July 28, 2006
Celebrating Puzzles, in 18,446,744,073,709,551,616 Moves (or So)By MARGARET WERTHEIM Correction Appended
Christianity sanctifies Sunday as a day of rest and worship. In the early 19th century, some Protestant communities interpreted the Sabbath sobriety as an injunction against dancing, games and other entertainments. But in Massachusetts a loophole was found. 
July 28, 2006
For teen math whiz, helping is part of human equationVolunteer hours at the Russell Home for Atypical Children add up to satisfaction for a 16yearold.Aline Mendelsohn  Sentinel Staff Writer Posted July 27, 2006 In one setting, Girish Sastry drills his peers on algebra and geometry. In another setting, he teaches severely disabled adults how to sign their names. The way Girish sees it, both endeavors strive to do the same thing: help others. Girish, 16, recently received a governor's Points of Light Award recognizing his volunteer efforts. "I really love helping people," says Girish, a rising senior at Trinity Preparatory School. In eighth grade, with his Hindu temple, Girish began volunteering at the Russell Home for Atypical Children in Orlando. There, he realized that many residents do not know how to sign their names. So he took it upon himself to teach them this skill. Girish's dad, Harry Sastry, says his son's visits to the Russell Home have been an important experience. "At a young age, he has learned what it is to have and not to have," says Sastry, a Winter Park anesthesiologist. Girish is particularly fond of a resident named Warren, who loves the Tampa Bay Buccaneers and was delighted when the Sastry family gave him a football. Russell administrator Judy Harris calls Girish an asset to the home. "They all [the residents] respond to him," Harris says. " . . . He's real quiet and calm and patient." He's also a math whiz: Girish earned a perfect score on his SAT, took advancedplacement calculus in ninth grade and takes advanced math classes at the University of Central Florida. He tutored other students at his temple in Casselberry, and his dad suggested that he tutor kids who couldn't afford to take SAT classes. So two years ago, Girish collaborated with two friends to host Saturday SAT math tutoring sessions at the Crooms Academy of Information Technology in Sanford. The trio continues to offer the classes, for free, during the school year. Girish finds reward in seeing students progress, such as a boy who raised his test score  and was accepted to the University of Florida. In addition to volunteer work, Girish maintains a heavy course load, takes tennis lessons and, he says, sleeps a lot: nine to 10 hours a night and however many catnaps he can sneak in on car rides. He hopes to pursue a career that combines medicine and technology. Girish recently returned from a summer chemistry program at Baylor University in Texas. For the rest of the summer, Girish plans to relax and continue his volunteer work at the Russell Home. There's also another item on the agenda: earning his drivers license. Girish doesn't seem too excited about it. He takes some of his best naps in the car. But Harry Sastry, who has spent hours behind the wheel carting Girish to his various volunteer and academic pursuits, is quite looking forward to Girish driving on his own. For teen math whiz, helping is part of human equation 
July 28, 2006
Dr. Lawrence J. Fogel Receives Inaugural IEEE Frank Rosenblatt Technical Field AwardVANCOUVER, British Columbia, July 25 /PRNewswire/  Dr. Lawrence J. Fogel, President of Natural Selection, Inc. in La Jolla, California, became the first recipient of the IEEE Frank Rosenblatt Technical Field Award on July 19. The award was presented at the 2006 IEEE World Congress on Computational Intelligence by IEEE Director Dr. Evangelia MicheliTzanakou. The IEEE is the world's largest association of professional engineers, with over 350,000 members internationally. The IEEE Frank Rosenblatt Award was established by the IEEE Board of Directors in 2004. The award is named in honor of Frank Rosenblatt, who is widely regarded as one of the founders of neural networks. His work influenced and even anticipated many modern neural network approaches. The award is presented for outstanding contributions to the advancement of the design, practice, techniques or theory in biologically and linguistically motivated computational paradigms, including but not limited to neural networks, connectionist systems, evolutionary computation, fuzzy systems, and hybrid intelligent systems in which these paradigms are contained. Dr. Lawrence J. Fogel was presented the award for "extraordinary and pioneering achievements in computational intelligence and evolutionary computation." Dr. Fogel, who has been described as a "father of computational intelligence," began in 1960 to devise evolutionary programming, a radical approach to artificial intelligence that simulated evolution to literally evolve solutions to problems. His 1964 doctoral dissertation at UCLA on evolutionary programming was the basis for the first book on evolutionary computation, Artificial Intelligence through Simulated Evolution, which he coauthored with Alvin Owens and Michael Walsh. In 1965, Dr. Fogel, with Owens and Walsh, founded Decision Science, Inc. in San Diego, California, the first company to focus on solving real problems via evolutionary computation. As president of Decision Science, Inc., he directed its activities, guiding research in areas such as computer simulation, mathematical prediction and control systems, realtime data processing and materials handling systems. He also developed evolutionary programming methods that led to the Adaptive Maneuvering Logic, a heuristic approach to missile evasion for simulated aerial combat. His method also has been used to discover new pharmaceuticals, improve industrial production and optimize mission planning in defense applications. In 1982, Decision Science merged with and became a division of Titan Systems, Inc. in San Diego. In 1993, Dr. Fogel founded Natural Selection, Inc. in La Jolla, California, which combines evolutionary computation with neural networks, fuzzy systems, and other computational intelligence technologies. The company has addressed and solved problems in many areas, including bioinformatics, medical diagnosis, pattern recognition, data mining, perimeter security, factory optimization, route scheduling, autonomous vehicle capabilities, and risk management. Dr. Fogel is an IEEE Life Fellow and recipient of the IEEE Neural Networks Council Evolutionary Computation Pioneer Award, the Lifetime Achievement Award from the Evolutionary Programming Society, and the Computational Intelligence Pioneer Award from the International Society for Optical Engineering. For additional information visit www.naturalselection.com. Dr. Lawrence J. Fogel Receives Inaugural IEEE Frank Rosenblatt Technical Field Award 
July 28, 2006
Award for mathematician Prof Seshadriautore Prof C S Seshadri, director, Chennai Mathematical Institute, has been awarded the Trieste Science Award for Mathematics for 2006 in recognition of his pioneering work in the field of Algebraic Geometry. Prof. Seshadri is the first Indian mathematician to receive this award, which is jointly shared with Prof J Palis of Brazil. The award consists of a cash prize of $ 50,000 and a plaque with a citation highlighting the recipients' major contributions. The award will be presented at a special ceremony at the tenth General Conference of the Academy for the Developing World in Brazil in September 2006. Governed by the Academy of Sciences for the Developing World, Italy (earlier known as the Third World Academy of Sciences, TWAS) and funded by Illy Caffe, an Italian Coffee Chain, this coveted award recognises outstanding scientific achievements made by researchers living and working in developing countries. A panel of internationally renowned scientists, headed by the president of TWAS, decides the winner after careful deliberation. This is the first time that the award has been given in the area of mathematics. "Mathematics is one of the great creations of the human mind. It is the basic language for all exact sciences. A significant feature in recent times is the use of highlevel mathematics in engineering sciences, computer science, economics, finance, biology and medicine. Modern society requires a substantial number of persons with advanced mathematical skills for the pursuit of pure sciences and in many activities touching daily life. The Chennai Mathematical Institute (CMI) is an institution of excellence devoted to research as well as teaching in mathematical sciences, where frontranking researchers involve themselves in training the younger generation of students at the formative stages of their studies," said Prof Seshadri. "I am delighted to receive the prestigious Trieste Science Award. I take this not just as a recognition of my work but as a tribute to CMI," he added. Prof Seshadri is a leading figure in such cuttingedge topics as the theory of vector bundles and quotient and compact homogenous spaces. He is recognised as the creator of the Standard Monomial Theory and Seshadri Constant, which have found important applications both in mathematics and physics. As founder, he was instrumental in ensuring that the CMI lends a platform for research in India. Under his leadership, CMI has become one of the bestknown institutes amongst the research community in India. He has held visiting positions in many universities abroad, including Harvard and Princeton. He is a Fellow of the Royal Society, UK, and is the recipient of many scientific awards. He has been recently appointed a National Research Professor by the Government of India. Chennai Mathematical Institute (www.cmi.ac.in) was founded in 1989 as a part of the SPIC Science Foundation, funded by the SPIC Group in Chennai. It is a centre of excellence for teaching and research in mathematical sciences. Since 1996, it has been an autonomous institution. The main areas of research at CMI are mathematics and computer science. In addition to a vibrant Ph.D. programme that is affiliated to both Madras University and BITS, Pilani, the institute conducts B.Sc. programmes in mathematics and physics and M.Sc. programmes in mathematics and computer science in conjunction with the Madhya Pradesh Bhoj Open University. A governing council, consisting of eminent persons, manages CMI. It receives substantial funding both from private sources as well as the Government of India and is an example of a wellfunctioning institution with publicprivate participation that is rather unique in higher education. R Rangaraj Award for mathematician Prof Seshadri 
July 28, 2006
The Geometer of Particle PhysicsAlain Connes's noncommutative geometry offers an alternative to string theory. In fact, being directly testable, it may be better than string theory By Alexander Hellemans
Alain Connes
If there is a mathematician eagerly waiting for the Large Hadron Collider near Geneva to start up next year, it is Alain Connes of the Collège de France in Paris. Like many physicists, Connes hopes that the Higgs particle will show up in detectors. The Higgs is the still missing crowning piece of the socalled Standard Modelthe theoretical framework that describes subatomic particles and their interactions. For Connes, the discovery of the Higgs, which supposedly endows the other particles with mass, is crucial: its existence, and even its mass, emerges from the arcane equations of a new form of mathematics called noncommutative geometry, of which he is the chief inventor. 
July 28, 2006
His work tied statistics to normal lifeResearch showed value of small class size, effect of finances on learning ADAM BERNSTEIN Washington Post Frederick Mosteller, who founded Harvard University's statistics department and used mathematical theories to explain everyday concerns, from health care to the World Series, died Sunday in Falls Church, Va. He was 89. Mosteller was a premier statistician of his generation and an early promoter of methodologies that can affect public policy, including analysis of how students can learn better and how some surgical practices can improve lives. He worked across many disciplines, wrote hundreds of papers and shared dozens of book credits with authors such as Princeton University statistician John Tukey and future U.S. Sen. Daniel Moynihan, DN.Y. Mosteller worked with Moynihan, then a Harvard government professor, on comprehensive studies involving the effects of a child's home life on educational development. Their book, "On Equality of Educational Opportunity" (1972), argued that raising the income of families was far more effective in elevating academic achievement than plowing more money into schools. His work in metaanalysis, a comprehensive study of other studies, was also notable. In 1995, he strongly supported a Tennessee study showing that smaller class size vastly improves the rate of learning for students. In 1962, Mosteller found himself in the news when one of his studies addressed the foundations of U.S. history. Mosteller and a colleague from the University of Chicago, David Wallace, proposed a solution to a lingering mystery of political science: Who had written 12 of the 85 Federalist papers? Those essays appeared in New York newspapers in 1787 and 1788, most under the pen name Publius, to urge the ratification of the U.S. Constitution. Although James Madison, Alexander Hamilton and John Jay were known to be "Publius," it was unclear which of the three had written a dozen of the pieces. Mosteller and Wallace spent three years on the project, applying Bayes' theorem, a method of interpreting probability of one event based on previous experience of other connected events. They had at their disposal a highspeed computer, which they fed the known Federalist writings of Madison and Hamilton. Among other things, they looked at sentence length (34.59 vs. 34.55 words, respectively, for Madison and Hamilton) and the frequency of such telltale words as "upon" and "whilst" in Madison and Hamilton's prose. But in the end, they used such noncontextual words as "by" and "from" to show that Madison had written the 12 disputed essays. Their analysis, published in their 1964 book "Inference and Disputed Authorship," spurred consensus among historians over their findings and was an early and persuasive demonstration of what has come to be called "stylometry." Stephen Fienberg, a former doctoral student of Mosteller's and a statistics professor at Carnegie Mellon University in Pittsburgh, placed Mosteller among "a dozen real giants of the last century in statistics." Fienberg said Mosteller's legacy was to show how adaptable many of his methodologies were to matters that were seemingly remote from one another. His work tied statistics to normal life 
July 28, 2006
UW Mathematician Earns Grant to Study Tornado TurbulenceJuly 25, 2006  Anyone who has seen a tornado has noticed its snakelike core weaving from an imaginary hole in the sky to threaten the ground below. However, not everyone who has witnessed a tornado calls it a "vortex filament" and views it as a window to advance energy science. The National Science Foundation has awarded a highlycompetitive single investigator grant to University of Wyoming Mathematics Professor Hakima Bessaih, who will determine how to use these mysterious vortex filaments to possibly uncover fundamental questions in engineering and energy science. "Professor Bessaih's research involves modeling the highlyswirling nature of turbulent fields such as tornadoes in the presence of random disturbances," says Sri Sritharan, UW professor of mathematics. He says vortex filaments also can be seen coming off from airplane wing tips, propeller blade tips and windmill blades. "Understanding the intricate dynamics of such vortex filaments is of fundamental importance in engineering and in energy sciences," he adds. Earning the grant is a major accomplishment for Bessaih, who just finished her second year at an American university. "For an early career scientist, winning a single investigator NSF grant in mathematical science is considered a major recognition by scientific peers," Sritharan says. She received $115,000 for the threeyear grant. The money will fund two summer undergraduate researcher positions each year and the research likely will have positive ramifications for the state of Wyoming. "Given the importance of renewable energy science to the state of Wyoming, it is expected that Professor Bessaih's fundamental contributions to the understanding of vortex filaments will someday help engineers to design windmill blades resistant to damage by turbulent gusts," Sritharan notes. Bessaih, who considers herself a traditional mathematical theorist, hopes to shed more light on the scientific community's understanding of turbulence. "The aim of this research is to understand a little bit more about turbulence from the mathematical point of view," she says. "Fluid mechanics represents turbulence models with differential equations, but we don't yet know how to quantify them mathematically. "The big idea is to be able to communicate more thoroughly with people in fluid mechanics. Combining our model (determined through Bessaih's forthcoming research) with those of fluid mechanics, should help us have a better overall understanding of turbulence," she adds. Before coming to UW in 2004, Bessaih taught for several years in Algeria and Italy. She earned her Ph.D. from the Scuola Normale Superiore in Pisa, Italy (1999), and is widely published in her field. Posted on Tuesday, July 25, 2006 UW Mathematician Earns Grant to Study Tornado Turbulence 
July 28, 2006
Let's get physicalAn eminent professor is lighting up the sciences in Australia, writes Cynthia Karena.
Professor Tanya Monro
SCIENCE is just as creative as playing music, according to one of the world's youngest professors. 
July 28, 2006
Rutgers team to monitor terror activityMathematicians to lead team of researchers for federal governmentThursday, July 27, 2006 BY KELLY HEYBOER StarLedger Staff Rutgers University researchers will lead a team designing ways to monitor news stories, blogs, Web sites and other information sources for signs of possible terrorist activities, school officials announced yesterday. The U.S. Department of Homeland Security awarded Rutgers a $3 million grant to oversee a group of computer scientists, mathematicians and other researchers working in information analysis, a field that has gained attention since the 9/11 terrorist attacks. Their research could help the U.S. government filter large amounts of data in the media and on the Internet to spot patterns that indicate someone is planning a terrorist attack. "The challenge involved in this endeavor is not only the massive amount of information out there, but also how quickly it flows and how fast the sources of information change," said Fred Roberts, director of Rutgers' Center for Discrete Mathematics and Theoretical Computer Science. Rutgers' mathematicians will work with researchers from AT&T Laboratories, Lucent Technologies Bell Labs, Princeton University, Rensselaer Polytechnic Institute and Texas Southern University on the project. "We will develop realtime streaming algorithms to find patterns and relationships in communications, such as among writers who may be hiding their identities, and to rate information sources for their reliability and trustworthiness," Roberts said. The Department of Homeland Security recently began investing money in similar research. Rutgers, the University of Southern California, the University of Illinois and the University of Pittsburgh will receive a total of $10.2 million in research grants over the next three years. Rutgers officials will coordinate the research at the other three universities in addition to overseeing nine research projects on their own campus. The state university also will develop degree and certificate programs to train students in any new technology it develops, school officials said. Rutgers team to monitor terror activity 
July 21, 2006
The Problem With 'NUMB3RS'Posted July 24, 2006 at 8:43 am · By ASU News Filed under App in the News Chronicle of Higher Education  By XIAOBO YUAN Sarah J. Greenwald, an associate professor of mathematics at Appalachian State University, is no stranger to popular culture. She runs Web sites that track math references in The Simpsons and Futurama, two smart cartoons that have alluded to subjects like "hyperbolic topology," and she even knows that five writers for The Simpsons have mathrelated degrees from Harvard. But there's one television bandwagon that Ms. Greenwald has hesitated to jump on: the CBS show NUMB3RS, a primetime drama starring a crimesolving math genius. Like other crime shows, NUMB3RS — which averaged 11.7 million viewers in the 20056 season — often opens with a murder scene or explosion. The difference is that its hero, a tousled academic named Charlie Eppes, played by David Krumholtz, uses equations — not guns or interrogations — to help his FBIagent brother solve crimes. Many mathematicians have embraced the show, whose math content is incorporated in an educational program, "We All Use Math Every Day," developed by Texas Instruments Inc. and the National Council of Teachers of Mathematics for use by middle and highschool students. But in an essay to be published in the August issue of Notices of the American Mathematics Society, Ms. Greenwald says the show may not always be appropriate for the classroom. "The violence, sexual innuendos, and representations of mathematicians on the show are complex for use with students," she writes. For one thing, Ms. Greenwald says, enough with the "genius" clichés. (Like other fictional brainiacs, Charlie is a bit of an eccentric.) Using the show in the classroom, she says, "reinforces the stereotype that you have to be a genius to do mathematics." She also thinks that the educational program should be tested in more classrooms before it becomes widely used. "The show's responsibility is not to educate but to entertain and make money," she says. "But if educators use the show as more than entertainment, how do we ensure good effects?" The critique has already inspired responses from Gary A. Lorden, head of the math department at the California Institute of Technology and chief consultant for NUMB3RS, and from Johnny A. Lott, a former president of the math teachers' council. Both of them have written letters to Notices countering Ms. Greenwald's criticisms. The educational program may not fit into any current school curricula, Mr. Lorden says, but it teaches students to think like real mathematicians. "Lots of kids think math is solved in books, or that everything is known by the teacher," he says, "yet in the real world there are plenty of mistakes — in textbooks and in journals." In the end, says Mr. Lott, who is director of the Center for Teaching Excellence at the University of Montana, mathematicians should appreciate NUMB3RS for its answer to the dreaded question posed by nearly every math student: "But when am I ever going to use this?" "The show gives kids a chance to see math in real use," he says. Even if that use is foiling Russian mobsters. The Problem With 'NUMB3RS' 
July 21, 2006
The Great Origami Maths and Science Show17 July 2006 Folding art into science! BOOK NOW for the Great Origami Maths and Science Show touring NZ in August 2006 Say the word 'origami' to most people and they will picture sharply creased models of birds, fish or frogs. But say it to Jonathan Baxter and Hugh Gribben, and they will tell you their origami is both a performance art and a science! These two master paperfolders have worked their way through a sheer mountain of paper as they prepare for the New Zealand tour of their uniquely titled Great Origami Maths and Science Show. As secondary teachers around the country start planning how to engage the enquiring minds of their maths and science students in Term 3, Jonathan and Hugh are offering up to them the ultimate maths class field trip – a one hour journey into the realms of a new field of origami – origami maths. If this all sounds a bit obscure, try googling the words science, maths and origami  you'll end up with half a millions hits and range of weird and wonderful websites that explore the application of origami in engineering, math and technology. It appears the ancient sculptural art form of origami has undergone a 21st century makeover! Across the globe, mathematicians and engineers with a fondness for origami have applied the rigour of scientific discipline to their hobby and yielded some fascinating results. Origamists are now able to fold, from a single, uncut square of paper, objects where no sheet of paper has gone before; and are able to portray levels of realism and expression never seen in the art form's lengthy history. The simple and stylized animals of the past, which relied as much on the viewer's imagination as on the folder's skill, have been joined by bugs and beasts bristling with anatomically correct legs and teeth. Some folders are exploring new subject matter, such as elaborate cuckoo clocks or working Swiss army knives. Others venture into the abstract world of mathematics, assembling spectacular interlocking polyhedra or tile mosaics, or defying straightline geometry to sculpt graceful curves. Professor Robert Lang, international advisor to the Origami Show and a laser physicist from Pleasanton, California, has been a key player in moving origami into the electronic age. Author of a computer program called TreeMaker, he can take any stick figure outline and calculate a pattern of creases that will produce that figure. This enabled him to create origami animals that were considered impossible years ago and pioneer a new field of mathematics called "computational origami" (the solution of origami problems by mathematical means). Origami can also be found in a range of everyday items. The folds in the top of a milk carton – origami. The way vehicle airbags are neatly squirreled away inside the driving column of your car – origami technology. The incredible way artery stents used in coronary surgery unfold inside the body – origami mechanism. Roadmaps  surely there must be a better way to fold them that makes them easier to return to their flattened state? Origamists are working on that one too and may soon have some answers for us! Clearly there is so much more to origami than just paper folding! Thanks to support from the Royal Society of New Zealand, the Great Origami Maths and Science Show will visit a town near you in August 2006. Come and explore with these expert paperfolders, just how much maths and science is tucked away in the creases of an origami model. Book now as venues are selling out fast! For more information, teacher resources and booking details visit http://www.nzamt.org.nz/origami.htm. The Great Origami Maths and Science Show 
July 21, 2006
Lacan dans ses oeuvres" Noeud borroméen de trois tétraèdres", estimé 1012000 euros(Photo DR)
Le mathématicien et psychanalyste JeanMichel Vappereau a rencontré Jacques Lacan en 1969 et cherché avec lui à réaliser « le noeud à quatre ». Sa collection d'oeuvres graphiques et de manuscrits du maître sera mise demain aux enchères. 
