Karl Pearson

Karl Pearson, 1912

Karl Pearson (27 March 1857 – 27 April 1936) was an influential English mathematician and biostatistician. He founded the world's first university statistics department at University College London in 1911.

Quotes

• Heredity. Given any organ in a parent and the same or any other organ in its offspring, the mathematical measure of heredity is the correlation of these organs for pairs of parent and offspring... The word organ here must be taken to include any characteristic which can be quantitatively measured.
  • "Mathematical Contributions to the Theory of Evolution III: Regression, Heredity and Panmixia", Philosophical Transactions of the Royal Society, Series A, Vol. 187 (1896) p. 259.

• 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.
  • As quoted by E.S. Pearson, Karl Pearson: An Appreciation of Some Aspects of his Life and Work (1938) and cited in Bernard J. Norton, "Karl Pearson and Statistics: The Social Origins of Scientific Innovation" in Social Studies of Science, Vol. 8, No. 1, Theme Issue: Sociology of Mathematics (Feb.,1978), pp. 3-34.

The Ethic of Freethought (Mar 6, 1883)

A Lecture Delivered at South Place Institute, source.

Karl Pearson

• [M]y axiom runs as follows: "The whole is not identical with a part." This axiom leads us at once to a problem. What relation has the part to the whole?

• I simply assert that the universe alters, is "becoming;" what it is becoming I will not venture to say. ...the individual too is altering, is not only a "being" but also a "becoming." These alterations... I shall—merely for convenience—term life.

• What relation has the life of the individual to the life of the universe? ...The former is absolutely subordinate, inconceivably infinitesimal compared with the latter. The becoming of the latter bears not the slightest apparent reference to the becoming of the former. ...The one seems finite, limited, temporal, the other by comparison infinite, boundless, eternal. This disparity has forced itself upon the attention of man ever since his first childlike attempts at thought.

• The "Eternal Why" begins to haunt his mind; "Why... am I here?" he asks. What relation do I, a part, bear to the whole—the sum of all things material and spiritual? What connection has the finite with the infinite? the temporal with the eternal?

• 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.

• [D]efinition... Religion is the relation of the finite to the infinite. ...is the relation. ...[T]here is only one relation, there can be only one religion. ...only so far true as it actually explains the relation of the finite to the infinite. In so far as it builds up an imaginary relation between finite and infinite it is false. ...[S]ince no existing religion lays out before us fully the relation of finite and infinite, all systems of religion are of necessity but half truths. ...not whole falsehoods, for many... may have made... small advance towards the solution...

• The great danger... not content with our real knowledge of the relation of the finite to the infinite, they slur over our vast ignorance by the help of the imagination. Myth supplies the place of true knowledge where we are ignorant of the connection between finite and infinite. Hence... most concrete systems of religion present us with a certain amount of knowledge but a great deal of myth.

• [O]ur [small] knowledge of the relation of finite to infinite... is... continually increasing—science and philosophy are continally presenting... broader views of the relation of man to nature and of individual thought to abstract thought.

• It follows... that... in every concrete religion the knowledge element ought to increase and the myth element decrease or... every concrete religion ought to be in a state of development.

• [S]mall as our increase in knowledge may be, concrete systems of religion have not kept pace with it. They persist in explaining by myth, portions of the relation of... which we have true knowledge. Hence we see the danger, if not the absolute evil of any myth at all.

• 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.

• The holding of a myth explanation of any problem whereon mankind has attained true knowledge is what I term enslaved thought or dogmatism.

• The rejection of all myth explanation, the reception of all ascertained truths with regard to the relation of the finite to the infinite is what I term freethought or true religious knowledge. ...[T]he freethinker ...possesses more real religion, more of the relation of the finite to the infinite than any mere believer in myth; his very knowledge makes him in the highest sense of the word a religious man.

The Common Sense of the Exact Sciences (1885)

Begun by William Kingdon Clifford prior to his death, then partially edited by R. C. Rowe until his death; then edited & completed by Pearson, source.

