Archives for November 2017

Ya-Wen Lei: Ideological Struggles and China’s Contentious Public Sphere

This post has been republished by the Fairbank Center for Chinese Studies at Harvard University.

Lei

Ideology was a critical theme at China’s 19th Party Congress in October 2017. In his speech, President Xi Jinping emphasized China’s “cultural confidence” as well as “Chinese values.” Attempting to import any other kind of political regime, he argued, would fail to match China’s social, historical and cultural conditions. Interestingly, however, at the same time that he rejected foreign political models, Xi promoted China’s particular version of modernization as a valuable model for other countries.

At the domestic level, Xi stressed the importance of controlling ideology, regulating the internet, and actively attacking “false” views within China’s public sphere. For Xi, ideology is a powerful tool that can, at best, unify the Chinese people or, at worst, turn them against the Chinese state.

In fact, ideology has been a priority for Xi ever since he became General Secretary of the Chinese Communist Party in 2012. This focus is understandable, I argue, precisely given the rising influence of liberal ideology within China’s public sphere.

Let me illustrate this by discussing one example, explored in greater depth in my book, The Contentious Public Sphere: Law, Media, and Authoritarian Rule in China. In Chapter 5, I analyze the political orientation of the top 100 opinion leaders on Weibo—one of China’s most popular social media sites—and the connections among them in 2015.

I classified Weibo opinion leaders into the following categories: political liberals, political conservatives, and others. I defined political liberals as those who express support on Weibo for constitutionalism (government authority derives from and should be limited by the constitution) and universal values (e.g., human rights, freedom, justice, equality), and political conservatives as those who argue against those principles. I classified as “others” those who expressed no views either way. I looked at people’s views on constitutionalism and universal values because these are particularly contested and politicized ideas in China given their association with Western liberal democracy. These are, in short, ideas that would not be popular in China if ideology were functioning “properly” from the government perspective.

Despite the Chinese government’s ideological control and censorship, I found that 58% of the top 100 Weibo opinion leaders in 2015 were political liberals, while only 15% were political conservatives. My analysis looked specifically at January of 2015, after the Chinese government launched its “purge the internet” campaign in August 2013 and arrested several opinion leaders. This was also after the government’s effort to use Weibo to create more “positive energy.” Presumably, then, the percentage of political liberals among opinion leaders might well have been even higher before the Chinese government’s intensified crackdowns.

In the following graph, I map the connections among the top 100 Weibo opinion leaders using social network analysis. Blue, red, and white nodes represent political liberals, political conservatives, and others, respectively. The graph reveals the greater level of influence of political liberals in general online, the dense connections among liberals themselves, and their seemingly greater influence on those who may be “on the fence” politically or simply more cautious about expressing their views of constitutionalism and universal values online. Importantly, political liberals would not have become so popular and influential had it not been for the direct and indirect endorsement of Chinese citizens.

Lei

Figure: Top 100 Weibo opinion leaders. Note: An edge between two opinion leaders is directional, showing that one opinion leader follows the other on Weibo. Blue, red, and white nodes represent political liberals, political conservatives, and others, respectively. Squares, triangles, boxes, diamonds, and circles denote media professionals, lawyers and legal scholars, scholars in non-law disciplines, entrepreneurs, and others, respectively. Gray and black edges show“following” across and between people with the same political orientation, respectively.

In short, the graph reveals a situation that contrasts sharply with the Chinese public sphere the government would like to see. The dissemination of liberal discourse and ideology, as well as growing public criticism of social and political problems in China, has only heightened the Chinese state’s concerns regarding ideology.

So, is ideology even “working” in China—at least in the way Xi would like? If constitutionalism and universal values are Western views that need to be discouraged and even attacked as “false,” this map of online opinion leaders in China suggests the government has its work cut out for it. How this happened, how it has changed China’s public sphere, and whether and how the govenment might attempt to regain ideological control moving foward are all questions I explore futher in my book, The Contentious Public Sphere: Law, Media, and Authoritarian Rule in China.

Ya-Wen Lei is an assistant professor in the Department of Sociology and an affiliate of the Fairbank Center for Chinese Studies at Harvard University. She is the author of The Contentious Public Sphere: Law, Media, and Authoritarian Rule in China.

Eelco J. Rohling on The Oceans: A Deep History

It has often been said that we know more about the moon than we do about our own oceans. In fact, we know a great deal more about the oceans than many people realize. Scientists know that our actions today are shaping the oceans and climate of tomorrow—and that if we continue to act recklessly, the consequences will be dire. In this timely and accessible book, Eelco Rohling traces the 4.4 billion-year history of Earth’s oceans while also shedding light on the critical role they play in our planet’s climate system. An invaluable introduction to the cutting-edge science of paleoceanography, The Oceans enables you to make your own informed opinions about the environmental challenges we face as a result of humanity’s unrelenting drive to exploit the world ocean and its vital resources. Read on to learn more about the ideas in Eelco Rohling’s new book.

