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.

Sociology is the science which has the most methods and the least results.

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.

I think I have already said somewhere that mathematics is the art of giving the same name to different things.

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.

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.

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.

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... The velocity of light... is adopted, such that the astronomic laws compatible with this value may be as simple as possible.

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. ...Causes which have produced a certain effect will never be reproduced except approximately.

We should say: 'Causes almost identical take almost the same time to produce almost the same effects.'

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

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.

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. ...This supreme intelligence would be only a demigod; 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.

Yet when we speak of time... do we not unconsciously adopt this hypothesis... and put ourselves in the place of this imperfect god... Do not even the atheists put themselves in the place where god would be..?

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.

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

Behold... the only... rule we can follow: when a phenomenon appears... as the cause of another, we regard it as anterior. ...Therefore 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. ...Shall we escape from this vicious circle?

Have we really the right to speak of the cause of a phenomenon?

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.

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.

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 principle of sufficient reason... furnishes us with a new rule for the investigation of simultaneity.

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.