• The original work as planned by Clifford was to have been entitled The First Principles of the Mathematical Sciences Explained to the Non-Mathematical and to have contained six chapters on Number, Space, Quantity, Position, Motion, and Mass respectively. ...Shortly before his death he expressed a wish that the book should only be published after very careful revision and that its title should be changed to [our title]. Upon Clifford's death the labour of revision and completion was entrusted to Mr. R. C. Rowe... On the sad death of Professor Rowe... I was requested... to take up the... editing thus left incomplete. ...For the latter half of Chapter III and for the whole of Chapter IV... I am alone responsible. Yet whatever there is in them of value I owe to Clifford; whatever is feeble or obscure is my own. ...With Chapter V. my task has been by no means light. ... I felt it impossible to rewrite the whole without depriving the work of its right to be called Clifford's, and yet at the same time it was absolutely necessary to make considerable changes. ...Without any notice of mass or force it seemed impossible to close a discussion on motion; something I felt must be added. I have accordingly introduced a few pages on the laws of motion [and] since found that Clifford intended to write a concluding chapter on mass. How to express the laws of motion in a form of which Clifford would have approved was indeed an insoluble riddle... because I was unaware of his having written on the subject. I have accordingly expressed... my own views on the subject [i.e.,] a strong desire to see the terms matter and force, together with the ideas associated with them, entirely removed from scientific terminology—to reduce, in fact, all dynamic to kinematic. I should hardly have ventured to put forward these views had I not recently discovered that they have... the weighty authority of Professor Mach... But since writing these pages I have also been referred to a discourse delivered by Clifford at the Royal Institution in 1873, some... of which appeared in Nature June 10, 1880 [pp. 122-123.] Therein it is stated that 'no mathematician can give any meaning to the language about matter, force, inertia used in current text-books of mechanics.' This fragmentary account of the discourse undoubtedly proves that Clifford held on the categories of matter and force as clear and original ideas as on all subjects of which he has treated; only, alas! they have not been preserved.
  Footnote: Mr. R. Tucker who... searched Clifford's note books... sends me... the following... in Clifford's handwriting: 'Force is not a fact at all, but an idea embodying what is approximately the fact.'
  • Preface, pp. v-ix.

• We may... be treating merely as physical variations effects which are really due to changes in the curvature of our space; whether, in fact, some or all of those causes which we term physical may not be due to the geometrical construction of our space. There are three kinds of variation in the curvature of our space which we ought to consider as within the range of possibility.
  (i) Our space is perhaps really possessed of a curvature varying from point to point, which we fail to appreciate because we are acquainted with only a small portion of space, or because we disguise its small variations under changes in our physical condition which we do not connect with our change of position. The mind that could recognise this varying curvature might be assumed to know the absolute position of a point. For such a mind the postulate of the relativity of position would cease to have a meaning. It does not seem so hard to conceive such a state of mind as the late Professor Clerk-Maxwell would have had us believe. It would be one capable of distinguishing those so-called physical changes which are really geometrical or due to a change of position in space.
  (ii) Our space may be really same (of equal curvature), but its degree of curvature may change as a whole with the time. In this way our geometry based on the sameness of space would still hold good for all parts of space, but the change of curvature might produce in space a succession of apparent physical changes.
  (iii) 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.'
  • Pearson & Clifford, Ch IV, Position, §19 On the Bending of Space, pp. 224-225.

A History of the Theory of Elasticity and of the Strength of Materials.. (1886)

..from Galilei to the Present Time, begun by Isaac Todhunter prior to his death, then edited & completed by Pearson, Vol. 1. Galilei to Saint-Venant, Preface, pp. x-xiii.

• 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.
  • Preface, pp. x-xi.

• The whole early history... is... so intimately connected with the names Galilei, Hooke, Mariotte and Leibniz that I have introduced some account of their work. The labours of Lagrange and Riccati also required some recognition. ...These early writers form the basis... not without interest, whether judged from the special standpoint of the elastician or from the wider footing of... the growth of human ideas. With a similar aim I have introduced throughout the volume... memoirs having purely historical value which had escaped Dr Hunter's notice.
  Another class of memoirs which I have inserted are... of mathematical value, omitted apparently by pure accident. For example all the memoirs of F. E. Neumann, the second memoir of Duhamel, those of [P. H.] Blanchet etc. I cannot hope that the work is complete in this respect even now, but I trust that nothing of equal importance has escaped...
  • Preface, pp. xi-xii.