How/Why did you become a specialist in past ocean and climate change?
When I was a boy, I actually wanted to become a brain surgeon. But I did not pass the lottery to get into medical school when I went to university. So I thought about what else to study for a year before trying again. I ended up doing geology, and never looked back—I pushed on with that instead of trying medical school again. In geology, I developed a fascination with the past environments in which animals and plants lived that we now find as fossils. So after my BSc, I did an MSc with a major in microfossils and palaeo-oceanography/-climatology, supported by minors in sedimentary systems and physical oceanography/climatology. Things started to really come together when I started my PhD project, for which I started to truly integrate these streams in a research context. That’s when my interest in past ocean and climate change became much deeper and more specific.

Why did you choose to write a book about the history of the oceans?
I discussed a few ideas with my editor Eric Henney, and we gradually brought the various ideas together into this book concept. We strongly felt that the vast existing knowledge about the past oceans (and past climate) needed to be better articulated, and placed in context of modern changes in these systems, and in the life that they sustain.

Why do we need to understand the history of the oceans?
The oceans’ past holds many fascinating pieces of information about how the ocean/climate system works, and how it interacts with life and the planet itself. No other field can bring that information to the table. The oceans’ history also holds important clues about how Earth may recover from human impact, and on what timescales such a recovery may be expected. This brings important context to the discussion about modern human impact.

Does the history of the oceans give any relevant information about their future?
Oh, yes. It illustrates the key processes by which carbon-cycle changes have occurred over Earth history, and whet the timescales were for these changes. It also illustrates which processes we might try to accelerate to drive atmospheric carbon-removal on timescales useful to humankind. Moreover, the history of the oceans provides insight into the developments (and extinctions) of life on Earth, which again gives context about the severity and rapidity of current changes on Earth.

Why does a book about the oceans contain so much about climate?
The oceans are an integral part of the climate system. The climate system is a complex beast that spans the atmosphere, hydrosphere (all forms of water), cryosphere (all forms of ice), lithosphere (the rocks), and biosphere (all forms of life, be it living or dead). The oceans are a vital link in all this, and one cannot talk about ocean changes without touching upon climate changes, or the other way around.

The oceans appear to have gone through very large changes in the past. How do the changes cause by humanity compare?
The human-caused changes are large, but not among the largest that have ever happened. But the human-caused changes are unique with respect to the rates of change: modern changes are 10 to 100 times faster than the fastest-ever natural changes any time before humans appeared on the scene. And, also, human-made changes have significant impacts from many different sides: warming, ocean acidification, physical (e.g., plastic) pollution, chemical pollution, eutrophication, overfishing, etc. Natural changes were not that all-encompassing. So modern changes are very scary in relation to the natural changes that have occurred, even when including major extinction events.

Are humans really causing damage to the enormous oceans and the life they contain?
Yes, for sure.Humans have trouble imagining how their (often little) actions can add up over time, and across the massive population numbers. But we’re on this planet with well over 7 billion people, all of whom at least partly rely on the ocean as a key resource for such things as: dumping waste/pollution from plastics to oil and from radioactive materials to chemical waste and fertilizers; transportation (with spillages), food production/fisheries; war-mongering, exploration/mining, energy production, etc. Added up over our massive human population and increasing technical infrastructure, all of these aspects alone have devastating impacts already, but taken together they are heading down a particularly terminal route.

OceansEelco J. Rohling is professor of ocean and climate change in the Research School of Earth Sciences at the Australian National University and at the University of Southampton’s National Oceanography Centre Southampton.

Browse Our Anthropology 2018 Catalog

Our Anthropology 2018 catalog includes a guide to thinking like an anthropologist, an in-depth ethnography of a would-be revolutionary middle school in New York, and a powerful argument that culture is the key driver of the success of humans as a species.

If you will be at the American Anthropological Association meeting in Washington DC this week, please visit us at booth 408, where you can pick up a copy of the catalog, and see our full range of titles in Anthropology.

Matthew Engelke’s How to Think Like an Anthropologist is a vivid and entertaining introduction to the key concepts and aims of anthropology. If you have ever been asked what it that anthropologists do and why you do it, How to Think Like an Anthropologist is the perfect answer.

How to Think Like an Anthropologist, by Matthew Engelke

Disruptive Fixation, by Christo Sims, examines the efforts of digital disruptors to revolutionize education through the lens of an innovative middle school project, from the earliest stages of planning to the graduation of its first eight-grade class, and analyzes the ways in which these efforts often fall short of their radical ambitions.

Disruptive Fixation, by Christo Sims

Robert Boyd argues that humans are A Different Kind of Animal, and that our growth to become the dominant species on the planet has been driven by our ability to learn from one another, and to establish the social norms that are the framework for human society—in a word, culture.

A Different Kind of Animal, by Robert Boyd

Find these titles, and many more, in our Anthropology 2018 catalog.

