On Motion (1800-1899)

"The determination of the average man is not merely a matter of speculative curiosity; it may be of the most important service to the science of man and the social system. It ought necessarily to precede every other inquiry into social physics, since it is, as it were, the basis. The average man, indeed, is in a nation what the centre of gravity is in a body; it is by having that central point in view that we arrive at the apprehension of all the phenomena of equilibrium and motion." (Adolphe Quetelet, "A Treatise on Man and the Development of his Faculties", 1842)

"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)

"The Mathematics, like language, (of which indeed they may be considered a species,) comprehending under that designation the whole science of number, space, form, time, and motion, as far as it can be expressed in abstract formulas, are evidently not only one of the most useful, but one of the grandest of studies." (Edward Everett, [address] 1857)

"When I have before my eyes a pair of stereoscopic drawings which are hard to combine, it is difficult to bring the lines and points that correspond, to cover each other, and with every little motion of the eyes they glide apart. But if I chance to gain a lively mental image (Anschauungsbild) of the represented solid form (a thing that often occurs by lucky chance), I then move my two eyes with perfect certainty over the figure without the picture separating again." (Hermann von Helmholtz, "Tonempfindungen" ["Sensations of Tone"], 1863)

"Consider an arbitrary figure in general position, indeterminate in the sense that it can be chosen from all such figures without upsetting the laws, conditions, and connections among the different parts of the system; suppose that given these data we have found one or more relations or properties, metric or descriptive, of that figure using the usual obvious inference (i.e., in a way regarded in certain cases as the only rigorous argument). Is it not obvious that if, preserving these very data, one begins to change the initial figure by insensible steps, or applies to some parts of the figure an arbitrary continuous motion, then is it not obvious that the properties and relations established for the initial system remain applicable to subsequent states of this system provided that one is mindful of particular changes, when, say, certain magnitudes vanish, change direction or sign, and so on - changes which one can always anticipate a priori on the basis of reliable rules." (Jean V Poncelet,"Treatise on Projective Properties of Figures", 1865)

"A strict materialist believes that everything depends on the motion of matter. He knows the form of the laws of motion though he does not know all their consequences when applied to systems of unknown complexity." (James C Maxwell, [Letter to Mark Pattison] 1868)

"Mathematics is the science of the functional laws and transformations which enable us to convert figured extension and rated motion into number." (George Holmes Howison, "The Departments of Mathematics, and their Mutual Relations", Journal of Speculative Philosophy Vol. 5, No. 2, 1871)

"We may conceive our space to have everywhere a nearly uniform curvature, but that slight variations of the curvature may occur from point to point, and themselves vary with the time. These variations of the curvature with the time may produce effects which we not unnaturally attribute to physical causes independent of the geometry of our space. We might even go so far as to assign to this variation of the curvature of space 'what really happens in that phenomenon which we term the motion of matter'." (William K Clifford, Richard C Rowe & Karl Pearson,"The Common Sense of the Exact Sciences", 1885)

"Since a given system can never of its own accord go over into another equally probable state but into a more probable one, it is likewise impossible to construct a system of bodies that after traversing various states returns periodically to its original state, that is a perpetual motion machine." (Ludwig E Boltzmann, "The Second Law of Thermodynamics", [Address to a Formal meeting of the Imperial Academy of Science], 1886)

"That branch of physics which is at once the oldest and the simplest and which is therefore treated as introductory to other departments of this science, is concerned with the motions and equilibrium of masses. It bears the name of mechanics." (Ernst Mach, "The Science of Mechanics: A Critical and Historical Account of Its Development", 1893)

"The first step, whenever a practical problem is set before a mathematician, is to form the mathematical hypothesis. It is neither needful nor practical that we should take account of the details of the structure as it will exist. We have to reason about a skeleton diagram in which bearings are reduced to points, pieces to lines, etc. and [in] which it is supposed that certain relations between motions are absolutely constrained, irrespective of forces. Some writers call such a hypothesis a fiction, and say that the mathematician does not solve the real problem, but only a fictitious one. That is one way of looking at the matter, to which I have no objection to make: only, I notice, that in precisely the same sense in which the mathematical hypothesis is 'false', so also is this statement 'false', that it is false. Namely, both representations are false in the sense that they omit subsidiary elements of the fact, provided that element of the case can be said to be subsidiary which those writers overlook, namely, that the skeleton diagram is true in the only sense in which from the nature of things any mental representation, or understanding, of the brute existent can be true. For every possible conception, by the very nature of thought, involves generalization; now generalization omits, means to omit, and professes to omit, the differences between the facts generalized." (Charles S Peirce, "Report on Live Loads", cca. 1895)

"Certainly, if a system moves under the action of given forces and its initial conditions have given values in the mathematical sense, its future motion and behavior are exactly known. But, in astronomical problems, the situation is quite different: the constants defining the motion are only physically known, that is with some errors; their sizes get reduced along the progresses of our observing devices, but these errors can never completely vanish." (Jacques Hadamard, "Les surfaces à courbures opposées et leurs lignes géodésiques", Journal de mathématiques pures et appliqués 5e (4), 1898)