Frasi di Henri Poincaré (62 frasi, pagina 2)

C'est même des hypothèses simples qu'il faut le plus se défier, parce que ce sont celles qui ont le plus de chances de passer inaperçues.
Thermodynamique: Leçons professées pendant le premier semestre 1888–1889 (1892), Preface

“If all the parts of the universe are interchained in a certain measure, any one phenomenon will not be the effect of a single cause, but the resultant of causes infinitely numerous; it is, one often says, the consequence of the state of the universe the moment before.”

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Henri Poincaré libro The Value of Science

Si toutes les parties de l’univers sont solidaires dans une certaine mesure, un phénomène quelconque ne sera pas l’effet d’une cause unique, mais la résultante de causes infiniment nombreuses ; il est, dit-on souvent, la conséquence de l’état de l’univers un instant auparavant.
Origine: The Value of Science (1905), Ch. 2: The Measure of Time

“We can not… escape the conclusion that the rule of reasoning by recurrence is irreducible to the principle of contradiction. …Neither can this rule come to us from experience… This rule, inaccessible to analytic demonstration and to experience, is the veritable type of the synthetic a priori judgment. On the other hand, we can not think of seeing in it a convention, as in some of the postulates of geometry. …it is only the affirmation of the power of the mind which knows itself capable of conceiving the indefinite repetition of the same act when once this act is possible. The mind has a direct intuition of this power, and experience can only give occasion for using it and thereby becoming conscious of it.”

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Henri Poincaré libro Science and Hypothesis

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

“If, then, a phenomenon admits of a complete mechanical explanation, it will admit of an infinity of others, that will render an account equally well of all the particulars revealed by experiment.”

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Henri Poincaré libro Science and Hypothesis

Si donc un phénomène comporte une explication mécanique complète, il en comportera une infinité d’autres qui rendront également bien compte de toutes les particularités révélées par l’expérience.
Origine: Science and Hypothesis (1901), Ch. XII: Optics and Electricity, as translated by George Bruce Halsted (1913)

“Mathematics have a triple aim. They must furnish an instrument for the study of nature. But that is not all: they have a philosophic aim and, I dare maintain, an esthetic aim. They must aid the philosopher to fathom the notions of number, of space, of time. And above all, their adepts find therein delights analogous to those given by painting and music. They admire the delicate harmony of numbers and forms; they marvel when a new discovery opens to them an unexpected perspective; and has not the joy they thus feel the esthetic character, even though the senses take no part therein? Only a privileged few are called to enjoy it fully, it is true, but is not this the case for all the noblest arts?
This is why I do not hesitate to say that mathematics deserve to be cultivated for their own sake, and the theories inapplicable to physics as well as the others. Even if the physical aim and the esthetic aim were not united, we ought not to sacrifice either.”

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Henri Poincaré libro The Value of Science

Origine: The Value of Science (1905), Ch. 5: Analysis and Physics

“It is by logic that we prove, but by intuition that we discover. To know how to criticize is good, to know how to create is better.”

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Henri Poincaré libro Science and Method

C'est par la logique qu'on démontre, c'est par l'intuition qu'on invente.
Part II. Ch. 2 : Mathematical Definitions and Education, p. 129
Science and Method (1908)

“What we call objective reality is, in the last analysis, what is common to many thinking beings, and could be common to all; this common part, we shall see, can only be the harmony expressed by mathematical laws. It is this harmony then which is the sole objective reality, the only truth we can attain; and when I add that the universal harmony of the world is the source of all beauty, it will be understood what price we should attach to the slow and difficult progress which little by little enables us to know it better.”

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Henri Poincaré libro The Value of Science

Introduction, p. 14
The Value of Science (1905)

“… treatises on mechanics do not clearly distinguish between what is experiment, what is mathematical reasoning, what is convention, and what is hypothesis.”

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Henri Poincaré libro Science and Hypothesis

... les traités de mécanique ne distinguent pas bien nettement ce qui est expérience, ce qui est raisonnement mathématique, ce qui est convention, ce qui est hypothèse.
Origine: Science and Hypothesis (1901), Ch. VI: The Classical Mechanics, Tr. George Bruce Halsted (1913)

“If we study the history of science we see happen two inverse phenomena… Sometimes simplicity hides under complex appearances; sometimes it is the simplicity which is apparent, and which disguises extremely complicated realities.
…No doubt, if our means of investigation should become more and more penetrating, we should discover the simple under the complex, then the complex under the simple, then again the simple under the complex, and so on, without our being able to foresee what will be the last term. We must stop somewhere, and that science may be possible, we must stop when we have found simplicity. This is the only ground on which we can rear the edifice of our generalizations.”

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Henri Poincaré libro Science and Hypothesis

Science and Hypothesis (1901)

“We have not a direct intuition of simultaneity, nor of the equality of two durations. If we think we have this intuition, this is an illusion. We replace it by the aid of certain rules which we apply almost always without taking count of them.
…We …choose these rules, not because they are true, but because they are the most convenient, and we may recapitulate them as follows: "The simultaneity of two events, or the order of their succession, the equality of two durations, are to be so defined that the enunciation of the natural laws may be as simple as possible. In other words, all these rules, all these definitions, are only the fruit of an unconscious opportunism."”

