October 31, 2004
E-Voting to Face Major Test TuesdayBy Keith Regan Among the security concerns that have been raised is the possibility of someone being able to cast multiple ballots. Other concerns are about a sudden power outage and whether data would be lost in such a scenario. An actual hacking could only be done if the voting machines were on a network. However, results from many of the machines will transmitted to election officials remotely.
Among the many questions that might be answered by the presidential election on Tuesday is whether electronic voting can silence its critics by turning in a seamless performance or, instead, will fall prey to any of the number of concerns that have been raised. |
October 31, 2004
Chomsky draws fervent crowdBy Mark Osmond and Monica Woll, For the Daily Students were crawling through windows and pushing through doors to hear Noam Chomsky in the Law School's Honigman Auditorium yesterday, as he spoke on the aggressive pattern of U.S. foreign policy at the 14th annual Lecture on Academic and Intellectual Freedom. Chomsky, a renowned linguist and linguistics and philosophy professor at the Massachusetts Institute of Technology, criticized the United States and its history from the era of President John Quincy Adams to the Iraq war, for engaging in military conflicts that violated international law. He said the United States has a tendency to exempt itself from international law, supporting his claim with various examples from world history. He spoke of the U.S. interventions in countries such as Nicaragua, Kosovo, Panama and Cuba, condemning each action as "illegal" by international standards but deemed "legitimate" by U.S. ones. International law states that war is justified only when all alternative options have been exhausted. The United States has continuously violated this rule, engaging in war without imploring alternatives, Chomsky said. For example, he said prior to bombing Serbia-Montenegro — a Balkan country which was practicing ethnic cleansing of Muslims in the state of Kosovo — a compromise had been drafted that would have made the war avoidable. Chomsky stated that before the United States and NATO went to war, this alternative to military action was hidden from the public. Chomsky also discussed instances when he said the United States was excused for war crimes. When Serbia-Montenegro brought charges against the United States to the world court, the United States asked to be and was excused from crimes against peace so that a precedent would not be established for inhibiting U.S. military action, he said.. Chomsky stated that U.S. military actions run contrary to the principle of universality, which means that nations should apply the same standard to themselves that they apply to others. For example, the United States embraces the right to use anticipatory self-defense against errorist threats. However, Chomsky said, anticipatory self-defense was not seen as an excuse for Japan to attack Pearl Harbor, despite the fact that the U.S. was plotting an attack against Japan that would have destroyed its wooden cities. The majority of the crowd was enthusiastic to Chomsky's message, giving him a standing ovation before and after his lecture. "If every person had a fraction of the insight that Noam Chomsky has, we would be in a much higher place," said Dave Kargol, editor of Eastern Michigan University's student newspaper, The Eastern Echo. "I can only try to hold onto a few things he said and think about them further." "I was particularly impressed by Chomsky's presence at his age," said LSA senior Michael Morgan " Although he is (75 years old), he spoke with more eloquence than our own president." There were, however, students who were skeptical of Chomsky's message. "I do not agree with everything Chomsky has to say," said RC freshman Miriam Liebman. "I think he is a little too extreme, and when you are too extreme you lose sight of reality." Liebman also mentioned what she called Chomsky's anti-Semitic reputation and his skepticism for considering Israel a Jewish state, although he himself is Jewish. The Lecture on Academic and Intellectual Freedom was established in 1990 to honor three University professors who were called to testify before the Congressional Committee on Un-American Activities during the McCarthy era. The University suspended all three professors and two of them, pharmacologist Mark Nickerson and mathematician Chandler Davis, were fired. The tour is meant to serve as a reminder that Americans' freedoms are vulnerable and ought not be taken for granted. Chomsky will give a lecture entitled "Biolinguistics and Human Cognitive Capacities" today at 2 p.m. in the Modern Languages Building. Chomsky has published more than 70 books and more than 1,000 articles in the fields of linguistics, philosophy, intellectual history, politics, cognitive sciences and psychology. His books include: Reflections on Language, Manufacturing Consent (with E.S. Herman), What Uncle Sam Really Wants and 9-11. Chomsky draws fervent crowd |
October 31, 2004
Math whizBy Alanna Mitchell China's prime math discovery has to do with the famously unprovable Goldbach conjecture. That's a theory scribbled on notes in 1742 in which Russia's Christian Goldbach and Swiss mathematician Leonhard Euler set out the theory that every even number greater than four is equal to the sum of two prime numbers. So, for example, 6=3+3, (3 is a prime), 8=5+3, 10=3+7, and so on. The theory has never been proved conclusively, despite great attention over the centuries. However, in 1966, Chen Jingrun came the closest. The Chen theorem proved that every large even number can be expressed as the sum of a prime number and a number with no more than two prime factors. As an added twist, Dr. Chen's work may play a role in the most famous mathematical contest currently on the go. In 2000, publisher Faber & Faber offered a $1-million prize for anyone who could find proof by March, 2002, and have it published in a respected journal by 2005. It was a marketing tool for a novel published in 2000 about the conjecture. Dr. Chen died in 1996, and so far there's no word on whether his survivors have a shot at the prize, or part of it. Math whiz |
October 29, 2004
US boosts e-voting software securityCeleste Biever A US federal body has come up with a new plan to help secure electronic voting, employing a mathematical technique used mainly by cryptographers. The US Election Assistance Commission (EAC) based in Washington DC, announced on Tuesday that it had persuaded the five largest electronic voting machine vendors to submit certified versions of their software to the National Software Reference Library (NSRL). "Their acceptance of our request begins the process that assures the country that we will have a higher level of security and therefore confidence in e-voting than we have ever had before," said DeForest Soaries, EAC chairman. At the NSRL, each program file submitted was converted via a mathematical function known as SHA-1 into a fixed-length string of digits, called a "hash". The hash is like a fingerprint for that piece of software - if the software changes, the hash changes. Smoke and mirrors Hashing is a cryptographic technique for representing large files with a small amount of data that is entirely dependent on the content of the files. But the EAC says that hashing is useful for e-voting software because even minor tampering or hacking of the code can be easily spotted by hashing the software and comparing the result with the certified version in the library. All the hashes of the e-voting software are available online. Barbara Guttman, computer security expert at the US National Institute of Standards and Technology in Gaithersburg, Maryland - which oversees the NSRL - says that election officials will be able to refer to the stored hashes to check that the piece of software they are about to install is indeed the certified version. But most computer scientists remain sceptical. "I think that the reference library is smoke and mirrors," says Avi Rubin, the computer scientist at Johns Hopkins University in Baltimore, Maryland, who spearheaded the criticism of e-voting machines with an analysis of the technology in July 2003. Pre-existing threats "Hashing will not catch malicious code that's already in the system, which is the biggest threat," he says. It will also fail to catch any bugs that are there by mistake, he adds. David Dill, a computer scientist at Stanford University, California, and founder of the lobby group Verified Voting, says e-voting software undergoes state testing and federal testing by Independent Testing Authorities. But he points out that bugs have slipped through before. He says the only safeguard against bugs, or the insertion of malicious code before the software is submitted for certification, is for the machine vendors to make their source code public - open to the full scrutiny of the security community. The companies that submitted their code to the NSRL were Diebold Election Systems, Sequoia Voting Systems, Election Systems and Software, Hart and VoteHere. "What's in it for us is a better election procedure," says David Bear of Diebold Election Systems in McKinney, Texas. US boosts e-voting software security |
October 29, 2004
The Science OrangutanIn a new weekly thing, we take an irreverent humour-based look at science. This week we look at the controversial topic of science jokes: The 'functions' joke f(x)=6x+3 walks into a bar. "Got any sandwiches?" f(x)=6x+3 asks the barman. "Sorry," he replies, "We don't cater for functions". "Why?" asks the function. "Cos the Sin on the door says so!" Noah's Ark The Flood is over and the ark has landed. Noah lets all the animals out and says: "Go forth and multiply." A few months later, Noah decides to take a stroll and see how the animals are doing. Everywhere he looks, he finds baby animals. Everyone is doing fine except for one pair of little snakes. "What's the problem?" says Noah. "Cut down some trees and let us live there", say the snakes. Noah follows their advice. Several more weeks pass. Noah checks on the snakes again. Lots of little snakes, everybody is happy. Noah asks, "Want to tell me how the trees helped?" "Certainly," say the snakes. "We're adders, so we need logs to multiply." Wife or mistress? A doctor, a lawyer and a mathematician were discussing the relative merits of having a wife or a mistress. The lawyer says: "For sure a mistress is better. If you have a wife and want a divorce, it causes all sorts of legal problems." The doctor says: "It's better to have a wife because the sense of security lowers your stress and is good for your health." The mathematician says: "You're both wrong. It's best to have both so that when the wife thinks you're with the mistress and the mistress thinks you're with your wife – you can do some mathematics." Hallowe'en and Christmas Why do Computer Scientists get Halloween and Christmas mixed up? Because Oct 31 = Dec 25 There are... There are three kinds of mathematicians: those who can count and those who can't. There are only 10 types of people in the world: those who understand binary and those who don't. The Science Orangutan |
October 26, 2004
A theory of everythingBy ANDREW CLIFFORD As awareness of the universe grows more intricate, astronomers, mathematicians and physicists need to negotiate sophisticated theories to reach a common understanding of what makes the cosmos tick. Paul Cullen may not understand the finer points of quantum physics or its latest string theory of matter and the universe, but he says he is intrigued by the oblique ways that complex ideas can be illustrated and explained. "They are presented in ways that can be really engaging and they are dealing with things that are deeply mysterious and inexplicable," he says. "One of the things that interests me about them is just the way that, for someone who isn't a mathematician or a physicist, they almost work in an evocative way, in the same way that art or music might work. "The responses we have to it are more subjective than an objective understanding of what's being articulated by those theories. It's that relationship through language and words [that is] perhaps the way the public comes to those things." One of the most important interpreters of popular science is the diagram, and Cullen considers his art to be like a diagram of a diagram. His explorations are presented like a sports debate in a restaurant where salt and pepper shakers become players and pieces of cutlery are goal posts. Everyday items are recruited into new roles, but in Cullen's curious constructions they don't represent actual objects but illustrate more abstract ideas like gravity and speed and, more specifically, the way we describe gravity and speed. Having grown up in the rural environs of Te Awamutu, Cullen began his career with a degree in science, majoring in botany. He says he decided there were more exciting vocational paths to follow so he took to art via a course in landscape architecture and now heads the sculpture department at Manukau School of Visual Arts, while completing a Doctorate in Fine Arts. However, Cullen's early training was not in vain; it still plays a vital role in his practice. Much of his previous work references gardens and the way they are a modified landscape, reconstructing and ordering our relationship to the physical world through ideas and imagination. Like gardens, his eccentric sculptures and wall-pieces are three-dimensional drawings; sketches that play with the way we use diagrams, maps, charts and models to depict ideas. He uses strangely modified tables and dissected textbooks to mimic the way numbers, letters and symbols become codes that define our understanding of the universe as well as underlining the uncertainty of that knowledge. Cullen recounts Italo Calvino's story of Mr Palomar's comical attempts at stargazing. After peering at a torch-lit star map, Palomar is unable to see anything in the dark until his eyes have adjusted. By the time he can see stars again, he has forgotten their arrangement on the chart. By repeating this routine, he negotiates the territory between diagram and reality. There is a similar humour in Cullen's assemblages, which could be seen as a science display from a Monty Python show, with the slightly surreal way they invert the usual physicality of common objects. Hundreds of bright yellow pencils are obsessively arranged in rows to penetrate and support old pieces of cut-up furniture, while pencil sharpener globes rise out of old books, which are glued shut, carved into and decorated with enigmatic jottings. An upturned stool, also balanced on pencils, is missing a leg, rendering it useless as a stool and reinforcing its new role as a depiction of surface, volume, gravity and more esoteric forces. It recalls the early conceptualism of Marcel Duchamp, who in 1917 famously named a urinal Fountain and placed it in a gallery, shifting its usual role to that of both art object and the representation of an idea. Duchamp also used a stool in the place of a plinth to display an upturned bicycle wheel, blurring the distinction between art object and its framing support. Cullen also acknowledges that his upturned furniture recalls a 1961 work of Italian artist Piero Manzoni, who presented an upside down plinth, slyly suggesting that the plinth supports the entire world and therefore that anything can be considered art. Everything engages concepts of a similarly grand scale, evoking through its title, the "Theory of Everything", a holy grail for mathematicians and physicists seeking a single law explaining the properties of all known phenomena. However, Cullen doesn't see his work as being quite as definitive. "I think it's more inclining towards the ridiculous rather than ultimately being something which can encompass all, and that's not intended as a comment on science. I think that it is really an amateur attempt at trying to do something in that way, which somehow is ultimately doomed to failure." Exhibition *What: Everything, by Paul Cullen *Where and when: 40 George St, Mt Eden, to Nov 6 (Thu-Sat only) A theory of everything |
October 26, 2004
Divine order for a gifted maths tutorBy Michael Winkler Gail Costello will become one of the first four teachers to be recognised as a highly accomplished teacher of mathematics by the Australian Association of Mathematics Teachers next year. Ms Costello says: "I think it is crucial that we recognise everybody can do maths. I've met people who have been scarred for life by bad experiences with maths at school. Seeing students start to love something you feel passionate about is so rewarding." What makes a great maths teacher? "Someone who knows the subject, knows how students learn, is passionate about maths and kids, and is always looking for new ways to communicate the information," Ms Costello says. She has just left Methodist Ladies College, where she was vice-principal, to pursue further study - not in mathematics, but divinity. Others might not see the connection, but Ms Costello does. "If you look at figures like Pascal and Descartes, mathematics and theology have often gone together. I am quite convinced that God is a mathematician!" Divine order for a gifted maths tutor |
October 25, 2004
