June 26, 2006
A&M-C math professor honored by Mathematical Association of AmericaBy Mary Lou Hazal  Dr. Stuart Anderson
COMMERCE, Texas -- Dr. Stuart Anderson of Texas A&M University-Commerce has been honored by the Texas Section of the Mathematical Association of America. |
June 26, 2006
Le petit Einstein de La MagdeleineVéronique Asselin  Alexandre Vincart-Émard Même s'il est le meilleur élève de son école, Alexandre demeure très humble. Il sait que beaucoup d'élèves doivent bûcher pour terminer leur scolarité.
DELSON - Il a la bosse des maths, du français, des sciences physiques, de l'histoire... Bref, Alexandre Vincart-Émard a l'école dans la peau même s'il n'est pas bossu pour autant.
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June 26, 2006
Cerca de 70 estudiantes de toda España participarán en la Olimpiada Nacional Matemática en Fuente de CantosEl programa de la misma contempla desde visitas culturales, actuaciones de teatro matemático, exposiciónes y charlas de Astronomía, así como resolución de problemas, utilizando rogramas de Software Libre bajo el Sistema Operativo Linex. La Olimpiada Nacional Matemática, que tendrá lugar en Fuente de Cantos entre los próximos días 25 y 29 de junio, contará con la participación de más de 70 estudiantes de entre 13 y 15 años de todas las comunidades autónomas y de centros educativos españoles en el extranjero. Se trata de un certamen organizado por la Sociedad Extremeña de Educación Matemática "Ventura Reyes Prósper" y auspiciadas por la Junta de Extremadura y el Ayuntamiento de Villafranca de los Barros con el apoyo organizativo y financiero de diversas instituciones y organismos. En estas pruebas, los diferentes escolares competirán entre ellos en la resolución de numerosos problemas de lógica matemática y de razonamiento. En cuanto a la prueba individual, ésta consistirá en la resolución de 5 problemas durante 2 horas y se realizará en el IES "Menéndez Valdés" de Villafranca de los Barros. Igualmente, las pruebas en grupo consistirán en una de Fotografía Matemática en la que se tendrán que reflejar algún concepto matemático en una fotografía así como dos circuitos matemáticos, uno en Fuente de Cantos y otro por la Ciudad Monumental de Cáceres. En ellos, se resolverán diferentes pruebas con un tiempo limitado que estarán basadas en la historia, las costumbres, la cultura y las tradiciones de ambas ciudades, de tal forma que a la vez que los alumnos resuelven problemas matemáticos conocen distintos aspectos de la ciudad. Así, el día 26 se someterán a una prueba escrita teórica y a la resolución de numerosos ejercicios prácticos, o problemas, relacionados con la cultura y el patrimonio de Fuente de Cantos, para lo que tendrán que recurrir a una serie de magnitudes, variables o herramientas matemáticas. Hasta llegar a esta fase final estatal, los 65 estudiantes que tomarán parte en la olimpiada matemática han debido superar previamente distintas fases locales o comarcales en sus respectivas comunidades autónomas, además de otra fase autonómica, igualmente en cada uno de sus territorios, que en la final extremeña concitó a 35 finalistas. Cabe recordar que los participantes proceden, además de las 17 comunidades autónomas, de las secciones españolas de Italia, Francia, Portugal y de Marruecos. Los jóvenes, además de participar en la resolución de los problemas matemáticos que se les plantee, tendrán también tiempo para el ocio y participarán en visitas turísticas por la población y la comarca de Tentudía, y en degustaciones gastronómicas de la zona, entre otras actividades. Cerca de 70 estudiantes de toda España participarán en la Olimpiada Nacional Matemática en Fuente de Cantos |
June 26, 2006
Top mathematician recognizes Chinese work on solving Poincare ConjectureWorld top mathematician Richard Hamilton has recognized the work of Chinese mathematicians on giving a complete proof of the century-old puzzle of Poincare Conjecture. "Chinese mathematicians have played a very important part in this development," Prof. Hamilton at Princeton University said in a video talk recorded two weeks ago in Beijing when he discussed the proof with Prof. Cao Huaidong, one investigator who unraveled the conjecture. "It's very nice to have such an account written by two outstanding people in the field of Ricci flow. They also introduced ideas of their own which makes the proof easier to understand," Prof. Hamilton said in the video that for the first time went to public at the ongoing International Conference on String Theory 2006. "All Chinese can be proud of the achievements of their mathematicians in differential geometry and their contributions to the completion of the proof of Poincare Conjecture," he said. Together with Prof. Cao, Prof. Zhu Xiping at Zhongshan University in Guangzhou, Guangdong Province, has put the final pieces together in the solution to the puzzle that has perplexed scientists in the world for more than a century. The pair has published a paper in the latest issue of the U.S.-based Asian Journal of Mathematics, providing complete proof of the Poincare Conjecture promulgated by French mathematician Henri Poincare in 1904. The work done by Zhu and Cao has given a new proof for the uniqueness of solutions on complete manifolds, a different idea for doing the backwards blowup in time and a proof of the canonical neighborhood theorem, Prof. Hamilton said. He said he will further discuss details of the proof next week with a few prominent mathematicians in Zurich, Switzerland. "We want to be complete certain that everything in the proof is beyond question before making a formal announcement, because many researchers will base their work on it," he said. Prof. Hamilton, member of the U.S. National Academy of Sciences, is recognized as "the father of Ricci flow", who introduced the Ricci flow equation and his development of it into one of the most powerful tools in geometry and topology. Hamilton's video talk was shown by Shing-Tung Yau, a Harvard mathematics professor and a Fields Medalist. His audience included legendary astrophysicist Stephen Hawking and 2004 Nobel physics laureate David Gross. "I'm very positive about Zhu and Cao's work," Prof. Yau said when he elaborated the proof to the audience. "Chinese mathematicians should have every reason to be proud of such a big success in completely solving the puzzle," Prof. Yau said. In his wheelchair, Prof. Hawking listened to the lecture of Yau. Prof. Hawking combines physical theories and mathematical methods to explore cosmic origins and black holes. "Professor Hawking's attendance at the lecture indicates that this is a very important work," Prof. Yau said. Source: Xinhua see also Chinese Mathematicians Unravel Century-Old Mathematical Problem, Has Poincare's Conjecture been solved? The conjecture continues, and make a freefind' search in these pages ... Top mathematician recognizes Chinese work on solving Poincare Conjecture |
June 26, 2006
Making music with mathematicsFind out how you can turn music into maths and maths into melodies at a free public lecture at The University of Queensland next week. UQ Mathematics Senior Lecturer Dr Michael Bulmer will talk about Making Music with Mathematics at 7pm on Thursday, July 6 in Room 222, Parnell Building, St Lucia campus. Dr Bulmer will show how the structure of music, and what makes it worth listening to, can be examined using a mathematical approach. He will apply the ideas behind fractal images to analyse music and will demonstrate how a similar principle, fractal noise, can be used to compose mathematical music. This easy-to-understand public lecture is open to all and a light supper will be served at 8pm. Please RSVP to Ms Helen Grey on 07 3365 2424 or hg@maths.uq.edu.au for catering. Dr Michael Bulmer is a Senior Lecturer in Mathematics and Statistics with a passion for maths, music and education. He has been vice-president of the Queensland Association of Mathematics Teachers since 2001 and last year won an Australian Award for University Teaching in recognition of his work in promoting student learning. Making music with mathematics |
June 26, 2006
IT Road Map: The quantum computer |
June 26, 2006
Cosmos as computer: It's more than a metaphorJAMES N. GARDNER E ach historical epoch is associated with a prevailing cosmological metaphor -- a canonical paradigm that embodies a collective societal vision of the ultimate nature of the universe. These metaphors invariably reflect the supreme technological or cultural accomplishments of a particular era. For example, for the ancient Greeks, the pre-eminent technology was musical-instrument construction, and Greek cosmology was dominated by the concept of harmony, order and the music of the spheres. For the leading playwright of the Elizabethan era, William Shakespeare, the world was "a stage, and all the men and women merely players." In Isaac Newton's era, the highest technological achievement was clockwork manufacture, and, unsurprisingly, the Newtonian metaphor for the universe was a great cosmic timepiece, ticking away with inexorable precision throughout eternal time and infinite space. In a subsequent era, the thermal power of internal and external combustion was harnessed to fuel the Industrial Revolution, and the dominant cosmological metaphor became a vision of the cosmos as a vast thermodynamic engine facing the inevitable fate of heat death. "Today," astrophysicist Paul Davies has observed, "the computer is the pinnacle of technology, so now it's fashionable to talk about nature as a computational process." This metaphor portrays the movements of every material object from quark to galaxy as subroutines in a vast computing system running on software that consists of the fundamental laws and constants of nature. This is the cosmic paradigm advocated with great enthusiasm and eloquence by MIT computer scientist Seth Lloyd in "Programming the Universe: A Quantum Computer Scientist Takes On the Cosmos." However, in Lloyd's view, computation is not merely a metaphor for the operations of the cosmos. He believes the universe is literally a giant computer -- indeed, that it is a very special kind of device known as a quantum computer. The difference between a quantum computer and the PC sitting on my desk is that the former exploits all the weird aspects of quantum physics to conduct super-fast calculations that are simply impossible on a traditional digital computer. For instance, rather than churning through various numerical combinations that might crack a top-secret NSA code, a quantum computer can explore all the possibilities simultaneously. (It is hardly surprising that the National Security Agency is one of the top sources of research funding for quantum computing research.) Lloyd believes the "history of the universe is, in effect, a huge and ongoing quantum computation. The universe is a quantum computer." And what precisely is the universe computing? Lloyd's answer is straightforward, if a trifle cryptic: "[The universe] computes itself. The universe computes its own behavior. As soon as the universe began, it began computing. At first the patterns were simple, comprising elementary particles and establishing the fundamental laws of physics. In time, as it processed more and more information, the universe spun out ever more intricate and complex patterns, including galaxies, stars and planets. Life, language, human beings, society, culture -- all owe their existence to the intrinsic ability of matter and energy to process information." Indeed, Lloyd believes that his insight explains one of the great mysteries of nature: Why is all that complexity out there? Why didn't the universe remain a uniform, dilute soup of featureless matter and energy after the Big Bang? Where did all the evident diversity come from -- matter clumped into stars, planets and giant pinwheel galaxies and, on at least one planet orbiting an ordinary sun, the seemingly miraculous emergence of life and intelligence? What is the source of this puzzling complexity, particularly the overwhelming complexity of living matter? Here is Lloyd's intriguing response: "The computational capability of the universe explains one of the great mysteries of nature: how complex systems such as living creatures can arise from fundamentally simple physical laws. . . . The computational universe necessarily generates complexity. Life, sex, the brain, and human civilization did not come about by mere accident." James N. Gardner is a Portland attorney and the author of "Biocosm." His new book, "The Intelligent Universe," will be published in 2007. Cosmos as computer: It's more than a metaphor |
