PUP math editor Vickie Kearn: How real mathematicians celebrate Pi Day

Who doesn’t love Pi (aka Pie) Day? Residents here in Princeton, NJ love it so much that we spend four days celebrating. Now, to be honest, we’re also celebrating Einstein’s birthday, so we do need the full four days. I know what I will be doing on 3.14159265 but I wondered what some of my friends will be doing. Not surprisingly, a lot will either be making or eating pie. These include Oscar Fernandez (Wellesley), Ron Graham (UCSD), and Art Benjamin (who will be performing his mathemagics show later in the week). Anna Pierrehumbert (who teaches in NYC) will be working with upper school students on a pi recitation and middle school students on making pi-day buttons. Brent Ferguson (The Lawrenceville School) has celebrated at The National Museum of Mathematics in NYC, Ireland, Greece, and this year Princeton. Here he is celebrating in Alaska:


The Princeton University Math Club will be celebrating with a party in Fine Hall. In addition to eating pie and playing games, they will have a digit reciting contest. Tim Chartier (Davidson College) will be spending his time demonstrating how to estimate pi with chocolate chips while also fielding interview requests for his expert opinion on March Madness (a lot going on this month for mathematicians). Dave Richeson (Dickinson College) goes to the local elementary school each year and talks with the fifth graders about pi and its history and then eats creatively rendered pi themed pie provided by the parents.

You might be wondering why we celebrate a mathematical constant every year. How did it get to be so important? Again I went back to my pi experts and asked them to tell me the most important uses of pi. This question is open to debate by mathematicians but many think that the most important is Euler’s Identity, e(i*pi) + 1 = 0. As Jenny Kaufmann (President of the Princeton University Math Club) puts it, “Besides elegantly encoding the way that multiplication by i results in a rotation in the complex plane, this identity unites what one might consider the five most important numbers in a single equation. That’s pretty impressive!” My most practical friend is Oscar and here is what he told me: “There are so many uses for pi, but given my interest in everyday explanations of math, here’s one I like: If you drive to work every day, you take many, many pi’s with you. That’s because the circumference of your car’s tires is pi multiplied by the tires’ diameter. The most common car tire has a diameter of about 29 inches, so one full revolution covers a distance of about 29 times pi (about 7.5 feet). Many, many revolutions of your tires later you arrive at work, with lots and lots of pi’s!” Anna is also practical in that she will be using pi to calculate the area of the circular pastry she will be eating, but she also likes the infinite series for pi (pi/4 = 1 – 1/3 + 1/5 – 1/7 etc.). Avner Ash (Boston College) sums it up nicely, “ We can’t live without pi—how would we have circles, normal distributions, etc.?”

One of the most important questions one asks on Pi Day is how many digits can you recite? The largest number I got was 300 from the Princeton Math Club. However, there are quite a few impressive numbers from others, as well as some creative answers and ways to remember the digits. For example, Oscar can remember 3/14/15 at 9:26:53 because it was an epic Day and Pi Time for him. Art Benjamin can recite 100 digits from a phonetic code and 5 silly sentences. Ron Graham can recite all of the digits of pi, even thousands, as long as they don’t have to be in order. Dave Richeson also knows all of the digits of pi which are 0,1,2,3,4,5,6,7,8,and 9.

No matter how you celebrate, remember math, especially pi(e) is useful, fun, and delicious.

Vickie Kearn is Executive Editor of Mathematics at Princeton University Press.

J. Richard Gott: What’s the Value of Pi in Your Universe?

Carl Sagan’s sci-fi novel Contact famously introduced wormholes for rapid transit between the stars. Carl had asked his friend Kip Thorne to tell him if the physics of wormholes was tenable and this led Thorne and his colleagues to investigate their properties. They found that traversable wormholes required exotic matter to prop them open and that, by moving the wormhole mouths one could find general relativity solutions allowing time travel to the past. A quantum state called the Casimir vacuum whose effects have been observed experimentally, could provide the exotic matter. To learn whether such time machines could be constructible in principle, we may have to master the laws of quantum gravity, which govern how gravity behaves on microscopic scales. It’s one of the reasons physicists find these solutions so interesting.

But in Contact there is lurking yet another fantastic sci-fi idea, which gets less publicity because it was not included in the movie version. In the book, the protagonist finds out from the extraterrestrials that the system of wormholes throughout the galaxy was not built by them, but by the long gone “old ones” who could manipulate not only the laws of physics but also the laws of mathematics! And they left a secret message in the digits of pi. In his movie Pi, Darren Aronofsky showed a man driven crazy by his search for hidden meanings in the digits of pi.

This opens the question: could pi have been something else? And if so, does pi depend on the laws of physics? Galileo said: “Philosophy is written in this grand book…. I mean the universe … which stands continually open to our gaze…. It is written in the language of mathematics.” The universe is written in the language of mathematics. Nobel laureate Eugene Wigner famously spoke of the “unreasonable effectiveness of mathematics” in explaining physics. Many philosophers take the Platonic view that mathematics would exist even the universe did not. And cosmologist Max Tegmark goes so far as to say that the universe actually is mathematics.