• My greatest difficulty arose with regard to the rigid line which Dr Todhunter had attempted to draw between mathematical and physical memoirs. Thus while including an account of Clausius' memoir of 1849, he had omitted Weber's of 1835, yet the consideration of the former demands the inclusion of the latter... [with respect to] elastic after-strain. What seemed... needful at... present... was to place before the mathematician the results of physical investigations that he might have some distinct guide to the direction in which research is required. ...I have endeavoured... to abrogate this divorce between mathematical elasticity on the one hand, and physical and technical elasticity on the other. With this aim... I have introduced the general conclusions of a considerable body of physical and technical memoirs in the hope that... I may bring the mathematician closer to the physicist and both to the practical engineer. I trust that in doing so I have rendered this History of value... and so increased the usefulness of Dr Todhunter's... years of patient historical research on the more purely mathematical side of elasticity. In this matter I have kept before me the labours of M. de Saint Venant as a true guide to the functions of the ideal elastician.
  • Preface, pp. xii-xiii. Here Pearson refers to Clausius' Ueber die Verdäderungen welche in den bisher gebräuchlichen Formeln für das Gleichgewicht und die Bewegung elastischer fester Körper durch neuere Beobachtungen nothwendig geworden sind, in Poggendorf's Annalen (1849) Vol. 76, pp. 46-67; and to Weber's Königliche Gesellschafl der Wissenschaflen (1835).

"The Scientific Aspect of Monte Carlo Roulette" (1894)

Fortnightly Review (Feb. 1894) as quoted in Karl Pearson, The Chances of Death, and Other Studies in Evolution (1897) Vol. 1, pp. 42-62.

• That it does not pay to gamble has been the oft repeated theme of the moralist, and has been demonstrated with much brave show of symbols by mathematicians from Lagrange to De Morgan and onwards.

• While the moralists have boldly asserted that the service of the goddess Chance leads to a complete demoralisation of her worshippers... the mathematicians... start from the hypothesis that gambling is a game of chance—chance being defined in their own perfectly clear and definite sense. My object... is to show that chance in this sense... as it applies to the tossing of an unloaded coin, has no application to Monte Carlo roulette.

• 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.

• 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.

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

• [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.

• [R]andom spinning being assumed, the distribution of chance in the game depends upon the mechanical perfection of the teetotum; it must be equally likely to fall on all its thirty-seven sides, i.e. the frequency of all the numbers must in the long run be very nearly the same.

• [W]e have an equal number of black and red possibilities... Thus in a very great number of throws there ought to be 50 per cent of both. ...In no case... are the results exactly reached, but in all the cases of large numbers we have but small deviations from 50 per cent. Thus 16,141 roulette throws give slightly better results than 12,000 and slightly worse results than 24,000 tosses. We notice that... 16,019 roulette throws give nearly the worst percentage 50.27 instead of 50.

• [F]or every type of experiment there is a numerical quantity, depending partly on the chance of the single event succeeding, and partly on the total number of the trials of it, which we may term the standard deviation. ... it gives us a measure of the frequency with which deviations of various sizes will occur.

• [W]e find out of 16,019 trials, 8053 red numbers instead of 8009 or 8010. We have a deviation of 43 to 44. The standard deviation is about 63; a deviation as great as or greater than 44 would occur in about half the number of times in which 16,019 returns were examined. It presents therefore nothing of the remarkable or improbable.

• 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.

• I felt somewhat taken aback. ...to have hit upon a month of roulette ...so improbable ...that it would only occur on the average once in 167,000 years of continuous roulette playing.

• 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$={\frac {1}{2}}$, of two heads succeeding each other ${\frac {1}{2}}\times {\frac {1}{2}}={\frac {1}{4}}$, of three heads ${\frac {1}{2}}\times {\frac {1}{2}}\times {\frac {1}{2}}={\frac {1}{8}}$, 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$={\frac {1}{2}}$, of a persistence followed by a change ${\frac {1}{2}}\times {\frac {1}{2}}={\frac {1}{4}}$, 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.

• The absence of the improbable, the redundancy of the probable, is just as much conclusive evidence against conformity with scientific law as the too frequent occurrence of the improbable itself.

• No statements of mere averages... are of the least avail against our statistics. Fluctuations from the averages are the sole reliable test...

• Monte Carlo roulette, if judged by returns which are published... is, if the laws of chance rule, from the standpoint of exact science the most prodigious miracle of the nineteenth century.

• [W]e are forced to accept... that the random spinning of a roulette manufactured and daily readjusted with extraordinary care is not obedient to the laws of chance, but is chaotic in its manifestations.

• [W]e appeal to the French Académie des Sciences, to obtain from its secretary, M. Bertrand... a report on the colour runs of the Monte Carlo roulette tables for... 1892. Should he confirm the conclusion... that these runs do not obey the scientific theory of chance, then science must reconstruct its theories to suit these inconvenient facts...

