Anurag Agrawal: The migration patterns of the monarch butterfly

by Anurag Agrawal

The plight of monarch butterflies if often in the news: many scientists around the world are working hard to understand their annual migratory cycle. How do the monarchs produced during summer in the northern reaches of America contribute to the overwintering population in Mexico? The origin of monarch butterflies that make it to Mexico has been hotly debated because it has profound consequences for how we approach monarch conservation.

A new study is remarkable in its use of historical collections over the past 40 years and modern isotopic analysis. The scientists address the most important regions in the U.S. for producing monarch butterflies that actually make it to Mexico. This sort of data has been very difficult to come by and there has been a lot of speculation. As outlined in my new book from Princeton, the midwest has dominated discussions as being the most important region in the U.S. for monarchs. In the study, the authors find that the Midwest contributes a whopping 38% of the butterflies that make it to Mexico.

Monarchs

The regions studied by Flockhart et al. separated to highlight their relative areas

I would add two points for discussion. The first is that the areas of land that the authors designated as Midwest, Northeast, etc., seemed totally reasonable, but also somewhat arbitrary. In particular, an issue arises when you consider that, as designated in the paper, the Midwest is about 2.5 times as big as the Northeast. It is therefore not surprising that the Midwest produces about 2.5 times as many butterflies that make it to Mexico (38% vs 15%). In other words, the butterflies that make it to Mexico have about an equal probability of coming from the Midwest and the Northeast when land area is considered. Yet another way to think about this is that two states that are about equal sizes in the two regions (for example, Indiana and Maine) will on average produce about the same number of butterflies that make it to Mexico.

Monarch2

The annual migratory cycle of the monarch butterfly from Monarchs and Milkweed. In my past research, we have opted for a three simple regions defined by the butterfly generations.

Quite interestingly, the North Central area (including my home in the Finger Lakes region of NY) is slightly more important for butterfly production given its size. When you factor out the area of the Great Lakes (where there are no monarch caterpillars), the area of North Central is small (36% of the size of the Midwest). Thus, about 20% more butterflies per square mile come out of the North Central than the Midwest or Northeast. Where does this leave us?  The agricultural Midwest is certainly important, but perhaps not as important as previously thought.

The other point worth thinking about is that the Southwest (read: Texas) comes out as big in terms of area (equal to the Midwest) and relatively less important in terms of contributing butterflies (11% of the total).  The critical importance of the Gulf States including Texas, however, is not in the last generation of butterflies produced in fall that migrate south, but rather in the first generation of butterflies that are produced in spring and that migrate north to the Midwest and Northeast.  In other words, the Gulf States are absolutely critical for the annual migratory cycle, even if that is not where fall migrants are produced.  Without a spring generation there, the Midwest and Northeast would be empty!  In chapter 9 of the book, I summarize the critical importance of Gulf States not only for the spring, but also in providing floral resources for fall migrating butterflies.

I hope we see more studies like this in the future, as it provides new important information and was inspiring to read.

AgrawalAnurag Agrawal is a professor in the Department of Ecology and Evolutionary Biology and the Department of Entomology at Cornell University. He is the author of Monarchs and Milkweed: A Migrating Butterfly, a Poisonous Plant, and Their Remarkable Story of Coevolution.

Jerald Podair: The story of Dodger Stadium

Dodger Stadium, which opened in Los Angeles on April 10, 1962, was the single most controversial building project in the city’s modern history. It was constructed in Chavez Ravine, a neighborhood overlooking downtown, whose Mexican American residents had been dispersed for a public housing project that was never built. In 1957, the city of Los Angeles attracted the Brooklyn Dodgers by promising team owner Walter O’Malley Chavez Ravine for his new stadium on favorable terms. O’Malley agreed to build Dodger Stadium at his own expense.

Critics of the contract between the city and the Dodgers under which the land was transferred labeled it a “giveaway.” Over the next five years they fought a multi-front battle to have the contract voided. They initiated a ballot referendum challenging the contract’s validity that failed by a razor-thin margin and brought a series of taxpayer lawsuits that were initially successful but eventually reversed by the Supreme Court of California. There was also a racially charged eviction of Mexican American homeowners from the Chavez Ravine land by city authorities.

The battle over Dodger Stadium was a civic war that divided Los Angeles in half. But it did not divide the city along the lines we might expect, especially if we adopt the essentialist view of race and class that seems to be in vogue today. It is tempting to view the Dodger Stadium story as a simple one of rich white people on one side and poor people of color on the other. But the truth is more complicated. There is no question that the city’s Latino community was deeply wounded by the Chavez Ravine removals. The evictions have been the subject of plays, films, and songs, and are credited with inspiring the Chicano movement in Los Angeles. They remain a subject of bitter memory today. But a majority of residents of the city’s heavily Latino East Los Angeles council district defied their own anti-contract councilman to vote in favor of the Dodger Stadium deal in the closely contested ballot referendum. Latinos have also constituted the Dodgers’ most loyal and enduring fan base through the years. Fair-weather fans come and go, but the Latino community remains Dodger Blue. The divided character of the Latino response to the Dodger Stadium controversy thus defeats attempts to cast it solely in racial terms.

