We Aren’t the World
Joe Henrich and his colleagues are shaking the foundations of psychology and economics—and hoping to change the way social scientists think about human behavior and culture.
(ILLUSTRATION: MARK MCGINNIS)
February 25, 2013 • By Ethan Watters •
IN THE SUMMER of 1995, a young graduate student in anthropology at UCLA named Joe Henrich traveled to Peru to carry out some fieldwork among the Machiguenga, an indigenous people who live north of Machu Picchu in the Amazon basin. The Machiguenga had traditionally been horticulturalists who lived in single-family, thatch-roofed houses in small hamlets composed of clusters of extended families. For sustenance, they relied on local game and produce from small-scale farming. They shared with their kin but rarely traded with outside groups.
While the setting was fairly typical for an anthropologist, Henrich’s research was not. Rather than practice traditional ethnography, he decided to run a behavioral experiment that had been developed by economists. Henrich used a “game”—along the lines of the famous prisoner’s dilemma—to see whether isolated cultures shared with the West the same basic instinct for fairness. In doing so, Henrich expected to confirm one of the foundational assumptions underlying such experiments, and indeed underpinning the entire fields of economics and psychology: that humans all share the same cognitive machinery—the same evolved rational and psychological hardwiring.
The test that Henrich introduced to the Machiguenga was called the ultimatum game. The rules are simple: in each game there are two players who remain anonymous to each other. The first player is given an amount of money, say $100, and told that he has to offer some of the cash, in an amount of his choosing, to the other subject. The second player can accept or refuse the split. But there’s a hitch: players know that if the recipient refuses the offer, both leave empty-handed. North Americans, who are the most common subjects for such experiments, usually offer a 50-50 split when on the giving end. When on the receiving end, they show an eagerness to punish the other player for uneven splits at their own expense. In short, Americans show the tendency to be equitable with strangers—and to punish those who are not.
Among the Machiguenga, word quickly spread of the young, square-jawed visitor from America giving away money. The stakes Henrich used in the game with the Machiguenga were not insubstantial—roughly equivalent to the few days’ wages they sometimes earned from episodic work with logging or oil companies. So Henrich had no problem finding volunteers. What he had great difficulty with, however, was explaining the rules, as the game struck the Machiguenga as deeply odd.
When he began to run the game it became immediately clear that Machiguengan behavior was dramatically different from that of the average North American. To begin with, the offers from the first player were much lower. In addition, when on the receiving end of the game, the Machiguenga rarely refused even the lowest possible amount. “It just seemed ridiculous to the Machiguenga that you would reject an offer of free money,” says Henrich. “They just didn’t understand why anyone would sacrifice money to punish someone who had the good luck of getting to play the other role in the game.”
Joe Henrich was a graduate student when he tested the ultimatum game on the Machiguenga of Peru.
The potential implications of the unexpected results were quickly apparent to Henrich. He knew that a vast amount of scholarly literature in the social sciences—particularly in economics and psychology—relied on the ultimatum game and similar experiments. At the heart of most of that research was the implicit assumption that the results revealed evolved psychological traits common to all humans, never mind that the test subjects were nearly always from the industrialized West. Henrich realized that if the Machiguenga results stood up, and if similar differences could be measured across other populations, this assumption of universality would have to be challenged.
Henrich had thought he would be adding a small branch to an established tree of knowledge. It turned out he was sawing at the very trunk. He began to wonder: What other certainties about “human nature” in social science research would need to be reconsidered when tested across diverse populations?
Henrich soon landed a grant from the MacArthur Foundation to take his fairness games on the road. With the help of a dozen other colleagues he led a study of 14 other small-scale societies, in locales from Tanzania to Indonesia. Differences abounded in the behavior of both players in the ultimatum game. In no society did he find people who were purely selfish (that is, who always offered the lowest amount, and never refused a split), but average offers from place to place varied widely and, in some societies—ones where gift-giving is heavily used to curry favor or gain allegiance—the first player would often make overly generous offers in excess of 60 percent, and the second player would often reject them, behaviors almost never observed among Americans.
The research established Henrich as an up-and-coming scholar. In 2004, he was given the U.S. Presidential Early Career Award for young scientists at the White House. But his work also made him a controversial figure. When he presented his research to the anthropology department at the University of British Columbia during a job interview a year later, he recalls a hostile reception. Anthropology is the social science most interested in cultural differences, but the young scholar’s methods of using games and statistics to test and compare cultures with the West seemed heavy-handed and invasive to some. “Professors from the anthropology department suggested it was a bad thing that I was doing,” Henrich remembers. “The word ‘unethical’ came up.”
So instead of toeing the line, he switched teams. A few well-placed people at the University of British Columbia saw great promise in Henrich’s work and created a position for him, split between the economics department and the psychology department. It was in the psychology department that he found two kindred spirits in Steven Heine and Ara Norenzayan. Together the three set about writing a paper that they hoped would fundamentally challenge the way social scientists thought about human behavior, cognition, and culture.
A MODERN LIBERAL ARTS education gives lots of lip service to the idea of cultural diversity. It’s generally agreed that all of us see the world in ways that are sometimes socially and culturally constructed, that pluralism is good, and that ethnocentrism is bad. But beyond that the ideas get muddy. That we should welcome and celebrate people of all backgrounds seems obvious, but the implied corollary—that people from different ethno-cultural origins have particular attributes that add spice to the body politic—becomes more problematic. To avoid stereotyping, it is rarely stated bluntly just exactly what those culturally derived qualities might be. Challenge liberal arts graduates on their appreciation of cultural diversity and you’ll often find them retreating to the anodyne notion that under the skin everyone is really alike.
If you take a broad look at the social science curriculum of the last few decades, it becomes a little more clear why modern graduates are so unmoored. The last generation or two of undergraduates have largely been taught by a cohort of social scientists busily doing penance for the racism and Eurocentrism of their predecessors, albeit in different ways. Many anthropologists took to the navel gazing of postmodernism and swore off attempts at rationality and science, which were disparaged as weapons of cultural imperialism.
Economists and psychologists, for their part, did an end run around the issue with the convenient assumption that their job was to study the human mind stripped of culture. The human brain is genetically comparable around the globe, it was agreed, so human hardwiring for much behavior, perception, and cognition should be similarly universal. No need, in that case, to look beyond the convenient population of undergraduates for test subjects. A 2008 survey of the top six psychology journals dramatically shows how common that assumption was: more than 96 percent of the subjects tested in psychological studies from 2003 to 2007 were Westerners—with nearly 70 percent from the United States alone. Put another way: 96 percent of human subjects in these studies came from countries that represent only 12 percent of the world’s population.
Henrich’s work with the ultimatum game was an example of a small but growing countertrend in the social sciences, one in which researchers look straight at the question of how deeply culture shapes human cognition. His new colleagues in the psychology department, Heine and Norenzayan, were also part of this trend. Heine focused on the different ways people in Western and Eastern cultures perceived the world, reasoned, and understood themselves in relationship to others. Norenzayan’s research focused on the ways religious belief influenced bonding and behavior. The three began to compile examples of cross-cultural research that, like Henrich’s work with the Machiguenga, challenged long-held assumptions of human psychological universality.
Some of that research went back a generation. It was in the 1960s, for instance, that researchers discovered that aspects of visual perception were different from place to place. One of the classics of the literature, the Müller-Lyer illusion, showed that where you grew up would determine to what degree you would fall prey to the illusion that these two lines are different in length:
Researchers found that Americans perceive the line with the ends feathered outward (B) as being longer than the line with the arrow tips (A). San foragers of the Kalahari, on the other hand, were more likely to see the lines as they are: equal in length. Subjects from more than a dozen cultures were tested, and Americans were at the far end of the distribution—seeing the illusion more dramatically than all others.
More recently psychologists had challenged the universality of research done in the 1950s by pioneering social psychologist Solomon Asch. Asch had discovered that test subjects were often willing to make incorrect judgments on simple perception tests to conform with group pressure. When the test was performed across 17 societies, however, it turned out that group pressure had a range of influence. Americans were again at the far end of the scale, in this case showing the least tendency to conform to group belief.
As Heine, Norenzayan, and Henrich furthered their search, they began to find research suggesting wide cultural differences almost everywhere they looked: in spatial reasoning, the way we infer the motivations of others, categorization, moral reasoning, the boundaries between the self and others, and other arenas. These differences, they believed, were not genetic. The distinct ways Americans and Machiguengans played the ultimatum game, for instance, wasn’t because they had differently evolved brains. Rather, Americans, without fully realizing it, were manifesting a psychological tendency shared with people in other industrialized countries that had been refined and handed down through thousands of generations in ever more complex market economies. When people are constantly doing business with strangers, it helps when they have the desire to go out of their way (with a lawsuit, a call to the Better Business Bureau, or a bad Yelp review) when they feel cheated. Because Machiguengan culture had a different history, their gut feeling about what was fair was distinctly their own. In the small-scale societies with a strong culture of gift-giving, yet another conception of fairness prevailed. There, generous financial offers were turned down because people’s minds had been shaped by a cultural norm that taught them that the acceptance of generous gifts brought burdensome obligations. Our economies hadn’t been shaped by our sense of fairness; it was the other way around.
