Benford’s Law: A curious statistical phenomenon that keeps getting curiouser

Ted Hill, one of the contributors to The Princeton Companion to Applied Mathematics, as well as the coauthor, with Arno Berger, of An Introduction to Benford’s Law, has written a post on this fascinating statistical phenomenon. You’ll be surprised at the rather unexpected places it pops up, from an analysis of Donald Trump’s finances, to earthquake detection.

Benford’s Law

The acclaimed business and technology news website Business Insider proudly offers this advice to its readers, in capital letters:


The curious statistical phenomenon known as Benford’s Law, first discovered by Newcomb in 1881 and later rediscovered and popularized by Benford in 1938, is currently experiencing an explosion of research activity, especially in fraud detection ranging from tax data and digital images to clinical trial statistics, and from voting returns to macroeconomic data. Complementing these new forensic Benford tools, recent applications also include earthquake detection, analysis of Big Data and of errors in scientific computations, and diagnostic tests for mathematical models. As is common in developing fields, the quality of this research is all over the map, from scholarly and insightful to amusing and outlandish. The most recent Benford article I have seen is an analysis of Donald Trump’s finances, and I will let interested readers have fun judging these Benford articles for themselves. Most may be found on the open access and fully searchable Benford Online Bibliography, which currently references more than 800 articles on Benford’s Law, as well as other resources (books, websites, lectures, etc.).

The First-digit Law

In its most common formulation, the special case of the first significant (i.e., first non-zero) decimal digit, Benford’s Law says that the leading decimal digit is not equally likely to be any one of the nine possible digits 1, 2, …, 9, but rather follows the logarithmic distribution

equationwhere D1 denotes the first significant decimal digit. Many numerical datasets follow this distribution, from mathematical tables like the Fibonacci numbers and powers of 2 to real-life data like the numbers appearing in newspapers, in tax returns, in eBay auctions, and in the meta-dataset of all numbers on the World Wide Web (see Figure 1).

For datasets like these that are close to being Benford, about 30% of the leading (nonzero) decimal digits are 1, about 18% are 2, and the other leading digit proportions decrease exponentially to about 5% that begin with 9.

fig 1
Figure 1. Empirical Evidence of Benford’s Law

The complete form of Benford’s Law also specifies the probabilities of occurrence of the second and higher significant digits, and more generally, the joint distribution of all the significant digits. For instance, the probability that a number has the same first three significant digits as π = 3.141… is

eqn 2(For non-decimal bases b, the analogous law simply replaces decimal logarithms with logarithms base b.)

Robustness of Benford’s Law

Benford’s Law is remarkably robust, which may help explain its ubiquity in both theory and applications. For example, it is the only distribution on significant digits that is scale invariant (e.g., converting from dollars to euros or feet to meters preserves Benford’s Law), and is the only continuous distribution on significant digits that is base-invariant.

As an example of stochastic robustness, if a random variable X satisfies Benford’s Law, then so does XY for all positive Y independent of X; thus in multiplying independent positive random variables, say to model stock prices, if you ever encounter a single Benford’s Law entry, the whole product will obey Benford’s Law. Moreover, if X follows Benford’s Law, then so do 1/X and X2, (and all other non-zero integral powers of X).

Benford’s Law is also robust under both additive and multiplicative errors: If an increasing unbounded sequence of values X obeys Benford’s Law, then so does X + E for every bounded “error” sequence E, and if X is Benford and E is any independent error with |E| < 1, then (1 + E)X is also exactly Benford.

Applications of Benford’s Law

The most widespread application of Benford’s Law currently is its use in detection of fraud. The idea here is simple: if true data of a certain type is known to be close to Benford’s Law, then chi-squared goodness-of-fit tests can be used as a simple “red flag” test for data fabrication or falsification. Whether the tested data are close to Benford’s Law or are not close proves nothing, but a poor fit raises the level of suspicion, at which time independent (non-Benford) tests or monitoring may be applied.

A similar application is being employed to detect changes in natural processes. If the significant digits are close to Benford’s Law when the process is in one particular state, but not when the process is in a different state, then comparison to Benford can help identify when changes in the state of the process occur. Recent studies have reported successful Benford’s Law tests to detect earthquakes, phase transitions in quantum many-body problems, different states of anesthesia, signal modulations in electrophysiological recordings, and output changes in interventional radiology.

Tests for goodness-of-fit to Benford are also useful as a diagnostic tool for assessing the appropriateness of mathematical models. If current and past data obey Benford’s Law, it is reasonable to expect that future data will also obey Benford’s Law. For example, the 1990, 2000, and 2010 census statistics of populations of the some three thousand counties in the United States follow Benford’s Law very closely (see Figure 1), so to evaluate a proposed mathematical model’s prediction of future populations, simply enter current values as input, and then check to see how closely the output of that model agrees with Benford’s Law (see Figure 2).

fig 2
Figure 2. Benford-in-Benford-out Diagnostic Test

The appearance of Benford’s law in real-life scientific computations is now widely accepted, both as an empirical fact (as reported in Knuth’s classic text), and as a mathematical fact (e.g., Newton’s method and related numerical algorithms have recently been shown to follow Benford’s Law). Thus, in those scientific calculations where Benford’s Law is expected to occur, knowledge of the distribution of the output of the algorithm permits better estimates of both round-off and overflow/underflow errors.

Recent Theoretical Developments

Complementing these applications are new theoretical advancements, which are useful in explaining and predicting when Benford analysis is appropriate, and which are also of independent mathematical interest. Recent results include:

  • The outputs of many numerical algorithms, including Newton’s method, obey Benford’s Law.
  • Iterations of most linear functions follow Benford’s Law exactly, and iterations of most functions close to linear, such as f(x) = 2x + ex, also follow Benford’s Law exactly.
  • Continuous functions with exponential or super-exponential growth or decay typically exhibit Benford’s Law behavior, and thus wide classes of initial value problems obey Benford’s Law exactly.
  • Powers and products of very general classes of random variables, including all random variables with densities, approach Benford’s law in the limit (see Figure 3 for the standard uniform case).
  • Many multidimensional systems such as powers of large classes of square matrices and Markov chains, obey Benford’s Law.
  • Large classes of stochastic processes, including geometric Brownian motion and many Levy processes, obey Benford’s Law.
  • If random samples from different randomly selected probability distributions are combined, the resulting meta-sample also typically converges to Benford’s Law. (This may help explain why numbers in the WWW and newspapers and combined financial data have been found to follow Benford’s Law.)


Fig 3
Figure 3. Powers of a Uniform Random Variable

The study of Benford’s Law has also at times been entertaining. I’ve been contacted about its use to support various religious philosophies (including evidence of Benford’s Law in the Bible and Quran, and its appearance in tables of the earth’s elements as evidence of Intelligent Design), as well as a website where Eastern European entrepreneurs sold Benford data to people who need it for 25 euros a pop. For me, however, the main attraction has been its wealth of fascinating and challenging mathematical questions.

Ted Hill is Professor Emeritus of Mathematics at the Georgia Institute of Technology, and currently Research Scholar in Residence at the California Polytechnic State University in San Luis Obispo. He is the co-author, with Arno Berger, of An Introduction to Benford’s Law, (Princeton University Press, 2015).

Intro to Benford's Law


An interview with Paul Wignall: How life on earth survived mass extinctions

Wignall jacketAs scientists ponder NASA’s recent announcement about the likelihood of water and the possibility of life, or extinct life on Mars, Paul Wignall, professor of palaeoenvironments at the University of Leeds, explores a calamitous period of environmental crisis in Earth’s own history. Wignall has been investigating mass extinctions for more than twenty-five years, a scientific quest that has taken him to dozens of countries around the world. Recently he took the time to answer some questions about his new book, The Worst of Times: How Life on Earth Survived Eighty Million Years of Extinctions.

