William Kingdon Clifford

William Kingdon Clifford

Infobox Scientist
name = William Clifford
box_width = 300px

image_width = 300px
caption = William Kingdon Clifford (1845-1879)
birth_date = birth date|1845|05|04
birth_place = Exeter, Devon, England
death_date = death date and age|1879|03|03|1845|05|04
death_place = Madeira, Portugal
residence = England
citizenship =
nationality = English
ethnicity =
field = Mathematician
work_institutions = University College London
alma_mater = King's College London
Trinity College, Cambridge
doctoral_advisor =
doctoral_students = Arthur Black
known_for = Clifford algebra
Klein-Clifford space
Clifford's theorem

Clifford-Klein form
Clifford parallelism
Bessel-Clifford function
author_abbrev_bot =
author_abbrev_zoo =
influences =
influenced = Georg Friedrich Bernhard Riemann
Nikolai Ivanovich Lobachevsky
prizes =
religion =
footnotes = He was married to the novelist Lucy Clifford.

William Kingdon Clifford FRS (May 4, 1845 – March 3, 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, where he was elected fellow in 1868, after being second wrangler in 1867 and second Smith's prizeman. 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. [cite book | author = Chisholm, M. | title = Such Silver Currents | year = 2002 | publisher = The Lutterworth Press | location = Cambridge | pages = 26 | isbn = 0-7188-3017-2]

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.

On April 7, 1875, Clifford married Lucy Lane. [Citation | last = Stephen | first = Leslie | last2 = Pollock | first2 = Frederick | title = Lectures and Essays by the Late William Kingdon Clifford, F.R.S | place = New York | publisher = Macmillan and Company | year = 1901 | volume = 1 | edition = | pages = 20 | url = http://www.openlibrary.org/details/lecturesessays01clifiala | format = dead link|date=June 2008 – [http://scholar.google.co.uk/scholar?hl=en&lr=&q=author%3AStephen+intitle%3ALectures+and+Essays+by+the+Late+William+Kingdon+Clifford%2C+F.R.S.&as_publication=&as_ylo=1901&as_yhi=1901&btnG=Search Scholar search] ] 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, leaving a widow with two children. Eleven days later, Albert Einstein was born, who would go on to develop the geometric theory of gravity that Clifford had suggested thirty-six years earlier.

Similar to Charles Dodgson, he enjoyed entertaining children, writing a collection of fairy stories, "The Little People".

Clifford and his wife are buried in London's Highgate Cemetery just north of the grave of Karl Marx, and near the graves of George Eliot and Herbert Spencer.


"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.


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, suggested to him by his reading of Spinoza. Sir Frederick Pollock wrote about Clifford as follows:

"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."

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 toward religion. Animated by an intense love of his conception 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 Darwinism; and Clifford was regarded as a dangerous champion of the antispiritual tendencies then imputed to modern science.

For arguing that it was immoral to believe things for which one lacks evidence, in his 1879 essay "The Ethics of Belief", which contains the famous principle: "it is wrong always, everywhere, and for anyone, to believe anything upon insufficient evidence." As such, he was arguing in direct opposition to religious thinkers for whom faith (i.e. belief in things in spite of the lack of evidence for them) was a virtue. This paper was famously attacked by pragmatist philosopher William James in his "Will to Believe" lecture. Often these two works are read and published together as touchstones for the debate over evidentialism, faith, and overbelief.

Selected writings

Most of his work was published posthumously.

*1877. "The Ethics of Belief," "Contemporary Review".
*1878. [http://books.google.com/books?id=pLgEAAAAYAAJ&printsec=frontcover&dq=william+kingdon+clifford&as_brr=1#PPR3,M1 "Elements of Dynamic"] , vol. 1.
*1879. [http://books.google.com/books?id=Tdrry7p7DeMC&printsec=frontcover&dq=william+kingdon+clifford&as_brr=1#PPP9,M1 "Seeing and Thinking"] , popular science lectures.
*1879. [http://www.openlibrary.org/details/lecturesessaysby02clifrich "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. [http://books.google.com/books?id=kAUAAAAAQAAJ&printsec=frontcover&dq=exact+sciences&as_brr=1#PPR3,M1 "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 University Press.
*1872. "On the aims and instruments of scientific thought", 524-41.
*1876. "On the space theory of matter", 523.


*"I ... hold that in the physical world nothing else takes place but this variation [of the curvature of space] ." "Mathematical Papers".
*"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)
*"I was not, and was conceived. I loved and did a little work. I am not and grieve not." - "epitaph".

See also

* Clifford's theorem
* Clifford-Klein form
* Clifford parallelism
* William James
* Will to Believe Doctrine


Further reading

* (The on-line version lacks the article's photographs.)


* (See especially pages 78 – 91)

* (See especially Chapter 11)

* – [http://scholar.google.co.uk/scholar?hl=en&lr=&q=author%3AStephen+intitle%3ALectures+and+Essays+by+the+Late+William+Kingdon+Clifford%2C+F.R.S.&as_publication=&as_ylo=1879&as_yhi=1879&btnG=Search Scholar search]

* – [http://scholar.google.co.uk/scholar?hl=en&lr=&q=author%3AStephen+intitle%3ALectures+and+Essays+by+the+Late+William+Kingdon+Clifford%2C+F.R.S.&as_publication=&as_ylo=1879&as_yhi=1879&btnG=Search Scholar search]

External links

* [http://www.williamandlucyclifford.com/ William and Lucy Clifford (with pictures)]
* " [http://www-gap.dcs.st-and.ac.uk/~history/Mathematicians/Clifford.html William Kingdon Clifford] ". School of Mathematics and Statistics, University of St Andrews, Scotland.
* Beichler, James E., " [http://members.aol.com/jebco1st/Paraphysics/twist1.htm Twist til' we tear the house down] !". Yggdrasil: The Journal of Paraphysics, 1996.
* Clifford, William Kingdon, William James, and A.J. Burger (Ed.), " [http://ajburger.homestead.com/ethics.html The Ethics of Belief] ".
* [http://www.findagrave.com/cgi-bin/fg.cgi?page=gr&GRid=10610&pt=William%20Kingdon%20Clifford Clifford's gravesite]
* " [http://www.1911encyclopedia.org/William_Kingdon_Clifford William Kingdon Clifford] ". 1911 Encyclopaedia Britannica.

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