May 30, 2006
Carnegie Mellon U. integrates math into global applications(Comtex Business Via Thomson Dialog NewsEdge)PITTSBURGH, May 26, 2006 (The Tartan, U-WIRE via COMTEX) --Past the piles of calculus homework and old theses strewn across the floor, a look into the Department of Mathematics at Carnegie Mellon University provides a startling surprise: Math is in everyone else's business. What's no surprise is that Carnegie Mellon values an interdisciplinary environment. Though it is the product of many generations, interdisciplinary research formally became part of the University's "Strategic Plan" in 1998. In the 21st century, mathematics at Carnegie Mellon is traveling not only to different departments, but out of the offices of Wean Hall and into the global centers of science and industry. "This is happening all over the world" According to David Kinderlehrer, professor of mathematics, the mathematics department at Carnegie Mellon and its peers at universities around the world have been doing a lot more "applied math" in recent years. For Kinderlehrer and his colleagues, "applied" necessarily means interdisciplinary. "Most often, I find myself in the company of colleagues who are not mathematicians," Kinderlehrer states on his website. "We are learning together what we could not do in our native disciplines: new science." Though journals of applied mathematics line his shelves, Kinderlehrer cannot give a concise definition for applied math -- because there isn't one. "[Mathematicians] are trying to get math into the laboratory to answer questions in biology, in mechanics, in physics," Kinderlehrer said, describing the implications of the move toward applied mathematics. "This is happening all over the world." According to Kinderlehrer, however, math should never be a service to other disciplines. The collaborative efforts of mathematicians around the world should serve to make mathematics a richer field of study. "We are working with [scientists] to create new science for them and new math for us," Kinderlehrer said. Kinderlehrer's breakthroughs are in materials science, and he uses mathematical simulations to control natural conditions in various materials. He is working to discover how to manipulate the granules present in almost all materials, elements that are often only few microns across. About two years ago, Kinderlehrer discovered a rational relationship to the composition of granules where there was previously thought to be no relationship. The discovery has far-reaching implications for materials science. With the knowledge of how materials are composed, Kinderlehrer and his partners can start to understand how to mold materials to do what they want. "We do our tango" One of Kinderlehrer's colleagues, professor Irene Fonseca, works on both the mathematics of materials and computer vision and imaging. "Mathematics is present in everything around, from [information technology] to biology to non-invasive surgery," Fonseca said. "The challenge to mathematics is that more and more the old way, [in which] you work with a pen and a pad, is no longer." Fonseca stresses the need to break down barriers and work across disciplines to create a new breed of mathematicians capable of tackling many different types of problems. "It's a long process," Fonseca said. "We are all aware there are things that need to be changed in the curriculum." Mathematical education is one of Fonseca's biggest concerns. She is worried that modern methods of mathematical instruction -- the computing environment and programming language Matlab, for instance -- are changing the way students of math think and closing them down to different methods of creative problem solving. "Are we creating technicians or thinkers?" Fonseca asked. "We cannot replace thinking creatively with all the gadgets." To tackle emerging issues in mathematical education, Fonseca will attend two different conferences in the coming weeks. She will travel first to the Georgia Institute of Technology to discuss the potential for more effective kindergarten-through-college math curriculums. From there, she will travel to Lisbon, Portugal, to meet with business and industrial leaders and discuss the role mathematics is playing in the global marketplace. On a broader level, the conference will deal with the ways in which the state of the economy impacts the educational curriculum. "To what extent are industries interested in universities? To what extent is that necessary?" Fonseca asked, indicating the need for an information pipeline between industry and academia to properly inform a study of mathematics. "It is a dance. We do our tango, we show what we have to offer, and they present their problems," Fonseca said. "What kind of math do I use?" If anyone knows the tango, it is professor Shlomo Ta'asan. He has been working closely with biologists and physicians at the University of Pittsburgh Medical Center (UPMC), trying to understand diseases by using mathematical tools. Carnegie Mellon and the University of Pittsburgh received a shared grant from the National Institute of Health in September to pay for this kind of research. Ta'asan is trying to develop mathematical models that will describe the progress of diseases and the inner workings of the immune system. "Once we know about it, we can stop it, slow it down, accelerate it," Ta'asan said. Though he is trying to answer some of the most daunting questions in immunology, Ta'asan doesn't have any degree in biology. "I've had to review my statistics," Ta'asan said. In addition to his work in immunology, Ta'asan also works on understanding mental illness, specifically depression. He had a hunch that the ups and downs characteristic of mild depression could be studied with a set of pre-existing simulations -- the ones used in the stock market to measure fluctuations. Ta'asan took some computational finance courses and borrowed the math he learned for use in his own biological computations. "This research has made me learn areas of math I didn't know," Ta'asan said. "I'm trying to use all the areas of math I ever learned. The question is, what kind of math do I use?" Like Fonseca, Ta'asan explained that every discipline has its own language and its own code. To cope with the language of biologists, Ta'asan has tried to take a qualitative approach to math, moving away from math that uses just real numbers and toward math with only a few levels. According to Ta'asan, biologists just do not speak and think the same way as mathematicians -- and vice versa. "It's not simple to convince them to change the way they are doing things," Ta'asan said. "I will change anything I need to." According to Ta'asan, the best way to get a feel for what scientists do is to make regular trips to medical research laboratories and communicate with scientists at work. "The purview of many fields" Across the Mall from Ta'asan's workspace is the office of dean John Lehoczky, who, in addition to leading the school of Humanities and Social Sciences, holds positions in both the statistics and mathematics departments. Lehoczky's work in computational finance has him running into many of the same difficulties that Ta'asan faces at UPMC -- the same ones that Fonseca is crossing the pond to talk about in Lisbon. He has to communicate mathematical research to the giants of finance through intermediaries who do not share his understanding of mathematics. Just like Ta'asan and Kinderlehrer, Lehoczky uses mathematical models to solve interdisciplinary problems in finance. According to Lehoczky, his collaborative work forms the basis for Carnegie Mellon's master of science in computational finance, the first program of its kind anywhere in the world. "We combined the statistics department, the math department, Tepper, and the Heinz school into a seamless program designed for students," Lehoczky said, explaining that while Wall Street had barely heard of Carnegie Mellon a decade ago, computational finance masters are now in high demand. Lehoczky attributes the program to the university's interdisciplinary nature of academics. According to Lehoczky, it is a model of academia toward which other institutions are moving out of necessity. "This is the era of big science projects," Lehoczky said. "The projects are not the purview of any [one] field; they are the purview of many fields." Carnegie Mellon U. integrates math into global applications |
May 30, 2006
Piero shows debt to ArchimedesRediscovered book on show in Siracusa by Denis Greenan (ANSA) - Siracusa, May 23 - A recently rediscovered book in which Renaissance great Piero Della Francesca shows his debt to Archimedes has gone on show for the first time in the Ancient Greek genius's home town Siracusa . The manuscript had languished in the archives of Florence's Riccardiana library for centuries before it was authenticated last year as the hand of Piero, the artist who brought the rigour of perspective studies into his masterpieces . Art historians were aware that Piero studied ancient art for the geometrically designed backgrounds of his luminous and other-worldy works, but his explorations of the great polymath of Siracusa had not been known . The manuscript, one of the art world's most sensational recent finds, has changed all that . Florentine art chiefs immediately set about bringing Piero's studies to the city where Archimedes made his great mathematical discoveries . "After the thrilling moment of discovery we immediately hatched the idea of exhibiting he manuscript on Archimedes' home ground, connecting the distant past, Piero's age and the present day," said the Riccardiana's director, Giovanni Lazzi . Physicist Franco Pezzella, who collaborated with famous architect Ettore Sottsass in creating a geometric room that leads into the show, said: "Piero Francesca, apart from a sincere interest in mathematics, embarked on a search for geometric notions by studying Archimedes" . Visitors are drawn into the exhibition by Sottsass's white, clean-lined room with geometric figures on the walls . They then pass through a dimly lit passage - "like the nave of a church," said Lazzi - which symbolises the artistic tone of the Middle Ages but is lined with lively scenes of daily life. Finally, they come into the room where the book is exhibited, decorated with one of his favourite colours: "an intensely luminous sky-blue, a light midway between the physical and the metaphysical" . Archimedes (287-212 BC) is best known for his famed cry 'Eureka!' ("I have found it!") as he splashed out of his bath and ran naked through the streets of Syracuse after cracking the theory of buoyancy . He also conceived a theory for calculating the number of grains of sand in the world, giant mirrors that could set fire to enemy sails, the water screw for raising water and giant pulleys that could hoist the biggest ships . "Give me a lever long enough, and a place to stand, and I'll move the world," he famously said . Piero Della Francesca (1416-1492) is celebrated for the mastery with which he placed realistic but ethereal characters inside a harmony of composition, in masterpieces such as The Legend of the True Cross fresco cycle, the Flagellation and the Baptism of Christ . His deep interest in the theoretical study of perspective is apparent in all his work . Late in life he wrote a treatise, De Prospectiva Pingendi, on the rules of mathematical foreshortening applied to any object, be it a cube or human head . He also wrote two treatises on arithmetic, algebra and solid geometry . Piero shows debt to Archimedes |
May 30, 2006