The growing body of cross-cultural research that the three researchers were compiling suggested that the mind’s capacity to mold itself to cultural and environmental settings was far greater than had been assumed. The most interesting thing about cultures may not be in the observable things they do—the rituals, eating preferences, codes of behavior, and the like—but in the way they mold our most fundamental conscious and unconscious thinking and perception.
For instance, the different ways people perceive the Müller-Lyer illusion likely reflects lifetimes spent in different physical environments. American children, for the most part, grow up in box-shaped rooms of varying dimensions. Surrounded by carpentered corners, visual perception adapts to this strange new environment (strange and new in terms of human history, that is) by learning to perceive converging lines in three dimensions.
When unconsciously translated in three dimensions, the line with the outward-feathered ends (C) appears farther away and the brain therefore judges it to be longer. The more time one spends in natural environments, where there are no carpentered corners, the less one sees the illusion.
As the three continued their work, they noticed something else that was remarkable: again and again one group of people appeared to be particularly unusual when compared to other populations—with perceptions, behaviors, and motivations that were almost always sliding down one end of the human bell curve.
In the end they titled their paper “The Weirdest People in the World?” (pdf) By “weird” they meant both unusual and Western, Educated, Industrialized, Rich, and Democratic. It is not just our Western habits and cultural preferences that are different from the rest of the world, it appears. The very way we think about ourselves and others—and even the way we perceive reality—makes us distinct from other humans on the planet, not to mention from the vast majority of our ancestors. Among Westerners, the data showed that Americans were often the most unusual, leading the researchers to conclude that “American participants are exceptional even within the unusual population of Westerners—outliers among outliers.”
Given the data, they concluded that social scientists could not possibly have picked a worse population from which to draw broad generalizations. Researchers had been doing the equivalent of studying penguins while believing that they were learning insights applicable to all birds.
NOT LONG AGO I met Henrich, Heine, and Norenzayan for dinner at a small French restaurant in Vancouver, British Columbia, to hear about the reception of their weird paper, which was published in the prestigious journal Behavioral and Brain Sciences in 2010. The trio of researchers are young—as professors go—good-humored family men. They recalled that they were nervous as the publication time approached. The paper basically suggested that much of what social scientists thought they knew about fundamental aspects of human cognition was likely only true of one small slice of humanity. They were making such a broadside challenge to whole libraries of research that they steeled themselves to the possibility of becoming outcasts in their own fields.
“We were scared,” admitted Henrich. “We were warned that a lot of people were going to be upset.”
“We were told we were going to get spit on,” interjected Norenzayan.
“Yes,” Henrich said. “That we’d go to conferences and no one was going to sit next to us at lunchtime.”
Interestingly, they seemed much less concerned that they had used the pejorative acronym WEIRD to describe a significant slice of humanity, although they did admit that they could only have done so to describe their own group. “Really,” said Henrich, “the only people we could have called weird are represented right here at this table.”
Still, I had to wonder whether describing the Western mind, and the American mind in particular, as weird suggested that our cognition is not just different but somehow malformed or twisted. In their paper the trio pointed out cross-cultural studies that suggest that the “weird” Western mind is the most self-aggrandizing and egotistical on the planet: we are more likely to promote ourselves as individuals versus advancing as a group. WEIRD minds are also more analytic, possessing the tendency to telescope in on an object of interest rather than understanding that object in the context of what is around it.
The WEIRD mind also appears to be unique in terms of how it comes to understand and interact with the natural world. Studies show that Western urban children grow up so closed off in man-made environments that their brains never form a deep or complex connection to the natural world. While studying children from the U.S., researchers have suggested a developmental timeline for what is called “folkbiological reasoning.” These studies posit that it is not until children are around 7 years old that they stop projecting human qualities onto animals and begin to understand that humans are one animal among many. Compared to Yucatec Maya communities in Mexico, however, Western urban children appear to be developmentally delayed in this regard. Children who grow up constantly interacting with the natural world are much less likely to anthropomorphize other living things into late childhood.
Given that people living in WEIRD societies don’t routinely encounter or interact with animals other than humans or pets, it’s not surprising that they end up with a rather cartoonish understanding of the natural world. “Indeed,” the report concluded, “studying the cognitive development of folkbiology in urban children would seem the equivalent of studying ‘normal’ physical growth in malnourished children.”
During our dinner, I admitted to Heine, Henrich, and Norenzayan that the idea that I can only perceive reality through a distorted cultural lens was unnerving. For me the notion raised all sorts of metaphysical questions: Is my thinking so strange that I have little hope of understanding people from other cultures? Can I mold my own psyche or the psyches of my children to be less WEIRD and more able to think like the rest of the world? If I did, would I be happier?
Henrich reacted with mild concern that I was taking this research so personally. He had not intended, he told me, for his work to be read as postmodern self-help advice. “I think we’re really interested in these questions for the questions’ sake,” he said.
The three insisted that their goal was not to say that one culturally shaped psychology was better or worse than another—only that we’ll never truly understand human behavior and cognition until we expand the sample pool beyond its current small slice of humanity. Despite these assurances, however, I found it hard not to read a message between the lines of their research. When they write, for example, that weird children develop their understanding of the natural world in a “culturally and experientially impoverished environment” and that they are in this way the equivalent of “malnourished children,” it’s difficult to see this as a good thing.
THE TURN THAT HENRICH, Heine, and Norenzayan are asking social scientists to make is not an easy one: accounting for the influence of culture on cognition will be a herculean task. Cultures are not monolithic; they can be endlessly parsed. Ethnic backgrounds, religious beliefs, economic status, parenting styles, rural upbringing versus urban or suburban—there are hundreds of cultural differences that individually and in endless combinations influence our conceptions of fairness, how we categorize things, our method of judging and decision making, and our deeply held beliefs about the nature of the self, among other aspects of our psychological makeup.
We are just at the beginning of learning how these fine-grained cultural differences affect our thinking. Recent research has shown that people in “tight” cultures, those with strong norms and low tolerance for deviant behavior (think India, Malaysia, and Pakistan), develop higher impulse control and more self-monitoring abilities than those from other places. Men raised in the honor culture of the American South have been shown to experience much larger surges of testosterone after insults than do Northerners. Research published late last year suggested psychological differences at the city level too. Compared to San Franciscans, Bostonians’ internal sense of self-worth is more dependent on community status and financial and educational achievement. “A cultural difference doesn’t have to be big to be important,” Norenzayan said. “We’re not just talking about comparing New York yuppies to the Dani tribesmen of Papua New Guinea.”
Norenzayan sees it, the last few generations of psychologists have suffered from “physics envy,” and they need to get over it. The job, experimental psychologists often assumed, was to push past the content of people’s thoughts and see the underlying universal hardware at work. “This is a deeply flawed way of studying human nature,” Norenzayan told me, “because the content of our thoughts and their process are intertwined.” In other words, if human cognition is shaped by cultural ideas and behavior, it can’t be studied without taking into account what those ideas and behaviors are and how they are different from place to place.
This new approach suggests the possibility of reverse-engineering psychological research: look at cultural content first; cognition and behavior second. Norenzayan’s recent work on religious belief is perhaps the best example of the intellectual landscape that is now open for study. When Norenzayan became a student of psychology in 1994, four years after his family had moved from Lebanon to America, he was excited to study the effect of religion on human psychology. “I remember opening textbook after textbook and turning to the index and looking for the word ‘religion,’ ” he told me, “Again and again the very word wouldn’t be listed. This was shocking. How could psychology be the science of human behavior and have nothing to say about religion? Where I grew up you’d have to be in a coma not to notice the importance of religion on how people perceive themselves and the world around them.”
Norenzayan became interested in how certain religious beliefs, handed down through generations, may have shaped human psychology to make possible the creation of large-scale societies. He has suggested that there may be a connection between the growth of religions that believe in “morally concerned deities”—that is, a god or gods who care if people are good or bad—and the evolution of large cities and nations. To be cooperative in large groups of relative strangers, in other words, might have required the shared belief that an all-powerful being was forever watching over your shoulder.
If religion was necessary in the development of large-scale societies, can large-scale societies survive without religion? Norenzayan points to parts of Scandinavia with atheist majorities that seem to be doing just fine. They may have climbed the ladder of religion and effectively kicked it away. Or perhaps, after a thousand years of religious belief, the idea of an unseen entity always watching your behavior remains in our culturally shaped thinking even after the belief in God dissipates or disappears.
Why, I asked Norenzayan, if religion might have been so central to human psychology, have researchers not delved into the topic? “Experimental psychologists are the weirdest of the weird,” said Norenzayan. “They are almost the least religious academics, next to biologists. And because academics mostly talk amongst themselves, they could look around and say, ‘No one who is important to me is religious, so this must not be very important.’” Indeed, almost every major theorist on human behavior in the last 100 years predicted that it was just a matter of time before religion was a vestige of the past. But the world persists in being a very religious place.