Alexander Thurston on Boko Haram: The History of an African Jihadist Movement

ThurstonBoko Haram is one of the world’s deadliest jihadist groups. It has killed more than twenty thousand people and displaced more than two million in a campaign of terror that began in Nigeria but has since spread to Chad, Niger, and Cameroon as well. This is the first book to tell the full story of this West African affiliate of the Islamic State, from its beginnings in the early 2000s to its most infamous violence, including the 2014 kidnapping of 276 Nigerian schoolgirls. In an in-depth account of a group that is menacing Africa’s most populous and richest country, Alexander Thurston also illuminates the dynamics of civil war in Africa and jihadist movements in other parts of the world. Read on to learn more about this deadly terrorist group and what is being done to stop them.

What is Boko Haram?

Boko Haram is a jihadist group, or rather cluster of groups, that emerged in northeastern Nigeria in the early 2000s. The group has called itself by various names, and “Boko Haram” is a nickname given by outsiders—it means “Western education is forbidden by Islam.” The nickname refers to a central theme that its founder Muhammad Yusuf used in his preaching, namely the idea that Western-style education (and democracy) were anti-Islamic. Boko Haram was involved sporadically in violence before 2009, but its transformation into a sustained insurgency occurred that year, when Yusuf and his followers clashed with authorities. Yusuf was killed during the initial uprising, but his followers regrouped under Abubakar Shekau and began to commit regular assassinations and attacks the next year. Boko Haram began to hold significant amounts of territory in northeastern Nigeria in 2014, which prompted Nigeria’s neighbors to intervene more strongly. In 2015, back on the defensive, Boko Haram pledged allegiance to the Islamic State (also known as ISIS and ISIL). Boko Haram continues to stage attacks in Nigeria, as well as in the neighboring countries, especially Niger. In summer 2016, a public schism emerged in the group, with one faction remaining loyal to Shekau and another following Abu Mus‘ab al-Barnawi, who has pledged to reduce civilian casualties and refocus Boko Haram’s efforts on fighting states and militaries. Boko Haram is most infamous for its mass kidnapping of 276 teenage schoolgirls in the town of Chibok, Nigeria in April 2014.

How has the Nigerian government responded to Boko Haram?

The Nigerian government has used a heavy-handed, military-focused approach to Boko Haram. The approach involves serious and systematic human rights violations—extrajudicial killings, collective arrests, detentions without trial, and torture. This approach has itself become a driver of the crisis, antagonizing civilians and reducing their willingness to work with authorities. In some cases, a desire for revenge has even pushed some civilians into joining or working with Boko Haram. Nigerian politicians repeatedly debated and haltingly pursued the idea of dialogue with Boko Haram starting around 2012, but it was not until 2016 that negotiations bore some fruit, resulting in two waves of releases/prisoner swaps of some of the “Chibok girls.” The current president, Muhammadu Buhari (elected 2015), has been quite eager to declare Boko Haram defeated, but its attacks continue to trouble the northeastern part of Nigeria.

What are the biggest misperceptions about Boko Haram?

One key misperception is the idea that Boko Haram is a direct consequence of demography, poverty, and underdevelopment in northern Nigeria. That thesis does not explain why Boko Haram emerged in the northeast, rather than elsewhere in the north, nor does it explain why there are not many more movements like Boko Haram in Nigeria’s neighbors, which suffer from many of the same problems. In a related way, many observers continue to believe that Boko Haram’s founder Muhammad Yusuf was a nonviolent critic of Nigerian government corruption; in truth, he rejected the entire premise of Nigeria’s secular state, and he flirted with violent jihadism from an early point in his career. By the time Yusuf’s message was fully developed, he was not calling for reform in the existing order, but for a complete overhaul of the system.

Another key misconception, however, is the claim that Boko Haram is merely an extension of the global jihadist movement—that it was created and managed by al-Qaeda, or that it now is merely a branch of the Islamic State. The reality is more complicated; Boko Haram’s early contacts with al-Qaeda were patchy, and al-Qaeda had trouble getting Yusuf and Shekau to follow their advice, so much so that al-Qaeda seems to have broken off contact with Yusuf well before the 2009 uprising, which was a disaster for Boko Haram. Given the flaws in these simplistic hypotheses—the poverty hypothesis or the global jihadism hypothesis—there is a need to develop more complicated understandings of Boko Haram. That’s what my book tries to do.

What are the key arguments of your book?

The main argument is that Boko Haram reflects a complicated intersection of politics and religion in northeastern Nigeria, and that this intersection can only be understood by examining developments at the local level, especially in the city of Maiduguri and the surrounding state of Borno. Political developments that contributed to Boko Haram’s rise included the implementation of “full shari‘a” in northern Nigerian states in the early 2000s, a highly competitive gubernatorial election in Borno in 2003, and bitter memories among northern Muslims regarding intercommunal violence dating back to the 1980s. Religious developments involved a rapidly shifting “religious field” in northeastern Nigeria. Yusuf’s rise coincided with new opportunities for young preachers to gain prominence as key scholars in Maiduguri were either aging and passing away, or were absent because they were studying in the Arab world.

Another, related argument is that although Boko Haram horrified and antagonized almost all Muslims in northern Nigeria, it did not come out of nowhere. Boko Haram and Yusuf picked up on ideas that had been circulating for several decades, particularly the idea that Nigeria needed to become an Islamic state, and the idea that Western-style education was undermining the moral fabric of northern Nigerian society.

