September 30, 2004
Maths genius is sum womanSam Preece At the age of 92 you'd expect world famous mathematician, Dame Kathleen Ollerenshaw, to be taking things easy. But then that's never been her style. Dame Kathleen, or Lady Manchester as she was once dubbed, cancelled her birthday celebrations this week because she's busy with her book. She has just finished an exhausting round of interviews with the local and national press to promote her autobiography, To Talk of Many Things. Although she has been partially deaf since the age of eight, her press assault included a lively discussion on Radio Four Woman's hour, which has proved so popular it has been repeated. Next week she will be the guest speaker at an important mathematical conference in London and she has just returned from an award ceremony at Lancashire University. She said: "I'm cancelling my birthday, they come around too quickly and I'm too busy. I've got so many things going on at the moment." Dame Kathleen of Pine Road, Didsbury, has had an astonishing career in mathematics, politics and education, as well as bringing up two children. Her achievements are even more significant because of her deafness, and until the age of 40 had to rely completely on lip reading. Dame Kathleen moved to Withington in 1919 and has lived in south Manchester ever since. She studied at Ladybarn School, where her teachers noticed she had a natural aptitude for mathematics and in 1931 she gained an Open Scholarship in Mathematics at Somerville College, Oxford. Dame Kathleen believes her love for mathematics is due to her hearing problem. She said: "Mathematics was one subject in which I was at no disadvantage. Nearly all equations are found in books or shown on the blackboard. The mathematics became my lifeline as well as an increasing source of joy." Dame Kathleen's other big passions are politics and education. She was Conservative councillor for Rusholme from 1956 to 1981 and Lord Mayor from 1975 to 1976. During her time as a councillor she sat on the education and finance committee and found herself the only woman in a male-dominated world. She said: "I used to call myself a kept woman. Years ago they called me Lady Manchester." A highly respected mathematician Dame Kathleen has served on the governing bodies of five universities in the north west, and in 1979 she was elected President of the Institute of Mathematics, the only woman ever to have held the position. She said: "My biggest passion is maths, I want to turn people on to it." Dame Kathleen is keen not to let age be a barrier to achieving her goals. At the age of 80 she took up astronomy and can now count famous star-gazer, Patrick Moore as a friend. Her autobiography, To Talk of Many Things, is published by University Press and available at all good bookshops. Maths genius is sum woman |
September 29, 2004
Biology and math merge in new curriculumBy Will Lloyd The National Science Foundation granted the College of Science $1.25 million to develop an interdisciplinary undergraduate program at Texas A&M that will incorporate biology with mathematics and statistics. The 1,144 undergraduate students in the Department of Biology are required to only take basic mathematical classes. Students on the biology track in the integrated program will be required to have 23 credits in mathematics, six credits in statistics and 104 credits in biology, chemistry and genetics. Students on the mathematics track will need 61 credits in mathematics, six credits in statistics and 60 credits in biology and the biology-related sciences. Dean of the College of Science Dr. H. Joseph Newton said the Interdisciplinary Training for Undergraduates in Biological & Mathematical Sciences (UBM) program is a four-year experiment and A&M is one of five places chosen to conduct the experiment. "Biology is becoming more and more mathematical, (although) it historically had been the least mathematical," Newton said. "For example, the students in biology were not required to take calculus. Now it has changed. Research projects like the Gene Project indicate a trend for biology majors to know about math." The program is designed to recruit 10 students to concentrate on biology with a minor in mathematics and 10 students to concentrate on mathematics with a minor in biology, but has recruited only 12 students this fall. Adam Stevenson, a senior computer engineering major, has been studying in the program since last December, even before it officially started. "I came to the program because it integrates computer science with math and biology. My goal is to be able to use mathematics to learn and understand concepts that cannot be understood without mathematics because of their abstract nature," Stevenson said. "Mathematics allows us to reduce complex biological problems into simple equations and to gain further insight into those problems that were not originally noticeable." Continued... Biology and math merge in new curriculum |
September 29, 2004
Geek salute: Purdue honors slide ruleWEST LAFAYETTE, Ind. -- A new Purdue University exhibit pays homage to slide rules, those somewhat geeky accessories that were a necessity for generations of scientists, engineers and mathematicians. Slide rules were rendered obsolete by electronic calculators in the 1970s, ending a run that stretched back nearly 400 years. But they are far from forgotten. Nearly 200 slide rules that once protruded from students and engineers' breast pockets are now on display at Purdue's Potter Engineering Center. All were donated by Purdue alumni, among them Neil Armstrong, the first man to walk on the moon. Jerry Ross, the man who has logged more time walking in space than any other astronaut, also donated one. So did two other astronauts. Although his colleagues began getting rid of their slide rules soon after the calculator's advent, James Alleman, a professor of civil engineering, held on to his. He began collecting slide rules as a hobby in 1982. Alleman's collection grew even larger in 1987 when he asked alumni to donate their retired slide rules to celebrate the 100th anniversary of Purdue's civil engineering department. Robert Miles, a Purdue professor emeritus of highway engineering, eventually approached him with the idea of making a display to commemorate the mathematical tool. "I told him this project had to be done. It's a demonstration of the evolution of technology," Miles said. The exhibit shows how slide rules changed over the years. It also provides a brief history of the device, which has columns of numbers that can be used to multiply and divide, calculate logarithms and trigonometric functions. English mathematician William Oughtred created the first slide rule in 1632 by taking two scales of numbers and sliding them directly opposite each other. At the end of the display lies the slide rule's nemesis -- the HP 35 calculator, which was introduced in 1972, ending the slide rule's reign. While Alleman and Miles concede that they are part of a dying breed, they say they appreciate the slide rule not just for its past usefulness, but for what it represents. "It's more than just a tool," Alleman said. "It's a symbol of an era. It makes you stop and ponder where we came from." Geek salute: Purdue honors slide rule |
September 28, 2004
Math phobiaEdmund X. DeJesus Recent stories in the press about potential mathematics breakthroughs are frightening computer security officers. The gist of these stories is that "imminent" advances in mathematics would allegedly make it possible to crack encryption schemes based on the difficulty of factoring humongous numbers -- like RSA. This would destroy the primary methods of protecting passwords, virtual private networks and Internet-based secure transactions. It's the end of the world as we know it. Again. However, there are good reasons for taking these stories with a grain of salt, due to the nature of mathematical research, the time involved and the difference between pure and applied mathematics. P vs. NP and the Riemann zeta function problem are the two areas of mathematics mentioned most often in this regard. Real mathematicians will froth at the mouth as I describe these problems, because my descriptions lack mathematical rigor. So, real mathematicians, just do some deep breathing exercises for a moment. The P versus NP problem involves the inherent difficulty of certain mathematical questions -- often those that have to do with optimization, such as the most efficient route for a delivery truck. No algorithm can solve such questions -- brute force guessing may eventually reveal a solution. Discovering the prime factors of huge numbers -- the basis of encryption schemes like RSA -- is a NP question. The news: NP problems really aren't as hard as we thought. The Riemann zeta function is intimately related to the distribution of prime numbers, which are notorious for being whimsically distributed. Since the Riemann zeta function is related to the distribution of prime numbers, it can help narrow down the search for prime numbers, and thus speed up the search. Still, keep in mind that mathematicians can consider a solution to be merely that an answer to a given question exists -- not what that answer might be or how to find it. A purely mathematical solution to these problems may be far from useful. Also, consider that some of these problems have been known for centuries and, while progress has been made, they still haven't been solved. So, when mathematicians talk about a breakthrough, it does not mean a solution is looming. The solution might be found tomorrow -- or a century from now -- or never. There's no way to tell, so why worry about something that may be decades away? Finally, the gulf between pure and applied mathematics is vast. Even if some genius announced tomorrow that an algorithm for finding factors of humongous numbers was possible, that wouldn't advance the search for that algorithm one nanometer. It's like an engineer announcing that it's possible to bridge a certain river: you wouldn't want to immediately drive up to the bank of the river and wait. Building that bridge will take time. The bottom line is simple. Don't let announcements about possible mathematical breakthroughs throw you. They might take years to crack, their application to reality is iffy and any uses will take years to develop. Remember: Math is our friend. Math phobia |
September 28, 2004
Saluting the data encryption legacyBy Bruce Schneier The Data Encryption Standard, or DES, was a mid-'70s brainchild of the National Bureau of Standards: the first modern, public, freely available encryption algorithm. For over two decades, DES was the workhorse of commercial cryptography. Over the decades, DES has been used to protect everything from databases in mainframe computers, to the communications links between ATMs and banks, to data transmissions between police cars and police stations. Whoever you are, I can guarantee that many times in your life, the security of your data was protected by DES. Just last month, the former National Bureau of Standards--the agency is now called the National Institute of Standards and Technology, or NIST--proposed withdrawing DES as an encryption standard, signifying the end of the federal government's most important technology standard, one more important than ASCII, I would argue. The strength of an algorithm is based on two things: how good the mathematics is, and how long the key is. A sure way of breaking an algorithm is to try every possible key. Modern algorithms have a key so long that this is impossible; even if you built a computer out of all the silicon atoms on the planet and ran it for millions of years, you couldn't do it. So cryptographers look for shortcuts. If the mathematics are weak, maybe there's a way to find the key faster: "breaking" the algorithm. The NSA's changes caused outcry among the few who paid attention, both regarding the "invisible hand" of the NSA--the tweaks were not made public, and no rationale was given for the final design--and the short key length. But with the outcry came research. It's not an exaggeration to say that the publication of DES created the modern academic discipline of cryptography. The first academic cryptographers began their careers by trying to break DES, or at least trying to understand the NSA's tweak. And almost all of the encryption algorithms--public-key cryptography, in particular--can trace their roots back to DES. Papers analyzing different aspects of DES are still being published today. So, how good is the NSA at cryptography? They're certainly better than the academic world. They have more mathematicians working on the problems, they've been working on them longer, and they have access to everything published in the academic world, while they don't have to make their own results public. But are they a year ahead of the state of the art? Five years? A decade? No one knows. It took the academic community two decades to figure out that the NSA "tweaks" actually improved the security of DES. This means that back in the '70s, the National Security Agency was two decades ahead of the state of the art. Today, the NSA is still smarter, but the rest of us are catching up quickly. In 1999, the academic community discovered a weakness in another NSA algorithm, SHA, that the NSA claimed to have discovered only four years previously. And just last week there was a published analysis of the NSA's SHA-1 that demonstrated weaknesses that we believe the NSA didn't know about at all. Maybe now we're just a couple of years behind. Saluting the data encryption legacy |
September 27, 2004