The most vociferous and passionate opponents of the Dodger Stadium deal, in fact, were white. They were the people the late California historian Kenneth Starr has called the “Folks”: middle-class homeowners, often with Midwestern or Southern roots, who lived in the peripheral areas of the city and harbored conservative cultural and economic sensibilities. Fearful of resources in their outlying communities being siphoned off for the benefit of large-scale undertakings downtown, the Folks were fiercely opposed to the Dodger Stadium project. Their campaign to keep it from being built allied them with the evicted residents of Chavez Ravine and their supporters in the city’s Latino community. Both groups united around the rights of property owners, no matter how humble, to keep what was rightfully theirs.

The coalition in favor of the stadium contract also defied simplistic race-and-class based expectations. Conservative downtown commercial and financial leaders lined up behind the stadium project, as did more liberal representatives of the city’s “Westside,” a center of the building-and-loan, construction, and entertainment sectors with a substantial Jewish population. Both shared an interest in revitalizing a downtown core whose civic and cultural amenities lagged significantly behind those of Los Angeles’s chief rival cities, New York and San Francisco.

These elites were joined by a crucial ally: the city’s African American community, which backed the stadium project overwhelmingly. The Dodgers, were, of course, closely associated with civil rights, having brought Jackie Robinson to the major leagues in 1947. Robinson was a Los Angeles-area native and his endorsement of the Dodger Stadium project was critical in gaining African American support for it.

The battle over Dodger Stadium thus produced interracial, cross-class alliances on both sides of the partisan divide. We can, of course, interpret these alignments as counterintuitive and even aberrational. But this view implies that identity is destiny, and that our political configurations can always be explained by the simple binaries of race and class. At Dodger Stadium, interest politics overcame identity politics. And that may not be a bad thing. In an identity-obsessed contemporary political environment, Dodger Stadium’s example of boundary-crossing allegiances is one we should take to heart.

PodairJerald Podair is professor of history and the Robert S. French Professor of American Studies at Lawrence University in Appleton, Wisconsin. He is a recipient of the Allan Nevins Prize, awarded by the Society of American Historians for “literary distinction in the writing of history.” He is the author of City of Dreams: Dodger Stadium and the Birth of Modern Los Angeles.

Favorite Lines: Fiona Sze-Lorrain

In honor of National Poetry Month, we’ve asked some of the poets who have published in the Princeton Series of Contemporary Poets to highlight and discuss a single line in their poetry that has special significance. Today Fiona Sze-Lorrain, author of The Ruined Elegance, talks about inspiration while writing “Midnight Almanac” (The Ruined Elegance, 34-35). Check this space weekly for more favorite lines throughout the month of April.

“All the parallel windows, different emptiness.”

—from “Midnight Almanac” in The Ruined Elegance (2016)

a

Lorrain

The image does not serve as an illustration.

b

This isn’t a favorite line of mine—it seems difficult for me to believe in the longevity of a favorite line—but one that has stopped me on a few occasions to think further about our current society. More precisely, the way we humans have chosen to live or exist, how we use the virtual space, for instance, to make ourselves “visible” or “audible” without necessarily engaging, face to face, with one another . . . and in what direction our civilization may be heading: if “we” —or should I say, the collective mass, their governments and institutions—continue to prioritize the economy and the industry, conform to social labels and homogeneity, or hide behind—as well as within—pigeonholed identities and comfort zones.

Human existence might become just that: a commodity.

Each to his/her own box or screen—

Perhaps this is why romanticizing solitude is a consolation prize for alienation, both physical and emotional.

c

Are our eyes still the windows to our souls?

d

When I came up with this verse, I had no specific address in mind.

I was, in fact, critiquing the possibilities of mediocrity. Being mediocre is safe. Banality works as a survival instinct.

I am also criticizing the hypocrisy of I agree, but . . .

Even windows now must look standardized.
jdjhbdjbagbdfbdfjvbdfhjbdgbrrOtherwise, we can’t (won’t) recognize them as windows.

LorrainFiona Sze-Lorrain is a poet, literary translator, editor, and zheng harpist. The author of two previous books of poetry in English, My Funeral Gondola and Water the Moon, she also writes and translates in French and Chinese. She lives in Paris. She is the author of The Ruined Elegance: Poems.

Anurag Agrawal: Monarch overwintering

by Anurag Agrawal

The estimates of the monarch butterfly overwintering population were announced February 9th by WWF Mexico. The butterflies are so dense at their dozen or so mountain-top clustering sites that overwintering butterflies cannot be individually counted. Instead, the area of forest that is densely coated with butterflies (at about 5,000 butterflies per square meter looking up into the canopy) is estimated as a measure of monarch abundance. Butterflies arrive in Mexico around early November and stay until March.

butterflies

This winter season (2016-2017), there were approximately 2.9 hectares of forest occupied with dense monarchs (somewhere in the neighborhood of 300,000 million overwintering butterflies). This estimate is down 27% compared to last year. Nonetheless, the previous two years were a 600% increase over the all-time low recorded in the winter of 2013-2014.

butterflies

Where does this leave us? This year’s population was higher than predicted by many. The season started with a late spring storm that killed an estimated 5-10% of monarchs in March 2016, and many reported low numbers of adults last summer. Nonetheless, the lower numbers this season compared to last are within the range of year-to-year variation, and overall, the population seems to be relatively stable over the past decade. With these 24 years of data, there are various ways to plot and assess the trends. Below I have plotted the four year averages for six periods beginning in 1992. Any way you slice it, the trend has been negative, and the population is not nearly what it once was. Nonetheless, the downward trend seems to have lessened this last period. Is this the new norm? How dangerously low are these numbers? And what can we do to reverse the trend?

butterfly

AgrawalAnurag Agrawal is a professor in the Department of Ecology and Evolutionary Biology and the Department of Entomology at Cornell University. He is the author of Monarchs and Milkweed: A Migrating Butterfly, a Poisonous Plant, and Their Remarkable Story of Coevolution.

