#ThanksEinstein: J.P. Ostriker on Einstein and the wonder of pure thought

Einstein meme

Questions with No Reply

J. P. Ostriker

J.P. Ostriker is an astrophysicist and the co-author of Heart of Darkness, which tells the saga of humankind’s quest to unravel the deepest secrets of the universe: dark matter and dark energy. Here is his story about how an Einstein thought experiment he encountered as a teenager changed his life.

When I was a high school student I drove my teachers crazy with incessant and insatiable curiosity about the natural world. Next to our pictures in the yearbook, one of the teachers had added a line for each student and for me it was “I thought of questions that have no reply.”

And for the questions that I had that my teachers could not or would not answer, I went to books. Einstein wrote several of these that were accessible to high school students, and they fascinated me. I remember a “thought experiment” presented in one of them: A scientist sets up an exquisite laboratory on a train and tests both Newton’s laws of mechanics and Maxwell’s laws of electricity and magnetism. And, hypothetically, one finds that both are correct to arbitrary precision.

train image, copyright: phildaintThen the train begins to move and E shows that, since the laws transform differently with the velocity of the observer, they can no longer both be true! Therefore one (or both) theories must be false.

This amazed me. No experiment was necessary. Pure thought was all that was needed and any high school student who thought about it could have come to the same conclusion as Einstein, and could have invented special relativity to solve the problem! I thought that this was wonderful, truly wonderful. I resolved that I would pursue physics and think about simple and fundamental matters. It looked easy.

Well, needless to say it was not always easy, but it has always been fun. I’m thankful I had access to Einstein’s popular books when I was a teenager with more questions than answers.

Jeremiah P. Ostriker is professor of astrophysical sciences at Princeton University. He is author, with Simon Mitton, of Heart of Darkness: Unraveling the Mysteries of the Invisible Universe. His books include Formation of Structure in the Universe and Unsolved Problems in Astrophysics (Princeton).


Train tracks image from Shutterstock, copyright: phildaint

Of Law and Love: Jon D. Levenson on THE LOVE OF GOD

The Love of God jacket

The love of God is perhaps the most essential element in Judaism—but also one of the most confounding. In biblical and rabbinic literature, the obligation to love God appears as a formal commandment. Yet most people today think of love as a feeling. How can an emotion be commanded? Jon D. Levenson, Albert A. List Professor of Jewish Studies at Harvard University, recently took the time to answer questions about his new book, The Love of God: Divine Gift, Human Gratitude, and Mutual Faithfulness in Judaism.

How did you first get the idea of writing a book on the love of God in Judaism?

JL:  To love God is actually taken as a formal commandment in the rabbinic sources, and the passages in Deuteronomy that mandate it appear in texts that Talmudic law requires to be recited every day of the year. So, for anyone who aspires to be a practicing Jew, the subject comes up rather obviously and regularly—even if many people in that category don’t give it much thought. But one of my professors in my doctoral program many moons ago was the distinguished Assyriologist and Biblicist William L. Moran, whose classic article on “The Ancient Near Eastern Background of the Love of God in Deuteronomy,” published in the Catholic Biblical Quarterly in 1963, had a huge effect on me when I read it my first year in graduate school.

In brief, Professor Moran shows that the idiom of the love of God (that is, the people Israel’s love for God) originates in ancient treaties, or covenants, and has to do with the lesser party’s exclusive and undivided service of the greater party. In an earlier book, Sinai and Zion: An Entry into the Jewish Bible, I dealt with this same transposition (as I put it) from the realm of politics and international relations to the realm of theology and national identity. In the first chapter of The Love of God, I try to draw out a number of further implications of Professor Moran’s argument but also to make some refinements on it and to enter respectful dissents from it.

What kind of refinements and dissents do you have in mind?