June 26, 2006
On Numb3rs, Krumholtz makes mathematics coolBy SEAN MITCHELL New York Times News Service LOS ANGELES - As one indication of how thoroughly he has mastered the part of a mathematics professor on the Friday-night CBS drama Numb3rs, David Krumholtz was invited to attend the commencement ceremony earlier this month at the California Institute of Technology in Pasadena. David Baltimore, the Nobel Prize-winning president of Caltech, even saluted Krumholtz and the show during his remarks to the graduating class. Not bad for Krumholtz, who never went to college, nevermind a powerhouse like Caltech. Krumholtz, who grew up in New York and appeared on Broadway at 13 with Judd Hirsch in Conversations With My Father, has won that kind of respect because as Charlie Eppes he has helped make math look cool. In Numb3rs, now in reruns after completing its second season, Krumholtz's character regularly helps his older brother, an FBI agent played by Rob Morrow, solve crimes by using his advanced knowledge of equations, numbers theory, algorithms and other mathematical tools. His role has been described by one reviewer as "Sherlock Holmes for the slide-rule set," though the show's weekly audience of more than 12 million last season — making it top-rated in its time slot — suggests an appeal well beyond the student bodies of Caltech and MIT. Krumholtz's uncanny facility with the language of math — uncanny for someone who readily admits he showed no aptitude for it in high school — won him the part over about 100 other actors who had auditioned for the role of a prodigy who teaches at a California university resembling Caltech. "We had some monologues with a lot of math language, and it's very difficult to sound like you say these words every day," said the show's co-executive producer, Cheryl Heuton. "We began to think we had written an uncastable part until David came in one morning." "I'm no mathematician," Krumholtz said. "I think it's more important that I learn who a mathematician is and how he sees the world than it is to actually learn the math." "The mathematics community has embraced us because the character is a great representation of their passion," he continued. Mathematicians are typically portrayed on on-screen "as mad or emotionally unstable or socially retarded," he said, "and that's not something we wanted to do at all." As a result, Krumholtz has been invited to three math conventions this year. And Texas Instruments, in association with the National Council of Teachers of Mathematics and CBS, has developed a program of math-education activities for teachers geared to the crime-solving techniques used on the show. In Numb3rs, Krumholtz has been reunited with Hirsch, who plays his father (again), and with his friend Peter MacNicol, who plays the meddling colleague Larry Fleinhardt. "Most procedural shows don't go into the characters that much," Hirsch said, suggesting that Charlie and his family have been an exception to the rule among crime-investigation series. When Charlie's mother died, for example, Krumholtz's character buried himself in a famously unsolvable math problem known as "P versus NP." It is a matter of pride to Krumholtz, 28, that he has won acceptance for his role in Numb3rs after being stuck for years in a Hollywood niche he found frustrating. "I was doing the whole New York neurotic schlub thing for a really long time," he said. "That or the nerd." While he earned praise for small roles in films like The Slums of Beverly Hills, The Santa Clause and Liberty Heights, he was worried that he was becoming a "show killer" in television after acting in five series (including The Trouble With Normal) that failed in their first seasons, as well as in five more pilots that never made it to the air. "That was very upsetting," he said. When he was rejected for a comedy series three years ago, he began to take stock. "The comedy thing wasn't working out," he said, even though he said people have found him funny since grade school in Queens. (His father, a postal worker, and his mother, a dental assistant, divorced when he was 2.) A turning point came in 2002, when he was cast in a guest role on ER as a deranged patient who stabbed two doctors. "Even that guy was a schlub," Krumholtz said, "but it was the first dramatic thing I'd done since the first play I did on Broadway. It opened up a whole new thing for me. People realized that I could do drama, that I could scream and be pretty serious and frightening." Numb3rs has proved to be an altogether different experience. "I knew after the pilot that if this thing went, it would be the best thing I'd ever done," he said, "and that it had the chance to influence people." Krumholtz has never studied acting, although he said that working alongside Hirsch on Broadway at a young age taught him a lot. "Here I was, assisting this brilliant Tony Award-winning performance every night with this guy who I just loved as a man." Hirsch, who earned a degree in physics at the City College of New York before becoming an actor, said there were two reasons he was eager to join the Numb3rs cast: "I knew it was about math and that David was in it." On Numb3rs, Krumholtz makes mathematics cool |
June 26, 2006
Wolfram Workbench IDE: come sposare matematica e programmazioneMathematica, il celebre pacchetto di calcolo numerico ed analisi matematica si arricchisce di uno specifico ambiente di programmazione, per unire gli algoritmi computazionali alla comodità di operazioni controllabili. Un IDE moderno in grado di interfacciarsi con la maggioranza dei prodotti di Wolfram. di Giuseppe De Maso Gentile Per molti anni il Fortran ha avuto il compito di far da ponte tra gli elementi programmativi e la complessità degli algoritmi matematici. Senza voler togliere nulla all'importanza di tale linguaggio, Wolfram Resarch ha pensato di favorire l'unione degli strumenti computazionali di Mathematica con i benefici di un ambiente di programmazione appositamente creato. E' nato così Wolfram Workbench, un IDE specifico per le tecnologie del pacchetto scientifico, basato su Eclipse (un analogo strumento per la programmazione Java). Nell'intento dei creatori, Wolfram Workbench favorirà la realizzazione di progetti scientifici e tecnici di vaste dimensioni potendo riutilizzare il codice generato nel linguaggio proprio di Mathematica. Tra le particolarità di rilievo segnaliamo una completa gestione dei file, risorse e linee di codice già create con Mathematica, analisi e correzione degli errori con segnalazioni e report, evidenziazione delle variabili locali utilizzate con colori diversi, proprio come ogni moderno IDE che si rispetti. Per mezzo del Workbench si potrà anche selezionare una porzione di codice per studiarla separatamente dal complesso, semplificando l'opera di individuazione dei problemi e dei bug. Saranno presenti specifiche opzioni per la gestione semplificata di versioni multiple dei propri lavori. Al momento la società mette a disposizione una pre-release di prova, gratuitamente a clienti selezionati, per saggiare la bontà del prodotto. La versione definitiva sarà disponibile dal prossimo luglio ad un costo di 145 dollari per le maggiori piattaforme: Mac OS X, Linux e Windows. L'esistenza di un tale prodotto è di importanza chiave, per il mondo Macintosh, essendo utilizzato da migliaia di ingegneri, scienziati, analisti finanziari, ricercatori e studenti in tutto il globo. Un vero e proprio standard presente in diversi campi che spaziano da quello industriale a quello accademico. Wolfram Workbench IDE: come sposare matematica e programmazione |
June 26, 2006
I motori di ricerca vanno alla conquista di MySpacedi Bernardo Parrella MySpace, stella indiscussa del social networking online, non vuole smettere di crescere. Nel mese di maggio ha registrato 51,4 milioni di visitatori unici, affermandosi come settimo sito assoluto per numero di hit, precedendo nomi quali Amazon, Apple e New York Times. Un bel balzo in avanti rispetto ai 17 milioni di visitatori unici contati poco meno di un anno fa, quando Rupert Murdoch decise di sborsare 580 milioni di dollari per inglobarlo nell'impero di News Corp - con l'ovvia speranza di trarne ricavi ancora maggiori, un giorno non troppo lontano. È vero che ora il sito non genera più di 100 milioni l'anno in entrate pubblicitarie (bruscolini per simili corporation), ma vari segnali sembrano indicare che quel giorno va avvicinandosi. Lo conferma soprattutto la "gara d'appalto" aperta nei giorni scorsi per la messa a punto di un motore di ricerca personalizzato per MySpace, notizia che ha scatenato una serie di dinamiche a tutto campo. Perché mai? Be', notoriamente le ricerche generano montagne di traffico e inserzionisti (Google docet), meglio ancora se si ha un profilo dettagliato del proprio target, come è chiaramente il caso con gli indaffarati adolescenti che popolano MySpace. Un enorme bacino di dati che garantisce parecchia crescita commerciale, ma che finora non è stato esplorato più di tanto dall'editore, al pari di altre entità online presenti nella scuderia di Fox Interactive Media. Scenario destinato a cambiare, ha spiegato il COO del gruppo Peter Chernin, nell'annunciare la nuova strategia interna sui search engine. Dopo aver considerato per qualche tempo il classico approccio, ovvero l'acquisto di un motore per poi modellarlo in base alle proprie esigenze e rilanciarlo alla grande, come hanno fatto in passato Yahoo! e MSN, l'odierna potenza di mercato conquistata da MySpace lo pone in ottima posizione per stipulare un accordo vantaggioso con uno dei grandi protagonisti del settore. Già oggi i suoi utenti producono oltre 100 milioni di ricerche, coprendo il 5% di tutte le ricerche effettuate sul web e l'8% di quelle che passano per Google. Come diretta conseguenza, spiegano gli esperti, MySpace potrebbe aggiudicarsi il 25-35% delle entrate pubblicitarie ricavate dalle pagine prodotte per il motore-partner—con annesse potenzialità per inventarsi business model ancor più remunerativi per entrambi. Non a caso «l'affare sarà dell'ordine di centinaia di milioni di dollari», spiega Chris Sherman, responsabile dell'osservatorio industriale Searchenginewatch.com, e per il posto al sole sono già in corsa i big Google, Yahoo! e MSN, i quali dovranno comunque garantire piene capacità audio e video onde soddisfare al meglio le sofisticate esigenze del pubblico di MySpace. Senza neppure escludere un possibile avvicinamento con Blinx, leader delle ricerche video che va conquistando sempre maggiore attenzione online. Insomma, l'aspra concorrenza tra i search engine per mettere solidamente piede nel giro (e nel business) di MySpace sembra tornare a tutto vantaggio degli utenti, oltre che