deodands

Turing's progress post 1951

As Turing's theory progresses from reaction-diffusion to lattices and then to parastichy transitions, the surviving documents becomes sparser and less coherent, so assessments of his progress between 1951 and his death on June 7th 1954 become correspondingly more speculative. But speculation is what this entry attempts.

There is no concrete archival support for that claim in 1951 to explain fir cone patterns. A possible explanation is that Turing saw clearly that he had a spot generation mechanism and assumed, incorrectly, that this would be sufficient to generate Fibonacci lattices. There is a quote from a Ferranti engineer, dated before the summer of 1953, that

...with a random starting disturbance the final configuration was displayed on the MkI's monitors. It was always of interest to those of us watching to see what Fibonacci configuration would result. (p65 of Bennett (1996))

Turing was certainly producing spotty patterns by 1953. But it seems more plausible that what the engineer saw was similar to those than explicitly Fibonacci patterns. Support for this comes from a letter of Turing's of May 1953.

None of the fragmentary material can be reliably dated; some of the probably relevant computer printouts are dated May 24th, but give no year. In addition several years of computing would have generated rather a lot of output, so the fact that all we have is a few sheets, and those not obviously archival records, hints that what we do have is the end of a series of ephemeral documents. So a speculation would date the latest analysis to within weeks of Turing's death. It is then likely that this was what Gandy was referring to when he wrote of hearing of Turing's individual and unmethodical computatiions.

In considering Turing's state of mind at his suicide, Hodges wrote that

Possibly the morphogenetic work had turned out plodding and laborious. It was three years since he had claimed he could account for the fir cone pattern and he had still not achieved it when he died. (p492 of Hodges)

The morphogenetic work was not, I think, plodding: the bifurcation tree of parastichy numbers was new and, as discussed below, on the right lines. The computer simulations, even for the author of Computable Numbers (or more relevantly of the first programming manual), must though have been laborious and frustratingly slow to get right. Although it was apparently producing at least some meaningful output, Turing might have become the first to appreciate the sheer craft needed by computational biologists. Probably Turing had not, indeed, accounted for Fibonacci phyllotaxis when he died, but he had got much further, and in the right direction, than he was in 1951.