Michael J. Ryan: A Taste for the Beautiful

Darwin developed the theory of sexual selection to explain why the animal world abounds in stunning beauty, from the brilliant colors of butterflies and fishes to the songs of birds and frogs. He argued that animals have “a taste for the beautiful” that drives their potential mates to evolve features that make them more sexually attractive and reproductively successful. But if Darwin explained why sexual beauty evolved in animals, he struggled to understand how. In A Taste for the Beautiful, Michael Ryan, one of the world’s leading authorities on animal behavior, tells the remarkable story of how he and other scientists have taken up where Darwin left off and transformed our understanding of sexual selection, shedding new light on human behavior in the process. Vividly written and filled with fascinating stories, A Taste for the Beautiful will change how you think about beauty and attraction. Read on to learn more about the evolution of beauty, why the sight of a peacock’s tail made Darwin sick, and why males tend to be the more “beautiful” in the animal kingdom.

What made you interested in the evolution of beauty?

For my Masters degree I was studying how male bullfrog set up and defend territories. They have a pretty imposing call that has been described as ‘jug-a-rum;’ it is used to repel neighboring males and to attract females. In those days it was thought that animal sexual displays functioned only to identify the species of the signaler. For example, in the pond where I worked you could easily tell the difference between bullfrogs, leopard frogs, green frogs, and spring peepers by listening to their calls. Females do the same so they can end up mating with the correct species. Variation among the calls within a species was thought of to be just noise, random variation that had little meaning to the females.

But sitting in this swamp night after night I was able to tell individual bullfrogs apart from one another and got used to seeing the same males with the loudest deepest calls in the same parts of the pond. I began to wonder that if I could hear these differences could the female bullfrogs, and could females decide who to mate with based on the male’s call? And also, if some calls sounded more beautiful to me, did female frogs share with me the same aesthetic?

I never got to answer these questions with the bullfrogs but I decided to pursue this general question when I started at Cornell University to work on my PhD degree.

Why did Darwin say that the sight of the peacock’s tail, an iconic example of sexual beauty, made him sick?

Darwin suffered all kinds of physical maladies, some probably brought on by his contraction of Chagas disease during his voyage on the Beagle. But this malady induced by the peacock’s tail probably resulted from cognitive dissonance. He had formulated a theory, natural selection, in which he was able to explain how animals evolve adaptations for survival. Alfred Russel Wallace developed a very similar theory. All seemed right with the world, at least for a while.

But then Darwin pointed out that many animal traits seem to hinder rather than promote survival. These included bright plumage and complex song in birds, flashing of fireflies, male fishes with swords, and of course the peacock with its magnificently long tail. All of these traits presented challenges to his theory of natural selection and the general idea of survival of the fittest. These sexy traits are ubiquitous throughout the animal kingdom but seem to harm rather than promote survival.

Sexual selection is Darwin’s theory that predicts the evolution of sexual beauty. How is this different from Darwin’s theory of natural selection?

The big difference between these two theories is that one focuses on survivorship while the other focuses on mating success. Both are important for promoting evolution, the disproportionate passage of genes from one generation to the next. An animal that survives for a long period of time but never reproduces is in a sense genetically dead. Animals that are extremely attractive but do not live long enough to reproduce also are at a genetic dead-end. It is the proper mix of survivorship and attractiveness that is most favored by selection. But the important point to realize is that natural selection and sexual selection are often opposed to one another; natural selection for example, favoring shorter tails in peacocks and sexual selection favoring longer tails. What the bird ends up with is a compromise between these two opposing selection forces.

In most of evolutionary biology the emphasis is still more on survival than mating success. But sometimes I think that surviving is just nature’s clever trick to keep individuals around long enough so that they can reproduce.

Why is it that in many animals the males are the more beautiful sex?

In most animals there are many differences between males and females. But what is the defining character? What makes a male a male and a female a female? It is not the way they act, the way they look, the way they behave. It is not even defined by the individual’s sex organs, penis versus vagina in many types of animals.

The defining characteristic of the sexes is gamete size. Males have many small gametes and females have fewer large gametes.  The maximum number of offspring that an animal can sire will be limited by the number of gametes. Therefore, males could potentially father many more offspring than a female could mother.

But of course males need females to reproduce. So this sets up competition where the many gametes of the males are competing to hook up with the fewer gametes of the females. Thus in many species males are under selection to mate often, they will never run out of gametes, while females are under selection to mate carefully and make good use of the fewer gametes they have. Thus males are competing for females, either through direct combat or by making themselves attractive to females, and females decide which males get to mate. The latter is the topic of this book.

Why is sexual beauty so dangerous?

The first step in communication is being noticed, standing out against the background. This is true whether animals communicate with sound, vision, or smells. It is especially true for sexual communication. The bind that males face is they need to make themselves conspicuous to females but their communication channel is not private, it is open to exploitation by eavesdroppers. These eavesdroppers can make a quick meal out of a sexually advertising male. One famous example, described in this book, involves the túngara frog and its nemesis, the frog-eating bat. Male túngara frogs add syllables, chucks, to their calls to increase their attractiveness to females. But it also makes them more attractive to bats, so when these males become more attractive they also become more likely to become a meal rather than a mate.

The túngara frog is only one example of the survival cost of attractive traits. When crickets call, for example, they can attract a parasitic fly. The fly lands on the calling male and her larvae crawl off of her onto the calling cricket. The larvae then burrow deep inside the cricket where they will develop. As they develop they eat the male from the inside out, and their first meal is the male’s singing muscle. This mutes the male so he will not attract other flies who would deposit their larvae on the male who would then become competitors.

Another cost of being attractive is tied up with the immune system. Many of the elaborate sexual traits of males develop in response to high levels of testosterone. Testosterone can have a negative effect on the immune system. So as males experience higher testosterone levels that might produce more attractive ornaments, but these males are paying the cost with their ability to resist disease.

How did you come to discover that frog eating bats are attracted to the calls of túngara frogs?

The credit for this initial discovery goes to Merlin Tuttle. Merlin is a well-known bat biologist and he was on BCI the year before I was. He captured a bat with a frog in its mouth. Merlin wondered how common this behavior was and whether the bats could hear the calls of the frogs and use those calls to find the frogs.

When Stan Rand and I discovered that túngara frogs become more attractive when they add chucks to their calls, we wondered why they didn’t produce chucks all the time. We were both convinced that there were some cost of producing chucks and we both thought it was likely the ultimate cost imposed by a predator.

Merlin contacted Stan about collaborating on research with the frog-eating bat and frog calls, and Stan then introduced Merlin to me. The rest is history as this research has blossomed into a major research program for a number of people.

Is beauty really in the eye of the beholder?

Yes, but it is also in the ears, the noses, the toes and any other sense organ recruited to check out potential mates. All of these sense organs forward information to the brain where judgements about beauty are made. So it is more accurate to say beauty is in the brain of the beholder. It might be true that the brain is our most important sex organ, but the brain has other things on its mind besides sex. It evolves under selection to perform a number of functions, and adaptations in one function can lead to unintended consequences for another function. For example, studies of some fish show that the color sensitivity of the eyes evolves to facilitate the fish’s ability to find its prey. Once this happens though, males evolve courtship colors to which their females’ eyes are particularly sensitive. This is called sensory exploitation.

A corollary of ‘beauty is in the brain of the beholder’ is that choosers, usually females, define what is beautiful. Females are not under selection to find out which males are attractive, by determining which males are attractive. They are in the driver’s seat when it comes to the evolution of beauty.

What is sensory exploitation?

