William Kingdon Clifford

William Kingdon Clifford

William Kingdon Clifford, FRS (May 4, 1845 - March 3, 1879) was an English mathematician and philosopher. Along with Hermann Grassmann, he invented what is now termed geometric algebra, a special case being the Clifford algebras named in his honour, which play a role in contemporary mathematical physics. He was the first to suggest that gravitation might be a manifestation of an underlying geometry. He was one of the first to synthesize Kant’s concept of a priori knowledge with Darwin’s evolutionary theory, suggesting that some types of innate knowledge may have been “phylo-genetically” learned and passed down through successive generations.

He coined the phrase "mind-stuff," to refer to the contents of which the conscience is composed. He supported the theory that mind was the ultimate reality, and proposed that human awareness of that reality was an evolutionary process. He also coined the term “tribal self” for the conscience, and developed a theory of ethics proposing that moral progress consist of subverting egotistical impulses to the “tribal self,” which ensure the well-being and survival of the tribe.

Biography

William Kingdon Clifford was born at Exeter, England, on May 4, 1845. His second name, Kingdon, was the maiden name of his mother, who died when he was nine years old. William Clifford showed exceptional ability school, especially in mathematics. At the age of fifteen, he went on to King's College London and in 1863 entered Trinity College, Cambridge, on a minor scholarship. He published his first mathematical paper just two months later. He was elected a member of “The Apostles,” an elite society at Cambridge whose membership included a number of British intellectuals. The society admitted only twelve students who were in residence at Cambridge, and in an effort to embody the “Spirit of the Apostles,” they were required, during their weekly debates, to give their honest opinions on the most inflammatory and sensitive issues, and to respect the views of the other members. Clifford studied Greek, German, Spanish, French, Arabic and Sanskrit, as well as Morse code and shorthand. He was responsible for the translation of Riemann’s 1854 paper on non-Euclidean geometry into English.

Clifford entered Cambridge a member of the Anglican high church, but after reading Darwin and meeting Herbert Spencer, he renounced his faith and became an advocate of agnosticism, and later, atheism. All the Members of Cambridge University were required to reaffirm their faith in the Church of England annually, by publicly signing a declaration of the 39 Articles of the Protestant Faith, which had been formulated three hundred years earlier. By refusing to sign this declaration in 1866, Clifford excluded himself from a professorship at Cambridge, but he was elected Fellow from 1868 to 1871, after being second “wrangler” in 1867 and second Smith's prizeman. (Being second was a fate he shared with others who became famous mathematicians, including William Thomson (Lord Kelvin) and James Clerk Maxwell).

In 1870, Clifford was part of an expedition to Italy to observe an eclipse, and survived a shipwreck along the Sicilian coast. In 1871, he was appointed Professor of Applied Mathematics and Mechanics at University College London, then known as the “godless college.” In 1874 became a fellow of the Royal Society. He was also a member of the London Mathematical Society and the Metaphysical Society.

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 1875, Clifford married Lucy Lane, originally from Barbados, who later became a well-known journalist and novelist in England. He had an engaging personality, enjoyed friendship and loved entertaining children. The couple had two daughters, and Clifford wrote, “The Little People,” a book of fairy stories for children. In 1876, Clifford suffered a serious breakdown, possibly brought on by overwork; he taught and administered by day, and wrote by night. A six-month holiday in Algeria and Spain allowed him to resume his duties at University College for eighteen months. To accommodate his failing health, the Senate of King’s College changed its statutes to allow Clifford to lecture only when he was able, and on topics of his own choosing. A Public Testimonial Fund was set up with the contributions of more than 200 friends and colleagues, so that he would know of their support before his death. Late in 1878 he collapsed again. He went to Madeira to recover, but died there of tuberculosis on March 3, 1879.

Thought and Works

William Clifford combined his mathematical aptitude with a broad and innovative mind to introduce and explore concepts which became basic elements of modern physics. He was sincerely committed to challenging existing preconceptions. His 1879 essay "The Ethics of Belief," contains the famous principle: "it is wrong always, everywhere, and for anyone, to believe anything upon insufficient evidence." This attitude led him to question not only existing scientific truths, but morality, ethics and religious beliefs.

Mathematics

William Clifford was an innovator against the excessively analytic tendency of Cambridge mathematicians. After his death, a British journalist described him as “being equally at home in Space of 3, 4 or x dimensions.” 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.

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. He employed octonions (biquaternions) 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).

