August 28, 2005
OYIBO'S DOCUMENTARY REVIEWAuthor: Ademola Bello For three hours the documentary movie of Professor Gabriel Audu Oyibo offer us insights into Africa's richness, history, and science through his own intricate method called God Almighty Grand Unified Theorem, GAGUT, or the theory of everything. This was the theory that Albert Einstein searched for unsuccessfully most of his life but which Oyibo discovered and considered to be the Holy Grail of Physics and Mathematics which proffer solutions to mankind problems and incurable diseases such as Aids and Cancer. The screening of Oyibo's documentary titled "GAGUT THEORY: A JOURNEY INTO THE AFRICAN SCIENCE OF THE UNIVERSE" opened for selected public viewing over this past weekat a Studio House in Brookyln, New York managed by Mr. Clemson Brown the producer of the documentary. Mr. Brown was assisted with the documentary by Mark Dunston, as the video editor. The documentary began with a mesmerizing opening with the drum beats and songs of the legendary drummer Babatunde Olatunji. Mr. Brown who is also the narrator of the movie fascinates us with the historical narratives of Africa and Nigeria. We follow Gabriel Oyibo's emotional and meditative journey as he landed at the Airport and how he was greeted by the ecstatic overwhelming crowd. The overstretched celebration took him into Kogi's State governor's office where his academic contributions to global community were cited and the Attah of Igala's Kingdom Palace where he was bestowed with a Chieftaincy title. The euphoria that heralded his arrival could be compared to the one a U.S Army Medic who was recognized after many years for his incredible bravery during the war got in a 2000 Fox Family channel documentary titled "Courage" that was narrated by the veteran Hollywood actor Danny Glover. But the main focus of that documentary was courage, heroism, and triumph. This Oyibo's documentary however aims at telling us about GAGUT's relevance but the obstruction of his mission with irrelevant Catch-22 incidents created in the minds of a curious observer an impression of a mere political jambore. The primary source of information we first digested about GAGUT'S theory came from Oyibo's himself when he talked to us through the waterfall background image that stifled the audible sound of his speech. There was a brief appearance of vetrean Professors Iya Abubakar and Alex Animalu both doctorate holders from Cambridge University as we are told and authority that was very much cited by Oyibo as having validated his theory. When he was asked a question on why he believed that Oyibo's theory is genuine. The only explanation Iya Abubakar gave was an assumption that belittle any great scholar. "I've looked at it, since American Mathematical Society says it's correct. Yes, I believe it's correct." Nevertheless, the most intriguing aspect of the documentary was in a close circuit hall at the Ahmadu Bello University in Zaria where something unfolded through ticking moments. Professor Oyibo devoted his articulation and brilliant mind to answer questions and to proof mathematically his theory. The spell-binding effect of that documentary came from Professor Singh the Head of Mathematics Department at Ahmadu Bello University, The Indian born don makes the perfunctory room to be more interractive and engaging. Professor Singh says there is no Mathematical equation now or in the near future that can actually represent the Almighty God who is absolutely infinite. He says, "Once you talk Mathematical equation the only thing is proof. All this probability equation cannot be proved of absolute God. God cannot be infinite, one or two. God cannot be treated mathematically. But Professor Oyibo responded by proving that GAGUT answers the most fundamental question for humanity which is: What is God or What is the Universe? GAGUT answers that question by saying that God represented by GIJ is an entity that remains unchangeable which can mathematically be written as GIJ, J=0 where the comma in the equation represents change. An entity that doesn't change is absolutely infinitely large space that is full of motion and so the GIJ, J=0 is valid at every point in the absolute large space. He also says that GAGUT also unified the three known accounts of creation which are the Holy Books, which says that the Universe came out of the Word of God, the Science which says that the Universe came out of the Big Bang, and the Ancient Africans who showed that the Universe came out of the roaring water waves of Nun out of which came out the building block called Atum, which was later mispronounced as Atom, and was further mispronounced as Adam. GAGUT unified those three accounts by demonstrating mathematically that the word of God is the Big Bang and sounded like the roaring water waves of Nun. The hallmark of any great academic institutions are the spirit of truth and freedom. Professor Oyibo should negotiate a deal with a local publisher that would make his book available at a cheaper rate so that Nigerian academics and students would be acquianted with his work and verified whether it was real or mere conjectures instead of absorbing dogmatic belief as we have seen through the documentary of notable scholars cited as believing in the theory including Jibril Aminu. Since late Awojobi, we have not yet seen another great practical scientist in Nigeria. Maybe, Oyibo could become one if he succeeds with his Grand Unified Theorem. Aside Professor Singh who expressed his skepticism, there is one student also who raised a vital question saying he would be confused substituting Atum for Atom. Surprisingly, others seems to be bought over by Oyibo's star power. Dr. Gabriel Audu Oyibo's career has been a singular journey, he earned his Ph. D in Aeronautics and Mathematics from Rensselaer Polytechnic Institute that is situated in Troy New York where he worked for four years on NASA, Afosr sponsored research. He is currently a full time Professor of Mathematics and Mathematical Sciences at the OFAPPIT Institute of Technology, Dix Hills New York, of which he is a founder and at the University of Bridgeport in Connecticut. Though, Professor Oyibo is very innovative with his ambitious project but he is yet to demonstrate to us convincingly as we have seen in the documentary that his controversial GAGUT theorem is a valuable or practical tool for solving the world's problems.
See also:
Mathematical Centre to Award Post Graduate, Doctorate Degrees Source URL: OYIBO'S DOCUMENTARY REVIEW |
August 25, 2005
Russian Engineer Proves Fermat's TheoremBorislav Kozlovsky The Omsk researcher's computations have not yet been published anywhere before appearing in a journal, they must be tested. A summery was published by Novaya Gazeta, but a number of inaccuracies makes the text too susceptible to criticism. It's also not exactly clear what has been proven at this point. The version (obviously false) published by Novaya Gazeta fully reproduces the remarks published on a personal Website dated from 2003 and signed by a different name. Then again, it's possible that there a lot more such proofs. Apart from what is mentioned above, not much is known about the mathematic discovery. Take, for example, reviewers' opinions: "The academician Leonid Gorynin and professor Sergei Shukanov also admitted that they see no faults in the proof," Newsru.com reported citing the Regions.ru website. However, Leonin Gorynin was not listed among the members of the Russian Academy of Science. Professor Sergei Chukanov, a doctor of technical sciences from Omsk who works at a department that deals in automated data processing, is clearly no specialist in number theory. That alone is enough to treat the Omsk researcher with a degree of skepticism. But several conclusions could have been drawn before that. There are certain words, after all, that any science journal editor or reviewer has to filter out immediately: "eternal engine, torsion field, and the like. Any time any of them are mentioned in earnest, it's usually a signal not to read any further. And Fermat's Last Theorem, through no fault of its own, was thus blacklisted. The famous theorem is probably the only serious mathematical problem that has attracted the interest of non-mathematicians. The reason is the relatively simple formula. Accessible to anyone ever taken a high-school algebra class, it looked as an invitation to test oneself against a puzzle. A 100-mark prize set up for anyone who could come up with a proof in 1908 helped create a whole new category of people: Fermatists. The first ones to suffer were number theory professionals: thousands of letters were addressed to them. It was Pierre de Fermat himself who gave laymen the confidence they needed. Written in 1637 on the pages of Diophantus's Arithmetica it was accompanied by the well-known commentary: I have discovered a truly remarkable proof which this margin is too small to contain. It was believed that the computational abilities of a 17th century mathematician would not be very demanding of a contemporary science college freshman. This is where the surface of the iceberg ends. It's known that Pierre de Fermat was later interested in exclusive cases of his statements, which would have been strange had he truly completed a full proof. Most likely, Fermat was mistaken a majority of mathematicians believe so. Fermat's Last Theorem was proven by Andrew Wiles, a professor of Princeton, in 1994. After being tested for about a year, his proofs were deemed accurate and published in the Annals of Mathematics. A long time before that, the problem was reduced to two theorems that complemented each other. One was proven in 1984 by the American mathematician Kenneth Allen Ribet. However, only about fifty people across the globe were capable of understanding the theorem. In 1997, Wiles was awarded the prestigious Fields Prize. The true rating of mathematical problems long ago grew apart from public attitudes as to their importance. Where "insolvability" is concerned, one can consult the "Gilbert list", which included 23 top unsolved problems at the start of the 20th century. Only three have remained unsolved today. Hardly any have an accessible formula. Talk of what would have happened had the "margins been big enough" is what algebraists do instead of talking about the weather. As more mathematicians acquired new instruments, the number of unsolvable problems grew as well. But they lacked the accessibility and the romanticism of the Fermat theorem. For the last 150 years, Fermat's theorem has had to share the limelight with Rieman's Hypothesis about zeros in zeta-functions. It is harder to formulate using school terminology, but a number of parallel consequences, such as the statement about the endless pairs of simple numbers two consecutive numbers apart, are well known. Anyone who proves (or disproves) the theorem will also get a considerable prize $1 million. Possibly, that is why laymen are not particularly disturbing the professional researchers their incompetence is readily noticed. But the existence of a closed science that does not demand much attention from the outside cannot but provoke someone to reexamine its very foundations. Fermat's theorem is just such an invitation. And there's no harm in search for proofs "in the margins." As long as amateurs don't get the airtime that real mathematicians can never afford. Russian Engineer Proves Fermat's Theorem |
August 25, 2005
Genes for mathematical genius?A British research team from the Autism Research Centre at the University of Cambridge has recently embarked upon the first-ever rigorous search for a maths gene. The scientists intend to search the DNA of 200 pairs of siblings for clues as to what makes a good mathematician. Mathematical ability is commonly thought of as an innate gift that some people are born with. Moreover, this gift, which often runs in the family, is coupled in many cases with other peculiar characteristics such as musical ability, spatial awareness and a lack of social skills. People with autism are not only challenged in terms of social skills, but can also show extremely high mathematical ability. The question remains as to whether this connection is due to genetics or due to nurture rather than nature. Mathematically minded families are more likely to foster the attraction of their children to this field by playing maths puzzles and games. Also, being a solitary business, maths is more likely to attract introverted individuals when they are still young. Trying to establish whether such a genetic link does exist, the Cambridge team of scientists, lead by Professor Baron-Cohen, intends to consider the genes of pairs of siblings who have both obtained an A grade at maths A level - the exams taken in the UK at the age of 18. Candidates will be asked to perform an online maths test and to send in a cheek swab by post. On average, siblings share 50 per cent of their genes. If the scientists find along the way a significantly higher number of genes that are shared, those genes would be candidates for being responsible for the common maths ability of the siblings. These candidate genes could then be subjected to further tests in order to see whether they really are connected to mathematical ability, or autism, or both. Understanding mathematical ability, and its origins, can help improve maths education and support those unable to get to grips with basic maths - a huge handicap for some people. Early identification of those that are likely to struggle, would allow provisions to be made so that they do not get left behind at school. Besides, knowledge of a maths gene, if it exists, may provide insights into how mathematically gifted people see the world, and may help scientist to pierce the mysteries of autism. The project team is asking for volunteers. They are particularly interested in brothers and sisters who both have an A grade in A Level maths. For further information, please visit the maths gene project website: http://www.cambridgepsychology.com/maths Genes for mathematical genius? |
