"Those who devised the eccentrics seen thereby in
large measure to have solved the problem of apparent motions with approximate
calculations. But meanwhile they introduced a good many ideas which apparently
contradict the first principles of uniform motion. Nor could they elicit or
deduce from the eccentrics the principal consideration, that is, the structure
of the universe and the true symmetry of its parts." (Nicolaus Copernicus, "De revolutionibus
orbium coelestium", 1543)
"Systems in physical science […] are no more than appropriate instruments to aid the weakness of our organs: they are, properly speaking, approximate methods which put us on the path to the solution of the problem; these are the hypotheses which, successively modified, corrected, and changed in proportion as they are found false, should lead us infallibly one day, by a process of exclusion, to the knowledge of the true laws of nature." (Antoine L Lavoisier, "Mémoires de l’Académie Royale des Sciences", 1777)
"[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)
"Force is not a fact at all, but an idea embodying
what is approximately the fact." (William K Clifford, "The Common
Sense of the Exact Sciences", 1823)
"The first steps in the path of discovery, and the first approximate measures, are those which add most to the existing knowledge of mankind." (Charles Babbage, "Reflections on the Decline of Science in England, And on Some of Its Causes", 1830)
"Experimental science hardly ever affords us more
than approximations to truth; and whenever many agents are concerned we are in
great danger of being mistaken." (Sir Humphry Davy, cca. 1836)
"With certain limited exceptions, the laws of
physical science are positive and absolute, both in their aggregate, and in
their elements, - in their sum, and in their details; but the ascertainable
laws of the science of life are approximative only, and not absolute."
(Elisha Bartlett, "An Essay on the Philosophy of Medical Science",
1844)
"Science gains from it [the pendulum] more than one
can expect. With its huge dimensions, the apparatus presents qualities that one
would try in vain to communicate by constructing it on a small [scale], no
matter how carefully. Already the regularity of its motion promises the most
conclusive results. One collects numbers that, compared with the predictions of
theory, permit one to appreciate how far the true pendulum approximates or
differs from the abstract system called 'the simple pendulum'."
(Jean-Bernard-Léon Foucault, "Demonstration Experimentale du Movement de
Rotation de la Terre", 1851)
"But in practical science, the question is - What
are we to do? - a question which involves the necessity for the immediate
adoption of some rule of working. In doubtful cases, we cannot allow our
machines and our works of improvement to wait for the advancement of science;
and if existing data are insufficient to give an exact solution of the
question, that approximate solution must be acted upon which the best data
attainable show to be the most probable. A prompt and sound judgment in cases
of this kind is one of the characteristics of a Practical Man in the right
sense of that term." (W J Macquorn Rankine, "On the Harmony of Theory
and Practice in Mechanics", 1856)
"We live in a system of approximations. Every end is prospective of some other end, which is also temporary; a round and final success nowhere. We are encamped in nature, not domesticated." (Ralph W Emerson, "Essays", 1865)
"Man’s mind cannot grasp the causes of events in
their completeness, but the desire to find those causes is implanted in man’s
soul. And without considering the multiplicity and complexity of the conditions
any one of which taken separately may seem to be the cause, he snatches at the
first approximation to a cause that seems to him intelligible and says: ‘This
is the cause!’" (Leo Tolstoy, "War and Peace", 1867)
"[...] very often the laws derived by physicists
from a large number of observations are not rigorous, but approximate."
(Augustin-Louis Cauchy, "Sept leçons de physique" ["Seven
lessons of Physics"], Bureau du Journal Les Mondes, 1868)
"Everything in physical science, from the law of gravitation to the building of bridges, from the spectroscope to the art of navigation, would be profoundly modified by any considerable inaccuracy in the hypothesis that our actual space is Euclidean. The observed truth of physical science, therefore, constitutes overwhelming empirical evidence that this hypothesis is very approximately correct, even if not rigidly true." (Bertrand Russell, "Foundations of Geometry", 1897)
"Science is about finding ever better approximations rather than pretending you have already found ultimate truth." (Friedrich Nietzsche)
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