G. Spencer-Brown
Encyclopedia
George Spencer-Brown is a polymath
best known as the author of Laws of Form
. He describes himself as a "mathematician
, consulting engineer
, psychologist
, educational consultant and practitioner, consulting psychotherapist, author, and poet
."http://www.lawsofform.org/gsb/vita.html.
Cambridge
, earning Honours in Philosophy (1950) and Psychology (1951), and where he met Bertrand Russell
. From 1952 to 1958, he taught philosophy at Christ Church, Oxford
, taking M.A. degrees in 1954 from both Oxford and Cambridge, and writing his 1957 book Probability and Scientific Inference.
During the 1960s, he became a disciple of the innovative Scottish psychiatrist R. D. Laing, frequently cited in Laws of Form. In 1964, on Bertrand Russell
's recommendation, he became a lecturer in formal mathematics at the University of London
. From 1969 onward, he was affiliated with the Department of Pure Mathematics and Mathematical Statistics at the University of Cambridge
. In the 1970s and 1980s, he was visiting professor at the University of Western Australia
, Stanford University
, and at the University of Maryland, College Park
.
During his time at Cambridge Spencer-Brown was a chess half-blue. He held two world records as a glider pilot
, and was a sports correspondent
to the Daily Express
. He has also written some novels and poems, sometimes employing the pen name James Keys.
, at once a work of mathematics
and of philosophy
, emerged out of work in electronic engineering Spencer-Brown did around 1960, and from lectures on mathematical logic
he later gave under the auspices of the University of London's extension program. First published in 1969, it has never been out of print. Spencer-Brown referred to the mathematical system of Laws of Form
as the "primary algebra" and the "calculus of indications"; others have termed it "boundary algebra." The primary algebra is essentially an elegant minimalist notation for the two-element Boolean algebra, very similar to formal system
s that Charles Sanders Peirce devised in work written in the 1880s and 90s (see entitative graph
and existential graph
), but in some cases not published until after the first edition of Laws of Form.
Laws of Form has influenced, among others, Heinz von Foerster
, Louis Kauffman
, Niklas Luhmann
, Humberto Maturana
, Francisco Varela
and William Bricken. Some of these authors have modified and extended the primary algebra, with interesting consequences.
Polymath
A polymath is a person whose expertise spans a significant number of different subject areas. In less formal terms, a polymath may simply be someone who is very knowledgeable...
best known as the author of Laws of Form
Laws of Form
Laws of Form is a book by G. Spencer-Brown, published in 1969, that straddles the boundary between mathematics and philosophy...
. He describes himself as a "mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
, consulting engineer
Engineer
An engineer is a professional practitioner of engineering, concerned with applying scientific knowledge, mathematics and ingenuity to develop solutions for technical problems. Engineers design materials, structures, machines and systems while considering the limitations imposed by practicality,...
, psychologist
Psychologist
Psychologist is a professional or academic title used by individuals who are either:* Clinical professionals who work with patients in a variety of therapeutic contexts .* Scientists conducting psychological research or teaching psychology in a college...
, educational consultant and practitioner, consulting psychotherapist, author, and poet
Poet
A poet is a person who writes poetry. A poet's work can be literal, meaning that his work is derived from a specific event, or metaphorical, meaning that his work can take on many meanings and forms. Poets have existed since antiquity, in nearly all languages, and have produced works that vary...
."http://www.lawsofform.org/gsb/vita.html.
Life
Spencer-Brown passed the First M.B. in 1940 at London Hospital Medical College (now part of Barts and The London School of Medicine and Dentistry). After serving in the Royal Navy (1943–47), he studied at Trinity CollegeTrinity College, Cambridge
Trinity College is a constituent college of the University of Cambridge. Trinity has more members than any other college in Cambridge or Oxford, with around 700 undergraduates, 430 graduates, and over 170 Fellows...
Cambridge
Cambridge
The city of Cambridge is a university town and the administrative centre of the county of Cambridgeshire, England. It lies in East Anglia about north of London. Cambridge is at the heart of the high-technology centre known as Silicon Fen – a play on Silicon Valley and the fens surrounding the...
