George Spencer-Brown (2 April 1923 – 25 August 2016) was an English

polymath A polymath or polyhistor is an individual whose knowledge spans many different subjects, known to draw on complex bodies of knowledge to solve specific problems. Polymaths often prefer a specific context in which to explain their knowledge, ...

best known as the author of ''

Laws of Form ''Laws of Form'' (hereinafter ''LoF'') is a book by G. Spencer-Brown, published in 1969, that straddles the boundary between mathematics and philosophy. ''LoF'' describes three distinct logical systems: * The primary arithmetic (described in Ch ...

''. He described himself as a "mathematician, consulting engineer,

psychologist A psychologist is a professional who practices psychology and studies mental states, perceptual, cognitive, emotional, and social processes and behavior. Their work often involves the experimentation, observation, and explanation, interpretatio ...

, educational consultant and practitioner, consulting

psychotherapist Psychotherapy (also psychological therapy, talk therapy, or talking therapy) is the use of Psychology, psychological methods, particularly when based on regular Conversation, personal interaction, to help a person change behavior, increase hap ...

, author, and poet".

Early life and education

Born in

Grimsby Grimsby or Great Grimsby is a port town in Lincolnshire, England with a population of 86,138 (as of 2021). It is located near the mouth on the south bank of the Humber that flows to the North Sea. Grimsby adjoins the town of Cleethorpes dir ...

, Lincolnshire, England, Spencer-Brown attended

Mill Hill School Mill Hill School is a 13–18 co-educational Private schools in the United Kingdom, private, Day school, day and boarding school in Mill Hill, London, England that was established in 1807. It is a member of the Headmasters' and Headmistresses' ...

and then passed the First M.B. in 1940 at

London Hospital Medical College The London Hospital Medical College was a medical school, medical and later dental school based at the London Hospital (later Royal London Hospital) in Whitechapel, London. Founded in 1785, it was the first purpose-built medical college in Englan ...

(now part of

Barts and The London School of Medicine and Dentistry Barts and The London School of Medicine and Dentistry, commonly known as Barts or BL, is a medical school, medical and dental school in London, England. The school is part of Queen Mary University of London, a constituent college of the federal ...

). After serving in the Royal Navy (1943–47), he studied at

Trinity College, Cambridge Trinity College is a Colleges of the University of Cambridge, constituent college of the University of Cambridge. Founded in 1546 by King Henry VIII, Trinity is one of the largest Cambridge colleges, with the largest financial endowment of any ...

, earning Honours in Philosophy (1950) and Psychology (1951), and where he met

Bertrand Russell Bertrand Arthur William Russell, 3rd Earl Russell, (18 May 1872 – 2 February 1970) was a British philosopher, logician, mathematician, and public intellectual. He had influence on mathematics, logic, set theory, and various areas of analytic ...

. From 1952 to 1958, he taught philosophy at

Christ Church, Oxford Christ Church (, the temple or house, ''wikt:aedes, ædes'', of Christ, and thus sometimes known as "The House") is a Colleges of the University of Oxford, constituent college of the University of Oxford in England. Founded in 1546 by Henry V ...

, took M.A. degrees in 1954 from both Oxford and Cambridge, and wrote his doctorate thesis ''Probability and Scientific Inference'' under the supervision of William Kneale which was published as a book in 1957.

Career

During the 1960s, he became a disciple of the innovative Scottish psychiatrist R. D. Laing, frequently cited in ''Laws of Form''. In 1964, on

's recommendation, he became a lecturer in formal mathematics at the

University of London The University of London (UoL; abbreviated as Lond or more rarely Londin in Post-nominal letters, post-nominals) is a collegiate university, federal Public university, public research university located in London, England, United Kingdom. The ...

. From 1969 onward, he was affiliated with the Department of Pure Mathematics and Mathematical Statistics at the

University of Cambridge The University of Cambridge is a Public university, public collegiate university, collegiate research university in Cambridge, England. Founded in 1209, the University of Cambridge is the List of oldest universities in continuous operation, wo ...

