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Henri Poincaré

Geburtstag: 29. April 1854
Todesdatum: 17. Juli 1912
Andere Namen: Анри Пуанкаре

Jules Henri Poincaré [pwɛ̃kaˈʀe] war ein bedeutender französischer Mathematiker, theoretischer Physiker, theoretischer Astronom und Philosoph.

Werk

„Die Reihenfolge, in die wir die Begebenheiten des Bewußtseins ordnen, duldet keinerlei Willkür; sie ist uns vorgeschrieben und wir können nichts daran ändern.“

—  Henri Poincaré

Das Maß der Zeit, in: Der Wert der Wissenschaft, B.G.Teubner, Leipzig 1906, Kap. I. S. 26 L’ordre dans lequel nous rangeons les phénomènes conscients ne comporte aucun arbitraire. Il nous est imposé et nous n’y pouvons rien changer. - :fr:s:La Valeur de la Science/Chapitre II. La mesure du temps

„Aus all diesen Resultaten würde, wenn sie sich bestätigten, eine ganz neue Methode hervorgehen, die hauptsächlich durch die Tatsache charakterisiert würde, daß keine Geschwindigkeit die des Lichtes übersteigen könnte, ebensowenig wie keine Temperatur unter den absoluten Nullpunkt fallen kann. Für einen Beobachter, der selbst in einer ihm unbewußten Bewegung mitgeführt wird, könnte ebenfalls, keine scheinbare Geschwindigkeit die des Lichtes übersteigen, und dies wäre ein Widerspruch, wenn man sich nicht daran erinnerte, daß sich dieser Beobachter nicht der gleichen Uhren bedient, wie ein feststehender Beobachter, sondern solcher Uhren, die die „lokale Zeit“ zeigen.“

—  Henri Poincaré

Der gegenwärtige Zustand und die Zukunft der mathematischen Physik, in: Der Wert der Wissenschaft, B.G.Teubner, Leipzig 1906, S. 149 f. De tous ces résultats, s’ils se confirmaient, sortirait une mécanique entièrement nouvelle qui serait surtout caractérisée par ce fait qu’aucune vitesse ne pourrait dépasser celle de la lumière [...] pas plus qu’aucune température ne peut tomber au-dessous du zéro absolu. Pour un observateur, entraîné lui-même dans une translation dont il ne se doute pas, aucune vitesse apparente ne pourrait non plus dépasser celle de la lumière ; et ce serait là une contradiction, si l’on ne se rappelait que cet observateur ne se servirait pas des mêmes horloges qu’un observateur fixe, mais bien d’horloges marquant le « temps local » . - :fr:s:La Valeur de la Science/Chapitre VIII. La crise actuelle de la physique mathématique, Flammarion, 1911, p. 197; Erstauflage 1905, zuvor in Bulletin des sciences mathématiques 28, Nr. 2, 1904

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Relativitätstheorie

„Das Prinzip der Relativität, nach dem die Gesetze der physikalischen Vorgänge für einen feststehenden Beobachter die gleichen sein sollen, wie für einen in gleichförmiger Translation fortbewegten, so daß wir gar kein Mittel haben oder haben können, zu unterscheiden, ob wir in einer derartigen Bewegung begriffen sind oder nicht.“

—  Henri Poincaré

Der gegenwärtige Zustand und die Zukunft der mathematischen Physik, in: Der Wert der Wissenschaft, B.G.Teubner, Leipzig 1906, S. 134 Le principe de la relativité, d’après lequel les lois des phénomènes physiques doivent être les mêmes, soit pour un observateur fixe, soit pour un observateur entraîné dans un mouvement de translation uniforme ; de sorte que nous n’avons et ne pouvons avoir aucun moyen de discerner si nous sommes, oui ou non, emportés dans un pareil mouvement ; - :fr:s:La Valeur de la Science/Chapitre VII. L’histoire de la physique mathématique, Flammarion, 1911, p. 176; Erstauflage 1905, zuvor in Bulletin des sciences mathématiques 28, Nr. 2, 1904

