Temas de relações internacionais, de política externa e de diplomacia brasileira, com ênfase em políticas econômicas, em viagens, livros e cultura em geral. Um quilombo de resistência intelectual em defesa da racionalidade, da inteligência e das liberdades democráticas.
O que é este blog?
Este blog trata basicamente de ideias, se possível inteligentes, para pessoas inteligentes. Ele também se ocupa de ideias aplicadas à política, em especial à política econômica. Ele constitui uma tentativa de manter um pensamento crítico e independente sobre livros, sobre questões culturais em geral, focando numa discussão bem informada sobre temas de relações internacionais e de política externa do Brasil. Para meus livros e ensaios ver o website: www.pralmeida.org. Para a maior parte de meus textos, ver minha página na plataforma Academia.edu, link: https://itamaraty.academia.edu/PauloRobertodeAlmeida.
Vejamos: antes de qualquer outro valor numérico figura a ética, à qual damos o número 1. Some-se honestidade, respeito, conhecimento, fraternidade, todos eles acrescentando zeros à direita do número 1. Agora, retire a ética do conjunto e o que é que sobra? Um monte de zeros...
Paulo Roberto de Almeida
Al Juarismi, o inventor da matemática moderna
Al Juarismi fue geógrafo, astrónomo y matemático. Su libro Al jabr, dio nombre a la disciplina que hoy conocemos como álgebra y en él se explicaba el método que utilizamos actualmente para resolver ecuaciones de segundo grado. Y, gracias a su tratado sobre aritmética, el mundo occidental tuvo conocimiento del sistema hindú de numeración decimal posicional, de la importancia del cero ―una novedad con respecto a los sistemas de numeración anteriores― y de los procedimientos para sumar, restar, multiplicar y dividir números en el sistema decimal que hoy aprenden todos los niños en la escuela. Y fue tan didáctico en exponer el método para operar con los números decimales, que esas operaciones recibieron el nombre de algoritmo, palabra formada a partir de su nombre.
ON Wednesday in Seoul, the International Congress of Mathematicians will announce the winners of the Fields Medal. First awarded in Oslo in 1936, the medal is given every four years to two to four mathematicians. It is considered the “Nobel Prize” of mathematics (even the organizers of the congress call it that), filling a gap left by Alfred Nobel, who did not include mathematics among the prizes endowed on his death in 1896.
Many mathematicians will tell you that Nobel omitted mathematics from his prizes to spite the Swedish mathematician Gosta Mittag-Leffler, a rival, and that the Canadian mathematician John Charles Fields created the award that bears his name to correct the omission. But this is a myth that needs debunking. First of all, there is no good evidence of a feud between Nobel and Mittag-Leffler. Nobel omitted mathematics simply because it was not as important to him as other endeavors were.
As for Fields, he proposed his award not as a substitute for the Nobel Prize but as a symbol of international unity. In the aftermath of World War I, the scientific community was fractured by national rivalries. When the International Mathematical Union was first founded, in 1920, it explicitly banned representatives of the former Central Powers. Fields so wanted “to avoid invidious comparisons” among candidates for his award that he suggested it be presented “with a view to encouraging further achievement” rather than just honoring past accomplishments. (This remark would later be used to justify the award’s age limit of 40, though Fields never intended the medal just for the young.)
For decades the Fields Medal was relatively obscure. In 1950, neither of the two recipients had heard of the award before being told that he had won it. So how did it become the Nobel Prize of mathematics? The true story helps illuminate the often neglected intersection of mathematics and politics.
On Aug. 5, 1966, The San Francisco Examiner reported that Stephen Smale, a mathematician at the University of California, Berkeley, who had been subpoenaed to appear before the House Un-American Activities Committee in connection with his anti-Vietnam War activism, had fled to Moscow. But Mr. Smale hadn’t fled. The subpoena hadn’t even reached him, for he was already in Europe. As Mr. Smale’s colleagues hurried to clarify to the press, he was on his way to attend the International Congress of Mathematicians, in Moscow, where he was to receive the Fields Medal on the day he was meant to testify.
Some saw Mr. Smale’s award as evidence of Communist affinities. “U.S. Math Teacher Wins Soviet Award” announced The Gettysburg Times. But The San Francisco Chronicle and The New York Times saw things differently. They credited Mr. Smale’s colleagues’ account, quoted in The Associated Press, that he was abroad to accept “mathematics’ closest award to the Nobel Prize” — an exaggeration that, by enhancing Mr. Smale’s stature, helped insulate him from criticism. The scandal faded.
The
following year, Mr. Smale returned to the headlines. It appeared that
his funding from the National Science Foundation had been blocked by
parties unhappy with his antiwar activism. But once again, the claim
that Mr. Smale held the equivalent of a Nobel Prize helped to protect
his cause, and he retained his funding. The close association between
the Fields Medal and the Nobel Prize, an artifact of Cold War politics,
would persist to this day.
Because
mathematics seems remote from “real world” concerns, people tend to
overlook how intertwined mathematics and politics can be. In Mr. Smale’s
case, his mathematical work was not directly tied to his political
activities (though his renown as a mathematician created opportunities
for his political engagement). But mathematics itself can be political,
too. After World War II, the United States military funded elite
mathematical research in areas ranging from topology and differential
equations to operations research and game theory.
Mathematicians have been some of the military-industrial complex’s biggest beneficiaries, but also some of its fiercest critics. Today, in the wake of the controversy about the National Security Agency’s surveillance, mathematicians are debating how they should relate to the agency, one of their largest employers and a longtime funder of their work. The Stanford mathematician Keith Devlin expressed the frustration of many of his peers when he said recently that mathematicians “should refuse to work for the N.S.A. until they both follow the U.S. Constitution and demonstrate responsible use of mathematical tools.”
Mr. Smale is not a mathematician who merely happened to oppose the Vietnam War, just as others are not mathematicians who merely happen to work for (or oppose) the N.S.A. Mathematics is a critical part of who they are and what they do, for better and sometimes for worse.
To say mathematics is political is not to diminish it, but rather to recognize its greater meaning, promise and responsibilities.
