School of Computer Science THE UNIVERSITY OF BIRMINGHAM Ghost Machine

AISB17 Symposium on Computing and Philosophy
Bath University April 2017

Compare Jiri earlier:
"Systems with self-improving theories"

(DRAFT: Liable to change)

Aaron Sloman
School of Computer Science, University of Birmingham

Installed: 18 Apr 2017
Last updated:
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A PDF version may be added later.

A partial index of discussion notes is in

Progress report on the Turing-inspired
Meta-Morphogenesis project


The Turing-inspired Meta-Morphogenesis project was proposed in the final
commentary in Alan Turing - His Work and Impact a collection of papers by and
about Turing published on the occasion of his centenary[6]. The project was also
summarised in a keynote talk at AISB2012, suggesting that an attempt to fill
gaps in our knowledge concerning evolution of biological information processing
may give clues regarding forms of computation in animal brains that have not yet
been re-invented by AI researchers, and this may account for some of the
enormous gaps between current AI and animal intelligence, including gaps between
ancient mathematicians, such as Euclid and current AI systems. Evolution of
information processing capabilities and mechanisms is much harder to study than
evolution of physical forms and physical behaviours, e.g. because fossil records
can provide only very indirect evidence regarding information processing in
ancient organisms. Moreover it is very hard to study all the internal details of
information processing in current organisms. Some of the reasons will be
familiar to programmers who have struggled to develop debugging aids for very
complex multi-component AI virtual machines. The paper presents challenges both
for the theory of evolution and for AI researchers aiming to replicate natural
intelligence, including mathematical intelligence. This is a partial progress
report on attempts to meet the challenges by studying evolution of biological
information processing, including evolved construction-kits.2

This is a brief progress report on the Meta-Morphogenesis (M-M)
project -- also  called The Self-Informing Universe project.

It extends ideas presented at AISB2012 (Turing Centenary).

The M-M project was based partly on my interest in defending Kant's
philosophy of mathematics, and partly on a conjectured answer to the
question: 'What would Alan Turing have worked on if he had not died two
years after publication of his 1952 paper on Chemistry and Morphogenesis

    This is now the most cited of his publications. though largely
    ignored by philosophers, cognitive scientists and AI researchers.

I suspect that if Turing had lived several decades longer, he would have
tried to understand forms of information processing needed to control
behaviour of increasingly complex organisms.

Protoplanetary disk

Controlled production of complex behaving structures needs increasingly
sophisticated information processing,

-- both in the processes of growth and development

and for

-- control of behaviour of complex organisms reacting to their environment,
   including other organisms.

In simple cases control uses presence or absence of sensed matter to turn
things on or off or sensed scalar values to specify and modify other values
(e.g. chemotaxis).

    Many artificial control systems are specified using collections of
    differential equations relating such measures.

    One of several influential attempts to generalise these ideas is the
    'Perceptual Control Theory (PCT)' of William T Powers.

But use of numerical/scalar information is not general enough.

It doesn't suffice for linguistic (e.g. grammatical structure) or for
reasoning about topological relationships, processes of structural change.

Turing's Morphogenesis paper also focused on scalar (numerical) changes, but as
a mathematician, a logician and a pioneer of modern computer science he was well
aware that the space of information-using control mechanisms is not restricted
to numerical control systems.

    For example a turing machine's operation involves changing linear
    sequences of distinct structures, not measures.

In the last half century human engineers have discovered, designed and built
additional increasingly complex and varied forms of control in interacting
physical and virtual machines.

That includes control based on

    grammars, parsers, planners, reasoners, rule interpreters, problem
    solvers and many forms of automated discovery and learning.

Long before that, biological evolution produced and used increasingly complex
and varied forms of information in construction, modification and control of
increasingly complex and varied behaving mechanisms.


    If Turing had lived several decades longer, he might have produced
    new theories about many intermediate forms of information in living
    systems and intermediate mechanisms for information-processing:
    intermediate between the very simplest forms and the most
    sophisticated current forms of life.

This would fill gaps in standard versions of the theory of natural selection:

    Namely, the theory does not explain what makes possible the many
    forms of life on this planet, and all the mechanisms they use,
    including the forms that might have evolved in the past or may
    evolve in the future.

    It merely assumes such possibilities and explains how a subset of
    realised possibilities persist and consequences that follow.

    For example, the noted biologist Graham Bell wrote in 'Living complexity
    cannot be explained except through selection and does not require any
    other category of explanation whatsoever'.

Only a few defenders of Darwinian evolution seem to have noticed the need to

    (a) what mechanisms make possible all the options between which
    choices are made, and

    (b) how what is possible changes, and depends on previously
    realised possibilities.


