*
Construction kits for biological evolution
Aaron Sloman
Invited contribution to: The Incomputable
Eds. Mariya Soskova and S Barry Cooper
DRAFT: Revised Apr 16, 2015
This is part of the Turing-inspired Meta-Morphogenesis project, which aims to
identify transitions in information-processing since the earliest
proto-organisms, in order to provide new understanding of varieties of
biological intelligence. Transitions depend on "construction-kits", including
the initial "Fundamental Construction Kit" (FCK) based on physics and Derived
Construction Kits (DCKs) produced by evolution, development, learning and
culture. Some construction kits (e.g. Lego, Meccano, plasticine, sand) are
concrete: using physical components and relationships. Others (e.g. grammars,
proof systems and programming languages) are abstract: producing abstract
entities, e.g. sentences, proofs, and new abstract construction kits. Mixtures
of the two are hybrid kits. Some are meta-construction kits: able to
create, modify or combine construction kits. Construction kits are generative:
they explain sets of possible construction processes, with mathematical
properties and limitations. Evolution and development demonstrate new
possibilities for construction kits: evolution as a "blind theorem prover",
proving "theorems" about what is and is not possible for the kits used,
including meta-cognitive abilities to think and reason about mathematical
discoveries, and discuss them with others. FCKs and DCKs help to provide new
answers to old philosophical questions, e.g. about the nature of mathematics,
language, mind, science, and life, and expose deep connections between science
and metaphysics. The requirement to show how the FCK makes everything else
possible provides a challenge for physicists: demonstrate that the fundamental
theory can explain how all the products of natural selection are possible. A
core thread is the connection of control and semantic information. The aim is
to explain, not reduce. This paper introduces a large research programme
that seems to have a chance of being progressive, in the sense of
Lakatos.
1 Background: What is science? Beyond Popper and Lakatos
How was it possible for
the known and unknown varieties of life to evolve from lifeless matter,
including some varieties that are able to make the mathematical discoveries
such as those in Euclid's Elements?1
The answer proposed here is based on construction kits, both fundamental and
derived.
Popper, [1934] distinguished scientific and non-scientific statements. He
required the former to be empirically falsifiable, otherwise they were
metaphysical. This criterion has been blindly followed by many scientists who
ignore the history of science. E.g. the ancient atomic theory of matter was not
falsifiable, but was an early example of a deep scientific theory. Popper
(unlike many of his admirers) acknowledged that some unfalsifiable
"metaphysical" theories were precursors of scientific theories. But labelling
them "metaphysics" rather than "science" is misleading, because of their
importance for science.2
Imre Lakatos () extended Popper's philosophy of science,
proposing ways of evaluating competing scientific research programmes, based on
their progress over time. He offered criteria for distinguishing "progressive"
from "degenerating" research programmes over time, on the basis of their
different patterns of development. What appears to be a decisive victory (like
Young's evidence of diffraction of light, apparently refuting Newton's particle
theory of light) may later be overturned (e.g. by evidence for the dual
wave-particle nature of light).
Chapter 2 of
Sloman, [1978]3
extended the ideas of Popper and Lakatos to accommodate scientific theories
concerned with what is possible, e.g. types of plant, types of animal,
types of reproduction, types of thinking, types of learning, types of verbal
communication, types of molecule, types of chemical interaction, and types of
biological information-processing - the focus of the Meta-Morphogenesis
project first presented in Sloman, [2013b]4
.
A separate paper5
discusses in more detail the general concept of "explaining possibilities",
its importance in science, the criteria for evaluating such explanations, and
how this notion conflicts with the falsifiability requirement for scientific
theories. Further examples are in Sloman, [1996a].
Insisting on sharp boundaries between science and metaphysics harms both. Each
can be pursued with rigour and openness to specific kinds of criticism. Some of
the criteria for evaluating theories of what is possible, including theories
that straddle science and metaphysics, were presented in sections 2.5.4-5 of
Sloman, [1978,Ch. 2], and in the section entitled
"Why allowing non-falsifiable theories doesn't make science soft and mushy" in
the companion paper to this (Note 5). The ideas presented here
are offered as a contribution to metaphysics as well as science - but
incomplete science, leaving much to be done. There are also connections with
Kant's philosophy of mathematics, extended here to biological/evolutionary
foundations of mathematics (BEFM). Possible engineering applications include
addressing current gaps between AI and animal intelligence.
2 Fundamental and Derived Construction Kits (FCK, DCKs)
Life requires construction kits supporting construction of machines with many
capabilities, including growing highly functional bodies, immune systems,
digestive systems, repair mechanisms, and reproductive machinery. The
requirements for life include information-processing (e.g. deciding what to
repair) as well as physical construction (assembling matter). The Fundamental
Construction Kit (FCK) provided by the physical universe when our planet came
into existence was sufficient to make possible all the forms of life that have
so far evolved on earth, meeting challenges that drove selection of new life
forms. The FCK also makes possible many unrealised but possible forms of life,
in possible but unrealised types of physical environment. How does it make all
these things possible?
Figure
Figure 1: This is a crude representation of the Fundamental
Construction Kit (FCK) (on left) and (on right) a collection of trajectories
from the FCK through the space of possible trajectories to increasingly complex
mechanisms.
Fig. 1 indicates crudely how a common initial construction kit
generates many possible trajectories in which components of the kit are
assembled to produce new instances (living or non-living). Products of a
construction kit can have mathematical features that are useful, e.g. negative
feedback. So evolution produces mathematical competences implicit in
biological mechanisms. This may lead later to explicit mathematical and
meta-mathematical competences in some species, eventually providing new
biological/evolutionary foundations for mathematics.
The history of technology, science and engineering includes many
transitions in which new construction kits are derived from old ones. That
includes the science and technology of digital computation, where new
advances used (among other things):
- punched cards, punched tape, and mechanical sorting devices,
-
electronic circuits, switches, mercury delay lines, vacuum tubes,
switchable magnets, and other devices,
-
arrays of transistors, connected electronically,
-
machine language instructions expressed as bit-patterns,
initially laboriously `loaded' into a computer by setting banks of switches,
-
symbolic machine languages composed of mnemonics that are "translated" by
mechanical devices into bit-patterns on punched cards or tapes that
can be read into a machine to get it set up to run a program,
-
compilers and assemblers that translate symbolic programs
into bit patterns,
-
operating systems: that manage other programs and hardware resources,
-
many types of higher level programming language that are compiled to
machine language or to intermediate
level languages before programs start running,
-
higher level programming languages that are never compiled (i.e.
translated into and replaced by programs in lower level languages) but are
interpreted at run time, with each interpreted instruction triggering a
collection of behaviours, possibly in a highly context sensitive way.
Products of evolutionary trajectories from the FCK may combine to form Derived
Construction Kits (DCKs) (some specified in genomes, and some designed or
discovered by individuals, or groups), that speed up construction of more
complex entities with new types of properties and behaviours, as crudely
indicated in Fig. 2. In convergent evolution, new DCKs evolve in
different species in different locations, with overlapping functionality, using
different mechanisms. A DCK producing mechanisms enabling elephants to learn to
use trunk, eyes, and brain to manipulate food may share features with a DCK
enabling primates to acquire abilities to use hands, eyes, and brains to
manipulate food. Both competences, apparently using related mathematical control
structures, evolved after the last common ancestor.
Figure
Figure 2: Further transitions: a
fundamental construction kit (FCK) on left gives rise to new evolved "derived"
construction kits, such as the DCK on the right, from which new trajectories can
begin, rapidly producing new more complex designs, e.g. organisms with new
morphologies and new information-processing mechanisms. The shapes and colours
(crudely) indicate qualitative differences between components of old and new
construction kits.
Biological evolution seems to have produced many branching lineages of
increasingly complex re-usable construction kits, adding new, more complex,
types of physical and chemical process (e.g. new forms of reproduction), and
increasingly complex forms of information-processing. Details of human-designed
forms of computation look very different from evolved biological layers of
machinery for assembling complex information-processing systems from simpler
ones. But there may be deep similarities of function, including use of virtual
machinery, discussed below. Over time, human designers use their evolved
mechanisms, to produce larger, more complex, and more powerful systems, with the
aid of increasingly complex tools for designing, building, testing and
debugging. Likewise evolution.