• Clearly, since the Casino does not serve the valuable end of huge laboratory for the preparation of probability statistics, it has no scientific raison d'être. Men of science cannot have their most refined theories disregarded in this shameless manner! The French Government must be urged by the hierarchy of science to close the gaming-saloons; it would be, of course, a graceful act to hand over the remaining resources of the Casino to the Académie des Sciences for the endowment of a laboratory of orthodox probability; in particular, of the new branch of that study, the application of the theory of chance to the biological problems of evolution, which is likely to occupy so much of men's thoughts in the near future.

"The Chances of Death" (1895)

Lecture before the Leeds Philosophical and Literary Society (Jan. 1895) as quoted in Karl Pearson, The Chances of Death, and Other Studies in Evolution (1897) Vol. 1, pp. 1-41.

• 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...

• This idea of Death as the lawless one... who strikes at random, arose early in mediaeval tradition, and is represented in the well known Dances of Death... Parallel with this notion... has run in the mind of the folk a vague idea of Chance as that which obeys no rule and defies all measure and prediction. The two conceptions cross one another in the medieval representation of Death seizing the gambler's dice-box and casting the dice with him for his life.

• Chance... the origin of the word itself is very possibly related to the falling of the dice from their box,—and certainly the first attempts at a theory of Chance arose from the general interest in gambling with dice.

• [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 broadsides, but as well in the sermons, the poetry, and the very turn of folk-sentiment.

• The shadow of death, more strongly even than blood or nation, maketh mankind akin; it arouses sympathy and understanding, which surmount all the barriers of caste and station.

• The old Dances of Death supplied what fails so much in our modern life—an artistic representation appealing to all classes of at least one experience common to the whole of humanity.

• Standing in 1875 on the well known wooden bridge at Luzern, with its pictures of the Dance of Death, it struck me that something might be done to resuscitate the mediaeval conception of the relation between Death and Chance and to express it in a more modern scientific form. ...[M]y aim in this essay is to place before the reader a modern conception of the Dance of Death.

• [O]ur conception of Chance is now utterly different from that of yore. Where we cannot predict, where we do not find order and regularity, there we should now assert... that something else than Chance is at work. What we are to understand by a chance distribution is one in accordance with law, and one the nature of which can... be closely predicted.

• It is not theory, but actual statistical experience, which forces us to the conclusion that, however little we know of what will happen in the individual instance, yet the frequency of a large number of instances is distributed round the mode in a manner more and more smooth and uniform the greater the number of individual instances. When this distribution round the mode does not take place... then we assert that some cause other than chance is at work.

• 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.

The Grammar of Science (1900)

Quotes are from second edition, unless otherwise noted. Source

• 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.
  • Preface to the Second Edition

• That all science is description and not explanation, that the mystery of change in the inorganic world is just as great and just as omnipresent as in the organic world, are statements which will appear platitudes to the next generation.
  • Preface to the Second Edition

• Formerly men had belief as to the supersensuous and thought they had knowledge of the sensuous. The science of the future, while agnostic as to the supersensuous, will replace knowledge by belief in the perceptual sphere, and reserve the term knowledge for the conceptual sphere—the region of their own concepts and ideas...
  • Preface to the Second Edition

• That this change of view as to the basis of science cannot take place without misunderstanding, or without giving an opportunity to those who dislike science to decry its weaknesses, is only natural. To change the basis of operations during a campaign always gives a chance to the enemy, but the chance must be risked if thereby we place ourselves permanently in a position of greater strength...
  • Preface to the Second Edition

• If the reader questions whether there is still war between science and dogma, I must reply that there always will be as long as knowledge is opposed to ignorance. To know requires exertion, and it is intellectually easiest to shirk effort altogether by accepting phrases which cloak the unknown in the undefinable.
  • Preface to the Second Edition

• [T]he need for remodelling the fundamental mechanical principles as we find them stated in elementary text-books of physics and dynamics remains as urgent as ever. Professor A. E. H. Love is, indeed, to be congratulated in having in his Theoretical Mechanics ventured a good way in the right direction, but his work will hardly be used for elementary science teaching, and it is through the latter only that we can hope to give the new and sounder scientific conceptions general currency.
  • Preface to the Second Edition

• For the present the Grammar may yet be of service. After an eight years' life and... 4000 copies, it reappears in a revised and enlarged form.
  • Preface to the Second Edition

• [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.
  • Preface to the Second Edition

• There are periods in the growth of science when it is well to turn our attention from its imposing superstructure and to carefully examine its foundations. The present book is primarily intended as a criticism of the fundamental concepts of modern science...
  • Preface to the First Edition