July 21, 2006
Un entretien avec JeanLuc Godard à propos de son exposition au Centre Pompidou : 
July 21, 2006
New European network on modelling control strategies for infectious diseasesEva Balla, 17/7/2006,12:04 The Commission's Directorate General for Health and Consumer Protection (DG SANCO) has announced its support for a new European network on modelling control strategies for infectious diseases and other health threats. The European Network on Mathematical Modelling (NEMO) will be composed mainly of national experts in the Member States in the field of mathematical modelling of the dynamics and control of diseases. The aim of the Network will be to develop and improve mathematical models, which would help to predict and simulate the behaviour and development of infectious diseases and their effect on society. This would help governments to be better prepared to respond in the event of flu pandemic for instance. The Network DG SANCO will chair the Network's Steering Committee in collaboration with the Commission's Joint Research Centre (JRC). The JRC, which is based in Ispra, Italy, will also manage the daytoday running of the project, as part of a wider programme of work on crisis management it is undertaking for DG SANCO. This includes the Health Emergency & Diseases Information System (HEDIS) http://hedis.jrc.it, which is a central hub to exchange healthrelated information between European health authorities, international organisations and international media. In addition, the Medical Intelligence System(MedISys) https://medisys.jrc.it is a web portal supporting DG SANCO and MemberStates, which monitors health related web sites and media every 20 minutes, and analyses the information to rapidly identify potential threats to public health. New European network on modelling control strategies for infectious diseases 
July 21, 2006
Matemáticos de todo el mundo se reúnen en Córdoba para crear un espacio de cooperación en el área mediterránea y latina17/07/2006  10:57 Redacción GD Córdoba acoge desde hoy a más de 150 matemáticos procedentes de universidades de todo del mundo para participar en el curso 'Matemáticas por la paz y el desarrollo', con el objetivo de crear un espacio de cooperación entre el área mediterránea y latina, y ello como paso previo al Congreso Internacional de Matemáticas, que por primera vez se celebra en España. Según la información facilitada a la prensa por la organización, Córdoba ha sido la ciudad española elegida para celebrar estas conferencias dado su pasado multicultural, ya que el trasfondo del evento es la cooperación, en el área de las Matemáticas, entre jóvenes pertenecientes a diferentes culturas y religiones, principalmente de países de Oriente Medio y Próximo, como Irán, Turquía, Palestina e Israel, y de países islámicos del Mediterráneo. Este curso, coordinado por el vicerrector de Comunicación y Coordinación Institucional de la Universidad de Córdoba (UCO), Manuel Torralbo, profesor titular de Matemáticas, será el preámbulo del ya indicado Congreso Internacional de Matemáticas que, por primera vez en sus más de 100 años de historia, se celebrará en España, concretamente en Madrid. 'Matemáticas para la paz y el desarrollo' se ha creado con la pretensión de ser la primera piedra para la construcción de un organismo estable que trabaje para facilitar el encuentro entre culturas en el ámbito específico de esta materia. La propuesta, que saldrá de este curso, ha de ser aprobada en el Congreso Internacional de las Matemáticas, que se celebra en Madrid a partir del próximo 22 de agosto y que volverá a reunir a los participantes de la conferencia de Córdoba, que se desarrollará hasta el próximo sábado. Las matemáticas aplicadas a diferentes ciencias como la Biología, la Física, las Finanzas o la Estadística, serán algunos de los temas que traten durante los seis días de conferencias los expertos que reunirán en torno a ellos a jóvenes matemáticos de países mediterráneos y latinos. Entre los conferenciantes destaca la presencia de Simon Donaldson, premio Crafoord en 1994, reconocimiento equivalente al Premio Nobel de las Matemáticas. Matemáticos de todo el mundo se reúnen en Córdoba para crear un espacio de cooperación en el área mediterránea y latina 
July 21, 2006
Cornell's Éva Tardos Awarded George B. Dantzig Prize at SIAM Annual MeetingEstablished in 1979, the George B. Dantzig Prize is awarded jointly by the Mathematical Programming Society (MPS) and the Society for Industrial and Applied Mathematics (SIAM). The prize is awarded for original research, which by its originality, breadth and scope, is having a major impact on the field of mathematical programming. Dr. Tardos was awarded the George B. Dantzig Prize at the SIAM Annual Meeting held in Boston from July 10 – 14, 2006. She received the prize in recognition for her deep and wideranging contributions to mathematical programming, including the first strongly polynomialtime algorithm for minimumcost flows, several other variants of network flows, integer programming, submodularity, circuit complexity, scheduling, approximation algorithms, and combinatorial auctions. Tardos' research interest focuses on the design and analysis of efficient methods for combinatorialoptimization problems on graphs or networks. Such problems arise in many applications such as vision, and the design, maintenance, and management of communication networks. She is mostly interested in fast combinatorial algorithms that provide provably optimal or closeto optimal results. She is most known for her work on networkflow algorithms, approximation algorithms for network flows, cut, and clustering problems. Her recent work focuses on algorithmic game theory, an emerging new area of designing systems and algorithms for selfish users. Éva Tardos received her Ph.D. at Eötvös University in Budapest, Hungary in 1984. After teaching at Eötvös and the Massachusetts Institute of Technology, she joined Cornell in 1989. She is currently a member of the American Academy of Arts and Sciences and an ACM Fellow. Tardos was a Guggenhaim Fellow, a Packard Fellow, a Sloan Fellow and an NSF Presidential Young Investigator. She received the Fulkerson Prize in 1988. Professor Tardos is the editor of several journals including SIAM Journal on Computing, Journal of the ACM, and Combinatorica. The Society for Industrial and Applied Mathematics (SIAM) was founded in 1952 to support and encourage the important industrial role that applied mathematics and computational science play in advancing science and technology. Along with publishing toprated journals, books, and SIAM News, SIAM holds about 12 conferences per year. There are also currently 45 SIAM Student Chapters and 15 SIAM Activity Groups. SIAM's 2006 Annual Meeting themes included dynamical systems, industrial problems, mathematical biology, numerical analysis, orthogonal polynomials and partial differential equations. For complete details, go to http://www.siam.org/meetings/an06/index.php . Cornell's Éva Tardos Awarded George B. Dantzig Prize at SIAM Annual Meeting 
July 21, 2006
SIAM's Julian Cole Lectureship awarded to Dr. Michael J. Shelley of the Courant InstituteThe Julian Cole Lectureship was established in 2001 and is given at the SIAM Annual Meeting. This year's meeting was held in Boston, July 10–14, 2006. The prize, funded by the students, friends, colleagues and family of Julian Cole, is awarded for an outstanding contribution to the mathematical characterization and solution of a challenging problem in the physical or biological sciences, or in engineering, or for the development of mathematical methods for the solution of such problems. The lectureship may be awarded to any member of the scientific or engineering community. SIAM selected Michael J. Shelly as this year's lecturer. His lecture was titled "Bodies Interacting With and Through Fluids." Professor Shelley's work, like that of Julian D. Cole, emphasizes mathematical modeling and scientific computation in fluid dynamics and other fields. He has worked collaboratively with many individuals, making significant advances in our understanding of basic phenomena from multicomponent fluids and multiphase materials to neuronal activity in the visual cortex. Michael J. Shelley received his B.A. in Mathematics from the University of Colorado in 1981, and his Ph.D. in Applied Mathematics from the University of Arizona in 1985. He was then a postdoctoral fellow in the Program in Applied and Computational Mathematics at Princeton University, following which he joined the mathematics faculty at the University of Chicago and where he was also an NSF Postdoctoral Fellow. In 1992, he joined the Courant Institute at New York University, where he is presently Professor of Mathematics and Neuroscience, and CoDirector of the Applied Mathematics Laboratory. He was previously an NSF Presidential Young Investigator, and received the Francois N. Frenkiel Award of the American Physical Society, Division of Fluid Dynamics, in 1998. His research interests include the mathematical modeling, analysis, and simulation of flowbody interactions and of complex fluids, often done in close connection with laboratory studies, as well as in understanding elements of visual perception, again using modeling and simulation, of the neuronal network dynamics of the primary visual cortex. SIAM's Julian Cole Lectureship awarded to Dr. Michael J. Shelley of the Courant Institute 
July 21, 2006
SIAM Awards Lagrange Prize to Roger Fletcher, Sven Leyffer and Philippe L. TointEstablished in 2002, the Lagrange Prize in Continuous Optimization is awarded jointly by the Mathematical Programming Society (MPS) and the Society for Industrial and Applied Mathematics (SIAM). SIAM awarded the Lagrange Prize at their annual meeting held in Boston from July 10–14, 2006. The recipients of this year's prize are Roger Fletcher of the University of Dundee, Scotland, Sven Leyffer of Argonne National Laboratory, and Philippe L. Toint of the University of Namur, Belgium. The prize is awarded for outstanding works in the area of continuous optimization. Judging of works is based primarily on their mathematical quality, significance, and originality. Clarity and excellence of the exposition and the value of the work in practical applications may be considered as secondary attributes. The 2006 recipients were recognized on behalf of their papers: "Nonlinear Programming Without A Penalty Function" by Roger Fletcher and Sven Leyffer, published in Mathematical Programming, 91 (2), pp. 239269 (2002) and "On the Global Convergence of a FilterSQP Algorithm" by Roger Fletcher, Sven Leyffer, and Philippe L. Toint, published in SIAM Journal on Optimization, Volume 13, pp. 4459 (2002) In the development of nonlinear programming over the last decade, an outstanding new idea has been the introduction of the filter. This new approach to balancing feasibility and optimality has been quickly picked up by other researchers, spurring the analysis and development of a number of optimization algorithms in such diverse contexts as constrained and unconstrained nonlinear optimization, solving systems of nonlinear equations, and derivativefree optimization. The generality of the filter idea allows its use, for example, in trust region and line search methods, as well as in active set and interior point frameworks. Currently, some of the most effective nonlinear optimization codes are based on filter methods. The importance of the work cited here will continue to grow as more algorithms and codes are developed. The filter sequential quadratic programming (SQP) method is proposed in the first of the two cited papers. Many of the key ideas that form the bases of later nonSQP implementations and analyses are motivated and developed. The paper includes extensive numerical results, which attest to the potential of the algorithm. The second paper complements the first, using novel techniques to provide a satisfying proof of correctness for the filter approach in its original SQP context. The earlier algorithm is simplified, and, in so doing, the analysis plays its natural role with respect to algorithmic design. SIAM Awards Lagrange Prize to Roger Fletcher, Sven Leyffer and Philippe L. Toint 
July 21, 2006
George F. Lawler, Oded Schramm and Wendelin Werner receive George Polya Prize in BostonThe Society for Industrial and Applied Mathematics' George Polya Prize was awarded to Gregory F. Lawler of Cornell University, Oded Schramm of Microsoft Corporation and Wendelin Werner of Université ParisSud at SIAM's Annual Meeting in Boston, July 10–14, 2006. The prize was established in 1969 and is given every two years, alternatively in two categories. One is a notable application of combinatorial theory. The other is for a notable contribution in another area of interest to George Polya such as approximation theory, complex analysis, number theory, orthogonal polynomials, probability theory, or mathematical discovery and learning. In 2006, the George Polya Prize is given for a notable contribution in another area of interest to George Polya. Lawler, Schramm and Werner received the prize for their groundbreaking work on the development and application of stochastic Loewner evolution (SLE). Of particular note is the rigorous establishment of the existence and conformal invariance of critical scaling limits of a number of 2D lattice models arising in statistical physics. Gregory F. Lawler received his B.A. from University of Virginia in 1976 and his Ph.D. from Princeton University in 1979. He went to Duke University in 1979, where he was named A. Hollis Edens Professor of Mathematics in 2001. Also, in 2001, he became Professor of Mathematics at Cornell University and this fall will start a new position as Professor of Mathematics at the University of Chicago. His research interests are random walk and Brownian motion with a particular emphasis on processes with strong interactions arising in statistical physics. Oded Schramm is a principal researcher working at Microsoft Research. He earned his B.Sc. and M.Sc. degrees in mathematics at the Hebrew University in Jerusalem and his Ph.D. in mathematics at Princeton University (advisor W. P. Thurston). After a twoyear appointment at the UCSD, he returned to Israel to work at the Weizmann Institute of Science. In 1999, he joined Microsoft Research at Redmond, Washington. He is the recipient of the Anna and Lajos Erdös Prize in Mathematics, the Salem Prize, Clay Research Award, Henri Poincaré Prize, and the Loeve Prize. Dr. Schramm's research interests include conformal mappings and probability. Wendelin Werner is Professor of Mathematics at the Université ParisSud. He completed his Ph.D. at Université Paris VI under the supervisioin of JeanFrancois Le Gall. His research interests lie in probability theory and especially in twodimensional structures. For his research, he has received prizes from the French Academy of Sciences, from the European Mathematical Society, as well as the Rollo Davidson, Fermat and Loeve prizes. George F. Lawler, Oded Schramm and Wendelin Werner receive George Polya Prize in Boston 
July 21, 2006
Stanford's George Papanicolaou selected speaker for the John von Neumann LectureDr. Papanicolaou was selected as this year's John von Neumann lecturer at the Society for Industrial and Applied Mathematics (SIAM) Annual Meeting held in Boston, July 10–14, 2006. The prize, established in 1959, is in the form of an honorarium for an invited lecture. The lecture includes a survey and evaluation of a significant and useful contribution to mathematics and its applications. It may be awarded to a mathematician or to a scientist in another field, but, in either case, the recipient should be one who has made distinguished contributions to pure and/or applied mathematics. Professor Papanicolaou was chosen lecturer in recognition of his wideranging development of penetrating analytic and stochastic methods and their application to a broad range of phenomena in the physical, geophysical, and financial sciences. Specifically, his research on imaging and time reversal in random media, on financial mathematics, and on nonlinear PDEs has been significant and influential. Dr. Papanicolaou's lecture was titled "Imaging in Random Media." George Papanicolaou received his Ph.D. in Mathematics from Courant Institute of Mathematical Sciences, New York University, in 1969 and joined the faculty of the Courant Institute. In 1993, he joined the faculty of Stanford University, and, in 1997, he was appointed the Robert Grimmett Professor of Mathematics. He has received an Alfred Sloan Fellowship and a John Guggenheim Fellowship and he is a Fellow of the American Academy of Arts and Sciences and a member of the National Academy of Sciences. His research interests include waves and diffusion in inhomogeneous or random media and in the mathematical analysis of multiscale phenomena that arise in their study, along with their application to electromagnetic wave propagation in the atmosphere, underwater sound, waves in the lithosphere, diffusion in porous media and, more recently, multipath effects in communication systems. He also is interested in asymptotics for stochastic equations in analyzing financial markets and in data analysis. Stanford's George Papanicolaou selected speaker for the John von Neumann Lecture 
July 21, 2006
Students awarded prizes at Society for Industrial and Applied Mathematics Annual Meeting in BostonThe SIAM Student Paper Prizes are awarded every year to the student author(s) of the most outstanding paper(s) submitted to the SIAM Student Paper Competition. These awards are based solely on the merit and content of the students' contribution to the submitted papers. The purpose of the SIAM Student Paper Prizes is to recognize outstanding scholarship by students in applied mathematics or computing. This year's winners represent the California Institute of Technology, Harvard University and the University of Florida. The 2006 winners are: Laurent Demanet of the California Institute of Technology for the paper titled "The Curvelet Representation of Wave Propagators is Optimally Sparse." The coauthor is Emmanuel J. Candès, California Institute of Technology Emanuele Viola of Harvard University for the paper titled "Pseudorandom Bits for Constant Depth Circuits with Few Arbitrary Symmetric Gates." Hongchao Zhang of the University of Florida for his paper titled: "A New Active Set Algorithm for Box Constrained Optimization." The coauthor is William W. Hager of the University of Florida. Students awarded prizes at Society for Industrial and Applied Mathematics Annual Meeting in Boston 
July 21, 2006
L'Université d'été des mathématiques de Safi rend hommage au mathématicien safiot Mohamed Chidamiwww.lematin.ma L'Université d'été des mathématiques de Safi, qui a ouvert mercredi 12 juillet 2006 ses portes pour aborder dans sa septième édition les travaux de l'analyse fonctionnelle, a honoré le professeur chercheur, Mohamed Chidami, un mathématicien safiot hors paire. Avant de relater brièvement cet événement, il convient de rappeler que l'Université d'été des mathématiques de Safi est un séminaire consacré à la recherche et à l'encadrement des élèves professeurs de maths, organisé chaque année, à pareille époque, par l'association Hawd Assafi. Plusieurs équipes d'analyse fonctionnelle du Royaume sont représentées dans ce congrès et pour ne citer que les équipes des villes de Rabat, de Fès, de Casablanca et d'Oujda. Même des équipes venues d'ailleurs y sont représentées, en l'occurrence celles de France et d'Espagne. Cependant pour rendre hommage au Pr. Mohamed Chidami, une cérémonie a été organisée à l'amphi de la wilaya en présence de présidents d'universités, de doyens de facultés, de directeurs de grandes écoles, d'enseignantschercheurs et de plusieurs autres personnalités. Nombreux étaient donc les collègues et amis qui avaient pris la parole pour présenter Mohamed Chidami ; cet homme à la fois modeste et courtois et combien pétri de qualités, de savoirfaire et de savoirêtre. "Tu es un homme dynamique et généreux", dira le Dr. Mohamed Akkar au moment où celui ci évoquait les qualités de ce professeur qui s'est investi dans une carrière totalement vouée à l'enseignement supérieur et à la recherche. Le professeur Mohamed Chidami est natif de Safi, en 1949 au quartier Achbar. Il a fait ses études d'abord à Safi, à l'école Hidaya Al Islamia, puis à Rabat où il obtint et son bac et sa licence pour aller, ensuite à Bordeaux et soutenir 4 ans après une thèse d'Etat. Professeurchercheur de l'enseignement supérieur, il a participé à des travaux extrêmement importants tant au niveau de l'enseignement secondaire qu'au niveau des ouvrages. Mohamed Chidami a également contribué à l'élaboration et mise en place des programmes de l'enseignement supérieur. Il a de même participé à de nombreux jurys d'examens, de concours et pour ne citer que l'agrégation et sa responsabilité pour l'enseignement des mathématiques à l'Académie Royale militaire de Meknès. Le professeur Chidami était aussi chef de département et a collaboré activement à la vie de la faculté des sciences de Rabat, etc. Enfin, il y a de quoi être fier de tout ce que Mohamed Chidami a entrepris pour l'enseignement, la recherche et pour l'université ; sans oublier aussi son action et ses interventions dans les congrès au niveau international. Salah Zentar  LE MATIN L'Université d'été des mathématiques de Safi rend hommage au mathématicien safiot Mohamed Chidami 
July 21, 2006
HK scoops record medal haul at International Mathematical OlympiadA team of secondary school students has won one gold, three silvers, two bronzes for Hong Kong at the 47th International Mathematical Olympiad (IMO), Information Services Department of Hong Kong Special Administrative Region government said Wednesday. Their outstanding performance lifted Hong Kong's ranking to an alltime high of 14th, up from 17th last year. Gold medallist Tsoi Yunpui is the first Hong Kong team member to win four gold medals in successive attempts in crossterritory mathematical competitions. Trainers Chan Jor Ting and Bobby Poon, as well as being IMO Hong Kong Committee members, were the leader and deputy leader of our HK team respectively. All Hong Kong team members are student members of the "Support Measures for the Exceptionally Gifted Students Scheme" under the Education and Manpower Bureau (EMB). In collaboration with the Olympiad's Hong Kong Committee, as one of the measures for nurturing the mathematically gifted, the EMB organizes the annual Olympiad Preliminary Selection Contest Hong Kong. Under the scheme, the students with an excellent performance in the selection contest receive training in a series of enhancement programs and have opportunity to represent Hong Kong in the International Mathematical Olympiad. The Olympiad was held from July 10 to 18, in Slovenia, with 90 teams of up to six members from various countries and territories participating. Among the 90 teams in the 47th International Mathematical Olympiad, China scored the highest overall marks while Russia ranked second and South Korea third. Source: Xinhua HK scoops record medal haul at International Mathematical Olympiad 
July 21, 2006
Japanese win gold at global math contestTwo Japanese high school students have won gold medals at this year's International Mathematical Olympiad in Slovenia, while four other Japanese contestants took silver and bronze, education ministry officials said Tuesday. The combined score of the Japan team was good enough for a seventh place finish, the highest ever for a Japanese team. In the competition held Wednesday and Thursday in Ljubljana, Yuta Ohashi and Masaki Watanabe, both 17 and from Senior High School at Komaba, University of Tsukuba, won top prizes, the Education, Culture, Sports, Science and Technology Ministry said. The two were among 42 gold medalists at the annual competition in which 498 contestants from 90 economies participated, the organizers said. Silver medals went to Yuki Ito, 18, of Nada Senior High School in Kobe, and Yuki Yoshida, 17, from the same school, as well as Toshiki Kataoka, 16, from Takada Senior High School in Tsu, Mie Prefecture. Teruhisa Koshikawa, 16, from Senior High School at Komaba, University of Tsukuba, won a bronze medal. Watanabe and Kataoka also won gold at last year's competition in Mexico. The International Mathematical Olympiad is the mathematics world championship for high school students and has been held every year since 1959. Japanese win gold at global math contest 
July 21, 2006
Students count successes at international Olympiads(18072006) HA NOI — All six Vietnamese who contested the 47th International Mathematics Olympiad in Slovenia won medals, the Education and Training Ministry reports. Twelfthgraders Nguyen Duy Manh, northern Hai Duong Province, and Hoang Manh Hung, Ha Noi, left with two gold medals. The other four secured two silver and two bronze medals. The silver medals went to Nguyen Xuan Tho, Vinh Phuc Province and Le Nam Truong, Ha Tinh Province; the bronze medals went to Dang Bao Duc, Ha Noi and Le Hong Qui, Nghe An Province. The eightday contest ends today. The effort added to the success of four of the five Vietnamese who won bronze medals at the 37th International Physics Olympiad that ended in Singapore yesterday. They were, Pham Huu Thanh, Nghe An Province, Tran Xuan Qui, Ha Noi, Pham Tuan Hiep, Hai Phong, and Nguyen Dang Phuong from Vinh Phuc Province. Four more students won bronze medals at the sevenday 2006 International Biology Olympiad in Cordoba, 1,000km southwest of Buenos Aires, that ended Saturday. They included 12thgrader Luu Thanh Thuy from the Ha NoiAmsterdam high school who added to the bronze medal she won at the 16th International Biology Olympiad in Beijing last year. Other medallists were her school mate Pham Duy, Tran Thi Thu Thuy, of the Ha Noi National University affiliate, the Natural Science University, and Nguyen Thi Quynh Giang, Vinh Phuc Province. All were born in 1988. — VNS Students count successes at international Olympiads 
July 21, 2006
Canada wins five silver and one bronze medal at the 47TH Mathematical Olympiad in Ljubljana, Slovenia.OTTAWA, July 18 /CNW Telbec/  Competing against students from 90 other countries, Canadian high school students have done extremely well with all six students winning medals at the 47th International Mathematical Olympiad (IMO) Ljubljana, Slovenia, from July 618, 2006. The six students who competed for Canada were: Farzin Barekat, Sutherland Secondary School, North Vancouver (British Columbia); Viktoriya Krakovna, Vaughan Road Academy Toronto (Ontario); Yang (Richard) Peng, Vaughan Road Academy, Toronto (Ontario); Dong Uk (David) Rhee, McNally High School, Edmonton (Alberta); Peng Shi, Sir John A. MacDonald Collegiate Institute, Toronto (Ontario); and Yufei Zhao, Don Mills Collegiate Institute, Toronto (Ontario). The team was accompanied by the Team Leader Robert Morewood (Crofton House School, Vancouver) and the Deputy Team Leader Naoki Sato (Art of Problem Solving (AoPS) Incorporated). At the Closing Ceremony on July 17th, Silver Medals were awarded to Farzin Barekat, Viktoriya Krakovna, Dong Uk (David) Rhee, Peng Shi and Yufei Zhao; and a Bronze Medal to Yang (Richard) Peng. "Our students really came together as a team. They trained hard and showed their individual strengths. They all made progress on every question in an extremely tough competition. I am proud of their achievements." said Robert Morewood. "The IMO is the world championship high school mathematics competition. The problems were very difficult and all the Canadian students have done very well. They demonstrated the problem solving skills, knowledge and creativity that is so essential to compete at this very high level," said Dr. Graham Wright, Executive Director of the Canadian Mathematical Society (CMS), the organization responsible for the selection and training of Canada's IMO team. Although students compete individually, country rankings are obtained by adding the teams' scores. The maximum score for each student is 42 and for a team of six students the maximum is 252. The Canadian team placed 15th out of 90 competing countries with a score of 123. Since 1981, Canadian students have received a total of 16 gold, 34 silver, and 58 bronze medals. The six members of the Canadian IMO team were selected from among more than 200,000 students who participated in local, provincial and national mathematics contests. Prior to leaving for the 47th IMO, the team trained at Dalhousie University from June 24th to July 2nd and in Ljubljana, Slovenia from July 3rd to July 10th. The 2006 IMO contest was set by an international jury of mathematicians, one from each country, and was written on Wednesday July 12th and Thursday July 13th. On each day of the contest, three questions had to be solved within a time limit of four and a half hours. Team members must be less than 20 years old when they write the IMO. The top 10 teams and their scores are: China (214); Russia (174); Korea (170); Germany (157); USA (154); Romania (152); Japan (146); Iran (145); Moldova (140); and Taiwan (136). The team will be returning to Canada today (July 18th), arriving at Pearson International Airport (Terminal 1) on Austrian Airlines flight 71 at 2:45 PM. Sponsors of the 2006 Canadian IMO team include: the Canadian Mathematical Society; NSERC PromoScience; the Imperial Oil Foundation; Sun Life Financial; the Ontario Ministry of Education; Alberta Learning; the Nova Scotia Department of Education; the Newfoundland and Labrador Ministry of Education; the Quebec Ministry of Education; the Northwest Territories Ministry of Education; the Saskatchewan Ministry of Education; the Samuel Beatty Fund; Maplesoft; the Centre de recherches mathématiques; the Fields Institute; the Pacific Institute for the Mathematical Sciences; the Centre for Education in Mathematics and Computing, University of Waterloo; the Department of Mathematics and Statistics, Dalhousie University; the Department of Mathematics and Statistics, University of Calgary; the Department of Mathematics and Statistics, University of New Brunswick at Fredericton; the Department of Mathematics and Statistics, University of Ottawa; the Department of Mathematics and Statistics, York University; and the Department of Mathematics, University of Toronto. The 48th International Mathematical Olympiad will take place in Hanoi, Vietnam, in July 2007. Canada wins five silver and one bronze medal at the 47TH Mathematical Olympiad in Ljubljana, Slovenia. 