porsi come elemento cruciale della futura strategia complessiva del mega-gruppo Fox Interactive Media. Nel frattempo il lucrativo mercato del web-search è tutt'altro che dormiente, e i maggiori soggetti sono costantemente alle calcagna della star Google. Anzi, dalle rilevazioni fornite da Nielsen Netratings per il mese di maggio si nota come Google e Yahoo! stiano accelerando il passo e incrementando le rispettive le quote di mercato, con un più 32% e 34%, rispettivamente. Da solo Google, che raggiunge un numero di ricerche più alto di Yahoo!, MSN, AOL e Ask messe insieme, raccoglie 2,78 miliardi di richieste (il 49,1%), mentre Yahoo! ne attrae 1,30 miliardi, pari al 22,9%. MSN è cresciuto più di Google e Yahoo! in termini percentuali (42%, con 601 milioni di ricerche), ma l'incremento non è stato sufficiente a tenere il passo, con quote passate dal 10,7% di aprile al 10,6% di maggio. Ancora più indietro troviamo AOL Search con il 6,4% e Ask.com con il 2,6%. Complessivamente, cresce ancora la popolarità delle ricerche online, con un più 7,5% rispetto ad aprile per un totale di 5,67 miliardi di ricerche. Il divario con Google si fa più evidente considerando il solo mercato statunitense, dove il motore californiano conquista il 43%, di fronte al 28% di Yahoo!, al 13% di MSN e al 6% per Ask, che è proprietà di IAC/Interactive Corp, conglomerato composto da circa 60 cyber-testate. Ma proprio questa generale superiorità di Google sta aprendo alcuni varchi nel settore, perché, suggerisce ancora Chris Sherman, «si considerano i migliori, eppure non sembrano avere sul serio una strategia chiara», riferendosi alla moltitudine di settori in cui il marchio va allargandosi spesso in maniera (apparentemente?) casuale. Ecco allora che Yahoo!, il cui portale, ricordiamolo, rimane il più grande su Internet, con circa 400 milioni di visitatori, va investendo non poco su differenziazione e personalizzazione delle ricerche e ha messo centinaia di ingegneri al lavoro. Anziché avere una fede "quasi-religiosa" negli algoritmi matematici che hanno fatto la fortuna di Google, Yahoo! «vuole integrare le persone migliori con la tecnologia migliore», chiarisce Eckart Walther, uno dei maggiori artefici di questa strategia. «L'idea è quella di non prendere in considerazione soltanto i link tra i vari siti ma anche tra le persone…fino a usare la ricerca sociale per risolvere richieste sempre più soggettive». Vanno in tal senso anche le dritte di Caterina Fake, co-fondatrice del popolare Flickr poi acquisito da Yahoo!, onde evitare la genericità per puntare invece a contenuti originali ed eclettici, come avviene con i ritorni offerti da MyWeb, altro engine del gruppo Yahoo!. Anche Ask (che da qualche mese ha abbandonato il suffisso iniziale, Jeeves) sta sperimentando con la differenziazione, presentando i link raggruppati in pagine ritenute popolari e affidabili dagli esperti di un particolare argomento, metodo che spesso procura risultati migliori dei ritorni massicci ma indifferenziati di Google. Motore di nicchia ma superaffidabile, dunque, che Searchenginewatch.com paragona alla Apple, con la sua ridotta eppure fidatissima folla di seguaci, pur se il gigante rimane Microsoft. A proposito, quest'ultima che dice? Anche per i search engine sembra seguire una strategia già vincente in passato: arrivare in ritardo sul mercato con un prodotto copiato e mediocre, ma che gradualmente migliora fino al punto di prevalere – ovviamente contando sull'egemonia del marchio software. A conferma del fatto che anche tra i motori di ricerca la battaglia rimane aperta, anzi apertissima. I motori di ricerca vanno alla conquista di MySpace |
June 20, 2006
García Ramos presenta hoy el libro de cuentos matemáticos de Luis Balbuena El profesor Luis Balbuena, con algunas de sus publicaciones anteriores
El premio Canarias de Literatura, Juan Manuel García Ramos, presentará esta tarde en el Ateneo de La Laguna un nuevo libro del matemático Luis Balbuena. En esta ocasión, Balbuena ofrece tanto a maestros, alumnos como al público en general en sus Cuentos del cero una forma divertida e ingeniosa de entender "la única asignatura que aparece en todos los planes de estudio del mundo". |
June 20, 2006
The New New Math of String Theory Mina Aganagic
Earlier this year, Mina Aganagic co-organized a Mathematical Sciences Research Institute (MSRI) program on New Topological Structures in Physics to encourage collaborations between mathematicians and physicists working on problems such as String Theory.
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June 20, 2006
Prix Mathématique-Léopold Sédar SenghorUn prix Mathématique-Léopold Sédar Senghor dénommé "Prix Maths-Senghor" a été institué par l'Espace Mathématique Francophone, Organisation mondiale des mathématiciens d'expression française, dans le cadre de la célébration du centenaire de la naissance de l'ancien président du Sénégal. Le Prix Maths-Senghor servira à encourager et à promouvoir les travaux originaux publiés en français dans le domaine de l'enseignement, de la recherche et des applications des Mathématiques, réalisés par de jeunes mathématiciens de moins de quarante ans d'Afrique et de la diaspora africaine mondiale. La présentation officielle du Prix Math-Senghor sera faite lors de la deuxième Conférence des intellectuels d'Afrique et de la Diaspora (CIAD2) qui se tiendra du 12 au 14 juillet 2006 à Salvador (Bahia), sous le patronage de la l'Union africaine et du président du Brésil, Luis Ignacio Lula da Silva. Prix Mathématique-Léopold Sédar Senghor |
June 20, 2006
Geometrie di aneurismaCome la matematica entra nella ricerca medica: progetto al Politecnico di Silvia Baglioni "Gli aneurismi si possono diagnosticare e curare, ma è molto difficile definire esattamente cosa sono, come si formano e, soprattutto, come evolvono". Alessandro Veneziani è un matematico del Laboratorio di Modellistica e Calcolo Scientifico MOX del Politecnico di Milano, ma non per questo ha difficoltà a definire gli aneurismi, anzi, con il suo prezioso aiuto i neurochirurghi del Niguarda hanno intrapreso, da un anno, un progetto di "chirurgia predittiva". "Utilizzando quel formidabile linguaggio che è la matematica", spiega Veneziani, "è possibile descrivere cosa succede nel cuore, nelle arterie, nel cervello. Il nostro studio, denominato ANEURISK (nato dalla collaborazione del mio dipartimento, del Laboratorio per le Strutture Biologiche dello stesso Politecnico, dell'ospedale Niguarda, dell'Istituto Mario Negri di Bergamo e della Siemens), si propone di analizzare le geometrie di aneurismi cerebrali, evidenziati con le Tac, sfruttando le tecniche di ricostruzione geometrica, analisi statistica e simulazione della dinamica del sangue. Vogliamo capire", continua Veneziani, "quanto la morfologia dei vasi sanguigni possa influire sulla nascita e sul destino di questi micidiali vortici. L'obiettivo ambizioso è scovare dei parametri geometrici, misurabili con gli esami di routine, che possano essere usati come "sentinelle" per quantificare i rischi di rottura dell'aneurisma (evento spesso mortale per il paziente) e dunque per aiutare il medico, indipendentemente dalla sua esperienza, a prendere decisioni appropriate". Da luglio, all'ospedale di Milano, sono stati studiati 75 casi di sospetto aneurisma cerebrale (a fine progetto, tra un anno, i casi esaminati saranno almeno 300). In queste circostanze il neurochirurgo sottopone il paziente ad una Tac che permette di evidenziare il punto critico. Una volta comprovata la presenza dell'aneurisma, al medico resta il dubbio se operare o aspettare l'evolvere degli eventi: un intervento può anche aumentare il rischio di rottura e quindi il pericolo di vita. In questo quadro le risposte che i matematici possono offrire diventano davvero preziose. Geometrie di aneurisma |
June 19, 2006
Mathematician colors his numbers into artworksBy Jennifer Flowers  Dr. Paul Sisson The complex landscapes he sees could take years to explain, and he rarely knows how to illustrate them. Many mathematicians will agree with Sisson, dean and professor of math at LSUS' College of Sciences department, that the often beautiful world of numbers will remain hidden from most people because it would take several years and a doctoral degree to learn the language needed to comprehend it. But Sisson jumped on a rare opportunity to give people a glimpse of the complex mental landscapes found in math. His resulting artwork now is hanging on the walls of Bistro 6301 on Line Avenue in Shreveport. "I'm just trying to get people to realize that math is beautiful," Sisson said. "It's not just the boring number crunching you did in high school." Bistro 6301 co-owner Amy Grosz never scouted artwork for her restaurant at a mathematician's office before, but admits she was fascinated by Sisson's digitally printed images, especially when Sisson explained the concepts behind them. "Just the basis behind it is very interesting," she said. "I thought that the colors are really brilliant in the pictures. They way they contrast just within one little area, they seem to glow. It's really amazing that he can do that just by assigning a color to a number, basically." Even without the theory, patrons have noticed the vibrant works, which are adding energy to the dining room, Grosz added. Many are more intrigued when they discover a mathematician made them. Sisson wrote the program he uses for his artwork more than a decade ago in a programming language called Mathematica, employed by mathematicians and scientists to study, analyze and visualize concepts and data. His intent was to research complex numbers, or a collection of numbers that extends past the numbers familiar to the average Joe. But soon he fell in love with the resulting patterns and began manipulating their aesthetic attributes. "In the simplest terms, it takes one complex number and turns it into another complex number," Sisson said. His images are anchored by one central mathematical reference point, which usually appears as a gold ring. That ring's mathematical qualities become the reference point for the other spatial relationships and patterns. Green in his work represents one iteration of the original pattern, while blue represents two. Red represents 12 iterations, but that's as far as he goes -- anything higher is blanketed in black. Sisson estimates his technique is 50 percent math and 50 percent art. "There's a lot of classic math here," he said. "But I also make up a function and look at it and see if I like it. If I don't like it, I try to modify it, and that's where the art comes in." Sisson is no stranger to visual art. As a teenager, he made stained-glass lamps and custom windows in Michigan and almost moved to Chicago to make a career out of it before studying math. Two summers ago, he rode his motorcycle all the way to Corning, N.Y., to take glass-blowing classes. Like Sisson, LSUS math professor Rick Mabry often is surprised at the beautiful images he sees when visualizing math and uses what he finds as examples in class. "It's like sculpting," said Mabry, describing Sisson's process. "He found the raw image and massaged it and tweaked it and explored it, really. "» He made some of those decisions based on some reaction to it." Even with his doctoral degree, Mabry needed Sisson to explain the mathematical process behind his work, especially since he added his own aesthetic choices. "Artists tell me the discovery part is the art of the process," he said. "I used to think picking the right color was part of it, and artists are quick to tell me that's not what art is. "» The imagining and the trials and so forth, that's the art part." Though math and art tend not to be uttered in the same breath, mathematicians and artists say they are deeply intertwined. Cubist Pablo Picasso, explained Sisson, used mathematical ideas by simultaneously representing multiple visual perspectives, or multiple points in time. Abstract expressionist Jackson Pollock left his work up to the randomness of his paint splatterings, but his process can be explained mathematically through chaos theory. Techniques like perspective and vanishing point all rely on basic mathematical principles. And then there are Mandelbrot sets, mathematical patterns discovered by Benoit Mandelbrot, which have been discussed extensively in the art world. They inspire fractal art, in which self-similar images are repeated numerous times while getting smaller and smaller, making irregular shapes and patterns that cannot be explained with classical geometry. And mathematicians are creating original art every time they break new ground in the field, according to Sisson. It's just not so easy to hang on the wall. "I hope that people look at my artwork and ask, 'what is that?'" Sisson said. "Every time they do that, I have five minutes to talk about math." Mathematician colors his numbers into artworks |
