Duration: 6' ca.

Composed in 2026

Perusal Score

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Written for Francesca Puro and Giorgiy Khokhlov

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The mathematical concept of Infinity can behave rather strangely. Infinity does not adhere to the same rules that finite numbers might. Hilbert’s Hotel Paradox is a thought experiment that demonstrates this unintuitive behavior. Hilbert invites us to imagine a hotel with infinitely many rooms, all of which are already occupied. Suppose a new guest arrives at the counter and requests a room. In a finite hotel, this guest would inevitably be turned away. But in Hilbert’s hotel, there’s no problem! Whoever is currently staying in room 1 simply needs to move to room 2, the guest in room 2 must move to room 3, and so on. Because every natural number n has a number n+1, there will always be another room to move into. After all is said and done, the new guest can take over room 1. Shockingly, even if an infinite bus with endless people shows up to Hilbert’s Hotel, they would still all be accommodable. The current guest in room n must simply move to room 2n, leaving all odd numbered rooms available. This paradox thusly demonstrates that an infinite set can contain one of its subsets.

 

I modeled the construction of this piece off of this idea–the music begins in room 1, which consists of just 1 eighth note. After many repetitions, we move to room 2, made of 2 eighth notes. This pattern continues, adding one eighth note per room, so that a full-length melody is constructed one piece at a time. The number of repetitions per room decreases as the size of each room increases. As the melody grows, the timbral interest within each measure changes. This piece begins like an empty black-and-white coloring book; as the rooms get bigger, more and more timbral “colors” are filled in, so that by the time a full melody is formed many different colors can be experienced. And of course, a few sudden surprises are thrown into the rooms at random to keep listeners on their toes.