Articles from the Institute Letter

Additional articles from new and past issues of the Institute Letter will continue to be posted over time and as they become available.

by Linda Goddard

Gauguin’s collaged images and text, seemingly artless (like a scrapbook), carefully project a particular self-image. (Credit: RMN Musée D'Orsay/Herve Lewandowski)

Self-portraiture on the margins of colonial power and local resistance

“When Paul Cézanne wants to speak ... he says with his picture what words could only falsify.” In The Voices of Silence (1951), French author and statesman André Malraux expressed his view that the Post-Impressionist painter could only “speak” with paint, not with words (his letters, according to Malraux, amounted to no more than a catalogue of petty-bourgeois concerns). This gives a fair idea of the reaction that a painter who tried their hand at writing could expect in the nineteenth and early twentieth centuries. But what did this mean for artists who wished to respond, verbally, to their critics, or for whom writing and painting were equal components of an interdisciplinary practice?

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by Daniel Rockmore

(Credit: Andrea Kane)

My earliest mathematical memories involve my father. One is of a walk from home to the edge of downtown Metuchen (the tiny central Jersey town where I grew up), to a little luncheonette called The Corner Confectionary. This wasn’t a frequent or regular event, but from time to time on a weekend morning we’d make our way there. It was about a mile as we first walked to the corner of Rose Street and Spring Street and then strolled up Spring—a beautiful leafy street with huge oak trees on which our friends the Kahns lived—to finally reach Main Street where we made a quick left, crossed the bridge over the railroad tracks to arrive at the store. I can still see its layout, even in the cluttered neural attic that holds my childhood memories: cash register by the door, rack filled with newspapers, magazines, and comic books, ice cream treats in the back corner, and of course, the long counter, lined with stools on which we would sit and spin—until told to stop.

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by Enrico Bombieri

The Ree Group Formula (Credit: Enrico Bombieri/Parasol Press, Ltd/Yale Art Gallery/Harlan & Weaver, Inc)

Does beauty exist in mathematics? The question concerns mathematical objects and their relations, the real subject of verifiable proofs. Mathematicians generally agree that beauty does exist in the structural beauty of theorems and proofs, even if most of the time it is largely visible only to mathematicians themselves.

The concept of group beautifully expresses symmetry in mathematics. What is a group? Consider any object, concrete or abstract. A symmetry of the object—mathematically, an automorphism—is a mapping of the object onto itself that preserves all of its properties. The product of two symmetries, one followed by the other, also is a symmetry, and every symmetry has an inverse that undoes it. Mathematicians consider continuous Lie groups, such as the rotations of a circle or of a sphere, to be a beautiful foundation for a great portion of mathematics, and for physics as well. Besides continuous Lie groups there are noncontinuous finite and discrete groups; some are obtainable from Lie groups by reduction to a finite or discrete setting.

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by Freeman Dyson

The MacDonald Equation (Credit: Freeman Dyson/Parasol Press, Ltd/Yale Art Gallery/Harlan & Weaver, Inc)

The MacDonald Equation is the most beautiful thing that I ever discovered. It belongs to the theory of numbers, the most useless and ancient branch of mathematics. My friend Ian MacDonald had the joy of discovering it first, and I had the almost equal joy of discovering it second. Neither of us knew that the other was working on it. We had daughters in the same class at school, so we talked about our daughters and not about mathematics. We discovered an equation for the “Tau-function” (written τ(n)), an object explored by the Indian genius Srinivasa Raman­ujan four years before he died at age thirty-two. Here I wrote down Mac­Donald’s equation for the Tau-function. The MacDonald equation has an amazing five-fold symmetry that Ramanujan missed. You can see the five-fold symmetry in the ten differences multiplied together on the right-hand side of the equation. We are grateful to Ramanujan, not only for the many beautiful things that he discovered, but also for the beautiful things that he left for other people to discover.

To explain how the Mac­Donald equation works, let us look at the first three cases, n=1, 2, 3. The sum is over sets of five integers a, b, c, d, e with sum zero and with the sum of their squares equal to 10n. The “(mod 5)” statement means that a is of the form 5j+1, b is of the form 5k+2, and so on up to e of the form 5p+5, where j, k, and p are positive or negative integers. The exclamation marks in the equation mean 1!=1, 2!=1×2=2, 3!=1×2×3=6, 4!=1×2×3×4=24. So when n=1, the only choice for a, b, c, d, e is 1, 2, -2, -1, 0, and we find tau(1)=1. When n=2, the only choice is 1, –3, 3, –1, 0, and we find tau(2)=–24. When n=3, there are two choices, 1, –3, –2, 4, 0 and –4, 2, 3, –1, 0, which give equal contributions, and we find tau(3)=252. It is easy to check that these three values of tau(n) agree with the values given by Ramanujan’s equation.

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by Hugh Gusterson

Under the Stockpile Stewardship program, laboratories like Livermore obtained some of the most powerful supercomputers in the world on which they could simulate nuclear tests.

And what would an anthropologist know about that?

In 1987, in my third year as a graduate student in anthropology, I arrived in the small California town of Livermore, host to one of two nuclear weapons design laboratories in the United States. Thanks to an indulgent dissertation committee, which had allowed me to abandon my original goal of doing fieldwork in Africa for a much more unconventional project, I came to Livermore intent on understanding the culture of the scientists, mainly physicists, who worked on the most powerful weapons on Earth. The anthropology of science did not yet exist as a recognized sub-field of anthropology but, in retrospect, that is what I was doing.

I came to Livermore at a moment when the nuclear weapons labs at Livermore and Los Alamos were on the defensive. The nuclear freeze campaign of the early 1980s had had some success in reframing the nuclear arms race as a danger to, not a guarantor of, security. “End the race or end the race,” as their slogan went. In 1982, more than a thousand protestors were arrested for civil disobedience at the gates of the Livermore Laboratory. Then, in 1985, the new Soviet leader, Mikhail Gorbachev, suspended Soviet nuclear testing for eighteen months, challenging the United States to join him. And at the Reykjavik Summit of 1986, Ronald Reagan and Mikhail Gorbachev astonished the world by coming close to an agreement to abolish nuclear weapons. 

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