Kenneth Iverson, Mathematician 1920-2004By JACK KAPICA Kenneth Iverson was a mathematician whose intense fascination with words and syntax led him to create an early programming language that inspired a generation of computer programmers. Born in Alberta in 1920 and educated in a one-room schoolhouse, Mr. Iverson harboured little intention of going to college, instead absorbing himself in textbooks his older brothers brought home, eventually teaching himself calculus. But the Second World War intervened; he became a flight engineer specializing in reconnaissance. When the war ended, a fellow serviceman who had taken note of his love of learning, told him, ''If you don't go to university I'm going to go down and beat your brains out,'' his widow, Jean, recalls. So when he was demobilized, Mr. Iverson enrolled at Queen's university, earning a Bachelor of Arts degree in mathematics. He continued his education at Harvard University, where he graduated with a Master of Arts and, in 1954, a doctorate in applied mathematics. He stayed at Harvard to teach mathematics and there developed a system of notation to describe to students a method of handling large groups of numbers. He published a book on it in 1962, titled A Programming Language, a name that was subsequently contracted to APL. International Business Machines Ltd. took note of what he had done, and in 1962 lured him from Harvard to develop APL as a language for use in its new IBM System 360 mainframe computers. He took three colleagues along with him to IBM -- Larry Breed, Roger Moore and Dick Lathwell -- who were later awarded the Grace Hopper Award for the subsequent implementation of APL based on the principles laid down by Mr. Iverson. As the computing revolution picked up speed, APL was not relegated to a dark corner of history, but embraced by a growing number of programmers who were in awe of its "elegance," a word the community uses to describe an especially simple but powerful language. APL's popularity lay in its ability to manipulate large amounts of data, therefore making it ideal for programming databases. Although it is compact, simple and easy to learn, APL's use of symbols can initially intimidate novice programmers. "You could write a program using APL 10 times faster than with any other languages," recalls Lib Gibson, an executive with Bell Canada who worked with Mr. Iverson in his later years at I.P. Sharp Associates Ltd., a Toronto-based time-sharing company. Initially, it was bundled with what are considered to be the world's first microcomputers, made in Toronto by MCM Computers Ltd., in 1974 -- at least two years before Apple introduced its desktop machine. APL maintained its devotees well into the 1980s, when it become a "niche language," said his son Eric. During his later years Mr. Iverson developed an advanced version called J -- more formally, the J Notation for the APL language -- that could run on a variety of computers. But he will remain known for APL. For more than 35 years he managed to turn it into a successful commercial property and, in the process, won the Harry Goode Award in 1975, the A.M. Turing Award in 1979, the IEEE Computer Pioneer Award in 1982 and the National Medal of Technology in 1991. His ability to create such languages came from his "sheer enjoyment of language and words," recalls his daughter Janet Cramer. "He read dictionaries like people read novels." Mr. Iverson thought it was important that language, both English and mathematics, could communicate clearly and concisely, she said, and he was always finding relationships between things. "If there was anyone who would have come up with the Universal Theory of Everything, it would have been him." Mr. Iverson was no pedant, however. A gregarious man, he attracted many young people around him. "He was a natural teacher," said his widow Jean. "He couldn't change a light bulb without showing the kids how it was done." In fact, he and his wife looked after many children, particularly during the years Jean worked in a youth advocacy program. The Iversons had four children of their own -- sons Eric, Paul and Keith and one daughter, Janet -- but still found room for some of Jean's troubled children. Two of them -- Robin Dick and Sherry Natusky -- ended up staying at the Iverson home, and are now part of the Iverson family. Mr. Iverson became a Fellow at IBM, a signal honour given only to its most prized employees. When he retired in 1980, he moved back to Toronto, where he worked at I.P. Sharp until 1987. For the rest of his life he dedicated himself the exploration of computer languages. "He didn't stop thinking or working in 1987, his son Eric said, "but continued his aggressive research until he died." And that's how he died. He was sitting at his computer at home, working on the J language, when he was felled by a stroke. Kenneth Iverson, mathematician, was born on Dec. 17, 1920, in Camrose, Alta. He died on Oct. 19, 2004. He was 83. Kenneth Iverson, Mathematician 1920-2004 |
October 25, 2004
What Makes an Equation BeautifulBy KENNETH CHANG CONSIDER a verbal description of the effect of gravity: drop a ball, and it will fall. That is a true enough fact, but fuzzy in the way that frustrates scientists. How fast does the ball fall? Does it fall at constant rate, or accelerate? Would a heavier ball fall faster? More words, more sentences could provide details, swelling into an unwieldy yet still incomplete paragraph. The wonder of mathematics is that it captures precisely in a few symbols what can only be described clumsily with many words. Those symbols, strung together in meaningful order, make equations - which in turn constitute the world's most concise and reliable body of knowledge. And so it is that physics offers a very simple equation for calculating the speed of a falling ball. Readers of Physics World magazine recently were asked an interesting question: Which equations are the greatest? Dr. Robert P. Crease, a professor of philosophy at the State University of New York at Stony Brook and a historian at Brookhaven National Laboratory, posed the question in his Critical Point column and received 120 responses, nominating 50 different equations. Some were nominated for the sheer beauty of their simplicity, some for the breadth of knowledge they capture, others for historical importance. In general, Dr. Crease said, a great equation "reshapes perception of the universe." The mathematical equation providing the speed of a falling ball is just four symbols long: v = gt. With it, you can calculate the ball's speed 2.5 seconds after release. (That's g, the acceleration of gravity, which is 32 feet per second squared, multiplied by 2.5 seconds, giving an answer of 80 feet per second.) This equation, a mainstay of high school physics, was not among those nominated as the greatest of all time, which is not surprising, because its use is limited. The pull of gravity varies with distance from the Earth's surface, and the equation also suggests that an object's speed could go on increasing toward infinity, past the known limit of the speed of light. The top vote-getters in the magazine poll were Maxwell's equations - a set of four that describe the interplay between electric and magnetic fields - and Euler's equation, a purely mathematical construct that finds wide use in theoretical physics. "It combines rational and irrational numbers to get zero," Dr. Crease said. "It's bizarre." Among the other nominees were the all-familiar E=mc2 from Einstein, which equates energy and matter; the Pythagorean theorem; and Isaac Newton's F=ma. Prominent scientists have their own favorites. Dr. Brian Greene, a theorist at Columbia University and author of "The Elegant Universe," cites Einstein's general relativity equations, which describe how matter warps the fabric of space, and the Schrödinger equation, the fundamental equation of quantum mechanics. "With a mere handful of symbols, those equations describe almost all phenomena in the universe," he said. "It is so amazing how so much of the universe is encapsulated in a few symbols." Dr. Neil deGrasse Tyson, director of the Hayden Planetarium, said he was disappointed that E=mc2 did not receive more votes. "I think the general physics community, they're a little bored with the equation," he said. "It's risen to the level of icon that people no longer pay attention to." But Dr. Tyson said that the equation was a fundamental underpinning not only of the universe, but also of the first five chapters of his book "Origins." "It's simple, yet profound," he said. "I'd be less impressed if it were a big complicated equation." A half-dozen of Dr. Crease's respondents, including Richard Harrison of Calgary, Alberta, chose one of the simplest possible equations. Mr. Harrison wrote: " '1 + 1 = 2' is the fairy tale of mathematics, the first equation I taught my son, the first expression of the miraculous power of the mind to change the real world. I remember my son holding up the index finger, the 'one finger,' of each hand as he learned the expression, and the moment of wonder, perhaps his first of true philosophical wonder, when he saw that the two fingers, separated by his whole body, could be joined in a single concept in his mind." What Makes an Equation Beautiful |
October 23, 2004
Tell me in joyful numbers…Syed Fattahul Alim The ability to count, like the ability to narrate, things in the objective world is a mental faculty that man is born with. He began to count immediately after he learnt to talk. Once it was thought that the ability to count is something that is not instinctive-- it is an acquired ability, a later-day development. But researches in behavioural science, especially those conducted on the lower animals have demonstrated beyond doubt that the ability to count is not an exclusive domain of man. And in man's case, his mathematical faculty is inborn. The numbers, whether they are intuitive or acquired, lie at the root of the phenomenal development of the modern-day science and technology. If words are the language of literature or worldly conversations, numbers make the language of science. The basic laws of the exact sciences are nothing but numerical relationships among the various properties of material objects. Scientists try to relate different properties of objects under study through quantitative relations using numbers. And the numbers come into the picture when they carry out the activity called measurement on the objects and the way in which they are connected with each other But that is about numbers as used in science as well as in the day-to-day business of life. These are in fact utilitarian uses of numbers. Such uses of numbers do not have the element or aura of mystery about them. They are mundane, tame and predictable. Now think about the numbers that we fear or love. Take the number 13, for example. People about everywhere in the world avoid the 13th day of any month for holding any auspicious occasion. While some numbers are treated as inauspicious, there are other numbers, such as 7, which is considered as the harbinger of good luck. There is the occult science of numerology which concerns itself with the auspicious or ominous properties of numbers. Persons are born with certain biases for or against special numbers, the numerologist would say. The sixth-century BC Greek philosopher and mathematician of Samos, Pythagoras believed that numbers are everything; all relations in the universe can be reduced to numbers. Such generalisation by Pythagoras and his pupils was prompted by their observations in the field of astronomy, mathematics and music. The study of stringed musical instruments, particularly the properties of the vibrating strings was the basis of their notion. The Pythagoreans, who were the followers of Pythagoras's thoughts and philosophy, (he also founded a religion and a philosophical society in Croton of southern Italy. The religious movement he initiated had some elements similar to the concept of Avatar or reincarnation in Hinduism) discovered that the ratios of the lengths of the vibrating strings that produce harmonious tones bear certain ratios with one another. The numbers that express these ratios are whole, integral digits, not fractional ones. So, the integral numbers, which are the natural numbers such as 0, 1, 2, etc., have some deeper significance, a mysterious connection with the greater order of things in the universe. In a similar vein the movements of the heavenly bodies in the Celestial Sphere was also governed by certain numerical relations which are nothing but the reflections of the greater cosmic harmony. The Pythagoreans called it the Music of the Spheres. The basic numbers representing the musical ratios, (the figures 4:3, 3:2 and 2:1) were thought to be the basis of structure of the universe itself. The philosophers of the classical antiquity were not blessed with the benefits of modern science and technology and as such they might have been prone to such mysticism about numbers. What about modern scientists, mathematicians or philosophers? Have they been entirely able to purge themselves of the mysticism that the ancients had about the numbers? There are certain numbers that still baffle the scientists. Suppose the velocity of light. It is a physical constant called 'c,' that pops up in electromagnetic equations. But Einstein made this number immortal by making it the limit of motion. There are similar other constants set the limits between different levels of physical realities. As for instance the Planck's constant denoted by the letter 'h'. This is also a number that draws the line between physical macro and the micro world. The physical scientists have to deal with dozens of such constants and they have learnt to live with these amazing numbers without question. The numbers that we have been talking about are connected with the physical sciences. They have something to do with the non-living world of the inert objects. Has the living world any bias for any such number strange numbers? There is a number called the 'golden ratio' which is expressed by the Greek letter Ö. It is a strange number that has something to do with beauty. The architects in their design of the buildings have been using this number from the time of the Greeks. The father of Geometry, Euclid of Alexandria, first described the uses and properties of this number. He also found its exact value to be an incommensurable number equivalent to 1.6180339887… or (1+v 5)/2. The columns of leaves on the vertical stem of a plant arrange themselves along a certain angle. It has been found that this angle (137.5 degree) is nothing but the part of the whole 360 degrees angle round the stem divided according to the golden ratio. The spirals the seashells have also follow the golden proportions. Science and mathematics are like the two hands of man. They developed together and complemented each other in the process. While growing together as twins in the house of human knowledge, they laid bare many unnecessary prejudices that people attributed to both. Man's fascination with the numbers has hardly ceased. Neither has the behaviour of numbers, especially of the very large ones could be unlocked. There are certain numbers called the prime numbers that have remained as elusive as ever. The greatest brains in science and mathematics, till now, have spent sleepless night over prime numbers in order that their incidence in the system of natural numbers may be made predictable. But so far no tangible progress could be made in this regard. Mathematicians in pursuit of the biggest ever prime number are greatly relieved that supercomputers have now appeared on the scene to help them break up the largest conceivable numbers to separate the biggest prime number discovered till date. Tell me in joyful numbers… |
October 23, 2004
Mathematical modelling is new buzzword in medicineOver the weekend, a few senior medical delegates were busy clicking away at their snazzy laptops at a suburban hotel. These clinicians, oncologists and gastroentrologists listened in rapt attention as a young man doled out a few mathematical formulae. At the first International Conference on Gastroenterology, city doctors were urged to shed their traditional phobia towards numbers. Instead, these medical practitioners were encouraged to explore the benefits of 'mathematical modelling'. Armed with up-to-date numerical data and mathematical programs, UK specialist Dr Simon Grummett spoke on the application of such modelling techniques for treatment of various ailments, including cancer. ''There is tremendous potential for using numerical readings to study the effects of the drug on the patient. Globally, this system is gradually being applied,'' explains Dr Grummett, professor of oncology, Oxford University. The accountant-turned-oncologist has been using mathematical formulae for six years to treat patients with colon cancer. He swears by the technique. Dr Grummett said that by comparing the growth of blood supply to a tumour and its invasion into the normal tissue, a mathematical model could predict what would happen to the tumour, whether it would respond to treatment or not. But most city doctors admitted to being intimidated and overwhelmed by all this number-crunching. They say that they prefer leaning on experience over relying on statistics for treating patients. ''Most of us were exposed to some statistics in med school, but the subject was often ignored. It's biology and anatomy that intrigues us more,'' said a candid Dr K G Nair, cardiologist, Holy Family hospital, Bandra. But a few sessions of data analysis convinced the greying experts about the importance of the discipline of mathematics and the increasing use of computer programming for diagnosis and treatment. ''It should become a serious part of our medical curriculum. Although bio-informatics does expose the students (to mathematics in medicine), such specialised techniques can open up a variety of approaches,'' said Dr M Yeolekar, dean, Sion hospital. Mathematical modelling is new buzzword in medicine |