Back to basics as maths problems multiplyBy Liz Lightfoot Education Correspondent (Filed: 27/05/2006) Modern methods of teaching maths which have mystified parents and confused many pupils are to be abandoned six years after the Government forced them on primary schools. The same unit at the Department for Education which devised the strategy now wants teachers to go back to the "standard written method" it abolished. The decision has prompted a backlash from some primary teachers and maths advisers who say children are better able to understand the concept of arithmetic when they break sums down into a series of units. They say the "back to basics" approach heralds a return to the "dark ages" of adding up, subtracting, multiplying and dividing in vertical rows without understanding what they are doing. But evidence has shown that many pupils are arriving at secondary school unable to do long division and multiplication and reliant on columns of workings out which take longer and are more prone to errors along the way. The proposed change, put out to consultation yesterday, has already won support from many teachers on the website of The Times Educational Supplement, who say it is better for pupils to master one, simple, standard method than struggle with many. Primary schools were inundated with complaints from parents when the new method came in and some organised meetings to explain the technique. However, many parents who gave it the benefit of the doubt began to panic when their children entered the teenage years unable, for example, to divide 196 by six or multiply 56 by 27 with speed and accuracy. The lesson plan for the numeracy hour introduced in 1999 instructs teachers to use the "grid" method for multiplication. Numbers are split into tens and units which are multiplied by each other in turn to give four totals which are then added together. In division pupils are taught to subtract multiples of the divisor until they end up with a number less than the divisor. They then add up the number of times they have multiplied the divisor and express the number less than the divisor as the remainder. Children are not allowed to "carry" numbers or put figures in vertical lines, such as 56 with x27 beneath it. They are also strongly discouraged from using the bracket form of dividing each number in turn with the answer above the line and the remainder placed before the next digit. The proposed new framework says the techniques of the last six years may still be used with younger children, especially to help with mental maths, but that by the time they reach the age of 11, pupils should be able to use the "standard written method", by which they mean the way parents were taught. In a joint statement, five leaders of the Mathematical Association opposed the change. "Don't let us go back to the bad old days with books full of pages of vertical sums when only a minute percentage of pupils understood what they were doing and only a third could carry out calculations," they said. National statistics for maths show that 25 per cent of 11-year-olds failed to reach the basic standard expected for their age last year rising to 26 per cent of 14-year-olds. The decision to return to the old methods will come as a relief to many parents. Christine Turno says she dreads the twice-weekly homework with her nine-year-old daughter. "She goes ballistic," she said. "We have massive rows because she says I'm doing it wrong and she has to do it the way the school says. But she can't understand what they want and it's a complete mystery to me." A 20-minute homework session turns into an hour. Mrs Turno, of west London, said: "The teachers say it is the new way and if the answer is wrong it doesn't matter as long as she is using the right method. It's quite bizarre." Of 30 in the class, 10 get private tuition. Back to basics as maths problems multiply |
May 22, 2006
Math prodigy wins $1,000 award Michael Anthony Viscardi
Providence, RI---Michael Anthony Viscardi from Josan Academy in San Diego (CA), who took calculus in eighth grade, is this year's first-place winner of the AMS Menger Awards for his project, "The solution of the Dirichlet Problem with Rational Boundary Data". Viscardi received $1000 for the project, awarded at the 2006 Intel-International Science and Engineering Fair (ISEF) in Indianapolis. Michael has done very well for himself this academic year, winning the top prize of a $100,000 scholarship in the Siemens-Westinghouse Competition in December, and $8000 in awards, including the Best of Category Award, at the 2006 ISEF. He will attend Harvard University. The Karl Menger Memorial Prizes are funded by income from the Karl Menger Fund, which was established by the family of the late Karl Menger. This is the 17th year that the awards have been presented at the ISEF. Karl Menger (1902-1985), a leading mathematician of the 20th century, was born in Vienna and received his PhD in mathematics from the University of Vienna. He was an active member in the Vienna Circle, which in the 1920s was at the center of cross-disciplinary intellectual developments. He emigrated to the United States in 1936 and joined the faculty of the Illinois Institute of Technology. A devoted teacher, he strove to convey to his students the beauty and power of mathematics. In 1989, his family donated funds to the AMS in his memory, and these funds have been used for the Menger Awards, a fitting tribute to Menger's commitment to inspiring young people in mathematics. More information about Karl Menger may be found at http://www.math.iit.edu/Menger/menger.html. The list of winners of Menger Awards, going back to 1990, may be found at http://www.ams.org/prizes/menger-award.html. For Further Information, Contact: Mike Breen, AMS Public Awareness Officer Email: myb@ams.org Telephone: 401-455-4109 Founded in 1888 to further mathematical research and scholarship, the 30,000-member AMS fulfills its mission through programs and services that promote mathematical research and its uses, strengthen mathematical education, and foster awareness and appreciation of mathematics and its connections to other disciplines and everyday life. Math prodigy wins $1,000 award |
May 22, 2006
Math in motionBy Joel McGrady
It may be a circus act to the rest of us, but for Ronald Graham it's a complex pattern
Dr. Ronald Graham's lecture on general mathematics Thursday became an impromptu lesson in the science of pattern and an art built of patterns. Using well-established mathematical logic and reasoning, he said, it is possible to transform movements like juggling into mathematical formulas. Why? To attempt to discover new and better ways of juggling. |
22 May, 2006
The Mathematical Structure of TerrorismThe complex patterns of the natural world often turn out to be governed by relatively simple mathematical relationships. A seashell grows at a rate proportional to its size, resulting in a delicate spiral. The gossamer network of galaxies results from the simple interplay between cosmic expansion and the force of gravity over a wide range of scales. As our catalogue of natural phenomena has grown more complete, more and more scientists have begun to look for interesting patterns in human society. The nature of war is a question of great interest to everyone, especially as the era of large-scale conflicts recedes into the past. The wars of today tend to be lopsided affairs, where guerilla forces, insurgent groups, and terrorists oppose incumbent governments. Instead of a few large-scale battles, this situation leads to an apparently random series of small-scale attacks against vulnerable targets of opportunity. While affected governments collect records of past attacks, the random nature of such wars means that these data are of limited use in predicting future attacks. When classified according to their frequency and intensity, however, the events of any insurgent war appear to follow a power law. It should come as no surprise that weaker attacks are more common than stronger attacks, but a power law distribution makes a much more specific prediction. It turns out that if individual conflicts (for example, a terrorist attack or a guerilla raid) are classified according to the resulting number of fatalities n, then the number of such conflicts occurring in any given year is proportional to n raised to a constant power. Let's look at a specific example. In the case of the Iraq war, we might ask how many conflicts causing ten casualties are expected to occur over a one-year period. According to the data, the answer is the average number of events per year times 10–2.3, or 0.005. If we instead ask how many events will cause twenty casualties, the answer is proportional to 20–2.3. Taking into account the entire history of any given war, one finds that the frequency of events on all scales can be predicted by exactly the same exponent. Professor Neil Johnson of Oxford University has come up with a remarkable result regarding these power laws: for several different wars, the exponent has about the same value. Johnson studied the long-standing conflict in Colombia, the war in Iraq, the global rate of terrorist attacks in non-G7 countries, and the war in Afghanistan. In each case, the power law exponent that predicted the distribution of conflicts was close to the value –2.5. What's more, in the case of Colombia and Iraq he was able to show that the exponent seemed to be evolving towards that value; Colombia from above, and Iraq from below. Does this hint at a simple underlying pattern driving the behavior of modern wars? Johnson thinks so, and has even developed a model that predicts a power law distribution of casualties with the correct exponent. In his model, the insurgent force consists of a fixed number of attack units (a general term which may include equipment or even information, as well as people) which may group together to form larger units. Each unit on its own is assigned a 'strength' of one, meaning that a conflict involving that unit will result in one death. Coalitions of units pool their strength, and cause proportionally more deaths. The key ingredient in this model is the evolution of groups over time. Terrorist organizations, for example, typically function in relatively small units. When an opportunity comes up that demands more resources, they may band together. When the authorities grow too close for comfort, on the other hand, they may split up. In time these competing pressures can create a stable arrangement of groups, with a fixed distribution of different sizes. Johnson's model adopts a very simple dynamic to model this evolution. In any given time step, one group of attack units is randomly chosen. Each group's chance to be chosen is proportional to its size, but the many small groups still see much more activity than the few large groups. The group selected is given a small probability (1%) of disbanding into individual units; if it doesn't disband, then it joins up with another randomly chosen group. These are the only rules of the model, and they turn out to work just fine. After the population is allowed to evolve for a long time, the result is a power law distribution of group sizes with an exponent of exactly –5/2. Since group size is proportional to attack strength, this distribution also predicts the frequency of attacks causing a given number of fatalities. It is also interesting that the result of this model depends only on the probability of fragmentation. As long as this probability is reasonably small, the distribution of attacking groups will settle into a steady state with a power law distribution. Is this new 'Law of Terrorism' really universal? "Power law patterns will emerge within any modern asymmetric war being fought by loosely organized insurgent groups." Johnson speculates, "Although future wars will provide the ultimate test." Johnson's research continues with the analysis of data from other conflicts, such as Senegal, Indonesia, Israel, and Northern Ireland. The Mathematical Structure of Terrorism |
May 22, 2006
Fun with numbersPaul Greenberg It sounds like a gigantic Sudoku puzzle, or maybe one of those abstruse mathematical challenges like finding the largest prime number. (That search is now into a million digits.) It's the kind of challenge that fascinates theoretical mathematicians. And also the National Security Agency. It seems three giant telecoms — AT&T, Verizon and BellSouth — have been supplying the counterspy agency with billions of phone numbers since 9/11, when the danger of terrorist attacks finally got the country's attention. Forcibly. The object of this numbers game is to see if some immense, computerized data search would reveal a suspicious numerical pattern — say, phone calls between a known terrorist overseas and a series of phone calls in this country. Talk about connecting the dots, this sounds like a search for something a lot smaller than a needle in a haystack. Maybe a better comparison would be looking for traces of where the needle had been. Good luck. To us innumerate types, finding such a pattern sounds impossible, or at least improbable to the nth degree. Then again, who would have thought only a few years back that one could type a name or phrase into a computer, and within seconds, no matter where it appears in literature or history or current events or anywhere else, the phrase appears on your screen in context, duly sourced, with cross-references and maybe an ad on top. Today it's called googling, and the big complaint about it is that it may take whole seconds too long. For that matter, even as far back as the Second World War, who would have believed Alan Turing and his fellow Brits at Bletchley Park would break the Nazis' unbreakable Enigma code? Not too long ago, a global network of computers deciphered one of Enigma's last remaining secret messages — during the computers' downtime. For those giants of Artificial Intelligence, it must have been a breeze — like solving the Mystery of the Great Pyramid during a lunch break. Strange and marvelous things, numbers, almost as strange and marvelous as the creatures