Ref: de.wikiquote.org - Henri Poincaré / Zitate mit Quellenangabe
Relativitätstheorie

„Wir haben keine unmittelbare Anschauung für die Gleichzeitigkeit, ebensowenig wie für die Gleichheit zweier Zeiträume. Wenn wir diese Anschauung zu haben glauben, so ist das eine Täuschung… Die Gleichzeitigkeit zweier Ereignisse oder ihre Aufeinanderfolge und die Gleichheit zweier Zeiträume müssen derart definiert werden, daß der Wortlaut der Naturgesetze so einfach als möglich wird.“

—  Henri Poincaré

Das Maß der Zeit, in: Der Wert der Wissenschaft, B.G.Teubner, Leipzig 1906, Kap. XIII. S. 42 Nous n’avons pas l’intuition directe de la simultanéité, pas plus que celle de l’égalité de deux durées. Si nous croyons avoir cette intuition, c’est une illusion. Nous y suppléons à l’aide de certaines règles que nous appliquons presque toujours sans nous en rendre compte. [...] Nous choisissons donc ces règles, non parce qu’elles sont vraies, mais parce qu’elles sont les plus commodes, et nous pourrions les résumer en disant : « La simultanéité de deux événements, ou l’ordre de leur succession, l’égalité de deux durées, doivent être définies de telle sorte que l’énoncé des lois naturelles soit aussi simple que possible. [...] » - :fr:s:La Valeur de la Science/Chapitre II. La mesure du temps

„Ich weiß nicht, ob ich an einer Stelle schon erwähnte, daß die Mathematik die Kunst ist, scheinbar verschiedenen Dingen denselben Namen zu geben. Nur müssen diese Dinge, wenn sie auch an Inhalt verschieden sind, in der äußeren Erscheinung sich ähnlich sein, und sie müssen sozusagen in dieselbe Form gegossen werden können. Wenn die Ausdrucksweise gut gewählt ist, so wird man mit Erstaunen bemerken, wie alle Beweisführungen, die für ein bekanntes Objekt gemacht werden, sofort auf viele neue Objekte anwendbar sind; man braucht nichts zu ändern, nicht einmal die Worte, weil die Benennungen die gleichen geworden sind.“

—  Henri Poincaré

Wissenschaft und Methode, Hrsg. F. und L. Lindemann, B. G. Teubner, Leipzig 1914, S. 23 f.,
Je ne sais si je n’ai déjà dit quelque part que la Mathématique est l’art de donner le même nom à des choses différentes. Il convient que ces choses, différentes par la matière, soient semblables par la forme, qu’elles puissent, pour ainsi dire, se couler dans le même moule. Quand le langage a été bien choisi, on est tout étonné de voir que toutes les démonstrations, faites pour un objet connu, s’appliquent immédiatement à beaucoup d’objets nouveaux ; on n’a rien à y changer, pas même les mots, puisque les noms sont devenus les mêmes. - :fr:s:Science et méthode/Livre premier, § II

„Die Mathematiker studieren nicht Objekte, sondern Beziehungen zwischen den Objekten; es kommt ihnen deshalb nicht darauf an, diese Objekte durch andere zu ersetzen, wenn dabei nur die Beziehungen ungeändert bleiben. Der Gegenstand ist für sie gleichgültig, die Formallein hat ihr Interesse.“

—  Henri Poincaré, buch Wissenschaft und Hypothese

Wissenschaft und Hypothese, Hrsg. F. und L. Lindemann, B. G. Teubner, Leipzig 1904, S. 20,
Les mathématiciens n’étudient pas des objets, mais des relations entre les objets ; il leur est donc indifférent de remplacer ces objets par d’autres, pourvu que les relations ne changent pas. La matière ne leur importe pas, la forme seule les intéresse. - :fr:s:La Science et l’Hypothèse/Chapitre 2

„All that is not thought is pure nothingness“

—  Henri Poincaré, buch The Value of Science

Quelle: The Value of Science (1905), Ch. 11: Science and Reality
Kontext: 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

