Statisticians

"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 and spiritualism."

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

"[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."

"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..."

"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."

"[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!"

"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."

"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."

"[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."

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

"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."

"[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."

"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."

"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..."

"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..."

"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."

"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."

"[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..."

"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..."

"[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."

"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."

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

"[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."

"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."

"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..."

"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 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."

"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..."

"[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..."

"[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."

"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..."

"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.""

"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."

"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."

"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..."

"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 ..."

"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."

"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."

"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."

"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."

"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."

"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."

"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."