who find patterns in them. And look for more. The odds may be against the mathematical sleuths at NSA in their quixotic mission, but if it can be accomplished, and even if it can't, human beings are going to try to pull it off, strange and marvelous and endlessly curious creatures that we are. Another name for Homo sapiens is Homo faber , man the toolmaker. In this case, the tools are those giant computer banks. And so long as we have such tools, some brain — like a four-star general named Michael Hayden, who once headed the NSA — will want to see what these battalions of brainiacs can come up with. To some of us, the whole idea sounds somewhere between highly improbable and definitely nuts, but there was a time when Einstein's idea of a space-time continuum sounded nuts, too. Just because we don't understand something doesn't mean better minds won't — or won't detect a terrorist cell lurking somewhere in the forest, the universe, of numbers. But it's not the mathematical wonder of it all, or the question of whether the whole project is just plain screwy, that intrigues minds of a constitutional bent. The question they ask isn't whether it can be done, but whether it can be done legally. Isn't this a violation of our privacy, to have the government go through billions of phone numbers — of which ours might be a part, however infinitesimal? There are at least a couple of court decisions (like Smith v. Maryland , a 1979 ruling by the U.S. Supreme Court) that make a distinction between eavesdropping on private conversations without a warrant, which may raise constitutional questions, and going through telephone company records in search of the bad guys, which may not. But the law on this point is still a work in slow progress, as opposed to high-speed Internet. The beginning and end of the constitutional debate over NSA's latest numbers game remains the Fourth Amendment: "The right of the people to be secure in their persons, houses, papers, and effects, against unreasonable searches and seizures, shall not be violated . . . ." That's the key word: unreasonable. What's reasonable mathematically may not be reasonable constitutionally. This whole scheme strikes me, like so much else in the world of numbers beyond my ken, as ultra-reasonable, like Newton's squeezing the idea of gravity out of mathematical proofs. NSA's data mine sounds like the Manhattan Project of numbers, and it, too, could prove a dramatic success. But is it reasonable law? As with so many other constitutional questions, the answer may depend on context. And motive. Things unreasonable in peacetime can become reasonable in war. What may be illegal snooping in one context may, in another, become a prudent precaution taken in good faith. Like running billions of phone numbers through vast computers to see what dangerous patterns show up. When the existence of this experiment was revealed, as almost any top secret is these days, I found myself less worried than assured. I had no idea our intelligence agencies were so imaginative and enterprising. Not to say intellectually adventuresome. JWR contributor Paul Greenberg, editorial page editor of the Arkansas Democrat-Gazette, has won the Pulitzer Prize for editorial writing. Fun with numbers |
May 22, 2006
Of math and men: The human side of mathAstrophysicist Mario Livio explains why we should care about natural symmetry By Mario Livio (May 19, 2006) Symmetry bridges science and art, psychology and mathematics, male and female. Start with the humble peahen, faced with the challenge of selecting a peacock mate. The female wants a male with strong genes. But how would she recognize strong genes? All she needs to do is take one look at the peacock's tail. A perfectly symmetric tail indicates that this male has conquered its parasites and thus must have strong genes. Closer to home, but no less instinctual, studies show that the mates men and women find attractive also tend to exhibit symmetric faces and bodies. But "symmetry" is more than just sameness on both sides of a peacock's tail or a supermodel's nose. It means immunity to possible change. Symmetry represents the stubborn cores of forms, music and mathematical objects that remain unchanged even while undergoing transformations. Mathematicians, scientists, stock market analysts and artists too navigate the labyrinths of the world's symmetries by using the language of group theory. Group theory Snowflakes, for instance, have sixfold rotational symmetry. Rotating them about an axis through their centers perpendicular to their plane by angles of 60, 120, 180, 240, 300 and 360 degrees leaves the shape unchanged. Any transformation that leaves something unchanged — such as the rotations of the snowflake — is called a "symmetry transformation." These types of transformations have an interesting property called "closure" — if you apply one symmetry transformation followed by another one, the result is yet another symmetry transformation. Turning halfway around twice is the same as turning all the way around once. This is easy to understand. If X is a symmetry transformation, this means that "doing X" leaves the system unaltered. If Y is another symmetry transformation, then clearly X followed by Y is also a symmetry transformation, which will by definition leave the system unchanged. This property implies that symmetry transformations can be described by mathematical structures called "groups." (See "The supreme art of numerical abstraction," page 32.) Like some posh country clubs, a group is composed of members that have to obey the same strict rules. Group theory identifies those unchanging cores of shapes, art forms or mathematical concepts, even if they are masquerading under disguises of different disciplines. This simple definition has led to a theory that embraces all the symmetries in the world, from snowflakes to peacocks to integers to abstract theories of quarks. Even seasoned mathematicians continue to be amazed. As the 20th-century English geometer Henry Frederick Baker once put it, "What a wealth, what a grandeur of thought may spring from what slight beginnings." Laws of nature Looking even deeper, it is interesting to think of symmetry as one of the many unseen "forces" that govern our lives — from the evolution of our brains to the laws of nature. One can see that the laws of nature do not change from place to place in the universe. A hydrogen atom in a galaxy that is a billion light-years away behaves precisely the same as a hydrogen atom here on Earth. If not for this remarkable symmetry, any attempt to explain the universe would have been hopeless. In some sense, this symmetry is the natural manifestation of the types of symmetries we see in wallpaper design or in pieces of music, where the same theme is repeated many times. Similarly, the laws of nature do not depend on our orientation in space. We can measure directions with respect to north, southwest or the nearest Starbucks, and the laws remain the same. The German mathematician Emmy Noether discovered a powerful connection between these symmetries and conservation laws. These laws reflect that some quantities can be neither created nor destroyed — they have the same values whether we measure them now, tomorrow or a thousand years from now. The expression "there is no free lunch," for instance, is the everyday representation of conservation of energy. We cannot create energy out of nothing. If we could, we wouldn't have to pay so much at the gas pump. Noether showed that for every continuous symmetry of the laws of nature there is a corresponding conservation law. The fact that the laws do not change from place to place manifests itself as conservation of linear momentum. We see this law in action every time two billiard balls collide. Symmetry also shapes the way we perceive the world around us. Imagine, for instance, a primitive man living in a world with no buildings, no cars, no airplanes. This man turns his head, and he sees something symmetrical. In this stage of the vision process, symmetry is a property that "catches the eye," allowing the prehistoric man to identify this symmetrical object as another animal. Experiments show that bilateral symmetry around a vertical axis is the easiest to recognize, and diagnostically it is used for "same-different" judgment. The man perhaps sees that this symmetrical object is another animal, and he quickly runs away. Or maybe he sees that it's food or an attractive female, and he sprints toward it. Detecting this symmetry quickly and learning to recognize it could have meant the difference between life and death. Because natural selection favors the fittest, those whose brains did not evolve to detect symmetries quickly did not live to tell about it. Therefore, the ability to avoid predators and select mates makes our brains fine-tuned to symmetries. If it weren't for symmetry, we wouldn't have evolved to see and understand the world around us. But that wouldn't matter, because without symmetry, the universe as we know it wouldn't exist. Not only does symmetry play a key role in the way the universe functions, it is also integral to the way we understand this functioning. Mario Livio is a senior astrophysicist at the Space Telescope Science Institute in Baltimore, and an adjunct professor of physics and astronomy at Johns Hopkins University. Of math and men: The human side of math |
22 May, 2006
The James Dean of mathematicsThe man who originated group theory was killed in a duel. Almost 175 years later, we find out why and how (May 19, 2006) In the morning hours of May 30, 1832, a single shot hit Evariste Galois in the stomach. Although fatally wounded, Galois did not die on the spot. He lay on the ground until a Good Samaritan picked him up and brought him to the Cochin Hospital in Paris. The following day, with his younger brother Alfred at his side, Galois died of peritonitis. His last known words were: "Don't cry, I need all my courage to die at 20." Galois is the originator of "group theory" — the mathematical language of symmetry. His premature death marked the unfortunate end of a man in whose mind the sweeping ideals of the French Revolution were inseparable from the revolutionary new branch of mathematics he had invented. So who killed Galois and why? It is undisputed that the young mathematician was involved in a duel regarding a coquette named Stéphanie-Felicie Poterin du Motel. Because Galois is said to have talked often about two people provoking the duel, I conclude that Denis Faultrier, a close friend of Potterin du Motel's family who later married her widowed mother, and Ernest Duchâtelet, Galois' republican friend and the young woman's presumed lover, were those two people. Duchâtelet fired the fatal bullet. The entire affair was a classic case of cherchez la femme. From pieces of Poterin du Motel's letters to Galois, we have learned that he had offended her and that she informed her lover and the family friend. When the two men confronted Galois, the hot-blooded young man added insult to injury, calling the entire incident a "miserable piece of gossip." This was more than enough for the two to challenge Galois. Why did Galois appear to have been left wounded on the ground? His autopsy report describes a large bruise on his head that was probably caused when he fell. He might have been knocked unconscious and presumed dead. One of the reports notes that a former officer brought Galois to the hospital. This is most likely Faultrier. Perhaps this closes the 174-year-old case. But with so many gaps in the hard evidence, uncertainties remain. What is certain, however, is that Galois will always be remembered as one of the most creative individuals who ever lived. The new branch of mathematics he established has expanded far beyond the boundaries of pure mathematics into the realms of music, visual arts, physics and wherever symmetries can be found. His romantic spirit makes him the James Dean of mathematics. Mario Livio is a senior astrophysicist at the Space Telescope Science Institute in Baltimore, and an adjunct professor of physics and astronomy at Johns Hopkins University. The James Dean of mathematics |
May 22, 2006