A possible defence of Darwinian evolution would enrich it
to include investigation of

    (a) the Fundamental Construction Kit (FCK) provided by physics and
    chemistry before life existed,

    (b) the many and varied 'Derived construction kits' (DCKs) produced
    by combinations of natural selection and other processes, including
    asteroid impacts, tides, changing seasons, volcanic eruptions and
    plate tectonics.



As new, more complicated, life forms evolved, with increasingly
complex bodies, increasingly complex changing needs, increasingly
broad behavioural repertoires, and richer branching possible actions
and futures to consider, their information processing needs and
opportunities also became more complex.

Somehow the available construction kits also diversified, in ways that

    construction not only of new  biological materials and body
    mechanisms, supporting new more complex and varied behaviours

    but also

    new more sophisticated information-processing mechanisms,
    enabling organisms, either alone or in collaboration, to deal with
    increasingly complex challenges and opportunities.


Evolution made many deep discoveries made by evolution including designs
for DCKs that make new forms of information processing possible,

These have important roles in animal intelligence, including perception,
conceptual development, motivation, planning, problem solving

also including topological reasoning about effects and limitations

possible continuous rearrangements of material objects: much harder than
planning moves in a discrete space.

Different species, with different needs, habitats and behaviours, use
information about different topological and geometrical relationships,

-- birds that build different sorts of nests,

-- carnivores that tear open their prey in order to feed,

-- human toddlers playing with (or sucking) body-parts, toys, etc.

Later on, in a smaller subset of species (perhaps only one species?) new
meta-cognitive abilities gradually allowed previous discoveries to be
noticed, reflected on, communicated, challenged, defended and deployed in
new contexts.

Such 'argumentative' interactions may have been important precursors for
chains of reasoning, including the proofs in Euclid's Elements.


This is part of an attempt to explain how it became possible for  evolution
to produce mathematical reasoners.

New deep theories, explanations, and working models t should emerge from
investigation of preconditions, biological and technological consequences,
limitations, variations, and supporting mechanisms for biological
 construction kits  of many kinds.

For example, biologists have pointed out that specialised construction
kits, sometimes called 'toolkits', supporting plant development were
produced by evolution, making upright plants possible on land

    (some of which were later found useful for many purposes by humans,
    e.g. ship-builders).

Specialised construction kits were also needed by vertebrates and others by
various classes of invertebrate forms of life.


Construction kits for biological information processing have received less

    One of the early exceptions was Schrdinger's little 1944 book
    What is life?

More general construction kits that are tailorable with extra
information for new applications can arise from discoveries of
parametrisable sub-spaces in the space of possible mechanisms

    e.g. common forms with different sizes, or different ratios of
    sizes, of body parts, different rates of growth of certain body
    parts, different shapes or sizes of feeding apparatus, different
    body coverings, etc.

Using a previously evolved construction kit with new parameters (specified
either in the genome, or by some aspect of the environment during
development) can produce new variants of organisms in a fraction of the
time it would take to evolve that type from the earliest life forms.

    Similar advantages have been claimed for the use of so-called
    Genetic Programming (GP) using evolved, structured, parametrised
    abstractions that can be re-deployed in different contexts, in
    contrast with Genetic Algorithms (GAs) that use randomly varied
    flat strings of bits or other basic units.

Evolution sometimes produces specifications for two or more different
designs for different stages of the same organism, e.g. one that feeds for
a while, and then produces a cocoon in which materials are transformed into
a chemical soup from which a new very different adult form (e.g. butterfly,
moth, or dragon fly) emerges, able to travel much greater distances than
the larval form to find a mate or lay eggs.

These species use mathematical commonality at a much lower level (common
molecular structures) than the structural and functional designs of larva
and adult, in contrast with the majority of organisms, which retain a
fixed, or gradually changing, structure while they grow after hatching or
being born, but not fixed sizes or size-ratios of parts, forces required,

Mathematical discoveries were implicit in evolved designs that support
parametrisable variable functionalities, such as evolution's discovery of
homeostatic control mechanisms that use negative feedback control, billions
of years before the Watt centrifugal governor was used to control speed of
steam engines.13 Of course, most instances of such designs would no more
have any awareness of the mathematical principles being used than a
Watt-governor, or a fan-tail windmill (with a small wind-driven wheel
turning the big wheel to face the wind) does.

In both cases a part of the mechanism acquires information about something
(e.g. whether speed is too high or too low, or the direction of maximum
wind strength) while another part does most of the work, e.g. transporting
energy obtained from heat or wind power to a new point of application.

Such transitions and decompositions in designs could lead to distinct
portions of genetic material concerned with separate control functions,
e.g. controlling individual development and controlling adult use of
products of development, both encoded in genetic material shared across

Very much later, some meta-cognitive products of evolution allowed
individuals (humans, or precursors) to attend to their own
information-processing (essential for debugging), thereby 'rediscovering'
the structures and processes, allowing them to be organised and
communicated -- in what we now call mathematical theories, going back to
Euclid and his predecessors (about whose achievements there are still many
unanswered questions).