JL: For one thing, although I totally agree that “love” has a technical, legal meaning in Deuteronomy and elsewhere in the Hebrew Bible (or Old Testament), I also agree with those who insist that the technical usage doesn’t preclude the emotional or affective connotations that the word has for most people. To put it differently, sometimes loving may simply mean loyal service and faithful obedience, but we need to guard against over-generalizing from such passages, just as we need to guard against interpreting “love” in this context as a purely subjective, emotional state without normative behavioral correlates. I try to show that in Deuteronomy God falls in love with Israel—I don’t think the language is exclusively technical but rather it connotes passion—and demands a response that has its own affective character. In other words, we have to reckon with both an outward and an inward dimension, though recognizing that the inward-outward dichotomy is not itself native to ancient Near Eastern culture and can lead interpreters of the Bible astray. In fact, the movement is in both directions. Actions awaken and deepen emotions, and emotions generate and make sense of actions.

I also stress more than Moran did the connection of the two meanings of “the love of God”—the love God receives and the love he gives. Both are found in Deuteronomy, though the rhetorical situation of that book leads it to emphasize the love the people Israel must give to God. An important part of the covenantal idea is that the greater party (in this case, God) has endowed the lesser party with gifts—like all true gifts, they are undeserved—and this should motivate the recipient to respond not only with gratitude and humility but also with acts of service. There is something in a gift that provokes reciprocity, and that reciprocity deepens the relationship of the two parties. This is what I mean by the words in the subtitle, “Divine Gift, Human Gratitude, and Mutual Faithfulness.” Simply to treat the norms of the Torah—the mitzvot as they are called in Hebrew—as impersonal injunctions divorced from that living relationship with that very personal God is to misunderstand them profoundly. In my experience, doing so makes the Torah itself seem incoherent and antique. It is a huge blunder to try to force the biblical commandments altogether into the Procrustean bed of ethics, morals, folkways, or whatever. In this book, I try to lay out the alternatives that the classical biblical and rabbinic sources offer to these very modern, and in my opinion not very successful, strategies.

I noticed that in your second chapter, “Heart, Soul, and Might,” you deal at length with suffering and martyrdom. Why?

JL: That chapter focuses on the ancient rabbinic interpretations of the famous commandment to “love the LORD [which is actually a proper name] your God with all your heart and with all your soul and with all your might.” The rabbis stress the unconditionality and supremacy of such love and consider ways in which a person might be tempted to prefer something else to that arduous commandment. So long as one puts self-interest above grateful and loving service, he or she has fallen short of the ideal. Part of the problem is that the biblical sources themselves (especially Deuteronomy again) promise all manner of good things to one who loves God, observing his commandments, and the opposite to one who fails to do so, breaking faith and breaching covenant. So, the rabbis are eager to stress that the hope for reward and the fear of punishment must not be the basis of the service. The Jew must persevere in his or her service; he or she must work at loving God even in the hardest and most frightful of situations. Here, the horrific martyrdom of Rabbi Akiva around 135 CE serves as a key object lesson.

One implication that I draw out from this is that the foundational narratives in which the God of Israel acts a generous benefactor establish the continuing norm. In other words, that situation overrides the immediate circumstances in which Jews find themselves—even circumstances of brutal persecution and death. The love that his gifts called forth was to remain firmly in place even when the gifts appear to have been withdrawn, replaced, in fact, by unspeakable hardship. This, in turn, leads me to reflect on the relationship of the unconditional to the conditional both in the love relationship of God and the Jewish people in these sources and in love relationships more generally.

It’s only in your third chapter that you develop the idea of a romance between God and the people Israel. Tell us why you didn’t do so earlier.

