364 | 33 PIONEER Of ARTIfICIAl lIfE
was that he couldn’t give a mathematical account of the origin of novel structure from some
prior structure, and that was a significant omission. For, as he pointed out, most examples of
structural development in biology involve the emergence of new forms (new patterns) from
pre-existing ones. (Think, for instance, of the appearance of fingers and then fingernails on
what were initially merely limb-buds.)
There was no notion, at that time, of the switching on and off of individual genes by other
(‘regulatory’) genes.^14 Nevertheless, Turing suggested that a succession of different chemicals
(morphogens) is brought into play as development proceeds. To understand the process, how-
ever, one would need to understand not only the simple diffusion reactions between morpho-
gens but also how (later) morphogens can react with pre-existing structures. This he couldn’t
do—at least not yet, as we shall see.
This imaginative paper, despite its many pages of challenging (and for many people, unfath-
omable) mathematics, was read with excitement by embryologists. It proved beyond doubt
what D’Arcy Thompson had suggested: that self-organization of a biologically plausible kind
could in principle result from relatively simple chemical processes describable by mathem-
atics. It intimated just which immortal hand had framed the tiger’s magnificent stripes and
symmetry—namely, the laws of physics, understood as reaction–diffusion equations. And it
was sufficiently general to cover lambs as well as tigers. (Blake’s ‘Lamb’, of course, had symbol-
ized Jesus: even Turing’s mathematics couldn’t cover that.)
Moreover, it suggested an exciting programme of biological research. For many years,
however, that excitement was doomed to disappointment. It was almost forty years before the
research programme implied by Turing’s ideas was taken up.
Turing and modern biology
Turing’s influence on modern biology is evident in three largely overlapping areas, each of
which covers a huge range of fascinating questions. The first concerns self-organization in
general—including brain development, for instance, briefly mentioned earlier. The second
is the computer-based field of artificial life (A-Life). The third is an unorthodox approach in
experimental biology known as ‘structuralism’.
A-Life is a form of mathematical biology.^15 It employs computational and dynamical ideas,
and computer models of various kinds, to understand living processes in general (including
development and evolution), and specific biological phenomena too, such as flocking, hexapod
locomotion, or the location of mates by hoverflies and crickets. Many A-Life scientists even
hope to understand the nature of ‘life as it could be’, not merely of ‘life as it is’.^16
That hope is reminiscent of D’Arcy Thompson’s goal in biology, which encompassed all pos-
sible organisms:^17
[I] have tried in comparatively simple cases to use mathematical methods and mathematical
terminology to describe and define the forms of organisms . . . [My] study of organic form . . . is
but a portion of that wider Science of Form which deals . . . with forms which are theoretically
imaginable.
Moreover, it is clear that D’Arcy Thompson would have become involved in A-Life had he lived
longer (he died in 1948, the year in which the Manchester Baby became operational). He him-
self had said:^18