Based on collaboration with
A partial index of discussion notes in this directory is in
Some of these ideas were in this IJCAI17 Workshop presentation
Video presentation with online notes
Why can't (current) machines reason like Euclid or even human toddlers?
(And many other intelligent animals)[*]
This is part of the Turing-inspired Meta-Morphogenesis project
A spin-off from the CogAff (Cognition and Affect) project:
The parameters required by the original system or its products may be simple entities such as numbers, labels (strings of characters), bits set on or off, or complex entities such as sets of numbers, other packages to be combined, or in some cases interfaces to hardware devices, such as cameras, microphones, keyboards, screens, or links to various parts of a complex functioning entity controlled by the new package, such as a chemical plant, an airliner automatic landing system, an assembly robot in a factory, a home security system, etc.
Biological evolution also produces designs for abstract re-usable structures or mechanisms that can be used in the production and functioning of individual organisms, or groups of organisms, as a result of insertion of parameters obtained either at later stages of evolution, or during development of individual organisms, or through formation of colonies, cultures or societies in which individuals interact, including transmitting information.
In these cases also, some parameters used for control decisions during development or during particular actions may be numerical values or scalar measures, e.g. temperature, concentrations of certain chemicals, sizes or weights of body parts, or speed of linear motion or angular rotation. But many parameters will be structures with parts and relationships, for instance a structured plan for action, an internal information structure representing a perceived physical structure or process, a theory about how something in the environment works, a structured question to be answered through active perception, experiment or exploration, or an intention to be achieved by performing an action or carrying out a plan involving multiple sub-actions. During physical development gene expression mechanisms may use structured 'inputs' in the form of molecular structures, e.g. molecules obtained from the organism's environment.
The parameters that are simple, such as measures or labels, are "atomic": their internal structure does not matter, only their location in some ordering or set of alternatives. The parameters that are complex are "molecular". They may be simple linear linked atomic items, or "tree" structures, where there is a "root" entity and all other components are reachable from the root via a unique path through a branching network of nodes and links, or a generalised "molecular" structure with parts that are related to other parts that are simultaneously related to several other parts, as indicated in typical diagrammatic representations used in chemistry. There may be several distinct routes between two nodes in such a network (referred to as a "graph" by mathematicians, but not in the same sense as a "graph" showing relationships between inputs and outputs of functions).
If evolution, like human package designers, is able to derive useful generic abstractions from specific cases, then more abstract products of evolution can be instantiated (e.g. by setting parameters) for use in contexts in which they did not evolve. The requirements for this are complex and subtle but it is clear that evolution found such powerful abstractions that are re-usable in new contexts long before human engineers did.
In many cases these included "discovered" mathematical generalities that are encoded in a relatively abstract form in genomes, able to be instantiated with different parameters both during development of individuals and when varied across species.
E.g. during individual growth (changing size, shape, strength etc.) and learning (acquiring/creating new information structures at various levels of abstraction) individual development mechanisms can combine information (parameters) from the environment with generic information in the genome to produce instances of a species tailored to the specific environment.
But the longer an individual lives the more likely it is that the environment will change during its lifetime either because of local changes or because of migration to new locations, or for other factors such as learning by prey or predators, or rapid evolution of other organisms (e.g. bacteria evolving resistance to medication).
Environmental pressures and opportunities on a species can be changed both during lifetimes of individuals, and more gradually across generations, by climate changes, geological changes (e.g. earthquakes, volcanic eruptions, sea-level changes, floods, etc.), invasion or migration of individuals of other species, removing resources and/or creating new threats and opportunities for previous inhabitants, diseases, crop failures, etc.
All of these cases provide opportunities for benefiting from adaptability both in genomes and in individuals. Resulting features of gene-expression mechanisms can lead to important new features of the interplay between evolution of new species, or new modifications of existing species, and advantages of new mechanisms of epigenesis: genetic influences on individual development.
Some new threats are so drastic that it is impossible for a genome to prepare for them, e.g. impact by a huge asteroid or huge fluctuations in cosmic radiation. Others may fit into a space of possibilities that allows defensive measures to be taken, or new opportunities to be grasped, by alteration of parameters derived from the new situation, in generic mechanisms.
If the parameters can be systematically derived from perceived structures in the new situation, such a process can be much faster than statistical search for appropriate parameters as happens in many current AI learning mechanisms.