August 23, 2005
Numbers gameStash your calculator, limber up your brain - a new radio series sets out to show maths can be interesting, and prove that the number 1,729 is special.  Maths ambassador Simon Singh
Imagine if school league tables reflected the popularity of individual subjects among pupils. It's a fair bet maths would not rank highly. |
August 23, 2005
REBUTTAL TO REVIEW OF GAGUTClemson Brown This is a rebuttal to the review of the film documentary of Professor Gabriel Audu Oyibo's God Almighty Grand Unified Theorem (GAGUT). The reviewer's objective was to create distrust and doubt as to whether Professor Oyibo has developed an equation for the Grand Unified Field Theorem. If this was just another documentary about aspects of a common issue, it would not merit a rebuttal. However, the honorable Anthony Agbo, Minister of Public Works in Ebonyi State in Nigeria stated that Professor Oyibo has discovered the holy grail of mathematics and physics. The search for the Unified Field Theorem has been the hottest contest among the greatest intellectual minds on the planet. The ultimate goal is to conceptualize the workings of the Universe and express it in one mathematical equation. What ever race is blessed with the knowledge of the equation of the Unified Field Theorem has been called by the creator to leadership in the world. This position is presently claimed by the western world as a matter of their technological supremacy. Leadership of the world is something that nations kill for every day. This is a position that the western world will not give up without a challenge. Therefore, we are writing in defense of our national legacy, security, and honor. Critics should scrutinize and present their professional opinion. They cannot however extend that liberty to outright lies and distortions. Especially if these deceptions help the enemies of Africa maintain their dominance and control over the Africa. Continent This film documents Professor Oyibo's International Presentation of GAGUT at the National Universities Commission (NUC) headquarters in Abuja Nigeria. Professor Oyibo gave 18 lectures at 8 specifically selected zones which covers the Nigerian University system. They were sponsored and organized by NEADS (Nigerian Experts and Academics in the Diaspora Scheme). The film also provides a historical perspective of the African origin of creation. It covers the enthusiastic celebration of Professor Oyibo's achievements and contribution as he is honored and welcomed home by his people. The film shows Prof. Oyibo's presentation to tens of thousands of Nigerians and over four hundred of Nigeria's professors of mathematics, science and engineering, vice chancellor and international representatives including a member of the United Nation Educational and Cultural Organization (UNESCO). Professor Oyibo has made himself available for any scrutiny by members of his genre. The reviewer failed to note Professor Oyibo's directive to unite the industrial sector with the university community. This, as Professor Oyibo stated, would provide students with grants for scholarly achievements toward the solution of problems holding back the growth and development of Africa through the use of GAGUT's principals. There has been many esteem journalists such as Laolu Akande of The Guardian newspaper, Kenneth Obechina Obo Reporter for Nigerian Television Authority (NTA), Herb Boyd of the Amsterdam News; Gary Byrd of WBAI Radio, and David Greaves of Our Times Press in the United States who spent hours interviewing and researching facts surrounding Professor work and have applauded Prof. Oyibo. The reviewer was given material from both the American Mathematical Society and the European Mathematical Society which verifies Professor Oyibo Theorem. These Societies in their review on 1) Generalized Mathematical proof of Einstein's theory using a new group theory 2) Exact closed form solution to the full Navier-Stokes equations and new perceptions for fluid and gas dynamics 3) Mathematical modeling for fluid and gas dynamic turbulence, among other qualifying relations, states that 'The Author (Oyibo) presents an exact solution of the steady Navier-Stokes equation'. Now The reviewer perhaps cannot follow the highly complicated scientific matter. The film also provides the viewer with the evidence of these reviews by five of the world's most noted mathematicians and physicist. Among the mathematicians who reviewed and supports Professor Oyibo's work is Dr. Iya Abubakar, who holds a PhD degree in Mathematics from Cambridge University in England, which hold the highest standards of excellence in mathematics in the world. He was former head of the mathematics department and the Vice Chancellor at Amadou Bello University In Zaria, Nigeria. He was the Nigerian Minister of Defense and is presently, of a member of the Nigerian Senate. The film shows an interview of Dr. Abubakar with the press, stating that ': 'I have looked at it and it is perfectly correct - you can rely on it. When you differentiate a constant, you get zero. In relation to the equation Gij,j = 0, this means that God is constant and that the change in God is zero'. The reviewer degraded Dr. Iya Abubakar by stating the following: 'when he was asked a question on why he believed that Oyibo's theory is genuine, the only explanation Iya Abubakar gave was an assumption that belittles any great scholar.' Another example is Dr. Alexander Animalu. Dr. Animalu is also a PhD graduate in mathematics from Cambridge University, whose Doctorate thesis was cited over 750 times, making it the most cited paper coming out of Cambridge University in the field of mathematics in over 50 years. He is a former head of the Nigerian Academy of Sciences. Dr. Animalu wrote a 22 page review of Professor Oyibo's theorem entitled 'The Dirac equation in 5 dimensions and consequences'. As the film shows, Dr. Animalu stated clearly that Professor Oyibo's theorem was a true unification with a methodology that goes beyond Einstein. The reviewer omitted the verification of Dr. Animalu completely. The reviewer was not interested in writing about any authorities who supported Professor Oyibo's Theorem. As a native born Nigerian, the reviewer could have taken pride in Professor Oyibo's discovery once the facts presented themselves. Instead he chose to insult the Nigerian people by insinuating that their Academic, religious and political leaders were 'mesmerized' by the star power of a snake oil salesman. Rather than taking pride at the sight of thousands of young students standing on the windows of the Kogi State University Auditorium for hours, for the chance to hear a lecture on mathematics, He chose to identify with the condescending attitude of a handful of dissenters who subconsciously reject their own color, culture and consciousness for some westernized model. The reviewer should log on to the web site www.geocities.com/igala1 if he can access it. GAGUT has been scrutinized, reviewed and verified by legendary Mathematicians, Scientists, and Physicists like Professors G. Tsagas, A.D. Khonkin, Jaume Carot, A. Cichoka, P.B. Duboski, A. Animalu, A. Pozzi, I. Abubakar just to name a few from the most prestigious universities and research centers around the world. In addition, some of the most brilliant journalists worldwide have published very thoroughly investigated reports about GAGUT. Some of these reports have attracted the intention of institutions like the Financial Times of London (August 9, 2004, October 27, 2004 and November 23, 2004), the Qtrade, Canada's leading on-line brokerage firm (October 24, 2004), the Baltimore Sun, one of the leading mainstream newspapers in America, featured article entitled Meet the Worlds Greatest Scientist ' Professor Oyibo(December 3, 2004), Wikiverse: A World of Knowledge (October 29, 2004). These News reports about GAGUT have been recognize d by the world's leading News Data base which is called NexisLexis in which news reports about GAGUT have been featured 23 times. The credibility of Nexis-Lexis is so high that news featured in Nexis-Lexis are used in legal court deliberations, by lawyers and legal experts. The news reports about GAGUT have also been featured on the Big News Network, which only reports Big News around the world (October 28, 2004). The American Mathematical Society and the European Mathematical Society have extensively reviewed GAGUT using legendary Mathematicians, Scientists, and Physicists above and others. There have been lots of Television News coverages about GAGUT. GAGUT has also been covered by Math News, an authoritative news source for significant developments in mathematics worldwide, and has recognized GAGUT as the HOLY GRAIL, a phrase that is used in the scientific and the mathematic world to represent the ultimate research goal for human beings, which is the Unified Field Theory, or the Theory of Everything. MathNews comes out of the University of Turin ( Torino), Italy, one of the oldest universities (1404) in Europe. One of the MathNews reports on GAGUT (July 23, 2005) entitled THE HOLY GRAIL!!! was featured with their report about significant research developments from Massachuttes Institute of Technology (MIT) as well as from Cambridge University in England, and other prestigious universities. MathNews is edited by Professor Umberto Cerruti, a very renown mathematician. GAGUT's classification as THE HOLY GRAIL by MathNews, therefore has confirmed for mathematicians and non-mathematicians that GAGUT is the long await ed discovery of the secret code to the universe. Many people all over the world are trying to gain access to the Nigerian Born American based, Nobel Prize nominee and cannot gain access so readily. People all over the world are attempting to gain access in order to find out what the Professor's latest discoveries are. Math News also states that: 'To underscore the extent of the impact of his work in the Western world the German armed forces through its nuclear bomb research, is now seriously understudying his work. On a famous German book web cite abebooks.de, the German Federal Armed Forces is offering and promoting one of Oyibo's works, 'Highlights of the Grand Unified Field Theorem' Also at DESY the library of the German Nuclear Bomb Research, Oyibo's Grand Unified Theorem the discovery of the Theory of Everything and the 'Fundamental Building Block of Quantum Theory' is listed. In the US, Oyibo's are mostly reserved in reference sections in major libraries including those in Stanford, Harvard and several top universities in Europe'. This work was supported by the National Institutes of Health. Patti Richards MIT News Office Brain scientists offer insight into vision
SEE ALSO:
Mathematical Centre to Award Post Graduate, Doctorate Degrees
AND |
August 22, 2005
