“Mathematics is the art of giving the same name to different things”*…
A few years back, 12 million of us clicked over to watch the “Pachelbel Rant” on YouTube. You might remember it. Strumming repetitive chords on his guitar, comedian Rob Paravonian confessed that when he was a cellist, he couldn’t stand the Pachelbel Canon in D. “It’s eight quarter notes that we repeated over and over again. They are as follows: D-A-B-F♯-G-D-G-A.” Pachelbel made the poor cellos play this sequence 54 times, but that wasn’t the real problem. Before the end of his rant, Paravonian showed how this same basic sequence has been used everywhere from pop (Vitamin C: “Graduation”) to punk (Green Day: “Basket Case”) to rock (The Beatles: “Let It Be”).
This rant emphasized what music geeks already knew—that musical structures are constantly reused, often to produce startlingly different effects. The same is true of mathematical structures in physical theories, which are used and reused to tell wildly dissimilar stories about the physical world. Scientists construct theories for one phenomena, then bend pitches and stretch beats to reveal a music whose progressions are synced, underneath it all, in the heart of the mathematical deep.
Eugene Wigner suggested a half-century ago that this “unreasonable effectiveness” of mathematics in the natural sciences was “something bordering on the mysterious,” but I’d like to suggest that reality may be more mundane. Physicists use whatever math tools they’re able to find to work on whatever problems they’re able to solve. When a new song comes on, there’s bound to be some overlap in the transcription. These overlaps help to bridge mutations of theory as we work our way toward a lead sheet for that universal hum…
Read the harmonious whole at “How Physics is Like Three-Chord Rock.”
* Henri Poincare
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As we hum the tune eternal, we might send astronomical birthday greetings to Allan Rex Sandage; he was born on this date in 1926. An astronomer, he spent his career first at the Palomar Observatory, then at the Carnegie Observatory in Pasadena, where at the outset, he was a research assistant to Edwin Hubble, whose work Sandage continued after Hubble’s death. Sandage was hugely influential on his field; he is probably best remembered for determining the first reasonably accurate value for the Hubble constant (there ate those chords again) and the age of the universe— and for discovering the first quasar (again, those chords).
