William Kingdon Clifford

William Kingdon Clifford, FRS (May 4, 1845 - March 3, 1879) was an English mathematician who also wrote a fair bit on philosophy. 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. His philosophical writings coined the phrase "mind-stuff". This image has been released into the public domain by the copyright holder, its copyright has expired, or it is ineligible for copyright. ... This image has been released into the public domain by the copyright holder, its copyright has expired, or it is ineligible for copyright. ... May 4 is the 124th day of the year in the Gregorian calendar (125th in leap years). ... 1845 was a common year starting on Wednesday (see link for calendar). ... March 3 is the 62nd day of the year in the Gregorian Calendar (63rd in leap years). ... 1879 (MDCCCLXXIX) was a common year starting on Wednesday (see link for calendar). ... Royal motto (French): Dieu et mon droit (Translated: God and my right) Englands location (dark green) within the United Kingdom (light green), with the Republic of Ireland (blue) to its west Languages None official English de facto Capital None official London de facto Largest city London Area – Total Ranked... Leonhard Euler is considered by many people to be one of the greatest mathematicians of all time A mathematician is a person whose primary area of study and research is mathematics. ... Philosopher in Meditation (detail), by Rembrandt. ... Hermann Günther Grassmann (April 15, 1809, Stettin – September 26, 1877, Stettin) was a German polymath, renowned in his day as a linguist and now admired as a mathematician. ... Geometric algebra is a Clifford algebra with a geometric interpretation. ... Clifford algebras are a type of associative algebra in mathematics. ... Mathematical physics is the scientific discipline concerned with the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories1. ... In physics, gravitation or gravity is the tendency of objects with mass to accelerate toward each other. ...

Biography

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. A number of other places have taken their names from Exeter The city of Exeter is the county town of Devon, in England, UK. It is located at 50° 43 25 N, 3° 31 39 W. In the 2001 census its population was recorded at 111,066. ... Kings College London, founded in 1829, is one of the oldest UK university institutions. ... Full name The College of the Holy and Undivided Trinity Motto Virtus vera nobilitas Virtue is true Nobility Named after The Holy Trinity Previous names Kings Hall and Michaelhouse (until merged in 1546) Established 1546 Sister College(s) Christ Church Master The Lord Rees of Ludlow Location Trinity Street... At the University of Cambridge in the United Kingdom, a wrangler is a student who has completed the third year (called Part II) of the Mathematical Tripos with first-class honours. ... There have been a number of people named William Thomson: William Thomson, 1st Baron Kelvin, usually known as Lord Kelvin, was a 19th century British physicist. ... James Clerk Maxwell (13 June 1831 – 5 November 1879) was a Scottish mathematical physicist, born in Edinburgh. ...

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. University College London, commonly known as UCL, is one of the colleges that make up the University of London. ... The premises of the Royal Society in London (first four properties only). ... The London Mathematical Society (LMS) is the leading mathematical society in England. ... The Metaphysical Society was a British society, founded in 1869 by James Knowles. ...

In 1875, he married Lucy Lane of Barbados. 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 Madeira to recover, but died there of tuberculosis after a few months, leaving a widow with two children. 11 days after his death, Albert Einstein was born, to develop thirty six years later the geometric theory of gravity that Clifford had suggested. 1875 (MDCCCLXXV) was a common year starting on Friday (see link for calendar). ... Lucy Clifford (1846 - April 21, 1929), better known as Mrs W K Clifford, was a British novelist and journalist, the wife of William Kingdon Clifford. ... Tuberculosis (commonly shortened to TB) is an infection caused by the bacterium Mycobacterium tuberculosis, which most commonly affects the lungs (pulmonary TB) but can also affect the central nervous system (meningitis), lymphatic system, circulatory system (Miliary tuberculosis), genitourinary system, bones and joints. ... Albert Einstein, photographed by Yousuf Karsh in 1948. ...

"If he had lived we might have known something." (Said by Isaac Newton of Roger Cotes, but applicable to Clifford.) Sir Isaac Newton, President of the Royal Society, (4 January 1643 – 31 March 1727) [OS: 25 December 1642 – 20 March 1727] was an English mathematician, physicist, astronomer, alchemist, chemist, inventor, and natural philosopher who is generally regarded as one of the most influential scientists and mathematicians in history. ... Roger Cotes (Burbage, Leicestershire July 10, 1682 – June 5, 1716 in Cambridge, Cambridgeshire) was a mathematician. ...

Similar to Charles Dodgson, he enjoyed entertaining children, writing a collection of fairy stories, The Little People. Photograph of Lewis Carroll taken by himself, with assistance Charles Lutwidge Dodgson (January 27, 1832 – January 14, 1898), better known by the pen name Lewis Carroll, was a British author, mathematician, Anglican clergyman, logician, and amateur photographer. ...

Mathematician

"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. Henry John Stephen Smith (November 2, 1826 - February 9, 1883) was an Irish mathematician, remembered for his work in number theory (elementary divisors, quadratic forms) and matrices. ... Bernhard Riemann. ... Nikolay Ivanovich Lobachevsky Nikolai Ivanovich Lobachevsky (Никола́й Ива́нович Лобаче́вский) (December 1, 1792 - February 24, 1856) was a Russian mathematician. ... Behavior of lines with a common perpendicular in each of the three types of geometry The term non-Euclidean geometry (also spelled: non-Euclidian geometry) describes both hyperbolic and elliptic geometry, which are contrasted with Euclidean geometry. ... Matter is commonly defined as the substance of which physical objects are composed. ... Albert Einstein, photographed by Yousuf Karsh in 1948. ... General relativity (GR) or general relativity theory (GRT) is the theory of gravitation published by Albert Einstein in 1915. ...