Step into the WORLD of M.C. EscherPhilip E. Bishop  'Belvedere' (M.C. ESCHER) Among the unlikely popular favorites of the '60s -- Buckminster Fuller, the Grateful Dead and Hermann Hesse's novels spring to mind -- the mind-bending prints of M.C. Escher are perhaps least expected. Escher's esoteric world of repeating patterns and playful illusion seems a long way from Hesse's Steppenwolf. But the opening of "M.C. Escher: Rhythm of Illusion" at Orlando Museum of Art still drew a crowd. There were probably a few ex-hippies with their children and grandchildren among the roughly 2,000 in attendance last weekend, contemplating the arcane pleasures of art and mathematics. The show of more than 80 prints and drawings was organized by the Portland Museum of Art in Oregon and includes about 10 works from a local private collection. Interactive games in the galleries engage young visitors. University of Central Florida professor Stella Sung composed ambient music that settles in the exhibition's quieter corners. The atmosphere is just right to clear the cliches around Escher and contemplate his deeply philosophical work anew. Maurits Cornelis Escher (1898-1972) began as a conventional artist and printmaker. Born in Holland, he was enamored of Italy, especially the picturesque villages of Sicily and the Amalfi coast. For 12 idyllic years, Escher created meticulous views of southern Italian villages, with their exotic blend of Norman, Moorish, Romanesque and Renaissance architecture. But in 1935, the rise of fascism forced Escher and his wife to abandon Italy. At home in flat, dull Holland, Escher later wrote, he withdrew "from the more or less direct and true-to-nature depiction of surroundings." His impoverished surroundings were "responsible for bringing my inner visions into being." Escher's inner visions eventually connected him to complex ideas of mathematics and physics. But the Orlando exhibition demonstrates that Escher's playful abstractions began in artistic ideas. These are works inspired, and sometimes haunted, by the idea of the double. In "Day & Night" (1938), a flight of ducks splits at the center, flying in opposite directions over the same landscape in night and day. At the image's center, the ducks embody Escher's principle of the "regular division of the plane." Mathematicians call this "tessellation," when interlocking figures completely fill a flat space, without blanks or overlap. The doubles can be funny. In "Encounter" (1944) two male figures, one a nagging pessimist and the other a smiling optimist, emerge from the background. The figures pace around a circular drum and shake hands at the front. Faith and redemption Escher's duality also has cosmic overtones. In "Circle Limit IV (Heaven and Hell)," a pattern of grinning demons and white angels covers a globe, stretching right to the horizon. As a technical tour de force, the print explores a tension between the confined figure and infinite space. As a philosophical speculation, it's aware that good and evil remain in eternal and unresolved tension. By the 1940s Escher was educating himself in crystallography and other esoteric branches of mathematics. His work was soon acclaimed by leading physicists and mathematicians, and the artist found himself a popular lecturer. In his art, Escher was exploring what mathematician Douglas Hofstadter called "the strange loop" in his cult classic Goedel, Escher, Bach. Take "Ascending and Descending," where monks climb (or descend) a cloister's staircase without ever reaching the top (or bottom). The print toys with "reality" and "illusion," creating an image that is real -- but a reality that is logically impossible. Orlando Museum's exhibition includes preparatory drawings that reveal Escher's trick, but this isn't just artistic sleight of hand. "Ascending" contains a brooding comment about human faith and its dogged pursuit of redemption. World of folly Artists have manipulated the conventions of perspective since the Renaissance, and Escher's "Belvedere" (1958) would seem to be a humorous play on perspective. Renaissance courtiers stand on balconies constructed in an impossible architecture, looking out upon grand vistas. Even here, though, there is a haunting undertone. Several figures are actually quoted from Hieronymus Bosch's bleak vision of hell in "The Garden of Earthly Delights." Escher's figures apparently don't realize that their world rests on folly. Even in his last works, Escher kept his feel for the tangible world that was lost to him in Italy. One of this exhibition's most compelling works is "Puddle," in which a mucky Earth records the tracks of shoes and tires. In the center, an irregular puddle reflects in perfect clarity the moon and trees above. The print seems a perfect metaphor for the fundamental duality in Escher's work between the natural world and his imaginative vision. His art is generated from complex and abstract ideas. But his fascinating patterns are always rooted in a reflection upon life as we live it. There's much more in this show than psychedelic trickery. Wear your tie-dyed T-shirt if you must. But go to see the real M.C. Escher. Philip E. Bishop is professor of humanities at Valencia Community College. MORE ONLINE To learn more about the artist, the composer of the exhibition's music and a University of Central Florida project that's bringing Escher's work to life, go www.OrlandoSentinel.com/art Step into the WORLD of M.C. Escher |
August 22, 2005
Outstanding Intellectual of the Twentieth Century Nominee Presents Paper at the 2005 Mathematical Association of America Conference in Albuquerque, New Mexico, USAEdited by Carly Zander  NORFOLK, VA - August 22 (SEND2PRESS NEWSWIRE) -- On Thursday, August 4, 2005, Dr. Archie W. Earl, Sr., nominated to the International Biographical Centre of Cambridge, England, for recognition as an "Outstanding Intellectual of the Twentieth Century," presented a paper at the MathFest 2005 Conference, of the Mathematical Association of America, in Albuquerque, New Mexico, USA. The paper Dr. Earl presented was entitled "A High-Tech In-Service Graduate Math Course." In the presentation, Dr. Earl discussed some of the technologies that were used in a mathematics course that Dr. Eurice Dawley, Mrs. Mary Copeland, and he team-taught, to in-service mathematics teachers, during the fall semester of 2004. Dr. Earl began his presentation with a discussion of the implementation of the Standards of Learning (SOLs) in public schools in the State of Virginia, USA. The SOLs are minimum standards that students in Virginia must achieve in order to graduate from high school. Dr. Earl stated that "Since the implementation of the SOLs, many school systems across Virginia, have experienced a need for teachers with more expertise in mathematics." The high-tech in-service graduate mathematics course, "Algebra & Elementary Functions," discussed in Dr. Earl's paper, was developed, at least partially, to address that need. Some of the technologies Dr. Earl discussed included, desktop computers; the PowerPoint presentation projector; the VCR; graphing calculators (the TI-73 and the TI-89); CBRs; Gizmos; Microsoft Excel; VHS, Online, and CD-ROM instructional mathematics videos; and online research. He said that "The use of the technologies were modeled, during the course, with the hope that, when the teachers returned to the classroom, they would include them in their teaching strategies and implement them." Dr. Earl is an Associate Professor of Mathematics, in the School of Science and Technology, at Norfolk State University, in Norfolk, Virginia, USA. He holds an earned Ed.D. from the College of William and Mary, in Williamsburgs, Virginia, USA. He has written several articles and books about mathematics and technology in colleges and universities. The Mathematical Association of America is the largest professional society of college and university mathematics teachers in the world, with over 30,000 members. Outstanding Intellectual of the Twentieth Century Nominee Presents Paper at the 2005 Mathematical Association of America Conference in Albuquerque, New Mexico, USA |
August 22, 2005
Engineer Charles ReVelle, 67, Creater of Location Analysis Charles ReVelle ReVelle was a chemical engineer who evolved into an applied mathematician specializing in environmental systems analysis. He earned his doctorate in sanitary engineering from Cornell University and served on the Cornell faculty from 1967 to 1970. He joined the Department of Geography and Environmental Engineering at Johns Hopkins in 1971. He quickly gained a reputation for his work in a broad range of environmental subjects. Location analysis, the science ReVelle pioneered, involves applying mathematical modeling to determine the optimal placement of facilities such as fire stations, hospitals and power plants. ReVelle's skills also were used in areas as diverse as nuclear disarmament, reservoir operation and the design of nature reserves. Promoted to a full professor in 1975, he was a prolific researcher, publishing more than 150 journal papers as well as authoring three books on mathematical modeling. With his wife, Penelope, he wrote and published five environmental science textbooks for undergraduates in the 1990s. Nick Jones, dean of the Whiting School of Engineering, said, "Chuck was absolutely devoted to the research and careers of his students, dozens of whom now hold faculty positions around the world. He was a gifted teacher, with an accessible and thorough style that extended beyond the classroom. A stream of visitors could always be found coming and going from his office." Among the friends and colleagues mourning the loss of ReVelle was Jared L. Cohon, president of Carnegie Mellon University. Before assuming his present post, Cohon spent 19 years as a faculty member and administrator at Johns Hopkins. He collaborated with ReVelle on research projects and course instruction. "Chuck ReVelle was a great teacher, scholar and innovator," Cohon said. "Chuck also had the discipline of mind and commitment to wrestle over long periods with the most challenging problems in environmental systems analysis and location theory, two fields in which he produced several seminal works and in which he is known as a pioneer and even founder. "He was, in addition, an incredibly gentle, thoughtful and generous person who earned the devotion of his colleagues and students. I was one of those people who had the good fortune of working closely with Chuck for many years. He meant a great deal to me as a colleague, mentor and friend. Like his many very successful students, I was educated by Chuck directly and by just being around him for almost two decades. We have lost a great person." ReVelle's many awards included a Lifetime Achievement Award in Locational Analysis in 1996 from the Section on Location Analysis of the Institute for Operations Research and Management Science and the Agamemnon Award from the Constantine Porphyrogenitus Association of Greece in 1995 for his contributions to Environmental Management and Public Decisions Making. In 2001 he was named the Mary Shephard B. Upson Visiting Professor in Civil and Environmental Engineering and Visiting Professor of City Planning and Regional Science at Cornell University's School of Civil and Environmental Engineering. Cornell subsequently appointed him adjunct professor of civil and environmental engineering, a position he held in addition to his Johns Hopkins appointment. His outside interests included building furniture, traveling and hiking. He also was known for his jokes and for puns that friends and colleagues affectionately described as "excruciating." He is survived by his wife, Penelope; daughters Cynthia ReVelle of Boston and Elizabeth ReVelle of New Castle, Australia; and a granddaughter. The family has requested that donations made in his honor be directed to the Charles S. ReVelle Scholarship Fund at Johns Hopkins, care of the Whiting School Development and Alumni Relations Office, 144 New Engineering Building. A memorial service for ReVelle will be held Sunday, Sept. 11, in 110 Hodson Hall on the Homewood campus. A reception will be held from 3:30 to 5 p.m., followed by a service from 5 to 6 p.m. Engineer Charles ReVelle, 67, Creater of Location Analysis |
August 19, 2005
Fibonacci series on microstructuresIt is a big challenge for materials scientists to produce highly ordered micro- and nanostructures in a designed pattern with uniform size and shape. By controlling the geometry and the stress upon cooling, CAS researchers coaxed a microstructure to self-assemble into the triangular tessellation and Fibonacci number patterns on its surface. Their work 'Triangular and Fibonacci number patterns driven by stress on core/shell microstructures' was published on the August 5 issue of Science. Fibonacci patterns come from a numerical sequence that fascinated the Italian mathematician Leonardo Fibonacci in the early 1200s. Each entry of the sequence is obtained by adding the two previous numbers together: 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144.... The patterns have been noted to frequently appear in biological settings, like the spiral arrangement of the florests, seeds, sepals and scales on such plants as pinecones, pineapples and sunflowers. For instance, people may find two sets of lines connecting the centers of each segment of the pinecone, 13 in clockwise and 8 in counterclockwise; or, in terms of sunflower spirals, the combinations can be in 21 by 34, 34 by 55 until 89 by 144. Using a core of silver and a shell of silicon oxide, Prof. Cao Zexian, together with his colleagues Li Chaorong and Zhang Xiaonan from the CAS Institute of Physics, set out on examining stresses in a microstructure about 10 micrometres in diameter. They first heated a mixture of Ag2O and SiO onto a substrate held at 1270 K, a temperature just above the melting point of silver but below that for SiO2, and then let the system cool down step by step. The researchers discovered that the shell shrank much less than the core, and bumpy patterns appeared on the shell as a result. These bumps appeared in different patterns with markedly uniform size and shape, depending on the geometry of the primary supporting surface.
