July 2006
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July 28, 2006

Celebrating Puzzles, in 18,446,744,073,709,551,616 Moves (or So)
Correction Appended
Puzzle 190

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.
Nowhere in the Bible could the church leaders of Salem find a prohibition against puzzles, and in the absence of a "no," they filled the gap with a resounding "yes." At the time, Salem was a center of brisk trade with China, and ship captains would often deliver a wooden chest filled with ivory puzzles as a gift for merchants, what came to be known as "Sunday boxes." A particularly fine example of a Sunday box is one of the centerpieces of a major new exhibition of mechanical puzzles to open next week at the Lilly Library at Indiana University.
The exhibition, which contains many world-class specimens of mathematical and physics-based puzzles, is the first taste of a collection of more than 30,000 puzzles being donated to the library by Jerry Slocum, a retired engineer and a former vice president of Hughes Aircraft, who has been collecting puzzles and researching their history for more than half a century.
Mr. Slocum is the author of 10 books on the history of puzzles, including a recently published account of the sudoku-like 15 Puzzle, which precipitated a puzzle mania across America in the 1880's.
Sitting in his private puzzle museum at his home in Beverly Hills, Calif., Mr. Slocum spoke about the exhibition and the convoluted, puzzlelike stories behind some of the pieces. Around him on shelves stacked from floor to ceiling sat thousands of puzzles of almost every conceivable shape and form: wooden, metal, wire, porcelain, plastic, glass and cardboard. There were Russian puzzle rattles, ancient Chinese puzzle mirrors and a rare example of an American Indian puzzle purse used to carry a version of gaming chips.
Of all the puzzles in the Sunday boxes, Mr. Slocum said, one of the most challenging was a deceptively simple-looking toy called Chinese rings. Its solution requires what mathematicians call a recursive sequence of moves.
The Chinese rings example in the library exhibition is particularly finely made. A set of rings are threaded over a long, thin loop with wires attached to each ring, tethering it below. Each ring can be taken off the loop or put back on only if the one next to it is on but the others farther down the chain are off. The goal is to get all the rings off.
According to legend, the puzzle was invented in the second century by a Chinese general who gave it to his wife to keep her busy while he was away at war.
Logically, Mr. Slocum said, the puzzle is closely related to the Towers of Hanoi problem, which requires one to move a tower of increasingly smaller blocks from one peg to another.
In recursive puzzles like these, as the number of rings (or blocks) increases, the number of moves required to solve the puzzle increases exponentially. Recursive problems are well known to computer scientists, but it is harder for most of us to get a grip on this elusive concept.
Chinese rings make the problem tangible, Mr. Slocum noted, and reveal in a hands-on fashion the exponential growth entailed. There are typically nine rings in a classic set of Chinese rings; if a player makes no mistakes, the puzzle requires 341 moves to solve. Mr. Slocum can solve it in three to four minutes.
But on a table next to the Sunday box sat a version with 65 rings. A perfect solution in that case would take 18,446,744,073,709,551,616 moves, Mr. Slocum said. "Assuming one move every second, that would be 56 billion years, or four times the age of the universe," he said.
This enigmatic object called to mind the White Queen's advice to Alice about how the more one practices, the better one gets at believing in impossible things. Though solvable in principle, in practice this puzzle can never be completed. Mr. Slocum's collection is a mind-boggling compendium of seemingly impossible, wildly improbable and sometimes breathtakingly difficult puzzles.
Breon Mitchell, director of the Lilly Library, said in an interview that the library was attracted to the collection "because we believe puzzles are important in the history of thought, in the history of mathematics and philosophy, and also the history of science."
Scott Kim, who writes a puzzle column for Discover magazine, said this was the first time a major collection of puzzles would be available in an academic setting. "Puzzles have always interested scientists and engineers," Mr. Kim said. "Many popular things, such as comic books, eventually become subjects for scholarly and academic study. Puzzles are on that cusp right now."
Among the star pieces in the Lilly Library show is an original Rubik's Cube signed by the Hungarian mathematician Erno Rubik, and a prototype of the first Rubik's Cube with six rows of six blocks on each side. That is an object long believed impossible to make, Mr. Slocum said. Finally, last year, the Greek inventor Panayotis Verdes managed to build one.
The Rubik's Cube is an example of a sequential movement puzzle, one of 10 basic categories in what Mr. Slocum called his "puzzle taxonomy." Other categories include disentanglement puzzles (Chinese rings), interlocking solid puzzles (three-dimensional jigsaws) and take-apart puzzles, which include among their subcategories trick locks, trick knives and secret-compartment puzzles.
A beautiful example of the compartment puzzle is another standout of the Lilly Library show. Made by the Japanese puzzle master Akio Kamei, it appears to be a simple, albeit finely crafted wooden cube. But on the top is a hint of how to gain access to its secret compartment. Inlaid in the dark wood is a series of tiny circles of paler wood. The pattern matches the arrangement of stars in the constellation Cassiopeia, and the box will open only when the constellation is correctly aligned. A mechanism inside the box includes a compass that triggers a hidden lock.
Mr. Kamei has made a specialty of such science-based puzzles, and the library exhibition includes several striking examples.
Perhaps the most famous class of physics-based puzzles is one of the most ancient: puzzle vessels. Usually built in the form of a cup or a jug, these vessels offer the challenge that one must drink from them, or fill them up, without spilling any liquid. They have strategically placed holes, so it is immediately clear that a trick is entailed. Early precursors to the form date to at least the 10th century B.C., and Mr. Slocum's collection includes examples from China, Peru, Germany, France and the Middle East.
Not all puzzles are complex. Mr. Slocum said that many of his favorites were the simplest, and that just because a puzzle was simple to look at did not mean it was easy to solve. He particularly likes one that consists of just two three-dimensional pieces that have to be arranged to form a tetrahedron. Another consists of four flat pieces that have to be arranged in the shape of the letter T.
"Both require geometrical reasoning that is counterintuitive," he said. "Good puzzles always go against the grain of our thinking."
Visitors to the Lilly Library will be able to play with a range of puzzles and view animations of various geometric puzzles. This involvement is a critical feature of the exhibition, said Dr. Mitchell, the library director.
"Generally," he said, "you can only study puzzles from books, but when you have three-dimensional puzzles, it's hard to get a sense of them from books alone." In keeping with the spirit of the show, the drawers and cupboards that hold the puzzles will themselves be puzzles.
"The first person who tries to open one each day will have to solve it," Mr. Slocum said, his eyebrows arching slyly. "With puzzles, there is really no substitute for trying them out yourself."
Correction: July 28, 2006
An article in Science Times on Tuesday about a new exhibition of mechanical puzzles at Indiana University included an incorrect estimate from a collector for the time it would take to solve his 65-piece Chinese ring puzzle. At a rate of one move per second, the 18,446,744,073,709,551,616 moves would take nearly 585 billion years, not 56 billion.
Celebrating Puzzles, in 18,446,744,073,709,551,616 Moves (or So)

July 28, 2006

For teen math whiz, helping is part of human equation

Volunteer hours at the Russell Home for Atypical Children add up to satisfaction for a 16-year-old.
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 advanced-placement 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 Award
VANCOUVER, 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 Micheli-Tzanakou. 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 co-authored 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, real-time 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
Dr. Lawrence J. Fogel Receives Inaugural IEEE Frank Rosenblatt Technical Field Award
July 28, 2006

Award for mathematician Prof Seshadri
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 high-level 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 front-ranking 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 cutting-edge 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 best-known 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 ( 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 well-functioning institution with public-private participation that is rather unique in higher education.
R Rangaraj
Award for mathematician Prof Seshadri
July 28, 2006

