March 31, 2005
Science groups to meet at KnoxISAS, ISMAA conventions coming in April to Galesburg GALESBURG - Hundreds of science and mathematics educators and students will converge on the Knox College campus from April 7 through April 9, as two state associations bring their annual conventions to Galesburg. An estimated 250 science faculty and students will attend the annual meeting of the Illinois State Academy of Science April 7-9 at Knox, while some 150 mathematics faculty and students will gather on the Knox campus April 8-9 for the annual meeting of the Illinois Section of the Mathematical Association of America. The conferences will include free, public lectures, as well as numerous sessions for registered attendees. The ISAS meeting will feature a free, public keynote lecture, "The Role of Science in Saving Nature: Fruits of the Illinois Natural Areas Inventory," by Brian Anderson of Lincoln Land Community College at 6 p.m. April 8 in Kresge Hall, Ford Center for the Fine Arts. Anderson most recently served as director of the Office of Scientific Research at the Illinois Department of Natural Resources, where he managed the state's natural history, geological and water surveys and the state museum. He has held posts with several Illinois natural resource agencies, including 10 years as director of the Illinois Nature Preserves Commission. Free, public lectures at the ISMAA conference will include: Phil Straffin of Beloit College will give a talk, "Explorations in the Mathematics of Other Cultures," at 12:45 p.m. April 8, in Kresge Hall, Ford Center for the Fine Arts. Straffin will discuss "ethnomathematics" a course he teaches on mathematical thinking in non-Western cultures. Examples include the traditional game of Achi from Ghana, and two kinds of sand drawings - "sona," created by the Tshokwe culture in Angola, and "nitus," which are drawn by people on Malekula, an island in the South Pacific nation of Vanuatu. Underwood Dudley of Florida State University will give a talk, "Formulas for Primes," at 7:30 p.m. April 8 at the Best Western Prairie Inn. A "prime" is a number that has only two factors, itself and the number one. Dan Kalman of American University will speak on "The Fibonacci Numbers Exposed" at 8:30 a.m. April 9 in Room A-110, Umbeck Science-Mathematics Center. Named after a 12th-century Italian mathematician, the Fibonacci series is a set of numbers in which each term is the sum of the preceding two numbers in the set. Jean Bee Chan of Sonoma State University will give a talk, "How Should We View an Art Gallery?" at noon April 9 in Room A-110, Umbeck Science-Mathematics Center. Chan will discuss the relationship between the shape of an art gallery and the number of objects that can be seen from any given point in the gallery. Science groups to meet at Knox |
March 31, 2005
Proof and beautyJust what does it mean to prove something? QUOD erat demonstrandum. These three words of Latin, meaning, "which was to be shown", traditionally mark the end of a mathematical proof. And, for centuries, a proof was exactly that: showing something by breaking it down into readily agreed-upon steps. Proving something was a matter of convincing one's peers that it has indeed been shown—no more, and no less. The rhetorical flourish of a Latin epigram also has served to indicate that the notion of proof is well understood, and commonly agreed. But that notion is now in flux. The use of computers to prove mathematical theorems is forcing mathematicians to re-examine the foundations of their discipline. Through much of the 20th century, questions of mathematical rigour were passed off to logicians and philosophers—working mathematicians have been, for the most part, content to work with an intuitive definition of proof. This notion works when each step of a proof is transparent, and can be examined by all. Proof is then just a process of reducing one big, non-obvious step, to a bunch of small, obvious ones. However, if a computer is used to make this reduction, then the number of small, obvious steps can be in the hundreds of thousands—impractical even for the most diligent mathematician to check by hand. Critics of computer-aided proof claim that this impracticability means that such proofs are inherently flawed. However, its defenders point out that some theorems that many mathematicians consider to have been proved in the classical manner also have proofs which are so long as to be uncheckable. The most famous case of this is something called the classification of finite simple groups. These are abstract objects with certain mathematical properties; the claim is that, over a 30-year span in a series of papers totalling some 15,000 pages, all possible such objects were enumerated. Though the mathematical consensus is that the classification (nicknamed the "enormous theorem") is complete, there are sceptics who point out that the dispersed proof is essentially unverifiable. What, then, does constitute a proof in the modern age? Two recent examples of how computers have been used to prove important mathematical results illustrate how the field is changing. A colouring problem The first is the "four colour theorem", which is perhaps the mathematical theorem most likely to bedevil a toddler. It states that any planar map (that is to say, a flat one) can be coloured with at most four colours in a way that no two regions with the same colour share a border. It was first proposed in 1852 but, despite efforts by a century's worth of mathematicians, went unproven until 1976, when Kenneth Appel and Wolfgang Harken, then of the University of Illinois, announced that they had proved the result. However, Dr Appel and Dr Harken used a computer to help them prove the result by examining about 10,000 cases. (Their proof also relied on a lot of old-fashioned gruntwork.) A new proof, in a paper just written by Georges Gonthier, of Microsoft Research, in Cambridge, England, also uses a computer. Dr Gonthier used similar techniques to those of Dr Appel and Dr Harken in his proof. However, rather than have part of the proof done by hand, and part by computer, he has automated the entire proof, and done so in such a manner that it is a formal proof. Formal proof is a notion developed in the early part of the 20th century by logicians such as Bertrand Russell and Gottlob Frege, along with mathematicians such as David Hilbert (who can fairly be described as the father of modern mathematics) and Nicolas Bourbaki, the pseudonym of a group of French mathematicians who sought to place all of mathematics on a rigorous footing. This effort was subtle, but its upshot can be described simply. It is to replace, in proofs, standard mathematical reasoning which, in essence, relies on hand-waving arguments (it should be obvious to everyone that B follows from A) with formal logic. The benefit of formal logic is that it is pure syntax. At no point does proceeding from one step to the next require understanding, let alone mathematical intuition. It is merely a matter of applying an agreed-upon set of rules (for instance, that any thing is equal to itself, or that if something is true for all members of a set of objects, it is true for any one specific object) to a set of agreed-upon structures, such as sets of objects. Formal proofs, however, never gained a foothold in the mainstream mathematical community because they are tedious—they take many steps to prove something in cases in which a mathematician might just take one. To those who would use a computer, however, they have two virtues. The first is that computers, with their tolerance for tedium, are particularly suited to writing the steps of a formal proof down. The second is that, by writing those steps down in what is called a "proof witness" instead of just announcing that a program had arrived at a true result, outsiders might gain greater confidence in a result derived from a computer. As Dr Gonthier, and other supporters of the use of computers, point out, there is no reason to think that humans are less fallible than computers when doing long computations or proofs. Indeed, the opposite might be true. The idea behind both proofs of the four colour theorem is to suppose that the theorem is violated—to assume, in other words, that there is some sort of map that requires five colours to fill in. The next step is to find the mathematically simplest versions of such maps. (What is meant by simplicity in this case is actually quite involved.) Dr Gonthier then showed that all these maps can, in fact, be re-coloured with only four colours, establishing the theorem by contradiction. The catch is that there are many such regions, which must be examined on a case-by-case basis; part of the mathematical difficulty lies in proving that the cases considered suffice to cover all possible maps, and part stems from proving that each individual case is indeed colourable with just four colours. Dr Gonthier says he is going to submit his paper to a scientific journal in the next few weeks. But he would do well not to get his hopes up about getting his paper published anytime soon. A 1998 paper which proved another long-standing conjecture using a computer, by Thomas Hales, of the University of Pittsburgh, has only recently been accepted by the Annals of Mathematics, perhaps the field's most prestigious journal, and is scheduled to be published later this year. The music of the spheres Dr Hales proved Kepler's conjecture, which is that the most efficient way to pack spheres in a box is the way grocers usually pack oranges—in a so-called "face-centred cubic lattice"—the arrangement whereby each layer of oranges is shifted so that an orange touches four oranges in the layer below. Kepler posited the conjecture in 1611, and it had long resisted efforts at proof. Indeed, Hilbert made it one of his list of the 23 most difficult and fundamental questions in mathematics, in 1900. Dr Hales proved the conjecture by using a trick different in nature to Dr Gonthier's. Rather than argue by contradiction, he reduced what was a problem about an infinite number of things (the Kepler conjecture considers an infinite number of spheres in an infinitely large space) to a statement about a finite, but very large, number of mathematical objects. He then used the computer to prove bounds about these objects, some of which, he says, can be thought of as sculptures made of cables and struts. Loosely speaking, he reduced the Kepler conjecture to a problem of considering whether, given a set of cables, which have no minimum length, but can only be stretched to a certain extent, and struts, which have a limit on how much they can be compressed, one can build a sculpture of a certain type. Dr Hales used a computer, as there were roughly 100,000 such structures that had to be considered in order to prove the Kepler conjecture. Although the Annals will publish Dr Hales's paper, Peter Sarnak, an editor of the Annals, whose own work does not involve the use of computers, says that the paper will be accompanied by an unusual disclaimer, stating that the computer programs accompanying the paper have not undergone peer review. There is a simple reason for that, Dr Sarnak says—it is impossible to find peers who are willing to review the computer code. However, there is a flip-side to the disclaimer as well—Dr Sarnak says that the editors of the Annals expect to receive, and publish, more papers of this type—for things, he believes, will change over the next 20-50 years. Dr Sarnak points out that maths may become "a bit like experimental physics" where certain results are taken on trust, and independent duplication of experiments replaces examination of a colleague's paper. Some of the movement towards that direction may be forestalled by efforts of Dr Gonthier's type to use computers to provide formal proofs and proof witnesses. It is possible that mathematicians will trust computer-based results more if they are backed up by transparent logical steps, rather than the arcane workings of computer code, which could more easily contain bugs that go undetected. Indeed, it is for this exact reason that Dr Hales is currently leading a collaborative project to provide a formal proof of the Kepler conjecture. In perhaps a more prosaic example of mathematics embracing technology, he is co-ordinating that effort using a blog called Flyspeck (the word, Dr Hales explains, means to examine closely). Why should the non-mathematician care about things of this nature? The foremost reason is that mathematics is beautiful, even if it is, sadly, more inaccessible than other forms of art. The second is that it is useful, and that its utility depends in part on its certainty, and that that certainty cannot come without a notion of proof. Dr Gonthier, for instance, and his sponsors at Microsoft, hope that the techniques he and his colleagues have developed to formally prove mathematical theorems can be used to "prove" that a computer program is free of bugs—and that would certainly be a useful proposition in today's software society if it does, indeed, turn out to be true Proof and beauty |
March 31, 2005
Math professor wins awardBy Michael Arcement II During the Mathematical Association of America's Louisiana-Mississippi regional meeting in Gulfport, Miss., associate professor of mathematics at NSU, Richard DeVault was awarded the Distinguished Teaching Award. Stan Chadick was the nominating professor. The award recognizes DeVault's accomplishments as a top educator among all collegiate teachers in Louisiana and Mississippi. As a result of his win at the regional level, DeVault was automatically nominated for the national Deborah and Franklin Tepper Haimo Award for Distinguished College or University Teaching of Mathematics. According to the MAA Web site, the national award carries a $1000 reward. It's only the attention his skills in the classroom and his lasting impact on students that really matter DeVault said. "Awards are more of a recognition thing," DeVault said. Previously DeVault had received an award for his research from NSU. "It was really nice to get recognized within the mathematical community for my teaching." DeVault said. Among the two major national mathematical associations, the MAA places a higher priority on teaching. The other association, the American Mathematical Society, is focused more on mathematical discovery and research. "I like to do the research, but if I had a choice between the two I would do the teaching," DeVault said. DeVault is the only recipient of this award among NSU faculty. Math professor wins award |
March 31, 2005
Girls' math scores add upBy Sharon Begley LEICESTER, England – In her 10th-grade math class, Frankie Teague dimmed the lights, switched on soothing music and handed each student a white board and a marker. Then, she projected an arithmetic problem onto a screen at the front of the room. "As soon as you get the answer, hold up your board," she said, setting off a round of squeaky scribbling. The simple step of having students hold up their work, instead of raising their hands or shouting out the answer, gives a leg up to a group of students who have long lagged in math classes – girls. Teague's teaching methods are part of broad changes in how math is taught in England's classrooms. Starting in the late 1980s, England's education department worried that lessons relied too heavily on teachers lecturing and students memorizing. So it began promoting changes in teaching methods, textbooks and testing in state-funded and private schools. The changes were designed to help all students, but educators have noticed a surprising side effect: Girls are closing a decades-old gender gap – and by many measures outscoring the boys. The English record goes against theories that boys are innately destined to dominate math and science – a view that caused a firestorm after recent remarks by Harvard University President Lawrence H. Summers. In discussing the preponderance of men in elite university science and engineering positions, Summers said "issues of intrinsic aptitude" might explain why more males than females score at the highest levels on measures of mathematical and scientific ability. Elaborating in the ensuing debate over his comments, however, Summers said in a letter to the Harvard faculty that his "January remarks substantially understated the impact of socialization and discrimination, including implicit attitudes." He added that his remarks about why more boys than girls score at the extremes on math tests and other assessments "went beyond what the research has established." The English experience with math education suggests that gender differences, even those that seem innate and based in biology, do not lead inevitably to any particular outcome. That view fits into a broader current sweeping over how scientists think of genetics. Many now believe that traits that seem intrinsic – meaning those grounded in the brain or shaped by a gene – are subject to cultural and social forces, and that these forces determine how a biological trait actually manifests itself in a person's behavior or abilities. An "intrinsic" trait, in other words, does not mean an inevitable outcome, as many scientists had long thought. "What's now in play is the question of what it means for a trait to be innate," says Eric Turkheimer, professor at the University of Virginia. In 2003, a study led by Turkheimer found that the influence of genes on intelligence varies with social class: In well-off children, genes seem to explain most IQ differences, but in disadvantaged minority children environmental influences have a greater impact. In another study, men carrying a gene linked to aggression and criminality were no more likely than other men to become violent adults – unless they were neglected or abused as children, according to a 2002 article published in the journal Science. And last summer, scientists in Canada reported that rats carrying a "neurotic" gene became more jumpy than their peers only if their mothers neglected them. In rats with attentive moms, the same DNA sequence produced mellow animals. "What we're learning is that culture and experience actually imprint themselves on the brain, on biology," says science historian Londa Schiebinger of Stanford University in Palo Alto, Calif. In other words, nature and nurture work together in a much more sophisticated way than many scientists had previously thought. England didn't take math education for girls seriously until the mid-1970s, when new anti-discrimination laws and a flood of gender research raised concerns about equality in the classroom. At the time, boys passed the math portion of an exam taken by all 16-year-olds, called the O-Level exam, at significantly higher rates than girls did. And more boys than girls achieved the top grades, educators say. Gender experts began having training courses for teachers, encouraging them to include girls more in classroom discussion and raise their own expectations of what girls could accomplish. Educators also began checking textbooks to eliminate gender stereotypes and include more positive images of girls excelling in math and science. A national curriculum, introduced in 1988, quickly added up to gains for girls. It required all students to take certain core subjects and prevented high-school girls from dropping out of math or science before age 16. The curriculum mandated that students learn to analyze mathematical theories to give them a deeper understanding of the topic. That had the side-benefit of helping girls because they – for what experts suspect is a combination of biological and social reasons – often excel at such analysis. Boys typically enjoy and excel at traditional problem-solving because many see it as a competition, educators say. The government also replaced the O-Levels with a new exam called the General Certificate of Secondary Education, or GCSE. That new exam required children to write an analysis of statistical data or a mathematical formula in the weeks before the exam and turn in their papers on exam day. Math exams in England also now give students partial credit for showing their work, even if they ultimately reach the wrong answer. This gives an advantage to girls, who are typically more methodical in writing out the problem step-by-step, educators says. Scotland and Wales, which also make up Great Britain, have separate educational systems and exams. Many math teachers in England attribute girls' rising scores to the changes in exam content, a view some scientists support. Leonard Sax, an American pediatrician and author of the book "Why Gender Matters," says there are hints that "girls' brains are built for complexity and boys' brains are built for speed." One of the most consistent findings in education, he notes, is that on time-constrained, high-pressure tests, boys on average do better than one would expect based on their classwork, while girls do worse. "There are no differences in what girls and boys can learn," Sax says. "If the environment is right, girls can excel to the same degree and in the same subjects that boys do." In 1988, the first year of the new test for 16-year-olds, 45.6 percent of boys and 38.2 percent of girls scored passing grades of A through C, according to government statistics. By the 1990s, boys and girls passed the math GCSE at nearly equal rates, but boys still outnumbered girls in achieving the top scores. In the mid-1990s, the government made a push to make lessons more interactive. That was a departure from the 1980s and early 1990s, when most lessons consisted of what teachers here call "chalk and talk," or standing at the board and lecturing. The new methods, although not specifically designed to benefit girls, draw more students into the lesson and help shy girls speak up and get noticed, teachers say. In 1997, for the first time, a higher percentage of girls (46.9 percent) than boys (46.8 percent) scored passing marks, ranging from A-star to C, on the math GCSE, according to the Department for Education and Skills. In 2003, 52 percent of girls and 50 percent of boys did so. In 2004, 53 percent of girls and 52 percent of boys. Although the percentages are close, the gains are a big change from the disparity of years past, educators say. Boys did come out on top in one area: 4.5 percent of boys, compared with 4 percent of girls, still achieved the highest possible score, called A-star. The boys' advantage didn't seem to hold up in the next level of testing. English girls now outperform boys on the "A-Level" exams taken by 18-year-olds. Comparable to Advanced Placement exams in the U.S., the A-Level tests college-level math. In 2003-04, 41 percent of the girls taking math A-Levels attained the highest grade, compared with 39 percent of the boys. "The perception of gender differences, that math is for boys, is vastly out of proportion to any evidence for them," says Jo Boaler, associate professor of mathematics education at Stanford and a former deputy director of national mathematics testing for 13-year-olds in the United Kingdom. Despite gains for girls in math, problems remain. Over the past decade, the number of students ages 16 and older opting to take A-Level math courses after they finish the mandatory curriculum has declined. And fewer students overall are studying math in college. The British government fears this could lead to a shortage of engineers and other technical professionals in years to come. It has tried to publicize the appeal of careers in science and math in an attempt to reverse the decline. By contrast, in the U.S., boys still outperform girls on standardized math tests. In 2004, for instance, 9.3 percent of boys and 4.4 percent of girls scored higher than 700 out of a possible 800 on the math portion of the SAT, according to the College Board, which administers the tests taken by college-bound high-school students. Also that year, 23.5 percent of boys and 17.1 percent of girls scored a 5 on one Advanced Placement calculus test, called the AB, where scores run from 1 through 5; 43.2 percent of boys and 34.8 percent of girls scored a 5 on the even more difficult Advanced Placement calculus BC test. Girls' math scores add up |
March 31, 2005
Israel's supercomputers become 'obsolete'By JUDY SIEGEL AND TALYA HALKIN For the lack of $3 million over three years, Israel has "fallen among Third World countries" because the government and academic institutions have refused to purchase advanced supercomputer equipment for research by 280 scientific teams in all the universities. Supercomputers are giant calculating machines with high-speed, high-capacity processing capabilities. Prof. Pinhas Bar-Yosef of the computational mechanics department of the Technion-Israel Institute of Technology and the scientific director of the Inter-University Computational Center's supercomputer project, said Wednesday that because there has been no investment in hardware and software, Israeli universities "dropped out four years ago from the list of the top academic institutions working with supercomputers." He accused the government, through the Council for Higher Education and the Ministry of Science and Technology, as well as the Israel Academy of Sciences of "doing nothing" to prevent this. Ironically, Israeli officials and scientists pleaded for years with a number of US administrations to change their long-standing policy that barred Israel from buying supercomputer equipment from any American firm. The US government feared that Israel was intending to use it for "nuclear weapons development at the Dimona nuclear reactor in the Negev" or "ballistic missile re-entry vehicles" -claims that Israel said were "nonsense." Eventually, the US dumped the policy and granted approval. The Technion, which produces two-thirds of all applied research in this country, was a leader in the push for as an effective tool for practical applications and theoretical research in the fields of physics, chemistry, and civil, mechanical and aeronautical engineering. There are hundreds of supercomputers in universities, research institutions and giant commercial firms in the U.S., dozens more in Europe and some even in Arab countries like Saudi Arabia. In 1995, the Education and Science Ministries, in coordination with the Council for Higher Education, purchased two supercomputers. The decision was made to install one at Tel Aviv University and the other at Ben-Gurion University in Beersheba. After the US realized the fear was baseless, it changed its mind, and in 2002, BGU was told told it could have the Cray, which was ungraded with then-innovative SV1 processors capable of executing 19.2 billion floating-point operations per second and a special vector-processing unit capable of carrying out simultaneous matrical actions -- especially important for science programs in computational fluid dynamics, weather forecasting, and searching for strings in large bio-informatics databases. Then-foreign minister Shimon Peres spoke at the dedication ceremony. The Council for Higher Education's powerful planning and budgeting committee, which was initially involved in funding, said it was agreed that the council's financial support would decline and responsibility for upgrading equipment be taken over by the universities. But the universities announced recently that they would no longer pay for supercomputers, and that the financial burden would be on the shoulders of "the individual researchers." Israel Academy of Sciences spokesman Avital Ber commented that she was surprised by the news, as "in recent years we never received one official request for help about supercomputers. But now that the issue has been raised, we will raise the issue with the head of our natural sciences unit." She added that there is some controversy among scientists whether supercomputers are too expensive and can be more effectively and efficiently replaced by parallel computing systems, in which individual PCs are linked together to process data together. Israel's supercomputers become 'obsolete' |
March 31, 2005