Finding Common Ground in the U.S. Math WarsJeffrey Mervis For years, mathematicians and math educators have blamed one another or the inadequacies of U.S. mathematics education. But both sides may finally be headed toward agreement on how to fix the system Like a sheriff summoned to restore order to a lawless town in the Wild West, Richard Schaar knew that taking on the Math Wars would be a rough assignment. An applied mathematician and former president of the calculator division at Texas Instruments (TI), Schaar was part of an industry-led panel trying to improve U.S. science and math education a few years back when he realized that a huge schism in the community would likely block any effort to reform elementary and secondary school mathematics. "I hate labels, but in general the professional mathematicians were on one side, and the math educators were on the other," says Schaar, describing a debate, triggered by a huge backlash to a 1990s reform movement, that has persisted despite mounting concern about how poorly U.S. students fare in international comparisons. "The argument over direct instruction versus discovery learning, as the two sides are commonly described, was pulling the field apart. The mutual respect had gone away. And in that climate, any attempt to improve math standards at the state level would have been doomed to failure." The solution seemed obvious to him: Bring together a handful of top guns from each side and hope for harmony rather than bloodshed. And that's exactly what Schaar has done, in the Common Ground initiative (www.maa.org/common-ground). The six-member group has made modest but impressive progress over the past 18 months in finding agreement on issues that for the last decade have led mathematicians and math educators, in the words of one mathematics society executive, "to sit on the sidelines and lob bombs at each other." (To be fair, both sides claim to be appalled by the analogy to warfare. But they use combat imagery repeatedly in conversations as a shorthand to describe their experiences.) The Common Ground initiative is one of several hopeful signs that the two sides may be ready to call a truce and work together to improve U.S. mathematics education. Last month, the country's largest group of mathematics educators, the National Council of Teachers of Mathematics (NCTM), endorsed a short list of math skills, by grade, that every elementary and middle school student needs to master. These skills, called Curriculum Focal Points, are an attempt to correct what math educators decry as "mile-wide, inch-deep" curricula in most U.S. schools that leave many students unprepared for high school and, ultimately, precludes them from pursuing careers in science and engineering. This week, the Department of Education named mathematicians, educators, and community leaders to a presidential panel that will review the state of mathematics education (see p. 982). Observers are hopeful that the easing of tensions will improve the quality of the panel's recommendations on bread-and-butter issues such as student instruction, teacher training, and the additional research needed to enhance each area, not to mention make those recommendations easier to sell. "I think Common Ground is a historic and groundbreaking exercise," says Frances "Skip" Fennell, a mathematics education professor at McDaniel College in Westminster, Maryland, and NCTM president. "I worked in the education directorate at NSF [National Science Foundation] in the late 1990s, and I was blown away by the anger in the community. This is exactly what we need to get things moving forward." All for algorithms Professional mathematicians blame themselves for some of those angry words. They were heavily involved in a major reform of the U.S. mathematics curriculum in the 1960s, after Sputnik, that was widely criticized as too difficult for the average student. In response, mathematicians largely withdrew from the fray and were silent when math educators promulgated the next round of reforms in response to a 1983 report that said low student achievement in reading and math was putting the country at risk. "There's been a divide between education and subject matter fields for a long time, but it's had its worst consequences in math," notes Roger Howe, a Yale University mathematician who has thought hard about the mathematical foundations of elementary principles such as place value. And when the mathematicians belatedly discovered aspects of the new courses that they didn't like, they unleashed their wrath upon federal officials and math educators, castigating them at every opportunity for demanding too little of students and watering down their discipline. Given the rancorous tone of the debate, Schaar knew that he needed to sign up leading figures from both sides. He spent a year picking his team: two mathematics professors who have been sharp, public critics of the reform curricula (R. James Milgram of Stanford University in Palo Alto, California, and Harvard University's Wilfried Schmid) and three math educators in the forefront of those reforms (Deborah Loewenberg Ball of the University of Michigan, Ann Arbor; Joan Ferrini-Mundi of Michigan State University in East Lansing; and Jeremy Kilpatrick of the University of Georgia, Athens). In December 2004, the same month he retired from TI, Schaar convened the first meeting of the Common Ground initiative, with himself as facilitator. Six months and six meetings later, the group issued a three-page document describing a handful of principles that should guide math education from kindergarten through high school. The principles include the automatic recall of basic facts, the importance of abstract reasoning, the need to acquire a mastery of key algorithms, and the judicious use of calculators and real-world problems. Two months ago, an expanded group met for a weekend to tackle the topics in greater detail, and last week, initial working papers from that meeting were posted. The core group met again last weekend to plot its next steps, as well as to clarify its earlier statement about setting high expectations for students--one that's been misinterpreted as an argument for making calculus a required course in high school. The document doesn't say when or how any of the concepts should be taught. Common Ground is not a curriculum, Schaar points out. The most its participants can hope to achieve is to influence the process by which states develop standards, adopt textbooks, and develop the assessment tools to measure what students should be learning. Even so, their carefully worded statements on selected topics reflect hard-fought compromises on core issues that have roiled the community for more than a decade and that, once resolved, could pave the way for continued progress. "There will always be differences," says Milgram, who in 2000 testified before Congress that "the sad state of U.S. mathematics education" is the result of "a constructivist philosophy" promoted by NCTM standards and endorsed by NSF and the Department of Education, the two leading federal sources of support for teaching mathematics. "But if we can agree on the essential content that students need to know, then the other fights become manageable. And I'd say that there has been far more agreement than disagreement." Ball, who has done pioneering work on what math teachers need to know to do their jobs well (i.e., not just how to teach long division but also to understand why Susie's method is incorrect), believes that the process has been just as important as the product. "Our goal was to provide leadership to the field, to say to everybody: 'If we can do it, then the rest of you can, too.' And I think we've shown that it's possible to come together on many of the flash points." One major flash point is the use of algorithms--how to do long division, for example--and the memorization of the facts upon which they are based. Many mathematicians maintain that current state standards and instructional materials downplay the use of such time-tested algorithms or allow students to bypass them entirely by using calculators. So when Common Ground asserts that "students should be able to use the basic algorithms of whole number arithmetic fluently, and they should understand how and why the algorithms work," the participants are trying to stitch up a vast rift in the community. "Of course kids have to know how to compute and know their basic facts. But they also have to make sense of what they are being taught and explore the ideas with open-ended problems," says Sybilla Beckmann Kazez, a mathematician at the University of Georgia, Athens, who is well respected by both camps. "If you put it that way, everybody would agree." Schaar concurs that the initiative has only scratched the surface on this contentious subject: The question of algorithms "is an incredibly challenging area that will require additional exploration." Getting to the (focal) point NCTM's new curriculum focal points, covering prekindergarten through grade eight, are also just beginning their long journey through the educational system. (The document won't even be released publicly until fall, officials say, although drafts have circulated and the council's executive board approved the latest version last month at the organization's annual meeting in St. Louis, Missouri.) With three per grade, the focal points address what math educators decry as overly broad and shallow curricula in most U.S. schools that hinder mastery and prepare students poorly for college-level work. NCTM President Fennell says the focal points are intended to provide "curricular relief " to elementary and middle school teachers whose school districts expect them to achieve as many as 100 objectives in mathematics. Many of those objectives span several grades, with teachers expected to tailor them to the maturing child. But there's no urgency because teachers know that their students will get another bite of the apple the following year. "While lots of things are important, we're saying to teachers that here are three things you need to zero in on," says Fennell. "For example, we'll teach some probability in the fourth grade. But it's not as important as multiplication," which takes center stage alongside fractions and decimals and the concept of area. Second graders should concentrate on addition and subtraction, place value, and linear measurement, says NCTM, even if their teachers also touch upon other topics. Although focal points must first be woven into state and district guidelines to have any real effect, the council's action already represents a significant move toward common ground: Professional mathematicians love to attack the 1989 and 2000 NCTM standards, and they see focal points as a tacit admission that some of their criticisms were on the mark. They also welcome the message that, for most students, less is more. "The idea of coming up with a few topics that should be addressed in K through 8 is a very needed step," says Richard Askey, a professor emeritus of mathematics at the University of Wisconsin, Madison, and an outspoken critic of earlier NCTM standards and curricula based on them. "I think that publishers, who now have to deal with all [different] state standards, will also like the idea" of a limited number of key objectives for each grade. Jane Schielack, a mathematician and math educator at Texas A&M University in College Station who led the NCTM task force that assembled the focal points, agrees that they are very much a product of the times. "This is something we couldn't have done 4 or 5 years ago," she says. In addition to the greater emphasis on accountability spawned by the 2001 federal No Child Left Behind law, Schielack cites the growing recognition that some countries, notably Singapore and China, excel on international student comparisons because of a national curriculum that focuses on a small number of topics and policies that give teachers the necessary training and resources to get the job done. "That's the biggest difference between the United States and the top-achieving nations," agrees Milgram. "Having NCTM come out with a statement to this effect should make an enormous difference on what we expect kids to learn." Even so, nobody expects Common Ground and focal points, by themselves, to usher in a golden age of quality mathematics education. There's too much that remains to be done. "It's a long, long journey," says Hung-Hsi Wu, a mathematician at the University of California, Berkeley, who runs summer institutes for classroom teachers whose grasp of basic mathematics is often poor or nonexistent. "Better mathematics education in the United States won't take place in the next 10 years. I think it will take 30 years." At the age of 60, Schaar doesn't plan on staying in the line of fire for quite that long. But he's not ready to saddle up and ride out of Dodge. Schaar believes that Common Ground, funded by NSF and TI and staffed by the Mathematical Association of America, has restored a measure of civility to the debate. And this month, after a coalition of 16 leading mathematical societies applauded his 2-hour presentation and told him to keep up the good work, he said that kind of support is exactly what's needed. "I'm not looking for an endorsement," he says. "I'm looking for help in getting more people involved." A bigger "in" crowd means fewer outcasts. And that's good news for a sheriff. Finding Common Ground in the U.S. Math Wars |
May 22, 2006
