CLIFFORD, WILLIAM KINGDON

born May 4, 1845, Exeter, Devon, Eng. died March 3, 1879, Madeira Islands, Portugal British philosopher and mathematician who developed the theory of biquaternions (a generalization of the Irish mathematician Sir William Rowan Hamilton's theory of quaternions) and then linked them with more general associative algebras. Clifford was educated at King's College, London, and at Trinity College, Cambridge, and was elected a fellow of the latter in 1868. In 1871 he was named professor of mathematics at University College, London. Three years later he was elected a fellow of the Royal Society of London. Influenced by the non-Euclidean geometries of Bernhard Riemann and Nikolay Lobachevsky, Clifford wrote On the Space-Theory of Matter (1870). He presented the idea that matter and energy are simply different types of curvature of space, thus foreshadowing Albert Einstein's general theory of relativity. In addition, he used biquaternions to study motion in non-Euclidean spaces and certain closed Euclidean manifolds (surfaces), now known as spaces of CliffordKlein. He showed that spaces of constant curvature could have several different topological structures and proved the topological equivalence of a Riemann surface to a box with holes in it. Karl Pearson of England further developed Clifford's views on the philosophy of science, which were related to those of Hermann von Helmholtz and Ernst Mach, both of Germany. In philosophy Clifford's name is chiefly associated with two phrases of his coining, mind-stuff (the simple elements of which consciousness is composed) and the tribal self. The latter gives the key to his ethical view, which explains conscience and moral law by the development in each individual of a self that prescribes conduct conducive to the welfare of the tribe. He recognized the serious difficulties created for certain features of Immanuel Kant's philosophy by the non-Euclidean geometries of Riemann and Lobachevsky. Clifford's works were for the most part published posthumously and include Elements of Dynamic, 2 vol. (1878, 1887), Seeing and Thinking (1879), Lectures and Essays (1879), Mathematical Papers (1882), and The Common Sense of the Exact Sciences, completed by Karl Pearson (1885).