Yet maybe it is the other way around. The laws of physics are just the laws by which matter behaves. They determine the nature of our universe. Maybe humans have simply developed the mathematics appropriate for describing our universe, and so of course it fits with what we see. The mathematician Leopold Kronecker said, “God created the integers, all the rest is the work of man.” Are the laws of mathematics discovered by us in the same way as we discover the laws of physics? And are the laws of mathematics we discover just those which would have occurred to creatures living in a universe with physics like ours? In our universe, physics produces individual identical particles: all electrons are the same for example. We know about integers because there are things that look the same (like apples) for us to count. If you were some strange creature in a fractal universe containing only one object—yourself—and you thought only recursively, you might not ever think of counting anything and would never discover integers.

What about π = 3.14159265.…? Might it have a different value in a different universe? In our universe we have a fundamental physical dimensionless constant, the fine structure constant α which is related to the square of the value of the electric charge of the proton in natural geometrical Planck units (where the speed of light is 1 and the reduced Planck constant is 1 and Newton’s gravitational constant is 1). Now 1/α = 137.035999… Some physicists hope that one day we may have a mathematical formula for 1/α using mathematical constants such as π and e. If a theory for the fine structure constant could be developed giving a value in agreement with observations but allowing it to be calculated uniquely from pure mathematics, and if more and more digits of the constant were discovered experimentally fulfilling its prediction, it would certainly merit a Nobel Prize. But many physicists feel that no such magic formula will ever be discovered. Inflation may produce an infinite number of bubble universes, each with different laws of physics. Different universes bubbling out of an original inflating sea could have different values of 1/α. As Martin Rees has said, the laws of physics we know may be just local bylaws in an infinite multiverse of universes. String theory, if correct, may eventually give us a probability distribution for 1/α and we may find that our universe is just somewhere in the predicted middle 95% of the distribution, for example. Maybe there could be different universes with different values of π.

Let’s consider one possible example: taxicab geometry. This was invented by Hermann Minkowski. Now this brilliant mathematician also invented the geometrical interpretation of time as a fourth dimension based on Einstein’s theory of special relativity, so his taxicab geometry merits a serious look. Imagine a city with a checkerboard pattern of equal-sized square blocks. Suppose you wanted to take a taxicab to a location 3 blocks east, and 1 block north of your location, the shortest total distance you would have to travel to get there is 4 blocks. Your taxi has to travel along the streets, it does not get to travel as the crow flies. You could go 1 block east, then 1 block north then 2 blocks east, and still get to your destination, but the total distance you traveled would also be 4 blocks. The distance to your destination would be ds = |dx| + |dy|, where |dx| is the absolute value of the difference in x coordinates and |dy| is the absolute value of the difference in y coordinates. This is not the Euclidean formula. We are not in Kansas anymore! The set of points equidistant from the origin is a set of dots in a diamond shape. See diagram.


Image showing an intuitive explanation of why circles in taxicab geometry look like diamonds. Wikipedia.

Now if the blocks were smaller, there would be more dots, still in a diamond shape. In the limit where the size of the blocks had shrunk to zero, one would have a smooth diamond shape as shown in the bottom section of the diagram. The set of points equidistant from the origin has a name—a “circle!” If the circle has a radius of 1 unit, the distance along one side of its diamond shape is 2 units: going from the East vertex of the diamond to the North vertex of the diamond along the diagonal requires you to change the x coordinate by 1 unit and the y coordinate by 1 unit, making the distance along one side of the diagonal equal to 2 units (ds = |dx| + |dy| = 1 + 1 units = 2 units). The diamond shape has 4 sides so the circumference of the diamond is 8 units. The diameter of the circle is twice the radius, and therefore 2 units. In the taxicab universe π = C/d = C/2r = 8/2 = 4. If different laws of physics dictate different laws of geometry, you can change the value of π.

This taxicab geometry applies in the classic etch-a-sketch toy (Look it up on google, if you have never seen one). It has a white screen, and an internal stylus that draws a black line, directed by horizontal and vertical control knobs. If you want to draw a vertical line, you turn the vertical knob. If you want to draw a horizontal line you turn the horizontal knob. If you want to draw a diagonal line, you must simultaneously turn both knobs smoothly. If the distance between two points is defined by the minimal amount of total turning of the two knobs required to get from one point to the other, then that is the “taxicab” distance between the two points. In Euclidean geometry there is one shortest line between two points: a straight line between them. In taxicab geometry there can be many different, equally short, broken lines (taxicab routes) connecting two points. Taxicab geometry does not obey the axioms of Euclidean geometry and therefore does not have the same theorems as Euclidean geometry. And π is 4.