 

 

 

butterfly

Anurag Agrawal on Monarchs and Milkweed

AgrawalMonarch butterflies are one of nature’s most recognizable creatures, known for their bright colors and epic annual migration from the United States and Canada to Mexico. Yet there is much more to the monarch than its distinctive presence and mythic journeying. In Monarchs and Milkweed, Anurag Agrawal presents a vivid investigation into how the monarch butterfly has evolved closely alongside the milkweed—a toxic plant named for the sticky white substance emitted when its leaves are damaged—and how this inextricable and intimate relationship has been like an arms race over the millennia, a battle of exploitation and defense between two fascinating species. Check the PUP blog each Monday for new installments in our “Monarch Monday” blog series by Anurag Agrawal.

What makes monarchs and milkweeds so special?

AA: Monarchs and milkweed are remarkable creatures, they’re on a wild ride! From the monarch’s perspective, its only food as a caterpillar is the milkweed plant. This makes them highly specialized, highly evolved, and very picky eaters indeed. They’re actually not that unique among butterflies, but they are extreme. Milkweed does everything in its power to defend itself against being eaten by monarchs. They make sandpapery leaves, toxins that can stop a human heart, and a thick poisonous goo that can glue an insect’s mouth shut. Again, although milkweed is not unique among plants, it is extreme. In what is called a coevolutionary arms race, monarchs and milkweed have been continually evolving over the eons to keep up with each other. As such, they have a lot to teach us about the way nature works, the way plants and animals interact, and about the various paths that evolution can take different species. And this is all to say nothing of the monarch’s spectacular annual migration, often over 3,000 miles flown by individual butterflies, using the sun to navigate, and having stored away milkweed’s poisons to protect themselves from being eaten by birds. Monarchs and milkweeds are royal representatives of all interacting species.

Why did you write this book?

AA: After studying monarchs and milkweed myself for over 15 years, I felt like I had a lot I wanted to share, especially with non-scientists and nature lovers. Monarchs and milkweed are such fascinating organisms, and yet so much of their beautiful biology is not widely known. I also wrote the book because there are areas of my own knowledge about monarchs and milkweed that I wanted to immerse myself in, but that I had not yet done any research on. So as an author, getting to visit the overwintering sites in Mexico, to study the population decline of monarch butterflies, and to understand their mating rituals were all fascinating detours from my everyday research life at Cornell University. The book was incredibly fun to write, and getting to work with artists and historians made it all the more rich. I hope that anybody that has an appreciation for nature, an interest in science, or just a curiosity about the ecology of plants and butterflies will enjoy this book. Working on this project has surely altered the course of my own research, the classes I teach, and how I see the natural world.

Why have you highlighted some of the personalities of the scientists studying monarchs and milkweeds in this book?

AA: One of the most amazing things about monarchs and milkweeds is the scientists who have studied them. They were such remarkable characters, especially those pioneering studies back in the 1950s: tremendously creative, sometimes competitive, and with some of their discoveries worthy of a Nobel prize. Getting to know them, both from their discoveries and their personalities, and how they interacted, has enriched my appreciation for how science is done. It also highlights the meandering and sometimes serendipitous nature of discoveries. I wanted to share the thrill of science, its ups and downs, and the process by which it is done with the curious reader.

Can you share one of your ah-ha! moments from studying monarchs and milkweeds?

AA: One of my favorites was from when I was an assistant professor at the University of Toronto. One day I was eating lunch by myself in a small downtown garden. Just by chance, I happened to sit on a bench beneath a very tall milkweed plant that had a very large monarch caterpillar feeding away. Without giving away all the details, that one hour encounter, in the middle of a city with 3 million people, changed my perspective on monarchs and milkweed forever. It was so unlikely an event, perhaps 1 in a 1,000 that a butterfly had been flying by and happened to lay an egg on this Toronto milkweed, and then a further 1 in 100 chance of that egg hatching and surviving to be that large caterpillar that I could watch it. And probably a 1 in a million event that I would happen to be eating lunch there, that day, to observe the events. In biology one has to work hard, be patient, and occasionally get very lucky! Throughout my studies on monarchs and milkweed, I have had tremendous luck in encountering wonderful biology that has had profound consequences.

Is the monarch butterfly going extinct?