Some new biological construction kits allow creation of new physical materials
with new properties - e.g. different weight/strength ratios, different kinds of
flexibility and elasticity, different sorts of permeability, different ways of
storing, releasing and using energy, different ways of producing motion,
different forms of reproduction, and many more, all making use of new chemical
mechanisms, including products of "biological nano-engineering".
Different life-forms (microbes, fungi, slime moulds, plants of many sizes and
shapes, invertebrate and vertebrate animals of many kinds) have produced
different sorts of physical materials used in constructing bodies, or extensions
of bodies such as webs, cocoons and egg-shells. Examples include the cellulose
and lignin structures that provide the strength of large plants that grow
upwards out of soil, the materials in animals that produce rigid or semi-rigid
structures (bones, shells, teeth, cartilage), the materials used in flexible
structures with high tensile strength (e.g. tendons, vines), materials used in
absorbing nutrients, oxygen, or water from the environment, materials
transported between body parts, for different purposes (nutrients, waste matter,
hormones, information, e.g. about stress or damage), materials concerned with
storage and transfer or deployment of energy, for heat, for applying forces, for
mobility, for reproduction, and many more.
Note on "Making Possible":
The assertion "X makes Y possible" does not imply that if X does not exist
then Y is impossible. All that is claimed is that one route to existence of Y is
via existence of X. If X is built, that makes construction of Y easier. However,
other things than X can make Y possible, for instance, an alternative
construction kit. So "makes possible" should be interpreted in our discussion
as a relation of sufficiency, not necessity. The exception is the case where X
is the FCK - the Fundamental Construction Kit - since all concrete
constructions must start from that. If X and Y are abstract, it is not clear
that there is something like the FCK to which they must be traceable. The space
of abstract construction kits may not have a fixed "root" kit. However, the
abstract construction kits that can be thought about by physically implemented
thinkers may be more constrained.
Note on Construction Kit Ontologies:
A construction kit (and its products) can exist without being described. However
scientists need to use various forms of language in order to describe the
entities they observe or postulate in explanations. So a physicist studying the
FCK will need one or more construction kits for defining concepts, formulating
questions, formulating theories and conjectures, constructing models, etc. Part
of the process of science is extending the construction kit for theory
formation, which includes extending the language used. Some of the later
theories about DCKs (including theories about virtual machines in computer
systems engineering) may include concepts that are not definable in terms
of the concepts used in theories about the FCK, even though everything created
using the DCK is fully implemented in the FCK. For more on this see
Sloman, [2013a].
2.1 The variety of biological construction kits
As products of physical construction kits become more complex, with more ways of
contributing to needs of organisms, and directly or indirectly to reproductive
fitness, their use requires increasingly sophisticated control mechanisms, for
which additional sorts of construction kit are required, including kits for
building various sorts of information-processing mechanisms.
The simplest microbes use only a few (usually chemical) sensors providing
information about internal states and the immediate external physical
environment, and have very few behavioural options. They acquire, use and
replace fragments of information, using the same types of internal information
throughout their life. More complex organisms acquire and use information about
enduring spatial locations in extended terrain whose contents include static and
changing resources and dangers. Some can construct and use complex (internal
or external) information stores about their environment. Some of them also
acquire and use information about information-processing, in themselves and in
others, e.g. conspecifics, predators and prey. What features of construction
kits support these developments?
Some controlled systems have states represented by a fixed set of physical
measures, often referred to as "variables" and "constants", representing
states of sensors, output signals, and internal states of various sorts.
Relationships between state-components are represented mathematically by
equations, including differential equations, and possibly also constraints (e.g.
inequalities) specifying restricted, possibly time-varying, ranges of values for
the variables. Such a system with N variables has a state of a fixed dimension,
N. The only way to store new information in such systems is in static or dynamic
values for the variables - changing "state vectors". A typical example is
Powers, [1973], inspired by Wiener, [1961] and Ashby, [1952].
There are many well understood special cases of this pattern, such as simple
forms of homeostatic control using negative feedback. Neural net controllers may
be very much more complex, with variables typically clustered into strongly
interacting sub-groups, and perhaps groups of groups, etc.
Recent discoveries indicate that some biological mechanisms use
quantum-mechanical features of the FCK that we do not yet fully understand,
providing forms of information-processing that are very different from what
current computers do. E.g. a presentation by Seth Lloyd, summarises quantum
phenomena used in deep sea photosynthesis, avian navigation, and odour
classification.6
This may turn out to be the tip of an iceberg of quantum-based
information-processing mechanisms (e.g.
Hameroff and Penrose, [2014]).
2.2 More varied mathematical structures
In the last century, the variety of types of control in artefacts exploded,
including use of logic, linguistics, and various parts of AI dealing with
planners, learning systems, problem solving systems, vision systems, theorem
provers, teaching systems, map-making explorers, automated circuit designers,
program checkers, and many more. The world wide web can be thought of as an
extreme case of a control system made up of millions of constantly changing
simpler control systems, interacting in parallel with each other and with
millions of display devices, sensors, mechanical controllers, humans, and many
other things. So the types of control mechanism in computer-based systems now
extend far beyond the sorts familiar to control engineers, and studied in
control theory.7
Many different sorts of control system may be required in the life of a single
organism, e.g. between an egg being fertilised and the death of the organism.
Not all natural control functions are numerical. A partially constructed
percept, thought, question, plan or terrain description has parts and
relationships, to which new components and relationships can be added and
others removed, as the construction proceeds and the product (percept, thought,
plan, map) becomes more complex - unlike a fixed size collection of changing
numerical values. Different branches of numerical and non-numerical mathematics
are suited to the problem of designing or understanding such systems, including
graph theory, lattice theory, knot theory, category theory, set theory, logic,
mathematical linguistics and others. For a full understanding of mechanisms and
processes of evolution and development, new branches of mathematics are likely
to be needed, including mathematics relevant to complex non-numerical structural
changes, such as revising a grammar for internal records of complex structured
information.
Traditional vector- and equation-based control theories, even with probabilistic
extensions, are not general enough for intelligent control systems that build
and use sentences, problem descriptions, changing ontologies, explanatory
theories, plans of varying complexity, new types of learning mechanism, systems
of motives, values, social rules, and rule-based games, among other things. A
fixed set of equations cannot adequately represent steady growth of increasingly
complex molecular structures [Anderson, 1972]. Evolution, like human
mathematicians and computer scientists millions of years later, built
construction kits and information structures able to cope with structures and
processes of changing complexity, unlike models and mechanisms based only on
fixed sets of variables linked by equations - unable to represent either the
meaning of a sentence, such as this one, or what can exist on a skyscraper
construction-site, or many other perceived processes, including waves breaking
on a rocky seashore, an intricately choreographed ballet, or a symphony.
It is unlikely that all the required forms of information, all the forms of
control, and all the types of physical mechanism required for implementation are
already understood by scientists and engineers. Yet the FCK along with the DCKs
produced directly or indirectly by natural selection must be sufficiently
general to model and explain everything that has evolved so far, and the things
they have created and will create in future.
The huge variety of types of construction kit cannot be surveyed here. Instead
of a complete theory: this paper merely presents a research framework within
which gaps in our understanding can be discovered and in some cases filled,
possibly over several decades, or even centuries. This first draft specifies
some features of old and new construction kits, in the hope that additional
research will extend the answers.
The planet on its own could not generate all those life forms. Energy from solar
radiation is crucial for life on earth (though future technologies may remove
that dependence). Other external influences that were important for the
particular forms of life that evolved on earth included asteroid impacts, and
cosmic radiation.8
Before our solar system formed, the fundamental construction-kit was potentially
available everywhere in the universe, making possible the formation of galaxies,
stars, clouds of dust, planets, asteroids, and many other lifeless entities, as
well as supporting all forms of life, possibly through derived construction kits
(DCKs) that exist only in special conditions. Local conditions e.g.
extremely high pressures, temperatures, gravitational fields, distribution of
kinds of matter, etc. can locally mask some parts of the FCK or prevent them
from functioning.