If all of this is correct then the physical universe, especially the
quantum mechanical aspects of chemistry discussed by Schrdinger provided
not only

    a construction kit for genetic material implicitly specifying
    design features of individual organisms,

but also

    a 'Fundamental' construction kit (FCK) that can produce a wide
    variety of 'derived' construction kits (DCKs)

some used in construction of individual organisms, others in construction
of new, more complex DCKs, making new types of organism possible.

Moreover, as Schrdinger and others pointed out, constructionkits that are
essential for micro-organisms developing in one part of the planet can
indirectly contribute to construction and maintenance processes in totally
different organisms in other locations, via food chains

    most species cannot synthesise the complex chemicals they need
    directly from freely available atoms or subatomic materials. So
    effects of DCKs can be very indirect.

Functional relationships between the smallest life forms and the largest
will be composed of many sub-relations.

Such dependency relations apply not only to mechanisms for construction and
empowerment of major physical parts of organisms, but also to mechanisms
for building information-processors, including brains, nervous systems, and
chemical information processors of many sorts.

    (E.g. digestion uses informed disassembly of complex structures to
    find valuable parts to be transported and used or stored

So far, in answer to Bell, I have tried to describe the need for
evolutionary selection mechanisms to be supported by enabling mechanisms.

Others have noticed the problem denied by Bell, e.g. Kirschner and Gerhart
added some important biological details to the theory of evolved
construction-kits, though not (as far as I can tell) the ideas (e.g. about
abstraction and parametrisation) presented in this paper.

Work by Ganti and Kauffman is also relevant.

-- and probably others unknown to me!


As organisms grow in size, weight and strength, the forces and torques
required at joints and at contact points with other objects change.

So the genome needs to use the same design with changing forces depending
on tasks. Special cases include forces needed to move and manipulate the
torso, limbs, gaze direction, chewed objects, etc. 'Hard-wiring' of useful
evolved control functions with mathematical properties can be avoided by
using designs that allow changeable parameters -- a strategy frequently
used by human programmers.

Such parametrisation can both allow for changes in size and shape of the
organism as it develops, and for many accidentally discovered biologically
useful abstractions that can be parametrised in such designs -- e.g.
allowing the same mechanism to be used for control of muscular forces at
different stages of development, with changing weights, sizes, moments of
inertia, etc.

Even more spectacular generalisation is achievable by re-use of evolved

-- not only across developmental stages of individuals within a species,

-- but also across different species that share underlying physical
parametrised design patterns,

-- with details that vary between species sharing the patterns

(as in vertebrates, or the more specialised variations among primates, or
among birds, or fish species).

Such shared design patterns across species can result either from species
having common ancestry or from convergent evolution 'driven' by common
features of the environment,

e.g. re-invention of visual processing mechanisms might be driven by
aspects of spatial structures and processes common to all locations on the
planet, despite the huge diversity of contents.

Such use of abstraction to achieve powerful re-usable design features
across different application domains is familiar to engineers, including
computer systems engineers.

'Design sharing' explains why the tree of evolution has many branch points,
instead of everything having to evolve from one common root node.

Symbiosis also allows combination of separately evolved features.

Similar 'structure-sharing' often produces enormous reductions
in search-spaces in AI systems.

It is also common in mathematics: most proofs build on a previously agreed
framework of concepts, formalisms, axioms, rules, and previously proved
theorems. They don't all start from some fundamental shared axioms.

If re-usable abstractions can be encoded in suitable formalisms
(with different application-specific parameters provided in different
design contexts), they can enormously speed up evolution of diverse
designs for functioning organisms.

This is partly analogous to the use of memo-functions in software design
(i.e. functions that store computed values so that they don't have to be
re-computed whenever required, speeding up computations enormously, e.g. in
the Fibonacci function).

Another type of re-use occurs in (unfortunately named) 'object-oriented'
programming paradigms that use hierarchies of powerful re-usable design
abstractions, that can be instantiated differently in different
combinations, to meet different sets of constraints in different
environments, without requiring each such solution to be coded from
scratch: 'parametric polymorphism' with multiple inheritance.

This is an important aspect of many biological mechanisms. For example,
there is enormous variation in what information perceptual mechanisms
acquire and how the information is processed, encoded, stored, used, and in
some cases communicated. But abstract commonalities of function and
mechanism (e.g. use of wings) can be combined with species specific
constraints (parameters).

Parametric polymorphism makes the concept of consciousness
difficult to analyse: there are many variants depending on what sort
of thing is conscious, what it is conscious of, what information is
acquired, what mechanisms are used, how the information contents
are encoded, how they are accessed, how they are used, etc.


Mathematical consciousness, still missing from AI, requires awareness of
possibilities and impossibilities not restricted to particular objects,
places or times -- as Kant pointed out.

