Tag Archives: math and

Math And: Arielle Saiber on Italian poetry and Italian algebra, Friday, Oct 23 at 4pm

Something to do tomorrow (besides eating the Beef n Brew slice): the Math And… seminar is very pleased to welcome Arielle Saiber from Bowdoin for our Fall 2009 lecture.  Arielle is an Italianist of very broad interests, with academic papers on Italian literature, the early history of algebra and geometry, Dali’s illustrations for Dante, and the polyvalent discourse of electronic music.  Tomorrow there will only be time to unite the first two.

23 Oct 2009, 4pm, Van Vleck B239: Arielle Saiber (Bowdoin, Italian)

Title “Nicollo Tartaglia’s Poetic Solution to the Cubic Equation.”

Niccolo Tartaglia’s (1449-1557) solution to solving cubic equations, which renowned mathematician and physician Girolamo Cardano wanted but Tartaglia resisted, led to one of the first intellectual property cases in Western history. Eventually, Tartaglia agreed to give Cardano what he so desired, but only if the latter promised he would not publish it. Cardano promised, and Tartaglia sent him the solution. Wasting little time, however, Cardano published the solution (along with a ‘general’ solution that he himself developed). Tartaglia was, not surprisingly, furious and began a vicious battle with Cardano’s assistant, Ludovico Ferrari (Cardano refused to engage Tartaglia directly). But vitriolic polemics aside, there is something else rather curious about this ordeal: the solution Tartaglia gave Cardano was encrypted in a poem. This talk looks at the motives behind his “poetic solution” and what it says about the close relationship between ‘poeisis’ and ‘mathesis’ in this period of mathematics’ history.

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The moduli space of chords: Dmitri Tymoczko on “Geometry and Music”, Friday 7 Mar, 2:30pm

The next installment of the “Math And…” seminar is coming next week:

7 Mar 2008, 2:30 PM, Birge 145: Dmitri Tymoczko (Princeton University, music)

Title: “Geometry and Music.”

In my talk, I will explain how to translate the basic concepts of music theory into the language of contemporary geometry. I will show that musicians commonly abstract away from five types of musical transformations, the “OPTIC transformations,” to form equivalence classes of musical objects. Examples include “chord,” “chord type,” “chord progression,” “voice leading,” and “pitch class.” These equivalence classes can be represented as points in a family of singular quotient spaces, or orbifolds: for example, two-note chords live on a Mobius strip whose boundary acts like a mirror, while four-note chord-types live on a cone over the real projective plane. Understanding the structure of these spaces can help us to understand general constraints on musical style, as well as specific pieces. The talk will be accessible to non-musicians, and will exploit interactive 3D computer models that allow us to see and hear music simultaneously.

The interactive 3D computer models are made by Dmitri’s program Chord Geometries, which you can download from his website. Or you can just watch the sample movies, and see what the opening of “Smoke on the Water” looks like on a Mobius strip. Dmitri comes by his mathematical know-how familially; his younger sister is the algebraic geometer Julianna Tymoczko (with whom I wrote this paper about diameters of finite groups) and his father was the philosopher of mathematics Thomas Tymoczko.

I’ve booked a big room, and the talk is open to the public, so if the abstract sounds interesting to you, please come!

On the other hand, perhaps the abstract puts you off by means of words like “real projective plane.” Well, it’s written for mathematicians; maybe it’s worth explaining in more down-to-earth language about what a guy like Dmitri means by “the space of chords,” or, as an algebraic geometer like me might put it, the moduli space of chords. Explanation below the fold: it’s essentially a brief version of an article called “The Idea of a Moduli Space” that I wrote for Imagine magazine when I was a grad student.

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