As a teacher, Clifford focused on teaching a student to think for himself, rather than on teaching the analytical solution to a problem. He introduced the graphical and geometrical methods of the Germans Mobius and Cullman to England.

His theory of graphs, or geometrical representations of algebraic functions, provided valuable suggestions for future mathematicians. He was interested in universal algebra and elliptic functions. His papers "Preliminary Sketch of Biquaternions" (1873), "On the Canonical Form and Dissection of a Riemann's Surface" (1877), and "Classification of Loci" (1878) are considered classics in mathematics.. He also published several papers on algebraic forms and projective geometry.

Ethics and Philosophy of Science

Clifford was one of the first to synthesize Kant’s ideas on a priori knowledge with Darwin’s evolutionary theory, suggesting that some types of innate knowledge may have been “phylo-genetically” learned and passed down through successive generations. Thus we can instinctively know certain concepts which our ancestors may have had to struggle to work out by trial and error.

Clifford's name is chiefly associated with two phrases which he coined, "mind-stuff" and the "tribal self." “Mind-stuff” refers to the contents of which the conscience is composed. Clifford, influenced by the ideas of Spinoza, suggested that all existence involved “mind,” and that man’s awareness of the content of this mind was evolutionary. The relationship a material object and the “mind” associated with it was similar to the relationship between the printed words of a sentence and the meaning it conveys when it is read by someone.

"Briefly put, 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." Sir Frederick Pollock writing about Clifford’s metaphysics.

The idea of the "tribal self" is essential to Clifford's ethical view. No human being exists in isolation; by nature man is part of a social organism. Moral progress involves the development in each individual of a "tribal self," or conscience, which directs the individual to behave in a way conducive to the welfare and survival of the "tribe." The ideal is to become a public-spirited and efficient citizen.

Much of Clifford's contemporary prominence was due to his attitude towards religion. Animated by a love of truth and devotion to public duty, he waged war on the ecclesiastical systems which seemed to him to favor Obscurantism, and to put the claims of their sect above those of human society. He referred to Christianity as a plague, and to the clergy as enemies of humanity. Clifford was regarded by the church as a dangerous champion of the antispiritual tendencies then imputed to modern science. His 1879 essay, "The Ethics of Belief", asserted that it was immoral to believe in something for which one did not have evidence, and criticized religious thinkers who proclaimed that blind faith was a virtue. This paper was attacked by pragmatist philosopher William James in his lecture, “Will to Believe.” These two works are often read and published together as touchstones for the debate over evidentialism, faith, and overbelief.

Works

Most of Clifford’s work was published posthumously.

• 1877. "The Ethics of Belief," Contemporary Review.
• 1878. Elements of Dynamic, vol. 1.
• 1879. Seeing and Thinking, popular science lectures.
• 1879. Lectures and Essays, with an introduction by Sir Frederick Pollock.
• 1882. Mathematical Papers, edited by R Tucker, with an introduction by Henry J. S. Smith.
• 1885. The Common Sense of the Exact Sciences. Completed by Karl Pearson.
• 1887. Elements of Dynamic, vol. 2.

In Ewald, William B., ed., 1996. From Kant to Hilbert: A Source Book in the Foundations of Mathematics, 2 vols. Oxford Uni. Press.

• 1872. On the aims and instruments of scientific thought, 524-41.
• 1876. On the space theory of matter, 523.

Quotations

• "I ... hold that in the physical world nothing else takes place but this variation [of the curvature of space]." Mathematical Papers.
• "We may always depend on it that algebra, which cannot be translated into good English and sound common sense, is bad algebra." Common Sense in the Exact Sciences.
• "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")
• "It is wrong always, everywhere, and for anyone, to believe anything upon insufficient evidence." The Ethics of Belief (1879)

References

ISBN links support NWE through referral fees

• Chisholm, M., 2002. Such Silver Currents - The Story of William and Lucy Clifford, 1845-1929. Cambridge UK: The Lutterworth Press. ISBN 0-7188-3017-2
• Penrose, Roger. The Road to Reality, Chapter 11. Alfred A. Knopf, 2004.

See also

• Geometric algebra
• Clifford algebra
• Clifford parallelism
• Clifford-Klein form
• Clifford's theorem
• William James
• Will to Believe Doctrine

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.
• http://www.clifford-algebras.org/monty/MONTY.pdf#search=%22William%20Kingdon%20Clifford%22 William Kingdon Clifford (1845-1878) and his Wife Lucy (1846-1829) Monty Chisholm

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This article incorporates text from the Encyclopædia Britannica Eleventh Edition, a publication now in the public domain.

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