jwilzewske: Marcus du Sautoy: Dark Side of Mathematics Populism

DSM: On Friday, 27 April, Marcus du Sautoy will give a lecture, at 5:15pm at the University of California Berkeley, in the Valley Life Sciences Building, Room 2050. Marcus is Professor of Mathematics at the University of Oxford, a Fellow of Wadham College. Also, he’s served as a visiting Professor at the École Normale Supérieure in Paris, the Max Planck Institute in Bonn, the Hebrew University in Jerusalem and the Australian National University in Canberra.

CMT: Notable among his other achievements was winning the Berwick Prize of the London Mathematical Society. But his activities in popularizing mathematics are extensive and are perhaps what has gained him the most notoriety. He’s a Senior Media Fellow at the EPSRC and has many involvements in print and broadcast journalism. Marcus writes for the London Times, the Daily Telegraph, the Independent and the Guardian and is a frequent guest on BBC radio and television programmes. And he’s the popular presenter of BBC4’s TV game show ‘Mind Games.’ His book, The Music of the Primes, has been widely acclaimed, and a one hour documentary based on his book was recently broadcast on BBC4. The lecture he’s giving at Berkeley on the 27th will be for an audience that will include some music theory faculty and students and mathematics people—but still it’s substantially similar to his offerings for lay non-specialist audiences.

DSM: It might be a bit much to say I look forward to attending Marcus’ lecture. It’s not that I don’t see why his style is so popular. Marcus’ flamboyance, his sensational attempts to bring ‘mathematics to the masses’ as he puts it—I find these hard to accept. Like Srinivasa Ramanujan, a mathematical Mozart who spent most of his career in Cambridge, Sautoy’s discussions of mathematical concepts lapse into atmospheric narrative that entertains but doesn’t really illuminate much. Pages 77 through 79, 84, and a few others in his book actually purport to be about music as such. But the following, for example, is dumbed-down to the point of being factually incorrect at multiple, multiple levels. It is not correct with regard to the two instruments’ waveforms. It is not correct with regard to Fourier analysis of the harmonics. It is overly-simplistic with regard to the physics of sound production in both of the instruments. It talks down to the reader by presuming that the reader doesn’t know what a square-wave is—while simultaneously presuming that such a stupefied reader does know what a ‘crenellation’ is. It’s appalling. Marcus’ popular journalistic writing is simply awful and panders to the consumeristic pseudo-science dramatization norm. It’s emblematic of the style of careless “page-turner” science writing that has filled the shelves since Dava Sobel’s 1996 book, ‘Longitude’. Doug Hofstadter’s 1980 ‘Gödel, Escher and Bach’ was a far better book, while still in the ‘popularizing’ idiom.

W hy does a clarinet sound so characteristically different to the sound of a violin playing the same note? The graph of the sound wave created by the clarinet looks like a square-wave function, like the crenellation of the top of a castle wall, instead of the spiky graph of the violin. The reason for the difference is that the clarinet is open at one end, whereas the string in the violin is fixed at both ends. This means that the harmonics produced by the clarinet vary from those of the violin, so the graph depicting the sound of the clarinet is built from sine waves oscillating at different frequencies.”
— Marcus du Sautoy, Music of the Primes, p. 95

CMT: Books like this trade on the mythology of “The Lone Genius Who Solved the Greatest Scientific Problem of His Time, By Means of an Other-Worldly Intelligence that Shall Never Be Equaled.” It’s a bit like the cult of Mozart. Breathless and uncritical worship of the Lone Virtuoso does nothing to advance the valuable participation of ordinary people in the field.

DSM: Do you suppose that this is partly why the mathematics of music theory has developed so slowly? –because of the back-handed discouragement of workmanly contributions by ordinary musicians who are not virtuoso mathematicians and ordinary mathematicians who are not virtuoso musicians, I mean. Musicians being misled to think that Mathematics is too complex for them. And mathematicians being misled to think that Music is not more broadly suitable for the formalisms and methods of analysis that they have developed for the ‘physical’ sciences.

CMT: Maybe a little. But I think it has more to do with temperament in both disciplines. There’s progress, yes—things you see published in Music Analysis and Computer Music Journal, things from IRCAM, from Guerino Mazzola and his students, and so on—but it strikes me that there are many branches of mathematics that could reasonably be applied to classical music analysis that have not yet ever been used. At least they haven’t yet appeared in published articles and books. Functional analysis; operator algebra; noncommutative geometry and matrix theoretic compactification; metric cohomologies for understanding rhythms and repetitions—lots of things.

DSM: There were a couple of the papers presented at this weekend’s Music Theory Midwest Conference (Music Theory Midwest (MTMW2007), Lawrence, Kansas) that included some functional analysis—for instance, Clare Sher Ling Eng’s paper, Being & Becoming: Rhythmic Function Analysis Applied to Brahms’ Alto Rhapsody, op. 53. Clare is currently at Yale, one of Allen Forte’s students. She presented an innovative and powerful analysis of the repetitive structures in the Brahms, in which she proposes two function-classes, with a real-valued index denoting (1) a scalar by which the duration of each motivic element is multiplied upon the application of the function, for the geometric function-class or (2) the duration of each motivic element to be added or elided, for the arithmetic function-class.

CMT: And yet, despite the elegance of her function-classes and her analysis, Clare nonetheless received some uncharitable feedback during the Q&A session after she read her paper. Her critic asserted that the index must be integer-valued or, at most, a rational number. He called it ‘infelicitous’. Hmmm. He couldn’t understand how a real-valued index on her functions would be useful—especially for electroacoustic or computer or other new music whose meter is not necessarily tightly periodic or a normal time-signature. More than that, he seemed to be holding himself forward in that Conference as an authority on mathematics—but the obtuseness of his argument made it abundantly clear that, as a musicologist, he actually had little understanding of operator algebra or functional analysis. Clare did an excellent job of responding in a positive way. But it was discouraging to see this dilettante musicologist/mathematician-poseur attack her work, attempting to build up his own ego at her expense.

jwilzewske

Monday, April 16, 2007

Marcus du Sautoy: Dark Side of Mathematics Populism

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