October 23, 2004
Can Computers Untangle the Neural Net?By Karen Heyman On a coffee break from the Methods in Computational Neuroscience class he codirects at the Marine Biological Laboratory (MBL) in Woods Hole, Mass., Bard Ermentrout is chatting with a student. It's unusually difficult to follow the conversation, because Ermentrout, a professor in the department of mathematics at the University of Pittsburgh, is talking entirely in equations--in near parody of most biologists' worst fears of a field populated largely by physicists and mathematicians. But despite the alien nature of the conversation, the questions that computational neuroscientists ask are becoming the questions that all neuroscientists ask. Indeed, "computational neuroscientist" eventually may become a redundant term. Computational neuroscientists are not to be confused with scientists who treat the brain as a biological blueprint for computer prototypes. Those researchers, often with computer science degrees, work in fields such as artificial intelligence, neural nets, or neuromorphic engineering. For the computational neuroscientist, the computer is not a goal, but a tool to create predictive models constrained by biology. There are those, such as field pioneers Sejnowski and Christof Koch at California Institute of Technology, who employ top-down, conceptual "simple" models, with only as much detail as necessary to derive fundamental principles. And then there are others, such as Jim Bower of the University of Texas at San Antonio, also a forefather of the field, who build data-driven, bottom-up models in which one feeds a supercomputer precise, mathematical descriptions of the individual pieces in order to create detailed simulations of individual neurons and neuronal networks. Thus, computational neuroscientists consider such questions as how many times per second a neuron spikes (called a rate code or independent-spike code), what patterns it makes with those spikes (a temporal or correlation code), and whether rate codes or temporal codes are important. A rate code considers how many times a neuron spikes in a given period of time, say 10 spikes per second. In a finer-grade temporal code, exactly when each individual spike occurs is significant as well. So neurons A and B may both fire 10 times in the same second, but if A fires seven times, pauses, then fires the last three times, and B fires five times, pauses, then fires five again, they are considered to be conveying different messages. But that is just the beginning of the code; what really matters is how populations of cells fire. "Information theory provides the natural mathematical language to ask questions about the neural code," says William Bialek of Princeton University. "Using information theory we can measure how much each spike tells us about the outside world, and we can start to dissect the language of the brain. If two different cells spike at the same time [i.e., synchronously], does this convey two independent pieces of information, or does it form a new symbol in the code, in the same way that we can put letters together to form new symbols in English, like 'th'?" To anyone considering a career in computational neuroscience, Abbott offers this advice: "You need a little math." Of course, as a physicist, his idea of a little math means at the very least calculus and college-level linear algebra. In computational neuroscience, as in bioinformatics, many of the breakthrough techniques are in the form of the applied math (featured in journals such as Neural Computation and the Journal of Computational Neuroscience) that is needed to analyze high-dimensional data sets, including neuronal population codes and data generated from functional magnetic resonance imaging. "There are orders of magnitude more interconnections in these systems," says Abbott. "In many physical systems researchers have concentrated on nearest-neighbor couplings; each unit might couple to its neighbor on the left or the right or above and below it. But in a system like a vertebrate brain, there are thousands of interconnecting synapses per neuron that must be considered." In addition, says Abbott, events occur over a wide variety of time scales in biological systems. "In most physical systems that mathematicians like to analyze, things change over a single time scale, say a second. But in a biological system changes range from milliseconds to days, months, and even years. So you have this incredible dynamic range you have to take into account. That one is an enormous challenge." Can Computers Untangle the Neural Net? |
October 21, 2004
Television commercials and AristotleSRINIVASAN SWAMY In 1988, the journal The Mathematical Intelligencer invited its readers to rank the proofs of a selection of 24 theorems for their beauty. The proof for 'incommensurability' was ranked seventh! When I mentioned this during an internal presentation, one of my colleagues asked me: "What has this got to do with advertising?" While he did have a point, I was ready for him. I told him that the gentleman who had supplied the proof and introduced the ingenious method called reductio ad absurdum (which lovers of mathematics still appreciate) also gave us the Theory of Rhetorical Discourse! Not many realise that the principles laid down by Aristotle in his Theory of Rhetorical Discourse 2,000 years ago have withstood the test of time and continue to guide the professionals who practice persuasion even today. He defined 'rhetoric' in terms of 'observing in a given case the available means of persuasion'. And 'available means' encompassed a range of appeals; some grounded in logic — called logos, others in emotion — pathos, and still others in the communicator — ethos. Now, that sounds very similar to the creative routes of a campaign which advertising professionals recommend: • Logical demonstration of superior product performance • Emotional appeals or • Celebrity endorsements In this receiver-oriented view of persuasion, Aristotle urged communicators to select the means of persuasion based on understanding and knowledge about the audiences to whom the communication was directed. The power of the logical argument was considered the most important tool of persuasion and at the heart of the logical argument was the concept of proposition and proof. Aristotle also invented structures to enable the communicator to organise his information and thoughts to create persuasive arguments. Marketers, by definition, are in the business of persuading their audiences to take some future action i.e., buy the brand. For this deliberative rhetoric, Aristotle's system of presentation — which some of us call the campaign structure — is fundamental to many a TV commercial even today. All those who understand what 'selling ideas' in advertising is all about, and those of us who talk about 'consumer insights', will immediately connect with the principle underlying the concept of persuasive proofs and propositions: these do not change the existing belief systems of the audiences, but rather build on them. The structure has four parts: 1. Exordium or the bait — which is essentially a statement that arouses audience interest, creates goodwill or puts them in a receptive frame of mind. Take Mark Antony's famous speech: 'Friends, Romans and countrymen, I've come to bury Caeser, not to praise him'. He ended up doing exactly the opposite, but Mark Antony did not start his speech by stating his intent upfront. Had he stated his intentions at the beginning, he probably would not have completed his speech. Instead, he put the audience in a receptive frame of mind by building his speech on points of agreement. 2. Narratio — the factual background wherein you pose the question or the problem that has to be answered. As was posed in this recent TV commercial, which I thought was quite entertaining, but am not sure if the audiences it was meant for feel the same. A frog turns into a prince and says: 'What knots? What tangles? What rubbish!' 3. Conformatio - where you resolve the issues that have been raised. • Demonstrate the benefits — 'stubborn stains have disappeared, no more tangles, whiter than whites, as good as new' • Appeal to the viewer's self-interest • Demonstrate superiority 4. Peroratio — is that part of the structure where you state the pay-off or benefit of adopting the recommended course of action — you get the job, mom-in-law appreciates you, everybody appreciates you, you look younger or transform into a handsome sexy young man! Quite a few TV commercials, which use logos as a persuasion tool, use this highly successful 'Bait-Problem-Solution-Payoff-Call for Action' format as their structure. Wonder how many realise that this structure is actually over 2,000 years old! Television commercials and Aristotle |
October 21, 2004
New Genomic Method Can Identify Disease-Causing Genes with Unprecedented Precision and SpeedPALO ALTO, Calif., Oct. 21 /PRNewswire/ -- A novel computational method to detect disease-causing genes accurately and rapidly was announced by Roche scientists in the October 22 issue of Science. This approach, another innovation in computational genetic analysis from Roche scientists, promises to accelerate markedly the discovery of mouse correlates of genetic risk factors for human disease. The new approach enables researchers to identify a single causative genetic factor by correlating a pattern of observable physiological or pathological differences among selected strains of mice with a pattern of genomic variation. Using conventional methods, pin-pointing a gene contributing to disease risk could take five scientists five years. With Roche's latest innovation, which has up to 1,000-fold greater precision than current methods, a single researcher may accomplish the task in a single afternoon. The method takes advantage of the block-like patterns of genomic variation in selected mouse strains, as illustrated on the cover of Science in which the article appears. "Our hope is that this new computational approach will increase the utility of the vast amount of DNA sequence information available today and help researchers more fully leverage mouse models of human disease to identify genes contributing to disease risk and drug response," said Gary Peltz, M.D., Ph.D., head of Genetics and Genomics at Roche Palo Alto. "It will help researchers understand the relationship between trait differences and variations in the mouse genome, which will move us a long way toward understanding the impact of human genetic differences. As that happens, we should be able to translate genetic data more effectively and efficiently into the development of both novel diagnostic tools and new medicines to treat human diseases." In this regard, Roche Palo Alto is engaged in research with several leading universities and government institutions to leverage the power of the new computational technique. The studies are directed toward better understanding the genetic causes of a range of human diseases and toward pharmacogenetic analysis of how various drugs that are used commonly to treat disease work in humans. The paper, entitled "In Silico Genetics: Identification of a Novel Functional Element Regulating H2-E alpha Gene Expression," reports that the new computational algorithm correctly identified the genetic basis for strain- specific differences in several biologically important traits, including differences in drug metabolism. The examples presented in the paper demonstrate the ability of the methodology to identify causative genetic factors accurately for a wide range of trait data. The technique also has the potential to uncover currently unknown genetic factors contributing to a host of different diseases. Roche scientists first published a computational method for mouse genome analysis in the June 8, 2001 issue of Science. That method predicted regions of a mouse chromosome responsible for a trait difference. The predicted regions contained hundreds of genes and the results were assessed by relative (percentile ranking) statistical criteria. The new method offers the same analytic speed, but is much more exact, linking a single gene to a trait difference. This method eliminates the need for follow-up studies to mine large chromosomal regions, saving researchers from months to years of experimentation. In addition, the results are assessed by absolute (p-value) statistical criteria, which give researchers greater confidence in their analyses. The pattern of genetic variation analyzed by this new computational method was created by mining a database of common genetic markers, called single nucleotide polymorphisms (SNPs), covering 1,900 genes across 16 commonly used inbred mouse strains. That database was created by Roche scientists in Palo Alto and Alameda, Calif., and Basel, Switzerland, and was partially sponsored by a National Human Genome Research Institute Grant. It was recently selected as the top SNP database by respondents to a survey of scientists conducted by Genome Technology and GenomeWeb Daily News. The genetic pattern maps are now available to the public for the first time as part of the Roche SNP database web site (http://mouseSNP.Roche.com). The web site delivers a wealth of genetic information about many mouse strains that are commonly used to model human disease. The mouse genome is similar to that of humans and mice can be genetically manipulated. Because of this, the mouse is the most commonly used experimental model for studying human disease, and the "mouse to man" approach is widely used. Since analyses of mouse genetic models by traditional methods are very time-consuming and costly, this novel computational approach represents a major advance for this entire field of research. Study participants from Roche included Guochun Liao, Jianmei Wang, Jingshu Guo, John Allard, Janet Cheng, Anh Nguyen, Gary Peltz, and Jonathan Usuka from the Roche Palo Alto campus, and Dorothee Foernzler from the Roche Center for Medical Genomics in Basel, Switzerland. Other study participants included: Steve Shafer from Stanford University, Stanford, California; Anne Peuch from the Centre National de Genotypage, France and John D. McPherson from the Washington University School of Medicine, St. Louis, Missouri. New Genomic Method Can Identify Disease-Causing Genes with Unprecedented Precision and Speed |
October 20, 2004
TANGO; towards faster prognosis of Alzheimer's and Parkinson's diseases?A large number of diseases - including Alzheimer's disease, Parkinson's disease, and mad cow disease - are the result of proteins that erroneously assume the wrong shape, causing them to stick to each other. This phenomenon is perceptible, but up to now it has been difficult to predict. Researchers from the Flanders Interuniversity Institute for Biotechnology (VIB) at the Free University of Brussels (VUB), in collaboration with a German research group, have developed TANGO - a statistical method that can predict the susceptibility of proteins to sticking together. Thus, for the first time, TANGO enables the prediction of risky protein alterations that underlie this group of diseases. When protein structure goes awry All living creatures, including humans, are made up of cells, and the vital functions within these cells are executed by proteins. The hereditary information for the production of proteins - including, among other things, their structure and length - is contained in our genes. But in order to be able to function properly, a protein must also fold itself correctly into its 3-dimensional structure. Sometimes this goes wrong and the proteins stick together, making them toxic and causing diseases like Alzheimer's. TANGO makes prediction of faulty protein structures possible Until recently, it was always thought that proteins stick together arbitrarily. But now it has become clear that a universal mechanism lies behind this process. Certain structural characteristics in proteins determine their susceptibility to sticking together. Using this information, Joost Schymkowitz and Frederic Rousseau have developed TANGO, a mathematical algorithm that looks at a large amount of data - including alterations of the protein and environmental factors - to indicate the degree of probability that particular proteins will stick together. TANGO thus opens possibilities for new diagnostic techniques for diseases that are caused by proteins that stick together erroneously. The VIB researchers also expect that TANGO will enable more efficient production of proteins for medical or industrial applications. The yield of these production processes is often low, because the proteins stick to each other and are therefore difficult to purify. With TANGO, one can determine under what conditions the solubility of the therapeutic proteins is large enough to purify them easily. Relevant scientific publications On 12 September, Schymkowitz and Rousseau's research was published online on the website of the authoritative journal, Nature Biotechnology (www.nature.com/nbt) Fernandez-Escamilla et al. TANGO; towards faster prognosis of Alzheimer's and Parkinson's diseases? |