A toy example: if you can map the perceived width of a new object into an appropriate extent of jaw opening then you don't need to spend a long time trying out different widths of opening.
So if individual members of a species have enough previously previously evolved generic design features into which parameters derived from perception or a small amount of interaction with new objects or situations can be inserted, then a large there will be no need for extended interactions searching for appropriate parameters.
This may also need to be a feature of design of future robots that have to be placed in their target environments in an under-developed state, enabling important features of their development to be influenced by inserting parameters derived from the environment into generic frameworks already in their design. That will require robots to have far more hard-wired generic, but parametrisable, intelligence than current machines have. Robots will be ignored in the rest of this paper.
Biological evolution involves mostly mindless processes of design, design evolution, and design instantiation combined with individual development, all in interaction with environments that can influence the developmental trajectories on different time-scales. Much of that process involves (cooperative, competitive or neutral) interactions with both conspecifics and members of other species. If previous evolution, combined with individual learning, has built enough abstract parametrised potential solutions into individual designs, then instantiation of abstract features of evolutionary history can enormously speed up development and learning by individuals, especially if the evolutionary history has captured some immutable reusable features of spatial structures and processes.
I think it is also consistent with Immanuel Kant's ideas about non-empirical knowledge of synthetic necessary truths, though that connection is far from obvious. [REF NEEDED]
There are close links with ideas about development and learning in Karmiloff-Smith(1992), including her ideas about "representational redescription" occurring as a type of competence develops.
Relevant recent evidence regarding epigenetic mechanisms is discussed by
neuroscientist Seth Grant, interviewed here by Ginger Campbell:
(I am grateful to Luc Beaudoin for the link.)
Bressloff focuses on mathematical features of of gene expression described at a level of detail that does not bring out some of the kinds of structure in epigenetic processes mentioned below, that seem to be much harder to investigate empirically, for example multi-layered highly structured forms of gene expression that involve instantiation of structural patterns with particular (often structured) parameters, as in formation of grammars, semantic categories, theories about space (geometry and topology), individually developed ontologies, values, preferences, and standards, and much more. Here are some samples from the paper that seem to be special cases of the general points being made I wish to make:
Page 4: "The presence of transcription factors means that cellular processes can be controlled by extremely complex gene networks with multiple negative and positive feedback loops. Identifying functional modules and motifs within such networks is a major component of systems biology . Gene regulation plays an essential role in viruses and bacteria, since it increases the versatility and adaptability of an organism within an environment. In multicellular organisms, gene regulation drives cellular differentiation and morphogenesis in the embryo, producing different cell types with different gene expression profiles from the same genome sequence."
Page 82: 5.3. Metastability in epigenetics
Aurell et al [21, 22] have developed a theoretical framework for studying the metastability of epigenetic states (see also ). Epigenetics concerns phenotypic states that are not encoded as genes, but as inherited patterns of gene expression originating from environmental factors. Examples of environmental influences range from changes in the supply of nutrients in bacteria to stress in humans.
Page 127 (In section 9)
One of the major challenges in furthering our understanding of biological switches, as well as other processes in systems biology, is dealing with the complexity of most gene regulatory and biochemical signaling networks. For example, typical reaction networks involve multiple nodes (complexes) and links (reactions) that represent a hierarchy of nonlinear feedback loops. Identifying characteristic modules and motifs within these networks (including switches) is a subject of intense research. The theory of chemical reaction networks touched upon in section 2.3 could be important in identifying non-equilibrium steady-states in complex networks, as could multi-scale analyses that exploit any separation of time-scales. Another source of complexity arises when spatial effects become important.
My main concern about this is whether human brains have the power to understand some of the kinds of complexity involved in the most complex forms of gene expression producing adult human brains, e.g. the interactions between genes in an embryo and the multiple levels of gene expression that in some ancient mathematicians produced major discoveries in geometry, topology and number theory. This paper is part of an attempt to make the process more tractable by provisionally abstracting from some of the more complex details.
A possible name for the Chappell-Sloman theory is "The Meta-Configured Genome" theory (producing a meta-configured epigenetic landscape?). The main ideas are summarised in Figure EPI, below,
One feature of the theory is that it claims that long before there were any human mathematicians, biological evolution (the blind mathematician?) implicitly made many mathematical discoveries, which were, in effect, encoded in parametrised designs for developmental processes, physical structures and useful behaviours in genomic structures that could be used (a) across different species (b) at different stages of development within a species.