• The obscurity which envelops the principia of science is not only due to an historical evolution influenced by the authority which attaches even to the phraseology used by great discoverers, but to the fact that science, as long as it had to carry on a difficult warfare with metaphysics and dogma, like a skilful general conceived it best to hide its own deficient organisation.
  • Preface to the First Edition

• [T]his deficient organisation will not only in time be perceived by the enemy, but... has already had a very discouraging influence both on scientific recruits and on intelligent laymen.
  • Preface to the First Edition

• Anything more hopelessly illogical than the statements with regard to force and matter current in elementary text-books of science, it is difficult to imagine; and the author, as a result of some ten years' teaching and examining, has been forced to the conclusion that these works possess little, if any, educational value; they neither encourage the growth of logical clearness nor form any exercise in scientific method.
  • Preface to the First Edition

• One result of this obscurity we probably find in the ease with which the physicist, as compared with either the pure mathematician or the historian, is entangled in the meshes of such pseudosciences as natural theology and spiritualism.
  • Preface to the First Edition

• [T]his work... is... intended to arouse and stimulate the reader's own thought, rather than to inculcate doctrine: this result is often best achieved by the assertion and contradiction which excite the reader to independent inquiry.
  • Preface to the First Edition

• 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...
  • Preface to the First Edition

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

• [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.
  • Introductory

• [T]he state may be reasonably called upon to place instruction in pure science within the reach of all its citizens. ...The scientific habit of mind is one which may be acquired by all, and the readiest means of attaining to it ought to be placed within the reach of all.
  • Introductory

• Minds trained to scientific methods are less likely to be led by mere appeal to the passions or by blind emotional excitement to sanction acts which in the end may lead to social disaster. ...therefore, I lay stress upon the educational side of modern science and state my position..:
  Modern Science, as training the mind to an exact and impartial analysis of facts, is an education specially fitted to promote sound citizenship.
  • Introductory

• [T]he value of science for practical life turns upon the efficient training it provides in method. ...to marshal facts... examine their complex mutual relations and predict... their inevitable sequences... which we term natural laws...[such a man ...will scarcely be content with merely superficial statement, with vague appeal to the imagination, to the emotions, to individual prejudices. He will demand a high standard of reasoning, a clear insight into facts and their results ...beneficial to the community at large.
  • Introductory

• If any... work gives a description of phenomena that appeals to... imagination rather than to... reason, then it is bad science.
  • Introductory

• The scientific method is one and the same in all branches, and that method is the method of all logically trained minds. In this respect the great classics of science are often the most intelligible of books, and... are far better worth reading than popularisations of them...
  • Introductory

• 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.
  • Introductory

• [T]he task of science can never end till man ceases to be, till history is no longer made, and development itself ceases.
  • Introductory

• 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.
  • Introductory

• When... a simple principle has been discovered... then this principle or law itself generally leads to the discovery of a still wider range of hitherto unregarded phenomena... Every great advance of science opens our eyes to facts which we had failed before to observe, and makes new demands...
  • Introductory

• Where [our great-grandfathers] interpreted the motions of planets in our own solar system, we discuss the chemical constitution of stars, many of which... their telescopes could not reach... Where they discovered the circulation of the blood, we see the physical conflict of living poisons within the blood whose battles would have been absurdities for them. Where they found void... we conceive of great systems in rapid motion capable of carrying through brick walls as light passes through glass. Great as the advance of scientific knowledge has been, it has not been greater than the growth of the material to be dealt with. The universe grows ever larger as we learn to understand more of our own corner of it.
  • Introductory

• [T]he material of science is coextensive with the whole life, physical and mental, of the universe, and... the limits to our perception of the universe are only apparent, not real.
  • Introductory

• The universe is a variable quantity, which depends upon the keenness and structure of our organs of sense, and upon the fineness of our powers and instruments of observation.
  • Introductory

• [T]he universe is largely the construction of each individual mind.
  • Introductory

• To say that there are certain fields—for example, metaphysics—from which science is excluded, wherein its methods have no application, is merely to say that the rules of methodical observation and the laws of logical thought do not apply to the facts, if any, which lie within such fields. These fields, if indeed such exist, must lie outside any intelligible definition which can be given of the word knowledge.
  • Introductory

• Each metaphysician has his own system, which to a large extent excludes that of his predecessors and colleagues. Hence... metaphysics are built either on air or on quicksands—either they start from no foundation in facts at all, or the superstructure has been raised before a basis has been found in the accurate classification facts.
  • Introductory

