Frases de Henri Poincaré

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Henri Poincaré

Data de nascimento: 29. Abril 1854
Data de falecimento: 17. Julho 1912
Outros nomes: Анри Пуанкаре

Jules Henri Poincaré foi um matemático, físico e filósofo da ciência francês.

Ingressou na Escola Politécnica em 1873, continuou seus estudos na Escola de Minas sob a tutela de Charles Hermite, e se doutorou em matemática em 1879. Foi nomeado professor de física matemática na Sorbonne , posto que manteve até sua morte. Antes de chegar aos trinta anos desenvolveu o conceito de funções automórficas, que usou para resolver equações diferenciais lineares de segunda ordem com coeficientes algébricos. Em 1895 publicou seu Analysis situs, um tratado sistemático sobre topologia. No âmbito das matemáticas aplicadas estudou numerosos problemas sobre óptica, eletricidade, telegrafia, capilaridade, elasticidade, termodinâmica, mecânica quântica, teoria da relatividade e cosmologia.

Foi descrito com frequência como o último universalista da disciplina matemática. No campo da mecânica elaborou diversos trabalhos sobre as teorias da luz e as ondas eletromagnéticas, e desenvolveu junto a Hendrik Lorentz a teoria da relatividade. A conjectura de Poincaré foi um dos problemas não resolvidos mais desafiantes da topologia algébrica, sendo resolvido apenas em 2003 pelo matemático russo Grigory Perelman, mais de um século após sua proposição; e foi o primeiro a considerar a possibilidade de caos num sistema determinista, em seu trabalho sobre órbitas planetárias. Este trabalho teve pouco interesse até que começou o estudo moderno da dinâmica caótica, em 1963. Em 1889 foi premiado por seus trabalhos sobre o problema dos três corpos.

Alguns de seus trabalhos mais importantes incluem os três volumes de Os novos métodos da mecânica celeste , publicados entre 1892 e 1899, e Lições de mecânica celeste . Também escreveu numerosas obras de divulgação científica que atingiram uma grande popularidade, como Ciência e hipótese , O valor da ciência e Ciência e método .

Obras

Science and Hypothesis
Henri Poincaré

„Faz-se ciência com os fatos, como se faz uma casa com pedras; mas uma acumulação de fatos não é ciência, assim como um monte de pedras não é uma casa.“

—  Henri Poincaré, livro Science and Hypothesis

on fait la Science avec des faits comme une maison avec des pierres ; mais une accumulation de faits n'est pas plus une science qu'un tas de pierres n'est une maison
La science et l'hypothèse (1902), como citado em "Système(s)" - página 25, Volume 607 de Annales littéraires de l'Université de Besançon, Yves Gilli, Editora Presses Univ. Franche-Comté, 1996, 104 páginas

„Duvidar de tudo ou crer em tudo. São duas soluções igualmente cômodas, que nos dispensam ambas de refletir.“

—  Henri Poincaré, livro Science and Hypothesis

La science et l'hypothèse (1902); citado em "Et si nous refaisions le monde?" - página 130, Joel Herbin, Editora Editions Le Manuscrit, 2004, ISBN 2748145038, 9782748145038
Fonte: Coletânea de Pensamentos http://www.espirito.org.br/portal/artigos/diversos/frases/coletanea-02.html
Douter de tout ou tout croire, ce sont les deux solutions également commodes qui l´une et l´autre nous dispensent de réfléchir.

„A mente usa a sua faculdade de criatividade apenas quando a experiência a obriga a fazê-lo.“

—  Henri Poincaré

The mind uses its faculty for creativity only when experience forces it to do so.
Henri Poincaré citado em "Changing core mathematics" - página 165, David C. Arney, Donald B. Small - Mathematical Association of America, 2002, ISBN 0883851725, 9780883851722 - 181 páginas

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„O pensamento é apenas um lampejo entre duas longas noites, mas este lambejo é tudo.“

—  Henri Poincaré

La pensée n'est qu'un éclair au milieu d'une longue nuit. Mais c'est cet éclair qui est tout.
La valeur de la science - página 276, Henri Poincaré - E. Flammarion, 1904 - 278 páginas

„O acaso é apenas a medida de nossa ignorância. Por definição, os fenômeno fortuitos são aqueles cujas leis desconhecemos. Seria essa definição de fato satisfatória? Quando os primeiros pastores caldeus observaram o movimento das estrelas, eles ainda não conheciam as leis da astronomia, mas teriam ousado dizer que as estrelas se moviam aleatoriamente?“

—  Henri Poincaré

Henri Poincaré, "Chance", em Science and Method. Trad. de Francis Maitland. mineola, Nova York: Dover, 2003. p. 65. Citado por James Gleick, "Uma história, uma teoria, uma enxurrada" [recurso eletrônico]; tradução Augusto Calil — 1a ed. — São Paulo : Companhia das Letras, 2013. p. 333.