In what way does religion matter for Boko Haram?

When the relationship between religion and jihadism gets discussed in the media and popular outlets, analysts often focus on the question of whether individuals really believe in what they’re saying—whether jihadists are pious and well-informed about religion, and whether recruits join jihadist groups out of conviction or opportunism. To me, those debates are of limited interest because it’s difficult to get inside the minds and hearts of individuals, and to know what they really believe. So for me, the most important way to think about religion’s role in jihadism is in terms of the “religious field”—the totality of actors and institutions vying to define and shape a religious tradition in a particular setting. Whether or not Boko Haram’s leaders and followers are truly religious and pious, they certainly see themselves as operating in a religious field. Their vocabulary, their propaganda, the leaders’ interactions with followers, and often the targets of their violence all reflect a self-conscious invocation of religion and Islam, or at least Islam as Boko Haram tries to define it. A big part of the book is an effort to show how Boko Haram found a niche in northern Nigeria’s religious field, and how it has tried to reshape the field around it.

ThurstonAlexander Thurston is visiting assistant professor of African studies at Georgetown University and the author of Salafism in Nigeria: Islam, Preaching, and Politics.

Big Pacific: The Galápagos Tortoise, a roaming reptile

From pages 116-118 of Big Pacific:

Perhaps the best known Galápagos inhabitants are the tortoises after which the archipelago was named — the word ‘galápago’ meaning tortoise in Spanish. Sometimes weighing in excess of 400 kilograms (900 pounds), they are the world’s largest tortoise, and also one of its longest lived.

Galápagos tortoises can survive without food or water for six months or more by breaking down body fat to produce sufficient water and nutrients. This remarkable adaptation helps them endure droughts on the islands’ arid lowlands, but also led to their mass exploitation by whalers and sealers who captured and kept the animals on board their ships as a convenient source of fresh meat for long sea voyages. This led not just to a rapid decline in Galápagos tortoise numbers but the extinction of several sub-species once found on the islands.

[Galápagos tortoises] move regularly from arid lowlands to lusher highlands, over time creating trails across the landscape.

Typically the herbivorous animals’ diet is the product of a daily routine which sees them wander along well-worn paths from the lower slopes of their island homes to the volcanic highlands. Here the tortoises enjoy the abundance of water and plants — including an introduced and highly invasive species of guava that now seems to be sustaining some tortoise populations.

Big Pacific: Passionate, Voracious, Mysterious, Violent
By Rebecca Tansley

The Pacific Ocean covers one-third of Earth’s surface—more than all of the planet’s landmasses combined. It contains half of the world’s water, hides its deepest places, and is home to some of the most dazzling creatures known to science. The companion book to the spectacular five-part series on PBS produced by Natural History New Zealand, Big Pacific breaks the boundaries between land and sea to present the Pacific Ocean and its inhabitants as you have never seen them before.

Illustrated in full color throughout, Big Pacific blends a wealth of stunning Ultra HD images with spellbinding storytelling to take you into a realm teeming with exotic life rarely witnessed up close—until now. The book is divided into four sections, each one focusing on an aspect of the Pacific. “Passionate Pacific” looks at the private lives of sea creatures, with topics ranging from the mating behaviors of great white sharks to the monogamy of wolf eels, while “Voracious Pacific” covers hunting and feeding. In “Mysterious Pacific,” you will be introduced to the Pacific’s more extraordinary creatures, like the pufferfish and firefly squid, and explore some of the region’s eerier locales, like the turtle tombs of Borneo and the skull caves of Papua New Guinea. “Violent Pacific” examines the effects of events like natural disasters on the development of the Pacific Ocean’s geography and the evolution of its marine life.

Providing an unparalleled look at a diverse range of species, locations, and natural phenomena, Big Pacific is truly an epic excursion to one of the world’s last great frontiers.

Learn more by watching Big Pacific, airing Sundays on PBS Guam and CPTV Spirit. Watch the trailer below:

 

 

Bird Fact Friday — The Variegated Fairywren

It’s Black Bird Fact Friday, so let’s celebrate with a look at another beautiful bird.

From page 230 of Birds of Australia:

Australia’s most widespread fairywren. Like males of several other fairywrens, the male Variegated has a blue crown contiguous with a pointed blue ear patch, a black throat and upper breast, a white lower breast, and a large chestnut shoulder patch. The blue markings are not uniform and have a bright, shimmering iridescent quality. There are distinct subspecies, which differ in the intensity of the blue crown colour. The males can be separated from those of Lovely, Blue-breasted, and Red-winged Fairywrens by the light blue edges at the sides of the breast, lacking in those species.

A female Variegated Fairywren (Malurus lamberti). Photo credit: Geoff Jones.