According to some physical theories, every physical particle is (or can be)
spread out over large areas, or possibly over the whole universe: nevertheless
there must be differences in what exists in different places, for different
processes can occur in different places.
The FCK must in some sense be available at the centre of the sun, but that does
not mean that animal life or plant life can exist there. Likewise if the cloud
of dust from which the earth is thought to have formed had been composed mostly
of grains of sand, then no DCK capable of supporting life as we know it could
have emerged, since earth-life depends on the presence of carbon,
oxygen, hydrogen, iron, and many other elements.
As the earth formed, the new physical conditions created new DCKs that made the
earliest life forms possible. Ganti, [2003] presents a deep analysis of
requirements for a DCK that supports primitive life forms. That DCK (building on
the FCK) made possible both the formation of pre-biotic chemical structures and
very simple life forms, and also the environments in which they could
survive and reproduce. But there's more to life than primitive life forms!
3 Construction kits generate possibilities and impossibilities
Explanations of how things are possible can refer to construction kits, either
manufactured, e.g. Meccano and Lego, or composed of naturally occurring
components, e.g. boulders, mud, or sand. (Not all construction kits have clear
boundaries.) Each kit makes possible certain types of construct, instances of
which can be built by assembling parts provided in the kit. Some construction
kits use products of products of biological evolution. For example, some birds'
nests are assembled from twigs or leaves.
In some cases, properties of components, such as shape, are inherited by
constructed objects. E.g. objects composed only of Lego bricks joined in the
"standard" way all have external surfaces that are divisible into faces
parallel to the surfaces of the first brick used. However, as Ron Chrisley
pointed out to me, when two Lego bricks are joined at a corner only, using only
one stud and socket, it is possible to have continuous relative rotation
(because studs and sockets are circular).
More generally, constructed objects can have features none of the components
have, e.g. a hinge is a non-rigid object that can be made from rigid objects:
two rigid objects with aligned holes through which a rod or screw is passed,
creating a flexible object from non-flexible parts. A connected structure in a
2-D film cannot have a channel going right through it, whereas a 3-D structure
can. There are many such examples of emergent novelty [Anderson, 1972]. I am
not aware of any exhaustive taxonomy of ways of producing novel powers,
structures and processes by combining old parts in new ways: apart from the
implicit taxonomy in life forms.
A construction kit that makes some things possible and others impossible can be
extended so as to remove some of the impossibilities, e.g. by adding a hinge to
Lego, or adding new parts from which hinges can be assembled. Another option is
to recruit something outside the kit, e.g. a gravitational field. Something like
a seesaw can be made using gravity (part of the FCK) to keep one piece
supporting another that behaves as if hinged at the centre.
Lego, meccano, twigs, mud, and stones, can all be used in construction kits
whose constructs are physical objects occupying space and time: concrete
construction kits. There are also non-spatial abstract construction kits,
for example components of languages, such as vocabulary and grammar, or methods
of construction of arguments or proofs. Physical representations of such
things, however, can occupy space and/or time, e.g. a spoken or written
sentence, a diagram, or a proof presented on paper, or orally. There are also
hybrid concrete+abstract construction kits, such as the physical
components of a chess set combined with abstract rules of chess.
In some hybrid construction kits the physical pieces are not essential. For an
expert, physical components of a chess set are dispensable: the abstract kit
suffices for representing the abstract structures, states and processes, though
communication of moves between players needs physical mechanisms, as does a
player's brain (in ways that are not yet understood). Related abstract
structures, states and processes can also be implemented in computers, which can
now play chess better than most humans, without replicating human brain
mechanisms, which have different strengths and weaknesses.
3.1 Construction kits for making information-users
Not everything that can play a role in acquisition, storage or transfer of
information has information-processing capabilities. Consider a construction kit
using material that can be deformed under pressure, e.g. plasticine or damp
clay. If some object, e.g. a coin, is pressed against a lump of the material the
lump will change its shape, acquiring a new depressed portion whose surface has
the inverted shape and size of part of the pressed object. Some entities with
information-processing capabilities (e.g. archaeologists, or detectives) may be
able to use the depression as a source of information about the coin. But the
lump of material is not an information user. Likewise the fact that some part of
a brain is changed by perceptual processes in an organism does not imply that
that portion of the brain is an information user. It may play a role analogous
to the lump of clay, or a portion of sand with footprints that last until the
next time rain falls or a wind blows.
The clay does not, in itself, have the ability to make use of those
relationships, but if something else can inspect the clay it may be able to take
decisions or answer questions about the things that have been pressed into it,
including quite abstract questions, e.g. whether any two of the objects were
similar in shape, or how they differ. But we must be careful not to jump to
conclusions from uses we can make of physical differences, as may happen
when scientists discover changes in brain states correlated with things for
which we have labels. Additional mechanisms are required if available
information is to be used: What sort of mechanism will depend on what sort of
use. A photocopier acquires information from a sheet of paper, but all it can do
with the information is produce a replica (possibly after slight modifications
such as changes in contrast, intensity or magnification).
Additional mechanisms are required for
recognising text, correcting spelling, analysing the structure of an image,
interpreting it as a picture of a 3-D scene, or using information about the
scene to guide a robot, or build a copy of the scene.
Different sorts of construction kit are required for producing those mechanisms.
In organisms, the kits have different evolutionary histories: for example,
mechanisms for finding, understanding, and correcting text evolved long after
mechanisms able to use visual information for avoiding obstacles or for grasping
objects. In some cases, the mechanisms that use information seem to be direct
products of biological evolution, including blinking as a defense mechanism, and
other reflexes. In other cases, the detailed mechanisms are developed by
individuals using mechanisms produced by evolution: for example: individual
humans in different cultures develop different language-understanding
mechanisms, but presumably they use a generic language construction kit shared
with other humans. After use of such a kit begins it may be modified in ways
that support further learning or development of a specific type of language. In
some species, especially those using sexual reproduction, there may be
considerable diversity in the construction kits produced by individual genomes,
leading to even greater diversity in adults, if they develop in different
physical and cultural environments.
3.2 Different roles for information
Across all the diversity of biological construction-kits and the mechanisms that
they produce in individuals there are some common recurring themes, including
requirements for different types of information-based control state, such as
information about how things actually are ("belief-like" information states),
information about how things need to be for the individual information user
("desire-like" information states), and information about steps to take to
achieve certain results ("procedural information states") - See
Sloman, [1996b]. Biological construction kits can support those cases in
different ways, depending on details of the environment, the animal's sensors,
its needs, the local opportunities, and the individual's history. In some cases
different mechanisms performing one of these functions share a common
evolutionary precursor that has been modified in different ways. In other cases
the mechanisms evolve independently - co-evolution.
A simple case is a thermostat that turns a heater on or off, discussed in
McCarthy, [1979]. It has two sorts of information: (a) about a target
temperature set by a user (desire-like information) and (b) about current
ambient temperature, provided by a sensor (belief-like information). The
discrepancy between the two information items is used by the thermostat to
select between turning a heater on, or off, or leaving it as it is.
This is a very simple homeostatic mechanism, using information and a source of
energy to maintain a state. Many biological and human-designed control
mechanisms acquire information through transducers and use the information in
combination with energy sources, to produce, maintain or avoid various states of
affairs. The causal role a physical state or change plays in controlling
something else, e.g. controlling deployment of energy, altering direction of
growth, selection of mode of analysis of information, among many others, can be
described as providing information, in this case control information.
As Gibson, [1966] pointed out, acquisition of information often requires
cooperation between processes of sensing and acting. In animal vision, saccades
are actions that constantly select new information samples from the environment
(e.g. from the optic cone). The use of that information is very different in
different contexts, e.g. controlling grasping, controlling preparation for a
jump, controlling avoidance actions, or sampling portions of text while reading.
