"Treatises on mechanics do not clearly distinguish between what is experiment, what is mathematical reasoning, what is convention, and what is hypothesis." (Henri Poincaré, "Science and Hypothesis", 1901)
"The laws of thermodynamics, as empirically determined, express the approximate and probable behavior of systems of a great number of particles, or, more precisely, they express the laws of mechanics for such systems as they appear to beings who have not the fineness of perception to enable them to appreciate quantities of the order of magnitude of those which relate to single particles, and who cannot repeat their experiments often enough to obtain any but the most probable results." (Josiah W Gibbs, "Elementary Principles in Statistical Mechanics", 1902)
"I never satisfy myself until I can make a mechanical model of a thing. If I can make a mechanical model, I understand it." (William T Kelvin, 1904)
"By laying down the relativity postulate from the outset, sufficient means have been created for deducing henceforth the complete series of Laws of Mechanics from the principle of conservation of energy (and statements concerning the form of the energy) alone." (Hermann Minkowski, "The Fundamental Equations for Electromagnetic Processes in Moving Bodies", 1907)
"The equations of Newton's mechanics exhibit a two-fold invariance. Their form remains unaltered, firstly, if we subject the underlying system of spatial coordinates to any arbitrary change of position ; secondly, if we change its state of motion, namely, by imparting to it any uniform translatory motion ; furthermore, the zero point of time is given no part to play. We are accustomed to look upon the axioms of geometry as finished with, when we feel ripe for the axioms of mechanics, and for that reason the two invariances are probably rarely mentioned in the same breath. Each of them by itself signifies, for the differential equations of mechanics, a certain group of transformations. The existence of the first group is looked upon as a fundamental characteristic of space. The second group is preferably treated with disdain, so that we with un-troubled minds may overcome the difficulty of never being able to decide, from physical phenomena, whether space, which is supposed to be stationary, may not be after all in a state of uniform translation. Thus the two groups, side by side, lead their lives entirely apart. Their utterly heterogeneous character may have discouraged any attempt to compound them. But it is precisely when they are compounded that the complete group, as a whole, gives us to think." (Hermann Minkowski, "Space and Time" ["Raum und Zeit"], [Address to the 80th Assembly of German Natural Scientists and Physicians] 1908)
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