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Friday, February 29, 2008Are our brains wired for math?
According to Stanislas Dehaene, humans have an inbuilt “number sense” capable of some basic calculations and estimates. The problems start when we learn mathematics and have to perform procedures that are anything but instinctive.
One morning in September, 1989, a former sales representative in his mid-forties entered an examination room with Stanislas Dehaene, a young neuroscientist based in Paris. Three years earlier, the man, whom researchers came to refer to as Mr. N, had sustained a brain hemorrhage that left him with an enormous lesion in the rear half of his left hemisphere. He suffered from severe handicaps: his right arm was in a sling; he couldn’t read; and his speech was painfully slow. He had once been married, with two daughters, but was now incapable of leading an independent life and lived with his elderly parents. Dehaene had been invited to see him because his impairments included severe acalculia, a general term for any one of several deficits in number processing. When asked to add 2 and 2, he answered “three.” He could still count and recite a sequence like 2, 4, 6, 8, but he was incapable of counting downward from 9, differentiating odd and even numbers, or recognizing the numeral 5 when it was flashed in front of him.
To Dehaene, these impairments were less interesting than the fragmentary capabilities Mr. N had managed to retain. When he was shown the numeral 5 for a few seconds, he knew it was a numeral rather than a letter and, by counting up from 1 until he got to the right integer, he eventually identified it as a 5. He did the same thing when asked the age of his seven-year-old daughter. In the 1997 book “The Number Sense,” Dehaene wrote, “He appears to know right from the start what quantities he wishes to express, but reciting the number series seems to be his only means of retrieving the corresponding word.”
Dehaene also noticed that although Mr. N could no longer read, he sometimes had an approximate sense of words that were flashed in front of him; when he was shown the word “ham,” he said, “It’s some kind of meat.” Dehaene decided to see if Mr. N still had a similar sense of number. He showed him the numerals 7 and 8. Mr. N was able to answer quickly that 8 was the larger number—far more quickly than if he had had to identify them by counting up to the right quantities. He could also judge whether various numbers were bigger or smaller than 55, slipping up only when they were very close to 55. Dehaene dubbed Mr. N “the Approximate Man.” The Approximate Man lived in a world where a year comprised “about 350 days” and an hour “about fifty minutes,” where there were five seasons, and where a dozen eggs amounted to “six or ten.” Dehaene asked him to add 2 and 2 several times and received answers ranging from three to five. But, he noted, “he never offers a result as absurd as 9.”
In cognitive science, incidents of brain damage are nature’s experiments. If a lesion knocks out one ability but leaves another intact, it is evidence that they are wired into different neural circuits. In this instance, Dehaene theorized that our ability to learn sophisticated mathematical procedures resided in an entirely different part of the brain from a rougher quantitative sense. Over the decades, evidence concerning cognitive deficits in brain-damaged patients has accumulated, and researchers have concluded that we have a sense of number that is independent of language, memory, and reasoning in general. Within neuroscience, numerical cognition has emerged as a vibrant field, and Dehaene, now in his early forties, has become one of its foremost researchers. His work is “completely pioneering,” Susan Carey, a psychology professor at Harvard who has studied numerical cognition, told me. “If you want to make sure the math that children are learning is meaningful, you have to know something about how the brain represents number at the kind of level that Stan is trying to understand.”
Dehaene has spent most of his career plotting the contours of our number sense and puzzling over which aspects of our mathematical ability are innate and which are learned, and how the two systems overlap and affect each other. He has approached the problem from every imaginable angle. Working with colleagues both in France and in the United States, he has carried out experiments that probe the way numbers are coded in our minds. He has studied the numerical abilities of animals, of Amazon tribespeople, of top French mathematics students. He has used brain-scanning technology to investigate precisely where in the folds and crevices of the cerebral cortex our numerical faculties are nestled. And he has weighed the extent to which some languages make numbers more difficult than others. His work raises crucial issues about the way mathematics is taught. In Dehaene’s view, we are all born with an evolutionarily ancient mathematical instinct. To become numerate, children must capitalize on this instinct, but they must also unlearn certain tendencies that were helpful to our primate ancestors but that clash with skills needed today. And some societies are evidently better than others at getting kids to do this. In both France and the United States, mathematics education is often felt to be in a state of crisis. The math skills of American children fare poorly in comparison with those of their peers in countries like Singapore, South Korea, and Japan. Fixing this state of affairs means grappling with the question that has taken up much of Dehaene’s career: What is it about the brain that makes numbers sometimes so easy and sometimes so hard?