Popular Science names two professors to 'Brilliant 10' listStephen Hsia The scientists you're about to meet aren't famous. Yet. Maria Chudnovsky GS '03 and Claire Gmachl have neither won the Nobel Prize nor penned a bestselling book, yet Popular Science magazine has named the two Princeton faculty members to its "Brilliant 10" list of young scientists. "'Brilliant 10' is our way of bringing some of the brightest, most promising minds in science to a mainstream audience," Mark Jannot, Editor-in-Chief of Popular Science, said. "This is a group of 10 people largely unfamiliar to most, but their work will change our lives." For mathematician Maria Chudnovsky, 27, the award came as a surprise. "A year ago, someone called me to find out more about my research," she said. "I must have put him to sleep, but a year later, he called me again and said 'Oh, we would like to do this article on you — you have been selected to [the Brilliant 10].'" What merited Chudnovsky such an honor? Along with her adviser, Paul Seymour, Chudnovsky unlocked a major, mathematical 40-year-old riddle known as the perfect graph conjecture. The conjecture explains why some organizational problems, like constructing a cell phone network using the fewest transmitters or assigning teachers to various classrooms, are harder than others. Popular Science credits Chudnovsky and her team as the first to prove this longstanding theory. Russian-born Chudnovsky came to Princeton in 2000 to pursue graduate work after her education in Israel. "I wanted to do my Ph.D. at a very good place and I was interested in combinatorics," Chudnovsky added, who received her doctorate last year. "At college in Israel, I had a very good combinatorics professor, and I liked math in high school, so graph theory was a natural choice for me." "It's like solving a crossword puzzle all day long," she said. Popular Science names two professors to 'Brilliant 10' list |
September 25, 2004
In nothing flatBrowns' Jeff Garcia found a reality check in Dallas with a 0.0 passer rating. Now, he looks to bounce backTony Grossi When the official game summary of the Browns' 19-12 loss to Dallas showed Jeff Garcia with a passer rating of 0.0 and Luke McCown with one of 39.6, a team official told a reporter it was a mistake, that the numbers should be reversed. He was wrong. It is hard to swallow that a quarterback could complete 8 of 27 passes and net a 0.0 rating, while one who goes 0-for-1 could top off at 39.6. "I'm disappointed in that one myself," sighed Seymour Siwoff, the founder of Elias Sports Bureau who helped originate the complex rating system more than 30 years ago. "This is the unfortunate part. No matter how many passes I throw, if I don't throw an interception, I will receive points." In 1973, Siwoff joined forces with Don Smith, formerly the director of communications with the Pro Football Hall of Fame in Canton, to devise a method by which quarterbacks of different years and different eras could be compared. A mathematician processed their thoughts into a formula that weighed six different passing categories. They were pared to four: Percentage of completions per attempt. Average yards gained per attempt. Percentage of touchdown passes per attempt. Percentage of interceptions per attempt. The numbers are crunched against the average standard in each category based on league history. The final number is multiplied by 100 to give it a more recognizable quantity. The result is a "passer rating" - not a "quarterback rating," Siwoff emphasized. The highest rating possible in the NFL system is 158.3. The lowest is 0.0. A negative rating is not possible. "The whole purpose was to have some kind of a way to judge a passer," he said. "It is not a rating of quarterbacks." In nothing flat |
September 25, 2004
Mr. Worm, you're the greatestLocal educator named state's teacher of the yearBy MELANIE ASMAR A teacher who encourages students to smash VCRs, inspires them to impersonate Richard Simmons and lets them eat pie in class received the New Hampshire Department of Education's Teacher of the Year award in a surprise ceremony yesterday. Known to his students as Mr. Worm, Belmont High School math teacher Randy Wormald accepted the honor wearing his signature paper clip tie-clip on a muted purple tie. He stood in front of the gymnasium bleachers and thanked the students and faculty. "I want to share this award with all of you," he said. "You make it fun to come to school each day. You guys rock!" Some would argue that the same could be said about Wormald, 38. Once a year, he dons a toga and slings a guitar over his shoulder to teach his students the Pythagorean Theorem. Dressed as ancient Greek mathematician Pythagoras, Wormald raps to the tune of the Sugar Hill Gang's "Rappers Delight," changing the lyrics to focus on right triangles: "I said uh P-Y-T, H-A-G, O-R-A-S/you see, I go by the unforgettable name of the one they call Pythagoras/well, my math is known all over the world . . . " That's not the only time he gets down. On Pi Day, March 14, Wormald has his students bake pies, bring them to class and then eat them while he sings them a song about 3.14 to the tune of Don McLean's "American Pie." "He always thinks of crazy projects for us," said senior Kayleigh Brown, a student in the class. "And he's easy to talk to. He's funny. He cares about what we want, and he's not there just to teach." Mr. Worm, you're the greatest |
September 24, 2004
Israelis among top innovatorsBy JUDY SIEGEL-ITZKOVICH For the first time, two Israelis under 35 - one at the Technion-Israel Institute of Technology in Haifa and the other at the Weizmann Institute of Science in Rehovot - are on the list of the world's "Top Young Innovators." The two Israelis are Dr. Kinneret Keren of the Technion and Ya'acov Benenson, a 29-year-old Weizmann Institute doctoral student. Selected from among almost 650 candidates from around the world, they will be honored, along with others on the list, at the Technology Review 2004 Emerging Technologies Conference at MIT on September 29 and 30. Benenson is also a candidate for "TR 100 Innovator of the Year" and the "TR 100 Humanitarian Award", which will be announced at the conference. This year's nominees are recognized for their contributions in transforming the nature of technology and business in industries such as biotechnology and medicine, computing, and nanotechnology. Keren, who is in the middle of doing post-doctoral work at Stanford University in California, studied at the Technion with Prof. Erez Baron and Prof. Uri Sivan of the physics faculty. Last year, the research team succeeded in finding a way to produce the first molecular transistor made out of DNA. Reports on this pioneering development were published in the prestigious journal Science and a variety of other print media. The Jerusalem-born researcher - whose father is a mathematician, mother was a computer scientist, and three siblings are all scientists - said that work at the Technion was very demanding, but also very rewarding, "because we invented something that was completely new and did not exist before. Science is usually composed of 90 percent frustration and 10 percent celebration. When you start from an idea, you experiment and often don't succeed. But there are those rare wonderful moments when they do succeed and something new is created." Benenson works with Prof. Ehud Shapiro of the Rehovot institute's department of computer science and applied mathematics, and its department of biological chemistry. Inspired by the world-famous Shapiro's vision of a "doctor in a cell", Benenson joined Weizmann in 1999 at age 24 and began to tackle the challenges of DNA-driven computing solutions for disease diagnosis and treatment. Benenson received the Wolf Foundation Prize for Excellence in Graduate Studies six years ago and is currently on the Dean's List of the Feinberg Graduate School at Weizmann for his achievements in PhD studies and research. He co-invented the world's smallest biological computing device - a bio-molecular finite-state automaton made from DNA strands and DNA-manipulating enzymes. The automaton, about a trillionth the size of a drop of water, was listed in the 2004 Guinness Book of World Records as the smallest biological computing device. Recently, this device was enhanced to detect and diagnose molecular symptoms of cancer in vitro and, in response, to release a drug to treat the cancer. Benenson's breakthrough in this area of research exceeded earlier progress predictions by Shapiro and others. Israelis among top innovators |
September 22, 2004
STUDY REVEALS WHY EYES IN SOME PAINTINGS SEEM TO FOLLOW VIEWERSCOLUMBUS, Ohio – You've seen it in horror movies, or even in real-life at the local museum: a painting in which the eyes of the person portrayed seem to follow you around the room, no matter where you go. People have described the effect as creepy or eerie, and some have thought it supernatural. But now researchers have demonstrated the very natural cause for this visual effect. All it takes for the effect to work is to have the person in the painting, or photograph, look straight ahead, said James Todd, co-author of the study and a professor of psychology at Ohio State University. Our visual perception takes care of the rest. "The core idea is simple: no matter what angle you look at a painting from, the painting itself doesn't change. You're looking at a flat surface. The pattern of light and dark remains the same," Todd said. "We found that our visual perception of a picture also remains largely unchanged as we look at it from different vantage points. If a person in a painting is looking straight out, it will always appear that way, regardless of the angle at which it is viewed." The study was conducted at the University of Utrecht in The Netherlands in collaboration with Jan Koenderink, Andrea van Doorn, and Astrid Kappers. Their results were published in a recent issue of the journal Perception. While scientists have considered the reasons behind this visual effect for more than a century, advances in the field of perception now allow for better ways to study why it occurs, Todd said. "Researchers have developed powerful techniques that allow us to measure the perception of complex shapes in a very precise way," he said. In this study, the authors viewed on a computer screen a picture of a medical mannequin human torso in a richly sculpted gilded frame, which appeared to be hanging on a brick wall. The wall and frame were shown in color, the torso in neutral gray. In order to answer their questions, the researchers needed to determine how the apparent 3D structure of the object depicted in the picture was influenced by changes in the viewing direction. They were particularly interested whether points that appeared to be closest or farthest in depth relative to other neighboring points would remain the same when the picture was observed at different viewing angles. They also wanted to determine how the relative magnitude of the perceived depth in different regions of the picture would be affected when viewed at different angles. In order to address these issues, the researchers did two types of tasks. In one, they moved a dot around on the computer screen to show which points on the torso appeared to be nearest and which appeared to be the furthest away. The researchers did this hundreds of times to find near points and far points on various parts of the torso. In a second task, they used a gauge figure (a circle with a needle sticking out) that had to be placed on the torso so it looked to be flat against the surface (The needle had to appear like it was perpendicular to the surface of the torso). This allowed the researchers to determine how viewers perceived the 3D shape of the depicted object. The researchers repeated this process for six different conditions, including sessions in which they looked straight at the monitor, and others in which they looked at it from an angle. Each researcher repeated these tasks three times for each of the six experimental conditions. "These experiments took hours," Todd said. "We made judgments at numerous probe points on each image, so that when all of the different conditions were completed we ended up making thousands of settings over the course of the experiment. "From all that data we were able to mathematically construct a surface that is most consistent with the overall pattern of judgments in each condition." However, the different viewing conditions didn't yield many different results. "It turned out that that changes in viewing direction had remarkably little effect on the observers' perceptions," Todd said. The only difference they found is that, when viewed from an angle, the torso looked "squashed" – in other words, it looked thinner to viewers. But the far points and near points, and the overall relief of the depicted object, remained proportionally the same. The key is that the near points and far points of the picture remained the same no matter the angle the picture was viewed from, Todd said. "When observing real surfaces in the natural environment the visual information that specifies near and far points varies when we change viewing direction," he said. "When we observe a picture on the wall, on the other hand, the visual information that defines near and far points is unaffected by viewing direction. Still, we interpret this perceptually as if it were a real object. That is why the eyes appear to follow you as you change your viewing direction." Todd said people may be surprised by this phenomenon because of the unique perceptual aspects of viewing a picture. We perceive the object depicted in a painting as a surface in 3-dimensional space, but we also perceive that the painting itself is a 2-dimensional surface that is hanging on the wall. "When we look at a picture, you have these two perceptions simultaneously, but it is difficult to make sense of that conceptually. That's why this issue has fascinated people for hundreds of years." In fact, many researchers have continued to follow the theories of La Gournerie, a French researcher who proposed a mathematical analysis in 1859 of why eyes in a painting seem to follow viewers. "One of the contributions of our study is that we showed that while La Gournerie had the basic idea right, his mathematical description was wrong," Todd said. "We were able to use new methodologies to give a more correct mathematical analysis of what is going on." STUDY REVEALS WHY EYES IN SOME PAINTINGS SEEM TO FOLLOW VIEWERS |
