BODEN | 371
Buried treasure
In 1940, when England was expecting a Nazi invasion, Turing buried some silver bars in
the grounds of Bletchley Park—or perhaps in Shenley Brook End, the village where he was
lodging—but despite repeated searches, many aided by metal-detectors, no-one has managed
to find them. Twelve years later he inspired another determined treasure hunt, for after his
tragically early death his friends found in his rooms many pages of handwritten notes com-
prised of largely unintelligible mathematical symbols.
They also found drafts of (and extensive notes for) three papers on ‘The morphogen theory
of phyllotaxis’—mentioned in his Royal Society publication.^38 These explained, among other
things, the prevalence of Fibonacci numbers in plant anatomy—the numbers of daisy petals for
example (see the Introduction). Versions partly corrected or prepared by his student Bernard
Richards, with notes by his close friend Robin Gandy, can be read in the Collected Works.^39
(Richards had been asked by Turing to solve the equations for spherical symmetry; his solu-
tions nearly matched various species of Radiolaria, but Turing died before seeing them: see
Chapter 35.^40 ) In short, these drafts were intelligible, at least to Turing’s collaborators.
The copious mathematical notes were a different matter. Gandy, no mean mathematician
himself, couldn’t make head or tail of them. The relevant folder in the Turing Archive bears
a manuscript note by Gandy, saying: ‘It will be difficult, in some places impossible, to know
exactly what the fragments are (exactly) about’.^41
There were four sorts of difficulty. The first was Turing’s often-illegible handwriting: this had
always been a problem—one of his schoolteachers had described it as ‘the worst I have ever
s e e n ’.^42 Another was his use of idiosyncratic abbreviations, many of which presumably referred
to equally idiosyncratic mathematical concepts. The third and fourth were identified by Gandy
as his unorthodox (‘so individual’) ways of doing mathematics and—more surprising—perhaps
even his ‘unmethodical’ thinking.^43 Faced with these obstacles, Gandy was not alone in being
unable to decipher Turing’s notes. They are still not fully understood.
It is inconceivable that there are no further mathematical insights in there of potential
relevance to theoretical biology; possibly they concerned the problem that Turing admitted he
had not solved—namely, the origin of new pattern not from homogeneity but from pre-existing
patterns. In other words, those handwritten pages are a treasure trove. But whereas the ‘trove’
(the finding) was all too easy, assessing the value of the treasure may forever prove too difficult.
In brief: yet another enigma.
The enigmatic embryo, however, has been demystified. Many unanswered questions remain,
to be sure. But thanks to Turing, this awe-inspiring biological phenomenon is significantly less
occult than it used to be. Blake might not be pleased about that—but perhaps ‘every schoolboy’
eventually will be.