Dehaene’s own gifts as a mathematician are considerable. Born in 1965, he grew up in Roubaix, a medium-sized industrial city near France’s border with Belgium. (His surname is Flemish.) His father, a pediatrician, was among the first to study fetal alcohol syndrome. As a teen-ager, Dehaene developed what he calls a “passion” for mathematics, and he attended the École Normale Supérieure in Paris, the training ground for France’s scholarly élite. Dehaene’s own interests tended toward computer modelling and artificial intelligence. He was drawn to brain science after reading, at the age of eighteen, the 1983 book “Neuronal Man,” by Jean-Pierre Changeux, France’s most distinguished neurobiologist. Changeux’s approach to the brain held out the tantalizing possibility of reconciling psychology with neuroscience. Dehaene met Changeux and began to work with him on abstract models of thinking and memory. He also linked up with the cognitive scientist Jacques Mehler. It was in Mehler’s lab that he met his future wife, Ghislaine Lambertz, a researcher in infant cognitive psychology.
In Chapter Four of her new book, Well-Behaved Women Seldom Make History, Pulitzer Prize-winning author Laurel Thatcher Ulrich describes Elizabeth Cady Stanton’s awakening as a young civil rights activist and gives context to her struggle. Stanton, who was one of the most outspoken advocates for women’s rights in the 19th century, identified strongly with those trapped by the institution of slavery.
From Chapter Four: Slaves in the Attic
On a bright autumn day in 1839, Elizabeth Cady and her sisters were singing in the parlor of the large country house owned by their cousin, the abolitionist Gerrit Smith. Suddenly, Smith walked in and with a mysterious air summoned them to the top of the house. Pledging them to secrecy, he opened the door to a little-used room. There sat a beautiful young woman—a runaway slave.
“Harriet,” Smith said, “I have brought all my young cousins to see you. I want you to make good abolitionists of them by telling them the history of your life—what you have seen and suffered in slavery.” For the next two hours the girls listened, weeping, as Harriet told of being sold for her beauty in a New Orleans market. The details were too horrible to repeat, except in whispers.
The tension deepened when at twilight they saw her slip out of the house into a waiting carriage wearing a Quaker bonnet. A few days later, they were relieved to hear that she had made her way safely to Canada.
Writing about this event half a century later, Stanton did not use Harriet Powell’s full name. Perhaps she had forgotten it. Perhaps she deliberately left it out. Whatever the reason, her omission adds to the mythical power of the story. Without a full name, one runaway can stand in for every slave who ever fled a master. Powell’s story can evoke other Harriets, other attics: Harriet Jacobs, for example, who in 1861, under the pseudonym “Linda Brent,” wrote about hiding in a cramped space above her grandmother’s shed for seven long years rather than submit to the sexual propositions of her master.
Or Harriet Tubman, the brave “general” of the Underground Railroad, who helped dozens of other slaves escape. Or Harriet Beecher Stowe, the white writer who filled Uncle Tom’s Cabin with beautiful quadroons and dramatic escapes, and who in the grim last section of the novel told a dark tale about a mysterious female slave hiding in the attic on a plantation owned by the evil Simon Legree.
All these Harriets made history, though not in Stanton’s memoir. In her telling, the encounter in the attic had less to do with the history of slavery than with her own evolution from naïve schoolgirl to public advocate for women’s rights. That was the autumn she fell in love with Henry Stanton, who as an agent for the radical American Anti-Slavery Society was a frequent visitor to Smith’s house. On a walk through the woods, Henry had “made one of those charming revelations of human feeling which brave knights have always found eloquent words to utter, and to which fair ladies have always listened with mingled emotions of pleasure and astonishment.” Although Elizabeth was smitten, she feared her father would never consent to her marrying an abolitionist. “So I lingered at Peterboro to prolong the dream of happiness and postpone the conflict I feared to meet.” For her, as for Harriet, Smith’s house became an oasis.
Harriet’s escape foreshadowed Elizabeth’s own. Seven months later, pressed into action by Henry’s imminent departure for London as a delegate to the World Anti-Slavery Convention, she braved her father’s displeasure and “without the slightest preparation for a wedding or a voyage,” married him. The runaway in the attic had introduced her to the horrors of slavery. The female abolitionists she met in London introduced her to feminism. When convention leaders refused to admit women as delegates, they collected in the gallery, pondering the insincerity of men “who, while eloquently defending the natural rights of slaves, denied freedom of speech to one-half the people of their own race.”
