Popular Science Monthly/Volume 15/June 1879/Sketch of Professor Clifford

PSM V15 D156 William Kingdon Clifford.jpg



WILLIAM KINGDON CLIFFORD was born at Exeter, May 4, 1845, and at the time of his death, which occurred on the 3d of March, he had therefore not reached the age of thirty-four years. His father was a justice of the peace, and his mother, from whom he inherited a portion of his genius and his constitutional weakness, died early. He first attended the school of Mr. Templeton, of that city, and went to King's College, London, in 1860. In 1863 he entered at Trinity College, Cambridge, in which he secured a foundation scholarship and got the honor of second wrangler in the mathematical Tripos of 1867. Soon after taking his degree he was elected to a fellowship at Trinity College, filling the post until his appointment to the chair of Applied Mathematics and Mechanics at University College, London, in August, 1871, a position which he held until his death. Professor Clifford was elected a Fellow of the Royal Society in June, 1874. He took prizes and honors wherever he went, which was the more remarkable, as his mind could not tolerate the usual school restraints, and he could not be induced to give much attention to the regular subjects of examination. He had consumption, which greatly impaired his working power in the latter portion of his life; and he died on the island of Madeira, where he had gone with his wife and two children to get the benefit of its milder climate.

Clifford was a genius, and brilliant from his boyhood. He early developed rare mathematical talent, and published the "Analogues of Pascal's Theorem" in the "Quarterly Journal of Mathematics" at the age of eighteen. His mind was at home in all highest mathematical questions, to which he made many profound and original contributions. Professor Sylvester remarked, "All that Professor Clifford adds is the very pith and marrow of the matter." Just before his death he published a little mathematical work, "The Elements of Dynamic," in which his faculty for the subject is fully displayed. It will probably not take high rank as a university text-book, for which it was intended, but is admired by mathematicians for the elegance, freshness, and originality displayed in the treatment of mathematical problems.

Clifford had no special taste for the acquisition of languages, but was interested in their mechanism, and took interest in short-hand, phonography, and telegraphic alphabets. Later in life, however, he mastered modern Greek and Spanish, and dabbled in Arabic and Sanskrit, which, in addition to his earlier Greek and Latin, French and German, landed him pretty heavily in the direction of vocabularies.

He was an early and devoted student of classics, and held extreme High-Church notions when he went to Cambridge. In his knowledge of the "Fathers" he is said to have surpassed the bishops, and his theological acquirements were of great use to him in his polemical and critical discussions. Not satisfied in addressing that very small portion of the public that understands mathematics, versatile in his powers, and of a restless temperament, he was powerfully attracted to those great subjects of scientific and speculative inquiry that have lately become so prominent in the world of thought. Into this field he entered vigorously, and made a strong impression upon the reading public by various able and elaborate articles which appeared in the "Fortnightly" and "Contemporary" Reviews, and in "The Nineteenth Century." He was an extreme and uncompromising rationalist, and although personally greatly liked on account of his gentleness and affability, he made many enemies by the relentless severity of his writing on topics that are conventionally handled with delicacy and caution. He discussed a variety of philosophical subjects, always in a striking and attractive manner, but can hardly be said to have developed any theories or system of his own.

As. an expositor, Professor Clifford was peculiarly and remarkably gifted. Aside from his mathematical attainments, this was the intellectual quality for which he was the most distinguished. His power in this direction is thus described by the "Pall Mall Gazette": "His faculty of explaining the results of scientific investigation in ordinary language, and to persons having little or no special preparation, was such as to amount of itself to genius. The grasp and width of his imagination enabled him to deal freely with the very ideas of the higher mathematics, unfettered by the symbolical expressions and machinery which had first made their conception possible; and he translated the ideas into forms of wonderful simplicity for hearers who little suspected the height and difficulty of the achievement. Long ago, in Cambridge days, he would discuss some complicated theorem of solid geometry, without aid of paper or diagram, in such a way as to make the whole thing seem visibly embodied in space and self-evident. Where the text-books gave a chaos of algebraical manipulation, he would instantly seize the real facts and relations and bring them out into manifest light. Nor did this power fail him even in the most arduous flights of modern geometrical speculation. He was the first in this country to see and enforce the important philosophical bearings of what is called imaginary geometry. His last published paper which saw the light only a few days before we knew that his work was irrevocably ended, was devoted to explaining with singular felicity and clearness the ultimate foundations of the science of number." The capacity here referred to was so unique and remarkable in Professor Clifford as to win for him a somewhat exaggerated reputation for originality; that is, he would so vividly and ingeniously present a difficult subject as almost to make the views expounded his own.