October 20, 2004
Those Brilliant Fall Outfits May Be Saving TreesBy CARL ZIMMER As trees across the northern United States turn gold and crimson, scientists are debating exactly what those colors are for. The scientists do agree on one thing: the colors are for something. That represents a major shift in thinking. For decades, textbooks claimed that autumn colors were just a byproduct of dying leaves. "I had always assumed that autumn leaves were waste baskets," said Dr. David Wilkinson, an evolutionary ecologist at Liverpool John Moores University in England. "That's what I was told as a student." During spring and summer, leaves get their green cast from chlorophyll, the pigment that plays a major role in capturing sunlight. But the leaves also contain other pigments whose colors are masked during the growing season. In autumn, trees break down their chlorophyll and draw some of the components back into their tissues. Conventional wisdom regards autumn colors as the product of the remaining pigments, which were finally unmasked. In other words, autumn leaves were a tree's gray hair. But in recent years, scientists have recognized that autumn colors probably play an important role in the life of many trees. Yellow leaves get their color from a class of pigments called carotenoids. Another group of molecules, anthocyanins, produce oranges and reds. Trees need energy to make carotenoids and anthocyanins, but they cannot reclaim that energy because the pigments stay in a leaf when it dies. If the pigments did not help the tree survive, they would be a waste. What's more, leaves actually start producing a lot of new anthocyanin when autumn arrives. "The reds are not unmasked-they are made in autumn," said Dr. David Lee, a botanist at Florida International University. Evolutionary biologists and plant physiologists offer two different explanations for why natural selection has made autumn colors so widespread, despite their cost. Dr. William Hamilton, an evolutionary biologist at Oxford University, proposed that bright autumn leaves contain a message: they warn insects to leave them alone. Dr. Hamilton's "leaf signal" hypothesis grew out of earlier work he had done on the extravagant plumage of birds. He proposed it served as an advertisement from males to females, indicating they had desirable genes. As females evolved a preference for those displays, males evolved more extravagant feathers as they competed for mates. In the case of trees, Dr. Hamilton proposed that the visual message was sent to insects. In the fall, aphids and other insects choose trees where they will lay their eggs. When the eggs hatch the next spring, the larvae feed on the tree, often with devastating results. A tree can ward off these pests with poisons. Dr. Hamilton speculated that trees with strong defenses might be able to protect themselves even further by letting egg-laying insects know what was in store for their eggs. By producing brilliant autumn colors, the trees advertised their lethality. As insects evolved to avoid the brightest leaves, natural selection favored trees that could become even brighter. "It was a beautiful idea," said Marco Archetti, a former student of Dr. Hamilton who is now at the University of Fribourg in Switzerland. Dr. Hamilton had Mr. Archetti turn the hypothesis into a mathematical model. The model showed that warning signals could indeed drive the evolution of bright leaves - at least in theory. Another student, Sam Brown, tested the leaf-signal hypothesis against real data about trees and insects. "It was a first stab to see what was out there," said Dr. Brown, now an evolutionary biologist the University of Texas. He studied 262 tree species, noting the leaf color and number of aphid species specialized on them. Dr. Brown found that trees with bright autumn leaves tended to be the victim of more specialist aphids. The correlation supported the leaf-signal hypothesis. Dr. Hamilton did not argue that the evolution of leaf signals would make all trees brilliantly colored. Instead, he said, only species that were under heavy attack experienced this evolutionary pressure. Those Brilliant Fall Outfits May Be Saving Trees |
October 20 2004
Scientists gingerly tap into brain's powerBy Kevin Maney, USA TODAY A 25-year-old quadriplegic sits in a wheelchair with wires coming out of a bottle-cap-size connector stuck in his skull. The wires run from 100 tiny sensors implanted in his brain and out to a computer. Using just his thoughts, this former high school football player is playing the computer game Pong. It is part of a breakthrough trial, the first of its kind, with far-reaching implications. Friday, early results were revealed at the American Academy of Physical Medicine and Rehabilitation annual conference. Cyberkinetics Neurotechnology Systems, the Foxborough-based company behind the technology, told attendees the man can use his thoughts to control a computer well enough to operate a TV, open e-mail and play Pong with 70% accuracy. "The patient tells me this device has changed his life," says Jon Mukand, a physician caring for him at a rehabilitation facility in Warwick, R.I. The significance of the technology, which Cyberkinetics calls Braingate, goes far beyond the initial effort to help quadriplegics. It is an early step toward learning to read signals from an array of neurons and use computers and algorithms to translate the signals into action. That could lead to artificial limbs that work like the real thing: The user could think of moving a finger, and the finger would move. The Cyberkinetics technology grew out of experiments with monkeys at Brown. Donoghue and his research team implanted sensors in the brains of monkeys, and got them to play a simple computer game - chasing dots around a screen with a cursor using a mouse - to get a food reward. As the monkeys played, computers read signals from the sensors and looked for patterns. From the patterns, the team developed mathematical models to determine which signals meant to move left, right, up, down and so on. After a while, the team disconnected the mouse and ran the cursor off the monkeys' thoughts. It worked: The monkeys could chase the dots by thinking of what they'd normally do with their hands. A driving concept is to make the computer control natural, so a patient doesn't have to learn new skills. Cyberkinetics technicians work with the former football player three times a week, trying to fine-tune the system so he can do more tasks. He can move a cursor around a screen. If he leaves the cursor on a spot and dwells on it, that works like a mouse click. Once he can control a computer, the possibilities get interesting. A computer could drive a motorized wheelchair, allowing him to go where he thinks about going. It could control his environment - lights, heat, locking or unlocking doors. And he could tap out e-mails, albeit slowly. At this point, though, the equipment is unwieldy. The computer, two screens and other parts of the system are stacked on a tall cart. The processor and software can't do all the computations quite fast enough to move the cursor in real time - not instantly, the way your hand moves when you tell it to move. And because the sensors tap no more than 100 neurons, the cursor doesn't always move precisely. That's why a one-time athlete can play Pong at only 70% accuracy. Though implanting a chip in the brain might seem alarming, devices are already regularly implanted in brains to help people who have severe epilepsy, Parkinson's disease or other neurological disorders. Scientists gingerly tap into brain's power |
October 20, 2004
Mathematical art: Making the ordinary chaoticBy Kristen DePalma Through unique and creative eyes, one can see beyond what is already evident and can create chaos from the ordinary and beauty from the bleak. With a brilliant mind, one can understand complex problems and derive solutions while curiosity will lead one to look past the answers and yearn to know and prove more. Bill Ralph is a mathematics professor at Brock University, but he has much more to teach to the world than algebra problems. Somewhere along the way, Ralph became fascinated by the algorithms that he was teaching in class and decided to experiment. The results were some of the most unique artwork to come out of mathematical formulas. Beginning with early mathematical models, Ralph transformed simple images into extremely complicated and chaotic visuals. Although they may appear to be paintings, Ralph's artworks are a unique blend of textures and shapes which are generated from algorithms, before being released as Giclee prints. The pieces take a great deal of creativity and plenty of experimentation before completion. "The process is much like creating a sculpture from a pile of leaves by blowing on them," said Ralph. "Each piece is like a little window into an exotic mathematical universe that has never been seen before." Viewing one of Ralph's works is ultimately like seeing into the unification of two generally separate worlds: mathematics and fine art. Even though his pieces are based on rather simple math rules, they carry an increasing complexity and spontaneity which would be almost impossible to duplicate. "As a teacher and mathematician, I hope that people can see the enormous complexity and unity that is inherent within the mathematical objects these images are built around," said Ralph. "My pieces ... parallel my philosophical fascination with the idea that much, if not all, of the complexity of the universe around us is the manifestation of a fairly simple set of rules of interaction." Ralph has always been interested in the visual process; several years ago, he designed a software program called Journey Through Calculus, which helped students to understand calculus through visual text. His mathematically generated artworks will no doubt open students' eyes to the capabilities of mathematics, as well as fine arts. "I think that my work shows my students the universal applicability of mathematical methods, even to areas as unusual and wonderful as fine art," said Ralph. "You can't see this type of work anywhere else; I think that's really exciting." The Brock professor's creations are receiving recognition and will essentially change the way that people view art and math, which is as one entity. Ralph's work has been displayed at the New York Art Exhibition and he recently received the Ontario Office for the Partnerships of Advanced Skills (OPAS) award for the development of educational technologies at universities. "Originally, I created images to help me understand mathematics, but as I've grown as an artist, I think that the images are now more about me understanding myself," said Ralph. "Mathematics is now playing the role of the technique and the medium, but the substance of the art has become something about my personal sense of mathematics and my relationship to it." Ralph carries a great enthusiasm about his work, as he inspires himself with his own interests in the mathematical field. What begins as an equation becomes an abstract masterpiece through a series of techniques which demand a nearly flawless understanding of the subject. "Each piece is a representation of a single mathematical system," said Ralph. "I find it fascinating, philosophically, that such enormous visual complexity and unity can arise out of a single nonrandom mathematical system. We seem to be living in such a system right now." If this is the first time that you have heard of Bill Ralph's mathematical art, it certainly won't be the last. The Brock professor stresses that art is a part of his life which comes natural to him and he will continue to create meaningful works which will surely have their impacts on the art world. "I would probably go on making images regardless of whether people liked them or understood them," said Ralph. "I make art because I feel compelled to." You can view Bill Ralph's exhibit at Rodman Hall until Nov. 21. Mathematical art: Making the ordinary chaotic |
October 20, 2004
Maths is his magic wordAnurita Rathore Ahmedabad, October 18: He has loved and pursued that which many wish to run away from or fear to associate with. Before you think too hard, it's Mathematics we are talking about. And, Dr Jean-Pierre Jouannaud of France is in Ahmedabad to discuss and share science research-related specificities and discoveries pertaining to Formal Mathematics when applied to computer science. He also enjoys climbing, fishing and writing poetry. But we can talk about that later. A Professor of Computer Science at the University of Paris-South, Orsay and at Ecole Polytecnique in Palaiseau, France, Jounnaud is currently ''researching on a programme without bugs''. ''Softwares around the world have bugs and my business is developing computer tools to make sure programmes are bug-free, i.e. they function properly. We employ Verification that ensures that a given software behaves according to its specification, which may further include security requirements. The first Pentium 2 chip had a bug in it and the computer didn't function. It cost Intel $700 million,'' says Jouannaud. He also cites credit card as one of the ''critical cases,'' a system that translates shortcomings into major loopholes. But what role does a mathematician — or Formal Mathematics — play here? ''There has been tremendous development of mathematical logic, formalising notions of reasoning and computation. In Formal Mathematics, the proof of a mathematical statement is itself proven to be correct through a calculation done on a computer. I moved to computer science since I loved solving problems,'' says the professor, who has also been an international research fellow at Stanford Research Institute at Palo Alto Institute, California and is currently a member of the board of the European Association for Theoretical Computer Science. Also a member of scientific committees for the NCSR (National Center for Scientific Research), Jouannaud is in India to tap the mathematically inclined talent of Indian students. He observes: ''In my trip to Ahmedabad, Bhopal, Chandigarh and Delhi, I will aim at attracting Indian students; we have very few Indians in France in the computer faculty. It is also amazing how more than half professors in American universities are either Indian or Chinese.'' Jouannaud's visit also results from the network of the Alliance Francaises and the Scientific Co-operation Section of the French Embassy in India's programme French Science Today, which aims at sharing the latest trends in science in France. Considering people's fear with numbers, how did he take to it himself? ''I was 10 when because of a great Mathematics teacher I found numbers interesting and easy. French words and phrases didn't lure me as much. Later, I moved to computer science and loved solving problems. I have been working in a big European project with seven groups from across Europe and for four years was heading Combination of Computational Logics. Types, another theoretical project, involves 15 groups. However, I am now working on practical projects. Averroes is a project that involves proving how certain protocols can be used in telecommunications. To put it briefly, we are proving that information is not leaked through Java,'' he explains. Explaining how mathematicians always co-ordinate some tool with some problem, Jouannaud says, ''It has taken upto 300 years to find a solution for certain problems. But, it is the capacity of reasoning that is most important coupled with the capacity to do it rightly.'' Getting back to the mathematician's interests, he sums up: ''Poetry can be very interesting, isn't it. Both, reading and writing.'' Maths is his magic word |
October 19, 2004
