All Things TOK

"PSYCHOTHERAPY is having yet another identity crisis. It has manifested itself in two recent trends in the profession in America: the first involves trying to make therapy into more of a "hard science" by putting a new emphasis on measurable factors; the other is a growing belief among therapists that the standard practice of using talk therapy to discover traumas in a patient's past is not only unnecessary but can be injurious. That psychotherapists of various orientations find themselves under pressure to prove to themselves and to society that they are doing a hard-core science - which was a leading theme of the landmark Evolution of Psychotherapy Conference in California in December - is not really surprising. Given the prestige and trust the modern world gives to scientific standards, psychotherapists, who always have to measure themselves against the medical profession, are going to want to demonstrate that they, too, deal in the predictable; that they, too, can provide evidence for the value of what they do."

"It was identified by Jonathan Haidt, a social psychologist at the University of Virginia who studies the intuitive foundations of morality and ideology. He polled his audience at the San Antonio Convention Center, starting by asking how many considered themselves politically liberal. A sea of hands appeared, and Dr. Haidt estimated that liberals made up 80 percent of the 1,000 psychologists in the ballroom. When he asked for centrists and libertarians, he spotted fewer than three dozen hands. And then, when he asked for conservatives, he counted a grand total of three. "This is a statistically impossible lack of diversity," Dr. Haidt concluded, noting polls showing that 40 percent of Americans are conservative and 20 percent are liberal. In his speech and in an interview, Dr. Haidt argued that social psychologists are a "tribal-moral community" united by "sacred values" that hinder research and damage their credibility - and blind them to the hostile climate they've created for non-liberals. "Anywhere in the world that social psychologists see women or minorities underrepresented by a factor of two or three, our minds jump to discrimination as the explanation," said Dr. Haidt, who called himself a longtime liberal turned centrist. "But when we find out that conservatives are underrepresented among us by a factor of more than 100, suddenly everyone finds it quite easy to generate alternate explanations." "

"WHEN colleges and universities finally decide to make full use of the Internet, most professors will lose their jobs. Enlarge This Image Many leading universities have put free videos online featuring their best lecturers. One aggregator site, Academic Earth, offers 150 courses. That includes me. I'm not worried, though, at least for the moment. Amid acute budget crises, state universities like mine can't afford to take that very big step - adopting the technology that renders human instructors obsolete. "

"In recent years popular science writing has bombarded us with titillating reports of discoveries of the brain's psychological prowess. Such reports invade even introductory patter in biology and psychology. We are told that the brain - or some area of it sees, decides, reasons, knows, emotes, is altruistic/egotistical, or wants to make love. For example, a recent article reports a researcher's "looking at love, quite literally, with the aid of an MRI machine." One wonders whether lovemaking is to occur between two brains, or between a brain and a human being. There are three things wrong with this talk."

"There has been much speculation that the lawyers for Jared Loughner, who has been charged in the Tucson shootings, may mount an insanity defense. Since John Hinckley Jr. was acquitted of trying to kill President Reagan, the use of the insanity defense has become very restricted in federal cases. Arizona, along with several other states, no longer allows a finding of not guilty by reason of insanity. In the three decades since the Hinckley case, brain research and brain scans have made many advances in diagnosing and categorizing mental illness. Yet this seems to have little bearing on how society deals with insanity and culpability in the legal arena. What has been learned in the decades since the Hinckley case? Should a better medical understanding of mental illness alter our legal definitions of insanity? Or is the insanity defense rooted in principles or traditions that actually don't have much to do with medicine?"

"Benno M. Nigg has become a leading researcher on orthotics - those shoe inserts that many athletes use to try to prevent injuries. And what he has found is not very reassuring. For more than 30 years Dr. Nigg, a professor of biomechanics and co-director of the Human Performance Lab at the University of Calgary in Alberta, has asked how orthotics affect motion, stress on joints and muscle activity. Do they help or harm athletes who use them? And is the huge orthotics industry - from customized shoe inserts costing hundreds of dollars to over-the-counter ones sold at every drugstore - based on science or on wishful thinking? "

"IN a great many fields, researchers would give their eyeteeth to have a direct glimpse of the past. Instead, they generally have to piece together remote conditions using remnants like weathered fossils, decaying parchments or mummified remains. Cosmology, the study of the origin and evolution of the universe, is different. It is the one arena in which we can actually witness history. Enlarge This Image Brendan Monroe The pinpoints of starlight we see with the naked eye are photons that have been streaming toward us for a few years or a few thousand. The light from more distant objects, captured by powerful telescopes, has been traveling toward us far longer than that, sometimes for billions of years. When we look at such ancient light, we are seeing - literally - ancient times. "