• There is no short cut to truth, no way to gain a knowledge of the universe except through the gateway of scientific method.
  • Introductory

• Our aesthetic judgment demands harmony between the representation, and the represented and in this sense science is often more artistic than modern art.
  • Introductory

• [T]he philosophical method seems based upon an analysis which does not start with the classification of facts, but reaches its judgments by some obscure process of internal cogitation. It is therefore dangerously liable to the influence of individual bias; it results... in an endless number of competing and contradictory systems. It is because the so-called philosophical method does not, when different individuals approach the same range of facts, lead, like the scientific, to practical unanimity of judgment, that science, rather than philosophy, offers the better training for modern citizenship.
  • Introductory

• Science can only answer to the great majority of "metaphysical" problems "I am ignorant." Meanwhile, it is idle to be impatient or to indulge in system-making.
  • Introductory

• [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!
  • Introductory

• Wherever there is the slightest possibility for the human mind to know, there is a legitimate problem of science. Outside the field of actual knowledge can only lie a region of the vaguest opinion and imagination, to which... men too often... pay higher respect than to knowledge.
  • Introduction

• The ignorance of science means the enforced ignorance of mankind.
  • Introductory

• Who can give us the assurance that the fields already occupied by science are alone those in which knowledge is possible? Who, in the words of Galilei, is willing to set limits to the human intellect?
  • Introductory

• Professor Huxley has invented the term Agnostic... for those who limit the possibility of knowledge in certain fields. ...Professor E. du Bois-Reymond has raised the cry "Ignorabimus" ("We shall be ignorant") and... undertaken the difficult task of demonstrating that with regard to certain problems human knowledge is impossible. ...Now ...there is great danger in this cry. ...[T]he attempt to demonstrate an endless futurity of ignorance ...approaches despair. ...Evolution has taught us of the continual growth of man's intellectual powers.
  • Introductory

• [M]ediaeval ...alchemy, astrology, witchcraft. ...Do we now know how the stars influence human lives or how witches turn milk blue? Not in the least. We have learnt to look upon the facts themselves as unreal, as vain imaginings of the untrained human mind; we have learnt that they could not be described scientifically because they involved notions which were in themselves contradictory and absurd. ...So soon as science entered the field of alchemy with a true classification and a true method, alchemy was converted into chemistry and became an important branch of human knowledge.
  • Introductory

• 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.
  • Introductory

• [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.
  • Introductory

• Although science claims the whole universe as its field... it confesses that its ignorance is more widely extended than its knowledge. In this very confession... it finds a safeguard for future progress. Science cannot... allow theologian or metaphysician... to the foreshore of our present ignorance, and so hinder the development in due time...
  • Introductory

• Each one of us is... called upon to give a judgment upon an immense variety of problems, crucial for our social existence. If that judgment confirms measures and conduct tending to the increased welfare of society, then it may be termed a moral, or, better, a social judgment. It follows, then, that to ensure a judgement's being moral, method and knowledge are essential to its formation. ...[T]he formation of a moral judgment—that is, one which the individual is reasonably certain will tend to social welfare—does not depend solely on the readiness to sacrifice individual gain or comfort, or on the impulse to act unselfishly: it depends in the first place on knowledge and method. The first demand of the state upon the individual is not for self-sacrifice but for self-development. ...[T]he man who gives a vote... in the choice of a representative, after forming a judgement based upon knowledge, is... acting socially, and is fulfilling a higher standard of citizenship.
  • Introductory

• All great scientists have, in a certain sense, been great artists; the man with no imagination may collect facts, but he cannot make great discoveries.
  • Introductory

• The single statement, the brief formula, the few words of which replace in our minds a wide range of relationships between isolated phenomena, is what we term a scientific law. Such a law, relieving our memory from the burden of individual sequences, enables us, with the minimum of intellectual fatigue, to grasp a vast complexity of natural or social phenomena. The discovery of law is... the peculiar function of the creative imagination. But this imagination has to be a disciplined one.
  • Introductory

• [W]hen the law is reached... it must be tested and criticised by its discoverer in every conceivable way, till he is certain that the imagination has not played him false, and that his law is in real agreement with the whole group of phenomena...
  • Introductory

• Hundreds of men have allowed their imagination to solve the universe, but the men who have contributed to our real understanding of natural phenomena have been those who were unstinting in their application of criticism to the product of their imaginations. It is such criticism which is the essence of the scientific use of the imagination, which is... the very life-blood of science.
  • Introductory

• Does not the beauty of the artist's work lie for us in the accuracy with which his symbols resume innumerable facts of our past emotional experience? ... [A]esthetic judgment... how exactly parallel it is to the scientific judgment.
  • Introductory. Pearson refers the reader to William Wordsworth's preface to the Lyrical Ballads (1815) "General View of Poetry".

