The purpose of the mathematical theory of statistics is to deal with the relationship between 2 or more variable quantities without assuming that one is a single-valued mathematical function of the rest. The statistician does not think a certain x will produce a single-valued y; not a causative relation but a correlation. The relationship between x and y will be somewhere within a zone and we have to work out the probability that the point (x,y) will lie in different parts of that zone. The physicist is limited and shrinks the zone into a line. Our treatment will fit all the vagueness of biology, sociology, etc. A very wide science.
English mathematician, biometrician, and eugenicist (1857–1936)
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The scientific conception of chance is that of a measure based on experience; a knowledge of the average results of many events is used to replace ignorance of the result of any individual event. ...The judgment which Science gives in this case is decisive; judged by the so called "permanences," or runs of colour, Monte Carlo roulette is no true worship of the goddess at all.
Scarcely any specialist of to-day is really master of all the work which has been done in his own comparatively small field. Facts and their classification have been accumulating at such a rate that nobody seems to have leisure to recognise the relations of sub-groups to the whole. It is as if individual workers... were bringing their stones to one great building and piling them on and cementing them... without regard to any general plan... only where some one has placed a great corner stone... the building... rises... more rapidly... till it... is stopped for want of side support. Yet this great structure... possesses a symmetry and unity... in scientific method. The smallest group of facts, if properly classified and logically dealt with, ...has its proper place... wholly independent of the individual workman who... shaped it. Even when two men work unwittingly at the same stone they will but modify and correct each other... In the face of all this enormous progress... when in all civilised lands men are applying the scientific method... the goal of science is and must be infinitely distant.
[S]uppose that the Emperor Karl V. had said to the learned of his day: "I want a method by which I can send a message in a few seconds to that new world, which my mariners take weeks in reaching. ..." ...It required centuries spent in the discovery and classification of new facts before the Atlantic cable became a possibility. It may require the like or even a longer time to unriddle... psychical and biological enigmas... but he who declares that they can never be solved by the scientific method is... as rash as the man of the early sixteenth century would have been had he declared it utterly impossible that the problem of talking across the Atlantic Ocean should ever be solved.
[I]n the seventeenth century... the system-mongers were the theologians who declared that cosmical problems were not the legitimate problems of science. It was vain for Galilei to assert that the theologians' classification of facts was hopelessly inadequate. ...[T]hey settled that:—
"The doctrine that the earth is neither the centre of the universe nor immovable, but moves even with a daily rotation, is absurd, and both philosophically and theologically false, and at the least an error of faith."
It took nearly two hundred years to convince the whole theological world that cosmical problems were the legitimate problems of science and science alone, for in 1819 the books of Galilei, Copernicus, and Keppler were still upon the index of forbidden books, and not till 1822 was a decree issued allowing books teaching the motion of the earth about the sun to be printed and published in Rome!
If my view be correct, Erasmus Darwin planted the seed of suggestion in questioning whether adaptation meant no more to man than illustration of creative ingenuity; the one grandson, Charles Darwin, collected the facts which had to be dealt with and linked them together by wide-reaching hypotheses; the other grandson, Francis Galton, provided the methods by which they could be tested...
Now it will, I think, be found that the fields of inquiry where science has not yet penetrated and where the scientist still confesses ignorance, are very like... alchemy astrology and witchcraft... Either they involve facts which are in themselves unreal—conceptions which are self-contradictory and absurd, and therefore incapable of analysis by the scientific or any other method,—or, on the other hand, our ignorance arises from an inadequate classification and a neglect of scientific method.
[B]ear these points in mind, the association of Death and Chance, the notion of both as chaotic in their action, and their embodiment in a great artistic ideal—the Dance of Death—which gave so much colouring to mediaeval thought and life. We find this sombre notion everywhere—on the church walls, on the bridges, in the engravings and s, but as well in the sermons, the poetry, and the very turn of folk-sentiment.
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The views expressed in this Grammar on the fundamental concepts of science, especially on those of force and matter, have formed part of the author's teaching since he was first called upon (1882) to think how the elements of dynamical science could be presented free from metaphysics to young students. But the endeavour to put them into popular language only dates from... 1891...