Dictionary of National Biography, 1885-1900/Clifford, William Kingdon

CLIFFORD, WILLIAM KINGDON (1845–1879), mathematician, was born on 4 May 1845 at Exeter. His father, William Clifford, was a well-known citizen of the town. His mother, whose maiden name was Kingdon, died in September 1854. He was a very precocious child. He was educated at Mr. Templeton's school at Exeter until 1860, when he was sent to King's College, London. Here he showed marked ability in classical and literary, as well as in mathematical studies. In October 1863 he entered Trinity College, Cambridge, having won a minor scholarship. His mathematical genius was at once recognised, and the most competent judges anticipated that he would rise to the highest place among contemporary men of science. His private tutor was Mr. Percival Frost. His originality led him to diverge from the regular course of study to independent researches. Like other eminent mathematicians, Whewell, Sylvester, Sir William Thomson, and Clerk Maxwell, he was second in the mathematical tripos. He was also second Smith's prizeman. He had become known for other qualities to his fellow-students. He took a boyish pride in his gymnastic prowess. Though slight, he was well made, and his great nervous energy enabled him to perform remarkable feats. He could pull up on the bar with either hand,' and once hung by his toes from the cross-bar of a weathercock on a church-tower. Praise of his athletic excellence gratified him even more than official recognition of his intellectual achievements. His literary power was shown by his winning the college declamation prize in 1866, in consequence of which he was appointed to deliver the usual oration at the college commemoration in the following December, when he pronounced a characteristic panegyric upon Whewell, then recently dead. He was a member of the well-known club generally called the 'Apostles,' and had many friends among his most distinguished contemporaries, especially Professor Pollock, afterwards his biographer. He was at this time a high churchman. He had studied Aquinas, and was fond of supporting catholic doctrines with ingenious scientific analogies. This phase was dispelled by his study of Darwin and Mr. Herbert Spencer, under whose influence he worked out the dominant ideas of his later writings.

In 1868 Clifford was elected to a fellowship at Trinity, and was a resident until 1871. In 1870 he joined the English Eclipse expedition, and was wrecked in the Psyche off Catania. The ship was entirely lost, but the instruments and all hands were saved. During his Cambridge residence he became intimate with Professor Fawcett, and was secretary to the Republican Club, of which Fawcett was a member. In 1871 he was appointed professor of applied mathematics at University College, London. In 1874 he was elected fellow of the Royal Society, a distinction for which he had modestly refused to be nominated at an earlier period. His reputation was rapidly spreadingbeyond purely scientific circles. He was a singularly effective lecturer. On 6 March 1868 he had delivered a discourse at the Royal Institution (upon 'Conditions of Mental Development'), showing the strong impression made upon him by Mr. Herbert Spencer, and another on 18 Feb. 1870 upon 'Theories of Physical Forces.' The last showed a remarkable power of giving a popular exposition of abstruse doctrines, which won general recog- nition when, on 19 Aug. 1872, he delivered an address before the British Association at Brighton upon 'The Aims and Instruments of Scientific Thought.' Clifford spoke with extreme facility, generally from a few brief notes. He would revise his lectures from a shorthand report, or write them out from memory. He found previous writing down to be only an encumbrance. The vivacity and quaint humour of his addresses, and the relarkable felicity of illustration, interested popular hearers, and persuaded them (not always correctly) that they could follow his reasoning. In the years 1872-5 he delivered several addresses to the Sunday Lecture Society, in which he took a deep interest. He sympathised with its aim of popularising the results of scientific inquiry, and was exceptionally qualified to aid in its promotion.

On 7 April 1875 Clifford married Lucy, daughter of Mr. John Lane, a well-known Barbadian. His marriage was a source of unmixed happiness. His house became the meeting-place of a varied circle of friends of all opinions and tastes, though especially of scientific friends. Clifford was a most attractive companion. His careless phrases had always the stamp of genius. His transparent simplicity and modesty, his unflagging vivacity and his keen interest in all speculative questions were combined with admirable delicacy of perception and a most affectionate nature. Childlike to the last, he had a special talent for attracting children, and a children's party was one of his greatest pleasures. He was equally at ease with the most eminent thinkers of his day, and was from 1874 a prominent member of the Metaphysical Society, in which distinguished men of the most opposite views met for a frank discussion of fundamental questions. Some of his papers read before this society were published in 'Mind ' and the 'Contemporary Review,' and may be found in his ' Essays and Lectures.' Clifford's freedom of speech and strong sense of the ridiculous occasionally gave some pretext for a charge of levity. But the utter absence of any wish to give pain prevented offence at the time, nor could there be any doubt of the fundamental seriousness of his purpose.

From 1875 to 1878 Clifford published several reviews, not previously delivered as lectures, for which his health was now becoming a disqualification. They give his latest philosophical views. One of them (a review of the 'Unseen Universe' in the 'Fortnightly Review ' for June 1875) was written between a quarter to ten at night and nine the next morning. Another upon Virchow's address ('Nineteenth Century' for April 1878) was written in the same way. Both at Cambridge and afterwards he would not unfrequently work through the night. The disproportion between his great nervous energy and his constitutional weakness tempted him to dangerous efforts, both physical and intellectual. It was difficult to persuade him to adopt prudential measures, and he persevered even in his gymnastic exercises till after serious warnings.

