Karl Pearson Quotes

The next point to which I turned my attention was the frequency with which the several numbers themselves occurred. ...Each number might be expected to have occurred either 447 or 448 times. ... I found that they fitted to a standard deviation of 15.85 while the theoretical standard was 20.87 giving a difference of 5. ...What is a reasonable amount for the standard deviation of an experiment of this kind to differ from its theoretical value..? The mathematician answers... by finding the standard deviation of the standard deviation. It turned out... to be 2.43... the odds against a divergence as large or larger than 5...were ...21 to 1. In every two years I might expect such a deviation from the most probable results to occur once. ...I ...increased ...by counting the numbers for each week in the month instead of the total month. Here the experimental standard deviation [was] 7.2, the theoretical being 10.34, a difference of 3.14, while the standard deviation between experiment and theory was only 0.60. The odds against a divergence so great as this are... about 2,000,000 to 1.

Primitive man... rushes to the satisfactory conclusion that that power must be itself infinite; that he, man, is not altogether finite, and so he constructs a doctrine of the soul and its immortality. Then he builds up myths, superstitions, primitive religions, dogmas, whereby the infinite is made subject to the finite—floating on this huge bladder of man's supposed immortality. The universe is given a purpose, and that purpose is man—the whole is made subordinate to the part. That is the first solution of the problem, the keystone of most concrete religions.

In my enthusiasm Monte Carlo appeared to me in a new light; it was clearly a scientific laboratory preparing material for the natural philosopher.

Step by step men of science are coming to recognise that mechanism is not at the bottom of phenomena, but is only the conceptual shorthand by aid of which they can briefly describe and resume phenomena.

[T]he tribal conscience ought for the sake of social welfare to be stronger than private interest...

[T]he records of the tables are published in... Le Monaco and issued weekly in Paris... eight weeks roulette gave a grand total of 33,000 events. ...M. Blanc deserved a niche in the temple of science and Le Monaco a shelf in every mathematician's library.

The field of science is unlimited; its material is endless, every group of natural phenomena, every phase of social life, every stage of past or present development is material for science. The unity of all science consists alone in its method, not in its material.

There is an old German proverb: "Death has no calendar," which taken in conjunction with our... "Death is no respecter of persons," strongly marks the folk conception... as of one who obeys no rule of time, or of place, or of age, or of sex, or of household...

I determined to... investigate how closely the runs, that is, successions of numbers of the same colour were in accord with theory. ...The chance of a head<math>=\frac{1}{2}</math>, of two heads succeeding each other <math>\frac{1}{2}\times\frac{1}{2} = \frac{1}{4}</math>, of three heads <math>\frac{1}{2}\times\frac{1}{2}\times\frac{1}{2} = \frac{1}{8}</math>, and so on. Calling a "set" the run of tosses or the throws of the roulette ball till a change of face or of colour comes, the chance of a change<math>=\frac{1}{2}</math>, of a persistence followed by a change <math>\frac{1}{2}\times\frac{1}{2} = \frac{1}{4}</math>, and so on. ...[I]n the case of the roulette on one occasion the actual deviation is nearly ten times the standard.... The odds are thousand millions to one against such a deviation as nine or ten times the standard. ..My pupil... tabulated... the runs in a second fortnight's play with the result... so improbable that it was only to be expected once in 5000 years of continuous roulette. ...Finally, Mr. de Whalley investigated 7976 throws of the ball, forming a fortnight's play, at a slightly later date... There resulted deviations 4.63, 4.62, and 4.44 times the standard deviation, or odds of upwards of 263,000 to 1... That one such fortnight of runs should have occurred in the year 1892 might be looked upon as a veritable miracle, that three should have occurred is absolutely conclusive. Roulette as played at Monte Carlo is not a scientific game of chance.

[T]he classification of facts and the formation of absolute judgments upon the basis of this classification—judgments independent of the idiosyncrasies of the individual mind—essentially sum up the aim and method of modern science. The scientific man has above all things to strive at self-elimination in his judgments, to provide an argument which is as true for each individual mind as for his own. The classification facts, the recognition of their sequence and relative significance is the function of science, and the habit of forming a judgment upon these facts unbiassed by personal feeling is characteristic of what may be termed the scientific frame of mind.

I fear that... I may appear to have exceeded the duty of an editor. For all the Articles in this volume whose numbers are enclosed in square brackets I am alone responsible, as well as for the corresponding footnotes, and the Appendix... The principle which has guided me throughout the additions I have made has been to make the work... a standard work of reference for its own branch of science. ...It forms ...the history of a peculiar phase of intellectual development, worth studying for the many side lights it throws on general human progress. On the other hand it serves as a guide to the investigator in what has been done, and what ought to be done. ...[T]he individualism of modern science has not infrequently led to a great waste of power; the same... work has been repeated in different countries at different times, owing to the absence of such histories... [T]he would-be researcher either wastes much of his time in learning the history... or else works away regardless of earlier investigators. ...I have endeavoured to give it completeness (1) as a history of developement, (2) as a guide to what has been accomplished.

[P]rogress... enables me to define several... conceptions much more accurately than was possible in 1892, and to indicate, if only in vague outline, what a fascinating field is being here transferred from the synoptic to the precise division of science.

Our conception of chance is one of law and order in large numbers; it is not that idea of chaotic incidence which vexed the mediaeval mind.

25,000 tosses of a shilling occupied a good portion of my vacation and... gave me... a bad reputation in the neighbourhood... A friend and former pupil supplemented... 8200 penny trials and the drawing of 9000 tickets from a bag while another kindly provided... nearly 23,000 drawings of coloured and numbered counters. In all these cases the results were in... strikingly close agreement with theory.

An imaginary explanation... too often impedes the true explanation when man has attained it. This gives rise to the so-called contests of religion and science or of religion and philosophy—the unintelligible conflicts of "faith" and "reason" which can only arise in the minds of those, who cannot perceive clearly the distinction between myth and knowledge.