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each of the little tips (calcium peaks) would have to behave (to soften, bulge, and grow) like the
main tip, but on a smaller scale: in principle, that is possible, but it would need the machine to
draw even more, and even tinier, lines. So it would be very costly computationally, requiring
the whole program to be repeated on a finer scale (to generate each lateral branch), and many
times over (to generate many laterals).
why such a long wait?
The examples given so far should suffice to show that biology today owes a significant intel-
lectual debt to the mathematician who cracked the Enigma code. What has not been explained
is why the world had to wait for so many years before this debt was acknowledged.
Even now, it hasn’t been acknowledged fully. As we noted at the beginning of this chapter,
Turing’s mathematical biology is less familiar to the general public than his ideas about com-
puter science and AI. And it is not only the ‘schoolboys’ who are unaware of it—indeed, on
mentioning his paper enthusiastically to various friends and colleagues on many occasions
between the mid-1950s (when I first read it) and 1990, I discovered to my amazement that most
of them had as little knowledge of its existence (not to mention its detail) as I had of Atahualpa.
Even now, in the 21st century, that is still often true.
Nevertheless, as we have seen, many people are at long last waking up to his ideas on mor-
phogenesis. But why only now? Why not immediately? After all, it’s not as though his paper
lay unread in an obscure journal hidden from public view, like Gregor Mendel’s little gem on
genetics.
One reason for this was pure bad luck—or bad timing. Only a year after Turing’s paper
appeared, Francis Crick and James Watson sent their epochal letter about the double helix to
Nature—and only a few years after that, they cracked the genetic code. Their efforts in crypt-
ography were at least as influential as Turing’s, for they resulted in an immediate switch of
interest on the part of biologists (including developmentalists) from whole-organism concerns
to molecular biology.
To be sure, questions about biochemistry were pushed to the fore, and Turing’s paper was
a theoretical exercise in biochemistry. But the emphasis in the new discipline of molecular
biology was more on the actual identity of the molecules (morphogens) than on their actions
and interactions. As for questions about biological form, whether of body or cell, these were
relegated to the background.^34
But there were also more intellectually substantive reasons for the neglect of Turing’s paper.
We have seen that D’Arcy Thompson’s mathematical approach was less influential than it might
have been, because he lacked the concepts and the machines needed to explore its implications
effectively. Partly thanks to his own earlier work, Turing possessed some of the concepts, and
even a machine: the world’s first modern-style digital computer. But that machine was unavoid-
ably primitive.
Turing used the Manchester University computer to calculate the successive steps of interac-
tion between the morphogens, but this was a time-consuming and tedious matter. Moreover, in
the absence of computer graphics, the computer’s numerical results had to be laboriously con-
verted by Turing by hand to a more easily intelligible visual representation. Turing remarked
that much better machines would be needed to follow up his ideas.