22 May: Microsoft Research Summer SchoolEFY News Network The annual event would seek to focus on critical areas that are not available in textbooks or covered in the academic syllabi. Friday, May 19, 2006: New Delhi: This summer, no vacation, only school. And, this is one school that tech graduates and researchers in cryptography, algorithms and security would certainly like to attend. For them, Microsoft Research India (MRI); Indian Institute of Science (IISc), Bangalore; and Indian Institute of Technology-Madras (IIT-M) have come together to organise a three-week summer school in Bangalore from 22 May to 10 June. The Microsoft Research Summer School, co-sponsored by the Indo-US Science and Technology Forum, will feature lectures by international experts in cryptography, algorithms, security, multimedia, protection, authentication and identification, auctions, game theory, number theory and elliptic curves. The school is reportedly roping in experts like Bela Bollobas from Cambridge University; Dan Boneh from Stanford University; Ravi Kannan from Yale University; Adi Shamir and Eran Tromer from Weizmann Institute of Science, Israel; and Kamal Jain, David Jao and Kivanc Mihcak from Microsoft Research, the US. According to P. Anandan, director, MRI, about 80 graduates and undergraduates from IITs and Indian Institutes of Information Technology (IIIT), and scientists and techocrats from R&D and defence institutes have been selected for the summer school. "Our objective is to enhance research pool and encourage basic research. We would also like to integrate talent among the Indian researchers who are already well advanced in their domain and are globally recognised too," said Ramaratnam Venkatesan, head-crytpography, security and algorithm, Microsoft. G. Rangarajan, chairman, mathematics department, IISc, said, "Such collaborations are aimed at helping scientists and engineers to solve complex research problems requiring inputs from mathematicians and help them to extend their expertise to applied areas." MRI is planning to forge partnerships with academics and institutions in the Indian subcontinent to advance education and research in computer science. The company has lined up many programmes to support basic research of local academia and foster alliances with universities in India. 22 May: Microsoft Research Summer School |
May 22, 2006
Linking Climate Change Across Time ScalesWOODS HOLE, Mass., May 18 (AScribe Newswire) -- What do month-to-month changes in temperature have to do with century-to-century changes in temperature? At first it might seem like not much. But in a report published in this week's Nature, scientists from the Woods Hole Oceanographic Institution (WHOI) have found some unifying themes in the global variations of temperature at time scales ranging from a single season to hundreds of thousands of years. These findings help place climate observed at individual places and times into a larger global and temporal context. "Much of the work went into assembling the different types of records needed to study such diverse time scales," said Peter Huybers, a paleoclimatologist in the Geology and Geophysics Department at WHOI and lead author on the study. "Data from instruments from around the world are available for recent periods, but it is not so easy for earlier times. We have few instrumental records before the 19th century, so we have to use measurements in corals, ice cores, and sediment cores to estimate past temperatures." These measurements and data compilations were made by scientists at WHOI and other research institutions. "While none of the measurements we use are new," Huybers said, "putting them together told us more than we could learn from any single record." Huybers and coauthor William Curry, a senior scientist and paleoceanographer at WHOI, found that temperature variations are more intimately linked across time scales than had previously been thought. For example, places that have a large annual cycle in temperature, like the high latitudes, also have a lot of interannual and decadal temperature variability. In fact, the relationship is so strong Huybers says you can fairly well predict how much decadal temperature change occurs at a given location simply by knowing the size of the annual cycle. At longer time scales, however, a different relationship seems to hold. Temperature variations at thousands and tens-of-thousands of years seem to follow temperature variations at the Milankovitch cycles. Milankovitch cycles are named after the Serbian mathematician Milutin Milankovitch who argued that periodic changes in the Earth's orbit around the Sun cause the advance and retreat of massive ice sheets. The changes in Earth's orbit cause redistributions in how much sunlight the Earth receives at different locations and seasons. "The overall impression is that energy is put into the climate system at the annual and Milankovitch time scales, causing temperature variations at those time scales, but also at the neighboring time scales," said Huybers. In the tropics the amplitude of the annual and Milankovitch cycles tends to be smaller than at high latitudes and, correspondingly, there is less tropical temperature change across interannual to thousand year time scales. Another notable feature is that the variability of temperature appears most similar globally at those time scales furthest removed from the annual and Milankovitch periods, indicating that away from these forcing periods climate relaxes to a more uniform background state. Climate varies at all time scales, from months to millions of years and longer. These changes are often studied independently of one another, but we now have a clearer idea of how climate change is linked across time scales. "These insights may help us to better understand past temperature changes, improve our models of the climate, and maybe even predict future climate change," Huybers said. Linking Climate Change Across Time Scales |
May 17, 2006
New Math - Recent Algorithmic Art at LACDALOS ANGELES, CA.-Los Angeles Center for Digital Art presents an international group exhibit of artists using computer algorithms, math based image generators and custom software for the production of abstract works. The show includes videos of animated algorithmic renderings, architecturally based works, internet generated images, 3D stereoscopes, art based on organic growth, as well as interactive pieces where visitors can create their own images. Andy Lomas is a mathematician, digital artist and Emmy award winning digital effects supervisor. His Aggregation series explores the complexity of organic form with intricate sculptural shapes generated by computer simulated growth systems. Using his own software to create the forms, biases and changes to environmental rules are used to create an incredible variety of structural shape. Nathan Selikoff has abandoned the predefined processes of production to more fully explore the computational landscape of mathematics and beauty. He uses custom software to investigate strange attractors – visual representations of chaotic dynamical systems. Fascinated by the diversity and complexity of the raw images that come from simple sets of iterated functions, he enjoys the interplay of technical problem solving and artistic spontaneous interactivity. Charles Fairbanks calls upon friends for an introduction: their laconic descriptions of the artist—ranging from "meaty" to "abstract dynamo"—lend linguistic thrust to his Googled Self-Portraits. The descriptions become keywords for a program to average the RGB data of the top fifty Google-Images. Determined by linguistic, personal, and virtual connections, the appropriated pictures become glowing color-fields of information while details linger at the threshold of perception. Hollis Cooper believes virtual environments have opened a new era in the experience of architectural space. Digital representation has produced perspectives that are no longer based on physical space but instead on multiple-user organization and efficiency – a limitless number of vanishing points. She regards these developments optimistically, as a means of expanding our ability to suspend disbelief and project ourselves into the world around us, interacting more actively with and within it. Tim Quinn is a nationally known Los Angeles sculptor and algorist. He has a long-standing love of recursion, which over the years he has applied to various visual material to produce a visually and conceptually stunning effect. His recent work explores a randomized kaleidoscope effect that defies easy understanding. Applying his own AppleScript Photoshop code to scanned images of his "Sculpey" objects, he achieves a global flattening of 3D space that doesn't flatten locally. Thomas Briggs is a veteran of the art world with a 20 year history in computer animation production and teaching. As an animator/programmer he was often concerned with the mathematical representation of fluid, lifelike gesture. He realized that this notion could be inverted, that the gesture could be realized from mathematics directly, and used to create drawings which retain some connection to the scratch of pen on paper. He eschews algorithmic, or procedural processes, instead using simple periodic functions evolving over time. Milos Rankovic received an Award for Doctoral Study in the Creative and Performing Arts from the UK's Arts and Humanities Research Council (AHRC) to pursue his study of the relationship between creativity and commitment. One of the key goals of the study was to develop an aesthetically relevant notion of complexity, which he now describes as "the tip-splitting instability and the infinite precision of the lossy incompressible". Inspired by Cairn-Smith's ideas regarding the pre-biotic (and therefore pre-phenotypic) evolution, and as a way of gaining some practical insight and intuition about the implications of this theoretical work, Milos designed an evolutionary algorithm featuring aesthetic selection of images as "naked genes". He implemented this algorithm as a computer program, ASNakedGene, that generated the images representing him in the show. Milos currently teaches digital art at the University of Leeds. New Math - Recent Algorithmic Art at LACDA |
May 17, 2006
NYU algorithm enhances ability to detect cancer genesResearchers at New York University's Courant Institute of Mathematical Sciences have developed a new algorithm that enhances the ability to detect a cancer gene, and have applied their algorithm to map the set of tumor-suppressor genes involved in lung cancer. The algorithm uses data from Affymetrix's gene-chips that can scan hundreds of patients' genomes to find gains and losses in gene-copies. The findings will appear in the July issue of the American Journal of Human Genetics. The study was conducted by Iuliana Ionita, a PhD student in computer science, Raoul-Sam Daruwala, a former research scientist from Courant Bioinformatics group and currently at Google, and Courant Professor Bud Mishra. Mishra is a professor of computer science and mathematics at the Courant Institute and also has an appointment in the Department of Cell Biology at NYU's School of Medicine. Previous research has found that certain gene-chips--a technology that allows the genome-wide screening for mutations in genes or changes in gene expressions all at once--shed light on genes and mechanisms involved in the onset and spread of cancer. Specifically, chromosomal segments, when deleted in a single or both copies of genomes of a group of cancer patients, point to locations of tumor suppressor genes implicated in the cancer. The NYU study focused on automatic methods for reliable detection of such genes, their locations, and their boundaries. For this purpose, the NYU scientists sought to devise an efficient and novel statistical algorithm to map tumor suppressor genes using a multi-point statistical score function. Their algorithm is unique in that it exploits the high resolution of gene-chips and prior biological models through Bayesian statistics in order to optimally pinpoint the genes involved in the cancer, even when these genomes may have many other unrelated deletions, which happen as "collateral damage" to the genomes as the cancer progresses to an advanced stage. The NYU algorithm estimates the location of tumor suppressor genes by analyzing segmental deletions in the genomes from cancer patients and the spatial relation of the deleted segments to any specific genomic interval. Since the gene-chip consists of many "probes"--each one characterizing an almost unique word and its location in the already-sequenced human genome--by combining these probe-measurements, one can estimate if an important genomic segment is missing. By analogy, this process is akin to guessing if a new edition of a book is missing an important paragraph by checking if some of the important key words in that paragraph are missing from the index of the new edition. The new algorithm computes a multipoint score for all intervals of consecutive probes, and the score reflects how well the deletion of that genomic interval may explain the cancer in these patients. In other words, the computed score measures how likely it is for a particular genomic interval to be a tumor suppressor gene implicated in the disease. In order to validate their algorithm, the authors produced a high fidelity in silico model of cancer, and checked how well they can detect the right genes, as they modified various parameters of the model in an adversarial manner. Encouraged by the success of their in silico study, they applied the algorithm to currently available patient data, and discovered that they were able to detect many genes that were already known in the literature, but also, several others that are statistically equally significant, but not found by the earlier studies. The findings also showed that the algorithm may be applied to a wider class of problems--including the detection of oncogenes, which promote the growth of cancer when they are mutated or overexpressed. As the technology and the statistical algorithms of this nature keep improving in cost and accuracy, it will prove useful in finding good biomarkers, drug discovery, disease diagnosis, and choosing correct therapeutic intervention. The members of the NYU group (the authors, Dr. Salvatore Paxia and Dr. Thomas Anantharaman) are in the process of creating a simpler user interface for their software, providing interoperability across many different chip technologies, and finally, making it publicly available in order to facilitate its free and wide-spread usage. NYU algorithm enhances ability to detect cancer genes |
