinity”

On a dark desert highway — not much scenery

Except this long hotel stretchin’ far as I could see.

Neon sign in front read “No Vacancy,”

But it was late and I was tired, so I went inside to plea.

The clerk said, “No problem. Here’s what can be done–

We’ll move those in a room to the next higher one.

That will free up the first room and that’s where you can stay.”

I tried understanding this as I heard him say:

CHORUS: “Welcome to the HOTEL INFINITY —

Where every room is full (every room is full)

Yet there’s room for more.

Yeah, plenty of room at the HOTEL INFINITY —

Move ‘em down the floor (move em’ down the floor)

To make room for more.”

I’d just gotten settled, I’d finally unpacked

When I saw 8 more cars pull into the back.

I had to move to room 9; others moved up 8 rooms as well.

Never more will I confuse a Hilton with a Hilbert Hotel!

My mind got more twisted when I saw a bus without end

With an infinite number of riders coming up to check in.

“Relax,” said the nightman. “Here’s what we’ll do:

Move to the double of your room number:

that frees the odd-numbered rooms.”

(Repeat Chorus)

Last thing I remember at the end of my stay–

It was time to pay the bill but I had no means to pay.

The man in 19 smiled, “Your bill is on me.

20 pays mine, and so on, so you get yours for free!”

lyric © 2000 Lawrence Mark Lesser, all rights reserved; May be sung to the tune of the Eagles’ 1976 #1 hit “Hotel California”.Previously appeared in Nov. 2004 Journal of Irreproducible Results, May 2001 Humanistic Mathematics Network Journal, Oct.2006 American Mathematical Monthly, Len Wapner’s 2005 A.K. Peters book The Pea and the Sun: A Mathematical Paradox, and of course, on Lesser’s math song webpage Mathemusician.

The last lecture of Calc II every year, I prove to the students that there is more than one infinity (coutable and uncountable infinity). When we talk about countable infinity, I may just have to break into song.

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