On Data (1850-1899)

"In every branch of knowledge the progress is proportional to the amount of facts on which to build, and therefore to the facility of obtaining data." (James C Maxwell, [letter to Lewis Campbell] 1851)

"In the original discovery of a proposition of practical utility, by deduction from general principles and from experimental data, a complex algebraical investigation is often not merely useful, but indispensable; but in expounding such a proposition as a part of practical science, and applying it to practical purposes, simplicity is of the importance: - and […] the more thoroughly a scientific man has studied higher mathematics, the more fully does he become aware of this truth - and […] the better qualified does he become to free the exposition and application of principles from mathematical intricacy." (William J M Rankine, "On the Harmony of Theory and Practice in Mechanics", 1856)

"It usually happens in scientific progress, that when a great fact is at length discovered, it approves itself at once to all competent judges. It furnishes a solution to so many problems, and harmonizes with so many other facts, - that all the other data as it were crystallize at once about it." (Edward Everett, "The Uses of Astronomy", [An Oration Delivered at Albany] 1856)

"The great problems which offer themselves on all hands for solution, problems which the wants of the age force upon us as practically interesting, and with which its intellect feels itself competent to deal, are far more complex in their conditions, and depend on data which to be of use must be accumulated in far greater masses, collected over an infinitely wider field, and worked upon with a greater and more systematized power than has sufficed for the necessities of astronomy. The collecting, arranging, and duly combining these data are operations which, to be carried out to the extent of the requirements of modern science, lie utterly beyond the reach of all private industry, mean, or enterprise. Our demands are not merely for a slight and casual sprinkling to refresh and invigorate an ornamental or luxurious product, but for a copious, steady, and well-directed stream, to call forth from a soil ready to yield it, an ample, healthful, and remunerating harvest." (Sir John F W Herschel, "Essays from the Edinburgh and Quarterly Reviews with Addresses and Other Pieces", 1857)

"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)

"Mathematics may be compared to a mill of exquisite workmanship, which grinds you stuff of any degree of fineness; but, nevertheless, what you get out depends upon what you put in; and as the grandest mill in the world will not extract wheat-flour from peascod, so pages of formulae will not get a definite result out of loose data." (Thomas H Huxley, "Geological Reform", Quarterly Journal of the Geological Society of London Vol. 25, 1869)

"The mathematician starts with a few propositions, the proof of which is so obvious that they are called self-evident, and the rest of his work consists of subtle deductions from them. The teaching of languages, at any rate as ordinarily practised, is of the same general nature: authority and tradition furnish the data, and the mental operations are deductive." (Thomas H Huxley, 1869)

"The ignoring of data is, in fact, the easiest and most popular mode of obtaining unity in one's thought." (William James, "The Sentiment of Rationality", Mind Vol. 4, 1879)

"It is a capital mistake to theorise before one has data." (Arthur C Doyle, "The Adventures of Sherlock Holmes", 1892)

"All deduction rests ultimately upon the data derived from experience. This is the tortoise that supports our conception of the cosmos." (Percival Lowell, "Mars", 1895)

"Physical research by experimental methods is both a broadening and a narrowing field. There are many gaps yet to be filled, data to be accumulated, measurements to be made with great precision, but the limits within which we must work are becoming, at the same time, more and more defined." (Elihu Thomson, "Annual Report of the Board of Regents of the Smithsonian Institution", 1899)