Mathematician and computer scientist John von Neumann invented a cellular automaton universe that obeys taxicab geometry. It starts with an infinite checkerboard of pixels. Pixels can be either black or white. The state of a pixel at time step t = n + 1 depends only on the state of its 4 neighbors (with which it shares a side: north, south, east, west of it) on the previous time step t = n. Causal, physical effects move like a taxicab. If the pixels are microscopic, we get a taxicab geometry. Here is a simple law of physics for this universe: a pixel stays in the same state, unless it is surrounded by an odd number of black pixels, in which case it switches to the opposite state on the next time step. Start with a white universe with only 1 black pixel at the origin. In the next time step it remains black while its 4 neighbors also become black. There is now a black cross of 5 pixels at the center. It has given birth to 4 black pixels like itself. Come back later and there will be 25 black pixels in a cross-shaped pattern of 5 cross-shaped patterns.

Come back still later and you can find 125 black pixels in 5 cross-shaped patterns (of 5 cross-shaped patterns). All these new black pixels lie inside a diamond-shaped region whose radius grows larger by one pixel per time step. In our universe, drop a rock in a pond, and a circular ripple spreads out. In the von Neumann universe, causal effects spread out in a diamond-shaped pattern.

If by “life” you mean a pattern able to reproduce itself, then this universe is luxuriant with life. Draw any pattern (say a drawing of a bicycle) in black pixels and at a later time you will find 5 bicycles, and then 25 bicycles, and 125 bicycles, etc. The laws of physics in this universe cause any object to copy itself. If you object that this is just a video game, I must tell you that some physicists seriously entertain the idea that we are living in an elaborate video game right now with quantum fuzziness at small scales providing the proof of microscopic “pixelization” at small scales.

Mathematicians in the von Neumann universe would know π = 4 (Or, if we had a taxicab universe with triangular pixels filling the plane, causal effects could spread out along three axes instead of two and a circle would look like a hexagon, giving π = 3.). In 1932, Stanislaw Golab showed that if we were clever enough in the way distances were measured in different directions, we could design laws of physics so that π might be anything we wanted from a low of 3 to a high of 4.

Back to the inhabitants of the von Neumann universe who think π = 4. Might they be familiar with number we know and love, 3.14159265…? They might:

3.14159265… = 4 {(1/1) – (1/3) + (1/5) – (1/7) + (1/9) + …} (Leibnitz)

If they were familiar with integers, they might be able to discover 3.14159265… But maybe the only integers they know are 1, 5, 25, 125, … and 4 of course. They would know that 5 = SQRT(25), so they would know what a square root was. In this case they could still find a formula for

3.14159265. . . =
SQRT(4) {SQRT(4)/SQRT(SQRT(4))}{SQRT(4)/SQRT(SQRT(4) + SQRT(SQRT(4)))}{SQRT(4)/ SQRT(SQRT(4) + SQRT(SQRT(4) + SQRT(SQRT(4))))} …

This infinite product involving only the integer 4 derives from one found by Vieta in 1594.

There are indeed many formulas equal to our old friend 3.14159265… including a spectacular one found by the renowned mathematician Ramanujan. Though every real number can be represented by such infinite series, products and continued fractions, these are particularly simple. So 3.14159265… does seem to have a special intimate relationship with integers, independent of geometry. If physics creates individual objects that can be counted, it seems difficult to avoid learning about 3.14159265… eventually—“If God made the integers,” as Kronecker suggested. So 3.14159265… appears not to be a random real number and we are still left with the mystery of the unreasonable effectiveness of mathematics in explaining the physics we see in our universe. We are also left with the mystery of why the universe is as comprehensible as it is. Why should we lowly carbon life forms be capable of finding out as much about how the universe works as we have done? Having the ability as intelligent observers to ask questions about the universe seems to come with the ability to actually answer some of them. That’s remarkable.

UniverseGottJ. Richard Gott is professor of astrophysics at Princeton University. His books include The Cosmic Web: Mysterious Architecture of the Universe. He is the coauthor of Welcome to the Universe: An Astrophysical Tour with Neil DeGrasse Tyson and Michael A. Strauss.

Just in time for Pi Day, presenting The Usefulness of Useless Knowledge

In his classic essay “The Usefulness of Useless Knowledge,” Abraham Flexner, the founding director of the Institute for Advanced Study in Princeton and the man who helped bring Albert Einstein to the United States, describes a great paradox of scientific research. The search for answers to deep questions, motivated solely by curiosity and without concern for applications, often leads not only to the greatest scientific discoveries but also to the most revolutionary technological breakthroughs. In short, no quantum mechanics, no computer chips. This brief book includes Flexner’s timeless 1939 essay alongside a new companion essay by Robbert Dijkgraaf, the Institute’s current director, in which he shows that Flexner’s defense of the value of “the unobstructed pursuit of useless knowledge” may be even more relevant today than it was in the early twentieth century. Watch the trailer to learn more:

The Usefulness of Useless Knowledge by Abraham Flexner from Princeton University Press on Vimeo.