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 octonions (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). Clifford algebras are a type of associative algebra in mathematics. ... Wikibooks Algebra has more about this subject: Complex numbers In mathematics, a complex number is an expression of the form where a and b are real numbers, and i is a specific imaginary number, called the imaginary unit, with the property i 2 = −1. ... William Rowan Hamilton Sir William Rowan Hamilton (August 4, 1805 – September 2, 1865) was an Irish mathematician, physicist, and astronomer who made important contributions to the development of optics, dynamics, and algebra. ... In mathematics, the quaternions are a non-commutative extension of the complex numbers. ... In mathematics, the octonions are a nonassociative extension of the quaternions. ... Topology (Greek topos, place and logos, study) is a branch of mathematics concerned with spatial properties preserved under bicontinuous deformation (stretching without tearing or gluing); these are the topological invariants. ... In mathematics, particularly in complex analysis, a Riemann surface is a one-dimensional complex manifold. ...

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. A labeled graph with 6 vertices and 7 edges. ... Universal algebra is the field of mathematics that studies the ideas common to all algebraic structures. ... In complex analysis, an elliptic function is, roughly speaking, a function defined on the complex plane which is periodic in two directions. ... In mathematics, a biquaternion is a numeric and geometric concept developed by William Kingdon Clifford, William Rowan Hamilton, and Alexander MacAuley in the nineteenth century. ... In mathematics, particularly in complex analysis, a Riemann surface is a one-dimensional complex manifold. ... The word locus (plural loci) is Latin for place: In biology and evolutionary computation, a locus is the position of a gene (or other significant sequence) on a chromosome. ... In the mathematics of the nineteenth century, an important role was played by the algebraic forms that generalise quadratic forms to degrees 3 and more, also known as quantics. ... Projective geometry is a non-metrical form of geometry that emerged in the early 19th century. ...

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, suggested to him by his reading of Spinoza. Sir Frederick Pollock wrote about Clifford as follows: Baruch Spinoza Benedictus de Spinoza (November 24, 1632 - February 21, 1677), named Baruch Spinoza by his synagogue elders and known as Bento de Spinoza or Bento dEspiñoza in the community in which he grew up. ... Sir Frederick Pollock (born London, December 10, 1845; died London, January 18, 1937) was an English jurist best known for his History of English Law before Edward I, written with F.W. Maitland, and his lifelong correspondence with Oliver Wendell Holmes. ...

"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." Properties In chemistry and physics, an atom (Greek άτομον meaning indivisible) is the smallest possible particle of a chemical element that retains its chemical properties. ... Consciousness is a quality of the mind generally regarded to comprise qualities such as subjectivity, self-awareness, sentience, sapience, and the ability to perceive the relationship between oneself and ones environment. ... In philosophy, materialism is that form of physicalism which holds that the only thing that can truly be said to exist is matter; that fundamentally, all things are composed of material and all phenomena are the result of material interactions. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... Monism is the metaphysical and theological view that all is of one essential essence, principle, substance or energy. ...

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 Darwinism; and Clifford was regarded as a dangerous champion of the antispiritual tendencies then imputed to modern science. Obscurantism is opposition to extension or dissemination of knowledge beyond certain limits and to questioning dogmas. ... Theology is reasoned discourse concerning God (Greek θεος, theos, God, + λογος, logos, word or reason). It can also refer to the study of other religious topics. ... Charles Darwin Darwinism is a term for the underlying theory in those ideas of Charles Darwin concerning evolution and natural selection. ...

He is also well known 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 which claim faith (i.e. belief in things in spite of the lack of evidence for them) to be virtuous.

Writings

Most of his 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. Sir Frederick Pollock (born London, December 10, 1845; died London, January 18, 1937) was an English jurist best known for his History of English Law before Edward I, written with F.W. Maitland, and his lifelong correspondence with Oliver Wendell Holmes. ... Henry John Stephen Smith (November 2, 1826 - February 9, 1883) was an Irish mathematician, remembered for his work in number theory (elementary divisors, quadratic forms) and matrices. ... Karl Pearson (pencil sketch in notebook; there is some see-through of writing on next page) Karl Pearson (March 27, 1857 – April 27, 1936) was a major contributor to the early development of statistics as a serious scientific discipline in its own right. ...

• 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")

References

• 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
• Roger Penrose, 2004. The Road to Reality. Alfred A. Knopf. Esp. chpt. 11.

Sir Roger Penrose, OM, FRS (born 8 August 1931) is an English mathematical physicist and Emeritus Rouse Ball Professor of Mathematics at the University of Oxford. ...

See also

• Geometric algebra
• Clifford algebra
• Clifford parallelism
• Clifford-Klein form
• Clifford's theorem

Geometric algebra is a Clifford algebra with a geometric interpretation. ... Clifford algebras are a type of associative algebra in mathematics. ... In mathematics, a Clifford-Klein form is a double coset space Γ/G H, where G is a reductive Lie group, H a closed subgroup of G, and Γ a discrete subgroup of G that acts properly discontinuously on the homogeneous space G H. A suitable discrete subgroup Γ may... In mathematics, Cliffords theorem on special divisors is a result of W. K. Clifford on algebraic curves, showing the constraints on special linear systems on a curve C. If D is a divisor on C, then D is (abstractly) a formal sum of points P on C (with integer...

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.

This article incorporates text from the Encyclopædia Britannica Eleventh Edition, a publication now in the public domain. Encyclopædia Britannica, the 11th edition The Encyclopædia Britannica Eleventh Edition (1910–1911) is perhaps the most famous edition of the Encyclopædia Britannica. ... The public domain comprises the body of all creative works and other knowledge—writing, artwork, music, science, inventions, and others—in which no person or organization has any proprietary interest. ...