G. Spencer-Brown

George Spencer-Brown (born April 2, 1923, Grimsby, Lincolnshire, England) 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] .

Life

Spencer-Brown obtained an M.B. in 1940 from London Hospital Medical College (now part of Queen Mary, University of London). 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, earning 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.

Spencer-Brown has 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 Charles 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.

Other mathematics

In a 1976 letter to the Editor of "Nature", Spencer-Brown claimed a noncomputational proof of the four-color theorem. While this claim of proof has yet to be verified, [http://www.arxiv.org/math.CO/0112266 Kauffman] has incorporated parts of Spencer-Brown's reasoning into his own work. The preface of the 1979 edition of "Laws of Form" repeats the four-color theorem claim, and further claims 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.

Spencer-Brown claimed in 1998 to have a proof of Goldbach's conjecture, and in 2006 to have a proof of the Riemann hypothesis. Spencer-Brown has also written on number theory, especially the determination of primality.

Quotation

:"...to teach pride in knowledge is to put up an effective barrier against any advance upon what is already known, since it makes one ashamed to look beyond the bounds imposed by one's own ignorance." "Laws of Form", Appendix 1.

ee also

*Laws of Form
*Charles Peirce
*Entitative graph
*existential graph
*two-element Boolean algebra

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
*" [http://www.lawsofform.org/gsb/nature.html Claim of Proof to Four Colour Theorem.] " Letter to the Editor of "Nature". 17 December 1976.

External links

* [http://forum.troonite.co.uk/gsb/index.html G Spencer-Brown: Laws of Form] , website with Tutorial, Flash animations, downloads.
* [http://www.lawsofform.org 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".
* [http://www.lawsofform.org/gsb/vita.html Brief bio] of G. Spencer-Brown.
* [http://www.laws-of-form.net/riemann.asp "A short proof of the Riemann hypothesis"] by G. Spencer-Brown (Juli 2006).
* [http://www.transordinator.de/edition/draw/0.html Draw a distinction...] The space of imagination based on Spencer-Brown.
*Kauffman, Louis H., " [http://www.arxiv.org/math.CO/0112266 Reformulating the Map Color Theorem] ".
* [http://www.lawsofform.org/aum/session1.html Transcript] of Spencer-Brown's talks at Esalen, 1973.