Physicists From France

"Toute définition implique un axiome, puisqu'elle affirme l'existence de l'objet défini. La définition ne sera donc justifiée, au point de vue purement logique, que quand on aura démontré qu'elle n'entraîne pas de contradiction, ni dans les termes, ni avec les vérités antérieurement admises."

"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."

"C'est par la logique qu'on démontre, c'est par l'intuition qu'on invente."

"Le but principal de l'enseignement mathématique est de développer certaines facultés de l'esprit et parmi elles l'intuition n'est pas la moins précieuse. C'est par elle que le monde mathématique reste en contact avec le monde réel et quand les mathématiques pures pourraient s'en passer, il faudrait toujours y avoir recours pour combler l'abîme qui sépare le symbole de la réalité."

"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."

"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."

"Le savant n'étudie pas la nature parce que cela est utile; il l'étudie parce qu'il y prend plaisir et il y prend plaisir parce qu'elle est belle. Si la nature n'était pas belle, elle ne vaudrait pas la peine d'être connue, la vie ne vaudrait pas la peine d'être vécue. Je ne parle pas ici, bien entendu, de cette beauté qui frappe les sens, de la beauté des qualités et des apparences; non que j'en fasse fi, loin de là, mais elle n'a rien à faire avec la science; je veux parler de cette beauté plus intime qui vient de l'ordre harmonieux des parties, et qu'une intelligence pure peut saisir."

"La sociologie est la science qui possède le plus de méthodes et le moins de résultats."

"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."

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

"Now what is science? ...it is before all a classification, a manner of bringing together facts which appearances separate, though they are bound together by some natural and hidden kinship. Science, in other words, is a system of relations. ...it is in relations alone that objectivity must be sought. ...it is relations alone which can be regarded as objective. External objects... are really objects and not fleeting and fugitive appearances, because they are not only groups of sensations, but groups cemented by a constant bond. It is this bond, and this bond alone, which is the object in itself, and this bond is a relation."

"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."

"Comme nous ne pouvons pas donner de l'énergie une définition générale, le principe de la conservation de l'énergie signifie simplement qu'il y a quelque chose qui demeure constant."

"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."

"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."

"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.""

"(1) The rules applied are exceedingly various. (2) It is difficult to separate the qualitative problem of simultaneity from the quantitative problem of the measurement of time; no matter whether a chronometer is used, or whether account must be taken of a velocity of transmission, as... of light, because such a velocity could not be measured without measuring a time."

"Or... they observe an astronomic phenomenon... an eclipse of the moon, and... suppose... this... is perceived simultaneously from all points of the earth. That is not altogether true, since the propagation of light is not instantaneous; if absolute exactitude were desired, there would be a correction... according to a complicated rule."

"When navigators... determine a ... they must... calculate Paris time...[with] a chronometer set for Paris. The qualitative problem of simultaneity is made to depend upon the quantitative problem of the measurement of time."

"Roemer used eclipses of the satellites of Jupiter, and sought how much the event fell behind its prediction. But... this prediction [is] made... by... astronomic laws; for instance Newton's... [T]he velocity of light... is adopted, such that the astronomic laws compatible with this value may be as simple as possible."

"He has begun by supposing that light has a constant velocity... the same in all directions. This... could never be verified directly by experiment... The postulate... resembling the ... furnishes us with a new rule for the investigation of simultaneity."

"When an astronomer tells me that some stellar phenomenon, which his telescope reveals to him at this moment, happened... fifty years ago... I... ask... how he has measured the velocity of light."

"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."

"[H]ave we really the right to speak of the cause of a phenomenon?"

"Behold... the only... [rule] we can follow: when a phenomenon appears... as the cause of another, we regard it as anterior. ...[T]herefore by cause... we define time; but...how do we recognize which is the cause and which the effect? We assume... the anterior fact, the antecedent, is the cause of the... consequent. It is then by time that we define cause. ...[S]hall we escape from this vicious circle?"