We have probably all envisioned the perfect sexual partner. And in many cases those visions do not exist in reality. In a sense, the same might be true in animals. Females can have preferences for traits that do not exist. Or at least do not yet exist. When males evolve traits that elicit these otherwise hidden preferences this is called sensory exploitation. We can think of the evolution of sexual beauty as evolutionary attempts to probe the ‘preference landscape’ of the female. When a trait matches one of these previously unexpressed preferences, the male trait is immediately favored by sexual selection because it increases his mating success.

A good example of this occurs in a fish called the swordtail. In these fishes males have sword-like appendages protruding from their tails. Female swordtails prefer males with swords to those without swords, and males with longer swords to males with shorter swords. Swordtails are related to platyfish, the sword of swordtails evolved after the platyfish and swordtails split off from one another thousands of years ago. But when researchers attach a plastic sword to a male platyfish he becomes more attractive to female platyfish. These females have never seen a sworded male but they have a preference for that trait nonetheless. Thus it appears that when the first male swordtail evolved a sword the females already had a preference for this trait.

Do the girls really get prettier at closing time, as Mickey Gilly once sang?

They sure do, and so do the boys. A study showed that both men and women in a bar perceive members of the opposite sex as more attractive as closing time approaches. This classic study was repeated in Australia where they measured blood alcohol levels and showed that the ‘closing time’ effect was not only due to drinking but to the closing time of the bar.

The interpretation is of these results is that if an individual wants to go home with a member of the opposite sex but none of the individuals meet her or his expectations of beauty, the individual has two choices. They can lower their standards of beauty or they can deceive themselves and perceive the same individuals as more attractive. They seem to do the latter.

Although we do not know what goes on in an animal’s head, they show a similar pattern of behavior. Guppies and roaches are much more permissive in accepting otherwise unattractive mates as they get closer to the ultimate closing time, the end of their lives. In a similar example, early in the night female túngara frogs will reject certain calls that are usually unattractive, but later in the night when females become desperate to find a mate they become more than willing to be attracted to these same calls.  It is also noteworthy that middle-aged women think about sex more and have sex more often than do younger women.

Deception seems to be widespread in human courtship. What about animals?

Males have a number of tricks to deceive females for the purpose of mating. One example involves moths in which males make clicking sounds to court females. When males string together these clicks in rapid succession it sounds like the ‘feeding buzz’ of a bat, the sound a bat makes as it zeros in on its prey. At least this is what the female moths think. When they hear these clicks they freeze and the male moth is then able to mount the female and mate with her with little resistance as she appears to be scared to death, not of the male moth but of what she thinks is a bat homing in on her for the kill.

Other animals imitate food to drive female’s attention. Male mites beat their legs on the water surface imitating vibrations caused by copepods, the main source of food for the water mites. When females approach the source of these were vibrations they find a potential mate rather than a potential meal.

What about peer pressure? We know this plays a role in human in interactions, and the influence our perceptions of beauty? What about animals, can they be subjected to peer pressure?

Suppose a woman looks at my picture and is told rate my attractiveness on the scale of 1 to 10. Another woman is asked to do the same but in this picture I am standing next to an attractive woman. Almost certainly I will get a higher score the second time; my attractiveness increases although nothing about my looks have changed, only that I was consorting with a good-looking person.  This is referred to as mate choice and it is widespread in the animal kingdom.

Mate choice copying was first experimentally demonstrated in guppies. Female guppies prefer males who have more orange over those who have less orange. In a classic experiment, females were given a choice between a more than a less colorful male. They preferred the more colorful male and then were returned to the center of the tank for another experiment. In this instance they saw the less colorful and less preferred male courting a female. That female was removed and the test female was tested for her preference for the same two males once again. Now the female changes her preference and prefers what previously had been the less preferred male. She too seems to be employing mate choice copying.

Many animals learn by observing others. Mate choice copying seems to be a type of observational learning that is common in many animals in many domains. It might suggest that we be careful with whom we hang out.

What is the link between sexual attraction in animals and pornography in humans?

Animal sexual beauty is often characterized by being extreme: long tails, complex songs, brilliant colors, and outrageous dances. The same is often true of sexual beauty in humans. Female supermodels, for example, tend to be much longer and thinner than most other women in the population, male supermodels are super-buff—hardly normal. Furthermore, in animals we can create sexual traits that are more extreme than what exists in males of the population, and in experiments females often prefer these artificially exaggerated traits, such as: even longer tales, more complex songs, and more brilliant colors than exhibited by their own males. These are called supernormal stimuli. Pornography also creates supernormal stimuli not only in showcasing individuals with extreme traits but also in creating social settings that hardly exist in most societies, this manufactured social setting is sometimes referred to as Pornotopia.

RyanMichael J. Ryan is the Clark Hubbs Regents Professor in Zoology at the University of Texas and a Senior Research Associate at the Smithsonian Tropical Research Institute in Panama. He is a leading researcher in the fields of sexual selection, mate choice, and animal communication. He lives in Austin, Texas.

 

Browse our 2018 Computer Science & Information Science Catalog

Our new Computer Science & Information Science catalog includes an accessible and rigorous textbook for introducing undergraduates to computer science theory, a fascinating account of the breakthrough ideas that transformed probability and statistics, and an amazing tour of many of history’s greatest unsolved ciphers.

If you’re attending the ITA Workshop-Information Theory and Its Application conference this week, please stop by our table to browse our full range of titles.

What Can Be Computed? is a uniquely accessible yet rigorous introduction to the most profound ideas at the heart of computer science. Crafted specifically for undergraduates who are studying the subject for the first time, and requiring minimal prerequisites, the book focuses on the essential fundamentals of computer science theory and features a practical approach that uses real computer programs (Python and Java) and encourages active experimentation. It is also ideal for self-study and reference.

Throughout, the book recasts traditional computer science concepts by considering how computer programs are used to solve real problems. Standard theorems are stated and proven with full mathematical rigor, but motivation and understanding are enhanced by considering concrete implementations. The book’s examples and other content allow readers to view demonstrations of–and to experiment with—a wide selection of the topics it covers. The result is an ideal text for an introduction to the theory of computation.

In the sixteenth and seventeenth centuries, gamblers and mathematicians transformed the idea of chance from a mystery into the discipline of probability, setting the stage for a series of breakthroughs that enabled or transformed innumerable fields, from gambling, mathematics, statistics, economics, and finance to physics and computer science. This book tells the story of ten great ideas about chance and the thinkers who developed them, tracing the philosophical implications of these ideas as well as their mathematical impact.

Complete with a brief probability refresher, Ten Great Ideas about Chance is certain to be a hit with anyone who wants to understand the secrets of probability and how they were discovered.

Unsolved! begins by explaining the basics of cryptology, and then explores the history behind an array of unsolved ciphers. It looks at ancient ciphers, ciphers created by artists and composers, ciphers left by killers and victims, Cold War ciphers, and many others. Some are infamous, like the ciphers in the Zodiac letters, while others were created purely as intellectual challenges by figures such as Nobel Prize–winning physicist Richard P. Feynman. Bauer lays out the evidence surrounding each cipher, describes the efforts of geniuses and eccentrics—in some cases both—to decipher it, and invites readers to try their hand at puzzles that have stymied so many others.

Browse Our 2018 Math Catalog

Our new Mathematics catalog includes the story of ten great ideas about chance and the thinkers who developed them, an introduction to the language of beautiful curves, and a look at how empowering mathematics can be.

If you plan on attending the Joint Mathematics Meeting this week, stop by Booths 504-506 to see our full range of Mathematics titles and more.

In the sixteenth and seventeenth centuries, gamblers and mathematicians transformed the idea of chance from a mystery into the discipline of probability, setting the stage for a series of breakthroughs that enabled or transformed innumerable fields, from gambling, mathematics, statistics, economics, and finance to physics and computer science. This book tells the story of ten great ideas about chance and the thinkers who developed them, tracing the philosophical implications of these ideas as well as their mathematical impact.

