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Count on It: Bach, Biology, and the Baroque

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If you haven’t yet watched our new short documentary based on geneticist Michael Denton’s work, The Biology of the Baroque, you must. As Denton shows, there is an excess and an opulence to the beauty and order of life that goes immeasurably beyond utilitarian evolutionary considerations of survival and reproduction. Perhaps, though, the parallel between what Denton calls “non-adaptive order” in biology, and the art of the Baroque period, goes a little further.

The video, scripted by our colleague Rachel Aldrich, asks:

Why do centipedes always have an odd number of body segments? How did that help the survive? Why do nearly all mammals, from mice to giraffes, have seven bones in their cervical vertebrae? All octopi have eight tentacles. Why not six, or ten? Jellyfish have a mesmerizing radial symmetry. Sand dollars and starfish both display a star-like pattern. Nature seems to have plenty of room to develop order and patterns that do no serve an immediate survival purpose.

Nature, it appears, has an interest in counting out abstract numeric patterns. Once such a pattern is hit upon, it sticks around — what Denton in his new book Evolution: Still a Theory in Crisis calls the “enigma of fixation.” He asks, “What adaptive forces fixed a previously fluid pattern at a particular moment in evolutionary history?” And: “Of course, the problem is not restricted to the pentadactyl limb. All the homologs must also have undergone the utterly un-Darwinian transformation from ‘evolvable’ to ‘immutable.'” Is the “fixation” arbitrary, or does it have an artistic purpose?

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Denton writes, “Take the different number of petals on different species of flowers. In many species the number of petals often corresponds to a Fibonacci number.” For more, see his section on “Numerics and Geometics.” It goes on and on.

Well, guess what. Such obsessions with numbers and patterns is also characteristic of certain artists, not least J.S. Bach, the foremost name in — yes — Baroque music. He was fixated on the number 14 and its mirror image, 41. Oxford mathematician Marcus du Sautoy contributed a fascinating article to The Guardian on numbers in music:

Bach’s name spells out a series of musical notes that Bach employs often in pieces as if he is musically signing his work. Other composers during the baroque used a cabalistic code that changes letters into numbers which could then be used in musical composition to hide words. For example, by replacing each letter with its number in the alphabet, Bach’s name translates into 2+1+3+8=14. Some commentators have tried to identify an obsession with the number 14 running throughout Bach’s work and life. Apparently when he was asked to join Mizler’s society of Musical Sciences he delayed until 1747 just to ensure that he could be the 14th member to join.

There’s much more. Mozart, while not part of the Baroque, exceeded Bach in his preoccupation with number symbolism:

What’s the next number in this sequence? 5, 10, 20, 30, 36 … ? And the next in this? 640, 231, 100, 91 … ?

If you know your Mozart then you’ll identify 43 as the number that comes after 36 in the first sequence. These are the opening lines of The Marriage of Figaro sung by Figaro as he measures out the room that he will share with Susanna once they are married. It’s a curious selection of numbers that when added together comes to 144, or 12 squared: perhaps a coincidence or maybe a numerical representation of the impending union of Figaro and his bride Susanna.

The second sequence continues with 1,003, the number of Don Giovanni’s female conquests in Spain. The other numbers are part of the famous Catalogue aria sung by Leporello, Don Giovanni’s servant, which include his other conquests: 640 in Italy, 231 in Germany, 100 in France, 91 in Turkey.

For these and other artists, particular numbers carried symbolic meaning that could be translated in this fashion. Is that true of the abstract geometric and number patterns in nature? Obviously I don’t know. But it seems to be not uncommon for creative minds to play with numbers this way, as if toying with their audience, or perhaps with a view to leaving clues, a kind of hidden signature, or just for fun. Numbers, too, have a beauty of their own, and that may be part of it. It’s, in any event, another way that nature calls to mind purposeful creativity, not mindless sifting.

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Image: J.S. Bach, by Elias Gottlob Haussmann [Public domain], via Wikimedia Commons.