A particular sensor can therefore be shared between many control subsystems
[Sloman, 1993], and the significance of particular sensor inputs will depend
partly on which subsystems are in control of the sensor at the time, partly on
which others happen to receive information from the sensor (assuming channels
can be turned on or off).
The study of varieties of use of information in organisms is exploding, and now
includes many mechanisms on molecular scales within much larger organisms as
well as many intermediate levels of informed control, including sub-cellular
levels (e.g. metabolism), physiological processes of breathing, temperature
maintenance, digestion of food, blood circulation, control of locomotion,
feeding and mating of large animals and coordination across communities, such as
collaborative foraging in insects and trading systems of humans. Slime moulds
include spectacular examples in which modes of acquisition and use of
information change dramatically.9
The earliest evolved machines must have acquired and used information about
things inside themselves and in their immediate vicinity, e.g. using chemical
detectors in an enclosing membrane. Later, evolution extended those capabilities
in dramatic ways. In the simplest cases, local information is used immediately
to select between alternative possible actions, as in a heating control, or
trail-following mechanism. Uses of motion in haptic and tactile sensing and use
of saccades, changing vergence, and other movements in visual perception all
exemplify the interplay between sensing and doing, in "online intelligence".
But there are cases ignored by Gibson and by researchers opposed to cognitive
theories, namely organisms that exhibit "offline intelligence", using
perceptual information for tasks other than controlling immediate reactions, for
example, reasoning about remote future possibilities or attempting to explain
something observed. Offline intelligence requires use of previously acquired
information about the environment including particular information about
individual objects and their locations or states, general information about
learnt laws or correlations and information about what is and is not possible.
One information-bearing structure (e.g. the impression of a foot, the shape
of a rock) can provide very different information to different
information-users, depending at least on (a) what kinds of sensors they can use
to get information from the structure, (b) what sorts of information-processing
(storing, analysing, comparing, combining, synthesizing, retrieving, deriving,
using...) mechanisms the users have, (c) what sorts of needs or goals they can
serve by using various sorts of information (knowingly or not).
So, from the fact that changes in some portion of a brain are strongly
correlated with changes in some aspect of the environment we cannot conclude
much about what information about the environment the brain acquires and uses or
how it does that - any more than discovering footprints in the sand where
animals walk, tells us that a beach perceives animals.
3.3 Motivational mechanisms
It is often assumed that every information user, U, must be trying to achieve
some reward or avoid some punishment (negative reward). In that case, the effect
of U acquiring some new item of information, I, will be to make some actions
more likely, and others less likely, on the basis of what U has previously
learnt about which actions increase positive rewards or decrease negative
rewards under conditions indicated by I. Many AI systems and psychological
theories are based on that assumption.
However, this ignores some of the sophistication of evolution. Animals are not
all restricted to acting on motives selected on the basis of rewards expected by
the individual. They may also have motive construction mechanisms that are
simply triggered as "internal reflexes" by certain states of affairs, without
having any knowledge or expectations regarding beneficial consequences of
achieving those motives, just as evolution produces phototropic reactions in
plants without giving plants any ability to anticipate benefits to be gained
from light. Some reflexes, instead of directly triggering behaviour instead
trigger construction of new motives, which may or may not lead to behaviour,
depending on how important other competing behaviours are. For example, in a
kind person, watching someone fall may trigger a motive to rush to help. But
that motive may not generate action if competing motives are too strong. Such a
motive need need not be selected because acting on it will produce some reward
for the actor, contrary to the widely held view that all motivation is
reward-based. Sloman, [2009] labelled such reflex motive
generation as "architecture-based motivation" in contrast with "reward-based
motivation" where motives are selected on the basis of anticipated rewards.
Behaviours apparently produced by architecture-based motivations can be observed
in young children and the young of other playful intelligent animals. When
watching such "idle" behaviours it may be tempting to invent hypothetical
rewards but the assumption that expected rewards must always play a role
in motive generation is just a prejudice. In some cases choosing between motives
can take rewards into account, but moral principles or mere habits, may suffice
instead.
One of the benefits of certain automatically triggered motives is that acting on
them will sometimes produce new information, by sampling properties of the
environment. That information may not be immediately usable, but in combination
with other episodes of information storage may enable some later processes to
analyse and reorganise the stored information. The individual need not have any
conception of that later process when the information is acquired, though the
ancestors of that individual may have benefited from the presence of the
mechanisms of information gathering later used for information reorganisation
(labelled "Representational Redescription" in Karmiloff-Smith, [1992]).
During evolution, and in some species also during individual development, the
sensor mechanisms, the types of information-processing, and the uses to which
various types of information are put, become more diverse and more complex,
while the information-processing architectures allow more of the processes to
occur in parallel (e.g. competing, collaborating, invoking, extending,
recording, controlling, redirecting, enriching, training, abstracting, refuting,
or terminating). If we don't understand the architecture and the many
information-processing functions it supports, and how they are related, and how
they grow and diversify, we are likely to reach wrong conclusions about
biological functions of the parts: e.g. over-simplifying the functions of
sensory subsystems, or over-simplifying the variety of concurrent control
mechanisms producing behaviours. The architectural knowledge about how such a
systems works may not be expressible in sets of differential equations, or
statistical learning mechanisms and relationships. (For important but partial
attempts to characterise some architectural roles in human
information-processing see
Minsky, [1987,Minsky, [2006,Laird et al, [1987,Sun, [2006]. Compare Sloman, [2003].)
The construction kits required for building information-processing
architectures, with multiple sensors and multiple motor subsystems developing in
complex and varied environments may differ in (a) what they provide as sources
of information, (b) whether their mechanisms allow only immediate use of
information or storage for future use, (c) whether the information is used only
in the form in which it is initially acquired or after modification by
mechanisms for analysing, parsing, interpreting, transforming, combining, or
deriving information, (d) how long they can maintain information and whether it
degrades with time, (e) what other types of information they can be combined
with, possibly different kinds in different contexts, (f) whether use of the
information requires additional information at various stages during the use
(e.g. approximate information used to control a grasping action may require more
detailed information to be added in late stages of the grasp, (g) whether the
additional information needs to have been acquired previously (like the
combination of a lock, which is not needed during approach to the lock) or needs
to be acquired from the environment while acting (like the precise locations of
the lock's controls used in controlling hand movements), (h) whether outcomes of
use of information can be used to modify previously acquired information (e.g.
because the world has changed), (i) whether all the acquired information can be
stored in the user, or whether external records are needed (e.g. diaries, filing
systems, marks on trees), (j) whether the process of using acquired information
can be terminated, temporarily suspended, or modified, by newly acquired,
unexpected information,
(k) whether information pathways through the system are fixed, or can be
modified slowly by learning processes, or rapidly by context sensitive
information management mechanisms,
(l) whether only information known or expected to be
true can be used or whether the organism can explore alternative hypothetical
situations in order to work out their consequences, (m) whether successes and
failures of processes using information merely cause adjustments in future
actions or whether they can lead to re-assessment of the theories used (e.g.
physical theories, chemical theories, theories about intentions of certain
individuals, etc.) and in some cases major revisions of those theories,
(n) whether surprising results can lead to modifications of the ontology used
(e.g.
adding new forces, new kinds of "stuff", genes, new quantum states, etc.).
This list is not meant to be complete: it merely illustrates the complexity and
variety of challenges in understanding the construction kits required for
producing theories or models of biological information-processing. Not all
biological information-processing systems have all these capabilities. Some are
required for all organisms, though their forms can vary. Others, including
abilities to reason about hypothetical possibilities, and to modify ontologies
used, must have been products of relatively recent evolution.
There is much we still do not know about the construction kits used in these
processes, and what they are used for. The Meta-Morphogenesis project aims to
investigate the variety of uses of information and how they evolved, partly in
the expectation there will turn out to be many mechanisms and many uses that we
have not noticed, that are essential for understanding, or replicating, the more
complex control phenomena in living things, including brain functions.