HENRICH, HEINE, AND NORENZAYAN’S FEAR of being ostracized after the publication of the WEIRD paper turned out to be misplaced. Response to the paper, both published and otherwise, has been nearly universally positive, with more than a few of their colleagues suggesting that the work will spark fundamental changes. “I have no doubt that this paper is going to change the social sciences,” said Richard Nisbett, an eminent psychologist at the University of Michigan. “It just puts it all in one place and makes such a bold statement.”
More remarkable still, after reading the paper, academics from other disciplines began to come forward with their own mea culpas. Commenting on the paper, two brain researchers from Northwestern University argued (pdf) that the nascent field of neuroimaging had made the same mistake as psychologists, noting that 90 percent of neuroimaging studies were performed in Western countries. Researchers in motor development similarly suggested that their discipline’s body of research ignored how different child-rearing practices around the world can dramatically influence states of development. Two psycholinguistics professors suggested that their colleagues had also made the same mistake: blithely assuming human homogeneity while focusing their research primarily on one rather small slice of humanity.
At its heart, the challenge of the WEIRD paper is not simply to the field of experimental human research (do more cross-cultural studies!); it is a challenge to our Western conception of human nature. For some time now, the most widely accepted answer to the question of why humans, among all animals, have so successfully adapted to environments across the globe is that we have big brains with the ability to learn, improvise, and problem-solve.
Henrich has challenged this “cognitive niche” hypothesis with the “cultural niche” hypothesis. He notes that the amount of knowledge in any culture is far greater than the capacity of individuals to learn or figure it all out on their own. He suggests that individuals tap that cultural storehouse of knowledge simply by mimicking (often unconsciously) the behavior and ways of thinking of those around them. We shape a tool in a certain manner, adhere to a food taboo, or think about fairness in a particular way, not because we individually have figured out that behavior’s adaptive value, but because we instinctively trust our culture to show us the way. When Henrich asked Fijian women why they avoided certain potentially toxic fish during pregnancy and breastfeeding, he found that many didn’t know or had fanciful reasons. Regardless of their personal understanding, by mimicking this culturally adaptive behavior they were protecting their offspring. The unique trick of human psychology, these researchers suggest, might be this: our big brains are evolved to let local culture lead us in life’s dance.
The applications of this new way of looking at the human mind are still in the offing. Henrich suggests that his research about fairness might first be applied to anyone working in international relations or development. People are not “plug and play,” as he puts it, and you cannot expect to drop a Western court system or form of government into another culture and expect it to work as it does back home. Those trying to use economic incentives to encourage sustainable land use will similarly need to understand local notions of fairness to have any chance of influencing behavior in predictable ways.
Because of our peculiarly Western way of thinking of ourselves as independent of others, this idea of the culturally shaped mind doesn’t go down very easily. Perhaps the richest and most established vein of cultural psychology—that which compares Western and Eastern concepts of the self—goes to the heart of this problem. Heine has spent much of his career following the lead of a seminal paper published in 1991 by Hazel Rose Markus, of Stanford University, and Shinobu Kitayama, who is now at the University of Michigan. Markus and Kitayama suggested that different cultures foster strikingly different views of the self, particularly along one axis: some cultures regard the self as independent from others; others see the self as interdependent. The interdependent self—which is more the norm in East Asian countries, including Japan and China—connects itself with others in a social group and favors social harmony over self-expression. The independent self—which is most prominent in America—focuses on individual attributes and preferences and thinks of the self as existing apart from the group.
The classic “rod and frame” task: Is the line in the center vertical?
That we in the West develop brains that are wired to see ourselves as separate from others may also be connected to differences in how we reason, Heine argues. Unlike the vast majority of the world, Westerners (and Americans in particular) tend to reason analytically as opposed to holistically. That is, the American mind strives to figure out the world by taking it apart and examining its pieces. Show a Japanese and an American the same cartoon of an aquarium, and the American will remember details mostly about the moving fish while the Japanese observer will likely later be able to describe the seaweed, the bubbles, and other objects in the background. Shown another way, in a different test analytic Americans will do better on something called the “rod and frame” task, where one has to judge whether a line is vertical even though the frame around it is skewed. Americans see the line as apart from the frame, just as they see themselves as apart from the group.
Heine and others suggest that such differences may be the echoes of cultural activities and trends going back thousands of years. Whether you think of yourself as interdependent or independent may depend on whether your distant ancestors farmed rice (which required a great deal of shared labor and group cooperation) or herded animals (which rewarded individualism and aggression). Heine points to Nisbett at Michigan, who has argued (pdf) that the analytic/holistic dichotomy in reasoning styles can be clearly seen, respectively, in Greek and Chinese philosophical writing dating back 2,500 years. These psychological trends and tendencies may echo down generations, hundreds of years after the activity or situation that brought them into existence has disappeared or fundamentally changed.
And here is the rub: the culturally shaped analytic/individualistic mind-sets may partly explain why Western researchers have so dramatically failed to take into account the interplay between culture and cognition. In the end, the goal of boiling down human psychology to hardwiring is not surprising given the type of mind that has been designing the studies. Taking an object (in this case the human mind) out of its context is, after all, what distinguishes the analytic reasoning style prevalent in the West. Similarly, we may have underestimated the impact of culture because the very ideas of being subject to the will of larger historical currents and of unconsciously mimicking the cognition of those around us challenges our Western conception of the self as independent and self-determined. The historical missteps of Western researchers, in other words, have been the predictable consequences of the WEIRD mind doing the thinking.
http://www.psmag.com/magazines/pacific-standard-cover-story/joe-henrich-weird-ultimatum-game-shaking-up-psychology-economics-53135/?utm_source=feedburner&utm_medium=feed&utm_campaign=Feed%3A+miller-mccune%2Fmain_feed+%28Pacific+Standard+-+Main+Feed%29&utm_content=Google+Reader
The title of this blogspot is a mix of the letter M, for mathematics, and a truncation of the number e, where e denotes the number 2.71828182845904523536028747135266249775724709369995, here truncated to 50 decimal plcs. In the clean world of math constructs, e is a prominant constant which has an infinite series for full representation. The blog itself covers news commentary, rational debates, quotes and humour on factual events and objectively understood ideas.
24 March 2013
Schoolchildren can learn complex subjects on their own
http://www.kurzweilai.net/schoolchildren-can-learn-complex-subjects-on-their-own
August 15, 2011
Educational researchers at the Technical University of Munich (TUM) have found that schoolchildren can independently develop strategies for solving complex mathematical tasks, with weaker students proving just as capable as their stronger classmates.
Researchers in mathematics education worked with approximately 1600 8th grade high-school students in various German states. Following an introduction to the general topic by their teachers, the school children were given a workbook of geometric tasks that they had to solve on paper and using a computer over four school periods. Calculating the surface area of Gran Canaria was one of the real-world, free-form assignments the students had to tackle. The workbook material included explanations and examples of various problem-solving approaches. The teachers took a back seat during the session but were on hand to answer questions from the children, who worked in pairs.
After testing the students’ skills before and after the session, the researchers recorded a significant improvement in their capabilities. The students learned to apply mathematics more effectively, the researchers said. The students were also able to call on these skills in a further test three months later.
“We expected students who were weaker at math to benefit more from a greater degree of guidance through the module,” said professor Kristina Reiss. ”But we didn’t see a significant difference between these and stronger students.”
The researchers also found that there were also no differences between boys and girls. “We now know that students — also those who are weaker in math — have the skills to master even very complex subject matters at their own pace,” said Reiss.
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http://www.psmag.com/magazines/pacific-standard-cover-story/joe-henrich-weird-ultimatum-game-shaking-up-psychology-economics-53135/?utm_source=feedburner&utm_medium=feed&utm_campaign=Feed%3A+miller-mccune%2Fmain_feed+%28Pacific+Standard+-+Main+Feed%29&utm_content=Google+Reader
22 March 2013
Women pioneering our understanding of chaos
Frank Y. Wang http://arxiv.org/pdf/0903.2671.pdf
The general public has been made aware of the research field of Chaos
by the book of that title by James Gleick.1 Since the publication of that best seller in 1987, the term ―chaos‖ has become a trendy word, and the title of the leading chapter ―butterfly effect‖ is a household name. While the idea of chaos seemed to emerge recently, it actually arose from the prize-winning work of one of the greatest mathematicians of the late nineteenth century—Henri Poincaré (1854–1912). Poincaré’s 1890 memoir on the three-body problem was the result of his entry in King Oscar II of Sweden’s 60th birthday competition. The Russian mathematician, Sonya Kovalevskaya (1850–1891), then a professor of the University of Stockholm, was consulted in the offering of the prize. About the same time, she finished her own celebrated work on the motion of a rigid body.2 From today’s point of view, with the benefit of 20/20 hindsight, the works of Poincaré and Kovalevskaya hinted at the failure of Newtonian determinism by using Newton’s own laws. The implication is that chaos is ubiquitous.