The Geometer of Particle Physics

Alain 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
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 so-called Standard Model--the 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.
Connes's idea was to extend the relation between geometric space and its commutative algebra of Cartesian coordinates, such as latitude and longitude, to a geometry based on noncommutative algebras. In commutative algebra, the product is independent of the order of the factors: 3 x 5 = 5 x 3. But some operations are noncommutative. Take, for example, a stunt plane that can aggressively roll (rotate over the longitudinal axis) and pitch (rotate over an axis parallel to the wings). Assume a pilot receives radio instructions to roll over 90 degrees and then to pitch over 90 degrees toward the underside of the plane. Everything will be fine if the pilot follows the commands in that order. But if the order is inverted, the plane will take a nosedive. Operations with Cartesian coordinates in space are commutative, but rotations over three dimensions are not.
To gain a clearer vision of what goes on in nature, physicists sometimes resort to "phase space." Such a space is an alternative to Cartesian coordinates--a researcher can plot the position of an electron against its momentum, rather than simply its x and y locations. Because of the Heisenberg uncertainty principle, one cannot measure both quantities simultaneously. As a consequence, position times momentum does not equal momentum times position. Hence, the quantum phase space is noncommutative. Moreover, introducing such noncommutativity into an ordinary space--say, by making the x and the y coordinates noncommutative--produces a space that has noncommutative geometry.
Through such analyses, Connes discovered the peculiar properties of his new geometry, properties that corresponded to the principles of quantum theory. He has spent three decades refining his thinking, and even though he laid down the basics in a 1994 book, researchers beat a path to listen to him. On a day plagued by typical March showers and wind, about 60 of the crème de la crème of French mathematicians fill Salle 5 at the Collège de France. Like a caged lion, the 59-year-old Connes walks quickly back and forth between two overhead projectors, talking rapidly, continually replacing transparencies filled with equations. Outside, police sirens scream amid student protestors trying to occupy the Sorbonne next door in response to the French government's proposed new employment law.
To Connes, physics calculations not only reflect reality but hide mathematical jewels.
Connes seems oblivious to the commotion--even afterward, while crossing the rue Saint-Jacques past blue police vans and officers in riot gear, he keeps talking about how his research has led him to new insights into physics. As an example, Connes refers to the way particle physics has grown: The concept of spacetime was derived from electrodynamics, but electrodynamics is only a small part of the Standard Model. New particles were added when required, and confirmation came when these predicted particles emerged in accelerators.
But the spacetime used in general relativity, also based on electrodynamics, was left unchanged. Connes proposed something quite different: "Instead of having new particles, we have a geometry that is more subtle, and the refinements of this geometry generate these new particles." In fact, he succeeded in creating a noncommutative space that contains all the abstract algebras (known as symmetry groups) that describe the properties of elementary particles in the Standard Model. The picture that emerges from the Standard Model, then, is that of spacetime as a noncommutative space that can be viewed as consisting of two layers of a continuum, like the two sides of a piece of paper. The space between the two sides of the paper is an extra discrete (noncontinuous), noncommutative space. The discrete part creates the Higgs, whereas the continuum parts generate the gauge bosons, such as the W and Z particles, which mediate the weak force.
Connes has become convinced that physics calculations not only reflect reality but hide mathematical jewels behind their apparent complexity. All that is needed is a tool to peer into the complexity, the way the electron microscope reveals molecular structure, remarks Connes, whose "electron microscope" is noncommutative geometry. "What I'm really interested in are the complicated computations performed by physicists and tested by experiment," he declares. "These calculations are tested at up to nine decimals, so one is certain to have come across a jewel, something to elucidate."
One jewel held infinities. Although the Standard Model proved phenomenally successful, it quickly hit an obstacle: infinite values appeared in many computations. Physicists, including Gerard 't Hooft and Martinus Veltman of the University of Utrecht in the Netherlands, solved this problem by introducing a mathematical technique called renormalization. By tweaking certain values in the models, physicists could avoid these infinities and calculate properties of particles that corresponded to reality.
Although some researchers viewed this technique as a bit like cheating, for Connes renormalization became another opportunity to explore the space in which physics lives. But it wasn't easy. "I spent 20 years trying to understand renormalization. Not that I didn't understand what the physicists were doing, but I didn't understand what the meaning of the mathematics was that was behind it," Connes says. He and physicist Dirk Kreimer of the Institut des Hautes Études Scientifiques near Paris soon realized that the recipe to eliminate infinities is in fact linked to one of the 23 great problems in mathematics formulated by David Hilbert in 1900--one that had been solved. The linkage gave renormalization a mathematically rigorous underpinning--no longer was it "cheating."
The relation between renormalization and noncommutative geometry serves as a starting point to unite relativity and quantum mechanics and thereby fully describe gravity. "We now have to make a next step--we have to try to understand how space with fractional dimensions," which occurs in noncommutative geometry, "couples with gravitation," Connes asserts. He has already shown, with physicist Carlo Rovelli of the University of Marseille, that time can emerge naturally from the noncommutativity of the observable quantities of gravity. Time can be compared with a property such as temperature, which needs atoms to exist, Rovelli explains. What about string theory? Doesn't that unify gravitation and the quantum world? Connes contends that his approach, looking for the mathematics behind the physical phenomena, is fundamentally different from that of string theorists. Whereas string theory cannot be tested directly--it deals with energies that cannot be created in the laboratory--Connes points out that noncommutative geometry makes testable predictions, such as the Higgs mass (160 billion electron volts), and he argues that even renormalization can be verified.
The Large Hadron Collider will not only test Connes's math but will also give him data to extend his work to smaller scales. "Noncommutative geometry now supplies us with a model of spacetime that reaches down to 10-16 centimeter, which still is a long way to go to reach the Planck scale, which is 10-33 centimeter," Connes says. That is not quite halfway. But to Connes, the glass undoubtedly appears half full.
The Geometer of Particle Physics

July 28, 2006

His work tied statistics to normal life
Research showed value of small class size, effect of finances on learning
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, D-N.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 meta-analysis, 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 high-speed 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 Turbulence
July 25, 2006 -- Anyone who has seen a tornado has noticed its snake-like 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 highly-competitive 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 highly-swirling 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 three-year 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 physical
An eminent professor is lighting up the sciences in Australia, writes Cynthia Karena.

Tanya Monro
Professor Tanya Monro

SCIENCE is just as creative as playing music, according to one of the world's youngest professors.
Professor Tanya Monro, 33, always wanted to be a musician, either a pianist or a cellist, but her year 9 science teacher opened her eyes to the "beauty and elegance" of science and she decided, aged 14, to become a physicist.
She still plays both the piano and the cello, and it continues to teach her to be persistent and patient in order to improve. Success is not all about being the best and brightest. "I've learnt (that) mainly you need perseverance and enthusiasm. While being bright helps, it takes a lot of stubbornness and doggedness to be a good researcher."
Author Richard Feynman was an inspiration when Professor Monro was first interested in physics. "He made me realise that physics doesn't have to be complicated to be profound and important. That simplicity of approach attracted me and I live by that even now."
She fell in love with photonics - the science and technology of the generation and control of light using glass optical fibres - during a summer job with a photonics research project in her first year at Sydney University.
"It's exciting. You can have a completely new idea, do the research, test the idea by making a new kind of optical fibre and putting light through it, and then take it forward to develop a solution to a real-world practical problem."
In 1998 she won the Bragg Gold Medal for the most outstanding PhD thesis in physics at an Australian institution, given by the Australian Institute of Physics. Professor Monro then left Australia for a research job at the University of Southampton in England, where she ran a project to develop a new class of optical fibres for patterning large plasma displays.
"I learnt to bring together the strengths of different specialities: chemists to develop new types of glass, engineers to make the optical fibre, mathematicians to predict how glass flows during the fibre fabrication process, physicists to predict how light travels through new classes of optical fibres and to test them experimentally, and people from industry to let us know what new type of fibres were of interest for their applications. Working with scientists from such diverse backgrounds allows for really creative and technologically important research to be done."
A position as the inaugural professor in photonics at the University of Adelaide lured her back to Australia last year. She is now also the director of the new Centre of Expertise in Photonics, which opened a few weeks ago at the University of Adelaide in partnership with the Defence Science and Technology Organisation. The organisation is giving $400,000 a year for up to five years, plus additional support for research so far exceeding $1 million. The South Australian Government has contributed more than $400,000.
The centre is working on the design, fabrication, development and applications of a new class of optical fibres - soft glass fibres - which have significant benefits over the conventional silica-based optical fibres.
"We heat the glass to soften it and push it at high pressure through extrusion dyes to get a wide range of different shapes and to introduce holes into the optical fibre cross-section," Professor Monro says. "The holes give you a great deal of freedom to control the way in which light travels along the fibre. This allows you to develop fibres that are very good at sending high power - a lot of light - down the fibre without melting. This is useful for optical computing, using optical fibres instead of electronic systems for data processing."
Professor Monro has learnt that industry works differently to the academic world. "Industry has a more closed and more competitive approach to science research. You don't collaborate as much as we should as academics. It's about finding the fine line (between commercial sensitivities and collaboration)."
Giving birth to twins recently has enforced Professor Monro's work philosophy. "I love the work I do, but there's more to life than work - even when it is as involving as research can sometimes be," she says. "It's important not to let work take over. Family forces you to strike a balance, because you never finish work - there is always something more to do. After a break, you come back to work fresh and with new perspectives. I learnt after my first child that if I didn't want to be at work, I was not effective."
· Be persistent and patient to improve your work.
· Working with scientists from diverse backgrounds allows for creative and technologically important research to be done.
· Be aware of the fine line between collaboration and competition.
· Success is not always about being the best and brightest - you need to be single-minded and enthusiastic.
· There is always more work to do - don't let it take over your life.
Let's get physical

July 28, 2006

Rutgers team to monitor terror activity

Mathematicians to lead team of researchers for federal government
Thursday, July 27, 2006
Star-Ledger 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 real-time 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 XIAO-BO 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 math-related degrees from Harvard.
But there's one television bandwagon that Ms. Greenwald has hesitated to jump on: the CBS show NUMB3RS, a prime-time drama starring a crime-solving math genius. Like other crime shows, NUMB3RS — which averaged 11.7 million viewers in the 2005-6 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 FBI-agent 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 high-school 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 Show
17 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 paper-folders 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 straight-line 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
The Great Origami Maths and Science Show
July 21, 2006

Lacan dans ses oeuvres
Noeud borroméen
" Noeud borroméen de trois tétraèdres", estimé 10-12000 euros(Photo DR)