JL: The reason is simple: love in the ancient world—and really in the modern as well—isn’t exclusively or even primarily sexual in nature, even though sexual love commands disproportionate attention at the moment, especially in the fashions of academia. The Hebrew Bible has many metaphors for the God-Israel relationship: suzerain and vassal, king and subject, father and son, shepherd and flock, etc. In order to understand the marital metaphor—God as husband, Israel as wife—it is important to have dealt with some of these others, especially the suzerain-vassal metaphor, beforehand. Otherwise, we’re likely to read all kinds of contemporary assumptions about sexuality and gender into literature that operates on completely different understandings. In particular, if we don’t grasp the dynamics of covenant, we’ll find God’s actions in that marriage to be bizarre and patently indefensible.

For example, in our modern American world, if the wife gives her affections and her body to other men, a common solution lies in divorce: the two parties just go their separate ways, hoping to end up with partners more to their liking. But that is exactly what doesn’t happen in the marital metaphor as the biblical prophets develop it! Here again, the element of unconditionality is crucial. God doesn’t walk away from the relationship, even if Israel has done so. He doesn’t replace her or even take a second wife (remember, ancient Israel had no legal or moral problem with polygamy). He punishes her, even harshly, but this turns out to be a preparation for a restoration of the marriage. The punishment is a consequence of his passionate love for her and faithfulness to her. Ultimately, it evinces a renewal of her love for him, in turn. All this, of course, is foreign to us and doesn’t comport with how we think human husbands ought to act. But that doesn’t authorize us to miss the underlying theology, satisfying ourselves with a simple characterization of it as immoral or whatever.

Later, in the case of the rabbis, the speakers in the great biblical love poem, the Song of Songs, come to be seen as God and Israel, again in their ideal state of mutual fidelity. That’s not the plain sense of the book taken as a stand-alone composition, but within the context of the rest of biblical literature, it is a very natural—and very productive and very moving—way to read it. Nowhere does one see the power of the love of God more dramatically than in the rabbinic interpretations of the Song of Songs. That biblical book enabled the rabbis to interpret the whole history of the God-Israel relationship as a romance—an extremely important move in the history of Jewish thought.

In your last two chapters, you deal with medieval and modern materials. What changes in the Middle Ages and modernity?

JL: The medieval thinkers continue the rabbinic legacy but also add to it. For example, they sometimes interpret the female speaker of the Song of Songs as the individual soul. They also provide practical guidance about how to attain the love of God. For them again, that’s something to work on; it doesn’t just happen to you. It’s also in the Middle Ages that we first see the sustained interaction of the rabbinic legacy with philosophy. In one case, that of Maimonides, the philosopher waxes passionate about humans’ love for God but has problems with the idea that God loves humans, or anything else. That’s because he believes all human language to describe God is akin to idolatry; a God who’s susceptible to love seems imperfect to Maimonides. But I show that other medieval Jewish philosophers develop sophisticated arguments against him on this. To them, to love is a sign of perfection, not imperfection, and God’s love—even his passionate, unpredictable love—is a sign of his greatness.

In modern times, momentous changes appear with emancipation and secularization. Now one can leave the Jewish community without having to convert to Christianity or anything else. This makes observance of the mitzvot (commandments) just one lifestyle option among many; it’s no longer a social necessity or an obvious response to a divine will. Martin Buber, one of the two thinkers I examine in my last chapter, believes deeply in a personal God, but he also argues that whether the commandments in the Torah really reflect his will has to be determined by each individual on a case-by-case basis. So, ultimately and perhaps also unwittingly, Buber opts for the disconnected, autonomous self of modern liberalism. But his friend and collaborator Franz Rosenzweig comes to see God’s love as something that transforms and enlarges the self and impels it towards acceptance of the mitzvot—though without the support of old and now discredited historical claims.

Will the reader find surprises in The Love of God? Do you say things that contradict what people are likely to expect?

JL: Yes, I think so. For one, most people have an image of law as cold, confining, and impersonal, and, in the case of Judaism, two millennia of Christian polemicizing about “Pharisaism” and the like continue to take their toll, even among people who don’t identify as Christian. The notion that God’s gift of the Torah and the Jews’ careful observance of it are both acts of intense love will surprise those who instinctively see law and love as necessarily in opposition or tension.