Evolutionary precursors of human mathematical abilities are a special case. But less spectacular versions seem to occur in many intelligent species, including crows, mentioned below.
Could a similar diagram represent physical/chemical evolution of the universe? Genes at the top of the diagram would have to be replaced by hitherto unknown aspects of fundamental physics playing the combined role of genome and environment.
The main difference can be summed up as follows: on the "Meta-configured" landscape, as the ball rolls down the landscape it changes the structure of the rest of the landscape, modifying the options available thereafter, partly on the basis of effects of its previous trajectory. Think of how the early years of learning a particular language alter language-development competences thereafter. Similarly the toys and games that a child, or other intelligent animal, learns to interact with or take part in may significantly alter the kinds of things that can be learnt, or the ease with which they can be learnt later.
But that analogy is too ill defined so we try to add more content in the discussion of Figure EPI, below, explained in some detail in the rest of the paper, though most of the details will have to be provided by future research.
The rightmost picture in Figure Evolution below, refers (crudely) to Betty, the New Caledonian crow, who made headlines in 2002 when she unexpectedly used a straight piece of wire to make a hook in order to fish a bucket of food out of a vertical tube. What the news headlines did not say, but can be checked in videos on the Oxford Ecology lab web site, was that she made hooks in several very different ways, all without any hesitation or trial and error, and apparently in full awareness of what she was doing and why.
Compare the discussion of toddler intelligence and weaver bird intelligence in
ths 42 minute video prepared for the IJCAI workshop presentation on 19th August
2017, available here:
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.
In Figure EPI, 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 instantiating generic patterns on the basis of results of earlier learning via feedback on left e.g. syntactic structures found, in the case of language development. Chris Miall helped with the original diagram in the Journal paper. Alan Bundy suggested the feedback loop extending meta-...competences: indicating that individual learning can expand the scope of genetic influences on acquired structures during epigenesis.
(a) Two (or more) types of species:
Newborn infants, or new hatchlings, of some species, e.g. deer, chickens, turtles, and many invertebrates, are highly competent, very soon after birth or hatching, including being able to move around and feed themselves or even run with the herd (e.g. newborn wildebeest foals), whereas others, e.g. crows, cats, other carnivores, and apes, including humans, are hatched or born incompetent and relatively immobile, depending crucially on parent feeding and care for some time. A biologist who attended my talk at a workshop in 1998 informed me that the former were called "precocial" and the latter "altricial" species. I later learnt from Jackie Chappell, a colleague in Biosciences, that these labels were more appropriate for specific competences than for species, as explained below.
(b) Differences in adult intelligence:
The second informal observation was that, paradoxically(?), adult members of species born less competent ("altricial" species) seem to have more sophisticated cognitive abilities than adult precocial animals that start life much smarter. E.g. adult squirrels, crows, apes and hunting mammals seem to have greater mastery over intricate spatial structures, processes and the problems they pose than horses and deer that find their way to the mother's nipple and, in some cases, run with the herd soon after birth, or chickens and ducks that extricate themselves from eggshells and feed themselves soon after, as do many insect grubs whose parents never meet their offspring.
Informally observed differences between the two types suggested that there might be some deep clues about natural intelligence, and the tradeoffs between innate information and acquired information. For example, is there great significance in the fact that for several years human brains develop in size and structure in parallel with increasingly complex physical and cognitive capabilities often involving performance of increasingly complex and varied physical actions?
Moreover, independently of those general ideas, there are very specific well known facts, such as the fact that in humans, some aspects of genetically determined morphology, and motivational and perceptual mechanisms related to reproduction, interest in and reactions to members of the opposite sex, seem to be genetically programmed to develop relatively late in life, i.e. at puberty. So expression of genes related to both physical characteristics and information-processing abilities can be delayed for several years.
There may be less obvious but equally important genetically controlled brain functions that are delayed till later, concerned with requirements for child care. Is there also delayed gene expression related to post-parental biological functions, such as grandparenting, and perhaps varieties of motivation and behaviour relevant to competitions for pack-leadership that need to be based on a lot of prior experience? Less well controlled motivational development could lead to premature production of ambitions -- e.g. before individuals have had enough time to gain relevant experience.