So why was this the worst of times and what died?

PW: For 80 million years, there was a whole series of mass extinctions; it was the most intense period of catastrophes the world has ever known. These extinctions included the end-Permian mass extinction, the worst disaster of all time. All life on earth was affected, from plankton in the oceans to forests on land. Coral reefs were repeatedly decimated, and land animals, dominated by primitive reptiles and amphibians, lost huge numbers of species.

What was responsible for all of these catastrophes?

PW: There is a giant smoking gun for every one of these mass extinctions: vast fields of lava called flood basalts. The problem is how to link their eruption to extinction. The key is understanding the role of volcanic gas emissions. Some of these gases, such as carbon dioxide, are very familiar to us today, and their climatic effects, especially global warming, seem to have been severe.

Why did these catastrophes stop happening?

PW: This is the $64,000 dollar question at the core of The Worst of Times. It seems to be because of a supercontinent. For 80 million years, all continents were united into a single entity called Pangea. This world was extremely bad at coping with rapid global warming because the usual feedbacks involved in removing gases from the atmosphere were not functioning very well. Since then, Pangea has broken up into the familiar multi-continent world of today, and flood basalt eruptions have not triggered any more mass extinctions.

What were the survivors like?

PW: Very tough and often very successful. It takes a lot to survive the world’s worst disasters, and many of the common plants and animals of today can trace their origin back to this time. For example, mollusks such as clams and snails were around before this worst of times, and their survival marks the start of their dominance in today’s oceans.

Are there any lessons we can apply to modern day environmental worries?

PW: Yes and no. Rapid global warming features in all of the mass extinctions of the past, which should obviously give us cause for concern. On the plus side, we no longer live in a supercontinent world. Flood basalt eruptions of the recent geological past have triggered short-lived phases of warming, but they have not tipped the world over the brink.

Paul Wignall at Otto Fiord at Cape St Andrew.

Paul Wignall conducting field research at Otto Fiord at Cape St Andrew.

Does this have anything to do with the dinosaurs?

PW: Sort of. Dinosaurs first appear towards the end of this series of calamities and to a great extent they owed their success to the elimination of their competitors, which allowed them to flourish and dominate the land for 140 million years. As we know, their reign was brought to an abrupt halt by a giant meteorite strike – a very different catastrophe to the earlier ones.

What would you say to those who want to know how you can claim knowledge of what happened so long ago?

PW: Geologists have a lot of ways to interpret past worlds. The clues lie in rocks, so mass extinction research first requires finding rocks of the right age. Then, once samples have been collected, analysis of fossils tells us the level where the extinctions happened. This level can then be analyzed to find out what the conditions were like. It’s like taking a sample of mud from the bottom of the ocean and then using it reconstruct environmental conditions. However, not everything gets “fossilized” in ocean sediments. For example, it is very hard to work out what past temperatures were like, and ocean acidity levels are even harder to determine. This leaves plenty of scope for debate, and The Worst of Times looks at some of these on-going scientific clashes.

Read chapter 1 here.

The Bees in Your Backyard – a slideshow

Bees are in decline, bringing many to embrace their value and think twice before decimating a hive. Even urban beekeeping has experienced an explosion in popularity. But the sheer number and variations that exist in the species can be confusing for novice (and seasoned) bee enthusiasts alike.

The Bees in Your Backyard by Joseph S. Wilson and Olivia Messinger Carril provides an engaging introduction to the roughly 4,000 different bee species found in the United States and Canada, dispelling common myths about bees while offering essential tips for telling them apart in the field. The authors are bee and wasp experts, and between them they have been studying these often misunderstood pollinators for more than three decades. The book contains over 900 stunningly detailed color photos, a few of which we’re excited to share with you here:


Image by Bob Peterson

Image by Jaco Visser

Image by Rick Avis

Image by B. Seth Topham

Image by Jillian H. Cowles

Image by Jillian H. Cowles

Image by USDA Bee Biology and Systematics Laboratory

Image by Jillian H. Cowles

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1.7_6_Strepsistera_JacoVissersmall thumbnail
1.7_10_mitesRAsmall thumbnail
2.1_1_bigandsmallBSTsmall thumbnail
3.1_8_AndrenaprimaJCsmall thumbnail
6.1_14_AgapostemonMelliventrisJCsmall thumbnail
7.0_1_MegachileHookedHairsBBSLsmall thumbnail
7.1_3_LithurgopsisJCsmall thumbnail

What does the Bible really say about infertility?

Moss jacket“If fertility is a blessing, then infertility ought to be a curse—so goes the logic of Genesis 1 and the creation story” write Candida Moss and Joel Baden, authors of Reconceiving Infertility, in their recent Daily Beast piece. In the secular view, infertility is a medical condition for which there is logical recourse: fertility treatment, adoption, or the decision to remain childless and pursue other means of fulfillment. But from ancient times to today, fertility through a biblical lens has often appeared as a sign of blessedness and moral uprightness, while infertility has been associated with sin and moral failing.

This week, the pope’s message carries the promise of many things: compassion for immigrants, vigilance about global warming, and redemption for those who have become alienated from the Catholic church because of its stance on divorce and other lifestyle choices. And yet, as Baden and Moss note in The Daily Beast:

Beyond the obvious—faceless corporations, greed, capitalistic exploitation, and so on—there is another group that Francis thinks is selfish: childless couples. In fact, during his tenure Francis has directly described those who choose not to have children as “selfish” and as obsessed with material things. He regularly uses sterility as a pejorative metaphor and fruitfulness as the primary image for that which flourishes. In so doing, he appears unaware of how this language alienates those without children and empowers others to negatively judge them.

Judgement of the childless, rooted as it may be in ancient biblical language, has long been a feature of modern life as well. Infertility carries a lingering stigma, and the decision not to procreate, often seen as a calculated choice, has led many to defend their “childless by choice” lifestyles. Yet according to Baden and Moss, biblical views on procreation and infertility were more diverse than we tend to think, particularly when we take into consideration the ancient contexts from which they emerged:

The good news is that the Bible, one of the primary ideological sources for discrimination against women, is in fact more complicated on the issue of infertility than it at first seems. While biological procreation is a perpetual blessing on God’s people, fertility is not always assumed to be the default human state. Certainly by the New Testament, the biblical “family” was less about biology than about a community drawn together by duty and responsibility. Informal adoption, mentorship as family, and concerns for others as a replacement for biological generation are the norm.

Read the rest of The Daily Beast piece here.

Candida Moss is professor of New Testament and Early Christianity at the University of Notre Dame, and is serving as a papal correspondent for CBS this week. Joel S. Baden is professor of Hebrew Bible at Yale Divinity School.

An interview with Eberhard Faber on “Building the Land of Dreams”

Faber jacketNew Orleans, iconic city of Mardi Gras, gumbo and jazz, was once little more than a sleepy outpost at the edge of Spain’s American empire. By the 1820s, with thriving cotton and sugar industries, the city was well on the way to becoming the urban capital of the antebellum South. Looking the ideological struggle, class politics, and powerful personalities that accompanied its transformation, Building the Land of Dreams is the narrative biography of a fascinating city at the most crucial turning point in its history. Recently, Eberhard Faber took the time to answer some questions about his book.

What inspired you to become a historian?

EF: It took a long time for me to become a professional historian; I was a touring musician for almost fifteen years before going back to school to study history. But I was always fascinated by history. As a kid I remember reading William Shirer’s Rise and Fall of the Third Reich. During my music years I remember reading Robert Caro’s The Power Broker in the back of the tour bus. History is simply a way of looking at the world and trying to understand it. I’ve always looked at the world this way.