Insects could hold the key to artificial intellegenceBy Lorraine Pace COMMERCE, Texas -- You have seen the movies in which robots are self-aware and joked about computer cockroaches, but scientists in their quest to understand intelligence and to develop artificial intelligence in robotics have actually turned to the study of insects and primitive vertebrates. They are looking at how these react to stimuli and how they develop memory, striving to replicate it in robotics for use in applications as diverse as medicine and space exploration. "Something eluded us," says Dr. Derek Harter, assistant professor of computer science and information systems at Texas A&M University-Commerce. "We started off by studying human intelligence, but did not find the answers we were searching for." Harter, a 2004 doctoral graduate from the University of Memphis, obtained his degree for research on applications of complex systems concepts to understanding intelligence and applying them to autonomous agents and robotic systems. Initially a pure computer scientist "not interested in how people produced cognition and intelligence, just in producing intelligent machines," his research as part of a team of scientists awarded a $900,000 grant from NASA has led him to straddle the fields of cognitive psychology, mathematics, and neuroscience. His work will eventually be applied to developing robotic space exploration and rescue vehicles that are better able to learn and navigate an unknown environment. "Initially a lot of research into artificial intelligence was focused on human cognition in a top-down approach. The human capabilities that most impressed were chess playing and logical reasoning. "However, we are now developing a different approach, starting with the study of insects and moving to primitive animals with a central nervous system -- like salamanders, in which we have found long-term brain memory." Harter says that psychologists are also interested in using robotic computer intelligence as a platform on which to study and build models of human cognition, even though artificial intelligence systems do not necessarily correlate directly with how humans might produce intelligence. "Cognitive psychologists want to model human cognition in a way that is concrete and real rather than the abstract, which is why they are now looking at robotics," Harter explains. Instinct, a reactive behavior, is being studied and chained together in sequence and applied as artificial intelligence in computers to get the same behavior. Chained sequences linked together create complex behavior, and these behaviors are being combined in an effort to create memory. Even simple mammals have an ability to build a cognitive map of the environment. They build representations of the environment to remember locations, especially of places that have importance to them, so they are able to navigate. Long-term memory is used to solve goals and satisfy needs. "Our first three-year NASA grant covered what is known as "proof of concept," which involves publications and work on theory. We have submitted the second stage of our work to NASA and are awaiting their approval on a $1 million grant. "NASA has something termed a "technology readiness level," which is when technology is considered mature enough to be put on a space mission. We expect it will take about three more years for our technology to reach the lowest level of this rung. "Our immediate focus is on vehicles and robots. If any succeed, there are a vast number of applications where increased intelligence can bring big benefits." Harter is collaborating loosely with scientists at the University of California-Berkley, the NASA Jet Propulsion Laboratory, the University of Florida and the University of Chicago. He is also working closely with his former adviser, Dr. Robert Kozma, professor in computer science at the University of Memphis. He received his bachelor's in computer science at Purdue University and computer science master's with a concentration in artificial intelligence at Johns Hopkins University. "I have always been fascinated by space and computers," Harter says, "so being able to work on this research has been a real treat for me." Insects could hold the key to artificial intellegence |
October 18, 2004
Montessori? Waldorf? Both methods can produce strong resultsEven Flora-Jane Hartford hadn't quite figured it out. The Waldorf school teacher who once ran her own Montessori school discovered that her kids didn't match the usual notions about those renowned and apparently opposite education systems. "I could see for my son, who was the mathematician and scientist, that he would prefer Montessori, but he actually liked Waldorf better," recounts Hartford, educator at the Halton Waldorf School in Burlington, Ont. "For my daughter who was the airy-fairy one, the order and structure of Montessori was a fit." In the long-running debate on the merits of the two pedagogical approaches, Hartford comes down firmly on the side of respecting both. "There are Montessori teachers who disparage Waldorf and vice-versa," she notes. "That's changing, fortunately. I find more interest now on both sides." With over 800 Waldorf schools worldwide and more than 4,000 of Montessori, there are a lot of families scratching their heads about how to make the choice. The good news is that as different as the philosophies are, they are generally observed to both produce strong results in Canada. For Candice Pascal van Alphen, Montessori has worked for her 5-year-old son in settings from Johannesburg to Toronto to Sudbury. "That says a lot about Montessori that the transition from one to the other school is very smooth," says Pascal van Alphen, a former educator herself. She's heard the usual reservations about a lack of play and creativity in the skills-oriented Montessori approach, but responds that, "with all three schools Jadon has been to, I couldn't disagree more." What it means is that parents have to spend at least as much time learning about a specific school as delving into the grand pedagogical traditions that inform Waldorf (started in Austria in 1919) and Montessori (Italy in 1907). "The independence of the schools is important," comments Dom Tassielli, chair of the Canadian Council of Montessori Administrators and co-founder of the Leonardo Da Vinci Academy of Arts & Sciences in Toronto. "It's almost like a local community. Especially Montessori, which is geared to young children. It serves the community and it needs to be independent." Tassielli's own academy has both Montessori and non-Montessori streams, and he isn't dogmatic about everyone cleaving to a single pedagogy for their kids. "When somebody develops an approach or a philosophy, they think theirs is the best of all but I'm not sure I buy that," he says. "If you provide a caring environment, that for me is the No. 1 requirement." Montessori? Waldorf? Both methods can produce strong results |
October 18, 2004
Optical art to bewilder gallery-goersAn art exhibition that opened in Hobart yesterday aims to draw people in to a disorientating space and provide an unsettling, heady experience. The work displayed in the Disorientate - colour, geometry and the body exhibition at the Plimsoll Gallery is influenced by the optical art paintings of the 1960s and 70s. Curator Paul Zika says included in the exhibition is the work of Tasmanian painter Paul Boam, who was at the forefront of optical art produced in the 1970s. Mr Zika says the paintings employ tricks of visual perception using the order of geometry. "They're using the geometry to feign some sort of logic," he said. "We look at the picture and we think this is order, this is rational, we know what's going on in front of us and very quickly that order seems to fall away from us - we're left in that bewildered state." Optical art to bewilder gallery-goers |
October 17, 2004
The geometry of MandelbrotBy Martin Baker Preposterous though it seems, there is something of the lone gunslinger about Benoit Mandelbrot. He is Sterling Professor of Mathematical Sciences at Yale University. And, yes, he is turning 80 next month. But if ever a man fixed the establishment in the eye and shot from the hip, it is Mandelbrot. Next week is the 75th anniversary of the Wall Street Crash of 1929 - now consider this extract from the book Mandelbrot is publishing next month: "The financiers and investors of the world are, at the moment, like mariners who heed no weather warnings." No, no, no. Surely it couldn't happen again? Conventional wisdom tells us that we understand risk so much better now. Those clever hedge fund chappies have got it all sewn up, surely. There has been the occasional disaster, such as the collapse of the huge US hedge fund Long Term Capital Management in the late 1990s. But we all survived. The investment industry has a sophisticated understanding of the riskiness of the market, and by using analytical tools such as chaos theory, the risks are managed and controlled. Unfortunately not, according to Mandelbrot. And he should know. As the founder of fractal geometry and the discoverer of the Mandelbrot set (pictorially represented as beautiful, complex swirls of coral) Mandelbrot is acknowledged as the father of chaos theory. Here are his views of the current state of play: "A few fund managers have experimented with these concepts [of price dependence, whatever that is, and volatility]. They often call it chaos theory - though strictly speaking that is marketing language riding on the coat-tails of a popular scientific trend. In reality, the mathematics is still young, the research barely begun, and reliable applications still distant." Mandelbrot has tweaked a few tails in the academic world, too. James Gleik, author of one of the many books on chaos theory, acknowledges Mandelbrot's contribution to the doctrine, while calling him "exasperating and indispensable". So what is the principal theory of this near-octogenarian, so often described as a maverick? It was clearly a good idea to find out before having lunch with him. Fractal geometry is a way of describing complex, irregular shapes that repeat themselves in nature. Take a leaf on a fir tree, for example. The leaf itself is a mini-me version of the whole tree. And if you look at the individual bits of the leaf, they look like the leaf that looks like the tree. So you have a complex mathematical formula that describes a pattern that keeps repeating itself. Thus a single formula describes lots and lots of data. This is the kind of thing that makes mathematicians happy. The practical applications of the theory are that it can be used to model and describe, though not predict, a huge number of complex phenomena such as coastlines, water and air turbulence, galaxy clusters, and the fluctuations of stock markets and commodity prices (there is an hilarious passage in the book describing early research on cotton price fluctuations that reads like a comedy thriller). By describing such phenomena, fractal geometry moves on from Euclidian geometry, which is confined to smooth shapes and planes. Armed with this very basic understanding of his work, I meet the man himself in a fantastically noisy French restaurant. Mandelbrot is tall, fairly robust, and has the thick-lensed spectacles of academic cliche. He has a Clouseau-esque accent, despite having worked at IBM in the US since 1958. But there is little of Peter Sellers about this man. His mind is like a steel trap. It turns out the publication of The (Mis)Behaviour of Markets - A Fractal View of Risk, Ruin and Reward is not entirely designed to upset the financial community. Mandelbrot, after all, is a teacher with a didactic urge: "Part of my business may be to return mathematics and geometry to its role as an instrument to organise and understand the patterns of nature." At this point readers may be crying out that markets are supposed to be rational phenomena, not natural ones. According to the efficient market hypothesis (a phrase coined by one of Mandelbrot's students, apparently) only rationally relevant information is priced into an asset or market. So what use is a formula that describes the natural world? Mandelbrot's point is that, whatever the causal factors that go into price movements, markets and prices behave as if they are natural phenomena. He says: "My purpose is always to observe the symptoms and have a model of what is being seen. In the case of markets, it is frightening because there are so many people of great brilliance and extraordinary greed who work there. They don't understand the market, but they understand the numbers." It is easy to see why Mandelbrot has a reputation for arrogance. He is, simply, very clever indeed, and is impatient with those who aren't. His fractal theory identifies three states of randomness - mild, slow and wild - and he believes that this model describes market behaviour far better than any other theories of randomness. If he is hard on the financial community, it is because he believes investment managers and advisers are failing investors: "A stockbroker wrote me a very plaintive letter asking why I was giving stockbrokers such a hard time. His argument was that what he did was right 98 percent of the time. Why bother about the events that occur in the rest of the time? The answer is that those events are the ones that really count." It is said that no one hurries like an old man, and Mandelbrot knows that at 79, time is precious. This only exacerbates his impatience with the financial community: "It is quite clear that some portfolios that were declared to be free of risk turned out not to be. They are very good for 90 percent or more of the time, but at the critical moment, they fail. They are just dreadful. Given the inter-connectedness of things, they may lead to very, very embarrassing complications for the whole world." His best attempt to save the world, or at least make society aware of its incomprehension of the riskiness of the markets it depends on so much, is probably contained in a book that is surprisingly entertaining (much credit must go to Richard Hudson, the former European bureau chief of The Wall Street Journal, and co-author). Now Mandelbrot is writing his memoirs - "purely what I remember. I won't research and check dates unless I absolutely have to". They should make compelling reading. Born in Warsaw in 1924, his family moved to Paris in 1936. As a Jew he was lucky to survive the Nazis, and had to move constantly. One possible benefit was the lack of a conventional education (he was tutored by an artist uncle who was also a professor of mathematics). Mandelbrot says he inherited his independent tendencies from a father who saved his own life by refusing to stay on the road with fellow Jews who had been liberated from an internment camp during the war. Mandelbrot senior set out on his own and took refuge in a wood; those who stayed on the road were strafed by Stuka fighter planes. Following his father's untimely death, the youthful Mandelbrot also learned about the market, selling the crude clothing his father had made to eke out a living at distressed seller prices. "It put food in our mouths," he says. Mandelbrot was a brilliant student and held a variety of academic positions, before resigning a post in France in 1958 in order to work in IBM's famous ideas factory (a group of oddball intellectuals paid to come up with great innovations). He was already seen as a cross-disciplinarian and a maverick and had created for himself "a very hostile intellectual environment. France does not like people not to belong". For the last five years he has been at Yale, feted for the long-delayed publication of his paper on fractal geometry. And now, in his memoirs, he's turning those fearsome analytical powers on himself: "There are many things I begin to understand better now." The geometry of Mandelbrot |
October 16, 2004
A Catalog of Random BitsMath Trek by Ivars Peterson Random numbers are a precious commodity, whether expressed as strings of decimal digits or simply 1s and 0s. Computer scientist George Marsaglia of Florida State University, however, likes giving them away. Marsaglia has spent most of his career producing and testing random numbers. He published his first paper on the topic more than 40 years ago. Since then, Marsaglia and his collaborators have identified a variety of flaws in computer-based random number generators, invented more robust versions of existing generators, and developed a suite of rigorous tests to check for randomness. Scientists, engineers, and others use random numbers for tackling a wide range of problems, from modeling molecular behavior and sampling opinion to solving certain equations and testing the efficiency of algorithms. Random numbers are also used in computer graphics for rendering realistic-looking images, such as mottled surfaces and other textures. They play a crucial role in a wide variety of games, including electronic versions of slot machines, lotteries, and other forms of gambling. Indeed, the world of gambling inspired use of the term "Monte Carlo method" to describe any algorithm that employs random numbers. During the 1990s, in a project funded by the National Science Foundation, Marsaglia packed his hard-won expertise onto a CD-ROM to create a catalog of random bits for the information age. Marsaglia's primary purpose was to provide a source of what he termed "unassailable random numbers" for serious Monte Carlo studies and simulations, which often require billions of such numbers. In smaller doses, these apparently patternless strings of bits are available to provide reliable and verifiable random choices in designing experiments and clinical trials, for running sample surveys and choosing jury panels, and in other applications of a statistical nature. The Marsaglia Random Number CD-ROM contained some 5 billion random bits, divided into 60 10-megabyte files, which could be read 1, 8, 16, or more bits at a time, depending on the application. The random bits were made by combining three sources of electronic white noise with the output from the best of the latest crop of deterministic random number generators. The result of combining a truly random string with any other bit string—no matter how patterned—is still random. So Marsaglia also mixed digital tracks from rap and classical music and even a few digitized pictures into some of the 10-megabyte files on the CD-ROM. Both the unadulterated and the mixed files passed Marsaglia's "Diehard" battery of randomness tests, which was also on the disk (along with text files explaining the theory underlying the tests and the random number generators used to create the random bits). "They seem to pass all tests I have put to them—and I have some very stringent tests," Marsaglia says. For example, in one of his Diehard tests he considers a string of random bits as a succession of overlapping 20-letter "words," made up of the "letters" 1 and 0. The first word starts with the first bit of the string, the second word with the second bit, and so on. Given that there are 220 possible 20-letter words, the test involves examining the first 2 million overlapping words derived from the random string to count how many of the possible words appear in the sequence. For a truly random sequence, the number of missing words should be very close to 142,000, according to probability theory. Marsaglia calls this a "monkey test," based on the proverbial monkey sitting at a keyboard and randomly hitting keys. "It's one of my most stringent tests," he says. "No commercial electronic generator of random bits that I know of can pass this test." Interestingly, generators that rely on electronic noise to produce random digits also fail. The playful names of other tests hint at alternative strategies for rooting out patterns in sequences purported to be random: the birthday-spacing test, the count-the-1s test, the parking-lot test, the minimum-distance test, the overlapping-sums test, and the craps test. Checking for randomness is difficult partly because it's the nature of randomness that anything can happen. Ironically, if a generator produces sequences of random numbers that always pass a given test, then it's probably flawed! As mathematician Robert R. Coveyou of Oak Ridge National Laboratory once put it, "The generation of random numbers is too important to be left to chance." A Catalog of Random Bits |