Marc Chamberland: Why π is important

On March 14, groups across the country will gather for Pi Day, a nerdy celebration of the number Pi, replete with fun facts about this mathematical constant, copious amounts pie, and of course, recitations of the digits of Pi. But why do we care about so many digits of Pi? How big is the room you want to wallpaper anyway? In 1706, 100 digits of Pi were known, and by 2013 over 12 trillion digits had been computed. I’ll give you five reasons why someone may claim that many digits of Pi is important, but they’re not all good.

Reason 1
It provides accuracy for scientific measurements


This argument had merit when only a few digits were known, but today this reason is as empty as space. The radius of the universe is 93 billion light years, and the radius of a hydrogen atom is about 0.1 nanometers. So knowing Pi to 38 places is enough to tell you precisely how many hydrogen atoms you need to encircle the universe. For any mechanical calculations, probably 3.1415 is more than enough precision.

Reason 2
It’s neat to see how far we can go


It’s true that great feats and discoveries have been done in the name of exploration. Ingenious techniques have been designed to crank out many digits of Pi and some of these ideas have led to remarkable discoveries in computing. But while this “because it is there” approach is beguiling, just because we can explore some phenomenon doesn’t mean we’ll find something valuable. Curiosity is great, but harnessing that energy with insight will take you farther.

Reason 3
Computer Integrity


The digits of Pi help with testing and developing new algorithms. The Japanese mathematician Yasumasa Kanada used two different formulas to generate and check over one trillion digits of Pi. To get agreement after all those arithmetic operations and data transfers is strong evidence that the computers are functioning error-free. A spin-off of the expansive Pi calculations has been the development of the Fast Fourier Transform, a ground-breaking tool used in digital signal processing.

Reason 4
It provides evidence that Pi is normal


A number is “normal” if any string of digits appears with the expected frequency. For example, you expect the number 4 to appear 1/10 of the time, or the string 28 to appear 1/100 of the time. It is suspected that Pi is normal, and this was evidenced from the first trillion digits when it was seen that each digit appears about 100 billion times. But proving that Pi is normal has been elusive. Why is the normality of numbers important? A normal number could be used to simulate a random number generator. Computer simulations are a vital tool in modeling any dynamic phenomena that involves randomness. Applications abound, including to climate science, physiological drug testing, computational fluid dynamics, and financial forecasting. If easily calculated numbers such as Pi can be proven to be normal, these precisely defined numbers could be used, paradoxically, in the service of generating randomness.

Reason 5
It helps us understand the prime numbers


Pi is intimately connected to the prime numbers. There are formulas involving the product of infinitely numbers that connect the primes and Pi. The knowledge flows both ways: knowing many primes helps one calculate Pi and knowing many digits of Pi allows one to generate many primes. The Riemann Hypothesis—an unsolved 150-year-old mathematical problem whose solution would earn the solver one million dollars—is intimately connected to both the primes and the number Pi.

And you thought that Pi was only good for circles.

SingleMarc Chamberland is the Myra Steele Professor of Mathematics and Natural Science at Grinnell College. His research in several areas of mathematics, including studying Pi, has led to many publications and speaking engagements in various countries. His interest in popularizing mathematics resulted in the recent book Single Digits: In Praise of Small Numbers with Princeton University Press. He also maintains his YouTube channel Tipping Point Math that tries to make mathematics accessible to a general audience. He is currently working on a book about the number Pi.

Jan C. Jansen and Jürgen Osterhammel on Decolonization

DecolonizationThe end of colonial rule in Asia, Africa, and the Caribbean was one of the most important and dramatic developments of the twentieth century. In the decades after World War II, dozens of new states emerged as actors in global politics. Long-established imperial regimes collapsed, some more or less peacefully, others amid mass violence. Decolonization by Jan C. Jansen and Jürgen Osterhammel takes an incisive look at decolonization and its long-term consequences, revealing it to be a coherent yet multidimensional process at the heart of modern history. Recently, the authors answered some questions about their new book:

You describe the dissolution of colonial empires as a major process of the twentieth century. What makes decolonization important?

In a way, decolonization is both among the most overrated and underrated historical processes of the twentieth century. On the one hand, many contemporaries pinned high expectations to the end of colonial rule: a new age of social and international equality, post-racism, peace, empowerment of the South, economic redistribution, cultural self-determination, democracy, technological progress, etc. Many of these expectations did not, or only partially, materialize. Hierarchies and inequality continue to shape the relations between formally independent states. It is thus only natural that many see decolonization through the prism of historical disappointment and disillusion. They regard decolonization as a failure. Yet we also have to see what decolonization did change: It dramatically altered the norms that govern the word-wide relations between nations and peoples. While in the late 1930s large parts of the world population still lived in territories that were under alien rule, this has become an anomaly in the present time. Racial hierarchy is no longer an accepted structuring principle of world order. This fundamental normative change is a major dimension—and yes, also an achievement—of the decolonization era. In general, it is important to go beyond these narratives of failure and success and to understand decolonization as a fundamental restructuring—and geopolitical fragmentation—of the international system. This is a perspective we put forward in the book.

How do you explain this international sea change?

