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 Andrej Bauer

Recommended Viewing: An animated visualization of the GitHub collaborations of over two dozen mathematicians working on the HoTT book over a period of six months may be viewed at http://vimeo.com/68761218/.

Since spring, and even before that, I have participated in a great collaborative effort to write a book on homotopy type theory. It is finally finished and ready for pub­lic consumption. You can get the book freely at http://homotopytypetheory.org/book/. Mike Shulman has written about the contents of the book (http://​golem.ph.u­te­x­as.edu/category/2013/06/the_hott_book.html), so I am not going to repeat that here. Instead, I would like to comment on the socio-technological aspects of making the book and in particular about what we learned from the open-source community about collaborative research.

We are a group of two dozen mathematicians who wrote a six-hundred-page book in less than half a year. This is quite amazing since mathematicians do not normally work together in large groups. A small group can get away with using obsolete technology, such as sending each other source LaTeX files by email, but with two dozen people even Dropbox or any other file synchronization system would have failed miserably. Luckily, many of us are computer scientists disguised as mathematicians, so we knew how to tackle the logistics. We used Git and GitHub.com. In the beginning, it took some convincing and getting used to, al­though it was not too bad. In the end, the repository served not only as an archive for our files but also as a central hub for planning and discussions. For several months, I checked GitHub more often than email and Facebook.

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By Boaz Katz, Subo Dong, and Doron Kushnir

Remnants of the type Ia supernova first observed by medieval astronomer Tycho Brahe

On the evening of November 11, 1572, twenty-six-year-old astronomer Tycho Brahe was about to make a discovery that would change his life and consequentially boost the scientific revolution significantly. While casually staring at the night sky, he suddenly noticed a very bright unfamiliar star in the Cassiopeia con­stellation. The star, which was as bright as Venus, was located in the inner parts of the famous W-shaped constellation, which was well known to many common people, let alone astronomers. What Tycho saw looked like the appearance of a new star (nova stella). He was so astonished that he sought the confirmation of others to assure himself that he was not hallucinating.

Unknown to Tycho, such new stars had appeared during the previous centuries (“guest stars” in Chinese records), with a much brighter star reported in 1006. While these events were very important to astrologers, they had no lasting effect on astronomical thinking at the time. Tycho, however, realized that such an event was revolutionary. By accurately and repeatedly measuring the position of the “nova,” Tycho showed that it was much further than the moon. In one night, Tycho managed to scientifically falsify the millennia-old Aristotelian belief that anything beyond the sphere of the moon cannot change. This convinced Tycho that the “known” cosmology was wrong and motivated him to devote his life to performing measurements of stars and planets to study the “true” cosmology. His hard, lifelong work paid off. His careful measurements of the positions of the planets enabled the discovery of the law of gravity by Johannes Kepler and Isaac Newton. Kepler would later say that if Tycho’s star did nothing else, it produced a great astro­nomer. Yet, even Tycho and Kepler could not have appreciated that what seemed like a new star was actually an explosion of unimaginable power and that such explosions are crucial for our existence.

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By Michael Lesnick

A still developing branch of statistics called topological data analysis seeks to extract useful information from big data sets. In the last fifteen years, there have been applications to several areas of science and engineering, including oncology, astronomy, neuroscience, image processing, and biophysics.

The story of the “data explosion” is by now a familiar one: throughout science, engineering, commerce, and government, we are collecting and storing data at an ever-increasing rate. We can hardly read the news or turn on a computer without encountering reminders of the ubiquity of big data sets in the many corners of our modern world and the important implications of this for our lives and society.

Our data often encodes extremely valuable information, but is typically large, noisy, and complex, so that extracting useful information from the data can be a real challenge. I am one of several researchers who worked at the Institute this year in a relatively new and still developing branch of statistics called topological data analysis (TDA), which seeks to address aspects of this challenge.

In the last fifteen years, there has been a surge of interest and activity in TDA, yielding not only practical new tools for studying data, but also some pleasant mathematical surprises. There have been applications of TDA to several areas of science and engineering, including oncology, astronomy, neuroscience, image processing, and biophysics.

The basic goal of TDA is to apply topology, one of the major branches of mathematics, to develop tools for studying geometric features of data. In what follows, I’ll make clear what we mean by “geometric features of data,” explain what topology is, and discuss how we use topology to study geometric features of data. To finish, I’ll describe one application of TDA to oncology, where insight into the geometric features of data offered by TDA led researchers to the discovery of a new subtype of breast cancer.

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Nima Arkani-Hamed (left), Professor in the School of Natural Sciences and a member of the Faculty Music Committee, describes Derek Bermel (right), whose four-year term as Artist-in-Residence ended in June, as a grand unifier, a fellow wanderer, and a continued inspiration.

Derek Bermel, the Institute’s Artist-in-Residence since 2009, organized the Edward T. Cone Concert Series as well as dozens of conversations with poets, writers, composers, and musicians during his appoint­ment, which ended in June. These included perform­ances in Wolfensohn Hall by violinist Midori, pianist Jeremy Denk, inventive groups like eighth blackbird and the Borromeo String Quartet, as well as a reading by Broadway actors of his musical Golden Motors. He created a new series of Writers Conversations that probed the nature of creativity and collaboration with artists, poets, directors, and writers, including Steve Bodow, producer and writer for the Daily Show, poet Tracy K. Smith shortly before she won the Pulitzer Prize, and composer Stephen Sondheim who called art “a kind of puzzle.”

While at the Institute, Bermel collaborated with Helmut Hofer, Professor in the School of Mathematics, on a musical piece inspired by symplectic dy­namics, a mathematical theory of dynamical systems. In Feb­ruary, the JACK Quartet performed Derek’s clarinet quintet “A Short History of the Universe (as related by Nima Arkani-Hamed),” inspired by lectures he attended by Arkani-Hamed, Professor in the School of Natural Sciences.

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What was your approach when you first started as the Institute’s Artist-in-Residence?

I’d say my approach has been fairly consistent. I’ve always been interested to make contact with people here. I only wish that I could have gone to more lectures, seen more presentations, participated even more. The Institute is a very rich place. There’s quite a bit below the surface, and it was clear to me right from the beginning that the Faculty and Members here were all working on fascinating projects; some of them I could only grasp skeletally, nonetheless it was well worth the effort.

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By Catherine Rottenberg

Children of the Hagar School and their families plant a community garden. The students learn to work as partners, using an array of skills.

Although I came to the Institute to research twentieth-century African-American and Jewish-American fiction, I would actually like to share with you a formative experience I have had as a parent. It all began in 2005, when my oldest child was turning one. My partner and I were living in Be’er-Sheva, a city in southern Israel, and, like many new parents, we began to worry about our child’s education. So one evening we invited a few friends, Jewish and Palestinian couples with young children, to our home to discuss daycare and school options for our toddlers. Like many parents around the world, we scouted the city to see what kinds of nurseries and kindergartens were available. The reality we found was depressing, since it was a reality of strict segregation between Arab and Jewish children.

Except for a handful of mixed cities like Haifa (which are also segregated by neighborhood), the 1,180 settlements in Israel are ethnically divided: they are either Jewish or Arab. This means that even though twenty percent of Israel’s population is Arab, Jewish and Arab children rarely if ever get to know each other as they grow up. They go to separate schools, play in different neighborhood playgrounds, and really don’t have an opportunity to meet one other until, perhaps, university. This segregation is not a result of legislation. There are no Jim Crow laws prohibiting Jews and Palestinians from learning together. Rather, the lack of contact has to do with, among other things, the way space has been organized.

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