June 19, 2006
INFINITE JESTEncountering the threshold of humankind's capacity for mathematical gamesmanship, at the annual Gathering for Gardner by Siobhan Roberts During his presentation in the chandelier-festooned ballroom of Atlanta's Ritz-Carlton Hotel, Akihiro Matsuura motioned to the Plexiglas cylinder lying horizontally in front of him and asked his audience what path a tennis ball would take if rolled along the cylinder's interior wall. "Spiral!" yelled one person in the audience. "Helix!" yelled another. The ball defied them both by rolling around the cylinder with a discrete elliptical route, returning to Matsuura's hand like a yo-yo tethered to a string. "NO!" The spectators gasped. There was a rumbling of flummoxed unease. With a mime's spare grace, Matsuura, a lecturer in computer science at Tokyo Denki University, then turned the transparent cylinder on its end and asked again: "Now what route will it travel?" The audience conferred: town, of course—but how? Would it drop straight, or curve like a corkscrew? Matsuura released the ball. It took a curving path downward, as expected, but then reversed course and climbed the cylinder, completing a three-dimensional figure eight—ending, again, in Matsuura's ready hand. Matsuura might well have announced the unification of quantum mechanics and special relativity in the Ritz-Carlton ballroom that day, judging by the cries of incredulity that erupted from his audience. But Matsuura just shrugged his shoulders. "I can't help myself," he said. So concluded the 43rd presentation of math and magic at "Gathering for Gardner," a bi-annual pilgrimage honoring Martin Gardner, who, from 1957 to 1981, enraptured mathematicians and scientists, hobbyists and professionals, magicians and puzzlists and skeptics alike with his "Mathematical Games" column in Scientific American. Known among the faithful as "G4G7" (as in "Gathering for Gardner," and seven because it is the seventh such gathering), the events are organized by Atlanta businessman Tom Rodgers, who one night had all 250-plus members of the international cult of Gardner over to his Japanese-style house, incongruously set atop red clay hills and a forest of Georgia pines, for sushi. The legend himself did not attend; living as he does in Norman, OK, and despising travel, Gardner has made it to only two of the events in his honor. Now a youthful 91, he performs his trademark tricks with more dexterity than ever. One Gardnerite, invoking George Bernard Shaw, observed that "We don't stop playing because we get old—we get old because we stop playing." Gardner himself has not stopped—currently he is writing a collection of essays, one on each of 12 books by the "prince of paradox," G.K. Chesterton. The conference equivalent of speed-dating, G4G7 was packed with math-and-magic presentations of 10, 20 or 30 minutes. Subjects addressed a curiosity cabinet of intellectual jewels, each revealing something quizzical about the world—like the presentation by Michael Cantor, an Atlanta experimental psychologist, on "Competence: Drivers, Aviators, Jugglers and More"—or concealing something magical, like the Swede Lennart Green's masterfully clumsy card tricks. Green doesn't deal cards, he fumbles and spills them, crumpled, in a seemingly chaotic mess—but reveals a royal flush. Then there was the talk by Bob Friedhoffer, who addressed an always-controversial issue: "Performing Fleas, Were They Up to Scratch?" Wiping his sweaty brow and repositioning his baseball cap (fittingly emblazoned with 3.141592) at the end of day two, Atlanta high-school teacher Steven Sigur willed himself to stay in his seat. "It's all very interesting, but I'm about to OD," he said. By day four, even Princeton's John Conway—typically the earliest to rise and last to bed—was lamenting the overload. "There's infinitely much to know," he said. "You simply can't know it all, despite the fact that that is my aim." This being the seventh Gathering for Gardner, the event celebrated "seven" in all its incarnations. The mathematician and physicist Sir Roger Penrose pondered "Seven: Geometry and Beyond." "Part of mathematics is like puzzle solving," said Sir Roger, "and it is a good way of getting people interested in mathematics without them realizing it is mathematics." Neil Sloane, a fellow at AT&T in Florham Park, NJ and creator of the On-Line Encyclopedia of Integer Sequences, expounded on "Seven Staggering Sequences." One in particular, discovered by Bernardo Recamán Santos, contained a pattern of numbers so difficult to decipher that those who've tried have dubbed it "How to Recamán's Life." And abiding by a rather lowbrow G4G tradition, the numerological riff by LA-based Scot Morris (best known as the erstwhile "Games" editor from Omni magazine) was a comprehensive chronicling of the importance of the "Cosmic Seven." He pointed out there are seven colors in the spectrum, seven notes in the diatonic scale, seven seas, seven continents, seven wonders of the world, seven dirty words (according to George Carlin) and seven holes in the typical human head. "That was such a load of crap," countered Robert Sandfield, a puzzle designer from Houston. As is the G4G custom with these two good-natured banterers, Sandfield followed with his own presentation, on "Anti-Seven." "Why did six fear seven?" asked this grown man, keeping an entirely straight face. "Because seven eight nine." INFINITE JEST |
June 19, 2006
The dean of debunkingIn challenging string theory, Peter Woit is taking on the self-interest of the entire scientific establishment NOT EVEN WRONG: The Failure of String Theory and the Continuing Challenge to Unify the Laws of Physics by Peter Woit Cape £18.99 pp290 What is the basic, unifying stuff of our universe? One philosopher in ancient Greece thought that everything was reducible to water; another plumped for air. Later, a philosopher called Democritus taught that the world is ultimately made up of tiny, eternal particles of varying weight known as "atoms", which form and reform as nature undergoes its constant round of change, death and rebirth. Today, 2,500 years on, and after several great revolutions in modern physics, a large and expanding community of scientists believes that the basic stuff of our universe is "strings". Hence "string theory". These are no ordinary strings. The physicists envisage tiny, vibrating, folding and elongating coils of energy, each 100 billion billion times smaller than the protons at the nucleus of an atom; so small,indeed, that they can be understood only in terms of extremely sophisticated mathematics impenetrable to all but an elite of specialists. String theory, which nowadays dominates the research programmes and main funding of theoretical physics in many western universities (at a recent conference in Cambridge some 440 of them gathered to discuss their subject), was not so much discovered as invented in order to solve a vexing explanatory deficit. In the early 1970s, physicists announced the so-called "standard model" — a theory that seeks agreement between the contrasting realms of super-huge objects, such as stars and planets, (known as relativity) and the super-small realms of the subatomic (known as quantum). The standard model, however, failed to explain gravity. Enter string theory to rectify the problem. In its simplest terms, this complex set of notions claims 10 or 11 space dimensions (as opposed to the three of everyday human perception), and assumes a "landscape" of myriad elementary bundles of energy (strings) that interface not only with the universe we inhabit but a multiplicity of unseen and unknowable parallel universes. But is string theory true? Peter Woit, a mathematician at Columbia University, has challenged the entire string-theory discipline by proclaiming that its topic is not a genuine theory at all and that many of its exponents do not understand the complex mathematics it employs. String theory, he avers, has become a form of science fiction. Hence his book's title, Not Even Wrong: an epithet created by Wolfgang Pauli, an irascible early 20th-century German physicist. Pauli had three escalating levels of insult for colleagues he deemed to be talking nonsense: "Wrong!", "Completely wrong!" and finally "Not even wrong!". By which he meant that a proposal was so completely outside the scientific ballpark as not to merit the least consideration. Woit's book, highly readable, accessible and powerfully persuasive, is designed to give a short history of recent particle and theoretical physics. Ultimately he seeks not only to rattle but to dismantle the cage of the string theorists. What gives the book its searingly provocative edge, moreover, is the fact that Woit isn't even a tenured professor, but a mere mathematics instructor specialising in computer systems. Yet he has formidable allies such as David Gross (the Nobel Llaureate theoretical physicist), Roger Penrose (the world-class mathematician) and Lee Smolin (the leading cosmologist), plus an accumulating constituency of other big-name supporters. Woit has taken on a group of the smartest minds in the world and told them that their intellectually imperial pretensions are naked. He has boldly published what many have thought but never dared to express so cogently, or at such length. He grants that an explanation for gravity is usefully embedded in string theory, but he challenges its authenticity as proper science. In his view, string theory offers no foreseeable prospect of making predictions, a crucial criterion for any theory worthy of the name. Matching the theory with the way we see the world, he argues, depends on believing in sixseveral tiny unobserved spatial dimensions wrapped around each other. Hence there is an infinite number of possible choices as to how one would make predictions, and nobody knows how to determine which choice is correct. The objection invokes the late Karl Popper's widely accepted definition of science. An explanation is scientific, according to Popper, only if it can be used to make predictions of a kind that can be falsified: in other words, can be checked to be right or wrong. Woit's second main objection is that string theory offers no possibility of producing experimental evidence. Even the proposed prodigiously expensive class of accelerators known as Superconducting Super Colliders (SSCs), he claims, would have failed to provide the merest clue as to whether the theory had merit. In the event, the SSCs fell