„All that is not thought is pure nothingness“

—  Henri Poincaré, livro The Value of Science

Fonte: The Value of Science (1905), Ch. 11: Science and Reality
Contexto: All that is not thought is pure nothingness; since we can think only thought and all the words we use to speak of things can express only thoughts, to say there is something other than thought, is therefore an affirmation which can have no meaning.
And yet—strange contradiction for those who believe in time—geologic history shows us that life is only a short episode between two eternities of death, and that, even in this episode, conscious thought has lasted and will last only a moment. Thought is only a gleam in the midst of a long night. But it is this gleam which is everything.<!--p.142

„When we say force is the cause of motion, we talk metaphysics“

—  Henri Poincaré, livro Science and Hypothesis

Fonte: Science and Hypothesis (1901), Ch. VI: The Classical Mechanics (1905) Tr. https://books.google.com/books?id=5nQSAAAAYAAJ George Bruce Halstead
Contexto: What is mass? According to Newton, it is the product of the volume by the density. According to Thomson and Tait, it would be better to say that density is the quotient of the mass by the volume. What is force? It, is replies Lagrange, that which moves or tends to move a body. It is, Kirchhoff will say, the product of the mass by the acceleration. But then, why not say the mass is the quotient of the force by the acceleration?
These difficulties are inextricable.
When we say force is the cause of motion, we talk metaphysics, and this definition, if one were content with it, would be absolutely sterile. For a definition to be of any use, it must teach us to measure force; moreover that suffices; it is not at all necessary that it teach us what force is in itself, nor whether it is the cause or the effect of motion.
We must therefore first define the equality of two forces. When shall we say two forces are equal? It is, we are told, when, applied to the same mass, they impress upon it the same acceleration, or when, opposed directly one to the other, they produce equilibrium. This definition is only a sham. A force applied to a body can not be uncoupled to hook it up to another body, as one uncouples a locomotive to attach it to another train. It is therefore impossible to know what acceleration such a force, applied to such a body, would impress upon such an other body, if it were applied to it. It is impossible to know how two forces which are not directly opposed would act, if they were directly opposed.
We are... obliged in the definition of the equality of the two forces to bring in the principle of the equality of action and reaction; on this account, this principle must no longer be regarded as an experimental law, but as a definition.<!--pp.73-74

„The very possibility of the science of mathematics seems an insoluble contradiction.“

—  Henri Poincaré, livro Science and Hypothesis

Fonte: Science and Hypothesis (1901), Ch. I: On the Nature of Mathematical Reasoning (1905) Tr. https://books.google.com/books?id=5nQSAAAAYAAJ George Bruce Halstead
Contexto: The very possibility of the science of mathematics seems an insoluble contradiction. If this science is deductive only in appearance, whence does it derive that perfect rigor no one dreams of doubting? If, on the contrary, all the propositions it enunciates can be deduced one from another by the rules of formal logic, why is not mathematics reduced to an immense tautology? The syllogism can teach us nothing essentially new, and, if everything is to spring from the principle of identity, everything should be capable of being reduced to it. Shall we then admit that the enunciations of all those theorems which fill so many volumes are nothing but devious ways of saying A is A!... Does the mathematical method proceed from particular to the general, and, if so, how can it be called deductive?... If we refuse to admit these consequences, it must be conceded that mathematical reasoning has of itself a sort of creative virtue and consequently differs from a syllogism.<!--pp.5-6

„For a definition to be of any use, it must teach us to measure force; moreover that suffices; it is not at all necessary that it teach us what force is in itself, nor whether it is the cause or the effect of motion.“

—  Henri Poincaré, livro Science and Hypothesis

Fonte: Science and Hypothesis (1901), Ch. VI: The Classical Mechanics (1905) Tr. https://books.google.com/books?id=5nQSAAAAYAAJ George Bruce Halstead
Contexto: What is mass? According to Newton, it is the product of the volume by the density. According to Thomson and Tait, it would be better to say that density is the quotient of the mass by the volume. What is force? It, is replies Lagrange, that which moves or tends to move a body. It is, Kirchhoff will say, the product of the mass by the acceleration. But then, why not say the mass is the quotient of the force by the acceleration?
These difficulties are inextricable.
When we say force is the cause of motion, we talk metaphysics, and this definition, if one were content with it, would be absolutely sterile. For a definition to be of any use, it must teach us to measure force; moreover that suffices; it is not at all necessary that it teach us what force is in itself, nor whether it is the cause or the effect of motion.
We must therefore first define the equality of two forces. When shall we say two forces are equal? It is, we are told, when, applied to the same mass, they impress upon it the same acceleration, or when, opposed directly one to the other, they produce equilibrium. This definition is only a sham. A force applied to a body can not be uncoupled to hook it up to another body, as one uncouples a locomotive to attach it to another train. It is therefore impossible to know what acceleration such a force, applied to such a body, would impress upon such an other body, if it were applied to it. It is impossible to know how two forces which are not directly opposed would act, if they were directly opposed.
We are... obliged in the definition of the equality of the two forces to bring in the principle of the equality of action and reaction; on this account, this principle must no longer be regarded as an experimental law, but as a definition.<!--pp.73-74

„It is only through science and art that civilization is of value.“

—  Henri Poincaré, livro The Value of Science

Some have wondered at the formula: science for its own sake; an yet it is as good as life for its own sake, if life is only misery; and even as happiness for its own sake, if we do not believe that all pleasures are of the same quality...
Every act should have an aim. We must suffer, we must work, we must pay for our place at the game, but this is for seeing's sake; or at the very least that others may one day see.
Fonte: The Value of Science (1905), Ch. 11: Science and Reality

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