October 15, 2004
Mathematical "truth serum" promotes honestyFew questions come with a clear-cut "right" answer, a solution as clear as the difference between black and white. Speculating on the future, making inferences about the past, and judging the present all involve a seemingly endless palette of greys. But eliciting truthful responses from people - who give subjective answers - is crucial to the surveys and expert analyses that determine government and financial policies. Finding out if someone is answering a question truthfully is a murky process, often inaccessible to the questioner - sometimes even the person answering cannot be sure. Now, Drazen Prelec, a psychologist at the Massachusetts Institute of Technology in Cambridge, US, has devised a scoring system, or "Bayesian truth serum" to encourage people to divulge their honest opinions. The method relies on asking questions in pairs and analysing the relationship between the answers in a so-called Bayesian approach – which assumes that the answers are interlinked. The first question queries the individual. For example: "Will you vote in the next presidential election?" or "Have you had more than 20 sexual partners in the last year?" While the second question goes on to focus on the person's estimate of how many other respondents would answer the same way. It is this perception of what other people's answer might be which gives hints as to whether the person is telling the truth – especially when their answer is the unusual or unpopular option. Conventional wisdom Prelec says if people truly hold a particular opinion, they tend to give higher estimates that other people share it. So if someone did have more than 20 recent sexual partners - but lied about it - that person would probably assume a higher rate of such behaviour in general than someone who had not had so many partners. "Normally we think of our own opinion as something no one else knows," Prelec told New Scientist. "But our judgments are related to those of others." The method is particularly useful for rooting out opinions that contradict conventional wisdom, he says. For example, he describes a situation where two paintings are viewed by a group of 10 people who are then asked, privately, to pick their favourite. Seven people say they prefer painting A, while three vote for painting B. If, on the second question, all 10 people said they thought everyone else would prefer painting A, then those three people expressing a personal preference for painting B might be thought of as a safer bet for having told the truth. That is because, argues Prelec, despite what they thought was more popular, those individuals still chose the other painting. True motivation But Prelec acknowledges the method cannot work as a lie detector to expose untruths at the level of a single question or even a single person. He says it works best on groups of at least 10 people. Using the mathematical formula Prelec has devised, truthful answers automatically produce higher scores. Prelec believes people enjoy scoring highly and so are motivated to be as truthful as possible. But Philip Reny, an economist at the University of Chicago in Illinois, says that such motivation may not be enough if, for some reason, someone has an incentive to lie. He believes that financial incentives might be necessary to use Prelec's system in a survey, which would be expensive on a large-scale. Drew Fudenberg, an economist at Harvard University in Cambridge, US, says the method is intriguing. But he adds that it has not been rigorously tested so "it remains to be seen how useful it is". Prelec plans to test his system using objectively verifiable questions. Mathematical "truth serum" promotes honesty |
October 15, 2004
Can you prove you're not a machine?By Christine Boese I've been thinking about something called the "Turing Test" lately because some of my personal e-mail has come back undeliverable. Evidently the servers, in an attempt to screen out machine-generated spam, think that my e-mail is spam, too. I hate spam as much as the next person, but I resent being censored and unable to communicate certain ideas in online discussions. Sometimes I like to make jokes about how spammers think everyone on Earth is a potential customer for Viagra. But if I use the word "Viagra," my e-mail bounces. Alan M. Turing was a mathematician and a co-founder of computer science and cryptography. He developed the Turing Test. Turing postulated that in developing a thinking machine or "artificial intelligence," the machine shouldn't have to duplicate human thinking processes exactly. All that should be required of a thinking machine is that it be able to "pass" as a human. The Turing Test imagines a questioner and two unseen correspondents, one human and one machine. The machine would pass the Turing Test if the questioner couldn't correctly guess which of the two was the machine. Josh Berman and Amy Bruckman at Georgia Tech created an online interface in the late 1990s that played with another aspect of the Turing Test: a gender test that went beyond gender to guessing all kinds of identities -- religious, ethnic, etc. Their work involved studying how people negotiated identities, made assumptions and acted or lied to outfox the questioner. It illustrated both how fluid online identities are and also how hard it is to lie about who we are. The other day I wrote an e-mail describing a favorite actress and her movies as part of a fun online film discussion. On one film in particular, I said this actress played a "sexpot." I think that is a perfectly fine discussion point about the kinds of two-dimensional roles that are available for women, but with the word "sexpot," one server kicked back my e-mail and banned me from sending e-mail through that server ever again. Actresses are still playing sexpots, but talking about them playing sexpots is verboten?! The servers (machines) suspect that I am a machine. The question is, online, how can I prove that I'm not? In the future, how much of my daily energy will have to go into acting sufficiently un-machinelike just to be able to "pass" as human? More recently, AOL (a division of Time Warner along with CNN Headline News) informed my friends with AOL accounts that they're banned from sending or receiving posts to a private mailing list I own. Our group of about 40 women discusses wide-ranging current events. We don't go out of our way to cuss, but we don't censor our language either. Our virtual air is hardly blue. What's going on here? I'm less likely to blame a culture of rigid morality than I am to blame spammers and pornographers who allow their machines to monopolize certain words, preventing the rest of us from using them in normal conversation and not be suspected as a machine by machine culture. What other words are being removed from our shrinking online vocabulary? Will we be able to write about breast cancer awareness, or will the word "breast" lead to e-mail bouncing? Now I wonder if anyone will be able to read this column because I've used the taboo words. At the very least, parental filters will block it. These are dangerous ideas after all. Can you prove you're not a machine? |
October 15, 2004
Fewer women in computer jobs these daysBy Ed Frauenheim A study released Wednesday by the Commission on Professionals in Science and Technology found a decline in the share of computer science jobs held by women in a recent 20-year period. In 1983, women held 30.5 percent of the jobs in the category of computer systems analysts and scientists, programmers and postsecondary computer science teachers, according to the commission. That figure declined to 27.2 percent in 2002. On the other hand, women have increased their share of jobs in the natural sciences and in engineering, according to the commission. The report comes in the wake of other concerns that have been raised about the U.S. science and engineering work force. Enrollments in leading computer science undergraduate programs are declining, the number of doctorates in science and engineering produced in the United States has dropped in recent years, and critics have argued that research in the country is not as bold as it could be. According to the commission's study, 44 percent of all jobs in the United States were held by women in 1983. By 2003, that level of participation had risen slightly, to 47 percent. The proportion of women in scientific, technological, engineering and mathematical jobs in 1983 ranged from 16 percent to 19 percent, depending on how such professions are defined to 23 percent to 26 percent in 2002, according to the commission. Women increased their representation in all the natural science professions, especially medical science, where they accounted for more than half of all employment in 2002, according to the report. When it comes to engineering, 10 percent of the jobs in 1983 were held by women, according to the commission. That figure rose to 14 percent in 2002. In 1983, women held 30.7 percent of the jobs in the category of mathematical and computer scientists, programmers and postsecondary math and computer science teachers, according to the commission. That figure declined to 29.9 percent in 2002. Fewer women in computer jobs these days |
October 13, 2004
Vantage Learning Announces Release of E-Fence, Advanced Detection of Non-legitimate Responses Submitted for IntelliMetric Automated Essay ScoringVantage Learning today announced the release of E-Fence(TM), a major advancement in detecting the legitimacy of essays submitted to IntelliMetric(TM). E-Fence is the product of several years of research by Vantage Laboratories' Natural Language and Text Processing Research and Development group. IntelliMetric uses a rich blend of artificial intelligence (AI) and the digitization of human expertise to accurately score and assess examinee responses to open-ended essay questions in a range of subjects. E-Fence improves IntelliMetric accuracy and functionality by identifying responses submitted to essays that are not legitimate. At times, IntelliMetric customers wish to restrict the submission of certain essay responses or types of responses for scoring. The E-Fence component ensures that pre-defined responses and/or classes of responses are restricted from scoring. "E-Fence employs several natural language processing, machine learning, and statistical tools to restrict certain essay responses from being scored. E-Fence learns the characteristics of restricted responses and evaluates essays submitted in relation to what it has learned," explains Scott Elliot, Chief Operating Officer of Vantage Learning. "It's as if a barbed wire fence is placed around IntelliMetric to keep out undesirable responses." Research conducted by both Vantage Learning and several third party agencies shows that IntelliMetric scores typically match those assigned by human expert scorers 99% to 100% of the time and show correlations with expert human scorers in the .82 to .92 range. "We expect to see the demand for automated essay scoring more than triple in the upcoming year. The volume of essays to be scored has increased dramatically, and we have responded by improving the accuracy and technical performance of the IntelliMetric engine," said Elliot. According to the company, E-Fence will be available to the market before the end of calendar year 2004. Initially, the E-Fence application will be offered to existing users of the IntelliMetric online essay scoring service. Vantage Learning Announces Release of E-Fence, Advanced Detection of Non-legitimate Responses Submitted for IntelliMetric Automated Essay Scoring |
October 12, 2004
Counting on the futureby Laura Durford, It's almost ten years since the most famous mathematical puzzle of all time – known as Fermat's Last Theorem - was solved after more than three centuries of tantalising and torturing the world's most gifted mathematicians. Now, two more major conundrums may be about to crumble. So is mathematics in a golden age or is it, in fact, in decline? If you listen to mathematicians, "both" may be the correct answer. Before the mid 1990s, no-one would have dreamt that a tale of high-level maths could ever prove a best-seller, but when Fermat's Last Theorem (the book, also titled Fermat's Enigma in the US) revealed the history of one of mathematics' most enduring enigmas, it was bought – and even read – by all kinds of people. Perhaps what lured them was the quest itself, but no doubt the fact that big money had been involved helped to spark public interest; in 1997 mathematician Andrew Wiles collected a 50,000-dollar prize for his proof of Fermat's Last Theorem. More cash A few years later, even bigger prizes were announced; a million dollars were offered for the solution of each of seven key mathematical problems. Keith Devlin of Stanford University in California helped to publicise these Millennium Maths Problems - the "Mount Everests of mathematics" as he terms these challenges - as set by the Clay Institute. But he also freely admits that the million dollar problems are a "publicity stunt" to help stimulate interest in mathematics. But is that really necessary? Simon Singh, the author of Fermat's Last Theorem, suggests that we might actually be seeing a golden age of mathematics, pointing out that two of the seven Clay questions have already attracted claims of proofs, while a raft of other riddles have also been solved in recent years and decades. "We're living in a mathematical age," he says. "There are more mathematicians alive today, doing more incredible maths, than ever before, and not just within Universities; these mathematicians are also finding roles within industry." The American Secret Service is the world's largest employer of mathematicians, while billion-dollar search-engine companies revolve around mathematical problem solving. And yet... Dr Singh changes direction almost as soon as he has started: he cannot shake the conviction that the apparently declining appeal of mathematics in schools is extremely dangerous. "The big problem is that we probably don't have enough mathematicians. Young people don't seem to want to do mathematics, and I think the problem is we just don't have enough teachers who are mathematicians." In addition to being tempted away from teaching by the more financially rewarding industries, many mathematicians also get attracted overseas in classic 'brain-drain' scenarios, leaving their home countries for higher salaries and status. It's a syndrome that's recognised by Professor Charles Chidume, who not only does maths teaching and research at the International Centre for Theoretical Physics in Trieste, Italy, but also heads the ICTP's initiatives to stimulate mathematics in developing countries. He says that in English-speaking sub-Saharan Africa in particular, mathematics is "a disaster". As part of an attempt to remedy such situations around the globe, the ICTP has recently announced a 10,000 dollar annual maths prize. New impetus Will such incentives really guarantee a continued interest in a discipline that is often unattractive and obscure to the greater part of humanity? Keith Devlin, for one, is optimistic, and believes that developments in other sciences will fuel a new era of mathematical discovery: "In the year 2100, I would be very surprised if there wasn't another competition announced with another five, seven, [or even] 10 problems. Mathematics will never be short of problems. There will be new problems about existing parts of mathematics, but there will also be new problems about new kinds of mathematics that we haven't even dreamt of yet. The 19th century was the century of chemistry and many of the mathematical problems related to chemistry. The 20th century was the century of physics - and many of the problems in mathematics of the 20th century came out of physics. The 21st century, as has been observed many times, is the century of biology; that's already giving rise to new problems. "In the new list of problems that I'm sure will come out in the year 2100, I'll bet about a half of them come out of biology, things like genetics, trying to understand the nature of life. That's where a lot of the new mathematics is coming from. And as in the past, at first the problems will be fairly practical. Then people will look for deeper abstract problems behind those ones and more abstract ones, so that by the year 2100, we will have analogues of the Poincaré Conjecture and the Navier-Stokes Conjecture [two of the Millennium Maths Problems]. The Navier Stokes problem is very much a problem of physics; the Poincaré Conjecture is a pure mathematical problem from physics. In the year 2100 we'll get both applicable problems from biology and we'll get pure mathematical problems that arise from biology. That's how mathematics grows and develops." Counting on the future |