19 March 2013
Butterflies and tornadoes
http://www.bbc.co.uk/news/magazine-21713163
A Point of View: Mary, queen of maths
Maths genius Mary Cartwright was a modest soul and one of the early founders of chaos theory. It's time we recognised her massive contribution, says historian Lisa Jardine.
In his Mathematician's Apology, published in 1940, the great mathematician GH Hardy argued emphatically that pure mathematics is never useful. Yet at the very moment he was insisting that - specifically - "real mathematics has no effect on war", a mathematical breakthrough was being made which contributed to the wartime defence of Britain against enemy air attack.
What is more, that breakthrough laid the groundwork - unrecognised at the time - for an entire new field of science.
In January 1938, with the threat of war hanging over Europe, the British Government's Department of Scientific and Industrial Research sent a memorandum to the London Mathematical Society appealing to pure mathematicians to help them solve a problem involving a tricky type of equation. Although this was not stated in the memo, it related to top-secret developments in Radio Detection and Ranging - what was soon to become known as radar.
Engineers working on the project were having difficulty with the erratic behaviour of high-frequency radio waves. The need had arisen, the memo said, for "a more complete understanding of the actual behaviour of certain assemblages of electrical apparatus". Could any of the Mathematical Society's members help?
The request caught the attention of Dr Mary Cartwright, lecturer in mathematics at Girton College Cambridge. She was already working on similar "very objectionable-looking differential equations" (as she later described them).
She brought the request to the attention of her long-term colleague at Trinity College, Professor JE Littlewood and suggested that they combine forces. In a memoir written later in her life, she explained that he already had the necessary experience in dynamics, having worked on the trajectories of anti-aircraft guns during World War I.
The distinguished physicist and public intellectual Freeman Dyson - who was born in Britain but has, since the 1950s, spent most of his professional life at the Princeton Institute for Advanced Studies in America - heard Cartwright lecture on this work when he was a student at Cambridge in 1942. He gives us a vivid account of the importance of the war work Cartwright and Littlewood did:
"The whole development of radar in World War Two depended on high power amplifiers, and it was a matter of life and death to have amplifiers that did what they were supposed to do. The soldiers were plagued with amplifiers that misbehaved, and blamed the manufacturers for their erratic behaviour. Cartwright and Littlewood discovered that the manufacturers were not to blame. The equation itself was to blame."
In other words, odd things happened when some sorts of values were fed into the standard equation they were using to predict the amplifiers' performance. Cartwright and Littlewood were able to show that as the wavelength of radio waves shortens, their performance ceases to be regular and periodic, and becomes unstable and unpredictable. This work helped explain some perplexing phenomena engineers were encountering.
Cartwright herself was always somewhat diffident when asked to assess the lasting importance of her war work. She and Littlewood had provided a scientific explanation for some peculiar features of the behaviour of radio waves, but they did not in the end supply the answer in time. They simply succeeded in directing the engineers' attention away from faulty equipment towards practical ways of compensating for the electrical "noise" - or erratic fluctuations - being produced.
So while Cartwright and Littlewood were producing significant results on the stability of solutions to the equation describing the oscillation of radio waves, the engineers working on radar systems decided they could not wait for precise mathematical results. Instead, once it had been identified, they worked around the problem, by keeping the equipment within predictable ranges.
Perhaps in part because of her own overly modest assessment of its importance, Cartwright's original work went relatively unnoticed when it was published in the Journal of the London Mathematical Society shortly after the end of the war. Freeman Dyson maintains that this is a classic example of the way in which real mathematical originality and innovation is missed until a generation after the work has been done:
"When I heard Cartwright lecture in 1942, I remember being delighted with the beauty of her results. I could see the beauty of her work but I could not see its importance. I said to myself, 'This is a lovely piece of work. Too bad it is only a practical wartime problem and not real mathematics.' I did not say, 'This is the birth of a new field of mathematics.' I shared the tastes and prejudices of my contemporaries."
The "new field" Dyson refers to here, which he and his contemporaries failed to recognise, is chaos theory. Cartwright's early contribution to the field is now acknowledged in all histories of the subject, but was largely overlooked for almost 20 years.
The results unexpectedly obtained from the equations predicting the oscillations of radio waves are part of the foundation for the modern theory that accounts for the unpredictable behaviour of all manner of physical phenomena, from swinging pendulums and fluid flow, to the stock market.
Steadily increase the rate of flow of water into a rotating waterwheel, for example, and the wheel will go correspondingly faster. But at a certain point the behaviour of the wheel becomes unpredictable - speeding up and slowing down without warning, or even changing direction.
Chaos theory has been used to explain stock market behaviour
The recognition that chaotic behaviour is a vital part of many physical systems in the world around us came in 1961, when Edward Lorenz was running a weather simulation through an early computer. When he tested a particular configuration a second time he found that the outcome differed dramatically from his earlier run. Eventually he tracked the difference down to a small alteration he had inadvertently made in transferring the initial data, by altering the number of decimal places.
Lorenz immortalised this discovery in a lecture entitled "Does the Flap of a Butterfly's Wings in Brazil set off a Tornado in Texas?".
Today, when we think of chaos theory we associate it with all kinds of fundamentally unstable situations - but one of the most vivid to imagine is still the idea that one flap of a butterfly's wing deep in the Amazon rainforest is the cause of a weather system thousands of miles away.
This is the same kind of unpredictability arising from small changes in initial conditions that Cartwright and Littlewood had recognised and drawn attention to in their work with radio waves several decades earlier.
After the war, Mary Cartwright moved away from knotty differential equations and ended her collaboration with Littlewood. She went on to have a distinguished academic career in pure mathematics and academic administration, earning a succession of honours.
Caused by the flap of a butterfly's wings?
In 1947 she was the first woman mathematician to be elected to the Royal Society. In 1948 she became Mistress of Girton College Cambridge, then reader in the theory of functions in the Cambridge mathematics department in 1959. From 1961 to 1963 she was president of the London Mathematical Society, and received its highest honour, the de Morgan Medal, in 1968. She was made a Dame Commander of the British Empire in 1969.
She lived long enough to see the field in which she had made those early, important discoveries become a major part of modern mathematics, and to see it take its place in the popular imagination. She was, however, characteristically modest to the end about the part she had played.
Freeman Dyson claims that Littlewood did not understand the importance of the work that he and Cartwright had done: "Only Cartwright understood the importance of her work as the foundation of chaos theory, and she is not a person who likes to blow her own trumpet."
He records, however, that shortly before her death, he received an indignant letter from Cartwright, scolding him for crediting her with more than she deserved.
Dame Mary Cartwright died in 1998 at the age of 97. In one of the many obituaries paying tribute to her, a friend and colleague described her as "a person who combined distinction of achievement with a notable lack of self-importance".
She left strict instructions that there were to be no eulogies at her memorial service.
However, March 8 was International Women's Day, so it feels like a particularly appropriate time to blow Dame Mary Cartwright's trumpet on her behalf - for her brilliance as a mathematician, and as one of the founders of the important field of chaos theory.
A Point of View: Mary, queen of maths
Maths genius Mary Cartwright was a modest soul and one of the early founders of chaos theory. It's time we recognised her massive contribution, says historian Lisa Jardine.
In his Mathematician's Apology, published in 1940, the great mathematician GH Hardy argued emphatically that pure mathematics is never useful. Yet at the very moment he was insisting that - specifically - "real mathematics has no effect on war", a mathematical breakthrough was being made which contributed to the wartime defence of Britain against enemy air attack.
What is more, that breakthrough laid the groundwork - unrecognised at the time - for an entire new field of science.
In January 1938, with the threat of war hanging over Europe, the British Government's Department of Scientific and Industrial Research sent a memorandum to the London Mathematical Society appealing to pure mathematicians to help them solve a problem involving a tricky type of equation. Although this was not stated in the memo, it related to top-secret developments in Radio Detection and Ranging - what was soon to become known as radar.
Engineers working on the project were having difficulty with the erratic behaviour of high-frequency radio waves. The need had arisen, the memo said, for "a more complete understanding of the actual behaviour of certain assemblages of electrical apparatus". Could any of the Mathematical Society's members help?
The request caught the attention of Dr Mary Cartwright, lecturer in mathematics at Girton College Cambridge. She was already working on similar "very objectionable-looking differential equations" (as she later described them).
She brought the request to the attention of her long-term colleague at Trinity College, Professor JE Littlewood and suggested that they combine forces. In a memoir written later in her life, she explained that he already had the necessary experience in dynamics, having worked on the trajectories of anti-aircraft guns during World War I.