• [W]e are frequently told that the growth of science is destroying the beauty and poetry of life. It is undoubtedly rendering many of the old interpretations of life meaningless, because it demonstrates that they are false to the facts which they profess to describe. It does not follow from this, however, that the aesthetic and scientific judgments are opposed; the fact is, that with the growth of our scientific knowledge the basis of the aesthetic judgment is changing and must change. There is more real beauty [satisfaction,.. permanent delight] in what science has to tell us of the chemistry of a distant star, or in the life history of a protozoon than in any cosmogony produced by the creative imagination of a pre-scientific age.
  • Introductory.

• [T]he laws of science are products of the human mind rather than factors of the external world.
  • Introductory

• [I]t is better to be content with the fraction of a right solution than to beguile ourselves with the whole of a wrong solution.
  • Introductory

• Step by step [aesthetic] judgment, restless under the growth of positive knowledge, has discarded creed after creed and philosophic system after philosophic system.
  • Introductory

• [O]nly little by little, slowly... man, by the aid of organised observation and careful reasoning, can hope to reach knowledge of the truth... science... is the sole gateway to a knowledge which can harmonise with our past as well as with our... future... As Clifford puts it, "Scientific thought is not an accompaniment or condition of human progress, but human progress itself."
  • Introductory

The Life, Letters and Labours of Francis Galton (1914)

Preface (April 8, 1914) to Volume 1.

Pearson with Galton (age 87).

• It was only the feeling that, at least in one or two aspects of Francis Galton's later life and of his scientific work, I could perhaps put his contributions to human knowledge more adequately than possibly one or another who might take up the task, if I resigned it, and who would hardly grasp the bearing of that long and intimate scientific correspondence between Galton, Weldon and myself, that I persevered in my endeavour to give some account of a life, wherein an important chapter of personal development must remain largely unrecorded.

• [I]t was soon clear to me that I was collecting as much information bearing on the family history of Charles Darwin as on that of Francis Galton. It seemed desirable to place the two men to some extent in contrast in my volume, showing in ancestry, in methods of work and in outlook on life what they had in common and how they differed.

• 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...

• Those who know the real history of the one occasion on which Galton and Darwin disagreed know how loyal Galton was to Darwin—loyal with a loyalty far rarer to-day. Galton would not have wished me to put him in the same rank as his master, but the reader who follows my story to the end may possibly see that the ramifications of Galton's methods are producing a renascence in innumerable branches of science...

• [T]his work... is intended fundamentally as a permanent memorial to the Founder of the Galton Laboratory, and embraces material which may easily perish or be ultimately lost sight of. ...My object is... to issue a volume to some extent worthy of the name of the man it bears,—which may be studied hereafter by those who wish to understand him, his origin and his aims...

• [T]his work is not written to gain a public, but piam memoriam prodere conditoris nostri and is intended especially for those who have known and loved Francis Galton in the past, or who may in the future desire to understand and honour him.

Quotes about Pearson

Karl Pearson, 1910

• The statistician Karl Pearson analyzed a large number of outcomes at certain roulette tables and suggested that the wheels were biased. He wrote in 1894:
  Clearly, since the Casino does not serve the valuable end of huge laboratory for the preparation of probability statistics, it has no scientific raison d’être...
  [E]arly experiments were suggestive and led to important discoveries in probability and statistics. They led Pearson to the chi-squared test, which is of great importance in testing whether observed data fit a given probability distribution.
  • Charles M. Grinstead, J. Laurie Snell, Introduction to Probability (1997) pp. 9-10.

• Before meeting with Weldon... Pearson had grown into a social Darwinist anxious to provide his particular form of Darwinism with a proper scientific basis, and to show that Darwin's ideas and socialism were complementary, and not opposed, as had been maintained by several leading thinkers of the nineteenth century. Biometry offered him the chance of pursuing these ends. Moreover... Pearson's conception of 'properly scientific'... was one that made it probable that the development of biometry... would yield a harvest of statistical methods. Statistics, thus formed, embodied the central tenets of Pearson's philosophy of science, and, as such, was to be universally recommended.
  • Bernard J. Norton, "Karl Pearson and Statistics: The Social Origins of Scientific Innovation" in Social Studies of Science, Vol. 8, No. 1, Theme Issue: Sociology of Mathematics (Feb. 1978), pp. 3-34.

