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.

Exploring the Arguments of Independence

The following text is excerpted from Our Declaration: A Reading of the ­Declaration of Independence in Defense of Equality (Liveright Publishing Corporation, 2014) by Danielle Allen, UPS Foundation Professor in the School of Social Science.

The Declaration of Independence matters because it helps us see that we cannot have freedom without equality. It is out of an egalitarian commitment that a people grows—a people that is capable of protecting us all collectively, and each of us individually, from domination. If the Declaration can stake a claim to freedom, it is only because it is so clear-eyed about the fact that the people’s strength resides in its equality.

The Declaration also conveys another lesson of paramount importance. It is this: language is one of the most potent resources each of us has for achieving our own political empowerment. The men who wrote the Declaration of Independence grasped the power of words. This reveals itself in the laborious processes by which they brought the Declaration, and their revolution, into being. It shows itself forcefully, of course, in the text’s own eloquence.

When we think about how to achieve political equality, we have to attend to things like voting rights and the right to hold office. We have to foster economic opportunity and understand when excessive material inequality undermines broad democratic political participation. But we also have to cultivate the capacity of citizens to use language effectively enough to influence the choices we make together.
 

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by Clyde Plumauzille

Professor Joan Scott at the School of Social Science’s twenty-fifth anniversary conference in 1997,  “25 Years: Social Science and Social Change”
Professor Joan Scott at the School of Social Science’s twenty-fifth anniversary conference in 1997, “25 Years: Social Science and Social Change” (Photo: Randall Hagadorn)

Revealing Implicit Structuring Norms and Challenging Categories of Difference

Critique will be the art of voluntary insubordination.”1 Epigraph to her essay ­”History-writing as Critique,”2 this quote from Michel Foucault is the key to understanding the epistemological journey of the American historian Joan W. Scott. Professor Emerita at the Institute for Advanced Study in Princeton, Scott is the author of numerous works on gender, feminism, and citizenship. A prolific and dynamic scholar, she has gone from studying social history to studying the history of women and then, in the 1980s, to studying the history of gender, becoming one of the first theorists in the field. With each shift in her historiographical focus, Scott has found the material needed to fuel her critical thought and shed light on the blind spots of social systems from the time of the French Revolution until the present day. Always on the lookout for history’s paradoxes, she has spent her entire career combatting the naturalization of differences and inequalities that stem from these contradictions.

As a historian and critical feminist, she has called for the concepts used in the social sciences to remain categories of critical intervention within political and academic debates. That’s why, from her seminal article “Gender: A Useful Category of Analysis,” published in 1986, to the recent publication in France of her book De l’utilité du genre in 2012, Scott has continued to highlight the political, social, and even imaginary issues that can only be understood through the conceptualization of sexual difference.3 To that end, she has zeroed in on French republican universalism, making it her preferred field of research, and has regularly weighed in on the public discussions surrounding its paradoxes. The politicization of sexual issues in France during the 1990s and the debates surrounding parité, domestic partnerships, and the wearing of Islamic headscarves have allowed her to reflect upon and discuss the reformulation of the republican contract by using real-life examples.

Now that “gender theory” has fallen under attack in France, denounced by its critics as an ideology that destroys the natural order and upsets the political and social balance, it seems fitting, if not crucial, that we take a look back on the ever-changing thoughts of a historian who has contributed greatly to the introduction of the concept of gender within the field of historiography.

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by Shiraz Minwalla

Shiraz Minwalla has uncovered an unexpected connection between the equations of fluid and superfluid dynamics and  Einstein’s equations of general relativity.
Shiraz Minwalla has uncovered an unexpected connection between the equations of fluid and superfluid dynamics and Einstein’s equations of general relativity. (Photo: McKay Savage)

How the Movement of Water Molecules Corresponds to Ripples in Spacetime

There is an interesting connection between two of the best-studied nonlinear partial differential equations in physics: the equations of hydrodynamics and the field equations of gravity.

Let’s start with a brief review of hydrodynamics. At the microscopic level a tank of water is a collection of, say, 1025 molecules that constantly collide with one another. The methods of physics may be used to model this collection of water molecules as follows: we set up equations that track the position and momentum of each of the water molecules and predict their time evolution. These conceptually complete equations have of order 1025 variables and so are clearly too difficult to handle in practice.

Does it then follow that tanks of water cannot be usefully studied using the methods of physics? As every plumber knows, this conclusion is false: a useful description of water is obtained by keeping track of average properties of water molecules, rather than each individual molecule.