For a spherical microstructure, a uniform triangular pattern appeared, containing some defects to enable it to cover a spherical surface - these took the form of five- or seven-fold triangles around a vertex. For conical microstructures, on the other hand, cooling led to the formation of the bumps in a spiral pattern, which were arranged in two sets of spirals, running in opposite directions. Curiously, the numbers of spirals in each pair of spiral sets were always adjacent members of the Fibonacci series. The researchers found sets with 5 by 8, 8 by 13, and 13 by 21 spirals. |
August 18, 2005
Barrier for China code breakerBy John Markoff The New York Times THURSDAY, AUGUST 18, 2005 SAN FRANCISCO Last year a Chinese mathematician, Xiaoyun Wang, shook up the insular world of code breakers by exposing a new vulnerability in a crucial American standard for data encryption. On Monday, she was scheduled to explain her discovery in a keynote address to an international group of researchers meeting in California. But a stand-in had to take her place, because she was not able to enter the country. Indeed, only one of nine Chinese researchers who sought to enter the country for the conference received a visa in time to attend. Although none of the scientists were officially denied visas by the United States Consulate, officials at the State Department and National Academy of Sciences said this week that the situation was not uncommon. Lengthy delays in issuing visas are now routine, they said, particularly for those involved in sensitive scientific and technical fields. The visa snag angered organizers of the annual meeting of the International Cryptology Conference, who argued that restrictions originally created to prevent the transfer of advanced technologies from the United States are now having the opposite effect. "It's not a question of them stealing our jobs," said Stuart Haber, a Hewlett-Packard computer security expert who is program chairman for the meeting, Crypto 2005, being held this week in Santa Barbara. "We need to learn from them, but we are shooting ourselves in the foot." Haber and other researchers stressed that progress is made in the field of cryptography by continually investigating existing algorithms and systems for weaknesses, in efforts like Wang's. Among scholars and software engineers, finding such obscure logical flaws is considered a badge of honor and not a hostile act. Wang, a mathematician at Tsinghua University in Beijing, and her student Hongbo Yu were scheduled to present a paper in Santa Barbara on Monday on their successful attack on a United States government cryptographic function called Sha-1. Sha-1 is a formula for creating what mathematicians call a hash, a single number used to represent a larger message or a data file. Such algorithms are routinely used in encryption and authentication systems. In addition to presenting the technical paper, Wang had been planning on detailing further advances in her work, according to several researchers attending the event. After Wang failed to obtain a visa, a third member of the research team, Yiqun Lisa Yin, presented the paper instead on Monday morning. A Chinese citizen, she is currently an independent security consultant in Connecticut and has been a student of Ronald Rivest, a prominent cryptographer. An official at the National Institute for Standards and Technology, which is responsible for maintaining U.S. cryptographic standards, said that he was disappointed by Wang's absence and that he had tried to intervene several times to persuade the State Department to allow her to appear at the conference. "I have no idea why she didn't get her visa," said the official, William Burr, the manager of the Security Technology Group at the institute. "But I attempted to convince them that this wasn't some strange woman. I wanted to let them know that there was someone whose business was affected by her work and who was anxious to see her." He said he was still hopeful that Wang would be permitted to attend a technology conference that the institute has scheduled for October. A State Department spokeswoman said Monday that the potential time it takes for visa applications to be approved is clearly outlined on Web sites maintained by United States embassies around the world. "I certainly do appreciate that this is a frustration," said the spokeswoman, Angela Aggeler, of the Bureau of Consular Affairs. She noted that Chinese visas that require review under a scientific and technical category, known as Mantis, routinely take more than two months. Wang and her student both applied in early July. Wang was interviewed by consular officials on Aug. 9, but typically two weeks are needed after such an interview for a visa to be processed. Last week, after the conference organizers realized that it was unlikely that Wang would obtain a visa in time to attend the event, they contacted the White House science adviser, John H. Marburger 3rd, asking him to intervene with the State Department. Chris Buckley contributed reporting from Beijing for this article. Barrier for China code breaker |
August 17, 2005
Famous scientist slams academic corruption in ChinaBEIJING, Aug. 17 (Xinhuanet) -- If academic corruption in China can not be curbed, scientific and technological development in the country will be delayed by 20 years, world-known mathematician Shing-Tung Yau warned recently. Yau, who is the only Chinese American winner of the Fields Medal, lashed out at rampant plagiarism in Chinese academia in an interview by a Beijing newspaper. Improving research quality and curbing violations of academic ethics is critical, he said. Yau, a professor at Harvard University, has many contacts with Chinese students and researchers and pays close attention to the training of mathematicians in China. He said the papers of some members of China's Academy of Sciences are not even up to the level of Harvard undergraduates. Many professors in Chinese universities prize the quantity of papers, while neglecting significant research. They even restrict talented students from conducting independent research by demanding their assistance in writing their own articles, said Yau. Breakthroughs and creativity also often attract jealousy and discrimination, said Yau. He mentioned that a Chinese student of his at Harvard plagiarized another professor's article. Yet when the student went back to China, he became a member of the Chinese Academy of Sciences and was put in charge of a science foundation. His salary was became 20 times that of other young researchers though his true expertise was far inferior. Yau said China's mathematical research was close to the top level in the world before the Cultural Revolution in the 1960s, when much of academia was purged in the campaign for ideological purity. With the rapid economic development in today's China, better achievements should be made by academia, he said. "Chinese students are talented. They can have great achievement if led by good teachers and doing research in a healthy academic environment," he said. Plagiarism is one of the chronic illnesses in Chinese academia. Several such cases of it involving recognized scholars have been uncovered in recent years. Some experts blame an imperfect Chinese academic evaluation system, which puts excessive emphasis on how many books a scholar writes and how many papers he publishes, as the root cause of academic inferiority. China made an effort to fight academic corruption last year, though its effectiveness remains to be seen. The Ministry of Education issued new criteria in 2004 for publication in philosophy and the social sciences. Regarded as the first "constitution" in Chinese academia, the regulations forbid plagiarism, encourage high-level research and require academics to shoulder legal responsibilities. Enditem Famous scientist slams academic corruption in China |
August 17, 2005
Brains, cancer and computersBy Daniel Winterstein Published Tuesday 16th August 2005 09:13 GMT The race is on to apply machine learning to biology. The starting gun was fired in 2002 when research company Correlogic stunned the medical world with the announcement of a vastly improved test for detecting ovarian cancer. The new test was simple - a few drops of blood are all that's required - yet reliable. What made it truly remarkable was that the test was discovered by machine. This formed a key theme at this month's International Joint Conference in AI (IJCAI) at Edinburgh. The computer program BLAST, which searches genetics databases looking for similar gene sequences, is now ubiquitous in genetics research. It suggests possible relations between genes, and is used as a tool for focusing research. In Seattle, a computer system recently deduced a complicated sequence of links between a dozen genes and the dangerous skin cancer melanoma. This particular link was already known about. The remarkable thing is that the machine discovered it independently with minimal human help. Researchers Zhang, Baral and Kim of Arizona University programmed the learning algorithm, pointed it at a biology database, and with a few clues - let it loose. This is the new mechanised biology, created by a combination of developments. Modern biology - especially genetics, molecular biology and medicine throws up vast amounts of data. These are now available in various vast international databases. Put this together with advances in statistical artificial intelligence (AI), and the conditions are ripe for the creation of a new subject. Known as bio-informatics (the word has become ubiquitous in AI project proposals), it is the application of computers to biology. Correlogic's test is slowly working its way through the approval process. Meanwhile, there have been few other clean-cut successes. This hasn't stopped researchers flocking to the field, as Edinburgh's recent International Joint Conference in AI showed. Developing RoboDoc Medicine attracts the most attention. There is interest from practically every area of AI. One striking project is the robot Penelope, who in June this year became the first autonomous robot to take part in an operation. Penelope manages the surgical instruments in an operating room, responding to voice requests such as "scalpel". Other work includes a system under development by Professor Jim Hunter's Scottish team that will automatically deliver oxygen to babies in intensive care. There are several hurdles to be overcome in the new science. One is that machine learning techniques depend upon large amounts of high-quality electronic data. Without this lifeblood - still in relatively short supply - they are useless. This is especially the case in medicine, were data must often be collected by doctors and nurses as part of their day-to-day work. Like all sane human beings, the medical profession do not really want to have anything to do with computers. In particular, they do not want to consult computers or input data (preferring clipboards and paper), they use conflicting clinical systems, they use words differently, and they enter data reluctantly and unreliably. In short, they are not machines and have no desire to become machines. It possibly doesn't help that many bio-informatics projects aim to make them redundant. Slowly, the researchers have learned to listen to their would-be users. Modern medical AI is often called by the less-threatening name of 'decision support', and at least tries to take into account the feelings and desires of the people who might have to use it. Psychology by numbers Computers are also being used to unlock that warped and weird construct, the human brain. Professor Daniel Wolpert gets schizophrenics to hit each other. He then models their behaviour on computer. He's testing a theory on how our perception is filtered by what we expect. Known events are largely ignored, whilst unexpected things grab our attention. One consequence of his model is that in quarrels, we consistently underestimate our own force (which we know about and expect). This can easily cause arguments to escalate, with both parties convinced that it is the other person who is to blame for shouting louder, or shoving harder. Wolpert demonstrated this with an experiment where volunteers exchanged taps, trying - and failing - to match each other's force. The computer predicts this - and also the surprising result that schizophrenics do better at this task. According to Wolpert, this is because schizophrenic patients are somewhat disassociated from their actions, and can be more objective. Old-school neuroscience had to rely on head-injury victims and torturing kittens. In the 70s and 80s, Colin Blakemore's performed ground-breaking work showing that vision must be learnt. He did this by experiments such as raising kittens in vertical striped boxes (they never learn horizontal and later fall off tables as they cannot see the edge). The man is either brilliant or twisted, depending on your view of the relative importance of science versus kittens. However the new wave of neuroscientists no longer need to abuse animals. Increasingly, scanners and computer simulations are used instead. With FMRI scanners able to pin down nerve-cell firing to within 3 millimetres, it is possible to take snapshots of roughly what the brain is doing. The reams of data produced by FMRI and EEG scans then provide the raw material for computational neuroscience. Brave New World? There is a sense of urgency to bio-informatics. Researchers and investors are scurrying to the field like old-time gold-rush prospectors. This may be motivated as much by the prospect of profitable patents as by scientific or medical aims. Machine-generated discoveries can still be used to patent genes - potentially privatising our biological heritage. If bio-informatics does deliver the hoped-for bio-riches, these may not be shared out. Yesterday, for example, Correlogic was awarded a US patent on using machine-learning to detect biological states. In accordance with US patent office policy, the new patent is obscenely broad and contravenes a good deal of prior art. The company is attempting to patent not a specific treatment, but a general process ("let's use computers and lots of clinical data") for finding treatments. This raises fears that - with greed outweighing scientific principles - bio-informatics may get bogged down in endless legal squabbles. Aggressive patenting is a real menace. The rush of modern science is exhilarating. But whilst it offers great potential, there are also grave dangers - dangers that we in the technology sector are perhaps too quick to dismiss. It is not clear what effects the new biology will have on society. The side-effects may come fast and they may not be altogether rosy. Of course, it may all turn out to be fool's gold. Brains, cancer and computers |