May 17, 2006
FACTBOX-Code-breaker NSA conducts top secret surveillanceMay 11 (Reuters) - The National Security Agency, which Thursday's USA Today said was secretly collecting telephone records of millions of Americans, has recently come under intense scrutiny for post-Sept. 11 surveillance activities. Following are some facts about the NSA, one of the most secretive U.S. spy agencies. - Founded in 1952, the NSA is the United States' cryptologic organization, which means it makes and breaks codes for the government. The Maryland-based Defense Department agency is one of the 16 U.S. intelligence agencies. - The agency uses high-tech equipment such as satellites and bugs to pick up and collect foreign electronic signals including telephone calls and computer messages to gather intelligence. It then disseminates the classified information to relevant U.S. government officials. - The agency's top-secret activities have come under intense scrutiny since the Bush administration acknowledged late last year that it had authorized the agency to eavesdrop on phone calls and emails to and from the United States by suspected militants without obtaining a court warrant. - The NSA's staff is half military, half civilian. The NSA director is always a high-ranking military officer, and the deputy director is always a civilian with technological expertise. - The agency's former director, Air Force Gen. Michael Hayden, currently the deputy intelligence czar, was nominated on Monday to succeed Porter Goss as the head of the CIA. Hayden served as NSA chief from 1999-2005. - Both the agency's budget and the number of staff members are confidential. But the NSA says that if it "were considered a corporation in terms of dollars spent, floor space occupied, and personnel employed, it would rank in the top 10 percent of the Fortune 500 companies." - According to the NSA's Web site, the agency "is said to be the largest employer of mathematicians in the United States and perhaps the world." Other staff members include engineers, physicists, linguists, computer scientists, researchers, analysts and security officers. FACTBOX-Code-breaker NSA conducts top secret surveillance |
May 17, 2006
New Math Model Finds That The Cochlea's Spiral Shape Enhances Low FrequenciesSource: Vanderbilt University Posted: May 11, 2006 The next time someone whispers in your ear, think "cochlea." The cochlea is the marvelous structure in the inner ear that is shaped like a snail shell and transforms sounds into the nerve impulses that your brain can process and interpret. You may remember learning about it in elementary school anatomy. This critical hearing organ consists of a fluid-filled tube about a cubic centimeter (three hundredths of an ounce) in volume. For decades, hearing experts thought that its spiral shape was simply an efficient packing job and its shape had no effect on how it functions. But a recent study headed by Vanderbilt mathematician Daphne Manoussaki calls this conventional wisdom into question. She and her colleagues, Richard Chadwick and Emilios Dimitriadis of the National Institutes of Health, have created a mathematical model of the cochlea that finds the spiral shape acts to enhance the low frequency sounds that we use to communicate with one another. They published the results recently in the journal Physical Review Letters. If the new model is correct, then the cochlea is more sophisticated than researchers have thought. "This would indicate we need to take a step back from the cell biology and see how the cochlea works as an integrated system," says Karl Grosh, who studies the ear's structure at the University of Michigan in Ann Arbor. "The more we understand how the cochlea works, the more success we will have in building signal processing systems that mimic its auditory characteristics â€" an important aspect in designing cochlear implants and analog cochlear processors." According to the National Institute on Deafness and Other Communications Disorders, about 59,000 people have received cochlear implants worldwide and about 250,000 are potential candidates. Manoussaki is an assistant professor of mathematics and her main interest is modeling cell movements. She got involved in studying the cochlea inadvertently. After she finished her doctoral degree from the University of Washington, she was looking for work. At NIH, Chadwick was looking for someone with computer skills. He saw her website, was impressed by the computer model of blood vessel formation that she had created and offered her a job as a visiting fellow. That is where she got involved in the workings of the inner ear. "I knew nothing about cochlea mechanics and I think that was to my advantage," Manoussaki says. "I looked at this organ that was shaped like a snail but that everyone was modeling as if it were a straight duct and I asked the obvious question." Chadwick informed her that it was well established that the spiral shape did not affect the way that the cochlea functions. In order to motivate her, however, he proposed that they review the papers that came to this conclusion. So that is what they did, one paper after another. It took them more than two years but they finally concluded that none of the existing proofs were persuasive. That realization led them to develop a mathematical model of the cochlea that included its helical structure. Their first model, which portrayed the cochlea as a helix of constant radius, did not show that the shape had any effects. At the end of her fellowship, Manoussaki returned home to Greece. In 2004, as she was preparing to return to the United States, she reconnected with her collaborators and began working on the problem once again. This time they developed a more sophisticated model. When sound waves enter the ear, they strike the ear drum and cause it to vibrate. Tiny bones in the ear transmit these vibrations to the fluid in the cochlea, where they travel along the narrowing tube that winds into a spiral. The tube is divided into two chambers by an elastic membrane that runs down its length. The mechanical properties of this "basilar" membrane vary from very stiff at the outer end and becomes increasingly flexible as the chambers narrow. These changing properties cause the waves to grow and then die away, much as ocean waves get taller and narrower in shoaling water. Different frequency waves peak at different positions along the tube. Hair cells sitting on the basilar membrane sense these motions by bending against the membrane and produce electrical signals that feed into the auditory nerve. Hair cells near the large end of the cochlea detect high-pitched sounds, such as the notes of a piccolo, while those at the narrow end of the tube detect lower frequency sounds, like a the oompah of a tuba. This basic frequency sorting works in the same fashion whether the cochlear tube is laid out straight or coiled in a spiral. That observation, in fact, was the major reason that the researchers studying cochlear mechanics concluded its shape didn't matter. Manoussaki's model comes to the same conclusion, but her calculations also reveal that the spiral shape causes the energy in the waves to accumulate against the outside edge of the chamber. She likens this to the "whispering gallery mode" effect where whispers traveling along curved walls of a large chamber can remain strong enough so they can be heard clearly on the opposite side of the room. This uneven energy distribution, in turn, causes the fluid to slosh higher on one side of the chamber, forcing the basilar membrane to tilt to one side, the direction to which the hair cells are most sensitive. The effect is strongest in the center of the spiral, where the lowest frequencies are detected. The researchers calculate the sensitivity increase can be as much as 20 decibels. That corresponds to the difference between the ambience of a quiet restaurant and the noise of a busy street. It could easily make the difference between understanding that whisper in the ear -- or not. The research was supported in part by the National Institutes of Health intramural program. Editor's Note: The original news release can be found here. New Math Model Finds That The Cochlea's Spiral Shape Enhances Low Frequencies |
May 17, 2006
Fuzzy mathsMay 11th 2006 | SAN FRANCISCO From The Economist print edition
MATHEMATICALLY confident drivers stuck in the usual jam on highway 101 through Silicon Valley were recently able to pass time contemplating a billboard that read: "{first 10-digit prime found in consecutive digits of e}.com." The number in question, 7427466391, is a sequence that starts at the 101st digit of e, a constant that is the base of the natural logarithm. The select few who worked this out and made it to the right website then encountered a "harder" riddle. Solving it led to another web page where they were finally invited to submit their curriculum vitae. |
May 17, 2006
Engineers Take Page Out of Nature's PlaybookNewswise — Designing complex systems such as nuclear reactors for space applications is a daunting task, but Oak Ridge National Laboratory researchers have made it less so by borrowing from nature. Using their genetic algorithm optimization tool, a takeoff of the natural selection process, Louis Qualls and colleagues can quickly perform searches of huge numbers of potential solutions to an engineering problem and identify the best options. An algorithm is a procedure for solving a mathematical problem. Advances in supercomputing and advanced optimization technologies are making it possible to sift through an enormous number of possibilities even for complex problems such as nuclear reactor design. "Designing space reactor power systems, nuclear reactors or safer automobiles is a long process that involves making perhaps thousands of choices," said Qualls, a nuclear systems integration specialist. "It can take months or years to perform all of the necessary calculations using traditional methods. "With genetic algorithms, however, we can perform those calculations and end up with a short list of potential solutions in a matter of just minutes or days, depending on the problem." As in nature and the survival of the fittest, the genetic algorithm approach evolves by removing poor solutions or designs that do not perform well and repopulates the next generation with only combinations – or mutations – of the better designs. Over time and with successive generations only the best options remain. Unlike traditional design analysis, which is limited to the specific input of engineers, complete with their biases, design optimization through genetic algorithms has virtually no boundaries. Each answer is created without sequential design information, which results in novel approaches that would likely never be generated with conventional methods. "Because of our individual education and training, we tend to approach problems with certain preconceptions," Qualls said. "Consequently, we often miss unique solutions to