Mechanisms and functions with mathematical aspects are also shared across
groups of species, such as phototropism in plants, use of two eyes with
lenses focused on a retina in many vertebrates, a subset of which evolved
mechanisms using binocular disparity for 3-D perception.

That's one of many implicit mathematical discoveries in evolved designs for
spatio-temporal perceptual, control and reasoning mechanisms, using the
fact that many forms of animal perception and action occur in 3D space plus
time, a fact that must have helped to drive evolution of mechanisms for
representing and reasoning about 2-D and 3-D structures and processes, as
in Euclidean geometry.

In a search for effective designs, enormous advantages come from (explicit
or implicit) discovery and use of mathematical abstractions that are
applicable across different designs or different instances of one design.

For example a common type of grammar (e.g. a phrase structure grammar)
allows many different languages to be implemented including sentence
generators and sentence analysers re-using the same program code with
different grammatical rules.

Evolution seems to have discovered something like this.

Likewise, a common design framework for flying animals may allow tradeoffs
between stability and maneouvreability to be used to adapt to different
environmental opportunities and challenges.

These are mathematical discoveries implicitly used by evolution.

Evolution's ability to use these discoveries depends in part on the
continual evolution of new DCKs providing materials, tools, and
principles that can be used in solving many design and manufacture

In recently evolved species, individuals e.g. humans and
other intelligent animals, are able to replicate some of evolution's
mathematical discoveries and make practical use of them in their own
intentions, plans and design decisions, far more quickly than natural
selection could.

Only (adult) humans seem to be aware of doing this.

Re-usable inherited abstractions allow different collections of
members of one species,
    e.g. humans living in deserts, in jungles, on mountain ranges, in
    arctic regions, etc.,

to acquire expertise suited to their particular environments in a much
shorter time than evolution would have required to produce the same variety
of packaged competences 'bottom up'.

This flexibility also allows particular groups to adapt to major changes in
a much shorter time than adaptation by natural selection would have
required. This requires some later developments in individuals to be
delayed until uses of earlier developments have provided enough information
about environmental features to influence the ways in which later
developments occur, as explained later.

This process is substantially enhanced by evolution of metacognitive
information processing mechanisms that allow individuals to reflect on
their own processes of perception, learning, reasoning, problem-solving,
etc. and (to some extent) modify them to meet new conditions.

Later, more sophisticated products of
evolution develop metameta-cognitive information processing
sub-architectures that enable them to notice their own adaptive processes,
and to reflect on and discuss what was going on, and in some cases
collaboratively improve the processes,

e.g. through explicit teaching

    at first in a limited social/cultural context,
    after which the activity was able to spread

    using previously evolved learning mechanisms.

As far as I know only humans have achieved that, though some other species
apparently have simpler variants.

These conjectures need far more research!

Human AI designs for intelligent machines created so far seem to have far
fewer layers of abstraction, and are far more primitive, than the re-usable
designs produced by evolution. Studying the differences is a major sub-task
facing the M-M project (and AI).

This requires a deep understanding of what needs to be explained.


Just as the designer of a programming language cannot know about, and does
not need to know about, all the applications for which the programming
language will be used, so also can the more abstract products of evolution
be instantiated (e.g. by setting parameters) for use in contexts in which
they did not evolve.


    Many discontinuities in physical forms, behavioural capabilities,
    environments, types of information acquired, types of use of
    information and mechanisms for information-processing are still
    waiting to be discovered.


One of the most spectacular cases is reuse of a common collection of
language-creation competences in a huge variety of geographical
and social contexts, allowing any individual human to acquire any
of several thousand enormously varied human languages, including
both spoken and signed languages.

A striking example was the cooperative creation by deaf children in
Nicaragua of a new sign language because their teachers had not learned
sign languages early enough to develop full adult competences. This
suggests that what is normally regarded as language learning is really
cooperative language creation, demonstrated in this video:

Re-use can  take different  forms, including

-- re-use of a general design across different species by
   instantiating a common pattern,

-- re-use based on powerful mechanisms for acquiring and using
   information about the available resources, opportunities and
   challenges during the development of each individual.

The first process happens across evolutionary lineages.

The second happens within individual organisms in their lifetime

Social/cultural evolution requires intermediate timescales.

Evolution seems to have produced multi-level design patterns, whose details
are filled in incrementally, during creation of instances of the patterns
in individual members of a species.

If all the members live in similar environments that will tend to produce
uniform end results.

However, if the genome is sufficiently abstract, then environments and
genomic structures may interact in more complex ways, allowing small
variations during development of individuals to cascade into significant
differences in the adult organism, as if natural selection had been sped up

A special case is evolution of an immune system with the ability to develop
different immune responses depending on the antigens encountered. Another
dramatic special case is the recent dramatic cascade of social, economic,
and educational changes supported jointly by the human genome and the


As living things become more complex, increasingly varied types of
information are required for increasingly varied uses.