victim to the hubris of physics. An infamous example is the one at Waxahachie, Texas. Budgeted at $11 billion, and designed to be 87km, it was cancelled by Congress in 1993 when $2 billion had been spent and 22km of tunnel constructed. Woit's most compelling accusation, however, is that the domination of string theory in universities has stifled progress in alternative research programmes within theoretical physics. As long as the leadership of the physics community refuses to accept that string theory is a "failed project", he writes, "there is little likelihood of new ideas finding fertile ground in which to grow". Finally, and most devastatingly, he follows the lead of the science writer John Horgan, who suggested in his controversial book, The End of Science (1996), that, having reached their limit, some areas of science are in danger of becoming what he terms "ironic science". In a passage of ultimate insult, Woit unpacks this notion further, suggesting that theoretical physics has become like the deconstructionist realms of literary criticism in the 1970s, which disappeared up its own fundament, "incapable of ever converging on the truth". Now that Woit has thrown a wild cat among the theoreticians, we can be sure that the ruffled string-theory advocates will be preparing a rebuttal. Woit, the humble maths instructor, has nothing to lose in terms of academic standing, but physics might have much to gain from his boldness. While his book tends to be negative, it may well shake up a community of scientists that has evidently become complacent if not entirely ossified in its thinking. If he can encourage string theorists to acknowledge the true difficulties of their discipline, and encourage young researchers to try neglected but promising alternatives, he will have succeeded in an important task. Available at the Sunday Times Books First price of £16.99 (inc p&p) on 0870 165 8585 |
June 19, 2006
Introduction à la pensée de Gottlob Frege : Qu'est-ce que penser ?Par Ramatoulaye Diagne Presses Universitaires de Dakar 2004 158 pages Une autre vision des rapports entre la philosophie et les sciences www.walf.sn Lorsque la philosophie se penche sur les sciences et leur histoire, elle est soupçonnée de chercher à se rapprocher ainsi des sciences afin d'acquérir ne serait-ce que l'apparence de l'objectivité scientifique. L'épistémologie ne serait que l'expression d'une nostalgie pour l'époque où la philosophie regroupait en son sein, telle une mère, toutes les sciences. Etudier la pensée de Frege, comme Ramatoulaye Diagne, ancienne élève du Lycée Louis-Le-Grand, docteur en philosophie et maître-assistant à l'université Cheikh Anta Diop de Dakar, propose de le faire ici, permet, entre autres objectifs, de corriger une vision aussi erronée des rapports entre la philosophie et les sciences. En effet, au dix-neuvième siècle, les Mathématiques font face à la crise la plus profonde de leur histoire. La naissance de nouvelles géométries remet en cause le statut jusque-là accordé à la géométrie euclidienne, d'être seule possible et vraie puisque correspondant à la réalité que nos sens perçoivent. Désormais, la conception d'une vérité correspondance cède la place à une définition de la vérité comme cohérence interne, c'est-à-dire validité. Des systèmes géométriques tout à fait cohérents dans lesquels ne figure pas le postulat des parallèles, sont possibles. Or, l'existence d'une pluralité de systèmes philosophiques est l'un des arguments brandis contre la philosophie pour lui reprocher d'être subjective et de n'être qu'un défilé de visions du monde de différents philosophes. S'il est dans la nature de la philosophie de refléter l'Absolu dans la pluralité des systèmes - pour arborer ici un langage hégélien - quelle réponse les mathématiques peuvent-elles apporter face à ce phénomène nouveau pour elles qui est l'émergence d'une pluralité de systèmes géométriques. Pour Frege, la recherche d'une réponse est l'affaire à la fois de la philosophie et des mathématiques. Même si Platon a vite pris conscience des problèmes que pose le langage et surtout de l'usage qui peut en être fait, la paternité de la logique entendue comme science du raisonnement est généralement attribuée à Aristote. Ce dernier reconnaît qu'il existait des travaux sur la rhétorique, et même de nombreux travaux des anciens mais que, sur le raisonnement, toutes les recherches et réflexions sont à construire (cf. Aristote, Réfutations sophistiques). L'objectif de la rhétorique, c'est le bien parler, la séduction par le langage, et le bien penser n'est pas forcément pris en charge. Les sophistes, ces prestidigitateurs des mots, comme le dit Platon, se soucient-ils véritablement du vrai ? En revanche, l'objectif d'une réflexion sur le raisonnement, puis la mise en place d'une science du raisonnement consiste à mettre en place les normes, auxquelles tout discours soucieux essentiellement de distinguer le vrai du faux doit se conformer. Réthorique et logique ne sauraient donc se confondre. Après Aristote, tantôt la logique sera tirée du rôle des sciences, tantôt du côté de la philosophie ou de la métaphysique. Contrairement à celle d'Aristote, la logique n'est pas exclusivement une logique de l'être, une ontologique, elle est aussi une logique du devenir. Aussi, certains spécialistes considèrent-ils que ce sont les stoïciens et non pas Aristote qui ont exercé véritablement une influence sur la logique moderne qui affiche la volonté d'affranchir la logique des liens de la métaphysique et d'en faire une logique mathématique. En effet, l'idée selon laquelle la logique et les mathématiques entretiennent des relations privilégiées, s'est imposée depuis le milieu du XIXe siècle. Cependant, cette appellation renvoie à deux conceptions différentes des relations qui doivent exister entre la logique et les mathématiques. Dès le XVIIe siècle, le philosophe allemand Leibniz a perçu l'importance des mathématiques pour la logique, en caressant le projet de créer une logique qui prendrait comme modèle le langage mathématique. Il crée une logique binaire reposant essentiellement sur les deux valeurs, 0 et 1. Dans une telle conception, c'est aux mathématiques qu'il est demandé de faire à la logique le don de la rigueur liée au symbolisme. Cependant, Leibniz n'a pas véritablement élaboré cette logique mathématique. Il estime que c'est avec George Boole qu'un système de logique mathématique est véritablement mis en place pour la première fois. Boole, en effet, se propose de reprendre la logique traditionnelle issue d'Aristote pour la reconstruire selon l'esprit mathématique. Il affirme avec force que la logique n'est pas faite pour servir de forme à des recherches métaphysiques, elle n'est pas un instrument pour démontrer l'existence de Dieu et mener la recherche des causes premières. Frege déplore l'état peu satisfaisant des mathématiques. Malgré tout, il conserve une foi inébranlable en la capacité des mathématiques à nous conduire au vrai. Seule la logique est capable de fonder les mathématiques en expliquant les principes des mathématiques et les règles d'inférence qu''elles mettent en œuvre. Telle est la démarche à la fois fondationniste et logiciste de Gottlob Frege. Avec le logicisme de Frege, s'affirme la volonté de construire un langage logique idéal dans lequel tout énoncé mathématique pourrait être exprimé. Le logicisme de Frege aura une forte influence sur Wittgenstein et sur le mouvement positiviste logique du cercle de Vienne. Jürgen Habermas insiste sur le recul du logicisme, pour mettre en évidence ce qu'on peut appeler le 'tournant pragmatique'. Il souligne la naissance d'une philosophe qui refuse de se réduire à l'autoréflexion des sciences, 'dont le regard n'est plus fixé sur le système des sciences et qui adopte un point de vue opposé pour se retourner vers cette forêt épaisse qu'est le monde vécu, se libère du logocentrisme. Elle découvre une raison qui opère déjà dans la pratique même de la communication quotidienne'. L'approche pragmatique et le refus du logicisme se retrouvent chez Austin, par exemple, qui va montrer l'importance des circonstances dans lesquelles nous employons le langage. Dans le chapitre II Frege : Philosophie du langage, philosophie de la pensée, Ramatoulaye Diagne retrace l'itinéraire de Frege. Elle montre l'existence d'une certaine continuité de la pensée de Frege par rapport à la pensée de Leibniz. Comme ce dernier, Frege cherche à peindre non point les mots, mais les pensées, comme l'indique le mot 'idéographie' qui est une symbolisation de la pensée. Même si le logicisme de Frege a rencontré des obstacles et des contestations, il n'en a pas moins joué un rôle déterminant dans la naissance et l'évolution de la philosophie analytique. En effet, les logiciens eux-mêmes vont remettre en question le caractère absolu et universel que Frege attribue à la vérité : à l'absolutisme de Frege, ils opposent la conception d'une vérité relative au modèle. De plus, l'unicité d'un langage formulaire universel sera récusé au profit de la multiplication des langues ; et enfin, le fondationnisme de Frege cèdera le pas à une perspective pragmatiste et universaliste. Cependant, tous ces divers mouvements philosophiques se posent dans un dialogue avec la pensée de Gottlob Frege. D'organon, instrument pour la pensée, la logique est-elle devenue un instrument de lutte, une arme pour la destruction d'un certain type de pensée, à savoir la métaphysique ? Chez Aristote, la logique n'est pas une science en elle-même, mais une propédeutique, une préparation que chacun doit recevoir avant d'entreprendre l'étude d'une science. En d'autres termes, la logique est une forme susceptible de recevoir comme matière n'importe quelle science. Avec le positivisme logique, sous l'influence plus ou moins directe de Frege, de Russell, etc., la logique apparaît davantage comme une arme redoutable qui devrait permettre de trancher cette barbe inutile qu'est la métaphysique. Peut-on alors proposer une lecture de l'histoire de la logique selon laquelle cette histoire apparaît comme le passage pour la métaphysique du sens, voire de la source de tout sens, vers un pur et simple non-sens ? Cependant, la question majeure est la suivante : même si, selon l'avis de R. Diagne, elle est l'arme la plus redoutable, la logique constitue-t-elle une arme suffisamment puissante pour ruiner à tout jamais la métaphysique ? L'ambition première de la philosophie, de l'attitude philosophique, c'est de mener à bien la quête du sens de l'existence de l'homme. La question de son être est fondamentale. La connaissance de soi est la question fondamentale de Socrate qui s'est approprié l'inscription du sanctuaire de l'Apollon Pythien à Delphes : 'Connais-toi toi-même'. Elle est aussi le fondement du système cartésien, dont le cogito est la pierre angulaire. La démarche métaphysique a, très tôt, subi de nombreuses critiques dans l'histoire de la philosophie. Pascal lui reproche de parler d'un Dieu qui n'est pas le véritable Dieu, le Dieu chrétien, le Dieu d'Abraham, d'Isaac et de Jacob. Jean-Paul Sartre s'oppose à certaines thèses métaphysiques plutôt qu'à la métaphysique elle-même. Or d'autres philosophes comme Auguste Comte remettent en cause la métaphysique, elle-même, de manière plus radicale. Dans la critique kantienne de la métaphysique, ce ne sont pas les questions elles-mêmes qui sont remises en cause, mais la prétention de la raison à y répondre. Ludwig Wittgenstein (1889 - 1951), philosophe et logicien autrichien naturalisé britannique, a mené une critique tout à fait radicale de la métaphysique. Cette critique sera amplifiée par le Cercle de Vienne, école néo-positiviste fondée à Vienne vers 1920 par Moritz Schlick. Ramatoulaye Diagne conclut sur l'idée selon laquelle, ce n'est pas de la logique que peut venir le coup de grâce pour la métaphysique. Le besoin d'une interprétation normative de soi et du monde demeure. R. Diagne a su, d'une manière très pédagogique et claire, amener les lecteurs à penser à travers les textes de Frege. On peut regretter qu'elle n'ait pas abordé les questions liées entre la philosophie et la logique chez les Africains qui ignorent massivement l'usage de l'écrit. Amady Aly DIENG Introduction à la pensée de Gottlob Frege : Qu'est-ce que penser ? |