The distinguished physicist and public intellectual Freeman Dyson - who was born in Britain but has, since the 1950s, spent most of his professional life at the Princeton Institute for Advanced Studies in America - heard Cartwright lecture on this work when he was a student at Cambridge in 1942. He gives us a vivid account of the importance of the war work Cartwright and Littlewood did:
"The whole development of radar in World War Two depended on high power amplifiers, and it was a matter of life and death to have amplifiers that did what they were supposed to do. The soldiers were plagued with amplifiers that misbehaved, and blamed the manufacturers for their erratic behaviour. Cartwright and Littlewood discovered that the manufacturers were not to blame. The equation itself was to blame."
In other words, odd things happened when some sorts of values were fed into the standard equation they were using to predict the amplifiers' performance. Cartwright and Littlewood were able to show that as the wavelength of radio waves shortens, their performance ceases to be regular and periodic, and becomes unstable and unpredictable. This work helped explain some perplexing phenomena engineers were encountering.
Cartwright herself was always somewhat diffident when asked to assess the lasting importance of her war work. She and Littlewood had provided a scientific explanation for some peculiar features of the behaviour of radio waves, but they did not in the end supply the answer in time. They simply succeeded in directing the engineers' attention away from faulty equipment towards practical ways of compensating for the electrical "noise" - or erratic fluctuations - being produced.
So while Cartwright and Littlewood were producing significant results on the stability of solutions to the equation describing the oscillation of radio waves, the engineers working on radar systems decided they could not wait for precise mathematical results. Instead, once it had been identified, they worked around the problem, by keeping the equipment within predictable ranges.
Perhaps in part because of her own overly modest assessment of its importance, Cartwright's original work went relatively unnoticed when it was published in the Journal of the London Mathematical Society shortly after the end of the war. Freeman Dyson maintains that this is a classic example of the way in which real mathematical originality and innovation is missed until a generation after the work has been done:
"When I heard Cartwright lecture in 1942, I remember being delighted with the beauty of her results. I could see the beauty of her work but I could not see its importance. I said to myself, 'This is a lovely piece of work. Too bad it is only a practical wartime problem and not real mathematics.' I did not say, 'This is the birth of a new field of mathematics.' I shared the tastes and prejudices of my contemporaries."
The "new field" Dyson refers to here, which he and his contemporaries failed to recognise, is chaos theory. Cartwright's early contribution to the field is now acknowledged in all histories of the subject, but was largely overlooked for almost 20 years.
The results unexpectedly obtained from the equations predicting the oscillations of radio waves are part of the foundation for the modern theory that accounts for the unpredictable behaviour of all manner of physical phenomena, from swinging pendulums and fluid flow, to the stock market.
Steadily increase the rate of flow of water into a rotating waterwheel, for example, and the wheel will go correspondingly faster. But at a certain point the behaviour of the wheel becomes unpredictable - speeding up and slowing down without warning, or even changing direction.
Chaos theory has been used to explain stock market behaviour
The recognition that chaotic behaviour is a vital part of many physical systems in the world around us came in 1961, when Edward Lorenz was running a weather simulation through an early computer. When he tested a particular configuration a second time he found that the outcome differed dramatically from his earlier run. Eventually he tracked the difference down to a small alteration he had inadvertently made in transferring the initial data, by altering the number of decimal places.
Lorenz immortalised this discovery in a lecture entitled "Does the Flap of a Butterfly's Wings in Brazil set off a Tornado in Texas?".
Today, when we think of chaos theory we associate it with all kinds of fundamentally unstable situations - but one of the most vivid to imagine is still the idea that one flap of a butterfly's wing deep in the Amazon rainforest is the cause of a weather system thousands of miles away.
This is the same kind of unpredictability arising from small changes in initial conditions that Cartwright and Littlewood had recognised and drawn attention to in their work with radio waves several decades earlier.
After the war, Mary Cartwright moved away from knotty differential equations and ended her collaboration with Littlewood. She went on to have a distinguished academic career in pure mathematics and academic administration, earning a succession of honours.
Caused by the flap of a butterfly's wings?
In 1947 she was the first woman mathematician to be elected to the Royal Society. In 1948 she became Mistress of Girton College Cambridge, then reader in the theory of functions in the Cambridge mathematics department in 1959. From 1961 to 1963 she was president of the London Mathematical Society, and received its highest honour, the de Morgan Medal, in 1968. She was made a Dame Commander of the British Empire in 1969.
She lived long enough to see the field in which she had made those early, important discoveries become a major part of modern mathematics, and to see it take its place in the popular imagination. She was, however, characteristically modest to the end about the part she had played.
Freeman Dyson claims that Littlewood did not understand the importance of the work that he and Cartwright had done: "Only Cartwright understood the importance of her work as the foundation of chaos theory, and she is not a person who likes to blow her own trumpet."
He records, however, that shortly before her death, he received an indignant letter from Cartwright, scolding him for crediting her with more than she deserved.
Dame Mary Cartwright died in 1998 at the age of 97. In one of the many obituaries paying tribute to her, a friend and colleague described her as "a person who combined distinction of achievement with a notable lack of self-importance".
She left strict instructions that there were to be no eulogies at her memorial service.
However, March 8 was International Women's Day, so it feels like a particularly appropriate time to blow Dame Mary Cartwright's trumpet on her behalf - for her brilliance as a mathematician, and as one of the founders of the important field of chaos theory.
11 March 2013
Global Warming's Terrifying New Math
Global Warming's Terrifying New Math
Three simple numbers that add up to global catastrophe - and that make clear who the real enemy is
by: Bill McKibben
Illustration by Edel
Rodriguez
Meteorologists reported that this spring was the warmest ever recorded for our nation – in fact, it crushed the old record by so much that it represented the "largest temperature departure from average of any season on record." The same week, Saudi authorities reported that it had rained in Mecca despite a temperature of 109 degrees, the hottest downpour in the planet's history.
Not that our leaders seemed to notice. Last month the world's nations, meeting in Rio for the 20th-anniversary reprise of a massive 1992 environmental summit, accomplished nothing. Unlike George H.W. Bush, who flew in for the first conclave, Barack Obama didn't even attend. It was "a ghost of the glad, confident meeting 20 years ago," the British journalist George Monbiot wrote; no one paid it much attention, footsteps echoing through the halls "once thronged by multitudes." Since I wrote one of the first books for a general audience about global warming way back in 1989, and since I've spent the intervening decades working ineffectively to slow that warming, I can say with some confidence that we're losing the fight, badly and quickly – losing it because, most of all, we remain in denial about the peril that human civilization is in.
When we think about global warming at all, the arguments tend to be ideological, theological and economic. But to grasp the seriousness of our predicament, you just need to do a little math. For the past year, an easy and powerful bit of arithmetical analysis first published by financial analysts in the U.K. has been making the rounds of environmental conferences and journals, but it hasn't yet broken through to the larger public. This analysis upends most of the conventional political thinking about climate change. And it allows us to understand our precarious – our almost-but-not-quite-finally hopeless – position with three simple numbers.
The First Number: 2° Celsius
If the movie had ended in Hollywood fashion, the Copenhagen climate conference in 2009 would have marked the culmination of the global fight to slow a changing climate. The world's nations had gathered in the December gloom of the Danish capital for what a leading climate economist, Sir Nicholas Stern of Britain, called the "most important gathering since the Second World War, given what is at stake." As Danish energy minister Connie Hedegaard, who presided over the conference, declared at the time: "This is our chance. If we miss it, it could take years before we get a new and better one. If ever."
In the event, of course, we missed it. Copenhagen failed spectacularly. Neither China nor the United States, which between them are responsible for 40 percent of global carbon emissions, was prepared to offer dramatic concessions, and so the conference drifted aimlessly for two weeks until world leaders jetted in for the final day. Amid considerable chaos, President Obama took the lead in drafting a face-saving "Copenhagen Accord" that fooled very few. Its purely voluntary agreements committed no one to anything, and even if countries signaled their intentions to cut carbon emissions, there was no enforcement mechanism. "Copenhagen is a crime scene tonight," an angry Greenpeace official declared, "with the guilty men and women fleeing to the airport." Headline writers were equally brutal: COPENHAGEN: THE MUNICH OF OUR TIMES? asked one.
The accord did contain one important number, however. In Paragraph 1, it formally recognized "the scientific view that the increase in global temperature should be below two degrees Celsius." And in the very next paragraph, it declared that "we agree that deep cuts in global emissions are required... so as to hold the increase in global temperature below two degrees Celsius." By insisting on two degrees – about 3.6 degrees Fahrenheit – the accord ratified positions taken earlier in 2009 by the G8, and the so-called Major Economies Forum. It was as conventional as conventional wisdom gets. The number first gained prominence, in fact, at a 1995 climate conference chaired by Angela Merkel, then the German minister of the environment and now the center-right chancellor of the nation.