Complete with a brief probability refresher, Ten Great Ideas about Chance is certain to be a hit with anyone who wants to understand the secrets of probability and how they were discovered.

Curves are seductive. These smooth, organic lines and surfaces—like those of the human body—appeal to us in an instinctive, visceral way that straight lines or the perfect shapes of classical geometry never could. In this large-format book, lavishly illustrated in color throughout, Allan McRobie takes the reader on an alluring exploration of the beautiful curves that shape our world—from our bodies to Salvador Dalí’s paintings and the space-time fabric of the universe itself.

The Seduction of Curves focuses on seven curves and describes the surprising origins of their taxonomy in the catastrophe theory of mathematician René Thom. In an accessible discussion illustrated with many photographs of the human nude, McRobie introduces these curves and then describes their role in nature, science, engineering, architecture, art, and other areas.  The book also discusses the role of these curves in the work of such artists as David Hockney, Henry Moore, and Anish Kapoor, with particular attention given to the delicate sculptures of Naum Gabo and the final paintings of Dalí, who said that Thom’s theory “bewitched all of my atoms.”

In The Calculus of Happiness, Oscar Fernandez shows us that math yields powerful insights into health, wealth, and love. Using only high-school-level math (precalculus with a dash of calculus), Fernandez guides us through several of the surprising results, including an easy rule of thumb for choosing foods that lower our risk for developing diabetes (and that help us lose weight too), simple “all-weather” investment portfolios with great returns, and math-backed strategies for achieving financial independence and searching for our soul mate. Moreover, the important formulas are linked to a dozen free online interactive calculators on the book’s website, allowing one to personalize the equations.

Fernandez uses everyday experiences—such as visiting a coffee shop—to provide context for his mathematical insights, making the math discussed more accessible, real-world, and relevant to our daily lives. A nutrition, personal finance, and relationship how-to guide all in one, this book invites you to discover how empowering mathematics can be.

SUMIT 2018: A math collaboration

by C. Kenneth Fan
President and Founder of Girls’ Angle, an organization that connects mentors with girls who love math

For decades, math extracurricular activity in the United States has been dominated by the math competition. I, myself, participated in and enjoyed math competitions when I was growing up. Many school math clubs are centered on math contest prep. Today, there are dozens upon dozens of math competitions. While many students gain much from math competitions, many others, for a variety of good reasons, do not find inspiration in math competitions to do more math, and the best way to learn math is to do math.

When I founded Girls’ Angle over ten years ago, a main task was to create new, non-competitive, mathematically compelling avenues into math that appeal to those who, for whatever reason, may not be so inspired by math competitions. To celebrate the end of our first year, we baked a brownie for the girls, but it wasn’t a rectangular brownie—it was a trapezoid, and nobody could have any brownie until members figured out how to split the brownie into equal pieces for all. We were counting on them to succeed because we wanted brownie!

It became a Girls’ Angle tradition to celebrate the conclusion of every semester with a collaborative math Single Digitspuzzle, and every semester the puzzle has grown more elaborate. It finally dawned on me that these collaborative end-of-session math puzzles could well serve as robust, mathematically-intense, but fully collaborative alternatives to the math competition. To directly contrast the concept with that of the math competition, we called these events “math collaborations.” On January 21, 2012, after 4 years of in-house development, we took the concept out of Girls’ Angle with SUMIT 2012, which took place at MIT in conjunction with MIT’s Undergraduate Society of Women in Mathematics. Then, on March 7, 2012, the Buckingham, Browne, and Nichols Middle School became the first school to host a math collaboration. The success of these events led to annual math collaborations at Buckingham, Browne, and Nichols, and, to date, over 100 other math collaborations at schools, libraries, and other venues, such as Girl Scout troops.

The upcoming SUMIT 2018 is going to be our biggest and best math collaboration ever. For girls in grades 6-10, participants will be put in a predicament from which they must extricate themselves using the currency of the world they’ll find themselves immersed in: mathematics! They must self-organize and communicate well as there will be no one to help them but themselves. It’ll be an epic journey where participants must become the heroines of their own saga.

Should they succeed, they’ll be rewarded with the knowledge of genuine accomplishment—and gifts, such as Marc Chamberland’s captivating book, Single Digits: In Praise of Small Numbers courtesy of long-time SUMIT sponsor Princeton University Press.

The best way to learn math is to do math, and what better way to do math than to do it while laughing out loud and making new friends?

There are a limited number of spots still available for 9th and 10th graders. Register today!

Browse Our 2018 Physics & Astrophysics Catalog

Our new Physics & Astrophysics catalog includes two new graduate-level textbooks from Kip S. Thorne, Co-Winner of the 2017 Noble Prize in Physics, as well as a look into the physics behind black holes.

If you plan on attending AAS 2018 in National Harbor, MD this weekend, please stop by Booth 1003 to see our full range of Physics and Astrophysics titles and more.

Black holes, predicted by Albert Einstein’s general theory of relativity more than a century ago, have long intrigued scientists and the public with their bizarre and fantastical properties. Although Einstein understood that black holes were mathematical solutions to his equations, he never accepted their physical reality—a viewpoint many shared. This all changed in the 1960s and 1970s, when a deeper conceptual understanding of black holes developed just as new observations revealed the existence of quasars and X-ray binary star systems, whose mysterious properties could be explained by the presence of black holes. Black holes have since been the subject of intense research—and the physics governing how they behave and affect their surroundings is stranger and more mind-bending than any fiction.

The Little Book of Black Holes takes readers deep into the mysterious heart of the subject, offering rare clarity of insight into the physics that makes black holes simple yet destructive manifestations of geometric destiny.

Modern Classical Physics is a long-awaited, first-year, graduate-level text and reference book covers the fundamental concepts and twenty-first-century applications of six major areas of classical physics that every masters- or PhD-level physicist should be exposed to, but often isn’t: statistical physics, optics (waves of all sorts), elastodynamics, fluid mechanics, plasma physics, and special and general relativity and cosmology. Growing out of a full-year course that the eminent researchers Kip Thorne and Roger Blandford taught at Caltech for almost three decades, this book is designed to broaden the training of physicists. Its six main topical sections are also designed so they can be used in separate courses, and the book provides an invaluable reference for researchers.

First published in 1973, Gravitation is a landmark graduate-level textbook that presents Einstein’s general theory of relativity and offers a rigorous, full-year course on the physics of gravitation. Upon publication, Science called it “a pedagogic masterpiece,” and it has since become a classic, considered essential reading for every serious student and researcher in the field of relativity. This authoritative text has shaped the research of generations of physicists and astronomers, and the book continues to influence the way experts think about the subject.

Pariah Moonshine Part III: Pariah Groups, Prime Factorizations, and Points on Elliptic Curves

by Joshua Holden

This post originally appeared on The Aperiodical. We republish it here with permission. 

In Part I of this series of posts, I introduced the sporadic groups, finite groups of symmetries which aren’t the symmetries of any obvious categories of shapes. The sporadic groups in turn are classified into the Happy Family, headed by the Monster group, and the Pariahs. In Part II, I discussed Monstrous Moonshine, the connection between the Monster group and a type of function called a modular form. This in turn ties the Monster group, and with it the Happy Family, to elliptic curves, Fermat’s Last Theorem, and string theory, among other things. But until 2017, the Pariah groups remained stubbornly outside these connections.