August 16, 2005
First Inca Word EmergesBy Rossella Lorenzi, Discovery News Aug. 16, 2005 Puruchuco the name of a city near modern Lima, Peru could be the first intelligible word to be heard from the vanished Inca civilization, according to a study published in the current issue of Science. The site of an Inca palace, the word Puruchuco would have appeared in the form of a characteristic series of three figure-of-eight knots at the start of several khipu. Khipu are mysterious assemblages of colored knotted strings that have been found at various Inca sites. Located in the Andean highlands of Chile and Colombia around 1200 A.D., the Inca ruled the largest empire on Earth by the time their last emperor, Atahualpa, was garroted by Spanish conquistadors in 1533. The advanced civilization left no written language, but it did leave hundreds of enigmatic khipu, decorative objects consisting of one main cord to which several pendant strings are attached. These strings can carry offshoot strings, and they bear clusters of knots. In 1923, science historian L. Leland Locke proved that the khipu were more than decorative; they were a sort of textile abacus, their knots used to record calculations. But Locke's rules decoded only a small percentage of the existing 700 khipu that survived the Spanish destruction, failing to take into account even one-half of the total information encoded in them. Anthropologist Gary Urton and mathematician Carrie Brezine at Harvard University have partly unravelled the knotty code by extracting the first Inca word and deciphering the math from a series of khipus. The knotty devices were used as ledger books in a sophisticated accounting system "in which census and tribute data were synthesized, manipulated, and transferred between different accounting levels in the Inca administrative system," said the researchers. Urton and Brezine used a computer database packed with any possible data on nearly half of the 700 known khipu to analyze 21 khipu recovered all together in 1956 near a palace at the Inca administrative center of Puruchuco. The computer data showed that seven of the 21 khipu were numerically related, uncovering the first mathematical bond between khipu. Basically, the summed values of all strings of the same color of one khipu matched the sums on the corresponding strings of another khipu, and so on. According to Urton, such compilation is consistent with the Inca state's enormous labor hierarchy, wherein groups of 10, 50, 100, 500 and more laborers nestled into increasingly large administrative units. "Tribute in the Inca state was levied in the form of a labor tax. Each taxpayer was required to work a specified number of days each year on state projects... .," Urton said. "Instructions of higher-level officials for lower-level ones would have moved, via khipu, from the top of the hierarchy down. This information would have been partitive in nature, with assignments made to groups of 1,000 workers broken down into two groups of 500, and so on. "In the reverse direction, local accountants would forward information on accomplished tasks upward through the hierarchy, with information at each successive level representing the summation of accounts from the levels below," said Urton. Moreover, all 21 khipu featured an "arrangement of three figure-eight knots at the start of the khipu," which the researchers believe represented "the place identifier, or toponym, Puruchuco." "We suggest that any khipu moving within the state administrative system bearing an initial arrangement of three figure-eight knots would have been immediately recognizable to Inca administrators as an account pertaining to the palace of Puruchuco," Urton said. Called "terrific, careful and great" by textile archaeologist Bill Conklin of the Textile Museum in Washington D.C., the research could pave the way to the first inventory of place names on khipu. First Inca Word Emerges |
August 16, 2005
Sophisticated Mathematics Applied to Plasma PhysicsUCLA mathematics professor Russel Caflisch has been awarded $630,000 by the U.S. Department of Energy's Office of Science to apply sophisticated mathematics to complex problems in plasma physics. "I hope our research will contribute to controlled fusion reactors for energy sources," said Caflisch, who is also a professor of materials science and engineering, and serves as a trustee of UCLA's Institute for Pure and Applied Mathematics. An applied mathematician who has conducted research on nanotechnology and computational finance, Caflisch and his research team will develop algorithms to solve plasma physics problems. The research is funded under the Office of Science's "Multiscale Mathematics" program. This program addresses those science problems that span many time scales from femtoseconds to years and many length scales from the atomic level to the macroscopic. "Computer simulations on even the most powerful present-day computers cannot handle these scientific problems, so new mathematics is needed," said Raymond L. Orbach, director of the DOE's Office of Science. "This research has very practical applications and will help to solve some of our most complex energy and environmental problems." In experiments that last but a hundred-millionth of a second, physicists are learning the secrets of plasma the turbulent, hot, ionized, gas-like matter that may help us destroy toxic waste and chemical and biological weapons, and perhaps help generate clean and virtually unlimited energy through fusion. In nuclear fusion, atoms collide inside a reactor at extremely high temperature and pressure, releasing energy that can be harnessed to produce electricity. The sun is powered by fusion reactions taking place in its hot dense core. Fusion is a nearly limitless energy source, which may be how electricity will be produced in the future. A viable fusion power plant requires an understanding of how plasma behaves. Plasma is a turbulent, hot, ionized, gas-like matter that is believed to make up more than 99 percent of the visible universe, including the sun, the stars, galaxies and the vast majority of the solar system. Plasma is a fourth state of matter, distinct from solids, liquids and gases, in which electrons have been stripped away to leave positively charged atoms or molecules. The Earth is too cold for plasmas to exist here naturally. Plasmas could have many practical uses, including plasma torches that cut through steel like butter, weigh no more than a pencil and may eventually be used to destroy toxic waste; devices that instantly destroy chemical and biological weapons; and devices into which garbage can be thrown and recycled. Much about plasmas and how they behave remain very poorly understood. "Mathematically describing and simulating the behavior of a plasma has been an enormous challenge," said Caflisch, also a member of the California NanoSystems Institute. "I am hopeful our research might be useful in making progress in this regard." Plasmas are very odd. Remarkably, the temperature in a plasma within a magnetic field can differ tremendously in different directions. Caflisch's plasma research is interdisciplinary, involving physics and engineering, as well as mathematics. The funds will enable him to hire postdoctoral scholars, as well as graduate students and undergraduates, who will collaborate on the research. He will work with researchers at Lawrence Livermore National Laboratory, as well as UCLA. UCLA runs a DOE-funded Fusion Science Center, called the Center for Multiscale Plasma Dynamics, along with the University of Maryland. The center is contributing to our understanding of plasma physics, and the quest for fusion. "Plasma physics has been a traditional strength at UCLA," said Physical Sciences Dean Tony Chan. He noted that UCLA's Basic Plasma Science Facility, federally funded by the U.S. Department of Energy and the National Science Foundation, is the country's first national research facility for scientists worldwide to study the mysterious properties of plasma, and a world-class facility. Under the Department of Energy's Office of Science "Multiscale Mathematics" program, researchers will use mathematics to help solve problems such as the production of clean energy, pollution cleanup, manufacturing ever smaller computer chips, and making new nanomaterials. DOE announced 13 major research awards to 17 universities and eight DOE national laboratories. The multiscale mathematics program seeks to help break through the current barriers in understanding complex physical processes that occur on a wide range of interacting length and time scales. The current state-of-the-science in the theory and modeling of complex physical systems generally requires that the physical phenomena being modeled either occur at a single scale, or widely separated scales with little or no interaction. Complex physical systems frequently involve interactions among many phenomena at many different scales. Increases in computational power over the last decade have enabled scientists to begin creating sophisticated models with fewer simplifying assumptions. For these new models to succeed, researchers will need a deeper understanding of the mathematics of phenomena at multiple scales and how they interact. DOE's Office of Science is the single largest supporter of basic research in the physical sciences in the nation. Posted 16th August 2005 Sophisticated Mathematics Applied to Plasma Physics |
August 16, 2005
Mental gymnasts dwell in kudos-free isolationPhilippa Stevenson 16.08.05 According to my mailbag even ardent sports fans believe we've been remiss in supporting and celebrating the full range of New Zealanders' achievement by all but ignoring competitive academic success. The comments I've received after bemoaning the lack of recognition for our biology, chemistry and maths Olympians have further highlighted our odd attitude towards academic pursuits. It's a baffling stance in a country that wants to ensure economic survival by jumping aboard a "knowledge wave". When I first questioned the lack of kudos accorded academic achievers, Auckland University mathematician Ivan Reilly responded with a tale that reflected the national conflict. In 1986, Reilly was asked to chair the new NZ Mathematical Olympiad Committee (NZMOC). "I declined on the grounds that what they proposed was elitist," the professor said. However, he was prevailed upon to do his "duty" for just one year and, 19 years on, still holds the job. "I saw very quickly that I had been wrong in my knee-jerk reaction. The activities organised by NZMOC filled a gap in NZ education - challenge for the brightest and most talented high school mathematics students." In other words Reilly discovered that the Olympiads are to the brightest what the First XV or First XI are to the sportiest. But the committee struggles as I suspect First XV coaches don't. "We never know from one year to the next if we shall have, or be able to raise, sufficient funds to organise our activities and send a team representing New Zealand to the International Mathematical Olympiad. But we keep doing it, and next year will be the 20th anniversary of the establishment of our committee," Reilly said. "We must be crazy." Or commended. The achievement record has been enviable. The six-member teams have come home with medals from 15 of the 18 annual Olympiads - 23 bronze, three silver and, in 2002, an historic gold for Simon Marshall of Onslow College. One reader - a migrant - has puzzled over our lack of pride in academic achievers in the 10 years she's lived here. "Unlike sports people, our intellectuals don't seem to have a big share in creating role models for the young generation. The continuous struggle of the universities and research institutes for funding casts a shadow on the future for our would-be scientists," she wrote. "The sad fact is that as a nation we continue wasting the talent of our best young minds and give them free into the hands of overseas corporates and various institutes." Mathematician Arkadii Slinko, also of Auckland University and the maths Olympiad team leader, also worries about the brain drain. "These kids are our future leaders in science, in industry, in politics - if we can keep them in New Zealand," he said. Maths teacher Alan Parris, president of the NZ Association of Maths Teachers and a NZMOC executive member, is optimistic that many of the academic achievers will return. And universities here do notice Olympiad success, he says. Three universities got into a bidding war over gold medal winner Simon Marshall who is now at Auckland University. Parris, who spends most of his year fundraising when he'd much rather be developing maths programmes to inspire young minds, is more worried about keeping the longest-running Olympiad effort on track. In 2001, a study funded by the Ministries of Education and Research, Science and Technology into the effectiveness of science and technology extension programmes such as Olympiads recommended that long-term and secure funding be provided for the Olympiad programmes. But the stop-start funding that has plagued the NZMOC from the beginning continues. a "The goal posts keep shifting," laments Parris, who notes that other disciplines such as geography, physics and IT are also keen to set up Olympiad teams. "We need a national programme - a new enterprise - that looks after our kids. Funding ebbs and flows now at the whim of politicians and ministries rather than the needs of the country." More than one of my correspondents would like to hear the views of electioneering politicians on the issue. I'm happy to field responses. Mental gymnasts dwell in kudos-free isolation |