In short, it seems that evolution somehow "discovered" that a type of genome for a long-lived intelligent species with many kinds of individual and social behaviours can increase evolutionary success if the processes of physical development then aging are accompanied by genetically delayed changes in cognitive mechanisms concerned with motivation, capabilities of various kinds, and relationships with conspecifics, that differ substantially across the lifespan.
These "delayed" developments could be based partly on processes of accumulation of information within the genome, over many generations, in contrast with information acquired through individual learning. But that would restrict the knowledge and competences individuals could acquire. In contrast, if if the specifications for later development are parametrised, allowing their manifestations to be tailored to specific circumstances, then parameters that vary widely across habitats and cultures could be derived from aspects of the environment during individual development, and later combined with the general design specifications, at appropriate times.
For example, genetic expression of a home-building instinct could be delayed until individuals have had time both to find out about available home-building resources in the environment and to acquire the required skills. Both of those could be facilitated by motivations connected with play and imitation of adult behaviours. Is this related to the complex nest-building achievements of some birds, such as weaver birds and crows? Perhaps also hunting and cadaver eating competences in some mammals?
However, if individuals also somehow acquire abilities to invent and create new home-building materials and new techniques, then that previously evolved delayed generation e.g. of home-building motives would also be applicable to use of new materials and techniques created in that location by previous generations, not just naturally occurring diversity in resources across different regions.
I suspect that many aspects of human technology, art and science depend on such mechanisms using inheritance of abstractions that can be combined with different "fillers", some of which may also be abstractions, and which may first have evolved to meet requirements of different terrains.
(Could this be a special case of the Baldwin effect, producing new inherited
abstractions rather than new inherited physical features or behaviours?
Such pre-programmed staggered development requires delayed expression of genetic features, e.g. taste preferences, or types of curiosity, or social motives, until physical changes or types of learning have occurred that are pre-requisites for the new feature to be useful.
Examples may include changes in food preferences with age, and delayed development of mating related interests, motives, and preferences.
A deeper reason for staggering development could be related to the need to match certain developmental processes to information that has been acquired about aspects of the environment, e.g. physical aspects that need to be learnt before major forms of motivation related to social functions, jobs, etc. can develop. This could explain how the same genome works for humans in ancient technologically primitive contexts, in more recent industrialised contexts, and in very recent contexts where very young children have internet connected games or toys requiring both new kinds of motivation and new forms of physical and intellectual knowledge and skill.
These cases require a genome that does not specify motives in detail, but allows a generic, genetic specification to be instantiated using locally acquired information: a crude case might be finding out what behaviours are currently admired by conspecifics, and then generating new motives to perform those behaviours. (The distinction between such architecture based and reward based motivation (ABM vs RBM) is explained in Sloman(2009) -- the latter presumes some generic form of reward involved in all motivation, which I claim is a myth.)
These ideas lead to a collection of hypotheses regarding genetic mechanisms concerned with motive generation. New types of motive may be triggered through delayed genomic expression at various stages of development. How new motives produce behaviour may be shaped by motivational mechanisms that use prior experience and knowledge of the individual, that provide parameters used to produce locally relevant special cases of generic abstract genetic specifications. So the genomic content must include "gaps" to be filled by such parameters.
In each case the expressed generic ("gappy") genes would combine with what the individual has already learnt (which can vary enormously with environment in combination with earlier gene-expression trajectories in the individual).
The engineering applications now take their most sophisticated forms in connection with software systems that use inheritance hierarchies and parametrised structures. In such contexts, parameters may be numbers, abstract symbols, procedures, complex data structures (e.g. a set of rules for a game) or even theories.
These ideas are now familiar in theoretical computer science, AI (especially symbolic AI), theoretical linguistics, and advanced software engineering, but seem to be unknown to many others who build computational models, including models of brain function, using only forms of abstraction based on numerical parameters.
The very misleading label "Object Oriented Programming" (OOP) has come to be used for the abstraction-based software design strategy, though the label unfortunately has several very different interpretations, some more sophisticated than others. What I am suggesting is that sophisticated versions of OOP were "discovered" and put to use long ago in biological evolution, though some of the not yet understood biological examples may turn out to be far more complex than anything developed by human engineers, so far.