July 21, 2006
Jóvenes peruanos regresan victoriosos de Olimpiada Internacional de MatemáticaEl puneño Daniel Soncco obtuvo una medalla de plata y Jossy Alva, una de bronce
Las sonrisas de satisfacción y orgullo son inevitables y no es para menos. Después de varios meses de preparación, la noche del pasado martes, los chicos de la delegación peruana de matemática retornaron triunfantes de su participación en la edición 47 de la Olimpiada Internacional de Matemática celebrada en Eslovenia del 8 al 18 de julio último. 
July 21, 2006
Un platense premiado en Olimpiada Matemática de EsloveniaSe trata de Roberto Morales, que con una medalla de bronce, formó parte del equipo argentino premiado en Eslovenia, donde participaron ochenta países
El equipo argentino, entrenado por profesoras del CBC, obtuvo en la competencia internacional de Eslovenia dos medallas de plata, dos de bronce y una mención de honor, informó la UBA. 
July 21, 2006
Turkey Wins 5 Medals in Mathematics OlympiadBy Muharrem Gokcen, Manisa Published: Monday, July 17, 2006 Turkish students achieved notable success at the Mathematics Olympiad, following the gold medal success of Turkish students at the International Chemistry Olympiad. At the 47th International Mathematics Olympiad, held between July 10 and July 16, 2006, in the Slovenian city of Ljubljana, the Turkish national team won four silver medals and one bronze medal, as well as an honorable mention. Out of the sixmember National Mathematics Team, selected by the Scientific and Technological Research Council of Turkey, Hale Nur Kazacesme, Hasan Huseyin Eruslu, Batuhan Karagoz, and Metehan Ozsoy won silver medals, and Cafer Tayyar Yildirim was awarded a bronze medal. Hale Nur Kazacesme was chosen the most successful female student of the competition. Ahmet Karabulak was also awarded an honorable mention in the competition. As Principal of Manisa Sehzade Mehmet Private High School, from which two students were awarded silver medals, Sebahattin Kasap said: "Our students' success in the 47th International Mathematics Olympiad, in which 516 students from 86 countries participated, is truly significant. Our school is proud of having secured 10 medals for Turkey at the International Mathematics Olympiad." In the 38th International Chemistry Olympiad, held in South Korea between July 2 and July 11, 2006, Hande Boyaci from Izmir Yamanlar Private High school was awarded a gold medal. Turkish National Team's Medal Winning Students: Silver: Hale Nur Kazacesme, Manisa Sehzade Mehmet Private High School Silver: Hasan Huseyin Eruslu, Manisa Sehzade Mehmet Private High School Silver: Batuhan Karagoz, Ankara Science High School Silver: Metehan Ozsoy, Ankara Yamanlar Science High School Bronze: Cafer Tayyar Yildirim, Ankara Yamanlar Science High School Honorable Mention: Ahmet Karabulak, Izmir Science High School Turkey Wins 5 Medals in Mathematics Olympiad 
July 21, 2006
Revisiting the Relevance of the Queen of SciencesMathematics is not all about numbers and statistics, the magic lies deeper, Prof. M. A. Sofi writes Mathematics, rightly viewed, possesses not only truth, but supreme beauty, a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as in poetry. (Bertrand Russell)
The raison d'etre of doing science is aptly summed up in the statement that 'if life was not beautiful, it won't be worth knowing and if life was not worth knowing, it won't be worth living'. 
July 13, 2006
Teen adds silver at math meetBY HUGH SON John Adams HS junior Fareed Mohammed with the silver medal he won at the National High School Math Championship in Okla.
Queens math whiz Fareed Mohammed had never seen a calculus problem before staring at four of the mindmelting equations at the National High School Mathematics Championship. 
July 13, 2006
Irving Kaplansky, 89, a Pioneer in Mathematical Exploration, Is DeadBy JEREMY PEARCE Published: July 13, 2006 Irving Kaplansky
Irving Kaplansky, a mathematician who broke ground in exploring concepts central to algebra and multiplication, died on June 25 at his home in the Los Angeles community of Sherman Oaks. He was 89. 
July 13, 2006
Gadanidis honoured for mathematical contributionsGeorge Gadanidis
Western Associate Education professor George Gadanidis has been honoured by the Fields Institute for his continuing work in the field of mathematics. 
July 13, 2006
How parachute spiders invade new territoryTwo male Erigone spiders on a grass seed head. The lower one is in a preballooning posture ready to disperse, known as the "tiptoe" position.
Researchers have developed a new model that explains how spiders are able to 'fly' or 'parachute' into new territory on single strands of silk – sometimes covering distances of hundreds of miles over open ocean. By casting a thread of silk into the breeze spiders are able to ride wind currents away from danger or to parachute into new areas. Often they travel a few metres but some spiders have been discovered hundreds of miles out to sea. Researchers have now found that in turbulent air the spiders' silk moulds to the eddies of the airflow to carry them further. Images available at: http://www.bbsrc.ac.uk/media/pressreleases/06_07_12_spiders.html 
July 13, 2006
Maths to peek in people's pursesBy Malcolm Keswell Accurately measuring income mobility is a notoriously difficult thing to achieve anywhere in the world. It's particularly hard to measure in South Africa. The country is lucky to have some very skilled economists, but until recently there has not been enough detailed, reliable, longterm information about income patterns and its underlying causes. Some of the data, to put it politely, is messy  often because it reflects the real world rather than a controlled laboratory experiment. In fact, even with trustworthy information about income, and even if the information covers a longenough timespan, understanding the shifting causes that lie beneath the data can be a nightmare. Yet it is impossible to take a decent snapshot of the changing face of South Africa  and to make progress in assessing the impact of government programmes  without this knowledge. Fortunately, data analysts at the Southern Africa Labour and Development Research Unit at the University of Cape Town are developing new mathematical techniques to piece together a more accurate picture of how far South African society has transformed (or not) in the last 10 years. We do know that at the end of apartheid, South Africa had among the highest levels of inequality in the world. How have things changed, more than a decade later? In theory, we should be becoming a more homogeneous, more middleclass society. In practice, this is far from clear. Think of a society formed of exactly three people: the first earns R2, the second earns R5 and the third earns R11. Total income in this society is therefore R18. Clearly, if this society were completely equal they would all earn R6. But what happens if, over time, the first person and the third person change positions? Then we would still have an unequal society, but one with rapid mobility. If you generalise this picture to the entire economy, then this is a straightforward case to analyse. But what if incomes are growing while inequality and mobility patterns also shift? Often, economists can't track mobility until they first understand what is happening to inequality  and with "dirty" data, we can't even begin to answer the inequality question. There are a few mathematical techniques that allow you to get around this problem, such as the Markov chain methods, but even these require you to make very restrictive assumptions and can bring with them other problems. Yet all is not lost. Recent advances in the field of nonparametric statistics (a branch of statistics which requires fewer behavioural assumptions about the data) provide innovative mathematical tools that until recently were rarely utilised to answer questions concerning income mobility. When combined with economic theory, these techniques still allow us to say something useful about the pace of change in society. Recent work using these techniques has shown that mobility patterns are much more nuanced than first meets the eye. In particular, my own work has shown that people in the middle of the incomeearning scale are in a fairly stable pattern. It is the very rich and the very poor  the people at either tail  who are experiencing radical changes in earnings. This idea of a "camel's humps" model goes against the standard assumption that all people are subject to the same forces. If my results are true, it would suggest that we have only scratched the surface in understanding the invisible forces at work here. For one, it makes clear that the urban black middle class represents a very, very tiny proportion of the black population. We can't therefore make any blanket statements about upward mobility for Africans, because the situation is very, very different depending on your starting position in the income distribution. And the upwardly mobile may not stay there. The data also seems to be suggesting, after we have weeded out other influences, that to a large extent the changes that we see are transitory, not permanent. That's a really bold statement, and clearly further work is required using the larger more representative data sets that have recently become available. Education may well be the reason why the middle stratum of earners is fairly stable  and education seems to be the one factor that helps buffer the nonpoor from wild swings in their economic position. Paradoxically, this appears to be less clear for those who escape poverty. The data seem to suggest that education is not the major determinant of these transitory shifts out of poverty. There are, of course, many open questions still about how to correctly interpret this finding, but one thing is certain: while education clearly does matter, we have very few clues about the true causal mechanisms behind its influence. The remaining challenge facing social scientists is how to devise better survey designs that provide opportunities to make causal inferences about patterns of inequality and mobility. Given the abundance of facts we now have to work with concerning levels of poverty and inequality in South Africa, the time is right for a shift in our focus to try to understand the causal mechanisms at play. Without this knowledge, it is hard to make progress in answering the biggest question of all: what are the most efficient policies (in terms of bang for buck) to eradicate poverty and deprivation in South Africa? We have only begun to scratch the surface on this count. l Keswell, deputy director of the Southern Africa Labour and Development Research Unit (www.saldru.uct.ac.za) at the University of Cape Town, won an award recently for his research into the most accurate way to track mobility. He received the Economics Society of South Africa's JJI Middleton Medal for best article by a new author for an article which appeared in the South African Journal of Economics, which is published by the society (www.essa.org.za). Published on the web by Cape Times on July 10, 2006.  © Cape Times 2006. All rights reserved. Maths to peek in people's purses 
July 09, 2006
Van Gogh painted perfect turbulencePhilip Ball Van Gogh  The Starry Nigth
Vincent van Gogh is known for his chaotic paintings and similarly tumultuous state of mind. Now a mathematical analysis of his works reveals that the stormy patterns in many of his paintings are uncannily like real turbulence, as seen in swirling water or the air from a jet engine. 