AA: The answer to this very important and timely question is both simple and complex. On the simple side, there is no way the monarch butterfly is going extinct anytime soon. Having said that, the butterfly, and especially the long-distance migration that occurs every fall from Southern Canada and the USA, all the way to Mexico’s highlands in Michoacán, is indeed declining at a rapid pace, and we should all be worried about the sustainability of the annual migration. There’s so much information and misinformation floating around in the news these days about the causes of the monarchs decline. What I’ve tried to do in the book is outline the best knowledge that we have to date and to examine the facts critically, so we can really understand what might be going on. Unfortunately, we don’t have all the answers, but we can reject some of the most prominent explanations for the population decline of the monarch butterfly. As I argue in the book, planting milkweed certainly won’t hurt, but it is unlikely to save the monarchs annual migratory cycle. It is perhaps ironic that I spend eight chapters of the book discussing and detailing the importance of milkweed for monarchs, and nothing could be more true than their intertwined and intense evolutionary battle, but at this stage, and thinking about their conservation, it does not appear that milkweed is what is limiting the monarch’s population. Monarchs will persist for a very long time, but given that they are migratory butterflies that taste their way across North America, their declining population is something we must try to understand. Much more than the monarch is at stake, these butterflies are sentinels for the health of our continent!

Anurag Agrawal is a professor in the Department of Ecology and Evolutionary Biology and the Department of Entomology at Cornell University. He lives in Ithaca, New York. He is the author of Monarchs and Milkweed: A Migrating Butterfly, a Poisonous Plant, and Their Remarkable Story of Coevolution.

Keith Devlin: Fibonacci introduced modern arithmetic —then disappeared

More than a decade ago, Keith Devlin, a math expositor, set out to research the life and legacy of the medieval mathematician Leonardo of Pisa, popularly known as Fibonacci, whose book Liber abbaci has quite literally affected the lives of everyone alive today. Although he is most famous for the Fibonacci numbers—which, it so happens, he didn’t invent—Fibonacci’s greatest contribution was as an expositor of mathematical ideas at a level ordinary people could understand. In 1202, Liber abbaci—the “Book of Calculation”—introduced modern arithmetic to the Western world. Yet Fibonacci was long forgotten after his death. Finding Fibonacci is a compelling firsthand account of his ten-year quest to tell Fibonacci’s story. Devlin recently answered some questions about his new book for the PUP blog:

You’ve written 33 math books, including many for general readers. What is different about this one?

KD: This is my third book about the history of mathematics, which already makes it different from most of my books where the focus was on abstract concepts and ideas, not how they were discovered. What makes it truly unique is that it’s the first book I have written that I have been in! It is a first-person account, based on a diary I kept during a research project spread over a decade.

If you had to convey the book’s flavor in a few sentences, what would you say?

KD: Finding Fibonacci is a first-person account of a ten-year quest to uncover and tell the story of one of the most influential figures in human history. It started out as a diary, a simple record of events. It turned into a story when it became clear that it was far more than a record of dates, sources consulted, places visited, and facts checked. Like any good story, it has false starts and disappointments, tragedies and unexpected turns, more than a few hilarious episodes, and several lucky breaks. Along the way, I encountered some amazing individuals who, each for their own reasons, became fascinated by Fibonacci: a Yale professor who traced modern finance back to Fibonacci, an Italian historian who made the crucial archival discovery that brought together all the threads of Fibonacci’s astonishing story, an American math professor who fought against cancer to complete the world’s first (and only) modern language translation of Liber abbaci, and the widow who took over and brought his efforts to fruition after he lost that battle. And behind it all, the man who was the focus of my quest. Fibonacci played a major role in creating the modern commercial world. Yet he vanished from the pages of history for five hundred years, made “obsolete,” and in consequence all but forgotten forever, by a new technology.

What made you decide to write this book?

KD: There were really two key decisions that led to this book. One was deciding, back in the year 2000, to keep a diary of my experiences writing The Man of Numbers. My first history book was The Unfinished Game. For that, all I had to do was consult a number of reference works. It was not intended to be original research. Basic Books asked me to write a short, readable account of a single mathematical document that changed the course of human history, to form part of a series they were bringing out. I chose the letter Pierre De Fermat wrote to his colleague Blaise Pascal in 1654, which most experts agree established modern probability theory, in particular how it can be used to predict the future.

In The Man of Numbers, in contrast, I set out to tell a story that no one had told before; indeed, the consensus among the historians was that it could not be told—there simply was not enough information available. So writing that book would require engaging in a lot of original historical research. I had never done that. I would be stepping well outside my comfort zone. That was in part why I decided to keep a diary. The other reason for keeping a record was to ensure I had enough anecdotes to use when the time came to promote the book—assuming I was able to complete it, that is. (I had written enough popular mathematics books to appreciate the need for author promotional activities!)

The second decision, to turn my diary into a book (which only at the end found the title, Finding Fibonacci), came after The Man of Numbers was published in 2011. The ten-year process of researching and writing that book had turned out to be so rich, and so full of unexpected twists and turns, including several strokes of immense luck, that it was clear there was a good story to be told. What was not clear was whether I would be able to write such a book. All my other books are third-person accounts, where I am simply the messenger. In Finding Fibonacci, I would of necessity be a central character. Once again, I would be stepping outside my comfort zone. In particular, I would be laying out on the printed page, part of my inner self. It took five years and a lot of help from my agent Ted Weinstein and then my Princeton University Press editor Vickie Kearn to find the right voice and make it work.

Who do you expect will enjoy reading this book?

