“The conclusion seems to be irresistible that such laws of nature as the principle of conservation of energy, the principle of conservation of momentum and the law of gravitation are necessary consequences of our modes of measurement. They are, in fact, elaborately disguised identities which could have been predicted a priori by a being of sufficiently powerful analytical insight who fully understood all that is implied in the way we measure space-time intervals.”

As quoted by Gerald James Whitrow, The Structure of the Universe: An Introduction to Cosmology (1949)

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Ernest Barnes 9
English mathematician and clergyman 1874–1953

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“Matter… could be measured as a quantity and… its characteristic expression as a substance was the Law of Conservation of Matter… This, which has hitherto represented our knowledge of space and matter, and which was in many quarters claimed by philosophers as a priori knowledge, absolutely general and necessary, stands to-day a tottering structure.”

Hermann Weyl (1885–1955) German mathematician

Introduction<!-- p. 1-2 -->
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Context: The Greeks made Space the subject-matter of a science of supreme simplicity and certainty. and certainty Out of it grew, in the mind of classical antiquity, the idea of pure science. Geometry became one of the most powerful expressions of that sovereignty of the intellect that inspired the thought of those times. At a later epoch, when the intellectual despotism of the Church... had crumbled, and a wave of scepticism threatened to sweep away all that had seemed most fixed, those who believed in Truth clung to Geometry as to a rock, and it was the highest ideal of every scientist to carry on his science "more geometrico". Matter... could be measured as a quantity and... its characteristic expression as a substance was the Law of Conservation of Matter... This, which has hitherto represented our knowledge of space and matter, and which was in many quarters claimed by philosophers as a priori knowledge, absolutely general and necessary, stands to-day a tottering structure.

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“We must all obey the great law of change. It is the most powerful law of nature, and the means perhaps of its conservation.”

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“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.”

Comme nous ne pouvons pas donner de l'énergie une définition générale, le principe de la conservation de l'énergie signifie simplement qu'il y a quelque chose qui demeure constant.
Source: The Value of Science (1905), Ch. 10: Is Science artificial?

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“Intelligence and free will here come into play, and these mystic forces are outside the law of conservation of energy as understood by physicists.”

William Crookes (1832–1919) British chemist and physicist

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Context: The clock runs down. I lift the weight by exerting the proper amount of energy, and in this action the law of conservation of energy is strictly obeyed. But now I have the choice of either letting the weight fall free in a fraction of a second, or, constrained by the wheelwork, in twenty-four hours. I can do which I like, and whichever way I decide, no more energy is developed in the fall of the weight. I strike a match; I can use it to light a cigarette or to set fire to a house. I write a telegram; it may be simply to say I shall be late for dinner, or it may produce fluctuations on the stock exchange that will ruin thousands. In these cases the actual force required in striking the match or in writing the telegram is governed by the law or conservation of energy; but the vastly more momentous part, which determines the words I use or the material I ignite, is beyond such a law. It is probable that no expenditure of energy need be used in the determination of direction one way more than another. Intelligence and free will here come into play, and these mystic forces are outside the law of conservation of energy as understood by physicists.

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