I suspect that assumptions made by neuroscientists about the
information-processing in brains omit some important types, and that AI
researchers influenced by those assumptions therefore fail to replicate
important functions of brains in their machines. Progress in this investigation
may require major conceptual advances regarding what the problems are and what
sorts of answers are relevant. E.g. "Where in the brain are discoveries made?"
"Where do emotions occur in the brain?" "Where in the brain is musical
ability?" "Where do visual experiences (qualia) occur in the brain?" "Where
does understanding occur when you read a sentence?" are all nonsensical
questions. But that does not mean there are no mental states and processes,
including detection of changes in qualia!
3.4 Biological construction kits
How did the FCK generate complex life forms? Is the
Darwin-Wallace theory of natural selection the whole answer?
Graham Bell wrote in [Bell, 2008]:
"Living complexity cannot be explained except through selection and does
not require any other category of explanation whatsoever."
No: the explanation must include both selection mechanisms and
generative mechanisms, without which selection processes will not have a supply
of new viable options. Moreover, insofar as environments providing
opportunities, challenges and threats are part of the selection process, the
construction kits used by evolution include mechanisms not intrinsically
concerned with life, e.g. volcanoes, earthquakes, asteroid impacts, lunar and
solar tides, and many more, in addition to evolved construction kits and their
products.
The idea of evolution producing construction kits is not new, though they are
often referred to as "toolkits".
Coates et al, [2014] ask whether there is "a genetic toolkit for
multicellularity" used by complex life-forms. Toolkits and construction kits
normally have users (e.g. humans or other animals), whereas the
construction kits we have been discussing (FCKs and DCKs) do not all need
external users. Ganti, [2003] explained how chemistry supports
self-sufficiency in very simple organisms.
Both generative mechanisms and selection mechanisms change during evolution
(partly by influencing each other). Natural selection (blindly) uses the initial
enabling mechanisms provided by physics and chemistry not only to produce new
organisms, but also to produce new richer DCKs, including increasingly complex
information-processing mechanisms. Since the mid 1900s, spectacular changes have
also occurred in human-designed computing mechanisms, including new forms of
hardware, new forms of virtual machinery, and networked social systems all
unimagined by early hardware designers. Similar changes during evolution
produced new biological construction kits whose products are
incomprehensible to thinkers familiar only with physics and chemistry.
Biological DCKs produce not only a huge variety of physical forms, and physical
behaviours, but also forms of information-processing required for
increasingly complex control problems, as organisms become more
complex and more intelligent in coping with their environments, including
interacting with predators, prey, mates, offspring, conspecifics, etc. In
humans, that includes abilities to form scientific theories and discover and
prove theorems in topology and geometry, some of which are also used unwittingly
in practical activities.10
I suspect many animals come close to this in their systematic but
unconscious abilities to perform complex actions that use mathematical features
of environments. Abilities used unconsciously in building nests or in hunting
and consuming prey may overlap with topological and geometrical competences of
human mathematicians. (See Section 7.2).
4 Concrete (physical), abstract and hybrid construction kits
Products of a construction kit may be concrete, i.e.
physical, or abstract, like a proof, a sentence, or a symphony; or hybrid,
e.g. a physical presentation of a proof or poem.
Concrete kits: Construction kits for children include physical parts that
can be combined in various ways to produce new physical objects that are not
only larger than the initial components but have new shapes and new behaviours.
Those are concrete construction kits. The FCK is a construction kit, with
concrete and abstract aspects, the subject of much research by physicists.
Abstract kits: Despite the current (deeply confused) fashion emphasising
embodied cognition, many examples of thinking, perceiving, reasoning and
planning, require abstract construction kits. For example, planning a journey to
a conference does not require physically trying possible actions, like water
finding a route to the sea by exploring possible route-fragments. Instead an
abstract construction kit representing possible options and ways of combining
them can be used. Being able to talk requires use of a grammar specifying a
abstract structures that can be assembled using a collection of grammatical
relationships to form new abstract structures with new properties relevant to
various tasks involving information. Sentences allowed by a grammar for English
can be thought of as abstract objects that can be instantiated in written text,
printed text, spoken sounds, morse code, semaphore, and other concrete forms: so
a grammar is an abstract construction kit whose constructs can have concrete
(physical) instances. The idea of a grammar is not restricted to verbal forms:
it can be extended to many kinds of complex structures, e.g. grammars for sign
languages, circuit diagrams, maps, architectural layouts and even molecules.
Human sign languages use different structures from spoken languages.
A grammar does not specify a language: a semantic construction kit,
structurally related to the grammar, is required for building possible
meanings for the language to express. Use of a language depends on language
users, for which more complex construction kits are required, also products of
evolution and learning. (Evolution of various types of language is discussed in
Sloman, [2008], which argues that internal languages must have evolved
first, then sign languages.)
Hybrid abstract+concrete kits: These are combinations, e.g. physical chess
board and chess pieces combined with the rules of chess, lines and circular arcs
on a physical surface instantiating Euclidean geometry, puzzles like the
mutilated chess-board puzzle, and many more. A particularly interesting hybrid
case is the use of physical objects (e.g. blocks) to instantiate arithmetic,
which may lead to the discovery of prime numbers when certain attempts at
rearrangement fail - and an explanation is found.
In computing technology, physical computers, programming languages, operating
systems and virtual machines form hybrid construction kits that can make things
happen when they run. A logical system with axioms and inference rules can be
thought of as an abstract kit supporting construction of logical
proof-sequences, usually combined with a physical notation for written proofs. A
purely logical system cannot have physical causal powers whereas its concrete
instances can, e.g. helping a student distinguish valid and invalid proofs.
Natural selection seems to have "discovered" the power of hybrid construction
kits, especially the use of sophisticated virtual machinery, long before human
engineers did. In particular, biological virtual machines used by animal minds
are more powerful than current engineering designs [Sloman, 2010]. All
examples of perception, learning, reasoning, and intelligent behaviour are based
on hybrid construction kits, though scientific study of such kits is still in
its infancy. This discussion merely scratches the surface of a huge
multi-disciplinary research area. Work done so far on the Meta-Morphogenesis
project suggests that natural selection "discovered" and used a staggering
variety of types of hybrid construction kits that were essential for
reproduction, for developmental processes (including physical development and
learning), for performing complex behaviours, and for social/cultural phenomena.
Jablonka and Lamb, [2005] seem to come close to making this point, though they use
different terminology.
4.1 Kits including external sensors and motors
Some toys interact with the environment by moving parts, e.g. wheels. A simple
toy car may include a spring that can be wound up. When started the potential
energy in the spring is transformed into mechanical energy via gears, axles and
wheels that are in contact with external surfaces. Further interactions,
altering the direction of motion, may result from collisions with fixed or
mobile objects in the environment.
Some construction kits allow assembly of such toys. More sophisticated kits
include sensors that can be used to provide information for an internal
mechanism that uses the information to take decisions concerning deployment of
available energy, for instance using light, sonar, or in the case of rats, using
whiskers, to gain information that allows frequent changes of direction or speed
of motion, e.g. in order to avoid collisions, or in order to move towards a
source of electrical or chemical energy when internals supplies are running low.
Some examples are provided in Braitenberg, [1984], though he (or at least some
of his admirers) unfortunately over-interpreted his vehicles as being capable of
love, fear, etc.11
In some cases the distinction between internal and external components is
arbitrary. For example, a musical box may perform a tune under the control of a
rotating disc with holes or spikes that cause a tone to be produced when they
reach a certain location, during the rotation. The disc can be thought of as
part of the music box. It can also be thought of as part of a changing
environment, in which case the devices that detect the holes or spikes are
external sensors.
If a toy train set has rails or tracks used to guide the motion of the train as
it moves, then the wheels of the train can be thought of as sensing the
environment and causing changes of direction in the train. This is partly like
and partly unlike a toy vehicle that uses an optical sensor linked to a steering
mechanism, so that a vehicle can follow a line painted on a surface. The railway
track provides both the information about where to go and the forces required to
change direction. The painted line, however, provides only the information, and
other parts of the vehicle have to supply the energy to change direction, e.g.
an internal battery that powers sensors and motors. Evolution uses both
sorts: e.g. wind blowing seeds away from parent plants and a wolf
following a scent trail left by its prey. An unseen wall uses force to stop your
forward motion in a dark room, whereas a perceived wall provides information,
not force, causing deceleration [Sloman, 2011].