July 09, 2006
The cocoa is in the can  the math is on itBy Ann D. Bingham Today I'm sipping my hot chocolate and thinking about mirrors. Did you ever go shopping for clothes with Mom when she made you stand in front of three mirrors together? From that angle you can see the back of yourself. Sometimes, when conditions are just right, you can see yourself multiple times. Try this: Take a mirror and put it next to another mirror. A bathroom is a great place to do this. Set something small between the two mirrors  a stack of five pennies perhaps. Put the mirrors almost at a corner. Can you see your pennies more than once? How many times can you see them? Now try moving one of the mirrors. Move them a little closer together. Ah ... more math. The shape that the mirrors make when they meet along their edge is called an angle. When we move the mirrors closer to each other, we are making a smaller angle. When we move them away from each other, it is considered a larger angle. This is geometry. See how many times you can see the pennies in the mirror. Do you see more copies of the pennies when the mirrors are closer together or farther apart? In mathematics we call that "recursion"  when we see something again and again and again. Anything that repeats itself is called recursion. Sometimes we see this in pictures. I had a book of stories one time. On the cover it showed a woman reading a book. And on the cover of that book was a picture of that very same book  with the woman reading that book again. Wow! How long could that go on? In mathematics we say it could go on to infinity  forever. (In real life the picture would get so small you couldn't see it anymore  but I like to think mathematically.) Mathematicians have a name for that effect. They call it the "Droste effect." It's named after a brand of cocoa made in the Netherlands. The Droste cocoa tin shows a picture of a woman wearing a large white hat. She's carrying a tray with a cup and a cocoa tin on it. What kind of cocoa do you think she is carrying? You guessed it! The cocoa she's carrying is a Droste cocoa can, and it has a picture of the woman on it. And in that picture she also is carrying a tray with a Droste cocoa can on it. And so on and so on. That's why mathematicians gave the name "Droste effect" to a recursive picture such as that. So as I take another sip of hot cocoa, I'll think about other times I've seen that kind of picture  one that goes on forever. Maybe you can, too. The cocoa is in the can  the math is on it 
July 09, 2006
Where brains meet gamesBy JOSEPH WILSON The scene is this year's e3 ( Electronic Entertainment Expo). Thousands of game junkies crowd around a giant video screen to witness the latest pinnacle of game programming: a little green bacterium in a pond of primordial goop. The usual Vegasstyle booths advertising the latest firstperson shooters empty out as technophiles grab at the opportunity to watch, enraptured, as the bacterium slowly evolves into a multicelled organism, then a landdweller, and finally a social being complete with buildings and spaceships. The 20minute demo is a preview of Spore (www.spore.com), the latest game by Will Wright, the creator of The Sims. The game reprises the openended structure of The Sims, where the usual gaming formula is reversed: usually, a gamer controls a main character in an environment of preset rules, but in The Sims, the player controls the environment, and the characters develop lives of their own. The focus of Spore is nothing less than the evolution of life itself, a fact sure to please the intelligent design lobby. Once you prove your worth in the primordial stew by eating smaller, weaker bacteria, you use DNA points to facilitate growth of complex structures, eventually allowing users to make decisions that would make Darwin swoon, such as trying out various adaptive features like green skin or sharper teeth. The virtual world of The Sims, released in 2000, made headlines by attracting more women players than men; a rarity in the maledominated world of gaming. The popularity across gender and generational divides spawned a slew of spinoffs including SimFarm, SimAnt, SimEarth and SimCity, the last of which was used by many city planers to prep eager apprentices. Similarly, Spore seems to be of interest to everyone from game geeks to casual players, and even science teachers anxious to promote the fundamental principles of natural selection. I can hear the collective happy sigh of biology teachers the world over as they hear the words of a stoned gamer: "Dude, you've totally got to get a flagellum to move better." Although graphically innovative, Spore is not the first instance where the complexity of life has been modelled through a gaming platform. In 1970, mathematician John Conway developed The Game Of Life, a set of animations showing how initially straightforward patterns can evolve into surprisingly complex shapes based on a simple set of mathematical rules. The Game has been used to illustrate the principles of complexity, which allow for socalled "emergent behaviour": completely unpredictable patterns can emerge from a simple set of conditions. Emergent behaviour is clearly evident in Spore. With one of his creations, Wright combined the action of eating with the action of movement and found to his surprise that the creature eventually decided on its own to drag its future prey to a set place for dinner. Once you've paid your dues mucking around in the prehistoric jungle, your creatures can form societies and complex communities, perhaps even venturing into space. The game itself is linked to other players online, so you can meet creatures on other planets that are the results of another player's game. Here, Spore veers into the territory of game theory, a philosophy that describes evolution as a scenario where creatures can either conquer or cooperate with new species, depending on the net benefit to their society. Simple interactions with other animals in Spore can lead to some pretty unpredictable results, something familiar to anyone who's tried to apply game theory to the world of international relations. So when Spore hits shelves in late 2006, try your hand at what Will Wright has called SimEverything, and see if you can survive as one of its fittest. Where brains meet games 
July 09, 2006
Il problema della fondazione dell'aritmetica come scienza sintetica a priori.Tempo ed aritmetica in Kant. FreePhilosofy: Vi è un elemento del sistema della Critica della Ragion Pura (1) che nella pur sterminata letteratura kantiana è stato assai discusso ma non sembra aver trovato soddisfacenti proposte di soluzione: si tratta del problema della fondazione dell'aritmetica come scienza sintetica a priori. Nell'occuparci principalmente di questo problema particolare, e solo secondariamente del problema più generale, ampiamente sviluppato nelle pagine kantiane e soprattutto nella letteratura critica, riguardante l'oggettività delle scienze matematiche, è da evidenziare come tale questione più generale, sviluppata senza riferimenti analitici alle scienze matematiche particolari, costituisce una parte integrante della teoria kantiana dello spazio e del tempo ad essa riferendosi il titolo del capitolo che nei Prolegomeni ad ogni futura metafisica che si presenterà come scienza (2) corrisponde all' "Estetica trascendentale" della Critica: "Della principale questione trascendentale: com'è possibile la matematica pura?"). In una prospettiva sintetica, questo problema può essere trattato genericamente, senza riferimento alle discipline matematiche particolari se non a scopo di esemplificazione. Infatti, tale è la prospettiva della Critica, come è stato spiegato da Ernst Cassirer (3): "A questo punto la filosofia non ha più un proprio campo, un ambito particolare di contenuti e di oggetti che le spetti unicamente ed esclusivamente, differenziandola dalle altre scienze; ma è la sola a cogliere la relazione delle funzioni spirituali fondamentali, nella sua vera universalità e profondità, ad un livello non accessibile ad alcuna di quelle scienze nella sua singolarità (...). Se, per mettere in luce questo fatto nei particolari, cominciamo con la struttura della matematica, allora qui non si tratterà tanto di svolgere il contenuto dei principi matematici, quanto piuttosto di mostrare il procedimento generale solo ed unicamente in forza del quale possono esservi per noi dei 'principi', ossia il procedimento in virtù del quale riusciamo a scorgere come ogni particolare posizione (Setzung) nello spazio ovvero ogni particolare posizione del numerare e del misurare restano legate a condizioni universali originarie dalle quali non possiamo uscire". Tuttavia, in Kant c'è anche una concezione della logica, del metodo e dei principi delle discipline matematiche considerate in particolare. La concezione della geometria che viene profilata nella Critica non è difficile da afferrarsi, nella sua generalità (nonostante alcuni problemi interpretativi): fondamentalmente, questa scienza viene analizzata e legittimata trascendentalmente grazie al suo riferimento necessario all'intuizione pura dello spazio, di cui determina a priori le proprietà ed in cui introduce un ordine intellettuale ed oggettivo, per cui lo spazio, che dapprima è soltanto forma della intuizione, priva di un adeguato ordine concettuale, diventa rappresentazione oggettiva, o "intuizione formale" (4). In altre parole: la possibilità della geometria possa poggiare sulla determinabilità concettuale a priori dell'intuizione esterna pura. Al contrario, la semplice lettura degli scritti kantiani non consente di formarsi un'idea chiara della concezione kantiana dell'aritmetica. Ai numeri ed all'aritmetica, infatti, Kant talvolta attribuisce una relazione con l'intuizione temporale che sembra analoga a quella tra lo spazio e la geometria: ma di questa relazione tra aritmetica e tempo manca in Kant una trattazione esauriente ed esplicita, e pertanto non se ne comprende se non l'elemento più generico: la relazione tra l'attività del numerare ed il succedersi del tempo. Inoltre, altre importanti questioni rimangono aperte: qual è per Kant l'oggetto specifico dell'aritmetica? Perché le proposizioni di questa scienza sono dette da Kant sintetiche a priori? Sulla base di alcuni passi kantiani, in generale né troppo estesi né troppo espliciti, si è cercato di ricostruire una teoria kantiana dell'aritmetica maggiormente articolata; la cosa è stata resa possibile dal ricorso ad alcuni documenti sino ad ora quasi del tutto trascurati dalla letteratura critica kantiana (5): le opere di uno dei primi esegeti contemporanei di Kant, Johann Schultz, professore di matematica nell'università di Königsberg. Schultz, da tempo in intensi rapporti personali con Kant, dopo la pubblicazione della Critica della Ragion Pura aderì alla filosofia trascendentale e compose due commentari della Critica (6), nei quali il tema della filosofia della matematica è dominante ed i problemi inerenti sono svolti in maniera assai più esplicita ed accurata che non nelle pagine di Kant. Il fatto più notevole è che le opere di Schultz possono essere accettate quasi fossero dei documenti di prima mano del pensiero di Kant: infatti, dallo studio dell'epistolario e della biografia di Kant risulta che Schultz svolse per Kant quasi un lavoro di portavoce ufficiale, e che nessuno dei suoi scritti filosofici potette essere pubblicato se non in seguito all'esame ed all'approvazione personale di Kant. Ciò non esclude tuttavia che i commentari di Schultz forniscano interessanti integrazioni e spiegazioni di parecchi temi della Critica della Ragion Pura, e soprattutto del pensiero matematico kantiano, che verosimilmente costituì l'interesse filosofico principale del matematico Schultz. Soprattutto, è notevole che egli si mostri consapevole della distinzione e dell'autonomia della ricerca filosofica sulla matematica rispetto alla ricerca scientifica propriamente matematica: non è privo di significato il fatto che egli usi proprio l'espressione "filosofia della matematica", non certo usuale nel contesto della cultura del 18° secolo (7): "Forse potrò compiacermi del fatto che questi appunti di filosofia della matematica non giungano sgraditi ai miei lettori..." In queste sue ricerche filosofiche lo Schultz precisò accuratamente il tema kantiano della sinteticità a priori dell'aritmetica; inoltre, in un'opera specificamente matematica (8), egli produsse anche una costruzione dell'aritmetica in cui concorrono alcuni dei concetti nati dalla riflessione kantiana. Quali siano per Kant l'oggetto specifico e la definizione della geometria non è dubbio (9): "La geometria è la scienza che determina le proprietà dello spazio sinteticamente, e nondimeno a priori.". Non ha senso, nella prospettiva kantiana, concepire la geometria come un costrutto di vuote forme logiche, il quale successivamente alla propria costruzione venga interpretato per un oggetto particolare, quale lo spazio; e questo perché per Kant la determinazione delle cose nella forma dell'intuizione spaziale è il primo momento necessario nella costituzione di ogni oggetto. La prospettiva formalistica sulla geometria al contrario è ordinaria nella logica e nella filosofia della matematica contemporanee. Si veda per esempio il seguente passo, tratto da un noto compendio di storia della logica (10): "Quando ricorrono in matematica pura, "spazio" e parole affini si riferiscono ad astratte strutture di ordinamento, che è possibile esemplificare con sistemi di oggetti molto differenti. Gli studi di geometria cominciarono, naturalmente, con la riflessione sullo spazio fisico, ma sono progrediti fino a considerare strutture che non si possono visualizzare." Per Kant, indipendentemente da ogni suo eventuale interesse per una visualizzazione in senso letterale dei costrutti geometrici, è da escludersi che la geometria possa risolversi in un sistema di mere forme logiche, il quale riceva successivamente alla propria costruzione un'interpretazione per qualche ambito di oggetti empirici; perciò la geometria non è scienza analitica, ma sintetica, ed è a priori, in quanto il suo oggetto è dato a priori (11): "Solo la nostra definizione [dello spazio come forma del senso esterno in generale, rappresentata necessariamente ed a priori] rende comprensibile la possibilità della geometria, come conoscenza sintetica a priori.". Poiché la geometria si riferisce alle proprietà dello spazio, l'aritmetica può essere interpretata, secondo una facile analogia, come una scienza della proprietà del tempo. Questa interpretazione, in generale non sviluppata né articolata, è tuttavia assai diffusa nella letteratura kantiana, ed anche nella filosofia della matematica non kantiana.. Si vedano per esempio i seguenti passi: "Solo nel secolo 19° questo concetto del numero [elaborato da Kant] fondato sulla rappresentazione del tempo fu accettato da alcuni matematici". (12) "Sull'assegnazione delle discipline matematiche alle due forme dell'intuizione sensibile Kant si è espresso in modo ambiguo; noi possiamo seguire qui la soluzione che, dopo il matematico G. Schultz, è stata generalmente adottata: al tempo corrisponde il calcolo (aritmetica, algebra, analisi), allo spazio la geometria". (13) Cassirer attribuisce a Kant di aver interpretato l'aritmetica come una scienza di ordinamenti di elementi successivi, avente perciò il proprio principio nel tempo: "Secondo Weyl, le ricerche moderne sui principi della matematica, che hanno distrutto la dogmatica teoria degli aggregati, hanno anche confermato la non deducibilità del puro concetto d'ordine ed hanno anche mostrato che il concetto di numero ordinale precede quello di numero cardinale. Con ciò l'algebra è nuovamente definita come la scienza del "tempo puro", nel senso di William Hamilton ed in armonia con un'idea fondamentale di Kant". (14) Vedremo come la conclusione del Cassirer è esatta ma mancante di una necessaria distinzione ulteriore. Per il fatto che la numerazione è una specie di sintesi che avviene successivamente, è evidente che l'aritmetica abbia un rapporto essenziale con il tempo, come forma di ogni successione in generale. Però, questo rapporto non è perfettamente analogo a quello della geometria con lo spazio, e per questo non si può dire che l'aritmetica sia una "scienza del tempo puro" nello stesso senso in cui lo si dice della geometria relativamente allo spazio. Si osservi, infatti, che proprio nel luogo dove più ci si attenderebbe la conferma del rapporto analogo tra aritmetica e tempo, geometria e spazio, e cioè la Sezione Seconda dell'"Estetica trascendentale", trattante del tempo, dell'aritmetica non viene fatta da Kant nessuna menzione, e si trova invece un accenno alla meccanica: "II nostro concetto di tempo spiega la possibilità di tante conoscenze sintetiche a priori, quante ce ne propone la teoria generale del moto, che non ne è poco feconda". (15) Non si vuole negare che nel pensiero di Kant vi sia un profondo rapporto tra intuizione temporale ed aritmetica; che vi sia un simile rapporto è cosa sempre affermata da Kant, sebbene sempre per brevissimi accenni; per esempio: "La geometria pone a fondamento l'intuizione pura dello spazio. L'aritmetica anche riesce a costruire i suoi concetti di numero mediante una successiva aggiunta delle unità nel tempo..." (16) Ciò che si vuole mettere in discussione è semplicemente la facile analogia finalizzata alla ricerca di un rapporto più esatto tra tempo ed aritmetica.  continua  Note bibliografiche (1) C.f.r. I. Kant, Kritik der reinen Vernunft. 1° ed. 1781, 2° ed. 1787; tr. it. Critica della Ragion Pura, a cura di Giovanni Gentile e Giuseppe Lombardo Radice, con Introduzione di Vittorio Mathieu, Roma  Bari, Laterza, 19797. La Critica della Ragion Pura si citerà sempre con la sigla CRP.; (2) Vd. I. Kant, Prolegomena zu jeder künftigen Metaphysik die als Wissenschaft wird auftreten können, 1783; tr. it. Prolegomeni ad ogni futura metafisica che si presenterà come scienza, a cura di Pantaleo Carabellese, edizione riveduta da Rosario Assunto, Roma  Bari, Laterza, 1979, p. 34, §6; (3) ,E. Cassirer, Vita e dottrina di Kant. tr. it., Firenze, La Nuova Italia, 1977, p. 186 ss.; (4) c.f.r. CRP, B l60 n.; (5) In relazione al pensiero matematico di Kant, di Johann Schultz si è occupato soltanto Gottfried Martin in Arithmetik und Kombinatorik bei Kant, opera del 1938 dalla quale noi abbiamo tratto moltissimi spunti. L'opera di Schultz come esegeta dei temi più generali della Critica della Ragion Pura è stata stroncata da Benno Erdmann in Kant's Kritizismus in der ersten und zweiten Auflage der Kritik der reinen Vernunft (1878), Vol. II, p. 112; al contrario essa è stata valutata positivamente da Hermann Johann De Vleeschauwer in La déduction transcendantale dans l'oeuvre de Kant (193537), specialmente nel vol. II, p.51112. Si coglie l'occasione per ringraziare la prof.ssa. Liliana Mittermayer, ricercatrice confermata di Lingua e letteratura tedesca per il notevole aiuto datomi nella traduzione (ed in definitiva comprensione) dell'opera di Gottfried Martin in Arithmetik und Kombinatorik bei Kan; (6) C.f.r. J. Schultz, Erläuterungen über Hrn. Professor Kant Critik der reinen Vernunft, del 1784, e Id.,Prüfung der Kantischen Critik der reinen Vernunft. 2 Voll., 178994; (7) J. Schultz, Prüfung der Kantischen Critik der reinen Vernunft, Vol. II, 1792, p. V); (8) I. Schultz, Anfangsgründe der reinen Mathesis, 1790; (9) I. Kant, CRP, B 40; (10) C.f.r. Kneale, William Calvert e Kneale, Martha, Storia della logica, tr. it. a cura di Amedeo G. Conte, Torino, Einaudi, 1972, p. 440; (11) I. Kant, CRP, B 41; (12) Vd. F. Cajori, "Zahlentheorie", in Vorlesungen über gesamte Geschichte der Mathematik. heraus. gegeben von Moritz Cantor, vol. IV, cap. XX; Leipzig, Teubner, 1908, Vol. IV, p. 79; (13) C.f.r. P. Martinetti, Kant. ristampa, Feltrinelli, Milano, 1968, p. 48; (14) C.f.r. E. Cassirer, Storia della filosofia moderna. Vol. IV, tomo I, Einaudi, Torino, 1963, p. 127; (15) I. Kant, CRP, B 49; (16) C.f.r. I. Kant, Prolegomeni ad ogni futura metafisica che si presenterà come scienza cit., Roma  Bari, Laterza, 1979, p. 34, §10, p. 37. di: Costantino D'Onorio De Meo Il problema della fondazione dell'aritmetica come scienza sintetica a priori. 
July 02, 2006
NJIT mathematician and geometry expert lauded for work, including notable publicationsVladislav Goldberg
Vladislav Goldberg, PhD, a distinguished professor in the department of mathematical sciences at New Jersey Institute of Technology (NJIT), and an expert in web geometry, was honored last month for a lifetime of scholarship. The International Geometry in Odessa Conference in the Ukraine lauded the 70yearold mathematician during a multiday conference. Goldberg, born and schooled in Moscow, emigrated to the US in 1979 during the immigration wave of the 1970s that brought into the US a number of highly educated Jewish scientists. Today, Goldberg has retained a network of scholarly friends in Russia, the US, Israel and many other countries. New Jersey Institute of Technology, the state's public technological research university, enrolls more than 8,100 students in bachelor's, master's and doctoral degrees in 100 degree programs offered by six colleges: Newark College of Engineering, New Jersey School of Architecture, College of Science and Liberal Arts, School of Management, Albert Dorman Honors College and College of Computing Sciences. NJIT is renowned for expertise in architecture, applied mathematics, wireless communications and networking, solar physics, advanced engineered particulate materials, nanotechnology, neural engineering and eLearning. In 2006, Princeton Review named NJIT among the nation's top 25 campuses for technology recognizing the university's tradition of research and learning at the edge in knowledge. NJIT mathematician and geometry expert lauded for work, including notable publications 
July 02, 2006
Prof. Dzinotyiwei joins Tsvangirai MDCBy Lance Guma The president of the Zimbabwe Integrated Programme (ZIP) Professor Heneri Dzinotyiwei has decided to join the Tsvangirai led MDC. The renowned mathematician made the announcement Wednesday and says his decision has been influenced by the clear link between the country's economic decline and its political policies. He told Newsreel, 'Many of us have been concerned largely with the economic decline…those who have been making efforts towards meaningful change have realized that no progress can be made if the political side is not supportive.' He says this has left him with no choice but to concentrate on the political side of Zimbabwe's problems. Asked why he chose Tsvangirai's side of the MDC divide, Dzinotyiwei says as far as he is concerned the differences in the MDC exist at leadership level and not within its general membership. He says many of its members have kept the structures intact at both branch and provincial levels. 'Ordinary members want focus on programmes for change and the differences are not expected to last,' Dzinotyiwei said. The University of Zimbabwe lecturer has been one of the country's most prominent political analysts and under his political party ZIP made attempts to influence an integrated approach to the country's politics. He says ZIP has not folded up but is now operating as a think tank and continues to advocate integration as a basis for governance. Meanwhile MDC spokesman Nelson Chamisa says they welcomed Dzinotyiwei into the fold. He told Newsreel 'the democratic train had sufficient space for all progressive forces and individuals in the country,' and that Dinotyiwei was one such individual. He described him as one of Africa's finest mathematicians and that his entry into the MDC will add weight to the party and increase its momentum towards confronting Mugabe's regime. Prof. Dzinotyiwei joins Tsvangirai MDC 
July 02, 2006
Math Lessons Get a Makeover: New Tools Spark Student Interest, Achievement in MathematicsTroy, N.Y.— A researcher at Rensselaer Polytechnic Institute has uncovered mathematics embedded in the designs of various aspects of native and contemporary culture, from traditional beadwork and basket weaving to modern hairstyles and music. Using the discovery, he's developed a series of interactive, Webbased teaching tools that are capturing the interest – and imagination – of students in math classes across the country.
Two qualitative evaluations conducted by teachers of predominately Latin American students found a statistically significant improvement in the mathematics performance scores of students using the CSDTs, compared to the achievement of students in classes where the tools were not used as a teaching aid. "Making realworld connections – especially connections that tie in students' heritage cultures – in math instruction has been recognized as increasingly important by educators. Culturally situated design tools provide a flexible space to do that, allowing students to reconfigure their relationship between culture, mathematics, and technology," said Eglash. "By challenging students to recreate a set of goal images or to construct their own shapes and designs, the tools give them a handson opportunity to explore and manipulate standard curriculum math concepts such as transformational geometry, scaling, Cartesian coordinates, and fractions, while connecting those concepts to their heritage as well as contemporary culture." The Fractal Factor In 1999, Eglash discovered that fractal geometry – the geometry of similar shapes repeated on evershrinking scales – is apparent in the designs of many cultures on the continent of Africa, revealing that traditional African mathematics may be much more complicated than previously thought. He documented fractal patterns in cornrow hairstyles, weavings, and the architecture of villages, as well as many forms of African art. Working with math teachers on ways to use this discovery to get African American students interested in the subject of math, Eglash began focusing on the geometry of cornrow hairstyles as a way to connect with popular culture. He developed his first CSDT, Cornrow Curves, which allows student to learn transformational geometry and iteration while they create simulated cornrow designs on the computer. Cornrow Curves was followed by a CSDT that focused on scaling iteration in the traditional ivory sculptures of Africa's Mangbetu people. "After students completed the Cornrow Curves and Mangbetu software experience, we asked them why they thought they were able to use iterative scaling for both simulations," said Eglash. "They quickly answered that it was because both designs were derived from African origins, an indication that math and computers have now become a potential bridge to their cultural heritage, rather than a barrier against it for these students." Additional CSDTs include Virtual Bead Loom (one of six programs focused on Native American culture), based on the geometric patterns present in ShosoneBannock beadwork, and Rhythm Wheels (one of two Latin Americangeared programs), which focuses on the concept of identifying the least common denominator between fractions. All of Ron Eglash's culturally situated design tools can be found and used – free of charge – on his Web site: www.rpi.edu/~eglash/csdt.html. Each CSDT program includes a tutorial, and a cultural background section explaining the social context of the practice as well as its underlying mathematics. Testing materials, ideas for assignment and student evaluation, and examples of student work also accompany each design tool. Eglash's research was funded by three federal grants: a U.S. Housing and Urban Development (HUD) Community Outreach Partnership Centers (COPC) grant, a Department of Education Fund for the Improvement of Postsecondary Education (FIPSE) grant, and a National Science Foundation (NSF) IT Workforce (ITWF) grant. The paper, titled "Culturally Situated Design Tools: Ethnocomputing from Field Site to Classroom," can be found on pages 347362 in Volume 108, Issue 2, of American Anthropologist.
About Rensselaer

July 02, 2006
Springer author wins the Alfried Krupp Science PrizeEberhard Zeidler awarded the prize for his life's work
The Alfried Krupp von Bohlen und Halbach Foundation was set up after the last direct descendant of the Krupp family, Arndt von Bohlen und Halbach, rejected his inheritance. The Alfried Krupp Science Prize is awarded every two years in recognition of outstanding research achievements in the field of natural sciences, engineering, the humanities, law and economics. 