October 12, 2004
Mathematician shows how to juggle with figuresA JUGGLING mathematician uses tricks to teach North Wales students the secrets of arithmetic. About 250 pupils were spellbound by the skills of Dr Colin Wright when they visited Bangor university. He juggled ceaselessly to introduce them to a range of higher maths principles, as part of Mathcymru's Maths Week. Tim Porter and Chris Wensley of the informatics maths school then challenged the teenagers, aged 15-18, with everyday arithmetic puzzles. The aim was to illustrate the types of applications mathematics have in the real world. "We are delighted to invite bright maths students to the university to have a glimpse at mathematics outside the classroom in real life situations, and to have an idea of the types of things that interest those of us who study mathematics beyond school," said Dr Porter. "I hope some will have been inspired to continue with their mathematics studies - or at the very least, to take up juggling". Mathematician shows how to juggle with figures |
October 11, 2004
Cells in retina found to behave like soap bubblesEVANSTON, Ill. --- Soap bubbles delight children and the young at heart, but they also have been objects of scientific study for centuries. Operating under the laws of physics, bubbles always try to minimize their surface area, even when many bubbles are aggregated together. Now two Northwestern University scientists have demonstrated that the tendency to minimize surface area is not limited to soap bubbles but extends to living things as well. In a paper published Oct. 7 in the journal Nature, they show that cells within the retina take on shapes and pack together like soap bubbles, ultimately forming a pattern that is repeated again and again across the eye. Gaining insight into these patterns can help researchers understand the interplay between genetics and physics in cell formation. "The cells we studied, those found in the retina of the fruit fly, adopt mathematically predictable shapes and configurations," said Richard W. Carthew, professor of biochemistry, molecular biology and cell biology and a co-author on the paper. "Like bubbles, life has co-opted a physical tendency for surfaces to be minimized and has harnessed it to design intricate cellular patterns within complex structures such as the eye." Similar to the colored dots in a Georges Seurat painting, though on a three-dimensional scale, the cell is the indivisible unit that gives shape to something larger and recognizable -- a butterfly, a maple tree, a human being. How is this amazing diversity of species created? "It is like designing the pieces of a jigsaw puzzle so that they fit together seamlessly," said Carthew. "Understanding how cells fit together in space is an underappreciated area of science that has started to gain serious momentum in the last decade. Cells are different shapes and pack together in different ways depending on where they are located in a living thing and what their function is." In investigating the physical basis of biological patterning in the retina, Carthew and co-author Takashi Hayashi, a post-doctoral fellow at Northwestern, looked at normal retinal cells where four cells group together to form an aperture that is circular in shape. They found that they did so in exactly the same pattern as a group of four soap bubbles. Then, they varied the number of cells in each aperture and looked at how the cells fit together. Again, the cell configurations correlated perfectly to those of bubbles of the same number. When an aperture had one to five cells each resulted in one configuration. If an aperture had six cells, three different configurations were possible, but always the same three. "By looking at one exquisitely structured tissue in one species, we discovered how the cells order themselves," said Carthew, who with Hayashi has been studying the form and function of the retina for years. "This experiment illustrates the importance of mathematics and physics in biology and points to a general principle of patterning found in a wide range of living things." Cells in retina found to behave like soap bubbles |
October 10, 2004
The rule in academic life is now 'publicise or perish'Richard Morrison THE WONDERS of modern science never cease to amaze. Last week an economist, a psychologist and a mathematician came up with a formula for predicting when Sod's Law is likely to hit you. In case you didn't jot it down — and it would be just Sod's Law that you didn't have a pencil handy — the formula is ((U+C+I) x (10-S))/20 x A x 1/(1 - sin (F/10)), where U stands for urgency, C for complexity, I for importance, S for skill, A for aggravation, F for frequency, and sin for "sine", that funny little button on your pocket calculator that you never understood. The idea, apparently, is that for any proposed activity you rate all these elements on a scale of one to nine, do the maths in your head (because Sod's Law dictates that the battery in your calculator will have run out), get an answer nowhere near what it is supposed to be, shout "oh, sod it!", do it all again with a completely different but no less absurd result, and stomp out of the house in a rage, only to find that it is raining and you left your umbrella inside. To which you can't return, because you left your house keys there as well. Thus the formula has fulfilled its purpose. You wanted to know when Sod's Law is most likely to strike? The answer is: at moments of maximum inconvenience or embarrassment, any time of the day or night. Well, I know what you are thinking now. "This is all very droll, but did I need the massed brain-power of an economist, a psychologist and a mathematician to tell me that? Couldn't I have worked out the sodding point of Sod's Law by myself?" Probably. But you are misreading the purpose of modern scientific research. Much of it has little to do with pushing out the boundaries of knowledge, and everything to do with scientists getting their names, and their universities' names, into the papers. "A few years ago," an Oxford don tells me, "the rule in universities was 'publish or perish'. Now it's 'publicise or perish'. And the more trivial or fatuous your research the better, because then it suggests that your university is trendy and populist. Just what the Government wants." The rule in academic life is now 'publicise or perish' |
October 09, 2004
Theoretical mathematicians offer unique help in the war on terrorBy MATT CRENSON You don't need political influence, military might or economic resources to plant bombs or take hostages but, without brains, terrorism is nothing more than random violence. Consider al-Qaida's attack on New York City and Washington, D.C., three years ago. It required a force of only 20 men armed with box cutters, yet it was so brilliantly conceived, meticulously planned and keenly attuned to global politics that it changed the world. "Terrorism is a thinking man's game," said terror expert Gordon Woo. Which is why a small group of thinking men and women convened at Rutgers University last month to consider how order theory - a branch of abstract mathematics that deals with hierarchical relationships - could be applied to the war on terror. It almost seems ridiculous for people who inhabit a world of concept lattices and partially ordered sets to think they can affect a war that is being fought on the streets of Baghdad and in the remote mountains of northern Pakistan. But the war on terror is also fought in cyberspace, and in the minds of people from Lahore to Los Angeles. Mathematicians are right at home in such abstract realms. "It's not just theoretical," said Fred Roberts, director of the Center for Discrete Mathematics and Theoretical Computer Science, the Rutgers research institute where the conference was held. Mathematician Jonathan Farley of the Massachusetts Institute of Technology said he was inspired to organize the meeting by the movie A Beautiful Mind. The film tells the story of mathematician John Forbes Nash, whose work in game theory found application in Cold War military strategy, international trade and the auctioning of broadcast frequencies by the Federal Communications Commission. "I'm a pure mathematician, so I'm completely useless for the most part," Farley said. "But it would be nice to take some of what we do and make it useful for some people - maybe even lifesaving." "Part of the war on terrorism is winning hearts and minds," said Woo, an analyst in the London office of Risk Management Solutions. The Newark, Calif.-based consulting firm assesses catastrophe risks for the banking and insurance industries. Minds are the specialty of Vladimir Lefebvre, a cognitive scientist at the University of California in Irvine. The Russian-born researcher has spent his career developing ways of reducing human decision-making to mathematical equations. The work stems from a top-secret Soviet research project that Lefebvre worked on during the 1970s. "I can compute feelings," he said with a grin. Lefebvre's ideas are so obvious that you wonder if he might be kidding. Every person, he argues, has a view of the self that he or she uses as a tool for making decisions. That view can be influenced by the outside environment. So in principle, there ought to be things we can do to make terrorists feel less sure about themselves or less ardent in their beliefs. The right strategy might even make them think of themselves as something other than terrorists. Lefebvre believes human decision-making is so straightforward that simple equations can describe how an individual's behaviour arises from his or her self-image as it is shaped by other people and the environment. Computer scientist Kathleen M. Carley heads a lab that tries to simulate all kinds of social groups, including terrorist organizations. The lab has built simulations of Hamas and al-Qaida by dumping newspaper articles and other publicly available information about the organizations into a computer database. A program then takes that information and looks for patterns and relationships between individuals. It finds weak and strong figures, power brokers, hidden relationships and people with crucial skills. Then another program can predict what would happen if a specific individual were removed from the organization. After Israel's assassination of Hamas founder Sheikh Ahmed Yassin in March, the program correctly predicted he would be succeeded by hard-liner Abdel Azziz Rantisi. Three weeks later Israel assassinated Rantisi as well. Carley's lab predicted that Hamas political director Khaled Mashaal would succeed him, and posted its pick on the Internet. This time, Hamas declined to reveal who had taken power for fear he too would be assassinated. But eventually it became known that Mashaal was indeed the one. At that point, Carley said, "we were told to quit putting such predictions on the Web" by federal officials. Theoretical mathematicians offer unique help in the war on terror |
October 09, 2004
NSF awards $20.1 million for new interdisciplinary science of learning centerBy Tim Stoddard Stephen Grossberg has been shedding light on the mysterious functions of the brain for the past 40 years. Now, the preeminent neuroscientist and artificial intelligence pioneer is assembling a different kind of central nervous system: a distinguished team of scientists from diverse fields who will work together to understand how brain function relates to behavior. Last week the National Science Foundation (NSF) awarded Grossberg a five-year, $20.1 million grant to launch the Center for Learning in Education, Science, and Technology (CELEST) at BU. The center's mandates are to better understand how the brain operates and to develop educational tools to advance the teaching of brain science in high schools and universities around the world. Just as the three-pound mass of interwoven nerve cells in our heads integrates sensory information, CELEST will synthesize and coordinate several research agendas. Based at the CAS department of cognitive and neural systems (CNS), the new center will pull together scientists, educators, and technologists from CNS, the CAS departments of mathematics and psychology, and the ENG department of biomedical engineering. It also will involve researchers at the Center for Adaptive Systems, the Center for Memory and the Brain, the Science and Mathematics Education Center, the Hearing Research Center, and the Center for Polymer Studies. Other CELEST collaborators include faculty at Brandeis University, MIT, and the University of Pennsylvania. The key to understanding how the brain learns and stores memories, Grossberg says, is to study how the organ's mechanisms give rise to behavioral functions. "You must have a theory that can describe the elements of the brain and how they interact, and how those interactions lead to emerging properties that map onto behavior as we know it," he says. "Our department of cognitive and neural systems is the leading department in the world for doing that." In addition to studying the biology of learning at several levels, as part of CELEST several BU faculty members will develop algorithms and artificial neural networks inspired by the brain's organizational structure for use in a wide variety of technological applications, including artificial intelligence. "The brain adapts autonomously to a changing world," Grossberg says, "and a lot of high-tech research is trying to find intelligent devices that can operate on their own in changing environments. The brain gives us new heuristics, new design principles, new circuits for understanding how to make systems that can adapt on their own to a changing world." CELEST's reach will extend nationally and internationally. The center will sponsor regular retreats, colloquia, and seminars for faculty and students throughout the Boston area to meet and share ideas about how the brain learns, and to discuss how to develop smarter algorithms for intelligent machines. The center will also run an annual international conference, bringing together scientists from all over the world to share the latest results from the psychological, biological, and technological aspects of learning. CELEST's research and educational goals are ambitious, but for Grossberg, an interdisciplinary approach is key to advancing the science of learning. He holds professorships in the departments of cognitive and neural systems, mathematics, psychology, and ENG's department of biomedical engineering and is founding director of the Center for Adaptive Systems and founding chairman of CNS. Always the interdisciplinarian, he requires CNS graduate students to follow a "three-quarter rule" — they must cultivate a strong background in three of the following subjects: psychology, neuroscience, mathematics, and computer science. Leading CELEST's scientific dream team "will be a lot of work, but we're really excited," says Grossberg. "I think of it as a dream come true." NSF awards $20.1 million for new interdisciplinary science of learning center |
October 09, 2004
The mathematics behind perfect piano tunes revealed!World News - Sydney, Oct 8 : Making a piano sound better may have more to do with maths than with the skill of actually playing it, if scientists at the CSIRO division of Mathematical and Information Sciences in Australia are to be believed. According to ABC online, the scientists led by Dr Bob Anderssen have worked out the mathematical formula that shows why Stuart & Sons grand pianos can produce notes of extraordinary clarity and tone. It has also fetched Anderssen the George Szekeres Medal for his contribution to maths. Australia's Stuart & Sons grand pianos use a different string clamp to traditional grand piano and so they play notes that produce sounds with more purity, sustain and volume. Anderssen used his speciality in "inverse problems" to work out the maths of piano string vibrations. "In order to explain the difference between the Stuart and traditional pianos, one has to take into account the fact that the tension changes and the string length changes slightly," he said. Anderssen used a non-linear string equation and included the tension and string length changes. He said inverse problems were used to translate between two-dimensions and three-dimensions. (ANI) The mathematics behind perfect piano tunes revealed! |