4.2 Mechanisms for storing, transforming and using information
Some information is acquired, used, then lost because it is immediately
over-written, e.g. sensor information in simple servo-control systems with
"online intelligence", where only the latest sensed state is used for deciding
whether to speed something up, slow it down, change direction, start to grasp,
etc. In more complex control systems, with "offline intelligence", some sensor
information is saved, possibly combined with other previously stored
information, and remains available for use on different occasions for different
purposes. In the second case, the underlying construction-kit needs to be able
to support stores of information that grow with time and can be used for
different purposes at different times. Sometimes a control decision at one time
can use items of information obtained at several different times and places, for
example information about properties of a material, where it can be found, and
how to transport it to where it is needed. Sensors used online may become faulty
or require adjustment. Evolution may provide mechanisms for testing and
adjusting. When used offline, stored information may need to be checked for
falsity caused by the environment changing, as opposed to sensor faults.
(The offline/online use of visual information
has caused much confusion among
researchers, including attempts to interpret the difference in terms of "what"
and `'where" information.12
Compare Sloman, [1983].
There are hugely varied ways of acquiring and using information, some of which
have been discovered (or re-discovered) and modelled by AI researchers,
psychologists, neuroscientists, biologists and others, though it seems that
evolution has achieved a great deal more, not only in humans, but in other
intelligent animals. Many of these achievements require not just additional
storage space but very different sorts of information-processing architectures.
A range of possible architectures is discussed in
Sloman, [1993,Sloman, [2006,Sloman, [2003]. Some types use sub-architectures
that evolved at different times, meeting different needs, in different
biological niches [Sloman, 2000].
This raises the question whether evolution produced "architecture kits" able
to combine evolved information-processing mechanisms in different ways, long
before software engineers discovered the need. Such a kit could be particularly
important for individuals that produce new subsystems, or modify old ones,
during individual development, e.g. during different phases of learning by apes,
elephants, and humans, as described in Section 5.13
4.3 Mechanisms for controlling position, motion and timing
All of the concrete construction kits (and some of the hybrid kits) share a deep
common feature insofar as their components, their constructs and their
construction processes involve space and time, both during construction
processes, as items are moved together and their relationships altered, and
during the behaviour of complex constructed objects. Those behaviours include
both relative motion of parts of an object, e.g. wheels rotating, joints
changing angles, and also motion of the whole object relative to other objects,
e.g. an ape grasping a berry. A consequence of the common spatiality is that
objects built from different construction kits can interact, by changing their
spatial relationships (e.g. if one object enters, encircles or grasps another),
by applying forces that are transmitted through space, and in other ways.
Products of different kits can interact in more complex ways, e.g. one being
used to manipulate another, or one providing energy or information for the
other. This contrasts starkly with the problems of getting software components
available on a computer to interact: merely co-locating them in the same virtual
machine on the same computer will not suffice. There are some rule-based systems
composed of condition-action rules, managed by an interpreter that constantly
checks for satisfaction of conditions. Newly added rules may then be invoked
simply because their conditions become satisfied, though special "conflict
resolution" mechanisms may be required if the conditions of more than one rule
are satisfied.14
Spatial embedding of products allows new construction kits to be formed by
combining two or more concrete kits. In some cases this will require
modification of a kit, e.g. supporting combinations of lego and meccano by
adding pieces with lego studs or holes alongside meccano sized screw holes. In
other cases mere spatial proximity and contact suffices, e.g. when one
construction kit is used to build a platform and others to assemble a house on
the platform. In organisms, products of different construction kits may use
complex mixtures of juxtaposition and adaptation. As mentioned in section
2.1, there is evidence that some organisms can also make use of
non-local quantum effects when complex mechanisms are made of interacting
components, a topic requiring much further research.
Another consequence of the fact that objects exist in space/time is the need for
timing mechanisms. Organisms use many "biological clocks" operating on
different time-scales controlling repetitive processes, including daily cycles,
heart-beats, breathing, and wing or limb movements required for locomotion. More
subtly there are adjustable speeds of motion or change, and adjustable rates of
change. Examples: a bird in flight approaching a perch on which it is to land;
an animal running towards a tree to escape a predator and having to decelerate
as it approaches the tree to avoid a dangerous crash; a hand moving to grasp a
stationary or moving object, with motion controlled by varying coordinated
changes of joint angles at waist, shoulder, elbow and finger joints so as to
bring the grasping points on the hand into a suitable location relative to the
selected grasping points on the object. (The last example is still very
difficult for robots, when grasping novel objects in novel situations: partly
because of designs that use only sensory-motor ontologies.)
There are also mechanisms for controlling or varying rates of production of
chemicals (e.g. hormones).
So biological construction kits need many mechanisms
with abilities to measure time intervals and to control rates of repetition or
rates of change of parts of the organism. These construction kits may be
combined with other sorts of construction kit that require temporal as well as
spatial control, e.g. changing speed and direction of motion simultaneously.
There are different requirements for controlling growth of fixed structures,
e.g. trees growing branches, and for mobile animals.
4.4 Combining construction kits
At the molecular level there is now a vast, and rapidly growing, amount of
research on interacting construction kits, for example interactions between
different parts of the reproductive mechanism during development of a fertilised
egg, interactions between invasive viral or bacterial structures and a host
organism, and interactions with chemicals produced in medical
research laboratories, among many other types.
In the realm of digital computation the ways of combining different toolkits
include the application of functions to arguments, although both functions and
their arguments can be far more complex than the simple cases most people
encounter in learning about arithmetic. For example a function could be a
compiler, its arguments could be arbitrarily complex programs in a high level
programming language, and the output of the function in each case might be
either a report on syntactic errors in the input program, or, if there are no
errors, a machine code program to run on a particular type of computer. The
application of functions to arguments is a very different process from
assembling structures in space time. In the latter case inputs to the process
form parts of the output, which need not be the case with a mathematical or
computational function. If computers are connected via digital to analog
interfaces, linking them to other things, e.g. surrounding matter, or if they
are mounted on machines that allow them to move around in space and interact,
that adds a kind of richness that goes beyond application of functions to
arguments.
That additional richness is present in the modes of interaction of
chemical structures which include both digital (on/off chemical bonds) and
continuous changes in relationships, as discussed by Turing in his paper on the
chemical basis of morphogenesis Turing, [1952] (the paper that inspired the
Meta-Morphogenesis project Sloman, [2013b]).
4.5 Combining abstract construction kits
The possibility of combining concrete construction kits results from the fact
that their instances occupy space and time. Combining abstract
construction kits is not so straightforward. A simple example is combining
letters and numbers to form coordinates for squares on a chess board, e.g.
"a2", "c5", etc. More complex examples include combining notations for a
human language and a musical system for writing songs, or combining a computer
operating system (e.g. Linux) with a programming language (e.g. Lisp). In living
organisms, there are interactions between products of the same or different kits
that involve information, e.g. use of information for sensing, predicting,
explaining or controlling, including information about information
Sloman, [2011].
Researchers on systems combining many kinds of functionality have found it
useful to design information-processing architectures that provide
frameworks for combining different mechanisms and information stores. This is
particularly important in large projects where different research groups are
working on sensors, learning mechanisms, motor subsystems, reasoning systems,
motivational systems, various kinds of meta-cognition, etc., with associated
sets of tools supporting processes of design, implementation, testing,
debugging. Our own SimAgent toolkit Sloman, [1996c], mentioned in Note
14 is one among very many. Some of the common principles
include the need to be able to support different sorts of virtual machines with
causal interactions between them and the physical environment
(including perception and physical actions).