Le mathématicien et psychanalyste Jean-Michel 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.
«DANS TRÈS PEU de temps, tout le monde s'en foutra de la psychanalyse», disait Jacques Lacan en 1977, quatre ans avant sa mort. On ne se fout pas, en tout cas, de la pensée lacanienne, comme devrait le montrer la vente aux enchères qui aura lieu demain à Paris (Artcurial-hôtel Dassault). En 1991, la vente de son cabinet de la rue de Lille avait fait salle comble et son précieux divan, mis à prix 2 000 F, avait été attribué pour 98 000 F. Pour la vente du 30 juin, qui n'est pas approuvée par la famille Lacan, le catalogue s'est déjà arraché. Il est vrai que c'est la première fois que des documents d'archives relatifs aux travaux du maître sont mis aux enchères. Près de 120 documents et dessins datant de 1972 à 1979, rassemblés par Jean-Michel Vappereau.
Ce mathématicien rencontre pour la première fois Jacques Lacan en 1969 par l'intermédiaire de Roland Dumas, qui fut son avocat. Il fera partie du cercle avec lequel le psychanalyste se penche sur des énigmes topologiques ; ensemble, ils chercheront à réaliser le « noeud à quatre ».
La collection qu'il met en vente «correspond aux années décisives de l'aventure topologique, de l'énigme des noeuds», commente Jacques Roubaud, mathématicien, écrivain, membre de l'Oulipo (Ouvroir de littérature potentielle), ami de Queneau et de Perec. «Ces documents témoignent d'une période décisive dans la recherche du DrLacan, dit Roubaud. Ils donnent accès au chantier d'une pensée de travail, avec ses tâtonnements, ses intuitions brusques, ses découvertes.»
Voici, avec des estimations allant de 1 000 à 10-12 000 euros, des chaînes, des tresses, des cercles, des tétraèdres, des quatresses, un triangle de Pascal, des noeuds borroméens. Ce noeud qui a pris tant d'importance dans ses théories, qui était devenu, comme le souligne Roland Dumas, «à la fois un symbole, un instrument de recherche et une éternelle interrogation».
Les manuscrits, écrits à l'encre bleue, sont pour la plupart de courts documents. Cela va de l'ordonnance de Valium aux lettres en passant par des textes humoristiques ou poétiques (un poème signé « là quand ») pleins de ces jeux de mots qui faisaient sa marque de fabrique («Le comble du comble, c'est que je suis comblé») ou une variation sur le syllogisme « Tous les hommes sont mortels ».
Lacan dans ses oeuvres

July 21, 2006

Un entretien avec Jean-Luc Godard à propos de son exposition au Centre Pompidou :
« Je n'ai plus envie d'expliquer »
Christophe Kantcheff
Jean-Luc Godard déambule dans les salles de « Voyage(s) en utopie, JLG, 1946-2006, À la recherche d'un théorème perdu ». Il évoque les origines de ce travail, la présence des mathématiques, le jugement critique, la platitude télévisuelle et... le cinéma.

Le lieu du rendez-vous était simple : Centre Pompidou, galerie Sud, niveau 1. Jean-Luc Godard avait décidé de parcourir ce Voyage(s) en utopie, JLG, 1946-2006, À la recherche d'un théorème perdu en compagnie d'un journaliste. Une exposition (voir critique p. 20) dont les prémices ont fait couler beaucoup d'encre. Parce qu'il y a, à l'origine de Voyage(s) en utopie... le projet d'une autre exposition, dont le titre devait être Collage(s) de France, qui n'a pu se faire. La presse a écrit sur les responsabilités de cet échec, et Dominique Païni, qui devait être le commissaire de l'exposition et qui a dû finalement se retirer après trois années de collaboration avec le cinéaste, est intervenu dans les médias à ce sujet.
Mais, aujourd'hui, Jean-Luc Godard n'est pas à Beaubourg pour revenir sur ces épisodes. Il est là, le cigare souvent à la bouche, pour accompagner son visiteur, dans la plus grande décontraction, à travers les trois pièces - nommées « Avant-hier », « Hier » et « Aujourd'hui » - qui constituent son exposition. Pendant plus de deux heures, celui qu'on a appelé « l'ermite de Rolle » déambule entre les maquettes ou les objets, les téléviseurs diffusant des extraits de films, les nombreuses citations sans auteur mentionné, en forme et en verve. Sa parole multiplie les changements de direction avec la même vélocité dont fait preuve l'équipe du Brésil avec un ballon : talonnades, déviations, passes de la poitrine. Et cela, aussi bien quand les mots brillent au soleil ou se camouflent dans la brume. Si Godard ne rechigne pas à s'arrêter devant tel ou tel élément exposé, il ne cache pas sa préférence en faveur d'une visite en mouvement, pour ne pas réduire la perception, fixer la sensation, figer le sens. Cet entretien ne doit pas se concevoir autrement.
L'exposition « Voyage(s) en utopie... » est née d'un premier projet d'exposition, dont le titre aurait été « Collage(s) de France », mais qui n'a pu être menée à bout. Comment les avez-vous articulées ?
Jean-Luc Godard : La première exposition a été empêchée, barrée ; la seconde a été pensée comme une introduction à cette impossibilité. Il y a donc des allers et retours entre les deux.
J'ai essayé d'être le plus clair possible, en disant : « Une exposition n'a pas pu avoir lieu. Il en reste quelques briques, quelques ruines, sous forme de maquettes. » Ce devait être le principe de la première exposition : édifier de grandes ruines. Les gens n'auraient rien compris, mais ils auraient senti. Dans l'exposition Voyage(s) en utopie..., on ne peut pas vraiment sentir, parce que j'ai essayé d'établir le scénario suivant : en soixante ans de cinéma, je suis finalement arrivé à ces ruines dont on n'a pas voulu. On peut toujours essayer de l'expliquer, comme un guide le ferait. Mais je n'ai rien à expliquer. Il s'agit d'une postface, sauf qu'on la met au début. Ce n'est donc pas du tout clair.
Vous vous refusez à toute explication, comme si vous vous méfiez du dire, de la parole sur, comme si vous en dénonciez même l'inanité...
Je ne peux plus parler sans images. Ce qui me revient immédiatement en mémoire, ce ne sont pas forcément des mots, mais des actions, des souvenirs... Je ne nie pas l'importance du texte. Personne n'aime autant les livres que moi, et personne ne l'a autant montré que moi. Mais il m'est difficile de tenir une discussion « de texte sur du texte », comme disait Péguy.
Si on se lance dans une discussion de mots au lieu de chercher à établir des rapports entre les choses, on reste en vase clos. C'est exactement ce qui se passe dans le domaine politique ou culturel. Dans Notre Musique (sorti sur les écrans en 2004, NDLR), l'écrivain Jean-Paul Curnier prononce cette phrase de Claude Lefort : « En faisant de la politique un domaine de pensée séparé, les démocraties modernes prédisposent au totalitarisme. » La science est plus forte parce qu'elle accepte un antagonisme entre l'expérience et la théorie. Dans l'art, il y a longtemps que cela n'existe plus. Il n'y a qu'à voir « l'exposition Duchamp » qui se déroule à côté (une exposition Claude Closky, artiste qui a reçu en 2005 le prix Marcel-Duchamp, se tient en effet actuellement au Centre Pompidou, juste à côté de l'exposition Voyage(s) en utopie..., NDLR).
Cette réticence à produire du « texte sur du texte » éclaire aussi les relations singulières que vous entretenez désormais avec les médias...
Nous - la Nouvelle Vague - avons cru qu'il fallait intervenir dans la presse pour nous faire une place, et nous avons pensé qu'on nous accepterait. J'ai cru, pris dans l'engrenage, que je pourrais convaincre qu'il était possible de faire de la télévision autrement. J'y suis donc apparu, un peu en clown, mais c'était très sincère. Aujourd'hui, je regarde cela avec un sentiment de honte, parce qu'il en reste un caractère prétentieux, autoritaire. Mais c'était bon enfant. Et puis, à un moment donné, la télévision n'a plus voulu de moi. Ce qui est bien, du reste. Aujourd'hui, je n'ai plus envie d'expliquer. Je peux, à la rigueur, déplier.
Dans l'exposition, les rapports que vous établissez entre les choses ne sont pas sans évoquer, selon vous, des formules mathématiques. Il est même question d'« un théorème perdu ». La présence des mathématiques y est forte, où l'on rencontre par exemple le nom d'un mathématicien comme Georg Friedrich Riemann...
Je fais des relations sous forme imagée. Si jamais un mathématicien vient voir l'exposition, je pourrais ainsi avoir avec lui un petit dialogue. Je lui dirais : « Vous êtes un littérateur, un écrivain. Il n'y a presque que des lettres dans vos théorèmes. Il y a très peu de chiffres. Et si vous êtes un écrivain, vous êtes un poète. » Jeune, je pensais que je me destinerais aux mathématiques. Je croyais être très doué. Ce ne fut pas le cas. Mais j'aimais bien ça.
Riemann est très difficile à lire. Certains mathématiciens sont plus linéaires dans leur démarche, plus explicatifs. Lui, il avance en faisant des sauts. Dans le même ordre d'idée, Fermat, qui était un contemporain de Pascal, a écrit dans la marge de son théorème : « Je n'ai pas beaucoup de place ici pour le démontrer, mais la solution de ce problème est extrêmement simple. » On a mis trois cents ans à le résoudre. C'étaient les débuts de l'algèbre géométrique et de la géométrie analytique, avec Descartes. Quand Fermat se plaignait de n'avoir pas assez de place, je crois qu'il voulait dire qu'il n'avait pas suffisamment de place pour exécuter des figures, contrairement aux mathématiciens arabes.
Les mathématiciens montrent mais ne disent rien. Je me suis longtemps identifié à des mathématiciens malheureux. Du début du XIXe siècle en particulier. À Évariste Galois, par exemple, qui est mort à 22 ans, et qui a fondé la théorie des ensembles. À Niels Abel aussi, un Norvégien très pauvre. Il avait démontré, à l'âge de 19 ans, l'impossibilité de résoudre les équations algébriques du 5e degré. Il a souhaité rencontrer, à Paris, un mathématicien très célèbre, Cauchy, de l'Académie des sciences, mais celui-ci n'a pas voulu le recevoir. Abel est reparti à pied en Norvège. Où il est mort aussi très jeune. Aujourd'hui, il existe un prix Abel en Norvège. Pour moi, ceux-là sont des amis.
Pour cette exposition, vous avez réalisé un film de montage, Vrai/faux passeport, où vous attribuez des bonus et des malus à des images de cinéma ou de télévision. En procédant ainsi, ne participez-vous pas à la faillite généralisée du jugement critique ?
Ce sont des citations à comparaître pour avoir la possibilité de juger des films. On m'a beaucoup reproché d'accorder des bonus et des malus. Or, c'est ce que pratiquent aujourd'hui tous les journaux : ils accordent des étoiles. Je ne fais rien d'autre que de partir de ce qui se pratique. Je mets un bonus ou un malus à telle ou telle séquence. Soit. Mais comme je procède par opposition dialectique - voici comment untel parle de la Palestine, voici comment tel autre en parle - le spectateur a la possibilité de juger du bien-fondé de ce bonus ou de ce malus. Les extraits de film sont comme des pièces à conviction.
Si je devais répondre explicitement à la question : « Pourquoi est-ce que je mets un malus ou un bonus ? », il me faudrait faire un autre film, ou un livre, qui me prendrait vingt ans. Ce ne serait pas la Critique de la raison pure, mais la Critique du cinéma pur... Mais dans Vrai/faux passeport, je ne m'intéresse pas au pourquoi, je pose la question du comment. Le spectateur, ensuite, peut voir ou revoir le film, même en DVD, et repasser le film en jugement. Et cela l'aidera peut-être ensuite pour d'autres films. Aujourd'hui, le spectateur a tous les moyens techniques pour regarder des films où et quand il le veut. Mais il préfère une autorité qui décrète, il a besoin d'être guidé, il a besoin de savoir combien on a mis d'étoiles...
Dans la pièce de l'exposition intitulée « Hier », et qui a pour sous-titre « Avoir », sont diffusés un certain nombre d'extraits de films du patrimoine, et des extraits de quelques-uns de vos films. C'est sans aucun doute la salle la plus sereine de l'exposition. Ressentez-vous de la nostalgie pour cet « Hier » ?
J'ai simplement voulu dire ceci : en soixante ans de cinéma, j'ai été influencé par ces films allemands, russes, américains..., et par quelques films français. Ça m'a amené à faire les films que j'ai réalisés, certains avec Anne-Marie Miéville, et de là je suis passé à l'archéologie du cinéma. Est-ce qu'il y a de la nostalgie ou de la mélancolie ? Non. Ma seule mélancolie personnelle vient du fait qu'on aurait pu m'aider mieux qu'on ne l'a fait. Je suis connu, mais pas reconnu. Mais aujourd'hui, c'est un peu tard.
Dans cette salle, les films dialoguent entre eux comme si vous vous effaciez derrière eux, ou comme si le visiteur se trouvait là où ils dialoguent en vous...
Imaginez que Scorcese ait eu à réaliser cette salle. Il n'aurait pas pu. Dans son histoire du cinéma italien, il raconte qu'il a vu tel film en telle année. Il a besoin de s'affirmer lui-même en s'appuyant sur l'existence de l'autre. C'est comme les livres sur moi. Ceux qui les écrivent touchent des droits d'auteur mais il ne connaissent rien. Tout est faux.
Dans la dernière salle, « Aujourd'hui », dont le sous-titre est « Etre », vous êtes en revanche, beaucoup plus sévère. La critique que vous faites de notre époque est implacable : nous sommes dans l'ère télévisuelle, c'est-à-dire celle du vide...
Il n'y a en effet que du rien : je ne le dis pas du monde entier, je le dis de la télé et de l'appartement où on regarde la télé. Si j'avais été plus explicite, j'aurais écrit en gros : « Là, à Pompidou, surnommé le garage, où on donne le moins d'argent possible, il n'y a rien ». Les gens se seraient dit : « Ah oui, d'accord, il est un peu vache avec le Centre Pompidou... »
Au début, je voulais garder ce qui restait de l'ancienne exposition. Comme ça, il y aurait eu au moins quelque chose. Et puis, petit à petit, j'ai fait tout enlever, jusqu'à ce qu'on arrive à l'idée d'un presque rien, à l'instar de ce qu'on dit par exemple du journal télévisé : ce n'est pas grand-chose... Beaucoup de gens vont se dire en entrant dans cette salle « Aujourd'hui » : ce n'est pas vrai, ce rien ne correspond pas à ce qui se passe aujourd'hui. Mais il s'agira d'une mauvaise interprétation. Il faut simplement voir ce qui est montré : des téléviseurs à plat dans un appartement. C'est décomposé. C'est un peu du Derrida. Mais, pour moi, c'est plus compréhensible que du Derrida...
Pourquoi ces écrans posés à plat ?
Puisqu'on les appelle des écrans plats, je ne vois pas pourquoi on ne les mettrait pas à plat. Dans cette salle, on est effectivement dans la platitude. On a la cuisine, la chambre à coucher, la cuisine, le bureau, c'est plat. Il n'y a pas de profondeur.
On y trouve aussi trois enveloppes vides, à côté d'une balance, sur lesquelles sont inscrits ces quelques mots : « Plus jamais ça », « Les lendemains qui chantent », et « L'Appel de Stockholm »...
Ces enveloppes introduisent un peu de profondeur, un peu de temps. Mais c'est mon temps à moi. Ce sont les premières phrases dont on m'a dit qu'elles étaient importantes. J'ai entendu : « Plus jamais ça ». On m'a parlé des « lendemains qui chantent ». Et j'ai signé l'appel de Stockholm à dix-sept ou dix-huit ans, sans savoir d'ailleurs ce dont il s'agissait exactement. Aujourd'hui, je constate que ces phrases ne pèsent plus grand chose. Le temps s'est effacé. Mais cette disparition du temps, elle, pèse lourd.
Et aujourd'hui, où en est le cinéma ?
Aujourd'hui, tout ce que je souhaite, c'est qu'un producteur me donne son avis sur le projet de film que je lui présente. Mais il ne me le donne plus. Il n'y a plus de producteur, il n'y a plus que des distributeurs. Le cinéma avait trois stades : la production (la caméra), la distribution (le projecteur), l'exploitation (la salle). Aujourd'hui, n'existe plus que la distribution qui produit pour distribuer. Du cinéma, il reste une métaphore. Mais à partir de cette métaphore, on peut encore expliquer le monde. Les mathématiciens croient que c'est à partir des mathématiques. Moi je crois que c'est à partir du cinéma. Je ne me dis pas cela depuis très longtemps, depuis sept ou huit ans seulement. Mais je crois que ce sera encore valable pour ce qu'il me reste de vie.