August 15, 2005
Maths isn't just for textbooksNowadays it's the inspiration for films, novels and art. But where do footballers' shirts enter the equation? By Boyd Tonkin Published: 15 August 2005 The progress of mathematics abounds in tall tales and unlikely stories. And they don't come much more improbable than this. Outside, the July sun of the Aegean is hammering down on a coastal hotel in Mykonos. Inside, America's most charismatic statistician addresses a gathering that can boast several of the world's top mathematicians as well as a motley assortment of science writers, novelists, historians and theatre people. And what is he doing? He's performing a card trick. Persi Diaconis, now of Stanford and Harvard Universities, once made his living this way. As a teenage prodigy, he toured the US as junior sidekick to one of the most famous magicians of the age. Then, via gamblers' after-hours talk of odds and probability, the sorcerer's apprentice caught the maths bug and took the first steps towards a career in another sort of spotlight. Diaconis was the expert who unmasked the delusions behind the so-called "Bible Codes" (which supposedly revealed hidden meanings within the text), but today in the Aegean, he's merely baffling his peers. He chucks a deck of cards towards this highly qualified audience. It's caught by Timothy Gowers, a professor at Cambridge and recipient of a Fields Medal - the maths equivalent of a Nobel Prize. Gowers cuts the pack, takes the top card, then passes it to a neighbouring titan, who himself passes it on. After five cuts, Diaconis asks holders of red-suited cards to stand up. Two do. He then proceeds to tell all five punters exactly which card they hold. Cue a burst of awestruck applause. How does he do it? Diaconis quips that "magicians aren't allowed to explain their secrets and mathematicians can't explain their secrets". But he tries. The root of card-recognition tricks lies in the De Bruijn Sequences, a branch of what's called "combinatorics" - a discipline with a long history that stretches from the counting patterns used in Indian classical music to the coded instructions for robots used today. The mathematicians grasp the theory easily enough, but the mind-boggling mental speed of the practice still confounds them, and me. This is a taste ofthe first Mykonos conference on Mathematics and Narrative. Arranged by a group known as Thales and Friends, after the ancient Greek geometer and philosopher who reputedly measured the Pyramids, this unprecedented project to bring scientists and storytellers together was the brainchild of the polymath Apostolos Doxiadis. Worried that the maths he loves has drifted too far out of the cultural mainstream, Doxiadis has already done more than his share of bridge-building. His novel Uncle Petros and Goldbach's Conjecture (Faber) helps to convey the life-enhancing, and life-consuming, attraction of pure mathematical research. Rebecca Goldstein, a philosopher and novelist who writes in her fiction about the "essentially tragic" lives of mathematicians, called her pet subjects "as bad as novelists in terms of ego". John Allen Paulos, who writes funny and instructive books, such as Innumeracy, about the misuse of statistics in the media, jokes: "How do you define an extravert mathematician? Someone who looks at your shoes when he's talking to you." If you want evidence of the problem that confronts them, look no further than today's newspapers. Millions of people now enjoy Sudoku puzzles. Forget the pseudo-Japanese baloney: sudoku grids are a version of the Latin Square created by the great Swiss mathematician Leonhard Euler in the late 18th century. Yet these legions of amateur problem-solvers tackle puzzles accompanied by the absurd assertion that "no maths is involved". In parts of popular culture, mathematics has become not so much the love that dare not speak its name as the love that doesn't even know its name. So, as the sun blazed and the sea sparkled off stage, we heard stories about the extraordinary rhythms of breakthrough and breakdown that punctuate the history of modern maths, and stories about the thinking and imagining that mathematicians do on the cutting edge of creation. John Barrow, another Cambridge professor, related the story of how his play Infinities reached the stage. Marcus du Sautoy, Oxford mathematician and Channel 4 pundit, delivered his multimedia gig about the mysteries of prime numbers and the long quest to prove Riemann's Hypothesis. The show took in David Beckham's Real Madrid shirt (a prime 23), some raucous audience participation and Professor du Sautoy himself on a surprisingly sweet trumpet. Less noisily, Tim Gowers ended his plea for concreteness and compression in mathematical explanations with some favourite passages from Alan Hollinghurst, Don DeLillo and Jonathan Franzen - to highlight the skills that good novelists have and most mathematicians lack. Of course, some writers and producers have turned to the lives and the works of mathematicians for inspiration. A gifted populariser such as Simon Singh can now sell in the hundreds of thousands - as he did with Fermat's Last Theorem. Sylvia Nasar's bestselling biography of the game-theory pioneer John Nash, and his decades-long mental illness, led to the big-screen adaptation of A Beautiful Mind. This familiar, Rain Man model of the pattern-seeking maths prodigy as a recluse, an idiot savant, or downright barking mad, recurs often - for instance, in fictionalised portraits (such as Enigma) of the computer prophet and Bletchley Park cryptographer Alan Turing. And it even underlies Mark Haddon's The Curious Incident of the Dog in the Night-time, with its Asperger-afflicted teenage narrator, always ready to reel off a series of prime numbers. Not surprisingly, real mathematicians have mixed feelings about mass-market yarns that present their domain as the stamping-ground of eccentrics, or even lunatics. But, for the most part, they applaud the endeavour to dramatise the human struggle of mathematical reasoning. Only one (absent) literary figure really fell foul of the Mykonos mob: the American writer David Foster Wallace, who in Everything and More wrote not a novel but a purported history of the mathematics of infinity. The computer-science guru Martin Davis counted "86 really egregious errors" in Wallace's book. "Are we so hard up for approval from the humanities that we have to accept this?" he thundered. And yet the history of modern maths features such a wealth of near-incredible narratives that certain kinds of faction or docu-drama will exert a huge appeal. After all, this is a field that, early in the last century, plunged into a "foundational crisis" that left its finest minds believing that they stood not on solid rock but on shifting sand. Out of that collective breakdown grew ideas about general computing machines that began as the purest theory but ended up as the intellectual inspiration of almost everything we now do with technology. If mathematics counts as the art of reality, then you might argue that its artistic crisis gave birth to the modern world. This is the theme of the mathematical narrative that Doxiadis and some colleagues will tell next. Collaborating with the Berkeley-based computer scientist Christos Papadimitriou and the Athenian artists Alecos Papadatos and Annie di Donna, Doxiadis has been working on a ground-breaking graphic novel about the development of 20th-century maths and its makers, from Russell and Hilbert to Gφdel and Turing. Due in 2007, Logicomix will tell an epic human, and political, story. On the one hand, Papadatos, the project's chief graphic artist, depicts the social turmoil, global warfare and deadly ideologies of the last century. On the other, the core story of maths - as with every other brand of creativity - will often come down to the journey of a single mind alone with its dreams, and its demons. "Like a mathematician," Papadatos notes, "a cartoonist works with paper, pens - and a waste-paper basket." www.thalesandfriends.org Maths isn't just for textbooks |
August 15, 2005
Surrealism and the MathematicianMonday, 15 August, 2005 Stop what you are doing and get a mirror.  It doesn't matter where from just polish up the nearest shiny surface or grab the nearest high-maintenance girl's handbag and steal her compact. Hold it in front of your face, but before you look at your reflection... close your eyes. Think. What do you expect to see? Open your eyes and there should be no surprises. This is because we have an innate knowledge about the physical laws that control our environment; we know how light behaves, including how it reflects. But what if light didn't obey normal physical laws? What if parallel lines bent away from each other, and our normal 2D representation of the world wasn't flat, but saddle-shaped? Welcome to the crazy world of Cormac Long: Southampton mathematician and keen climber. Cormac investigates problems in hyperbolic, or 'bendy', space; a world view that is, well, bendy. He explains, "Draw a triangle on a sphere and measure it's interior angles. The sum of these angles is greater than 180 degrees. "On a plane (Euclidean space) the sum is exactly 180 degrees. In hyperbolic space, the sum is less than 180 degrees the sides of the triangle 'bend in' towards the middle." Cormac builds 3D images to describe events in hyperbolic space, including reflections. He computes 3D visualisations analogous to the 2D interlocking tiles, or tessellations, that 1950's artist M.C. Escher used as the basis for his surreal mathematical artwork. Escher used art to represent mathematical concepts, often using unusual perspective and viewpoints. His brain-teasing works include an endless staircase, that seems to simultaneously ascend and descend, a waterfall that flows uphill, and hands that draw themselves. So how do people like Escher and Cormac keep their sanity in a world where straight lines are bent, and reality is the reflection of a dimension that is separate from normality? Cormac explains, "In some ways it is like sculpture: Start with an amorphous blob of stuff, then hack at it until you get something strange but beautiful. Your only limit is your imagination." Chris Lane Surrealism and the Mathematician |
August 15, 2005
University library's collection tells story of secret codesPosted on Mon, Aug. 15, 2005 Associated Press ST. LOUIS - The invention of the printing press didn't just make it easier to disseminate information. It made it easier to hide it, too - as the collection of books in a vault at Washington University shows. The books, some more than 500 years old, chronicle the history of secret codes - some concealed so intricately that art professor Ken Botnick regularly shows them to his students. "(The books) explore a very sophisticated relationship of type to the page that I'm not sure has ever been surpassed," Botnick said. "They're using typography in a visual way that kind of fell by the wayside." In some of the books, circular pieces of paper, decorated with angels and ivy and sewn onto the pages, serve the same function as the decoder rings found in children's "spy kits." In others, messages are hidden in musical scores or in lines of poetry, with the message revealed when another design is laid over the poem. The messages could take months to design and produce. "To put a message like 'The King of Spain is going to attack you in July' into a poem is not so easy," said David Kahn, a historian of cryptology. Modern codes still use some of the same techniques, Kahn said - and without one hazard that plagued their 16th-century counterparts. "In those days," he said, cryptography "was regarded partly as black magic." The museum's collection includes "Polygraphique," the first book printed about coding. Its author, Trithemius, had to swear in writing: "I have no commerce with daemons, never had any, and with God's protection will never have any; no studies in magic, necromancy or the profane arts." The older books are part of the 1,600-volume Philip Mills Arnold Semeiology Collection, and the library continues to add books on encrypted communications. "To grow the collection, we'll have to collect books on computer cryptography because people 200 years from now will be interested," said Anne Posega, the university's head of special collections. "It will all seem very old some day." University library's collection tells story of secret codes |
August 14, 2005