A fairly elementary, somewhat idiosyncratic, tutorial introduction to OOP can be found here:
The meta-configured genome theory suggests that biological evolution
"discovered" (or "stumbled across"?) the value of such parametrised design
specifications (as in OOP) long before human scientists and engineers did, and
as a result parametrised specifications are used in genomes for many complex
species, especially portions of genomes required for information processing
mechanisms and control functions. Some of them will use virtual machinery
implemented in physical machinery, as explained here:
All of these ideas need to be expanded in the context of the theory of evolved construction kits, under development here:
I suspect that the most important consequences of these ideas for patterns of development controlled by genomes (epigenetic processes) have not yet been understood.
There are some brain mechanisms that should not begin development until their development can be accompanied with actions that require a certain level of size, strength and self control. The burden of natural selection can be reduced if it does not need to encode full information about required brain features into the genome because control parameters can be picked up during earlier interactions with the environment while the relevant portions of the brain are still growing.
I am not talking about acquiring statistical regularities, but fitting generic
patterns to parameters, such as muscular strength, lengths of bones, angles of
rotation, moments of inertia, etc. In some cases this requires relevant physical
growth to have been achieved, e.g. bones, muscles, and nervous connections,
along with under-developed but usable motor control mechanisms. If relevant
control parameters can be acquired from physiological sensors or from the
environment, then control patterns can be instantiated using those parameters,
to produce effective actions, modulated appropriately as the organism changes
size, weight, strength, shape, etc.
(Add ref to D'Arcy Thompson's work, Brian Goodwin, etc.)
N.B. This proposal does not require acquired parameters to be very precise, if homeostatic (negative feedback) control mechanisms manage the details of actions. Greater precision is required, however, for ballistic actions, e.g. leaping across gaps, throwing objects at targets, etc. (Ref Alain Berthoz and Philippe Rochat?)
These ideas contradict the hypothesis that in humans there is a single very powerful, uniform, learning capability that is combined with a large initially empty, uniform, information store, as suggested (seriously??) by Turing in his Mind 1950 paper in Section 7 Learning Machines, where he wrote:
(p.456) "Instead of trying to produce a programme to simulate the adult mind, why not rather try to produce one which simulates the child's? If this were then subjected to an appropriate course of education one would obtain the adult brain. Presumably the child-brain is something like a note-book as one buys it from the stationers. Rather little mechanism, and lots of blank sheets. (Mechanism and writing are from our point of view almost synonymous.) Our hope is that there is so little mechanism in the child-brain that something like it can be easily programmed. The amount of work in the education we can assume, as a first approximation, to be much the same as for the human child."
I find it hard to believe that around 1950 Turing really believed that human brains start with "so little mechanism". He was far too intelligent and too widely read.
In contrast, the facts summarised above, but not described in detail, suggest that more intelligent species may have various sorts of learning abilities that get switched on at different stages of development. Learning abilities related to use of relatively large limbs controlled by relatively strong muscles might use specialised brain mechanisms that develop only when they are needed at a relatively late stage, and could be different from mechanisms that acquire/learn strategies for control of gaze direction, which seems to develop very early in many intelligent species.
Some mammals are born blind and begin to see some time after their birth. In those cases the required visual learning mechanisms should not begin to function until other aspects of the organism have developed, e.g. retinal functions, neural connections, and muscles required for control of gaze direction and visual focusing?
There are alternative strategies used in some genomes that produce what is known as "Biological metamorphosis", e.g. insect forms that change from caterpillar to moth or butterfly via a pupal stage in which molecules undergo drastic genetically controlled reorganisation, as described by Ferris Jabr in Scientific American.
How Did Insect Metamorphosis Evolve?
There is an additional, more subtle requirement for development of some brain mechanisms to be delayed in organisms whose evolution equips them for life in widely varying environments. There can be extreme variations in the environment that are out of the control of the genome, some of which are results of differences in terrain, climate, predators, food sources, or competitors in different parts of the planet, and some of which are results of cultural differences that are produced by earlier products of evolution. In those cases, the full details of related competences should not be encoded in the genome: each individual needs to find out what is required in the environment of its birth, or hatching, or development.
It is often assumed that this requires collection of large amounts of statistical data and computing derived regularities. The alternative assumed here is that abstract possibilities for structural variation previously "discovered" by evolutionary mechanisms are implicitly encoded in the genome but with parameters of various kinds missing, and the learning process discovers those parameters. The learning process need not be totally general (as suggested in the quotation from Turing) and the parameters acquired may be structural rather than numerical in many cases (e.g. linguistic structures that work in a community).