Un entretien avec Jean-Luc Godard à propos de son exposition au Centre Pompidou : « Je n'ai plus envie d'expliquer »

July 21, 2006

New European network on modelling control strategies for infectious diseases
Eva 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 day-to-day 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), which is a central hub to exchange health-related information between European health authorities, international organisations and international media.
In addition, the Medical Intelligence System(MedISys) 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 latina
17/07/2006 - 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 Meeting
Established 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 wide-ranging contributions to mathematical programming, including the first strongly polynomial-time algorithm for minimum-cost 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 combinatorial-optimization 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 close-to optimal results. She is most known for her work on network-flow 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 top-rated 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 .
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 Institute
The 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 Co-Director 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 flow-body 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. Toint
Established 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. 239-269 (2002) and "On the Global Convergence of a Filter-SQP Algorithm" by Roger Fletcher, Sven Leyffer, and Philippe L. Toint, published in SIAM Journal on Optimization, Volume 13, pp. 44-59 (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 derivative-free 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 non-SQP 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 Boston
The 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 Paris-Sud 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 two-year 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 Paris-Sud. He completed his Ph.D. at Université Paris VI under the supervisioin of Jean-Francois Le Gall. His research interests lie in probability theory and especially in two-dimensional 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 Lecture
Dr. 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 wide-ranging 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 multi-scale 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, multi-path 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 Boston
The 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 co-author 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 co-author 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 Chidami
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'enseignants-chercheurs 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 savoir-faire et de savoir-être. "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. Professeur-chercheur 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 Olympiad
A 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 all-time high of 14th, up from 17th last year.
Gold medallist Tsoi Yun-pui is the first Hong Kong team member to win four gold medals in successive attempts in cross-territory 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 contest
Two 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
HA NOI — All six Vietnamese who contested the 47th International Mathematics Olympiad in Slovenia won medals, the Education and Training Ministry reports. Twelfth-graders 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 eight-day 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 seven-day 2006 International Biology Olympiad in Cordoba, 1,000km south-west of Buenos Aires, that ended Saturday.
They included 12th-grader Luu Thanh Thuy from the Ha Noi-Amsterdam 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 6-18, 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 Matemática
El 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.
Daniel Chen Soncco con tan solo 15 años ganó una de las medallas de plata: "Estoy recontracontento. No pensé que en esta prueba tan difícil iba a lograr esto". Jossy Alva, también de 15 años, se hizo merecedora de una de bronce. Franco Vargas, María Teresa Huánuco, Paolo Aguilar y Aldo Quillas recibieron mención honrosa. Con estos resultados, de un total de 90 países, estos chicos dejaron al Perú en el puesto 40 del ránking general de la olimpiada con un total de 85 puntos acumulados. El país ganador fue China con 214 puntos, seguido por Rusia y Corea del Sur.
Además de la competencia, nuestros representantes tuvieron la oportunidad de recorrer la ciudad de Luvenia y conocer un poco sobre su cultura. "Este año la organización estuvo mejor que el año anterior, pero los problemas estuvieron más difíciles", cuenta Daniel Chen Soncco, sin que sus manos dejen de jugar con la medalla cuadrada que le cuelga del cuello.
Durante dos días los concursantes se volcaron en la resolución de seis problemas. El que Jossy disfrutó más fue una inecuación por la manera bastante creativa de resolverlo. Sin embargo, nos cuenta que el más difícil fue uno en el que le daban un polígono que había que dividirlo en varios triángulos. "Te pedían demostrar que la suma de algunos de ellos era mayor que el doble del área del polígono", explica.
Otro problema, no de tipo matemático, que la delegación tuvo que resolver fue el financiamiento del viaje. A diferencia de años anteriores, este año no contaron con el auspicio de alguna entidad. Solo gracias a la unión de esfuerzos de los padres de familia y de los colegios en los que estudian, se pudo cubrir el costo de los pasajes. El sector privado y público bien gracias.
Jóvenes peruanos regresan victoriosos de Olimpiada Internacional de Matemática