In my previous Princeton University Press book, Inheriting Abraham: The Legacy of the Patriarch in Judaism, Christianity, and Islam, I tried to shed new light on the vexing question of the chosenness, or election, of the Jews, and I’ve continued that, but with a somewhat different tack, in the new book. When chosenness is put into a framework of justice, the lack of objective merit of the chosen becomes a huge obstacle. But love isn’t based on objective assessments of merit. It has an unpredictable or irrational dimension, what today people call the “chemistry” the two parties experience. And love, because it’s relational, is necessarily particular. There’s room in Judaism for the idea that God loves all humanity, but his love for the people Israel cannot be identified with his love for everybody.

Actually, in speaking about this subject around the country, I’ve found that many people are unaware that the idea of a personal relationship with a loving God is part of Judaism at all. Partly, this is because of the legacy of the Christian caricature of the Old Testament as a book of harsh legalisms enforced by an angry, judgmental God (though there have long been many, many Christians who don’t subscribe to that notion). Partly, it’s because modern Judaism has tended to stress the mitzvot as manifested in ethics and social action over than the traditional theological claim that the mitzvot make a connection with the personal, loving God.

Finally, I think many readers will be surprised by the stress in medieval sources on solitary devotion and contemplation and on abstinence as key elements in Jewish spirituality. Almost all versions of modern Judaism have long been propounding a view of Judaism as communal, active, and world-affirming, but that is a gross over-simplification of the older tradition. As for abstinence or asceticism, one must always ask what the positive gain is that the renunciation or self-control at issue delivers. In the case of Baḥya ibn Paquda, one of the medieval thinkers examined in chapter 4, the asceticism serves the interest of increasing one’s love of God, which for Baḥya is the “consummation of the spiritual life,” as I entitle that chapter.

There may be other surprises, but to find out what they are, people will just have to read the book!

Jon D. Levenson is the Albert A. List Professor of Jewish Studies at Harvard University. His many books include The Love of God, as well as Resurrection and the Restoration of Israel, which won the National Jewish Book Award, and Inheriting Abraham and Creation and the Persistence of Evil (both Princeton).













Publishing for a digital age: A word from Peter Dougherty #UPWeek


Scholarly Kitchen ran a terrific article yesterday on the important contributions of university presses, and how many are redefining their role in the digital age. At Princeton University Press, the past year has brought the successful launch of a major intellectual, digital, and global undertaking. A word from our director, Peter Dougherty:

EinsteinProbably the most stunning development at Princeton University Press is the successful launch of our Digital Edition of The Collected Papers of Albert EinsteinThe Digital Einstein Papers has given scientists and historians alike all over the world free access to the first thirteen volumes of the Einstein Papers, one of the most important intellectual archives in all of scholarly publishing.  According to Kenneth Reed, PUP’s Digital Production Manager, usage statistics suggest that the Digital Einstein Papers has been a truly successful global project:

“Since its launch, there have have been 2.7 million page views from across the world. Outside the United States, Germany and India represent the second and third most visitors to the site. Visitors view an average of over nine pages per visit, and returning visitors are 75%. Mobile users account for over 30% of the site usage, which is not surprising given the global appeal of the site.”

The Digital Einstein Papers also represents a global success by way of being a great international and cross-institutional collaboration, drawing on the talents and effort of colleagues not only at PUP, but at our partner institutions, The Einstein Papers Project at Caltech, the Albert Einstein Archive at the Hebrew University in Jerusalem, and the online platform firm, Tizra.  PUP will add new volumes as they appear roughly every eighteen months.