. In the 1970s and 1980s, he was visiting professor at the

University of Western Australia University of Western Australia (UWA) is a public research university in the Australian state of Western Australia. The university's main campus is in Crawley, Western Australia, Crawley, a suburb in the City of Perth local government area. UW ...

Stanford University Leland Stanford Junior University, commonly referred to as Stanford University, is a Private university, private research university in Stanford, California, United States. It was founded in 1885 by railroad magnate Leland Stanford (the eighth ...

, and at the

University of Maryland, College Park The University of Maryland, College Park (University of Maryland, UMD, or simply Maryland) is a public university, public Land-grant university, land-grant research university in College Park, Maryland, United States. Founded in 1856, UMD i ...

''Laws of Form''

'', at once a work of mathematics and of philosophy, emerged from work in electronic engineering Spencer-Brown did around 1960, and from lectures on

mathematical logic Mathematical logic is the study of Logic#Formal logic, formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory (also known as computability theory). Research in mathematical logic com ...

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 ''

'' 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 In mathematics and abstract algebra, the two-element Boolean algebra is the Boolean algebra whose ''underlying set'' (or universe or ''carrier'') ''B'' is the Boolean domain. The elements of the Boolean domain are 1 and 0 by convention, so that ''B ...

. One core aspect of the text is the 'observer dilemma' that arises from the very situation of the observer to have decided on the object of observation - while inevitably leaving aside other objects. Such an un-observed object is attributed the 'unmarked state', the realm of all 'unmarked space'. ''Laws of Form'' has influenced, among others,

Heinz von Foerster Heinz von Foerster (; November 13, 1911 – October 2, 2002) was an Austrian-American scientist combining physics and philosophy, and widely attributed as the originator of second-order cybernetics. He was twice a Guggenheim fellow (1956–57 and ...

Louis Kauffman Louis Hirsch Kauffman (born February 3, 1945) is an American mathematician, mathematical physicist, and professor of mathematics in the Department of Mathematics, Statistics, and Computer Science at the University of Illinois at Chicago. He doe ...

Niklas Luhmann Niklas Luhmann (; ; December 8, 1927 – November 11, 1998) was a German sociologist, philosopher of social science, and systems theorist. Niklas Luhmann is one of the most influential German sociologists of the 20th century. His thinking was ...

Humberto Maturana Humberto Maturana Romesín (September 14, 1928 – May 6, 2021) was a Chilean biologist and philosopher. Some name him a second-order cybernetics theoretician alongside the likes of Heinz von Foerster, Gordon Pask, Herbert Brün and Ern ...

Francisco Varela Francisco Javier Varela García (September 7, 1946 – May 28, 2001) was a Chilean biologist, philosopher, cybernetician, and neuroscientist who, together with his mentor Humberto Maturana, is best known for introducing the concept of autopoie ...

, Leon Conrad, and William Bricken. Some of these authors have modified and extended the primary algebra, with interesting consequences.

Controversial mathematics

In a 1976 letter to the Editor of ''Nature'', Spencer-Brown claimed a proof of the

four-color theorem In mathematics, the four color theorem, or the four color map theorem, states that no more than four colors are required to color the regions of any map so that no two adjacent regions have the same color. ''Adjacent'' means that two regions shar ...

, 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. The 6th edition of ''Laws of Form'' advertises that it includes "the first-ever proof of

Riemann's hypothesis In mathematics, the Riemann hypothesis is the conjecture that the Riemann zeta function has its Root of a function, zeros only at the negative even integers and complex numbers with real part . Many consider it to be the most important List of u ...