July 21, 2006

Un platense premiado en Olimpiada Matemática de Eslovenia
Se 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.
La 47. Olimpíada Internacional de Matemática, realizada el domingo en la República de Eslovenia, fue como las anteriores favorable para la actuación del equipo argentino, que obtuvo dos medallas de plata, dos de bronce y una mención especial.
Los estudiantes fueron preparados, como es habitual, por las profesoras del CBC Patricia Fauring y Flora Gutiérrez.
Los alumnos distinguidos fueron Julián Eisenschlos, de la Ciudad de Buenos Aires, con medalla de plata; Ignacio Rossi, de Escobar, provincia de Buenos Aires, también con medalla de plata; Roberto Morales, de la ciudad de La Plata, con medalla de bronce, premio que también obtuvo Pablo Nicolás Zimmermann, de Rosario.
Por último, Fernando Martín Vidal, de Villa Cañás, Santa Fe, fue premiado con Mención de Honor.
La Olimpíada Internacional de Matemática es la más exigente en su género.
Un platense premiado en Olimpiada Matemática de Eslovenia

July 21, 2006

Turkey Wins 5 Medals in Mathematics Olympiad
By 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 six-member 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 Sciences
Mathematics 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'.
Before deliberating upon the subliminal text of the above statements in the context of Mathematics, I should begin by trying to dispel certain myths about Mathematics that have been in currency for a long time now. To begin with, mathematicians have very little to do with numbers in the same way as a research scientist has hardly anything to do with technology which is merely a welcome outcome of the hard work that he is supposed to put in with a view to understanding the mysteries of nature. In fact, the definition of mathematics as 'working with numbers' has been out of date for nearly 2500 years now. One can no more expect a mathematician to be able to add a column of numbers rapidly and correctly than one can expect a painter to draw a line or a surgeon to carve a turkey- popular legend attributes such skills to these professions- but popular legend is wrong. There is, to be sure, a part of mathematics called number theory, but even that doesn't deal with numbers in the legendary sense. A number theorist and an adding machine would find very little to talk about. A machine might enjoy proving that the sum of the first five cubes is 225 but many mathematicians would enjoy the theorem that sum of the cubes of the first n integers is always a perfect square, whereas the 'infinity' involving the word 'every' in that statement would frighten and paralyze any computing machine. Plainly, mathematics is not numbers or machines. It is also not determination of heights of mountains by trigonometry or compound interest by algebra. A more altruistic but an equally important view of mathematics consists basically in the idea of 'doing things for their own sake'. Thus, one may encounter this attitude in music as much as in Art or even in medicine. To quote a famous mathematician P.R.Halmos " I never quite trust a doctor who says he chose his profession out of a desire to benefit humanity. I am uncomfortable and skeptical when I hear such things. I must prefer the doctor to say that he became one because he liked the idea, because he thought he would be good at it, or even because he got good grades in biology. I like the subject for its own sake in medicine as much as in music and I like it in Maths." What is it then that mathematics is all about?
To answer this question, let me begin by saying that mathematics is an important human endeavour, essentially a science of patterns- real or imagined- visual or mental, arising from the natural world or from within the human mind. Far from being too abstract to matter and besides being a uniquely human endeavour , mathematics helps us understand the universe and ourselves. It informs our perceptions of reality-both the physical, biological and the social worlds without, and the realms of ideas and thought within. Like a scientist who does not study nature because it is useful to do so, but because he takes pleasure in his subject, so does a mathematician take pleasure in mathematics because it is beautiful. What I mean is that intimate beauty of mathematics that comes from the harmonising order of its parts and which only pure intelligence can grasp. Here I quote the famous French mathematician Henri Poincare who said" Intellectual beauty is self-sufficing and it is for it, more perhaps than for the future good of humanity, that the scientist condemns himself to long and painful labour". In that sense, mathematics has a lot in common with poetry where it is the search for beauty that inspires the activity of the poet as it does that of the mathematician. Pushkin had captured this analogy succinctly when he had said" Inspiration is needed as much in geometry as it is needed in poetry". This puts into perspective Bertrand Russel's quote stated in the beginning of this article, not only in the context of mathematics but equally pertinently from the viewpoint of natural sciences where it is invariably the search for beauty that drives a scientist's work in understanding the myteries of nature. And that entails not merely a comprehension of the processes involved in how do the things work but, perhaps more importantly, why do the things behave the way they do. This is precisely what constitutes the scientific temper which, however, should not be deemed to be at variance with other forms of intellectual activity. It is a pity that there are those swearing fealty to the cause of education whose vision of a 'reformed and modernized' system of education is to do away with the 'traditional' in favour of the more contemporary curriculum, as if that would act as a panacea for all our educational ills. They would do well to remember that no worthwhile purpose of education can be hoped to be served if 'modernising' the curriculum is achieved at the cost of 'traditional' subjects like literature, philosophy or history etc. which are at least as vital for human development as are the more contemporary ones that are fancied to be in accord with the 'zeitgeist'.
On the other hand - and at a more utilitarian level - mathematics surpasses every other human endeavour in terms of the value it has brought to human life through science and technology where the role of mathematics has been immense. It is this unexpected role of mathematics it has played in the development of science over the centuries that it is the topic of a famous and widely-read classic by the Physics Nobel Laureate Eigene Wigner 'The unreasonable effectiveness of mathematics in the natural sciences", a theme that is echoed by the fact that mathematics has come to be recognised as the language of Science, where its role is not limited to the physical sciences alone but more recently to biological sciences as well. Contemporary research pertaining to the 'topology' of the DNA molecules is a case in point where the ideas and techniques from 'Knot Theory'- a branch of modern differential topology- have been employed to gain a deeper understanding of the 'geometry' of the DNA molecule. There is also this ubiquitous individual phenomenon of mathematicians being motivated primarily by a subtle mixture of ambition and intellectual curiosity, and not by a wish to benefit society. According to Professor Timothy Gowers, the Field Medalist ( equivalent of Nobel Laureate in Mathematics), this is because mathematics is cheap and occasionally produces breakthroughs of enormous economic benefit, either directly as in the case of public-key cryptography, or indirectly as a result of providing the necessary theoretical underpinnings of science. Here it is pertinent to briefly talk about the oft-quoted division of mathematics into 'pure' and 'applied' mathematics. As things stand, the main difference between these parts of mathematics is the intellectual curiosity that motivates the work or, perhaps more accurately, the kind of intellectual curiosity that is relevant. How in the first place does one choose one's research problem and what is it about the problem that attracts a mathematician? Do you want to know about Nature or about Logic" Do you prefer concrete facts to abstract relations? If it is nature you want to study, in other words, if the concrete has the greater appeal, then you are an applied mathematician. In this case, the question always comes from outside, from the 'real' world and the satisfaction the scientist/mathematician gets from the solution comes, to a large extent, from the light it throws on facts. The conclusion from these speculations is inescapable: between the two-pure and applied- there is identity with small differences instead of diversity with important connections! We have a case for saying that mathematics is a glorious creation of the human spirit and deserves to live even in the absence of any practical applications which, in any case, are aplenty.
A study of the growth and development of mathematics reveals that care for the beautiful invariably leads to the same selection as care for the useful. This is borne out by developments, say in 'Group theory' and 'Hilbert spaces'- important areas of mathematics- that have been witnessed over a period of time, resulting in epoch-making discoveries in the theoretical underpinnings of the processes unfolding in the physical world. After all, today's research is tomorrow's technology! All the same, it may be of no practical use that ? ( read as pi)- an important number in mathematics-is irrational, but if we can know, it would surely be intolerable not to know! The so-called pure mathematicians do mathematics because for them it is fun in the same way perhaps that people climb mountains for fun. It may be an extremely arduous and even fatal pursuit, but is fun nevertheless. Mathematicians enjoy themselves because they do sometimes get to the top of their mountain and, anyhow trying to get up there does seem to be worthwhile. In essence, mathematicians are engaged in discovering and mapping out a real world- a world of thought, which is of a kind on the basis of which the physical world is, to a certain extent, also constructed. And the most inscrutable object in this world of thought is surely the concept of infinity and the ways to tackle it. Thus for the most part, mathematics ought to be looked upon as a philosophy to deal with the ways to tackle and tame the 'infinite'.
While hoping that the idea of 'what mathematics is not about' has been reasonably hammered home, there still is a need for identifying ways in which it is possible to tell a good piece of mathematics from one which is not. The bottomline is that it has to be new without being silly. Mere accuracy in performance does not make good music nor does resemblance in appearance qualify for good painting. In the same way, mere logical correctness doesn't make good mathematics. The fact is that one of the greatest joys of the subject has to do with discovering surprising connections between various branches of mathematics, which are-on the face of it- as different as the chalk is from the cheese. The interplay of ideas from 'Knot Theory' which belongs to Differential Topology and 'Operator Algebras'( a branch of Functional Analysis) within mathematics on the one hand and 'Knot Theory' and the study of the DNA molecule (outside of mathematics) on the other , is a case in point. It is sad that at least in this part of the country, Science is merely perceived as a profession where you learn the skill say, to play the computer keyboard or transacting business with your credit card. This is symptomatic of an affliction where scientific temper has not been allowed to flourish. In a similar vein, mathematics has been touted purely as a number game which is supposed to be learnt-and mastered!- through rote learning which, sadly, is the flavour of the month in most of the educational institutions, both public and private. This prurient thirst for trivia involving encouragement of rote learning and similar other tips for 'passing the exam' is not going to enhance the cause of education unless the entire educational system is overhauled at all levels involving the school, college and the university level where comprehension and not memorizing the material is emphasized. The incorporation of negative marks in the recently held entrance tests in the university of Kashmir is no doubt a small but an important beginning in this direction.
Mathematics is by no means a spectator's game where one can hope to have fun without participating in the game in the first place. In order to enjoy the thrill of discovery in mathematics, one has to 'get one's hands dirty' as it were, by 'doing' mathematics, which entails a willingness for 'slogging it out', for total commitment and a self-effacing obsession with the problem under study. Among other factors responsible for an unwillingness, even among bright students, to pursue a career in science is the abysmally low quality of teaching of science in general and of mathematics in particular in our educational institutions. Unless the system of education is drastically reformed where such values are cultivated and nurtured as part of a system, we are condemned to be second-raters in the field of science where nothing substantial can be achieved in the absence of a culture in which scientific ethos tempered by pure thought and reason would flourish. I conclude with the following quote of Professor Steven Weinberg which sums up the essence of the scientific activity as discussed in the above lines in no uncertain terms: The effort to understand the universe is one of those few things that lifts human life a little above the level of farce and gives it some grace of tragedy.
(The author is Professor of Mathematics and Dean Academics, Kashmir University, Srinagar. He can be mailed at
Revisiting the Relevance of the Queen of Sciences