In some cases the processes of development and learning do not directly produce
structures and behaviours but instead produce
construction kits (including physical construction
kits and abstract construction kits) tailored to the current environment,
which then create the final products, as proposed in
Striking examples of the use of evolved construction kits and generic patterns that are instantiated differently in different environments are differences in processes of language acquisition used by humans in different parts of this planet. Differences between spoken and sign languages are among the most spectacular examples, and will be mentioned later in connection with the question: are languages learnt or created? See the section on evolution of language below.
Some of the later forms of learning derive from previously evolved genetic mechanisms with a very high level of abstraction that are sensitive to abstract and complex features of the development environment. So instead of later forms of learning merely having parameters that can be replaced by different constants in different environments, they may have generalised learning mechanisms or construction kits that are instantiated in more complex ways in different environments, e.g. depending on more complex and structured parameters. Compare sophisticated uses of parametric polymorphism in modern programming languages.
Moreover, the types of learning required at different stages of development are not uniform. For example, if the claims made by Chomsky and others that language development requires particular forms of information processing related to production and perception of grammatical structures, and use of language based on those structures depends on other previously developed competences, then that might be a reason for delaying growth of relevant portions of the brain until the more basic physical and information processing mechanisms had been grown and assembled into well functioning components, and some basic features of the form of language used in the infant's culture have been absorbed -- e.g. whether it's a sign language or vocal language, etc.
That argument could apply to other capabilities also. For example, if there are forms of learning that use brain mechanisms relevant to coordination of motor control in upright sitting, standing, or walking postures, then the brain mechanisms required for planning and control functions of those coordinated late developing mechanisms need not grow until they are needed. Moreover it is possible that if grown too soon they would be stimulated in inappropriate ways and learn the wrong things, which may be an irreversible process.
In all these cases different forms of learning and development may be required that cannot be pre-encoded uniformly in the genome. For example, if very different sound patterns or signing patterns have developed in different cultures, then the mechanisms for utilising those patterns to express different forms of communication syntax may not be able to use a general purpose learning engine effectively. Instead, the genome may allow each individual to grow a tailored "syntax learning system" suited to the local language culture.
If other forms of development are delayed until this mechanism has been deployed, then after they have started building on linguistic accomplishments so far, attempts to learn a new language later may not produce a second-language competence that is so well integrated into the whole system.
This may also require different forms of learning to deal with differences in semantic structures and syntactic-semantic relationships that depend on both environmental influences and previously evolved cultural structures. (Musical notation is a clear example where the latter influence is dominant.)
There are also differences that relate to culture-specific games and rituals, though it is likely that the ability to cope with those was not a selecting factor in language evolution, but a consequence of the generality of evolved mechanisms.
In Figure EPI, 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 instantiating generic patterns on the basis of results of earlier learning via feedback on left e.g. syntactic structures found, in the case of language development. Chris Miall helped with the original diagram in the Journal paper. Alan Bundy suggested the feedback loop extending meta-...competences: indicating that individual learning can expand the scope of genetic influences on acquired structures during epigenesis.
A possible name for the Chappell-Sloman theory is "The Meta-Configured Genome" (producing a meta-configured epigenetic landscape?). Could a similar diagram represent physical/chemical evolution of the universe? Genes would have to be replaced by hitherto unknown aspects of fundamental physics.
This idea, generalising claims previously made regarding language development, was developed jointly with Jackie Chappell and presented in Sloman and Chappell (2005a), after which we were invited to write a paper for a journal in which the ideas were developed further Chappell and Sloman (2007). The ideas have developed since then, adding detail summarised in Figure EPI below.
That figure summarises the key ideas in the 2007 paper and some ideas developed
later. Additional work is being done on the special case of evolution and
development of mathematical abilities, especially the abilities that led to
(non-numerical) geometric and topological discoveries of ancient mathematicians.
Some recent related work in progress can be found in:
The latter is an incomplete draft specification of a kind of (virtual) multi-membrane machine, very different from a Turing machine, that seems to be required by an organism or machine able to make the ancient discoveries made by Archimedes, Euclid, Zeno and their (mostly unknown) predecessors. I don't yet know whether such a machine could be implemented as a virtual machine on a digital computer. Neither does anyone know how it could be implemented in brain mechanisms. I think Trehub (1991) had some ideas that could be adapted for these purposes, though he was not thinking of these problems.
