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(Blake’s question) marks one of the most intriguing—and most in-your-face unavoidable—
puzzles of biology. Only the nature of life itself is deeper.
Turing’s paper on the chemical basis of morphogenesis contained what, in conversations
with friends, he called ‘my mathematical theory of embryology’. It concerned questions that he
had been pondering ever since his youth—for instance, taking a rest from his wartime work
on the Germans’ Enigma code, when he lay on the grass of Bletchley Park picking daisies and
carefully counting their petals.
How daisy petals might be relevant to mathematics isn’t immediately obvious. And what
about tigers or lambs? (Remember Blake’s question.) Are they relevant too? Having written the
first programming manual for the Manchester ‘Baby’ computer in 1950, why did Turing irritate
his Manchester colleagues by neglecting his duties in the computing laboratory there in favour
of this other interest? And why did he look forward eagerly to the delivery of the first Ferranti
computer in February 1951, planning to use it immediately for calculations to be reported in
his about-to-be-submitted biological manuscript?
Well, read on.
Turing’s mathematical theory of embryology
Turing was nothing if not a mathematician—and he knew it. His embryology paper, published
in the biological strand (Series B) of the Royal Society’s Philosophical Transactions, was a pre-
cursor of certain aspects of what is now called complexity theory. It contained specific warnings
for its biologist readers about the difficulty of the mathematics involved. It gave directions about
which sections to read or omit, depending on one’s level of mathematical literacy. It would be
fully understood, he said, only by those ‘definitely trained as mathematicians’.^6 In fact, even
what he termed ‘only a very moderate understanding of mathematics’ was doubtless too much
to expect from many of his readers.
Nonetheless, the general message was clear enough. It was also intoxicating. For the paper
showed how biological structure or form could arise out of a homogeneous origin—in particu-
lar, how cell differentiation and (eventually) various organs could emerge from the unstruc-
tured protoplasm of the fertilized ovum. (As his Abstract put it: how ‘the genes of a zygote may
determine the anatomical structure of the resulting organism’.^7 )
As we saw earlier, the origin of biological form (morphogenesis) was still hugely mysterious
at that time. Hard-headed biologists spoke of vaguely conceptualized ‘morphogenetic fields’
governing cell differentiation, controlled by hypothetical, presumably biochemical, forces
called ‘organizers’. But just what these were, and just how they might work, was an enigma much
harder to crack than the Enigma code.
In other words, embryologists’ talk of organizers and morphogenetic fields was largely empty.
It certainly didn’t answer the question posed forty years before in a children’s book which (so he
told his mother) had first awakened Turing to science:^8
The body is a machine. It is a vastly complex machine, many, many times more complicated than
any machine ever made with hands; but still after all a machine . . . [But if we ask how its] living
bricks find out when and where to grow fast, and when and where to grow slowly, and when and
where not to grow at all [we must admit that this is something which] nobody has yet made the
smallest beginning at finding out.