—Peter Dougherty

Read what these other university presses have to say on the future of scholarly publishing, from the value of acquisitions work and the meaning of gatekeeping in the digital era, to how university presses are picking up the slack left by trade publishers:

Indiana University Press

Oxford University Press

George Mason University Press

University Press of Colorado

University Press of Kansas

UNC Press

West Virginia University Press

Johns Hopkins University Press

University of Georgia Press

Children’s Literature for Grownups #ReadUp

Have you ever found yourself returning to a book considered “children’s literature?” There’s just something about our favorite children’s books that can draw us in. What’s with the magnetism? Children’s books are a part of our literary foundation, and some of the best ones hold a special place in our hearts. Or is it something more?

k10538Remember reading Alice’s Adventures in Wonderland? First published in 1865, PUP is publishing a new edition in honor of the 150th anniversary, illustrated by none other than the famous surrealist, Salvador Dalí.

The whimsical world of Wonderland holds a special charm for both children and adults. You can bet more adults will be purchasing this item for themselves than for their children, both for the sense of nostalgia and for the promise of new things that children’s books inevitably hold. This promise is much more prominent in children’s books than it is in adult books because children’s books are written differently. They are written with the idea that they will likely be revisited, often including multiple layers and facets. Just ask Neil Gaiman. In a recent article, Gaiman notes that “When I’m writing for kids, I’m always assuming that a story, if it is loved, is going to be re-read. So I try and be much more conscious of it than I am with adults.”

Re-reading a children’s book as an adult brings the gift of new perspective. Would you read A Wrinkle in Time or The Hobbit the same way now as you did when you were 10? We might find and identify common themes, or develop sympathies for characters we formerly loved to hate. When we revisit these stories later in life, we read them with a new lens, one altered by experience and time, often picking up on new and interesting tidbits that we never knew existed. This is particularly true of fairy tales. If these Disney-esque stories are meant for children, why do we, as adults, enjoy them so much? The answer probably lies in their adult origins. One of PUP’s most popular recent books is The Original Folk and Fairy Tales of the Brothers Grimm: The Complete First Edition. The first edition. Take note.k10300

AndreaDezso_BrothersGrimm3As David Barnett states in The Guardian in a piece titled, Adult content warning: beware fairy stories, “Wilhelm and Jacob Grimm . . . did not set out to collect the stories that bear their name in order to entertain children. They were primarily collectors and philologists, who assembled their tales as part of a life’s work. . . . And they were surprised when the adults who bought their collections of fairy tales to read to their children began to complain about the adult nature of the content.”

These stories were not polished and sanitized until much later. Originally, they were filled with violence and other adult content. (As evidenced by the picture on the above left, by Andrea Dezsö, featured in PUP’s The Original Folk and Fairy Tales of the Brothers Grimm). This image is from a tale entitled Herr Fix-It-Up. Herr Fix-It-Up must complete tasks denoted by a lord and king in order to win the lord his princess bride. One of the tasks is to kill a unicorn that’s been “causing a great deal of damage.” By today’s standards, beheading of unicorns is hardly the stuff of children’s tales, but these tales are more sociological accounts than children’s stories, reflecting the sensibilities of the time period and place in which they were written.

UntitledOthk10312er “children’s” books expand on this very aspect of fairy tales, including The Fourth Pig by Naomi Mitchison. Mitchison takes many of the classic tales of our childhood including Hansel and Gretel and The Little Mermaid and re-imagines them for an older audience.

As a fairly new member of the press, it never occurred to me that some titles on our list would include some of my old favorites. What children’s books do you love more as an adult?


You can take a tour of the gorgeous interior of Alice’s Adventures in Wonderland here:



Feature image by Steve Czajka – https://www.flickr.com/photos/steveczajka/11392783794

Frontispiece designed by Gertrude Hermes


New video trailer for THE SECRET OF OUR SUCCESS by Joe Henrich

Henrich jacketThe premise of Survivor, in which 16 previously unacquainted humans were routinely abandoned in forbidding locations to brave the elements, was no doubt wildly popular because of the simple fact that we humans, on our own, are virtually helpless. We aren’t particularly adept at building shelter, fending off predatory animals, and the thought of having to procure a meal with nothing but our bare hands and our wits is enough to make many of us run for our nearest Whole Foods. How on earth have we managed to dominate the globe when we can’t survive in the wild? As Joseph Henrich points out, human groups are far less hopeless than lone individuals, and our collective brains have produced ingenious technologies, sophisticated languages, and complex institutions that have not only allowed us to inhabit diverse environments, but have actually shaped biology. Check out the trailer for his new book, The Secret of our Success: How Culture is Driving Human Evolution, Domesticating our Species, and Making Us Smarter.