Personal life and death

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 A correspondent or on-the-scene reporter is usually a journalist or commentator for a magazine, or an agent who contributes reports to a newspaper, or radio or television news, or another type of company, from a remote, often distant, locati ...

to the ''

Daily Express The ''Daily Express'' is a national daily United Kingdom middle-market newspaper printed in Tabloid (newspaper format), tabloid format. Published in London, it is the flagship of Express Newspapers, owned by publisher Reach plc. It was first ...

''. He also wrote some novels and poems, sometimes employing the pen name ''James Keys''. Spencer-Brown died on 25 August 2016. He was buried at the London Necropolis, Brookwood,

Surrey Surrey () is a Ceremonial counties of England, ceremonial county in South East England. It is bordered by Greater London to the northeast, Kent to the east, East Sussex, East and West Sussex to the south, and Hampshire and Berkshire to the wes ...

Reception

While not denying some of his talent, not all critics of Spencer-Brown's claims and writings have been willing to assess them at his own valuation; the poetry is at the most charitable reading an idiosyncratic taste, and some prominent voices have been decidedly dismissive of the value of his formal material. For example

Martin Gardner Martin Gardner (October 21, 1914May 22, 2010) was an American popular mathematics and popular science writer with interests also encompassing magic, scientific skepticism, micromagic, philosophy, religion, and literatureespecially the writin ...

wrote in his essay: "''M-Pire Maps''":

In December of 1976 G. Spencer-Brown, the maverick British mathematician, startled his colleagues by announcing he had a proof of the four-color theorem that did not require computer checking. Spencer-Brown's supreme confidence and his reputation as a mathematician brought him an invitation to give a seminar on his proof at Stanford University. At the end of three months all the experts who attended the seminar agreed that the proofs logic was laced with holes, but Spencer-Brown returned to England still sure of its validity. The "proof' has not yet been published.
Spencer-Brown is the author of a curious little book called ''Laws of Form'',George Spencer-Brown. Laws of form. 1969, Pub. George Allen and Unwin. SBN 04 510028 4 which is essentially a reconstruction of the
propositional calculus The propositional calculus is a branch of logic. It is also called propositional logic, statement logic, sentential calculus, sentential logic, or sometimes zeroth-order logic. Sometimes, it is called ''first-order'' propositional logic to contra ...
by means of an eccentric notation. The book, which the British mathematician John Horton Conway once described as ''beautifully written but "content-free,"'' has a large circle of
counterculture A counterculture is a culture whose values and norms of behavior differ substantially from those of mainstream society, sometimes diametrically opposed to mainstream cultural mores.Eric Donald Hirsch. ''The Dictionary of Cultural Literacy''. Ho ...
devotees.Martin Gardner. The last recreations: hydras, eggs, and other mathematical mystifications. ISBN 0-387-94929-1

Selected publications

* 1957. ''Probability and Scientific Inference''. * 1961. ''Design with the Nor'' (first published in 2021). * 1970. ''23 degrees of Paradise''. * 1971. ''Only Two Can Play This Game'' (under pseudonym James Keys) *Selected editions of ''Laws of Form'': ** 1969. London: Allen & Unwin. ** 1972. Crown Publishers, hardcover. ** 1994. Cognizer Company, paperback. ** 1997. German translation titled ''Gesetze der Form''. Lübeck: Bohmeier Verlag. *"Claim of Proof to Four Colour Theorem." Letter to the Editor of ''Nature''. 17 December 1976.

References

External links

G Spencer-Brown: Laws of Form
website with Tutorial, Flash animations, downloads. Site not found
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''.

of G. Spencer-Brown.

of Spencer-Brown's talks at Esalen, 1973.
YouTube Course
offering a close reading of ''Laws of Form'' by his last student, Leon Conrad. {{DEFAULTSORT:Spencer-Brown, G. 1923 births 2016 deaths 20th-century English mathematicians People educated at Mill Hill School Alumni of the London Hospital Medical College Alumni of Trinity College, Cambridge Fellows of Christ Church, Oxford People from Grimsby Royal Navy personnel of World War II Military personnel from Lincolnshire Royal Navy sailors