Back Pain Succumbs to Star Trek MedicineUsing sound frequencies to diagnose and eliminate back pain evokes images of Star Trek medicine; a pleasant fantasy but not quite in our realm of belief, until now. (PRWEB) March 31, 2005 -- Back pain suffered by an estimated 65 million Americans may be calmed by a frequency based device being made available, on a limited basis, by nVoice Technologies, a pioneering biotech marketing company. Using sound frequencies to diagnose and eliminate back pain evokes images of Star Trek medicine; a pleasant fantasy but not quite in our realm of belief, until now. Trials conducted during the last four years utilized a small hand-held frequency generator containing a sequenced set of sounds that supported the ability to significantly decrease, and in a number of cases, completely eliminate pain for research subjects. Varying degrees of back pain were evaluated. During tone trials, the experimental frequency sequences were delivered via a prototype later dubbed the "Little Back Box" that is now being made available to the public primarily through back pain clinics and health professionals. "It is hard to believe that the brain can be entrained, in less than ten minutes, to provide signals to muscles in such a way that the body relieves its own pain – not only back pain but other muscles as well are influenced. I've experienced the pain relief for myself," states Barbara McNeil, an Ohio chiropractor. Although these results may not be representative of everyone, they certainly seem to be consistent if the appropriate frequencies can be identified and applied. It is not just a simple matter of listening to these low pitched tones which sound somewhat like soft rumbling background noise. The frequency sets, which were specifically designed for the Little Back Box, "sonically massage" the tiny muscles that support the spine through a controlled combination of oscillations, frequencies and patterns. So novel is the design that the device is patent pending. Many of the study participants were confounded, yet pleased, by the fact that merely listening to a sound could provide pain relief that felt so natural that many of them did not attribute the relief to the Little Back Box. Pain measurements included trauma as well as reported discomfort from everyday muscle stress. Low back pain is the fifth-leading cause of doctor visits. Back injuries are the leading cause of work-related disability. Even though back pain is rarely life-threatening, the annual cost in terms of lost productivity, medical expenses and workers' compensation benefits account for $26 billion a year, which translates to 2.5% of the total health care bill in America. The Little Back Box is not designed for relief of pain from serious back trauma or surgery but professionals report that their clients don't care how the Little Back Box works, they only care that pain relief has been provided. The idea that frequency oscillation can be used to mechanically block pain signals is evidenced by devices such as the TENS unit which must be attached to the body. Frequency is also used via compression bursts to assist in shattering kidney stones and heel spurs. Both of the latter techniques are cumbersome, time consuming and cost thousands of dollars. What is different about The Little Back Box is the fact that the frequencies are delivered ambiently (through the air) via a speaker as a form of entrainment to engage the brain in creating the signals required for the pain relief. Headphones can be used but subjects reported pain relief to be five times more effective and faster if the frequencies were provided through a speaker. The Little Back Box, costing less than $200, comes with headphones but can be used with either headphones or an amplified subwoofer. James Gimzewski, a UCLA nanophysicist, has discovered that each human cell emits a frequency that can be accurately measured. It is his belief that if the sounds of the body can be decoded into known frequency patterns, those patterns may be the key to optimal health and the elimination of disease. Gimzewski was surprised to learn that the original research in this genre has been ongoing for nearly 20 years by Sound Health, a southern Ohio independent biotech facility that employs fundamental mathematical concepts, uniquely expressed to distinguish novel biometric frequency associations of the body. The facility is dedicated to the study of low frequency sound and vocal profiling as an opportunity to develop individualized "Designer Frequencies" for everything from conception to anti-aging to disease detection. This type of intervention would fall under the auspices of complementary or functional medicine. The Journal of Manipulative Physiology Therapy reported in February, 1999 that experts favor alternative modalities of treatment for uncomplicated acute and chronic back pain. The Yale Medical Group specializing in back pain estimates that 70-85% of all people have had back pain at some time in their lifetime. Often experts do not agree concerning the exact cause and diagnosis of back pain. Dr. James Weinstein, head of orthopedics at Dartmouth Medical School and Dr. Richard Deyo, professor of medicine at the University of Washington state that 85% of patients with lower back pain often cannot be given a precise diagnosis. Non specific terms such as strain, sprain or degenerative processes are commonly used to describe back pain. Providing frequencies ambiently is non-invasive and relatively inexpensive. On-going research has been designed to evaluate the potential to use frequency, through vocal analysis, to predict and evaluate disease states. "As the study longitudinally unfolds, the implications of biofrequency markers continue to expand into unpredicted venues. We were astonished when degenerated discs seemed to restructure themselves after a patient started using the tones," declared Liz Lonergan, RN and founder of the Body and Soul Health Clinic in Chicago. The Little Back Box is a first step in making available many such devices and techniques which use frequency to monitor health and wellness. Pharmaceutical companies are beginning to realize that frequency holds an amazing potential to complement current medical protocols. Pfizer Pharmaceutical recently reported using similar techniques to those historically used by Sound Health, to predict Parkinson's disease. Research plans include the development of other tone delivery devices which would have the ability to eliminate snoring, muscle cramps, heart arrhythmia, allergic reactions, skin wrinkles and collagen formation; and those that can increase stamina, immune response, muscle strength and sexual response. The ability to predict and manage disease states through the use of mathematical modeling may be moving us quickly toward a medical paradigm that we can presently only imagine. Back Pain Succumbs to Star Trek Medicine |
March 31, 2005
Worcester Polytechnic Institute Announces Ray Kurzweil as Commencement SpeakerPRNewswire/ -- Ray Kurzweil, world-renowned inventor, entrepreneur, author, and futurist, will be the commencement speaker at Worcester Polytechnic Institute's (http://www.wpi.edu) 137th graduation ceremony on Saturday, May 21. Kurzweil will discuss his ideas on the future interplay between mankind and artificial intelligence with WPI's graduates and community in his speech, "When Humans Transcend Biology." After Kurzweil's talk, the university will confer upon him an honorary degree. Widely regarded as one of the preeminent inventors and innovators of our time, Kurzweil foresees an era when the human body will be enhanced by software and computers, enabling humans to download intelligence and to live long past the current life expectancy. Kurzweil has laid out his vision in this area through his writing. He has authored five books and hundreds of articles. His first book, The Age of Intelligent Machines, was named Best Computer Science Book of 1990. His best- selling book, The Age of Spiritual Machines, When Computers Exceed Human Intelligence, has been published in nine languages and achieved the #1 best selling book on Amazon.com in the categories of "science" and "artificial intelligence." Kurzweil's most recent work, coauthored with Terry Grossman, M.D., is Fantastic Voyage: Live Long Enough to Live Forever. His next book, The Singularity is Near, When Humans Transcend Biology, is due to be published in September 2005. "As our graduates begin the next chapter of their lives, Ray Kurzweil is an excellent role model -- providing a firsthand example of an innovative career that has used science, technology and engineering to benefit the world," says Dennis D. Berkey, president of WPI. Kurzweil launched his thriving career in high school when he appeared on the television show "I've Got a Secret," hosted by Steve Allen. His secret was that he programmed his computer to analyze abstract patterns in musical compositions and then composed original melodies in a similar style. With this project, Kurzweil won first prize in the International Science Fair, and he was named one of the 40 Westinghouse Science Talent Search winners who were able to meet President Lyndon Johnson in a White House ceremony. Kurzweil subsequently rose to even greater success with the invention of several devices, including the first omni-font optical character recognition (OCR), the first print-to-speech reading machine for the blind, the first CCD flat-bed scanner, the first text-to-speech synthesizer, the first music synthesizer capable of recreating the grand piano and other orchestral instruments, and the first commercially marketed large-vocabulary speech recognition. He has founded and developed nine businesses in OCR, music synthesis, speech recognition, reading technology, virtual reality, financial investment, cybernetic art, and other areas of artificial intelligence. As a result of his accomplishments, Kurzweil was named in 2002 to the National Inventors Hall of Fame, which was established by the U.S. Patent Office. He has also been the recipient of numerous awards, including the $500,000 Lemelson-MIT Prize, the nation's largest award in invention and innovation, and the 1999 National Medal of Technology, the nation's highest honor in technology, from President Bill Clinton in a White House ceremony. About Worcester Polytechnic Institute Founded in 1865 as one of the nation's first technological universities, WPI is renowned for its innovative project-based undergraduate curriculum and global projects program. With 2,770 undergraduates and 1,040 full- and part- time graduate students, WPI offers undergraduate and graduate degrees in more than 30 disciplines in engineering, science and the management of technology. Working in more than 30 research institutes, centers and laboratories, the university's faculty and students are engaged in cutting-edge research in a broad range of fields. Worcester Polytechnic Institute Announces Ray Kurzweil as Commencement Speaker |
March 30, 2005
Mathematics could be solution to hospital waiting listsMathematics is being applied to the problem of long waiting lists for surgery at Queensland's hospitals. Researchers at the Queensland University of Technology are attempting to apply formulas to the elective surgery list at the Royal Alexandra Hospital, with a view to making it more efficient. Sam McHardy says it may be possible to reduce waiting times without increasing resources by mathematically controlling the way the hospital processes and prioritises patients. He says if the project is successful, it could be applied to other areas of the hospital. "We're looking at using techniques to either take over or aid the decision making process for the admissions, which will allow the resources to be used more efficiently and decisions to be made quicker," Mr McHardy said. "We hope to reduce the elective patient waiting list as well as reducing the cost of running the intensive care unit by being able to manage it more efficiently." Mathematics could be solution to hospital waiting lists |
March 30, 2005
New director believes in "vibrant" Swiss cultureMathematician Jean-Frédéric Jauslin is to take over as director of the Federal Culture Office on April 1. swissinfo caught up with Jauslin in Bern, where he spent the past 15 years at the helm of the Swiss National Library, which he restructured and modernised. Handpicked by Interior Minister Pascal Couchepin as successor to David Streiff, Jauslin - a mathematician by training - may appear on the surface an unusual choice for the job. swissinfo: You have three children, the youngest of whom is 12 years old ? how do you explain culture to him? Jean-Frédéric Jauslin: You cannot define culture or, to put it better, I wouldn't dare to define it. You have to live it, breathe it and, above all, get young people involved. It's important to demonstrate that culture is not elitist or dusty or boring, as people frequently think. Culture is something that is vibrant and which can be practised every day. swissinfo: You have a degree in mathematics and a doctorate in IT and are the new head of Swiss culture. Isn't that out of the ordinary? J.-F.J.: When I was named director of the National Library, people found it strange that a mathematician could be chosen for the post. I have now been in the world of culture for 15 years... so [it is no longer] anything peculiar. I am an ardent believer in humanism in the purest sense of the word, that is to say, [one should] keep an open mind. I see no incompatibility between the worlds of maths, culture, IT, biology and other sectors. Our society needs to open its mind and that's how I see my arrival at the culture office. swissinfo: What did your time at the National Library teach you about the Swiss political world? J.-F.J.: Switzerland is a complex country. The ties among the federal government, the cantons and the communes in the field of culture are extremely complicated and the experiences I gathered at the National Library will stand me in good stead. We are a multicultural country and the essence of my role is to guarantee that each culture can express itself. swissinfo: Some politicians have raised their voices over "leftist" networks that would like to govern the world of culture in Switzerland. As a man of the right, are you there to swing the balance in the other direction? J.-F.J: I did not have to bring politics into my function at the National Library and I am not convinced that there's any need in this instance to bring a political counterbalance. There are different cultures, we are a multicultural country, and my basic task will be to make sure that everyone can express themselves. There is at present a debate between the state that is a patron and a state that sponsors. I lean quite clearly in favour of a state that acts as a patron, but for me the state should not get involved with content. We are there to put the framework and infrastructure in place but not to intervene when it comes to content, except to guarantee certain limits that are already defined by law. swissinfo: Which tasks will you undertake first? J.-F. J.: The first job will be to push through parliament the law on promoting culture, followed by another on the National Museum. That should be followed by legislation on the role of languages and a final law on coordinating institutions and bodies in the culture field. It's about trying to bring people together around the same table. Everyone will have to make an effort but there aren't that many differences of opinion. We will find a way to work together. The cultural nucleus of this country is incredible ? we are just not aware of it enough. swissinfo-interview New director believes in "vibrant" Swiss culture |
March 30, 2005
Mathematicians promise animation revolutionKevin Cryan of CSIRO Mathematical and Information Sciences says that current approaches to animating fluids like water, smoke, gases, lava and molten metals are based on relatively simplistic calculations and do not deliver anything like realistic motion. "Audiences are very good at assessing realism, so a poorly animated scene involving water or another fluid can reduce the overall impact of a production, causing the audience to be distracted from the story," says Mr Cryan. "What we are doing is taking the mathematical equations used to model complex fluid interactions, such as the aerodynamics of aircraft or the behaviour of mined ores in crushing mills, and applying them to animating fluids for motion pictures and computer games." When one or more fluids interact in a space, predicting flow behaviours like waves, bubbles, splashes, eddies and whirlpools requires extremely complex mathematical models. The science of Computational Fluid Dynamics (CFD) helps engineers understand how fluids behave so they can design better products and processes. "In recent times it has become clear that the equations developed by CSIRO to model how fluids behave can be used to analyse other complex phenomena. For example, we have created a software product, Reditus, which uses CFD methods for pricing complex financial options," says Mr Cryan. "Now CSIRO is working with the Korean Electronics and Telecommunications Research Institute (ETRI) to deliver new tools for animators working with fluids." "Korea is a global leader in animation and ETRI has chosen to work with CSIRO because they understand that the leap forward in animating liquids can only come from advanced mathematics." Prototype examples of CSIRO animations can be seen at http://www.cmis.csiro.au/mediarel/etrirelease.htm Mathematicians promise animation revolution |
March 30, 2005
Joint effort in fluid artsSelina Mitchell CSIRO mathematicians, more accustomed to modelling industrial processes, may soon provide the animation sector with a solution to a long-standing problem — realistic depiction of fluids. Fast, faithful animation of water, gasses, smoke, lava and molten metals in movies, computer games and advertisements has long been one of the biggest challenges of animation. The CSIRO team has joined forces with world-renowned Korean animators in a four-year project that aims to produce tools to speed up the process, and provide images so realistic viewers will reach for their umbrellas, CSIRO mathematical and information sciences business development manager Kevin Cryan says. The Korean Electronics and Telecommunications Research Institute approached the CSIRO to help it advance the technology used by Korean companies – and push its role in the industry from animating episodes of The Simpsons on the cheap to providing large-scale productions of their own. Next month, CSIRO scientists will meet local special effects and animation companies to assess their interest in the project. "We're taking the equations used to model complex fluid interactions, such as the aerodynamics of aircraft or the behaviour of mined ores in crushing mills, and applying them to animating fluids for motion pictures and computer games," Cryan says. The tools will deliver animations of fluids that are better than anything currently possible because of the high level of accuracy already attained in modelling industrial processes, he says. Perhaps more importantly, such tools can save production costs by speeding up the complex animation process, he says. Chris Spry, head of 3D at post-production facility, the LaB, says his group is looking forward to discussions with CSIRO. "Speed is our biggest problem," he says. "It can take three days to run through a simulation of one sequence of 100 frames, which is about four seconds worth. "Often we only have one or two weeks to produce the end result. Even though computers get faster, nothing gets quicker, the quality just gets better," Spry says. The LaB recently produced a Mizone drink commercial for the Chinese market that involved complex fluid animation. Animal Logic research and development director Guy Griffiths says representatives of his digital production company will meet CSIRO scientists in April to discuss the project. Griffiths says animating fluids is difficult, but the big issues is to have artistic control over the simulation. "Scientists ask, given the initial conditions, where will the fluid end up, but we want to be able to direct it." Computational fluid dynamics methods are already used in animation, Griffiths says. "We're trying to create a plausible reality." The CSIRO's achievements so far are the result of 15 years of work in computational fluid dynamics. The same work could also lead to breakthroughs in biotechnology (modelling the flow of blood through and around objects), financial services (risk analysis tools) and boatbuilding (next-generation fast ships), Cryan says. "If you make significant investments in core mathematics, you get benefits in ways you can't at the time begin to contemplate," Cryan says. "You're getting real innovation where the disciplines collide, such as IT and art, or IT and biology." The Australian Joint effort in fluid arts |
March 27, 2005
Martyn CundyTalented mathematician who played an influential role in the reform of school maths teaching in Britain - and Malawi TO BE awarded, after competition, one of the most prestigious prizes that the University of Cambridge can offer must be a crowning moment for every good young mathematician. And so it was for Martyn Cundy, who took the Rayleigh Prize in 1937 for his essay Motion in a Tetrahedral Field. Cundy's contemporaries were men such as Alan Turing, Harry Pitt and Fred Hoyle, all future Fellows of the Royal Society. With his background of distinctions in higher certificate in mathematics, divinity, Latin and Greek, and a starred examinee in part III of the mathematical tripos in 1935, Cundy might have been expected to take an immediate research fellowship at Trinity. Instead, he went a year later to Sherborne School, to teach mathematics. And so he became, gradually, the greatest teacher of the subject of his generation. Even in the golden interwar years of education when it was still common for those with good first-class degrees to go into the grammar schools and the better independents, it was astonishing that a Rayleigh prizewinner should do so. But if Cundy was a loss to university mathematics, he was an even greater gain to schools. Born in 1913, he must, as a boy, have picked up his deep Christian faith from his priest father who even named him after a forebear — the missionary Henry Martyn who had been Senior Wrangler in 1801. So at Cambridge, on becoming secretary of the 1934 Cambridge Prayer Fellowship, he began an active life of Christian witness. In turn, he was a Methodist lay preacher, the author of The Faith of a Christian, an elder in the Malawi Presbyterian Church, a lay reader in Kendal (and organist), and winner of the Diocese of Carlisle 850th anniversary hymnwriting competition. Each year his friends received a Christmas card with a delightful line drawing and a brief Nativity verse. His excellent personal relations must have been at least partly due to the serenity and composure which went hand in hand with his spiritual strength. He first came to the notice of the wider mathematical community in 1951 with the publication of Mathematical Models, jointly with A. P. Rollett. Still in print, this book became an inspiration for generations of mathematics teachers. But throughout his life there poured forth a continuous stream of at least 50 delightful and erudite articles published in the Mathematical Gazette. It was typical that many were based on some everyday artefact. But many others revolved round his fascination with triangles and their associated lines, circles and cubic curves. Such a paper in 2003 was voted Article of the Year and the last, published at the end of 2004, contained what must be the most complicated geometrical figure ever printed — and that despite the failing eyesight which distressed him in later years. More substantial research papers were published in the Journal of Geometry. In 1961 there came the opportunity to exert a decisive influence on school mathematics. Three heads of mathematics — Tom Jones, from Winchester, Douglas Quadling, from Marlborough and Cundy, from Sherborne — met, largely at the instigation of Bryan Thwaites (then a professor at Southampton and now Sir Bryan) to consider new syllabuses at O and A level. They were an exceptional trio, and it is hard to imagine that such a powerful group could be formed nowadays from schools. They were hugely ambitious in their plans, which included not merely new content but the writing of new, and novel, texts and teachers' guides, together with a large continuing programme of residential teacher-training courses. As more teachers became involved, a formal organisation was created: the School Mathematics Project. The SMP (as it became known) rapidly became the dominant player in the reform of school mathematics and its influence spread internationally, most notably in Africa. It is the only project of those heady years of curriculum reform in the early 1960s that still operates. In this great and complicated exercise Cundy played a hugely influential role in two respects. First, his profound knowledge enabled him to see mathematics in the round. There were connections between geometry and calculus and algebra which could be explored to the great advantage of the texts and which could kindle the interest of pupils. His own writing was always of the highest quality, clear and concise, and his tactful comments on the writing of others were always gratefully received. He edited both volumes of Advanced Mathematics (1968), which many would say were the finest sixth-form texts written. He exerted a quiet influence within working groups. The SMP necessarily spawned committees and planning meetings of all sorts. But Cundy was no committee man in the bureaucratic sense. Instead he was the great conciliator. He would look around an argumentative group without taking much part and simply make some quizzical remark which would not only suggest a solution but also settle tempers. Nevertheless, he was for a time deputy director and an initial trustee when the SMP became a registered charity in 1967. The SMP's growing involvement in overseas education led Cundy to the chair of mathematics in Malawi in 1968. His latent missionary zeal no doubt played a part in his decision to help the fledgeling university which was to move in 1973 from Limbe, near Blantyre, to Zomba, and he threw himself with gusto into its development. Mathematics may have been his first responsibility there, but he was also involved with other matters such as student housing, staff welfare and provision for religious worship. He had little difficulty in responding appropriately to local culture and customs, learning the local language Chichewa on the way. He was admirably supported by his wife Kittie, whom he married in 1939. She was a mathematics student at Cambridge where they first met. Cundy had a love affair with mountains, so he and Kittie took a special joy in walking the great African spaces. Their many guests from the UK were almost invariably offered a couple of days high on Mount Mulanje, the wonderful granite inselberg immortalised by Laurens van der Post in his novel Venture into the Interior. Nearer home was the Zomba plateau, for which they wrote and published a walkers ' guide. And it was typical of Cundy's approach to mathematics that he composed an A-level question based on his observation of the plateau's afternoon shadow moving on the plain below. The couple returned to Britain in 1975. After a brief stint in the Caribbean for the British Council, they settled in Kendal so as to be members of a lively church encompassed by mountains. There followed nearly 30 years of wideranging activity during which he always gave more than he received. Cundy was a man of huge talent and influence, beloved and respected by all who knew him and greatly admired by so many who did not. His bequest, with Kittie, spans their two chief interests, Christianity and mathematics, for two of their sons were heads of mathematics and the other is Bishop of Peterborough. Martyn Cundy, mathematician, was born on December 23, 1913. He died on February 25, 2005, aged 91. Martyn Cundy |
March 27, 2005