The processes of reproduction normally produce new individuals that have
seriously under-developed physical structures and behavioural competences.

Self-development requires physical materials, but it also requires
information about what to do with the materials, including disassembling
and reassembling chemical structures at a sub-microscopic level and using
the products to assemble larger body parts, while constantly providing new
materials, removing waste products and consuming energy.

Some energy is stored and some is used in assembly and other processes.

The earliest (simplest?) organisms can acquire and use information about
(i.e. sense) only internal states and processes and the immediate external
environment, e.g. pressure, temperature, and presence of chemicals in the
surrounding soup, with all uses of information taking the form of immediate
local reactions, e.g. allowing a molecule through a membrane.

Changes in types of information, types of use of information and types of
biological mechanism for processing information have repeatedly altered the
processes of evolutionary morphogenesis that produce such changes: a
positive feedback process.

An example is the influence of mate selection on evolution in intelligent
organisms: mate selection is itself dependent on previous evolution of
cognitive mechanisms. Hence the prefix 'Meta-' in 'Meta-Morphogenesis'.

This is a process with multiple feedback loops between new designs
and new requirements (niches), as suggested in

As Figure 1 suggests, evolution constantly produces new organisms that may
or may not be larger than predecessors, but are more complex both in the
types of physical action they can produce and also the types of information
and types of information processing required for selection and control of
such actions.

Some of that information is used immediately and discarded (online
perceptual intelligence) while other kinds are stored, possibly in
transformed formats, and used later, possibly on many occasions (offline
perceptual intelligence) -- a distinction often mislabelled as 'where' vs
'what' perception.

This generalises Gibson's theory that perception mainly provides
information about 'affordances' rather than information about visible
surfaces of perceived objects.

These ideas, like Karmiloff-Smith's Beyond Modularity suggest that one of
the effects of biological evolution was fairly recent production of more or
less abstract construction kits that come into play at different stages in
development, producing new more rapid changes in variety and complexity of
information processing across generations as explained below (See fig 2)

It's not clear how much longer this can continue: perhaps limitations of
human brains constrain this process. But humans working with intelligent
machines may be able to stretch the limits.

At some much later date, probably in another century, we may be able to
make machines that do it all themselves -- unless it turns out that the
fundamental information processing mechanisms in brains cannot be modelled
in computer technology developed by humans.

Species can differ in the variety of types of sensory information
they can acquire, in the variety of uses to which they put that
information, in the variety of types of physical actions they can
produce, in the extent to which they can combine perceptual and
action processes to achieve novel purposes or solve novel problems,
and the extent to which they can educate, reason about, collaborate
with, compete against conspecifics, and prey or competitor species.

As competences become more varied and complex, the more disembodied must
the information processing be, i.e. disconnected from current sensory and
motor signals (while preserving low level reflexes and sensory-motor
control loops for special cases).

This may have been a precursor to mathematical abilities to think about
transfinite set theory and high dimensional vector spaces or modern
scientific theories.

E.g. Darwin's thinking about ancient evolutionary processes. was detached
from particular sensory-motor processes. This applies also to affective
states, e.g. compare being startled and being obsessed with ambition.

The fashionable emphasis on embodied cognition may be appropriate to the
study of organisms such as plants and microbes, or even insects, but
evolved intelligence increasingly used disembodied cognition, most
strikingly in the production of ancient mathematical minds.

        A picture of epigenesis (beyond Waddington)


      Figure 2. Cascaded, staggered, developmental trajectories
      proposed by Chappell and Sloman 2007.

Early genome-driven learning from the environment occurs in loops on the
left. Downward arrows further right represent later gene-triggered processes
during individual development modulated by results of earlier learning via
feedback on left.

(Chris Miall suggested the structure of the original diagram.)


The description given so far is very abstract and allows significantly
different instantiations in different species, addressing different sorts
of functionality and different types of design, e.g. of physical forms,
behaviours, control mechanisms, reproductive mechanisms, etc.

At one extreme the reproductive process produces individuals whose genome
exercises a fixed pattern of control during development, leading to
'adults' with only minor variations.

At another extreme, instead of the process of development from one stage to
another being fixed in the genome, it could be created during development
through the use of more than one level of design in the genome.

E.g. if there are two levels then results of environmental interaction at
the first level could transform what happens at the second level. If there
are multiple levels then what happens at each new level may be influenced
by results of earlier developments.

In a species with such multi-stage development, at intermediate stages not
only are there different developmental trajectories due to different
environmental influences, there are also selections among the intermediate
level patterns to be instantiated, so that in one environment development
may include much learning concerned with protection from freezing, whereas
in other environments individual species may vary more in the ways they
seek water during dry seasons.

