Introducing the new video trailer for The Quotable Feynman

Nobel Prize-winning physicist Richard P. Feynman (1918–88) is widely known for his scientific genius. But during his life, he became as famous for the wit, wisdom, and lucidity of his popular lectures and writings as for his fundamental contributions to physics. We are pleased to present the new video trailer for The Quotable Feynman, including approximately 500 quotations carefully selected by his daughter, Michelle Feynman, from his spoken and written legacy:

Check out chapter one here.





Announcing the First Annual Humanities Lecture with the New York Institute for the Humanities at NYU

Humanities lecturePrinceton University Press and the New York Institute for the Humanities at New York University are pleased to announce the first Annual Humanities Lecture. With the aim of highlighting both the value and the relevance of the humanities, this new lecture will be given annually in New York by notable figures from a wide range of fields and will explore humanistic topics and themes.

The inaugural lecture will be given at New York University on October 29 by Thomas Laqueur, the Helen Fawcett Professor of History at the University of California, Berkeley and author of the forthcoming book The Work of the Dead: A Cultural History of Mortal Remains.

Laqueur’s lecture, “The Work of the Dead: How Caring for Mortal Remains has Shaped Humanity,” will speak to compelling questions: Why do we as a species care for the bodies of our dead?  What work do the dead do for the living?  How do specific ways of disposing of the dead and specific memorial practices create communities, nations, and culture more generally?

According to Princeton University Press Director Peter Dougherty: “We at PUP welcome the opportunity to collaborate with the esteemed New York Institute for the Humanities in sponsoring this new annual lecture to showcase the work of the world’s most exciting and important scholars working in the humanities, beginning next month with historian Thomas Laqueur’s fascinating study of how care for the dead has shaped humanity. We are also extremely pleased at the prospect of an annual PUP cosponsored event in New York City, a capital of global culture and intellect.”

The Annual Humanities Lecture follows in the footsteps of Princeton in Europe, a PUP-sponsored lecture that has been presented annually in London since launching at the London Book Fair in 2011.

According to New York Institute for the Humanities Director Eric Banks: “I’m delighted that Princeton University Press has decided to partner with the New York Institute for the Humanities in endowing an annual series of lectures in the humanities. For four decades, the Institute has offered public programming and weekly fellows’ luncheons that have explored a range of issues that engage the role of the humanities in our broader civic life. Princeton University Press has long published some of the most provocative and thought-provoking titles, of interest, not only to scholars but to an intellectually curious larger readership. We are excited to inaugurate our collaboration with a scholar of the caliber of Thomas Laqueur, who has combined erudition, public engagement, and a flair for style as a writer in a unique body of work. We look forward to developing our annual lecture series over the years to come to continue to highlight intriguing and far-reaching work in the humanities.”

The Work of the DeadProfessor Laqueur’s October 29 lecture is cosponsored by the College of Arts and Science at New York University and will be free and open to the public, though preregistration is required. The lecture begins at 6:30 p.m at Hemmerdinger Hall, 100 Washington Square East, New York University.

About Princeton University Press

Princeton University Press is an independent publisher with close connections, both formal and informal, to Princeton University. As such it has overlapping responsibilities to the University, the academic community, and the reading public and a fundamental mission to disseminate scholarship both within academia and to society at large. Founded in 1905, it has offices in Princeton, Oxford, and Beijing.

About the New York Institute for the Humanities

Established in 1976, the New York Institute for the Humanities at New York University is a leading forum for promoting the exchange of ideas between academics, professionals, politicians, diplomats, writers, journalists, musicians, painters, and other artists in New York City. Comprising more than two hundred distinguished fellows, the NYIH serves to facilitate conversations about the role of the humanities in public life.


Introducing the new video trailer for The Princeton Companion to Applied Mathematics

We are pleased to present the new video trailer for The Princeton Companion to Applied Mathematics. Modeled on the popular Princeton Companion to Mathematics, this is an indispensable resource for undergraduate and graduate students, researchers, and practitioners in other disciplines seeking a user-friendly reference book. Check out the video in which editor Nicholas Higham, Richardson Professor of Applied Mathematics at The University of Manchester, talks about the major ideas covered in this expansive project, which includes nearly 200 entries organized thematically and written by an international team of distinguished contributors.