any given design challenge." Specific areas of interest for the Department of Energy's ORNL are in materials research and development and understanding how various metals and alloys respond to extreme radiation. Qualls noted that these are areas for which ORNL has established a long tradition of excellence and continues to play a key role in the nation's efforts to develop nuclear reactors for the space program and commercial nuclear reactors. Qualls illustrated the advantage of genetic algorithm-based design methods with a recent example proposed by the Nuclear Science and Technology Division irradiation engineering team. The challenge was to optimize the design of an experiment in which 128 material test specimens were to be irradiated in ORNL's High Flux Isotope Reactor. The specimens were composed of four different materials that were to be distributed over three different temperatures to obtain the broadest range of evenly spaced irradiation damage levels. "There are literally billions and billions of possible combinations of temperature and specimen arrangements," Qualls said. "While this is something that can be solved manually given some time, it makes a lot of sense to use genetic algorithms to quickly find the most promising solutions. In just a few minutes we found four solutions that were marginally better than the manually derived solutions." From the perspective of Sherrell Greene, director of Nuclear Technology Programs at ORNL, the genetics algorithm method is providing new design approaches and innovative designs for terrestrial and space-based reactor power and propulsion systems. "The tools developed by ORNL researchers have already made valuable contributions to our space power programs by enabling us to rapidly explore new concepts and designs," Greene said. "Now we are beginning to harness the power and flexibility of the genetic algorithm approach to improve the design of irradiation experiments and maximize the value of our R&D facilities to our researchers." In addition to Qualls, others involved in developing the genetic algorithm optimization tool are Ken Childs of the Computational Sciences and Engineering Division and Ed Blakeman, Seokho Kim, Jeff Johnson and John Neal of the Nuclear Science and Technology Division. This research has been funded by DOE Office of Science, NASA and by the Laboratory Directed Research and Development program. UT-Battelle manages Oak Ridge National Laboratory for the Department of Energy. Engineers Take Page Out of Nature's Playbook |
May 17, 2006
17-yr-old wins Cowbell Maths competitionBy Wale Ajao Posted to the Web: Thursday, May 11, 2006 IT was glamour, joy and admiration as 17 year old Mobolaji Tunde James was crowned king of young Mathematicians last Thursday at NICON NOGA Hilton Abuja. He won this year's Cowbell Mathematics competition in the Senior Secondary School category with a total of 89%. The significant thing is that Mobolaji is a student of a public secondary school. The name of the school is Iwa Community Grammar School, Ayetoro, Oke-ho, Oyo State. He got N130,000 cash prize. He also got a trophy, a medal and certificate. His school got a Riso digital printer, mathematics textbooks, high class metal sign post and plague. His mathematics teacher, who was visiting Abuja for the first time courtesy of Cowbell got N10,000. Elated Master Mobolaji James told journalists, "I'm very very happy. I thank Cowbell for this opportunity. He said he hopes to become an Engineer. The second prize in the same category was won by Tunde Emmanuel of Commercial College Gboko Benue State. He is a friend of Mobolaji James because they have met at various mathematics competitions in the past. Emmanuel is also 17. He scored 87%. He got N100,000, plaque, medal and certificate. His school got mathematics textbooks, high class metal sign post and plague. Like all the other winners in both junior and senior categories, Emmanuel's mathematics teacher also got N10,000; 15 year old Master Adebayo Afeez Adedotun came third. He got N75,000, plague, medal and certificate. His school got mathematics textbooks, high class metal sign post plus plague. He is a student of Mayflower Secondary School, Ikenne Ogun State. In the junior category 13 years old Ogbuagu Joy Chinasa of Federal Government Girls College Onitsha came first. She scored 95%. She got N100,000, a trophy, medal and certificate. Her school got Riso digital printer, mathematics textbooks, high class metal sign post and plaque. The second position was won by 13 year old Durojaye Damilola of Mayflower Junior Secondary School, Ikenne Ogun State. He scored 93%. He got N75,000, plague plus medal. His school got mathematics textbooks, high class metal sign post plus plaque. The third position in the junior category was won by 15 year old Adegboyega Abdul Wasiu. He is from Islamic Commercial College, Ede, Osun State. He scored 91% and got N75,000, a plaque and metal. His school got mathematics textbooks, high class metal sign post and plaque. In both senior and junior categories there were a total of six star prize winners. Fourteen others, also got various prizes. They were made up of seven in the junior categories and seven in the senior categories. In effect twenty students and their mathematics teachers went home with prizes and Cowbell products and souvenirs. Addressing the ceremony, Mr. David Draude, Finance Director Promasidor said that the race for supremacy in this year's competition started with the first stage examination held in 126 centres across the country on 23 participated. They were pruned down to 74 who sat the second stage examination at Lagos Airport Hotel on Saturday April 6. It is out of the 74 students that twenty were selected and honoured last thursday. Also speaking on the occasion, the Director General, National Mathematical Centre, Professor Sam Ale praised Promasidor makers of Cowbell Milk for continuously sponsoring the competition since 1998. He spoke further, "this event is therefore historical as it is another step towards addressing the problem of apparent loss of students interest in mathematics due to the perceived difficulty of the subject. Promasidor and Cowbell Milk therefore deserves commendation for stimulating and developing interest of students in Mathematics." The Minister of State for Education, Dr. Mrs Grace Oguche also graced the occasion. She congratulated the winners and urged parents to always pay more attention to the academic and social activities of their wards. Dr. Mrs Oguche who had been a school principal for twenty two years expressed the determination of government to continue to give education adequate attention. She also thanked Promasidor for sponsoring the competition. Honourable Abike Dabiri sneaked out of the National Assembly and joined the ceremony. She thanked Promasidor for an enduring relationship with her organisation. She had with the support of Cowbell Milk. She congratulated the students and urged them to always be of good behaviour. She craved the indulgence of the audience to quickly return to the House of Representatives where she said a crucial debate on the political situation in the country was going on. Veteran broadcaster, Yinka Craig was Master of Ceremony. Side attractions included cultural dances and drama sketches. 17-yr-old wins Cowbell Maths competition |
May 11, 2006
PRESIDENTS, PULITZER PRIZE WINNERS JOIN UH PROF IN HIGH HONOR |
May 11, 2006
World-Famous Mathematician Ronald Graham To Give Lecture At Oregon's PSU, |
May 11, 2006
Scientists Have Identified Basic Principles of CommunicationNewswise — How do we succeed in putting our ideas into words, so that another person can understand them? This complex undertaking involves translating an idea into a one-dimensional sequence, a string of words to be read or spoken one after the other. Of course the person on the receiving end might not get the intended point: The effective expression of one's ideas is considered an art, or at least a desirable and important skill. A team of scientists that included physicists and language researchers at the Weizmann Institute of Science recently investigated this process by applying scientific methods to some of our culture's most successful models for effective transfer of ideas – classic writings that, by common agreement, get their messages across well. They created mathematical tools that allowed them to trace the development of ideas throughout a book. The international team included Prof. Elisha Moses of the Weizmann Institute's Physics of Complex Systems Department and Prof. Jean-Pierre Eckmann, a frequent visitor from the University of Geneva, as well as postdoctoral fellow Enrique Alvarez Lacalle and research student Beate Dorow from the University of Stuttgart. The paper describing their research was recently published in the Proceedings of the National Academy of Sciences (PNAS). Because strings of words are one-dimensional, they literally lack depth. Our minds and memories aid us in recreating complex ideas from this string. The narration "encodes" a hierarchical structure. (An obvious hierarchical structure in a text is chapter-paragraph-sentence.) The implication is that our minds decipher the encoded structure, allowing us to comprehend the abstract concept. To test for an underlying structure in strings of words that are known for their ability to convey ideas, the scientists applied their mathematical tools to a number of books, including writings of Albert Einstein, Mark Twain's Tom Sawyer, Metamorphosis by Franz Kafka and other classics of different styles and periods. They defined "windows of attention" of around 200 words (about a paragraph) and within these windows, they identified pairs of words that frequently occurred near each other (after eliminating "meaningless" words such as pronouns). From the resulting word lists and the frequencies with which the single words appeared in the text, the scientists' mathematical analysis was used to construct a sort of network of "concept vectors" – linked words that convey the principal ideas of the text. Mathematically, these concept vectors can go in many directions, and reading the text can be thought of as a tour along paths in the resulting network. The multidimensional concept vectors seem to span a "web of ideas." The scientists' work suggests this network is based on a tree-like hierarchy that may be a basic underpinning of language. The reader or listener can reconstruct the hierarchical structure of a text, and thus the multidimensional space of ideas, in his or her mind to grasp "the author's meaning." Moses: "Philosophers from Wittgenstein to Chomsky have taught us that language plays a central evolutionary role in shaping the human brain, and that revealing the structure of language is an essential step to comprehending brain structure. Our contribution to research in this basic field is in the creation of mathematical tools that can be used to make the connection between concepts or ideas and the words used to express them, making it possible to trace in a speech or text the path of an idea in an abstract mathematical space. We can understand theoretically how the structure of the wording serves to transmit concepts and reconstruct them in the mind of the reader. A deep question that remains open is if and how the correlations we uncovered serve the aesthetics of the text." Prof. Elisha Moses' research is supported by the Clore Center for Biological Physics; the Center for Experimental Physics; and the Rosa and Emilio Segre Research Award.
The Weizmann Institute of Science in Rehovot, Israel, is one of the world's top-ranking multidisciplinary research institutions. Noted for its wide-ranging exploration of the natural and exact sciences, the Institute is home to 2,500 scientists, students, technicians and supporting staff. Institute research efforts include the search for new ways of fighting disease and hunger, examining leading questions in mathematics and computer science, probing the physics of matter and the universe, creating novel materials and developing new strategies for protecting the environment.
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May 11, 2006
KEYFITZ BECOMES SECOND MEMBER OF
HER FAMILY TO EARN |
May 11, 2006
Stony Brook Hillel Welcomes Nobel Prize-Winning Mathematician Robert J. Aumann
Stony Brook Hillel recently hosted Robert J. Aumann, the Israeli mathematician who was awarded the Nobel Prize in economics for 2005, at a reception for its Jewish student leaders. Dr. Aumann, a professor emeritus at Hebrew University and leading visiting professor at Stony Brook University for the past 16 years, was awarded the Nobel Prize for his groundbreaking work on game theory. While at Stony Brook he delivered a public lecture on "War and Peace," based on his Nobel lecture delivered in Stockholm in October.