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Henri Poincaré libro The Value of Science

Origine: The Value of Science (1905), Ch. 2: The Measure of Time

“We see that experience plays an indispensable role in the genesis of geometry; but it would be an error thence to conclude that geometry is, even in part, an experimental science. If it were experimental it would be only approximative and provisional. And what rough approximation!
…The object of geometry is the study of a particular 'group'; but the general group concept pre-exists… in our minds. It is imposed on us, not as form of our sense, but as form of our understanding. Only, from among all the possible groups, that must be chosen… will be… the standard to which we shall refer natural phenomena.
Experience guides us in this choice without forcing it upon us; it tells us not which is the truest geometry, but which is the most convenient.
Notice that I have been able to describe the fantastic worlds… imagined without ceasing to employ the language of ordinary geometry.”

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Henri Poincaré libro Science and Hypothesis

Origine: Science and Hypothesis (1901), Ch. IV: Space and Geometry, Conclusions (1905) Tr. https://books.google.com/books?id=5nQSAAAAYAAJ George Bruce Halstead

“The advance of science is not comparable to the changes of a city, where old edifices are pitilessly torn down to give place to new, but to the continuous evolution of zoologic types which develop ceaselessly and end by becoming unrecognizable to the common sight, but where an expert eye finds always traces of the prior work of the centuries past. One must not think then that the old-fashioned theories have been sterile or vain.”

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Henri Poincaré libro The Value of Science

Il ne faut pas comparer la marche de la science aux transformations d’une ville, où les édifices vieillis sont impitoyablement jetés à bas pour faire place aux constructions nouvelles, mais à l’évolution continue des types zoologiques qui se développent sans cesse et finissent par devenir méconnaissables aux regards vulgaires, mais où un œil exercé retrouve toujours les traces du travail antérieur des siècles passés. Il ne faut donc pas croire que les théories démodées ont été stériles et vaines.
Introduction, p. 14
The Value of Science (1905)

“Thought must never submit, neither to a dogma, nor to a party, nor to a passion, nor to an interest, nor to a preconceived idea, nor to whatever it may be, save to the facts themselves, because, for thought, submission would mean ceasing to be.”

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Henri Poincaré

La pensée ne doit jamais se soumettre, ni à un dogme, ni à un parti, ni à une passion, ni à un intérêt, ni à une idée préconçue, ni à quoi que ce soit, si ce n'est aux faits eux-mêmes, parce que, pour elle, se soumettre, ce serait cesser d'être.
Speech, University of Brussels (19 November 1909), during the festival for the 75th anniversary of the university's foundation; published in Œuvres de Henri Poincaré (1956), p. 152

“There is no science apart from the general. It may even be said that the very object of the exact sciences is to spare us these direct verifications.”

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Henri Poincaré libro Science and Hypothesis

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

“Logic teaches us that on such and such a road we are sure of not meeting an obstacle; it does not tell us which is the road that leads to the desired end. For this, it is necessary to see the end from afar, and the faculty which teaches us to see is intuition. Without it, the geometrician would be like a writer well up in grammar but destitute of ideas.”

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Henri Poincaré libro Science and Method

La logique nous apprend que sur tel ou tel chemin nous sommes sûrs de ne pas rencontrer d'obstacle ; elle ne nous dit pas quel est celui qui mène au but. Pour cela il faut voir le but de loin, et la faculté qui nous apprend à voir, c'est l'intuition. Sans elle, le géomètre serait comme un écrivain qui serait ferré sur la grammaire, mais qui n'aurait pas d'idées.
Part II. Ch. 2 : Mathematical Definitions and Education, p. 130
Science and Method (1908)

“What is objective must be common to many minds and consequently transmissible from one to the other, and as this transmission can only come about by… discourse… we are even forced to conclude: no discourse no objectivity.”

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Henri Poincaré libro The Value of Science

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

“Does the harmony the human intelligence thinks it discovers in nature exist outside of this intelligence? No, beyond doubt, a reality completely independent of the mind which conceives it, sees or feels it, is an impossibility.”

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Henri Poincaré libro The Value of Science

Cette harmonie que l’intelligence humaine croit découvrir dans la nature, existe-t-elle en dehors de cette intelligence ? Non, sans doute, une réalité complètement indépendante de l’esprit qui la conçoit, la voit ou la sent, c’est une impossibilité.
Introduction, p. 14
The Value of Science (1905)

“Scientists believe there is a hierarchy of facts and that among them may be made a judicious choice. They are right, since otherwise there would be no science… One need only open the eyes to see that the conquests of industry which have enriched so many practical men would never have seen the light, if these practical men alone had existed and if they had not been preceded by unselfish devotees who died poor, who never thought of utility, and yet had a guide far other than caprice.
As Mach says, these devotees have spared their successors the trouble of thinking.”

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Henri Poincaré libro The Value of Science

Author's Essay Prefatory to the Translation: "The Choice of Facts," p.4
The Value of Science (1905)

“It is because simplicity and vastness are both beautiful that we seek by preference simple facts and vast facts; that we take delight, now in following the giant courses of the stars, now in scrutinizing the microscope that prodigious smallness which is also a vastness, and now in seeking in geological ages the traces of a past that attracts us because of its remoteness.”

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Henri Poincaré libro Science and Method

C’est parce que la simplicité, parce que la grandeur est belle, que nous rechercherons de préférence les faits simples et les faits grandioses, que nous nous complairons tantôt à suivre la course gigantesque des astres, tantôt à scruter avec le microscope cette prodigieuse petitesse qui est aussi une grandeur, tantôt à rechercher dans les temps géologiques les traces d’un passé qui nous attire parce qu’il est lointain.
Part I. Ch. 1 : The Selection of Facts, p. 23
Science and Method (1908)