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.
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.
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."
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 longitude... 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... The 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 principle of sufficient reason... 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.