KD: I have a solid readership around the world. I am sure they will all read it. In particular, everyone who read The Man of Numbers will likely end up taking a look. Not least because, in addition to providing a window into the process of writing that earlier book, I also put in some details of that story that I did not fully appreciate until after the book had been published. But I hope, and in fact expect, that Finding Fibonacci will appeal to a whole new group of readers. Whereas the star of all my previous books was a discipline, mathematics, this is a book about people, for the most part people alive today. It’s a human story. It has a number of stars, all people, connected by having embarked on a quest to try to tell parts of the story of one of the most influential figures in human history: Leonardo of Pisa, popularly known as Fibonacci.

Now that the book is out, in one sentence if you can, how would you summarize writing it?

KD: Leaving my author’s comfort zone. Without a doubt. I’ve never been less certain how a book would be received.

DevlinKeith Devlin is a mathematician at Stanford University and cofounder and president of BrainQuake, an educational technology company that creates mathematics learning video games. His many books include The Unfinished Game: Pascal, Fermat, and the Seventeenth-Century Letter That Made the World Modern and The Man of Numbers: Fibonacci’s Arithmetic Revolution. He is the author of Finding Fibonacci: The Quest to Rediscover the Forgotten Mathematical Genius Who Changed the World.

Evgeny Finkel on his new book, Ordinary Jews

Focusing on the choices and actions of Jews during the Holocaust, Ordinary Jews: Choice and Survival During the Holocaust examines the different patterns of behavior of civilians targeted by mass violence. Relying on rich archival material and hundreds of survivors’ testimonies, Evgeny Finkel presents a new framework for understanding the survival strategies in which Jews engaged: cooperation and collaboration, coping and compliance, evasion, and resistance. Rather than looking at the Holocaust as a whole, Ordinary Jews focuses on three Jewish communities—those of Minsk, Kraków, and Białystok—to try to understand why Jews in these communities had very different responses when faced with similar Nazi policies. Recently, Finkel took the time to answer some questions about his new book.

The Holocaust is one of the most researched episodes of human history. What new angle does your book contribute?

EF: It is true that the Holocaust had been extensively researched, but we still know very little about why European Jews chose different responses to the genocide—why some rebelled against the Nazis while others collaborated with them; why some escaped while others did nothing. This book is different from the existing research in that it focuses exclusively on the Holocaust’s Jewish victims and on what made individual Jews choose different survival strategies in response to the Nazi genocide. Instead of looking at the Holocaust as a whole or focusing on one place, as historians usually do, I compare three Jewish communities—those of Minsk, Kraków, and Białystok—and try to understand why, when faced with similar Nazi policies, the Jews in these communities reacted in dramatically different ways.

So what could the Jews do during the Holocaust and why did they behave in different ways?

EF: I identify four main strategies used by the Jews: cooperation and collaboration with the Germans; coping with the danger and attempting to survive while staying put; evasion via escape and hiding among the non-Jews; and armed resistance to the Nazis. What I discovered is that the choice of a particular survival strategy was shaped more by the Jews’ pre-WWII lives and the regimes under which they lived—decades before the Holocaust—than by what the Nazis did. People who were politically active before the Holocaust were more likely to choose cooperation with or resistance to the Nazis. Jews who were more integrated into the non-Jewish society were much more likely to escape and hide, and the stronger the pre-WWII local Jewish community was, the higher was the number of people who chose coping.

But eventually, no matter what the Jews did they almost all died?

EF: True, in those parts of Eastern Europe that were occupied by the Nazis most Jews did not survive the Holocaust, but this general observation obscures important local dynamics: for instance, those who chose evasion were more likely to survive than those who stayed put. Even more so, buying fake documents and going to Germany proper (and often to Berlin!) as a Polish or Russian laborer was likely the most successful survival strategy. The tragedy was that the evasion strategy was not available to everyone because it heavily depended on the Jews’ pre-WWII lives and interactions with non-Jewish people. Even very basic contacts such as having non-Jewish janitors in one’s workplace or apartment building could sometimes be the difference between death and survival. Speaking Polish or Russian without a Yiddish accent was much more important than having “non-Jewish looks” or being rich. For minorities, integration into the majority’s culture takes decades. In places where pre-WWII government encouraged such policies, Jews were more likely to have the tools to successfully escape and hide than in places where segregation between the Jews and the Christians was almost complete. In Kraków, the Austro-Hungarian Empire allowed and encouraged the Jews’ integration before Hitler was even born. The Empire itself collapsed twenty years before the WWII, but the legacy of its policies allowed quite a few Jews to successfully hide and eventually survive. In Białystok, neither the Russian Empire nor the interwar Polish state encouraged Jews to integrate into the broader society. When the Nazis came, for the local Jews, evasion was simply not an option because very few spoke Polish or had non-Jewish acquaintances to ask for help.

What about resistance?

EF: Actually, Jewish armed resistance was not as rare as people think. We tend to equate Jewish resistance with open uprisings like that of the Warsaw ghetto. But there were several ways to fight the Nazis and not all of them involved rebellions. The three communities I study all had Jewish armed resistance groups, but only the Białystok ghetto rebelled. In Kraków, the Jewish resistance bombed a coffee shop packed with German servicemen and engaged in anti-Nazi sabotage. In Minsk, the Jewish underground helped to establish and supply communist guerilla units in the forests around the city and smuggled numerous Jews out of the ghetto. Yet, because the Białystok ghetto uprising was a highly visible, symbolic act of resistance, it tends to be widely remembered, while the Kraków and Minsk Jewish undergrounds are largely overlooked and forgotten, in spite of the fact that they likely killed more Nazis than the Białystok uprising did.