Females differmuch more among subspecies; over most of Australia they are sandy brown above and buff below, with a white-tipped blue tail and chestnut lores and eye rings that create a masked appearance. Superb Fairywren females differ in lacking a fine white tip to the tail. Variegated females from Arnhem Land (NT) and the Kimberley region (WA) are white below and have black wings and beautiful powder-blue upperparts. Small groups of this common bird generally favour undergrowth and clearings within habitats such as open woodlands, eucalypt forests, mallee, mulga, and even rainforest edges in e.Australia. Variegated is found all over mainland Australia except the s. and n. extremities.

Birds of Australia
By Iain Campbell, Sam Woods & Nick Leseberg
With photography by Geoff Jones

Australia is home to a spectacular diversity of birdlife, from parrots and penguins to emus and vibrant passerines. Birds of Australia covers all 714 species of resident birds and regularly occurring migrants and features more than 1,100 stunning color photographs, including many photos of subspecies and plumage variations never before seen in a field guide. Detailed facing-page species accounts describe key identification features such as size, plumage, distribution, behavior, and voice. This one-of-a-kind guide also provides extensive habitat descriptions with a large number of accompanying photos. The text relies on the very latest IOC taxonomy and the distribution maps incorporate the most current mapping data, making this the most up-to-date guide to Australian birds.

  • Covers all 714 species of resident birds and regularly occurring migrants
  • Features more than 1,100 stunning color photos
  • Includes facing-page species accounts, habitat descriptions, and distribution maps
  • The ideal photographic guide for beginners and seasoned birders alike

Pariah Moonshine Part II: For Whom the Moon Shines

by Joshua Holden

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

HoldenI ended Part I with the observation that the Monster group was connected with the symmetries of a group sitting in 196883-dimensional space, whereas the number 196884 appeared as part of a function used in number theory, the study of the properties of whole numbers.  In particular, a mathematician named John McKay noticed the number as one of the coefficients of a modular form.  Modular forms also exhibit a type of symmetry, namely if F is a modular form then there is some number k for which

Figure 1

for every set of whole numbers a, b, c, and d such that adbc=1.  (There are also some conditions as the real part of z goes to infinity.)

Modular forms, elliptic curves, and Fermat’s Last Theorem

In 1954, Martin Eichler was studying modular forms and observing patterns in their coefficients.  For example, take the modular form

Figure 2

(I don’t know whether Eichler actually looked at this particular form, but he definitely looked at similar ones.)  The coefficients of this modular form seem to be related to the number of whole number solutions of the equation

y2 = x3 – 4 x2 + 16

This equation is an example of what is known as an elliptic curve, which is a curve given by an equation of the form

y2 = x3 + ax2 + bx + c

Note that elliptic curves are not ellipses!  Elliptic curves have one line of symmetry, two open ends, and either one or two pieces, as shown in Figures 1 and 2. They are called elliptic curves because the equations came up in the seventeenth century when mathematicians started studying the arc length of an ellipse.  These curves are considered the next most complicated type of curve after lines and conic sections, both of which have been understood pretty well since at least the ancient Greeks.   They are useful for a lot of things, including cryptography, as I describe in Section 8.3 of The Mathematics of Secrets.

Figure 1

Figure 1. The elliptic curve y2= x3 + x has one line of symmetry, two open ends, and one piece.

Figure 2

Figure 2. The elliptic curve y2 = x3 – x has one line of symmetry, two open ends, and two pieces.

 

In the late 1950’s it was conjectured that every elliptic curve was related to a modular form in the way that the example above is.  Proving this “Modularity Conjecture” took on more urgency in the 1980’s, when it was shown that showing the conjecture was true would also prove Fermat’s famous Last Theorem.  In 1995 Andrew Wiles, with help from Richard Taylor, proved enough of the Modularity Conjecture to show that Fermat’s Last Theorem was true, and the rest of the Modularity Conjecture was filled in over the next six years by Taylor and several of his associates.

Modular forms, the Monster, and Moonshine

Modular forms are also related to other shapes besides elliptic curves, and in the 1970’s John McKay and John Thompson became convinced that the modular form

J(z) = e -2 π i z + 196884 e 2 π i z + 21493760 e 4 π i z  + 864299970 e 6 π i z  + …

was related to the Monster.  Not only was 196884 equal to 196883 + 1, but 21493760 was equal to 21296876 + 196883 + 1, and 21296876 was also a number that came up in the study of the Monster.  Thompson suggested that there should be a natural way of associating the Monster with an infinite-dimensional shape, where the infinite-dimensional shape broke up into finite-dimensional pieces with each piece having a dimension corresponding to one of the coefficients of J(z).   This shape was (later) given the name V♮, using the natural sign from musical notation in a typically mathematical pun.  (Terry Gannon points out that there is also a hint that the conjectures “distill information illegally” from the Monster.) John Conway and Simon Norton formulated some guesses about the exact connection between the Monster and V♮, and gave them the name “Moonshine Conjectures” to reflect their speculative and rather unlikely-seeming nature. A plausible candidate for V♮ was constructed in the 1980’s and Richard Borcherds proved in 1992 that the candidate satisfied the Moonshine Conjectures.  This work was specifically cited when Borcherds was awarded the Fields medal in 1998.