• During the first two terms of 1881 he deputised for W. H. Drew, Professor of Mathematics at King's College, London, taking the senior mathematical teaching. It was in 1882... that he was engaged in his first considerable piece of mathematical work, according to his friend W. H. Macaulay "a theory of pulsating spheres in a fluid, forming an Atomic Theory,... a thing in spherical harmonics of the Clerk-Maxwell type." This work, or part of it, was probably not published till 1887. In 1883 two papers were printed "On the Motion of Spherical and Ellipsoidal Bodies in Fluid Media", and another "Note on Twists in an Infinite Elastic Solid". It was a natural step from such research to the completion of Clifford's Common Sense of the Exact Sciences and Todhunter's History of the Theory of Elasticity. We see from the subject-matter of these papers how Pearson's mind was already at work puzzling over the laws of the physical universe, which in terms of the Grammar of Science describe the "how" rather than the "why."
  • Egon Sharpe Pearson, Karl Pearson: An Appreciation of Some Aspects of His Life and Work (1938) p.8.

• It was Karl Pearson, a man with an unquenchable ambition for scholarly recognition and the kind of drive and determination that had taken Hannibal over the Alps and Marco Polo to China, who recognized the power in Edgeworth's formulations of Galton's ideas. Pearson lacked Galton's originality and Edgeworth's depth of understanding, but it was his zeal, with a vital assist from G. Udny Yule, that created the methodology and sold it to the world.
  • Stephen M. Stigler (1986). The History of Statistics: The Measurement of Uncertainty Before 1900. Harvard University Press. p. 266. ISBN 978-0-674-40341-3. 

• I wish I could communicate to you, and especially to those of you who are just now beginning your professional careers in a world of statistics incredibly more sophisticated than that of Karl Pearson's day, something of the thrill in meeting in person and studying under a man of Pearson's immense reputation. Author of the Grammar of Science, perfector of simple linear correlations; inventor of multiple and partial correlation, of curvilinear correlation, of tetrachoric and bi- serial correlation; discoverer of the $\chi ^{2}$ function for summarizing multinomial data with magnificent simplicity; builder of a beautiful system of frequency curves derived from a single differential equation which in turn harked back to the hypergeometric series; founder of Biometrika and author or co-author of a prolific literature applying these new statistics to biological and sociological data - Karl Pearson was a hero of Asgard to an American boy vouchsafed a visit to the home of the gods. Indeed, Pearson was Thor himself - for the thunderbolts with which he attacked unsparingly those who dared oppose him were echoing and reechoing.
  • S.A. Stouffer, "Karl Pearson - An Appreciation on the 100th Anniversary of His Birth", Journal of the American Statistical Association, Vol. 53 (1958), pp. 23-27.

• Professor Karl Pearson... devised the first test of nonrandomness (...in reality, deviation from normality ...for all intents and purposes, the same thing). He examined millions of runs of what was called a Monte Carlo (the old name for a roulette wheel) during... July 1902... He discovered... with a high degree of statistical significance... the runs were not purely random. ...Pearson was greatly surprised ...Philosophers of statistics call this the reference case problem to explain that there is no true attainable randomness in practice, only in theory.
  • Nassim Nicholas Taleb, Fooled by Randomness: The Hidden Role of Chance in Life and in the Markets (2001) Nine: It is Easier to Buy and Sell than to Fry an Egg | Comparative Luck | Professor Pearson Goes to Monte Carlo (Literally): Randomness does not Look Random!

• Even the fathers of statistical science forgot that a random series is bound to exhibit some pattern... Professor Pearson was among the first scholars interested in creating artificial random number generators, tables one could use as inputs for... simulations (precursors of our Monte Carlo simulator). ...[T]hey did not want these tables to exhibit... regularity. Yet real randomness does not look random!...A single random run is bound to exhibit some pattern ...
  • Nassim Nicholas Taleb, Fooled by Randomness: The Hidden Role of Chance in Life and in the Markets (2001) Nine: It is Easier to Buy and Sell than to Fry an Egg | Comparative Luck | Professor Pearson Goes to Monte Carlo (Literally): Randomness does not Look Random!

See also

• Francis Galton
• Eugenics