Biographers From England

"[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."

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

"[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."

"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?"

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

"[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."

"The ignorance of science means the enforced ignorance of mankind."

"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..."

"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."

"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."

"[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."

"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 ."

"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."

"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."

"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."

"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..."

"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."

"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 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.'"

"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."

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

"[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."

"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.'"

"[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."

"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."

"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..."

"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."

"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."

"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?"

"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.""

"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 ' and author or co-author of a prolific literature applying these new statistics to biological and sociological data - Karl Pearson was a hero of 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."

"[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."

"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 ', which is of great importance in testing whether observed data fit a given ."

"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."

"[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."

"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."

"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."

"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..."

"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."

"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..."

"[T]his work... is intended fundamentally as a permanent memorial to the Founder of the , 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..."

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

"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..."

"[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."

"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."

"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."

"[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."