A Replicating MachineA revolutionary machine which can make everything from a cup to a clarinet quickly and cheaply, could be in all our homes in the decade. Research by engineers at the University of Bath could transform the manufacture of almost all everyday household objects by allowing people to produce them in their own homes at the cost of a few pounds. The new system is based upon rapid prototype machines, which are now used to produce plastic components for industry such as vehicle parts. The method they use, in which plastic is laid down in designs produced in 3D on computers, could be adapted to make many household items. However, conventional rapid prototype machines cost around £25,000 to buy. But the latest idea, by Dr Adrian Bowyer, of the University's Centre for Biomimetics, is that these machines should begin making copies of themselves. These can be used to make further copies of themselves until there are so many machines that they become cheap enough for people to buy and use in their homes. Dr Bowyer is working on creating the 3D models needed for a rapid prototype machine to make a copy of itself. When this is complete, he will put these on a website so that all owners of an existing conventional machine can download them for free and begin making copies of his machine. The new copies can then be sold to other people, who can in turn copy the machine and sell on. As the number of the self-replicating machines – there are now thousands of conventional rapid prototype machines – grows rapidly, so the price will fall from £25,000 to a few hundred pounds. "People have been talking for years about the cost of these machines dropping to be about the same as a computer printer," said Dr Bowyer. "But it hasn't happened. Maybe my idea will allow this to occur." A machine could, for instance, make a complete set of plates, dishes and bowls out of plastic, coloured and decorated to a design. It could also make metal objects out of a special alloy that melts at low temperatures, making it suitable for use in printed circuit boards for electronics. The machines would not be able to produce glass items or complex parts such as microchips, or objects that would work under intense heat, such as toasters. But a digital camera could be made for a few pounds, and a lens and computer chip bought separately and added later. The rapid prototype machines would be useful for producing items that are now expensive, such as small musical instruments. The items produced could be from a few millimetres (0.25 inches) to 300 millimetres (12 inches) in length, width and height. Larger items could be made simply by clipping together parts of this size. Dr Bowyer said all that would be needed for a machine owner would be to buy the plastic and low-temperature alloy for a few pounds, and items could then be created in a few minutes or a few hours depending on their size. Designs for items could be bought – or downloaded free – from the web. Alternatively, people could create them for themselves on their own PCs. He said that he would publish the 3D designs and computer code for the machine to replicate itself on the web over the next four years as they are developed, until the entire machine could be copied. He said that he has not taken out a patent and will not charge for creating the design for the machine. "The most interesting part of this is that we're going to give it away," he said. "At the moment an industrial company consists of hundreds of people building and making things. If these machines take off, it will give individual people the chance to do this themselves, and we are talking about making a lot of our consumer goods – the effect this has on industry and society could be dramatic." The machines would be about the size of a refrigerator, and would self-reproduce by making a copy of themselves, part by part. These parts would then have to be assembled manually by their owners. Dr Bowyer said the machines were a form of Universal Constructor, first proposed theoretically by the mathematician John von Neumann in the 1950s. He also said their progress would be similar to that of a species in nature – as the machines replicated, so their users would vary them to suit their needs, some making larger objects, some more accurate devices and some making devices more quickly. Dr Bowyer, and his colleague Ed Sells, have already created a demonstration robot with an electrical circuit built in using this technology and funding from the Nuffield Foundation. They hope to get new funding soon to begin work on the other stages of development. A Replicating Machine |
March 27, 2005
Natural Selection, Inc. Wins U.S. Air Force SBIR Phase IINatural Selection, Inc. has been awarded a $748,848 Phase II Small Business Innovation Research (SBIR) contract from the U.S. Air Force Research Laboratory to develop technology to evolve courses of action for mission planning, such as is required in unmanned aerial vehicle (UAV) operations. The contract's principal investigator is Dr. David Fogel, CEO of Natural Selection, Inc.: "There is a critical need for combat simulations to incorporate intelligently interactive agents, both for mission planning and training. The technology we are developing will allow mission planners to optimize courses of action on-the-fly, while considering what the responses of opposing forces are likely to be." The technology relies on evolutionary computing to adapt plans in light of evolved enemy courses of action (known as eCOAs) in a sequential manner, where each side anticipates what the other will do for a period of time projected into the future. "We have developed new methods of employing evolutionary algorithms to make real-time course-of-action planning and replanning feasible," said Dr. Fogel. Part of the SBIR Phase II project involves the parallelization of Natural Selection, Inc.'s evolutionary computing tools on a cluster of personal computers. "There are numerous commercial applications of this technology as well," offered Dr. Fogel. "One in particular involves improving the design of intelligent agents in entertainment software as found in massively multiplayer online games." Natural Selection, Inc. is now in the second year of a National Science Foundation SBIR Phase II grant to develop evolutionary computing and neural network technology to improve the performance of characters in entertainment software and reduce the time required to develop and test new games. Natural Selection, Inc. was founded in 1993 to address complex problems in industry, medicine, and defense. The company possesses unique expertise in computational intelligence techniques, including evolutionary computation, neural networks, and fuzzy logic. The corporation's research efforts support the discovery of new pharmaceuticals, the automated detection and discovery of important patterns and processes in bioinformatics and medical informatics, computer-assisted diagnosis, and a variety of military and industrial projects. Natural Selection, Inc. Wins U.S. Air Force SBIR Phase II |
March 27, 2005
Jeff Hawkins' Bold BrainstormBy Peter Burrows The man who launched Palm thinks he can give machines the smarts to work just like the human mind. Ambitious? Yes, but the experts aren't laughing It's a few days before the public launch of his new company, and Jeff Hawkins is excited but also concerned. "We don't want this to get overhyped," he says, slumping down with his head nearly on the conference table of his small Menlo Park (Calif.) office. And worry about overexposure he should. For starters, Hawkins is a proven entrepreneur. The world's most famous designer of handheld computers, he co-founded Palm Computing and its offspring, Handspring (see BW Online, 10/21/04, "Wizard of the Wireless Future"). UNIFIED THEORY. This time, he's aiming at a far bigger opportunity than selling handheld gizmos. With his new company, Numenta, which he'll unveil on Mar. 24, he's trying to do no less than create machines that work just like the human brain. "This could radically change the way that computer systems work," says Harry Saal, a Silicon Valley veteran and one of a handful of investors in the company. Certainly, Hawkins' pedigree, coupled with the vast implications of his new quest, will garner a lot of attention. But before you ask, the answer is no -- Hawkins' inquisitive brain hasn't taken him around the bend. Neuroscience, the study of the brain, has fascinated him since 1979, when he read a Scientific American article on the roots of intelligence. It started his obsession with finding the Holy Grail of neuroscience: a unified theory of how the brain works. While neuroscientists over the years have parsed the problem into more digestible chunks -- say, how a neuron fires -- he says no one has put all the pieces together. "I tried several times to make this my career," says Hawkins, who three years ago created the self-funded Redwood Neuroscience Institute, where he spends most of his time. "Nobody had done the theoretical analysis of the brain." "GENTLEMAN SCIENTIST?" Now, he thinks he has figured it all out and believes that he and an associate have come up with a way to translate his theories into electronic terms. Their company will license -- for free, at least for the first few years -- technology to others who may want to create what he predicts will be truly intelligent machines. "He's moving from the neuroscience to the computer science," says Palm and Handspring co-founder Donna Dubinsky, who will serve as Numenta's chief executive. (Hawkins' title will simply be "founder.") Of course, Hawkins' goal carries long odds, and critics say he has tried to take a shortcut by skirting peer review and letting the market, rather than more research, prove or disprove his theories. Some compare him to a certain 18th-century gentleman scientist -- a rich man using his personal wealth to pursue a radical vision. Of course, for every Ben Franklin, there were scores of others whose aspirations never panned out. Not surprisingly, Hawkins' work is raising big questions from the hard-core science crowd. "He's a man of action, and he wants to get things done," says Terrence Sejnowski, head of the Computational Neurobiology Laboratory at the Salk Institute for Biological Studies in San Diego. "That's a different mode from most scientists, who are more interested in taking small steps and getting each step right." NEURAL HIERARCHY. Hawkins' basic theory, laid out in his 2004 book, On Intelligence (see BW, 11/08/04, "Redefining Smart"), says the brain doesn't function as a miraculously fast processing unit, like a microchip. Instead, it represents a rather simple memory system that keeps track of all kinds of patterns over time -- whether they are sights, sounds, textures, or any other kind of input. He believes this system is hierarchical -- that there are lower-level bits of brain that note specific details, which humans later synthesize into overall experiences. That allows someone, for example, to know that the combination of the touch of a finger on the shoulder and the sight of a masseuse's pillow means a massage will ensue. By gathering an uncountable number of these patterns every instant of every day, the brain -- actually, the neocortex, or "the big wrinkly thing on top of the brain that does all the higher-level functions," as Hawkins puts it -- can predict what to make of any situation it encounters. COMPUTERIZED CLAIRVOYANCE. If Hawkins' idea works, it could have an almost limitless number of applications. Attached to electronic eyes, such systems could pick out a terror suspect's face in a crowd as quickly as you could spot your mother -- a task today's computers can't handle. The systems would also have military uses. Unmanned aircraft could go far beyond the rudimentary drones now in use. Or, the Army could outfit soldiers with a small device and various sensors enabling them to see, hear, and detect all manner of threats -- from an enemy creeping up from behind, to footsteps around the corner. Plug in enough weather data, and one of Hawkins' computers might predict rain or snow -- not based on an actual forecast, but with a kind of electronic sixth sense akin to what experienced fishermen feel when they scan the skies. FREE SAMPLES. Since 2003, Hawkins and co-founder Dileep George, who will serve as principal engineer at Numenta, have been working on software that incorporates such basic memory architecture. So far, they've developed a proof-of-concept program. By "showing" their program 90 simple line drawings -- one of a helicopter, another of a dog, for example -- they can teach it enough to identify another drawing of that object, even if it's poorly drawn or incomplete. While science has already made similar efforts at machine vision, Hawkins insists this marks the first time a piece of software has had such predictive power. "If I see a cat behind a chair, I don't think it's half a cat," he says. And neither does his software, he claims. While there is no undeniable proof of his sweeping unified theory, Hawkins has enough to take the next step: to develop the software and related tools so that engineers from various disciplines can try it out in their worlds. INSTANT DEMAND. To encourage such widespread use, Numenta will initially charge nothing for its technology. Hawkins and Dubinsky, who have raised an undisclosed amount from a handful of friends and associates, will supply most of the $1 million-plus annual budget themselves. They still need to figure out the licensing details. "The next step in the evolution of this is to create a profit motive for people to rally around," says Hawkins. Adds Gary Bradski, a machine-learning expert at Intel (INTC ): "Even if he's wrong, his theory is better than nothing. And it's 'attackable' -- and that's a good thing." Certainly, indications point to Hawkins receiving lots of interest. Raj Kent, a technologist with Lockheed Martin Advanced Technology Labs (LMT ), says he has already spoken with Numenta about seeking grants for "cognitive computing" research the Defense Advanced Research Projects Agency will offer. "THE MOST IMPORTANT THING." And Ajay Bakshi, a consultant in McKinsey & Co.'s health-care practice, read Hawkins' book and plans to contact him about using his ideas to help pharmaceutical companies discover new drugs. "Nobody was stepping back and looking at the big picture [of how the brain works]," he says. "Hawkins has given us a very big picture. It's a low-resolution picture -- but it will lead to a whole bunch of experiments." That's just what Hawkins wants. "I don't need to run another company," he says. "But I think this is the most important thing I can do with my life. I'm trying to create a movement. Artificial intelligence had one for years, and neural networks had its time. But they were flawed theories. And I think we've got it right." Experts caution against making such a claim too soon. But even if Hawkins finds only a small sliver of the Holy Grail he seeks, he'll add yet another industry-moving startup to his résumé. Jeff Hawkins' Bold Brainstorm |
March 27, 2005
A New Company to Focus on Artificial IntelligenceBy JOHN MARKOFF The technologist and the marketing executive who co-founded Palm Computing in 1992 are starting a new company that plans to license software technologies based on a novel theory of how the mind works. Jeff Hawkins and Donna Dubinsky will remain involved with what is now called PalmOne, but on Thursday they plan to announce the creation of Numenta, a technology development firm that will conduct research in an effort to extend Mr. Hawkins's theories. Those ideas were initially sketched out last year in his book "On Intelligence: How a New Understanding of the Brain Will Lead to the Creation of Truly Intelligent Machines," co-written with Sandra Blakeslee, who also writes for The New York Times. Dileep George, a Stanford University graduate student who has worked with Mr. Hawkins in translating his theory into software, is joining the firm as a co-founder. Mr. Hawkins has long been interested in research in the field of intelligence, and in 2002 he founded the Redwood Neuroscience Institute. He now spends part of his time there while continuing to serve as chief technology officer of PalmOne. Artificial intelligence, which first attracted computer scientists in the 1960's, was commercialized in the 1970's and 1980's in products like software that mimicked the thought process of a human expert in a particular field. But the initial excitement about machines that could see, hear and reason gave way to disappointment in the mid-1980's, when artificial intelligence technology became widely viewed as a failure in the real world. In recent years, vision and listening systems have made steady progress, and Mr. Hawkins said that while he was uncomfortable with the term artificial intelligence, he believed that a renaissance in intelligent systems was possible. He said that he believed there would soon be a new wave of software based on new theoretical understanding of the brain's operations. "Once you know how the brain works, you can describe it with math," he said. Mr. Hawkins acknowledged, however, that full-scale applications of his theoretical approach had not yet been developed or proved . Mr. Hawkins is now demonstrating a pattern-recognition application using a version of his software. It allows a computer to correctly identify a line drawing of a dog from many different patterns. Commercial uses for the technology might include speech recognition for telephone customer service or vision systems for quality control in factories. Initially, the company will offer free licenses to the Numenta software to permit experimentation and help build a research community to develop the technology, Ms. Dubinsky said. Neuroscience researchers said Mr. Hawkins's theories were promising but still unproved. "Jeff is doing interesting work, and he may well recharge the field, whether or not his particular algorithms play out," said Gary Bradski, a neuroscientist who manages the machine learning group at the Intel Corporation. "He's had good instincts on his last two ventures." Mr. Hawkins and Ms. Dubinsky left Palm Computing in 1998 to form Handspring. They then returned to Palm in 2003 when it acquired Handspring in an effort to speed its entry into the market for smart phones. Ms. Dubinsky is currently a PalmOne board member. Mr. Hawkins said that in addition to his work with Numenta he was developing a new product for PalmOne. A New Company to Focus on Artificial Intelligence |
March 27, 2005
THE CRYPTOGRAPHY GURUBy Dan Lee Bruce Schneier, founder and chief technical officer of Counterpane Internet Security, might be as close as the computer security industry gets to its own celebrity. Although not as well known as Larry Ellison at Oracle or Bill Gates at Microsoft, Schneier is still the public face of his company, recognized by industry insiders as one of their gurus. Businesses hire Counterpane to guard their networks from hackers and viruses in the same way a nervous homeowner would pay a home-security provider like ADT to watch for fires or burglars. But unlike most entrepreneurs, Schneier admits that he spends much of his time not focused on his creation. Schneier helped build the Mountain View start-up through his technical expertise and the exposure he brings as a high-profile security guru, but he has turned its operations over to others to run. While they introduce new services to make the company profitable after five years and $78 million in venture funding, he focuses on what he sees as loftier issues. ``I tell people how to think about security: what works, what doesn't and why,'' Schneier, 42, a New York native, said of his role. ``I'm not involved day to day with Counterpane, but I never intended to be.'' Schneier, who lives in Minneapolis, divides his time between Counterpane and writing and speaking on security. He tackles issues from the debate over national ID cards to how scam artists trick computer users into divulging personal information. He began his career in search of a perfect mathematical solution to computer security through cryptography, the technology of putting data into a secret code so it's unreadable except by those allowed to see it. His book ``Applied Cryptography'' remains a widely read introduction to the complex field. Paul ``Tony'' Watson, a network security architect for Google, credited Schneier with ``bringing an understanding of encryption to the masses.'' Rare exposure Counterpane Chief Executive Paul Stich said Schneier's witty and opinionated ways bring the company a level of exposure rare for a start-up with just 100 employees. ``A lot of people say, `the reason we trust Counterpane is we trust Bruce,' '' Stich said. ``He does it naturally. It would be foolish to discourage him.'' And when Schneier talks, it can be wild. Some cheer. Others fume. At last month's RSA Conference in San Francisco, the nation's largest gathering of computer security professionals, Schneier said he couldn't even grab a meal at a hotel bar without being mobbed by strangers. Tom Rowley, who founded Counterpane with Schneier in 1999 after a lunch conversation and served as its first chief executive until Stich took over in 2003, told a similar story about Schneier at a security gathering. ``As we walked down the hall, there were people who were bowing to him,'' he said. ``They were kind of joking but kind of not.'' His Crypto-Gram newsletter goes to 120,000 e-mail inboxes each month, and he said his blog at www.schneier.com has an audience of 20,000. But Schneier's exposure has also caused Rowley some headaches. Schneier's newsletter showcases a ``Doghouse'' for what he calls ``stupid security companies or products.'' He dismisses some technology as ``snake-oil cryptography.'' ``I used to get sued or threatened to be sued about once a quarter by someone who Bruce had offended,'' said Rowley. Counterpane began by monitoring corporate customers' networks for security breaches but has since added more offerings. That includes services added last month for scanning e-mail or protecting against attacks known as a Distributed Denial of Service, in which a Web site is flooded with junk data in an effort to cripple it. The company feeds information from a customer's existing security hardware -- such as firewalls and intrusion-detection devices -- through its own security device and analysis system to thwart attacks. Counterpane said its 65 security analysts in Mountain View and Chantilly, Va., provide constant watch over 500 networks in 38 countries. Counterpane's approach to watching so many networks gives it expertise in spotting new attacks and security trends, said Peter Christy, principal analyst with NetsEdge Research. ``Security is exactly one of those things where you want some of the best people in the world sleeping in the firehouse, eating chili waiting for the fire alarm to go off,'' he said. At odds with Cisco? However, Christy added that Counterpane could find itself at odds with networking giant Cisco Systems, a leading seller of firewalls and other devices to protect corporate networks. He said the start-up has tended to recommend that customers go with a mix of mostly non-Cisco products, an approach that holds risks if Cisco comes to dominate the security field as it has networking. Counterpane also faces competition from security-software maker Symantec and Internet services company VeriSign. The company is ``close to breaking even,'' Stich said. It has about 150 business customers, including Pacific Gas and Electric, General Mills and Royal Bank of Canada. Stich said an average customer spends roughly $15,000 to $20,000 a month for Counterpane's services. Watson, the Google security expert, remembered when Counterpane came up during a chat he had with Schneier several years ago while the two sat in heavy Chicago traffic. ``He made an offhand comment about how all the traffic seemed so unnecessarily, wasteful and inefficient,'' Watson recalled. ``We debated the issue, and at some point I commented that without commerce and traffic, his new Counterpane business wouldn't make any money. ``The response I received was that he would be more than happy to trade his business if it would help make the world a little better. At the time, it struck me as somewhat eccentric, odd and idealistic, but I believe those are terms that describe Bruce quite well.'' THE CRYPTOGRAPHY GURU |
March 27, 2005
RSA Finds More Flaws in RFIDBy Jacqueline Emigh After uncovering a security weakness in a radio-frequency identification tag from Texas Instruments Inc., researchers from RSA Security Inc.'s RSA Laboratories and The Johns Hopkins University are now eyeing future exploits against other RFID products in the interests of better security, one of the researchers said this week. Meanwhile, TI will keep making the compromised RFID tag in order to meet the needs of applications more sensitive to speed and pricing than to privacy, according to a TI official. The Johns Hopkins University Information Security Institute and RSA first publicized their findings about the RFID security hole in January. In a paper posted at www.rfidanalysis.org, the researchers claim that by cracking a proprietary cipher, or encryption algorithm in one of TI's DST (digital signature transponder) RFID tags, they were able to circumvent the tags' built-in security enough to buy gasoline and turn on a car's ignition. Paul Sabetti, global business manager for TI's RFID Systems, acknowledged that the DSTs contain some proven vulnerabilities. But Sabetti also described the security risk as relatively minimal, calling it a "tradeoff" that some makers of electronic payment and vehicle immobilization systems are willing to accept. Some of TI's customers in these niches produce car keys or tokens, and others, complete systems. The RFID tags compromised by Johns Hopkins and RSA—part of TI's DST-40 tag lineup—use a proprietary 40-bit encryption algorithm first written in 1999. "Why are we using a proprietary algorithm? Because it's faster [that way] to produce inexpensive chips," Sabetti said. The researchers from Johns Hopkins and RSA reverse-engineered and emulated the 40-bit encryption over two months. But DST-40 tags are only one part of a larger RFID portfolio that also includes a DST "Plus" edition—featuring "a series of memory features and encryption scalable to 80 bits"—as well as an "RFID credit card" lineup with industry-standard 128-bit Triple DES encryption, he said. RSA Finds More Flaws in RFID |
March 23, 2005
Why Science Can't Show Us GodBy Margaret Wertheim This month, the Nobel Prize-winning physicist Charles Townes won the $1.5-million Templeton Prize, an award given out for "progress toward research or discoveries about spiritual realities." What does it mean that a religious prize is being given to a physicist? Townes, in fact, is the fifth scientist to have won the award (the world's most lucrative academic prize). Fellow physicist winners include Freeman Dyson of the Institute for Advanced Study in Princeton, N.J., cosmologist Paul Davies, general-relativity expert George Ellis and particle physicist John Polkinghorne. "Religion," Townes told the journal Physics World, "is aimed at understanding the purpose and meaning of our universe, including our own lives. If the universe has a purpose and meaning, this must be reflected in its structure and functioning, and hence in science." In 1966, in the wake of his Nobel Prize, Townes was even bolder. In an article published in MIT's Technology Review, he wrote that differences between science and religion "are largely superficial … the two become almost indistinguishable if we look at the real nature of each." The idea that science and religion coalesce in the structure of the universe has been expressed by a slew of physicists in recent years. Among them are Davies, in his bestselling book "God and the New Physics," and Stephen Hawking, in "A Brief History of Time." In this view, science and religion both find their apotheosis in a Theory of Everything — a unified account of all the world's forces and particles. Know the final equations, Hawking tells us, and you will know "the mind of God." There is nothing new about this notion, but there is something fundamentally missing from this portrayal of the religious enterprise, at least from a Christian point of view. Contrary to widespread belief, religion and science have not always been at odds. The idea that science may illuminate the divine predates Christianity and goes back to the great pioneer of mathematics, Pythagoras of Samos in the 5th century BC. Pythagoras believed that numbers were literally gods, and he associated the numbers 1 through 10 with the major gods of the Greek pantheon. In Pythagorean science, to find mathematical relations behind physical phenomena was to find the divine harmonia by which the universe had been created. This was the original "music of the spheres," an idea that was to have a profound effect on the evolution of modern physics. From the 13th through 17th centuries, the Pythagorean notion of an underlying cosmic harmony gradually gave rise to the idea that the Judeo-Christian God had created the world according to a divine mathematical plan — the "laws of nature." To discover and understand these laws was to decipher God's plan, and therefore an essentially religious act. As Isaac Newton's great predecessor, Johannes Kepler, wrote: "For a long time, I wanted to become a theologian…. Now, however, behold how through my effort God is being celebrated in astronomy." Newton himself saw his scientific work as one long argument for a beneficent Creator. The elision of God and physics today follows directly from this tradition, but there is a critical difference between the scientific theologizing of Kepler and Newton and that of physicists like Hawking and Townes. The Christian God has two aspects: God the Creator and God the Redeemer. The former acts at the beginning of time, the latter reigns at the end. For most of Christian history, intellectual reflection was focused on God the Redeemer, for the core of Christian theology and faith has always been the end-time promise of resurrection and atonement. Christ died and rose to heaven as the guarantee that eventually all true believers would follow him into the everlasting bliss of paradise. Kepler and Newton were adamant that the value of their work lay in its support for God's salvific function. Yet as time went by, God the Redeemer has gone missing from the "god and physics" discourse. That is because material science can say nothing about sin and grace, let alone heaven, a place that by definition is beyond the purview of modern science. Of the five physicists who have won the Templeton Prize, four are practicing Christians. (Townes, for example, is a member of the First Congregational Church in Berkeley.) While the claim they make for the discoveries of science supporting their faith in God the Creator is certainly, legitimate, that is surely only half the task. "Progress" in religion must be judged not by our knowledge of particles and forces but by action toward a more just, equitable and humane society. By equating God with the "structure and function" of the material world, Christians play a losing game. As the Jesuit philosopher Michael Buckley has pointed out, rational inference can never substitute for personal experience of the divine — which is, and must remain, the grounding of faith. Why Science Can't Show Us God |