The origin of the biology debate Intelligent design movement says the science isn't settled on how life is shaped.Posted on Sun, Aug. 14, 2005 As Minnesota high school educators who are also, respectively, a theologian and a biologist, we sympathize with President Bush's remark that intelligent design should be taught alongside evolutionary theory, even in public schools. Predictably, the media have cast the issue as a demand for equal classroom attention to science and religion. The Associated Press reported flatly, "Scientists have rejected (intelligent design) as an attempt to force religion into science education." Yet, while Bush is not a scientist, his remark actually reflects a greater scientific openness than one might first suppose indeed, an openness greater than that of many evolutionary biologists. "Intelligent design" is not a term that denotes a religious, but rather a scientific, movement. Bush was implying, too, that something educationally important here transcends the scientific question. Ideas about life, especially human life, have moral and philosophical consequences. Should students be led to assume that science demands philosophical materialism? Should students be led to assume that science is settled in favor of randomness and dumb accident in the origins of life? The science is not settled. What we have in today's Darwinism is a dominant theory. Intelligent design theory is, by contrast, a young movement spawned by a recognition among many scientists that mounting evidence undermines some explanatory elements of the dominant theory. For example, the fossil record suggests many sudden appearances of fully formed species. Another example is that, while today's Darwinists have studied millions of instances of mutations in species, they have yet to show any one species has mutated into another. What is needed on the part of Darwinian theorists is humility in the face of incomplete and contradictory evidence. The problems with Darwinism have been identified by scientists; they have not been trumped up by religious fanatics. A growing number of scientists are at work developing testable hypotheses that detect design in nature. Among the most compelling is mathematician William Dembski's "explanatory filter," which detects complexity at levels statistically consistent with design. Scientists at work in this field may be ill served by the moniker "intelligent design theorists," since they freely admit that the existence of a Designer (i.e. God) is beyond the scope of empirical science. Their scientific goal is to follow the evidence where it leads. It is Darwinists who increasingly seem to be adhering dogmatically to a creed. Rather than confront troubling evidence, many of the dominant theorists seem satisfied to classify alternative lines of inquiry as "religious" precisely in order to discount that evidence. This is not surprising. Forty years ago, Thomas Kuhn's "The Structure of Scientific Revolutions" showed how scientific progress is often stalled by entrenched scientific (and personal) interests and convictions. Last year, a group of over 300 scientists issued a national "Scientific Dissent from Darwin" statement. "We are skeptical," they wrote, "of claims for the ability of random mutation and natural selection to account for the complexity of life. Careful examination of the evidence for Darwinian theory should be encouraged." The time has come for Darwinists to stop hiding behind the claim that all their opponents are Scopes trial-style "creationists" and face the fact that there is a growing contingent of scientists who have found the evidence for Darwinian evolution wanting and who are ready and willing to debate Darwinists on scientific grounds. Thus, why should schools, indeed public schools, not teach this academic dispute? Should educators insist that dominant theories be immune from criticism, much as in an earlier time the Inquisition insisted against Galileo? Surely, in science education first and foremost, the notion that you can't use evidence to criticize is a bad idea. The key educational value of including intelligent design theory in secondary education is scientific. But philosophic concerns about life and its meaning are by no means unimportant. All schools convey philosophical perspectives. Most schools, including ours, try hard to teach young people such values as respect, tolerance, fairness and honesty. Fair-minded people are not out of line in questioning how a dogmatic presentation of the random and accidental character of human life supports any given moral code, let alone a school's. The kids, too, are smart enough to wonder. Flanders is headmaster of Providence Academy in Plymouth and adjunct scholar with the Acton Institute for the Study of Religion and Liberty. Boldt is science department chair at Providence. The origin of the biology debate Intelligent design movement says the science isn't settled on how life is shaped. |
August 13, 2005
Inca code came with strings attached, but researchers closer to cracking it
Washington: A series of three figure-of-eight knots tied into strings may be the first word from the ancient Inca in centuries. |
August 12, 2005
IQ test for AI devices gets experts thinking16:16 12 August 2005 NewScientist.com news service Duncan Graham-Rowe How do you tell just how smart your robot is? Give it a universal IQ test, researchers suggest. Traditional measures of human intelligence would often be inappropriate for systems that have senses, environments, and cognitive capacities very different from our own. So Shane Legg and Marcus Hutter at the Swiss Institute for Artificial Intelligence in Manno-Lugano, have drafted an idea for an alternative test which will allow the intelligence of vision systems, robots, natural-language processing programs or trading agents to be compared and contrasted despite their broad and disparate functions. Although there is no consensus on exactly what human intelligence is, most views cluster around the idea that it hinges on a general ability to achieve goals in a wide range of environments, says Legg. The same concept can be applied to an AI system, by measuring its ability to carry out complex tasks within its particular environment and then comparing the complexity of its environment with those of a wide range of other AI systems. "But there is a problem," he says. Before putting this into practice the AI community will have to thrash out an agreement on what counts as the average environment. And that will not be easy. Thrown gauntlet Under Legg and Hutter's definition, for example, the chess-playing computer Deep Blue would come out as less intelligent than a generalist learning algorithm, as Deep Blue is only designed to carry out a very specific task. But consensus or no consensus, the test is likely to face a lot of resistance, says Blay Whitby, an expert in human and artificial intelligence at the University of Sussex in Brighton, UK. For one thing, some people would even dispute that intelligence involves goals, he says. Also it may imply that rather a lot of computer programs should suddenly be considered intelligent, he says: "Some people may object to this." But Legg's test is a good place to start, says Whitby, not least because it throws down the gauntlet to the AI community to come up with a definition of intelligence that will work for all AI. "This is a very important perhaps the most important issue to be resolved for the future of AI," says Whitby. He adds that all too often intelligence is identified with human intelligence but, given the wide range of systems in AI, this anthropomorphic approach is not always appropriate. The Turing Test, for example, is often seen as the ultimate challenge for artificial intelligence. This is typified by the annual Loebner Prize where computers converse with people in an attempt to convince them they too are human, frequently with very limited success. IQ test for AI devices gets experts thinking |
August 09, 2005
Cracked! Maths solves old war codeJudy Skatssoon The Japanese navy was brought down by a fatal flaw in its secret war code that Allied code breakers exploited during the Pacific War, an Australian mathematician has revealed. Dr Peter Donovan, a senior lecturer at the University of New South Wales, says he is the first to identify the truth about Japan's operational code JN-25 since archives became available in 1975. Donovan discussed his discovery ahead of Australia's 60th anniversary of Victory in the Pacific Day on 15 August. The cipher used groups of numbers that were multiples of three, he discovered. For instance, 0009 may have stood for a certain type of fuel oil, he says. "The truth was that having multiples of three in the code book was a flawed process which was systematically exploited by the Allies," he says. The US, Australia and the UK had originally decided to keep the code-breaking secret for ever, but this decision was reversed, giving Donovan and his colleagues access to reams of previously unseen archives. Having a recognisable pattern made it easy for Allied code busters, including a team of 10 Australians working from a converted office block in Melbourne, to decipher encoded messages between Japanese navy ships. "Recognising that pattern and putting an awful lot of time into it, [the code] became breakable," he says. Code busters The Japanese navy introduced JN-25 in 1939. But by 1940, UK computer scientist and code breaker Alan Turing, who had also cracked the code used by German submarines in the Atlantic, had worked it out. By 1942, the Allies were beginning to read the code, the next stage after cracking it. By that time the Japanese had revised the code several times, but it was still based on the same flawed code book. Cracking the code came too late to prevent Pearl Harbour in 1941 but it gave the Allies a leg-up in the Coral Sea Battle of 1942 and provided knowledge about the Japanese advance in what was then New Guinea in the same year. It also made it possible for the Allies to ambush and sink Japanese aircraft carriers in the crucial Battle of Midway in 1942, Donovan says. An army of code breakers At the peak of activity around 35,000 people were engaged in Allied code breaking. During the Pacific War this involved intercepting Japanese radio waves and using a machine made from old cash register parts as part of the deciphering process. None of these devices are believed to remain today but Donovan has made a working model. "It's just wheels turning and being pushed by rods and you win when you've got the right pattern of colours," he says. Dead codes Today the old codes and the methods used to break them are obsolete thanks to advances in technology and code breaking techniques, Donovan says. New codes, for example those used to send banking information over telephone wires, are virtually unbreakable. "The old codes are totally dead," he says. "The modern codes are essentially uncrackable, which is why no sane person would ever reinvent JN-25." Donovan reported his finding in a paper published in the journal Cryptologia and is writing a book on the subject. Cracked! Maths solves old war code |
August 8, 2005
Blair junior dominates international math competitionBrian Lawrence achieves perfect score at International Mathematical Olympiad Varun Gulati, Online Managing Editor 8/12/2005 Junior Brian Lawrence earned a gold medal for achieving an individual perfect score at the 46th International Mathematical Olympiad (IMO), arguably the world's most prestigious high-school math competition. He and the other five members of the USA team finished second overall. At the IMO, held in Merida, Mexico, from July 4 to July 18, 513 participants from 93 countries were given nine hours each to solve six math problems. Lawrence contributed 42 points, the highest individual score attainable, to the U.S. team's cumulative score of 213 points. China placed first with 235 points, Russia third with 212 points, Iran fourth with 201 points and Korea fifth with 200 points. Lawrence also excelled in the USA Mathematical Olympiad (USAMO), a multi-stage nationwide competition. Of the 300,000 participants from over 4,000 schools, 300 students became eligible for the USAMO after taking the American Mathematics Contest and American Invitational Mathematics Exam qualifiers. Lawrence scored the highest at USAMO and received a $20,000 scholarship from the Akamai Foundation. Two of the other five USA team members, Thomas Mildorf and Eric Price, attend Thomas Jefferson High School of Science and Technology in Alexandria, Virginia. Blair junior dominates international math competition |
August 7, 2005
What we definitely know about endlessly possibleReviewed by Jenn Shreve The Infinite Book A Short Guide to the Boundless, Timeless and Endless By John D. Barrow PANTHEON; 328 Pages; $26 While science and religion often make for odd, if not hostile, bedfellows, at times they have been quite cozy indeed. Take the strange case of Georg Cantor. After being relegated to an obscure mid-tier university, blocked from leading journals and openly mocked by his peers, including his former mentor, the late 19th century German mathematician found refuge for his groundbreaking work on infinities in, of all places, the Roman Catholic Church. Yes, the very same church that in 1600 burned philosopher Giordano Bruno at the stake for espousing his belief in an infinite universe was in Cantor's day seeking to reconcile science and religion through, among other things, repercussion-free dialogue. Catholic theologians welcomed Cantor's ideas, which provided a workable way of understanding mathematical infinities, as evidence that humans could grasp the infinite and could also, therefore, have a greater understanding of God, himself infinite. What a welcome relief this must have been to the chronically depressed Cantor! As John D. Barrow writes in "The Infinite Book: A Short Guide to the Boundless, Timeless and Endless," Cantor "started to tell his friends that he had not been the inventor of the ideas about infinity that he had published. He was merely a mouthpiece, inspired by God to communicate parts of the mind of God to everyone else." Today, Cantor's work on infinity is taken for granted by mathematicians, and religious authorities seem more wont to ban sound science from schools than foster it. But the story demonstrates the unusual position infinity occupies in intellectual history, broad enough in scope to engage the minds of philosophers, astronomers, physicists, theologians and literary authors alike. And not just in the past, but the present as well. Barrow eloquently explains: "Infinity is a player of great significance who appears on the stage only when the crucial questions of existence are raised. Infinity offers its services when we seek to know if the Universe began or whether it will ever end, whether life will always be part of its landscape, and whether there are tasks which can never be accomplished. Infinity challenges us to contemplate the duplication of ourselves and all that we hold dear, and to ponder the cogency of all possibilities, potential and actual. It undermines our sense of the precious by suggesting a randomly infinite universe will eventually conjure up the works