Invited contribution to Cybertalk Magazine, September 2013
In Cybertalk Three, pages 48-9.
Alan Turing Commemorative Year Centenary Edition
Published by: SBL

Extending Turing's Pattern:
   From Morphogenesis to Meta-morphogenesis

Aaron Sloman
School of Computer Science, University of Birmingham, UK

(Revised: 28 Aug 2013)
Turing's 1952 paper on chemical morphogenesis can be compared with his earlier work
on Turing machines (TMs). Both demonstrate that some very simple local interactions
can produce strikingly varied and complex large scale results. In a TM, many small,
discrete changes in contents of a linear tape, with an engine controlled by very
simple rules, can transform initial linear patterns, representing many different
problems, into patterns representing solutions. This requires two important features:
representational power: the ability of the patterns used to support a wide
variety of rich and complex problems and solutions, for a fixed interpreter of
the patterns, and inference power: the ability of the engine to transform those
patterns from representations of problems to representations of solutions.
The 20th century saw major advances in digital electronic machines with those
capabilities. An electronic computer can be understood as a TM with a finite, very
fast, tape, nowadays often linked in networks and connected with various physical
interfaces between the memory (tape) and things in the environment, allowing them not
only to solve problems but also to produce useful behaviours by monitoring and
controlling external devices.
Turing's 1952 paper showed, among other things, that in chemical morphogenesis local
processes, in which chemicals diffuse through a growing structure and interact when
they meet, can produce complex and varied global patterns, like dots, stripes,
blotches, spirals, and others. Patterns on organisms can have rich biological
functions, including camouflage, mate selection, attraction of pollinators, deception
of predators, and probably many others. (His paper discussed far more than this.)
His 1936 computing machine was originally intended to replicate analogues of processes
that occur in familiar human mathematical reasoning, whereas his chemical theory was
intended to account for some familiar biological phenomena. In the first case all the
structures and operations are discrete, whereas in the second case, continuous
diffusion and changes of concentration play a role. However, molecular changes are
discrete: there are not infinitely many intermediate cases between any two molecules
(e.g. between O2 and H2O) as there are between two rational numbers, such as
three fifths and seven eighths.
In 2011, reading the morphogenesis paper made me wonder whether, if Turing had lived,
he might have attempted an even bigger challenge, namely showing how local interactions
between molecules in a lifeless world might eventually produce the huge variety of
living organisms now found on our planet: a far greater challenge than explaining the
development of structure in a developing embryo, or the production of a proof in a
symbol-manipulating engine.
The Darwin-Wallace theory of natural selection shows that, in principle, diverse and
complex organisms, and ecosystems containing them, could emerge from much simpler
systems by many small steps, provided that the mechanisms operated on by selection
had the power to accommodate that diversity and complexity. But that left open the
question: what sorts of underlying machinery could do that?
Computational experiments on artificial evolution suggested that in principle modern
computers could replicate evolution of all living phenomena. However, combining and
extending Turing's ideas about computation and morphogenesis may reveal previously
unnoticed potential in the mixture of continuity and discreteness found in chemical
information processing but unavailable in discrete symbol manipulators.
A possible clue: transformations from one molecular structure to another often
require rotation, and a complex 3D molecule can be rotated without losing any
information, whereas rotation of digitised images or models will lose information
except for special cases (e.g. 90 degree array rotation). Non-rigid discrete
transformations e.g. forming a spiral, are also problematic.
A mixture of discrete and continuous mechanisms may turn out to be crucial for
providing new, deep and general explanations of processes in which a dust cloud
condenses to form a planet that several billion years later includes microbes,
monkeys, music, mathematics, manslaughter, metropolitan cultures and other marvels.
Would Turing have contributed to developing that idea? Thousands of researchers have
investigated trajectories in the evolutionary history of the planet, but they have
tended, with a few exceptions, to leave out one of the most important types of
change, partly because they are invisible and hard to study, namely changes in
information processing, including perception, learning, decision-making,
problem-solving and control of many internal functions and external actions.
There is masses of evidence about the diversity of physical forms and physiological
that evolution has produced. Our knowledge of that diversity increases
with developments in technology for inspecting and experimenting on life at very
small scales, and technology for accessing more varied environments, such as deep sea
It is possible to acquire vast amounts of information about the diversity of behaviours
of organisms, by direct observation of living systems, using inferences from fossil