For Stanton, slavery became a metaphor for the female condition. Years later, in a speech at Waterloo, New York, she accused men in all parts of the world of enslaving women, “from the Mahometan who forbids pigs, dogs, women and other impure animals to enter a mosque, and does not allow a fool, madman or woman to proclaim the hour of prayer,—from the German who complacently smokes his meerschaum while his wife, yoked with the ox, draws the plough through its furrow,—from the delectable gentleman who thinks an inferior style of conversation adapted to women—to the legislator who considers her incapable of saying what laws shall govern her.” Women everywhere were subject to men. “I am a slave, a favoured slave,” she exclaimed, quoting a line given to a harem girl in Lord Byron’s poem “The Corsair.”
“I am a slave, a favoured slave...”
At one level, the rhetoric was nonsensical. Stanton was not a slave. Nor, whatever his deficiencies as a husband, was Henry a sultan. But the language was well chosen. For a white woman to declare herself a slave was the ultimate misbehavior. It was one thing to reach out to a poor suffering creature like Harriet. It was another to identify with her degradation. In Stanton’s lifetime, nearly everyone assumed that middle-class white women were among the most privileged and pampered creatures on earth. They were the mothers, the muses, and the lovers of men, the caregivers of children, and the hope of the weary. Stanton cut through that sentimental view. To be a perpetual dependent was to be a slave, regardless of how comfortable one ’s position. At Seneca Falls in 1848, she and her collaborators gave up the deference due to them as fair ladies and demanded “all the rights and privileges which belong to them as citizens of the United States.”
For Stanton, the antislavery movement was a way station on the road to something bigger. That is the way it has been treated in many histories of the women’s suffrage movement. Recent accounts do better. They help explain how Harriet Powell ended up in Smith’s attic and where she went when she left there, and they show the complex interplay between sentimental literature, evangelical religion, abolitionism, and women’s rights. Stanton’s story looks different when placed alongside the lives of Harriet Powell and her namesakes. The biographies of the four Harriets—Powell, Jacobs, Stowe, and Tubman—take slaves out of the attic.
Three Runaways and a Novelist
In Stanton’s memoir, Harriet Powell appears from nowhere. In reality, her escape was managed by a powerful network that linked wealthy patrons like Gerrit Smith with free blacks who risked social ostracism, violence, and even death to help others gain their liberty. Powell had come to upstate New York from Mississippi as a nursemaid in the family of John Davenport, who had booked them into the best hotel in Syracuse. Powell was terrified that she might be sold when they returned to Mississippi. Somehow she communicated her anxieties to a black waiter who, with the help of antislavery allies, arranged for her escape. On October 7, while her master and mistress were attending a party, she left their child asleep in its room and slipped out of the hotel into a carriage, where two respectable white citizens were waiting with her disguise—a man’s cloak and hat. They delivered her to a farmer in a neighboring town, changing carriages along the way to avoid detection. Eventually she reached Smith’s house in Peterboro.
Well-Behaved Women Seldom Make History
from the Pulitzer Prize-winning author Laurel Thatcher Ulrich.
Outraged to discover his slave missing, Davenport offered a $200 reward for information leading to her recovery. He described her as a young woman “of a full and well proportioned form” and “so fair that she would generally be taken for white,” adding that a discerning person would recognize certain African traits, such as “a prominent mouth with depressed nostrils, and receding forehead.” She had worn a black print dress, small rings in her ears, and three gold rings on her fingers. She had left her bonnet behind.
The local abolitionist newspaper, The Friend of Man, hooted at the spectacle of a supposed gentleman advertising as property a woman who might have passed for white. “Some of the anti-abolition gentry at Syracuse, begin to think it rather too bad to enslave handsome white ladies, with gold rings on their fingers,” the editor wrote. In December, the paper reprinted a piece from the Toronto Free Press dated Jubilee 12, 1839” which parodied Davenport’s advertisement. “Found on the Canadian shore, a young woman who says her name is Harriet Powell,” it began, adding, “When found, her head dress consisted of a Freedom Bonnet, and a Liberty Cap.”
All the abolitionist accounts of Harriet’s rescue emphasized her physical attractiveness and her fear of being sold. One paper said that in Mississippi “a man of bad character” had tried to purchase her. A Toronto writer was more explicit: “From her admissions and style of dress, I suppose she came from the seraglio of some ‘Patriarch.’” There was some foundation for such stereotypes. In slave markets, color defined a person’s capacity for work. Dark-skinned slaves, female as well as male, were deemed healthier, stronger, and more likely to perform well in the fields. Light-skinned women, often described as “delicate,” supposedly made better seamstresses, house servants—or concubines. In the New Orleans market especially, there was no ambiguity about the “fancy trade.” Men openly bid for light-skinned women, often paying three times the median price for young women who fulfilled their fantasies. Flirting with propriety, they listed their purchases as seamstresses or cooks, then unabashedly flaunted them as mistresses. Not they, but those who questioned their behavior, were guilty of indiscretion.