September 22, 2004
Drumming Up Answer to Math MysteryBy Lisa De Nike A $975,398 National Science Foundation grant is allowing a team including mathematicians at Johns Hopkins' Krieger School of Arts and Sciences to tackle a 200-year-old question: How does the shape of drums influence the frequency and geometry of their vibrations when they are struck? The $402,000 portion of the grant coming to Johns Hopkins is the largest ever awarded to faculty in the Department of Mathematics, according to Christopher Sogge, department chair, who has teamed up with Professor Steven Zelditch for the three-year investigation. The Johns Hopkins team is sharing the grant with fellow mathematicians Daniel Tataru and Maciej Zworski at University of California, Berkeley, and Hart Smith at the University of Washington, who are taking on the same challenge. According to Sogge, the purpose of the grant is to get like-minded researchers collaborating. "At the heart of our project is a 200-year-old question that remains largely unanswered today," Sogge says. "Mathematicians are interested in what can be known, and even better, proven, about vibrating shapes. This is important in mathematics and physics because it deals with what we call 'modes of vibration' of objects ranging from drums to atoms and molecules to the whole universe." The question dates back to the early 19th century, when a German scientist named Ernst Chladni impressed Emperor Napoleon Bonaparte with his ability to make sound waves "visible" using a simple experiment. When Chaldni sprinkled sand onto metal plates and drew a violin bow across the edges, the grains scattered and settled into intricate geometric designs on the portions that were not shaking with sound. Intrigued by those results, the emperor offered a reward to anyone who could explain how the sand's patterns--and the invisible sound waves that produced them--related to the shape of the metal surface upon which they settled. Sogge and Zelditch have chosen to study various drum shapes because their contours provide a simple model for any vibrating object, including atoms and molecules. The general question of how the frequencies and shapes of vibration reflect the shape of the object is the same, whether one is talking about drums or atoms, they say. "The shapes we are dealing with range from the kind a drummer would use in a rock band to drums of any dimension and shape," Zelditch says. "We are especially interested in what we call 'extreme drums': those capable of making extreme sounds at a given frequency. Extreme to most people would mean 'loud.' But we think geometrically." It's important to note that no actual drums are involved in the team's inquiry. Sogge and Zelditch are operating entirely in the realm of the theoretical: Their only hands-on work involves putting chalk to blackboard or pen to paper in the quest for the formula or proof that solves the question at hand. And though some mathematicians and physicists are tackling this challenge with the help of computers, the Johns Hopkins pair is using old-fashioned brainpower. "It's pure thought research; we do it by thinking and brainstorming," Sogge says. "The best way to visualize what we are doing is to imagine playing billiards on a drumhead and using math to predict and describe the trajectory of the ball when you hit it. For instance, the usual billiard table is rectangular, and the path of a ball hit upon it is, therefore, predictable. But if one makes a pool table in the shape of a football stadium, it turns out that the ball, no matter how you hit it, will move around in a chaotic way. It's as if we are playing an imaginary game of billiards atop drums of various shapes to determine what their vibrations will look like." Though the Johns Hopkins team anticipates having some answers by the end of the three-year grant, Sogge and Zelditch say they expect to be grappling with similar problems and theories for the rest of their careers. "What we're doing is of interest to the math world because the properties we are talking about are very basic to lots of areas of mathematics, from number theory to partial differential equations to differential geometry," Sogge says. "But it also is of interest to physicists who study dynamical systems and nanostructures, such as quantum dots and electron corals. In both cases, the concentration patterns of waves and excited states play a fundamental role in the systems they study." Drumming Up Answer to Math Mystery |
September 20, 2004
For Fry's, It's a Prime Time to Support Higher MathMichael Hiltzik Shopping at Fry's Electronics Inc. stores has always struck me as a form of geek penance: Its indifferent customer service, onerous returns system and not-always-so-low prices are legendary among the clientele drawn in by the chain's vast inventory. This is, admittedly, a churlish way to lead up to an aspect of Fry's that merits our unalloyed admiration: Under its publicity-shy founder, John Fry, the San Jose company has endowed one of the most remarkable academic institutes in the country. The American Institute of Mathematics lies behind a heavy steel door situated just next to the main entrance of Fry's Palo Alto store. A bright mural hangs on the outside wall as a signpost, explains AIM Executive Director Brian Conrey, because visitors used to have trouble finding the nondescript doorway even with explicit directions. AIM currently receives about $1 million a year from the closely held company and a Fry family foundation, and another $1 million from the National Science Foundation. Since its 1994 founding, the institute has been devoted to cracking the most elusive problems in higher math by organizing workshops that bring together leading experts for top-level brainstorming. To appreciate the uniqueness of such collaboration one must understand the traditionally hermetic work habits of mathematicians. "If you look at the literature you will find that maybe 70 years ago, almost every paper was single-authored," says Peter Sarnak, a Princeton University mathematician. "AIM was the first to bring together teams with major success." For example, AIM can claim a hand in the 2002 proof of the "perfect graph conjecture," an important problem in communications networking, by members of a group that the institute had funded. But mathematics being what it is, a large part of AIM's work has been a quest for the Holy Grail of number theory: a proof of the Riemann Hypothesis. In this space I couldn't explain the Riemann Hypothesis without simplifying it to the point of caricature. Suffice to say that it's an 1859 guess by the mathematician Bernhard Riemann that certain solutions to a mathematical operation known as the zeta function — its "zeros," or inputs that make the function equal 0 — can be graphed with startling symmetry along a certain straight line. The hypothesis fascinates mathematicians in part because the zeta function is closely related to the distribution of prime numbers (numbers divisible only by themselves and 1). Primes are important in number theory because every integer is either a prime or the product of primes. The search for a proof has been driven by discoveries that zeta functions lie behind a wide range of mathematical relationships. "It's the tip of a much bigger thing we're struggling with," Conrey told me, "and the last elementary function we don't understand." It doesn't hurt that a $1-million prize — one of seven that a Boston businessman, Landon Clay, established in 2000 for the solutions to seven top mathematical challenges — awaits the victor in the race. So far, experts have verified the Riemann Hypothesis for points on the number line out to the tens of billions, but that's not the same as proving its fundamental truth. Conrey himself holds the world record for the largest percentage of zeros proved to lie on Riemann's line — a mere 40%, a mark he set in 1987. Now and then a mathematician will suggest that the hypothesis has resisted proof for so long because it's inherently unprovable or even false, but that's a distinctly minority view. The hypothesis, as it happens, was instrumental in bringing Conrey to AIM. Conrey, now 49, had done his undergraduate work at Santa Clara University, where John Fry was a fellow mathematics student. Gerald Alexanderson, who later became AIM's board chairman, had headed the math department. At a convocation in 1996, Conrey told the AIM advisory board that the hypothesis would be an ideal target for the collaborative approach the institute was promoting. The result later that year was the first AIM workshop, which brought together 70 physicists, computer scientists, number theorists and analytical mathematicians — representing all the varied disciplines then taking stabs at the hypothesis, mostly in snug isolation. The stage was set for a new paradigm in math research. "People said there was no way you could make it work," Conrey recalls, "but that whole week it felt like something different was happening." He became AIM's executive director the next year. AIM is working toward a schedule of 24 workshops a year, each with a maximum of 32 participants, devoted to a wide range of issues. That will be a lot easier once the institute moves into a spacious permanent home it plans to build in Morgan Hill, south of San Jose, as a temple to the pursuit of pure knowledge. For that's the aspect of the field that sets mathematicians apart. Although prime numbers recently acquired commercial value as keys to secure encryption systems — and notwithstanding Clay's $1-million prize — most seem to be searching for an orderliness belying nature's apparent dishevelment. Riemann's Hypothesis is central to AIM because it symbolizes that absolute tidiness. "The primes on the one hand seem very unruly and unpredictable," Conrey says. "On the other hand, having these zeros all on the line is just spectacular." When I asked whether he harbored any doubts about the truth of the hypothesis, he answered with a sort of mathematician's credo. "That would be a really mean trick, somehow," he says. "It's too beautiful not to be true." For Fry's, It's a Prime Time to Support Higher Math |
September 20, 2004
Alice chatbot wins for third timeA computer chat program called Alice has won a prestigious prize for human-like conversation for the third time. It was judged to be chattiest bot out of the four finalists in the Loebner Prize for artificial intelligence held in New York on Sunday. British hopeful, Jabberwacky, came second in the annual competition. The event is based on the Turing Test, which suggests computers could be seen as intelligent if their chat was indistinguishable from those of humans. Alice won the international competition for the most convincing entry in 2000 and 2001. Its creator, American Richard Wallace, started work on the software in 1995. Since then, he has been refining the conversational skills of the software through the Alice Foundation. Alice works by following a complex set of rules that govern its responses to a question. It managed to see off three other contenders to take the bronze award in the Loebner Prize for a third time, convincing judges with its life-like responses. The British contender, Jabberwacky by Rollo Carpenter, had to settle for second place. "I'm disappointed as I did believe I would win," Mr Carpenter told BBC News Online. However, he remained hopeful that his program would be more successful in the years to come. "Alice is based around a set of big and complex 'if statements' that analyses the text and respond to the one thing that you have immediately said. "My program is more open and free," he said. "I believe the day of the learning AI will come soon. It is inevitable because a hand-coded system cannot keep up with an exponentially growing system which learns dynamically." The Loebner Prize was started in 1990. It hands medals and cash prizes to the inventors of computer programs that can maintain the most life-like dialogue. The competition is a variant of a stricter test first thought up by pioneering mathematician Alan Turing. He suggested that computers could be said to be intelligent if their responses to conversational cues were indistinguishable from those of humans. The contest in New York was hosted by American philanthropist Dr Hugh Loebner, who started the prize in 1990. The Gold Medal, and a cash prize of $100,000 (Ł69,000), is awarded to the program that convinces half the judges that they are talking to a believable virtual person on screen. The Silver Medal, plus a cash prize of $25,000 (Ł17,000), goes to the text-based program that convinces half the judges. No Gold or Silver medals have ever been awarded. But every year, a bronze medal, and $2,000 (Ł1,400) cash, goes to the most convincing entry. Alice chatbot wins for third time |
September 19, 2004