Think of a tank of water as a union of non-overlapping lumps of water. Each lump is big enough to contain a large number of molecules but small enough so that gross macroscopic properties of the water (energy density, number density, momentum density) are approximately uniform. The fundamental assumption of hydrodynamics is that under appropriate conditions, all the “average” properties of any lump are completely determined by its conserved charge densities (in the case of water, molecule number density, energy density, and momentum density). In particular, the conserved current for molecule number jµ and the conserved current for energy and momentum Tµν are themselves dynamically determined functionals of local thermodynamical densities in a locally equilibrated system (fluctuations away from these dynamically determined values are suppressed by a factor proportional to the square root of the number of molecules in each lump). The equations that express conserved currents as functionals of conserved densities are difficult to compute theoretically but are easily measured experimentally and are known as constitutive relations.

When supplemented with constitutive relations, the conservation equations ∂µ jµ =0, and ∂µ Tµν=0(2) turn into a well-posed initial value problem for the dynamic of conserved densities. They are the equations of hydrodynamics. Let me reemphasize that the effect of the ignored degrees on the evolution of conserved densities is inversely proportional to the square root of the number of molecules in a lump, and so is negligible in an appropriate thermodynamic limit, allowing the formulation of a closed dynamical system for conserved densities.

My research concerns how the equations of hydrodynamics pop up in an apparently completely unrelated setting: in the study of the long wavelength dynamics of black holes governed by Einstein’s equations with a negative cosmological constant.

Einstein’s gravitational equations describe the dynamics of the geometry of spacetime. The ripples of spacetime (gravitational waves) have interesting dynamics even in the absence of any matter. For most of this article, I will be referring to Einstein’s equations in the absence of matter.
 

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By Olga Holtz

Olga Holtz lecturing at the Women and Mathematics Program at the Institute for Advanced Study (2014)
Olga Holtz (Photo: Dan Komoda)

The Making of a Mathematician

My love affair with George Pólya began when I was seventeen. It was in Chelyabinsk, Russia, and my first year at the university was coming to an end. I had come across a tiny local library with an even tinier math section, which nobody ever seemed to visit, and had taken out most of those math books one by one before I came across The Book. It was George Pólya’s Mathematics and Plausible Reasoning.

By that time I was a total bookworm, having devoured almost a thousand volumes of my parents’ home library, mostly fiction. My familiarity with math books was much poorer although, growing up, I had enjoyed Yakov Perelman’s popular books for children on math and physics. I was a proud graduate of a specialized math and physics school, the only one in town, and had had a few wins at local olympiads in math and science. A top kid in class as far back as I could remember, I was arrogant as hell.

I read the introduction to Mathematics and Plausible Reasoning and its Chapter I standing up next to the bookshelf. It read like a novel. A cerebral one alright, which made you pay quick attention. Chapter I started out in the least orthodox way, comparing mathematical induction to a domino chain. The book endeavoured to explain not only what was mathematically true but how and why. I was hooked. Chapter I ended with a list of problems. I solved a couple of them still standing up but quickly came to a halt on Problem 3.

The arrogance kicked in––I had to solve those problems. I still remember carrying that book home after I checked it out. It was late spring, gorgeous weather, bird songs in the air, romantic couples––you get the picture. I was besotted with The Book.

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By Lucy Colwell

How do proteins self-assemble into functional molecules?

Proteins are typically cited as the molecules that enable life; the word protein stems from the Greek proteois meaning “primary,” “in the lead,” or “standing in front.” Living systems are made up of a vast array of different proteins. There are around 50,000 different proteins encoded in the human genome, and in a single cell there may be as many as 20,000,000 copies of a single protein.1

Each protein provides a fas­cinating example of a self-organ­izing system. The molecule is assembled as a chain of amino acid building blocks, which are bonded together by peptide bonds to form a linear polymer. Once synthesized, this polymer spontaneously self-assembles into the correct and highly ordered three-dimensional structure required for function. This ability to self-assemble is remarkable—each linear polypeptide chain is highly disorganized, and has the potential to adopt an array of conformations so vast that we cannot enumerate them, yet within less than a second a typical protein spontaneously assumes the correct, highly ordered three-dimensional structure required for function. The identity and order of the amino acids that make up this polypeptide, that is the protein sequence, typically contain all the information necessary to specify the folded functional molecule.2

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