This is a question that many contemporaries and witnesses of decolonization were already debating, and today’s historians and political scientists have inherited several ways of explaining the end of colonial rule: that the colonial powers simply could not stem against the rising tide of national liberation movements, that the new postwar international scene of the Cold War and international organizations forced Europe’s colonial powers to give up colonial rule, or that the colonial powers, in association with influential big business interests, realized that they could pursue their interests in more cost-effective ways than colonial rule, the classical “neo-colonialism” theory. In our book, in line with today’s excellent scholarship, we try to avoid overtly simplified models. Decolonization was a multifaceted and complex historical process, and its sheer geographical breadth should caution us against one-factor-theories. The book seeks to provide an analytical grid that takes into account various levels of historical action (local, imperial, international) and time frames. This grid may be used by our readers to analyze and describe specific cases, and may also help to explain decolonization in comparative perspective.

How irreversible is this process, in light of the current international scene? Are there no clear signs that the international order marked by decolonization is coming to an end?

Decolonization never did away with power structures between nations and peoples. Rather, it changed the ways in which these hierarchies are arranged and exercised. The formally sovereign nation-state—and no longer the empire—has become the basis of the international system. Despite the current renaissance of “spheres of interest” and “interventions,” as worrisome as these tendencies are, we do not see the reemergence of internationally codified hierarchies between “metropoles” and “colonies.” To be sure, the post-1989 international order has been under great pressure. Yet, there are no historical precedents for the reappearance of once collapsed empires. If current talk of a “Greater Russia” really leads to Russian “re-imperialization” remains to be seen. In that case, Russian ambitions will eventually clash with a self-confident China, ironically its old Asian rival, which, by the way, has never really ceased to be an empire. Elsewhere, the rise of xenophobic and racist movements throughout the Western world hardly seems to be inspired by the desire to be again at the pinnacle of a diverse and multi-ethnic empire. These movements want to minimize interaction with what they conceive as the inferior and dangerous other (be they Syrians, Eastern Europeans, or Mexicans); their new symbol is “the Wall.” Colonial re-expansion would necessarily go in a different direction.

You also argue that decolonization marked “a crucial phase in West European nation-building.” What do you mean by this?

Of course, decolonization did not bring about new European nation-states. This happened in the global South. Yet, it did have a considerable impact on the European metropoles, and also on Japan, which had built up its own colonial empire in Asia from the late nineteenth century on. These metropoles were closely tied to their overseas possessions, and it is one of the paradoxes of the decolonization era that such ties intensified at the very moment of imperial demise. After the Second World War, Great Britain and France, the two leading colonial powers, sought to facilitate mobility within their imperial spheres and set up, by today’s standards, relatively liberal citizenship laws for people from their respective empires. Decolonization, in this context, came as no less than a rupture in longstanding geopolitical orientations. It set off a new phase in European nation-building, a sort of nation-building by way of contraction. The metropoles had to dissolve or redefine the many—economic, political, social, also mental—ties to their respective empires. In light of increased immigration from their former colonial territories, they also had to redefine what it meant to be British, French, or Dutch. Though not produced by the end of empire, European supranational integration became enmeshed in European decolonization: the postcolonial European nation-states started to focus on Europe and the European market, which more than made up for their losses in former imperial trade. Great Britain, marked by a long-standing ambivalence toward continental Europe, made its first attempt to join the European Common Market in 1961, after the disaster of the Suez crisis and at the apogee of African decolonization. In a way, the 2016 “Brexit” vote to drop out of the European Union concluded this period of postimperial British supra-nationalism.

How present is the history of decolonization today?

Remnants of the colonial past and the decolonization era are pervasive. They remind us that our current world was built out of the ruins of empire. For example, a large portion of international borders between states, including the conflicts they sometimes nourish, have been the result of colonial rule. Decolonization basically enshrined most of them as the borders between sovereign nation-states. Some of the most troubling conflicts in the world—such as the Israeli-Palestinian conflict or the conflict between Pakistan and India—can be traced back to the decolonization era. Yet, notwithstanding the many apparent links, assessing the long-term impact of decolonization and the colonial past remains a tricky operation. Postcolonial countries have taken very different trajectories, sometimes starting from the same colonial system. Consider the two Koreas which had been under Japanese rule and which took diverging paths. The Syrian civil war, to cite another case, can hardly be seen as the ineluctable result of Franco-British quasi-colonial rule in the Middle East during the interwar years.

While the impact of the colonial past and the decolonization process may be fading with time, memories relating to this period have experienced a boom over the past two decades. Certainly, many episodes of the decolonization period remain largely forgotten. Who remembers the bloody repression of a major insurrection in Madagascar in 1947–49? Yet, debates about the colonial past and its end have attracted a great deal of attention not only in formerly colonized countries, but also in Japan and in many European countries. These memories have even become a concern in the diplomatic world. Internationally concerted efforts at remembering the effects—and the many victims—of colonial rule, similar to what we have seen with regard to the Holocaust or the world wars, however, are still no more than a wild dream by some historians.

Why did you write this book?