July 02, 2006
Of Biocultural Mathematics and MindReflections On and Around The Origin and Evolution of Cultures by Robert Boyd and Peter J. Richerson. New York: Oxford University Press, 2005. Charles J. Lumsden, Room 7313, Medical Science Building, University of Toronto, 1 King's College Circle, Toronto, Ontario, Canada M5S 1A8. My comments on and around this fine book proceed from three basic premises. If you do not share them, be advised there is little to follow that you will find reassuring or informative, except perhaps as filler for a void in chat when you're next together with associates who, like yourself, also have little use for evolutionary science, mathematics, and their connections. So please be warned. Time is precious; I have no interest in wasting yours. My first premise is that evolution, including the biological, genetic evolution of our human species, is a fact. Thus, what follows is not a defense of evolutionary thinking and why it is important in coming to terms with human beings and the societies they form. Nor is it an argument against the alleged attacks on evolutionary science by people with beliefs attributing human origins to divine intervention or to the actions on our universe of beings identical to (or, for us, indistinguishable from) gods. If you are of the former school and find surprising the assertion that humans, like all life on Earth, are evolved organic beings, then as far as I am concerned you have either been asleep the past century or cast away on a very remote island. If you adhere to the latter belief system and see the proper understanding of humankind as a matter for priests rather than scientists, then you have my respect, and my best wishes for a life good to yourself and others. But you will find little of value in what follows. The fact of human evolution (taken here as selfevident) is of course not the same as the understanding of how that evolution occurred (still a scientific mystery, largely unexplained), It is also not the same as knowing why this evolution occurred the way it did over the millions of years needed to transform our hominid ancestors into us, rather than taking place some other possible way. Scientific conjectures about how human evolution occurs, and why our branch of the hominid evolution tree flourished while those nearby withered, have always attracted plenty of attention. Human beings find themselves interesting. Since the ratio of conjectures to hard data has traditionally been quite high, the debate surrounding these conjectures has gone on for a long time. Polarizing this range of conjectures has been the importance of evolved biological (read "genetic") elements in understanding human nature. One extreme position sees genetic change nudging the bodies, brains, and minds of ancestral hominids over an evolutionary threshold, into human form, and then "switching off" as cultural innovation and social evolution took over. Another extreme sees in the data a densely innate pattern of biologically evolved drives and needs wired into the brain right up to the present day, a stone age genetic strait jacket from which we cannot escape. If you are not a fan of simple alternatives, you can pick a comfortable spot somewhere between these two extremes and wait for more data to roll in. Thirty years ago last year, the eminent Harvard evolutionary biologist Edward O. Wilson took a profoundly more subtle and complex approach to the question of behavior and psyche in human beings and, indeed, in all social animals. In a pair of landmark books  Sociobiology: The New Synthesis (1975) and On Human Nature (1978)  Wilson explored the diverse literatures bearing on human history, psychology, and social life, concluding that Darwinian genetic evolution cannot be ignored if we are to grasp what made us human. The whirl of controversy which quickly enveloped the human sciences in answer to Wilson's books is itself the focus of a growing literature (Segerstråle, 2000). For our purposes here, suffice it to say that by the late 1970s, genes, Darwin, and Darwinian evolution were part of a new agenda for understanding the history and psychology of human beings  an agenda to which the subsequent rise of the Human Genome Project and the field of evolutionary developmental genetics ("evodevo": Carroll, Grenier, and Weatherbee, 2005; Davidson, 2006) has added impressive empirical depth. The new agenda also marked a time of striking innovation in the way evolutionary hypotheses about human nature were expressed and investigated. This brings us to my second premise, which is that in understanding the evolution of human nature, mathematics matters. That is, we must explore the exciting possibility that explanations of human mental organization, social dynamics, and evolution are irreducibly mathematical in form: that the truth about us is encoded in a mathematics, albeit one with properties still largely undiscovered. Please note that my second premise is not that mathematics is essential. The premise is that, given the enormous effectiveness of mathematical reasoning in other sciences, we should find out whether or not it is the best way to talk about the human mind, culture, and history. A premise assigning high priority to mathematics is not, I think, horridly provocative or controversial in itself, at least not any more. Mathematics is everywhere. Perhaps we should thank our currency economies, with all their acounting. Any disinterested student who has yawned through an introductory economics course has seen the curves of supply and demand intersect at their optimal attractor point. In the areas of serious research, mathematical models and equations have been studied in psychology, sociology, and anthropology throughout the twentieth century (Ball, 2004; Epstein and Axtell, 1996; Fararo, 1978; Hamlin, Jacobsen, and Miller, 1973; and Rashevsky, 1951 provide a small sampling). Even literary theorists are using nonlinear attractors and chaotic dynamics (e.g. Hayles, 1990). Within evolutionary science, population biology and genetics have received extensive mathematical development over the past century, first in the hands of pioneers like J. B. S. Haldane, Ronald Fisher, and Sewall Wright, then with the axiomatics of the neoDarwinian synthesis, and most recently with the mathematics of biocultural evolution.. Certainly, the priority of mathematics in getting to the bottom of things in physics, chemistry, and engineering, has been evident for centuries. Try building a television set or airliner without it. So by the late 1970s, mathematics was "in the air" across the natural and social sciences. You'll note a missing link, however: a system of mathematical reasoning that would connect the human sciences not just within themselves, but also crossbridge them to the mathematical structures of the biological/evolutionary sciences and, beyond that, to the rest of the physical and natural sciences as well. Stimulated in part by Wilson's sociobiology controversy, the search was on for such connections and their ability to predict testable outcomes about human psychological and social evolution. From time to time new science seems to be the province of the great solitaries, thinkers who, like the White Whale, somehow slip beneath the surface of existence and penetrate deep into reality, far below the realm accessible to the rest of us: Newton, Darwin, Einstein, Hamilton, Goodall. At other times, it seems to belong to huge teams of investigators, such as those whose dedication drives the mapping of whole genomes at the molecular biology institutes or of the world of elementary particles at the giant accelerator labs. Sometimes, though, good things seem to come in (or through) pairs: Louis and Mary Leakey for example, or the brothers Wright, or Watson and Crick, or Cousteau and Gagnan. For reasons still to be unraveled by historians of science, the mathematical explorations of human biological evolution, cultural evolution, and social history born of those controversies and opportunities of the late 1970s took shape in the work of several pairs of scholars: Ed Wilson and myself (1981) writing from a sociobiological perspective, Luigi CavalliSforza and Marc Feldman (1981) from the standpoint of social networks, Robert Boyd and Peter Richerson (1985) from the direction of population biology and cultural transmission, and Leda Cosmides and John Tooby (1989) from the vantage of axiomatic evolutionary psychology. The books by Ed Wilson and me, and by CavalliSforza and Feldman, appeared first in the early progression, in 1981. Wilson and I, introducing the term geneculture coevolution perhaps for the first time, took a mathematical approach to human genes, minds, and culture anchored in developmental psychology. CavalliSforza and Feldman, for their part, mapped the remarkable effects exerted by the directions of information transmission through social networks treated as mathematical patterns. With their work the adjectives horizontal, vertical, and oblique took on new meaning and significance for evolutionary biologists. Boyd and Richerson's (BR hereafter) influential monograph followed several years later, in 1985, and they have continued with studies that steadily deepened our understanding of the strengths, and limitations of simple mathematical models as probes of human evolution. In the present book, Boyd and Richerson provide a much needed compilation of key papers marking this further development of their approach. The assembled publications span a period of almost fifteen years, from 1989 through 2003. Each is given its own chapter, for a total of twenty chapters. The set is headed by a concise but wideranging introduction that summarizes the history of their collaboration and their progress in this exciting field, along with the core propositions around which their mathematical models are organized. Scholars new to mathematical modeling are right to wonder if the method's abstract beauties also have meaningful content. Nature seems exuberantly complex; the mathematical models are deliberately simple. Where's the matchup? The standard apologies offered in the face of such justifiable skepticism are relevant to appreciating the importance of books like this one, as well as the literature of which it is a part. So it makes sense to touch on them briefly here. Indeed, a flip through the book under review reveals more than a few formulas and equations, some rather thickly laid onto the pages. The casual browser who normally spends her time dissecting Chaucer or tracing Fellini's source material might ask if a close reading of this book is worth the time, given all the maths and graphs and charts. It is worth it. The text is well accessible despite the technical nature of its mathematical approach. In the main body of each chapter, equations are used when essential and their terminology is presented in a logical manner and tied directly to the biocultural problem. Although the cadence from time to time favors the applied mathematician, for the most part detailed math is kept in technical appendices. Since the works assembled, as we shall see in a moment, cover a wide range of topics in biocultural science, the reader is at liberty to sample the chapters or chapter sections as personal interest dictates. There is no need to slog through from first chapter to last, initial equation to final. The sequence chosen for the chapters, however, very nicely showcases the progression of BR's ideas and modeling strategy over the years. The structure of the volume therefore will benefit both the general reader as well as the specialist or the student wishing a strong technical introduction to their methods. The closer reading will, however, give certain pause, because the equations BR deploy seem strikingly simplistic, at least to a postmodern eye keyed to deeply subtle phenomena of mind and culture. In this book, culture's dense forest of symbols (Turner, 1967) has faded into a thin shimmer of "replicators" housed in formulas bearing abstractions like "frequencies," "adaptive character," and so on. To dismiss such fare as pale beer would, however, be to overlook the astonishing impact simple mathematical readings of Nature have effected, right across the sciences. Philosophers may from time to time moan and groan, but simple works. Sometimes. The first apology as to why, when it comes to human nature and history, simple mathematical models are worthwhile makes slight extension of the appeal to mathematical beauty. It notes that by taking a mathematical approach, we are forced to clarify our thinking to the point at which specific mathematical terms can be defined and arranged into formulas that connect logically one to another, and to the reasoning apparatus of mathematics as a whole. That may not sound like much, but in practice such formalization (as it is called) helps throw fuzzy thinking about mind and culture into harsh relief, along with the lexical bafflegab and ideative twaddle such thinking comes packaged in. This is not to say suspect notions (memes? culturgens?) cannot be hidden under the mathematical bush  indeed they can be  but the axiomatic structure of math spreads the branches of the bush more thinly than otherwise, making the bafflegab tougher to keep out of sight. The second apology is an appeal to that scientific favorite, "simpler first." Experimental science uses more or less the same apology, pointing out the virtues of tightly controlled arrangements in which the normal flux of reality is confined to just a few independent variables. Correlations can then be monitored, null hypotheses maybe rejected. In mathematical modeling, it also makes sense to begin with axiomatic bindings among a few variables suspected to be crucial in the relationship of cause to effect. Thus, compared to the real developing human mind or evolving culture, the mathematical model is a stripped down representation. But so, by deliberate intent, is what happens in the experimental laboratory  again, not an unfamiliar scenario. The goal, of course, is to strip away only the inessential, keeping the gist in a mathematical model with helpful properties, and perhaps even leading to deep insights. The evolutionary theorists of the past century  Haldane, Fisher, Wright, Crow, Kimura, Maynard Smith, Hamilton  racked up impressive gains following this path. It is a cognitive strategy that is not confined to mathematical or experimental science, but suggestive of the informed workings of our everyday attention. In learning to drive a car, for example, we are well advised to concentrate on our control inputs and the rules of the road, not on the color of our roadster's paint job or the metallurgy of its engine block. In this apology the mathematical model is not the whole truth, nor is it nothing but the truth. The gist expressed by its few formal terms is intended as a telling caricature. Many mathematical models, including those studied in the book, are offered in this spirit. Indeed, in their Chapter 19, entitled "Simple models of complex phenomena: The case of cultural evolution" BR wrestle with the problem from a stance quite similar to the one I've outlined in the preceding paragraph. They introduce some specialized terminology ("generalized sample theories," "modularization of analysis") to help make the point, but if I read them at all accurately it boils down to "go for the gist." A third apology for why apparently simple math models can work very well is more abstruse and less familiar, but also of potentially deep significance. It is the appeal to socalled universality and so far has been worked mostly within the physical sciences and by physical scientists who are interested in complex biological systems. Universality is a bold epistemic position on the organization of nature in relation to mathematics, including human nature and biosocial evolution. Essentially, a universality hypothesis says the world is organized into categories or classes in which apparently simple and apparently complex phenomena belong together. They do so because, deep down, they all follow identically the same simple mathematical rules, at least in certain key conditions, despite their differences in apparent complexity. Notice how different this apology for math is, compared to the natural appeal of "simplest first" as outlined above: under universality, the parsimonious mathematical formulation is not a first, crude caricature of a more subtle, intricate reality. It is the exact formal description of that reality, shared identically by the simple mathematical model and the actual, realworld system. The discovery, for example, that real geneculture coevolution (GCC for now) works in exactly the same way as the hugely simple GCC mathematical models studied to date would be an example of universality in action. I'm not aware of any such universality proof or measurement for human GCC models as yet, but there is already some hint of the idea's potential relevance. For example, Geoff Clarke and I (2005a,b) have recently found signs of universality in the developmental mathematics of cell death in neural cell populations in the brain and peripheral nervous system, across a range of species and diverse developmental conditions. A fourth apology for mathematics, the appeal to vulgar reductionism, merits a quick look. In using the term "vulgar" I show my age as a child of the 1960s and 70s, perhaps, but my purpose in doing so is as follows. A science of GCC must connect events of diverse kinds: signaling among genes drives neurogenesis which sculpts nerve cell circuits that are shaped by experience that responds to cultural setting that influences survival, reproduction, artifact production, and so on. Mathematical treatments of GCC are therefore "consilient" (Wilson, 1998) or "holistic" (Lumsden, 1997) insofar as such diverse elements draw together into meaningful patterns. These connections are not "vulgar reductionism" (VR). VR is the claim that notions like cognition or the collapse of a civilization are of no scientific merit, and should be cast out. To VR they are epiphenomena, nothing but fuzzy minded standins for the molecules comprising the creatures and ecosystems. VR wants explanations via the molecules and atoms. A VR modeler might insist that mathematics is the optimal language of GCC because, to explain biocultural evolution scientifically, we just need get all the right DNA molecule data etc. into the biggest computer and solve the molecular equations. Then absolutely everything can be predicted, completely and rigorously, through those solutions. A point of view like VR seems far fetched because we really do not have computers this powerful, or databases of information so complete that we can write down all of the molecules in a nerve cell or a collapsing civilization. Given the pace of advance in computer engineering and the empirical mapping of cells and tissues in molecular terms, however, it might not be outlandlish to contemplate a day when we do have this much information and so undertake simulations of this kind. I think, therefore, that appeals to current empirical ignorance will not quite do in seeing what is really wrong with VR as a context for the mathematics (or anything else). For, even if successful, a VR simulation succeeds only in tracking the molecules. Watching only molecules, it has nothing to say about us in terms of cells, brains, humans, or cultures. I take it as uncontroversial, however, to say in present company that science is about understanding as well as prediction. If so, then we have no reason to suspect that making sense of human nature and its evolution is possible (for brains and minds like ours) with a sciencespeak in which the vocabulary is just molecules or elementary particles. Cells, brains, humans, and cultures are pivotal way points in our consilient map of human science. We don't want to get rid of them in favor of molecules or quarks. The only thing a VR model and simulation can show us in GCC is that nonrelativistic quantum mechanics is an accurate theory of molecules under the conditions prevailing on the surface of our planet. This we already know, however, to enormous accuracy, from physics itself. The authors of this important book rightly ignore VR, as do all practitioners of GCC mathematics of whose work I'm aware. The one possible exception is Roger Penrose's hotly debated conjecture that human consciousness is a noncomputable natural phenomenon (Penrose, 1994). I shall return to this briefly below. The book's twenty chapters are organized into five groups of mathematical applications carried out using simple models: The Evolution of Social Learning (five chapters), Ethnic Groups and Markers (two chapters), Human Cooperation, Reciprocity, and Group Selection (seven chapters), Archaeology and Culture History (three chapters), and Links to Other Disciplines (three chapters). To a reader like myself, who spends a lot of time wondering about mind and culture, all these sections are strikingly useful because of the clarity of their exposition and the potential significance of their results. More general readers, interested in what culture change and biocultural evolution are, and what theories of these phenomena look like, also will find the entire book highly relevant. BR's explanations of the relative likelihood of cultural evolution per se, of social learning as an evolved strategy, and of the novel pathways to cooperation and multilevel evolution open to culturebearing creatures, will deservedly attract further attention now that they are available via this well organized compilation. BR have done us all a favor by using their Introduction to state, and discuss, the propositions at the heart of their work. They are five. Some, such as "Genes and culture coevolve", that "Culture is part of human biology", and that "Culture makes human evolution very different from the evolution of other organisms", will sit happily with a lot of people, including myself. The other propositions less so. Their second one, that culture should be modeled as a Darwinian evolutionary process, strikes me as just a retread of Don Campbell's old "selection/retention" culture change model and an excuse to hide a lot of important questions about the mind inside empty parameters about preference and utility. This may have been best practice at one time, but I think we now need to do better, for reasons I'll get to in a moment. Their first proposition, "Culture is information that people acquire from others by teaching, imitation, and other forms of social learning" really will not do any more either; it just begs the question of what we mean by information, social, learning, acquire and so on in such work. The 1980s attitude of "I knows it when I sees it" does not meet our need for evolutionarymathematical approaches that say more about the interior life of culture and of mind. A little earlier I alluded to Victor Turner's "forest of symbols" when I touched on culture. This sounds like poetry rather than mathematics, but thanks, famously, to Nelson Goodman and his memetic descendants we now have hardnosed theories of symbols. When combined with other recent ideas, it may promise a next stage of major progress in geneculture mathematical studies. Certainly, if I have any complaint at all about this book, it is the purely minor one that RB themselves have little to say  beyond a chaste "there is still much to explain"  about their view of what lies ahead as they review their thirty years of effort in this field. Nevertheless, researchers and students in the human sciences, sociobiology, evolutionary psychology, and GCC research will welcome this book, which compiles and synthesizes results heretofore available only by digging through the scattered specialist literature. The material is important both for what it accomplishes and for all that it leaves undone. Well showcased are merits of simple mathematical models as an aid to exploring specific evolutionary effects in the geneculture linkage. Also on display are the potential limitations of the current mathematical approaches and their underlying premises, but in this Boyd and Richerson do not stand alone. All of us GCC modelers share in them. Changes are needed before there can be a next striking wave of research innovation in this subject. Why is this so? In a nutshell, it is because we GCC modelers have been too content to labor in the shadow of 19th century physics and applied mathematics, and so to fit our needs and conceptions into that axiomatic frame, instead of building one that fits geneculture coevolution and evolutionary psychology ab initio. A first step, by means of old frameworks well proven in terms of prior applications, is reasonable. But after a quartercentury the big questions about the evolution of mind and culture are as elusive as ever, and new mathematical frameworks are needed. Admittedly, it is in part better math allowing better experimental measurement and testing of the models. But only in part: The deductions of CavalliSforza and Feldman about the respective roles of horizontal, oblique, and vertical meme transmission routes, the inferences of Lumsden and Wilson about the amplification of developmental genetic changes into shifts of largescale cultural patterns, the conclusions of Boyd and Richerson about the evolution of cooperation and cultural group selection in biocultural populations  these are examples of predictions stimulated by the mathematical work so far. So already there are key inferences about what we should be seeing in the human mind and the biocultural record. For the most part, experimental science has not yet caught up to them. The program of Cosmides, Tooby, and their colleagues is an outstanding example of the progress that can be achieved in evolutionary psychology when formal models and experiment are in synch. The need for predictions is not the driving force for radical progress in GCC mathematics. The force I see is internal to the subject itself, given what we (want to) know about human nature. Evolution is about change, and in the mathematical language of approaches to date, change is about "dynamics," i.e. the solution of differential equations or their ilk that make up the "equations of motion" for the evolutionary process. BR are fond of discrete timestep equations for the dynamics in their models, rather than the continuous axis of temporal change in differential equations, but the point is the same: discrete or continuous, deterministic or stochastic, we want the equations of motion; they are our Rosetta Stone for translating the pattern of evolutionary forces into predictions of the evolutionary path the population tracks, in response to those forces. So far so good, but then we turn to the kinds of mathematical arenas, invented between the time of Newton and the time of Einstein, used to represent this evolutionary change. By and large these arenas are sets of elements, each element representing or "marking" a possible state of the evolving system. Usually the elements are labeled with numbers, or strings of numbers, that demarcate them quantitatively. The equations of motion specify the rates (or something similar) at which any one state gives way to others accessible from it, and so on through each moment of time in the evolutionary progression. The set of elements often has a metric, or natural measure of distance, associated with it, which allows us to say when a state has changed a little or a lot, and by how much. When suitably posed, the metric can be read as equipping the set of elements with geometric properties. These properties are intrinsic to the evolutionary change and can be freed from the arbitrary manner in which we might map, or link, the state elements to their numerical