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 Amy Singer

With a vision to enrich and advance the field of Islamic and Near Eastern studies, Sabine Schmidtke (far left) and Amy Singer (right) are among the DOP participants compiling the pages of Ottoman history. (Credit Andrea Kane)

What makes a digital Ottoman project different from other digital projects and why isn’t it a straightforward endeavor but rather one that will probably take several years to develop successfully? And why isn’t there one already? Why would twenty-four people need one week together even to figure out where to begin? The Digital Ottoman Platform (DOP) workshop convened at the Institute June 8–12, 2015 to establish a transnational digital space in which to create, collect, and manage source materials, datasets, and scholarly work related to the Ottoman world. The goal is that these resources will be transparently and reliably authored, referenced, and reviewed to ensure that scholarly standards of research and publication are maintained for materials created and made available. The site, its materials, and its datasets will be sustainably managed to serve the global community of scholars, many of whom will also have contributed to the platform from their own research. At the same time, the space will be accessible to students, researchers, and readers worldwide.

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by Siobhan Roberts

In this caricature sketched by his friend, John Conway’s head has grown a “horned sphere,” a topological entity that is counterintuitive and ill-behaved, much like the ­mathematician himself. (Credit: Simon J. Fraser)

The elusive nature of biographical truth

During a visit to the Institute in the 1970s, the mathematician John Horton Conway, then of Cambridge, spent the ten most interesting minutes of his life. Invited to deliver a talk to the undergraduate math club at Princeton, Conway made his way across town and wangled himself a private audience with the God of logic, Kurt Gödel.

Conway had recently enjoyed his self-proclaimed annus mirabilis: In a period of twelve months in and around 1969 (which he usually rounds up to 1970), he invented the cellular automaton Game of Life, he discovered the 24-dimensional symmetrical entity named the Conway group, and while playing around with trivial children’s games he happened upon the aptly named surreal numbers. While Conway might be most popular among the masses for Life and its cult following, and while he might be most highly regarded among mathematicians for his big group, Conway himself is proudest of his surreal numbers. The surreals are a souped-up continuum of numbers including all the merely real numbers—integers, fractions, and irrationals such as π—and then going above and beyond and below and within, gathering in all the infinites and infinitesimals; the surreals are the largest possible extension of the real number line. And deferring to Scientific American columnist Martin Gardner’s reliable assessment, the surreals are “infinite classes of weird numbers never before seen by man. They provide a secure foundation on which Conway … carefully builds a vast and fantastic edifice.”

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by Timothy Brandt

Star clusters have a range not of ages, but of aging rates. Above: NGC 6811 (Credit: Anthony Ayiomamitis)

Might stellar rotation explain the variance of ages seen in star clusters?

“How big” is almost always an easier question to answer than “how old.” Though we can measure the sizes of animals and plants easily enough, we can often only guess at their ages. The same was long true of the cosmos. The ancient Greeks Eratosthenes and Aristarchus measured the size of the Earth and Moon, but could not begin to understand how old they were. With space telescopes, we can now even measure the distances to stars thousands of light-years away using parallax, the same geometric technique proposed by Aristarchus, but no new technology can overcome the fundamental mismatch between the human lifespan and the timescales of the Earth, stars, and universe itself. Despite this, we now know the ages of the Earth and the universe to much better than 1 percent, and are beginning to date individual stars. Our ability to measure ages, to place ourselves in time as well as in space, stands as one of the greatest achievements of the last one hundred years.

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by Timothy Brandt

Five years ago, NASA’s Fermi Gamma-ray Space ­Telescope saw more gamma rays than expected from the area around the center of our galaxy. Many scientists suggest that the extra gamma rays could be from the annihilation of dark matter particles. This exotic interpretation, however, requires ruling out all other possible sources of the gamma rays. While working at IAS as Members in the School of Natural Sciences, Bence Kocsis and I have discovered an ideal candidate source.

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by Stephen Adler

Fig. 1. Fermion loop diagram contributions to the axial-vector vertex part. Solid lines are fermions and dashed lines are photons. (a) The smallest loop, the AVV triangle diagram. (b) Larger loops with four or more vector vertices, which (when summed over vertex orderings) obey normal Ward identities.

Exploring the connection between anomalies and counting quark degrees of freedom

The article by Wally Greenberg in the spring 2015 Institute Letter mentions the anomalous axial current triangle diagram and describes its connection with counting quark degrees of freedom. This derives from a calculation I did when a long-term Member at the Institute in 1968, so I thought it would be useful to describe in detail the work done by me and by Bill Bardeen at the Institute on axial-vector or chiral anomalies. At first, this work was considered to be quantum field theory esoterica, but it has turned out to have wide and continuing implications.

But first, what is an axial-vector? A vector is a directed arrow. If you hold your right hand up to a mirror with the thumb pointing towards the mirror, you will see as the image a left hand with the thumb pointing towards you. This reversal of direction is characteristic of a vector under inversion of the coordinate axes (in this case, inversion of the axis perpendicular to the mirror). But another behavior is possible: a directed arrow that remains the same under inversion of the coordinate axes. Such a quantity is called an axial-vector or pseudovector. In the Maxwell equations for electromagnetism, electric fields behave as vectors and magnetic fields behave as axial-vectors under coordinate inversion, so this distinction has been around for many years.

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