In the spring of 1876 grave symptoms of pulmonary disease showed themselves. He was induced, very reluctantly, to take six months' leave of absence, which he spent with his wife in Algiers and Spain. The next year and a half was spent in England; but the death of his father (February 1878) and the strain of literary work hastened another collapse, and in April 1878 he again visited the Mediterranean, and afterwards spent some time at the Monte Generoso. In August 1878 he had improved sufficiently to return to England, but another collapse followed at the end of September. As a last chance he was sent to Madeira. The senate of University College recommended that he should retain his chair, and that, if he should recover sufficiently, he should be invited to lecture upon special subjects not involving the strain of regular work. Before the council could act upon this suggestion the end had come. After a brief interval of comparative ease, the case became hopeless, and he died at Madeira 3 March 1879. He was buried in Highgate cemetery. He left a widow and two daughters.

An excellent portrait of Clifford by his intimate friend Mr. John Collier is in possession of Mrs. Clifford. Two portraits after photographs are engraved in the 'Essays and Lectures.'

Clifford's health prevented him from giving more than a fragmentary exposition of views which still needed fuller elaboration. As a philosopher, he was a follower of the English school, and radically opposed to the teaching of modern Hegelians. He venerated Berkeley and Hume, but held that their teaching requires the modification implied in modern theories of evolution. His mathematical genius led him to take a special interest in one doctrine. He thought that Kant's argument, based upon the universality and necessity of geometrical truths, was invincible as against Hume. But he thought that the 'imaginary geometry ' of Lobatschewsky and Riemann supplied the true answer, and showed that even geometrical truths must be regarded as a product of experience. His view is most fully given in his essay on the 'Philosophy of the Pure Sciences.' The metaphysical theory to which he inclined is given in the essays on 'Body and Mind' and the 'Nature of Things in themselves.' He was more inclined than most English psychologists to believe in the possibility of constructing a definite metaphysical system, in which he was probably influenced by his admiration for Spinoza. His doctrine is described by Professor Pollock as an 'idealist monism.' He agreed with Berkeley that mind is the ultimate reality; but held that consciousness as known to us is built up out of simple elements or atoms of 'mind-stuff' − the characteristic phrase which gives the keynote of theories full of suggestion, and showing curious affinities to other philosophies, but not fully worked out. His ethical system, strongly influenced by evolutionist doctrines, was also congenial to his own temperament. He attaches supreme importance to freedom, since all progress implies variation, and the implicit acceptance of formulas is equivalent to death. Here he was also influenced by Mazzini from another side. But in his later work more importance is attached to the 'social factor' and the 'tribal judgment' regarded as an embodiment of the past experience of the race. The second volume of 'Essays and Lectures' contains his application of his leading ideas to ethical and religious questions; especially in the essays upon the 'Scientific Basis of Morals,' 'Right and Wrong,' and 'Cosmic Emotion.' He had contemplated a recasting of his work in a book to be called 'The Creed of Science.' A sketch of the intended contents is given in the 'Essays and Lectures' (i. 71, 72). As he had not the opportunity of completing his design, the essays must be taken only as a collection of fragmentary though luminous suggestions.

As a mathematician, says Professor Karl Pearson, Clifford may be regarded as marking an epoch in the history of this science in England. He was among the first by his writings to raise a protest against the analytical bias of the Cambridge school. Essentially a geometrician he yet regarded geometry as a 'physical science,' whose axioms are the outcome of human experience. So great was his belief in geometry that he even went the length of attempting to explain matter on geometrical principles; an attempt which, however it may be regarded in the future, will at least remain as a witness to future investigators of Clifford's consciousness of the often disregarded truth that matter cannot be explained by mechanism. As a mathematical writer Clifford was marked by a keen power of imagination, rich in its suggestions of new lines of thought and discovery; he was a standing example of the fact that the true man of science, especially the mathematician, is the man of speculation, of tested theory, of keen, albeit disciplined imagination. His 'Canonical Dissection of a Riemann's Surface,' his theory of 'Biquaternions,' and his unfinished memoir 'On the Classification of Loci,' belong to the classics of mathematical literature. As a mathematical teacher Clifford did much (and his influence is still working) to revolutionise the teaching of elementary mathematics; he introduced into England the graphical and geometrical methods of Möbius, Culmann, and other Germans. His uncompleted text- book on 'Dynamics,' his fragmentary 'Common Sense of the Exact Sciences' and the 'Lectures on Geometry' represent especially the direction and novelty of his elementary teaching; its fundamental aim was not to teach a student the analytical solution of a problem, but to force him to think for himself.

Clifford's works as posthumously published are:

  1. 'Lectures and Essays,' edited by F. Pollock and L. Stephen, 1879.
  2. 'Mathematical Fragments, being facsimiles of his unfinished papers relating to the theory of Graphs,' 1881.
  3. 'Mathematical Papers,' edited by R. Tucker, with a very interesting introduction by H. J. S. Smith, late Savilian professor at Oxford, 1882. A careful bibliography is added.
  4. 'Common Sense of the Exact Sciences,' edited and partly written by Karl Pearson, 1885.
  5. 'Elements of Dynamic.'

We may mention, in addition to the works already referred to, the little volume of elementary science entitled 'Seeing and Thinking.'

[Life by F. Pollock prefixed to Lectures and Essays; information from Mrs. Clifford; personal knowledge.]

L. S.