indices. It is then natural to think of such a set, equipped with a natural geometry, as a "space" of "points," each point marking a state, and of the evolutionary change as tracing out a path or trajectory though this space. So, for example, a state element or point represents a population in which the frequency of a gene variant has a specific value and that of a meme variant also has a specific value. Points with slightly different frequency values are nearby in the space. The equations of motion connect the points in an axiomatic game of "jointhedots," to predict which point will follow which as the population evolves. A glance in any textbook about mathematical population genetics, ecology, or neural network theory, for instance, will reveal endless content based on this general point of view. Equations tracing evolutionary paths down to quantitative precision sounds pretty good, and indeed they certainly are not bad. Equations of motion on such spaces are made from the getgo for being solved, at least in approximate numerical terms. The solutions are therefore quantitative predictions about what happens as the evolutionary process unfolds. Deterministic and probabilistic changes can be handled, as can discrete as well as continuous alterations. No sweat. The predictions either are confirmed by experiment, or not, so such models are not flybynight stories that can elude scientific scrutiny by, chameleonlike, switching their intended meaning at the last minute. But let's take a closer look. Tagged to each of those state points is a number or a set of numbers. Numbers are good when we want to count things, and points are good when we have reason to believe the states of our system reduce to geometric singularities. Sometimes we do want to count things  the number of variants of a kind of gene variant (sickle cell or not?) or meme (conservative or liberal today?), for instance, or of a certain style of clay pot. Without doubt this is the kind of "actuarial" dynamics in which GCC mathematics has excelled since the early 1980s monographs by Lumsden and Wilson (1981) and CavalliSforza and Feldman (1981). It fills the BR book from cover to cover. At other times, however, we might want to do more than count pots. Psychologists in particular, I think, need take a guarded view of mathematical models framed as state changes over spaces of numerically labeled points. Why? As I see it, we cannot have an adequate mathematics of geneculture coevolution without an adequate mathematics of behavior. How could we, since to feign otherwise would merely be to sweep the effects of learning, choice, and decision into "preference functions" that simply hide behavior inside some innocent looking mathematical parameters? Similarly for culture, whatever that esoteric thing finally turns out to be in mathematical terms. In the psychological part of the problem we need mathematical constructs that express specific conditions of the evolved embodied mind. It may prove ill advised to squeeze such a representation down to a single number or number string. To see what I am getting at here, let us do a short experimental run, in which you gather data on my current mood and on one or more items in my store of declarative knowledge. In Run 1 you get the mood data first and then the declarative item, while in Run 2 you get the declarative item first and then the mood item. Run 1: if you ask me how I feel just now, I'll report the positive feelings allied to the pleasant task our Editor has set me in composing this essay on and around an excellent book. If you then ask me what is the size of the tumor now growing in my kidney, I'll tell you suchandsuch a diameter based on my recent medical imaging scans. So you get the positive mood datum and the tumor size datum. Run 2: We reverse the order of the queries. You ask me about the tumor size first and get the same number as in Run 1. But now I am thinking about the tumor and likely to start ruminating on the future, so when you ask me about my mood you will get a more somber report than in Run 1. Bottom line: the order in which you have made observations matters. From the standpoint of mathematical theory there is a lot going on in a thought experiment like this, which it is well beyond the scope of this assignment to unpack. I think, however, that in part such considerations are telling us that the algebra of observables, defined over the space of states characterizing mind and culture, does not fully commute. Numbers, and the usual functions of numbers, do commute, so they cannot be the whole mathematical story about us. Other mathematical objects, however, are more suited to the noncommutative job. For example, the netlike structure of a brain circuit or a semantic network or a pattern of cultural meaning has a natural associative pattern, i.e. a netlike pattern in which elements are interconnected. The mathematical objects that quantify such patterns of associative connection are matrices, rather than single numbers. Matrices do not in general commute. Imagine then a biocultural space in which, as we shrink down and zoom in on single states, the view resolves not into the point singularities of current conception, but into mathematical objects perhaps akin to matrices. Mathematicians are exploring such spaces as homes for generalized concepts of our familiar geometric theorems; the next few years will no doubt see their further extensions into human evolutionary science. I for one would find a mathematics of human evolution that shortchanged reason, or passion, or both, quite uninteresting. There is a further troubling feature of these mathematical spaces used to house models of GCC. Once again it descends from the well established needs of the physical and engineering sciences. We saw above that, at each point of the space, there is a number or collection of numbers labeling the state of the system. If we have a hurtling rocket, for example, the numbers might label the missile's current position, its velocity, and its angular heading relative to the fixed stars. Similarly, in an evolving geneculture system the numbers might label the current frequencies of the genes and memes we are tracking. The point is that, once determined by the specifications of the dynamics problem, this list of traits does not change. Consider, however, a society in which there is innovation (the creation of new memes, and the spread of said memes to others in the population; all human cultures have this). From the mathematical point of view, after the innovation event there is something new to be counted and tracked, and it is not in the list of numbers attached to any of the points in the model's evolutionary space. A new equation has suddenly appeared in our list of equations of motion. The mathematical spaces used in current work don't like this. They are built for problems in which the equations of motion do not morph and mutate and jump around. That's okay for the trajectories prescribed by the equations of motion  they can twist and turn  but not for the population of motion equations themselves. This "tight bind of the fixed dimensions" will have to be circumvented if mathematical treatments of geneculture coevolution are to become nontrivial, i.e. if they are to predict what is not already obviously built into the model. Mathematicians and physical theorists have cooked up some interesting possibilities for spaces that don't mind having their dimensions and equations of motion come and go. They have imposing names, like "Fock space" and "superspace," but tend to make use of a trick which makes them of little use to the psychologist who takes creativity, innovation, and other dynamicsbusting traits of human nature seriously: they hide the problem within an infinitude of possibilities worked out in advance by the modeler. This really is of no use at all to us, since one wants a biocultural mathematics with room for the unforeseen and its consequences, i.e., of creativity and innovation. Indeed, I do not think we can score significant further advances in biocultural mathematics unless we create a deep mathematics of mind. What ties genes to culture in human history except the activities of mind? That is, surely, equivalent to saying the GCC problem contains the mind problem, which for our human species contains the problem of consciousness (Cs). What to do about Cs in sociobiology and evolutionary science is beyond the scope of this essay, but I will note I have considered the Cs issue at somewhat more length elsewhere (Lumsden, 2005) and conclude that all is not lost (maybe)  especially if those following a mathematical approach are willing to consider still more general spaces in which the ground symbols stretch past numbers and begin expressing the nature of cultural and mental things. Also in play, of course, is Roger Penrose's unpopular idea about Cs noted above (Penrose, 1994). If I understand Professor Penrose, this is the possibility that Cs may be impervious to any current means of scientific calculation, prediction, or understanding because Cs  at least in its manifestations of creativity and subjective self awareness  entails properties of our Universe currently beyond the ken even of our most up to date quantum theories of nature. Its explanation, Penrose anticipates, will require a revolution in physics, with all the shock waves that may send through the natural and human sciences. Such caveats still fall within the purview of the third premise I promised you earlier. This premise states that geneculture coevolution is compressible, i.e. that it is amenable to explanations more concise than a straight chronicle or full narrative record of all of biocultural history itself. Science, from the point of view championed by this premise, is the art of the highly compressible, in other words of apprehending those parts of existence that can be wrapped up in short explanations. Otherwise, simple explanations of apparently complex things are a contradiction in terms. Physics currently reigns supreme in this regard, having found a mode of mathematical explanation in which the paths of footballs, planets, stars, and galaxies all follow from a few lines of mathematical equations. Indeed, we hear physical scientists talk about the imminent arrival of a "theory of everything," but given my remarks on the downside of vulgar reductionism, we must be prepared for a restrained reading of the term "everything," even if current efforts to blend quantum theory and Einstein's gravitation work out. We have seen above how influential the mathematical tools championed by physical theorists have been in other fields, including the modeling of geneculture coevolution. We have also seen a few of the reasons why GCC may require more than such tools can at present deliver. The human sciences are, I think, absolutely justified in demanding to know why a premise of high compressibility should apply to their subject matter. Just how concise can we get in these disciplines? Are the evolved mind and its geneculture history, or at least their gist, tied up in a few lines of equations? Or are they their own shortest possible explanation? The only straight answer is that, at present, no one yet knows the epistemic compressibility of minds, human evolutionary history, and geneculture coevolution. A long time ago I estimated that the brain and mind are highly incompressible from the gene's point of view (Lumsden and Wilson, 1981), but that is a different story. We are reflecting on the goals of scientific explanation, not on the role hereditary molecules play in development. The mathematician Gregory Chaitin, (1987) has developed an ingenious way of thinking about this problem, which is very helpful here. The idea appears baldly simple but can be shown to have remarkable consequences. In step one of Chaitin's approach, we assess a measure of the size of our original description or depiction of the phenomenon. Let that size be D. In step two, we determine the size of the smallest computer program capable of producing the description D as output. Let that size be P. (In what follows I will also use the symbols D and P to refer to the description and the program themselves, as well as to their sizes.) In the final step we just figure the ratio P/D. If it is considerably less than one, we have distilled D into a very concise computer program (our "model" or "theory" of D) and say that D is highly compressible. We have squeezed it down into a tiny mathematical formulation. If P/D is no different from unity, then our description D is quite incompressible. D is then its own shortest possible explanation. For example, if D is the enormously long string of numbers giving the orbital position of our Moon since first it formed and settled into its path round the Earth, an astronomer could regenerate D with a computer code P containing the concise equations of celestial mechanics. A D like that is highly compressible. For things like the mind and its evolution, however, we must ask if there is any reason to think P/D might be small, and research using simple mathematical models thus motivated. This sounds like a very abstract problem. As a problem asking about mind and culture in general, it certainly is abstract, and no doubt difficult, at least for now. But a specific example, which can readily be generalized, can help us see what is involved in posing such questions in specific terms. For example, I am very attached to Homer's Iliad but, my archaic Greek being what it is, I have a shelf full of English translations, all wellthumbed. Some are more concise than others. The full text of Alexander Pope's rhyming couplets and notes (1996/17151720), for instance, considerably outweighs Stanley Lombardo's (1997) sinewy English vernacular. Where on the shelf of variously sized translations is the "real" Iliad? To streamline the formalities let us take as the Iliad one of the standard editions in Greek (Monro and Allen, 1920, for example) our master translators use in rendering Homer's artistry into English. Such an Iliad is a long poem  almost 16,000 lines by many counts. A glance through my English translations gives, say, roughly ten words per each of these 16,000 lines, for 160,000 words of Homeric action. That's an approximate word count but will do here. Now let those words, in sequence from first to last, be our D, the initial description or cultural object. Since the Iliad is, canonically, a founding text of Western culture, it makes a useful touchstone indeed. Is this D compressible, and so recoverable from a small mathematical model? If it is, then we mean something like the following is true: There exists a mathematical equation FIliad with two properties: If k is a word from the Iliad, i.e. if k is the kth word from D, then FIliad (k) = k + 1, i.e., the next word in the text, for k running from the first word right through to the nextbutlast word of the epic. So the first few steps in using this equation would be (my crude rendering into English): FIliad (Sing) = oh FIliad (oh) = ye FIliad (ye) = Goddess, FIliad (Goddess,) = Rage and so on. FIliad (k) requires far less than 160,000 words to write down. Taken separately, these two criteria are each easy to fulfill. For example, the formula F(k) = k2 + 1 is very concise, but will not generate the Iliad. On the other hand, we could readily devise an exactly accurate FIliad (k) by loading Homer's text into a computer program, then just having the program print out word k + 1 whenever we input word k. This would give us a FIliad all right, but it would be even longer than the original work, not shorter  this "easy" FIliad would contain not only all of the Iliad text D we started with, but the lines of code for printing it out too. So its size P would be even greater than the Iliad's and we would get no compressibility at all. (A strict approach might encourage us also to include the size of the computer's operating system, compiler, printer drivers, and so on in estimating the size of our FIliad, in which case the amount of spare room we are left with to write down a working FIliad is going to be quite tight indeed.) Meeting both criteria at once  completeness and concision  is going to be hard. We can appreciate the magnitude of the task by considering the Iliad against the background space of all possible texts of the same length. My morning paper has reported that the English language is expected to officially assimilate its millionth word by summer or autumn 2006 (Kesterton, 2006; Peritz, 2006). One count currently stands at 986,120 words. Let us take the store of English as an even million, or 106, and go back to D, our 160,000 words of a hypothetical translated Iliad text. Consider again the operation of the mathematical equation FIliad. At each step k for English readers, it must pick out the one "right" word from a million possibilities, and do so 160,000 times in sequence. The possibilities grow very big very fast. If there are 106 options at each step k, then there are (106)160,000 ~ 101,000,000 alternative texts 160,000 words long in a language of a million words, ignoring the niceties of punctuation and whatnot. FIliad must zero in on the one matching D. Even at the first word (Sing, in my take above), there are a million possible choices for where to go next, then a million beyond each of those million choices, and so on. The psycholinguists could trim the size of this space by imposing constraints of grammatical structure, but many alternatives would remain. How big is 101,000,000? It's big compared to what physical (as opposed to cultural) nature presents us. The Universe is roughly 15 billion years, or 5 ´ 1016 seconds, old. The Planck time  considered by some cosmologists as the increment below which time's passage becomes quantumdiscrete rather than a continuous flow  is some 1043 seconds. So roughly 1060 steps of Planck time (all the time there has been thus far) have elapsed since the Big Bang. That number is essentially zero when compared to numerical behemoths like 101,000,000. These kinds of number games can of course be taken too far. The intent of the above is to give us some appreciation of the magnitude of the cultural diversity lingering behind objects like the Iliad, apparent to us once we start putting the issue in mathematical terms. This in turn allows us to appreciate the targeting precision needed from mathematical models FIliad as they regenerate D from their equation P. It is quite clear, however, that targeting is not the issue in itself. Take the F(k) = k2 + 1 equation we dealt with above. Give it a real number k to start, and this little formula will happily pick exactly the right subsequent value (i.e., k2 + 1) from the continuum of the real number line. That continuum holds a range of options (of magnitude c, the cardinality of the real numbers) that dwarfs magnitudes like 101,000,000, but our little F(k) selects the right trajectory each and every time we give it the starting k. The real issue whether a fully accurate equation F(k) = FIliad(k) can have P >> D to boot. Let us think about this in psychological terms. Since FIliad essentially "authors" the Iliad once we feed it the initial prompt "Sing," we are in effect asking whether an equation describing what went through Homer's mind as he created his 16,000line epic can itself be written down in far less than 16,000 lines of computer code, i.e. in P >> D. The real "Homer" may have been one creative genius or a group of bardic masters spun out over time and place, but the point about compressibility stands regardless. In fact the Iliad as our example D is all the more interesting in this regard, since its origins in an oral culture of bardic performance suggest the existence of a FIliad(k)Oral  a learnably concise set of rules for composing an Iliad in one's head on the fly, as it were  a folk theory of the Iliad  capable of oral transmission from bard to bard, in contrast to the rote memorization of a 16,000line poem (for which there is very little evidence). The Iliad's many levels of modular organization are commonly thought to be signs of a more concise plan or narrative blueprint anchoring the fully elaborated recitations, each a unique but valid "Iliad." The equation FIliad(k)Oral would stand in contrast to a mathematical equation FIliad(k)Text capable of outputting exactly and fully the complete "official" Iliad text (e.g. Monro and Allen, 1920), which was achieved in a mammoth editorial effort by scholars in the centuries after Homer  and, of course, the fruit of a literate, rather than strictly oral, system of culture transmission. In view of the completeness and precision demanded of FIliad(k)Text (the full exact text) compared to FIliad(k)Oral (a recitation valid to listeners of the time) we would not be surprised if the former equation's length greatly exceeded the latter's, perhaps even compared to the size D of the full text itself. Literate culture, with its received texts, is then radically less compressible, for both learner and for mathematical model, than is oral culture. If Penrose's conjecture is right, the foregoing considerations are not even well posed, since FIliad points to something not computable by any notions of science or mathematics we now have. Theories of geneculture coevolution will then have to await (or help provoke) seismic displacements in mathematical physics. And yet one does not have to believe in the need for such revolutions to doubt the premise that, for mind and culture, high compressibility and the concision of general laws will prevail. Creativity simply may be its own shortest possible description. For example Deep Blue, the famous IBM computer that took on world champion chess grand master Garry Kasparov in 1996 and, in upgraded form, again in 1997 (http://www.research.ibm.com/deepblue/) is reported to have used some 8,000 terms in the evaluation function (its FChess) by which possible next moves on the chess board were evaluated (http://en.wikipedia.org/wiki/Deep_Blue). Deep Blue also had an enormous chess move database and hardware designed especially for generating vast numbers of chess piece positions (some 200,000,000) per second. But let us for simplicity ignore the database and specialized hardware, and just use P ~ 8,000. And yet D, the complete narrative of the battle fought out on the chess board in these games, requires only about 50 short lines per game (see http://www.research.ibm.com/deepblue/watch/html/c.shtml), giving P/D ~ 400 >> 1, i.e. hugely incompressible. Is a game of chess, even a grand master game of chess, more creative than the Iliad, or will the challenges to mathematical science posed by such manifestations of mind and culture be even greater? Until firmer results are available, mathematical models will continue the practical strategy of their experimental counterparts, namely assuming that the simplest conceivable formulations are helpful and then testing them with hard data. It is said that Achilles, Iliadic champion of the Greek invaders, sat in a funk on the Trojan shore, gazing out on the wine dark sea as carnage raged and bronze clad warriors perished in the dunes behind him, the sand red with their blood. Epic history does not report much about what Achilles saw as he looked out, apart from his goddess mother rising from the waves in answer to his prayerful behest. For us, regardless of how the Penrose Conjecture, compressibility lemmas, and new methods play out, it is clear that a small band of very real scholars has established a beachhead on the shores of psychohistory. From this vantage point we can already see that much of the apparatus used in the first assault lies disused or in wreckage, ready to be superceded by new ideas. That seems to me as it should be. Science is about the future, as well as the now and the past (Lumsden, 2004). Boyd and Richerson have been pioneers in grounding biocultural studies as a young but thriving science in which mathematical theory is a partner to empirical discovery. Their book is of permanent value in gauging the view back and in considering what will come in the years ahead. References Ball, P. (2004). Critical mass: how one thing leads to another. New York: Farrar, Straus and Giroux. Boyd, R. and Richerson, P. J. (1985). Culture and the evolutionary process. Chicago: University of Chicago Press. Carroll, S. B., Grenier, J. K. and Weatherbee, S. D. (2005). From DNA to diversity: Molecular genetics and the evolution of animal design. Second edition. Malden, MA: Blackwell Science. CavalliSforza, L. L. and Feldman, M. (1981). Cultural transmission and evolution: A quantitative approach. Princeton, N. J.: Princeton University Press. Chaitin, G. J. (1987). Information, randomness and incompleteness: Papers on algorithmic information theory. Singapore and London: World Scientific. Clarke, G. and Lumsden, C. J. (2005a). Heterogeneous cellular environments modulate onehit neuronal death kinetics. Brain Research Bulletin, 65, 5967. Clarke, G. and Lumsden, C. J. (2005b). Scalefree neurodegeneration: Cellular heterogeneity and the kinetics of neuronal cell death. Journal of Theoretical Biology, 233, 515525. Cosmides, L. (1989). The logic of social exchange: has natural selection shaped how humans reason? Studies with the Wason selection task. Cognition, 31, 187276. Cosmides, L. and Tooby, J. (1989). Evolutionary psychology and the generation of culture, II: a computational theory of social exchange. Ethology and Sociobiology, 10, 5197. Davidson, E. (2006). The regulatory genome: Gene regulatory networks in development and evolution. New York: Academic Press. Epstein, J. M. and Axtell, R. (1996). Growing artificial societies: Social science from the bottom up. Washington, D.C.: The Brookings Institution. Fararo, T. J. (1978). Mathematical sociology: An introduction to the fundamentals. Robert Huntington, N. Y.: E. Krieger Publishing. Hamlin, R. L., Jacobsen, R. B. and Miller. J. L. L. (1973). A mathematical theory of social change. New York: John Wiley and Sons. Hayles, N. K. (1990). Chaos bound: Orderly disorder in contemporary literature and science. Ithaca, N. Y.: Cornell University Press. Kesterton, M. (2006). The millionth word? The Globe and Mail (Toronto, Canada), Wednesday, February 8, 2006, pg. A20. Lombardo, S., Trans. (1997). The Iliad, by Homer. Indianapolis, IN: Hackett. Lumsden, C. J. (1997). Holism and reduction. In C. J. Lumsden, W. A. Brandts, and L. E. H. Trainor (Eds.), Physical theory in biology: Foundations and explorations (pp. 1744). London and Singapore: World Scientific. Lumsden, C. J. (2004). Sociobiology. In G. Adelman and B. H. Smith (Eds.), Encyclopedia of neuroscience. Third edition. (085SociobiologyE.pdf, 085SociobiologyE.html). New York: Elsevier. Lumsden, C. J. (2005). The next synthesis: 25 years of genes, mind, and culture. In C. J. Lumsden and E. O. Wilson, Genes, mind, and culture: The coevolutionary process. 25th Anniversary Edition, (pp. xvlxiii). London and Singapore: World Scientific. Lumsden, C. J. and Wilson, E. O. (1981). Genes, mind and culture: The coevolutionary process. Cambridge, MA: Harvard University Press. Monro, D. B. and Allen, T. W., Eds. (1920). Homeri opera. Vols. I and II. New York: Oxford University Press. Penrose, R. (1994). Shadows of the mind: A search for the missing science of consciousness. New York: Oxford University Press. Peritz, I. (2006). Spreading the (English) word. The Globe and Mail (Toronto, Canada), Saturday, February 11, 2006, pp. A1, A7. Pope, A., transl. (1996/17151720). The Iliad of Homer. S. Shankman (Ed.). New York: Penguin Books. Rashevsky, N. (1951). Mathematical biology of social behavior. Chicago: University of Chicago Press. Segerstråle, U. (2000). Defenders of the truth: the battle for science in the sociobiology debate and beyond. New York: Oxford University Press. Tooby, J., and Cosmides, L. (1989). Evolutionary psychology and the generation of culture, I: Theoretical considerations. Ethology and Sociobiology, 10, 2949. Wilson, E. O. (1975). Sociobiology: The new synthesis. Cambridge, MA: The Belknap Press of Harvard University Press. Wilson, E. O. (1978). On human nature. Cambridge, MA: Harvard University Press. Wilson, E. O. (1998). Consilience: The unity of knowledge. New York: Alfred A. Knopf. Citation Lumsden, C. (2006). Of Biocultural Mathematics and Mind. Evolutionary Psychology, 4:5774. Date of article 30 June 2006 Email Charles Lumsden Links 