Woodrow Wilson Papers to go online with new partnership

Princeton University Press, The Woodrow Wilson Presidential Library, and the University of Virginia Press Partner To Create Digital Edition of THE PAPERS OF WOODROW WILSON

wilson portraitPRINCETON UNIVERSITY PRESS (PUP), the WOODROW WILSON PRESIDENTIAL LIBRARY(WWPL), and the UNIVERSITY OF VIRGINIA PRESS (UVaP) announced today an agreement to create THE PAPERS OF WOODROW WILSON DIGITAL EDITION (PWWDE). Edited by Arthur S. Link and published by Princeton University Press, The Papers of Woodrow Wilson will be digitized and made available online in UVaP’s Rotunda American History collection, with the permission of PUP and the generous support of friends of the WWPL.

“This partnership among two university presses and a presidential library harnesses the intellectual investment and publishing expertise represented in the great documentary editions of the last century,” said Peter Dougherty, Director of Princeton University Press, “and makes them more accessible and valuable through this century’s digital technologies.”

Princeton University Press published the print edition of the Papers of Woodrow Wilson, consisting of 69 volumes with a 5-part index, between 1966 and 1994. The edition’s editor, Arthur Stanley Link (1920–1998),Edwards Professor of History Emeritus at Princeton University, was widely considered a pioneer in the field of documentary editing as well as the foremost scholar of Woodrow Wilson, the 28th President of the United States. The Link edition includes Wilson’s personal correspondence, academic works, and speeches, minutes of the Paris Peace Conference, and diary entries of close associates Edward House, Cary Grayson, and Josephus Daniels, totaling approximately 38,400 documents from a vast range of government and academic sources. The most significant sources of Wilson material in the published volumes are stored in the Library of Congress and Princeton University.  The Journal of American History described the Papers of Woodrow Wilson as “an unprecedented illumination of Wilson’s activities and ideas.”

Woodrow Wilson is one of the most accessible presidents in American history due to the precise organization, annotation, and indexing of the Papers of Woodrow Wilson. The Rotunda digital edition will enhance discovery of Wilson’s papers by adapting the documents, annotation, and indexing created by Arthur Link and his fellow editors to a state-of-the-art electronic publishing platform. “Inclusion in Rotunda not only provides the most up-to-date digital publishing technology,” said Mark H. Saunders, Director of UVaP. “It puts the Wilson material in conversation with other important figures in American political history, from the Founding Fathers to participants in the civil rights and Vietnam eras. Comparing the view of Thomas Jefferson, Woodrow Wilson, and Lyndon Johnson on a subject such as race or presidential power can provide new scholarly insights that were hard to imagine in an age of analog information or siloed digital repositories.”

The WWPL anticipates digitizing further materials in its collection and the collection of the Library of Congress, including a selection of Wilson’s correspondence during World War I and documents from Wilson’s later public career, and making them available in the coming years. “There is a vast array of important Wilson material that could not be included due to the constraints of a print edition,” said Don W. Wilson, President of WWPL Foundation. “Those documents will now be made available to scholars, students, and the interested public.” Additional collections held at Princeton University, among them letters between Woodrow Wilson and his wives, Edith and Ellen, and his daughter Jessie Sayre, would also be added to the PWWDE.

Press contacts:

Emily Grandstaff :

Debra Liese:

An interview with Nicholas Higham on The Princeton Companion to Applied Mathematics

Higham jacket

We are excited to be running a series of posts on applied mathematics by Nicholas Higham over the next few weeks. Higham is editor of The Princeton Companion to Applied Mathematics, new this month. Recently he took the time to answer some questions about the book, and where the field is headed. Read his popular first post on color in mathematics here.

What is Applied Mathematics?

NH: There isn’t any generally agreed definition, but I rather like Lord Rayleigh’s comment that applied mathematics is about using mathematics to solve real-world problems “neither seeking nor avoiding mathematical difficulties”. This means that in applied mathematics we don’t go out of our way to consider special cases that will never arise in practice, but equally we do not sidestep genuine difficulties.

What is the purpose of The Companion?

NH: The Companion is intended to give an overview of the main areas of applied mathematics, to give examples of particular problems and connections with other areas, and to explain what applied mathematicians do—which includes writing, teaching, and promoting mathematics as well as studying the subject. The coverage of the book is not meant to be exhaustive, but it is certainly very broad and I hope that everyone from undergraduate students and mathematically interested lay readers to professionals in mathematics and related subjects will find it useful.