But there was also a literary quality to the stories abolitionists told. Rescued from slavery, Powell became the captive instead of a centuries-old story that originated in lurid “tales from the harem.” To be worthy of rescue, escaped slaves needed to be well-behaved. That is why all the stories about her emphasized her refinement. Although she was ignorant of religion (an indictment of her master), her manners were graceful, her voice soft. Even better, she was duly grateful for the help she received: “the trickling tear told that her heart felt far more than her tongue could utter.”
In April, The Friend of Man printed a letter that Powell purportedly dictated to the Canadian woman in whose home she was then living.
Dear Sir—I am sure you will be happy to learn that I am
well and quite contented in my present situation. I am still in
Kingston, and living with Mr. and Mrs. Hale, where I have an
opportunity of attending the Methodist Chapel every
Sunday. I am very much obliged to all my kind friends who
assisted me in gaining my liberty; and I think, not all the
money in the United States could induce me to return to
slavery. I am most anxious to hear something of my dear
mother and sister; Mrs. Hale wrote to Mr. Gerrit Smith for
me, some time ago, but we have not received any answer. I
should be most thankful to receive any intelligence. Please
give my love to all my friends, and accept the same yourself from,
There is no reason to doubt Harriet’s concern for her mother and sister. Davenport, like other slave owners, counted on family bonds to keep slaves, especially female slaves, from fleeing.
How Harriet felt about life in Ontario we do not know, though The Friend of Man soon reported that she had married Mr. Henry Kelly, “a respectable colored man, in good pecuniary circumstances.”Canadian records show that in the next fifteen years, she gave birth to eight children, three of whom died in infancy. Little else is known about her life except that she died in Kingston, Ontario, in 1861. Crossing the border into liberty, she moved out of history.
Excerpted from Well-Behaved Women Seldom Make History by Laurel Thatcher Ulrich Copyright ©2007 by Laurel Thatcher Ulrich. Excerpted by permission of Knopf, a division of Random House, Inc.
—Laurel Thatcher Ulrich is a 300th Anniversary University Professor at Harvard and the author of A Midwife’s Tale: The Life of Martha Ballard, Based on her Diary, 1785–1812 for which she won the Pulitzer Prize in History.
Human beings have never lacked for things to fight over, but for the last two millennia, they have fought the most over ideas involving the divine. Politics, technology, military capacity, and diseases have all played decisive roles in shaping history, yet it is impossible to understand the rise and fall of empires, the clash of civilizations, and the evolving balance of power without appreciating the unique fervor that religion inspires, and the speed with which new religions can spread.
Christianity, a minority sect during much of the Roman Empire, became a world religion with a vast following after the Emperor Constantine converted to it, in the fourth century A.D. Then came Islam, in the seventh century: just a hundred years after Muhammad’s death, in 632, the religion he founded reached beyond the Middle East to Africa, India, and significant parts of Spain and France. The Protestant Reformation of 1517 quickly engulfed half of Europe, migrated to the New World, and fueled the Counter-Reformation in the remaining Catholic states on the Continent—by 1618, the Thirty Years’ War had begun, resulting in the devastation of large swaths of western Europe and the death of some 30 percent of Germany’s population. Every new outburst of religious passion, while producing ecstasy and revelation for some, has disrupted established loyalties, fueled intolerance, and led to violence between the chosen and the damned.
It may seem, at first glance, that little has changed. A recent cover story in The Economist, titled “The New Wars of Religion,” proclaimed, “Faith will unsettle politics everywhere this century.” Some scholars of religion have found new sport in predicting which religions will gain the most adherents (and upset the most applecarts) during the coming decades. Pentecostalism is one favorite candidate; it is sweeping through Latin America and Africa, already claiming some half-billion followers around the world. Catholicism is vying for the same conservative turf; Pope Benedict XVI’s insistence on stricter religious teachings, though not likely to grow the Church in Boston, appears intended to win more souls in Bogotá and Brazzaville. Islam claims a fifth of the world’s population, and its share is climbing quickly; it is only a matter of time, many believe, before it surpasses Christianity, which is embraced by a third of the world’s population, to become the predominant faith. Hindus and Buddhists together make up 20 percent of the world’s people, and high birthrates in the countries in which they are dominant suggest that this proportion will grow. Some think that other religions will have to make room for Mormonism, an infant compared with many other faiths. (Those others will have ample time to do so—although the Church of Jesus Christ of Latter-Day Saints is growing quickly, it has just 12 million members, half in the United States.) All in all, The Economist forecasts, by mid-century, 80 percent of the world’s people will adhere to one of the major faiths.