July 13, 2006

Teen adds silver at math meet
Mohammed Fareed
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 mind-melting equations at the National High School Mathematics Championship.
But that didn't stop the John Adams High School junior from solving the problems - and snagging a silver medal at the prestigious annual math competition July 1 and 2.
"It was the hardest thing I've ever seen, I never did calculus in my whole life," Mohammed, 17, told the News. "I had to use my past knowledge to figure it out."
Mohammed was one of just 24 other finalists selected to participate in the annual two-day math melee held by the American Society for Mathematics in Oklahoma City.
Other New York finalists included Matt Zee, 18, of West Nyack; Sulinya Ramanan, 17, of Poughkeepsie and Kenneth Mandel, 16, of Sea Cliff, L.I. Outreach programs that help find the math whiz kids in New York schools are sponsored by the Daily News Educational Dept.
Despite the grueling mathematical challenges, Mohammed said he made friends with many of the other finalists - fellow bright kids with whom he will stay in touch via e-mail.
"I'm a normal kid, right; I like to kid around and have fun," he said. "I made a lot of friends from [places] like Texas and Georgia, all over the United States."
American Society for Mathematics president Richard Neal called Mohammed the "most liked" person of the competition, which tests students on topics unfamiliar to them unless they've taken college courses.
"The areas are pretty expansive; logic, modular arithmetic and other things they wouldn't normally encounter in their curriculum," Neal said.
The finalists have bright futures, he said, adding that "about half of them are going to MIT."
Mohammed - who moved from his native Republic of Trinidad and Tobago to Richmond Hill in Queens two years ago - got a boost from Councilman Joseph Addabbo (D-Howard Beach) and State Sen. Ada Smith (D-Jamaica), who helped collect $800 for his airfare and expenses.
"It was money well spent," Addabbo said. "He did very well and represented not only the school, not only the borough, but the whole state."
Mohammed said that after attending college, he wants to be a medical engineer and "as a sideline, also find a cure for cancer."
Before curing cancer, however, he said he wants to return to the math competition. "Next year, I plan on getting the gold medal."
Originally published on July 13, 2006
Teen adds silver at math meet

July 13, 2006

Irving Kaplansky, 89, a Pioneer in Mathematical Exploration, Is Dead

Published: July 13, 2006
Irving Kaplansky
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.
The cause was respiratory failure, his family said.
From 1945 to 1984, Dr. Kaplansky taught at the University of Chicago, where he joined his famous former teacher, Saunders Mac Lane, who worked on topology and category theory, an abstract branch of algebra with applications in computer science. Dr. Mac Lane died in 2005.
Dr. Kaplansky's interests were similarly broad, and he explored the properties of groups of numbers called commutative groups, also known as Abelian groups, in which the order that a group's members are multiplied does not affect their outcome.
He published "Infinite Abelian Groups" (1954, 1969) and "took a big step in showing how far you could go with infinite elements" that are commutative, said David Eisenbud, director of the Mathematics Sciences Research Institute in Berkeley, Calif. From 1984 to 1992, Dr. Kaplansky directed the institute.
J. Peter May, a former student of Dr. Kaplansky and a professor of mathematics at the University of Chicago, praised his "exceedingly incisive mind that saw through to the essentials in mathematical arguments with precision and clarity."
Dr. Kaplansky went on to write "Commutative Rings" (1970), a work that Dr. Eisenbud said remained in use and was "narrowly focused on its subject, a subject that, partly because of this book, has since gone much further." Dr. Kaplansky later wrote about an area bridging algebra and topology, a field that involves the study of real or abstract spaces, in "Lie Algebras and Locally Compact Groups" (1971).
A noted pianist, he also composed music, often on mathematical themes, and contributed to performances of Gilbert and Sullivan productions in Chicago.
Irving Kaplansky was born in Toronto. He received his bachelor's and master's degrees from the University of Toronto before earning a doctorate in mathematics from Harvard in 1941.
After early work at Columbia, Dr. Kaplansky moved to Chicago in 1945. He was named a professor of mathematics there in 1955, and a professor emeritus in 1984. He became an American citizen in the 1950's.
Dr. Kaplansky was a member of the Institute for Advanced Study in Princeton, N.J., and was elected to the National Academy of Sciences in 1966. He also was president of the American Mathematical Society.
In 1989, the society awarded him its Leroy P. Steele Prize for Lifetime Achievement.
Dr. Kaplansky is survived by his wife of 55 years, the former Chellie Brenner.
He is also survived by a daughter, Lucy, a singer-songwriter, of Manhattan; two sons, Alex, of Hillsborough, N.J., and Steven, of Sherman Oaks; and two grandchildren.
As a musician entranced with the mathematical possibilities of music, Dr. Kaplansky once wrote a melody based on assigning notes to the first 14 decimal places of pi. Called "A Song About Pi,'' it received lyrics in 1971 from a Chicago colleague, Enid Rieser, and has been sung by Dr. Kaplansky's daughter in her act.
Irving Kaplansky, 89, a Pioneer in Mathematical Exploration, Is Dead

July 13, 2006

Gadanidis honoured for mathematical contributions
George Gadanidis
George Gadanidis

Western Associate Education professor George Gadanidis has been honoured by the Fields Institute for his continuing work in the field of mathematics.
Gadanidis was one of six Canadians recently inducted as a Fields Institute Fellow, a lifetime appointment conferred on individuals who have made outstanding contributions to the Fields Institute, its programs, and to the Canadian mathematical community. a The Fields Institute, located in Toronto, is recognized as one of the world's leading independent mathematical research institutions. With a wide array of pure, applied, industrial, financial and educational programs, the Institute attracts over 1,000 visitors annually from every corner of the globe, to collaborate on leading-edge research programs in the mathematical sciences.
Gadanidis has given significant support to the Fields program in Mathematics Education and continues to serve on the steering committee of the Fields Mathematics Education Forum.
Gadanidis honoured for mathematical contributions

July 13, 2006

How parachute spiders invade new territory
Erigone spiders
Two male Erigone spiders on a grass seed head.
The lower one is in a pre-ballooning posture
ready to disperse, known as the "tip-toe" 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.
The team at Rothamsted Research, a sponsored institute of the Biotechnology and Biological Sciences Research Council (BBSRC), realised that the existing 20 year old models to explain this phenomenon – known as 'ballooning' – failed to adequately deal with anything other than perfectly still air. Called Humphrey's model it made assumptions that the spider silk was rigid and straight and the spiders were just blobs hanging on the bottom. It could not explain why spiders were able to travel long distances over water, to colonise new volcanic islands or why they were found on ships. The new Rothamsted mathematical model allows for elasticity and flexibility of a ballooning spider's dragline – and when a dragline is caught in turbulent air the model shows how it can become highly contorted, preventing the spider from controlling the distance it travels and propelling it over potentially epic distances.
Dr Andy Reynolds, one of the scientists at Rothamsted Research, explained: "Researchers knew that spiders could use ballooning to cover long distances but no previous model has adequately explained how this worked. By factoring in the flexibility of the dragline that the spiders cast into the breeze have shown how it can contort and twist with turbulence, affecting its aerodynamic properties and carrying its rider unpredictable distances. Spiders are key predators of insects and can alleviate the need for farmers to spray large quantities of pesticide. But they can only perform this function in the ecosystem if they arrive at the right time. With our mathematical model we can start to examine how human activity, such as farming, affects the dispersal of spider populations."
Dr Dave Bohan, a member of the research team, commented on how mathematical models and traditional bioscience observation come together: "To really understand the factors at play on ballooning spiders we need to watch them in action. We have already observed spiders ballooning through still air and we are now planning to take them into a wind tunnel to watch how they handle turbulent flows. Once we have done that we can refine the model further." Professor Julia Goodfellow, Chief Executive of BBSRC, the organisation which funded the project, said: "The exciting thing about this research is that it not only explains a long-standing question but also shows how ecologists, mathematicians and physical scientists can draw on each others strengths. The future face of bioscience is highly interdisciplinary and will require more collaboration between, for example, mathematicians and ecologists working together to answer biological questions."