What is an example of something aspect of applied mathematics that you’ve learned while editing the book?

NH: Applied mathematics is a big subject and so there are many articles on topics outside my particular areas of expertise. A good example concerns applications of computational fluid dynamics in sport. An article by Nicola Parolini and Alfio Quarteroni describes the mathematical modeling of yachts for the America’s cup. The designer wishes to minimize water resistance on the hull and maximize the thrust produced by the sails. Numerical computations allow designs to be simulated without building and testing them. The article also describes mathematical modeling of the hi-tech swimsuits that are now banned from competition. The model enables the benefit of the suits on race times to be estimated.

The Companion is about 1000 pages. How would advise people to read the book.

NH: The book has a logical structure, with eight parts ranging from introductory material in Part I, the main areas of applied mathematics in Part IV (the longest part), through to broader essays in the final part. It is a good idea to start by reading some of the articles in Part I, especially if you are less familiar with the subject. But a perfectly sensible alternative approach is to select articles of interest from the table of contents, read them, and follow cross-references. Or, you can just choose a random article and start reading—or simply follow interesting index entries! We worked very hard on the cross-references and index so an unstructured approach to reading should lead you around the book and allow you to discover a lot of relevant material.

What was the hardest thing about editing The Companion?

NH: The hardest aspect of the project was ensuring that it was completed in a reasonable time-frame. With 165 authors it’s hard to keep track of everything and to to ensure that drafts, revisions, and corrected proofs are delivered on time.

How much of the book did you write?

NH: I wrote about 100 of the 1000 pages. This was great fun, but it was some of the hardest writing I’ve done. The reason is partly that I was sometimes writing about topics that I don’t normally write about. But it was also because Companion articles are quite different from the papers I’m used to writing: they should have a minimal number of equations and formal statements of theorems, lots of diagrams and illustrations, and no citations (just Further Reading at the end of the article).

How did you choose the cover?

NH: We considered many different ideas. But after a lot of thought we settled on the motor boat picture, which captures the important topics of fluid mechanics, waves, and ocean, all of which are covered in the book in a number of articles.

What is the most unexpected article?

NH: Perhaps the article Mediated Mathematics: Representations of Mathematics in Popular Culture and Why These Matter by sociologist of education Heather Mendick. She discusses the way mathematics is represented in numerous TV shows and films.

What would you be doing if you hadn’t become a mathematician?

NH: I’d be playing a Hammond B3 organ in a jazz or blues band. I’m a keen musician and played keyboards semi-professionally for many years, starting in my teens.

How did you go about organizing the book?

NH: I recruited five Associate Editors with expertise in different areas and we met and planned out the eight parts of the book and the articles, along with a list of authors to invite. We looked for authors who are leading international experts in their field and are at the same time excellent expositors. Signing up the 165 authors was quite a long process. We were able to find authors for almost every article, so just a very small number had to be dropped. In some cases the authors suggested changes of content or emphasis that we were happy to agree with.

What range of readers is The Companion aimed at?

NH: The target audience for The Companion is very broad. It includes mathematicians at undergraduate level or above, students, researchers, and professionals in other subjects who use mathematics, and mathematically interested lay readers. Some articles will also be accessible to students studying mathematics at pre-university level.

Why not just seek information online? Why is there a need for a book?

NH: When Princeton University Press asked me to edit The Companion they told me that reference books still have great value. Many people have trouble navigating the vast amount of information available online and so the need for carefully curated thematic reference works, written by high calibre authors, is as great as ever. So PUP’s experience is that print is definitely not dead, and indeed my own experience is that I have many books in PDF form on my computer, but if I want to read them seriously I use a hard copy.

How have you ensured that the book will not go out of date quickly?

NH: This was a major consideration. This was a five and a half year project and we wanted to make sure that the book will still be relevant 10, 20, or 50 years from now. To do that we were careful to choose articles on topics that have proven long-term value and are not likely to be of short-term interest. This is not to say that we don’t cover some relatively new, hot topics. For example, there are articles on compressed sensing (recovering sparse, high-dimensional data from a small number of indirect measurements) and on cloaking (hiding an object from an observer who is using electromagnetic, or other, forms of imaging, as in Harry Potter or Romulan space ships in Star Trek), both of which are areas that have grown tremendously in the last decade.