A lot rides on which of these predictions turn out to be true, and on how and where different religions bump up against one another. A common worry is that intense competition for souls could produce another era in which religious conflict leads to religious war—only this time with nuclear weapons. If we are really in for anything like the kind of zeal that accompanied earlier periods of religious expansion, we might as well say goodbye to the Enlightenment and its principles of tolerance.
Yet breathless warnings about rising religious fervor and conflicts to come ignore two basic facts. First, many areas of the world are experiencing a decline in religious belief and practice. Second, where religions are flourishing, they are also generally evolving—very often in ways that allow them to fit more easily into secular societies, and that weaken them as politically disruptive forces. The French philosopher Blaise Pascal once famously showed that it would be irrational to bet against the existence of God. It would be equally foolish, in the long run, to bet against the power of the Enlightenment. The answer to the question of which religion will dominate the future, at least politically, may well be: None of the above.
Until relatively recently, most social theorists, from Marx to Freud to Weber, believed that as societies became more modern, religion would lose its capacity to inspire. Industrialization would substitute the rational pursuit of self-interest for blind submission to authority. Science would undermine belief in miracles. Democracy would encourage the separation of church and state. Gender equality would undermine patriarchy, and with it, clerical authority. However one defined modernity, it always seemed likely to involve societies focused on this world rather than on some other.
But intellectual fashions are fickle, and the idea of inevitable secularization has fallen out of favor with many scholars and journalists. Still, its most basic tenet—that material progress will slowly erode religious fervor—appears unassailable. Last October, the Pew Global Attitudes Project plotted 44 countries according to per capita gross domestic product and intensity of religious belief, gauged by the responses to several questions about faith (a rendition of the Pew data appears on the opposite page). The pattern, as seen in the Pew study and a number of other sources, is hard to miss: when God and Mammon collide, Mammon usually wins.
Toward the right edge of the graph—in the realm of the most-prosperous countries—and at the very bottom lies western Europe, where God, if not dead, has only a faint pulse. Islam, to be sure, is increasingly prevalent in countries such as France and Great Britain, and one can also detect a slight uptick in Christian religiosity across much of the Continent in the past decade or so. But at the same time, the region’s last significant pockets of concentrated religiosity are collapsing. Fifty years ago, Spain and Ireland were two of the most religious countries in Europe; now they are among the least. Not long ago, Spain was governed by a fascist dictator in close collaboration with the Catholic Church; now it allows both gay marriage and adoption by gay couples, making it as liberal as Massachusetts. Ireland once gave us, in the form of James Joyce’s Portrait of the Artist as a Young Man, one of the most chilling depictions of damnation in world literature; these days, Dublin’s churches are emptying out, and the few parishioners are apt to be Polish immigrants, most of whom presumably came to Ireland to nourish their bank accounts, not their souls.
Eastern Europe lies to the left of western Europe on the graph. Poland is of course well known for its religiosity; the Communists who governed the country for nearly half a century tried to suppress the Church but were ousted by Solidarity, in large part a faith-based movement, with the encouragement of a native-son pope. But most of the countries of eastern Europe, though poorer than their counterparts in the West, are not very different from them in religious terms. And increasing prosperity in eastern Europe may lower religiosity even more. Poland shows signs of this already. The country’s outspokenly Catholic prime minister, Jaroslaw Kaczynski, who governed in collaboration with his equally devout twin brother, was defeated late last year by Donald Tusk. Tusk is far less religious in his personal life than the Kaczynskis— he was married in a civil ceremony, and held a church wedding later only to further his political career. During the election campaign, he attacked Kaczynski’s ties to a right-wing, ultra-Catholic broadcasting station, and took more-liberal positions on in vitro fertilization and abortion (although he does not support legalized abortion, he opposed a Church-sponsored constitutional amendment to ban it). The first European states to fully embrace secularism did so over hundreds of years. The last holdouts appear to be making the shift in a generation.
by Alan Wolfe
Read Full Text:http://www.theatlantic.com/doc/print/200803/secularism