Images available at:
Image available is: Two male Erigone spiders on a grass seed head. The lower one is in a pre-ballooning posture ready to disperse, known as the 'tip-toe' position.
Dr David Bohan, Rothamsted Research, Tel: 01582 763133 ext. 2454, email
Dr Andy Reynolds, Rothamsted Research, email:
Dr James Bell, Rothamsted Research, email:
Rothamsted Research
Elspeth Bartlet, Tel: 01582 763133 ext 2260, email:
BBSRC Media Office
Matt Goode, Tel: 01793 413299, email:
Tracey Jewitt, Tel: 01793 414694, email:
Notes to Editors
An article on this research appears in the July 2006 issue of BBSRC Business available soon. Business is the quarterly research highlights magazine of the UK's Biotechnology and Biological Sciences Research Council.
Further information about the Ecosystem Dynamics and Biodiversity Group at Rothamsted Research is available at: Rothamsted Research in Harpenden, Hertfordshire is one of the largest agricultural research institutes in the country and is sponsored by the BBSRC. For more information please visit:
The Biotechnology and Biological Sciences Research Council (BBSRC) is the UK funding agency for research in the life sciences. Sponsored by Government, BBSRC annually invests around £350 million in a wide range of research that makes a significant contribution to the quality of life for UK citizens and supports a number of important industrial stakeholders including the agriculture, food, chemical, healthcare and pharmaceutical sectors.
How parachute spiders invade new territory

July 13, 2006

Maths to peek in people's purses
By 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, long-term 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 long-enough 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 middle-class 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 income-earning 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 non-poor 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 ( 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 ( 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 turbulence
Philip Ball
The disturbed artist intuited the deep forms of fluid flow.

Van Gogh - The Starry Nigth
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.
Physicist Jose Luis Aragon of the National Autonomous University of Mexico in Queretaro and his co-workers have found that the Dutch artist's works have a pattern of light and dark that closely follows the deep mathematical structure of turbulent flow.
The swirling skies of The Starry Night, painted in 1889, Road with Cypress and Star (1890) and Wheat Field with Crows (1890) — one of the van Gogh's last pictures before he shot himself at the age of 37 — all contain the characteristic statistical imprint of turbulence, say the researchers.
These works were created when van Gogh was mentally unstable: the artist is known to have experienced psychotic episodes in which he had hallucinations, minor fits and lapses of consciousness, perhaps indicating epilepsy.
"We think that van Gogh had a unique ability to depict turbulence in periods of prolonged psychotic agitation," says Aragon.
In contrast, the Self-portrait with Pipe and Bandaged Ear (1888) shows no such signs of turbulence. Van Gogh said that he painted this image in a state of "absolute calm", having been prescribed the drug potassium bromide following his famous self-mutilation.
Measured chaos
Scientists have struggled for centuries to describe turbulent flow — some are said to have considered the problem harder than quantum mechanics. It is still unsolved, but one of the foundations of the modern theory of turbulence was laid by the Soviet scientist Andrei Kolmogorov in the 1940s.
He predicted a particular mathematical relationship between the fluctuations in a flow's speed and the rate at which it dissipates energy as friction. Kolmogorov's work led to equations describing the probability of finding a particular velocity difference between any two points in the fluid. These relationships are called Kolmogorov scaling.
Aragón and colleagues looked at van Gogh's paintings to see whether they bear the fingerprint of turbulence that Kolmogorov identified. "'Turbulent' is the main adjective used to describe van Gogh's work," says Aragn. "We tried to quantify this."
Darkness and light
The researchers took digital images of the paintings and calculated the probability that two pixels a certain distance apart would have the same brightness, or luminance. "The eye is more sensitive to luminance changes than to colour changes," they say, "and most of the information in a scene is contained in its luminance."
Several of van Gogh's works show Kolmogorov scaling in their luminance probability distributions. To the eye, this pattern can be seen as eddies of different sizes, including both large swirls and tiny eddies created by the brushwork.
Van Gogh seems to be the only painter able to render turbulence with such mathematical precision. "We have examined other apparently turbulent paintings of several artists and find no evidence of Kolmogorov scaling," says Aragon.
Edvard Munch's The Scream, for example, looks to be superficially full of van Gogh-like swirls, and was painted by a similarly tumultuous artist, but the luminance probability distribution doesn't fit Kolmogorov's theory.
The distinctive styles of other artists can be described by mathematical formulae. Jackson Pollock's drip paintings, for example, bear distinct fractal patterns.
Van Gogh painted perfect turbulence

July 09, 2006

The cocoa is in the can - the math is on it
By Ann D. Bingham
Mathematicians gave the name 'Droste effect' to a recursive picture, one that repeats itself forever.
Droste Cacao
I love math, don't you? Math is all around us, and I like to find it when it's hidden.
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 games
New Spore game is making geeks and science teachers swoon

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 Vegas-style booths advertising the latest first-person shooters empty out as technophiles grab at the opportunity to watch, enraptured, as the bacterium slowly evolves into a multi-celled organism, then a land-dweller, and finally a social being complete with buildings and spaceships. The 20-minute demo is a preview of Spore (, the latest game by Will Wright, the creator of The Sims.
The game reprises the open-ended structure of The Sims, where the usual gaming formula is reversed: usually, a gamer controls a main character in an environment of pre-set 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 male-dominated world of gaming.
The popularity across gender and generational divides spawned a slew of spin-offs 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 so-called "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 co-operate 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 (1935-37), specialmente nel vol. II, p.511-12. 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., 1789-94;
(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 publications
Vladislav Goldberg
Vladislav 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 70-year-old mathematician during a multi-day 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.
Goldberg is renowned for his understanding of a little-known branch of geometry: web geometry. Only a small number of scholars study this field, although their expertise is frequently tapped by economists and physicists, especially those scientists studying thermodynamics. The late S.S. Chern, PhD, of the University of California, Berkeley, numbered among the past century's noted mathematicians who worked in web geometry.
Web geometry focuses on the non-changing, or invariant, properties of a series of curved lines laid over a grid of horizontal and vertical lines.
Goldberg and a small international group of other web mathematicians create the rules for studying or understanding web geometry. If there is only one family of curves to overlay the grid, a curvilinear three-web is produced," said Goldberg. "Two families of curves produce a curvilinear four-web. We can use an infinite number of curves in each web family, but only a finite number of families produce a web. The grid, which is the foundation, or starting point, always counts as the first two families."
Economists and physicists use web geometry as a tool to prove their theories. Through the years, Goldberg has served many colleagues in other disciplines. His most memorable collaboration was in 2003 with Nobel Prize economists Paul A. Samuelson of MIT, Thomas Russell of University of Santa Clara and James B. Cooper of Johannes Kepler Universität Linz, Austria. The trio challenged him to answer an unsolved problem. "They asked to me find the conditions under which a curvilinear web can be mapped into a web with all transversal families being families of straight lines," said Goldberg.
Goldberg accepted the challenge and in 2004 and again in 2006, he co-authored two breakthrough works refuting a 1938 assertion by Wilhelm Blaschke, a noted German mathematician credited with founding the field of web geometry. Blaschke (1862-1955), a colorful character in his own right, ended up snubbed by nations and academics later in life for his public Nazi sympathies during World War II.
In Einfuehrung in die Geometrie der Waben (1955) Blaschke wrote that it was "hopeless" for mathematicians to find the conditions under which a curvilinear web can be mapped into a new web with transversal, nonintersecting straight lines.
"By hopeless, he meant that the problem had impossible calculations to carry out by hand," explained Goldberg. Of course, Blaschke's words were penned prior to the arrival of personal computing. Some 60 years later, Goldberg and coauthors, with the aid of advanced computer software programs, proved Blaschke wrong. In 2004, Maks A. Akivis, of the Jerusalem Institute of Technology, Goldberg and Valentin V. Lychagin, of the University of Tromso, Norway, each a renowned mathematical author and scholar, solved the problem for all webs, except three-webs. Selecta Mathematica published "Linearizability of d-webs, d> 4, on two-dimensional manifolds" in December of 2004. Then, in 2005, Goldberg and Lychagin solved the more difficult variant of the problem, finding the conditions under which a curvilinear three-web can be mapped into a linear three-web with transversal straight lines. The Journal of Geometric Analysis published "On the Blaschke conjecture for 3-webs" in March of 2006. Comptes Rendus Mathematique, published a six-page version of the same work in August of 2005.
Since 1958, Goldberg has published four monographs, eight textbooks, three book chapters and more than 120 scientific papers. Goldberg received his master's and doctoral degrees in mathematics from Moscow State University. From 1964 to 1978, Goldberg was a professor in the department of mathematics at Moscow Institute of Steel and Alloys. In 1979, after immigrating to the US, Goldberg worked at Lehigh University for two years as a visiting professor. In 1981, he joined NJIT as a full professor. In 1985, NJIT made Goldberg one of the university's earliest distinguished professors. At the ceremony this past May in Ukraine, Goldberg's colleagues from different countries warmly lauded his contribution to science and education. They presented him with a formal bound document which was read aloud to him at the ceremony. The document said: "We wish that you continuously move ahead and successfully complete all your plans and intentions. Let the welfare and success and health of all your family members assure your peace of mind and good mood. Let your loyal friends and your highly professional colleagues, united by joint goals, support your professional success which will bring progress and success to our common cause."