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May 11, 2006
Coexistence through math is a winning equationBy Sima Borkovski May 07, 2006 A group of Israeli academics believe that peaceful coexistence between Israelis and Palestinians could be as easy as adding 2 plus 2. In fact, along with Palestinian professors, they've put that theory to practice by developing and launching a new museum exhibit called Meet Math, a project intended to inspire young minds to pursue the wonders of numbers. The exhibit, which opened last month at the Bloomfield Science Museum after several years of preparation, represents a joint effort between the Jerusalem educational facility, the Italian Institute of Science (La Citta' della Scienza) and East Jerusalem's Al Quds University, and serves as a testament to cooperation between Israeli, Palestinian and Italian mathematicians, designers, builders, curators and educators. "Math is a language used by all, and at the same time there are so many people, especially school students, who are terrified of it and feel it is beyond their grasp," Ehud de Shalit, a professor at Hebrew University and academic consultant for the exhibit, told ISRAEL21c. "This exhibition allows its visitor an accessible route to Math, one that even children will find enjoyable." The project came about as part of an initiative to open an interactive science center at Al Quds - the site where the exhibit will become permanently stationed when it moves there later this year. The Bloomfield Science Center seemed like a natural choice for this joint enterprise, as they have long been involved in efforts promoting Arab-Israeli coexistence. "We have been hosting Arab teachers and schoolchildren in our museum since our very first days as a museum," says Maya Halevi, director of the Bloomfield Science Museum in Jerusalem. "This made us natural partners for the project of creating a new science center for Al Quds University. Our experience showed us that when children work together, hostility and language barriers are put aside." The concept proved true, according to Halevi, even in the formative stages of the exhibit. "The same thing happened with our crew and the Palestinian crew when the latter came to our workshops and we all worked together. Working on a mutual exhibition made us the best of friends." The project was aided by the Citta' della Scienza in Naples, who helped with the overall design for the exhibit, and who provided a meeting place when security restrictions made it too difficult for the Palestinian and Israeli crew to meet in Israel. The inspiration for the exhibition centered on the idea that through finding neutral common ground, a road towards coexistence could be paved. "We hope this effort will prove to be a step in showing how the universal language of mathematics can be translated into a shared language of political and moral values," says Professor Sari Nusseibeh, President of Al Quds University. Dr. Hasan Dweik, director of Science education programs at Al Quds agrees. "We chose math because it is the language of logic. Math is the base for all science, and even though I'm not a mathematician I acknowledge the importance of this 'language' in the process of scientific studies." The exhibit itself is interactive and didactic, combining humorous elements with graphic panels that explore the history of mathematics. Using light and color, the exhibit intends to intrigue children, and encourage them to engage in numerous educational activities that are components of the exhibit. The specific subject of math was chosen after consideration was given to a number of themes, says Professor Peter Hillman. "Mathematics was chosen because of its universality, the major Islamic contributions to its history, and the need for a program of enrichment in mathematics teaching. We also welcomed the challenge of doing something new and different, exploring something that was perceived as an inaccessible, abstract subject. Our mission was to make it interactive and attractive for the children who will visit the exhibit." De Shalit, who spent hours working on the mathematical content of the exhibit, says that he was drawn to the idea of trying to make a child understand the concept and beauty of mathematics. He ended up employing the help of his school-age son, who became enamored with the concept of the exhibit as well. Finding a way to make math understandable to children fills an important need in the Palestinian community. "We have a real need for teachers that will be able to cope with the challenge of teaching math and science to our children," says Dweik. "With the help of the Bloomfield Science Museum and our Israeli friends it was made possible for us to establish an institution where our teachers could be trained for this purpose." While the end goal was an exhibit that would find common ground for coexistence, the means to the end emphasized coexistence as well. Halevi notes, "It was important for us that the Palestinians would actually build the exhibit themselves, and would not rely on ready-made ones created by the Italian or Israeli staff. This was actually the first time that the Palestinians were not simply donated an exhibition, but were involved in every step of its making." Hillman echoes that sentiment, referring to the creation of the exhibition as "the courage to cooperate." The emphasis on constant coexistence was not always easy, and was constantly fraught with hurdles that needed to be overcome. "Difficulties arose from both sides as Israel frequently closed key border crossings, and there were voices on the Palestinian side that demanded our [Palestinian] partners stop cooperating with Israelis," Hillman recalls. "Many times our Palestinian partners' lives were threatened and there was real danger for them to continue working with us." But through all of the difficulties, the team remained committed to the project, and to the concept of peace. And like so many others before him, Dweik accepts the sacrifices of today in hopes for a safer tomorrow, "After all, we are making this effort for the sake of our children and for the promise of a better future." Coexistence through math is a winning equation |
May 06, 2006
Centenarian publishes article in Springer's Japanese Journal of MathematicsContribution mentioned in Japan's most popular newspaper Yomiuri Shimbun
 Shokichi Iyanaga
Shokichi Iyanaga, a one-hundred-year-old mathematician, continues to publish in the Springer journal Japanese Journal of Mathematics. His most recent article, which explains the contributions of Claude Chevalley to class field theory, was published in the April 2006 issue.
Contact Joan Robinson, tel +49-6221-487-8130
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May 06, 2006
Scientists moot Romulan-style cloaking deviceBy Lester Haines Two mathematicians have boldly gone where no boffin has gone before and described the theoretical possibility of a cloaking device, the BBC reports. However, before the Trekkies among you don your Romulan cozzies and rush for a copy of the Royal Society publication in which Nicolae Nicorovici and Graeme Milton expound their cloak of invisibility, be aware it's very much a paper concept, currently applicable only to small objects of a particular range of shapes. The theory is based on "anomalous localised resonance" - analogous to the effect by which a vibrating tuning fork placed close to a wine glass will cause the latter to vibrate, as the Beeb notes. Nicorovici and Milton say an illuminated speck of dust (yup, that's the scale we're talking about), in close proximity to a "superlens*" cloaking material, would "scatter light at frequencies that induce a strong, finely tuned resonance in a cloaking material placed very close by". Said resonance cancels out the light coming from the speck, and voila! - invisibility. At least, that's the plan. Superlens pioneer Sir John Pendry, of Imperial College London, said of the mathematicians' admission that "the cloaking effect works only at certain frequencies of light, so that some objects placed near the cloak might only partially disappear": "I believe their claims about the speck of dust and a certain class of objects. In the paper, they do give an instance about a particular shape of material they can't cloak. So they can't cloak everything." He further explained: "Providing the specks of dust are within the cloaked area, the effect will happen. A cloak that only fits one particular set of circumstances is very restrictive - you can't redesign the furniture without redesigning the cloak." Accordingly, we don't think Starfleet Command will be losing any sleep over this one just yet. Nicorovici and Milton's research is published in the Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. ® Bootnote *The superlens's basic purpose is to break the "diffraction limit" which "restricts the resolution of microscopes and other optical devices to the wavelength of light used", as physicsweb puts it in its illuminating and comprehensive technical description. Here's more: Diffraction restricts the resolution of microscopes and other optical devices to the wavelength of light used. To see why, imagine two widely spaced apertures that are illuminated by the same beam of light so that each aperture produces its own diffraction pattern. If the apertures are moved closer together, their diffraction patterns overlap until they eventually merge to form a single peak. The individual apertures can then no longer be resolved by observing the transmitted light. This unwanted effect is known as the diffraction limit. As is often the case in physics, this simple picture is a little more complicated in practice because light that squeezes through a sub-wavelength aperture emerges in two portions. First there is a "far-field" portion that propagates away from the aperture and can be refocused by conventional lenses. Then there is a "near-field" portion that stays put, remaining localsed around the aperture over a region less than a wavelength in size. The near-field portion contains all of the sub-wavelength spatial details about an object, but it decays quickly as a function of distance from the object. Conventional optical devices are therefore unable to convey these finer details to an image. Instead, such instruments are constrained to recover as much of the far-field light as possible, limiting their resolution to roughly the wavelength of light.The idea, then, is to produce a lens capable of recovering the near-field and far-field components, in which case "an exact image of the object could be formed with perfect resolution". That's exactly what two teams did with a thin layer of silver which, working with visible light, "can be used to image structures with a resolution as high as one-quarter the wavelength of the incident light". Scientists moot Romulan-style cloaking device |
May 06, 2006
Physicists push against big bang, say time's infiniteBY STEVEN BODZIN BLOOMBERG NEWS Space and time go on forever, and the so-called big bang said to have started the universe is actually part of a repeating cycle, according to a new paper that challenges conventional wisdom in physics. Infinite space and time would contradict the generally accepted notion of a universe expanding abruptly out of nothing 14 billion years ago, said Neil Turok, a professor of mathematical physics at University of Cambridge in England. Turok wrote the paper -- which builds on a theory set forth in 2002 -- in the May 4 issue of Science Express with Paul Steinhardt of Princeton University in New Jersey. An ongoing expansion and contraction is more likely than a big bang as supported by Cambridge physicist Stephen Hawking and other cosmologists building on the work of the late Albert Einstein, Turok said. Rather than proving "the big bang happened," such work shows only that "Einstein's theory fails at a singularity 14 billion years ago," Turok said. The new study began as an attempt to explain the energy found in vacuums, which is credited with accelerating the universe's expansion. If the energy had been around since the big bang, Turok said, it should have blown the universe apart. The study's authors looked at why the force of the expanding universe, known as the cosmological constant, is much smaller than would be expected under the big bang. Physicists previously explained the discrepancy by introducing so-called inflationary energy, Turok said. This intensely powerful force blew the universe up to huge size in a fraction of a second and disappeared. Five billion years later, "the cosmological constant shows up," he said. Using a mathematical model, Turok and Steinhardt showed that space and time could continue forever. Two infinite three-dimensional spaces, called branes, touch one another every trillion years or so, sparking great explosions of radiation and creating new matter, a process that had been detected as the big bang. The authors' theory faces skepticism. In a companion article in Science, Alexander Vilenkin, director of the Tufts Institute of Cosmology in Medford, Mass., said the traditional big-bang theory remains more convincing. The authors' new cyclic theory of the universe can be disproved by observations of gravitational waves in the universe, Vilenkin said. A NASA probe a million miles from Earth is trying to find the waves, which the new theory says shouldn't exist. Physicists push against big bang, say time's infinite |