As far as how I got interested in New Orleans and the South, it happened early in grad school at Princeton; I wrote a research paper for Linda Colley about the short-lived British colony in West Florida formed in 1763, and all the sources that I read pointed to New Orleans as a crucial strategic point in that era. The next year I wrote a paper for John Murrin about the South in the War of 1812, culminating with the Battle of New Orleans. The year after that I moved down to New Orleans for what was to have been a year of research; we got hooked and live here still.

What was the most interesting thing you learned from writing Building the Land of Dreams?

EF: Well, so many things. But perhaps it would be the biographies of the many people who moved to New Orleans in the months following the Louisiana Purchase, from the northern United States but also from across the Atlantic: England, Ireland, and France especially. In the book I call them the “generation of 1804” because they arrived right after the Louisiana Purchase. They were a varied cohort, and they fought amongst each other a lot, but I found their energy, ambition and idealism very appealing. One common characteristic was that they were all sincere believers in the world-changing possibilities of republican rule. They thought this radical experiment that the United States had only recently embarked upon was going to rewrite everything about human history. In New Orleans they ran into a conservative creole planter class that believed in none of those things, and they had a rude awakening of sorts. It’s a fascinating encounter.

What do you think is the book’s most important contribution?

EF: I think it has been a very common assumption that the United States imposed certain changes on Louisiana after 1803. That the course New Orleans and its wider region took, in the early nineteenth century, was an outcome of the policies of Thomas Jefferson and other American statesmen. What Building the Land of Dreams shows is that there were already very powerful entrenched interests in the area and that they, not the United States, ultimately had the power to dictate outcomes. What Jefferson and Madison could do was actually very limited; while the creole elite, on the other hand, initially threatened by republicanism, figured out that it actually gave them tremendous power to design the regimes – of law, of slavery, and race – that they had long wanted under colonial rule.

What is the biggest misunderstanding people have about what you do?

EF: Well, as far as my work in particular, I don’t think enough people know it for any major misunderstandings to have developed. As for the profession, I think there is a very wide gap between what the general public thinks of as “history” and what historians do in colleges and universities. If you go into a book store, many of the history books will be about military history (and at least half of those will be about the Civil War) and of the rest, a good portion will have Presidents on the cover. This leads many people to believe history is mostly about battles and Presidents, whereas in fact the field is so much bigger than that. The fact that it’s not understood is the fault of the field, of course. We need to do a better job of reaching the public and engaging their interest in historical issues.

What is your next project?

EF: I have two. One is a biography of the lawyer, legal reformer, and politician Edward Livingston, who was Mayor of New York and then fled from a scandal in 1803 to New Orleans. He ended up deeply entangled in New Orleans politics and power struggles and plays a major role in Building the Land of Dreams. I read almost all his personal papers in the course of writing the book and would love to focus on him exclusively for my next project.

The other one is totally different: a history of the music industry in the United States since the invention of the gramophone in the 1890s, with an emphasis on the parallel history of the rise of American capitalism.

What would you have been if not a historian?

EF: Well, that’s easy, since I was a musician (guitar player, songwriter, bandleader, arranger, record producer) for fifteen years before turning to history. I still play actively, too, within the limits imposed by writing and teaching. If the question is what would I have been if I was neither a musician nor a historian – well, my original hope was to be a professional baseball player, but at 5’ 5” that was never entirely realistic.

What are you reading right now?

EF: I’m currently reading Walter Johnson’s River of Dark Dreams. It covers some of the same historical ground as my book – even including the word Dreams in the title! – but from a very different attitude and perspective. I find it alternately infuriating and revelatory. Either way it’s certain to become an important part of the discussion on the antebellum South. Other wonderful books I’ve read lately include Sarah Carr’s brilliant exposé on the New Orleans public school system since Katrina, Hope Against Hope; Robert Gordon’s classic history of Stax Records, Respect Yourself; and Greg Iles’ epic Southern mystery novel Natchez Burning.

What was the most influential book you’ve read?

EF: I always come back to Thomas Mann’s The Magic Mountain, an allegorical novel about Europe before the Great War. Although it’s fiction, it contains great intellectual history, and combines themes that are essentially historical with deep exploration of human psychology. The same is true of War and Peace, which also had a profound effect on me: a meditation on the meaning of history and the sources of historical change, inextricably intertwined with such “interior” issues as the nature of human suffering and the attempt to find meaning in the universe. All historians should read these books. They remind us of the spiritual dimension behind the often dry academic debates that tend to cloud the field.

Meanwhile, in the realm of historical scholarship, I could mention so many – Henry Adams, Schlesinger, Hofstadter, Genovese, Gordon Wood, Rhys Isaac, William Cronon, Alan Taylor, my mentors Linda Colley and Sean Wilentz – but the one book that truly did influence me more deeply and permanently than any other was Richard White’s The Middle Ground. I don’t even think I’m very much like White as a historian, temperamentally and aesthetically; he’s a burrower, while I’m a wanderer; he eschews drama completely, while I am simply incapable of living without it. But the method, the dedication, the integrity, the matching of evidence to ideas, the rigor of the concepts, the sense of change over time, in that book, all of that is just so beautiful to me, and it remains a very distant and unreachable benchmark of sorts.

Describe your writing process. How long did it take you to finish your book? Where do you write?

EF: I like to write in libraries. I really love a nice library: the sensation that you are being enveloped in quiet and ideas and books, and that your work is going to merge into this enormous sea of scholarship that surrounds you. I wrote most of the first draft of Building the Land of Dreams on the C Floor of Princeton’s Firestone Library, 3 floors below ground level, in a tiny carrel. I wrote most of the revised version at the Community Coffee shop at the corner of Jefferson Ave. and Magazine St. in New Orleans (which is appropriate, because developing Thomas Jefferson’s part in the story was one of the biggest changes in the second draft).

As far as method and process, I think research and preparation is really 80% of the task, the actual writing is the final 20%. I spent lots of time on research; I read Edward Livingston’s papers in their entirety (140-some boxes worth), I read the New Orleans Conseil de Ville records in their entirety from 1803 to 1819, I have read pretty much every piece of secondary literature on early Louisiana ever written. It all goes into a big database (although, life being what it is, there’s always lots of stuff that never makes it into the database, too). By the time I actually start writing I have a very good idea of what I am going to say, including exact phrasing in many cases. The phrases have been building up in my head during showers and long drives for the months prior to writing them down. When I actually get going I write fast, and I write a lot. I have to trim a lot, too, eventually. The final version of Building the Land of Dreams is probably about equal in size to the pile of stuff that got left out and discarded along the way.

The whole project took almost seven years from beginning to end – three of which were spent working on the project pretty much full time, and four of which were spent balancing the writing and research with teaching.

Why did you write this book?

EF: I think I wrote the book because I had the very good fortune to have the institutional backing of Princeton University and Loyola University New Orleans; because I have a wonderfully supportive family; because I have a terrific network of colleagues and peers including a handful of close friends in my grad student cohort, my mentors at Princeton and in New Orleans, and the brother/sisterhood of Louisiana historians; in short because I am a very fortunate person in many ways. Good work doesn’t just spring from the genius of the author, but from very particular social circumstances in which the author is embedded. When I switched from a music career to an academic one, I knew I still wanted to be a creative person. I was lucky to find a great topic I could throw myself into and a great network of supporters to help me towards the finish. And lastly, in the final phase of turning this from a “project” into an actual book, I have also benefited greatly from the support and advice of Brigitta van Rheinberg, Quinn Fusting, and everyone else at Princeton University Press.

How did you come up with the title or jacket?