March 23, 2005
Genius with big ideaJUDY SIEGEL-ITZKOVICH A Jerusalem high school pupil who "improved on" an algorithm formulated by a 19th-century British mathematician to study black holes has won first prize in the eighth annual Intel-Israel Young Scientists Competition. Elad Oster of the Jerusalem High School for the Sciences and Arts was awarded a scholarship from Intel for his achievement, which was hailed by President Moshe Katsav at Beit Hanassi on Tuesday. Oster looked at the Newton-Raphson algorithm, which is a dynamic system to solve concrete numerical equations but is not effective on complex equations. Over a century ago, a British mathematician published a short article in which he asked whether the algorithm can solve complex equations, but there has been no answer until now. Oster took the problem to the three-dimensional sphere and suggested ways of improving the algorithm and finding solutions in a way that has practical applications for raising the level of accuracy in calculations. The team of judges, headed by Hebrew University physicist Prof. Hanoch Guttfreund, said the teenager had contributed to a real breakthrough in solving the mathematician's problem. Second prize was awarded to three teams: Liron Mark of the Leo Baeck School in Haifa, who studied the role of the Israeli press in the great crisis that occurred in the wake of the Yom Kippur War, changing from a "voice of the establishment" to "the watchdog of democracy"; to San Bitan, Yuval Nativ and Yehonatan Weintraub of the Practical Engineering School in Tel Aviv, for developing algorithmic solar sensors to support a project for sending nano-satellites to revolve around Earth; and Hasouna Fuad of the Orthodox High School in Ramle, who investigated the influence of replication conditions of DNA in on the frequency and type of mutations in Im7 genes. Third prize was given to Harel Cohen and Daniel Mazor of the Ma'ayan Shahar educational complex, who designed inflated plastic suits worn during occupational therapy sessions by children with cerebral palsy and the mentally disabled and used in interaction with animations on a computer screen; and Avraham Dayan of Petah Tikva, who studied the influence of the RTP801 gene in protecting the heart muscle when it is starved of oxygen and opened possibilities of gene therapy for heart attack victims. Anna Tatrov and Tim Mitnick of Herzliya shared fourth place for studying the connection between urban air pollution and biochemical and neurological mechanisms, especially the role of pollution in causing headaches misdiagnosed as migraines. Seven others received citations of excellence. These young geniuses were the cream of a crop of 69 finalists who presented 39 scientific projects for consideration at the Bloomfield Science Museum in Jerusalem. The top eight winners will represent Israel at the Intel International Young Scientists Contest. Genius with big idea |
March 23, 2005
NYU's Peter Lax Wins 'Nobel Prize of Mathematics'BY GARY SHAPIRO A New York University professor emeritus at the Courant Institute of Mathematical Sciences, Peter Lax, has won the $980,000 Abel Prize, popularly known as the Nobel Prize of mathematics. That's $1 million minus only $20,000, for those of who are not mathematically inclined. The 78-year-old will travel to Oslo, Norway, May 24 to receive the prize, established by the Norwegian Academy of Science and Letters. "Besides being the dominant figure in applied mathematics in his time, he's also one of the world's central figures in pure mathematics," a New York University professor, Sylvain Cappell, said. Of all fields of mathematics, that of differential equations, which allows an understanding of how quantities vary over time, is probably the most important for applications, a Princeton and NYU professor, Peter Sarnak, said. "Lax has made fundamental contributions to almost every aspect of this topic," he said. Mr. Lax immigrated to America from Budapest at 15. After traveling through Germany by train, he and his parents - both doctors - boarded the last boat from Portugal on December 5, 1941. Before Mr. Lax was 16, the eminent John von Neumann paid him a visit him at his parents' Upper West Side apartment after two of his former Budapest teachers recommended him as a promising mathematician. Mr. Lax, who attended Stuyvesant High School, had once won a competition of high school students involving geometry, and von Neumann probed him with questions about what problems he had worked on. Over a tea in Princeton in spring 1942, the kindly mathematician Paul Erdos introduced Mr. Lax to Albert Einstein as a talented young Hungarian mathematician. Einstein turned to Erdos and asked: Why mention Hungarian? Mr. Lax's Ph.D. studies at New York University dealt with hyperbolic equations, which describe motions of sound, light, and electromagnetic waves, and compressible fluids. During World War II, Mr. Lax was a GI whose basic training in Florida took place at an "infantry replacement training center," which he said "sounded like cannon fodder." Assigned to the Manhattan Project at Los Alamos, N.M., in 1945-46, he worked on neutron transport. During trips in subsequent years to Los Alamos, von Neumann helped spark Mr. Lax's interest in shock waves, an area to which Mr. Lax later made important research contributions. Mr. Lax did foundational work on finding solution to equations that describe the way a single wave moves. It has been long noticed, for example, that a single water wave down a canal will preserve its shape for astonishing distances; his work furthered understanding of such phenomena. Mr. Lax's varied contributions touch areas such as scattering theory (which addresses, for example, how a wave goes around an obstacle) and modern computational mathematics. Mr. Lax's ideas - often at the intersection of mathematics and physics - have importance for aerodynamics and weather prediction, as well as for CAT scans and oil rigs. He modestly said: "It is typical of mathematics that its ideas are very generally applicable." He praised the Courant Institute's supportive atmosphere and published a paper in 1956 with its founder, Richard Courant, his former thesis advisor, on how signals propagate. Mr. Lax recalled the sense of humor of another teacher, Fritz John, who reputedly said, "What is the reward of mathematicians? The grudging admiration of a few friends." The Abel Prize, Mr. Lax said, shows that there are other rewards. The call informing Mr. Lax that he had won the prize came at 5:30 a.m. He was asked if it had awoken him. It had. "It was a Norwegian accent, so I thought it was probably true," he said. Mr. Lax won the Wolf Prize in 1987 and the Chauvenet Prize in 1974, among other awards. President Reagan presented him the National Medal of Science in 1986. He has been president of the American Mathematical Society and directed the Courant Institute from 1972 to 1980. His late wife, an important leader in American college mathematics teaching, also taught at NYU. One son is a doctor; the other, who was working toward a Ph.D. at Columbia in history, was killed by a drunk driver. Mr. Lax is currently working on a second edition of his book "Linear Algebra" (Wiley-InterScience) to make it more "user-friendly." "All of us who have admired his work are pleased that he has gotten this recognition," said Ed Witten of the Institute for Advanced Study at Princeton, whose own research has utilized "Lax pairs" (named for Mr. Lax), by which integrable or soluble nonlinear equations are understood. "Since his father was still playing tennis and had a girlfriend in his late 90s," Mr. Cappell said, "we expect Lax to continue to earn awards." NYU's Peter Lax Wins 'Nobel Prize of Mathematics' |
March 23, 2005
Retired prof scores top math awardby Emily Tan NYU alum and professor emeritus Peter D. Lax will be awarded the Abel Prize, known as the "Nobel Prize" of mathematics in May, the Norwegian Academy of Science and Letters announced Thursday. Lax will receive the prize - and $980,000 - for work he did in the 1950s and '60s. Some of his contributions to mathematics include forming the foundations of the modern theory of nonlinear equations for hyperbolic systems, and developing the "Lax equivalence theorem" for modern numerical analysis. "Peter D. Lax has been described as the most versatile mathematician of his generation," the academy wrote in a statement. "He has had a profound influence, not only by his research, but also by his writing, his lifelong commitment to education and his generosity to younger mathematics." Partly because there is no Nobel Prize category for mathematics, the Norwegian Academy of Science and Letters established the Abel Prize in January 2002 to honor individuals who have done outstanding work in mathematics. But Lax, 78, said the honor was not expected. "One doesn't count on these things," he said. "I was very pleasantly surprised. It's like a dream come true." Lax worked on the Manhattan Project at Los Alamos from 1945-46 and then earned his bachelor's degree in 1947 and his Ph.D. in 1949 from NYU. He became an NYU assistant professor of mathematics in 1949 and served as director of the Courant Institute of Mathematical Sciences from 1972 to 80. Courant named Lax a professor emeritus in 1999. Since forming the theories that earned him the Abel Prize, Lax said, he has continued his work, writing books and serving on the National Science Board for six years. Lax said he hasn't thought much about how he will spend his monetary prize, but he does have some idea of what he will do. "It's nice to have money," he said. "I guess I can help my grandchildren with education. That's always very expensive." Lax's wife passed away five years ago and his oldest son was killed by a drunk driver at the age of 28. His one surviving son has three kids, the oldest of whom is 21. Courant Director Charles Newman said in a statement that Lax is "a wonderful person and a cherished colleague" who is very deserving of the prize. "He exemplifies the philosophy of the [Courant] Institute that there are no real divisions between the applied and pure mathematical sciences," he said. Lax will receive the Abel Prize from King Harald V of Norway in Oslo on May 24 Retired prof scores top math award |
March 23, 2005
Classic maths puzzle cracked at lastMaggie McKee A number puzzle originating in the work of self-taught maths genius Srinivasa Ramanujan nearly a century ago has been solved. The solution may one day lead to advances in particle physics and computer security. Karl Mahlburg, a graduate student at the University of Wisconsin in Madison, US, has spent a year putting together the final pieces to the puzzle, which involves understanding patterns of numbers. "I have filled notebook upon notebook with calculations and equations," says Mahlburg, who has submitted a 10-page paper of his results to the Proceedings of the National Academy of Sciences. The patterns were first discovered by Ramanujan, who was born in India in 1887 and flunked out of college after just a year because he neglected his studies in subjects outside of mathematics. But he was so passionate about the subject he wrote to mathematicians in England outlining his theories, and one realised his innate talent. Ramanujan was brought to England in 1914 and worked there until shortly before his untimely death in 1920 following a mystery illness. Curious patterns Ramanujan noticed that whole numbers can be broken into sums of smaller numbers, called partitions. The number 4, for example, contains five partitions: 4, 3+1, 2+2, 1+1+2, and 1+1+1+1. He further realised that curious patterns - called congruences - occurred for some numbers in that the number of partitions was divisible by 5, 7, and 11. For example, the number of partitions for any number ending in 4 or 9 is divisible by 5. "But in some sense, no one understood why you could divide the partitions of 4 or 9 into five equal groups," says George Andrews, a mathematician at Pennsylvania State University in University Park, US. That changed in the 1940s, when physicist Freeman Dyson discovered a rule, called a "rank", explaining the congruences for 5 and 7. That set off a concerted search for a rule that covered 11 as well - a solution called the "crank" that Andrews and colleague Frank Garvan of the University of Florida, US, helped deduce in the 1980s. Patterns everywhere Then in the late 1990s, Mahlburg's advisor, Ken Ono, stumbled across an equation in one of Ramanujan's notebooks that led him to discover that any prime number - not just 5, 7, and 11 - had congruences. "He found, amazingly, that Ramanujan's congruences were just the tip of the iceberg - there were really patterns everywhere," Mahlburg told New Scientist. "That was a revolutionary and shocking result." But again, it was not clear why prime numbers showed these patterns - until Mahlburg proved the crank can be generalised to all primes. He likens the problem to a gymnasium full of people and a "big, complicated theory" saying there is an even number of people in the gym. Rather than counting every person, Mahlburg uses a "combinatorial" approach showing that the people are dancing in pairs. "Then, it's quite easy to see there's an even number," he says. "This is a major step forward," Andrews told New Scientist. "We would not have expected that the crank would have been the right answer to so many of these congruence theorems." Andrews says the methods used to arrive at the result will probably be applicable to problems in areas far afield from mathematics. He and Mahlburg note partitions have been used previously in understanding the various ways particles can arrange themselves, as well as in encrypting credit card information sent over the internet. Classic maths puzzle cracked at last |
March 23, 2005
Math Guy: The Birthday ProblemKeith Devlin What is the probability that in a room filled with 23 people at least two of them have the same birthday? (It's more than half!) Devlin explains: The birthday problem asks how many people you need to have at a party so that there is a better-than-even chance that two of them will share the same birthday. Most people think the answer is 183, the smallest whole number larger than 365/2. In fact, you need just 23. The answer 183 is the correct answer to a very different question: How many people do you need to have at a party so that there is a better-than-even chance that one of them will share YOUR birthday? If there is no restriction on which two people will share a birthday, it makes an enormous difference. With 23 people in a room, there are 253 different ways of pairing two people together, and that gives a lot of possibilities of finding a pair with the same birthday. Here is the precise calculation. To figure out the exact probability of finding two people with the same birthday in a given group, it turns out to be easier to ask the opposite question: what is the probability that NO two will share a birthday, i.e., that they will all have different birthdays? With just two people, the probability that they have different birthdays is 364/365, or about .997. If a third person joins them, the probability that this new person has a different birthday from those two (i.e., the probability that all three will have different birthdays) is (364/365) x (363/365), about .992. With a fourth person, the probability that all four have different birthdays is (364/365) x (363/365) x (362/365), which comes out at around .983. And so on. The answers to these multiplications get steadily smaller. When a twenty-third person enters the room, the final fraction that you multiply by is 343/365, and the answer you get drops below .5 for the first time, being approximately .493. This is the probability that all 23 people have a different birthday. So, the probability that at least two people share a birthday is 1 - .493 = .507, just greater than 1/2. The Children Puzzle I tell you that a couple has two children and that (at least) one of them is a boy. I ask you what is the probability that their other child is a boy. Most people think the answer is 1/2, arguing that it is equally likely that the other child is a boy or a girl. But that's not the right answer for the question I have asked you. Here's why. In terms of order of birth, there are four possibilities for the couple's children: BB, BG, GB, GG. When I tell you that at least one child is a boy, I rule out the possibility GG. That leaves three possibilities: BB, BG, GB. With two of these, the other child is a girl; so the probability of the other child being a girl is 2/3. Leaving the probability of the other child being a boy at 1/3. Math Guy: The Birthday Problem |
March 23, 2005
IBM computing algorithm thinks like an animalMichael Kanellos IBM has devised a way to let computers think like vertebrates. Charles Peck and James Kozloski of IBM's Biometaphorical Computing team say they have created a mathematical model that mimics the behavior of neocortal minicolumns, thin strands of tissue that aggregate impulses from neurons. Further research could one day lead to robots that can "see" like humans and/or make appropriate decisions when bombarded with sensory information. A research paper on the model is expected to come out this week. The brain consists of roughly 28 billion cells, Peck explained. The 200 million minicolumns essentially gather sensory data and organize it for higher parts of the brain. The minicolumns also communicate with each other through interconnections. Minicolumns are roughly 1/20 of a millimeter in diameter and extend through the cortex. The mathematical model created at IBM simulates the behavior of 500,000 minicolumns connected by 400 million connections. With it, "we were able to demonstrate self-organization" and behavior similar to that seen in the real world, Peck said. "What we are trying to do is study the brain at the highest level of abstraction without masking the underlying function," he said. In a test outlined in the upcoming paper, the system was able to solve a pattern recognition problem that will cause errors on ordinary computers. Ideally, the algorithm could one day help scientists more fully understand the underlying processing that takes place when people see things. In a nutshell, an image is received, decomposed into color, shape, texture and other attributes and then reassembled, prompting the animal to change its behavior. Not all parts of the process are fully understood, Peck said. Over the past two years, researchers have increasingly looked toward nature as a model to emulate. Some companies, such as Cambrios, are trying to develop new compounds by exploiting proteins secreted by biological viruses. PalmOne founder Jeff Hawkins, meanwhile, is creating a company that will sell systems that use the same thought processes as the human brain. Intel co-founder Gordon Moore recently said that computers won't likely be able to think like humans unless they are redesigned. Brains typically think by making predictions about future events by looking at a vast array of past experiences, Hawkins said in a speech Monday at an event unrelated to IBM. Hawkins showed off a prototype application that can recognize shapes it has "seen" in the past. IBM is presenting the paper at the International Conference on Adaptive and Natural Computing Algorithms in Coimbra, Portugal. IBM computing algorithm thinks like an animal |
March 23, 2005
Computers gain power, but it's not what you thinkPerforming complex tasks at lightning speed is the machine's greatest strength; thinking, intelligence still in our heads By Jon Van Donald McLellan has a pretty smart computer. It watches what he reads and writes and can go online for information it thinks he might need. "If I didn't have it, I'd have to hire a research analyst to sit next to me," said the corporate vice president at Motorola Inc. McLellan uses software called Watson, developed at Northwestern University and marketed by Chicago's Intellext Inc., which is part of a new wave of programs that provide computers with something akin to human intelligence. But these programs do not think for their users. Rather, after decades of trying to create machines that can think, researchers now just want to make computers that are less stupid. The results are impressive. "Computers haven't gotten more deep cognitively, but they have gotten a lot faster," said Steve White, a senior IBM research manager. "What we can do is use that speed to do brute force calculations to solve problems." Intellext's Watson is one example of software that takes advantage of more powerful computers. Another is a program that tracks the emotions of people talking on the phone, created by a firm that monitors call center conversations. Computers have long been likened to human brains, sparking fears and hopes that someday a collection of silicon and wires would think like a person. But even today's most powerful units are not smart enough to tie a shoelace or do anything most human 4-year-olds accomplish thoughtlessly. Even so, escalating computing power enables machines to recognize patterns and operate in ways that seem eerily intelligent. When Watson sees a technical term McLellan types, it has no idea of the meaning. But by using pattern recognition, it can put the term into a context, enabling it to find relevant documents created by others at Motorola. McLellan directs Motorola's strategic transactions group, and he receives many proposals from people outside the firm. With Watson, he is able to quickly find the appropriate people within the company to help evaluate those proposals. As McLellan delves into something Watson finds, the program takes note of what interests him and drills down further to get additional related material. Watson is a remarkably useful tool, he said. Watson debuted last month, and costs range from $99 for an individual user to thousands of dollars for large companies. Northwestern professor Kristian Hammond, a co-founder of Intellext, was active in the artificial intelligence branch of computer science for years at Yale University and the University of Chicago before joining Northwestern. He no longer embraces the notion of intelligence commonly shared by artificial intelligence researchers. "That model is that people have a clear, crisp idea of what they're thinking," Hammond said. "Our model is that there's never a clear idea; often it's just a collection of ideas in a context. You change the context and you change the intelligence." A similar philosophy is at work at NICE Systems Inc., a Rutherford, N.J., firm that records call center conversations to monitor for quality. Its software can determine when a caller becomes emotional and can recognize specific words. "We didn't start with artificial intelligence in mind, but that's the direction we've gone," said Eyal Danon, the firm's marketing director. NICE systems record 500 calls a second for clients around the world. Managers never listen to even 1 percent of those calls, and the ones they hear are usually bland. Those provide few valuable insights about customers. But identifying conversations where customers get emotional can make a big difference. Those are generally more interesting and useful, Danon said. About 300 scientists worked for three years to develop 26 algorithms that make the NICE monitoring system work. "It's similar to a lie detector," Danon said. "It looks at the pitch, volume, tone, speed and tempo of the caller's voice and watches how those change over time. It looks for words like `cancel' and any mentions of the company's competitors." Sharon Whitwam, vice president of member services for WPS Health Insurance in Madison, Wis., said the system is most helpful. "We have 100 representatives taking calls," she said. "Getting your arms around customer information here is like herding cats." Tapping into calls where the caller is emotional has saved WPS a lot of headaches, she said. "If we see a high level of emotion in a call, management will listen to it and make a call back to the customer if necessary." Complicated problems are being solved these days by using approaches having little to do with artificial intelligence, said IBM's White. Computers now plan how to assemble complex information technology systems for businesses, stringing hundreds of machines together in networks, he said. Machines can do in hours or days the network assembly tasks that take weeks or months of human labor. Contrary to the once fairly widespread belief, computers don't work the way human brains do, White said. Adding more speed makes computers more useful but doesn't endow them with intelligence. "We need to better understand the brain's architecture--bundles of interconnected neurons," said White. "They're very slow as computing elements, but their connections make them very powerful and intelligent. We might build a different kind of computer modeled after that." Some researchers are trying to do just that. Jeff Hawkins, a respected Silicon Valley computer architect who started high-tech firms Palm Computing and Handspring, is developing a computer that mimics the human brain. Hawkins founded the Redwood Neuroscience Institute in Palo Alto, Calif., to further his research. A working computer that demonstrates humanlike intelligence will be ready by the end of this decade, he predicts. "It can be done," Hawkins said. "We are over the hump." Such an intelligent computer could be taught to look at random images and tell the difference between a cat and a dog or a duck and a chicken, much as young children learn to do. The machine might also learn to walk down a hill or drive a car, he said. In a book published last year, "On Intelligence," Hawkins outlined the theories needed to make machines with genuine intelligence. Instead of using computers to duplicate tasks humans do, he suggests that intelligent machines will be used to do things that neither people nor computers do well today. An intelligent machine connected to sensors across the globe feeding information about weather could become a weather brain, for instance. It would think about weather patterns the way a person understands objects and people, Hawkins said. Its deeper understanding should enable the computer to discern subtle patterns, such as El Nino, that affect weather greatly but were only noticed by scientists in the last 40 years. "Our weather brain could find more patterns like El Nino, or learn how to predict tornadoes or monsoons far better than humans," Hawkins wrote. "Putting large amounts of weather data into a form that humans can readily understand is difficult; our weather brain, in contrast, would sense and think about weather directly." Computers gain power, but it's not what you think |
March 23, 2005
