Glass and Lace

Two unrelated events in January, 2020, on opposite coasts of North America, precipitated these inconclusive musings.

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Two unrelated events in January, 2020, on opposite coasts of North America, precipitated these inconclusive musings. • January 12: a concert in Northampton, Massachusetts, where I live. A mindboggling and mindbending afternoon: cellist Matt Haimovitz and pianist Simone Dinnerstein playing Beethoven sonatas and solo works by Philip Glass. • January 20: the first corona virus case in the United States was confirmed in faraway Seattle. It spread eastward with the speed of sound. In what seemed an instant, my calendar was erased for the foreseeable future, except for my weekly piano lessons, which moved to Zoom. Unusual juxtapositions, to say the least! The concert and the coronavirus, and also Beethoven and Glass. Beethoven is the predominant musical figure in the transi tional period between the Classical and Romantic eras; orchestras around the world had planned 250th birthday galas, but the virus cut them short. By contrast, Glass’s work has been called “minimalist;” he himself describes it as “music with repetitive structures.” Either way, at 83 he is one of the most influential composers of the late 20th century. So I had expected dissonances in style, sound, and centuries. Instead, I heard consonances that seemed, somehow, familiar. The two duos, the composers and the performers, pointed me to a rabbit hole. The lockdown of normal life set me free to explore it. I grabbed my piano and jumped in. To explore, in a time of corona virus, is to remember, reread, listen, probe, and search online. Here are some of the things I found.

Electronic Supplementary Material The online version of this chapter (https://doi.org/10.1007/ 16618_2020_18) contains supplementary material, which is available to authorized users. M. Senechal (*) Smith College, Northampton, MA, USA e-mail: [email protected] © The Author(s), under exclusive license to Springer Nature Switzerland AG 2020 A. Wonders (ed.) Math in the Time of Corona, Mathematics Online First Collections, https://doi.org/10.1007/16618_2020_18

M. Senechal

An interview with the young Icelandic pianist, Vikingur Olafsson, who had recently released an album of Philip Glass's piano works. Said Olafsson of Glass, To me, he's like the Mondrian of music. He's taking primary colors and exploring what that means. At his best he's getting to the essence of music. . . . I came to the conclusion that it’s not a repetition. It’s a rebirth. It’s not treading the same path, but traveling in a spiral.

An aside in Milan Kundera's The Book of Laughter and Forgetting.1 Variation form was Beethoven's favorite toward the end of his life. At first glance, it seems the most superficial of forms, a simple showcase of musical technique, work better suited to a lacemaker than to a Beethoven. But Beethoven made it a sovereign form (for the first time in the history of music), inscribing in it his most beautiful meditations.

A memory. It's 1998. Geometers from around the world have gathered in Rome to celebrate the work of the Dutch graphic artist M. C. Escher and the centennial of his birth.2 The progr