EF: Building the Land of Dreams – well, the phrase “Land of Dreams” comes from two places. One is William Blake’s poem, from the Pickering Manuscript, written around the time of the Louisiana Purchase. Blake never traveled to New Orleans, but the poem suggests the expanded mental universe of possibilities in the midst of the Age of Revolutions – and those world-changing possibilities were very much a part of the mental landscape of early 19th century New Orleans in the years after 1803. The second source, of course, is Spencer Williams’ “Basin Street Blues,” made famous by Louis Armstrong’s 1926 recording, which led to the “Land of Dreams” becoming one of the Crescent City’s many nicknames – and which, in the line about the banks of the Mississippi being “the place where dark and light folks meet,” also speaks to the central place of race in the city’s history and in my understanding of it.

The book’s jacket is a painting by John Boqueta de Woiserie, A View of New Orleans Taken from the Plantation of Marigny. It was painted in 1803, in celebration of the Louisiana Purchase and the American takeover, and it shows an eagle hovering over New Orleans, with a banner in its beak that reads “Under my wings/everything prospers.” It shows the enormous optimism with which some people, at least, greeted the prospect of American rule; the linked faith in personal liberty and material prosperity; and an unironic faith in the American promise that seems, in this cynical era, all too naïve. The book is the story of the various ways that promise was both betrayed and fulfilled.

Eberhard L. Faber teaches history and music industry studies at Loyola University, New Orleans. Previously, he spent twelve years leading the New York-based rock band God Street Wine. He blogs on New Orleans history and other topics at

An interview with Louise Fresco on “Hamburgers in Paradise”

Fresco JacketIn Louise Fresco’s new book, Hamburgers in Paradise, the term “Paradise”, in her own words, is “a metaphor that refers to the landscapes on our planet, the collective Garden of Eden which, according to some views, we have irreversibly destroyed through large scale food production.” It is a view shared by many in a world simultaneously plagued by food shortages and GMO fears. In such a climate, is there room for optimism? Fresco looks at our food situation in all its complexity, taking the stance that there is no one perfect way to produce or consume food, and that balance and trade-offs between different goals are central to any long term solution. You can see her TED talk here, and the English subtitled version to a documentary she made about the food industry here. Recently Fresco took some time to answer some questions about her book.

What’s new in this book?

LF: Human history has been one of continuous scarcity. The abundance of food that has emerged for the majority of the world population in the last decades is so unique that we have not yet learnt to deal with it. We are still scared that there will not be enough, and that we will destroy our environment. Scarcity is our default mode, and that of our bodies, hence our difficulties to balance our diets and to reduce our ecological footprint. Abundance is a triumph of science and trade; it allows us to shed our fears of shortages. But the book argues that we require new ways of thinking, to reign in our needs (for example of meat) while producing food sustainably for all, with new methods (for example through recycling or using algae). The book demonstrates in detail that there is not one perfect way to produce and consume food, but that we always have to balance the trade-offs between different goals, such as large scale production (i.e. low food prices) and biodiversity. What is best depends on our goals and our insight in unintended side effects (we may like to see free roaming chickens but they may be more prone to disease that way).

Can you explain the title Hamburgers in Paradise?

LF: The title refers to a thought experiment: if Eve were alive today, what food would she offer Adam as a temptation? Paradise as a metaphor also refers to the landscapes on our planet, the collective Garden of Eden which, according to some views, we have irreversibly destroyed through large scale food production. These semi-conscious images of a pre-Industrial and idealized past are still guiding many of our reactions to modernization. The hamburger, of course, is the iconic food that symbolizes the rise of the modern middle class, from suburban America to places like Moscow or Mumbai, as well as the critical counterforces: slow food, vegetarian and organic products. The hamburger illustrates also the adaptation to new demands: fat and salt contents have been lowered, information on calories and nutritional values are published, wrappings are made of recycled materials and advertising to children is limited. In the most recent twist of history, the hamburger becomes popular once again in upper class restaurants, dipped in liquid Nitrogen, or in a vegetarian reincarnation.

Food is the source of much confusion today, we hear so many, contradictory stories about what we must or mustn’t eat and why. What is the reason for this confusion?

LF: Food and agriculture are the basis human survival. Food conjures up strong feelings, based on individual memories, strict convictions and long traditions, especially in times of rapid modernization. Many people, even in rural areas, are hardly aware of how food is really produced and how it lands on their plates. Nearly all of us rely on others, often far away, to feed us. Ignorance and dependency make us feel vulnerable and worried about food.

But we can also turn this around: behind every meal there is a story, one that is nearly always fascinating and often complex, but always worth telling. Food connects us with the past and the future.

Is there room for optimism?

LF: With current knowledge, we can feed nine or ten billion people quite easily. This doesn’t mean that there is no world food problem. Even if enough food can be produced this is not easy and more production does not mean food reaches people automatically. The current gap between actual and attainable yields is still enormous. At the same time, agricultural research and innovation continue to be needed to tackle specific problems of animal and plant diseases, poor soils and climate variation. The application of existing knowledge is hampered by poor infrastructure, unavailability of irrigation or fertilizer, dysfunctional markets and policy.

Food shortage is more a matter of distribution than just production. Hunger is caused by poverty, so creating employment is essential. The great improvements in agricultural production since the 1970s have benefitted the urban poor more than the rural poor. These improvements involve higher yields, through better agricultural techniques such as irrigation, leading to lower food prices that benefit those who buy food (those living in cities), while farmers selling foods are at a disadvantage. Today more than 850 million people go hungry and perhaps as many as 2 billion may lack balanced nutrition. Most of the hungry live in areas of civil war or frequent natural disasters, so peace and resettlement are priorities.

There seems to be much concern about Genetically Modified Organisms, is this concern justified?

LF: This is a very complex issue about which it is impossible to generalize and about which there are many misunderstandings. For example, if cows are fed genetically modified soy bean, their milk does not become genetically modified, even if some people fear this. The modified genes and cells do not survive the gut. What the effects and risks are depends very much on what crop or animal, what genes are used for what purpose and where. Certain problems, for example diseases in banana, can only be tackled with biotechnology, a large toolkit which does not necessarily result in GMOs. There are two types of risk, for human and animal health. While we need to continue to monitor the situation, there are no indications that GM crops lead to additional food related risks in human beings or animals. So far, there are no indications of environment effects (such as insect mortality or genes “escaping “), but ecosystems are complex and difficult to monitor. Finally, there is also the issue of intellectual property rights: while a fair reward is needed for the companies developing the biotechnology or GMOs, we must also make sure that farmers and scientists and breeders elsewhere can keep access to varieties or breeds. Here the U.S. and EU legislation and traditions do not coincide.

What about chemical inputs such as fertilizer. Are we not destroying the land?

LF: Plants and animals need food just as we do. These nutrients come nearly exclusively from the soil (and through water, transported from soils elsewhere). Only very few soils can sustain production for long periods and their nutrient reserve needs to be built up through other sources of nutrients. Whilst manure from animals can be used for this, this does not solve the problem, it just means that animals have to graze somewhere from where they take up the nutrients. Almost without exception agriculture requires fertilizer to be sustainable. Fertilizer has a bad name mainly because it has been overused in the past with detrimental effects on surface water, but in itself, if wisely used, it is a blessing. More land is depleted through lack of fertilizer than is affected through its use.

Is fast food the source of all evils?

LF: Fast food is part of a complex process of transformation of society: greater mobility, work pressures, urbanization, diversification through trade, smaller and singe households, greater affluence of young, ubiquitous equipment like microwaves and fridges people all lead to out of home eating and pre-packed meals. As with all foods, it is not the individual item that is “bad” but the pattern. Eating fast food from time to time is acceptable in an otherwise healthy lifestyle. However, fast food often contains too many calories and we should be concerned if there are no other options, In so-called food deserts, neighbourhoods devoid of shops selling vegetables, fast food is often the recourse for single parents.

