Mathematicians From England

"[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..."

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

"[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."

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

"[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 produced by the creative imagination of a pre-scientific age."

"[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..."

"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."

"[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.""

"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."

"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..."

"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."

"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."

"[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."

"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."

"[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."

"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."

"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]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!"

"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."

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

"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."

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

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

"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 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."

"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."

"[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."

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

"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."

"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."

"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."

"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."

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

"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..."

"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."

"[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."

"[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."

"[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."

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

"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."

"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."

"[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."

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

"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."

"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."

"[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."

"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."