Part 12 of Turing: a natural philosopher (1997)
Growing CrisisIn any case, by 1950 Turing had an excited interest in a new field. Turing was interested in the body in Nature as well as the brain; his boyhood experiments had been chemical rather than mathematical, and he retained the eyes to see biological structure as intensely puzzling. We recall the early fascination with determinism, and 'the rest of the body amplifies this'; his thesis had interested him in brain cells, and he attacked a simplified problem in biological growth by postulating non-linear differential equations. He showed how inhomogeneity could arise from homogeneous initial conditions, using a symmetry-breaking effect of chemical instability. He described his philosophical outlook as countering the theological argument from design, suggesting a future Richard Dawkins of physiology. He set himself as a goal the explanation of Fibonacci patterns in plants; this was perhaps unfortunate as this problem remains unsolved, but his research, as a first user of electronic computation for serious mathematical investigation, was twenty years ahead of its time and full of potential for discovery. With hindsight we notice that the elucidation of chaotic dynamics was later to come from just such computational experiment.
This work struggled against personal catastrophe. In December 1951 he met a young man in Manchester, and told him of his work on 'the electronic brain.' An unsatisfactory affair led to indirect blackmail, exploiting the fact that all sex between men was then criminal. Resisting it by going to the police, he was arrested. Unrepentant and unashamed at his trial, he had to agree to the injection of oestrogen, supposed to neutralize his supposedly unnatural nature. The alternative would have been prison. Deemed a security risk by post-war regulations, he was stopped from the work he had continued to do from GCHQ, the Cold War successor to Bletchley Park. He found himself under watch; and other pressures may have been placed on him.
Turing complained that he lacked concentration, yet for two years he developed a mass of geometric and analytic ideas; he also turned to new topics, or rather old ones revived. In particular, he puzzled over the standard view of reduction of the wave-function in quantum mechanics, noting the paradox that continuous observation freezes the dynamics. He told Robin Gandy of his new idea for quantum mechanics: 'Description must be non-linear, prediction must be linear' . Possibly he had in mind a non-linear quantum theory in which reduction would arise as did the symmetry breaking in his non-linear morphogenetic theory.
To relieve depression and anger he had turned to Jungian therapy, and found new interest in writing down his dreams. On a visit to Blackpool in early 1954 with the therapist's family, he consulted the Gypsy Queen fortune-teller, and emerged 'white as a sheet.' He remained silent for the rest of that day; nor did he leave a public word at his suicide on Whit Monday, 7 June 1954. Symbolism, in the cyanide-poisoned apple he ate, was his language. What words could have sufficed? Jokes, as perhaps in the 1950 paper, were his serious defence from the ineffable irony of the world. After his arrest he wrote :
Turing believes machines think
and shortly before he died, he wrote postcards headed 'Messages from the Unseen World' — explicitly referring to Eddington, some with schoolboy allusions, and a hymn-like relativistic verse :
Hyperboloids of wondrous Light
Had an earlier agenda, the nature of spirit, resurfaced? Would he have reconsidered his philosophy, bringing quantum mechanical substrate into the discrete-state picture? In my biography I suggested that the emotional intensity and gross interference of this period might have undermined his certainty in the mechanical model of mind, but offered no evidence, for there is none. His last publication  was in Penguin Science News, written like a modern Scientific American article, and entitled Solvable and unsolvable problems. Written vividly but from the perspective of a pure mathematician, its final words concerned the interpretation of unsolvable problems, such as the halting problem for Turing machines. They were lame: 'These... may be regarded as going some way towards a demonstration, within mathematics itself, of the inadequacy of "reason" unsupported by common sense.' No clues are offered here.
Alan Turing's philosophy might appear the ultimate in reductionism, in its atomizing of mental process, its scorn for the non-material. Yet it depends upon a synthesis of vision running against the grain of an intellectual world split into many verbal or mathematical or technical specialisms. He preached the computable, but never lost natural wonder; the law killed and the spirit gave life.
A. M. Turing. 'The chemical basis of morphogenesis.' Phil. Trans. R. Soc. London B 237 (1952) pp. 37-72.
© 1997, Andrew Hodges.