In September 2017, John Duncan, Michael Mertens, and Ken Ono published a paper announcing a connection between the Pariah group known as the O’Nan group (after Michael O’Nan, who discovered it in 1976) and another modular form. Like Monstrous Moonshine, the new connection is through an infinite-dimensional shape which breaks up into finite-dimensional pieces. Also like Monstrous Moonshine, the modular form in question has a deep connection with elliptic curves. In this case, however, the connection is more subtle and leads through yet another set of important mathematical objects: the quadratic fields.

At play in the fields quadratic

What mathematicians call a field is a set of objects which are closed under addition, subtraction, multiplication, and division (except division by zero). The rational numbers form a field, and so do the real numbers and the complex numbers. The integers don’t form a field because they aren’t closed under division, and the positive real numbers don’t form a field because they aren’t closed under subtraction.  (It’s also possible to have fields of things that aren’t numbers, which are useful in lots of other situations; see Section 4.5 of The Mathematics of Secrets for a cryptographic example.)

A common way to make a new field is to take a known field and enlarge it a bit. For example, if you start with the real numbers and enlarge them by including the number i (the square root of -1), then you also have to include all of the imaginary numbers, which are multiples of i, and then all of the numbers which are real numbers plus imaginary numbers, which gets you the complex numbers. Or you could start with the rational numbers, include the square root of 2, and then you have to include the numbers that are rational multiples of the square root of 2, and then the numbers which are rational numbers plus the multiples of the square root of 2. Then you get to stop, because if you multiply two of those numbers you get

Holden

which is another number of the same form. Likewise, if you divide two numbers of this form, you can rationalize the denominator and get another number of the same form. We call the resulting field the rational numbers “adjoined with” the square root of 2. Fields which are obtained by starting with the rational numbers and adjoining the square root of a rational number (positive or negative) are called quadratic fields.

Identifying a quadratic field is almost, but not quite, as easy as identifying the square root you are adjoining. For instance, consider adjoining the square root of 8. The square root of 8 is twice the square root of 2, so if you adjoin the square root of 2 you get the square root of 8 for free. And since you can also divide by 2, if you adjoin the square root of 8 you get the square root of 2 for free. So these two square roots give you the same field.  For technical reasons, a quadratic field is identified by taking all of the integers whose square roots would give you that field, and picking out the integer D with the smallest absolute value that can be written in the form b2 – 4ac for integers a, b, and c.  (This is the same b2 – 4ac as in the quadratic formula.)  This number D is called the fundamental discriminant of the field. So, for example, 8 is the fundamental discriminant of the quadratic field we’ve been talking about, not 2, because 8 = 42 – 4 × 2 × 1, but 2 can’t be written in that form.

Prime suspects

After addition, subtraction, multiplication, and division, one of the really important things you can do with rational numbers is factor their numerators and denominators into primes. In fact, you can do it uniquely, aside from the order of the factors. If you have number in a quadratic field, you can still factor it into primes, but the primes might not be unique. For example, in the rational numbers adjoined with the square root of negative 5 we have

Holden

where 2, 5, 1 + √–5, and 1 – √–5 are all primes. You’ll have to trust me on that last part, since it’s not always obvious which numbers in a quadratic field are prime. Figures 1 and 2 show some small primes in the rational numbers adjoined with the square roots of negative 1 and negative 3, respectively, plotted as points in the complex plane.

Holden 3

Figure 1. Some small primes in the rational numbers adjoined with the square root of -1 (D = -4), plotted as points in the complex plane. By Wikimedia Commons User Georg-Johann.)

 

Holden

Figure 2. Some small primes in the rational numbers adjoined with the square root of -3 (D = -3), plotted as points in the complex plane. By Wikimedia Commons User Fropuff.)

We express this by saying the rational numbers have unique factorization, but not all quadratic fields do. The question of which quadratic fields have unique factorization is an important open problem in general. For negative fundamental discriminants, we know that D = ‑3, ‑4, ‑7, ‑8, ‑11, ‑19, ‑43, ‑67, ‑163 are the only such quadratic fields; an equivalent form of this was conjectured by Gauss but fully acceptable proofs were not given until 1966 by Alan Baker and 1967 by Harold Stark. For positive fundamental discriminants, Gauss conjectured that there were infinitely many quadratic fields with unique factorization but this is still unproved.

Furthermore, Gauss identified a number, called the class number, which in some sense measures how far from unique factorization a field is. If the class number is 1, the field has unique factorization, otherwise not. The rational numbers adjoined with the square root of negative 5 (D = -20) have class number 2, and therefore do not have unique factorization. Gauss also conjectured that the class number of a quadratic field went to infinity as its discriminant went to negative infinity; this was proved by Hans Heilbronn in 1934.

Moonshine with class (numbers)

What about Moonshine? Duncan, Mertens, and Ono proved that the O’Nan group was associated with the modular form

F(z) = e -8 π i z + 2 + 26752 e 6 π i z + 143376 e 8 π i z  + 8288256 e 14 π i z  + …

which has the property that the coefficient of e 2 |D| π I z  is related to the class number of the field with fundamental discriminant < 0.  Furthermore, looking at elements of the O’Nan group sometimes gives us very specific relationships between the coefficients and the class number.  For example, the O’Nan group includes a symmetry which is like a 180 degree rotation, in that if you do it twice you get back to where you started.  Using that symmetry, Duncan, Mertens, and Ono showed that for even D < -8, 16 always divides a(D)+24h(D), where a(D) is the coefficient of  e 2 |D| π i z  and h(D) is the class number of the field with fundamental discriminant D.  For the example D = -20 from above, a(D) = 798588584512 and h(D) = 2, and 16 does in fact divide 798588584512 + 48.  Similarly, other elements of the O’Nan group show that 9 always divides a(D)+24h(D) if D = 3k+2 for some integer k and that 5 and 7 always divide a(D)+24h(D) under other similar conditions on And 11 and 19 divide a(D)+24h(D) under (much) more complicated conditions related to points on an elliptic curve associated with each D, which brings us back nicely to the connection between Moonshine and elliptic curves.

How much Moonshine is out there?

Monstrous Moonshine showed that the Monster, and therefore the Happy Family, was related to modular forms and elliptic curves, as well as string theory. O’Nan Moonshine brings in two more sporadic groups, the O’Nan group and its subgroup the “first Janko group”. (Figure 3 shows the connections between the sporadic groups. “M” is the Monster group, “O’N” is the O’Nan group, and “J1” is the first Janko group.) It also connects the sporadic groups not just to modular forms and elliptic curves, but also to quadratic fields, primes, and class numbers. Furthermore, the modular form used in Monstrous Moonshine is “weight 0”, meaning that k = 0 in the definition of a modular form given in Part II. That ties this modular form very closely to elliptic curves.

Holden

Figure 3. Connections between the sporadic groups. Lines indicate that the lower group is a subgroup or a quotient of a subgroup of the upper group. “M” is the Monster group and “O’N” is the O’Nan group; the groups connected below the Monster group are the rest of the Happy Family. (By Wikimedia Commons User Drschawrz.)

The modular form in O’Nan Moonshine is “weight 3/2”. Weight 3/2 modular forms are less closely tied to elliptic curves, but are tied to yet more ideas in mathematical physics, like higher-dimensional generalizations of strings called “branes” and functions that might count the number of states that a black hole can be in. That still leaves four more pariah groups, and the smart money predicts that Moonshine connections will be found for them, too. But will they come from weight 0 modular forms, weight 3/2 modular forms, or yet another type of modular form with yet more connections? Stay tuned! Maybe someday soon there will be a Part IV.

Joshua Holden is professor of mathematics at the Rose-Hulman Institute of Technology. He is the author of The Mathematics of Secrets: Cryptography from Caesar Ciphers to Digital Encryption.