Then differences in adults come partly from the influence of the
environment in selecting patterns to instantiate. E.g. one group may learn
and pass on information about where the main water holes are, and in
another group individuals may learn and pass on information about which
plants are good sources of water.

If these conjectures are correct, patterns of development will
automatically be varied because of patterns and meta-patterns picked up by
earlier generations and instantiated in cascades during individual

So different cultures produced jointly by a genome and previous
environments can produce very different expressions of the same genome,
even though individuals share similar physical forms.

The main differences are in the kinds of information acquired and used, and
the information processing mechanisms developed. Not all cultures use
advanced mathematics in designing buildings, but all build on previously
evolved understanding of space, time and motion.

Evolution seems to have found how to provide rich developmental variation
by allowing information gathered by young individuals not merely to select
and use pre-stored design patterns, but to create new patterns by
assembling fragments of information during earlier development, then using
more abstract processes to construct new abstract patterns, partly shaped
by the current environment, but with the power to be used in new

Developments in culture (including language, science, engineering,
mathematics, music, literature, etc.) all show such combinations of data
collection and enormous creativity, including creative ontology extension
(e.g. the Nicaraguan children mentioned above.

Unless I have misunderstood her, this is the type of process
Karmiloff-Smith called 'Representational Re-description' (RR).

Genome-encoded previously acquired abstractions 'wait' to be instantiated
at different stages of development, using cascading alternations between
data-collection and abstraction formation (RR) by instantiating higher
level generative abstractions (e.g. meta-grammars), not by forming
statistical generalisations.

This could account for both the great diversity of human languages and
cultures, and the power of each one, all supported by a common genome
operating in very different environments.

Jackie Chappell noticed the implication that instead of the genome
specifying a fixed 'epigenetic landscape' (proposed by Waddington) it
provides a schematic landscape and mechanisms that allow each individual
(or in same cases groups of individuals) to modify the landscape while
moving down it (e.g. adding new hills, valleys, channels and barriers).

Though most visible in language development, the process is not unique to
language development, but occurs throughout childhood (and beyond) in
connection with many aspects of development of information processing
abilities, construction of new ontologies, theory formation, etc.

This differs from forms of learning or development that use uniform
statistics-based methods for repeatedly finding patterns at different
levels of abstraction.

Instead, Figure 2 indicates that the genome encodes increasingly abstract
and powerful creative mechanisms developed at different stages of
evolution, that are 'awakened' (a notion used by Kant) in individuals only
when appropriate, so that they can build on what has already been learned
or created in a manner that is tailored to the current environment.

For example, in young (non-deaf) humans, processes giving sound sequences a
syntactic interpretation develop after the child has learnt to produce and
to distinguish some of the actual speech sounds used in that location.

In social species, the later stages of Figure 2 include mechanisms for
discovering non-linguistic ontologies and facts that older members of the
community have acquired, and incorporating relevant subsets in combination
with new individually acquired information.

Instead of merely absorbing the details of what older members have learnt,
the young can absorb forms of creative learning, reasoning and
representation that older members have found useful and apply them in new
environments to produce new results.

In humans, this has produced spectacular effects, especially in the last
few decades.

The evolved mechanisms for representing and reasoning about possibilities,
impossibilities and necessities were essential for both perception and use
of affordances and for making mathematical discoveries, something
statistical learning cannot achieve.


An invariant for all species in this universe is space-time embedding, and
changing spatial relationships between body parts and things in the

The relationships vary between waterdwellers, cave-dwellers, tree-dwellers,
flying animals, and modern city-dwellers.

Representational requirements depend on body parts and their controllable
relationships to one another and other objects.

So aeons of evolution will produce neither a tabula rasa nor geographically
specific spatial information, but a collection of generic mechanisms for
finding out what sorts of spatial structures have been bequeathed by
ancestors as well as physics and geography, and learning to make use of
whatever is available (McCarthy[17]): that's why embodiment is relevant to
evolved cognition.

Kant's ideas about geometric knowledge are relevant though he assumed that
the innate apparatus was geared only to structures in Euclidean space,
whereas our space is only approximately Euclidean.

Somehow the mechanisms conjectured in Figure 2 eventually (after many
generations) made it possible for humans to make the amazing discoveries
recorded in Euclid's Elements, still used world-wide by scientists and

If we remove the parallel axiom we are left with a very rich collection of
facts about space and time, especially topological facts about varieties of
structural change, e.g. formation of networks of relationships,
deformations of surfaces, and possible trajectories constrained by fixed

It is well known (though non-trivial to prove!) that trisection of an
arbitrary angle is impossible in Euclidean geometry, whereas bisection is

However, some ancient mathematicians (e.g. Archimedes) knew that there is a
fairly simple addition to Euclidean geometry that makes trisecting an
arbitrary angle easy, namely the 'neusis' construction that allows a
movable straight edge to have two marks fixed on it that can be used to
specify constraints on motion of the edge.