Some context: So far, we've raised the average temperature of the planet just under 0.8 degrees Celsius, and that has caused far more damage than most scientists expected. (A third of summer sea ice in the Arctic is gone, the oceans are 30 percent more acidic, and since warm air holds more water vapor than cold, the atmosphere over the oceans is a shocking five percent wetter, loading the dice for devastating floods.) Given those impacts, in fact, many scientists have come to think that two degrees is far too lenient a target. "Any number much above one degree involves a gamble," writes Kerry Emanuel of MIT, a leading authority on hurricanes, "and the odds become less and less favorable as the temperature goes up." Thomas Lovejoy, once the World Bank's chief biodiversity adviser, puts it like this: "If we're seeing what we're seeing today at 0.8 degrees Celsius, two degrees is simply too much." NASA scientist James Hansen, the planet's most prominent climatologist, is even blunter: "The target that has been talked about in international negotiations for two degrees of warming is actually a prescription for long-term disaster." At the Copenhagen summit, a spokesman for small island nations warned that many would not survive a two-degree rise: "Some countries will flat-out disappear." When delegates from developing nations were warned that two degrees would represent a "suicide pact" for drought-stricken Africa, many of them started chanting, "One degree, one Africa."
Despite such well-founded misgivings, political realism bested scientific data, and the world settled on the two-degree target – indeed, it's fair to say that it's the only thing about climate change the world has settled on. All told, 167 countries responsible for more than 87 percent of the world's carbon emissions have signed on to the Copenhagen Accord, endorsing the two-degree target. Only a few dozen countries have rejected it, including Kuwait, Nicaragua and Venezuela. Even the United Arab Emirates, which makes most of its money exporting oil and gas, signed on. The official position of planet Earth at the moment is that we can't raise the temperature more than two degrees Celsius – it's become the bottomest of bottom lines. Two degrees.
The Second Number: 565 Gigatons
Scientists estimate that humans can pour roughly 565 more gigatons of carbon dioxide into the atmosphere by midcentury and still have some reasonable hope of staying below two degrees. ("Reasonable," in this case, means four chances in five, or somewhat worse odds than playing Russian roulette with a six-shooter.)
This idea of a global "carbon budget" emerged about a decade ago, as scientists began to calculate how much oil, coal and gas could still safely be burned. Since we've increased the Earth's temperature by 0.8 degrees so far, we're currently less than halfway to the target. But, in fact, computer models calculate that even if we stopped increasing CO2 now, the temperature would likely still rise another 0.8 degrees, as previously released carbon continues to overheat the atmosphere. That means we're already three-quarters of the way to the two-degree target.
How good are these numbers? No one is insisting that they're exact, but few dispute that they're generally right. The 565-gigaton figure was derived from one of the most sophisticated computer-simulation models that have been built by climate scientists around the world over the past few decades. And the number is being further confirmed by the latest climate-simulation models currently being finalized in advance of the next report by the Intergovernmental Panel on Climate Change. "Looking at them as they come in, they hardly differ at all," says Tom Wigley, an Australian climatologist at the National Center for Atmospheric Research. "There's maybe 40 models in the data set now, compared with 20 before. But so far the numbers are pretty much the same. We're just fine-tuning things. I don't think much has changed over the last decade." William Collins, a senior climate scientist at the Lawrence Berkeley National Laboratory, agrees. "I think the results of this round of simulations will be quite similar," he says. "We're not getting any free lunch from additional understanding of the climate system."
We're not getting any free lunch from the world's economies, either. With only a single year's lull in 2009 at the height of the financial crisis, we've continued to pour record amounts of carbon into the atmosphere, year after year. In late May, the International Energy Agency published its latest figures – CO2 emissions last year rose to 31.6 gigatons, up 3.2 percent from the year before. America had a warm winter and converted more coal-fired power plants to natural gas, so its emissions fell slightly; China kept booming, so its carbon output (which recently surpassed the U.S.) rose 9.3 percent; the Japanese shut down their fleet of nukes post-Fukushima, so their emissions edged up 2.4 percent. "There have been efforts to use more renewable energy and improve energy efficiency," said Corinne Le Quéré, who runs England's Tyndall Centre for Climate Change Research. "But what this shows is that so far the effects have been marginal." In fact, study after study predicts that carbon emissions will keep growing by roughly three percent a year – and at that rate, we'll blow through our 565-gigaton allowance in 16 years, around the time today's preschoolers will be graduating from high school. "The new data provide further evidence that the door to a two-degree trajectory is about to close," said Fatih Birol, the IEA's chief economist. In fact, he continued, "When I look at this data, the trend is perfectly in line with a temperature increase of about six degrees." That's almost 11 degrees Fahrenheit, which would create a planet straight out of science fiction.
So, new data in hand, everyone at the Rio conference renewed their ritual calls for serious international action to move us back to a two-degree trajectory. The charade will continue in November, when the next Conference of the Parties (COP) of the U.N. Framework Convention on Climate Change convenes in Qatar. This will be COP 18 – COP 1 was held in Berlin in 1995, and since then the process has accomplished essentially nothing. Even scientists, who are notoriously reluctant to speak out, are slowly overcoming their natural preference to simply provide data. "The message has been consistent for close to 30 years now," Collins says with a wry laugh, "and we have the instrumentation and the computer power required to present the evidence in detail. If we choose to continue on our present course of action, it should be done with a full evaluation of the evidence the scientific community has presented." He pauses, suddenly conscious of being on the record. "I should say, a fuller evaluation of the evidence."
So far, though, such calls have had little effect. We're in the same position we've been in for a quarter-century: scientific warning followed by political inaction. Among scientists speaking off the record, disgusted candor is the rule. One senior scientist told me, "You know those new cigarette packs, where governments make them put a picture of someone with a hole in their throats? Gas pumps should have something like that."
The Third Number: 2,795 Gigatons
This number is the scariest of all – one that, for the first time, meshes the political and scientific dimensions of our dilemma. It was highlighted last summer by the Carbon Tracker Initiative, a team of London financial analysts and environmentalists who published a report in an effort to educate investors about the possible risks that climate change poses to their stock portfolios. The number describes the amount of carbon already contained in the proven coal and oil and gas reserves of the fossil-fuel companies, and the countries (think Venezuela or Kuwait) that act like fossil-fuel companies. In short, it's the fossil fuel we're currently planning to burn. And the key point is that this new number – 2,795 – is higher than 565. Five times higher.
The Carbon Tracker Initiative – led by James Leaton, an environmentalist who served as an adviser at the accounting giant PricewaterhouseCoopers – combed through proprietary databases to figure out how much oil, gas and coal the world's major energy companies hold in reserve. The numbers aren't perfect – they don't fully reflect the recent surge in unconventional energy sources like shale gas, and they don't accurately reflect coal reserves, which are subject to less stringent reporting requirements than oil and gas. But for the biggest companies, the figures are quite exact: If you burned everything in the inventories of Russia's Lukoil and America's ExxonMobil, for instance, which lead the list of oil and gas companies, each would release more than 40 gigatons of carbon dioxide into the atmosphere.
Which is exactly why this new number, 2,795 gigatons, is such a big deal. Think of two degrees Celsius as the legal drinking limit – equivalent to the 0.08 blood-alcohol level below which you might get away with driving home. The 565 gigatons is how many drinks you could have and still stay below that limit – the six beers, say, you might consume in an evening. And the 2,795 gigatons? That's the three 12-packs the fossil-fuel industry has on the table, already opened and ready to pour.
We have five times as much oil and coal and gas on the books as climate scientists think is safe to burn. We'd have to keep 80 percent of those reserves locked away underground to avoid that fate. Before we knew those numbers, our fate had been likely. Now, barring some massive intervention, it seems certain.
Yes, this coal and gas and oil is still technically in the soil. But it's already economically aboveground – it's figured into share prices, companies are borrowing money against it, nations are basing their budgets on the presumed returns from their patrimony. It explains why the big fossil-fuel companies have fought so hard to prevent the regulation of carbon dioxide – those reserves are their primary asset, the holding that gives their companies their value. It's why they've worked so hard these past years to figure out how to unlock the oil in Canada's tar sands, or how to drill miles beneath the sea, or how to frack the Appalachians.
If you told Exxon or Lukoil that, in order to avoid wrecking the climate, they couldn't pump out their reserves, the value of their companies would plummet. John Fullerton, a former managing director at JP Morgan who now runs the Capital Institute, calculates that at today's market value, those 2,795 gigatons of carbon emissions are worth about $27 trillion. Which is to say, if you paid attention to the scientists and kept 80 percent of it underground, you'd be writing off $20 trillion in assets. The numbers aren't exact, of course, but that carbon bubble makes the housing bubble look small by comparison. It won't necessarily burst – we might well burn all that carbon, in which case investors will do fine. But if we do, the planet will crater. You can have a healthy fossil-fuel balance sheet, or a relatively healthy planet – but now that we know the numbers, it looks like you can't have both. Do the math: 2,795 is five times 565. That's how the story ends.