of Shakespeare, somewhere, as if created by a regiment of monkeys armed with typewriters. Infinity also seeks to guard us from taking the wrong path in our quest to unravel the deepest of Nature's secrets about the ultimate structure of mass and energy." Barrow, a mathematician and popular science writer who in previous books tackled "Theories of Everything" and the scientifically impossible, captures many of humanity's attempts to grasp the ungraspable in this engaging read. "The Infinite Book" starts with a quick tour of early philosophers' crude attempts to define, dismiss or otherwise contain the infinite. Without telescopes, microscopes, calculators or other modern tools to guide them, these thinkers' understanding of the world was informed by a sense of their own limits and a belief in the transcendent. Their views on the infinite reflected this. Aristotle dealt with the paradoxes of infinity by dividing it into actual and potential infinities, the former being impossible. A sequence of numbers could go on forever but, as nobody could ever count it, could not exist in actuality. St. Augustine posited that what seemed infinite to humans was finite to God. In the 17th century, Pascal believed that humans encountered infinities regularly, but could never fully grasp them. Eighteenth century philosopher Immanuel Kant took a similar path, arguing that infinities existed, but humans' perceptive powers were too limited to perceive them. Not being able to comprehend infinity didn't stop people from trying and eventually succeeding. Galileo described some of mathematical infinity's most troubling paradoxes, such as the fact that an infinite sequence of whole numbers (one, two, three, four, five ...) and an infinite sequence of even numbers (two, four, six, eight ...) would be the same size even though the latter would appear to contain far fewer numbers. It was Cantor who made sense of such conundrums, dividing infinities into the countable, which could be put into a one-to-one correspondence with a list of natural numbers, as Galileo's could, and uncountable, which could not. He showed that mathematical infinities could, in fact, exist and be understood. Some infinities were even bigger than others. Catholic theologian Constantin Gutberlet, Barrow writes, "responded by seizing upon Cantor's mathematical work to argue that it provided clear evidence that the human mind could contemplate the actual infinite," and therefore "get closer to the true nature of the Divine." Of course, as Barrow is quick to point out, "infinity is not a big number. " It behaves quite differently and is riddled with problems that can lead the imagination to some very unsettling places. For instance, the infinite replication paradox, which the author sums up succinctly as such: "In a universe of infinite size, anything that has a non-zero probability of occurring must occur infinitely often. Thus at any instant of time, for example the present moment, there must be an infinite number of identical copies of each of us doing precisely what each of us is now doing." Yikes! In such examples one can see why, when it comes to infinities, science and the "softer" pursuits of theology, philosophy and ethics -- to say nothing of literature -- to this day frequently find themselves traversing the same territory. It is also in the midst of such mixed company that we find the agile mind of Barrow at its best: moving from science's attempts to evade the implications of the infinite replication paradox to converse with the works of Jorge Luis Borges that embrace them; pausing to acknowledge St. Augustine's worry that multiple worlds would require multiple crucifixions; as well as paying his respects to Friedrich Nietzsche, who, Barrow writes, argued "that we should act as if we knew our actions would be infinitely repeated." One only wishes that Barrow would escape the clutches of the Western canon every now and then to dialogue with Eastern philosophy and religion's own fascinating takes on the infinite. That's one quibble with this book. Here's another. While Barrow's remarkable ability to provide clear, concise, engaging and distinctly finite explanations -- even when describing some fairly advanced concepts -- will, for the most part, be much appreciated, this approach occasionally breaks down and mathematical equations like L'=L(1-V²/c²){+ 1/2} get tossed onto the page without much explanation, as though they read as clearly as 1 + 2 = 3. Readers without the proper background in science and math will probably find themselves feeling a bit left behind at times. At the same time, armchair cosmologists who've pored over every book and theory may find some of Barrow's more scientific material a bit too familiar. This is the fine line every popular-science writer must walk. Fortunately, Barrows maintains his balance more often than not. So where does all this talk of infinity leave us? Right back where we started, of course, smack dab in the land of conjecture or, specifically, the question of eternal life. In Barrow's exploration of this final topic, we see clearly science's uncanny ability to provide many answers (but no Answer) juxtaposed against religion's ability to supply a ready Answer but no real answers. How appropriate, really, that from the mixed roots of the infinite should spring up so many unanswerables. Rather than pick a side, Barrow seems content throughout this book to simply acknowledge these, in one case ending a chapter on whether there can be other planets and universes with the quizzically titled subsection, "How should we then live?" How indeed! And when he writes, "You can discover whether the Universe is infinite, but the learning will take an infinite time, '' one gets the eerie feeling that we haven't progressed as far from Aristotle's conjectures as we'd like to think. But this, too, is the charm of the infinite: that one can learn so much about it yet know so little, can finish a book, but never reach the subject's end. What we definitely know about endlessly possible |
August 06, 2005
Sea spray likely whips winds to hurricane forceMichelle Lefort, USA Today For thousands of years, sailors have been known to throw oil overboard to calm stormy seas. Hurricane experts are beginning to see scientific rationale behind this practice. In a study out last week, researchers from the University of California, Berkeley, and a Russian colleague argue that sea spray kicked up by storms has a lubricating effect that helps accelerate wind. Suppress the sea spray, as ancient sailors tried to do with oil tossed on the water, and you may be able to affect the strength in the wind, the research suggests. The computer model by Berkeley mathematician Alexandre Chorin and his colleagues appears in the current Proceedings of the National Academy of Sciences. Chorin says that sea spray reduces turbulence, chaotic fluctuations in wind velocity and direction, like a comb through unruly hair. At the air-sea boundary, turbulence is the primary source of the friction that would dissipate hurricane energy, just as eddies and swirls in water slow the speed of ships and flowing rivers. According to Chorin, this reduction in turbulence allows for much faster wind speeds. There are other reasons why sea spray accelerates winds in a storm. When ocean water is tossed into the air as droplets, the hurricane has more access to the heat it needs for strength. Physicist Edgar Andreas at the U.S. Army Cold Regions Research and Engineering Laboratory in Hanover, N.H., did a calculation to show that at around 70 mph, near the wind speed that signals the formation of a hurricane, sea spray effectively doubles the surface area of the ocean. When "spray increases the ocean surface area, it becomes intuitively obvious that spray can play a role. Spray transfers heat and moisture better than ocean," Andreas says. "A hurricane is a machine that pulls heat out of the ocean. It's an engine, actually," says physicist Chris Fairall at the National Oceanic and Atmospheric Administration's environmental technology lab. This is why hurricanes only form over tropical waters that are at least 80 degrees Fahrenheit. The hurricane's strength is determined by the energy it is able to gain from the warm ocean and the energy it loses to friction between the air and the waves. Strangely, Fairall says, estimates from computer models indicate that storms don't get enough energy from the ocean and lose too much of their energy to friction to even develop into hurricanes or tropical storms. So scientists have looked to sea spray to explain the fury of beasts like hurricanes Hugo, Ivan or Andrew. Scientists believe that sea spray likely plays a role in hurricane generation. But without measurement from the ocean surface during a hurricane, it is difficult to determine exactly how sea spray is influencing heat energy or friction. "I've been working in it for 15 years and I am still kind of skeptical," Fairall says. "My personal opinion is that sea spray does have an effect on hurricanes, but I don't know whether it is a 5 percent effect or 50 percent effect." Sea spray likely whips winds to hurricane force |
August 03, 2005
The Race For The Lost ArkBy Dvora Waysman Thousands of people saw the movie "Raiders of the Lost Ark", and most of them knew that Indiana Jones was based on a real person, famous archaeologist Dr. Vendyl Jones. Less well-known is another charismatic contender, who believes he will be the first to uncover the hiding place of this fabulous prize. He was recently in Jerusalem, and his name is Lt. Barry S. Roffman of the U.S. Coast Guard. Roffman is basing his search on the Bible Code ... a code encrypted in the Bible some 3,000 years ago, now unlocked by computer. The mathematician who discovered the code was Dr. Eliyahu Rips, one of the world`s leading experts in group theory, the field that underlies quantum physics. Jones is basing his research on the Talmud. Once a Christian pastor, he left his post to become a leader of the Noahide movement, Gentiles who observe the seven laws of Noah. His search is aided by an ancient document found in Qumran together with the Dead Sea Scrolls, known as the "Copper Scroll." He is convinced that he has pinpointed the ark`s location. (Vendyljones.org.il/copperscroll). For Roffman`s research, you can hear a 30 minute radio broadcast by accessing www.biblecodenews.com In the case of Vendyl Jones, he plans to uncover the lost Ark of the Covenant by Tisha b`Av. It was the resting place of the Ten Commandments, given to the Jews at Mt. Sinai and supposedly hidden just before the First Temple was destroyed. Although the Talmud says the Ark is hidden under the Temple Mount, Jones believes the tunnel continues 18 miles to the south and is now in the Judean Desert. Jones is not Jewish, although his daughter Sarah has converted and lives in Samaria (Shomron). However, he is learned in Torah and Talmud and has contact with a mysterious kabbalist who has now given him his blessing to reveal the Ark by Tisha B`Av (August 14th), the anniversary of the destruction of both the First and Second Temples. But Jones is not alone in his search. Barry Roffman, an Orthodox Jew and a Lieutenant in the U.S. Coast Guard and author of Ark Code, (www.amazon.com ) believes that the Torah codes he has discovered can unlock the secret of the Ark`s location, and his findings are very different from those of Vendyl Jones. According to Roffman, there are maps encoded in the Torah. Key site names are encoded in such a way that the angles between Jerusalem, Arabic sites and a suspect Egyptian Ark site correspond to actual course headings on real world maps. The site, which he describes as 31 degrees 9 minutes North, 33 degrees 4 minutes East, is where a cloud of fire blocked the Egyptian army from the Israelites before we crossed the Sea of Reeds (Yam Suf) at Lake Bardawil in Northern Sinai, Egypt. He cites Jeremiah as the last prophet to control the Ark before finishing his life in that area of Egypt. Roffman`s research is unique, quite different from methods used by other Bible code researchers. It is rooted in his expertise as a Coast Guard military planner. He has explanations as to why Jeremiah took the Ark to the site of the splitting of the sea, and believes that the Ark`s purpose is to prevent a nuclear war between Israel and its enemies. Barry Roffman was born in 1947 in Philadelphia and now lives in California with his second wife, Katherine Kim Roffman and their young son David. He has a distinguished Navy background, and was also a high school teacher of earth science, biology, chemistry and physical science. In 1989, his book, A Matter of Spiritual Custody, dealt with an interfaith child custody battle in which the Catholic Church, possibly for the first and only time, annulled his older son`s baptism on a ruling by Edward A. McCarthy, Archbishop of Miami, on the grounds that it was carried out without the father`s knowledge or consent when the boy was seven and considered himself to be Jewish. Today, that son, Robert Altair Roffman, is an Orthodox Rabbi in the U.S. Air Force. So now, the world is waiting with bated breath. Will it be Jones or Roffman who finds the Ark of the Covenant? Will it be found in Israel or in Egypt? Will it be discovered by means of ground-penetrating radar? What will be the religious, political and scientific implications and ramifications if it is found? And what else can we learn of the future from the words encrypted in the Bible codes or the secrets of the Talmud? We may not have long to wait. The Nobel Laureate physicist, Richard Feynman, put it this way: "To solve any problem that has never been solved before, you have to leave the door to the unknown, ajar." Dvora Waysman is a writer living in Jerusalem. She is the author of nine books, including Woman of Jerusalem; Esther and newly-released in paperback in English and Hebrew by Chaim Mazo Publishers The Pomegranate Pendant. She can be reached at ways@netvision.net.il or website: www.dvorawaysman.com The Race For The Lost Ark |