Geoff Mulgan on Big Mind: How Collective Intelligence Can Change Our World

A new field of collective intelligence has emerged in the last few years, prompted by a wave of digital technologies that make it possible for organizations and societies to think at large scale. This “bigger mind”—human and machine capabilities working together—has the potential to solve the great challenges of our time. So why do smart technologies not automatically lead to smart results? Gathering insights from diverse fields, including philosophy, computer science, and biology, Big Mind reveals how collective intelligence can guide corporations, governments, universities, and societies to make the most of human brains and digital technologies. Highlighting differences between environments that stimulate intelligence and those that blunt it, Geoff Mulgan shows how human and machine intelligence could solve challenges in business, climate change, democracy, and public health. Read on to learn more about the ideas in Big Mind.

So what is collective intelligence?

My interest is in how thought happens at a large scale, involving many people and often many machines. Over the last few years many experiments have shown how thousands of people can collaborate online analyzing data or solving problems, and there’s been an explosion of new technologies to sense, analyze and predict. My focus is on how we use these new kinds of collective intelligence to solve problems like climate change or disease—and what risks we need to avoid. My claim is that every organization can work more successfully if it taps into a bigger mind—mobilizing more brains and computers to help it.

How is it different from artificial intelligence?

Artificial intelligence is going through another boom, embedded in everyday things like mobile phones and achieving remarkable break throughs in medicine or games. But for most things that really matter we need human intelligence as well as AI, and an over reliance on algorithms can have horrible effects, whether in financial markets or in politics.

What’s the problem?

The problem is that although there’s huge investment in artificial intelligence there’s been little progress in how intelligently our most important systems work—democracy and politics, business and the economy. You can see this in the most everyday aspect of collective intelligence—how we organize meetings, which ignores almost everything that’s known about how to make meetings effective.

What solutions do you recommend?

I show how you can make sense of the collective intelligence of the organizations you’re in—whether universities or businesses—and how to become better. Much of this is about how we organize our information commons. I also show the importance of countering the many enemies of collective intelligence—distortions, lies, gaming and trolls.

Is this new?

Many of the examples I look at are quite old—like the emergence of an international community of scientists in the 17th and 18th centuries, the Oxford English Dictionary which mobilized tens of thousands of volunteers in the 19th century, or NASA’s Apollo program which at its height employed over half a million people in more than 20,000 organizations. But the tools at our disposal are radically different—and more powerful than ever before.

Who do you hope will read the book?

I’m biased but think this is the most fascinating topic in the world today—how to think our way out of the many crises and pressures that surround us. But I hope it’s of particular interest to anyone involved in running organizations or trying to work on big problems.

Are you optimistic?

It’s easy to be depressed by the many examples of collective stupidity around us. But my instinct is to be optimistic that we’ll figure out how to make the smart machines we’ve created serve us well and that we could on the cusp of a dramatic enhancement of our shared intelligence. That’s a pretty exciting prospect, and much too important to be left in the hands of the geeks alone.

MulganGeoff Mulgan is chief executive of Nesta, the UK’s National Endowment for Science, Technology and the Arts, and a senior visiting scholar at Harvard University’s Ash Center. He was the founder of the think tank Demos and director of the Prime Minister’s Strategy Unit and head of policy under Tony Blair. His books include The Locust and the Bee.

Kyle Harper: How climate change and disease helped the fall of Rome

HarperAt some time or another, every historian of Rome has been asked to say where we are, today, on Rome’s cycle of decline. Historians might squirm at such attempts to use the past but, even if history does not repeat itself, nor come packaged into moral lessons, it can deepen our sense of what it means to be human and how fragile our societies are.

In the middle of the second century, the Romans controlled a huge, geographically diverse part of the globe, from northern Britain to the edges of the Sahara, from the Atlantic to Mesopotamia. The generally prosperous population peaked at 75 million. Eventually, all free inhabitants of the empire came to enjoy the rights of Roman citizenship. Little wonder that the 18th-century English historian Edward Gibbon judged this age the ‘most happy’ in the history of our species – yet today we are more likely to see the advance of Roman civilisation as unwittingly planting the seeds of its own demise.

Five centuries later, the Roman empire was a small Byzantine rump-state controlled from Constantinople, its near-eastern provinces lost to Islamic invasions, its western lands covered by a patchwork of Germanic kingdoms. Trade receded, cities shrank, and technological advance halted. Despite the cultural vitality and spiritual legacy of these centuries, this period was marked by a declining population, political fragmentation, and lower levels of material complexity. When the historian Ian Morris at Stanford University created a universal social-development index, the fall of Rome emerged as the greatest setback in the history of human civilisation.

Explanations for a phenomenon of this magnitude abound: in 1984, the German classicist Alexander Demandt catalogued more than 200 hypotheses. Most scholars have looked to the internal political dynamics of the imperial system or the shifting geopolitical context of an empire whose neighbours gradually caught up in the sophistication of their military and political technologies. But new evidence has started to unveil the crucial role played by changes in the natural environment. The paradoxes of social development, and the inherent unpredictability of nature, worked in concert to bring about Rome’s demise.

Climate change did not begin with the exhaust fumes of industrialisation, but has been a permanent feature of human existence. Orbital mechanics (small variations in the tilt, spin and eccentricity of the Earth’s orbit) and solar cycles alter the amount and distribution of energy received from the Sun. And volcanic eruptions spew reflective sulphates into the atmosphere, sometimes with long-reaching effects. Modern, anthropogenic climate change is so perilous because it is happening quickly and in conjunction with so many other irreversible changes in the Earth’s biosphere. But climate change per se is nothing new.

The need to understand the natural context of modern climate change has been an unmitigated boon for historians. Earth scientists have scoured the planet for paleoclimate proxies, natural archives of the past environment. The effort to put climate change in the foreground of Roman history is motivated both by troves of new data and a heightened sensitivity to the importance of the physical environment. It turns out that climate had a major role in the rise and fall of Roman civilisation. The empire-builders benefitted from impeccable timing: the characteristic warm, wet and stable weather was conducive to economic productivity in an agrarian society. The benefits of economic growth supported the political and social bargains by which the Roman empire controlled its vast territory. The favourable climate, in ways subtle and profound, was baked into the empire’s innermost structure.

The end of this lucky climate regime did not immediately, or in any simple deterministic sense, spell the doom of Rome. Rather, a less favourable climate undermined its power just when the empire was imperilled by more dangerous enemies – Germans, Persians – from without. Climate instability peaked in the sixth century, during the reign of Justinian. Work by dendro-chronologists and ice-core experts points to an enormous spasm of volcanic activity in the 530s and 540s CE, unlike anything else in the past few thousand years. This violent sequence of eruptions triggered what is now called the ‘Late Antique Little Ice Age’, when much colder temperatures endured for at least 150 years. This phase of climate deterioration had decisive effects in Rome’s unravelling. It was also intimately linked to a catastrophe of even greater moment: the outbreak of the first pandemic of bubonic plague.

Disruptions in the biological environment were even more consequential to Rome’s destiny. For all the empire’s precocious advances, life expectancies ranged in the mid-20s, with infectious diseases the leading cause of death. But the array of diseases that preyed upon Romans was not static and, here too, new sensibilities and technologies are radically changing the way we understand the dynamics of evolutionary history – both for our own species, and for our microbial allies and adversaries.

The highly urbanised, highly interconnected Roman empire was a boon to its microbial inhabitants. Humble gastro-enteric diseases such as Shigellosis and paratyphoid fevers spread via contamination of food and water, and flourished in densely packed cities. Where swamps were drained and highways laid, the potential of malaria was unlocked in its worst form – Plasmodium falciparum – a deadly mosquito-borne protozoon. The Romans also connected societies by land and by sea as never before, with the unintended consequence that germs moved as never before, too. Slow killers such as tuberculosis and leprosy enjoyed a heyday in the web of interconnected cities fostered by Roman development.