Prepare yourself for rise of the machinesKEVIN HURLEY THE coming of a robot age, with mechanical helpers at our beck and call, moved a step closer yesterday with news of a revolutionary British invention that could soon change our lives. Science fiction writers from HG Wells onwards have long brought us visions of machines that respond to our every whim. Many of their imaginings have been given life on cinema screens in films such as The Terminator and I, Robot, portraying machines both as friends and enemies. Now engineers are working on a device capable of churning out a host of household items and gadgets, including kitchenware, cameras and even small musical instruments. The invention, named the "self-replicating rapid prototyper" or "RepRap", will one day even reproduce itself by fabricating its own component parts. Scientists behind the invention believe this capability will mean the machine will cost a few hundred pounds or less within years. Dr Adrian Bowyer, who is leading the project at the University of Bath's Centre for Biomimetrics, hopes initially to use the computer controlled machines, which mass-produce components for industry, such as vehicle parts, to make parts for the RepRap. Once assembled, however, his invention can then be programmed to make further copies of itself, increasing its numbers dramatically and slashing its costs. Mr Bowyer revealed the RepRap machine could become a reality within four years and his aim is to make it a universal feature of the home. He said his invention - about the size of a refrigerator, could render many forms of traditional manufacturing obsolete. "Four hundred years ago almost every human being was employed in agriculture, and now it's only a couple of per cent," he said. "I suspect the same thing is going to happen to manufacturing." Rapid prototype machines work by fusing together layers of plastic according to a blueprint fed into the computer. Mr Bowyer's machine would also be able to incorporate simple metal components and circuits out of an alloy that melts at low temperatures. The machines could, for instance, make complete sets of coloured and decorated plastic plates, dishes and bowls. The objects they produce would measure no more than 12 inches in length, width and height. Larger items could be made by clipping together smaller manufactured parts. Glass items, complex parts such as microchips, and anything exposed to intense heat - such as a toaster - could not be directly assembled. Components the machine is unable to make could easily be added. A basic digital camera could be made with the lens and computer chip bought separately and slotted in later. Mr Bowyer plans to make the 3D designs and computer code needed for an existing machine to make one of his devices freely available on the internet. "The most interesting part of this is that we're going to give it away," he said. "At the moment an industrial company consists of hundreds of people building and making things. "If these machines take off, it will give individual people the chance to do this for themselves. The effect this has on industry and society could be dramatic." The RepRap invention will effectively be a form of Universal Constructor - the theoretical self-replicating machine first proposed by mathematician John von Neumann in the 1950s. Bath University engineers have already built a simple demonstration robot. They are now looking for funding for the next stages of development. HACKING GROWS COMPUTER hackers have stepped up their efforts to target unsuspecting online bank customers, according to a report published today. The internet security firm Symantec noticed a huge jump in attempted "phishing" attacks in the second half of last year. The company filters millions of e-mails a day on behalf of companies around the world. In July last year the firm's anti-virus software was preventing about nine million e-mails containing a phishing attack from getting through to intended victims per week. Within six months the number of phishing attacks blocked had soared to an average of 33 million a week, according to the report. A typical phishing attack starts with a spoof e-mail directing users to a fake website for their bank. Fraudsters try to trick customers into giving away their log-in details or other personal information. One in every 250 e-mail messages filtered between July and December last year contained a phishing attack. The firm also reported a continuing problem with junk e-mails - otherwise known as "spam". More than 60 per cent of e-mails filtered during the six months were classified as spam. Symantec also highlighted the growing threat from software which infects computers to relay information on what tasks the user performs back to hackers. So-called "spyware" has been used to obtain password information based on the order in which users press keys. Richard Archdeacon, director of technical services at Symantec, said: "New forms of attack that use underhand and subtle methods are becoming increasingly prevalent. We predicted that these methods would become more popular with attackers and this has proved to be the case, with spam and phishing e-mails becoming a way of life for every computer user today." Prepare yourself for rise of the machines |
March 23, 2005
Studies probe secrets behind baby's mind |
March 19, 2005
Dubey, a mathematician-philanthropistSailaja Kumar What is the sum total, the meaning of life? Ask a certain mathematician and he will tell you this. Add sports, healthy food and music for recreation, divide your troubles with logical thinking and multiply your joy with friends. The sum of this equals life. So says Manoj Dubey, the Principal of Texmaco DPS International School (TDIS) in Karawang. Living by numbers, Dubey's career has been a series of discoveries, of incrementally increasing awareness and knowledge. In the field of education for more than two decades, he began teaching in DPS R.K. Puram, New Delhi in 1983; one the best schools in India, and shifted to TDIS Karawang in 1999. The school follows the Indian Central Board of Secondary Education (CBSE) curriculum. TDIS Karawang is affiliated to the Delhi Public School Society, which groups more than 100 schools, and CBSE has over 7,200 schools based in India that are internationally recognized. Mathematics for Dubey is not merely a hobby or profession but a passion, he says, and he has developed an intense love for the workings of numbers. The subject scares off many students and Dubey says much of his job involves passing on his enjoyment and mastery of the subject to his classes. "Do not allow mathematics to take you over, you must take over mathematics...," he frequently says to his students. His analytical approach teaches them not only how to solve specific problems in steps but also how to find solutions logically to other problems they face in life. A veteran of math seminars and workshops, Dubey has a deep insight into the teaching of math. A keen reader of technical literature, he has written more than 10 text books on math published by Tata McGraw Hill for sixth to 12th grade students. Learning math, he says, teaches one analytical and logical approaches, which can be applied to any problem. Students should always question things and never banish the "hows" and "whys" from their minds. "Doubts signify an intelligent mind. Speak them, empty your mind -- and make room for more doubts to surface." The school of ancient Greek philosopher-mathematician Plato had a motto: "Students having no interest in math are not welcome here." This is a maxim Dubey says he also he follows. However, Dubey is well-known among his colleagues for leaving no stone unturned in his search to find interesting new ways to teach math concepts. He is equally known for teaching economically disadvantaged students outside of class hours for free. But life is not only mathematics. Sport, he says, helps people make friends and keeps them fit. A self-confessed badminton and tennis freak, he spends his evenings playing lawn tennis, badminton and table tennis and coaches his students. The mathematician also has a love of classical music, which he says inspires him to action. An environmentalist, the principal feels it is his responsibility to encourage the respect and understanding of nature -- the theme of the school's environmental club, which has made students aware of pollution and the need to plant more trees for cleaner air. At his behest, other welfare programs in the spirit of community service have been organized in the school, including a blood donation scheme. Dubey is pained by the religious extremism currently prevalent in the world and the ruthless massacres that occur in the name of different gods. A proper understanding of subjects like science and math would definitely enlighten the intellect and reduce fanaticism, he says. He feels the success of Indians in the field of information technology internationally can be attributed to the strong foundation of Indian students in math. Like his favorite subject, Dubey is multifaceted, and he can be complex. But it is possible to sum him up. One part each philanthropist and mathematician, with a dash of sportsmanship, a touch of creativity and an eco-friendly heart that is powered by a teaching fervor, Dubey is also a man of peace. A strong believer of Gandhian philosophy, he feels that all the problems faced by the world can be resolved through nonviolent means, like negotiated settlements. Violence, he says, only brings more destruction. "There is no way to peace," Dubey quotes Gandhi, "... peace is the only way". Dubey, a mathematician-philanthropist |
March 19, 2005
Mathematician untangles legendary problemParoma Basu Karl Mahlburg, a young mathematician, has solved a crucial chunk of a puzzle that has haunted number theorists since the math legend Srinivasa Ramanujan scribbled his revolutionary notions into a tattered notebook. "In a nutshell, this [work] is the final chapter in one of the most famous subjects in the story of Ramanujan," says Ken Ono, Mahlburg's graduate advisor and an expert on Ramanujan's work. Ono is a Manasse Professor of Letters and Science in mathematics. "Mahlburg's achievement is a striking one, " agrees George Andrews, a mathematics professor at Penn State University who has also worked deeply with Ramanujan's ideas. The father of modern number theory, Ramanujan died prematurely in 1920 at the age of 32. The Indian mathematician's work is vast but he is particularly famous for noticing curious patterns in the way whole numbers can be broken down into sums of smaller numbers, or "partitions." The number 4, for example, has five partitions because it can be expressed in five ways, including 4, 3+1, 2+2, 1+1+2, and 1+1+1+1. Ramanujan, who had little formal training in mathematics, made partition lists for the first 200 integers and observed a peculiar regularity. For any number that ends in 4 or 9, he found, the number of partitions is always divisible by 5. Similarly, starting at 5, the number of partitions for every seventh integer is a multiple of 7, and, starting with 6, the partitions for every 11th integer are a multiple of 11. The finding was an intriguing one, says Richard Askey a emeritus mathematics professor who also works with aspects of Ramanujan's work. "There was no reason at all that multiplicative behaviors should have anything to do with additive structures involved in partitions." The strange numerical relationships Ramanujan discovered, now called the three Ramanujan "congruences," mystified scores of number theorists. During the Second World War, one mathematician and physicist named Freeman Dyson began to search for more elementary ways to prove Ramanujan's congruences. He developed a tool, called a "rank," that allowed him to split partitions of whole numbers into numerical groups of equal sizes. The idea worked with 5 and 7 but did not extend to 11. Dyson postulated that there must be a mathematical tool--what he jokingly called a "crank"--that could apply to all three congruences. Four decades later, Andrews and fellow mathematician Frank Garvan discovered the elusive crank function and for the moment, at least, the congruence chapter seemed complete. But in a chance turn of events in the late nineties, Ono came upon one of Ramanujan's original notebooks. Looking through the illegible scrawl, he noticed an obscure numerical formula that seemed to have no connection to partitions, but was strangely associated with unrelated work Ono was doing at the time. "I was floored," recalls Ono. Following the lead, Ono quickly made the startling discovery that partition congruences not only exist for the prime number 5, 7 and 11, but can be found for all larger primes. To prove this, Ono found a connection between partition numbers and special mathematical relationships called modular forms. But now that Ono had unveiled infinite numbers of partition congruences, the obvious question was whether the crank universally applied to all of them. In what Ono calls "a fantastically clever argument," Mahlburg has shown that it does. A UW-Madison doctoral student, Mahlburg says he spent a year manipulating "ugly, horribly complicated" numerical formulae, or functions, that emerged when he applied the crank tool to various prime numbers. "Though I was working with a large collection of functions, under the surface I slowly began to see a uniformity between them," says Mahlburg. Building on Ono's work with modular forms, Mahlburg found that instead of dividing numbers into equal groups, such as putting the number 115 into five equal groups of 23 (which are not multiples of 5), the partition congruence idea still holds if numbers are broken down differently. In other words, 115 could also break down as 25, 25, 25, 10 and 30. Since each part is a multiple of 5, it follows that the sum of the parts is also a multiple of 5. Mahlburg shows the idea extends to every prime number. "This is an incredible result," says Askey. Mahlburg's work completes the hunt for the crank function, says Penn State's Andrews, but is only a "tidy beginning" to the quest for simpler proofs of Ramanujan's findings. "Mahlburg has shown the great depth of one particular well that Ramanujan drew interesting things out of," Andrews adds, "but there are still plenty of wells we don't understand." Mathematician untangles legendary problem |
March 19, 2005
UW-Madison grad student makes math historyRon Seely Wisconsin State Journal If you ask Karl Mahlburg about his mathematical breakthrough, he will, typically, smile a very shy smile, duck his head, and say something self- effacing. But Mahlburg, a 25-year-old UW-Madison graduate student, has solved what may be the last part of a historic mathematical problem that has challenged the brightest minds in the field of number theory for 75 years. It is a feat that has drawn praise from the elite in the math world. So daunting was this part of the problem that Mahlburg's professor and mentor, Ken Ono, Manasse Professor of Letters and Science - who made his own startling breakthrough on another piece of the same problem - advised against him even trying. But Mahlburg forged ahead. For 1 years, working mostly in his modest cubby hole of an office on the fourth floor of Van Vleck Hall, he labored away, scrawling equation after equation on pages of lined notebook paper. And in the last few weeks, he has succeeded. "It is beautiful," the renowned Princeton physicist Freeman Dyson said of Mahlburg's work Thursday. "Beautiful and totally unexpected." Dyson is perhaps one of the ultimate and most learned sources on this particular accomplishment. Better known among lovers of science writing for books such as "Infinite in All Directions," and among scientists for his seminal work in quantum theory and particle physics, Dyson also plays a crucial role in the history of the problem on which Mahlburg worked. Though the math itself quickly becomes a thorny tangle to the lay person, the broad outlines of Mahlburg's work can be understood and appreciated as well as a few of its implications, though it is early to discern many. Such work, Ono said, can have important applications in number-related fields such as cryptology. As important, the story of Mahlburg's effort affords a look into the brainy and infrequently revealed depths of scholarly life on the UW- Madison campus. And it shows, too, how math is done and has been done since the ancients, how theory and proof are slowly built upon through the decades, bricks becoming walls and walls eventually becoming a house. As for this particular structure of mathematical thought, Mahlburg may have added the roof. "He's whip-smart," Ono said of his student. "He's very clever. And, frankly, he's quite stubborn, stubborn in not letting go of a problem." Mahlburg's problem has its roots in the life of one of history's most unlikely mathematicians. Srinivasa Ramanujan was born in southern India in 1887. With no formal training, the short, pudgy boy who was slow to learn to speak, grew into one of history's most famous and gifted mathematicians. Much of Ramanujan's work was in number theory, the study of the relationships and properties of numbers. Partitions are a good and relatively uncomplicated place to start in understanding the complexities of what Mahlburg has done. A partition, simply, is the expression of a number as a sum of numbers less than or equal to the given number. Four, as an example, has five partitions. They are: 1+1+1+1, 2+1+1, 3+1, 2+2, and 4. The interesting thing about partitions and one of the things that makes them intriguing to study is that they start out simple but quickly become complicated. While the number four has five partitions, for example, the number 10 has 42. And by the time you get to 100, you are dealing with a number that has 190,569,292 partitions. Number theorists look for patterns and for predictability in those patterns when they look at long lists of numbers. Eventually, studying lists of partitions, Ramanujan discerned a pattern that became a historic discovery. He found that, starting with four, the number of partitions for every fifth integer is a multiple of 5. For example, the number of partitions for 9 is 30 and for 14 is 135. Such a relationship is called a congruence. Ramanujan found congruences for 5, 7, and 11. The congruences were an unexpected finding and mathematicians through the years have been obsessed with figuring out why they exist and why there were apparently only congruences for those three prime numbers. They wanted to know the reason behind the rhyme. Years passed with little or no progress. Then, in the 1940s, a young Dyson took up the task. He made advances the math world had been waiting on for years. In 1944, he published a paper theorizing the existence of a mathematical tool he called a "crank" that would explain congruences and could be used to find more of them. And there the so-called "crank conjecture" sat for 40 years. But, beginning in the 1980s, there came a series of discoveries related to the problem. The actual existence of the crank was proven by another famous mathematician, George Andrews of Penn State University and a student of his, Frank Garvan. This is where the story turns toward Madison and the Van Vleck offices of Ono and Mahlburg. After the work by Andrews and Garvan, it was widely believed there would be no new major discoveries regarding partition congruences. But after long hours spent studying a lost notebook of Ramanujan's, Ono shocked the math world by proving in 2000 that Ramanujan's three congruences were merely the easy ones to see. In research Science News called "a remarkable tour de force," Ono showed Ramanujan congruences are everywhere. Once again, many in the math world believed the work on congruences would end with Ono's accomplishments. But as Ono explained, mathematicians come in a couple of types: theoreticians who make the grand connections, and problem solvers who make the theories work on paper. Mahlburg, Ono said, is a problem solver. Ono said that in his four years as a graduate student at UW-Madison, Mahlburg has already written three papers, more than enough to earn a Ph.D. So when the young man said he wanted to continue Ono's work on congruences, Ono was nervous. He didn't want his student to fail. But Mahlburg could not be dissuaded. "Not everyone," Ono said, "has the ability to work out a problem that at the end of a year, might not work out at all." In summary, Mahlburg described exactly how the famous crank works. It took calculations that even Ono found exhausting, pages and pages of mind-bending work. Mahlburg, who plays classical piano to get the numbers out of his head when he needs a break, lived with his problem day in and day out. He did much of his best thinking, he said, just before going to sleep at night. But he succeeded. Even as monumental a figure in the field as Andrews said Thursday that he is deeply impressed with Mahlburg's work. Now, Andrews said, Mahlburg's work, along with Ono's breakthrough, allows for a more complete explanation of the intricacies of partitions and congruences than ever before. "This is something way beyond what anybody has done before," Andrews said. "This is a very bright guy who has done something very hard." UW-Madison grad student makes math history |
March 19, 2005
Snow Moebius Strip: Doing the TwistBy SHARON TANG-QUAN The next time you enter a snow-sculpting contest, you may want to consult a mathematician for help. A team including a UC Berkeley computer engineer entered the International Snow Sculpture Championships in Breckenridge, Colorado. This year the team took on the challenge of creating a knotted Moebius strip—and then splitting that band along its whole length. Carlo H. Séquin, a UC Berkeley electrical engineering and computer science professor, created the team's design based on a triply twisted Moebius strip. Such a Moebius strip is constructed by joining the two ends of a rectangular piece of paper, after rotating one end by 540 degrees. Séquin created three-dimensional scale models of the structure on a rapid prototyping machine in Etcheverry Hall to help the snow carvers visualize this complicated geometry. For the past seven years, "Team Minnesota" has been headed by Stan Wagon, a professor at Macalester College in Minnesota. The team has typically chosen mathematical schemes for its entries. This year, Team Minnesota consisted of Séquin, Wagon, John Sullivan of the Technical University of Berlin, Dan Schwalbe of Minneapolis and Richard Seeley of Silverthorne, Colorado. The 2005 theme originated from the realm of knot theory. "The roots and inspiration for my design go back to an encounter with sculptor Keizo Ushio from Japan, who carved a split torus at the 1999 Art+Mathematics conference," Séquin said. "Since then, I have constructed ever more complex split tori, Mobius bands, and knots," he said. The team abandoned the basic three-fold symmetry of the triply twisted band in order to make a more dramatic-looking sculpture and to make the best possible use of the provided snow blocks, which measured several feet tall. Special attention was spent on raising the three lobes of the Moebius band to different heights for a more artistic sculpture. "Since the original ribbon has an odd number of half-twists and thus is single sided, the splitting operation will not actually divide the knot into two parts, but will just produce a single strand of twice the length of the original ribbon—thus the name of the sculpture: 'Knot Divided,'" he said. The snow carvers were allowed four and a half days to carve their creations. Within the first three days of the competition, the team experienced unseasonably warm weather, with a strong sun and temperatures climbing into the 40 degree range. The team's major concern was the structural stability of the large, leaning arched lobes. "To reduce weight at the top, we slightly tapered down the cross section towards the top," Séquin said. "To increase support, we let the bottom of the lobes touch at a couple of points, and we did not split the original band into two strands all the way down to the platform on which the sculpture rested," he said. The dropping temperatures on the fourth day allowed the structure to stand in place for the judging and public viewing. At the end of the contest, judges awarded the winning prize to a sculpture of the shell of a nautilus. The nautilus was also created using mathematical planning. Séquin's involvement comes as a lifelong interest in geometry and topology. He has actively collaborated with some sculptors for 11 years now, which he says has enabled him to combine his mathematical and artistic interests. Snow Moebius Strip: Doing the Twist |
March 19, 2005
Russian scientists say Egyptian frescoes are medieval workA Russian mathematician will argue at a news conference on Thursday that famous fresco horoscopes in ancient Egyptian temples that have been a source of disputes for two centuries were actually painted in the Middle Ages. Anatoly Fomenko, a member of the Russian Academy of Sciences, will for the first time disclose the results of many years of work on the horoscopes and comment on new statistical methods of studying world history at the news conference, which will be held at the Interfax headquarters in Moscow and start at noon. According to Fomenko and Gleb Nosovsky of Moscow State University, many of the Egyptian temple frescoes conceal dates ciphered as constellation maps and the earliest of the dates go back to the 12th century A.D. Fomenko is known as the founder of "new chronology," a study of history via mathematical statistics, astronomy-based dating, and the computer processing of written sources. Russian scientists say Egyptian frescoes are medieval work |
March 19, 2005
No matter how you slice it, they've got your numberBy LEANNE JOSEPHSON Clatsop College students revel in Pi Day In a perfect world, pie would be everywhere: luscious fruit pies growing on bushes, cream pies floating through the air. But instead we've got the less edible Pi all over the place – on the head of a sunflower and in the calculations used to make a bridge. Pi definitely has a lot more uses, but even math instructors agree it isn't as tasty as the kind that comes out of the oven. Given the option between Pi and pie, Clatsop Community College math instructor James McGlothin didn't hesitate. "I'd take the edible pie, for sure," he said. But on Monday McGlothin didn't have to choose. Pie and Pi merged in a Pi Day event at the college. Organized by the mathematics department, Pi Day celebrates the mysteries of the mathematical constant with Pi quizzes, pie throwing, pie eating, Pi necklace-making, Pi quilt-making and a Pie walk. "Most people are afraid of math, so this is a way to make them a little less afraid," McGlothin said. "Pi has been around for thousands of years. It's not a new concept. So when people struggle with numbers like Pi, it's been going on for a long time." Pi was of practical importance before 2000 B.C. Although ancient civilizations used different values, scholars have chased the number for almost 4,000 years. Renowned mathematician Leonhard Euler standardized the currently used symbol in 1737. Pi captivates mathematicians both because no one has been able to find the end of the number, and because it is found in so many places in nature. "Pi is everywhere," said college math instructor Liz Hylton. "If it involves a circle, it involves Pi. Circular motion, figuring out the area of a circle. ... If we didn't have Pi we wouldn't find the volume of the earth." There's even Pi in pie. Cut a pie in half and Pi is the number of times the length of that cut will go around the outside of the pie. The Pi of pie? That would be a piece for three people, with .14159 part of a piece left over. There weren't many pie pieces left over at Pi Day, which started off with Pi songs, including a corrupted Elton John tune: "And you can tell everybody it's three point one four But that's not it exactly, 'cause there's so much more One four one five nine, one four one five nine I hope we can learn How wonderful life is, with Pi in the world." After singing, the crowd split to, among other things, throw pies at college President Greg Hamann. The pies were actually paper plates covered with canned whipping cream and chocolate syrup. For a dollar, students, faculty and community members could have a shot. Hamann would have preferred pecan pies, but they're a little heavy when heading for one's face. One of the most popular Pi Day spots was the pie table. The college honor society, Phi Theta Kappa, sold pies as a fund-raiser for scholarships. Pie-eyed math enthusiasts were supposed to order in terms of radians, with 2p equaling one pie, p equaling half a pie and p/3, p/4 and p/6 equaling a slice, but most were too eager to dig into pumpkin, peanut butter, pecan, apple and key lime desserts to bother. "I think most people are here for the actual pie," said Glenda Miller, vice president of the honor society. They also knew more about pie than Pi. Jacob Penden, 6, scrunched up his face as he tried to define Pi. "Sometimes it's good," he said, adding that his favorite kind is blueberry. Annika Wolters, 13, from Ilwaco Middle school, had a few more math classes behind her. "It's got like 10,000 digits," she said. "I know it has something to do with circumference." For all the excitement about Pi and pie, there was at least one person at the event who was pied out. Jon Padgett, a sophomore at the college, said Pi has its applications, but he doesn't have any particular fondness for the number. "I don't really like it because it deals with circles and I've never really liked calculating circles," he said. "You never get an exact number." Padgett wasn't much for pie either. He'll doesn't like fruit pies, will tolerate a cream pie, but would be happiest with a carton of ice cream. But even for his dislike of Pi and pie, Padgett wants to be an engineer, and is enrolled in calculus this quarter. Pi Day organizers hope other students will see the necessity of math for certain careers and not be scared off, and that maybe Pi Day will help kids connect math with happy memories. "Just because you study math doesn't mean you have to be good at it," Hylton said. "You have to believe it's okay to make mistakes. Anyone can become good at math if they're stubborn and persistent." Did you know? The carefully chosen date for the Pi Day celebration mimics the first digits of Pi, which are 3.1415926. Thus, Pi Day is celebrated March 14, with the event beginning at 1:59 p.m. and continuing to 6 p.m. No matter how you slice it, they've got your number |
March 19, 2005