In addition to design patterns for physical mechanisms, biological evolution
also discovered re-usable frameworks for assembling complex
information-processing architectures, accommodating multiple interacting
virtual machines, with different modifications developed by different species -
including humans [Minsky, 1987,Minsky, 2006]. This is a topic for further
research, which will provide new insights into complex mental states and
processes, including forms of self-consciousness, varieties of affective states,
and processes of cognitive development that help to explain mathematical
development.15
Adding a new DCK can make some possible further developments quicker to
reach - fewer additional steps are required than were originally required, and
the total search space for a suitable sequence of steps to a solution may be
considerably reduced. This is partly analogous to the role of previously proved
theorems in a new proof. Using previous results can considerably shorten a
proof, make it more comprehensible, and have a dramatic effect on the size of
the search-space when searching for a proof. If the number of steps to a
solution has been reduced by 10 and there are two options at every step, the
search for a complete design may have been reduced by a factor of 210, i.e.
1024: reducing the remaining evolutionary search space required by a factor
over a thousandfold - if a solution exists in the remaining search space.
Evolutionary search spaces are very much larger, and in principle re-use of
designs
could have an even larger impact on search spaces. So, the ability to
re-use modified versions of useful designs could dramatically reduce an
evolutionary search space - if there is a solution in the remaining search
space.
Creation of new construction kits may start by simply recording parts of
successful assemblies, so that they can easily be reproduced. At later stages
previous stores may be combined to form an appropriate "meta-construction
kit" able to extend or modify or combine previously created construction kits.
Evolution needs to be able to create new meta-construction kits using natural
selection. Natural selection, the great creator/meta-creator, is now
spectacularly aided and abetted by its products, especially humans and their
products!
5 Construction kits built during individual development
Some new construction kits are products of the process of evolution of a species
and are shared between all members of the species (barring genetic
abnormalities), alongside construction kits shared between species, such as
those used in mechanisms of reproduction and growth in related species. But
evolution has also discovered the benefits of what might be called
"meta-construction-kits", namely mechanisms provided for members of a species
that allow individuals to build new construction kits during their own
development.
Examples include mechanisms for learning that are developed by individuals on
the basis of their own previously encountered learning experiences, which may be
different in different environments for members of the same species. Human
language learning is a striking example: things learnt at earlier stages make
new things learnable that might not be learnable by an individual transferred
from a different environment, having experienced a different language.
This contrast between genetically specified and individually built capabilities
for learning and development was labelled a difference between
"pre-configured" and "meta-configured" competences in
Chappell and Sloman, [2007], summarised below in Fig. 3.
Mathematical development in humans seems to be a
special case of growth of meta-configured competences.
Figure
Figure 3: A construction kit gives rise to very
different individuals if the genome interacts with the environment in
increasingly complex ways during development. Precocial species use only the
downward routes on the left, producing preconfigured competences. Competences of
altricial species, using staggered development, may be far more varied. Results
of using earlier competences interact with the genome,
producing meta-configured
competences on the right.
The construction kits used for assembly of new organisms that start as a seed or
an egg enable many different processes in which components are assembled in
parallel, using abilities of the different sub-processes to constrain one
another. As far as I can tell, nobody knows the full variety of
ways in which parallel construction processes can exercise mutual control in
developing organisms. One implication is that there are not simple correlations
between genes and organism features.
Turing's () examples of diffusing chemicals causing
patterns when they interact include only formation of superficial 2-D patterns.
Explaining the different ways in which features of a genome can directly or
indirectly orchestrate many parallel processes of growth, development, formation
of connections, etc. is a far greater challenge. A possible framework for
allowing abstract specifications in the genome to interact with details of the
environment in instantiating complex designs is illustrated schematically in
Fig. 3. This generalises Waddington's "epigenetic landscape"
metaphor Waddington, [1957], by allowing individual members of a species to
partially construct their own epigenetic landscapes instead of merely following
paths in a landscape that is common to the species. Related ideas are in
Karmiloff-Smith, [1992].
Some of the implications of these ideas for attempts to understand genetic
abnormalities such as autism are discussed in
http://www.cs.bham.ac.uk/research/projects/cogaff/misc/autism.html
6 Some constructions exclude or necessitate others
Physical construction kits (e.g. lego, plasticine, or a
combination of paper, scissors and paste) have parts and materials with
physical properties (e.g. rigidity, strength, flexibility, elasticity,
adhesion, etc.), possible relationships between parts and possible processes
that can occur when the parts are in those relationships (e.g. rotation,
bending, twisting and elastic or inelastic resistance to deformation).
Features of a physical construction kit - including the shapes and materials of
the basic components, the ways in which the parts can be assembled into larger
wholes, the kinds of relationships between parts and the processes that can
occur involving them - all contribute to explaining the possibility of
entities that can be constructed from those components, and the possibility of
processes, including both the processes of construction and the behaviours
of the constructs.
Construction kits can also explain necessity and impossibility. A construction
kit that has a very large set of generative powers initially can be used to
build a structure realising some of the kit's possibilities, in which some
further possibilities are excluded, namely all extensions that do not
include what has so far been constructed. Some of the extensions that were
possible before the last addition become impossible unless the last step is
undone.
Figure
Figure 4: Interactions between structure and remaining possibilities:
If a rod that can swing about a point in a plane is in a gap, then
the wider the gap the wider the possible swing, and the shorter the rod for a
fixed size gap, the wider the possible swing. In general, interactions between
structures and possibilities are more complex than this.
Moreover, what has been done may make some further steps possible and others
impossible: e.g. the size of a gap between two rigidly assembled components will
make it impossible to extend the structure by placing some components in the
gap: A beam of 20cm square cross section cannot fit in a 10cm gap. Narrower
beams can fit in the gap, but the angles by which their orientations can vary
will depend on their diameter, the diameter of the gap, and other spatial
relations. the narrower or shorter a beam in the gap, is the wider the angle
through which it can rotate in a plane through the gap. The wider the gap is the
wider the angle through which a beam of a certain width can rotate, while the
longer the gap is the narrower the angle of rotation possible in that plane.
Examples are in Figure 4. Both human engineers and evolution can
make use of similar, though usually more complex, mathematical relationships, in
skeletal geometry for example.
Figure
Figure 5: The sequence of figures, demonstrates how the three-cornered shape has
the consequence that summing the three angles necessarily produces half a
rotation (180 degrees). Since the position, size, orientation, and precise shape
of the triangle can be varied without affecting the possibility of constructing
the sequence, this is a proof that generalises to any planar triangle. This is
an unpublished proof reported to me by Mary Pardoe in the early 1970s.
Figure 5 illustrates a different sort of example, where no
physical properties of a structure (e.g. rigidity or impenetrability of
materials) are involved, only spatial relationships. It presents a proof, found
by Mary Pardoe, that internal angles of a triangle sum to a straight line, or
180 degrees. Unlike the "standard" proofs, this proof makes no explicit
reference to Euclid's parallel axiom. The human mathematical ability to look at
a physical situation, or a diagram representing a class of physical situations,
and reason about constraints on a class of possibilities sharing certain
constraints may have evolved from earlier abilities to reason about changing
affordances in the environment [Gibson, 1979]. Current AI perceptual and
reasoning systems still lack most of these abilities, though that may change.
These are simple examples of the mathematical properties of construction kits
(partly analogous to mathematical properties of formal deductive systems and
AI problem solving systems).
As parts (or instances of parts) of the FCK are combined, structural relations
between components of the kit have two opposed sorts of consequences: they make
some further structures possible, and they make other structures
impossible - and their absence or opposites, e.g. geometrical or topological
properties, will then be necessary consequences of previous selection
steps.
These examples illustrate how a construction kit with mathematical relationships
can provide the basis for necessary truths and necessary falsehoods in some
constructions (as in Sloman, [1962,Chap 7]). Such relationships between
possibilities provide a deeper, more natural, basis for understanding modality
(necessity, possibility, impossibility) than so called "possible world
semantics". Being able to think about and reason about alterations in some
limited portion of the environment is very common and a requirement for
intelligent action [Sloman, 1996a]. In contrast being able to think about the
whole world, past, present and future, and the set of alternative complete
worlds is a far more demanding requirement. Moreover it is not clear how we
could decide whether an individual language user has that capability.