Is it true that only a minority of the Jews resisted? Why wasn’t there unified resistance as the Nazi agenda became clear?

EF: Overall, only a minority of Jews chose resistance, but the expectation that all, or even the majority of Jews should or could have resisted is naive. Resistance, especially organized resistance, is not a matter of spontaneous decision taken on the spot. It required time, money, and resources that most Jews, especially those with families to provide for, simply did not have. It also required cooperation with likeminded and equally committed comrades, which is why this strategy attracted mostly Jews who were politically active before the Holocaust. Most importantly, skills to outfox the Nazi security services were essential. Without these skills, a resistance group was doomed to fail. As with other strategies, pre-Holocaust realities influenced who could become skillful resisters to the Nazis. In pre-WWII Poland, communism was repressed by the government and Jewish communists had to go underground. In the Soviet Union, the communists were the ruling party and therefore no young Jewish communist had underground resistance skills. On the other hand, the Zionists were persecuted in the USSR, but not in Poland. As a result, organized Jewish resistance to the Nazis was most widespread in Eastern Poland – an area that was briefly occupied by the Soviets in 1939-1941 prior to the Nazi takeover, and in which both the Zionists and the Jewish communists had the skills to fight back.

Can your argument explain the behavior of victims of mass violence beyond the Holocaust?

EF: Obviously, there are differences between the Holocaust and other instances of mass murder and genocide, but I think the overall list of possible behaviors is the same everywhere, be it during the Holocaust or in areas currently under the control of ISIS. That the behavior of victims of mass violence is heavily influenced by their pre-war lives is, I believe, also true beyond the specific case of the Holocaust. And if we know which potential victims of mass violence are more likely to try to escape, and who is more likely to fight back, then the hope is we would be better equipped to assist these people as the violence unfolds.

FinkelEvgeny Finkel is assistant professor of political science and international affairs at George Washington University. He is the author of Ordinary Jews: Choice and Survival during the Holocaust.

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

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

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

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

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

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

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

Gott

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Marc Chamberland: Why π is important

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

Reason 1
It provides accuracy for scientific measurements

Pi1

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

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

Pi2

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

Reason 3
Computer Integrity

Pi3

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

Reason 4
It provides evidence that Pi is normal

Pi4

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

Reason 5
It helps us understand the prime numbers

Pi5

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

And you thought that Pi was only good for circles.

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

James Gibson: Voters Beware! TV ads may damage Supreme Court legitimacy

The right-wing Judicial Crisis Network has launched a $10 million advertising campaign to put public pressure on Democratic politicians who oppose President Trump’s nomination of Judge Neil Gorsuch to the U.S. Supreme Court.

While ideological fights over who controls the courts are nothing new, my research suggests that this use of political advertising to sway public opinion of a nominee may do real damage to the the institutional legitimacy of the U.S. Supreme Court in the eyes of the American people.

In Citizens, Courts, and Confirmations, Gregory Caldeira and I focused on the 2006 nomination of Samuel Alito to the U.S. Supreme Court. During that confirmation battle, proponents and opponents of Alito’s confirmation ran intensely politicized television ads trying to shape public opinion on the nomination.

Using surveys of public opinion, we demonstrated that the ads spilled over to infect support for the Court as an institution, subtracting from its legitimacy. In order to understand how and why this happened, it’s important to consider what political scientists (including Caldeira and I) have discovered is the main source of the Court’s legitimacy.

Despite the arguments of some judges to the contrary, the American people do not believe that judges somehow mystically “find” the law. They realize, instead, that judges’ ideologies matter, that liberal and conservative judges make different decisions, and that they do so on the basis of honest intellectual differences. This philosophy is called “legal realism,” and it is widely embraced by the American people.

But there is a difference between honest ideological differences and the politicization of the courts. When people believe that a judge “is just another politician,” or that courts are filled with such judges, legitimacy suffers. The American people do not think highly of politicians. Politicians are seen as self-interested and insincere. That means one can rarely believe what politicians say because they so rarely say what they believe. It is not ideology that Americans oppose, but rather the insincere and strategic way that contemporary politics is fought.

Our analysis discovered that it is not damaging to the Court when Americans recognize that judges hold different ideologies and that those ideologies strongly influence their decisions. But when judges cross the line, when they engage in overly politicized behavior—either on the bench or off—then the Court’s legitimacy is threatened. Scalia’s intemperate language in his opinions is one such example of judges venturing into partisanship; so, too, is Ginsburg’s attempt to influence last year’s presidential election. Still, events like these do not widely penetrate the consciousness of the American people, and so in the end, they likely have small effects on institutional legitimacy.

The same cannot be said of televised advertisements. Millions of Americans are exposed to these churlish and politicized ads, and so they take their toll. The lesson of these ads is too often the same: The “Supreme Court is just another political institution,” worthy of no more esteem than the other institutions of government. As this belief becomes widespread, the institution of the Court is harmed.

Our analysis demonstrates that while Alito got his seat on the Supreme Court, the court he joined had a diminished supply of goodwill among the Court’s constituents, the American people. It also makes clear that the upcoming nomination fights have implications beyond who does and doesn’t get a seat on the bench. At stake is the very legitimacy of the U.S. Supreme Court.