June 19, 2006
Mind-boggling mathematical show by a child prodigyMUSCAT — Nischal, a 10-year-old child prodigy from India, has put in a mind-boggling show that left a packed audience at the Indian Social Club's multi-purpose hall amazed. Indian Social Club, in cooperation with the Telugu Wing, hosted this multi-faceted genius prodigy and wizard of numbers who demonstrated an exceptional ability of mental mathematics and memory skills. For many in the audience, seeing was believing. Nischal was the guest of honour at the formal inauguration of ISC's Children's Wing. He, along with chief guest T.R. Mohana, vice-principal of the senior section at Indian School Muscat lighted the traditional lamp marking the ceremony. The show focused on Nischal's extraordinary wizardy with numbers and memory power. Nischal took the stage and his feats left the audience of children and their parents wondering in awe. Teachers from the ISM Mathematics Department fired complicated questions at Nischal and he obliged them with the correct answers within seconds using only his memory. Among the many solutions the 10-year-old math-genius worked out in the matter of seconds was the total of 12345 x 99999. Nischal was given the least side of a right-angled triangle and he worked out the lengths of the other two sides applying the Pythagoras theorem. Nischal also worked out square roots, the fifth root, products of six-digit numbers, fractions, percentages and within a matter of seconds, came out precisely with the day of a given date in the month of February in 1983. Nischal also filled 16 squares with two-digit numbers in such a way that the total of the columns and the rows and diagonally, were the same (130). What was amazing is that the numbers were not repeated. Nischal also involved the children from the audience and, in a mind-boggling demonstration, gave a display of his prowess to work with numbers. He recalled from memory a 26-digit number left to right and right to left with consummate ease. Using only his extraordinary mental skills, Nischal worked out the square root of 569 and then left the audience amazed when he worked out the fifth root of a 2073071515. Nischal is the second child of industrialist N. Nageswara Rao and Dr Padmavathy, a scholar in Sanskrit. The lad is a GradeV student of Gitanjali School, Hyderabad, South India. But it is his mother who has totally devoted herself to the grooming of his inherent talents and interest that lie beyond the realm of numbers. Nischal has also authored several books on maths for children. He has recently created the Nischal Math Lab, which consists of six volumes of books and mathematical equipment which enable youngsters to master challenging math concepts in an enjoyable manner. Milind Bhagwat, honourable general secretary of ISC, proposed a vote of thanks. At the end of the show, Nischal was felicitated by the Telugu Wing. The Tamil Wing also felicitated Nischal. Mind-boggling mathematical show by a child prodigy |
June 10, 2006
Sound investment: A new mathematical method provides a better way to analyze noise
Humans have 200 million light receptors in their eyes, 10 to 20 million receptors devoted to smell, but only 8,000 dedicated to sound. Yet despite this miniscule number, the auditory system is the fastest of the five senses. Researchers credit this discrepancy to a series of lightning-fast calculations in the brain that translate minimal input into maximal understanding. And whatever those calculations are, they're far more precise than any sound-analysis program that exists today. |
June 10, 2006
A mathematical framework shows new five-dimensional theory of gravity in Hyperspace that challenges the General Theory of Relativity of EinsteinCharles R. Keeton of Rutgers University and Arlie O. Petters of Duke University have unleashed the type II Randall-Sundrum braneworld gravity model. The theory holds that the visible universe is a membrane (hence "braneworld") embedded within a larger universe, much like a strand of filmy seaweed floating in the ocean. It has four spatial dimensions and the time. It is the conceptual Hyperspace in which our universe in floating like a bubble. Preparations are being made to test the braneworld theory through satellites in the space. It would confirm that there is a fourth dimension to space. It will all on a sudden change the views of classical physics. Physics and Astro-physics will have to be rethought again. According to brane theory (as proposed by physicists Lisa Randall of Harvard University and Raman Sundrum of Johns Hopkins University) a mathematical description of how gravity shapes the universe that differs from the description offered by the General Theory of Relativity is available According to some scientists the Hyperspace has five spatial dimension with no time dimension. The braneworld theory predicts that relatively small "black holes" created in the early universe have survived to the present. The black holes, with mass similar to a tiny asteroid, would be part of the "dark matter" in the universe. These small black holes are in thousands in our solar system. In Pluto's orbit one can observe the effects of our terrestrial science of a time black hole. The braneworld black hole produces an interference pattern in a passing burst of gamma rays as they travel to Earth. The resulting bright and dark "fringes" in the interference pattern provides a means of inferring characteristics of braneworld black holes and, in turn, of space and time. There are several methods of gamma-ray fringe pattern detection and measurement. The computer models are already showing its existence. The fourth spatial dimension will be further confirmed using the Gamma-ray Large Area Space Telescope, which is scheduled to be launched on a spacecraft in August 2007 by NASA in collaboration with U.S. Department of Energy, and France, Germany, Japan, Italy and Sweden. A mathematical framework shows new five-dimensional theory of gravity in Hyperspace that challenges the General Theory of Relativity of Einstein |
June 10, 2006
Springfield Theory |
Jaune 10, 2006
Mathematician pens book about famous mathematician foibles and funniesBy Alison Drain June 8, 2006 -- Steven G. Krantz, Ph.D., professor of mathematics at Washington University in St. Louis, illuminates mathematicians' very human brilliance in his book, Mathematical Apocrypha Redux, his sequel to his successful, original Mathematical Apocrypha, published in 2002, both by the Mathematical Association of America. The book is a collection of anecdotes about famous mathematicians and their frivolity, wisdom and situations, revealing more vulnerable, human versions of the remote and often eccentric savants. Krantz, who, in mid-career, has published a remarkable 53 books, once wrote: "Being a mathematician is a bit like being a manic depressive: you spend your life alternating between giddy elation and black despair," lives a very normal, public life. His office is filled with toys and gadgets; his head with stories and jokes — and math. He's approachable, engaging, funny and a widely recognized mathematical whiz himself. "The truth is, there isn't anybody who can productively think about mathematics more than four or five hours a day," Krantz says. "You just can't do it. So I spend the rest of the day writing books. Other people spend the rest of the day banging their head against a wall. I decided I'd rather do something productive with my time." Krantz received his bachelor's degree in mathematics in 1971 from the University of California, Santa Cruz before he could legally drink a beer. In 1974, at age 23, he was awarded his Ph.D. in mathematics from Princeton University. That same year he joined the faculty of UCLA as an assistant professor, moving to Pennsylvania State University as associate professor in 1981. He joined the Washington University faculty as professor of mathematics in 1986. Many have recognized his writing prowess: Krantz has received the coveted Chauvenet Prize of the Mathematics Association of America (MAA) in 1992 for expository writing, and the Beckenbach Prize of the MAA in 1994 for his book, Complex Analysis: The Geometric Viewpoint, published in 1992. So far, Mathematical Apocrypha Redux has been very well received. A Krantz sampling In the book, Krantz offers insight into the lives of many dozens of mathematicians, while minimizing the mathematical lexicon. "I really try to make the stories accessible to a broad audience," he says. And what's more accessible than stories? In Krantz 's own words, here is a sampling of the hundreds of anecdotes: • One day, a very famous mathematician at Princeton University named Willie Feller and his wife were trying to move a large table from their living room into their dining room. But they couldn't get it through the door. They struggled and they struggled and they just couldn't do it, and finally, in exhaustion and frustration, Feller sat down and did a mathematical derivation to prove that the table couldn't be gotten through the door. Meanwhile, as he was doing that, his wife got the table through the door. • My friend Ken Rosen is most successful textbook authors around — he has a very successful book on discrete math. And this book is actually used in Kuwait. In fact, the Kuwaitis had some trouble with this book's section on logic. And one of the things you do in sentential logic is you teach the students to analyze the truth value of the various sentences. There are some famous examples that you always use. So, one of the examples in this book is: if one plus one equals three, then God does not exist. Another example is: if two plus two equals four, then pigs can fly. He has these in his book. And the Kuwaitis were very unhappy with him because they thought the first sentence was blasphemous, and the second sentence somehow associated the unclean pig with God. They had to undergo some negotiation. • John Nash gave a talk in 2002, after the movie "A Beautiful Mind" had come out. It was very well attended. I think 2000 people went to the talk, and it was a very technical talk. The next day, my friend from Sweden, Christer Kiselman, went up to John Nash and congratulated him on the talk. He said, "Gee, I was very pleased to see how many people came out to your talk." And Nash said, "Well there's this movie starring Russell Crowe that seems to have gotten a lot of attention." Apocrypha, the sequel Unlike his first book, which was written entirely from his own experience at Princeton University's Institute for Advanced Study (home to Einstein and to many of the country's famous intellectuals ), these stories were assembled after many hours of diligent research. "I put every story I knew in the first book, and I thought, what am I going to do with a second book? " Krantz says. "Well, I had to do a lot of research, is what I had to do. So I worked like a dog to assemble good stories for the second book. But the good news is, everybody agrees the second book is much better than the first book." Of his writing regiment, Krantz says that while he might spend three to four hours writing on a teaching day, he'll spend up to eight to ten hours writing when he has the time. "I'm lucky in that I don't have problems with carpel tunnel, I don't have problems with my back, I don't have headaches, so I can just work," he says. His writing affects people worldwide: other professors read excerpts from his book of funny anecdotes to their rapt college kids. He's authored a how-to book for young people hoping to become mathematicians "This is all the stuff I wish somebody had told me 30 years ago," he says, of that work. Krantz's writing life has brought him into contact with legions of people from all over. One, having read his quote about the ups and downs of being a mathematician in her mathematics textbook, was even inspired to write his biography. That was even before she knew that Krantz published a whopping 12 books last year. Another contacted him from prison. "An inmate at Huntsville Penitentiary in Texas — arguably the worst prison in the country — contacted me because he was working his way through my real analysis book and he had some questions," Krantz recalled. "This guy turned out to be quite bright and we conducted considerable correspondence over quite a long period of time. I was quite impressed by the progress he made. He is now out and trying to re-establish himself in the computer business." Mathematician pens book about famous mathematician foibles and funnies |