July 02, 2006
Ecologie et libéralisme: Deux visions du monde inconciliablesPar Laurent OZON Fondés en 1944 à Bretton Woods aux ÉtatsUnis, la Banque mondiale et le fonds monétaire international (FMI), puis l'Organisation Mondiale du Commerce, l'OMC qui a succédé au GATT en 1996, sont les instruments d'une logique planétaire de développement économique et de libéralisation des échanges voulus par les firmes transnationales. Leur modèle de développement prétend apporter le bienêtre général et le dogme du libéralisme économique qu'elles défendent exalte les vertus du marché sans entraves comme « valeur universelle », et fondement de la démocratie. Or, après plusieurs dizaines d'années de croissance et d'expansion du système technoéconomique occidental, il nous est bien permis d'apprécier ses résultats et en définitive de juger de sa désidérabilité . Pour toute personne lucide, le constat est facile à faire. Edward Goldsmith nous en livre une synthèse qui se passe de commentaires : « Le commerce mondial a été multiplié par onze depuis 1950 et la croissance économique par cinq et pourtant au cours de cette période, il y a eu un accroissement sans précédent de la pauvreté, du chômage, de la désintégration sociale et de la destruction de l'environnement. Il n'y a donc pas de preuve que le commerce ou le développement économique soient d'une grande valeur pour l'humanité..». En cela, rien d'étonnant donc à ce que les valeurs libérales soient, prioritairement à tout autre, la cible des critiques que les écologistes ont adressé à la société. Le but de mon intervention est de vous présenter ce que postulent l'écologie et le libéralisme, à mon sens de façon inconciliable, à l'heure où certains politiciens prétendent éclairer les électeurs sur leur démarche en se réclamant de l'une et de l'autre. Le libéralisme n'est pas simplement une conception du monde reposant sur une valorisation de la liberté sous toutes ses formes (économique, politique, morale ou religieuse). Cette définition dont certains libéraux peuvent user pour définir leur démarche ne nous permettrait en effet pas de comprendre ce qu'est historiquement le libéralisme et ce qui le distinguerait par exemple de l'anarchisme ou du libertarisme, même si, de l'avis de nombreux commentateurs, ces doctrines ne sont pas sans rapports. Pour être bref, nous dirons que le libéralisme est, au même titre que le socialisme, une doctrine de gestion du capitalisme, de la « richesse matérielle» générée par l'activité industrielle. La vulgate libérale qui se ramène aujourd'hui plus prosaïquement en économie à un éloge de la croissance et de la libreentreprise peut se résumer ainsi : Chaque homme en poursuivant librement la satisfaction de son intérêt propre contribue, si tous les autres hommes en ont la même liberté, à la satisfaction de l'intérêt collectif. Pour les libéraux, « la liberté pour l'individu de concourir à son propre bienêtre est la condition nécessaire et suffisante du bienêtre social » c'est ce qu'on appelle la coïncidence naturelle des intérêts. Pour les libéraux, l'individu est intégré à un monde régi par des lois mécaniques et complexes, qui ne doivent directement rien, ni au Dieu chrétien, ni au Cosmos des Anciens. La cause de toute action humaine serait ainsi la recherche de la satisfaction individuelle, et l'activité de l'homme conformément à la recherche de son intérêt reposerait toujours sur un processus de comparaison comptable (exact ou non, conscient ou non) et donc in fine sur un calcul coût  profit. La possibilité d'un calcul économique rationnel reposerait enfin sur la possibilité d'une interprétation objective préalable du résultat des actions humaines en termes d'utilité et impliquerait donc une évaluation mathématique du résultat de ces actions (en fonction du rapport coûtprofit). Pour finir, le Produit National Brut (PNB) mesurant ce que chacun peut, en moyenne, acquérir serait le concept le plus réaliste et le plus pratique pour évaluer le bienêtre collectif. Il en ressortirait alors que « plus le PNB est élevé et plus le bienêtre général est important ». Pour un libéral, l'objectif poursuivi par la société doit être la Croissance du PNB ou du Produit National Net réel par tête d'habitant. Parce que l'organisation de l'économie selon les principes de la libre concurrence des individus (liberté de circulation des biens et des valeurs sans intervention de l'Etat), est , selon lui, la seule qui permette la Croissance du PNB, les politiques qui ont en charge les intérêts de la collectivité doivent prioritairement se donner pour objectif d'assurer une croissance la plus importante possible. Il leur incombe donc de veiller à maintenir la paix sociale, sans laquelle il n'y a pas de liberté économique, tout en se gardant d'intervenir en tant que « agent économique » sur un marché en voie de planétarisation. L'influence des valeurs de la modernité sur la formation épistémologique de la science économique orthodoxe dont le libéralisme est l'émanation est admis par tous ou presque. Le libéralisme est une doctrine qui n'est tout simplement pas pensable sans les valeurs de la modernité. Certains ont même vu à l'instar de Louis DUMONT1 dans l'idéologie économique contemporaine l'incarnation la plus aboutie des valeurs modernes. Le libéralisme prend appui sur un système de valeurs, ce que Thomas KUHN2 a appelé un paradigme, le paradigme moderne, pour partie déjà constitué au XVIIIe siècle, au moment où le philosophe écossais Adam SMITH, fondateur de l'économie politique anglaise fait publier en 1776 son fameux Recherches sur la nature et les causes de la richesse des nations, considéré encore aujourd'hui comme un livremanifeste pour les libéraux . L'écologie comme science apparaît à la fin du XIXe siècle au carrefour de plusieurs disciplines scientifiques (la pédologie, la botanique, l'agrochimie, la phytogéographie et la biologie) de la nécessité d'étudier les espèces vivantes en contexte, c'estàdire sur leur lieu de vie et dans le réseau de liens qui les lient aux autres espèces. Cette méthode sera spontanément adoptée par les scientifiques qui, à partir du XVIIe siècle se lancent dans l'exploration du monde pour étudier et découvrir ce que ne pouvait leur révéler l'étude d'individus isolés dans des espaces artificiels. Il parut clair que cette approche offrait beaucoup plus de potentialités. Elle impliquait que les individus en question étant fortement dépendants de leurs communautés multiples d'appartenance, il n'était possible de comprendre certaines de leurs particularités physiologiques ou comportementales, qu'en les replaçant dans le système naturel de relations complexes au sein duquel ils remplissaient des fonctions particulières et dont ils dépendaient par ailleurs pour leur survie, à savoir leur milieu:, Leur milieu, c'estàdire le contexte le plus approprié pour leur fournir les informations nécessaires à l'adoption d'un comportement conforme à la préservation de leur équilibre. Le mot « Oekologie » sera forgé par le biologiste allemand Ernst HAECKEL (18341919), et utilisé pour la première fois en 1866 dans la première édition de sa Morphologie générale des organismes . Il est formé de deux racines grecques : oïkos et logos, la science. Le mot, « écologie » est construit comme « économie » et dérive comme le note Pascal ACOT3 , « pour une partie, du thème indoeuropéen weik, qui désigne une unité sociale immédiatement supérieure à la maison familiale. Ce thème donna, entre autres, le sanskrit veçah (maison), le latin vicus qui désigne un quartier, et le grec oïkos, l'habitat, la maison ». L'écologie signifie donc littéralement « la science de l'habitat » . Haeckel la définit ainsi : « par écologie, nous entendons la totalité de la science des relations de l'organisme avec l'environnement, comprenant au sens large toutes les conditions d'existence »4. Cette définition constitue encore le fond de la plupart des définitions actuelles de l'écologie scientifique. L'écologie est une science tout entière tournée vers l'étude des relations entre les groupes. On pourrait presque dire que, pour les écologistes, et du point de vue de la priorité donnée dans l'approche de leur objet d'étude : la relation précède l'essence. Victor Émile SHELFORD, pionnier de l'écologie américaine la définira lui comme "la science des communautés" et écrira : « Une étude des rapports d'une seule espèce donnée avec son environnement, qui ne tient pas compte des communautés et, en définitive, des liens avec les phénomènes naturels de son milieu et de sa communauté, ne s'inscrit pas correctement dans le champ de l'écologie »5. Ce seront les théories organicistes de l'américain Frédéric CLÉMENT et plus tard la systémique de Ludwig VON BERTALLANFFY qui fourniront des éléments de compréhension des communautés biotiques, qui seront désormais considérées comme des systèmes vivants. Cette comparaison de la communauté à un organisme biologique sera si bien établie que Daniel SIMBERLOFF la considère comme « le premier paradigme de l'écologie ». C'est en réaction à cette théorie qu'il jugeait excessive que le biologiste Sir Arthur TANSLEY élaborera son concept d'écosystème à savoir « l'ensemble formé par une communauté, son substrat géologique et son environnement atmosphérique. » pour désigner ce qu'il considère lui comme un quasiorganisme. Cette théorie des écosystèmes (ou biorégion) intégrant des règnes différents, sera validée ultérieurement dans les années 20 par les travaux de l'école d'Uppsala fondée par le botaniste suédois EINAR DU RIETZ, grâce à la méthode dite des "aires minima", puis par ceux de l'Ecole de Zurich Montpellier de Josias BRAUNBLANQUET. Après une éclipse d'une cinquantaine d'années, l'organicisme fit un retour en force dans la pensée écologiste grâce aux travaux de James LOVELOCK qui étudiera le caractère autorégulé et autocréateur de la Biosphère dans son fameux livre « l'hypothèse Gaïa », qu'il fera soustitrer « la Terre est un être vivant », et par l'effort de vulgarisation entrepris par le courant culturel écologiste baptisé par le philosophe Norvégien Arne NAESS « Deep Ecology », écologie profonde. A l'opposé de cette approche, les modernes, se représentent la nature de façon mécaniciste. Rompant avec la physique aristotélicienne et organiciste d'un Cosmos, d'une nature ordonnée, hiérarchisée et finalisée, la physique de GALILÉE, mettait en scène un espace infini de masseénergie, mathématisable et géométrisable, une nature obéissant à des lois présentant partout les mêmes propriétés (isotropes) et où la cause déterministe et retardée d'un phénomène est seule efficace (causalistes). Repris par tous les tenants de la modernité occidentale, ce nouveau paradigme scientifique postule, à l'inverse de toute perspective organiciste, que « La nature ne peut s'expliquer que par ellemême et ses lois sont identiques à celles de la mécanique » 6. De plus, pour les libéraux, la seule unité naturelle et originaire est l'individu et c'est en lui que réside toute souveraineté. Il faut qu'il la transfère momentanément à la société pour que celleci puisse s'en prévaloir. L'individu (naturel, premier et principiel) préexiste à la collectivité (artificielle dérivée et conventionnelle) qui n'en est que la simple addition à un moment donné. En conséquence de quoi, l'intérêt de la totalité sociale est  pour les libéraux  secondaire, car constitué de la somme des intérêts particuliers qui la composent. Découlant de l'organicisme, le holisme (du grec holos entier), se fonde sur le constat que « l'organisme vivant est un tout, et que ce tout est plus et autre que la somme de ses parties ». Que l'individu ne peutêtre vraiment compris dans ses aptitudes et ses besoins sans le contexte des communautés et des écosystèmes auxquels il est adapté. Le systémisme écologiste s'inspire des principes dégagés par la théorie des systèmes et la cybernétique et récuse les doctrines atomistes (subordination de l'intérêt collectif aux intérêts individuels) pour lui préférer les doctrines holistes (subordination des intérêts individuels à l'intérêt collectif). Ces points de vue contiennent respectivement une part de vérité lorsqu'ils sont pensés complémentairement. Et, dans ce cadre là, de notre point de vue, l'intérêt individuel est de faire primer l'intérêt général uniquement lorsque celui ci s'identifie aussi à celui de la préservation de l'intégrité de la Biosphère. Pour être clair, le holisme écologiste a ceci de spécifique qu'il considère que l'ensemble à respecter s'étend audelà de la communauté humaine d'appartenance ou d'identification pour s'étendre à la hiérarchie des systèmes vivants, dont l'intégrité est une condition sine qua non de la préservation à terme de l'intérêt collectif. Pour reprendre une sentence du célèbre savant Russe et précurseur de l'écologie Vladimir Ivanovich VERNADSKY « L'homme en tant qu'être vivant est indéfectiblement lié aux phénomènes matériels et énergétiques d'une des enveloppes géologiques de la Terre : la Biosphère. Et il ne peut en être physiquement indépendant un seul instant ». Autres point de divergence entre écologistes et libéraux, leurs visions des lois du monde et les bases de leurs naturalismes. Les écologistes affirment le caractère « coopératif, ordonné et évolutif » de tous les systèmes vivants par opposition à une interprétation strictement « compétitive, aléatoire et non directive » portée par les élites économiques acquises à une interprétation superficielle des travaux de DARWIN. Pour l'écologie, les relations entre les êtres vivants sont essentiellement coopératives et accessoirement compétitives lorsque le système, (la communauté ou l'organisme) parvient à préserver son Homéostase, c'estàdire ses capacités à préserver sa stabilité face aux agressions internes et externes. Cette situation peut changer, et généraliser la compétition et les comportements d'agressions (qu'il faut distinguer de la prédation), lorsque l'ensemble ne parvient plus à faire face aux discontinuités qui le menace. C'est à la généralisation des perturbations sociales et naturelles que nous devons la montée des comportements relevant d'une lutte de tous contre tous, et qui ne sont qu'exceptionnels en situation normale. Cette divergence d'appréciation, de perception de la nature, dominée par, la diversité, l'adaptabilité et la stabilité, pour les écologistes et l'isotropie, le chaos et la compétition pour les libéraux traduit bien, audelà des différences d'opinions et de valeurs, des différences de sensibilité. Différences de sensibilité et donc différences dans l'appréciation des finalités ultimes, pour l'individu, le groupe, la vie ou la matière. Les Anciens à l'instar d'ARISTOTE distinguaient, à côté d'une notion de cause efficace de nature déterministe et se déroulant du passé vers l'avenir, une notion de cause finale, de nature téléologique se déroulant de l'avenir en direction du passé. Comme le note Roberto FONDI10 : « Cette théorie introduisait l'idée selon laquelle les phénomènes naturels ne dépendent pas seulement de causes situées dans le passé, mais aussi de causes situées dans le futur ». Pour nous, l'intentionnalité est la caractéristique essentielle du comportement des êtres vivants. Les organismes vivants sont conçus et se développent « comme s'il leur fallait poursuivre intentionnellement un dessein conscient »11. L'évolution d'un être vivant est téléologique (de telos, le but), c'est à dire orientée vers un but, qui est de prendre une place particulière dans un ensemble dynamique. Il n'est donc pas là par hasard, et ne se développe pas (s'il est sain) de façon aléatoire. Or, d'une façon générale, les libéraux comme les socialistes en tiennent pour ce que Serge LATOUCHE a appelé la métaphysique du progressisme. L'idée de progrès, qui nous l'avons vu l'année dernière, lors de notre premier forum, repose sur une conception linéaire et orientée du temps, sur une interprétation profondément optimiste du mouvement des sciences et des techniques et sur une valorisation intrinsèque de la nouveauté. A cette conception fondamentalement optimiste, les écologistes préfèrent une perception plus réaliste et moins teintée de métaphysique, qui s'inspire d'une autre grande loi du monde, physique cellelà, l'Entropie. L'Entropie désigne le second principe de la thermodynamique né d'un mémoire de Sadi CARNOT amélioré par l'autrichien Rudolf CLAUSIUS, qui s'inspire d'un fait élémentaire : la chaleur s'écoule naturellement du corps le plus chaud au corps le plus froid. Carnot en déduit que, inversement, le passage de la chaleur d'un corps froid à un corps chaud ne peut se faire sans l'intervention d'un travail. La conséquence la plus générale est qu'il y a une dégradation continuelle et irréversible de l'énergie dans n'importe quel système clos. Désignant la mesure de la dissipation ou du désordre, la loi de l'Entropie est aussi l'énoncé général à partir duquel peuvent se comprendre tous les phénomènes de dégradation d'énergie, ainsi que leur caractère irréversible. Nicholas GEORGESCUROEGEN, mathématicien et théoricien d'une bioéconomie, demande, quant à lui, que l'on ne restreigne pas l'entropie au seul domaine de l'énergie, mais qu'on en étende aussi l'application à la matière : car qu'estce que l'usure des matériaux, sinon une forme particulière d'entropie? GeorgescueRoegen publiera en 1973 son livre « La décroissance »13, une analyse thermodynamique appliquée à l'économie et démontrant l'irréversibilité du cycle de transformation des énergies et des matières et donc les limites matérielles de la croissance économique prônée par les libéraux. Le processus économique consistant pour l'essentiel selon lui en un prélèvement de matières à basse entropie dans les stocks de ressources « libres » ou accessibles mais limitées et en un rejet de matière à haute entropie, aggravant ainsi le phénomène de dissipation de ressources indispensables mais nonrenouvelables14. Edward GOLDSMITH, le directeur de la revue The Ecologist, met pour sa part, en doute la viabilité de l'entropie pour rendre compte des lois du vivant15, tout en admettant sa pertinence pour rendre compte des lois physiques de l'inerte. Au regard des lois physiques la vie constitue ainsi un phénomène de boucles syntropiques qui compense temporairement par son « travail », l'inéluctabilité de la dégradation entropique de l'énergie et la matière inerte. Le phénomène vivant est désormais perçu comme une exception, une formidable mais fragile exception dont les caractéristiques contredisent temporairement l'entropie fondamentale de l'énergie et de la matière. La vie, se maintient à l'intérieur d'ensembles organisés et diversifiés en compensant temporairement la mort, l'Entropie, le processus fatal et continuel de dissipation de désorganisation et d'homogénéisation des masseénergies abandonnées par la vie. Précisément, la biosphère, semble, à bien des égards engagée dans un processus dominant menant à une progressive et mortelle entropie sous la pression croissante de l'impact des activités humaines. Les exemples qui en témoignent sont nombreux : La France comptait plus de 4000 espèces de pommes au début du siècle, Il est devenu difficile d'en recenser une centaine et 5 espèces assurent à elles seules 95 % de la consommation. En France, là où étaient répertoriées au XIXe siècles 88 variétés de melons, on n'en trouve plus guère que 5. Jacques Barrau, un ethnobotaniste, écrit, qu'en 1853, les frères Audibert, pépiniéristes provençaux offraient à la vente 28 variétés de figues, alors qu'on n'en trouve plus guère que 2 ou 3 aujourd'hui. On pourrait continuer comme cela durant des heures. Le biocide est aussi à l'oeuvre pour écraser la diversité interspécifique et intraspécifique des communautés humaines. Je pense aux cultures, régionales, locales, en France, mais aussi partout en Europe et dans le monde. Je pense à ces communautés chassées de leurs terres par des projets pharaoniques imposés par les multinationales et leurs relais, en Inde, ou ailleurs. Je pense à ces peuples broyés par la mécanique implacable de la colonisation occidentale : Les indiens guaranis parqués comme du bétail et qui ne survivent plus qu'en louant leurs bras aux industries d'alcool qui les empoisonnent comme avant eux plus de 90% des indiens d'Amazonie ont déjà disparu. Ailleurs, ce sont Les Bushmen chassés de leur territoire pour faire place aux industries touristiques, Les Aborigènes déplacés de leurs terres ancestrales pour y effectuer des essais nucléaires, les paysans en Europe en Afrique ou ailleurs. Pensons encore aux tibétains dont les autorités chinoises organisent méthodiquement le génocide par l'assimilation, l'acculturation et la terreur policière, pendant que le chef de l'Etat français se fait en Chine le VRP d'une industrie qu'il croit encore nationale. Pensons encore aujourd'hui aux indiens Wayampi, Emerillon et Wayanna qui luttent contre la colonisation et la normalisation imposée simultanément par l'état français au nom de la mise en valeur du territoire, les médias au nom du droit à l'information, et des firmes au nom de la liberté du commerce. Car en Guyane dans ce département du bout du monde L'Etat français y poursuit l'occidentalisation et la normalisation des indiens dans la continuité des grands ancêtres qui ont appliqué les méthodes d'assimilation et de destruction des peuples en Bretagne, en Corse, en Alsace, en Provence, au Pays Basque et ailleurs. Le carnet de commande y a remplacé la Bible ou le Code Civil, mais la logique coloniale reste la même. Cette homogénéisation culturelle conduit, précisément, par un significatif phénomène de rétroaction à l'accélération de l'homogénéisation et de la standardisation des paysages. Car les paysages que nous connaissons, en Europe en particulier sont le résultat d'une longue interaction entre les communautés humaines et l'ensemble des autres espèces vivantes qui composent son milieu, comme de la nature de ses sols et de son climat. Et parce que l'homme est un être qui intervient sur son milieu, à la diversité des écosystèmes répond la diversité des cultures et des modes de représentation du monde et rétroactivement, à la diversité des modes de représentations du monde répond la diversité des écosystèmes. Pour le dire autrement, lorsque les hommes vivent, parlent et pensent différemment, ils interviennent différemment sur leurs milieux, et leurs activités peuvent ainsi contribuer à renforcer la typicité d'un paysage. La diversité des cultures participe ainsi de et à la diversité des écosystèmes. En conséquence, dans une vision écologiste qui reconnaît l'humanité comme espèce et comme partie de la nature, la diversité culturelle  et l'organisation spécifique qui lui correspond  sont à la fois une valeur et une nécessité. Aujourd'hui, de nombreux penseurs écologistes défendent bien la thèse selon laquelle, un système, en augmentant sa diversité, élargit la gamme des pressions écologiques auxquelles il est capable de faire face. En un mot que la biodiversité accroît la stabilité d'un système en augmentant ses possibilités d'adaptation aux discontinuités qui le menacent. Nous dirons plutôt que c'est l'accroissement de la complexité (à ne pas comprendre avec la diversité), qui augmente la stabilité du vivant. Même si, évidemment, la diversité des parties d'un ensemble est la condition sine qua non de sa capacité de complexification. Il faut comprendre le terme « complexe » dans son sens étymologique, « ce qui est tissé ensemble » (voir sur ce sujet l'œuvre d'Edgard MORIN17), non pas les parties différentes d'un conglomérat aléatoire, mais les parties ordonnées d'un système vivant. Pour être plus clair, la diversité n'est facteur de stabilité pour les systèmes vivants que si les parties sont complémentaires, homéothéliques c'estàdire de simplement différenciées, deviennent « complexes », organisées en écosystème, à l'intérieur duquel ils remplissent tous une fonction compatible avec la préservation de l'écosystème tout entier. Jean DORST écrivait « Le maintien de la diversité de la nature et des espèces est la première loi de l'écologie »16. Les valeurs modernes postulent quant à elles, un humanisme anthropocentrique, c'estàdire la conception d'un homme à qui son statut d'être rationnel confère une valeur morale rendant ses intérêts moralement plus importants que les intérêts de la nature dans son ensemble. Une nature qui n'est plus perçue que comme ressource tout entière dévolue au bienêtre du genre humain., avec la valeur utilitaire que lui confère ce statut19. Or, les écologistes les plus conséquents portent contre la civilisation universaliste et anthropocentriste occidentale, une critique comparable à celle qui fut adressée aux nationalismes durant le XXe siècle. Cette critique s'articulait autour d'un processus de relativisation des appartenances nationales et ethniques par le dessus, en valorisant l'appartenance zoologique à l'espèce humaine. Et par le dessous en défendant les communautés locales, les petits peuples opprimés par les regroupements et les annexionnismes nationaux. De la même manière les écologistes radicaux relativisent l'appartenance à l'espèce humaine et dénoncent l'attitude spéciste (l'égoïsme d'espèce comparable en tout point au racisme) en rappelant qu'audelà de l'humanité nous appartenons à la communauté biotique planétaire, la Biosphère et que notre solidarité doit s'exercer à l'endroit des animaux, des plantes et de toute vie en général. Cette Biosphère est organisée à la base en communautés peuplant des écosystèmes et nous sommes reliés par notre culture, notre ethnie, ou notre histoire à des communautés intermédiaires, à l'intérieur desquelles notre existence sociale prend une signification. C'est donc dans ses formes d'organisation que nous devons chercher à comprendre, puis respecter et aimer la nature. Non pas de façon abstraite et globale, mais de façon concrète en respectant sa diversité et son organisation. L'écologie postule que tout être vivant mérite le respect moral. Ce postulat contrairement à ce qu'écrit Luc FERRY20, n'implique a priori aucun égalitarisme. Il est compatible avec une attitude différencialiste dans l'esprit de ce qu'écrivait Claude LÉVISTRAUSS, dans son livre Le Regard éloigné en 1983. Ce point de vue consistant à considérer comme normale une attitude de « préférence » ou de survalorisation d'une espèce plutôt qu'une autre, liée à des phénomènes d'identification, d'utilité, de coappartenance ou de rareté. Ce biocentrisme n'est pas incompatible, à la rigueur, avec un humanisme châtié, protégeant l'homme dans sa totalité, non pas seulement comme être pensant, comme être rationnel, mais aussi et d'abord comme être vivant complet, dans toutes ses dimensions, y compris physiques et spirituelles. Ecologie et libéralisme: Deux visions du monde inconciliables 
July 02, 2006
La matematica: fra oppio e linguaggio
Da quasi due mesi a Palazzo Ducale a Genova la gente paga (2 euro) per fare matematica. Sono quasi 2000 le persone che hanno partecipato finora a MateFitness, la Palestra della Matematica. Con l'aiuto di studenti universitarianimatori persone di tutti i generi si sono divertite col «puzzle di Pitagora», con le «fette di torta» di legno per capire le frazioni, con i sudoku e con un altro centinaio di attrazioni matematiche. 