However, the decisive factor in Rome’s biological history was the arrival of new germs capable of causing pandemic events. The empire was rocked by three such intercontinental disease events. The Antonine plague coincided with the end of the optimal climate regime, and was probably the global debut of the smallpox virus. The empire recovered, but never regained its previous commanding dominance. Then, in the mid-third century, a mysterious affliction of unknown origin called the Plague of Cyprian sent the empire into a tailspin. Though it rebounded, the empire was profoundly altered – with a new kind of emperor, a new kind of money, a new kind of society, and soon a new religion known as Christianity. Most dramatically, in the sixth century a resurgent empire led by Justinian faced a pandemic of bubonic plague, a prelude to the medieval Black Death. The toll was unfathomable – maybe half the population was felled.

The plague of Justinian is a case study in the extraordinarily complex relationship between human and natural systems. The culprit, the Yersinia pestis bacterium, is not a particularly ancient nemesis; evolving just 4,000 years ago, almost certainly in central Asia, it was an evolutionary newborn when it caused the first plague pandemic. The disease is permanently present in colonies of social, burrowing rodents such as marmots or gerbils. However, the historic plague pandemics were colossal accidents, spillover events involving at least five different species: the bacterium, the reservoir rodent, the amplification host (the black rat, which lives close to humans), the fleas that spread the germ, and the people caught in the crossfire.

Genetic evidence suggests that the strain of Yersinia pestis that generated the plague of Justinian originated somewhere near western China. It first appeared on the southern shores of the Mediterranean and, in all likelihood, was smuggled in along the southern, seaborne trading networks that carried silk and spices to Roman consumers. It was an accident of early globalisation. Once the germ reached the seething colonies of commensal rodents, fattened on the empire’s giant stores of grain, the mortality was unstoppable.

The plague pandemic was an event of astonishing ecological complexity. It required purely chance conjunctions, especially if the initial outbreak beyond the reservoir rodents in central Asia was triggered by those massive volcanic eruptions in the years preceding it. It also involved the unintended consequences of the built human environment – such as the global trade networks that shuttled the germ onto Roman shores, or the proliferation of rats inside the empire. The pandemic baffles our distinctions between structure and chance, pattern and contingency. Therein lies one of the lessons of Rome. Humans shape nature – above all, the ecological conditions within which evolution plays out. But nature remains blind to our intentions, and other organisms and ecosystems do not obey our rules. Climate change and disease evolution have been the wild cards of human history.

Our world now is very different from ancient Rome. We have public health, germ theory and antibiotic pharmaceuticals. We will not be as helpless as the Romans, if we are wise enough to recognise the grave threats looming around us, and to use the tools at our disposal to mitigate them. But the centrality of nature in Rome’s fall gives us reason to reconsider the power of the physical and biological environment to tilt the fortunes of human societies. Perhaps we could come to see the Romans not so much as an ancient civilisation, standing across an impassable divide from our modern age, but rather as the makers of our world today. They built a civilisation where global networks, emerging infectious diseases and ecological instability were decisive forces in the fate of human societies. The Romans, too, thought they had the upper hand over the fickle and furious power of the natural environment. History warns us: they were wrong.Aeon counter – do not remove

Kyle Harper is professor of classics and letters and senior vice president and provost at the University of Oklahoma. He is the author of The Fate of Rome, recently released, as well as Slavery in the Late Roman World, AD 275–425 and From Shame to Sin: The Christian Transformation of Sexual Morality in Late Antiquity. He lives in Norman, Oklahoma.

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

Sean Fleming: The Water Year in Review

The top five water-related news stories of 2017—and what to expect for 2018

FlemingThe thing about water is that something’s always happening, and the implications of that fact are growing – fast.  What are the top five water-related news stories of 2017?  Read on to see, along with a little context and some implications for next year and beyond.

Oops!  (The Oroville Dam evacuation)

Possibly the most obvious water story of 2017 happened right after the New Year: nearly 200,000 Californians were evacuated beneath Oroville Dam as it threatened to fail under record flooding, which in turn ended a historic drought that had cost the state billions of dollars.  Previously of little note to most living outside the region, Oroville is in fact the tallest dam in the US.  It’s located on the Feather River, a headwater basin to the Sacramento River that drains the western slopes of the snow-laden Sierra Nevada and Cascades in the wet, northern part of California.  Oroville Dam is a key component the California State Water Project, shifting water into the California Aqueduct to help irrigate the Central Valley, which produces about 25% of the food consumed in the US, and to transport water to southern Californian urban centers.  Critics charge that in spite of its size and status as a cornerstone of the civil works in a heavily populated but largely arid state where water is everything, dam maintenance and upgrading lagged far behind, setting the stage for problems.  Record rains in February provided the trigger, and the main spillway failed – which might in turn have undermined the dam as a whole, sending the entirety of massive Lake Oroville downstream all at once in a wave of destruction and death.  Disaster was averted, but the costs were tremendous and the risks were real.  For thoughts on improving America’s river infrastructure, see my recent Scientific American post.

Water goes bang on the India-China border

The most exciting, yet perhaps most under-reported water story of 2017 took place on the India-China border.  A military buildup and tense standoff over disputed ownership of a Himalayan frontier area shared by China, Nepal, Bhutan, and India this summer may have cooled off, but India charges that China followed up by using water as a weapon – withholding key data that India needs to manage lethal monsoon flooding on transboundary rivers.  Violent international conflict solely over water is extremely rare because it usually doesn’t work strategically, though it does happen from time to time.  For instance, in 1965, when Syria was building an upstream diversion of a tributary to the River Jordan that would deeply reduce Israel’s water supply – a catastrophe for a desert nation – Israel responded with air strikes against the facility.  And water has been used as a weapon in wars that were being fought for other reasons: Chiang Kai-shek’s Nationalist government in China opened the dikes on the Yellow River in 1938 in an effort to hold back the invading Imperial Japanese army. The action was only partially successful and had a disastrous humanitarian cost.  The soaring mountain ranges wrapping around the Tibetan Plateau – including the Hindu Kush, Karakoram, and Himalayas, spanning China, India, Pakistan, and  several other countries – host one of the world’s largest remaining icefields and are the source of the Indus, Yangtze, Yellow, Ganges, Brahmaputra, and Mekong Rivers among others, and thus help provide water to a full quarter of the global human population.  Perhaps nowhere else on Earth is it more important for nations to cooperate over water.

Two inter-state water lawsuits go to the US Supreme Court

The volume was turned up in the country’s water wars, with SCOTUS announcing this fall it will hear both Texas’s lawsuit against New Mexico over Rio Grande water rights, and Florida’s lawsuit against Georgia over the Apalachicola.  Rivers and aquifers don’t respect borders.  The geophysics of where water comes from and how and where it flows is complex, fascinating, and full of surprises, such as flash floods, alternating drought and flood sequences, and abrupt and catastrophic changes in river channel location.  And those are just the natural aspects – the engineering and management part can be just as complicated for some basins, and a high ratio of demand to supply, as we have in the increasingly heavily populated deserts of the Southwest for instance, exacerbates these issues.  Originating from snowy headwaters in the mountains of southern Colorado and northern New Mexico, the Rio Grande flows south through increasingly arid country and then turns southeastward, forming the US-Mexico border until emptying in the Gulf of Mexico.  Water projects abound on the Rio Grande, and each influences the other in some way.  For example, the San Juan-Chama project diverts water from the Colorado River into the Rio Grande, municipal groundwater pumping in Albuquerque interacts with Rio Grande flows through subterranean geologic pathways, and a series of dams withdraws water from the river for agriculture, reducing what’s left for downstream users.  Water law is complicated.  Texas says New Mexico is taking more than its fair share of Rio Grande water; New Mexico says it isn’t.  The potential for disagreement over water will only continue to grow in the Southwest, though there are success stories as well: after some earlier missteps, Las Vegas has invented one of the most advanced and successful water conservation programs around, reportedly reducing its water consumption by almost a quarter over a ten-year period while its population grew by half a million.

