George Spencer-Brown (born April 2, 1923) 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."
Born in Grimsby, Lincolnshire, England, 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 College 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.
Laws of Form
Laws of Form, 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 systems 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.
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.
- 1957. Probability and Scientific Inference.
- Selected editions of Laws of Form:
- "Claim of Proof to Four Colour Theorem." Letter to the Editor of Nature. 17 December 1976.
- Brief bio of G. Spencer-Brown.
- Cf. Spencer-Brown, George: Laws of Form, New York: Dutton, (1969/1979), S. 143 (About the Author).
- Robert Spencer (6 January 1977). "A colourful character". New Scientist. p. 6.
- Kauffman, Louis H. (2001). "On the map theorem". Discrete Math. 229 (1-3): 171–184. ISSN 0012-365X.
- Kauffman, L. (2005). "Reformulating the map color theorem". Discrete Mathematics 302 (1–3): 145–172. doi:10.1016/j.disc.2004.07.031. , preprint available online.
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- 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.