What type of agriculture is most sustainable?

LF: There is no blueprint for an agricultural model that fits all situations. Agriculture is the art of the location-specific and always depends on soils, climate, geography, culture and economics. Agriculture is forever changing, adapting to new consumer demands and new technology. However, using resources as efficiently as possible is essential to avoid wasting labour, water, land, fertilizer, seeds or animals as well as reducing post harvest losses in the entire value chain. Efficiency is often misunderstood as large-scale and anonymous, but it applies at all scales. No farmer can afford to waste resources, nor can we as humanity. The World will need 50% more calories in 2030.

Would the world be better off if all meat would be prohibited?

LF: No, meat is necessary for certain groups such as pregnant and lactating women, children, the elderly and sick and of course the malnourished. Meat is not only a source of proteins but also of essential nutrients such as iron and certain vitamins (B12). Humans evolved as omnivores; vegetarians, even in India, have always been a small minority. Also, there are areas in the world where nothing else can be produced but grazing land and animals. The growth in demand for meat and fish is expected to increase faster than the growth in population, especially in Asia and Africa.

However, there are major problems associated with meat production: environmental (water, emissions, production and transportation of feed) veterinary public health, human health (diseases associated with high red meat intake and overuse of antibiotics) as well as animal welfare. These can all be solved with adequate research and regulation. Reducing meat consumption through substitution of animal proteins in healthy individuals in affluent societies is part of that.

Louise O. Fresco is president of Wageningen University and Research Centre in the Netherlands. The author of several books, she is a member of the Council of Advisors for the World Food Prize and has worked extensively in developing countries for many years. She lives in Amsterdam.

A Letter From Your Publicist


Happy pub date to you, happy pub date….

Congratulations on your new book! Whether you’ve just put the finishing touches on your first book or have been down this road before, you’re probably eager to see what you can do to help to give your baby a proper send-off into the wild world of book critics and Amazon reviewers alike. Though I may not be your publicist, here’s hoping this guide can address the publicity questions you have, but were hesitant to ask.

Will you send my book out for review?

Absolutely! We are as invested in seeing your book land in the right hands as you are. Many months ago you should have filled out an Author Promotion Form (APF). Every press calls these forms something different, but this is an opportunity for you to share any suggestions for publications or special contacts that should receive a copy of your book. Didn’t fill it out? Don’t fear. You can contact your publicist at any time with leads for reviewers. Your publicist has also been familiarizing herself with your book and compiling a list of contacts that are just right for the target audience. Your book will be sent to a well-curated list. We also send out press releases and targeted email pitches.

My book is out and I haven’t seen any reviews in journals. What’s going on?

Don’t despair. Reviews in scholarly journals can happen at a glacial pace. Often they appear many months (or even a year) after publication date. This is also the case for major publications like the New York Review of Books, The London Review of Books, and the Times Literary Supplement.

What can I do to help?

writingA lot. One of the best things you can do after writing a book is… write some more! If your book’s research can be leveraged to comment on current events and you’re able to write a short (750 words) piece with a definite argument, you can pen an op ed positioning yourself as an expert, mentioning your book in the byline. Your publicist can help you  to get this into the hands of the right people. Never written an op ed before? Start by reading them.

Notice they are free of jargon, written for a general audience, and feature a strong point of view. Here’s a good place to read about the dos and don’ts of op ed writing.

Take advantage of other writing opportunities too. Guest blog if you are asked. Respond quickly to reporters who solicit your expertise. Reach out to personal contacts and colleagues who may have an affinity with your work and be interested in covering it.

Should I promote my book on Facebook/Twitter? Something else?

If you’re already active on social media, get more active now. The three months following the publication of your book is no time for modesty. You can follow people working on or writing about similar topics, retweet your book’s reviews or your own opinion pieces, use twitter to engage with others on your topic, or simply tweet ‘thanks!’ at someone for sharing your piece. If you know of an organization or individual that might be interested in your book, you can tag them in tweets to let them know about it.  But whatever you do, make sure to use your twitter feed to do more than self promote. Pay attention to what others are writing and be generous. If you share someone else’s work, there’s a good chance they’ll pay attention to the next thing you write as well. Finally, don’t worry about jumping onto every social platform there is. Use whatever is most comfortable for you, and where you have a natural following.

Should my book have its own hash tag?

Probably not.  Instead, use a popular tag on a topic you cover (like #edchat or  #behavioraleconomics).

I’ve never used social media and feel silly tweeting. Do I have to?

dislike buttonThere is no pressure at all to engage in these activities. If you’re on the fence about social media, now might be a time to give it a whirl. But if social media use is painful for you, forcing yourself into that territory it isn’t likely to benefit you or your book. No need to worry. Your publicist and press’s social media manager will be pushing out posts on your book themselves. Just sit back and enjoy the show.

Can my university help?

Definitely leverage the power of your university. Be in touch with your communications office to see what resources or plans they may have to promote your book. Some will share special features on social media, put out a press release on your book, post interviews with you their own website, or even be willing to produce a video interview or book trailer. Make sure to keep your book publicist in the loop about any plans to avoid duplication of effort, and offer both your university and your publisher opportunities to cross post.

I was interviewed, but the reporter used my quote without mentioning my book. How can I make sure my book is mentioned next time?

Just ask. Most reporters are amenable to referring to you as ‘author of…’ when using your quote. Don’t be shy about making the request.

Help! My book got a bad review! Should I respond?

angry manSome reviewers may draw conclusions about your research that you think are off base; in rare cases, they may even write caustic takedowns. There is no absolute rule covering how or whether to respond, though in many cases, the best response is no response at all. At times, we may counsel authors to reply, especially in the New York Review of Books, which has a long tradition of spirited exchanges between reviewer and author in their “Letters” section. Above all, if you do respond, you should keep it respectful and stick, as much as possible, to correcting errors of fact. Avoid the polemics the reviewer may have engaged in. You’ll come off better if you take the high ground. Kill’em with kindness.

I still feel frustrated.

troll signCompletely understandable. Post the offending review to your personal Facebook wall if you’re inclined, where no doubt your friends and colleagues will rally to your cause. But don’t feel the need to reply to everything, rectify every misunderstanding, or haunt the comments section under your own op eds. Remember the old chestnut that even bad publicity is good publicity? It’s true. The interest of readers and other reviewers is likely to be piqued by the very controversy that has you steaming, and that can only be a good thing.

Thanks for the tips, but I wish I could talk to another author. Someone who’s traveled this road before.

Jane Austen, Game Theorist cover artYou’re in luck! For another perspective and more ideas on how you can get creative with book publicity, check out this post by Michael Chwe, whose exuberant, hands-on efforts helped his book, Jane Austen: Game Theorist, to garner widespread attention. This is a man who said he’d stop at nothing—not even Jane Austen kitten memes—to get his scholarly book out there.

If you’re not as proactively disposed as Chwe, don’t worry. Successful publicity campaigns come in many forms. Remember, too, that your book is supported by the collaborative efforts of multiple people and departments. Although every new author’s journey comes with a bit of anxiety, take a deep breath, set up a Google alert for your name, and raise a glass to yourself. Whatever you do, try to enjoy the ride.