So far, as I said at the start, environmental efforts to tackle global warming have failed. The planet's emissions of carbon dioxide continue to soar, especially as developing countries emulate (and supplant) the industries of the West. Even in rich countries, small reductions in emissions offer no sign of the real break with the status quo we'd need to upend the iron logic of these three numbers. Germany is one of the only big countries that has actually tried hard to change its energy mix; on one sunny Saturday in late May, that northern-latitude nation generated nearly half its power from solar panels within its borders. That's a small miracle – and it demonstrates that we have the technology to solve our problems. But we lack the will. So far, Germany's the exception; the rule is ever more carbon.
This record of failure means we know a lot about what strategies don't work. Green groups, for instance, have spent a lot of time trying to change individual lifestyles: the iconic twisty light bulb has been installed by the millions, but so have a new generation of energy-sucking flatscreen TVs. Most of us are fundamentally ambivalent about going green: We like cheap flights to warm places, and we're certainly not going to give them up if everyone else is still taking them. Since all of us are in some way the beneficiaries of cheap fossil fuel, tackling climate change has been like trying to build a movement against yourself – it's as if the gay-rights movement had to be constructed entirely from evangelical preachers, or the abolition movement from slaveholders.
People perceive – correctly – that their individual actions will not make a decisive difference in the atmospheric concentration of CO2; by 2010, a poll found that "while recycling is widespread in America and 73 percent of those polled are paying bills online in order to save paper," only four percent had reduced their utility use and only three percent had purchased hybrid cars. Given a hundred years, you could conceivably change lifestyles enough to matter – but time is precisely what we lack.
A more efficient method, of course, would be to work through the political system, and environmentalists have tried that, too, with the same limited success. They've patiently lobbied leaders, trying to convince them of our peril and assuming that politicians would heed the warnings. Sometimes it has seemed to work. Barack Obama, for instance, campaigned more aggressively about climate change than any president before him – the night he won the nomination, he told supporters that his election would mark the moment "the rise of the oceans began to slow and the planet began to heal." And he has achieved one significant change: a steady increase in the fuel efficiency mandated for automobiles. It's the kind of measure, adopted a quarter-century ago, that would have helped enormously. But in light of the numbers I've just described, it's obviously a very small start indeed.
At this point, effective action would require actually keeping most of the carbon the fossil-fuel industry wants to burn safely in the soil, not just changing slightly the speed at which it's burned. And there the president, apparently haunted by the still-echoing cry of "Drill, baby, drill," has gone out of his way to frack and mine. His secretary of interior, for instance, opened up a huge swath of the Powder River Basin in Wyoming for coal extraction: The total basin contains some 67.5 gigatons worth of carbon (or more than 10 percent of the available atmospheric space). He's doing the same thing with Arctic and offshore drilling; in fact, as he explained on the stump in March, "You have my word that we will keep drilling everywhere we can... That's a commitment that I make." The next day, in a yard full of oil pipe in Cushing, Oklahoma, the president promised to work on wind and solar energy but, at the same time, to speed up fossil-fuel development: "Producing more oil and gas here at home has been, and will continue to be, a critical part of an all-of-the-above energy strategy." That is, he's committed to finding even more stock to add to the 2,795-gigaton inventory of unburned carbon.
Sometimes the irony is almost Borat-scale obvious: In early June, Secretary of State Hillary Clinton traveled on a Norwegian research trawler to see firsthand the growing damage from climate change. "Many of the predictions about warming in the Arctic are being surpassed by the actual data," she said, describing the sight as "sobering." But the discussions she traveled to Scandinavia to have with other foreign ministers were mostly about how to make sure Western nations get their share of the estimated $9 trillion in oil (that's more than 90 billion barrels, or 37 gigatons of carbon) that will become accessible as the Arctic ice melts. Last month, the Obama administration indicated that it would give Shell permission to start drilling in sections of the Arctic.
Almost every government with deposits of hydrocarbons straddles the same divide. Canada, for instance, is a liberal democracy renowned for its internationalism – no wonder, then, that it signed on to the Kyoto treaty, promising to cut its carbon emissions substantially by 2012. But the rising price of oil suddenly made the tar sands of Alberta economically attractive – and since, as NASA climatologist James Hansen pointed out in May, they contain as much as 240 gigatons of carbon (or almost half of the available space if we take the 565 limit seriously), that meant Canada's commitment to Kyoto was nonsense. In December, the Canadian government withdrew from the treaty before it faced fines for failing to meet its commitments.
The same kind of hypocrisy applies across the ideological board: In his speech to the Copenhagen conference, Venezuela's Hugo Chavez quoted Rosa Luxemburg, Jean-Jacques Rousseau and "Christ the Redeemer," insisting that "climate change is undoubtedly the most devastating environmental problem of this century." But the next spring, in the Simon Bolivar Hall of the state-run oil company, he signed an agreement with a consortium of international players to develop the vast Orinoco tar sands as "the most significant engine for a comprehensive development of the entire territory and Venezuelan population." The Orinoco deposits are larger than Alberta's – taken together, they'd fill up the whole available atmospheric space.
So: the paths we have tried to tackle global warming have so far produced only gradual, halting shifts. A rapid, transformative change would require building a movement, and movements require enemies. As John F. Kennedy put it, "The civil rights movement should thank God for Bull Connor. He's helped it as much as Abraham Lincoln." And enemies are what climate change has lacked.
But what all these climate numbers make painfully, usefully clear is that the planet does indeed have an enemy – one far more committed to action than governments or individuals. Given this hard math, we need to view the fossil-fuel industry in a new light. It has become a rogue industry, reckless like no other force on Earth. It is Public Enemy Number One to the survival of our planetary civilization. "Lots of companies do rotten things in the course of their business – pay terrible wages, make people work in sweatshops – and we pressure them to change those practices," says veteran anti-corporate leader Naomi Klein, who is at work on a book about the climate crisis. "But these numbers make clear that with the fossil-fuel industry, wrecking the planet is their business model. It's what they do."
According to the Carbon Tracker report, if Exxon burns its current reserves, it would use up more than seven percent of the available atmospheric space between us and the risk of two degrees. BP is just behind, followed by the Russian firm Gazprom, then Chevron, ConocoPhillips and Shell, each of which would fill between three and four percent. Taken together, just these six firms, of the 200 listed in the Carbon Tracker report, would use up more than a quarter of the remaining two-degree budget. Severstal, the Russian mining giant, leads the list of coal companies, followed by firms like BHP Billiton and Peabody. The numbers are simply staggering – this industry, and this industry alone, holds the power to change the physics and chemistry of our planet, and they're planning to use it.
They're clearly cognizant of global warming – they employ some of the world's best scientists, after all, and they're bidding on all those oil leases made possible by the staggering melt of Arctic ice. And yet they relentlessly search for more hydrocarbons – in early March, Exxon CEO Rex Tillerson told Wall Street analysts that the company plans to spend $37 billion a year through 2016 (about $100 million a day) searching for yet more oil and gas.
There's not a more reckless man on the planet than Tillerson. Late last month, on the same day the Colorado fires reached their height, he told a New York audience that global warming is real, but dismissed it as an "engineering problem" that has "engineering solutions." Such as? "Changes to weather patterns that move crop-production areas around – we'll adapt to that." This in a week when Kentucky farmers were reporting that corn kernels were "aborting" in record heat, threatening a spike in global food prices. "The fear factor that people want to throw out there to say, 'We just have to stop this,' I do not accept," Tillerson said. Of course not – if he did accept it, he'd have to keep his reserves in the ground. Which would cost him money. It's not an engineering problem, in other words – it's a greed problem.
You could argue that this is simply in the nature of these companies – that having found a profitable vein, they're compelled to keep mining it, more like efficient automatons than people with free will. But as the Supreme Court has made clear, they are people of a sort. In fact, thanks to the size of its bankroll, the fossil-fuel industry has far more free will than the rest of us. These companies don't simply exist in a world whose hungers they fulfill – they help create the boundaries of that world.
Left to our own devices, citizens might decide to regulate carbon and stop short of the brink; according to a recent poll, nearly two-thirds of Americans would back an international agreement that cut carbon emissions 90 percent by 2050. But we aren't left to our own devices. The Koch brothers, for instance, have a combined wealth of $50 billion, meaning they trail only Bill Gates on the list of richest Americans. They've made most of their money in hydrocarbons, they know any system to regulate carbon would cut those profits, and they reportedly plan to lavish as much as $200 million on this year's elections. In 2009, for the first time, the U.S. Chamber of Commerce surpassed both the Republican and Democratic National Committees on political spending; the following year, more than 90 percent of the Chamber's cash went to GOP candidates, many of whom deny the existence of global warming. Not long ago, the Chamber even filed a brief with the EPA urging the agency not to regulate carbon – should the world's scientists turn out to be right and the planet heats up, the Chamber advised, "populations can acclimatize to warmer climates via a range of behavioral, physiological and technological adaptations." As radical goes, demanding that we change our physiology seems right up there.