GibsonJames L. Gibson is the Sidney W. Souers Professor of Government at Washington University. He is the coauthor of Citizens, Courts, and Confirmations: Positivity Theory and the Judgments of the American People.

Michael Strauss: Our universe is too vast for even the most imaginative sci-fi

As an astrophysicist, I am always struck by the fact that even the wildest science-fiction stories tend to be distinctly human in character. No matter how exotic the locale or how unusual the scientific concepts, most science fiction ends up being about quintessentially human (or human-like) interactions, problems, foibles and challenges. This is what we respond to; it is what we can best understand. In practice, this means that most science fiction takes place in relatively relatable settings, on a planet or spacecraft. The real challenge is to tie the story to human emotions, and human sizes and timescales, while still capturing the enormous scales of the Universe itself.

Just how large the Universe actually is never fails to boggle the mind. We say that the observable Universe extends for tens of billions of light years, but the only way to really comprehend this, as humans, is to break matters down into a series of steps, starting with our visceral understanding of the size of the Earth. A non-stop flight from Dubai to San Francisco covers a distance of about 8,000 miles – roughly equal to the diameter of the Earth. The Sun is much bigger; its diameter is just over 100 times Earth’s. And the distance between the Earth and the Sun is about 100 times larger than that, close to 100 million miles. This distance, the radius of the Earth’s orbit around the Sun, is a fundamental measure in astronomy; the Astronomical Unit, or AU. The spacecraft Voyager 1, for example, launched in 1977 and, travelling at 11 miles per second, is now 137 AU from the Sun.

But the stars are far more distant than this. The nearest, Proxima Centauri, is about 270,000 AU, or 4.25 light years away. You would have to line up 30 million Suns to span the gap between the Sun and Proxima Centauri. The Vogons in Douglas Adams’s The Hitchhiker’s Guide to the Galaxy (1979) are shocked that humans have not travelled to the Proxima Centauri system to see the Earth’s demolition notice; the joke is just how impossibly large the distance is.

Four light years turns out to be about the average distance between stars in the Milky Way Galaxy, of which the Sun is a member. That is a lot of empty space! The Milky Way contains about 300 billion stars, in a vast structure roughly 100,000 light years in diameter. One of the truly exciting discoveries of the past two decades is that our Sun is far from unique in hosting a retinue of planets: evidence shows that the majority of Sun-like stars in the Milky Way have planets orbiting them, many with a size and distance from their parent star allowing them to host life as we know it.

Yet getting to these planets is another matter entirely: Voyager 1 would arrive at Proxima Centauri in 75,000 years if it were travelling in the right direction – which it isn’t. Science-fiction writers use a variety of tricks to span these interstellar distances: putting their passengers into states of suspended animation during the long voyages, or travelling close to the speed of light (to take advantage of the time dilation predicted in Albert Einstein’s theory of special relativity). Or they invoke warp drives, wormholes or other as-yet undiscovered phenomena.

When astronomers made the first definitive measurements of the scale of our Galaxy a century ago, they were overwhelmed by the size of the Universe they had mapped. Initially, there was great skepticism that the so-called ‘spiral nebulae’ seen in deep photographs of the sky were in fact ‘island universes’ – structures as large as the Milky Way, but at much larger distances still. While the vast majority of science-fiction stories stay within our Milky Way, much of the story of the past 100 years of astronomy has been the discovery of just how much larger than that the Universe is. Our nearest galactic neighbour is about 2 million light years away, while the light from the most distant galaxies our telescopes can see has been travelling to us for most of the age of the Universe, about 13 billion years.

We discovered in the 1920s that the Universe has been expanding since the Big Bang. But about 20 years ago, astronomers found that this expansion was speeding up, driven by a force whose physical nature we do not understand, but to which we give the stop-gap name of ‘dark energy’. Dark energy operates on length- and time-scales of the Universe as a whole: how could we capture such a concept in a piece of fiction?

The story doesn’t stop there. We can’t see galaxies from those parts of the Universe for which there hasn’t been enough time since the Big Bang for the light to reach us. What lies beyond the observable bounds of the Universe? Our simplest cosmological models suggest that the Universe is uniform in its properties on the largest scales, and extends forever. A variant idea says that the Big Bang that birthed our Universe is only one of a (possibly infinite) number of such explosions, and that the resulting ‘multiverse’ has an extent utterly beyond our comprehension.

The US astronomer Neil deGrasse Tyson once said: ‘The Universe is under no obligation to make sense to you.’ Similarly, the wonders of the Universe are under no obligation to make it easy for science-fiction writers to tell stories about them. The Universe is mostly empty space, and the distances between stars in galaxies, and between galaxies in the Universe, are incomprehensibly vast on human scales. Capturing the true scale of the Universe, while somehow tying it to human endeavours and emotions, is a daunting challenge for any science-fiction writer. Olaf Stapledon took up that challenge in his novel Star Maker (1937), in which the stars and nebulae, and cosmos as a whole, are conscious. While we are humbled by our tiny size relative to the cosmos, our brains can none the less comprehend, to some extent, just how large the Universe we inhabit is. This is hopeful, since, as the astrobiologist Caleb Scharf of Columbia University has said: ‘In a finite world, a cosmic perspective isn’t a luxury, it is a necessity.’ Conveying this to the public is the real challenge faced by astronomers and science-fiction writers alike. Aeon counter – do not remove

UniverseMichael A. Strauss is professor of astrophysics at Princeton University and coauthor with Richard Gott and Neil DeGrasse Tyson of Welcome to The Universe: An Astrophysical Tour.