This multi-layered pattern of individual development driven by a genome specifying required mechanisms at high levels of abstraction, allows evolution to produce and re-use very general abstractions that can be instantiated to produce very different types of information processing, based partly on the environment of development of each individual, which in turn can be influenced partly by what earlier generations have achieved (which is most obviously the case in humans, but may also apply to some other species).
A consequence of this type of genome is that intermediate learning mechanisms are constructed by instantiating very abstract "parametrised" learning mechanisms in different ways, using different parameters picked up at earlier stages of development, that can vary enormously as environments vary. In particular, this can use "construction kits" that the individual has created, on the basis of genetically specified construction kits of greater generality produced at earlier stages of evolution. See Sloman.
We call a genome of that sort a Metaconfigured Genome in contrast with a Preconfigured genome of the kind implied by Waddington's epigenetic landscape depicted below.
These mechanisms allow individual development to be deeply influenced by aspects of the environment that have been changed by their ancestors and ancestors of other species with whom they interact. Obvious examples include types of agriculture, types of urban development, types of machinery that have been found useful, forms of energy that have been used, and many more. In Sloman & Chrisley (2005) the label "Extended genotype" was proposed for this, echoing Dawkins' "Extended Phenotype".
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 or more levels then results of environmental interaction at earlier levels could determine how generic potential is later instantiated at higher levels -- e.g. what sorts of verbal morphology, grammatical structure or semantic structure develop at later stages. If there are multiple levels then what happens at each new level may be influenced partly by results of earlier developments.
If the abstract structures are not mere numeric formulae whose instantiation involves insertion of numeric values, but also allow previously acquired structures (e.g. spatial structures, process structures, grammatical structures) to be inserted at later stages of development, then the results can differ far more than if numerical values are used. The same is true if different chemical structures are inserted into the same chemical framework. This may have been one of the insights driving Schrödinger(1944).
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.
As the development of linguistic competence shows, these processes can produce new construction kits within individuals, including construction kits for creating new (to the learner) forms of representation and reasoning. The theory of "architecture-based motivation" Sloman(2009) implies that similar structural variation can occur in patterns of motivation.
Differences in adults with a shared genome can then result partly from the influence of the environment, including the social environment, in triggering instantiation of motivational patterns. 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. Further details within individuals may be results of different individual experiences, or complex interactions with products of previously instantiated genetic patterns.
If these conjectures are correct, patterns of individual development in a species will automatically be varied because of patterns and meta-patterns picked up by earlier generations and instantiated in cascades during individual development.
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, the information processing mechanisms developed, and the motivations triggered in various contexts. But some aspects of these mechanisms will be common across the species. For example, not all cultures use advanced mathematics in designing buildings, but all use previously evolved understanding of space, time and motion.
All of this implies that evolution has 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 environments.
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 Annette 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' (as proposed at one stage 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, barriers, taps that can be turned on or off, etc.).
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 EPI 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 EPI 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.
Evolution and use of derived construction kits (DCKs), both concrete and abstract (as required for many forms of information processing), uses a process of multi-layer feedback partly like the Chappell-Sloman conjectures depicted in Figure EPI.
The repeated use by evolution of increasingly complex and abstract designs, shows that the theory of evolution by design is basically correct except that there is no single initial design: new designs are repeatedly created and put to use. That seems to include designs used in ancient mathematical minds, still available in the human genome, that have so far eluded AI researchers, and everyone else.
The relationships vary between water-dwellers, 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 (2008): that's the main reason why embodiment is relevant to evolved cognition. However, as organisms grow more complex, with more complex behavioural alternatives and more options to choose between, requiring actions extended over space and time, cognitive processing must become increasingly disembodied, i.e. disconnected from sensory and motor subsystems. For example, if some plan unexpectedly goes badly wrong, working out how that happened may require reflecting in detail on the processes that occurred and the un-tried alternatives. The results of that process of analysis may prove life-saving at some future time. Enactivist, anti-cognitivist, anti-computational theories of cognition are rightly given short shrift in Rescorla (2015). (Most of the achievements of human mathematics, science and engineering, and even philosophy, would have been impossible if enactivist/embodied theories of cognition were close to the truth. Developing an enactivist/disembodied theory of cognition is itself a mostly disembodied process!)
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 engineers.
If the parallel axiom is removed what remains is still 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 obstacles.
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 types of affordance that as far as I know he did not consider, namely reasoning about possible and impossible alterations to spatial configurations and necessary consequences of possible alterations. How brains represent possibilities, impossibilities, and necessary consequences (as opposed to learnt associations) is, as far as I know, still open.