What sort of overview of applied mathematics does the book give?

NH: Applied mathematics is a huge subject, so we cannot cover everything in 1000 pages. We have tried to include the main areas of research as well as key underlying concepts, key equations, function and laws, as well as lots of example of applied mathematics problems. The examples range from the flight of a golf ball, to robotics, to ranking web pages. We also cover the use of applied mathematics in other disciplines such as engineering, biology, computer science, and physics. Indeed the book also has a significant mathematical physics component.

Where is the field going?

NH: Prior to the 20th century, applied mathematics was driven by problems in astronomy and mechanics. In the 20th century physics became the main driver, with other areas such as biology, chemistry, economics, engineering, and medicine also providing many challenging mathematical problems from the 1950s onwards. With the massive and still growing amounts of data available to us in today’s digital society information, in its many guises, will be an increasingly important influence on applied mathematics in the 21st century.

To what extent does The Companion discuss the history of applied mathematics?

NH: We have an excellent 25-page article in Part I titled The History of Applied Mathematics by historians of mathematics June Barrow-Green and Reinhard Siegmund-Schultze. Many articles contain historical information and anecdotes. So while The Companion looks to the future it also gives an appreciation of the history of the subject.

How do you see the connections between applied mathematics and other disciplines developing?

NH: Applied mathematics is becoming ever more interdisciplinary. Many articles in The Companion illustrate this. For example,

  • various facets of imaging feature in several articles, including those on compressed sensing, medical imaging, radar, and airport baggage screening,
  • the article on max-plus algebras shows how what may seem like an esoteric area of pure mathematics has applications to all kinds of scheduling processes,
  • the article on the spread of infectious diseases shows the value of mathematical models in epidemiology,
  • several articles show how mathematics can be used to help understand the earth’s weather and climate, focusing on topics such as weather prediction, tsunamis, and sea ice.

What are you thoughts on the role of computing in applied mathematics?

NH: Computation has been a growing aspect of applied mathematics ever since the first stored program computer was invented here in Manchester. More and more it is the case that numerical computations and simulations are used in tandem with, or even in place of, the classical analysis that relies just on pen and paper. What I find particularly interesting is that while the needs of mathematics and of science in general have, naturally, influenced the development of computers and programming languages, there have been influences in the other direction. For example, the notation for the ceiling and floor functions that map a real number to the next larger or smaller integer, respectively, was first introduced in the programming language APL.

Of course numerical computations are expressed in terms of algorithms, and algorithms are ubiquitous in applied mathematics, and strongly represented in the book.

Do you have any views on ensuring the correctness of work in applied mathematics?

NH: As the problems we solve become every more complicated, and the computations we perform run for longer and longer, questions about the correctness of our results become more important. Applied mathematicians have always been good at estimating answers, perhaps by an asymptotic analysis, so we usually know roughly what the answer should look like and we may be able to spot gross errors. Several particular aspects of treating correctness are covered in The Companion.

Uncertainty quantification is about understanding how uncertainties in the data of a problem affect the solution. It’s particularly important because often we don’t know the problem data exactly—for example, in analyzing groundwater flow we don’t know the exact structure of what lies under the ground and so have to make statistical assumptions, and we want to know how these impact the computed flows.

A different aspect of correctness concerns the reproducibility of our computations and treats issues such as whether another scientist can reproduce our results and whether a computation on a high-performance computer will produce exactly the same answer when the computation is repeated.

All of these issues are covered in multiple articles in the book.

Nicholas J. Higham is the Richardson Professor of Applied Mathematics at The University of Manchester. Mark R. Dennis is professor of theoretical physics at the University of Bristol. Paul Glendinning is professor of applied mathematics at The University of Manchester. Paul A. Martin is professor of applied mathematics at the Colorado School of Mines. Fadil Santosa is professor of mathematics at the University of Minnesota. Jared Tanner is professor of the mathematics of information at the University of Oxford.