Feynman on the historic debate between Einstein & Bohr

The golden age of quantum theory put many of the greatest minds of the 20th century in contact with some of the most significant scientific and philosophical questions of their era. But it also put these minds in contact with one another in ways that have themselves been a source of curiosity and ongoing scientific debate.

Richard Feynman and Albert Einstein, two towering geniuses of their time, were both as revered for their scientific contributions as they were beloved for their bursts of wisdom on a wide range of subjects. It’s hard not to wonder just what these men thought of one another. Princeton University Press, which published The Ultimate Quotable Einstein in 2010 publishes The Quotable Feynman this fall. The book includes reflections by Feynman on Einstein, from his memorable mannerisms to his contributions to some of the most heated debates in 20th century science.Feynman quote

Perhaps because of the gap between their career high points, (Einstein died in 1955; Feynman didn’t receive his Nobel Prize until 1965), there are no verified quotes where Einstein alludes to Feynman or his expansive body of work. But Feynman had made observations on the older physicist, several of which revolve around Einstein’s famous 1927 public debate with Niels Bohr on the correctness of  quantum mechanics. Central to the debate was this question: Were electrons, light, and similar entities waves or particles? In some experiments they behaved like the former, and in others, the latter.

In an attempt to resolve the contradictory observations, Einstein proposed a series of “thought experiments”, which Bohr responded to. Bohr essentially took the stance that the very act of measuring alters reality, whereas Einstein insisted that reality exists, independent of the act of measurement. Key to the philosophy of science, the dispute between the two giants is detailed by Bohr in “Discussions with Einstein on Epistemological Problems in Atomic Physics”. Richard Feynman is quoted as commenting on the debate:Feynman quote 2

An Einstein Encyclopedia contains a section on the Einstein-Bohr debates, as well as a wealth of other information on Einstein’s career, family, friends. There is an entire section dedicated to righting the various misconceptions that swirl around the man, and another on his romantic interests (actual, probable, and possible).

In spite of their differences, Bohr and Einstein were friends and shared great respect for each others’ work. Until Einstein’s death 3 decades later, they continued their debates, which became, in essence, a debate about the nature of reality itself.  feynman quote 3

Check out other new Einstein publications this fall, including:

An Einstein Encyclopedia
The Road to Relativity

Why Calculus Will Save You from the Zombie Apocalypse

To survive a zombie apocalypse, one will need more than instinct and short term solutions – one will need logic and, most importantly, math. A thought-out plan comprised of sophisticated calculus equations will ensure long-term safety objectives. Thankfully, Zombies and Calculus by Colin Adams colorfully illustrates the critical implementation of calculus components when going head-to-head with zombies. Adams demonstrates how a professor and his students successfully exercise calculus to survive the attacks of zombies who not only disrupt their calculus class (the horror!), but are also out for human flesh.

Here are a few need-to-knows:

Zombies travel approximately at one yard per second – a constant derivative.

A derivative of a function is its rate of change. If a function is changing quickly, its derivate will be high, while if a function is changing slowly, its derivate will be low. Adams explains that we can measure the function’s rate of change through the steepness of the tangent line. zombies and calculus rate of change
Since speed is defined as distance divided by time, one can calculate the speed required to get from Point A to Point B in a specific time, while being able to evade any unwanted visitors (zombies). Keep in mind — speed tends to vary (not for zombies, remember, they travel in a constant derivative!), so the derivate of the function has the potential to increase or decrease. Using these simple formulas, one is able to plan out the distance, time, and speed needed to outrun these deadly predators.