Math whiz hopes to make the world more intelligent through his Web siteBy Douglas Sams DULUTH — Those frustrating after-school sessions with the math tutor — a common experience for generations of Algebra-challenged students — may soon be a thing of the past. At least, that's the trend that information technology entrepreneur and mathematician Jeetan Singh sees taking shape. So rather than build a traditional learning center, where students come after school to practice math with an instructor, Singh took a different approach. Called iCoachMath.com, his new venture is a Web-based resource of thousands of math problems, where students can hone their math abilities online, rather than in a classroom. Math teachers have also been using the program to sharpen their skills, with several from the Atlanta School System sending letters to Singh's business to say how impressed they are by his idea. "I want every child in the world to be able to go to this Web site and practice math," Singh said. "You don't need the learning center or the math tutor anymore. I'm bringing the service to you." Singh is founder of Duluth-based Datamatics, a software consulting company he started in his one-bedroom Dunwoody apartment, just as the dot-com boom was beginning to surge in the early-to-mid 1990s. Datamatics Consultants Inc. now has 85 employees, 70 clients across various industries and offices in several different countries, including Canada and India. At one time, he said Datamatics was ranked by Inc. 500 as the 81st-fastest growing U.S. company. And even with all that success, Singh believes iCoachMath.com may become a more impressive profit-making machine than his first company. For one, this offshoot of Datamatics has already gained nearly 22,000 regular users since February. The current generation of school-aged children is also more comfortable working and learning on the Internet. Another reason — though a more discouraging one — is the state of math education in the country. "It is severely lacking," Singh said. Raised in New Deli, Singh earned degrees in mathematics and a masters in computer science, a background that fueled his belief in the power of a good education and the endless possibilities of technology. When his daughter came to him one evening to ask for help on a math problem, the idea for iCoachMath was born. "I thought, 'how many more children are coming to their parents right now asking them for help on their math homework, and, more importantly, how many of those parents have the time or the knowledge to actually help?'" Singh said. "Some of those children had nowhere to go, and that's such a terrible thing because childrens' minds are like a sponge — they absorb everything. But if they have no access to the knowledge, all that potential is denied." So Singh spent more than three years building an online database of math problems, seeking answers to the questions from mathematicians he knew from around the world. He then built the Web-based bank of math problems, solutions and tips. A passionate advocate for a more egalitarian educational system, Singh also offers his online service at reduce rates for children whose families are struggling financially. While Singh is a successful businessman who thinks his new creation can be a big revenue-maker, he says he also has another more noble goal than making a lot of money — making the world more intelligent and productive. "Math makes the mind think faster all the time," he said. "And a faster, more powerful mind helps you achieve new heights in life." Math whiz hopes to make the world more intelligent through his Web site |
September 18, 2004
Code created for shape-shifting robotsNewScientist.com news service Robots that change shape and even split into smaller parts to explore unfamiliar terrain could soon be feasible thanks to new algorithms designed to enable such metamorphic tricks. Zack Butler and colleagues at Dartmouth College in New Hampshire, US, developed algorithms to control robots made from identical components, each capable of moving on their own but also able to attach to one another. As this is beyond current hardware, they constructed virtual modular bots and used a software simulator to test them. The modular robot can move along as a complete unit, built up of around 100 smaller parts. But when faced with an impassable obstacle, some of these modules can detach and proceed as a smaller unit, or even on their own. Once the obstacle has been passed, however, the smaller units will automatically recombine into the larger whole, enabling them to travel over different terrain once more. "These algorithms are the first step toward using the power of modularity to work in parallel," Butler told New Scientist. "They could allow the use of modular robots to perform parallel exploration, dividing up and recombining to cover ground faster while still having the capability of the original system." Normally a robot has a single central control component. But the researcher's goal was to develop distributed software for each module, so that the robot could split and still carry on with its mission. Simulations showed that complex shape shifting robots could be controlled by giving each module an identical algorithm with its own relatively simple set of rules to follow. In a paper published in the International Journal of Robotics Research, the researchers also demonstrated mathematically that the algorithms would work under any circumstances for the geometry of the simulated robots. Marsette Vona, a robotics researcher at MIT in Massachusetts, US, says developing distributed algorithms should prove useful in other areas of research, such as sensor networking. But he adds that there these algorithms could still be a lot more efficient. "Even in the simulated world, the problems are tremendously challenging," he says. Code created for shape-shifting robots |
September 17, 2004
Say hello to Jabberwacky, our best 'human' computerBy Charles Arthur A computer program will attempt to pull off the ultimate con trick tomorrow: fooling an adult into believing it is human - and in doing so claim the greatest prize in artificial intelligence. The program in question - called Jabberwacky - started life in 1982 on a Sinclair home computer. Written by Rollo Carpenter, a British computer consultant, it is one of four that have been picked by the millionaire Hugh Loebner to take part in the annual Loebner Prize contest, where computer programs try to pass the "Turing Test". That challenge, originally set by the British mathematician Alan Turing in 1950, is straightforward. In a text conversation with no fixed topic a human should be unable to tell whether they are communicating with another person or a computer. If successful, the machine would have passed at least one of the requirements to be described as "thinking" - though Turing himself said it would be better described as "imitation". "I suspect in the future there will be ever-increasing move away from things like TV to things like the internet and other communications devices. Imagine where you have an iPod or mobile phone or little robot that sits on your shoulder which keeps you company as you walk along the street, or advises you on what to do. My approach is about making something that gives you companionship." He has been running the Jabberwacky program at its website for some years, where it will engage human visitors in conversation. So far it has sorted through more than 3.3 million responses in 200,000 conversations to try to build a database of sensible responses. "Right now [the program] is still pretty strange," admits Mr Carpenter. "It says unexpected things, which if you're of a certain mind is amusing, and makes people stay on the site. But that won't necessarily impress somebody who's coming to test it." The Loebner Prize is run under strict conditions, where the competing programs must be run on a computer that is not connected to the internet, and run on their own on a computer in a room shared with a human being. In an adjacent room, a human "interrogator" will quiz the four computer programs and one human - without any clues to their identity - and decide which are the machines and which the person. That meant that Mr Carpenter had to add an extra layer to his program: simulated typing, including mistakes. Say hello to Jabberwacky, our best 'human' computer |
September 16, 2004
Dembski to head seminary's new science & theology centerBy Jeff Robinson LOUISVILLE, Ky. (BP)--Southern Baptist Theological Seminary President R. Albert Mohler Jr. announced Sept. 16 the establishment of the Center for Science and Theology along with the appointment of renowned philosopher of science William A. Dembski as its first director. Since 1999, Dembski has served as associate research professor at Baylor University's Institute for Faith and Learning. He also serves as a senior fellow for the Discovery Institute's Center for the Renewal of Science and Culture in Seattle, Wash., and is executive director of the International Society of Complexity, Information and Design. Mohler said that the new center, along with Dembski, will represent a major component of Southern Seminary's commitment to develop and articulate a comprehensive Christian worldview. Dembski, who will begin June 1, will serve as the Carl F.H. Henry Professor of Theology and Science. Dembski said he desires to help students understand how science should be understood in terms of Christian theology. Theology, he said, underpins all of his views of science and intelligent design. "I started out as a straight research mathematician but got into these questions of philosophy and theology because I was so exercised in my spirit about the unbelief I saw in the academy [and] why it seemed so reasonable to disbelieve the Christian faith," Dembski said. "That is what really motivated me to work on Christian worldviews and apologetics and it is in the background of my work on intelligent design as well. "Theology is where my ultimate passion is and I think that is where I can uniquely contribute ... I am looking forward to engaging students and theological students have always been my favorite to deal with because for theology students, it's not just a job, but a passion, especially at a place like Southern, because they want to change the world." A mathematician and philosopher, Dembski is the author of a number of influential books, including "Intelligent Design: The Bridge Between Science & Theology," "The Design Inference," and his latest, "The Design Revolution," published by Cambridge University Press. Dembski previously taught at Northwestern University, the University of Notre Dame and the University of Dallas. Dembski holds seven degrees, including two Ph.D. degrees -- one in mathematics from the University of Chicago and the other in philosophy from the University of Illinois at Chicago. He holds a Master of Divinity degree from Princeton Theological Seminary and also holds a Bachelor of Arts degree in psychology and a Master of Science degree in statistics. In addition, Dembski has done postdoctoral work in mathematics at MIT, in physics at the University of Chicago and in computer science at Princeton. Dembski to head seminary's new science & theology center |
September 15, 2004
Govt Invites Oyibo to Head NEADSautore IN appreciation of his scientific discovery in mathematical physics, the Federal Government has invited Prof. Gabriel Oyibo to head the Nigerian Experts and Academics in the Diaspora Scheme (NEADS). Executive Secretary of the National Universities Commission (NUC), Prof. Peter Okebukola, in a letter to the New York based researcher, said government decision was informed by his scientific accomplishment. Prof. Oyibo who is a three-time nominee for the prestigious Nobel Prize in mathematical physics, has attracted the interest of world leaders, including President Olusegun Obasanjo, the European and the U.S. Mathematical societies, as well as the German Army. "NEADS is aimed at attracting experts and academics of Nigerian origin in the diaspora to contribute their quota to the development of the Nigerian University System, and hence to the development of the nation through short-term academic appointments" Prof. Okebukola noted. It is in the above context that the NUC has considered it appropriate to invite you to flag-off the scheme, through a series of lectures and professional interactions across Nigeria, at your convenience, between October and December 2004, and for up to one month, he added. The NUC boss explained that the thrust of the activity is centred on Mathematics and Physics interfacing for human development," expectedly infusing the applications of your widely acclaimed GAGUT Theorem." He asked Prof. Oyibo to arrange a month-long visit to Nigeria between October and December for the purpose of a nationwide lecture series on the relevance of GAGUT to the country, adding that NEADS activities would commence fully next January. Govt Invites Oyibo to Head NEADS |
September 14, 2004
Searching for the Best Women's Chess Player in the WorldThe Russian Samovar, 1pm Thursday September 16, 2004