This article was originally published at Aeon and has been republished under Creative Commons.

Rahul Sagar: Are There “Good” Leaks and “Bad” Leaks?

Washington is awash in leaks. Should these leaks be praised or should they be condemned, as the president argues? President Trump’s supporters may argue that his critics—Democrats in particular—praise or condemn leaks as it suits them. Consider the hypocrisy, they will say:

First, since Democrats criticized Wikileaks’ publication of John Podesta’s emails, shouldn’t they also criticize NSA and FBI employees who have disclosed information about contacts between Trump Administration officials and Russian officials? Second, if it was wrong for Edward Snowden to have disclosed communications intelligence, as many Democrats argued at the time, then shouldn’t they also think it is wrong for NSA and FBI employees to disclose communications intelligence about Russian contacts with the Trump Administration?

These questions aren’t trivial. So how to respond?

The answer to the first question hinges on what kind of leaks are in question—those that expose wrongful or unlawful activities as opposed to those that reveal private behavior or information. The former variety further the public interest because they bring to light information that citizens and overseers require in order to hold representatives to account. Leaks about contacts between Trump Administration officials and Russian officials clearly fall into this category. The latter variety may have only a faint connection to the public interest. It may be of some interest to have an unvarnished account of the private conduct of public officials, but this interest hardly seems weighty enough to justify the violation of a person’s privacy (especially when the violation is wholesale). Leaks about Podesta’s pizza orders and office politicking fall into the latter category.

The answer to the second question hinges on knowing when unauthorized disclosures are justified. The president’s supporters may argue that intelligence leaks are never justified because they are illegal. To this the press and First Amendment aficionados may respond that leaks are never unlawful. In their view, the Espionage Act, often used to prosecute leakers, was never meant to be used in this fashion. This response is untenable, but even supposing it were true, it is irrelevant. The Communications Intelligence Act (18 USC §798) plainly makes it unlawful—without exception—for persons to communicate or publish classified information “concerning” or “obtained by” the “processes of communication intelligence.”

So the president is right to say that government employees who have disclosed intercepts pertaining to Russian actions, and even the reporters and newspapers that have published these leaks, have broken the law. But must the law always be followed? Suppose you witness a hit-and-run. There are clear signs saying that you are not to stop or park along the road. You would of course nonetheless stop on the reasonable calculation that disobedience is justified since a weighty interest is involved, and when there aren’t other means of aiding the victim. This is the position that intelligence officers sometimes find themselves in—only they can assist the victim, because only they are aware of the harm that has been done. Indeed when the harm they are witnessing is sufficiently acute, government employees may not only be justified in breaking the law, they may even be obliged to do so.

This is not the end of the story, however. Much depends on how a government employee breaks the law. Let us return to the analogy. As you rush the victim to the hospital are you morally obliged to stop at every red light along the way? It depends, surely, on how crowded the roads are, and how badly the victim is injured. If the roads are busy, jumping a light will likely endanger more lives than it will save. But if the roads are clear, and the victim is hemorrhaging, then it is ethical to run a red light. This is the standard that government employees and the press ought to hold themselves to. If they act rashly they will end up doing more harm than good. Arguably, this is why Snowden does not deserve a pardon—he disclosed classified information without much regard for consequences, seemingly driven by his own pet peeves. Did we really need to learn precisely how the United States spies on foreign powers, for instance. Far better then to act temperately—disclosing only as much information as is necessary to kick start the processes of oversight and accountability. This may be where we are today. But it is not easy to be certain. Since ordinary citizens are not privy to the contents of the intercepts, we must hope that the government employees responsible have faithfully calculated that the cost of disclosing such intelligence is worth bearing because the danger confronting the nation is so great.

There are costs, to be clear. The recent disclosures are likely to have exposed sources and methods since Russian agents have presumably learnt that their communication channels are not secure. There are also political costs for the intelligence community, since the leaks can be—indeed are being—portrayed as an effort to subvert the president.

It now remains for Congress to credibly investigate the worrying claims that have been aired. Should the claims prove true, then we will be indebted to the individuals that have made these disclosures at great risk to themselves. Should the disclosures prove unfounded, however, then President Trump’s supporters will have reason to think that politically motivated insiders have engaged in sabotage, and recriminations may well follow. It is also worth pointing out that should Congress fail to conduct a credible investigation, then further disclosures may be justified. This would be not unlike how the driver in our analogy may drive the victim to a different hospital should the first one prove unwilling to attend to the emergency.

It cannot be said enough that with great power comes great responsibility. This aphorism applies as much to presidents as it does to the press. There are “good” and “bad” leaks. To make the distinction, officials, reporters, and citizens must think carefully about the what, when, and how of unauthorized disclosures.

LeaksRahul Sagar is Global Network Associate Professor of Political Science at New York University in Abu Dhabi and Washington Square Fellow at New York University in New York. He is the author of Secrets and Leaks: The Dilemma of State Secrecy.