June 07, 2006
Chinese Mathematicians Unravel Century-Old Mathematical ProblemAccording to Mingpao News, two Chinese mathematicians have successfully completed the proof of the Poincaré Conjecture, which has been one of the great unsolved mathematical puzzles since 1904. Professor Qiu Chengtong (Shing-Tung Yau) of Harvard University, a world renowned Chinese mathematician who has won the Fields prize, announced at the Morning Star Institute of Mathematics, Chinese Academy of Sciences in Beijing, on June 3, that based on the theoretical foundation laid by American and Russian scientists, Professor Zhu Xiping at Zhongshan University in Guangzhou City, and Professor Cao Huaidong at Lehigh University in Pennsylvania, who is also a visiting Professor at Beijing's Qinghua University, have completely proved this conjecture. Professor Qiu said this achievement is far more important than the Goldbach Conjecture. The mathematician Yang Le said that, as a result of the outstanding mathematical work, it is the first time that a complete proof of the Poincaré conjecture has been published in an international journal of mathematics. In the June issue of the U.S.-based Asian Journal of Mathematics, the two scientists published a 334-page paper, "A Complete Proof of the Poincaré and Geometrization Conjectures - application of the Hamilton-Perelman theory of the Ricci flow." The Poincaré Conjecture, first stated by French mathematician Henri Poincaré in 1904, is that, in topology, if in a closed three-dimensional space, any closed curves can shrink to a point, this space is topologically equivalent to the three-dimensional sphere. Like the Riemann Hypothesis, the Hodge Conjecture and the Yang-Mills Existence and Mass Gap, the Poincaré Conjecture has been rated as one of the seven "Millennium Prize problems"for proofs of which the Clay Mathematics Institute of Cambridge, Massachusetts was offering prizes of US$1,000,000 each, in May 2000. By the end of the 1970s, U.S. mathematician William P. Thurston had produced partial proof of Poincaré Conjecture on geometric structure, and was awarded the Fields Prize for the achievement. Fellow American Richard Hamilton completed the majority of the program and the geometrization conjecture. In 2003, Russian mathematician Grigory Perelman made key new contributions. Utilizing the Hamilton-Perelman theory of Ricci flow, Zhu and Cao have successfully provided the complete proof of the Poincaré Conjecture in the paper. Zhu and Cao were invited by Harvard University to give a three-hour lecture every week, between last September and March, to five mathematicians, including the head of Harvard's Mathematics Department. Chinese Mathematicians Unravel Century-Old Mathematical Problem |
June 07, 2006
Has Poincare's Conjecture been solved? The conjecture continuesBy Charles Arthur / Challenges The never-knowingly-undersold Chinese news agency Xinhua is reporting that a team of Chinese scientists has solved Poincaré's Conjecture, one of the longest-outstanding mathematical problems that is also reckoned to be capable of solution. Two Chinese mathematicians, Zhu Xiping and Cao Huaidong, have put the final pieces together in the solution to the puzzle that has perplexed scientists around the globe for more than a century. The two scientists have published a paper in the latest U.S.-based Asian Journal of Mathematics , providing complete proof of the Poincaré Conjecture promulgated by French mathematician Henri Poincaré in 1904. But it's not as though they did it in their lunch hour, or indeed on a single side of A4. This has taken them years, after others worked on it - and achieved part solutions - for decades. Harvard mathematics professor Shing-Tung Yau, winner of the Fields Prize, said the excellent job done by Zhu and Cao was the final strike on a global collaborative work for a complete proof. Now it's at about this time that you start looking at the ceiling and saying "What was Poincaré's Conjecture again?" Come on, you remember - if in a closed three-dimensional space, any closed curves can shrink to a point continuously, this space can be deformed to a sphere. Got that? No? All right, here's the more easily understood version from the Clay Mathematics Institute's Millennium Prize website: If we stretch a rubber band around the surface of an apple, then we can shrink it down to a point by moving it slowly, without tearing it and without allowing it to leave the surface. On the other hand, if we imagine that the same rubber band has somehow been stretched in the appropriate direction around a doughnut, then there is no way of shrinking it to a point without breaking either the rubber band or the doughnut. We say the surface of the apple is "simply connected," but that the surface of the doughnut is not.However, the claim doesn't amount to a proof. Even the publication doesn't amount to a proof. Only once it has been chewed over by mathematicians will we have confirmation on whether the conjecture has truly been solved. In fact, they're still chewing over a possible solution proposed in 2003 by Grisha Perelman, a Russian mathematician, which many have thought would prove to be true. (He'd already solved some special cases of the conjecture.) You're also wondering: what use is it? Well, Perelman seems to be active in string theory. If the conjecture is right, perhaps we'll be able to put a rubber band around the universe. Or not. Which would tell us what shape it is, which might in turn tell us.. something more useful. You can read the rest of the Clay Millennnium challenges, but some do take degree-level maths even to begin to understand. Not like good old Fermat's Last Theorem, where any GCSE-level maths student could understand the problem, but only a mathematician at the top of his game could hit the solution. (Which is: It's true. But you have to show your working. Still, it did bring the phrase "Taniyama-Shimura Conjecture" to deserved popularity.) You may also ask: what's this to do with technology? Well, it's got doughnuts in it, which are always popular with the geekerati. Plus we're sure this news will soon be followed by the release of Google Conjecture, a desktop program that will see whether you can slide rubber bands off differently-shaped objects drawn on your screen. And that will be closely followed by Microsoft Live! Bandstretcher, which will show you 3D graphics of rubber bands stretching. And a week later, Yahoo! will open a portal to the stock prices of differently-shaped rubber bands. We can hardly wait.. Has Poincare's Conjecture been solved? The conjecture continues |
June 07, 2006
Daniel Zheng wins SIAM's first prize at INTEL-ISEFContact: Michelle Montgomery montgomery@siam.org Daniel Zheng, an eleventh grader at St. Paul Academy and Summit School in St. Paul, Minnesota was awarded first prize in SIAM's Special Awards Organizations at the INTEL International Science and Engineering Fair (ISEF) held in Indianapolis, Indiana, May 7 – 12, 2006. Established in 2006, the SIAM award recognizes the projects that explore the ties between mathematics and applications that may not easily fit within a formal engineering, science, or mathematical discipline. Projects that include non-trivial mathematical analysis in the context of an engineering or science problem are considered. Examples of qualifying projects include mathematical analysis of a problem in science or engineering; projects that bridge the gap between math and an application; mathematical methods applied to solving a problem in science or engineering, optimization, scientific computing; or numerical analysis. Zheng received the prize in recognition of his project titled "Mathematical Modeling of Smoking Effect on Down Syndrome." His entry, which examined the long term effects of smoking on the incidence of Down Syndrome, impressed Kelly Black, a judge and Associate Professor of Mathematics at Union College of Schenectady, New York. "Mr. Zheng was able to clearly describe the mathematical model and explain the motivations as to how certain terms in the equations had been simplified…his project made use of a wide range of skills and techniques," says Black. "I was partly inspired to select this topic because of my father," says Zheng. "He has done some research in the field of birth defects. I was also motivated to look into this topic by curiosity. Not a lot is known about maternal-age-related defects and I thought that with mathematics I could provide some insight into the problem." The eleventh grader plans to write and submit an article on his project for publication in a peer-reviewed medical journal. Chang-Jiang (C.J.) Zheng, a physician specializing in preventative medicine, is thrilled with his son's interests in applied math and epidemiology. "Dan is my free assistant. He's been helping me in the office for years. He started doing some data entry, then he and his friend started downloading data from hospital labs for me, and then he started modeling some of my research interests. I know some math but not at the level he is doing," Dr. Zheng laughs. "I need this young guy to help me but so far I've been unable to pay him." Zheng learned algebra before he started fourth grade. He has attended the University of Minnesota Talent Youth Mathematics Program (UMTYMP) for five years. UMTYMP is a program that allows high school and middle school students to take advanced mathematics courses. Through the program, Zheng completed courses in single and multivariable calculus, linear algebra, and introductory differential geometry. He hopes to pursue a college major in computational biology or double major in mathematics and biology at MIT, Caltech or Brown. "Daniel is an extraordinary student, passionate about all areas of learning, although most especially about math and science. He is one of those rare students who pushes himself well beyond the assigned material to satisfy his own curiosity," says Tom Fones, Zheng's teacher and debate coach of Saint Paul Academy. "Daniel is really capable of pursuing virtually any profession that he's interested in. I could very easily see him as a researcher, professor, or an engineer." Mary Hill, Zheng's college counselor concurs with Fones. "I'm impressed by Daniel's