Among his other accomplishments, Clifford was a skillful gymnast, and as original in his performances as in his intellectual work. He was always executing some striking or eccentric feat, such as hanging head downward, by his toes, and drinking a glass of wine without spilling it; or going up to his room in the college by the water-spout and through the window, instead of the regular staircase. He had more pride in the invention of adventurous and daring gymnastic feats than in his intellectual work. He seems, indeed, to have used his gymnastic exercises as expressions of his genius rather than as means of promoting health. He was of a slender constitution, which was ever on the strain, in one direction or another; and there is reason to think that he was deficient in the important art of taking care of himself, and that, if he had conformed to the first requirement of morality, the duty of doing good to the nature that was in his own charge, he might have done, far more good to the world by a prolonged and increasingly useful life.

What shall we say of an education or a culture which not only fails to teach a man how to continue his own life, but which is itself the means of destroying it? On this point Clifford's intimate friend, Pollock, writing about him in "The Fortnightly Review," says: "This was the perilous excess in his own frame of nervous energy over constitutional strength and endurance. He was able to call upon himself, with a facility which in the result was fatal, for the expenditure of power in ways and to an extent which only a very strong constitution could have permanently supported; and here the constitution was feeble. He tried experiments on himself when he ought to have been taking precautions. He thought, I believe, that he was really training his body to versatility and disregard of circumstances, and fancied himself to be making investments when he was in fact living on his capital. At Cambridge he would constantly sit up most of the night working or talking. In London it was not very different, and once or twice he wrote the whole night through; and this without any proportionate reduction of his occupations in more usual hours. The paper on ‘The Unseen Universe’ was composed in this way, except a page or two at the beginning, at a single sitting which lasted from a quarter to ten in the evening till nine o'clock the following morning. So, too, was the article on Virchow's address. But Clifford's rashness extended much further than this one particular. He could not be induced, or only with the utmost difficulty, to pay even moderate attention to the cautions and observances which are commonly and aptly described as taking care of one's self. Had he been asked if it was wrong to neglect the conditions of health in one's own person, as well as to approve or tolerate their neglect on a larger scale, he would certainly have answered ‘Yes.’ But to be careful about himself was a thing that never occurred to him."

We append a portion of the estimate of Clifford made in the columns of the "Saturday Review": "The unexpected news of the death of Professor Clifford at Madeira will have brought sadness to an unusally large body of devoted friends, who had hoped that his strength had not waned so far that it might not be recovered under the influence of the mild climate to which he had gone. Nor will it be only by those who had the pleasure of a personal acquaintance with Professor Clifford that the news of his untimely death will be deeply felt. Few men who have passed away at so early an age have been so central a figure as he was in the view of a large portion of the most highly educated among us; and still fewer have achieved this distinction, while at the same time they retained the esteem and admiration of the select few who were competent to estimate their powers and know whether they had been put to a worthy use. But it was always his fate to be conspicuous in whatever circumstances or society he was placed. This was primarily due to his intellectual power, for, without the wonderful rapidity and vigor of thought which he possessed, such a reputation as his could not have been sustained; but it was in no small degree due also to the peculiar originality of his character, both intellectual and moral, and to the absolutely tireless energy of his versatile mind.

"Those who remember Cambridge some ten or fifteen years ago will readily call to mind his fame while an undergraduate there. From the time when he came up to the university, with the high reputation which he had won while a schoolboy, to the time he left it some eight years afterward to become Professor of Mathematics at University College, London, he was more universally known and discussed among all classes at the university, whether undergraduates, graduates, or dons, than any of his contemporaries. He was indeed at all times a contrast to the normal type. At first, when fresh from school, he appeared as an ardent High Churchman, but he gradually became known as a devoted follower of Mr. Herbert Spencer, and as the champion of those views with which his name has since been identified. But, whatever was the precise phase of thought in which he might be, there was the same brilliant though paradoxical style of asserting and defending his beliefs which made him the terror of authorities and the delight of younger men. He never was in any sense the head of a party there. He was far too eccentric and original to have many followers or imitators. But no one had a wider circle of intimate friends, and no one could be in intimate intercourse with him without being deeply influenced by his views; and it was at that time chiefly by his direct influence on those personally acquainted with him that he produced his effect on the university. But the many-sidedness of his character caused this direct personal influence to be much more widely extended than would have seemed possible to those unacquainted with him. Gifted with an almost equal love for science, mathematics, history, and literature—we may even add gymnastics—he was the center of a knot of devotees of each of these studies, each of whom welcomed him as a comrade and regarded with jealousy his attention to other subjects as being likely to seduce him from the true bent of his genius into less important and congenial studies. And no doubt it was a fortunate thing in this instance that the arrangements for retaining the ablest men at the English universities are so imperfect, that Professor Clifford found no certainty of sufficient scope for his energies there, and resolved to leave that abode of learned leisure, and come to London, to become a mathematical professor, inasmuch as it was this that prevented him from wasting his life in desultory essays in a great variety of directions. No doubt all of these would have shown a power which would have made them remarkable, but they would have been dearly purchased by the sacrifice of the far greater and more abiding results that followed the concentration of his energies on the one or two subjects to which he devoted himself after his departure from the university.