The (topological) impossibility of solid linked rings becoming unlinked is usually obvious even to children without any mathematical education. E.g.
This rubber-band example is harder to understand:
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. Weaver birds are among the most obvious candidates.
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.
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 (1952). E.g. it seems that recognition of transitivity of one-one correspondence is not achieved until about the 5th or 6th year. (What would have to change in brains to make that occur?)
However, I suspect that (as Kant seems to have realised) the genetically provided mathematical powers of intelligent animals make more use of topological and semi-metrical geometric reasoning, using analogical, non-Fregean, representations, than the logical, algebraic, and statistical capabilities that have so far dominated AI and robotics. (Sloman (1971) and chapter 7 of Sloman 1978)
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. http://www.cs.bham.ac.uk/research/projects/cogaff/crp/#chap8.html
(NB 'analogical' does not imply 'isomorphic' as often suggested. A typical 2D picture (an analogical representation) of a 3D scene cannot be isomorphic with the scene depicted. A 3D to 2D projection is not an isomorphism except in special cases. There is a deeper distinction between Fregean and Analogical forms of representation Sloman (1971), concerned with the relationships between representation and what is represented.
Such transitions occur both in individual development in intelligent species and also in evolution of complex organisms.
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), including abstract construction kits needed for intelligent organisms (e.g. grammar construction kits in humans), enhances both the mathematical and the ontological creativity of evolution, which is indirectly responsible for all the other known types of creativity.
Although I have not developed the idea in this paper, the work on construction kits and their essential role in evolution on this planet, suggests that there are weak but important analogies between epigenetic processes in individual humans illustrated in Figure EPI, and some evolutionary processes. In both cases, the development depends on discovery of powerful abstractions ("moving upwards") that can be instantiated in different ways in different species or the same species at different times ("moving downwards"), instead of all evolution being simply "sideways" movement at a fixed level of abstraction in design.
(This distinction is ignored by theories of mathematical discovery by humans that emphasise use of metaphor and analogy instead of use of abstraction and multiple re-instantiation.)
The fact that many evolved construction kits, and their products, depended on natural selection "discovering" enormously powerful re-usable mathematical abstractions, whose re-use involved not just copying, but instantiation of a generic schema with new parameters, illustrates a partial analogy between epigenesis in intelligent organisms and epigenesis in evolution. To that extent I am proposing that some aspects of evolution need intelligent design, more precisely intelligent abstraction of powerful re-usable structures from special cases, but all the intelligence used in evolutionary design processes was previously produced by evolution.
This helps to counter both the view that all of 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, to include 'Meta-Descriptive Metaphysics'.
This contrasts with the once-popular theory that humans are born so helpless because if they were retained in the mother until their brains were fully formed the mothers would be more likely to die in childbirth; or the alternative theory that walking upright is not compatible with having a large enough pelvic aperture for a birth several years later. A different explanation is offered in this Scientific American blog:
"Rosenberg additionally noted-and I found this especially fascinating-that the authors mention the possibility that the timing of birth actually optimizes cognitive and motor neuronal development. That idea, first proposed by Swiss zoologist Adolf Portman in the 1960s, is worth pursuing, she says. 'Maybe human newborns are adapted to soaking up all this cultural stuff and maybe being born earlier lets you do this,' she muses. 'Maybe being born earlier is better if you're a cultural animal.' Food for thought."
Types of competence, rather than types of species
When Jackie Chappell came to the University of Birmingham in 2004 we began to discuss these ideas and she quickly pointed out that it was incorrect to assume that altricial species were uniformly incompetent at birth. For example, most are very competent at sucking soon after birth. She suggested that it would be more appropriate to contrast precocial and altricial competences, allowing that species may differ in the initial variety and proportions of competences of both sorts. She also helped me see that future intelligent robots would require similar mixtures -- including precocial competences used for bootstrapping and altricial competences that begin to develop only after information gained by using precocial competences has been acquired, analysed and organised. This also allowed some species with a long process of development to have genomes that initiated development of more sophisticated altricial competences at different stages of development.
In 2005, we presented a paper suggesting that future intelligent robots would also require such layers of development in which more sophisticated types of competence could begin their development at later stages, building on earlier competences.
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NOTE: some of the links to other researchers' web pages are out of date, but in most cases a search engine should take you to the new location.
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