"We are, I believe, witnessing something new in American politics. Last year, looking at claims that we can cut taxes, avoid cuts to any popular program and still balance the budget, I observed that Republicans seemed to have lost interest in the war on terror and shifted focus to the war on arithmetic. But now the G.O.P. has moved on to an even bigger project: the war on logic. "

"Chaser, a border collie who lives in Spartanburg, S.C., has the largest vocabulary of any known dog. She knows 1,022 proper nouns, a record that displays unexpected depths of the canine mind and may help explain how children acquire language. "

"HERE IS A mathematician's nightmare I heard in the 1980s when that irritating, unconforming, self-regarding provocateur Benoît Mandelbrot was suddenly famous - fractals, fractals everywhere. The mathematician dreamed that Mandelbrot died, and God spoke: "You know, there really was something to that Mandelbrot." Sure enough. Mandelbrot created nothing less than a new geometry, to stand side by side with Euclid's - a geometry to mirror not the ideal forms of thought but the real complexity of nature. He was a mathematician who was never welcomed into the fraternity ("Fortress Mathematics," he said, where "the highest ambition is to wall off the windows and preserve only one door"), and he pretended that was fine with him. When Yale first hired him to teach, it was in engineering and applied science; for most of his career he was supported at I.B.M.'s Westchester research lab. He called himself a "nomad by choice." He considered himself an experienced refugee: born to a Jewish family in Warsaw in 1924, he immigrated to Paris ahead of the Nazis, then fled farther and farther into the French countryside."

"Grisha Perelman, where are you? Three years ago, a Russian mathematician by the name of Grigory Perelman, a k a Grisha, in St. Petersburg, announced that he had solved a famous and intractable mathematical problem, known as the Poincaré conjecture, about the nature of space. After posting a few short papers on the Internet and making a whirlwind lecture tour of the United States, Dr. Perelman disappeared back into the Russian woods in the spring of 2003, leaving the world's mathematicians to pick up the pieces and decide if he was right. Now they say they have finished his work, and the evidence is circulating among scholars in the form of three book-length papers with about 1,000 pages of dense mathematics and prose between them. As a result there is a growing feeling, a cautious optimism that they have finally achieved a landmark not just of mathematics, but of human thought."

"True art would never be mistaken for a crude, paint-by-the-numbers copy. But a researcher has developed a statistical tool for determining whether a purported masterpiece is only a skilled imitation, suggesting that art may be a numbers game after all. Using high-resolution digital images and complex mathematical formulas, associate professor Hany Farid of Dartmouth College analyzed works by Renaissance artists to determine their authenticity. His computer program was able to accurately separate eight drawings by 16th century Flemish artist Pieter Bruegel the Elder from five drawings by imitators. It also found that portions of a painting by Italian artist Pietro di Cristoforo Vannucci, known as Perugino, were probably done by Perugino's apprentices. Farid described his work, presented Monday in the Proceedings of the National Academy of Sciences, as "simply another tool that is contributing to the dialogue of art authenticating" and said more work is needed before digital analysis of art could be done on a wider scale. Art experts reacted warily to the prospect that a masterpiece could be reduced to the sum of its digital parts. "

"What is mathematics? It's neither physical nor mental, it's social. It's part of culture, it's part of history. It's like law, like religion, like money, like all those other things which are very real, but only as part of collective human consciousness. That's what math is. For mathematician Reuben Hersh, mathematics has existence or reality only as part of human culture. Despite its seeming timelessness and infallibility, it is a social-cultural- historic phenomenon. He takes the long view. He thinks a lot about the ancient problems. What are numbers? What are triangles, squares and circles? What are infinite sets? What is the fourth dimension? What is the meaning and nature of mathematics? In so doing he explains and criticizes current and past theories of the nature of mathematics. His main purpose is to confront philosophical problems: In what sense do mathematical objects exist? How can we have knowledge of them? Why do mathematicians think mathematical entities exist forever, independent of human action and knowledge? "

"In the beauty and geometric complexity of tile mosaics on walls of medieval Islamic buildings, scientists have recognized patterns suggesting that the designers had made a conceptual breakthrough in mathematics beginning as early as the 13th century. A new study shows that the Islamic pattern-making process, far more intricate than the laying of one's bathroom floor, appears to have involved an advanced math of quasi crystals, which was not understood by modern scientists until three decades ago. The findings, reported in the current issue of the journal Science, are a reminder of the sophistication of art, architecture and science long ago in the Islamic culture. They also challenge the assumption that the designers somehow created these elaborate patterns with only a ruler and a compass. Instead, experts say, they may have had other tools and concepts."

