"The phenomena of nature are most often enveloped by so many strange circumstances, and so great a number of disturbing causes mix their influence, that it is very difficult to recognize them. We may arrive at them only by multiplying the observations or the experiences, so that the strange effects finally destroy reciprocally each other." (Pierre-Simon Laplace, "A Philosophical Essays on Probabilities", 1814)
"The Laws of Nature are merely truths or generalized facts, in regard to matter, derived by induction from experience, observation, arid experiment. The laws of mathematical science are generalized truths derived from the consideration of Number and Space." (Charles Davies, "The Logic and Utility of Mathematics", 1850)
"The laws of nature are drawn from experience, but to express them one needs a special language: for, ordinary language is too poor and too vague to express relations so subtle, so rich, so precise. Here then is the first reason why a physicist cannot dispense with mathematics: it provides him with the one language he can speak […]. Who has taught us the true analogies, the profound analogies which the eyes do not see, but which reason can divine? It is the mathematical mind, which scorns content and clings to pure form." (Henri Poincaré, "The Value of Science", 1905)
"The scientific worker has elected primarily to know, not do. He does not directly seek, like the practical man, to realize the ideal of exploiting nature and controlling life – though he makes this more possible; he seeks rather to idealize – to conceptualize – the real, or at least those aspects of reality that are available in his experience. He thinks more of lucidity and formulae than of loaves and fishes. He is more concerned with knowing Nature than with enjoying her. His main intention is to describe the sequences in Nature in the simplest possible formulae, to make a working thought-model of the known world. He would make the world translucent, not that emotion may catch the glimmer of the indefinable light that shines through, but for other reasons – because of his inborn inquisitiveness, because of his dislike of obscurities, because of his craving for a system – an intellectual system in which phenomena are at least provisionally unified." (Sir John A Thomson," Introduction to Science", 1911)
"It is experience which has given us our first real knowledge of Nature and her laws. It is experience, in the shape of observation and experiment, which has given us the raw material out of which hypothesis and inference have slowly elaborated that richer conception of the material world which constitutes perhaps the chief, and certainly the most characteristic, glory of the modern mind." (Arthur J Balfour, "The Foundations of Belief", 1912)
"Everything we think we know about the world is a model. Every word and every language is a model. All maps and statistics, books and databases, equations and computer programs are models. So are the ways I picture the world in my head - my mental models. None of these is or ever will be the real world. […] Our models usually have a strong congruence with the world. That is why we are such a successful species in the biosphere. Especially complex and sophisticated are the mental models we develop from direct, intimate experience of nature, people, and organizations immediately around us." (Donella Meadows, "Limits to Growth", 1972)
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