The construction of V♮ turned out also to have a close connection with mathematical physics.  The reconciliation of gravity with quantum mechanics is one of the central problems of modern physics, and most physicists think that string theory is likely to be key to this resolution.  In string theory, the objects we traditionally think of as particles, like electrons and quarks, are really tiny strings curled up in many dimensions, most of which are two small for us to see.  An important question about this theory is exactly what shape these dimensions curl into.  One possibility is a 24-dimensional shape where the possible configurations of strings in the shape are described by V♮.  However, there are many other possible shapes and it is not known how to determine which one really corresponds to our world.

More Moonshine?

Since Borcherds’ proof, many variations of the original “Monstrous Moonshine” have been explored.  The other members of the Happy Family can be shown to have Moonshine relationships similar to those of the Monster.  “Modular Moonshine” says that certain elements of the Monster group should have their own infinite dimensional shapes, related to but not the same as V♮.  (The “modular” in “Modular Moonshine” is related to the one in “modular form” because they are both related to modular arithmetic, although the chain of connections is kind of long. )  “Mathieu Moonshine” shows that one particular group in the Happy Family has its own shape, entirely different from V♮, and “Umbral Moonshine” extends this to 23 other related groups which are not simple groups.  But the Pariah groups remained outsiders, rejected by both the Happy Family and by Moonshine — until September 2017.

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.

A peek inside ‘Paul Cézanne: Painting People’

This beautifully illustrated book features twenty-four masterpieces in portraiture by celebrated French artist Paul Cézanne (1839–1906), offering an excellent introduction to this important aspect of his work. Art historian Mary Tompkins Lewis contributes an illuminating essay on Cézanne and his portraiture for general readers, alongside an illustrated chronology of the artist’s life and work. Check out the trailer to see a preview of Cézanne’s stunning portraiture.

Mary Tompkins Lewis is an art historian, critic, and visiting associate professor of fine arts at Trinity College, Hartford. Her books include Cézanne: Art and Ideas and Cézanne’s Early Imagery.

Pariah Moonshine Part I: The Happy Family and the Pariah Groups

by Joshua Holden

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

HoldenBeing a mathematician, I often get asked if I’m good at calculating tips. I’m not. In fact, mathematicians study lots of other things besides numbers. As most people know, if they stop to think about it, one of the other things mathematicians study is shapes. Some of us are especially interested in the symmetries of those shapes, and a few of us are interested in both numbers and symmetries. The recent announcement of “Pariah Moonshine” has been one of the most exciting developments in the relationship between numbers and symmetries in quite some time. In this blog post I hope to explain the “Pariah” part, which deals mostly with symmetries. The “Moonshine”, which connects the symmetries to numbers, will follow in the next post.

What is a symmetry?

First I want to give a little more detail about what I mean by the symmetries of shapes. If you have a square made out of paper, there are basically eight ways you can pick it up, turn it, and put it down in exactly the same place. You can rotate it 90 degrees clockwise or counterclockwise. You can rotate it 180 degrees. You can turn it over, so the front becomes the back and vice versa. You can turn in over and then rotate it 90 degrees either way, or 180 degrees. And you can rotate it 360 degrees, which basically does nothing. We call these the eight symmetries of the square, and they are shown in Figure 1.

Figure1

Figure 1. The square can be rotated into four different positions, without or without being flipped over, for eight symmetries total.

If you have an equilateral triangle, there are six symmetries. If you have a pentagon, there are ten. If you have a pinwheel with four arms, there are only four symmetries, as shown in Figure 2, because now you can rotate it but if you turn it over it looks different. If you have a pinwheel with six arms, there are six ways. If you have a cube, there are 24 if the cube is solid, as shown in Figure 3. If the cube is just a wire frame and you are allowed to turn it inside out, then you get 24 more, for a total of 48.

Figure 2

Figure 2. The pinwheel can be rotated but not flipped, for four symmetries total.

Figure 3

Figure 3. The cube can be rotated along three different axes, resulting in 24 different symmetries.

These symmetries don’t just come with a count, they also come with a structure. If you turn a square over and then rotate it 90 degrees, it’s not the same thing as if you rotate it first and then flip it over. (Try it and see.) In this way, symmetries of shapes are like the permutations I discuss in Chapter 3 of my book, The Mathematics of Secrets: you can take products, which obey some of the same rules as products of numbers but not all of them. These sets of symmetries, which their structures, are called groups.

Groups are sets of symmetries with structure

Some sets of symmetries can be placed inside other sets. For example, the symmetries of the four-armed pinwheel are the same as the four rotations in the symmetries of the square. We say the symmetries of the pinwheel are a subgroup of the symmetries of the square. Likewise, the symmetries of the square are a subgroup of the symmetries of the solid cube, if you allow yourself to turn the cube over but not tip it 90 degrees, as shown in Figure 4.

Figure 4

Figure 4. The symmetries of the square are contained inside the symmetries of the cube if you are allowed to rotate and flip the cube but not tip it 90 degrees.

