I am no expert in classical music. In fact, I know very little. I received the same classical education we all got from Looney Tunes so many years ago, but I couldn’t tell Brahms from Beethoven. This is an actual text I sent to a friend a few months ago:

What’s the famous classical piece that goes “do do do do dih do dih, dih do dih, dih do dih, do do do do dih do do do dih do do do dih?”

I have great friends, because here was his immediate answer:

Peer Gynt – In the Hall of the Mountain King.

There is a composer that has fascinated me for some time though: J. S. Bach. Apart from being a good churchgoing Lutheran (like myself), and deeply into mathematics (like myself), he was also something of a completist (like myself). He published a book entitled The Well-Tempered Clavier in 1722. (A clavier was a generic term for a keyboard instrument, like a harpsichord, a piano, or an organ.) This opus had a total of 48 pieces of music in it: one prelude and one fugue for each of the 24 musical keys, major and minor. In other words, it contained:

  • Prelude in C Major
  • Fugue in C Major
  • Prelude in C Minor
  • Fugue in C Minor
  • Prelude in C# Major
  • Fugue in C# Major

and so on, completing with Fugue in B Minor. Forty-eight pieces of music, and why? In Bach’s words (well, in English translation of Bach’s words), “for the profit and use of musical youth desirous of learning, and especially for the pastime of those already skilled in this study.” But why all 48? Well, just because he could, I suppose.

Most of what I know about Bach comes not from listening to his work, but from a book I devoured a while back called Gödel, Escher, Bach: An Eternal Golden Braid by Douglas Hofstadter. The book describes itself as “a metaphorical fugue on minds and machines in the spirit of Lewis Carroll.” On one level, it’s an exploration into artificial intelligence, how it arises and what it would mean. On another level, it’s a deep dive into the shared rhythms and connections among the mathematical work of Kurt Gödel, the artistic work of M. C. Escher, and the musical work of J. S. Bach. Among the three of them, Hofstadter found a shared fascination with intricate fractal-like patterns of recursion and depth. Escher’s artwork is filled with impossible structures and repeating designs. Bach’s fugues are filled with intricate repeating themes and secret hidden codes. And Kurt Gödel discovered (invented?) the Incompleteness Theorems. In hopelessly simplified format, Gödel’s Incompleteness Theorems state that in any system of mathematics, there are some questions that simply cannot be answered. Gödel states that no matter how complete you try to create your system, it simply cannot answer every question. And on another level, the book itself is a self-referential, recursive creation that somehow holds together like a perfect crystal. It’s like a gift from the early seconds of the universe, a time when the laws of physics and mathematics were one, and everything was both intricately complex yet gracefully simple.

It’s a hard read at parts, but I love it. If you enjoy Escher, or Bach, or mathematics (or all three!), pick up a copy. At the very least, read all the “dialogues” between Achilles and the Tortoise that come between each of the chapters. My big takeaway from the book: intelligence arises due to complexity. The reason our brains provide us with consciousness and intelligence is because of how complex they are. Our level of sentience and intelligence exceeds that of other animals precisely because our brains are more complex. And my other big takeaway: intelligence arises at a higher “level” than its component parts. The neurons in our brain are not intelligent, or sentient. The cells in our body have no idea that they are part of a human, nor do the atoms within them know that they’re in cells. They’re just going about their atomic, and cellular, business. It’s because of the complexity of our brains that something arose higher than them, namely, you and me. (Please note: this is not a statement in favor of, or against, a belief in God. Perhaps God planned it this way; or perhaps there is no God, and this arose naturally. Certainly I have my own thoughts on that, but either way works.)

Someday I should listen to the preludes and fugues from Well-Tempered Clavier. But for now, I might just pull out my old copy of Gödel, Escher, Bach.

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