Ode to Hilbert's Grand Hotel

Lyrics

The sign says No Vacancy.
Every light is on.
Every key is turned.
The sign is a liar.

Down the corridor, the numbers never end.
Room Aleph-Null. Room Aleph-Null plus one.
A thread of light under every door.
You can hear a life in every room.
The night clerk polishes the front desk bell.
He knows the secret of the floor plan.
The hotel is completely full.
And it has been, forever.

Then the call goes out along the wire.
From the front desk to the farthest star.
Guest in Room 1, please take your things to Room 2.
Guest in Room 2, you're moving to Room 3.
The shuffle begins, a wave down the hall.
A rustle of sheets, a turning of keys.
And Room 1 is empty now.
We have a room for you.

David Hilbert drew it on the board in Göttingen.
The year was 1924.
You could smell the chalk dust in the air.
Hear the wooden chairs scrape on the stone floor.
He said, "Imagine a hotel with infinite rooms..."
And every single one is occupied.
Years later, George Gamow wrote it down for the rest of us.
In a little book from 1947.

And the call goes out along the wire.
From the front desk to the farthest star.
Guest in Room 1, please take your things to Room 2.
Guest in Room 2, you're moving to Room 3.
The shuffle begins, a wave down the hall.
A rustle of sheets, a turning of keys.
And Room 1 is empty now.
We always have a room for you.

Now a bus arrives with an infinite number of souls.
And the night clerk doesn't even blink.
He just sends another call down the wire:
"Guest in Room N, please move to Room 2N."
One moves to two. Two moves to four. Three to six.
And suddenly all the odd-numbered rooms are empty.
An infinity of vacancies.
Waiting for an infinity of guests.

So here is your key.
It's for Room 1.
Listen.
Can you hear the doors closing, all the way down?
Welcome to the Grand Hotel.
There's always room.