, earning Honours in Philosophy (1950) and Psychology (1951), and where he met Bertrand Russell
Bertrand Russell
Bertrand Arthur William Russell, 3rd Earl Russell, OM, FRS was a British philosopher, logician, mathematician, historian, and social critic. At various points in his life he considered himself a liberal, a socialist, and a pacifist, but he also admitted that he had never been any of these things...
. From 1952 to 1958, he taught philosophy at Christ Church, Oxford
Christ Church, Oxford
Christ Church or house of Christ, and thus sometimes known as The House), is one of the largest constituent colleges of the University of Oxford in England...
, taking M.A. degrees in 1954 from both Oxford and Cambridge, and writing his 1957 book Probability and Scientific Inference.
During the 1960s, he became a disciple of the innovative Scottish psychiatrist R. D. Laing, frequently cited in Laws of Form. In 1964, on Bertrand Russell
Bertrand Russell
Bertrand Arthur William Russell, 3rd Earl Russell, OM, FRS was a British philosopher, logician, mathematician, historian, and social critic. At various points in his life he considered himself a liberal, a socialist, and a pacifist, but he also admitted that he had never been any of these things...
's recommendation, he became a lecturer in formal mathematics at the University of London
University of London
-20th century:Shortly after 6 Burlington Gardens was vacated, the University went through a period of rapid expansion. Bedford College, Royal Holloway and the London School of Economics all joined in 1900, Regent's Park College, which had affiliated in 1841 became an official divinity school of the...
. From 1969 onward, he was affiliated with the Department of Pure Mathematics and Mathematical Statistics at the University of Cambridge
University of Cambridge
The University of Cambridge is a public research university located in Cambridge, United Kingdom. It is the second-oldest university in both the United Kingdom and the English-speaking world , and the seventh-oldest globally...
. In the 1970s and 1980s, he was visiting professor at the University of Western Australia
University of Western Australia
The University of Western Australia was established by an Act of the Western Australian Parliament in February 1911, and began teaching students for the first time in 1913. It is the oldest university in the state of Western Australia and the only university in the state to be a member of the...
, Stanford University
Stanford University
The Leland Stanford Junior University, commonly referred to as Stanford University or Stanford, is a private research university on an campus located near Palo Alto, California. It is situated in the northwestern Santa Clara Valley on the San Francisco Peninsula, approximately northwest of San...
, and at the University of Maryland, College Park
University of Maryland, College Park
The University of Maryland, College Park is a top-ranked public research university located in the city of College Park in Prince George's County, Maryland, just outside Washington, D.C...
.
During his time at Cambridge Spencer-Brown was a chess half-blue. He held two world records as a glider pilot
Glider (sailplane)
A glider or sailplane is a type of glider aircraft used in the sport of gliding. Some gliders, known as motor gliders are used for gliding and soaring as well, but have engines which can, in some cases, be used for take-off or for extending a flight...
, and was a sports correspondent
Correspondent
A correspondent or on-the-scene reporter is a journalist or commentator, or more general speaking, an agent who contributes reports to a newspaper, or radio or television news, or another type of company, from a remote, often distant, location. A foreign correspondent is stationed in a foreign...
to the Daily Express
Daily Express
The Daily Express switched from broadsheet to tabloid in 1977 and was bought by the construction company Trafalgar House in the same year. Its publishing company, Beaverbrook Newspapers, was renamed Express Newspapers...
. He has also written some novels and poems, sometimes employing the pen name James Keys.
Laws of Form
Laws of FormLaws of Form
Laws of Form is a book by G. Spencer-Brown, published in 1969, that straddles the boundary between mathematics and philosophy...
, at once a work of mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
and of philosophy
Philosophy
Philosophy is the study of general and fundamental problems, such as those connected with existence, knowledge, values, reason, mind, and language. Philosophy is distinguished from other ways of addressing such problems by its critical, generally systematic approach and its reliance on rational...