"Female physicists, astronomers and mathematicians are up against more than 2,000 years of convention that has long portrayed these fields as inherently male. Though women are no longer barred from university laboratories and scientific societies, the idea that they are innately less suited to mathematical science is deeply ingrained in our cultural genes. The problem goes back to the ancient Greeks, particularly to Pythagoras, the philosophical giant who dreamed the dream that became modern physics. Pythagoras almost certainly learned his famous theorem about right-angled triangles from the Babylonians, but we owe to him a far greater idea: "All is number," he declared, becoming the first person to say that the physical world could be described by the language of mathematics. Pythagoras also gave us the idea of the "music of the spheres," a set of mathematical relationships that would describe the structure of the universe itself. His vision would eventually give rise to the scientific revolution led by Copernicus, Kepler, Galileo and Newton. The search for a theory of everything today is the latest version of the ancient Pythagorean quest for divine "cosmic harmonies.""

"IF there is ever a class in how to remain calm while trapped beneath $250,000 in loans, Michael Wallerstein ought to teach it. Here he is, sitting one afternoon at a restaurant on the Upper East Side of Manhattan, a tall, sandy-haired, 27-year-old radiating a kind of surfer-dude serenity. His secret, if that's the right word, is to pretty much ignore all the calls and letters that he receives every day from the dozen or so creditors now hounding him for cash. "And I don't open the e-mail alerts with my credit score," he adds. "I can't look at my credit score any more." Mr. Wallerstein, who can't afford to pay down interest and thus watches the outstanding loan balance grow, is in roughly the same financial hell as people who bought more home than they could afford during the real estate boom. But creditors can't foreclose on him because he didn't spend the money on a house. "

December 2005 Over the millennia, many mathematicians have hoped that mathematics would one day produce a Theory of Everything (TOE); a finite set of axioms and rules from which every mathematical truth could be derived. But in 1931 this hope received a serious blow: Kurt Gödel published his famous Incompleteness Theorem, which states that in every mathematical theory, no matter how extensive, there will always be statements which can't be proven to be true or false. Gregory Chaitin has been fascinated by this theorem ever since he was a child, and now, in time for the centenary of Gödel's birth in 2006, he has published his own book, called Meta Math! on the subject (you can read a review in this issue of Plus). It describes his journey, which, from the work of Gödel via that of Leibniz and Turing, led him to the number Omega, which is so complex that no mathematical theory can ever describe it. In this article he explains what Omega is all about, why maths can have no Theory of Everything, and what this means for mathematicians."

Recent theories in cognitive psychology allow us to understand that emotions are not especially irrational. Rather, they are important in the management of our goals and actions . "We are ambivalent about our emotions. Sometimes they seem to make us think in a distorted way. To say that someone is being emotional is to be insulting. But on the other hand, we regard emotions as important to our humanity. To be without them would be less than human. This ambivalence is depicted in science fiction. Mr Spock of Star Trek is superintelligent and without emotion. But he is a lonely figure - not the person to identify with as one boldly goes across the universe. So the question is, do emotions impede rationality? If we were fully rational, would we need them? Would an intelligent being from another planet have emotions? Would a robot? Are emotions an important part of being human? And if so, how? Perhaps science can help to answer such questions. Most important here has been the work of Charles Darwin. His book published in 1872, The Expression of the Emotions in Man and the Animals, touches on a fundamental dilemma about the nature of emotions, and the way we view them. "

"When discussing what to eat and how much, people often come to the conclusion "Everything in moderation." This is too vague for me. What exactly is "everything"? Every kind of Drake's Cake and candy bar? There's a lot I could justify with this "directive." Twinkies in moderation? Pop-Tarts in moderation? Ice cream in moderation? I could make an entire "everything in moderation" diet in which I eat nothing but crap.\n\nOf course, this is not what "everything in moderation" means. It means lumping these foods into one category (junk food, or refined carbohydrates, or sugar, or desserts, or processed foods) and taking the whole category in moderation. But what exactly is "moderation"? What, pray tell, would a "moderate" amount of chocolate be? An ounce a day, a week, or only on special occasions? And what would a moderate amount of trans fat be? Aren't some things better avoided altogether, or is this what people mean when they say, "Everything in moderation. Even moderation"?\n\nAnd where did this "Everything in moderation" come from? "

"It is difficult to get through a day in an American school without hearing maxims such as these: "To succeed, you must believe in yourself," and "To teach, you must relate the subject to the lives of students." But the Brookings Institution is reporting today that countries such as the United States that embrace self-esteem, joy and real-world relevance in learning mathematics are lagging behind others that don't promote all that self-regard. Consider Korea and Japan. According to the Washington think tank's annual Brown Center report on education, 6 percent of Korean eighth-graders surveyed expressed confidence in their math skills, compared with 39 percent of U.S. eighth-graders. But a respected international math assessment showed Koreans scoring far ahead of their peers in the United States, raising questions about the importance of self-esteem. In Japan, the report found, 14 percent of math teachers surveyed said they aim to connect lessons to students' lives, compared with 66 percent of U.S. math teachers. Yet the U.S. scores in eighth-grade math trail those of the Japanese, raising similar questions about the importance of practical relevance. "