How music became a mathematical practice

He was born in a Jewish family in the Middle-West.

He is said to be brash and never bothers being mean with lesser mortals.

Part of his work is said to be a synthesis of some others’ contributions, rather than a fully original creation.

Some people think he’s a traitor to the political left’s cause he embraced in his youth.

He doesn’t really like historical accounts of his life and prefers reinventing his own history.

But in spite of all these controversies, it is rather difficult to deny him genius, acute intelligence and an amazing sense of humor and self-derision. All in all, he is considered as one of the greatest minds of the past century.

For all these reasons, we can think there are some similarities between Bob Dylan and Paul Samuelson.

But here is an excerpt of Dylan’s Chronicles that I find particularly striking. At the end of the 1980s, while he is in New Orleans, in the process of recording one of his masterful albums, Oh Mercy, with Canadian producer Daniel Lanois, Bob (re)discovers a way of playing  guitar that, he thinks, might change his life (it’s pages 158-161 of the paperback edition, emphasis added):

The system works in a cyclical way. Because you’re thinking in odd numbers instead of even numbers, you’re playing with a different value system … I had too long been freeze in the secular temple of a museum anyway. It’s not a complicated thing. There are thousands if not millions of these patterns so you never run out of ideas. You’re always at some unexploited fixed point. It’s not a heavy theorized thing, it’s geometrical. I’m not that good at math but I do know that the universe is formed with mathematical principles whether I understand them or not, and I was going to let that guide me. My playing was going to be an impellent in equanimity to my voice and I would use different algorithms that the ear is not accustomed to. It should be, but it’s not.

Okay. That might sound a little bit confused and obfuscating … but I think I definitely love it ! And I think it captures the mathematical zeitgeist of the second half of the twentieth century quite well. I hope a music writer will write a piece like “Dylan as a positivist” in the near future.

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7 thoughts on “How music became a mathematical practice

  1. Music have been linked to mathematics and mathematical practice for a long time. The first name that comes to mind is J.-S. Bach whose virtuosity have often been compared to mathematical principles. Another thing is that in the mathematical recreations literature of 17th and 18th century always had a “music” sections with problems using music or linked to music.

  2. Do mathematicians play by ear?
    Aesthetics seems to play a role in the history of mathematics and even physics, if you accept the statements of practitioners. Arthur Miller at UCL was making this point evoking painting not music.

    Slightly on the side, Hunter S. Thompson while writing his freak fest FEAR AND LOATHING IN LAS VEGAS listened to the same live concert of the Rollings Stones over and over again until he had burned through three tapes of it. This sounds slightly deranged, as all hunter stories, but it might suggest that music does offer you a sense of order and theme and chromatic unity that links with other cognitive efforts.

  3. I understand that music has been linked to mathematics for a long time, and I assume that so have been other artistic practices. But in Dylan’s quote, what I find interesting is that he thinks that the world obeys to some kind of mathematical order, so that music can be derived from mathematics. I think – but I can be totally wrong – that it is not the way people would have seen it before the 19th century. I suppose that when people used to say that Bach’s music is similar to mathematics, they believed that music is in some ways an imitation of nature, in the same way that mathematics was considered as an imitation of nature … Indeed, both music and mathematics can be derived from some natural order. Moreover, Dylan does not say that mathematics can be a convenient tool to understand (or practice) music, he says that you do not need to understand the maths, but you just have to be sure there are some mathematics working behind that … It’s a bit more modern statement, I think, but maybe my “exegesis” of Dylan’s writings are too influenced by my utter admiration for his music !

  4. Let me quote wikipedia on Kepler to give a sense of what I had in mind when writing my comment:
    “Kepler was convinced “that the geometrical things have provided the Creator with the model for decorating the whole world.” In Harmonices Mundi, he attempted to explain the proportions of the natural world — particularly the astronomical and astrological aspects — in terms of music. The central set of “harmonies” was the musica universalis or “music of the spheres,” which had been studied by Pythagoras, Ptolemy and many others before Kepler; in fact, soon after publishing Harmonices Mundi, Kepler was embroiled in a priority dispute with Robert Fludd, who had recently published his own harmonic theory.”
    If we take that literally, then it is nature which is an imitation of music. Ido not say that it the same thing that Dylan was saying, but there is definitely a common ground in my opinion.
    What do you think?

  5. My dusty high school memories contain a reference to Schonberg-Berg dodecaphonism, an attempt to “formalize” the method of musical composition with mathematical notions of series, transformations, symetry, etc. conducted in Vienna during the twenties. I was taught that it was an attempt to “unify” mathematics and musics, but maybe it was an attempt modelled on Vienna mathematicians’ interest in completedness, I don’t know. But knowing what was going on among economists in Vienna at the moment make the parallel interesting.

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