The Value of Science

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.

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.

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.

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.

As we can not give a general definition of energy, the principle of the conservation of energy signifies simply that there is something which remains constant.

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.

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.

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.

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.

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?

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.

[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?

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.

The mathematician is born, not made.

[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..?

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.

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.

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

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."

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.

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.

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.

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

(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.

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

[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...

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.

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...

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.

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.

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.

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.

[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.

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

[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?

[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]!