July 02, 2006
What is Intuition?Sam Vaknin, Ph.D.  6/28/2006 I. The Three Intuitions IA. Eidetic Intuitions Intuition is supposed to be a form of direct access. Yet, direct access to what? Does it access directly "intuitions" (abstract objects, akin to numbers or properties  see "Bestowed Existence")? Are intuitions the objects of the mental act of Intuition? Perhaps intuition is the mind's way of interacting directly with Platonic ideals or Phenomenological "essences"? By "directly" I mean without the intellectual mediation of a manipulated symbol system, and without the benefits of inference, observation, experience, or reason. Kant thought that both (Euclidean) space and time are intuited. In other words, he thought that the senses interact with our (transcendental) intuitions to produce synthetic apriori knowledge. The raw data obtained by our senses our sensa or sensory experience  presuppose intuition. One could argue that intuition is independent of our senses. Thus, these intuitions (call them "eidetic intuitions") would not be the result of sensory data, or of calculation, or of the processing and manipulation of same. Kant's "Erscheiung" ("phenomenon", or "appearance" of an object to the senses) is actually a kind of senseintuition later processed by the categories of substance and cause. As opposed to the phenomenon, the "nuomenon" (thing in itself) is not subject to these categories. Descartes' "I (think therefore I) am" is an immediate and indubitable innate intuition from which his metaphysical system is derived. Descartes' work in this respect is reminiscent of Gnosticism in which the intuition of the mystery of the self leads to revelation. Bergson described a kind of instinctual empathic intuition which penetrates objects and persons, identifies with them and, in this way, derives knowledge about the absolutes  "duration" (the essence of all living things) and "élan vital" (the creative life force). He wrote: "(Intuition is an) instinct that has become disinterested, selfconscious, capable of reflecting upon its object and of enlarging it indefinitely." Thus, to him, science (the use of symbols by our intelligence to describe reality) is the falsification of reality. Only art, based on intuition, unhindered by mediating thought, not warped by symbols  provides one with access to reality. Spinoza's and Bergson's intuited knowledge of the world as an interconnected whole is also an "eidetic intuition". Spinoza thought that intuitive knowledge is superior to both empirical (sense) knowledge and scientific (reasoning) knowledge. It unites the mind with the Infinite Being and reveals to it an orderly, holistic, Universe. Friedrich Schleiermacher and Rudolf Otto discussed the religious experience of the "numinous" (God, or the spiritual power) as a kind of intuitive, prelingual, and immediate feeling. Croce distinguished "concept" (representation or classification) from "intuition" (_expression of the individuality of an objet d'art). Aesthetic interest is intuitive. Art, according to Croce and Collingwood, should be mainly concerned with _expression (i.e., with intuition) as an end unto itself, unconcerned with other ends (e.g., expressing certain states of mind). Eidetic intuitions are also similar to "paramartha satya" (the "ultimate truth") in the Madhyamika school of Buddhist thought. The ultimate truth cannot be expressed verbally and is beyond empirical (and illusory) phenomena. Eastern thought (e.g. Zen Buddhism) uses intuition (or experience) to study reality in a nondualistic manner. IB. Emergent Intuitions A second type of intuition is the "emergent intuition". Subjectively, the intuiting person has the impression of a "shortcut" or even a "short circuiting" of his usually linear thought processes often based on trial and error. This type of intuition feels "magical", a quantum leap from premise to conclusion, the parsimonious selection of the useful and the workable from a myriad possibilities. Intuition, in other words, is rather like a dreamlike truncated thought process, the subjective equivalent of a wormhole in Cosmology. It is often preceded by periods of frustration, dead ends, failures, and blind alleys in one's work. Artists  especially performing artists (like musicians)  often describe their interpretation of an artwork (e.g., a musical piece) in terms of this type of intuition. Many mathematicians and physicists (following a kind of Pythagorean tradition) use emergent intuitions in solving general nonlinear equations (by guessing the approximants) or partial differential equations. Henri Poincaret insisted (in a presentation to the Psychological Society of Paris, 1901) that even simple mathematical operations require an "intuition of mathematical order" without which no creativity in mathematics is possible. He described how some of his creative work occurred to him out of the blue and without any preparation, the result of emergent intuitions. These intuitions had "the characteristics of brevity, suddenness and immediate certainty... Most striking at first is this appearance of sudden illumination, a manifest sign of long, unconscious prior work. The role of this unconscious work in mathematical invention appears to me incontestable, and traces of it would be found in other cases where it is less evident." Subjectively, emergent intuitions are indistinguishable from insights. Yet insight is more "cognitive" and structured and concerned with objective learning and knowledge. It is a novel reaction or solution, based on already acquired responses and skills, to new stimuli and challenges. Still, a strong emotional (e.g., aesthetic) correlate usually exists in both insight and emergent intuition. Intuition and insight are strong elements in creativity, the human response to an ever changing environment. They are shock inducers and destabilizers. Their aim is to move the organism from one established equilibrium to the next and thus better prepare it to cope with new possibilities, challenges, and experiences. Both insight and intuition are in the realm of the unconscious, the simple, and the mentally disordered. Hence the great importance of obtaining insights and integrating them in psychoanalysis  an equilibrium altering therapy. IC. Ideal Intuitions The third type of intuition is the "ideal intuition". These are thoughts and feelings that precede any intellectual analysis and underlie it. Moral ideals and rules may be such intuitions (see "Morality  a State of Mind?"). Mathematical and logical axioms and basic rules of inference ("necessary truths") may also turn out to be intuitions. These moral, mathematical, and logical selfevident conventions do not relate to the world. They are elements of the languages we use to describe the world (or of the codes that regulate our conduct in it). It follows that these apriori languages and codes are nothing but the set of our embedded ideal intuitions. As the Rationalists realized, ideal intuitions (a class of undeniable, selfevident truths and principles) can be accessed by our intellect. Rationalism is concerned with intuitions  though only with those intuitions available to reason and intellect. Sometimes, the boundary between intuition and deductive reasoning is blurred as they both yield the same results. Moreover, intuitions can be combined to yield metaphysical or philosophical systems. Descartes applied ideal intuitions (e.g., reason) to his eidetic intuitions to yield his metaphysics. Husserl, Twardowki, even Bolzano did the same in developing the philosophical school of Phenomenology. The apriori nature of intuitions of the first and the third kind led thinkers, such as Adolf Lasson, to associate it with Mysticism. He called it an "intellectual vision" which leads to the "essence of things". Earlier philosophers and theologians labeled the methodical application of intuitions  the "science of the ultimates". Of course, this misses the strong emotional content of mystical experiences. Confucius talked about fulfilling and seeking one's "human nature" (or "ren") as "the Way". This nature is not the result of learning or deliberation. It is innate. It is intuitive and, in turn, produces additional, clear intuitions ("yong") as to right and wrong, productive and destructive, good and evil. The "operation of the natural law" requires that there be no rigid codex, but only constant change guided by the central and harmonious intuition of life. II. Philosophers on Intuition  An Overview IIA. Locke But are intuitions really apriori  or do they develop in response to a relatively stable reality and in interaction with it? Would we have had intuitions in a chaotic, capricious, and utterly unpredictable and disordered universe? Do intuitions emerge to counterbalance surprises? Locke thought that intuition is a learned and cumulative response to sensation. The assumption of innate ideas is unnecessary. The mind is like a blank sheet of paper, filled gradually by experience  by the sum total of observations of external objects and of internal "reflections" (i.e., operations of the mind). Ideas (i.e., what the mind perceives in itself or in immediate objects) are triggered by the qualities of objects. But, despite himself, Locke was also reduced to ideal (innate) intuitions. According to Locke, a colour, for instance, can be either an idea in the mind (i.e., ideal intuition)  or the quality of an object that causes this idea in the mind (i.e., that evokes the ideal intuition). Moreover, his "primary qualities" (qualities shared by all objects) come close to being eidetic intuitions. Locke himself admits that there is no resemblance or correlation between the idea in the mind and the (secondary) qualities that provoked it. Berkeley demolished Locke's preposterous claim that there is such resemblance (or mapping) between PRIMARY qualities and the ideas that they provoke in the mind. It would seem therefore that Locke's "ideas in the mind" are in the mind irrespective and independent of the qualities that produce them. In other words, they are apriori. Locke resorts to abstraction in order to repudiate it. Locke himself talks about "intuitive knowledge". It is when the mind "perceives the agreement or disagreement of two ideas immediately by themselves, without the intervention of any other... the knowledge of our own being we have by intuition... the mind is presently filled with the clear light of it. It is on this intuition that depends all the certainty and evidence of all our knowledge... (Knowledge is the) perception of the connection of and agreement, or disagreement and repugnancy, of any of our ideas." Knowledge is intuitive intellectual perception. Even when demonstrated (and few things, mainly ideas, can be intuited and demonstrated  relations within the physical realm cannot be grasped intuitively), each step in the demonstration is observed intuitionally. Locke's "sensitive knowledge" is also a form of intuition (known as "intuitive cognition" in the Middle Ages). It is the perceived certainty that there exist finite objects outside us. The knowledge of one's existence is an intuition as well. But both these intuitions are judgmental and rely on probabilities. IIB. Hume Hume denied the existence of innate ideas. According to him, all ideas are based either on sense impressions or on simpler ideas. But even Hume accepted that there are propositions known by the pure intellect (as opposed to propositions dependent on sensory input). These deal with the relations between ideas and they are (logically) necessarily true. Even though reason is used in order to prove them  they are independently true all the same because they merely reveal the meaning or information implicit in the definitions of their own terms. These propositions teach us nothing about the nature of things because they are, at bottom, self referential (equivalent to Kant's "analytic propositions"). IIC. Kant According to Kant, our senses acquaint us with the particulars of things and thus provide us with intuitions. The faculty of understanding provided us with useful taxonomies of particulars ("concepts"). Yet, concepts without intuitions were as empty and futile as intuitions without concepts. Perceptions ("phenomena") are the composite of the sensations caused by the perceived objects and the mind's reactions to such sensations ("form"). These reactions are the product of intuition. IID. The Absolute Idealists Schelling suggested a featureless, undifferentiated, union of opposites as the Absolute Ideal. Intellectual intuition entails such a union of opposites (subject and object) and, thus, is immersed and assimilated by the Absolute and becomes as featureless and undifferentiated as the Absolute is. Objective Idealists claimed that we can know ultimate (spiritual) reality by intuition (or thought) independent of the senses (the mystical argument). The mediation of words and symbol systems only distorts the "signal" and inhibits the effective application of one's intuition to the attainment of real, immutable, knowledge. IIE. The Phenomenologists The Phenomenological point of view is that every thing has an invariable and irreducible "essence" ("Eidos", as distinguished from contingent information about the thing). We can grasp this essence only intuitively ("Eidetic Reduction"). This process  of transcending the concrete and reaching for the essential  is independent of facts, concrete objects, or mental constructs. But it is not free from methodology ("free variation"), from factual knowledge, or from ideal intuitions. The Phenomenologist is forced to make the knowledge of facts his point of departure. He then applies a certain methodology (he varies the nature and specifications of the studied object to reveal its essence) which relies entirely on ideal intuitions (such as the rules of logic). Phenomenology, in other words, is an Idealistic form of Rationalism. It applies reason to discover Platonic (Idealism) essences. Like Rationalism, it is not empirical (it is not based on sense data). Actually, it is antiempirical  it "brackets" the concrete and the factual in its attempt to delve beyond appearances and into essences. It calls for the application of intuition (Anschauung) to discover essential insights (Wesenseinsichten). "Phenomenon" in Phenomenology is that which is known by consciousness and in it. Phenomenologists regarded intuition as a "pure", direct, and primitive way of reducing clutter in reality. It is immediate and the basis of a higher level perception. A philosophical system built on intuition would, perforce, be non speculative. Hence, Phenomenology's emphasis on the study of consciousness (and intuition) rather than on the study of (deceiving) reality. It is through "Wesensschau" (the intuition of essences) that one reaches the invariant nature of things (by applying free variation techniques).
Sam Vaknin, Ph.D. is the author of Malignant Self Love  Narcissism Revisited and After the Rain  How the West Lost the East. He served as a columnist for Central Europe Review, PopMatters, Bellaonline, and eBookWeb, a United Press International (UPI) Senior Business Correspondent, and the editor of mental health and Central East Europe categories in The Open Directory and Suite101.
Until recently, he served as the Economic Advisor to the Government of Macedonia. Sam Vaknin's Web site is at http://samvak.tripod.com 
July 02, 2006
PORTRAIT OF THE PSYCHOANALYST AS AN ARTISTDrawings by the late French psychoanalyst Jacques Lacan (19011981) are going under the hammer this week at Paris' Artcurial. As Le Monde's Clarisse Fabre reports, JeanMichel Vappereau—a mathematician and analyst who owns the 130 works, including manuscripts—decided to sell the collection. The profits from the auction—estimated at €450,000 ($566,275)—will be used to purchase an apartment in Paris to serve as a home for Lacan's vast archives. Lacan began to draw in the 1970s with a group of mathematicians in an attempt to solve various enigmas. "A series of graphs, sketched for the most part on A4 sheets of paper, came from this emulation, if not obsession," writes Fabre. The graphs include "chains, braids, circles, Borromean knots (three interlaced rings), drawn with ink or a felttip pen." What would the sale be without a few Oedipal conflicts? As Fabre reports, Lacan's family has opposed the sale. According to Artcurial, the analyst's daughter Judith Miller—also a psychoanalyst—did not allow photographs of her father, published in her book Album Jacques Lacan: Visages de mon père (Jacques Lacan Album: Faces of my Father) (Seuil, 1991), to be used in the catalogue for the Artcurial sale. DAVID WEISS AT SIXTY Die Frankfurter Allgemeine Zeitung's Niklas Maak congratulates David Weiss—one half of the Swiss duo Fischli & Weiss—on his sixtieth birthday. "Without him, [Peter] Fischli is nothing," writes Maak in his admiring assessment of the pair's impact, giving special praise to their film Der Lauf der Dinge (The Way Things Go), which was shown at Documenta 8 in 1987. "Without Lauf der Dinge," notes Maak, "artists like John Bock would surely be doing another type of art today." Born in Zurich in 1946, Weiss started working with Fischli in 1979. For Maak, one of the duo's most memorable efforts involved dressing up for a film as a rat and bear, "a nightmare of the art market circa 1980." At the Venice Biennale in 2003, Fischli & Weiss were honored with the Golden Lion for posing a series of questions, including "Should I leave reality in peace?"; "Is my stupidity a warm coat?"; "Does the dog bark the whole night?"; and—the most pressing—"Does the world also exist without me?" 130,000 FEEL THE "FORCE DE L'ART" "La Force de l'Art"—the controversial exhibition of contemporary French art initiated by French prime minister Dominique de Villepin—has closed its doors on a successful note. As Agence FrancePresse reports, 130,000 people saw the exhibition, which included 350 works produced by 200 French and Francebased artists. Minister of culture Renaud Donnedieu de Vabres called the event "a popular success," especially for a public unfamiliar with contemporary art. But the "Force" is far from over. Donnedieu de Vabres announced that he will appoint a team to organize a second edition of the exhibition, which is now destined to become a triennial for Paris. According to the minister, the team for the next "Force"—slated for 2009—would be finalized by the beginning of September. According to AFP, the "Force" pales in comparison to the Musée du Quai Branly, the new ethnographic museum that just opened its doors across the Seine. In the first three days, Quai Branly welcomed 28,000 visitors, including the Uranthropologist Claude LéviStrauss, now ninetyeight years old. WALDVOGEL SPEAKS OUT ON MANIFESTA 6 Die Tageszeitung features an interview with Florian Waldvogel, part of the curatorial team for the troubled Manifesta 6, which was slated to take place in the divided city of Nicosia on Cyprus in the fall. Recently, the city and the organization Nicosia for Art (NFA) effectively cancelled the event by relieving Waldvogel, Anton Vidokle, and Mai Abu ElDahab of their curatorial duties. The municipal government and NFA disagreed with the curators' plan to include the northern part of Nicosia—occupied by Turkey since 1974—in the exhibition. Yet according to the curators, their original contract stipulated that the event would take place in both the Greek and Turkish zones of the city. "It was clear to us from the beginning that we did not want to organize another group exhibition on Cyprus," says Waldvogel, "which would reproduce the commercial logic of art tourism. Our idea was to establish a longterm school on both sides of the Green Line." Waldvogel explains that the interdisciplinary school would have buttressed the infrastructure and supported the local artist scene. "From the start, it was important for us to integrate both sides, the Greek and the Turkish, so no one would be left out. We had this ensured in the contract." Does the failure of Manifesta 6 spell the end of Manifesta and its goal to bring contemporary art to new EU member countries? "The Manifesta Foundation must ask itself if its model is still legitimate," said Waldvogel. "I hope this occasion sparks a caesura in the art world and that people will consider the expansion of the concept of art and not only expanding capital markets." Along with these queries, Waldvogel is looking to the International Foundation Manifesta to compensate the travel costs for both artists and curators. When asked if moving Manifesta 6 to another location might indeed be a lastminute option, Waldvogel is not giving any definitive answers. "For me," the curator told the newspaper, "the failure of the project is the project."
—Jennifer Allen