The World's First Artificial Intelligence Search Engine, NEW YORK, Sept. 14 /PRNewswire/ -- Two of the World's best women Chess Players are set to face off in the ACCOONA French-American Women's Chess Championship on Thursday September 16, at the Russian Samovar*, in the heart of Times Square, New York City. French Champion, Almira Skripchenko, will meet American Champion, Irina Krush, in this ACCOONA World Chess Championship Series Match. The winner earns the right to challenge Zhu Chen, Women's World Champion from China, in the ACCOONA Women's World Chess Championship Finals, slated for December 7, 2004 at the ABC Television Times Square Studios. Skripchenko (French Champion) vs. Krush (American Champion) The match-up between Almira Skripchenko and Irina Krush is extremely close. Irina is nominally six points stronger than Almira, but the French Champion has more international titles and championship wins to her name. 28-year-old Almira Skripchenko was recently crowned French Champion, solidifying her status as the #1 woman player in France. Skripchenko was crowned European Women's Chess Champion in 2001, and earlier this year won the first ever women's chess super tournament in Krasnoturinsk, Russia. Skripchenko has twice made it to the quarterfinals of the World Championships. Just recently Almira won the strongest women's chess tournament ever held, the North Urals Cup. 20-year-old Irina Krush is one of the best American woman chess players of all time. She became the youngest woman ever to compete in the US Women's Chess Championship at age 11, and became the youngest ever to win the same event at the age of 14. Krush has participated in several US Championships, and represented the USA at both the Chess Olympiad and the Women's World Chess Championship on multiple occasions. Krush is currently the #1 rated female player in the USA. ABOUT ZHU CHEN (Women's World Chess Champion, from China) 28-year-old Zhu Chen rose to the pinnacle of the chess world in 2002 when she won the Women's World Championship in Moscow. She has had much success at the international level, winning the World Girls Under 12 championship and also winning the World Girls Under 20 championship twice. She also became the first ever Woman's World Champion to defeat the reigning World Champion when she stunned Ruslan Ponomariov in Dubai in 2002. Zhu Chen has represented China worldwide at the highest level. Searching for the Best Women's Chess Player in the World |
September 14, 2004
Were Newton, Einstein plagiarists?Ashutosh Shukla CHALLENGING THE theories of two most eminent physicists the world has known – Isaac Newton and Albert Einstein- is indeed a nerve-wreaking enterprise fraught with the grave risk of being dismissed either as a lunatic or a fanatic. But, Bhopal-based physicist and mathematician C K Raju is doing just that all the same. And, he appears well-equipped to challenge the fundamental notions regarding the theories attributed to the two physicists when he will visit Europe later this month for lectures. He plans to tell how Einstein 'stole' his most seminal thesis -the theory of relativity- from the works of his lesser-known contemporaries in Europe. Also, he plans to 'reveal' that Newton, who is credited to have invented calculus, had no idea of even key series expansions whereas Indians had been using it for navigation, time measurement and agriculture in ancient times. Raju, author of three famous books on physics, mathematics and philosophy governing these sciences, has an invitation from Harvard university as well for lecture. But, he says, he will be too tied up in Europe to accept the invitation for now. As far as Isaac Newton, Raju's premise is that the scientist of eighteen century was more of a theologian than a physicist. And his concern was more on corrections in Bible that he thought had been distorted rather than inventing laws of physics or calculus. He believes that as BJP is accused of 'saffronising' history books in India, the Church colluded with the State for centuries in Europe to not just distort history as a subject but also history of all subjects. " If you misrepresent history of a subject, the subject itself gets distorted", he asserts. Raju says that the popular doctrine of Christian discovery in the 18th and 19th century, which had an inherent belief that only Christians could discover or invent something and the principle or thing so invented would belong to the first person who does it, has taken away credit for several inventions and discoveries made in ancient civilizations like India, Arab or Egypt and were attributed to Europeans. " Europe had taken 250 years to fully understand calculus but Newton and Leinbiz are credited with having invented it", Raju bemoans. " The standard theory that the calculus was invented by Newton and Leibniz is placed in the context of the systematic manipulation of history as an instrument of western religious politics. Newton and Leibniz themselves claimed credit for certain key series expansions known in India for three centuries before them; and this prior Indian work has been publicly known to western historians for the last two centuries" he claims. Nevertheless, Raju was the first to take up the study of the possible transmission of the Calculus to Europe from India in 1995. Were Newton, Einstein plagiarists? |
September 13, 2004
Scientists Ravi Vakil and Sandeep Shukla HonoredFrancis C. Assisi Boston, 13 Sept. -- Ravi Vakil, a mathematician, and Sandeep Shukla, a computer scientist, are the two Indian-Americans among this year´s 57 young scientists to receive the Presidential Early Career Award (PECASE) for Scientists and Engineers. Considered the nation´s most prestigious award for new faculty members, these awards honor the most promising young researchers in science and engineering fields who have translated their work into significant education activities. For their leadership role they also receive monetary awards, ranging from $400,000 to nearly $1 million over five years to support their career research and education goals. This year´s awards, announced September 9th, bring to 160 the number of PECASE recipients since 1996. LEADER IN MATHEMATICS Vakil, a theoretical mathematician at Stanford University, is at the forefront of modern algebraic geometry. He is a leading figure in the study of the moduli space of curves, to deepen a growing understanding of the “universal facts” of these objects. This is adding much to core mathematics theory as well as applications such as String Theory and physics. Originally from Toronto, Vakil received his undergraduate degree at the University of Toronto, where he was a four-time Putnam Competition winner. After completing a PhD at Harvard, he taught at Princeton and MIT before moving to Stanford in 2001. His field of research is algebraic geometry, with connections to nearby fields, including combinatorics, topology, number theory, and physics. He has long been interested in teaching mathematics through problem solving; he coached the Canadian team to the International Mathematical Olympiad from1989 to 1996, and has written two books related to problem-solving (one on the Putnam competition, and one titled "A Mathematical Mosaic:Patterns and Problem Solving"). Vakil has established significant educational outreach to Bay-Area groups devoted to stimulating mathematics learning among high-school students, and he has established a journal introducing high-school students to mathematics through hands-on problem solving. A three-time medalist (including two golds) in the International Mathematical Olympiad, he has worked extensively with gifted high school students. He is author of A Mathematical Mosaic: Patterns and Problem Solving where he tries to encourage curiosity, a sense of beauty, and the love of knowledge. The book which is a collection of puzzles, mathematical explanations and historical tidbits, speaks in an interesting and understandable way about number theory, combinatorics, game theory, geometry, and calculus to say nothing about magic tricks, and other digressions, weaving them into a mosaic that reveals their interconnections. It is a must for teachers seeking to challenge their best students and for students preparing for mathematics competitions. In his public seminars Vakil likes to show that lurking behind even the most trivial-looking doodles can be mathematics of surprising beauty and power. According to Vakil, doodling has many mathematical aspects: patterns, shapes, numbers, and more. Not surprisingly, he says, there is often some sophisticated and fun mathematics buried inside common doodles. Vakil is interested in attracting talented high school and undergraduate students into the mathematical sciences, by exposing them to exciting and advanced yet accessible ideas, for example through problem solving; this will be done primarily through the Stanford University Math Camp, a problem solving seminar at Stanford, the Berkeley Math Circle, and various writings. In particular, his goal is to attract students from previously untapped pools of talent. In addition he hopes to build a center for algebraic geometry at Stanford, by providing resources for graduate students and postdoctoral students, developing new courses, inviting visitors, and sponsoring seminars and conferences, often jointly with other institutions. Finally he hopes to continue to bring sophisticated mathematical ideas (of all levels) to a wider audience through expository writing. Scientists Ravi Vakil and Sandeep Shukla Honored |
September 13, 2004
Tiny robot walks on waterMike Crissey in Pittsburgh IT could be called a mechanical miracle — a robot that walks on water. With inspiration from nature and some help from research at the Massachusetts Institute of Technology, a team led by Carnegie Mellon engineering professor Metin Sitti built a tiny robot that can walk on water, much like the insects known as water skimmers or Jesus bugs. It's only a prototype, but some researchers imagine the water-skimming robot could have many uses. With a chemical sensor, it could monitor water supplies for toxins; with a camera it could be a spy or an explorer; with a net or a boom, it could skim contaminants off the top of water. Producing it was "the final challenge of microrobotics," said Professor Sitti, who runs Carnegie Mellon's NanoRobotics Lab. "It needs to be so light and so compact." The robot is little more than a 13mm boxy body made from carbon fibre and eight 5cm steel-wire legs coated with a water-repelling plastic (technically making it a water spider). The prototype is especially impressive given researchers didn't know how water skimmers walked on water until last year. Massachusetts Institute of Technology mathematician John Bush and two graduate students solved the riddle by placing dyes and particles in water and using a high-speed video camera. The MIT team discovered that water striders move by pushing down on the surface of water with enough force to create valleys, but not enough to break the surface. The water then bounces back like a trampoline to push the insect forward. Tiny robot walks on water |
Septwmber 13, 2004
Out of sight, not out of hopeI AM aged 19, and hail from a middle class family. I had glaucoma since birth; however, this was rectified when I was five years old and I could see clearly. But, unfortunately, a couple of years later, while in my fifth standard, I met with an accident and lost my eyesight. Despite specialised medical treatment from reputed medical institutions I could not get my vision back. Permanent loss of eyesight is a handicap I have to live with, I realised. A couple of years back, when playing with a friend of my age, I was awestruck by his knowledge on various things. Initially, I was sceptical whether I could pursue my studies in a normal school. Rather than wallow in self-pity, I went about finding ways to make a mark in life. I continued my studies steadfastly and completed my 12th standard with more than 95 per cent marks. This performance could not have been possible but for the encouragement and motivation provided by my parents, friends, relatives, and the senior principal, teaching staff, president and secretary of the `Reading Association of Blind'. I am always grateful to them for their special care and services. My ambition in my life is to become a mathematician. I have found a short-cut method for solving squares and cubes. In addition, I love playing the keyboard and writing poetry. I have also composed a number of tunes. At present, I am doing my B.Com at Vivekananda College and also the CA (PE I) course. I am optimistic that I will come out with flying colours. I receive excellent support and guidance from my college and the ICAI. I am confident that with the help of appropriate software I will be able handle my studies. B. Ramkumar Out of sight, not out of hope |
September 13, 2004
Parrots might be able to talk as distinctly as humans: Study:This one is definitely for all the bird enthusiasts, soon parrots might graduate from being mere mimics with a limited vocabulary to proper talking birds as a new study has found that that parrots and humans use their tongues to craft and shape sound in a similar manner. The study, which has been published in this month's issue of Current Biology, indicates that both parrots and humans rely on extremely specialized vibrating organs in their throats. The study also found that even tiny changes in the position of a parrot's tongue could lead to big differences in sound. This is the first direct evidence that parrots are able to use their large tongues to change the acoustic properties of their vocalizations which means that parrots now make many more distinctive sounds than previously believed. Earlier it was believed that the complexity of parrot communication was because of the syrinx, an organ in their throats but now it has been found that the tongue is involved, just like with human speech. The researchers studied five monk parakeets, small parrots native to South America. While a speaker swept through a series of tones, from 500 to 11,000 Hz the researchers measured how much the birds' tongue position influenced the outgoing sound. They found that a change of just a fraction of a millimeter in tongue position could significantly affect the qualities of the emerging sound. The scientists also suggest that there are four acoustic "formants" in parakeet sounds. Formants are small ranges of frequencies that remain strongly audible as sound travels past the throat, tongue, mouth and nasal cavities. The geometry of these passages deadens some frequencies but leaves others relatively unaffected. What's left distinguishes the character of a sound, in this case, the voice of a parakeet Parrots might be able to talk as distinctly as humans: Study: |