Decolonization has become an important topic in international historical scholarship, a development not completely detached from the memory boom we just talked about. Over the past two decades, historians and social scientists around the world have worked at piecing together a complex picture of this process and its reverberations. In many cases they have unearthed new archival evidence, a lot of which has only recently become accessible. Decolonization is in the process of turning into a highly productive—and specialized—research field. The wealth of new empirical studies, however, has been rarely accompanied by attempts at synthesis or general interpretation. The book offers such a broader survey. We sought to write it in a clear, accessible prose which addresses students and scholars, but also readers from outside the historical profession who are interested in this process.

Jan C. Jansen is a research fellow at the German Historical Institute in Washington, DC. Jürgen Osterhammel is professor of modern and contemporary history at the University of Konstanz. He is a recipient of the Gottfried Wilhelm Leibniz Prize, Germany’s most prestigious academic award. His books include The Transformation of the World: A Global History of the Nineteenth Century (Princeton).




Craig Clunas on Chinese Painting and its Audiences

ClunasWhat is Chinese painting? When did it begin? And what are the different associations of this term in China and the West? In Chinese Painting and Its Audiences, which is based on the A. W. Mellon Lectures in the Fine Arts given at the National Gallery of Art, leading art historian Craig Clunas draws from a wealth of artistic masterpieces and lesser-known pictures to show how Chinese painting has been understood by a range of audiences over five centuries, from the Ming Dynasty to today. Recently, Clunas took the time to answer some questions about the book.

There are lots of books about Chinese art, what’s the particular scope of this one?

CC: This book isn’t about the whole of Chinese art, but it looks at the important art of painting in China over the last five hundred years or so, from the Ming Dynasty (1368-1644) to the very recent past. It does it not from the point of view of the creation of Chinese painting but through a history of looking at it, and a history of the types of viewers who have formed the very diverse audiences for it over those centuries.

If I don’t know much about Chinese culture, will I be able to understand this book?

CC: I hope anybody interested in art can get something from this book. It has its origins in a lecture series, the A. W. Mellon Lectures in the Fine Arts, held regularly at the National Gallery of Art in Washington, DC, since 1953. In 2012 I gave these lectures (with the same title as the book); that’s only the second time in over sixty years that art from China has been the focus of a Mellon Lecture series. So I was very conscious of addressing a non-specialist audience, of people with an interest in the visual arts generally but without any specific expertise, and I’ve tried to keep the technicalities to a minimum in the main text, while still providing the evidence for other scholars to judge the strength of my arguments. When people say, ‘I don’t know anything about Chinese art,’ they often in fact already have a strong set of preconceptions, and I want to dispel some of these by showing the actual variety of painting being produced over a long time span, including work made in China in the past which tends to get left out of the category called ‘Chinese painting’ today.

How would you break down the main argument? 

CC: Obviously, back in the sixteenth century people in China who viewed a work by a famous painter of the day, or an old master from the past, didn’t think of what they were looking at as ‘Chinese painting.’ To them, it was just ‘painting.’ Today, whether in the Chinese-speaking world or outside it, the category ‘Chinese painting’ is the meaningful one we use to describe both historic painting and contemporary work of certain kinds. The book looks at how this came about, and shows how it was through the actions of viewers that this cultural category was formed, concentrating on certain kinds of pictures and marginalizing others. I’m claiming that the understanding of Chinese painting in some ways ran before it could walk, making big generalizations about the subject before much of the detailed work was done. These generalizations then fed into art history as a whole, where ‘Chinese painting’ stands as probably the major counter-example to the western tradition of art. I’m arguing here that the category ‘Chinese painting’ isn’t a timeless essence of Chinese culture, or an imposition on China from outside, but the result of a complex set of historical processes involving different types of audiences.

How does the book do this? 

CC: Firstly, by showing a fresh and broad set of images, you can’t write about pictures without showing them! The book is very heavily illustrated; it includes some familiar paintings which everybody already interested in the topic might recognize (though I hope they are talked about in a new way), but it also has lots of unfamiliar images, pictures which haven’t been widely reproduced before. I hope every reader will see something surprising and something beautiful. At the book’s heart are a sequence of what to me are really interesting paintings of different types of people – men and women, emperors and merchants, scholars and gallery-goers – looking at paintings. These pictures which take viewing as their subject can tell us a lot. They are at the core of a sequence of chapters which roughly speaking takes the topic from the fifteenth century to our own time, looking at a number of ideal audiences for Chinese painting; I’ve called these: the gentleman, the emperor, the merchant, the nation, the people. I’ve tried to balance analysis of the images themselves with the context in which they were produced, and to look at audiences both inside and outside China, which go back a lot longer than people might imagine. I’m obviously dependent on the specialist scholarship of other writers, and I’ve tried to pull together some of this work to give readers who might be interested in knowing more about a particular topic a sense of some of the great work being done now on Chinese painting. You can now read extensively in English about Chinese painting theory and criticism, and the lives of individual artists, over a broad time span. I’d be pleased if this book made people just a bit more aware of that great body of knowledge, and of the sheer scale of China’s artistic production.