"Is not my present nearer my past of yesterday than the present of Sirius?"

"[This] shows, perhaps, why we have tried to put all physical phenomena into the same frame. But that can not pass for a definition of simultaneity, since this hypothetical intelligence, even if it existed, would be for us impenetrable. It is... necessary to seek something else."

"[Y]et when we speak of time... do we not unconsciously adopt this hypothesis... [and] put ourselves in the place of this imperfect god... [D]o not even the atheists put themselves in the place where god would be..?"

"We should like to represent... the... universe, and... feel... we understood it. We... never can attain this representation: our weakness is too great. But... we desire... to conceive an infinite intelligence... which should see all, and... classify all in its time, as we classify, in our time, the little we see. ...[T]his supreme intelligence would be only a ; infinite in one sense... limited in another, since it would have... imperfect recollection of the past... otherwise all recollections would be equally present... and for it there would be no time."

"If... it be supposed that another way of measuring time is adopted... enunciation of the law would be... translated into another language... much less simple. So that the definition implicitly adopted by the astronomers may be summed up..: Time should be so defined that the equations of mechanics may be as simple as possible... [i.e.,] there is not one way of measuring time more true... only more convenient."

"[A]stronomers... define duration in the following way: time... so defined that Newton's law and that of vis viva [or of the ] may be verified. Newton's law is an experimental truth... only approximate... [W]e still have only a definition by approximation."

"[W]e should say: 'Causes almost identical take almost the same time to produce almost the same effects.'"

"In physical reality one cause does not produce a given effect, but a multitude of distinct causes contribute to produce it, without our having any means of discriminating the part of each of them. ...[C]auses which have produced a certain effect will never be reproduced except approximately."

"[W]hat postulate do we implicitly admit? It is that the duration of two identical phenomena is the same; or... that the same causes take the same time to produce the same effects. ...Is it impossible that experiment may some day contradict our postulate?"

"[I]t is the sidereal day, that is, the duration of the rotation of the earth, which is the constant unit of time. ...However ...[many] astronomers ...think that the tides act as a check on our globe, and that the rotation of the earth is becoming slower and slower. Thus would be explained the apparent acceleration of the motion of the moon..."

"We have not a direct intuition of the equality of two intervals of time."

"[T]wo difficulties: (1) Can we transform psychologic time, which is qualitative, into a quantitative time? (2) Can we reduce to one and the same measure facts which transpire in different worlds [of conscious beings]!"

"But these labels can only be finite in number. On that score, psychologic time should be discontinuous."

"Pour qu’un ensemble de sensations soit devenu un souvenir susceptible d’être classé dans le temps, il faut qu’il ait cessé d’être actuel, que nous ayons perdu le sens de son infinie complexité, sans quoi il serait resté actuel. Il faut qu’il ait pour ainsi dire cristallisé autour d’un centre d’associations d’idées qui sera comme une sorte d’étiquette. Ce n’est que quand ils auront ainsi perdu toute vie que nous pourrons classer nos souvenirs dans le temps, comme un botaniste range dans son herbier les fleurs desséchées."

"The mathematician is born, not made."

"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... 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."

"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. Un monde si extérieur que cela, si même il existait, nous serait à jamais inaccessible. Un monde si extérieur que cela, si même il existait, nous serait à jamais inaccessible."

"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."

"Le temps et l’espace... Ce n’est pas la nature qui nous les impose, c’est nous qui les imposons à la nature parce que nous les trouvons commodes."

"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."

"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..."

"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."

"It is often said that experiments should be made without preconceived ideas. That is impossible. Not only would it make every experiment fruitless, but even if we wished to do so, it could not be done. Every man has his own conception of the world, and this he cannot so easily lay aside. We must, for example, use language, and our language is necessarily steeped in preconceived ideas."

"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."

"Le savant doit ordonner ; 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."