September 12, 2004
Einstein's Days in the Sun, Among the Hollywood StarsBy Cecilia Rasmussen, Times Staff Writer He was perhaps the greatest thinker of the 20th century, but like many L.A. newcomers, he relaxed in the California sun, hobnobbed with Hollywood celebrities and watched the Rose Parade. He even helped children with their homework. Seldom has a scientist won such public acclaim as Albert Einstein when he wintered in Pasadena in 1931, 1932 and 1933. An amateur violinist, he played one on one with the conductor of the Los Angeles Philharmonic. Local artists painted his portrait, sculpted him in bronze, and turned him into a puppet figure. Master violin maker Frank J. Callier carved a bow and special case with Einstein's name inlaid in the wood. But the FBI was watching too. He was one of four German scientists to sign an antiwar petition during World War I, and he joined the Zionist movement, which called for Jews to regain their biblical homeland in Palestine. Excerpts from his FBI file — which eventually filled 1,500 pages — will be on exhibit at the Skirball Cultural Center beginning Tuesday, along with his love letters, manuscripts, diary and high school report card. (He earned top marks in algebra, geometry and physics and lower ones in French and geography.) The exhibit includes a science lesson simulating a black hole and an interactive computer screen that allows visitors to delve into Einstein's life. A video traces his birth in Germany in 1879, his lifelong battle with dyslexia, his Nobel Prize and his stands against segregation, anti-Semitism, McCarthyism and nuclear armament — a type of weapon that his own theories helped to make possible. The exhibit, which runs through May 2005, coincides with the centennial of Einstein's "miracle year," when he published his theories — one of which is expressed by E=mc2. Sometimes Einstein seemed to lose sight of the respect he had inspired. Late in life, he described himself in a letter to a friend as "a lonely old fellow … a kind of patriarchal figure who is known chiefly because he does not wear socks." Today, schoolchildren are more familiar with his formulas than his footwear. Einstein's Days in the Sun, Among the Hollywood Stars |
September 10, 2004
Perplexing proof |
September 10, 2004
da Vinci and the divine proportionBY KIRAN KRISHNAMURTHY Like the man he admires, Bulent Atalay straddles the worlds of art and science. Atalay, an artist and University of Mary Washington physics professor, suggests in his new book, "Math and the Mona Lisa: The Art and Science of Leonardo da Vinci," that the enduring appeal of da Vinci's paintings may lie in the painter-scientist-engineer's conscious use of perspective, pattern and symmetry, all of which are rooted in math. Also known as the golden mean or golden ratio, the divine proportion is a mathematical formulation exhibited in everything from the logarithmic spirals of a nautilus shell to the structure of a pine cone, from the double-helix of DNA to the form of the human body itself. In the example of the "Mona Lisa," Atalay shows that the area from the top of her head to the top of her bodice can be encompassed in a "golden rectangle," which adheres to the divine proportion. Forming a square using the base of the subject's chin, Atalay shows how the diagonals of the square intersect at the "compositionally dominant" eye. A vertical line bisecting the portrait passes through the same eye, a phenomenon that neuroscientist Christopher Tyler explored in the late 1990s. The same geometric construction is evident in the only other two known portraits that da Vinci painted: "Ginevra de Benci" and "Lady with an Ermine (Portrait of Cecilia Gallerani)," which is Atalay's favorite of the three. Atalay's passion for da Vinci sprang from his childhood. Born in Turkey, Atalay recalls always being surrounded by art in his youth. He took art lessons and now is an accomplished artist himself. His pen-and-ink drawings are included in collections in the White House, Buckingham Palace and the Smithsonian. Atalay said "Math and the Mona Lisa" began simply as notes for a physics class at the University of Mary Washington in Fredericksburg in spring 2000. "In a weak moment, I told the students not to take notes in class," he said, recounting how he often stayed up until midnight typing notes for his class on his computer. "Those notes became the seeds of this book." Atalay said the book took him 3˝ years to complete. He says he did not read "The Da Vinci Code" until later, and he thought it was "a good mystery." Atalay, 63, said he plans to write another book, focusing on genius and certain to include da Vinci. He said that while Beethoven is known for his music and Isaac Newton for his scientific insight, the products of da Vinci's mind spanned myriad disciplines. Da Vinci's designs for the tank, the helicopter, the submarine and the parachute predated the actual invention of each by hundreds of years. He studied anatomy, geology and, of course, produced some of the world's most renowned paintings. "He was a transformative genius. He was inventing civilization, inventing technology from scratch," Atalay said. "Here was a man who did it all." da Vinci and the divine proportion |
September 10, 2004
Using Maths to Help Diagnose Disease From Medical ImagesFrom X-rays to Magnetic Resonance Imaging (MRI), there are a wide variety of medical imaging methods available today in hospitals around the world. The purpose of these imaging methods is to assist doctors in diagnosing disease without the need for surgery, by providing images of regions deep inside the human body. The problem is, that even in healthy individuals, biological structures - such as regions of the brain, for example - can vary widely from person to person, making it difficult to reliably detect diseases from these images. Complicating the matter, the appearance of disease on the images can also vary a great deal amongst individuals. Dr Stephen Marsland, a recently-appointed lecturer at Massey University, has been awarded a 2-year Fast-Start Marsden grant to develop advanced mathematical and statistical approaches for dealing with data from MRI scanners. The Fast-Start programme is an initiative to give emerging researchers an opportunity to explore an innovative idea, developing their capabilities and helping them establish their research career. Dr Marsland will develop new methods to help measure the differences in the 'shapes' of biological structures between individuals, and thereby improve the detection of irregularities that are due to disease rather than natural variation. The new techniques involve a combination of advanced and challenging mathematical and statistical techniques. Overall, the aim is to help doctors more accurately diagnose diseases such as brain tumours, Alzheimer's disease and other conditions. Using Maths to Help Diagnose Disease From Medical Images |
September 10, 2004
Following the signs to a job at GoogleCambridge, Mass, September 10: You can't miss the three new 50-foot-wide beige banners hanging from the ceiling of the Harvard Square subway station. But you may need a Massachusetts Institute of Technology degree to have the foggiest idea what they mean. "(First 10-digit prime found in consecutive digits of e).com," is all the banners say. It may take a few seconds for commuters to realize there's a math question being asked here. But T riders passing through this stop in the shadow of Harvard University may be more likely than average Bostonians to recognize "e" as an important irrational number — kind of a distant cousin of pi — widely used in calculus and other higher mathematics. However, anyone who solves the puzzle (by combining the first 10-digit prime found in consecutive digits of e with ".com" and entering it into a Web browser) discovers that the website named for the solution, www.7427466391.com, only gives you directions to another website with another vexing math problem. Solve that, and you get to an internal Google page that praises "your big, magnificent brain" and invites you to apply for a job. Google, which recently had a high-profile IPO, has long prided itself on its deep talent base of engineers, mathematicians, and computer scientists who fashion complex algorithms for searching Web pages. "The limit to our growth is our ability to get the best talent on the planet and get them working on the toughest computing problems around," Google engineering vice president Wayne Rosing said in a Reuters interview earlier this year. E — formally known as the base of the natural logarithm — begins 2.718281828 and goes on forever. An indication of how much Google brainiacs love e: When they filed for their initial public stock offering, they put down as $2,718,281,828 the amount they hoped to raise. Following the signs to a job at Google |
September 09, 2004
Mathematician knows his odds at card tableBy VINCE DEVLIN of the Missoulian Poker players may have a notion that their three of a kind in a game of five-card draw seems to hold up better than it does in seven-card stud. Then again, they may not. Those are the players Brian Alspach hopes to find when the mathematician sits down in a card room. Alspach, professor emeritus at Simon Fraser University and adjunct professor at the University of Regina, has figured out the probability of being dealt various hands in dozens of games. For instance, in a five-card game, the probability of getting three of a kind is 0.0211, while the probability of having a straight tails off to 0.0039. "A straight whomps three of a kind in five-card draw," says Alspach, who Thursday delivers a lecture on "Mathematics and Poker" at the University of Montana. But when a player has seven cards from which to choose five, the probability changes dramatically: 0.046 for a straight; 0.048 for three of a kind. Alspach, 66, started playing poker as a graduate student in 1960, but didn't move from in-home games and into card rooms until the early 1990s. "When you play in card rooms you're playing better players, and I was getting absolutely killed," Alspach says. "You either adapt, or go back down a level." .... Mathematician knows his odds at card table |
September 09, 2004
'MATHS BY ROTE IS BEST'SCHOOLS 2 RECITING 'times tables' by rote is the best way to improve mathematical skills, a study has shown. Out of 241 children tested, aged seven to 12, those who learnt multiplication tables by traditional methods were four times faster than others. The slowest and least accurate were those who counted either on their fingers or in their mind. Dr Sylvia Steel, from Royal Holloway University, who carried out the six-year study, revealed the findings at the British Association's Festival of Science, in Exeter, Devon. She said: "Learning multiplication tables was almost extinct in State schools because it was considered boring and unlikely to lead to understanding. "Our study shows it is very effective." 'MATHS BY ROTE IS BEST' |
September 07, 2004
Is Encryption Doomed?Our entire information society rests on a fragile foundation that mathematicians are racing to dismantle.It's not often that results from conferences on mathematics make the news, but that's precisely what happened last month at the annual Crypto conference in Santa Barbara, CA when researchers from France, Israel, and China all showed that they had discovered flaws in a widely used algorithm called MD5—an algorithm that I wrote about in some detail last month. The "when life gives you lemons, make lemonade" message that came out of the conference was that this process of breaking codes and developing even stronger ones is all part of the cryptographer's game.But what if a fundamental breakthrough in mathematics rendered useless all of the fancy encryption that the world now depends upon? For more than 30 years, mathematicians have sought in vain the answer to a simple problem in theoretical computer science. The problem is what's known as an open question —it's a simple equation that is either true or false. It can't be both. The problem—independently formalized by the mathematicians Stephen Cook and Leonid Levin in 1971—remains one of the central unsolved questions of modern mathematics. It is a problem about other problems. Cook and Levin asked whether there exist mathematical puzzles that are hard to solve, but that have solutions that are easy to verify. As the problem is commonly phrased, the mathematicians asked whether P is equal or not equal to NP. P is the set of problems that are easy to solve. Strictly speaking, it is the set of problems that can be solved in "polynomial" time—that is, in an amount of time that is roughly proportional to the size of the problem's description. Most of these problems are so easy, in fact, that we hardly even consider them to be problems at all. For example, multiplying two numbers together is a P problem: the solution can be found in polynomial time. Another P problem is searching for a book that's lost in your house. Even if all of your books are packed away in boxes in your basement, it's still an "easy" problem to solve, at least by mathematical standards: just open up every box and look. It might take you days, but if you can do a thorough