In some cases, ignoring a subgroup of the symmetries of a shape gets us another group, which we call the quotient group. If you ignore the subgroup of how the square is rotated, you get the quotient group where the square is flipped over or not, and that’s it. Those are the same as the symmetries of the capital letter A, so the quotient group is really a group. In other cases, for technical reasons, you can’t get a quotient group. If you ignore the symmetries of a square inside the symmetries of a cube, what’s left turns out not to be the symmetries of any shape.

You can always ignore all the symmetries of a shape and get just the do nothing (or trivial) symmetry, which is the symmetries of the capital letter P, in the quotient group. And you can always ignore none of the nontrivial symmetries, and get all of the original symmetries still in the quotient group. If these are the only two possible quotient groups, we say that the group is simple. The group of symmetries of a pinwheel with a prime number of arms is simple. So is the group of symmetries of a solid icosahedron, like a twenty-sided die in Dungeons and Dragons. The group of symmetries of a square is not simple, because of the subgroup of rotations. The group of symmetries of a solid cube is not simple, not because of the symmetries of the square, but because of the smaller subgroup of symmetries of a square with a line through it, as shown in Figures 5 and 6. The quotient group there is the same as the symmetries of the equilateral triangle created by cutting diagonally through a cube near a corner.

Figure 5

Figure 5. The symmetries of a square with line through it. We can turn the square 180 degrees and/or flip it, but not rotate it 90 degrees, so there are four.

Figure 6

Figure 6. The symmetries of the square with a line through it inside of the symmetries of the cube.

Categorizing the Pariah groups

As early as 1892, Otto Hölder asked if we could categorize all of the finite simple groups. (There are also shapes, like the circle, which have an infinite number of symmetries. We won’t worry about them now.)  It wasn’t until 1972 that Daniel Gorenstein made a concrete proposal for how to make a complete categorization, and the project wasn’t finished until 2002, producing along the way thousands of pages of proofs. The end result was that almost all of the finite simple groups fell into a few infinitely large categories: the cyclic groups, which are the groups of symmetries of pinwheels with a prime number of arms, the alternating groups, which are the groups of symmetries of solid hypertetrahedra in 5 or more dimensions, and the “groups of Lie type”, which are related to matrix multiplication over finite fields and describe certain symmetries of objects known as finite projective planes and finite projective spaces. (Finite fields are used in the AES cipher and I talk about them in Section 4.5 of The Mathematics of Secrets.)

Even before 1892, a few finite simple groups were discovered that didn’t seem to fit into any of these categories. Eventually it was proved that there were 26 “sporadic” groups, which didn’t fit into any of the categories and didn’t describe the symmetries of anything obvious — basically, you had to construct the shape to fit the group of symmetries that you knew existed, instead of starting with the shape and finding the symmetries. The smallest of the sporadic groups has 7920 symmetries in it, and the largest, known as the Monster, has over 800 sexdecillion symmetries. (That’s an 8 with 53 zeros after it!) Nineteen of the other sporadic groups turn out to be subgroups or quotient groups of subgroups of the Monster. These 20 became known as the Happy Family. The other 6 sporadic groups became known as the ‘Pariahs’.

The shape that was constructed to fit the Monster lives in 196883-dimensional space. In the late 1970’s a mathematician named John McKay noticed the number 196884 turning up in a different area of mathematics. It appeared as part of a function used in number theory, the study of the properties of whole numbers. Was there a connection between the Monster and number theory? Or was the idea of a connection just … moonshine?

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.

Big Pacific: Palolo Worms, the sprawling spectacle

From pages 23-24 of Big Pacific:

Mysteriously driven by the moon’s cycle, the mass spawning of Palolo worms leads to a unique annual harvest on many Pacific islands. In Samoa it is an eagerly anticipated, communal event. Equidistant between Hawai‘i and New Zealand, Samoa is part of the group of islands known as Polynesia. Samoans have long been sustained by the Pacific’s bounty, and they regard the protein-rich Palolo worms as an extra-special gift of the sea.

Between midnight and dawn — the timing depends on the exact location — the first few worms emerge from the coral reefs. Soon their writhing forms swirl upwards in the water like a frenzy of animated scribbles.

Harvested epitokes are eaten raw, fried in butter or cooked with egg or onion.

Measuring around 30 centimeters (12 inches) in length, these animals spend most of their lives buried inside the substrate of the ocean floor. Once a year they undergo a remarkable transformation, sprouting an extended tail segment, called an epitoke, that is filled with either eggs or sperm. The epitoke — colored either pale tan (male) or bluegreen (female) — also sports a primitive, light-sensitive eye that guides it to the sea’s surface.

Prompted somehow by lunar phases, all the worms in one area release their epitokes more or less in unison. This simultaneous timing maximizes the chances of fertilization and creates one of the ocean’s greatest mass spawning events.

After fertilization, the eggs drift away on the currents to hatch into larvae. For a time these form part of the ocean’s planktonic biomass, but eventually the maturing worms settle on the seafloor to begin the miraculous and mysterious cycle again.