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 MDC
By 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 Mathematics
Troy, 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, Web-based teaching tools that are capturing the interest – and imagination – of students in math classes across the country.
Ron Eglash, associate professor of science and technology studies at Rensselaer, has created a suite of 11 computer software programs that focus on individual facets of African American, Native American, or Latin American culture where math plays a role in design. Called "culturally situated design tools" (CSDTs), the programs educate students about the mathematics principles used to design cornrow hairstyles, Mangbetu art, Navajo rugs, Yupik parka patterns, Pre-Columbian pyramids, and Latin music, among others. New research reported in the June 2006 issue of American Anthropologist suggests that use of CSDTs can raise math achievement and may improve technological career aspirations for ethnic minority students.
Preliminary surveys of students – 83 percent of which were under-represented minorities – who used the design tools for two hours per day over a two-week period displayed a statistically significant increase in their attitudes toward computers, compared to 175 randomly selected students who had not used a CSDT. The statistical upsurge in the first group of students may indicate an increase in positive attitudes toward IT careers for students exposed to CSDTs, according to Eglash, lead author on the paper.
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 real-world 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 hands-on 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 ever-shrinking 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 Shosone-Bannock beadwork, and Rhythm Wheels (one of two Latin American-geared 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: 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 347-362 in Volume 108, Issue 2, of American Anthropologist.

About Rensselaer
Rensselaer Polytechnic Institute, founded in 1824, is the nation's oldest technological university. The university offers bachelor's, master's, and doctoral degrees in engineering, the sciences, information technology, architecture, management, and the humanities and social sciences. Institute programs serve undergraduates, graduate students, and working professionals around the world. Rensselaer faculty are known for pre-eminence in research conducted in a wide range of fields, with particular emphasis in biotechnology, nanotechnology, information technology, and the media arts and technology. The Institute is well known for its success in the transfer of technology from the laboratory to the marketplace so that new discoveries and inventions benefit human life, protect the environment, and strengthen economic development.
Math Lessons Get a Makeover: New Tools Spark Student Interest, Achievement in Mathematics

July 02, 2006

Springer author wins the Alfried Krupp Science Prize

Eberhard Zeidler awarded the prize for his life's work

Eberhard Zeidler
Eberhard Zeidler (66) was awarded the prestigious Alfried Krupp Prize at a ceremony in Essen (Germany) on 13 June 2006. The prize is awarded to leading scientists for their life's work by the Alfried Krupp von Bohlen und Halbach Foundation. The prize was given in recognition of Zeidler's achievements in the field of non-linear functional analysis and for his scientific contribution to issues concerning the application of mathematical research in the natural sciences. The award was set up in 1998 and carries prize money of €52,000.
Zeidler has been lecturing at Leipzig University since 1974. His five-volume monography Nonlinear Functional Analysis and Its Applications, which was published by Springer-Verlag in the 1980s, is one of the standard works in the field. This was followed by books such as Applied Functional Analysis, Vol 108, Vol 109, A Singular Introduction to Communicative Algebra and Quantum Field Theory I: Basics in Mathematics and Physics, also published by Springer. Zeidler helped set up the Max Planck Institute for Mathematics in the Sciences between 1995 and 2003 and became its director. He is regarded as one of the leading mathematicians of the former East Germany, particularly in the application of mathematics in the natural sciences.
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.

Springer author wins the Alfried Krupp Science Prize

July 02, 2006

Of Biocultural Mathematics and Mind
Reflections 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 self-evident) 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 ("evo-devo": 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 a-counting. 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 neo-Darwinian 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 cross-bridge 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 Cavalli-Sforza 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 Cavalli-Sforza and Feldman, appeared first in the early progression, in 1981. Wilson and I, introducing the term gene-culture coevolution perhaps for the first time, took a mathematical approach to human genes, minds, and culture anchored in developmental psychology. Cavalli-Sforza 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 wide-ranging 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 match-up? 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 so-called 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, real-world system. The discovery, for example, that real gene-culture 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 epi-phenomena, nothing but fuzzy minded stand-ins 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 science-speak 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 non-computable 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 multi-level evolution open to culture-bearing 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 evolutionary-mathematical 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 hard-nosed theories of symbols. When combined with other recent ideas, it may promise a next stage of major progress in gene-culture 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 gene-culture 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 gene-culture 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 quarter-century 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 Cavalli-Sforza 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 large-scale 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 time-step 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 "join-the-dots," 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 get-go 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 fly-by-night stories that can elude scientific scrutiny by, chameleon-like, 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 Cavalli-Sforza 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 gene-culture 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 such-and-such 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 non-commutative job. For example, the net-like structure of a brain circuit or a semantic network or a pattern of cultural meaning has a natural associative pattern, i.e. a net-like 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 short-changed 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 gene-culture 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 gene-culture 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 dynamics-busting 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 gene-culture 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 gene-culture 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 gene-culture 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 gene-culture 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 well-thumbed. Some are more concise than others. The full text of Alexander Pope's rhyming couplets and notes (1996/1715-1720), 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 k-th 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 next-but-last 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 quantum-discrete rather than a continuous flow - is some 10-43 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 16,000-line 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 16,000-line 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 gene-culture 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 ( 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 ( 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, 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.
Cavalli-Sforza, 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 one-hit neuronal death kinetics. Brain Research Bulletin, 65, 59-67.
Clarke, G. and Lumsden, C. J. (2005b). Scale-free neurodegeneration: Cellular heterogeneity and the kinetics of neuronal cell death. Journal of Theoretical Biology, 233, 515-525.
Cosmides, L. (1989). The logic of social exchange: has natural selection shaped how humans reason? Studies with the Wason selection task. Cognition, 31, 187­-276.
Cosmides, L. and Tooby, J. (1989). Evolutionary psychology and the generation of culture, II: a computational theory of social exchange. Ethology and Sociobiology, 10, 51-97.
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. 17-44). 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. xv-lxiii). 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. (1996/1715-1720). The Iliad of Homer. S. Shankman (Ed.). New York: Penguin Books.
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Lumsden, C. (2006). Of Biocultural Mathematics and Mind. Evolutionary Psychology, 4:57-74.

Date of article 30 June 2006 Email Charles Lumsden Links

Of Biocultural Mathematics and Mind

July 02, 2006

Ecologie et libéralisme: Deux visions du monde inconciliables
Par Laurent OZON
Fondés en 1944 à Bretton Woods aux États-Unis, 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 bien-être 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 techno-économique 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 libre-entreprise 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 bien-être est la condition nécessaire et suffisante du bien-être 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 coût-profit).
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 bien-être collectif. Il en ressortirait alors que « plus le PNB est élevé et plus le bien-être 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 livre-manifeste 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'est-à-dire 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'est-à-dire 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 (1834-1919), 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 indo-européen 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 quasi-organisme.
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 BRAUN-BLANQUET.
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 sous-titrer « 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 masse-énergie, 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 elle-même 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 celle-ci 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 peut-être 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 au-delà 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'est-à-dire 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, au-delà 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 celle-là, 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 GEORGESCU-ROEGEN, 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'est-ce que l'usure des matériaux, sinon une forme particulière d'entropie?
Georgescue-Roegen 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 non-renouvelables14.
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 masse-énergies 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'est-à-dire 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'est-à-dire 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 bien-être 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'au-delà 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 LÉVI-STRAUSS, dans son livre Le Regard éloigné en 1983. Ce point de vue consistant à considérer comme normale une attitude de « préférence » ou de sur-valorisation d'une espèce plutôt qu'une autre, liée à des phénomènes d'identification, d'utilité, de co-appartenance 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 universitari-animatori 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.
Nonostante la sua pessima fama di materia barbosa e complessa, se presentata al pubblico in maniera accessibile, la matematica diventa interessante e autenticamente divertente.
Secondo uno studio condotto da Irving Biederman della Southern California University, apparso su American Scientist, il cervello si gratifica per aver afferrato un concetto difficile o interessante producendo sostanze simili agli oppiacei. E allora forse, una volta vinta la resistenza iniziale, si può diventare "dipendenti" dalla matematica!
Un meccanismo gratificante di questo tipo è il mezzo che l'evoluzione ha scelto per sviluppare l'intelligenza, e spiega in maniera plausibile la curiosità cognitiva in generale.
Sempre a proposito di matematica un altro recentissimo studio condotto da Yijun Liu, Yiyuan Tang e colleghi della Dalian University of Technology, di Dalian, in Cina, ha ipotizzato che essa sia strettamente legata al linguaggio, e che la lingua madre abbia un'influenza sul modo in cui il cervello affronta diversi compiti numerici. Sottoponendo a risonanza magnetica funzionale volontari sottoposti a test di aritmetica è stato riscontrato che per risolvere un problema di addizione, i soggetti di madrelingua inglese mostrano la presenza di attività nell'area che sovrintende al linguaggio, mentre i soggetti di madrelingua cinese utilizzano regioni cerebrali più legate all'elaborazione delle informazioni visive, in accordo con la tipologia ideografica della loro lingua.
Link | Una bella risorsa on line è il sito Matematica dell'Università Bocconi

La matematica: fra oppio e linguaggio

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 a-priori 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 sense-intuition 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, self-conscious, 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, pre-lingual, 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 non-dualistic 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 self-evident 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 a-priori languages and codes are nothing but the set of our embedded ideal intuitions.
As the Rationalists realized, ideal intuitions (a class of undeniable, self-evident 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 a-priori 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 a-priori - 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 counter-balance 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 a-priori. 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 anti-empirical - 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
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What is Intuition?

July 02, 2006

Drawings by the late French psychoanalyst Jacques Lacan (1901-1981) are going under the hammer this week at Paris' Artcurial. As Le Monde's Clarisse Fabre reports, Jean-Michel 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 felt-tip 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.
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?"
"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 France-Presse reports, 130,000 people saw the exhibition, which included 350 works produced by 200 French and France-based 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 Ur-anthropologist Claude Lévi-Strauss, now ninety-eight years old.
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 long-term 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 last-minute 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