search, you will find the book. NP problems, on the other hand, are hard problems. NP standards for "nondeterministic polynomial"—it's a formalism that describes a kind of computer that can't be built, but that can be mathematically modeled. An NP computer can simultaneously try every possible solution to a problem and recognize which one is correct. It turns out that NP computers are really good at solving any kind of problem where the answer can be found only by searching. One of the best examples of these problems today is code breaking. Say the FBI raids a terrorist hideout and grabs a laptop with encrypted files on it. The only feasible way to decrypt the data today is to try every possible encrypt key, hoping that one will work. A small network of modern computers can try every possible 40-bit key in just a few weeks. But a technically advanced terrorist would be more likely to use 128-bit encryption. And cracking a single 128-bit key, even harnessing the power of every computer on the planet, could take thousands of billions of years. For all practical purposes, it's impossible to break such a code, because today's computers can only try one or a few keys at a time. An NP computer, if one existed, could try all of the possible keys at the same time, and recognize instantly which key was correct. Code breaking is an NP problem. Factoring is another NP problem. Although there are various techniques for factoring large numbers, all of them involve searching through large numbers of, well, numbers. But an NP computer could simultaneously try to multiply every number with every other number and somehow pick out the pair of numbers that yielded as a product the number that the computer was told to factor. The difficulty of factoring large numbers is at the basis of the RSA encryption algorithm, which is built into practically every Web browser and is the basis of most e-commerce. As described above, NP computers seem like magical things that could never exist today. But that might not be the case. It's easy to see that there exist many NP problems, including—code breaking and factoring. But nobody has ever been able to mathematically prove that it's impossible to solve all NP problems in polynomial time on an ordinary computer—in other words, that P is not equal to NP. Many experts now believe, however, that it's just a matter of time before the question will be resolved. One mathematician who was willing to back that belief with gold is Michael Sipser, who this month becomes the new head of the MIT Mathematics Department. Back when he was a graduate student at the University of California, Berkeley, Sipser went so far as to bet a fellow graduate student an ounce of gold that by the end of the twentieth century, P would be found to be not equal to NP. Sipser lost, of course. As it turns out, the graduate student that accepted Sipser's offer was Len Adelman—the "A" in RSA. "I thought then that the problem was just not ripe for any resolution," says Adelman, explaining why he accepted Sipser's wager. After he made the bet, Sipser ended up becoming a professor of mathematics at MIT and taught MIT's course on the theory of computation. He enjoyed the course so much that he wrote an introductory textbook that has become one of the subject's bibles. And he has published extensively on the history of the P vs. NP question. There is a lot riding on the answer to that question. That's because what Cook and Levin realized simultaneously back in 1971 is that there exists a large number of NP problems that can be thought of as "perfect" or "complete." Each of these so-called NP-complete problems encompasses everything that it means to be an NP problem. That means that if a solution for any NP-complete problem could be found that could be solved in polynomial time, then a short-cut solution could be found for every NP problem. In practical terms, that would spell the end of encryption as we know it. The Internet would be vulnerable to hackers and computer viruses. As the twentieth century neared its conclusion, it became clear to Sipser that nobody was going to find a solution anytime soon. This left the matter of the bet."There was a little bit of a controversy as to when the entry of the century was," he recalls. "Was it January 1, 2000, or January 1, 2001? I decided not to quibble because it didn't look like [a solution] was imminent. So somewhere early in 2000, I bought an American Gold Eagle—I spent an extra $10 to make it a Year 2000 Gold Eagle—and I sent it to him." Adelman had long since left his professorship at MIT and taken up residence at the University of Southern California, where he works on cryptography and DNA-based computers. Reached by e-mail, Adelman confirmed that he received the gold coin. Today, however, there is a lot more than an ounce of gold riding on the question. Shortly after Sipser sent Adelman the coin, the Clay Mathematics Institute of Cambridge, MA, named the P and NP question as one of the Institute's seven "Millennium Problems." The institute set aside $7 million, with a $1 million prize offered to the person (or machine) that can solve each problem. Adelman thinks that we'll be waiting for the solution for a long time. Resolving the question of P and NP, he says, "would require new and brilliant ideas and not routine incremental progress. From my perspective, we are no nearer to solving the problem now that we were when bell-bottom pants were cool." Is Encryption Doomed? |
September 07 2004
Famous Chinese-American mathematician applies for "Green Card" of ChinaHearing that China officially began implementing its Regulations on Examination and Approval of Permanent Residence of Aliens in China, world-famous mathematician Chen Xingshen (Shiing-Shen Chern), a Chinese-American, submitted his application documents to Tianjin entry/exit authority on September 3, becoming one of the first foreigners applying for Chinese "Green Card". This is the second time for Chen's application according to the new regulation after gaining permanent residence in 2000. As "Father of differential geometry", Chen created Nankai Mathematics Research Institute in 1985, and is now honorary president of the Institute and a foreign member of the Chinese Academy of Sciences. After returning from overseas in 2000, Chen settled down in Nankai University, Tianjin. In the same year, he was granted according to law permanent residence in China for his outstanding contribution to the country. Permanent residence is a kind of qualification of unlimited stay in a country granted by a government according to law to foreigners who meet a certain requirements. The permanent residence permit issued is what we call "green card". By now Tianjin city has seen 11 foreigners applying for "green cards" in China. Famous Chinese-American mathematician applies for "Green Card" of China |
September 06, 2004
Math wizard makes it simpleCAROL GOAR Each school year, John Miton thinks he's finally met a student whose mathematical aptitude is so low that he or she can't be taught to add, subtract, multiply, divide and see patterns. So far, he's been wrong every time. In 15 years of tutoring — in inner-city schools, hospital wards, even youth detention centres — Miton hasn't had a single failure. Under his guidance, weak students have raced ahead of their peers, kids with behavioural problems have learned to concentrate, children who'd given up on themselves have regained their confidence. "If a kid gets stuck, it means you haven't made the steps simple enough," he says. "If a kid is failing, it means you haven't figured out where the blockage is." That is the philosophy behind JUMP (Junior Undiscovered Math Prodigies), a non-profit program that Miton runs out of the Fields Institute for Research in Mathematical Sciences at the University of Toronto. He launched it four years ago, tutoring in a few classrooms. Now, he and his team of volunteers are coaching 3,000 kids in 17 elementary schools. Another 400 schools are on the waiting list. The funny thing is, Miton didn't set out to be a mathematician. The 46-year-old Hamilton native almost flunked the subject in high school. "Like most kids, I'd give up when I encountered a difficulty." He studied philosophy at university and made his mark as a playwright, winning a Dora Award for his first play, Scientific Americans and a Governor General's Award for his second, Possible Worlds. But numbers always fascinated him. In the mid '90s, he returned to university, earning a master's degree in mathematics, then a Ph.D. While doing his research, he approached the principal of a nearby elementary school and offered free tutoring to kids who had fallen behind in math. "What we've shown at JUMP is that you can raise the proficiency of virtually all children to the point where they could choose to go into sciences or math, if they wanted to." Students seldom ask Miton why they should learn math. He makes it so exciting that they just want to play the game. "If you allow kids to exercise their minds and succeed, they don't give a damn if it has an application. "Of course it does," he adds. "It trains them to think. You need that in every career." Math wizard makes it simple |
September 06, 2004
Mathematical Mystery Believed to Have Been SolvedBy John von Radowitz One of the seven great unsolved mysteries of mathematics may have been cracked by a reclusive Russian who is not remotely interested in the Ł560,000 prize his solution could win him, it emerged today. The Poincare Conjecture involves the study of shapes, spaces and surfaces and makes predictions about the topology of multi-dimensional objects. Basically, it says that a three-dimensional sphere can be used in an analogous way to describe higher-dimensional objects that are impossible to visualise. Since Henri Poincare suggested the theorem in 1904, some of the greatest mathematicians of the 20th century have struggled to prove it either right or wrong. All have failed. But now the world of maths is buzzing with the news that an answer might at long last have been found. Dr Grigori Perelman, from the Steklove Institute of Mathematics at the Russian Academy of Sciences in St Petersburg, has published two papers offering a solution to a larger-scale problem called the Geometrization Conjecture. This is also concerned with geometry, and experts say that contained within it is proof that the Poincare Conjecture works. If Perelman can satisfy his peers that this is the case, he stands to win a one million dollar cash prize from the Clay Mathematics Institute in the United States. The Institute is offering million dollar prizes for solutions to each of the mathematical conundrums it calls the Seven Millennium Problems. But there is a more fundamental problem the general community of mathematicians needs to solve first.... Mathematical Mystery Believed to Have Been Solved |
September 06, 2004
A Lewis Carroll ScrapbookCharles Lutwidge Dodgson, a lecturer in mathematics at the University of Oxford, is better known as Lewis Carroll, author of Alice's Adventures in Wonderland and other works. A scrapbook kept by Dodgson is now available online, via the Library of Congress. It contains a variety of items, including newspaper clippings, illustrations, and photographs. The Web site also has a timeline of Dodgson's life and other supporting materials. Go to: http://international.loc.gov/intldl/carrollhtml/ A Lewis Carroll Scrapbook |
September 06, 2004
Women in MathematicsFrom Maria Gaetana Agnesi to Lai-Sang Young, these Web pages provide biographies of prominent women in mathematics. Prepared by students at Agnes Scott College in Atlanta, the biographical essays describe the achievements of women in a variety of mathematical fields. Some essays include portraits and other illustrations. Go to: http://www.agnesscott.edu/lriddle/women/Women.htm Women in Mathematics |
September 04, 2004
A game of numbersDevlin's Angle The approach of the 2004 World Series sees the publication of not one but two books on the use of statistics in baseball. By statistics, I don't mean what most fans seem to think this means, namely collecting and tabulating game stats, but the use of sophisticated mathematical techniques to examine players' performance and the effectiveness of various plays in depth, to help clubs make hiring and salary decisions, and to decide on game strategy. Alan Schwartz, a senior writer at Baseball America, has written a book called The Numbers Game, and math professor and former MAA President Ken Ross of the University of Oregon has published A Mathematician at the Ballpark. These books come close on the heels of last year's bestseller Moneyball, by Michael Lewis, which described how the Oakland As used mathematics to turn itself into one of the most successful teams in the league, despite being one of the poorest. The Schwartz book is a history of the use of statistics in baseball; it fills in a lot of the details that Lewis skipped over in Moneyball. Ross's book tries to explain the math itself. All the facts in this article are taken from one or more of these three books. At this point, I need to admit up front that I am not a baseball fan. I attended my first Major League game only this year. Not that I have anything against the game. Just that, growing up in England, baseball looked to me like rounders played by men in pyjamas who seemed to wear very scratchy underpants that required constant adjustment and who had an unusual propensity for spitting. Baseball is a natural game both to collect little-s statistics in and to apply big-S Statistics to. One reason is obvious: there are lots of things to count. Another reason may be a bit less obvious: for all the skill and artistry of the great players, there is an enormous random element to the game. From those two observations, it doesn't take much mathematical knowledge to realize that it is likely to be quite hard to separate mirages from reality. There have been over 11 million batter-pitcher confrontations in the more than 150,000 games that have been played since the major leagues began. With so much raw data and so many things you can do with that data, coupled with a big random element, you are going to get lots of patterns. Figuring out whether they tell you anything useful is likely to be very difficult. As several experts have observed, many of the most hallowed streaks and other records that made players famous are quite likely simply the result of pure luck. Like winning the lottery, sooner or later one player or another would have done it. For instance, if the outcome of every play in major league history had been decided purely on luck, with no skill involved, someone would have chalked up a .424 batting average (as Rogers Hornsby did), someone would have scored three home runs in a World Series game (as Babe Ruth and Reggie Jackson did), and a whole ton of players would have earned a reputation for being clutch hitters (as many did). The only record that would not have arisen through pure luck is DiMaggio's 56-game hitting streak. The best that would have happened by chance is a 46-game streak, or thereabouts. This does not mean that there isn't a lot of skill involved in baseball. Nor does it mean that some players aren't better than others. It does suggest that there is a lot more that happens due to pure luck than most fans (or record holding players) would like to admit. A game of numbers |