Your Publicist




Leah Wright Rigueur on Making Sense of Ben Carson

Leah Wright Rigueur

Photo Credit: Chion Wolf WNPR

Harvard Kennedy School of Government Professor of Public Policy, Leah Wright Rigueur, who was extensively quoted in the Washington Post  this week on Ben Carson, has written the first in a series of posts she’ll be contributing to the PUP blog. Today she explains the surge in Carson’s popularity among Republican voters in a race that has, until recently, been dominated by Donald Trump. Leah’s recent book, The Loneliness of the Black Republican, offers further insight into the seemingly incongruous intersection of civil rights and American conservatism. We’re delighted to have her. –PUP Blog Editor

Making Sense of Ben Carson

A modified version of this post appears at The Monkey Cage blog of the Washington Post

According to recent polls, Ben Carson has surged in popularity among likely Republican voters and now finds himself at the top of the GOP presidential primary pack. A recent poll of Iowa Republicans, for example, found Carson tied with Donald Trump for first place, with each candidate garnering 23 percent support. That an African American with zero political experience is now a front-runner in the Republican primaries is shocking. A political campaign that many dubbed a joke now appears to have political legs, and the public and press are scrambling to make sense of it.

The idea of a black conservative and/or a black Republican often feels a little like an oxymoron. Black people are partisan voters, overwhelmingly affiliating with the Democratic Party since 1948. In 2012, more than 90 percent of black voters cast ballots for Barack Obama. Their partisanship was, and continues to be, strategic – after all, many of the post-World War II advances in racial and social justice have come by way of Democratic liberalism. Coupled this with the modern – as in, post 1960s – GOP’s move to the extreme right and hostility toward racial justice and race-conscious solutions, and it would appear that politically, black voters have nothing in common with the Republican Party or modern conservatism.

But clearly we know that there are exceptions to this rule. According to the Pew Research Center, between five and eleven percent of the black public either identify as Republican or Lean Republican. Carson is not the first black Republican to run for president, and he won’t be the last. He’s also not the first black Republican to be discussed as part of a potential Republican presidential ticket. Speculation has long surrounded moderate Republican Colin Powell, who has declined to run, time and time again. In 1968 Richard Nixon toyed with tapping liberal Republican Edward Brooke as his vice-presidential running mate, while Gerald Ford placed the black senator high on a private list of potential vice-presidential appointees, in 1974.

Carson, Powell and Brooke, of course, all exhibit different forms of black Republicanism, ranging from liberal to the extreme right. But to some degree, their belief in Republicanism is undergirded by a kind of general black conservatism. African Americans are no strangers to conservatism. We see strong strands of it crop up in nineteenth and early twentieth century religious thought, especially among black churches, despite their political radicalism. Despite their beliefs in racial equality and justice, we see conservative thought in the behaviors of even some of the most progressive of civil rights leaders of the 1960s and 1970s. Conservatism also underscores the respectability politics of the black middle and working class, historically and in the present-day. Even today, studies have shown that about a third of black people self identify as conservative, although their conservatism rarely translates into support for the Republican Party.

And this is how we make sense of Ben Carson. He comes from a long conservative tradition, one that is rooted in a belief in religious morality, personal responsibility, self-help, individualism and free-market enterprise, and one that sometimes exists outside the boundaries of partisanship. Some have attributed Carson’s switch from ardent Democrat to conservative Republican as a matter of opportunism. That may very well be true, but one read of Gifted Hands, indicates that Carson has long exhibited the kind of “everyday black conservatism” that defines a portion of black communities.

Carson also comes from a partisan tradition that has given us figures like Clarence Thomas, Mia Love, Tim Scott, and many others. Organizations like the Black Silent Majority Committee in the 1970s, and the Lincoln Institute for Research and Education in the 1980s and 1990s, built on the black conservatism of past, cultivating a harsher kind of partisan Republican activism and rhetoric that Ben Carson currently articulates.

It’s the kind of position that conservative audiences, almost exclusively white, embrace. Carson is unique no doubt in attracting so much popularity. Historically, black Republicans have been unsuccessful at commanding this kind of attention, at this level of politics. And there are many, many reasons why Carson is surging in the polls: his religious roots, his “niceness” especially when contrasted with Donald Trump, his image as a brilliant surgeon, his position as a political outsider at a moment when people universally distrust politicians, his plain-spoken ability to “tell it like it is,” and his willingness to criticize, unapologetically, Barack Obama, and more broadly, black social justice movements like Black Lives Matter (BLM).

For white conservative audiences, Carson is “safe.” His words on racism, for instance, while profoundly critical of racist acts, are striking when compared to criticisms employed by black liberals. For Carson, racism is something to be changed through individual acts rather than something to be eradicated through structural change. In an era when explicit acts of racism are taboo, Carson’s rhetoric is both palatable to white audiences and comforting. In fact, Carson’s race lends a certain level of legitimacy to his remarks. In other words, conservative voters can look at Carson and have their personal beliefs on race validated, because a black man is articulating their exact same ideas. Historically, we consistently see this, as the GOP moved further to the right. Republicans in 1975, for example, used the Black Silent Majority Committee’s various conservative platforms to validate their views on various racial issues – even as African American voters routinely rejected the organization’s positions. This fraught relationship even led Clarence Thomas to once quip that black converts to the GOP’s acceptance hinged on becoming – in Thomas’ own words – a “caricature of sorts, providing sideshows of anti-black quips and attacks.”

Given all of this, what are we to make of Ben Carson? Are we to take him seriously? Well, in short, yes – we absolutely should take his candidacy seriously. Regardless of whether or not his campaign fizzles or he ends up at the top of the Republican presidential ticket, the general public, scholars, and journalists need to grapple with what, exactly, Carson represents. At this point, the scenarios are nuanced – at the extreme end of the spectrum, Carson could end up as the Republican nominee. He could also end up as vice-presidential nominee, a future presidential cabinet member, a member of Congress, or as a consultant to various public and private Republican factions. There’s a very real chance that Carson may ultimately end up influencing public policies, either directly or indirectly. After all, over the course of the last 80 years, the GOP has implemented black Republicans policies and programs, often favoring those ideas that are firmly couched within right-wing thought. And as we have seen in the past, previous Republican contenders rarely fade from the limelight, choosing instead to use their popularity to influence popular opinion. Ultimately then, we must pay attention to how Carson uses this platform, no matter how precarious, to influence American politics and life.

Leah Wright Rigueur is an Assistant Professor of Public Policy at the Harvard Kennedy School. She is the author of The Loneliness of the Black Republican: Pragmatic Politics and the Pursuit of Power (Princeton University Press, 2015).

Ethicist Jason Brennan on why smart politicians say dumb things

Jason BrennanEthicist Jason Brennan, whose posts on the ethics of voting for our 2012 Election 101 series were enormously popular, will be writing a series of posts for the PUP blog offering unique perspectives on ethics, voting, not voting, democracy, public policy and strategy. He is currently Flanagan Family Associate Professor of Strategy, Economics, Ethics, and Public Policy at the McDonough School of Business at Georgetown University, and is writing Against Politics, under contract with Princeton University Press. We’re excited to have him back, and to kick it off with his first post. –PUP Blog Editor

Saying stupid things to would-be voters is a very smart thing to do.

The Onion jokes: Donald Trump is “an eccentric, megalomaniac billionaire still more relatable to average Americans than anyone willing to dedicate life to politics”. Every other day, he says something outrageous or blatantly false, and yet he continues to grow in the polls. He seems to be getting by on empty slogans, with no well thought out policy ideas.
 When you see a politician saying something outrageous or blatantly false, you might be tempted to decry the quality of our politicians. If only someone better came along.

But there’s a reason we have the kind of politicians we do, and it’s not because no one better is willing to step up to the plate. Nor is it because great and evil villains (insert the Koch Brothers or George Soros, depending on your political predilection) are keeping our saviors down. Donald Trump may or may not be an eccentric megalomaniac, and he has indeed said many substantively stupid things. But he’s not a stupid man, and saying stupid things to would-be voters is a very smart thing to do.

