Utilizador:Mateuszica/Deus e a Matemática: diferenças entre revisões

Conteúdo apagado Conteúdo adicionado
Mateuszica (discussão | contribs)
Mateuszica (discussão | contribs)
Linha 32:
 
Why does math describe reality so well? A scientist offers tentative answers.Livio (The Equation that Couldn't Be Solved: How Mathematical Genius Discovered the Language of Symmetry, 2005, etc.), an astrophysicist at the Hubble Space Telescope Science Institute, frames his investigation with a history of math, beginning with the key question: Are mathematical truths discovered or invented? Pythagoras came down firmly on the side of discovery. His argument convinced Plato, and thus almost every ancient philosopher of note. The default assumption throughout most of history was that numbers, geometric figures and other mathematical truths are real. Galileo was the first to argue that scientific truth was necessarily expressed in mathematical terms. Newton's highly accurate calculations of the gravitational force drove the point home, implying that math and physical reality were two sides of the same coin. Even probability and statistics, which seem fuzzier than the hard equations of physics, give useful answers in the world of quantum interactions. But then math began to explore realms of thought that had no obvious relation to the world as we experience it: non-Euclidean geometry, or the paradoxes of set theory and symbolic logic. The idea that math was a game invented by mathematicians rather than something inherent in reality became fashionable, perhaps even inescapable. Also, it became clear that certain undeniably useful scientific disciplines—Darwinian evolution, to name one salient example—resisted mathematical treatment. Even so, Livio shows that correspondences between mathematical discoveries and physical phenomena continued to crop up, often in abstract mathematics created without any idea of practical applications, such as Einstein's use of non-Euclidean geometry. Knot topology, devised to explain a long-discredited model of the atom, turned out to have application to string theory. The author gives no final answer to the central question of math's relationship to reality. There are physical phenomena that are modeled by math, he asserts, but we also understand reality with a brain wired to find mathematical relations all around it.The conclusion falls a bit flat, but Livio's trip through mathematical history is thoroughly enjoyable and requires no special training to follow it.
 
=== Johannes Kepler ===
 
http://www.spaceandmotion.com/Physics-Johannes-Kepler.htm
 
At University, Kepler had learned about Copernicus' system and had immediately accepted heliocentrism as a real picture of the world: 'I have attested it as true in my deepest soul,' he later wrote. Nevertheless, he did not exhibit much interest in the subject until the day in Gratz when the figure on the blackboard suggested to him that he could explain the details of the heliocentric cosmos in terms of a beautiful underlying geometric pattern. Copernicus had discovered the general arrangement of the heavens - the sun at the center and the planets revolving around it. Now Kepler would explain precisely the orbital sizes and spacings. That there was a precise mathematical explanation for the cosmic plan was an article of faith with Kepler, because for him the world was a reflection of the supremely Pythagorean God.
Following Nicholas of Cusa, Kepler saw the world as the material embodiment of mathematical forms present within God before the act of creation. 'Why waste words?' he wrote, 'Geometry existed before the Creation, is co-eternal with the mind of God, is God himself ... geometry provided God with a model for the Creation.' Thus, 'where matter is, there is geometry.'
Because he believed that the world was a reflection of God, who was a perfect being, according to Kepler it must necessarily be a perfect world, and therefore the manifestation of sublime geometric principles. 'It is absolutely necessary that the work of such a perfect creator should be of the greatest beauty.' (Kepler) (Wertheim, Pythagoras' Trousers, 1997)
 
=== Citações de Grandes Mentes ===
Antes de começar o livro exponho aqui um lista de citações de grandes mentes que relacionam Deus e a matemática