Environmentalists, understandably, have been loath to make the fossil-fuel industry their enemy, respecting its political power and hoping instead to convince these giants that they should turn away from coal, oil and gas and transform themselves more broadly into "energy companies." Sometimes that strategy appeared to be working – emphasis on appeared. Around the turn of the century, for instance, BP made a brief attempt to restyle itself as "Beyond Petroleum," adapting a logo that looked like the sun and sticking solar panels on some of its gas stations. But its investments in alternative energy were never more than a tiny fraction of its budget for hydrocarbon exploration, and after a few years, many of those were wound down as new CEOs insisted on returning to the company's "core business." In December, BP finally closed its solar division. Shell shut down its solar and wind efforts in 2009. The five biggest oil companies have made more than $1 trillion in profits since the millennium – there's simply too much money to be made on oil and gas and coal to go chasing after zephyrs and sunbeams.
Much of that profit stems from a single historical accident: Alone among businesses, the fossil-fuel industry is allowed to dump its main waste, carbon dioxide, for free. Nobody else gets that break – if you own a restaurant, you have to pay someone to cart away your trash, since piling it in the street would breed rats. But the fossil-fuel industry is different, and for sound historical reasons: Until a quarter-century ago, almost no one knew that CO2 was dangerous. But now that we understand that carbon is heating the planet and acidifying the oceans, its price becomes the central issue.
If you put a price on carbon, through a direct tax or other methods, it would enlist markets in the fight against global warming. Once Exxon has to pay for the damage its carbon is doing to the atmosphere, the price of its products would rise. Consumers would get a strong signal to use less fossil fuel – every time they stopped at the pump, they'd be reminded that you don't need a semimilitary vehicle to go to the grocery store. The economic playing field would now be a level one for nonpolluting energy sources. And you could do it all without bankrupting citizens – a so-called "fee-and-dividend" scheme would put a hefty tax on coal and gas and oil, then simply divide up the proceeds, sending everyone in the country a check each month for their share of the added costs of carbon. By switching to cleaner energy sources, most people would actually come out ahead.
There's only one problem: Putting a price on carbon would reduce the profitability of the fossil-fuel industry. After all, the answer to the question "How high should the price of carbon be?" is "High enough to keep those carbon reserves that would take us past two degrees safely in the ground." The higher the price on carbon, the more of those reserves would be worthless. The fight, in the end, is about whether the industry will succeed in its fight to keep its special pollution break alive past the point of climate catastrophe, or whether, in the economists' parlance, we'll make them internalize those externalities.
It's not clear, of course, that the power of the fossil-fuel industry can be broken. The U.K. analysts who wrote the Carbon Tracker report and drew attention to these numbers had a relatively modest goal – they simply wanted to remind investors that climate change poses a very real risk to the stock prices of energy companies. Say something so big finally happens (a giant hurricane swamps Manhattan, a megadrought wipes out Midwest agriculture) that even the political power of the industry is inadequate to restrain legislators, who manage to regulate carbon. Suddenly those Chevron reserves would be a lot less valuable, and the stock would tank. Given that risk, the Carbon Tracker report warned investors to lessen their exposure, hedge it with some big plays in alternative energy.
"The regular process of economic evolution is that businesses are left with stranded assets all the time," says Nick Robins, who runs HSBC's Climate Change Centre. "Think of film cameras, or typewriters. The question is not whether this will happen. It will. Pension systems have been hit by the dot-com and credit crunch. They'll be hit by this." Still, it hasn't been easy to convince investors, who have shared in the oil industry's record profits. "The reason you get bubbles," sighs Leaton, "is that everyone thinks they're the best analyst – that they'll go to the edge of the cliff and then jump back when everyone else goes over."
So pure self-interest probably won't spark a transformative challenge to fossil fuel. But moral outrage just might – and that's the real meaning of this new math. It could, plausibly, give rise to a real movement.
Once, in recent corporate history, anger forced an industry to make basic changes. That was the campaign in the 1980s demanding divestment from companies doing business in South Africa. It rose first on college campuses and then spread to municipal and state governments; 155 campuses eventually divested, and by the end of the decade, more than 80 cities, 25 states and 19 counties had taken some form of binding economic action against companies connected to the apartheid regime. "The end of apartheid stands as one of the crowning accomplishments of the past century," as Archbishop Desmond Tutu put it, "but we would not have succeeded without the help of international pressure," especially from "the divestment movement of the 1980s."
The fossil-fuel industry is obviously a tougher opponent, and even if you could force the hand of particular companies, you'd still have to figure out a strategy for dealing with all the sovereign nations that, in effect, act as fossil-fuel companies. But the link for college students is even more obvious in this case. If their college's endowment portfolio has fossil-fuel stock, then their educations are being subsidized by investments that guarantee they won't have much of a planet on which to make use of their degree. (The same logic applies to the world's largest investors, pension funds, which are also theoretically interested in the future – that's when their members will "enjoy their retirement.") "Given the severity of the climate crisis, a comparable demand that our institutions dump stock from companies that are destroying the planet would not only be appropriate but effective," says Bob Massie, a former anti-apartheid activist who helped found the Investor Network on Climate Risk. "The message is simple: We have had enough. We must sever the ties with those who profit from climate change – now."
Movements rarely have predictable outcomes. But any campaign that weakens the fossil-fuel industry's political standing clearly increases the chances of retiring its special breaks. Consider President Obama's signal achievement in the climate fight, the large increase he won in mileage requirements for cars. Scientists, environmentalists and engineers had advocated such policies for decades, but until Detroit came under severe financial pressure, it was politically powerful enough to fend them off. If people come to understand the cold, mathematical truth – that the fossil-fuel industry is systematically undermining the planet's physical systems – it might weaken it enough to matter politically. Exxon and their ilk might drop their opposition to a fee-and-dividend solution; they might even decide to become true energy companies, this time for real.
Even if such a campaign is possible, however, we may have waited too long to start it. To make a real difference – to keep us under a temperature increase of two degrees – you'd need to change carbon pricing in Washington, and then use that victory to leverage similar shifts around the world. At this point, what happens in the U.S. is most important for how it will influence China and India, where emissions are growing fastest. (In early June, researchers concluded that China has probably under-reported its emissions by up to 20 percent.) The three numbers I've described are daunting – they may define an essentially impossible future. But at least they provide intellectual clarity about the greatest challenge humans have ever faced. We know how much we can burn, and we know who's planning to burn more. Climate change operates on a geological scale and time frame, but it's not an impersonal force of nature; the more carefully you do the math, the more thoroughly you realize that this is, at bottom, a moral issue; we have met the enemy and they is Shell.
Meanwhile the tide of numbers continues. The week after the Rio conference limped to its conclusion, Arctic sea ice hit the lowest level ever recorded for that date. Last month, on a single weekend, Tropical Storm Debby dumped more than 20 inches of rain on Florida – the earliest the season's fourth-named cyclone has ever arrived. At the same time, the largest fire in New Mexico history burned on, and the most destructive fire in Colorado's annals claimed 346 homes in Colorado Springs – breaking a record set the week before in Fort Collins. This month, scientists issued a new study concluding that global warming has dramatically increased the likelihood of severe heat and drought – days after a heat wave across the Plains and Midwest broke records that had stood since the Dust Bowl, threatening this year's harvest. You want a big number? In the course of this month, a quadrillion kernels of corn need to pollinate across the grain belt, something they can't do if temperatures remain off the charts. Just like us, our crops are adapted to the Holocene, the 11,000-year period of climatic stability we're now leaving... in the dust.
This story is from the August 2nd, 2012 issue of Rolling Stone.
01 March 2013
Topology and Data
Listen to Robert Ghrist explain how topology helps make sense of large data sets:
http://www.ams.org/samplings/mathmoments/mm77-topology-data-podcast
For More Information: “Topology and Data”, Gunnar Carlson, Bulletin of the American Mathematical Society (Vol. 46, No. 2), April 2009.
http://www.ams.org/samplings/mathmoments/mm77-topology-data-podcast
For More Information: “Topology and Data”, Gunnar Carlson, Bulletin of the American Mathematical Society (Vol. 46, No. 2), April 2009.
Much of modern research—from genome sequencing to digital surveys of outer space—generates tremendous amounts of multi-dimensional data. Unfortunately, visualizing dimensions higher than three is not easy, which makes analyzing and understanding the data difficult. Topology, a branch of mathematics concerned with the properties of geometrical structures, helps make sense of large data sets by providing a way of classifying the shapes of these sets. It’s especially useful for locating groups of similar points called “clusters”, which can, for example, distinguish between distinct types of a given disease, each requiring its own treatment.
Topology (specifically algebraic topology) is also important in the operation of wireless sensor networks, which are used in applications as diverse as monitoring automobile traffic and controlling irrigation. Combined with numerical integration, results from algebraic topology provide the complete picture based on strictly local data. The advantage is that such sensor networks, maintained without GPS or other distance measures, are generally much cheaper to operate. So, in the case of irrigation, mathematical discoveries made almost a century before the advent of today’s technology save money while helping us use precious water wisely. In topological terms, just like the Möbius strip: What goes around, comes around.
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