How do you think this book might be received in China? 

CC: I’ve written other books on Chinese art, mostly of the Ming period, which have been translated into Chinese, and what I find interesting (and a bit surprising) is how some Chinese readers find contemporary resonances in books which I thought of when I wrote them as being ‘just’ about history. So I’ve come to accept that the history we write is never ‘just’ about the past. I’ve also learned (and this would be one of the main arguments of the book) that it’s wrong to imagine some homogeneous ‘Chinese view’ of painting or anything else, as if everybody in that huge country thought the same way. I hope some readers there might find it intriguing, and that even if they don’t like its way of arguing they would recognise the respect I feel for one of the world’s great bodies of art and human creativity.

How do you see the story of Chinese painting and its audiences developing in the future? 

CC: Painting, whether in brush and ink or oil on canvas, is only one of the practices of the visual arts in China today, but it remains an extremely important one. This is not least because the boom in the art market in China makes works of both past and present hugely valuable commodities. It seems pretty unlikely to me that the significant collections of Chinese painting outside China (whether in museums or in private hands) will grow very much in the future, the gravitational pull of the Chinese market is now just too strong. But the digital reproduction of artworks, which is proceeding now at a terrific pace, may mean that the physical location of paintings will matter less and less, their audiences will become more global and the composition of these audiences will get more and more diverse. That’s perhaps going to make it harder and harder for a restrictive definition of ‘Chinese painting’ to sustain itself, and maybe in time it will just be part of something called ‘painting’ again, or – who knows – even the dominant strand within it.

Craig Clunas is the Professor of History of Art of Oxford University in England. His books include Screen of Kings: Royal Art and Power in Ming China, Empire of Great Brightness: Visual and Material Culture and Social Status in Early Modern China, and Art in China.

Asia Week New York: March 9–18

Asia Week New York is an annual event in which top-tier Asian art specialists, major auction houses, museums, and Asian cultural institutions collaborate to honor and promote Asian art in New York City. Since 2009, the Asia Week New York Association has focused its efforts on putting together an event-filled week that draws collectors and curators from across the globe. If you’re going to be in the area, be sure to make time for some of the exciting special sales, lectures, receptions, and tours taking place in NYC. Here at PUP, we’re thrilled to be publishing two books that celebrate Asian art this season—Chinese Painting and Its Audiences by Craig Clunas and Kanban by Alan Scott Pate—and to revisit a favorite backlist title—Preserving the Dharma by John M. Rosenfield. If you can’t attend the events, you can always join the conversation on social media using the hashtag #AsiaWeekNY.

Exploring the complex relationships between works of art and those who look at them, Chinese Painting and Its Audiences sheds new light on how the concept of Chinese painting has been formed and reformed over hundreds of years.


Providing a look into a unique, handmade world, Alan Scott Pate offers new insights into Japan’s commercial and artistic roots, the evolution of trade, the links between commerce and entertainment, and the emergence of mass consumer culture in Kanban: Traditional Shop Signs of Japan.


In Preserving the Dharma: Hōzan Tankai and Japanese Buddhist Art of the Early Modern Era, eminent art historian John Rosenfield explores the life and art of the Japanese Buddhist monk Hozan Tankai (1629–1716).


Featured image: The Art of Japan (Medina, WA) Torii Kotondo Beauty Combing her Hair 1933

When the Women Set Sail

In 1852, after the publication of Harriet Beecher Stowe’s Uncle Tom’s Cabin, Elizabeth Barrett Browning urged her friend, art critic and memoirist Anna Jameson to read the novel, and expressed her indignation when Jameson found the subject of the novel too incendiary for a woman to tackle. Barrett Browning wrote in her letter to Jameson: “[I]s it possible that you think a woman has no business with questions like the question of slavery? Then she had better use a pen no more.” Elizabeth Barrett Browning’s assertion of her obligations as a female writer and poet is just one example of female writers’ active participation in the debates about the crucial concerns of civil society. Instead of concerning themselves solely with their domestic lives, women writers over the centuries have devoted themselves to aspiration, adventure, and public discourse. With stories about traveling, emigration, escape, and exodus, they have confronted ideas such as class formation, slavery, warfare, feminism, globalism, and the clash of cultures.

At Home in the World by Maria DiBattista and Deborah Epstein Nord is a reevaluation of the works of women writers, from canonical figures such as Jane Austen and George Eliot, to contemporary writers like Nadine Gordimer and Anita Desai. The authors argue that a complicated relationship and a recurring dialectic of home and abroad remain central in the literary expression of women’s experiences over two centuries. Searching for a “promised land” or a site of true belonging (the Home with a capital “H”), these women writers find the idea of Home in need of constant rediscovery and reinvention.

