Frasi di Henri Poincaré

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Henri Poincaré

Data di nascita: 29. Aprile 1854
Data di morte: 17. Luglio 1912
Altri nomi: Анри Пуанкаре

Jules Henri Poincaré è stato un matematico e un fisico teorico francese, che si è occupato anche di struttura e metodi della scienza.

Poincaré viene considerato un enciclopedico e in matematica l'ultimo universalista, dal momento che eccelse in tutti i campi della disciplina nota ai suoi giorni.

Come matematico e fisico, diede molti contributi originali alla matematica pura, alla matematica applicata, alla fisica matematica e alla meccanica celeste. A lui si deve la formulazione della congettura di Poincaré, uno dei più famosi problemi in matematica. Nelle sue ricerche sul problema dei tre corpi, Poincaré fu la prima persona a scoprire un sistema caotico deterministico, ponendo in tal modo le basi della moderna teoria del caos. Viene inoltre considerato uno dei fondatori della topologia.

Poincaré introdusse il moderno principio di relatività e fu il primo a presentare le trasformazioni di Lorentz nella loro moderna forma simmetrica. Poincaré completò le trasformazioni concernenti la velocità relativistica e le trascrisse in una lettera a Lorentz nel 1905. Ottenne così la perfetta invarianza delle equazioni di Maxwell, un passo importante nella formulazione della teoria della relatività ristretta.

Il gruppo di Poincaré usato in fisica e matematica deve a lui il suo nome.

Era zio del matematico e storico della scienza Pierre Boutroux .

Frasi Henri Poincaré

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„Supponiamo, ad esempio, un mondo rinchiuso un una grande sfera e soggetto alle seguenti leggi:
1) la temperatura non è uniforme;
2) è massima al centro, diminuisce man mano che ci si allontana da esso, per ridursi allo Zero Assoluto quando si raggiunge la superficie della sfera che racchiude questo mondo.
Preciso meglio la legge secondo cui la temperatura varia. Sia R il raggio della sfera limite: sia r la distanza fra il punto considerato e il centro di tale sfera. La temperatura assoluta sarà proporzionale a R2 – r2. Suppongo ancora che, in questo mondo, tutti i corpi abbiano lo stesso coefficiente di dilatazione, in modo tale che la lunghezza di un qualunque regolo sia proporzionale alla sua temperatura assoluta. Supporrò infine che un oggetto, trasportato da un punto all'altro, essendo diversa la sua temperatura, si ponga immediatamente in equilibrio calorifico con il suo nuovo ambiente. In queste ipotesi, nulla è contraddittorio o inimmaginabile. Un oggetto mobile diverrà allora sempre più piccolo nella misura in cui ci si avvicinerà alla sfera limite. Osserviamo innanzitutto che, se questo mondo è limitato sul piano della nostra abituale geometria, apparirà come infinito ai suoi abitanti. Se essi volessero avvicinarsi alla sfera limite, si raffredderebbero e diverrebbero sempre più piccoli. I loro passi sarebbero sempre più brevi, al punto che essi non potrebbero mai raggiungere la sfera limite. […] Farò ancora un'altra ipotesi. Supporrò che la luce attraversi mezzi diversamente rifrangenti e in modo tale che l'indice di rifrazione sia inversamente proporzionale a R2 – r2. E' facile constatare che, in queste condizioni, i raggi luminosi non sarebbero rettilinei, ma circolari. […] Se fondassero una geometria, essa non sarebbe come la nostra, e cioè uno studio dei movimenti dei solidi invariabili. Sarebbe […] la geometria non euclidea. Così, individui come noi, la cui educazione si realizzasse in un mondo simile, non avrebbero la nostra stessa geometria.“

—  Henri Poincaré
La scienza e l'ipotesi, pp. 73-ss.

„All that is not thought is pure nothingness“

—  Henri Poincaré, libro The Value of Science
The Value of Science (1905), Context: 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 Ch. 11: Science and Reality

„Every definition implies an axiom, since it asserts the existence of the object defined.“

—  Henri Poincaré, libro Science and Method
Science and Method (1908), Context: Every definition implies an axiom, since it asserts the existence of the object defined. The definition then will not be justified, from the purely logical point of view, until we have proved that it involves no contradiction either in its terms or with the truths previously admitted. Part II. Ch. 2 : Mathematical Definitions and Education, p. 131

„The principal aim of mathematical education is to develop certain faculties of the mind, and among these intuition is not the least precious.“

—  Henri Poincaré, libro Science and Method
Science and Method (1908), Context: The principal aim of mathematical education is to develop certain faculties of the mind, and among these intuition is not the least precious. It is through it that the mathematical world remains in touch with the real world, and even if pure mathematics could do without it, we should still have to have recourse to it to fill up the gulf that separates the symbol from reality. Part II. Ch. 2 : Mathematical Definitions and Education, p. 128 Variant translation: The chief aim of mathematics teaching is to develop certain faculties of the mind, and among these intuition is by no means the least valuable.

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

—  Henri Poincaré, libro Science and Hypothesis
Science and Hypothesis (1901), Context: 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 Ch. I: On the Nature of Mathematical Reasoning (1905) Tr. https://books.google.com/books?id=5nQSAAAAYAAJ George Bruce Halstead

„When shall we say two forces are equal?“

—  Henri Poincaré, libro Science and Hypothesis
Science and Hypothesis (1901), Context: 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 Ch. VI: The Classical Mechanics (1905) Tr. https://books.google.com/books?id=5nQSAAAAYAAJ George Bruce Halstead

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

—  Henri Poincaré, libro The Value of Science
The Value of Science (1905), 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. Ch. 11: Science and Reality

„Induction applied to the physical sciences is always uncertain, because it rests on the belief in a general order of the universe, an order outside of us.“

—  Henri Poincaré, libro Science and Hypothesis
Science and Hypothesis (1901), Context: But, one will say, if raw experience can not legitimatize reasoning by recurrence, is it so of experiment aided by induction? We see successively that a theorem is true of the number 1, of the number 2, of the number 3 and so on; the law is evident, we say, and it has the same warranty as every physical law based on observations, whose number is very great but limited. But there is an essential difference. Induction applied to the physical sciences is always uncertain, because it rests on the belief in a general order of the universe, an order outside of us. Mathematical induction, that is, demonstration by recurrence, on the contrary, imposes itself necessarily, because it is only the affirmation of a property of the mind itself.<!--pp.13-14 Ch. I. (1905) Tr. George Bruce Halstead

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