Facebook YEAR OF BOOKS live Q&A with authors of “Portfolios of the Poor”

Collins jacketPortfolios of the Poor: How the World’s Poor Live on $2 a Day by Daryl Collins, Jonathan Morduch, Stuart Rutherford & Orlanda Ruthven is a recent choice by Mark Zuckerberg for his Year of Books project. An unusual investigation of the staggering problem of global poverty, the authors conducted year-long interviews with impoverished villagers and slum dwellers in Bangladesh, India, and South Africa. This morning the authors are taking part in a live Q&A on the Year of Books Facebook page to share the surprising and systematic methods these families used to survive on an income that is, for many, unimaginably small.

Mark Zuckerberg announced the book’s selection on his personal Facebook page with the following thoughts:

It’s mind-blowing that almost half the world — almost 3 billion people — live on $2.50 a day or less. More than one billion people live on $1 a day or less.

This book explains how these families invest their money to best support themselves.

I hope reading this provides some insight into ways we can all work to support them better as well.

You can follow the discussion here.

Paul Krugman hosting free discussion at Cooper Union with authors of THRIVE

Thrive jacketTonight, Nobel-prize-winning economist Paul Krugman will host a free public discussion at Cooper Union with Richard Layard & David M. Clark, co-authors of Thrive: How Better Mental Health Care Transforms Lives and Saves Money. Richard Layard discussed the book with Tom Keene on Bloomberg Surveillance here, and both authors answered some questions on mental health policy for the PUP blog here.

Mental illness is a leading cause of suffering in the modern world. In sheer numbers, it afflicts at least 20 percent of people in developed countries. It reduces life expectancy as much as smoking does, accounts for nearly half of all disability claims, is behind half of all worker sick days, and affects educational achievement and income. There are effective tools for alleviating mental illness, but most sufferers remain untreated or undertreated. What should be done to change this? In Thrive, Richard Layard and David Clark argue for fresh policy approaches to how we think about and deal with mental illness, and they explore effective solutions to its miseries and injustices.

Richard Layard is one of the world’s leading labor economists and a member of the House of Lords. He is the author of Happiness: Lessons from a New Science, which has been translated into twenty languages.

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.

Paul Krugman is an author and economist who teaches at Princeton, the London School of Economics and elsewhere. He won the 2008 Nobel Prize in economics. He is also an Op-Ed columnist for the New York Times.

September 29, 2015 @ 6:30 pm – 9:30 pm
The Great Hall
Foundation Building
7 E 7th St, New York, NY 10003

Please RSVP here.

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.

Behind every meal you eat, there is a story

Louise Fresco, president of Wageningen University and Research Centre in the Netherlands and author of Hamburgers in Paradise, talks about that story here:


Patterns are math we love to look at

This piece by Frank Farris was originally published on The Conversation.

Frank A Farris, Santa Clara University

Why do humans love to look at patterns? I can only guess, but I’ve written a whole book about new mathematical ways to make them. In Creating Symmetry, The Artful Mathematics of Wallpaper Patterns, I include a comprehensive set of recipes for turning photographs into patterns. The official definition of “pattern” is cumbersome; but you can think of a pattern as an image that repeats in some way, perhaps when we rotate, perhaps when we jump one unit along.

Here’s a pattern I made, using the logo of The Conversation, along with some strawberries and a lemon:

Repeating forever left and right.
Frank A Farris, CC BY-ND

Mathematicians call this a frieze pattern because it repeats over and over again left and right. Your mind leads you to believe that this pattern repeats indefinitely in either direction; somehow you know how to continue the pattern beyond the frame. You also can see that the pattern along the bottom of the image is the same as the pattern along the top, only flipped and slid over a bit.

When we can do something to a pattern that leaves it unchanged, we call that a symmetry of the pattern. So sliding this pattern sideways just the right amount – let’s call that translation by one unit – is a symmetry of my pattern. The flip-and-slide motion is called a glide reflection, so we say the above pattern has glide symmetry.

A row of A’s has multiple symmetries.
Frank A Farris, CC BY-ND

You can make frieze patterns from rows of letters, as long as you can imagine that the row continues indefinitely left and right. I’ll indicate that idea by …AAAAA…. This row of letters definitely has what we call translational symmetry, since we can slide along the row, one A at a time, and wind up with the same pattern.

What other symmetries does it have? If you use a different font for your A’s, that could mess up the symmetry, but if the legs of the letter A are the same, as above, then this row has reflection symmetry about a vertical axis drawn through the center of each A.