They proved this without modern logic, algebra, set theory, proof theory
etc. However, there is no current AI reasoner capable of discovering such a
construct, or considering whether it is an acceptable extension to Euclid's
straight-edge and compasses constructs.

If we can identify a type of construction-kit that produces
young robot minds able to develop or evaluate those ideas in
varied spatial environments, we may find important clues about
what is missing in current AI.

Long before logical and algebraic
notations were used in
mathematical proofs, evolution had produced abilities to represent
and reason about what Gibson called 'affordances', including
possible and impossible alterations to spatial configurations

    the (topological) impossibility of solid linked rings becoming
    unlinked, or vice versa.

I suspect brains of many intelligent animals make use of topological
reasoning mechanisms that have so far not been discovered by brain
scientists or AI researchers.

Addition of meta-cognitive mechanisms able to inspect and experiment with
reasoning processes may have led both to enhanced spatial intelligence and
meta-cognition, and also to meta-metacognitive reasoning about other
intelligent individuals.


I conjecture that further investigation will reveal varieties of
information processing (computation) that have so far escaped the attention
of researchers, but which play important roles in many intelligent species,
including not only humans and apes but also elephants, corvids, squirrels,
cetaceans and others.

In particular, some intelligent non-human animals and pre-verbal human
toddlers seem to be able to use mathematical structures and relationships
(e.g. partial orderings and topological relationships) unwittingly.
Mathematical meta-meta...-cognition seems to be restricted to humans, but
develops in stages, as Piaget found, partially confirming Kant's ideas
about mathematical knowledge in.

However, I suspect that (as Kant seems to have realised) the genetically
provided mathematical powers of intelligent animals make more use of
topological and geometric reasoning, using analogical, non-Fregean,
representations, as suggested in  than the logical, algebraic, and
statistical capabilities that have so far dominated AI and robotics.

    (NB 'analogical' does not imply 'isomorphic'.)

For example, even the concepts of cardinal and ordinal number are crucially
related to concepts of one-one correspondence between components of
structures, most naturally understood as a topological relationship rather
than a logically definable relationship.


All this  shows  why  increasing  complexity  of  physical  structures  and
capabilities, providing richer collections of alternatives and more complex
internal  and  external  action-selection  criteria,  requires   increasing
disembodiment of information processing.

The fact that evolution is not stuck with the Fundamental Construction Kit
(FCK) provided by physics and chemistry, but also produces and uses new
'derived' construction-kits (DCKs), enhances both the mathematical and the
ontological creativity of evolution, which is indirectly responsible for
all the other known types of creativity.

This counters both the view that mathematics is a product of human minds,
and a view of metaphysics as being concerned with something unchangeable.

The notion of 'Descriptive Metaphysics' presented by Strawson (1959) needs
to be revised.

I also conjecture that filling in some of the missing details in this
theory (a huge challenge) will help us understand both the evolutionary
changes that introduced unique features of human minds and why it is not
obvious that Turing-equivalent digital computers, or even asynchronous
networks of such computers running sophisticated interacting virtual
machines, will suffice to replicate the human mathematical capabilities
that preceded modern logic, algebra, set-theory, and theory of computation.

It will all depend on the precise forms of virtual information processing
machinery that evolution has managed to produce, about which I suspect
current methods of neuroscientific investigation cannot yield deep

Current AI cannot produce reasoners like Euclid, Zeno, Archimedes, or even
reasoners like pre-verbal toddlers, weaver birds and squirrels.

This indicates serious gaps, despite many impressive achievements. I see no
reason to believe that uniform, statistics based learning mechanisms will
have the power to bridge those gaps.


Whether the addition of logic-based reasoners will suffice (as suggested by
McCarthy and Hayes in 1969) is not clear.

The discoveries made by ancient mathematicians preceded the discoveries of
modern algebra and logic, and the arithmetisation of geometry by Descartes.

Evolved mechanisms that use previously acquired abstract forms of
meta-learning with genetically orchestrated instantiation triggered by
developmental changes (as in the above diagram), may do much better.

These mechanisms depend on rich internal languages that evolved for
use in perception, reasoning, learning, intention formation, plan formation
and control of actions before communicative languages.

This generalises claims made by Chomsky in, and his later works, focused
only on development of human spoken languages, ignoring how much language
and nonlinguistic cognition develop with mutual support.


Building a new computer for every task was made unnecessary
by allowing computers to have changeable programs.

Initially each program, specifying instructions to be run, had to be loaded
(via modified wiring, switch settings, punched cards, or punched tape), but
later developments provided more and more flexibility and generality, with
higher level programming languages providing reusable domain specific
languages and tools, some translated to machine code, others run on a task
specific virtual computer provided by an interpreter.

Later developments provided time-sharing operating systems supporting
multiple interacting programs running effectively in parallel performing
different, interacting, tasks on a single processor.

