Kingdon Clifford 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".
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, 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.
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.
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
he had lived we might have known something." (Said by Isaac
Newton of Roger Cotes, but applicable to Clifford.)
to Charles Dodgson, he enjoyed entertaining children, writing
a collection of fairy stories, The Little People.
"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.
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.
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
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:
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.
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."
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
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.
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.
"I ... hold that in the physical world nothing else takes
place but this variation [of the curvature of space]."
"We may always depend on it that algebra, which cannot be
translated into good English and sound common sense, is bad algebra."
"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."