, emerged out of work in electronic engineering Spencer-Brown did around 1960, and from lectures on mathematical logic
Mathematical logic
Mathematical logic is a subfield of mathematics with close connections to foundations of mathematics, theoretical computer science and philosophical logic. The field includes both the mathematical study of logic and the applications of formal logic to other areas of mathematics...
he later gave under the auspices of the University of London's extension program. First published in 1969, it has never been out of print. Spencer-Brown referred to the mathematical system of Laws of Form
Laws of Form
Laws of Form is a book by G. Spencer-Brown, published in 1969, that straddles the boundary between mathematics and philosophy...
as the "primary algebra" and the "calculus of indications"; others have termed it "boundary algebra." The primary algebra is essentially an elegant minimalist notation for the two-element Boolean algebra, very similar to formal system
Formal system
In formal logic, a formal system consists of a formal language and a set of inference rules, used to derive an expression from one or more other premises that are antecedently supposed or derived . The axioms and rules may be called a deductive apparatus...
s that Charles Sanders Peirce devised in work written in the 1880s and 90s (see entitative graph
Entitative graph
An entitative graph is an element of the diagrammatic syntax for logic that Charles Sanders Peirce developed under the name of qualitative logic beginning in the 1880's, taking the coverage of the formalism only as far as the propositional or sentential aspects of logic are concerned...
and existential graph
Existential graph
An existential graph is a type of diagrammatic or visual notation for logical expressions, proposed by Charles Sanders Peirce, who wrote on graphical logic as early as 1882, and continued to develop the method until his death in 1914.-The graphs:...
), but in some cases not published until after the first edition of Laws of Form.
Laws of Form has influenced, among others, Heinz von Foerster
Heinz von Foerster
Heinz von Foerster was an Austrian American scientist combining physics and philosophy. Together with Warren McCulloch, Norbert Wiener, John von Neumann, Lawrence J. Fogel, and others, Heinz von Foerster was an architect of cybernetics.-Biography:Von Foerster was born in 1911 in Vienna, Austria,...
, Louis Kauffman
Louis Kauffman
Louis H. Kauffman is an American mathematician, topologist, and professor of Mathematics in the Department of Mathematics, Statistics, and Computer science at the University of Illinois at Chicago...
, Niklas Luhmann
Niklas Luhmann
Niklas Luhmann was a German sociologist, and a prominent thinker in sociological systems theory.-Biography:...
, Humberto Maturana
Humberto Maturana
Humberto Maturana is a Chilean biologist and philosopher. He is considered a member of the second wave of cybernetics, known for developing a theory of autopoiesis about the nature of reflexive feedback control in living systems.- Biography :After completing secondary school at the Liceo Manuel de...
, Francisco Varela
Francisco Varela
Francisco Javier Varela García , was a Chilean biologist, philosopher and neuroscientist who, together with his teacher Humberto Maturana, is best known for introducing the concept of autopoiesis to biology.-Biography:...
and William Bricken. Some of these authors have modified and extended the primary algebra, with interesting consequences.
Other mathematics
In a 1976 letter to the Editor of Nature, Spencer-Brown claimed a proof of the four-color theorem, which is not computer-assisted. The preface of the 1979 edition of Laws of Form repeats that claim, and further states that the generally accepted computational proof by Appel, Haken, and Koch has 'failed' (page xii). Spencer-Brown's claimed proof of the four-color theorem has yet to find any defenders; Kauffman provides a detailed review of parts of that work.Selected publications
- 1957. Probability and Scientific Inference.
- Selected editions of Laws of Form:
- 1969. London: Allen & Unwin.
- 1972. Crown Publishers, hardcover. ISBN 0-517-52776-6
- 1994. Cognizer Company, paperback. ISBN 0-9639899-0-1
- 1997. German translation titled Gesetze der Form. Lübeck: Bohmeier Verlag. ISBN 3-89094-321-7
- "Claim of Proof to Four Colour Theorem." Letter to the Editor of Nature. 17 December 1976.
External links
- G Spencer-Brown: Laws of Form, website with Tutorial, Flash animations, downloads.
- Richard Shoup's website devoted to Spencer-Brown, his work, and related ideas. Includes an extensive bibliography of the secondary literature on Laws of Form.
- Brief bio of G. Spencer-Brown.
- Draw a distinction... The space of imagination based on Spencer-Brown.
- Kauffman, Louis H., "Reformulating the Map Color Theorem".
- Transcript of Spencer-Brown's talks at Esalen, 1973.