As networks developed, these collaborating virtual machines became more
numerous, more varied, more geographically distributed, and more
sophisticated in their functionality, often extended with sensors of
different kinds and attached devices for manipulation, carrying, moving,
and communicating.

These developments suggest the possibility that each biological mind is
also implemented as a collection of concurrently active nonphysical, but
physically implemented, virtual machines interacting with one another and
with the physical environment through sensor and motor interfaces.

Such 'virtual machine functionalism' could accommodate a large variety of
coexisting, interacting, cognitive, motivational and emotional states,
including essentially private qualia as explained by Sloman and Chrisley

Long before human engineers produced such designs, biological evolution had
already encountered the need and produced virtual machinery of even greater
complexity and sophistication, serving information processing requirements
for organisms, whose virtual machinery included interacting sensory qualia,
motivations, intentions, plans, emotions, attitudes, preferences, learning
processes, and various aspects of self-consciousness.


We still don't know how to make machines able to replicate the mathematical
insights of ancient mathematicians like Euclid e.g. with 'triangle qualia'
that include awareness of mathematical possibilities and constraints23 or
minds that can discover the possibility of extending Euclidean geometry
with the neusis construction.

It is not clear whether we simply have not been clever enough at
understanding the problems and developing the programs, or whether we need
to extend the class of virtual machines that can be run on computers, or
whether the problem is that animal brains use kinds of virtual machinery
that cannot be implemented using the construction kits known to modern
computer science and software engineering. As Turing hinted in his 1950
paper: aspects of chemical computation may be essential.

Biological organisms also cannot build such minds directly from
atoms and molecules. They need many intermediate DCKs, some of
them concrete and some abstract, insofar as some construction kits,
like some animal minds, use virtual machines.

Evolutionary processes must have produced construction kits for abstract
information processing machinery supporting increasingly complex
multi-functional virtual machines, long before human engineers discovered
the need for such things and began to implement them in the 20th Century.

Studying such processes is very difficult because virtual machines don't
leave fossils (though some of their products do). Moreover details of
recently evolved virtual machinery may be at least as hard to inspect as
running software systems without built-in run-time debugging 'hooks'. This
could, in principle, defeat all known brain scanners.

'Information' here is not used in Shannon's sense (concerned
with mechanisms and vehicles for storage, encoding, transmission,
decoding, etc.), but in the much older sense familiar to Jane Austen
and used in her novels e.g. Pride and Prejudice, in which how
information content is used is important, not how information bearers
are encoded, stored, transmitted, received, etc. The primary use of
information is for control.

Communication, storage, reorganisation, compression, encryption,
translation, and many other ways of dealing with information are all
secondary to the use for control. Long before humans used structured
languages for communication, intelligent animals must have used rich
languages with structural variability and compositional semantics
internally, e.g. in perception, reasoning, intention formation, wondering
whether, planning and execution of actions, and learning.

We can search for previously unnoticed evolutionary transitions going
beyond the examples here (e.g. Figure 1), e.g. transitions between
organisms that merely react to immediate chemical environments in a
primaeval soup, and organisms that use temporal information about changing
concentrations in deciding whether to move or not.

Another class of examples seems to be the new mechanisms required after the
transition from a liquid based life form to life on a surface with more
stable structures (e.g. different static resources and obstacles in
different places), or a later transition to hunting down and eating mobile
land-based prey, or transitions to reproductive mechanisms requiring young
to be cared for, etc.? Perhaps we'll then understand how to significantly
extend AI.

Compare Schro|dinger's discussion in [19] of the relevance of quantum
mechanisms and chemistry to the storage, copying, and processing of genetic
information.26 I am suggesting that questions about evolved intermediate
forms of information processing are linked to philosophical questions about
the nature of mind, the nature of mathematical discovery, and deep gaps in
current AI.27

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[23] A. Sloman, "Interacting trajectories in design space and niche space:
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[26] Aaron Sloman, "Virtual machinery and evolution of mind (part 3) metamorphogenesis: Evolution of information-processing machinery', in
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[28] Aaron Sloman and David Vernon. A First Draft Analysis of some MetaRequirements for Cognitive Systems in Robots, 2007. Contribution to
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Maintained by Aaron Sloman
School of Computer Science
The University of Birmingham

Computer Science, Univ. of Birmingham. email: An extended abstract for a closely related invited talk at the Symposium on computational modelling of emotions is also available online at http:// 19 Boden [2] distinguishes H-Creativity, which involves being historically original, and P-Creativity, which requires only personal originality. The distinction is echoed in the phenomenon of convergent evolution, illustrated in of examples of convergent evolution. The first species with some design solution exhibits H-creativity of evolution. Species in which that solution evolves independently later exhibit a form of P-creativity. 20 Why did Turing write in his [30] that chemistry may turn out to be as important as electricity in brains?