17 January 2023

On Precision II: Precision in Science

"[It] may be laid down as a general rule that, if the result of a long series of precise observations approximates a simple relation so closely that the remaining difference is undetectable by observation and may be attributed to the errors to which they are liable, then this relation is probably that of nature." (Pierre-Simon Laplace, "Mémoire sur les Inégalites Séculaires des Planètes et des Satellites", 1787)

"Simplicity and precision ought to be the characteristics of a scientific nomenclature: words should signify things, or the analogies of things, and not opinions." (Sir Humphry Davy, Elements of Chemical Philosophy", 1812)

"[Precision] is the very soul of science; and its attainment afford the only criterion, or at least the best, of the truth of theories, and the correctness of experiments." (John F W Herschel, "A Preliminary Discourse on the Study of Natural Philosophy", 1830)

"One is almost tempted to assert that quite apart from its intellectual mission, theory is the most practical thing conceivable, the quintessence of practice as it were, since the precision of its conclusions cannot be reached by any routine of estimating or trial and error; although given the hidden ways of theory, this will hold only for those who walk them with complete confidence." (Ludwig E Boltzmann, "On the Significance of Theories", 1890)

"As scientific men we have all, no doubt, felt that our fellow men have become more and more satisfying as fish have taken up their work which has been put often to base uses, which must lead to disaster. But what sin is to the moralist and crime to the jurist so to the scientific man is ignorance. On our plane, knowledge and ignorance are the immemorial adversaries. Scientific men can hardly escape the charge of ignorance with regard to the precise effect of the impact of modern science upon the mode of living of the people and upon their civilisation. For them, such a charge is worse than that of crime." (Frederick Soddy, [Nobel prize speech] 1922)

"The scientist explores the world of phenomena by successive approximations. He knows that his data are not precise and that his theories must always be tested. It is quite natural that he tends to develop healthy skepticism, suspended judgment, and disciplined imagination." (Edwin P Hubble, 1938)

"Starting from statistical observations, it is possible to arrive at conclusions which not less reliable or useful than those obtained in any other exact science. It is only necessary to apply a clear and precise concept of probability to such observations. " (Richard von Mises, "Probability, Statistics, and Truth", 1939)

"It is never possible to predict a physical occurrence with unlimited precision." (Max Planck, "A Scientific Autobiography", 1949)

"It is never possible to predict a physical occurrence with unlimited precision." (Max Planck, "The Meaning of Causality in Physics", 1953)

"Scientists whose work has no clear, practical implications would want to make their decisions considering such things as: the relative worth of (1) more observations, (2) greater scope of his conceptual model, (3) simplicity, (4) precision of language, (5) accuracy of the probability assignment." (C West Churchman, "Costs, Utilities, and Values", 1956)

"The most important maxim for data analysis to heed, and one which many statisticians seem to have shunned is this: ‘Far better an approximate answer to the right question, which is often vague, than an exact answer to the wrong question, which can always be made precise.’ Data analysis must progress by approximate answers, at best, since its knowledge of what the problem really is will at best be approximate." (John W Tukey, "The Future of Data Analysis", Annals of Mathematical Statistics, Vol. 33, No. 1, 1962)

"It is of course desirable to work with manageable models which maximize generality, realism, and precision toward the overlapping but not identical goals of understanding, predicting, and modifying nature. But this cannot be done."(Richard Levins, "The strategy of model building in population biology", American Scientist Vol. 54 (4), 1966)

"A scientific theory is a concise and coherent set of concepts, claims, and laws (frequently expressed mathematically) that can be used to precisely and accurately explain and predict natural phenomena." (Mordechai Ben-Ari, "Just a Theory: Exploring the Nature of Science", 2005)

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