intellectual versatility as much as his depth of knowledge and research skills in math and science. He excels in history, debate, English, and Chinese. He is becoming a fine painter as well. With deep-seated curiosity about the world around him, Daniel finds joy in learning through debate, conversation and reading in all fields," she says. Zheng is also a member of the Saint Paul Academy and Summit School's Math Team, Debate Team, Science Bowl, Quiz Bowl, and Science Olympiad. According to his teacher and coach Bill Boulger, Zheng brings a broad and deep background to the Math Team. "He is able to assume several key roles on the Math Team: introducing younger students to ideas they have not studied, volunteering for the most difficult events during competitions, and leading problem-solving exercises on the team events. Dan fills all of these roles with ease, poise, and graciousness," says Boulger. Tina Barsky, a Biology teacher at St. Paul Academy notes Zheng's joy and enthusiasm for all things scientific. "He is wonderfully open and upbeat without an ounce of arrogance -- very refreshing," she says. Aside from math and science, Zheng enjoys painting, playing Dance Dance Revolution, reading science fiction, fantasy and war history, as well as watching SG-1, Atlantis, and Star Trek. SIAM's S.A.O. honorable mention prize was awarded at INTEL-ISEF to Gabriel Joel Mendoza and Frederic Rojas of El Paso, Texas for their project titled, "Stochastic/Deterministic Analysis of Arboviral Transovarial Transmission in Culicidae." Their entry focused on the spread of West Nile virus. SIAM, headquartered in Philadelphia, PA, is an international community of over 10,000 individual members, including applied and computational mathematicians, computer scientists, and other scientists and engineers. The Society advances these fields through a series of premier journals and a wide selection of conferences. With over 500 academic and corporate institutional members, SIAM serves the disciplines of applied mathematics and computational science by publishing a variety of books and prestigious peer-reviewed research journals, by conducting conferences, and by hosting activity groups in various areas of mathematics. SIAM supports regional sections and student chapters that provide many opportunities for students. One of the primary goals of SIAM is to increase the pipeline of students into applied math studies and careers. More information about SIAM is available at www.siam.org. Daniel Zheng wins SIAM's first prize at INTEL-ISEF |
June 07, 2006
Four mathematical pioneers highlight NJIT's Third Annual Math ConferenceContact: Sheryl Weinstein sheryl.m.weinstein@njit.edu More than 120 mathematicians from around the world descended last month upon New Jersey Institute of Technology (NJIT) for news of the foremost advances in mathematical fluid dynamics at the university's annual conference on applied and computational mathematics. Plenary speakers included mathematician Charles S. Peskin, PhD, of the Courant Institute of Mathematical Sciences at New York University, well known for his research on mathematical models of the beating heart. Other key speakers were John Hinch, PhD, department of applied mathematics and theoretical physics at Cambridge University, England and a Fellow of the Royal Society; Grigory Barenblatt, PhD, a renowned applied mathematician from the University of California at Berkeley who studies the flow of fluids, and Tom Hou, PhD, a professor at California Institute of Technology, also famous for his work on the flow of fluids. Today mathematicians, thanks to the ability of supercomputers, employ mathematical modeling to create remarkably accurate scenarios of unexplained phenomena in the physical and natural sciences. "In turn," said Robert Miura, PhD, acting chair, of the department of mathematical sciences at NJIT, "scientific researchers find themselves teaming up with mathematicians to learn of better ways to eliminate or control the damage from natural disasters and other crises." Barenblatt's research attracts the attention of not only mathematicians, but engineers and physicists. Using mathematics, he studies the flow of fluids, said Michael Siegel, PhD, professor in the department of mathematical sciences at NJIT. When gases and liquids, such as air and water, do not follow a uniform motion and become chaotic-- the behavior of physical systems become unpredictable. Barenblatt understands the mathematics behind these turbulent chaotic fluid motions. "We have many mathematicians who wanted to hear Barenblatt," said Siegel. "His theories may be useful in understanding why materials like metals crack, how flame waves move and the mechanics of explosions." Barenblatt's presentation, "Incomplete Similarity in Continuum Mechanics," focused on the chaotic or whirling motions of fluids (also known as turbulence), special similarity solutions and scaling laws in fluid dynamics. Peskin is famous for his mathematical models using a computer representation of a beating heart. "This is very impressive stuff," said Siegel. For example, Peskin might be able to work out for heart surgeons precise worst-case scenarios showing what happens next to the blood flow if, say, a heart were to develop an atrial fibrillation. Siegel said that Peskin creates a mathematical model of the human heart, modeled as an elastic object embedded in a fluid. The difficulty of what he does is to link the fluid flow to the heart's elastic motion. Peskin has been working on this research for more than 20 years. The new element, which he discussed at the meeting, was mathematically incorporating electric signals into his models. Signals are important because they govern the coordination and control of the heartbeat, said Siegel. The electric signal tells the heart when to contract and when to relax. Peskin's talk was entitled "Cardiac Mechanics and Electrophysiology by the Immersed Boundary Method." Hinch's presentation analyzed the collapse of a column of grains. His research is motivated by the desire to understand landslides, explained Siegel. Hinch is well known for his work on the dynamics of drops and bubbles in fluids and for his work on suspensions. Hinch showed mathematically how the column of grains collapsed onto a horizontal, flat plain. Such an experiment offers researchers a better understanding of the distance the grains run out. His research is really important because his model imitates the motion of particles in a landslide, Siegel explained. The model leads to simple rules concerning the distance the grains run out, which is in agreement with experimental and numerical simulations. Hou presented recent work on what is considered an outstanding open problem in mathematical fluid dynamics. He asked and answered the question: Do the equations that govern the motion of frictionless fluids have reasonable solutions? The title of the presentation was: "The Interplay Between Local Geometric Properties and the Global Regularity of the 3-D Incompressible Euler Equations." To learn more about the conference or the department of mathematical sciences at NJIT, contact Susan Sutton at 973-596-3235. 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. Four mathematical pioneers highlight NJIT's Third Annual Math Conference |
June 07, 2006
Number mania: TV shows go on integer alertBy Jackie Burrell CONTRA COSTA TIMES 325? 325? As if "Lost" devotees didn't have enough to ponder, with 4, 8, 15, 16, 23 and 42. Now that they've been handed three more integers, the conclusion is inescapable: Hollywood has been invaded by numbers. It's not just the maddening numerical sequence on "Lost" or the crime drama "Numb3rs" with tousled mathematician Charlie Eppes. Numbers are sprinkled through next fall's TV line-up, too, with seven new integer-heavy titles including "The Nine," "3 Lbs." and "Six Degrees." "Numbers have always been hot," says Keith Devlin, Stanford math professor and former dean of math and science at Moraga's St. Mary's College. "It's just that until recently, the media did not shine the spotlight on the heat." Moviegoers may have flocked to see Matt Damon in "Good Will Hunting" and Russell Crowe in "A Brilliant Mind," but mathematicians weren't exactly sex symbols. "The Simpsons" managed to sneak math into its plots every so often -- one of the writers has a Ph.D in applied mathematics -- but math was subjecta non grata on prime time until recently. But there was nothing understated about the intentions behind "Numb3rs," says Cal Tech professor Gary Lorden, who serves as the show's mathematical consultant. The creators designed the show specifically about the way -- to quote the program's weekly intro -- "We all use math every day." The crime element was a vehicle to get it into prime time, Lorden said during a panel discussion on National Public Radio last year. The pilot featured an FBI agent, his brilliant mathematician brother, a serial rapist and a killer math equation. Critics disapproved of the "unbelievable" plotline, but the story was based on an actual case in Louisiana. And the equation that "Charlie Eppes" -- actor David Krumholtz -- used to pinpoint the rapist's neighborhood was the one a real forensics mathematician used to solve the case. Most mathematicians are not as cute as Krumholtz, admits Devlin, but the math is always spot on. Test audiences, armed with dials to turn whenever their interest was piqued, went wild for the math, says co-executive producer Andrew Dettmann. "When we asked, 'Why did you turn up the dial when the math sequences were explained?' they said they suddenly felt smart," Dettmann recounts. Lorden enjoyed the crime-solving, but he was absolutely delighted by the mathematical tidbits writers dropped into the show almost offhandedly -- Fibonacci numbers, game theory and strange mathematical puzzles. The show has taken off, both in the ratings and with an unlikely television fan base -- teachers. At a national math educators conference last year, more than a thousand teachers lined up to see a screening and meet Lorden and Krumholtz. "They (acted) like we were the Beatles," Lorden said. Last month, the National Council of Teachers of Mathematics launched "We All Use Math Every Day," an educational outreach program based on the show. Executive producer and co-creator Cheryl Heuton was delighted by the chance "to spread the word that 'Math is cool!'" The cool factor is no surprise to Devlin. "The fascination with numbers that many people have -- not everyone, to be sure -- sometimes goes deep," he says. "It seems that people want there to be hidden mathematics in everyday life. And there is." While "Numb3rs" uncovers how we, well, use math every day, "Lost" goes for strange coincidences and mathematical relationships. And its mysterious numerical sequence -- 4, 8, 15, 16, 23 and 42 -- is giving old Fibonacci some serious competition in the popularity sweepstakes. The "Lost" numbers show up on a lottery ticket, a hatch cover and a mysterious radio broadcast. They have to be re-entered into the hatch's computer every 108 seconds -- and 108 is the sum of the numbers. It's strange and compelling stuff. There's hope for numbers junkies next fall, too. "Lost" co-creator J.J. Abrams is at the helm of "Six Degrees," one of those seven numerically-rich TV shows for fall. He plays off the "degrees of separation" idea with a story arc involving six New York strangers and -- one hopes -- strange numerical sequences and odd coincidences that might be explained using a logistic regression equation or iterative processes or that other thing Charlie Eppes explained so well. Number mania: TV shows go on integer alert |