Politicians are trying to win elections. To win elections, they need to get the most votes. To do that, they need to appeal to as many voters as possible. In an election, what every smart politician is trying to do is behave in ways that he or she hopes will appeal to the typical voter. Politicians are like this because they respond rationally to the incentives democracy creates.

 If voters were well-informed, dispassionate policy-wonks, then political campaigns would resemble peer-reviewed economics journals. But few voters or potential voters are like that. As I’ll document at greater length in future blog posts here, most voters are poorly informed, passionate, biased, overconfident, and tribalistic. Most non-voters are not dispassionate truth-seekers; rather, they just don’t care much at all.

Voters are like this because they respond rationally to the incentives democracy creates. The problem is that our individual votes count for very little. Economists and political scientists debate just how to calculate the probability that your vote will make a difference. Still, even on the most optimistic estimate in the literature, your vote (in a presidential election) has a 1 in 10 million chance of making a difference, but only if you live one of handful of swing states and vote Democrat or Republican. Otherwise, your vote has no real chance of mattering. Polls show that citizens more or less realize this.

Voters do not consume much information, nor do they discipline themselves to think rationally about the information they consume, because their votes make little difference. As economists like to say, voters are rationally ignorant. Consider, as an analogy. Suppose a billionaire offers you a million dollars if you can ace the Advance Placement Economics and Political Science exams. You’d probably be willing to learn basic economics and political science for that price. But now suppose the billionaire instead offers you a 1 in 20 million chance of earning that million dollars if you ace the exams. Now it’s not worth your time—it doesn’t pay to learn economics or political science.

Indeed, it’s not clear that voters are even trying to change the outcome of the election when they vote.  One popular theory of voter behavior is that voters vote in order to express themselves. Though the act of voting is private, voters regard voting as a uniquely apt way to demonstrate their commitment to their political team. Voting is like wearing a Metallica T-shirt at a concert or doing the wave at a sports game. Sports fans who paint their faces the team colors do not generally believe they will change the outcome of the game, but instead wish to demonstrate their commitment to their team. Even when watching games alone, sports fans cheer and clap for their teams. Perhaps voting is like this.

When you see politicians saying dumb things, remember that these politicians are not fools. They are responding rationally to the incentives before them. They say dumb things because they expect voters want to hear dumb things. When you see that voters want to hear dumb things, remember that the voters are only foolish because they are responding rationally to the incentives before them. How we vote matters, but for each individual person, how she votes does not. Thus, most individuals vote as if very little is at stake.Trump’s popularity is an indictment of democracy, not a conviction (yet). Democracy may make us dumb, but that doesn’t mean that in the end, democracies always make dumb decisions.

Jason Brennan is Flanagan Family Associate Professor of Strategy, Economics, Ethics, and Public Policy at the McDonough School of Business at Georgetown University. He is the author of Markets without Limits, with Peter Jaworski (2015), Why Not Capitalism? (2014), Compulsory Voting, with Lisa Hill (2014), Libertarianism (2012), The Ethics of Voting (2011), and A Brief Hisotry of Liberty, with David Schmidtz (2010). He is currently writing Against Politics, under contract with Princeton University Press, and Global Justice as Global Freedom, with Bas von der Vossen.

Five places you didn’t expect to encounter applied math

You don’t need to step into a classroom to have a run-in with mathematics. Professionals from a range of backgrounds — engineering, economics, physics, biology, computer science — use mathematics every day. To celebrate the publication of the much-anticipated Princeton Companion to Applied Mathematics, edited by Nicholas J. Higham, we’re thinking about all of the unique places and situations where applied mathematics is at work. Here is a list of just a few, compiled with a little help from our numerically inclined friends.

On the Golf Course


Golf involves mathematics, and not just when keeping score. The flight of your golf ball is affected by how air interacts with the surface of the ball. Did you know that the dimples in golf balls have a purpose, one with a mathematical explanation? Douglas N. Arnold, professor of Mathematics at the University of Minnesota, tells us more:

In the middle of the nineteenth century, when rubber golf balls were introduced, golfers noticed that old scuffed golf balls traveled farther than new smooth balls, although no one could explain this unintuitive behavior. This eventually gave rise to the modern dimpled golf ball. Along the way a great deal was learned about aerodynamics and its mathematical modeling. Hundreds of different dimple patterns have been devised, marketed, and patented. However, even today the optimal dimple pattern lies beyond our reach, and its discovery remains a tough challenge for applied mathematics and computational science.

Check out Dr. Arnold’s entry, “The Flight of a Golf Ball,” where he explains why golf ball dimples are an important part of your Saturday morning tee time.

On Wall Street


Wall Street is all about the numbers. Whether modeling the risk of a single stock or mapping the complex interactions that make up the world’s financial structure, mathematics helps the financial sector to study and evaluate systemic risk.

“The complexity, unpredictability, and evolving nature of financial markets continues to provide an enormous challenge to mathematicians, engineers, and economists in identifying, analyzing, and quantifying the issues and risks they pose,” write Dr. René A. Carmona and Dr. Ronnie Sircar of Princeton University.

In their entry, “Financial Mathematics,” Dr. Carmona and Dr. Sircar discuss how the finance industry uses mathematics. They also examine the role of mathematics in understanding and regulating financial markets in light of the financial crisis of 2008.

On Your Phone’s Weather App

Do you check the 10-day forecast during the weekend before a big outdoor event, fingers crossed for clear skies and no rain? There’s math behind that “chance of thunderstorms” prediction. NWP [numerical weather prediction] helps meteorologists to predict weather patterns for more than a week ahead. Better numerical schemes are partially responsible for moving us forward from the weather prediction methods of fifty years ago.

In his article “Numerical Weather Prediction,” Peter Lynch presents the mathematical principles of NWP and illustrates the process by considering some specific models and their application to practical forecasting. Dr. Lynch describes the many conditions that can be better predicted using NWP:

NWP models are used to generate special guidance for the marine community. Predicted winds are used to drive wave models, which predict sea and swell heights and periods. Prediction of road ice is performed by specially designed models that use forecasts of temperature, humidity, precipitation, cloudiness, and other parameters to estimate the conditions on the road surface. Trajectories are easily derived from limited-area models. These are vital for modeling pollution drift, for nuclear fallout, smoke from forest fires, and so on. Aviation benefits significantly from NWP guidance, which provides warnings of hazards such as lightning, icing, and clear-air turbulence.

In the Airport Security Line

baggage claim

On your next trip through airport security, take a look at the x-ray machine. Once an object, like your suitcase, is scanned, the image can be viewed from multiple angles by a security officer. Threat detection software can also be used to locate problematic items. There is math at work here too.

W. R. B. Lionheart, professor of Applied Mathematics at the University of Manchester, explains this technology in his entry “Airport Baggage Screening with X-Ray Tomography.”

While Researching Your Next Vacation


Getting ready for your first vacation of the fall? Buying tickets, making dinner reservations, researching tourist attractions — what did we do without the internet? Or rather, what did we do before the organized internet?

When the internet was still in its early stages, search engines were not as advanced as they are today, and webpage results were ranked by simple rules. Searching for “New York sightseeing” may have led you to the page where the search term appears the most, instead of a page with the most useful information. Today, search engines use a more advanced method for ranking web pages: grouping pages into authority pages, which have many links to them, and hub pages, which point to many authorities. The catch is that these terms depend on one another. How does this work? In the Princeton Companion to Applied Mathematics, editor Nicholas Higham explains the mathematics behind webpage ranking.

Looking for more examples of math in the world? Check out this video from SIAM, where SIAM conference attendees are asked how they use math in their work. Math really is all around us.

