Saturday, December 19, 2009

William Kingdon Clifford

William Kingdon Clifford (1845-1879)

From Wiki:


"I was not, and was conceived. I loved and did a little work. I am not and grieve not." - epitaph

"It is wrong always, everywhere, and for anyone, to believe anything upon insufficient evidence." The Ethics of Belief (1879)

"There is no scientific discoverer, no poet, no painter, no musician, who will not tell you that he found ready made his discovery or poem or picture - that it came to him from outside, and that he did not consciously create it from within." (From a lecture to the Royal Institution titled "Some of the conditions of mental development")

"I ... hold that in the physical world nothing else takes place but this variation [of the curvature of space]." Mathematical Papers.

William Kingdon Clifford FRS (4 May 1845 – 3 March 1879) was an English mathematician and philosopher. Along with Hermann Grassmann, he introduced what is now termed geometric algebra, a special case of the Clifford algebra named in his honour, with interesting applications in contemporary mathematical physics and geometry. He was the first to suggest that gravitation might be a manifestation of an underlying geometry. In his philosophical writings he coined the expression "mind-stuff".

Born at Exeter, William Clifford showed great promise at school. He went on to King's College London (at age 15) and Trinity College, Cambridge. At the latter, he was second wrangler in 1867 and second Smith's prizeman. He was elected fellow in 1868.[1] Being second was a fate he shared with others who became famous mathematicians. e.g., William Thomson (Lord Kelvin), James Clerk Maxwell. In 1870, he was part of an expedition to Italy to observe an eclipse, and survived a shipwreck along the Sicilian coast.[2]

In 1871, he was appointed professor of mathematics and mechanics at University College London, and in 1874 became a fellow of the Royal Society. He was also a member of the London Mathematical Society and the Metaphysical Society.

In 1876, Clifford suffered a breakdown, probably brought on by overwork; he taught and administered by day, and wrote by night. A half-year holiday in Algeria and Spain allowed him to resume his duties for 18 months, after which he collapsed again. He went to the island of Madeira to recover, but died there of tuberculosis after a few months. Eleven days later, Albert Einstein was born, who would go on to develop the geometric theory of gravity that Clifford had suggested nine years earlier.

"Clifford was above all and before all a geometer." (H. J. S. Smith). In this he was an innovator against the excessively analytic tendency of Cambridge mathematicians. Influenced by Riemann and Lobachevsky, Clifford studied non-Euclidean geometry. In 1870, he wrote On the Space-Theory of Matter, arguing that energy and matter are simply different types of curvature of space. These ideas later played a fundamental role in Albert Einstein's general theory of relativity.

Yet Clifford is now best remembered for his eponymous Clifford algebras, a type of associative algebra that generalizes the complex numbers and William Rowan Hamilton's quaternions. The latter resulted in the complex quaternions (biquaternions), which he employed to study motion in non-Euclidean spaces and on certain surfaces, now known as Klein-Clifford spaces. He showed that spaces of constant curvature could differ in topological structure. He also proved that a Riemann surface is topologically equivalent to a box with holes in it. On Clifford algebras, quaternions, and their role in contemporary mathematical physics, see Penrose (2004).

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. 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 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.

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