Program encourages mathematical thinkingBy Judy Jackson Math Investigations helps make learning fun Do you remember what it was like when you were studying math in elementary school? To most of us, things that come to mind are formulas and times tables to memorize, and long tedious assignments of one problem after another. Beloit elementary school students are finding out that there is more to mathematics than memorizing formulas and figuring out where to use them. Teachers are enthusiastic about "Math Investigations," a program developed by the Technical Education Research Center, a non-profit company that works to improve math and science education, according to Director of Student Achievement Pam Kiefert. "It emphasizes high expectations for all students, and provides the tools and technology for supporting thinking," Kiefert said. "The students are engaged from the minute they walk into the room." said Educational Program and Professional Development Coordinator Carol Healless. The first part of the hour-long class is called the launch, Kiefert explained. The teacher poses a problem, reads a story, or explains the rules of a game. No matter which it is, each gives the students a problem to solve. The students are encouraged to try various types of problem solving strategies, to arrive at the answer. All are designed to encourage higher level mathematical thinking, rather than memorization, Kiefert said. After the launch, the students delve into that problem. Working alone or in groups, the students record data, build a geometric model, record solutions or use a number of other strategies. The teacher acts as a facilitator, going from one student to the next and asking questions designed to encourage critical thinking. The third part is the summary and reflection, which gives students a chance to reflect on the math they learned, asking themselves questions such as, "What did I learn? What would have happened if I had done this?" This allows the students to articulate their mathematical thinking, Healless said. "The understanding part is huge," Healless said. Emily Allen, a second grade teacher at Morgan Elementary School, is sold on Math Investigations. "Research indicates that Math Investigations closes the achievement gap and raises test scores, so as teachers, we need to trust this curriculum. We will be successful," she said. "The kids are extremely motivated." Math Investigations makes it easier to reach each student at his or her ability level, since they have so many choices for problem solving strategies, and so many games are incorporated into the teaching that the students enjoy learning without realizing it, according to Allen. Program encourages mathematical thinking |
March 15, 2005
Now world can browse through Ramanujan's Lost Notebook, 29 years after its discoveryRESHMA PATIL MUMBAI, MARCH 12: Twenty-nine years after an American mathematician pottering around the Trinity College Library (UK) stumbled upon hundreds of forgotten formulas scribbled by math genius Srinivasa Ramanujan in his last years, their secrets are on the verge of being revealed with pathbreaking and complete answers. The formulas were noted by a dying, bed-ridden Ramanujan a year or two before his untimely death aged 32, at Chennai in 1920. In 1976 these pages shot to fame as Ramanujan's invaluable Lost Notebook that quickly became contemporary mathematics' great riddle. Mathematics duo George Andrews—he found the notebook—and Bruce Berndt have spent years solving Ramanujan's last enigmas. Written over 85 years ago, they still point to questions of current interest. ''This manuscript took me by complete surprise,'' Andrews, faculty at Pennsylvania State University, told The Sunday Express. The first edited volume, with 442 entries of the Lost Notebook and some unpublished papers, will be published within a couple of months. ''Unfortunately, Ramanujan wrote these formulas without any explanatory comments,'' says Andrews. ''Some proofs are very difficult and unilluminating. There was never a moment when I did not wish that Ramanujan was around to explain himself.'' The authors—world experts on Ramanujan—are now writing volume two. But volume three will be the ''hardest'' says Andrews, with the hope of finishing. ''In a few years.'' Questioned on the significance of the forthcoming volume, Andrews replies that ''most everything is new. There are some results that were rediscovered between 1920 and 1976, but not a large percentage. There have been many research articles on the Lost Notebook, but this is the first complete account.'' Bruce Berndt (65) a distinguished research professor at the University of Illinois mathematics department joined this project during the late nineties, working exclusively on it since summer 2003. Sometimes he struggled with the feverish handwriting. ''His writing is clear, but on some pages it runs at all angles,'' sighs Berndt. ''Some entries are cryptic or incomplete. Some scratchwork we will likely never figure out. But less than 10 per cent formulas are yet to be proved.'' Berndt emphasises that Ramanujan was not ''old-fashioned''. Mathematical research, though largely theoretical, underpins applications from aircraft design to computer science and nuclear physics. In the past months Berndt and colleague Alexandru Zaharescu proved a formula from the Lost Notebook that has connections with the ''deepest and famous'' unsolved problems in number theory—the circle problem and the divisor problem. ''This formula is one of a pair on one page of the notebook,'' says Berndt, confessing he always wished he could ask Ramanujan his motivations. ''At this moment, we cannot prove the second formula!'' The original Lost Notebook is at the Trinity College Library, Cambridge. ''I have turned to it again and again for inspiration,'' recalls Andrews, ''always coming upon new challenges that had escaped my notice. It played a major role in most of my work.'' Andrews, Berndt and his students have ''pretty much proved'' all of Ramanujan's assertions. ''Some entries are routine for experts but many point to questions of current interest,'' says Andrews. ''A lot still needs to be don.'' Four number theorists at the University of Florida's mathematics department— including the department chairman Krishnaswami Alladi—work in areas influenced by Ramanujan. ''The Lost Notebook is very much our interest,'' Alladi says. ''Edited versions of Ramanujan's original notebooks by Berndt had tremendous impact, earning him the Steele Prize of the American Mathematical Society,'' he adds. ''We expect publication of edited versions of the Lost Notebook to have equally significant impact.'' At Chennai's Institute of Mathematical Sciences, director R Balasubramanian emphasises that Andrews and Berndt are putting Ramanujan's work in the modern context. ''It's very important that the Lost Notebook is being edited and published.'' But Andrews humbly concludes that the world would have been richer if Ramanujan had lived to explain his lost discoveries. Now world can browse through Ramanujan's Lost Notebook, 29 years after its discovery |
March 15, 2005
IISc gives maths study a new edgeJOHNSON T.A. BANGALORE: Mathematics, long relegated to being the back room boy of science, is making a comeback on the wings of the changing equations in modern science. Teaching jobs are no longer the only choice available to mathematics professionals. A whole world is opening up at the interface between mathematics and other sciences -promising higher incomes than IT jobs. Communication networks, the financial markets, coding theory, genetic engineering, designer drugs, cryptography, data mining, computational neuroscience, image compression, population dynamics and mathematical physics are just some of the areas beckoning mathematics expertise. Across developed countries, efforts are on to create a greater pool of people with mathematics knowledge to meet the needs of the changing times. In India, finding professionals with the necessary mathematics domain knowledge is naturally a difficult task, given the backseat mathematics has been relegated to in education. A mathematics initiative that has germinated at the Indian Institute of Science here is now trying to bridge the gap that exists between mathematics and other science disciplines. Its aim: To kickstart research in cutting areas of science and technology where mathematics plays an important role. The scene has dramatically changed in India over the last three to four years. Earlier, mathematics was thought fit only for academic research. Many companies are now realising they need people who have a very sophisticated mathematics background, says themes. Govindan Rangarajan, head of the mathematics department, IISc and convener of the IISc Mathematics Initiative. The initiative is just a starting point. We are involving people from all over the country, especially research students, engineers, scientists from national labs and industry personnel, says Rangarajan. With funding of a little over Rs 50 lakh from the National Board for Higher Mathematics and the Defence Research Development Organisation, the IISc Mathematics Initiative has arrived at a plan to declare a cutting edge mathematics theme for each year and to conduct workshops, compact courses, seminars and conferences around these themes. The workshops and courses are conducted by either Indian or foreign faculty. For instance, a French scientist is now conducting a course based on the first years theme Scientific computation, numerical analysis and applications. This is of great value to scientists from Indias defence and space labs. For the second year, the mathematics initiative has zeroed in on Coding theory and cryptography which has applications in areas like communication networks and defence. Stochastic processes and applications is the theme for the third year and holds out value for financial institutions, neuroscientists, defence and communication network companies. Those at the helm of the initiative admit that there is a lag between opportunities opening up for mathematics professionals and the number of people taking up mathematics. Industry has realised they need mathematics professionals, but the general public has not realised mathematics can provide good jobs. It will take some time, says Prof Rangarajan. IISc gives maths study a new edge |
March 15, 2005
Giving robots a human faceDALLAS, Texas (AP) -- With her sparkling blue eyes, wispy eyelashes and demure smile, Hertz is the center of attention wherever she goes. If you're lucky enough to meet her, try to ignore the tangle of wires slinking from behind her face. If you speak with her, talk slowly and loudly. And no matter what you say, don't be offended if she looks at you blankly and repeatedly asks, "What did you say?" Hertz isn't really a she, but rather an it, an animated robot head built in about nine months by self-titled "sculptor roboticist" David Hanson. Hanson and other robot makers believe social robots will one day serve a variety of functions: tutor, companion, even security guard. But should they look human? Hanson, who has worked as a designer, sculptor, and robotics developer for Walt Disney Imagineering, Universal Studios and MTV, thinks precise human looks are a must if people are going to effectively communicate with robots. Like his previous project, K-bot, Hanson sculpted Hertz to resemble his girlfriend. It's sheathed in a high-tech polymer Hanson invented called "f'rubber," which resembles human skin. The face is embedded with tiny electronic motors, so Hertz can smile, frown or wrinkle its forehead. For now, Hertz is a face mounted to a wooden stool, its disembodied brain a laptop computer. It has no arms, legs or body, although Hanson is planning those enhancements someday. Hertz's eyes have video cameras, enabling it to gaze at a human face and follow you around, provided you don't move too quickly or beyond its limited field of vision. That and the limited speech skills are the extent of Hertz's abilities. Despite the embryonic state of his work, Hanson insists he's on to something. "Most people doing social robots believe that human faces will turn people off and will disturb them. I think that's ridiculous," Hanson said. "The human face is perhaps the most natural paradigm for us to interact with." Not quite human Most experts disagree. They cite one of the principles of social robotics, the so-called "Uncanny Valley" theory. First described by pioneering Japanese roboticist Masahiro Mori, the theory goes like this: humans have a positive psychological reaction to robots that look somewhat like humans. But if a robot is made to look very realistic but somehow isn't quite right (it has an odd smile, or it doesn't blink, for example) it seems grotesque instead of comforting. "Our experience has shown that people quickly lose the suspension of disbelief needed to interact with these creations once they start interacting with them for any length of time, because the artificial intelligence is not capable of producing human-level behavior," said Reid Simmons, a researcher at Carnegie Mellon University's Robotics Institute. "I strongly believe that this problem would be exacerbated by having a more humanly realistic robot." Science fiction has long taken different approaches to imbue robots with personal appeal. In "Star Wars," the blinks, blurps and beeps of R2-D2 were enough to give the trashcan-shaped machine a wide range of human emotions such as fear and excitement. There was the strikingly human, but emotionally clueless, Data from "Star Trek: The Next Generation." And in 2001's "Artificial Intelligence: AI," unblinking robot boy David Swinton yearned to become real so his flesh-and-blood mother would love him. Hanson apart, most of today's roboticists are taking Mori's theory into consideration. Sony Corp.'s QRIO robot looks like a young boy in a space suit, but Sony researchers say they didn't want to make it too similar to a human. "If your design is too close to human form, at a certain point it becomes just too uncanny," Toshitada Doi, head of Sony's Intelligent Dynamics Research Institute, says on Sony's Web site. Others include GRACE, short for Graduate Robot Attending a ConferencE. Built by Simmons and researchers at several other schools, GRACE's "face" is a flat-screen television capable of displaying a range of emotions. Kismet, a product of the Massachusetts Institute of Technology's Humanoid Robotics Group, has exaggerated, fuzzy eyebrows, big blue eyes and floppy ears but its face is mostly metal and plastic. Captivating or disturbing? Inventor and author Ray Kurzweil thinks Hanson's work is significant because realistic facial movement will play an important role in the way future androids respond to humans. First, however, robots will have to become significantly more intelligent, able to gauge the expressions of the people they encounter. Kurzweil estimates that we'll begin to see this human level of artificial intelligence around 2029. Until then, he believes less-realistic robots will be more successful. "If a robot has a face that is not human, then we are more accepting of less-than-human behavior, as we would with an animal or doll," he said. "Intelligence significantly below that of normal humans stands out more with a robot that looks strikingly human. This creates the impression of a human with impaired intelligence, which may strike some as disturbing." For now, Hanson is taking a semester off from pursuing his doctoral thesis at the University of Texas-Dallas so he can tinker with his bots. Most of the work on Hertz was done in his apartment and funded mostly with student loans. Last summer, Hanson formed a company, Human Emulation Robotics, with the hopes of raising venture capital. "This is like a first step," he said. "This looks like a monster because it is a severed head. But once you get used to it, it's not. I haven't proven that it's not disturbing yet, but I have shown that it is captivating." No matter what, we can expected future social robots to be more alien than human, said Will Wright, creator of The Sims video games and a robot enthusiast. "The fact is, I will share much more evolutionary history, and hence, brain circuitry and behavior, with my cat than I ever will with a machine intelligence," he said. "The AIs we will be inventing soon will almost certainly be the first true alien intelligences humans will meet." Giving robots a human face |
March 11, 2005
New Mathematical Model to Predict Ecological Invasion and Species SurvivalResearchers at Rensselaer Polytechnic Institute and University at Albany have proposed a new mathematical model that predicts the survival of invasive biological species upon introduction to an ecosystem. The model analyzes the struggle for space between clusters of invasive species and native species to predict which species will survive. According to Gyorgy Korniss, assistant professor of physics at Rensselaer Polytechnic Institute, a predictive understanding of the ecological invasion process should lead to better techniques in preventing the proliferation of invasive species such as milfoil. A submerged aquatic weed that invades lakes, ponds, and reservoirs, milfoil often restricts natural water flow, clogs water intakes, and eliminates native species from ecosystems. This new model explains what happens when invasive and resident species are competing for space and how the invasion process evolves over time," said Korniss. "We have shown that it is possible to quantitatively predict the lifetime of invasive and native species based on analysis of the species' cluster patterns." Korniss collaborates with Thomas Caraco, associate professor of biological sciences at University at Albany, on the project which has also benefited from contributions by Rensselaer graduate student Lauren O'Malley (physics), Rensselaer undergraduate student Joseph Yasi (computer science, physics), and UAlbany undergraduate student Andrew Allstadt (biology, computer science). The work was supported by the National Science Foundation (NSF). "Our collaboration offers students a perspective to better prepare them for scientific careers that increasingly require an integration of disciplines," said Caraco. The research findings are reported today in the Journal of Theoretical Biology in a paper titled "Spatial Dynamics of Invasion: The Geometry of Introduced Species." To approach this biological problem from a computational perspective, researchers applied statistical physics to complex ecosystems. The researchers predicted the invading species' population growth in time based on its spatially-distributed cluster patterns by applying the theory of nucleation. Nucleation theory has been used to explain growth processes such as crystal growth, magnetic domain formation, and DNA replication. Korniss said that additional research will combine spatial elements of species growth with more complicated temporal elements. "The next step in our research is to further develop the model to explain how the change of seasons affects the probability of an invasive species' survival," he said. New Mathematical Model to Predict Ecological Invasion and Species Survival |
March 11, 2005
Does Gödel Matter?By Jordan Ellenberg The reticent and relentlessly abstract logician Kurt Gödel might seem an unlikely candidate for popular appreciation. But that's what Rebecca Goldstein aims for in her new book Incompleteness, an account of Gödel's most famous theorem, which was announced 75 years ago this October. Goldstein calls Gödel's incompleteness theorem "the third leg, together with Heisenberg's uncertainty principle and Einstein's relativity, of that tripod of theoretical cataclysms that have been felt to force disturbances deep down in the foundations of the 'exact sciences.' " What is this great theorem? And what difference does it really make? Mathematicians, like other scientists, strive for simplicity; we want to boil messy phenomena down to some short list of first principles called axioms, akin to basic physical laws, from which everything we see can be derived. This tendency goes back as far as Euclid, who used just five postulates to deduce his geometrical theorems. But plane geometry isn't all of mathematics, and other fields proved surprisingly resistant to axiomatization; irritating paradoxes kept springing up, to be knocked down again by more refined axiomatic systems. The so-called "formalist program" aimed to find a master list of axioms, from which all of mathematics could be derived by rigid logical deduction. Goldstein cleverly compares this objective to a "Communist takeover of mathematics" in which individuality and intuition would be subjugated, for the common good, to logical rules. By the early 20th century, this outcome was understood to be the condition toward which mathematics must strive. Then Gödel kicked the whole thing over. Gödel's incompleteness theorem says: Given any system of axioms that produces no paradoxes, there exist statements about numbers which are true, but which cannot be proved using the given axioms. In other words, there is no hope of reducing even mere arithmetic, the starting point of mathematics, to axioms; any such system will miss out on some truths. And Gödel not only shows that true-but-unprovable statements exist—he produces one! His method is a marvel of ingenuity; he encodes the notion of "provability" itself into arithmetic and thereby devises an arithmetic statement P that, when decoded, reads: P is not provable using the given axioms. So a proof of P would imply that P was false—in other words, the proof of P would itself constitute a disproof of P, and we have found a paradox. So we're forced to concede that P is not provable—which is precisely what P claims. So P is a true statement that cannot be proved with the given axioms. (The dizzy-making self-reference inherent in this argument is the subject of Douglas Hofstadter's Pulitzer Prize-winning Gödel, Escher, Bach, a mathematical exposition of clarity, liveliness, and scope unequalled since its publication in 1979.) One way to understand Gödel's theorem (in combination with his 1929 "completeness theorem") is that no system of logical axioms can produce all truths about numbers because no system of logical axioms can pin down exactly what numbers are. My fourth-grade teacher used to ask the class to define a peanut butter sandwich, with comic results. Whatever definition you propose (say, "two slices of bread with peanut butter in between"), there are still lots of non-peanut-butter-sandwiches that fall within its scope (say, two pieces of bread laid side by side with a stripe of peanut butter spread on the table between them). Mathematics, post-Gödel, is very similar: There are many different things we could mean by the word "number," all of which will be perfectly compatible with our axioms. Now Gödel's undecidable statement P doesn't seem so paradoxical. Under some interpretations of the word "number," it is true; under others, it is false. In his recent New York Times review of Incompleteness, Edward Rothstein wrote that it's "difficult to overstate the impact of Gödel's theorem." But actually, it's easy to overstate it: Goldstein does it when she likens the impact of Gödel's incompleteness theorem to that of relativity and quantum mechanics and calls him "the most famous mathematician that you have most likely never heard of." But what's most startling about Gödel's theorem, given its conceptual importance, is not how much it's changed mathematics, but how little. No theoretical physicist could start a career today without a thorough understanding of Einstein's and Heisenberg's contributions. But most pure mathematicians can easily go through life with only a vague acquaintance with Gödel's work. So far, I've done it myself. How can this be, when Gödel cuts the very definition of "number" out from under us? Well, don't forget that just as there are some statements that are true under any definition of "peanut butter sandwich"—for instance, "peanut butter sandwiches contain peanut butter"—there are some statements that are true under any definition of "number"—for instance, "2 + 2 = 4." It turns out that, at least so far, interesting statements about number theory are much more likely to resemble "2 + 2 = 4" than Gödel's vexing "P." Gödel's theorem, for most working mathematicians, is like a sign warning us away from logical terrain we'd never visit anyway. What is it about Gödel's theorem that so captures the imagination? Probably that its oversimplified plain-English form—"There are true things which cannot be proved"—is naturally appealing to anyone with a remotely romantic sensibility. Call it "the curse of the slogan": Any scientific result that can be approximated by an aphorism is ripe for misappropriation. The precise mathematical formulation that is Gödel's theorem doesn't really say "there are true things which cannot be proved" any more than Einstein's theory means "everything is relative, dude, it just depends on your point of view." And it certainly doesn't say anything directly about the world outside mathematics, though the physicist Roger Penrose does use the incompleteness theorem in making his controversial case for the role of quantum mechanics in human consciousness. Yet, Gödel is routinely deployed by people with antirationalist agendas as a stick to whack any offending piece of science that happens by. A typical recent article, "Why Evolutionary Theories Are Unbelievable," claims, "Basically, Gödel's theorems prove the Doctrine of Original Sin, the need for the sacrament of penance, and that there is a future eternity." If Gödel's theorems could prove that, he'd be even more important than Einstein and Heisenberg! One person who would not have been surprised about the relative inconsequence of Gödel's theorem is Gödel himself. He believed that mathematical objects, like numbers, were not human constructions but real things, as real as peanut butter sandwiches. Goldstein, whose training is in philosophy, is at her strongest when tracing the relation between Gödel's mathematical results and his philosophical commitments. If numbers are real things, independent of our minds, they don't care whether or not we can define them; we apprehend them through some intuitive faculty whose nature remains a mystery. From this point of view, it's not at all strange that the mathematics we do today is very much like the mathematics we'd be doing if Gödel had never knocked out the possibility of axiomatic foundations. For Gödel, axiomatic foundations, however useful, were never truly necessary in the first place. His work was revolutionary, yes, but it was a revolution of the most unusual kind: one that abolished the constitution while leaving the material circumstances of the citizens more or less unchanged. Does Gödel Matter? |
March 10, 2005
EU project helps recover hidden Archimedes treatyEurope, perhaps more than other region in the world, has a heritage of manuscripts and archive documents that are steadily deteriorating or are in less than optimum condition due to fire, water damage, stains or poor restoration work. The physical deterioration of these documents is a major loss to European cultural heritage. In 2003, the European Commission therefore decided to fund a two year innovative project aimed at developing a user-friendly and cost-effective tool for the digitalisation, virtual restoration and archiving of ancient, degraded texts and manuscripts. The IsyReaDeT project, funded under the CRAFT scheme of the Fifth Framework Programme (FP5), has now achieved this goal and developed a successful modular prototype based on a multispectral camera and image processing algorithms. In an interview with CORDIS News, Elena Console and Rossella Tassone from TEASAS in Italy, who have been coordinating the project, explained how this novel system works. 'Multispectral imaging, by using a selection of spectral bands such as ultraviolet and infrared rays, makes it possible for the user to obtain the images of damaged documents and see what is invisible to the naked eye,' explained Dr Console. 'Depending on the type of ink used, infrared rays enable us to see hidden characters or even characters that have disappeared over time. Ultraviolet rays enable us to see what caused the degradation of the text without having to touch the document and without a chemical test that would further damage and even destroy the document,' added Dr Console. Once the multispectral camera has revealed the hidden features in the damaged document, the digital image can then be enhanced with various image-processing techniques to erase stains and increase the readability of the text. As Dr Console and Dr Tassone explained, the IsyReaDeT algorithms were tested on a document provided by the Walters Art Museum of Baltimore in the US. This document, the Archimedes Palimpsest, is an ancient manuscript of several treatises by the great philosopher and mathematician, which had been re-used and over-written with a Byzantine prayer in the 12th century. Thanks to the IsyReaDeT system, it was possible to recover what had been written under the prayer and recuperate some pages of the Archimedes texts. 'We are extremely happy with the results of the project,' Dr Console told CORDIS News. 'We have achieved a prototype of a modular system which is small in size, small in price and simple to use even for people with no expertise in mathematics.' 'Furthermore,' added Dr Console, 'the system can be used preventively and is not restricted to damaged documents. It enables the virtual reproduction and diffusion through the Internet, as well as on multimedia CD-ROMs, of books and documents. Our aim is to disseminate culture in order to reach more people.' The fact that the system is modular also means that a user interested only in multispectral acquisition or only in image enhancement can use the modules separately. 'The prototype still needs some fine-tuning of course as it can always be improved. We are now looking for other sources of financing to turn this prototype into a marketable product,' concluded Dr Console. For further information on IsyReaDeT, please visit: http://www.isyreadet.net/ Or contact: Elena Console: elena@teacz.191.it EU project helps recover hidden Archimedes treaty |
