1911 Encyclopædia Britannica/Clifford, William Kingdon

CLIFFORD, WILLIAM KINGDON (1845–1879), English mathematician and philosopher, was born on the 4th of May 1845 at Exeter, where his father was a prominent citizen. He was educated at a private school in his native town, at King’s College, London, and at Trinity College, Cambridge, where he was elected fellow in 1868, after being second wrangler in 1867 and second Smith’s prizeman. In 1871 he was appointed professor of mathematics at University College, London, and in 1874 became fellow of the Royal Society. In 1875 he married Lucy, daughter of John Lane of Barbados. In 1876 Clifford, a man of high-strung and athletic, but not robust, physique, began to fall into ill-health, and after two voyages to the South, died during the third of pulmonary consumption at Madeira, on the 3rd of March 1879, leaving his widow with two daughters. Mrs W. K. Clifford soon earned for herself a prominent place in English literary life as a novelist, and later as a dramatist. Her best-known story, Mrs Keith’s Crime (1885), was followed by several other volumes, the best of which is Aunt Anne (1893); and the literary talent in the family was inherited by her daughter Ethel (Mrs Fisher Dilke), a writer of some charming verse.

Owing to his early death, Professor Clifford’s abilities and achievements cannot be fairly judged without reference to the opinion formed of him by his contemporaries. He impressed every one as a man of extraordinary acuteness and originality; and these solid gifts were set off to the highest advantage by quickness of thought and speech, a lucid style, wit and poetic fancy, and a social warmth which made him delightful as a friend and companion. His powers as a mathematician were of the highest order. It harmonizes with the concrete visualizing turn of his mind that, to quote Professor Henry Smith, “Clifford was above all and before all a geometer.” In this he was an innovator against the excessively analytic tendency of Cambridge mathematicians. In his theory of graphs, or geometrical representations of algebraic functions, there are valuable suggestions which have been worked out by others. He was much interested, too, in universal algebra, non-Euclidean geometry and elliptic functions, his papers “Preliminary Sketch of Bi-quaternions” (1873) and “On the Canonical Form and Dissection of a Riemann’s Surface” (1877) ranking as classics. Another important paper is his “Classification of Loci” (1878). He also published several papers on algebraic forms and projective geometry.

As a philosopher Clifford’s name is chiefly associated with two phrases of his coining, “mind-stuff” and the “tribal self.” The former symbolizes his metaphysical conception, which was suggested to him by his reading of Spinoza. “Briefly put,” says Sir F. Pollock, “the conception is that mind is the one ultimate reality; not mind as we know it in the complex forms of conscious feeling and thought, but the simpler elements out of which thought and feeling are built up. The hypothetical ultimate element of mind, or atom of mind-stuff, precisely corresponds to the hypothetical atom of matter, being the ultimate fact of which the material atom is the phenomenon. Matter and the sensible universe are the relations between particular organisms, that is, mind organized into consciousness, and the rest of the world. This leads to results which would in a loose and popular sense be called materialist. But the theory must, as a metaphysical theory, be reckoned on the idealist side. To speak technically, it is an idealist monism.” The other phrase, “tribal self,” gives the key to Clifford’s ethical view, which explains conscience and the moral law by the development in each individual of a “self,” which prescribes the conduct conducive to the welfare of the “tribe.” Much of Clifford’s contemporary prominence was due to his attitude towards religion. Animated by an intense love of truth and devotion to public duty, he waged war on such ecclesiastical systems as seemed to him to favour obscurantism, and to put the claims of sect above those of human society. The alarm was greater, as theology was still unreconciled with the Darwinian theory; and Clifford was regarded as a dangerous champion of the anti-spiritual tendencies then imputed to modern science.

His works, published wholly or in part since his death, are Elements of Dynamic (1879–1887); Seeing and Thinking, popular science lectures (1879); Lectures and Essays, with an introduction by Sir F. Pollock (1879); Mathematical Papers, edited by R. Tucker, with an introduction by Henry J. S. Smith (1882); and The Common Sense of the Exact Sciences, completed by Professor Karl Pearson (1885).