Saying goodbye to the Paris Agreement on climate change

Why is climate change important to rivers?  Lots of natural processes and human activities affect how high rivers run and how much water arrives at your tap, and climate variables like precipitation and temperature rank high among these influences.  While the new administration’s withdrawal from the Paris Agreement in 2017 was obviously a setback for action on climate change, it was also a democratic response to widespread sentiment.  And this fact suggests that explaining climate change may be turning into the greatest science communication failure in history.  As scientists, we clearly need to adjust course – but in what direction?  Consider a recent article by a multi-disciplinary team in the respected research journal, Global Environmental Change.  Applying complex network theory (kind of a mathematical formalization of the seven degrees of Kevin Bacon) to social media feeds about climate change, they demonstrated the dominance of so-called echo chambers, and that constructive progress is made only when groups with opposing views actually talk with each other.  Consider also that populism – which is by nature skeptical around the competence and integrity of designated experts – has been growing over the last decade on both the left and right, as evidenced by the mayoralties of Rob Ford in Toronto and Boris Johnson in London, the Tea Party and Occupy movements, Brexit, and Bernie and The Donald.  If there is a silver lining to withdrawal from the Paris accords, it’s that it may teach us valuable lessons around communicating about climate change: reach out to people who don’t believe us yet, treat them with respect, and focus on just explaining our science.

Houston, we have a problem

Hurricane Harvey hit Houston hard.  In late August, the fourth largest city in the US, with over 4 million residents counting Harris County, was at the epicenter of what some are saying will be the costliest natural disaster in US history.  Though no hurricane is to be trifled with, why was the flooding so intense in this case?  To be sure, the rainfall generated by this particular storm was unusually heavy.  But risk is, by definition, what you get when you take the probability that something bad will happen (like record rainfall under a hurricane) and multiply it by the impact it will have if it does happen (like flooding and the associated economic cost and human suffering).  In the case of Harvey’s visit to Houston, it had a lot to do with local-scale choices that affected the second part of that equation.  In fact, parts of the greater Houston metropolitan area have seen a spate of floods over the last few years, and they weren’t all associated with huge storms.  The region has experienced an explosion of population growth and urban sprawl.  Lots of residences were built in low-lying, flood-prone areas, which is the single best of way of increasing flood risk.  And urbanization – the conversion of wild or agricultural land to rooftops, parking lots, and roadways – is another powerful flood risk factor.  Soils and wetlands hold on to rainwater for a while, and then gently release it to natural drainage systems like aquifers and rivers.  If you pave and build over these things, their ability to attenuate flooding is removed.  While these effects are particularly noticeable in Houston, and especially so when the city gets hit by a major hurricane, they’re ubiquitous; increased flooding in the UK over the last decade has been attributed to exactly the same causes.

What will 2018 have in store for us?  If we can be sure about one thing, it’s to expect the unexpected.  But the larger trends are clear.  Global water demand will increase 55% in the next few decades, urbanization will spread, tens of millions more will congregate in floodplain-located megacities, the climate will subtly but profoundly shift overhead, and cooperation and conflict over water will vie for supremacy.  We can, in short, expect that water stories will make the news with increasing frequency and force.

Sean W. Fleming has two decades of experience in the private, public, and nonprofit sectors in the United States, Canada, England, and Mexico, ranging from oil exploration to operational river forecasting to glacier science. He holds faculty positions in the geophysical sciences at the University of British Columbia and Oregon State University. He is the author of Where the River Flows: Scientific Reflections on Earth’s Waterways.

Anurag Agrawal: Monarch butterflies—out of sight, but not out of mind!

By Anurag Agrawal

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The annual migratory calendar for monarch butterflies in eastern North America.

As winter approaches, monarch butterflies are not in sight for most Americans. Beginning in the fall, hundreds of millions of butterflies east of the Rocky Mountains oriented south and began their migration. And indeed the story of how they navigate is truly remarkable: the little insect uses a sun compass that is adjustable depending on the time of day to find its way. Details of the migration and much more are in Monarchs and Milkweed: A Migrating Butterfly, a Poisonous Plant, and their Remarkable Story of Coevolution. And 2017 was a spectacular fall season for monarch butterflies. As far as most monarch biologists can remember, this was perhaps the biggest summer season on record, with monarchs in epic numbers congregating and flying south.

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Southward migrating monarchs in Ontario during autumn. Although monarchs are usually dispersed in the summer, as the fall migration takes hold, butterflies congregate in larger clusters.

As the holiday season approaches, it is useful to keep in to keep in mind where monarchs are and what they are doing.  Cool and concentrated, they huddle en masse for nearly five months.  Will the numbers of butterflies overwintering in Mexico this year show a rebound from their precipitous decline?  If the migration was successful, yes, we all expect (hope!) the numbers to be up.  But only time will tell, as the official numbers are typically announced each February by World Wildlife Fund Mexico.  The monitoring of these unimaginable aggregations of butterflies has been a critical piece in the conservation puzzle for monarchs.

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The state license plate in Michoacán State, Mexico.

In November around the Day of the Dead and leading to American Thanksgiving, monarchs arrive to their overwintering grounds in the highlands Michoacán, Mexico. And legend has it that the butterflies are the returning souls of loved ones. They form clusters that are so dense, they weigh down the Oyamel Fir trees they inhabit above 10,000 feet of elevation in these exquisite sites. The sites are terribly small, with all of them fitting into area smaller than New York City.

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A congregation of monarchs within the Monarch Butterfly Biosphere Reserve, a UNESCO World Heritage Site. Most wings are closed, but look for the orange spots of open butterfly wings.

But before 1975, there was no conservation conversation about monarchs, because scientists simply did not know where monarchs went in the winter (of course native Mexicans of the region have known for centuries).  More importantly, we didn’t know how restricted and sensitive their overwintering sites are. The story of how the monarchs were found is too lengthy to recount here, but it is an astonishing story. In short, Professor Urquhart from the University of Toronto was hot on the trail, and knew that they flew south into Mexico during the fall.  Nora and Fred Urquhart marshaled a citizen science campaign that included a massive effort to engage folks far and wide in the search for the overwintering grounds.  In fact, in 1973, they wrote an article in an English language newspaper in Mexico City requesting help in finding the monarch overwintering sites.

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I obtained this reproduction of the original article outlining monarch butterfly biology and requesting help finding the overwintering grounds from the Library of Congress. It came on microfiche and was a treasure to hold and read.

Still, it was another two years before the overwintering colonies were found and reported to the world. After thirty years of tagging butterflies, enlisting thousands of citizen scientists, and much speculation, shortly after new year’s day in January 1975, the great discovery was made. The Urquharts wrote to their thousands of volunteers: “We now wish to announce to our associates, that, after these many years of intensive study, after having tagged thousands of migrants, we have, finally located the exact area where they overwinter, with the very able assistance of Ken Brugger and Cathy Brugger of Mexico City”. And the rest is history.

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.