March 10, 2005
Thinking robots – not quite yetProfessor Noel Sharkey left school at the age of 15 but is now one of our leading robotics experts. Chris Bond talked to him about the future of artificial intelligence. NOEL Sharkey is in the mood to debunk a few myths. The 56-year-old professor of computer science at Sheffield University is at the forefront of robotic technology in this country and there's a few things he wants to get off his chest. "Everybody wants to hear that robots are going to take over the world but it's not going to happen," he says. "You get a lot of scientists, particularly American scientists, saying that robotics is about at the level of the rat at the moment, I would say it's not anywhere near even a simple bacteria." With his gentle Irish lilt, long grey hair held back in a ponytail, this softly-spoken 56-year-old grandfather appears every bit the wacky scientist – he looks somewhere between The Fast Show's mad professor, Denzil Dexter, and a Grateful Dead fan. But there is an incredibly sharp mind behind the slightly unkempt facade and he's a man in demand. As well as being a senior fellow on the Engineering Physical Research Council, Prof Sharkey was the chief judge on the BBC's Robot Wars, and has recently been interviewed by Sky Movies for a documentary into the making of the animated sci-fi film Robots, starring the voices of Ewan McGregor, Halle Berry and Robin Williams. Oh and he also happens to edit three robotics and neurocomputing journals – "I'm an efficient worker," he says modestly. Prof Sharkey has just returned from the national robotics championships in Egypt where he supplied all the robots and taught the students how to programme them. At the weekend he heads to China where, among other things, he will chair a debate into whether robots can ever gain consciousness. "We've been saying that since the 50s but there's not much chance of it happening," he says. Not that he's trying to rubbish the detailed field of robotics research – far from it – he simply feels compelled to inject a degree of realism into a topic which readily surrenders itself to the fantastical. "We are getting on incredibly well mechanically and with computers, but artificial intelligence (AI) is still not forthcoming compared to what you see in the movies." Put simply, Prof Sharkey's job is to "raise awareness of engineering and science" but he is worried by the apparent apathy in this country. "The number of engineers is dropping dramatically, it seems dull and boring to people, whereas if you go to India or China everybody there wants to be an engineer and we need to do something about this," he says. "In this country we are brilliant with sticky tape and that kind of thing but we don't have the manufacturers. Japan is so far ahead technologically it's impossible to catch up. "They have running robots and somersaulting robots," he says. Humanoid walking robots have only been developed in the last couple of years but it cost Honda millions of pounds to make the breakthrough with its asimo robot. "I had a chance to play with that and it is extraordinary," the professor says. "When I saw it my immediate thought was there's a kid in there. It can do Michael Jackson's moonwalk, it can run and it can walk in slow motion. "But these are the kind of things we're only developing now after 50 years of research. But it's still what I would call artificially stupid – it can do all these things but it has no capacity to think." Prof Sharkey has come a long way since leaving school at the age of 15. Brought up in a mixed Catholic-Protestant household in Coleraine he found school tedious and boring, preferring instead to ferret himself away at home where he devoured books on everything from geometry to history. "I used to keep it a secret because people would have laughed at me. I used to come out of bookshops as if I was carrying pornography in a brown paper bag." One of the few fond memories he has of his schooldays is beating his headmaster at chess as a 14-year-old. "He wouldn't believe that I played chess, he thought I was stupid. But I humiliated him in front of the whole class and just as I was about to check mate him he said he had an appointment and walked out with the whole of the class on their tables cheering." After leaving school he trained as a psychiatric nurse and came top of his year at Exeter University with a first in psychology. He finished his PhD and was offered a research post at Yale University in America, working with artificial intelligence and cognitive science groups. This led him towards the field of robotics research and in 1989 he built his first robot – a mathematical model of the nervous system. "You can simulate things but you can't beat the physics of the real world and my first experiment involved moving a robot down a corridor. It avoided people and turned corners and from that point I was hooked." He has since created all sorts of robots, including one that can fly, but admits the technological developments are slow. "The difficult things are the ones you wouldn't think are difficult, like vision. You can programme something to take photographs but there's no one inside to understand them, it's a bit like a television." The professor is halfway through a book, called The Tin Man, which is both a history of robotics and an investigation into man as machine. "Robotics, or automatons," he says, "goes back to around 3000BC and has always been associated with a kind of trickery and magic. Some Egyptian temples had talking statues, they had people inside but it was the same kind of fascination." The first time a robot was seen in a film was in Fritz Lang's masterpiece Metropolis, but Prof Sharkey argues in reality we haven't come close to re-creating that. But he believes today's films can have a bearing on the future. "The good thing about movies like Robots is that youngsters will look at what robots can do in it and that will be their creative aim. "I continually meet children who come up with solutions to things that engineers couldn't come up with because they haven't learned constraints. "I've seen two boys who built a unicycle which could drive on its own and it looked like magic and all the engineers with me said 'no, no, that's not possible, we can't be seeing this.' "But the boys didn't think of the problems they came up with solutions." Perhaps robots will actually take over the world one day because sometimes the impossible does actually happen. Thinking robots – not quite yet |
March 10, 2005
Indian women put nurture ahead of natureMUMBAI: In the age of the Kalpana Chawlas and Sudha Murthys, is the notion that men are better at science and maths at all relevant? Apparently it is, going by the prolonged controversy over Harvard president Larry Summer's remarks on the issue. Last month, Summers suggested in a speech that "intrinsic aptitude" might have something to do with the lower representation of women in the sciences, particularly engineering and mathematics. The economist's largely misquoted venture into the explosive territory overlapping sexual politics and evolutionary biology created outrage in academic circles worldwide, particularly among women. Summers' remarks may seem like a throwback to the 19th century when women were considered emotional creatures only fit to raise families—but they come at a time when certain studies have claimed that male and female brains are wired differently, making men quicker with better visual-spatial skills and giving women better emotional and verbal skills. The findings contradict prevalent beliefs that humans have no innate traits, but are "blank slates". Indian women scientists are reassuringly unfazed by the recent events, asserting that individual ability and nurture determines scientific success. "Even in ancient history, we have examples like Lilavati, the daughter of the mathematician Bhaskara, for whom he wrote his calculus verses," says Swati Piramal of pharma Nicolas Piramal India Ltd, adding, "Choice of subjects depends on the environment you are brought up in, the kind of training you get." If there are more men in engineering and more women in "soft" life sciences like biology, says Piramal, it's because of gender stereotypes. "Men are supposed to go out and build bridges," she says, noting that medical colleges were once male bastions but are now flooded with women. Adds 55-year-old Uma Rao, a biochemist and an activemember of the BhabaAtomic Research Centre's women cell, "Inmy time, it was unthinkable for girls to go in for engineering and maths but nowadays, so many girls are opting for it." That stereotypes may influence talent development is supported by studies which show that girls do better in maths and science when segregated from the other sex. "Choice has a lot to do with perception," agrees Sugra Chunawalla of the Homi Babha Centre for Science Education, citing a study last year which found that school students, when asked to draw a scientist, drew mostly men. Intellectuals also fear that such generalisations about innate ability may be used to justify inequality and discrimination. "One of the reasons for the extreme reaction to Summers' remarks is the fear that these ideas might translate into hiring practices," notes Shubha Tole, of the biological science department in the TIFR. Jitendra Shah, an engineering professor for 24 years, says he has found differences in intellectual approach. "The boys are better at rapidfire response and the girls are better at thinking comprehensively, resolving conflicting conditions to arrive at an answer, '' he says, adding that unfortunately, engineering admission exams with their emphasis on speed are skewed towards the boys. "In practice, what engineering needs is comprehensive thinking so a filtering system which puts the partial capacity of speed at a premium is really skewed. I get many graduates who do well in the exams but are unemployable because they can't handle real-life problems." Even if mental talent is not entirely gender-neutral, it doesn't matter, suggest others. "So what if people's brains are wired differently?" asks Tole, "To say that men on average perform better on maths tests cannot be stretched to say they are better mathematicians. Women are supposed to be better at languages but does that mean they are better novelists?" In fact, a complex and diverse set of skills go into making a good scientist. "You need creative as well as logical skills," she says. "You have to have mentoring and managerial skills, you need to be able to ideate in groups, to attract funding, to produce data, achieve closure and publish it before anyone else. There's a lot more to it than just scoring well on tests." Indian women put nurture ahead of nature |
March 10, 2005
CMU MATHEMATICS BOOK CONTAINS NEW RESULTS ON SYMMETRIC DESIGNSMEDIA CONTACT: Pat Housley CMU CONTACTS: Mohan Shrikhande, Yury Ionin Two Central Michigan University faculty members identify recent developments in the theory of symmetric designs in a mathematics book to be published this year by Cambridge University Press in England. "Combinatorics of Symmetric Designs" by CMU Professors Yury Ionin and Mohan Shrikhande will be published in the series, New Mathematical Monographs. "The book is primarily a research monograph that gives a unifying exposition of the theory of symmetric designs with an emphasis on recent developments," said Shrikhande. "The book covers the combinatorial aspects of the theory with particular attention to constructing symmetric designs and related objects." The last five chapters of the book are devoted to results that have never previously appeared in book format. The book has an extensive bibliography of more than 400 entries that makes it valuable to researchers. It also could be used as a text for a course in combinatorial designs. Ionin and Shrikhande were awarded the Cambridge contract in 2001after submitting initial ideas on the monograph and some sample chapters. To support the project, each faculty member also received a CMU Research Professorship, which gives faculty members a semester off to conduct research. Cambridge University Press is the oldest printing and publishing house in the world. It was founded on a royal charter granted by Henry VIII in 1534 and has been operating continuously as a printer and publisher since the first press book in 1584. The New Mathematical Monographs are dedicated to books containing an in-depth discussion of a substantial area of mathematics. Design theory is a well-established branch of combinatorial mathematics. Combinatorics is a branch of mathematics that deals with counting objects in finite collections and calculating the number of ways patterns can be formed in the objects, such as the number of possible orderings of a deck of playing cards. The origins of the subject can be traced back to the pioneering works of renowned statisticians. From the beginning, one of the central objects of design theory has been symmetric design. The prototype of a symmetric design is a finite projective plane, and the theory of symmetric designs borrows its methods and ideas from finite geometries, group theory, number theory and linear algebra. This is Shrikhande's second Cambridge University Press monograph. The first, "Quasi-Symmetric Designs," with S.S. Sane was published in 1991. It also was the result of a CMU Research Professorship award in 1988. An editorial board that includes noted professors Bela Bollobas, William Fulton, Anatole Katok, Frances Kirwan, Peter Sarnak and Barry Simon directs the New Mathematical Monographs series. CMU MATHEMATICS BOOK CONTAINS NEW RESULTS ON SYMMETRIC DESIGNS |
March 10, 2005
Hans Bethe, A Titan Of Physics And Conscience Of Science, Dies At Age 98ITHACA, N.Y. -- Nobel laureate Hans Bethe, the last of the giants of the golden age of 20th-century physics and the birth of modern atomic theory, and one of science's most universally admired figures, died quietly yesterday evening at his home in Ithaca, N.Y. He was 98. At his death, Bethe was emeritus professor of physics at Cornell University, the institution he joined in 1935 after fleeing Nazi Germany because his mother was Jewish. He was one of the most honored members of the faculty in the university's 140-year history for his work in revolutionizing our perception of the real world. But he was equally admired for his reputation for integrity, humility and concern that made him the conscience of science. In tribute, Jeffrey S. Lehman, president of Cornell, said; "The world has lost one of the great pioneers of 20th century physics, and Cornell has lost a beloved teacher, mentor and friend. In the breadth of his insight, the rigor of his research, the depth of his social conscience and the steadfastness of his commitment to Cornell, Hans Bethe set the standard for engaged scientific citizenship that will serve as a beacon for generations to come." Bethe's fellow Nobel laureate, physicist Robert C. Richardson, who is Cornell's vice provost for research, said; "Hans Bethe was a giant of 20th century science. He has been revered by his Cornell colleagues. He left profound and enduring marks of his intellectual leadership on Cornell, the United States, and the entire world. Bethe had an important influence upon me as a young faculty member when I arrived at Cornell in 1966. He demonstrated a clarity of thought that I could only hope to emulate some day." Bethe's deep and abiding belief in science was unaffected by his work on developing the first atomic bomb. "The intellectual achievements of pure research are one of the things that make life worth living," he once said. Even when he had just witnessed the blinding flash from the detonation of the first nuclear explosion at Trinity site in the New Mexico desert on July 16, 1945, he professed only to a concern about the atomic bomb's functioning . "I am not a philosopher," he explained. Yet he was deeply committed to humanitarian values, as shown in his efforts to limit the use of nuclear weapons and his work to promote the peaceful use of nuclear energy. "Science is always more unsolved questions, and its great advantage is that you can prove something is true or something is false. You can't do that about human affairs -- most human things can be right from one point of view and wrong from another," he once said. Eminent astrophysicist, Edwin E. Salpeter, who arrived at Cornell in 1949 to study under Bethe, said of his former mentor, "He brought clarity to an amazing number of fields of science -- especially in astrophysics -- where he had to work in the face of uncertainty." Despite the turmoil of history, Bethe remained committed to the idea of physics as a thing of beauty leading to discovery and understanding, a quest that he called "the spirit of physics." It was a spirit enunciated by his famously optimistic phrase "I can do that," always said in the face of opposition or adversity. Salpeter noted that Bethe's optimism sprang from knowing how to use the minimum mathematical complexity compatible with each problem he faced. "In his hands, approximations were not a loss of elegance but a device to bring out the basic simplicity and beauty of each field," he said. During World War II Bethe was a key figure in the building of the first atomic bomb as head of the theoretical physics division at Los Alamos. Bethe would later recall how "two elder statesmen" told J. Robert Oppenheimer, director of the Manhattan Project, " 'Look here, you can't run the theoretical division if you run the laboratory at the same time, and there has to be a theoretical division. It has to be organized. And so the obvious person to put in charge of the theoretical division is Bethe.' " But after World War II Bethe became a persistent champion of nuclear arms control, helping to persuade the White House to ban atmospheric nuclear tests in 1963 and antiballistic missile systems in 1972. And he stood firm in his opposition to President Ronald Reagan's Strategic Defense Initiative, the missile defense system known as Star Wars. "The Star Wars system involved impossible tasks to make lasers of unheard of power [and then] to deploy them on satellites in space," he argued. Bethe also was a deeply committed, even sensitive, teacher, and from 1945 until his retirement from active teaching in 1975 he trained and inspired a large number of graduate students. One of them, Freeman Dyson of the Institute for Advanced Study at Princeton, once noted that Bethe would often continue classes over lunch "and that's where most of the teaching was really done." His presence at Cornell was a magnet that attracted a world-class faculty to the university's physics department. During the 20 years following the war he became more involved in what he called "political physics," an attempt to educate the public and politicians about the consequences of the existence of nuclear weapons. He was on the President's Scientific Advisory Committee which gave advice to President Eisenhower and, later, to Presidents Kennedy and Johnson on such matters as ways to limit nuclear proliferation and further development of atomic weapons. Bethe was truly indefatigable. In his 90s, with his left arm and shoulder wasted by a degenerative muscle disease, he continued to arrive regularly at his office at the Newman Laboratory on the Cornell campus although, he admitted, "not every day do I find anything interesting." Every day began with a 45-minute hot bath, because, he said, "You sleep, and things get somewhat unscrambled in your mind; then in the bath, I can become conscious of that." And he always carried with him his old slide rule on which he could with ease perform calculations to the sixth power. Hans Albrecht Bethe was born July 2, 1906, in Strasbourg, now in France but then part of Germany. He showed an early genius as a mathematician, studying physics at the University of Frankfurt and doing research in theoretical physics at the University of Munich, where he was a student of Arnold Sommerfeld, the teacher of Wolfgang Pauli and Werner Heisenberg, and where he received his doctorate in 1928. In 1930 and 1931 he received fellowships, first to the University of Cambridge and then to the Institute of Physics in Rome, where he worked with Enrico Fermi. He taught at Frankfurt and Munich. At the Technical University of Stuttgart he was assistant to Paul Ewald, professor of theoretical physics, who would become his father-in-law a decade later when Bethe married Rose Ewald, then a student at Smith College in Massachusetts, and who graduated from Cornell in 1941. Bethe's father, a professor of physiology, was a Protestant, but his mother was Jewish. This brought him into conflict with Nazi race laws after Hitler came to power, and Bethe was dismissed from his post at the University of Tubingen. He left Germany, going first to England, then to the United States and Cornell in 1935. Bethe later said of his arrival at Cornell; "I came to America expecting to be among strangers. I came home to Ithaca." And he regarded it as home for the next 70 years. It was Bethe who propelled Cornell's physics department into the top rank. And it was at Cornell during the late 1930s that he wrote his famous reviews of nuclear physics and, in 1938, published his seminal paper on the theory of energy production in stars that explained how the sun shines. The work was to win him the Nobel Prize in 1967. During his years as a physicist he published papers in every decade from the 1920s through the 2000s. In 1995 Bethe's colleagues, students and friends marked his 60 years at Cornell with a two-day tribute to his life and work. "If you know his work," said John Bahcall of the Institute for Advanced Study, delivering his own appreciation, "you might be inclined to think he is really several people, all of whom are engaged in a conspiracy to sign their work with the same name." After World War II Bethe brought some of the most outstanding young physicists at Los Alamos to Cornell, among them Richard Feynman and Robert Wilson. Under their leadership Cornell became a world center for high energy elementary particle physics. Bethe and Feynman played a central role in developing quantum electrodynamics, work for which Feynman shared the Nobel Prize in 1965. During this period Bethe also produced the first major paper on the theory of order-disorder transitions in alloys. After his retirement from teaching he devoted much of his time to astrophysics, and wrote papers with Bahcall trying to explain why the sun produced fewer particles called neutrinos than predicted by Bethe's theory of stellar energy production. And at the age of 83 he apprenticed himself to Gerald E. Brown of the State University of New York at Stony Brook in order to learn lattice gauge theory. The theory, which predicts how nuclear matter is transformed at extremely high temperatures into a plasma of particles called quarks and gluons, is one of the most challenging in all of physics. "I'm interested in learning new things," Bethe explained. The two scientists went on to publish numerous papers together on astrophysics. He was deeply in love with the mountains, spending at least two or three weeks every summer walking in the U.S. Rockies or the Swiss Alps. He was also a stamp collector, a hobby he took up in his teens and resumed in his late 40s and continued until his death. "It was the one place in the world where all countries sat together peacefully," he said. He also was passionately interested in history. In addition to his wife, he is survived by two children, Henry, of Ithaca, and Monica, who lives near Kyoto, Japan, and three grandchildren. Hans Bethe, A Titan Of Physics And Conscience Of Science, Dies At Age 98 |
March 07, 2005
Scientific advance: creating wrinklesBy Glennda Chui Wrinkles? Who needs 'em? The fewer the better, most people would say, whether on your face or your shirt. Not scientists. They are busy creating wrinkles in the lab -- layer upon layer of them, in an effect worthy of Robert Redford. Wrinkles, researchers note in a report released today, ``have been typically treated as a nuisance to be avoided rather than an exquisite pattern to be exploited.'' In fact, they say, learning how to precisely craft such exquisite wrinkles could have practical value for making tiny gadgets and flexible electronic displays, among other things. It could also shed light on why our eyes sprout crow's feet -- even if it turns out we can't do much to stop it. The report in the journal Nature Materials, is the latest step in a fascination that goes back 500 years, said Lakshminarayanan Mahadevan, an applied mathematician at Harvard University. Renaissance artists made careful studies of wrinkles in skin and drapery, he said. And science has been weighing in for at least half a century. Two years ago, Mahadevan and a colleague laid out a general theory to explain how wrinkles form at scales as small as a cell and as big as a mountain range. The latest discovery came about by accident. Jan Genzer, a materials scientist at North Carolina State University, was working with clear sheets of silicone rubber, which is more elastic than a rubber band. His team tried to make the rubber stickier by stretching and baking it under ultraviolet light. They overdid it: The top of the sheet hardened into a rigid skin. When they released the ends of the sheet, the skin wrinkled. Genzer wondered: Could these wrinkles be good for something? Mahadevan encouraged him to push the technique further. So far they have made five layers of wrinkles on a single sheet. The finest wrinkles form first, on the top; then ever-bigger wrinkles form in the layers below. ``We have not invented wrinkles,'' Genzer said. ``But we have shown you can make multiple generations of wrinkles situated on top of each other.'' The group has used the wrinkled surface to sort tiny spheres by size: The smallest ones settle into the tiniest wrinkles, and so on. Whether this could be turned into a practical tool is unclear. ``It's an early demonstration. I really don't know how realistic it is,'' said Meyya Meyyappan, director of the Center for Nanotechnology at NASA's Ames Research Center in Mountain View, who was not involved in the study. Mahadevan said he doesn't really care. Over the years, he has tried to explain such ordinary phenomena as the way a card tumbles through the air and how honey dropped from a spoon forms a surprisingly neat coil on toast. ``It's nice if there are applications,'' he said. But ``I'm quite happy to study phenomena because they're there. Knowledge is never useless.'' Scientific advance: creating wrinkles |
March 07, 2005
Speaker decodes codes for curious |
March 07, 2005
Instructor puts the "Math" in "Mathios" |
March 06, 2005