October 09, 2004
The Murphy's Law formulaBoffins have come up with a mathematical formula which they claim proves Murphy's Law really does strike at the worst possible time. Ordinary people have long known that computers crash on deadline and cars break down in emergencies, while previous studies have shown the Law, also called Sod's Law, is not a myth and toast really does fall buttered side down. But now a panel of experts has provided the statistical rule for predicting the Law of "anything that can go wrong, will go wrong" - or ((U+C+I) x (10-S))/20 x A x 1/(1-sin(F/10)). And after tests of the experiences of 1,000 people, they have discovered "things don't just go wrong, they do so at the most annoying moment". Now the experts commissioned by British Gas - a psychologist, a mathematician and an economist - say the formula allows people to calculate the chances of Sod's law striking, and even try to beat the bad luck. Project psychologist Dr David Lewis said: "The lesson from this is that, to cut the seemingly unbeatable Murphy's Law gremlins down to size you need to change one of the elements in the equation. "So, if you haven't got the skill to do something important, leave it alone. If something is urgent or complex, find a simple way to do it. If something going wrong will particularly aggravate you, make certain you know how to do it." But he added a note of caution: "There is, of course, a Sod's Law factor to the equation. If you judge your ratings wrongly, you might become too optimistic - and calamity will strike." In the calculation, five factors have to be assessed: urgency (U), complexity (C), importance (I), skill (S) and frequency (F) and each given a score between one and nine. A sixth, aggravation (A), was set at 0.7 by the experts after their poll. Top of the most likely - and most annoying - events was spilling something down yourself before a date and the boiler breaking down in cold weather, followed by rush hour being worse when you're already late. The equation has seven steps to forecasting a potential Murphy's Law moment, so you can work out which factors you need to change to avoid it: 1. Rate the urgency, importance and complexity on a scale of one to nine and add the three figures together 2. Rate from one to nine how skilled you are at the task, then subtract this from 10 3. Multiply answers to 1 and 2 and divide by 20 4. Rate from one to nine how frequently you perform the task and divide this by 10 5. Rate the sine (or sin) of your answer to step 4 and subtract this from 1 6. Divide 1 by your answer to step 5 7. Multiply your answer to step 3 by 0.7 and multiply this by your answer to step 6, and that's your Sod's Law rating. The closer to 10 it is, the higher your risk of falling victim. The Murphy's Law formula |
October 06, 2004
Cross-strait tensions are more than just a gameBy Kung Ming-hsin Rational behavior and ideals are diametrically opposed concepts. In economics, rationality is normally explained as using all possible past and current information to avoid systemic mistakes from occurring. In other words, rationality is more pragmatic, while ideals normally mean elevating a goal to a level where compromise is no longer possible. The mathematician John Nash formulated a definition of equilibrium in game theory, the Nash Equilibrium, for which he was awarded the Nobel prize in economics. This point of equilibrium describes the situation most beneficial to all parties given their assumed existing choices. But such an equilibrium could lead to the creation of a "Priso-ner's Dilemma." Two thieves get caught for theft, and are interrogated separately. If neither con-fesses, they will only go to prison for a short period of time. But if one confesses, he will get a reduced sentence and only be imprisoned for a few days, while the other thief will be given a longer sentence. If both confess, neither will be given a reduced sentence. The resulting equilibrium is that they will both confess. Although they know that the best solution would be for both not to confess, the problem is that if one confesses, the other would be better off also confessing. In the current anti-arms procurement atmosphere, two former and one incumbent university presidents have issued a statement saying they want to "alert the government to the fact that if, when two people quarrel, one constantly clenches his fist, the other party will have to do the same. In the end, one of the two will strike out. There is no longer any sense in debating who will strike first, but one of the two has to relax his clenched fist and offer a true sign of good will. That is the only way to evade danger." Game theory says that if Tai-wan is first to relax its clenched fist, China's best choice would be to strike, because if Beijing also relaxed, the unification issue would never be resolved, which is diametrically opposed to China's goal. Thus, from a rational standpoint, if our government relaxes first, it is staking the lives of 23 million Taiwanese on its good intentions and ideals. To turn the issue around: Taipei maintaining good military preparedness actually means that there may be a smaller risk of war. The rational behavior of rulers always overrides the ideals they held while in opposition. Has the Democratic Progressive Party government compromised its Tai-wan independence stance since its years in opposition? The "Five Noes" and the decision that a new constitution will not affect the national title or territory are examples of rational behavior taking precedence over ideals. So, can the cross-strait conflict be resolved? A look at the behavior of the US and the Soviet Union during the Cold War suggests that it is situational misjudgements that are the main cause of war. Although the two nations never ceased enhancing their arsenals, mutual communication and negotiations also continued uninterrupted. If the two sides of the Taiwan Strait harbor good intentions, why not show it by no longer making "one China" or "Taiwan independence" a premise for negotiations? Cross-strait tensions are more than just a game |
October 06, 2004
MTSSR students measure earth's circumferenceBy Zalia Zaini An experiment called "Eratosthenes" was conducted worldwide on the 22nd of September to calculate the circumference of earth by measuring the altitude of the sun at a specified date and time. In Brunei, the experiment was held at Maktab Teknik Sultan Saiful Rijal and participated by fifty students and instructors of the college. The event was organised by the Mathematics Department through the initiative of its newly formed Mathematics Club. Eratosthenes, a Greek scholar (about 276 to 194 B.C.), made a surprisingly accurate estimate of the earth's circumference. In the great library in Alexandria he read that a deep vertical well near Syene, in southern Egypt, was entirely lit up by the sun at noon once a year. Eratosthenes reasoned that at this time the sun must be directly overhead, with its rays shining directly into the well. In Alexandria, almost due north of Syene, he knew that the sun was not directly overhead at noon on the same day because a vertical object cast a shadow. Eratosthenes could now measure the circumference of the earth (sorry Columbus) by making two assumptions - that the earth is round and that the sun's rays are essentially parallel. He set up a vertical post at Alexandria and measured the angle of its shadow when the well at Syene was completely sunlit. Eratosthenes knew from geometry that the size of the measured angle equalled the size of the angle at the earth's centre between Syene and Alexandria. Results obtained by the MTSSR teams from the experiment have been submitted to the organisers for verification. Two teams have produced highly commendable results with a mere 1.7% error from the actual circumference of the earth. The activity created great enthusiasm amongst the students and instructors involved. Students are able to see how mathematics could be integrated with subjects like geography, for instance, to identify and solve problems. It is the hope of the department to make mathematics an interesting and practical subject. More activities of this nature have been outlined by the Mathematics Department for the benefit of the students at MTSSR and also the community as a whole. MTSSR students measure earth's circumference |
October 04, 2004
WelTec gets fuzzy feelingBy TOM PULLAR-STRECKER Wellington Institute of Technology has reinforced its credentials as a centre for research into fuzzy logic and artificial intelligence, thanks to the efforts of Romanian-born Professor Mircea Negoita. Professor Negoita, director of WelTec's Centre of Computational Intelligence, arranged for Wellington to host this year's International Conference on Knowledge-Based Intelligent Information and Engineering Systems, KES 2004. Last year the conference was hosted by Oxford University. The event attracted 480 academics from 50 countries, including the "father" of fuzzy logic, Berkeley University Professor Lotfi Zadeh, who has been appointed honorary chairman of the Centre for Computational Intelligence at WelTec. It also attracted 168 academics from Japan, including the president of the Japanese Society of Fuzzy Systems and Intelligent Informatics, Professor Takeshi Yamakawa. About a third of the attendees were PhD students from around the world. Professor Negoita, who in 1997 emigrated to New Zealand from Romania where he had established his international reputation, has been invited by Nasa to serve as a visiting professor at its 6000-strong Jet Propulsion Laboratory next year. He says WelTec will bid to host KES again in 2010. WelTec gets fuzzy feeling |
October 02, 2004
Professors wrestle question: creation, evolutionBy DEEPIKA RAO Members of the audience sat and stood out of the doors as University science professors Wyatt Anderson and Henry Schaefer argued about the validity of evolutionary theory Thursday afternoon at the Student Learning Center. The theory of evolution -- that species evolved through natural selection -- was published in naturalist Charles Darwin's "The Origin of Species" in 1859. Anderson, former dean of the Franklin College of Arts and Sciences whose specialty is genetics, supported the evolutionary side of the debate. Schaefer, who currently works in computational quantum chemistry, has written more than 900 scientific publications and teaches a seven-week freshman seminar titled "Science and Christianity: Conflict or Coherence?" The discussion was moderated by Betty Jean Craige, a University comparative literature professor and director of the Center for Humanities and Arts -- the organization that sponsored the event. In the 10-minute introductory presentation each panelist was allowed, Schaefer said he adopted the creationist position after accepting Jesus Christ and subsequently began "taking reservations about the evolutionary theory." "I grew up in an environment that accepted evolution not just as a good theory but a sacred truth," he said. He posed the question, "Is evolution a good theory?" He then explained the theory of evolution does a "good job of categorizing and systemizing" the earth's fossil record, but the topic covers too broad an area for the theory to be valid. Anderson responded, saying evolutionary biology is a science that works like other sciences -- it involves finding hypotheses, conducting experiments and collecting data. "Darwin defined evolution as descent with modification, which is still acceptable, and natural selection is a mechanism of evolution," Anderson said. "Evolution has led to better study of human origins, which originated in Africa," he said. The discussion, which lasted about an hour-and-a-half, hit on one aspect of evolutionary theory more than once -- the amount of time it took for the understood gradual process of evolution to occur. Schaefer said the fossil record, once closed, will show some stages of evolution occurred much more rapidly than the theory suggests. Anderson attributed inconsistencies in rapid versus gradual stages of the evolutionary process to conditions in the environment either hindering or encouraging the speed of the progression. Schaefer said he would like to see more discussion of evolution in the classrooms but a balance of emphasis on the theory's weaknesses as well as its strengths. Anderson said this area of discussion in science is less cut-and-dry and more personal. "It's not just about science -- we are talking about an area of science that bears on people's beliefs," he said. "(Schaefer) is a wonderful person and a wonderful scientist; we just happen to disagree." Craige said she chose this topic because it will continue to be a point of debate that students will encounter. "I believe students in science and students in humanities struggle with this issue and have discussions in the classroom," she said. "It is important for students to see that brilliant academic scholars can disagree profoundly with each other and appreciate each other." Professors wrestle question: creation, evolution |
October 01, 2004
Quantum cryptography gets practicalOpinion by Bob Gelfond, MagiQ Technologies Inc In theory and in labs, quantum cryptography -- cryptography based on the laws of physics rather than traditional, computational difficulty -- has been around for years. Advancements in science and in the world's telecommunications infrastructure, however, have led to the commercialization of this technology and its practical application in industries where high-value assets must be secure. Protecting information today usually involves the use of a cryptographic protocol where sensitive information is encrypted into a form that would be unreadable by anyone without a "key." For this system to work effectively, the key must be absolutely random and kept secret from everyone except the communicating parties. It must also be refreshed regularly to keep the communications channel safe. The challenge resides in the techniques used for the encryption and distribution of this key to its intended parties to avoid any interception of the key or any eavesdropping by a third party. Many organizations are advancing quantum technology and bringing it outside academia. Research labs, private companies, international alliances such as the European Union and agencies such as the Defense Advanced Research Projects Agency are investing tens of millions of dollars in quantum research, with projects specifically focused on the challenge of key distribution. Quantum cryptography gets practical |
October 01, 2004
'Most Recent Common Ancestor' Of All Living Humans Surprisingly RecentNew Haven, Conn. -- In this week's issue of Nature, a Yale mathematician presents models showing that the most recent person who was a direct ancestor of all humans currently alive may have lived just a few thousand years ago. "While we may not all be 'brothers,' the models suggest we are all hundredth cousins or so," said Joseph T. Chang, professor in the Department of Statistics at Yale University and senior author on the paper. Chang established the basis of this research in a previous publication with an intentionally simplified model that ignored such complexities as geography and migration. Those precise mathematical results showed that in a world obeying the simplified assumptions, the most recent common ancestor would have lived less than 1,000 years ago. He also introduced the "identical ancestors point," the most recent time -- less than 2,000 years ago in the simplified model -- when each person was an ancestor to all or ancestor to none of the people alive today. The current paper presents more realistic mathematical and computer models. It incorporates factors such as socially driven mating, physical barriers of geography and migration, and recorded historical events. Although such complexities make pure mathematical analysis difficult, it was possible to integrate them into an elaborate computer simulation model. The computer repeatedly simulated history under varying assumptions, tracking the lives, movements, and reproduction of all people who lived within the last 20,000 years. These more realistic models estimate that the most recent common ancestor of mankind lived as recently as about 3,000 years ago, and the identical ancestors point was as recent as several thousand years ago. The paper suggests, "No matter the languages we speak or the color of our skin, we share ancestors who planted rice on the banks of the Yangtze, who first domesticated horses on the steppes of the Ukraine, who hunted giant sloths in the forests of North and South America, and who labored to build the Great Pyramid of Khufu." 'Most Recent Common Ancestor' Of All Living Humans Surprisingly Recent |