Uma reavaliação do pensamento lógico de George Boole à luz da história da matemática

The aim of the present study is to reevaluate the logical thought of the English mathematician George Boole (1815 - 1864). Thus, our research centers on the mathematical analysis of logic in the context of the history of mathematics. In order to do so, we present various biographical considerations about Boole in the light of events that happened in the 19th century and their consequences for mathematical production. We briefly describe Boole's innovations in the areas of differential equations and invariant theory and undertake an analysis of Boole's logic, especially as formulated in the book The Mathematical Analysis of Logic, comparing it not only with the traditional Aristotelian logic, but also with modern symbolic logic. We conclude that Boole, as he intended, expanded logic both in terms of its content and also in terms of its methods and formal elaboration. We further conclude that his purpose was the mathematical modeling of deductive reasoning, which led him to present an innovative formalism for logic and, because the different ways it can be interpreted, a new conception of mathematics

Anagramas do corpo, processos de repetição e representação da condição humana: um diálogo entre Hans Bellmer e Pina Bausch

La relation entre l`ignorance, l`apprentissage et de la création composent un décor provocant pour nous faire réfléchir sur l`éducation et la science. Pour éclaircir cette réflexion, nous démarrons sur les propositions de Ilya Prigogine (1986), pour qui l`art est une métaphore qui représente la science au XXe siècle, les idées d`Edgar Morin (2004), en soulignant la contribution fondamentale de l`art à l`état humain, et Maurice Merleau- Ponty (1980), qui crédite à l`art la possibilité d`un nouveau regard sur le monde, un regard sensible, esthétique. Ayant par référence la présence de ces arguments, nous réaffirmons la thèse de que l`art peut présenter des métaphores pour considérer la science, l`éducation et la condition humaine sur des bases complexes et transdisciplinaires. Nous nous concentrons sur des catégories particulières de la déformation et de la répétition. La première est considérée comme un désordre nécessaire au corps, à la science et à l`éducation, des lieux de métamorphose constante, d`après les principes de la complexité. La seconde est appréciée comme un opérateur sans lequel la variation, l`écart, le nouveau et l`invention ne peuvent pas émerger. Nos métaphores ressortent des travaux esthétiques de deux artistes de renom: Pina Bausch et Hans Bellmer, les délinquants qui certainement se rebellent contre la trivialité dans l`art et la vie. Ils exploitent des rêves, des démonstrations affectueuses impertinentes, esthétiques inaugurales, antiparadigmatiques et audacieuses. En un mot, ils incarnent ce qu`on appelle une pensée complexe. Nous comprenons que les deux artistes déclenchent des dispositifs qui dialoguent avec le manifeste de Merleau-Ponty lorsque l`on cherche dans l "aisthesis" la possibilité d`une production naturelle qui est en elle-même, créative. Ayant comme horizon cette puissance créatrice nous concentrons notre regard sur les anagrammes du corps proposés par Bellmer et sur la répétition exprimée par Pina Bausch. La déformation et la répétition sont des étapes embryonnaires de la création

Gravitomagnetismo e o teste da sonda gravidade B

The so-called gravitomagnetic field arised as an old conjecture that currents of matter (no charges) would produce gravitational effects similar to those produced by electric currents in electromagnetism. Hans Thirring in 1918, using the weak field approximation to the Einsteins field equations, deduced that a slowly rotating massive shell drags the inertial frames in the direction of its rotation. In the same year, Joseph Lense applied to astronomy the calculations of Thirring. Later, that effect came to be known as the Lense- Thirring effect. Along with the de Sitter effect, those phenomena were recently tested by a gyroscope in orbit around the Earth, as proposed by George E. Pugh in 1959 and Leonard I. Schiff in 1960. In this dissertation, we study the gravitational effects associated with the rotation of massive bodies in the light of the Einsteins General Theory of Relativity. With that finality, we develop the weak field approximation to General Relativity and obtain the various associated gravitational effects: gravitomagnetic time-delay, de Sitter effect (geodesic precession) and the Lense-Thirring effect (drag of inertial frames). We discus the measures of the Lense-Thirring effect done by LAGEOS Satellite (Laser Geodynamics Satellite) and the Gravity Probe B - GPB - mission. The GPB satellite was launched into orbit around the Earth at an altitude of 642 km by NASA in 2004. Results presented in May 2011 clearly show the existence of the Lense-Thirring effect- a drag of inertial frames of 37:2 7:2 mas/year (mas = milliarcsec)- and de Sitter effect - a geodesic precession of 6; 601:8 18:3 mas/year- measured with an accuracy of 19 % and of 0.28 % respectively (1 mas = 4:84810��9 radian). These results are in a good agreement with the General Relativity predictions of 41 mas/year for the Lense-Thirring effect and 6,606.1 mas/year for the de Sitter effect.