"When resident in London the same qualities that had won him so many friends at Cambridge still stood him in good stead, and he rapidly drew round him a large circle of warm friends and admirers, among whom might be found almost all the best known names in science or literature. This power of winding the affections of those who were most worthy of friendship was due mainly to the peculiarly winning gentleness and tenderness which characterized him, and made it impossible to resist the charm of personal intercourse with him. Although the nature of his opinions and his style of championing them raised him countless enemies among those who knew him only from his writings and lectures, yet there was no school of thought among the members of which he did not possess some intimate friends. However widely their opinions might differ, it seemed to be quite impossible for any one to feel hostility toward him after becoming personally acquainted with him. The versatility of his mind aided this greatly, for it gave to his conversation a charm which was quite peculiar, and which was felt alike by the most different classes of minds. There was no subject from which he used not to draw apt illustrations or expressive metaphors, which came clothed in language as quaint and as original as it was appropriate. Whatever he discussed seemed to become full of suggestiveness. These qualities gave great additional value to his mathematical lectures.

"With his style of teaching, the most valuable part of the instruction was the indirect effect of the lessons; the actual matter in hand was distinctly subordinate to the general training in the fundamental ideas and principles of the subject which its discussion enabled him to give. Everything was treated from the point of view in which it least needed the aid of artificial methods and conventions, so that its direct connection with the broad underlying principles common to a whole class of subjects might be immediately perceived. This dislike to artificial methods was almost a passion with him. He had great faith in the superiority of this style of teaching, and always maintained that it was the easiest as well as the best, a proposition to which the experience of most teachers would not lead them to assent. Perhaps it was his own special power of clear exposition which enabled him to succeed so well in thus handling his subjects in their most general form, instead of starting from simple and particular cases, and only taking up more general theorems after the simpler ones had been mastered by his pupils; but, whether or not this was the case, it is certain that he had all the success in his teaching that he could desire.

"It is a signal proof of the beauty of Professor Clifford's personal character that, in forming an estimate of him, one should so naturally and inevitably think first of his general qualities, and only in the second place of his claims to fame as a mathematician. For it was in the latter character that he first gained his great reputation, and it is in that that his claims to genius are the strongest. No one of his contemporaries ever approached Professor Clifford in his marvelous. power over the intricate and abstruse branches of mathematics to which he gave his main affections, and to find his equal we should have to look among veterans whose names will for ever be identified with these subjects. Such was his prodigious grasp over the phantoms that people these remoter regions of thought, that while little more than a boy he seemed fit to take his place among the masters of these studies. And there can be no doubt that, if the innate restlessness of his nature would have permitted him to accept the quiet of a mathematician's life, he might have left behind him what would have entitled him to take rank as one of our greatest mathematicians. But it is hard to forego the pleasure of using powers which one is conscious of possessing, and the temptation to which the versatility of his mind subjected him was wellnigh fatal to his reputation as a specialist. Every now and then something would turn his energy into these lines, and he would show by some fragment what magnificent work he was capable of doing; but it was for a long time doubtful whether he would ever do justice to himself in this respect, and by more continuous application to some special subject produce results worthy of his powers. As time went on, however, this changed; during the last few years there were fewer signs of the old desultoriness, and both in his 'Elements of Dynamic' and his various mathematical papers there were abundant traces of the concentration of effort which alone was needed to secure success. But, alas! this was only too speedily succeeded by the leisure of the sick-bed. Perhaps it was the feeling of decaying strength which first made Professor Clifford limit the sphere of his efforts, and seek to finish some of his many projects, instead of forming new ones. Whether this was so or not, it was not the less a gain to the world, though even now what we possess should be considered only as indications of what his powers would have been when fully developed. Few, if any, have done such brilliant work and yet died leaving us to feel that it must be taken only as the promise, and not as the measure, of their powers.

"But what the mathematical world lost in this want of specialization of Professor Clifford's powers was gained by the general educated public. His powers as a scientific expositor were as remarkable as his mathematical abilities. His talent did not lie in experimental illustration; on the contrary, he seldom, if ever, resorted to it. Nor did he ever condescend to the nurse-like prattle by which some scientific lecturers make themselves comprehensible to the meanest intellects—but to those only. There was not a sentence, or a scientific statement, in one of Professor Clifford's lectures of which he need have been ashamed in an address to the most scientific or learned society."