September 03, 2004
Good news greets D65 teachersBY KAREN BERKOWITZ Teachers were greeted with good news on two fronts as they headed back into their classrooms in preparation for the opening of school Monday. For starters, a tentative settlement had been reached after months of contract talks between the District Educators' Council and the District 65 Board of Education. Specifics were to be presented to teachers during an after-school meeting Monday. (See story on Page 16.) The second morale boost came with the news that District 65 students had posted higher test scores in reading, mathematics and writing at all grade levels on the Illinois Standards Achievement Test (ISAT) taken in April. Addressing teachers during a start-of-school pep rally last Thursday, Superintendent Hardy Murphy said the preliminary results suggested the district was starting to get some traction from its initiatives. "The results are the highest they have been in three years," reported Murphy, in his opening-of-schools address to teachers, aides, child-care workers and custodians. "Once again, we exceeded state averages in every grade level in reading, math and writing. Congratulations to you for that." Murphy told his audience that adequate financing for public education would not happen "without people looking in the mirror and saying, I had the best that our country had to offer and they deserve more from us. "We have to make sure that everyone understands that teachers are deserving, that public schools are the best place for their children and that the political system has one major responsibility - to make sure classrooms and schools have everything they need to educate children." Good news greets D65 teachers |
September 02, 2004
Underwater Photos Made Crystal-clear by Mathematical SolutionNewswise — Thanks to mathematics, the quality of underwater photographs is about to get dramatically better. The first-of-its-kind method for radically improving underwater shots combines a mathematical formula or algorithm with a filter normally used for land photography. The findings by researchers at the Technion-Israel Institute of Technology were presented at the IEEE* Conference on Computer Vision and Pattern Recognition in Washington, DC in June. "This is a brand new solution to solving the problem of underwater image degradation," notes lead researcher Professor Yoav Schechner of the Technion Faculty of Electrical Engineering. "Underwater photos tend to be degraded and lacking in clear details because of the 'veiling' effect of ambient light," explains Schechner. "From above the water's surface, ambient light scatters into the line of sight – an effect commonly known as 'backscatter.' This causes poor visibility in even the clearest water." He adds that the veiling effect increases with distance, making many details undetectable. Schechner and graduate student Nir Karpel realized that photographic images could be greatly improved by eliminating the backscatter effect. The two then developed an algorithm that – combined with a polarizing filter readily available for $20 to $100 – compensates for backscatter. Once the photographs are taken using the filter, they are transferred to a computer program, which then applies the algorithm, compensating for the underwater image degradation caused by backscatter. Unlike standard photo imaging programs that treat a photographic image as a whole, the new method corrects different elements – such as objects that are closer or distant – individually, according to need. According to the researchers, this process also provides estimates of underwater distances, resulting in improved picture quality and photographs with three-dimensional depth. Schechner says the program could be placed on a chip embedded within the camera or be integrated with existing video systems to vastly improve underwater video quality. In the future, it could be utilized for a myriad of applications including engineering, marine biology and archeology, underwater mapping, recreational photography and underwater rescue. The researchers are negotiating commercialization of the program. Underwater Photos Made Crystal-clear by Mathematical Solution |
September 02, 2004
For Ken Ono, the mysteries of math swirl just below the surfaceRon Seely Wisconsin State Journal Ken Ono seldom tells anyone what he does for a living. He's a mathematician. But if he told you that, what's the first thing you would say? Almost always, Ono lamented, people respond, "I'm not good at math." And after that, the conversation doesn't have much of anyplace to go. That's too bad, because Ono, who teaches at UW-Madison, is a pretty interesting fellow. In fact, he is one of those Madisonians who lead intriguing double lives. On the one hand, he is the guy next door trimming his hedge. On the other, he's also the guy who lectured President Bill Clinton on numbers theory during a visit to the White House and who came up with a proof a few years ago that left the math world gasping. Mathematicians don't need much in the way of equipment to do what they do. They think. They pencil intricate lines of math notation on paper. And then they think some more. Ono does some of his best thinking on airplanes or in the quiet of early morning before he gets out of bed. While Ono deeply values his relationship with students and the important task of teaching and guiding them, he remains at heart a numbers theorist, a mathematician in love with numbers and able to see in them elegance and mystery that eludes most. He has been enamored of numbers since he was a boy collecting baseball cards, lining them up face down and studying the statistics on the back. Eventually he followed in the footsteps of his father, Takashi, also a mathematician specializing in numbers theory. The younger Ono's career has already been stellar - numerous awards and honors, including a Guggenheim Fellowship and a Presidential Early Career Award (which afforded him the audience with Clinton). He has studied and worked at some of the country's most prestigious institutions, from the University of Chicago to UCLA to, for the last four years, UW-Madison. There are also practical applications to what Ono and mathematicians do, especially in the fields of physics and cryptography, or the writing and deciphering of codes. Always, it seems, there is interest from the military. Ono tells of the time he was called to the Department of Defense and asked to describe one of this theories and submit a paper. The military never explained its interest and he never saw the paper again. But Ono cares less about practicality than he does about the numbers themselves, clicking around forever in his head, and the miraculous patterns in their ranks yet to be discovered. That is the secret behind the life of this particular member of the campus community, whom you may see at times walking distractedly up Bascom Hill toward Van Vleck Hall. "I like to do battle with problems," Ono says. "And I've lived with some of these problems for so long that they are my friends. I can't imagine doing anything else." For Ken Ono, the mysteries of math swirl just below the surface |
September 01, 2004
Cheating in nature: why rotting food could hold the keyFrom salting and drying to pickling and irradiating, humans have devised many ingenious ways of preserving their food from spoilage by microbes. The question of what microbes gain from making food go off in the first place has attracted less attention, but research presented at this years British Ecological Society Annual Meeting will shed new light on the problem. Speaking at the meeting, taking place at Lancaster University on 7-9 September 2004, Dr Dave Wilkinson of Liverpool John Moores University and Dr Thomas Sherratt of Carleton University in Canada will cast doubt over Professor Dan Janzen's seductive 1977 theory that microbes make food go off in order to make it objectionable or unusable by the larger animals they are competing with for food. Janzen illustrated his theory thus: imagine a child left alone for a short time in the kitchen with two strawberries, one fresh and one mouldy. If the youngster pops the fresh one into its mouth, then the microbe has won. Wilkinson and Sherratt used mathematical models for the first time to test Janzen's theory . According to Wilkinson: "In our current model it is difficult to see how spoiling behaviour could evolve as an adaptation to deter larger animals. Janzen's idea, while intuitively attractive, may be unworkable. Our main result is that in the mathematical model we have developed so far, we have been unable to find realistic conditions under which cheats will not undermine the system." "If microbes are expending energy producing chemicals to deter birds and other animals from eating their food, then what is to stop them from cheating by not producing the chemical but just relying on protection from chemicals produced by other microbes?" As well as challenging Janzen's theory, Wilkinson and Sherratt's work could help ecologists understand cheating in other areas of nature. "The problem of cheats destroying systems of mutually cooperating organisms is a major problem in evolutionary ecology. Janzen's system has great merit because it is relatively simple and therefore open to mathematical study, so it may yet help identify the conditions under which cooperation is favoured over cheating," Wilkinson says. Wilkinson and Sherratt are currently building more complex models to see if this helps rescue Janzen's theory. Dr Wilkinson will present his full findings at 08:40 on Thursday 9 September 2004. Cheating in nature: why rotting food could hold the key |
September 01, 2004
Here's more computer muscle to simulate real-life problemsBy Ho Ka Wei POWERFUL computers are being used more and more by industry for simulations so as to design better buildings against fires and oil rigs that don't collapse out at sea. How powerful? Over at the Institute of High Performance Computing in Science Park II near Pasir Panjang, the machines can go up to one tera- flop - one trillion calculations a second. A flop, or a floating-point operation, is a widely-used measure of computing muscle. Industries are heading there to tap into the number-crunching power needed for complicated simulations used to build better machines and structures. The institute's acting executive director, Associate Professor Lee Heow Pueh, said at a media briefing yesterday: 'It's about transferring real-life problems into mathematical equations that are then used to create simulations for us to study the issue.' The result is the field of computational science and engineering research, which combines applied mathematics, computer science, engineering and science. It uses computer-generated 3D diagrams and models to simulate how products will perform even before they are made. One application is in the simulation of air flow within buildings to predict how conditions such as wind drafts, temperature and humidity, change within an enclosed space. This is especially important for fire safety as it can provide valuable information like the time those inside have to evacuate. Another application is designing jack-up rigs, the three-legged outposts in the sea used by the oil and gas industries. Mr Ng Khim Kiong, general manager for engineering of PPL Shipyard, which makes such rigs, said such simulations can lead to better and safer rigs. 'It offers an accurate analysis of specific areas of the rigs, which would otherwise have to be tested physically and may be more costly,' he told The Straits Times. 'It's a short cut to a high level of confidence in our system.' The institute, formed in April 1998 after a merger of the Centre for Computational Mechanics and the National Supercomputing Research Centre, is now working with some 40 to 50 partners from various fields, including engineering and electronics, on long and short-term projects. Here's more computer muscle to simulate real-life problems |