Introduction and welcome
In 1977, having previously studied the mathematical foundational work of Boole, Frege, Russell, Whitehead, Wittgenstein and Gödel, Graham was given a copy of George Spencer-Brown's Laws of Form and quickly recognized it as a work of the highest order.
Over the following years, Graham thoroughly analysed the calculus presented in Laws, and in 1983 sent his demonstration of the primary algebra from a single initial-equation to Spencer-Brown who invited him to his home in Cambridge, their discussions initially focusing on formal algebras and Spencer-Brown's work on the four-colour conjecture. A friendship quickly developed with Graham becoming Spencer-Brown's principal friend and confidant for more than three decades, frequently visiting him at his successive homes in Cambridge, London and Horningsham.
Graham is the leading authority on the primary algebra, with Spencer-Brown once remarking, "You have made the field your own", and is the custodian of Spencer-Brown's personal effects, notebooks, unpublished papers, poetry, miscellaneous writings, and photographs. These documents and several hundred hours of their discussions and other audio recordings are being digitised with the intention that they will form an archive for possible future publication online. Graham initiated the Laws of Form conferences now being generously hosted by the University of Liverpool.
In addition to formal algebras, Graham's interests include cryptography, having written a detailed description of, and a computer program which emulates, the logical operations of the bombe, the machine devised by Alan Turing and Gordon Welchman, which broke the German Enigma machine on an industrial scale; the philosophy of physics; binocular stargazing; and chess. Graham has an MSc in Computing Science from Birkbeck, University of London.