Agrawal

Matthew J. Salganik on Bit by Bit: Social Research in the Digital Age

In just the past several years, we have witnessed the birth and rapid spread of social media, mobile phones, and numerous other digital marvels. In addition to changing how we live, these tools enable us to collect and process data about human behavior on a scale never before imaginable, offering entirely new approaches to core questions about social behavior. Bit by Bit is the key to unlocking these powerful methods—a landmark book that will fundamentally change how the next generation of social scientists and data scientists explores the world around us. Matthew Salganik has provided an invaluable resource for social scientists who want to harness the research potential of big data and a must-read for data scientists interested in applying the lessons of social science to tomorrow’s technologies. Read on to learn more about the ideas in Bit by Bit.

Your book begins with a story about something that happened to you in graduate school. Can you talk a bit about that? How did that lead to the book?

That’s right. My dissertation research was about fads, something that social scientists have been studying for about as long as there have been social scientists. But because I happened to be in the right place at the right time, I had access to an incredibly powerful tool that my predecessors didn’t: the Internet. For my dissertation, rather than doing an experiment in a laboratory on campus—as many of my predecessors might have—we built a website where people could listen to and download new music. This website allowed us to run an experiment that just wasn’t possible in the past. In my book, I talk more about the scientific findings from that experiment, but while it was happening there was a specific moment that changed me and that directly led to this book. One morning, when I came into my basement office, I discovered that overnight about 100 people from Brazil had participated in my experiment. To me, this was completely shocking. At that time, I had friends running traditional lab experiments, and I knew how hard they had to work to have even 10 people participate. However, with my online experiment, 100 people participated while I was sleeping. Doing your research while you are sleeping might sound too good to be true, but it isn’t. Changes in technology—specifically the transition from the analog age to the digital age—mean that we can now collect and analyze social data in new ways. Bit by Bit is about doing social research in these new ways.

Who is this book for?

This book is for social scientists who want to do more data science, data scientists who want to do more social science, and anyone interested in the hybrid of these two fields. I spend time with both social scientists and data scientists, and this book is my attempt to bring the ideas from the communities together in a way that avoids the jargon of either community.  

In your talks, I’ve heard that you compare data science to a urinal.  What’s that about?

Well, I compare data science to a very specific, very special urinal: Fountain by the great French artist Marcel Duchamp. To create Fountain, Duchamp had a flash of creativity where he took something that was created for one purpose—going to the bathroom—and turned it a piece of art. But most artists don’t work that way. For example, Michelangelo, didn’t repurpose. When he wanted to create a statue of David, he didn’t look for a piece of marble that kind of looked like David: he spent three years laboring to create his masterpiece. David is not a readymade; it is a custommade.

These two styles—readymades and custommades—roughly map onto styles that can be employed for social research in the digital age. My book has examples of data scientists cleverly repurposing big data sources that were originally created by companies and governments. In other examples, however, social scientists start with a specific question and then used the tools of the digital age to create the data needed to answer that question. When done well, both of these styles can be incredibly powerful. Therefore, I expect that social research in the digital age will involve both readymades and custommades; it will involve both Duchamps and Michelangelos.

Bit by Bit devotes a lot attention to ethics.  Why?

The book provides many of examples of how researchers can use the capabilities of the digital age to conduct exciting and important research. But, in my experience, researchers who wish to take advantage of these new opportunities will confront difficult ethical decisions. In the digital age, researchers—often in collaboration with companies and governments—have increasing power over the lives of participants. By power, I mean the ability to do things to people without their consent or even awareness. For example, researchers can now observe the behavior of millions of people, and researchers can also enroll millions of people in massive experiments. As the power of researchers is increasing, there has not been an equivalent increase in clarity about how that power should be used. In fact, researchers must decide how to exercise their power based on inconsistent and overlapping rules, laws, and norms. This combination of powerful capabilities and vague guidelines can force even well-meaning researchers to grapple with difficult decisions. In the book, I try to provide principles that can help researchers—whether they are in universities, governments, or companies—balance these issues and move forward in a responsible way.

Your book went through an unusual Open Review process in addition to peer review. Tell me about that.

That’s right. This book is about social research in the digital age, so I also wanted to publish it in a digital age way. As soon as I submitted the book manuscript for peer review, I also posted it online for an Open Review during which anyone in the world could read it and annotate it. During this Open Review process dozens of people left hundreds of annotations, and I combined these annotations with the feedback from peer review to produce a final manuscript. I was really happy with the annotations that I received, and they really helped me improve the book.

The Open Review process also allowed us to collect valuable data. Just as the New York Times is tracking which stories get read and for how long, we could see which parts of the book were being read, how people arrived to the book, and which parts of the book were causing people to stop reading.

Finally, the Open Review process helped us get the ideas in the book in front of the largest possible audience. During Open Review, we had readers from all over the world, and we even had a few course adoptions. Also, in addition to posting the manuscript in English, we machine translated it into more than 100 languages, and we saw that these other languages increased our traffic by about 20%.

Was putting your book through Open Review scary?

No, it was exhilarating. Our back-end analytics allowed me see that people from around the world were reading it, and I loved the feedback that I received. Of course, I didn’t agree with all the annotations, but they were offered in a helpful spirit, and, as I said, many of them really improved the book.

Actually, the thing that is really scary to me is putting out a physical book that can’t be changed anymore. I wanted to get as much feedback as possible before the really scary thing happened.

And now you’ve made it easy for other authors to put their manuscripts through Open Review?

Absolutely. With a grant from the Sloan Foundation, we’ve released the Open Review Toolkit. It is open source software that enables authors and publishers to convert book manuscripts into a website that can be used for Open Review. And, as I said, during Open Review, you can receive valuable feedback to help improve your manuscript, feedback that is very complimentary to the feedback from peer review. During Open Review, you can also collect valuable data to help launch your book. Furthermore, all of these good things are happening at the same time that you are increasing access to scientific research, which is a core value of many authors and academic publishers.

SalganikMatthew J. Salganik is professor of sociology at Princeton University, where he is also affiliated with the Center for Information Technology Policy and the Center for Statistics and Machine Learning. His research has been funded by Microsoft, Facebook, and Google, and has been featured on NPR and in such publications as the New Yorker, the New York Times, and the Wall Street Journal.

Browse Our Earth Science 2018 Catalog

Our new Earth Science 2018 catalog ranges from the northernmost reaches of the globe to the unfathomable depths of its oceans, while also covering essential techniques and concepts in the fields of complexity and predictive ecology. 

If you will be attending the American Geophysical Union 2017 meeting in New Orleans this weekend, please stop by booth 730, where you can pick up a copy of the catalog in person and see our full range of books in Earth Science.

In the forthcoming Brave New Arctic, Mark Serreze details the history and the science of the precipitous warming of the Arctic, and its potentially devastating consequences for the planet as a whole. Drawing on his own work, as well as that of pioneering climate scientists, Brave New Arctic is a fascinating account of the not-so-frozen North. 

Brave New Arctic, by Mark Serreze

Eelco Rohling’s The Oceans traces the history of the planet’s oceans from the Earth’s formation to the present day, demonstrating the critical role they play in the Earth’s climate system. Concise but comprehensive, The Oceans is an essential introduction to paleoceanography, from one of AGU’s newest fellows.  

The Oceans, by Eelco Rohling

Drawing on simple computational models, Natural Complexity by Paul Charbonneau analyzes the emergence of complex behaviors and structure in natural phenomena from forest fires to epidemic diseases. Including complete source code in Python, Natural Complexity is a straightforward introduction to complexity in all its forms.

Natural Complexity, by Paul Charbonneau

What is involved in making ecology a more predictive science? In Ecological Forecasting, Michael Dietze covers the cutting-edge techniques that are driving modern ecology, complete with case studies and hands-on examples using R.

Ecological Forecasting, by Michael C. Dietze