The magic numberAll day yesterday people were asking me just what was so interesting about breaking the world record for giant prime numbers. It was certainly surprising to see this week's breakthrough in primes sandwiched in between articles about Iraq and the Michael Jackson trial, but Dr Nowak and his 7,816,230-digit prime number did indeed deserve their place on the front page because this discovery of a new biggest prime symbolises mankind's progress in confronting a challenge of epic proportions. It is an intellectual struggle that dates back to the Ancient Greeks and which holds some of the deepest, most beautiful mysteries imaginable. First, a quick reminder. A prime number is simply one that cannot be divided by any other number except 1 and itself. So 21 is not a prime number, because it can be divided by 3 and 7, but 3 and 7 are both primes because nothing will divide into either of them. Hence, the primes are the building blocks of mathematics, the numerical equivalent of atoms. Just as a molecule of water can be broken down into two atoms of hydrogen and one atom of oxygen, so can a big chunky number such as 90 be broken down into its prime atoms 2, 3, 3 and 5, because 2 x 3 x 3 x 5 =90. Consequently, a complete understanding of prime numbers would lead to a more profound understanding of all numbers. One of the first people to explore primes was Euclid in around 300BC in Alexandria. He noticed that primes become increasingly rare as numbers increase. For example, between 10 and 20 there are four primes (11, 13, 17, 19), but between 110 and 120 there is only one (113). He wondered whether the primes eventually became extinct or whether they go on forever? Is there a biggest prime or is there an infinite number of primes? In one of the most staggeringly bril liant and gorgeous breakthroughs in the history of human thought, Euclid proved that there is an infinite number of primes. He started by assuming the opposite, namely that there is a finite list of primes. Let's assume that 2 and 3 are the only primes in the world. However, if we multiply them together (2x3) and add 1 we get 7. Clearly 2 and 3 will not go into 7, so we have a new prime. But still our list of primes is not complete, because we can multiply all our known primes (2x3x7) and add 1 and we get 43, and once again we have discovered yet another prime. The argument needs a little refinement, but Euclid was basically saying that with any finite list of primes it is always possible to multiply them together and add 1 and demonstrate that the list is incomplete. If there is an infinite number of primes, then why is it so hard to find newer, bigger primes? The primes become increasingly rare, until eventually there are vast deserts of numbers where none exist. In between the deserts there will be an oasis where one prime sits quietly, but finding the location of these oases is a hit and miss affair. The location of primes is apparently unpredictable. And this leads to the greatest prime mystery in the world, namely the Riemann hypothesis. In 1859 the German mathematician Bernhard Riemann made a conjecture about the approximate distribution of primes, but after almost 150 years nobody has yet been able to prove its veracity. It is undoubtedly the single greatest outstanding conundrum in mathematics. For pure mathematicians, proving the Riemann hypothesis would provide a firm foundation for their subject and allow them to explore the rest of mathematics with renewed vigour, but this probably seems too abstract for most people. Researching into primes might still seem like rather an arcane pursuit. What's the point? The mathematical motivation for proving the Riemann hypothesis and understanding primes is merely the search for truth. Pure mathematicians are simply curious and are intrigued by such challenges. Proving theorems is akin to climbing mountains - you prove them because they are there. Or proving theorems is like writing a symphony - the result is something that lifts the human spirit. But if you insist on something that benefits society on a more material level, then research into prime numbers can still justify itself. Modern encryption relies on the strange property that multiplying prime numbers is relatively easy (7 x 13 = ?), but working out what two prime numbers multiply together to give a certain result is much harder (? x ? = 323). Indeed, with very large numbers it becomes virtually impossible to solve such problems, and this leads to effectively unbreakable codes. Thanks to the mathematics of primes and these codes it is possible to send credit card details over the internet, which gives rise to e-commerce, more efficient businesses, lower inflation, stronger economies and a wealthier society. And thanks to primes our emails can be encrypted and made safe from prying eyes. Prime numbers mean that our privacy can be protected. And on a global scale, these prime number codes allow every government and army in the world to defend themselves against eavesdroppers and phone-tap pers. America's National Security Agency (NSA) is the biggest employer of mathematicians in the world. And if that still isn't enough, and you want to have a direct personal financial benefit, then primes can deliver again. RSA, an encryption corporation in the United States, offers $20,000 to anybody who can work out which two primes multiply together to give 31074182404900437213507500358885679300373460228427275457201619488232064405 18081504556346829671723286782437916272838033415471073108501919548529007337 724822783525742386454014691736602477652346609. Solving this problem would help gauge the strength of today's codes. Or, you can try to break Nowak's record for the biggest prime. Download some free software and join the Great Internet Mersenne Prime Search (Gimps). You will become one of 40,000 Gimps around the world and if you happen to be the Gimp that discovers a prime with more than 10m digits then you can claim a reward of $100,000 from the Electronic Frontier Foundation. For the really big bucks then you just have to prove the Riemann hypothesis. The Clay mathematics institute in Massachusetts is offering $1m for what will be the most important proof in modern mathematics. And not only will you become rich, you will become famous and achieve the closest thing to immortality. Scientific theories are often proved incorrect or at least refined over the course of time, but mathematical theorems last for ever. We laugh at Pythagoras's ideas about medicine, but we still learn his mathematical theorem at school. Or, as the British mathematician GH Hardy put it, "Archimedes will be remembered when Aeschylus is forgotten, because languages die and mathematical ideas do not. 'Immortality' may be a silly word, but probably a mathematician has the best chance of whatever it may mean." · Simon Singh is the author of Fermat's Last Theorem. His latest book is Big Bang, a history of cosmology. The magic number |
March 06, 2005
NSA names ECC as the exclusive technology for key agreement and digital signature standards for the U.S. governmentElliptic Curve Cryptography (ECC), a strong, efficient public key cryptosystem, will soon become the standard to protect U.S. government communications. On February 16, 2005 at the RSA conference, the National Security Agency (NSA) presented its strategy and recommendations for securing U.S. government sensitive and unclassified communications. The strategy included a recommended set of advanced cryptography algorithms known as Suite B for securing sensitive and unclassified data. The only public key protocols included in Suite B are Elliptic Curve Menezes-Qu-Vanstone (ECMQV) and Elliptic Curve Diffie-Hellman (ECDH) for key agreement and Elliptic Curve Digital Signature Algorithm (ECDSA) for authentication. The Advanced Encryption Standard (AES) for data encryption and SHA for hashing are also included. All of the Suite B algorithms are consistent with the National Institute of Standards and Technology (NIST) publications. Interoperability and information sharing are two key principles in the NSA strategy. In his remarks, Daniel Wolf, the NSA's information assurance director discussed the importance of sharing information between departments and using consistent and strong standards to protect that information. The NSA recommends that the same level of security that is used to protect mission critical information - ECC-based protocols - now be extended to protect sensitive and unclassified data. "The NSA strategy is major news for the security industry and all government agencies or suppliers because it sets the security standards for at least the next few decades. The NSA has stated that there are more than 1.3 million cryptographic devices in the U.S. inventory, over 75 percent of which will be replaced during the next decade under the U.S. Crypto Modernization Program," said Scott Vanstone, Certicom's founder & executive vice-president strategic technology. "A system is only as strong as its weakest link. By using the same high level of protection for all communications, especially security that is standards-based and interoperable, agencies and all organizations can establish a trusted system that is much harder to compromise." ECC is a publicly-available algorithm and Certicom is known as the ECC pioneer and expert, having researched and developed ECC-based implementations and security for the past 20 years. In 1997, Certicom developed the industry's first toolkit to include ECC which has since been adopted by over 300 organizations. Today, its Certicom Security Architecture, a modular set of security services, software cryptographic providers (including a FIPS 140-2 Validated cryptographic module), and board support packages, enables device manufacturers and other government suppliers to easily add strong, efficient cryptography that meets the NSA recommendations and NIST publications. NSA names ECC as the exclusive technology for key agreement and digital signature standards for the U.S. government |
March 02, 2005
Pi = 3.14 = March 14 = Texas Pi Day = Pies!Holt Sponsors Texas Pi Day to Focus Attention on Mathematics and Gives Teachers Free Lesson Plans AUSTIN, Texas, March 2 /PRNewswire/ -- To highlight the importance of mathematics education and help students see that mathematics affects their everyday lives, Holt, Rinehart and Winston is sponsoring Texas Pi Day on March 14 by giving K-8 teachers in Texas free math lesson plans and a serving of reality-based fun. Pi is a mathematical concept that is taught and understood around the world. Texas Pi Day will occur on March 14, 2005, in recognition of the numeric significance of the date: 3.14. Holt's free teaching activities encourage teachers to give their students a fun experience with mathematics while they discover how math affects their lives in seemingly hidden ways. Teachers are encouraged to use the all-American dessert, pie, as a foundation for exploring the number pi. Not only do pie and pi sound alike, but pies are circular and the number pi is used in geometric equations related to circles. "We created this activity in an effort to raise awareness of the importance of mathematics in our daily lives and to focus on mathematics education," said Judy Fowler, president of Holt. "Mathematics literacy is a core component of our country's plan to bring US students to the forefront of education success. We hope that this event will inspire students to look at mathematics in a new light and be more interested in their math classes." During the first two weeks of March, Holt staff will deliver the free lesson plans to schools throughout Texas. Many schools will also receive free pies from Holt in an effort to encourage participation and thank them for their extraordinary daily efforts in teaching our youth. Public and private schools throughout Texas can download the activities at www.hrw.com. About Holt, Rinehart and Winston Holt, Rinehart and Winston is a leading publisher of textbooks and educational materials for grades six through 12 and is part of Harcourt Education, a global education provider serving students and teachers in PreK through grade 12, adult learners, and readers of all ages. The Harcourt companies are Harcourt School Publishers; Holt, Rinehart and Winston; Harcourt Achieve (including the Rigby, Steck-Vaughn, and Saxon imprints); Harcourt Assessment; Classroom Connect; Harcourt Canada; and Harcourt Trade Publishers. For further information, please call 800-992-1627 or visit www.hrw.com or www.harcourt.com. Pi = 3.14 = March 14 = Texas Pi Day = Pies! |
March 02, 2005
Prime movers' odyssey to infinityBy Richard Macey They do it for the same reason people climb mountains: because it's there. For almost 10 years, thousands of people around the world have been linking their personal computers to create a supermachine for a cyber voyage of exploration, seeking ever bigger prime numbers. A prime number is a number bigger than one that is divisible by itself and one only - 2, 3, 5, 7, 11 and 13 are the first six primes. Mathematicians have known for more than 2000 years that there are infinitely many primes. Now the computer of MartinNowak, a German eye surgeon, has discovered the largest one known to mankind. It has 7,816,230 digits, "over half a million digits larger than the previous largest known prime number", announced the Great Internet Mersenne Prime Search, or GIMPS. "You do it because it's there," James Franklin, an associate professor of mathematics at the University of NSW, said yesterday. "You can feel that you have done something for world knowledge. You become famous, but it's the computers that do all the work." The computer project is seeking a special type of prime called a Mersenne prime, named after a French monk, Marin Mersenne, who studied them over 350 years ago. A Mersenne prime is a prime number that can be expressed as 2n - 1. For example, 22 -1 equals 3, which is a prime, while 211 - 1 equals 2047, which is not. "People will go on finding prime numbers forever, slowly," said Mike Hirschhorn, a senior lecturer in mathematics at the University of NSW. But, he said, no one knows if there are infinitely many Mersenne primes. Dr Hirschhorn said the late Paul Erdos, a Hungarian-born mathematician, had predicted that "by the year 5000 we should know if there are infinitely many Mersenne prime numbers". There is a $US50,000 ($64,000) prize for the first GIMPS team member to find a Mersenne prime with 10 million digits. But Dr Hirschhorn suspected the money should be safe for quite a while. Finding such a number with 10 million digits, he said, "could be a thousand years away. Who knows?" Prime movers' odyssey to infinity |
March 02, 2005
COOL 2 KNOWBY JAMES LYNN; James Lynn is a former Newsday editorial writer A NEW HOOK Those crafty scientists A 200-year-old hole in the fabric of mathematics has finally been mended. In a recent lecture at The Kitchen theater in Chelsea, a brainy - and dexterous - Cornell mathematician described how she made a real-life model of a principle that has mystified scientists for centuries. She crocheted it. Since the early 1800s, mathematicians have known about something called "hyperbolic space," but they couldn't figure out a way to illustrate it. Enter Daina Taimina. After watching her husband, fellow mathematician David Henderson, make a rather flimsy version out of paper, she decided to use her knowledge of handicrafts to create a more durable one. When her knitted model proved too droopy, she tried crocheting it with coarse synthetic yarn and the rendering turned out exactly as she had hoped. One of the models is now on display at the Smithsonian, and the scientific community is abuzz with requests for her handicrafts. So what is hyperbolic space? "The easiest way of understanding it is that it's the geometric opposite of a sphere," Taimina says. "On a sphere, the surface curves in on itself and is closed. But on a hyperbolic plane, the surface is space that curves away from itself at every point." Still confused? That's where her models come in. Verbal descriptions are so hard to understand that, until recently, only a small group of mathematicians really knew what it all meant. And even they overlooked naturally occurring examples, like some kinds of lettuce and seaweed. Now, using the crocheted models, fifth graders are learning about hyperbolic planes. Neurosurgeons also find the models useful because the planes' surface is similar to that of the brain. Henderson says scientists speculate that this kind of folding allows the brain to store information and retrieve it more quickly than if the surface were stretched out flat. Even cartoons can benefit from the models. Pixar animators use this kind of geometry to make certain surfaces, like fabric and skin, appear three-dimensional on screen. COOL 2 KNOW |
March 01, 2005
Maths literacy vital for life todayBy Aarnout Brombacher When Premier Ebrahim Rasool calls for increased participation in mathematics and goes on to suggest that all pupils in the Western Cape should be doing higher grade mathematics (in his State of the Province address of February 18), does he really mean what he is saying? When the premier calls for increased capacity and the development of human capital and at the same time links this to success in mathematics he is, of course, correct. The development of our economy and nation is intimately linked to the development of certain kinds of skills - skills that appear to be mathematical in nature. However, the sad truth is that higher grade mathematics does not necessarily develop these skills. These skills may well be better developed by the new subject, mathematical literacy, that is being introduced in the Further Education and Training (FET) curriculum. Mathematics is important for enrolling in many higher education programmes. But is it the mathematical skills themselves that are needed, or is ability in maths simply considered a useful standard for selecting pupils? Higher grade mathematics provides a crucial and important foundation for those who go on to study further courses in mathematics, and in mathematics-related fields such as science, engineering, technology and the life and physical sciences. However, it does not necessarily develop the skills we think we need when we advocate "mathematics for all". The influence of increasingly powerful computers and the pervasive nature of the media have ensured that the world we live in is data driven. Data is presented in numbers, tables, graphs, formulae and words - artefacts we associate with mathematics. Some of us who feel intimidated by all this assume that to make sense of the data we need more mathematics - a subject that we associate with bad memories from our school days. Not wanting our children to experience the same feelings of inadequacy about the data that pervades our lives, we call for mathematics for all. Individuals need to be mathematically literate in all spheres of their lives. At a personal health level, people need to understand the importance of an adherence regimen for the success of ARVs and TB treatments - that is, they need to have an understanding of tolerances. To manage their finances, individuals need to understand the impact of hire-purchase agreements on their disposable income, to understand that there are no "free" cellphones, and to understand that there are no "hot" and "cold" numbers in the national lottery. They need to be able to make choices from information presented in tables and through statistics. As workers, we need to be able to negotiate a fair wage, to be able to argue for conditions of service and to know when our trade unions are effectively losing our money by prolonging a negotiation process. Employers increasingly demand that their employees can make decisions based on data that is presented through numbers, in tables, graphs and sometimes even through formulae. Computers produce data that is presented in spreadsheets and employees need to be able to interpret it. As critical citizens, we need to be able to understand and engage with the statistics that appear in the daily media - statistics that deal with crime, allocation of public funds and the transformation of society and lately even discussions about the role of Stats SA. What good does it do to know that crime is down 2% when we do not have other information? The actual amount of crime may have increased and people are simply not reporting it, or big crimes may have increased even though the total is down. Mathematically literate people can ask the right questions to make sense of, to engage with and to critique the information, that bombards them as individuals, workers and citizens rather than accepting that they "don't understand it" because they were not good at maths. In fact many people who were "good at maths" are also unable to make sense of such information. Why? Because that maths was designed purely to prepare them for further study in mathematics, not to equip them for the rigours of the modern world. I agree with the premier that the modern world requires skills that appear to be mathematical in nature and I would go so far as to say that a modern democracy can be threatened by an absence of such skills. However, the skills the premier is talking about would be developed more effectively by the new subject of mathematical literacy. That is not to say that mathematics higher grade has no place; the two subjects need to exist side by side, equal in status yet serving different roles. While mathematics higher grade provides the foundation for further study in the fields of mathematics, engineering and the life and physical sciences, mathematical literacy provides one with the skills to make sense of, and contribute to, the world in which they live. As an aside, I also agree with the premier's implicit acknowledgement that mathematics standard grade is not, in general, of much use to those who take it. It is, to all intents and purposes, a dead-end subject that does little more than boost school pass rates. It is for this reason that I am at peace with the new FET curriculum, in which there will no mathematics standard grade as we know it today - only mathematics (offered and assessed as a high-quality robust course in mathematics, the discipline). What I really worry about is the possibility that mathematical literacy may be interpreted as the new mathematics standard grade. Let me be emphatic about this: it is not! Mathematical literacy is a different kind of mathematics, not a different, lower level of mathematics. mathematical literacy will be at least as demanding as mathematics to teach and certainly as challenging for pupils to learn. The world has changed dramatically and mathematical literacy is the new currency. I support the premier's call for increased mathematical skills for all. However, I want to caution that the skills he is calling for may not be found where he suggests they are. Brombacher is a former high school mathematics teacher and past president of the Association for Mathematics Education of South Africa (Amesa). He now works as a consultant in mathematics education. Maths literacy vital for life today |
March 01, 2005
Spam key to help solve HIVBy Tom Paulson Biomedical researchers at Royal Perth Hospital in Western Australia are helping software scientists at Microsoft Research in the US see if computer techniques used to defeat email spam can also design a vaccine to beat AIDS. The plan to use "machine learning" and data mining was announced last week at an AIDS conference in the US. Researchers hope to use computational techniques to decipher HIV's wildly creative genetic ability to constantly change and disguise itself from immune system deletion. "HIV mutates like crazy but it does show a pattern," says Dr David Heckerman, a physician and computer scientist at Microsoft Research. "It isn't completely random," says his colleague Nebojsa Jojic, adding that just as a spammer can only add so much nonsense without obscuring the message, so can the AIDS virus only vary so much without disabling itself. Professor Simon Mallal, executive director of the Centre for Clinical Immunology and Biomedical Statistics at Royal Perth Hospital, says: "A few vaccines are in clinical trials, but none have overcome the primary challenge, the enormous diversity of the virus. Our tests on 473 HIV patients in Perth found 473 different strains of the virus." Researchers hope they will be able to train the immune system to reject HIV once they can uncover the patterns by which it mutates, Mallal says. Dr James Mullins, a University of Washington microbiologist and AIDS researcher, says standard vaccine development requires extensive experimental testing against specific strains or select groupings of similar strains. Machine learning, a form of artificial intelligence, will make this search more manageable by letting a computer sort and analyse all the information and variations to look for revealing, repeat genetic patterns in HIV. Just as a computer's spam filter learns to recognise variations from the same spammer, it is hoped a computer can learn to decipher fundamental repeat patterns about HIV's genetic variability and narrow the search for vaccine targets. Spam key to help solve HIV |
March 01, 2005
A Brilliant Mind and an Anguished LifeBy CORNELIA DEAN "Dark Hero of the Information Age: In Search of Norbert Wiener, the Father of Cybernetics," by Flo Conway and Jim Siegelman. Basic Books, 423 pages, $27.50. It is hardly the greatest scientific mystery of the 20th century, but it is a riddle just the same: why did Norbert Wiener - gray eminence of gray matter, inventor of cybernetics, founding theorist of the information age - abandon his closest young colleagues just as they were about to embark on an exciting new collaboration on the workings of the brain? Historians of science, and even some of Wiener's associates, have long puzzled over this question. Now Ms. Conway and Mr. Siegelman offer an answer. In their new biography, they tell a tale of jealousy, false accusations of sexual misconduct and twisted family relations. Their account might be dismissed as a 50-year-old soap opera, were it not for Wiener's stature. He pioneered the study of the ways mechanical, biological and electronic systems communicate and interact. His groundbreaking research at the Massachusetts Institute of Technology defined the parameters of what we know today as computer science. His book "Cybernetics" is widely regarded as a major work of 20th century science. And he was already famous, before he even started. Born in 1894, he grew up in eastern Massachusetts under the harsh tutelage of a father whose unorthodox home schooling methods and relentless pushing turned Wiener into a child prodigy. By the time he was 14 he had a diploma from Tufts and by 18 he had earned a doctorate in mathematical philosophy from Harvard. One newspaper called him "the most remarkable boy in the world." But these achievements came at a cost. After a childhood taken up almost exclusively with study, his adulthood was plagued by clumsiness, tubbiness, nearsightedness and absentmindedness so extreme they eventually became the stuff of legend. Years of devastating paternal criticism left him hypersensitive, and he suffered periodic episodes of deep depression. Nevertheless, he married, and the woman he married is the villain of this tale. She was Margaret Engemann, a young immigrant from Germany whom he met through his parents. The younger Wieners had two daughters and initially, it seemed, the marriage was more or less happy. But it was Margaret Wiener's dream, the authors write, to be a high-status professor's wife, presiding over an intellectual salon in the Teutonic mold. Instead, her husband had surrounded himself with a number of imaginative young students and protégés, as intent as he was on figuring out how the brain talks to itself and how machines could be made to perform similar feats. One in particular incited her ire. He was Warren McCulloch, a neurophysiologist and free-wheeling bohemian with a thirst for alcohol and an inventive mind. The authors theorize that she disliked his way of life and at the same time feared he would threaten Wiener's prominence at M.I.T. To prevent that, they say, she tried to quash plans for McCulloch and his associates to move to M.I.T. When that failed, she told Wiener an invented story, that one or more of "the boys," as Wiener called them, had seduced their elder daughter. The authors say this explains why Wiener broke with the boys - immediately, utterly and apparently without a word of real explanation to anyone. Read from a distance of decades, it seems incredible that such a promising collaboration could have collapsed so completely. It is particularly poignant that Wiener, who suffered so much from paternal disdain, would abandon young men who thought of him as a father. The boys waited in vain for Wiener's antipathy to fade. Years later, scientists still wonder what their collaboration might have produced, had they continued to work together. As the book recounts, the rest of Wiener's life was hardly bereft of accomplishment. Among other things, he collaborated on major advances in robotics and automation. In 1964, shortly before he died at age 69, he received the National Medal of Science. But often, the authors say, Wiener missed out on credit he should have had because he was chronically ahead of his time or because he shared his findings readily, allowing less generous colleagues and competitors to capitalize on his insights. Wiener's interest in cybernetics in the Soviet Union and his support of it brought him unwelcome government attention in the anti-Communist 1950's. And his ardent opposition to secrecy and commercialism left him at odds with many scientists. (One can only wonder what he would have said about the commercialization of science today.) Over the years, Wiener has been described again and again as a great mathematician, gifted with imagination and insight that soared over the artificial boundaries that divide disciplines in science. Recent findings in neuroscience, for example, confirmed his early hunches about the workings of the brain, and he is still revered at M.I.T. But in the prosaic realm of real life, he was often disappointed, discouraged and downhearted. His may have been one of the great minds of the 20th century, but in reading this book one can only feel sorry for him. A Brilliant Mind and an Anguished Life |