It’s hard to crack a zombie’s skull. It’s easier to knock a zombie unconscious.

As detailed in Zombies and Calculus, the amount of force necessary to crack a human skull is 10,000 newtons (a newton is a measurement for force that equals 1 kilogram meter per second squared). Adams offers an example: if a baseball is going 90 miles per hour (40.2 meters/second), weighs 5 ounces (0.145 kilograms), and comes into contact with a head for .007 seconds, its force can be calculated through:Screen Shot 2015-10-29 at 4.44.31 PMSo since a baseball, with said specifications, can only create approximately 800 newtons, imagine how much force is needed to produce 10,000 newtons! When attacking a zombie with force, do not try to go for the easy kill — rather play strategically by knocking the zombie unconscious with a sudden sharp blow to the head. This will create a dramatic head jerk, causing the brain to get knocked around in the cranial cavity, thus causing a short circuit. The benefit of knocking a zombie unconscious, of course, is additional planning and escape time!

Zombies pursue in a radiodrome path.

Like a dog pursues a rabbit, a zombie pursues its human prey. A zombie will follow its prey’s path at the prey’s given location at that specific instant. In a scene from Zombies and Calculus, (pause to imagine it), a Dean is running towards the safe haven of an academic building in a straight line. However, a zombie is present and begins to pursue the Dean, always having its tangent vector pointing at the Dean. The zombie is going to travel to wherever the Dean is in that current moment. Screen Shot 2015-10-29 at 4.39.23 PM

Since zombies are incapable of developing an efficient plan, the zombie does not run at a diagonal towards the academic building, which would cut-off the dean’s path. Instead of recognizing the Dean’s travel pattern or destination, the zombie is chasing the dean like a dog chasing a bunny’s tail to the rabbit hole. If only the dog knew that its radiodrome procedure was flawed, the dog would be able (with a speed higher than the rabbit) to cut-off the rabbit at its hole and claim victory. If dogs were to catch on, there would probably be fewer bunnies hopping around.

Cold-blooded creatures are unable to regulate their body heat.

Like other cold-blooded creatures, zombies hibernate. A zombie’s body temperature will decrease according to the differential equation that guides the temperature change of an object placed in a space with a different temperature (so for instance, if a zombie with a temperature of 60 degrees is placed a room of 30 degrees.) According to Newton’s Law of Cooling (remember Newton from discussing the measurement ‘newton’ for force?), the temperature of a body’s rate of change is proportional to the difference between the present temperature of that body and the ambient temperature (basically, the temperature of its surroundings). Given as a function of time, the zombie’s temperature (where Tg is the specific location):Screen Shot 2015-10-29 at 4.42.31 PMThe larger the contrast of temperatures, the faster the body temperature will drop. As the characters in the book discover, if there is a zombie apocalypse, it might be time to consider a move to our friendly neighbor to the north, Canada.


Zombies and CalculusTo discover more lifesaving tips, fun and entertaining mathematical applications, and learn the fate of the brave calculus professor and his students, read Colin Adam’s  Zombies and Calculus. Just in case the zombie apocalypse does occurs (maybe tomorrow?) it should be comforting to know there’s a mathematical guide to survival on your bookshelf.

(Stanley) Fish Food for Thought: Cultural Reflections

Welcome to Part 5 of PUP’s Stanley Fish series, Fish Food for Thought. All selections are excerpted from Fish’s new book, Think Again: Contrarian Reflections on Life, Culture, Politics, Religion, Law, and Education.


Fish Food for Thought

Part 5: Cultural Reflections

3.1 Professor Sokal’s Bad Joke

May 21, 1996

Fish on why Professor Sokal is wrong about sociologists.