„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, buch Wissenschaft und Hypothese

Quelle: Science and Hypothesis (1901), Ch. I. (1905) Tr. George Bruce Halstead
Kontext: 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

„To doubt everything or to believe everything are two equally convenient solutions; both dispense with the necessity of reflection.“

—  Henri Poincaré, buch Wissenschaft und Hypothese

Douter de tout ou tout croire, ce sont deux solutions également commodes, qui l'une et l'autre nous dispensent de réfléchir.
Preface, Dover abridged edition (1952), p. xxii
Science and Hypothesis (1901)

„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, buch Science and Method

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.
Science and Method (1908)
Kontext: 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.

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

—  Henri Poincaré, buch Wissenschaft und Hypothese

Quelle: Science and Hypothesis (1901), Ch. VI: The Classical Mechanics (1905) Tr. https://books.google.com/books?id=5nQSAAAAYAAJ George Bruce Halstead
Kontext: 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 scientist does not study nature because it is useful to do so. He studies it because he takes pleasure in it, and he takes pleasure in it because it is beautiful.“

—  Henri Poincaré, buch Science and Method

Part I. Ch. 1 : The Selection of Facts, p. 22
Science and Method (1908)
Kontext: The scientist does not study nature because it is useful to do so. He studies it because he takes pleasure in it, and he takes pleasure in it because it is beautiful. If nature were not beautiful it would not be worth knowing, and life would not be worth living. I am not speaking, of course, of the beauty which strikes the senses, of the beauty of qualities and appearances. I am far from despising this, but it has nothing to do with science. What I mean is that more intimate beauty which comes from the harmonious order of its parts, and which a pure intelligence can grasp.

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

—  Henri Poincaré, buch Wissenschaft und Hypothese

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

„A scientist worthy of the name, above all a mathematician, experiences in his work the same impression as an artist; his pleasure is as great and of the same nature.“

—  Henri Poincaré

"Notice sur Halphen," Journal de l'École Polytechnique (Paris, 1890), 60ème cahier, p. 143. See also Tobias Dantzig, Henri Poincaré, Critic of Crisis: Reflections on His Universe of Discourse (1954) p. 8
Kontext: A scientist worthy of the name, above all a mathematician, experiences in his work the same impression as an artist; his pleasure is as great and of the same nature.... we work not only to obtain the positive results which, according to the profane, constitute our one and only affection, as to experience this esthetic emotion and to convey it to others who are capable of experiencing it.

„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, buch Wissenschaft und Hypothese

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

„Science is built up with facts, as a house is with stones. But a collection of facts is no more a science than a heap of stones is a house.“

—  Henri Poincaré, buch Wissenschaft und Hypothese

Quelle: Science and Hypothesis (1901), Ch. IX: Hypotheses in Physics, Tr. George Bruce Halsted (1913)
Kontext: The Scientist must set in order. Science is built up with facts, as a house is with stones. But a collection of facts is no more a science than a heap of stones is a house.

„What has taught us to know the true profound analogies, those the eyes do not see but reason divines?
It is the mathematical spirit, which disdains matter to cling only to pure form.“

—  Henri Poincaré, buch The Value of Science

Quelle: The Value of Science (1905), Ch. 5: Analysis and Physics
Kontext: All laws are... deduced from experiment; but to enunciate them, a special language is needful... ordinary language is too poor...
This... is one reason why the physicist can not do without mathematics; it furnishes him the only language he can speak. And a well-made language is no indifferent thing;
... the analyst, who pursues a purely esthetic aim, helps create, just by that, a language more fit to satisfy the physicist.
... law springs from experiment, but not immediately. Experiment is individual, the law deduced from it is general; experiment is only approximate, the law is precise...
In a word, to get the law from experiment, it is necessary to generalize... But how generalize?... in this choice what shall guide us?
It can only be analogy.... What has taught us to know the true profound analogies, those the eyes do not see but reason divines?
It is the mathematical spirit, which disdains matter to cling only to pure form.<!--pp.76-77

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

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

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