Washington Post highlights historic clash between Einstein and Bergson on the nature of time

2015_Einstein_bannerWith the 100th anniversary of the general theory of relativity coming up in November, Einstein is popping up everywhere. Yesterday’s Washington Post ran a terrific feature on Einstein books, including three of our own: Hanoch Gutfreund and Jürgen Renn’s The Road to Relativity, Einstein’s Relativity: The Special and the General Theory, and Jimena Canales’s The Physicist and the Philosopher.

One of the most fascinating chapters of Einstein’s public life revolves around an encounter he had with Henri Bergson, the renowned philosopher, on April 6, 1922, in Paris. It was on this day that Einstein and Bergson publicly debated the nature of time, touching off a clash of worldviews between science and the humanities that persists today. The philosopher Bergson argued that time was not merely mechanical, and should be seen in terms of lived experience; Einstein dismissed Bergson’s psychological notions as irreconcilable with the realities of physics. The Physicist and the Philosopher tells the remarkable story of how this explosive debate between two famous thinkers created intellectual rifts and revolutionized an entire generation’s understanding of time.

Nancy Szokan’s piece in Washington Post recounts the dramatic collision:

In The Physicist and the Philosopher, Canales recounts how Bergson challenged Einstein’s theories, arguing that time is not a fourth dimension definable by scientists but a ‘vital impulse,’ the source of creativity. It was an incendiary topic at the time, and it shaped a split between science and humanities that persisted for decades—though Einstein was generally seen as the winner and Bergson is all but forgotten.

Bergson and Einstein, toward the end of their lives, each reflected on his rival’s legacy and dedication to the pursuit of truth: Bergson during the Nazi occupation of Paris and Einstein in the wake of the first hydrogen bomb. Referencing Einstein’s quest for scientific truth, Hanoch Gutfreund recently had an article in the Huffington Post on how Einstein helped shape the Hebrew University of Jerusalem (home of the Albert Einstein Archives online):

On the occasion of the opening of the university, Albert Einstein published a manifesto “The Mission of our University”, which generated interest and excitement in the entire Jewish and academic worlds.

It states: “The opening of our Hebrew University on Mount Scopus, at Jerusalem, is an event which should not only fill us with just pride, but should also inspire us to serious reflection. … A University is a place where the universality of human spirit manifests itself. Science and investigation recognize as their aim the truth only.”

Read the rest here.

November’s big anniversary serves as a reminder of the enduring commitment to scientific investigation that continues at The Hebrew University and centers of learning all over the world today.

Read sample chapters of The Physicist and the Philosopher here, The Road to Relativity here, and Relativity here.

You can find information on the Digital Einstein Papers, an open access site for The Collected Papers of Albert Einstein, comprising more than 30,000 unique documents here.

A Q&A with Richard Layard and David Clark, authors of THRIVE

Thrive jacketHow can mental illness—an affliction that affects at least 20 percent of people in developed countries, reduces life expectancy, and wrecks havoc on educational potential—remain chronically under-treated? The answer is simple: mental and physical pain are not viewed equally, and even in a relatively progressive culture, the former remains profoundly stigmatized. As a result, most who suffer from mental health issues suffer in silence, or receive inadequate support. Can this change? Richard Layard and David Clark say it can.

In Thrive, Layard and Clark look at the practical politics of increasing access to mental health care, arguing that the therapies that exist—and work—are available at little to no cost. Recently, both took the time to answer some questions about the book, and the transformative power of mental health care.

What is the message of your book?

Depression and anxiety disorders are the biggest single cause of misery in Western societies. They also cause enormous damage to the economy. But they are curable, in most cases, by modern evidence-based psychological therapy. The shocking thing is that very few of those who need it get any help and fewer still get help based on evidence. In England such help is now becoming available to many of millions who need it. As we show, this help involves no net cost to society. It’s a no-brainer.

What is the scale of the problem?

Surveys of households in rich countries show that around 1 in 6 adults have depression or anxiety disorders severe enough to cause major distress and impair the person’s functioning. Only a quarter of these people are in any form of treatment, most usually medication. This is shocking. For surveys show that mental illness is the biggest single reason why people feel dissatisfied with their lives – accounting for more of the misery in our societies than either poverty or unemployment do.

What is its economic cost?

Mental illness accounts for nearly a half of all absenteeism from work and for nearly a half of all those who do not work because of disability. This imposes huge costs on employers and taxpayers. Mental illness also increases the use of physical healthcare. People with a given physical illness of a given severity use 50% more physical healthcare if they are also mentally ill. This is a huge cost to those who fund healthcare.

Does psychological therapy help?

In the last 40 years considerable progress has been made in developing effective psychological therapies. The most studied therapy is CBT – cognitive behavioural therapy, which is a broad heading for therapies which focus on directly influencing thoughts and behaviours – in order to affect the quality of human experience. In hundreds of randomised controlled trials CBT has been shown to produce recovery rates of over 50% for depression and anxiety disorders. For anxiety, recovery is generally sustained; for depression, the risk of relapse is greatly reduced.

The range of therapies which have been shown to work has been surveyed internationally by the Cochrane Collaboration and in England by the National Institute for Health and Care Excellence (NICE). Besides CBT, NICE also recommend for all depressions Interpersonal Therapy (IPT) and, for mild to moderate depression, Brief Psychodynamic Therapy, Couples Therapy and Counselling. Modern psychological therapies have also been shown to be effective in a wide range of other mental health conditions.

Do these therapies really cost nothing?

Yes. If delivered to a representative group of patients they pay for themselves twice over. First, they pay in reduced invalidity benefits and lost taxes due to invalidity. We know this from a series of controlled trials. Second, they pay for themselves in reduced costs of physical healthcare. Again we know this from controlled trials. It is so partly because the typical cost of an evidence-based course of treatment is only about $2,000.

How can these therapies become more widely available?

Two things are needed. First, there have to be enough people trained to deliver these therapies. This is the responsibility of universities and colleges, including of course supervised on-the-job training. Second, there have to be effective frameworks where trained people can be employed. The evidence is that recovery rates are higher where people are employed in teams where they can get supervision, in-service training, and clear career progression.

Those who fund healthcare have in the USA and UK the legal obligation to provide parity of esteem for mental and physical healthcare, and this requires that they are willing to fund high quality evidence-based therapies that are made easily available and provide the necessary duration of treatment, based on evidence. Insurers never fund half a hip replacement and they should not fund only half a proper course of psychological therapy.

What can be learnt from the English experience?

The English National Health Service has in recent years developed a totally new service to deliver evidence-based psychological therapies. (It’s called Improving Access to Psychological Therapies (IAPT)). This service has, over six years, trained altogether 6,000 therapists and is now treating nearly half a million people a year, with a recovery rate of 46% and rising. The prestigious journal Nature has called it “world-beating”.

How can we prevent mental illness in the first place?

First we must of course treat it as soon as it appears. This is often in childhood, where the same evidence-based treatments for depression and anxiety disorders apply as in adulthood. For children’s behaviour problems, parent training and family therapy are recommended.

But we must also reduce the overall prevalence of mental illness. This requires major changes throughout society. First, more support and education for parents. Second, schools which give more priority to the well-being of children. Third, employers who treat their workers with appreciation and encouragement and not as income-maximising machines. Fourth, more positively-oriented media. And finally, a new citizens’ culture giving more priority to compassion, both as an emotion and as a spring for action.

Richard Layard is one of the world’s leading labor economists and a member of the House of Lords.  David M. Clark is professor of psychology at the University of Oxford. Layard and Clark were the main drivers behind the UK’s Improving Access to Psychological Therapies program.

Read chapter one here.