Big Pacific: Passionate, Voracious, Mysterious, Violent
By Rebecca Tansley

The Pacific Ocean covers one-third of Earth’s surface—more than all of the planet’s landmasses combined. It contains half of the world’s water, hides its deepest places, and is home to some of the most dazzling creatures known to science. The companion book to the spectacular five-part series on PBS produced by Natural History New Zealand, Big Pacific breaks the boundaries between land and sea to present the Pacific Ocean and its inhabitants as you have never seen them before.

Illustrated in full color throughout, Big Pacific blends a wealth of stunning Ultra HD images with spellbinding storytelling to take you into a realm teeming with exotic life rarely witnessed up close—until now. The book is divided into four sections, each one focusing on an aspect of the Pacific. “Passionate Pacific” looks at the private lives of sea creatures, with topics ranging from the mating behaviors of great white sharks to the monogamy of wolf eels, while “Voracious Pacific” covers hunting and feeding. In “Mysterious Pacific,” you will be introduced to the Pacific’s more extraordinary creatures, like the pufferfish and firefly squid, and explore some of the region’s eerier locales, like the turtle tombs of Borneo and the skull caves of Papua New Guinea. “Violent Pacific” examines the effects of events like natural disasters on the development of the Pacific Ocean’s geography and the evolution of its marine life.

Providing an unparalleled look at a diverse range of species, locations, and natural phenomena, Big Pacific is truly an epic excursion to one of the world’s last great frontiers.

Learn more by watching Big Pacific, airing Sundays on PBS Guam and CPTV Spirit. Watch the trailer below:

 

 

Browse Our Religion 2018 Catalog

The offerings in our new Religion catalog include an in-depth investigation of the philanthropic projects of the billionaire evangelical owners of the craft chain Hobby Lobby and their plans to make America a “Bible Nation” once again, a new historically-grounded critique of the religious nationalism and radical secularism found on both sides of America’s culture war, and an examination of the key cognitive process that makes religion possible.

If you’ll be at the joint Annual Meetings of AAR-SBL in Boston this weekend, please join us at Booth 2627 in the Exhibit Hall. Stop by any time to see our full range of religion titles.

 

Like many evangelical Christians, the Green family of Oklahoma City believes that America was founded as a Christian nation, based on a “biblical worldview.” But the Greens are far from typical evangelicals. As America’s biggest financial supporters of Christian causes they are spending hundreds of millions of dollars in an ambitious effort to increase the Bible’s influence on American society. The crown jewel of their efforts, the lavishly-appointed Museum of the Bible, is opening this weekend in Washington DC around the corner from the National Mall. In Bible Nation, Candida Moss and Joel Baden provide the first in-depth investigative account of the Greens’ sweeping Bible projects and the many questions they raise.

Was the United States founded as a Christian nation or a secular democracy? Neither,argues Philip Gorski in his new history of “civil religion” in the United States, American Covenant. What the founders actually envisioned was a prophetic republic that would weave together the ethical vision of the Hebrew prophets and the Western political heritage of civic republicanism. In this ambitious book, Gorski shows why this civil religious tradition is now in peril—and with it the American experiment.

Religion remains a crucial influence in the world today, yet as sociologist of religion Christian Smith argues, the social sciences are still not adequately equipped to understand and explain it. Building on recent developments in social science theory and philosophy, this book advances an innovative theory of religion that addresses key questions about the nature, powers, workings, appeal, and future of religion.

 

Bird Fact Friday — Red-Rumped Parrot

From page 194 of Birds of Australia:

The male Red-Rumped Parrot is a bright green parrot with a red rump, lemon-yellow belly and vent, and a subtle blue wash on the shoulder and forehead. It is told from male Mulga Parrot by its lack of red on the nape and vent and absence of a yellow shoulder patch. Females are dull brownish-green with little colour except some green on the rump. The lack of any strong shoulder mark or reddish nape patch separates this species from female Mulga Parrot.

A male Red-Rumped Parrot (Psephotus haematonotus)

Red-rumped parrot is most likely to be found in pairs or small flocks. It readily perches in the open, is often conspicuous and approachable, and is more regularly found around country towns than Mulga Parrot. Red-rumped is a common species of the south-east, where it occurs in farmlands with scattered trees and grassy and other open woodlands, often around watercourses.

Birds of Australia
By Iain Campbell, Sam Woods & Nick Leseberg
With photography by Geoff Jones

Australia is home to a spectacular diversity of birdlife, from parrots and penguins to emus and vibrant passerines. Birds of Australia covers all 714 species of resident birds and regularly occurring migrants and features more than 1,100 stunning color photographs, including many photos of subspecies and plumage variations never before seen in a field guide. Detailed facing-page species accounts describe key identification features such as size, plumage, distribution, behavior, and voice. This one-of-a-kind guide also provides extensive habitat descriptions with a large number of accompanying photos. The text relies on the very latest IOC taxonomy and the distribution maps incorporate the most current mapping data, making this the most up-to-date guide to Australian birds.

  • Covers all 714 species of resident birds and regularly occurring migrants
  • Features more than 1,100 stunning color photos
  • Includes facing-page species accounts, habitat descriptions, and distribution maps
  • The ideal photographic guide for beginners and seasoned birders alike