William Kingdon Clifford (May 4, 1845 - March 3, 1879) was an English mathematician and philosopher. Along with Hermann Grassmann he discovered what is now often called geometric algebra, which is a special case of the Clifford algebras named in his honor. He was also the first to suggest that gravitation might be due to an underlying geometry, and in his philosophical work coined the phrase "mind-stuff".

Biography

He was born at Exeter, and educated at a private school there. He went on to King's College, London and 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 a fellow of the Royal Society. He was also a member of the Metaphysical Society In 1875 he married Lucy, daughter of John Lane of Barbados. In 1876, however, he began to suffer ill-health, and after two voyages to the South, died during the third of pulmonary consumption at Madeira, leaving his widow with two daughters.

Geometry

His contemporaries considered him a man of extraordinary acuteness and originality, gifted with quickness of thought and speech, a lucid style, wit and poetic fancy, and a social warmth. To quote H. J. S. 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 Biquaternions" (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.

Philosopher

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 Frederick 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 antispiritual tendencies then imputed to modern science.

Books

His works, published wholly or in part after 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);
• The Common Sense of the Exact Sciences, completed by Professor Karl Pearson (1885).
• The Ethics of Belief, Originally published in Contemporary Review, (1877)

Reference

Such Silver Currents - The Story of William and Lucy Clifford, 1845-1929 by M. Chisholm, The Lutterworth Press, Cambridge, 2002. ISBN 0-7188-3017-2

See also

• Math: Geometric algebra, Clifford algebra, Clifford parallelism , Clifford-Klein form
• Lists: List of mathematical topics, List of algebraic geometry topics
• Timelines: Timeline of gravitational physics and relativity, Timeline of black hole physics
• Other: Clifford, Lucy Clifford, Metaphysical Society
• Panpsychism: List of Pantheists

External links and reference

• "William Kingdon Clifford". School of Mathematics and Statistics, University of St Andrews, Scotland.
• Beichler, James E., "Twist til' we tear the house down!". Yggdrasil: The Journal of Paraphysics, 1996.
• Clifford, William Kingdon, William James, and A.J. Burger (Ed.), "The Ethics of Belief".
• "William Kingdon Clifford". Find a grave.com.
• "William Kingdon Clifford". 1911 Encyclopaedia Britannica.