And rediscover they do. At the conclusion of Jane Austen’s Persuasion, Anne Elliot takes a brave step to liberation by accepting a future life of possible distress and impending war. Anne ends in a “non-place,” her possible life on a ship will be a life with indefinite location; however, this might offer her a true Home alongside Captain Wentworth, which promises conjugal happiness and a loving companionship. In Charlotte Brontë’s Villette, Lucy Snowe leaves England abruptly and impulsively for the town of Villette, and starts a journey of adventure and dislocation. She increasingly comes to “mark her place”, not as wife or keeper of a household, but as traveler, writer, and teacher. She retreats from bourgeois domesticity and begins to envision a new model of Home: a place that enables a woman to live and thrive alone in the world. Stepping out of the private realm and a conventional home provides a space of possibility—a new incarnation of Home begins to take shape at the moment when the women set sail.

When explaining the title of their book, DiBattista and Nord write: “Our title is meant to conjure the image of those dauntless women writers who ventured across the threshold that leads from home into the public thoroughfares of thought and action where history is made, the world reformed and reimagined. The peripatetics whose work and tradition we chronicle in these pages are determinedly and inventively moving toward a promised land—for so many called it that—where they hope to feel, at last, at home in the great world” (11). However, the discovery of a true Home is always problematic or even impossible, for its discovery or search often takes the form of “creating, writing, recording, and reporting back—activities that never really find a terminus” (248).

Public engagement by women writers is an ongoing process. Through continued dissent and active involvement with the most pressing issues in public life, they continue to forge an artistic path home in the world.

You can read the introduction to At Home in the World: Women Writers and Public Life, From Austen to the Present, by Maria DiBattista and Deborah Epstein Nord here.

Cass Sunstein on the echo chamber and his new book, #Republic

SunsteinSocial media gives us ways to nurture ever more elaborate online communities, but is it friendly to the kind of democracy diverse societies need? In #Republic: Divided Democracy in the Age of Social Media, Cass Sunstein, the New York Times bestselling author of Nudge and The World According to Star Wars, shows exactly how today’s Internet is driving political fragmentation, polarization, and even extremism—and what can be done about it. Recently, Sunstein answered a few questions about his timely new book.

Why did you write this book, and how does it relate to your previous work?

Well, we are obviously in a time of national division. The splits between Americans across political lines are striking and disturbing, and there’s a lot of division and mutual misunderstanding out there. There is distrust and anger as well. Social media contributes to those splits. So I wanted to get hold of what is a really serious problem in a nation that aspires to E Pluribus Unum. The book grows out of my previous books on the general subject—but the media environment has changed so rapidly that some of the central arguments, e.g. about Twitter and Facebook, are entirely new.

What new threats to democracy does the internet pose now that it didn’t pose, say, five years ago? Haven’t people always sorted themselves into like-minded groups?

We used to have a much larger role for general interest intermediaries, such as the Wall Street Journal and the New York Times. That’s diminished, and with it, trust in them has diminished too. The use of niches—especially for people who are politically engaged—is pretty dramatic. Hashtag Nation (#Nation) isn’t really something we’ve seen before. I wouldn’t want to say that things are getting worse, but they’re getting differently bad.

We’ve all heard the term “echo chamber,” perhaps particularly in the recent election cycle. Can you talk a bit about this idea and the implicit dangers?

Echo chambers breed extremism. If you hang out with like-minded people, you’ll get more confident and more extreme—and the group will get more unified. Pretty soon, people in different echo chambers live in different political universes. That makes problem-solving really hard, and it makes enmity really easy. My own work in the White House showed me the importance of focusing on objective truths and of not insulating oneself—echo chambers are destructive to those endeavors.

How can the internet be made friendlier to democratic deliberation?

A big question. Let’s start with Facebook: It should redo its News Feed so as to ensure that there’s less in the way of informational cocoons. Let’s end with each of us: We should make choices so that we hear lots of points of view, including from people we think we disagree with. If you can’t learn something from someone with a very different political orientation, you’re missing a lot. You’re not an ideal citizen, or close to it.

What kind of democracy is needed in diverse societies, and how can your book help us to get there?

We need deliberative democracy—one in which people deliberate with people who are unlike themselves, and learn from them. We need to put a premium on science and facts. We need serendipitous encounters with people and ideas that we would not choose to engage. We need a lot more technocracy, not less. The book might have a few ideas on those subjects.

Cass R. Sunstein is the Robert Walmsley University Professor at Harvard Law School. His many books include the New York Times bestsellers Nudge: Improving Decisions about Health, Wealth, and Happiness (with Richard H. Thaler), The World According to Star Wars, and #Republic: Divided Democracy in the Age of Social Media.

An interview with Andrea Carandini, editor of The Atlas of Ancient Rome

We’re thrilled to announce that The Atlas of Ancient Rome is now available for purchase. Take a moment to watch this interview with the volume editor, Andrea Carandini, in which he discusses why Rome merits its own Atlas, the appeal of the book as an object, and what makes this project unique. And be sure to check out the microsite for more information on this gorgeous tour through centuries of Roman history.

An Interview of Andrea Carandini Author of Atlas of Ancient Rome from Princeton University Press on Vimeo.