When Professor Sokal declares that “theorizing about ‘the social construction of reality’ won’t help us find an effective treatment for AIDS,” he is at once right and wrong. He is right that sociologists will never do the job assigned properly to scientists. He is wrong to imply that the failure of the sociology of science to do something it never set out to do is a mark against it, (95)

3.3 Dorothy and the Tree: A Lesson in Epistemology

April 25, 2011apples

Fish on why Dorothy picked an apple from a speaking tree without thinking.

Another way to put this is to say that changes of mind tend to be local and piecemeal, not systemic. Wholesale conversions like Paul’s on the road to Damascus do occur, but more often a change will affect only a small corner of one’s conceptual universe. After her conversation with the tree, Dorothy may no longer place trees and persons in completely different compartments, but much that she used to think, she will still think, (107)

3.5 What Did Watson the Computer Do?

February 21, 2011

computerFish on the difference between computers and humans when following the rules.

The inability or unwillingness of human beings to follow the rules or be
content with their guidance is not a weakness but a strength; it is the strength of being able to adjust when the rules have nothing helpful to say or produce absurd results in a situation the rule-markers did not anticipate. Only a fool will persist in adhering o a rule or set of directives when its application is clearly counterintuitive and even disastrous… The computer I am writing this column on is a fool,

3.7 Can I Put You on Hold?

November 16, 2009

Fish on the annoying little things everyone encounters.

There is a class of utterances that, when encountered, produces irritation, distress and, in some cases, the desire to kill… Mine is a three-word announcement on the TV Screen, “To Be Continued,” which says, “I know that you have become invested in this story and are eager to find out how it ends, but you’re going to have to wait for a few days or a week or a month or forever.” In the great order of things, it is only a minor inconvenience, but it is experience as a deprivation; you were banking on something and now it has been taken away, (120)

3.10 Favoritism is Good

January 7, 2013

Fish on why favoritism is sometimes the preferred thing.

Favoritism – giving more than an even break to your own kind – is not a distortion of judgment, but the basis of judgment. And being impartial to those who are a part of you – through blood or creed or association or profession (think of the thin blue line) – is not to be virtuous but to be ungrateful and disloyal, more concerned with hewing to some abstract principle of respect for all than with discharging the obligations that come along with your most intimate relations, (129-130)


Anat Admati on the stark reality of post-2008 banking

Admati-BankersNewClothes_pbkThere are a few lessons still unlearned from the 2008 financial recession, according to Anat Admati, co-author of The Banker’s New Clothes: What’s Wrong with Banking and What to Do about it. “After such a major trauma, we want to believe all is well again,” Admati wrote in her Bloomberg piece on Monday. “But the reality in banking is different and stark.”

Admati turns her attention to former chair of the Federal Reserve, Ben Bernanke’s new book, The Courage to Act. While she applauds Bernanke for appreciating the significance of “equity capital in protecting the economy from financial shocks”, she is skeptical of the supposed progress resulting from regulations implemented by the Federal Reserve post-2008. Admati writes in Bloomberg:

A clear lesson is that banks need much more capital, specifically in the form of equity. In this area, the reforms engendered by the crisis have fallen far short. Regulators focus on “risk-weighted” and accounting-based capital ratios that, among their many flaws, rely on banks to assess the riskiness of their assets. Using off-balance-sheet accounting, derivatives and other tools, banks have become adept at manipulating these ratios. Annual stress tests aren’t much better: They employ the same flawed measures and cannot reliably predict how an actual crisis, which may come from an unexpected direction, would play out in an opaque and interconnected financial system.

Admati argues that a larger amount of equity given to banks would offer substantial benefits to society with minimal costs, halting the precarious practice of creditors allowing the largest banks in the world to borrow money under the assumption of government intervention in dire situations.

Read the rest of Admati’s analysis here .

Anat Admati is the George G. C. Parker Professor of Finance and Economics at Stanford’s Graduate School of Business.

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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