records, analysing requirements posed by environmental changes, and using laboratory
There has also been rapid expansion in our knowledge of the chemical mechanisms
and structures
underpinning biological evolution and individual development,
including chemically implemented genetic mechanisms that, together with the
environment of growing organisms, control the diverse developmental trajectories of
organisms as different as bacteria, earthworms, giant fungi, daisies, giant redwood
trees, squirrels, bats, crows, elephants and whales.
To that rich and growing store of knowledge about long past and very recent changes
in structure, in behaviours, and in chemical mechanisms, Turing might have
contributed new theories about the changes in information processing,
combining and extending the kinds of thinking displayed in his work on morphogenesis
and on Turing machines and computability.
There is a deep, rich, and largely unknown, repertoire of forms of information-processing
required for the types of reproduction, development, control of behaviour, learning,
perception, reasoning, communicating, forms of social interaction, and, in the case
of humans, construction of powerful new explanatory theories and technologies and
works of art. Research in psychology, linguistics, psychiatry, education, and other
fields has enriched the set of facts to be explained by theories about biological
information processing, but only in very complex systems most of whose details are
inaccessible, and mostly cannot be inferred from their effects. What we've learnt
from neuroscience leaves many explanatory gaps between physical mechanisms and
information-processing, e.g. musical composition or mathematical reasoning.
Forms of information processing required in microbes, plants and animals of various
kinds differ enormously. Sources of diversity include: sensory-motor morphologies
restricting what information is available and what actions can be controlled,
environments constraining what the information needs to refer to and diverse
requirements for cooperation and competition using different forms of communication.
Those variations in information contents and types of information processing (e.g.
acquiring, analysing, interpreting, deriving, storing, matching, communicating, and
using information) suggest the need for variations in information processing
mechanisms over evolutionary times, and in some cases during individual development
-- e.g. changes in information processing capabilities between a caterpillar and the
moth it turns into, and changes between a new-born baby and the physics professor
some years later. Besides mechanisms for producing new forms of information-processing
there were also new mechanisms for producing those mechanisms, e.g. mate-selection
and cultural evolution.
Researchers interested in what Turing might have done are invited to join the
Meta-morphogenesis project: a multi-pronged attack on the problem of identifying
unobvious forms of biological information-processing, such as explaining how the same
genome can enable learning of thousands of possible languages, but not all possible
languages, and explaining how our ancestors acquired the ability to make mathematical
discoveries before there were mathematics teachers.
We can try to fill gaps in our knowledge about current systems by creating plausible,
and, wherever possible, observationally tested, hypotheses about intermediate states
between the earliest, simplest forms of life and the ones we are now trying to
For example, microbes can detect the presence of chemicals in contact with their
membrane and let some enter, others not. More complex mechanisms may use internal
state sensors and admit different substances at different times, according to sensed
needs. Still more complex organisms may not only sense external stimulation and react
immediately, but sense changes over time, and, use the direction of change to
influence motion: e.g. if the intensity of something harmful is increasing make a
move. Later the moves might be controlled so as to follow trajectories of increasing
or decreasing density. Even more complex changes in the mechanisms are required to
allow organisms to acquire, store and use information about the spatial layout of
important parts of the environment, near and far, or information about things that
process information, e.g. other animals and themselves, or information about states
of the environment that can be observed only from close up. Further complexity comes
from abilities to take account of multiple needs. All of those changes require
changes in information processing, often supported by new physical/chemical
Researchers wishing to join this very ambitious Turing-inspired project, can start
by analysing what is already known about evolutionary changes and individual
development, in order to come up with good theories about changes in the mechanisms
The following web pages (still under development) present many more examples of
changes in information processing during evolution, and in development of young humans:


Turing, A. M. (1936).
        On computable numbers, with an application to the Entscheidungsproblem.
        Proc. London Math. Soc., 42(2), 230-265.

Turing, A. M. (1952).
        The Chemical Basis Of Morphogenesis. Phil. Trans. R. Soc. London B 237, 37-72.

Sloman, A (2013).
        Virtual Machinery and Evolution of Mind (Part 3) Meta-Morphogenesis:
          Evolution of Information-Processing Machinery.
        In Alan Turing - His Work and Impact, Eds. S. B. Cooper and J. van Leeuwen,
        Elsevier, Amsterdam, pp. 849-856, . .