Now here’s where some interesting mathematics comes in: did you notice the reflection axis between the As? It turns out that every frieze pattern with one vertical mirror axis, and hence an infinite row of them (by the translational symmetry shared by all friezes), must necessarily have an additional set of vertical mirror axes exactly halfway between the others. And the mathematical explanation is not too hard.

Suppose a pattern stays the same when you flip it about a mirror axis. And suppose the same pattern is preserved if you slide it one unit to the right. If doing the first motion leaves the pattern alone and doing the second motion also leaves the pattern alone, then doing first one and then the other leaves the pattern alone.

Flipping and then sliding is the same as one big flip.
Frank A Farris, CC BY-ND

You can act this out with your hand: put your right hand face down on a table with the mirror axis through your middle finger. First flip your hand over (the mirror symmetry), then slide it one unit to the right (the translation). Observe that this is exactly the same motion as flipping your hand about an axis half a unit from the first.

That proves it! No one can create a pattern with translational symmetry and mirrors without also creating those intermediate mirror symmetries. This is the essence of the mathematical concept of group: if a pattern has some symmetries, then it must have all the others that arise from combining those.

The surprising thing is that there are only a few different types of frieze symmetry. When I talk about types, I mean that a row of A’s has the same type as a row of V’s. (Look for those intermediate mirror axes!) Mathematicians say that the two groups of symmetries are isomorphic, meaning of the same form.

It turns out there are exactly seven different frieze groups. Surprised? You can probably figure out what they are, with some help. Let me explain how to name them, according to the International Union of Crystallographers.

The naming symbol uses the template prvh, where the p is just a placeholder, the r denotes rotational symmetry (think of a row of N’s), the v marks vertical qualities and the h is for horizontal. The name for the pattern of A’s is p1m1: no rotation, vertical mirror, no horizontal feature beyond translation. They use 1 as a placeholder when that particular kind of symmetry does not occur in the pattern.

What do I mean by horizontal stuff? My introductory frieze was p11g, because there’s glide symmetry in the horizontal directions and no symmetry in the other slots.

Another frieze pattern, this one based on a photo of a persimmon.
Frank A Farris, CC BY-ND

Write down a bunch of rows of letters and see what types of symmetry you can name. Hint: the persimmon pattern above (or that row of N’s) would be named p211. There can’t be a p1g1 because we insist that our frieze has translational symmetry in the horizontal direction. There can’t be a p1mg because if you have the m in the vertical direction and a g in the horizontal, you’re forced (not by me, but by the nature of reality) to have rotational symmetry, which lands you in p2mg.

A p2mg pattern based on some of the same raw materials as our first frieze pattern.

It’s hard to make p2mg patterns with letters, so here’s one made from the same lemon and strawberries. I left out the logo, as the words became too distorted. Look for the horizontal glides, vertical mirrors, and centers of twofold rotational symmetry. (Here’s a funny feature: the smiling strawberry faces turn sad when you see them upside down.)

One consequence of the limitation on wallpaper groups is that honeybees cannot make combs with fivefold symmetry.
LHG Creative Photography, CC BY-NC-ND

In my book, I focus more on wallpaper patterns: those that repeat forever along two different axes. I explain how to use mathematical formulas called complex wave forms to construct wallpaper patterns. I prove that every wallpaper group is isomorphic – a mathematical concept meaning of the same form – to one of only 17 prototype groups. Since pattern types limit the possible structures of crystals and even atoms, all results of this type say something deep about the nature of reality.

Ancient Roman mosaic floor in Carranque, Spain.
a_marga, CC BY-SA

Whatever the adaptive reasons for our human love for patterns, we have been making them for a long time. Every decorative tradition includes the same limited set of pattern types, though sometimes there are cultural reasons for breaking symmetry or omitting certain types. Did our visual love for recognizing that “Yes, this is the same as that!” originally have a useful root, perhaps evolving from an advantage in distinguishing edible from poisonous plants, for instance? Or do we just like them? Whyever it is, we still get pleasure from these repetitive patterns tens of thousands of years later.

Frank A Farris, Associate Professor of Mathematics, Santa Clara University. He is the author of Creating Symmetry.

This article was originally published on The Conversation. Read the original article.


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