Henri Poincaré Quotes

[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.

For an aggregate of sensations to have become a remembrance capable of classification in time, it must have ceased to be actual, we must have lost the sense of its infinite complexity, otherwise it would have remained present. It must, so to speak, have crystallized around a center of associations of ideas which will be a sort of label. It is only when they have lost all life that we can classify our memories in time as a botanist arranges dried flowers in his herbarium.

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.

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. A world as exterior as that, even if it existed, would for us be forever inaccessible.

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.

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.

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.

Time and Space … It is not nature which imposes them upon us, it is we who impose them upon nature because we find them convenient.

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.