Since our examples of making things possible or
impossible, or changing ranges of possibilities, are examples of causation, this
also provides the basis for a Kantian notion of causation based on mathematical
necessity [Kant, 1781], so that not all uses of the notion of "cause" are
Humean (i.e. based on correlations), even if some are. Compare
Section 6.3.16
Varieties of causation that do not involve mathematical necessity, only
probabilities (Hume?) or propensities (Popper) will not be discussed here.
6.1 Proof-like features of evolution
An unknown subset of the FCK produced fortuitously as a side effect of formation
of the earth, supported (a) primitive life forms and (b) processes of evolution
that produced more and more complex forms of life, including new, more complex,
derived, DCKs. New products of natural selection can make more complex products
more reachable, as with toy construction kits, and mathematical proofs.
Assembling a set of pre-built house parts (walls, door-frames, window-frames,
etc.) provides routes to a collection of possible houses using those parts,
where the routes are much shorter than routes starting from the primitive
components. However starting from those parts will make some designs unreachable
except by disassembling some of the parts first.
Moreover, there was not just one sequence of DCKs: different evolutionary
lineages evolving in parallel can produce different DCKs. According to the
"Symbiogenesis" theory, different DCKs produced independently can sometimes
merge to support new forms of life combining different evolutionary
strands.17 So creation
of new DCKs in parallel evolutionary streams with combinable products can hugely
reduce part of the search space for complex designs, at the cost of excluding
parts of the search space reachable from the FCK. For example, use of DCKs in
the human genome may speed up development of language and typical human
cognitive competences, while excluding the possibility of "evolving back" to
microbe forms that might be the only survivors after a cataclysm. Likewise
adding previously proved theorems to a set of axioms, for use as starting
points for new proofs will reduce the search space for proofs of related
theorems.
6.2 Euclid's construction kit
A much older example, of great significance for philosophy of mathematics, is
the construction kit specified in Euclidean geometry, starting with points,
lines, surfaces, and volumes, and methods of constructing new more complex
geometrical configurations using a straight edge for drawing straight lines in a
plane surface, and a pair of compasses, for drawing circular arcs in a surface.
A different sort of geometry allows line segments to be translated and rotated
in a plane while preserving their length. This is an assumption underlying the
use of rulers for measuring length. Adding movable and rotatable line segments
to Euclidean geometry allows an arbitrary angle to be divided into three equal
parts, which is not possible in standard Euclidean geometry. See
http://www.cs.bham.ac.uk/research/projects/cogaff/misc/trisect.html
A related construction is possible using "Origami geometry".
The idea of spaces of possibilities generated by different sorts of physical
construction kit may be easier for most people to understand than the
comparison with generative powers of grammars or formal systems, though the two
are closely connected, since grammars and axiom systems are both abstract
construction kits that can be parts of hybrid construction kits.
Concrete construction kits corresponding to grammars can be built out of
physical structures: for example a collection of small squares with letters and
punctuation marks can be used to form sequences that correspond to the words in
a lexicon. Adding some blank squares and specifying rules of a grammar based on
that lexicon, produces a new grammar that can be applied to sequences of
squares, with blanks as word-separators, generating a set of possible physical
sentences conforming to the grammar. The use of cursive ("joined up") script
provides a more complex physical construction kit.
Some challenges for construction kits used by evolution, and also challenges for
artificial intelligence and philosophy, arise from the need to explain both how
natural selection makes use of mathematical properties of construction kits
related to geometry and topology, in producing organisms with spatial
structures and spatial competences, and also how various subsets of those
organisms developed specific topological and geometrical reasoning abilities
used in controlling actions and solving problems, and finally how at least one
species developed abilities to reflect on the nature of those competences and
eventually, through unknown processes of individual development and social
interaction, using unknown representational and reasoning mechanisms, managed to
produce the rich, deep and highly organised body of knowledge published as
Euclid's Elements (Note 1).
There are important aspects of those mathematical competences that as far as I
know have not yet been replicated in Artificial Intelligence or
Robotics,18
Is it possible that currently understood forms of digital computation are
inadequate for the tasks, whereas chemistry-based information-processing systems
used in brains are richer?
6.3 Mathematical discoveries based on exploring construction kits
Some mathematical discoveries result from observation of naturally occurring
physical construction kits and noticing how constraints on modes of composition
of components generate constraints on resulting constructs. E.g. straight line
segments on a surface can be joined end to end to enclose a region of the
surface, but that is impossible with only two lines, as noted in
Kant, [1781]. Likewise flat surfaces can be combined to enclose a volume,
such as a tetrahedron or cube, but it is impossible for only three flat surfaces
to enclose a finite space. It is not clear how humans detect such
impossibilities: no amount of trying and failing can establish impossibility.
Many mathematical domains (perhaps all of them) can be thought of as sets of
possibilities generated by construction kits of various kinds. Engineers deal
with hybrid concrete and abstract construction kits. The space of possible
construction kits is also an example, though as far as I know this is
not a domain that has been explored systematically by mathematicians, though
many special cases have.
In order to understand how the sorts of biological evolution that occurred on
this planet are possible we need to understand the sorts of construction kits
made possible by the existence of the physical universe, and in particular the
variety of construction kits inherent in the physics and chemistry of the
materials of which our planet was formed, along with the influences of its
environment (e.g. solar radiation, asteroid impacts). An interesting research
question is whether any construction kit capable of producing all the non-living
structures on the planet would also suffice for evolution of all the forms of
life on this planet, or whether life and evolution have additional requirements,
e.g. external influences such as cosmic radiation.
Insofar as construction kits have mathematical properties, life and mathematics
are closely interconnected, as we have already seen. More complex relationships
arise after evolution of mathematical meta-cognitive mechanisms.
6.4 Evolution's (blind) mathematical discoveries
On the way to achieving those results, natural selection often works as "a blind
theorem-prover". The theorems are mainly about new possible structures,
processes, organisms, ecosystems, etc. The proofs that they are possible are
implicit in the evolutionary trajectories that lead to such occurrences.
Proofs are often thought of as abstract entities that can be represented
physically in different ways (e.g. using different formalisms) for the purpose
of communication or persuasion (including self-persuasion), predicting,
explaining and planning. It can also be argued that a physical sequence produced
unintentionally, e.g. by natural selection, or by growth in a plant, that leads
to a new sort of entity is a sort of (unwitting) proof that some construction
kit makes that sort of entity possible. The evolutionary or developmental trail
answers the question: how is that sort of thing possible? In that sense
biological evolution can be construed as a "blind theorem prover", despite
there being no intention behind the proof.
Proofs of impossibility (or necessity) raise more complex issues, to
be discussed elsewhere.
These observations seem to support a new kind of "Biological-evolutionary"
foundation for mathematics, that is closely related to Immanuel Kant's
philosophy of mathematics in his Critique of Pure Reason (1781), and my
attempt to defend his ideas in Sloman, [1962]. This answers questions like
"How is it possible for things that make mathematical discoveries
to exist?", an example of explaining a possibility (See Note 5).
Those who try to go too directly from hypothesized properties of the primordial
construction kit to explaining advanced capabilities such as human
self-awareness (e.g. Schrödinger, [1944,Penrose, [1994]) are likely to
fail, because short-cuts will omit essential details of both the problems and
the solutions, like mathematical proofs with gaps.
The success of many of the "mathematical discoveries" (or inventions?) produced
(blindly) by evolution, depend on mathematical properties of physical
structures or processes or problem types, whether they are specific solutions to
particular problems (e.g. use of negative feedback control loops), or new
construction-kit components that are usable across a very wide range of
different species (e.g. the use of a powerful "genetic code", the use of various
kinds of learning from experience, the use of new forms of representation for
information, use of new physical morphologies to support sensing, or locomotion,
or consumption of nutrients etc.)
These mathematical "discoveries" (discussed in more detail on the
Meta-Morphogenesis web site19)
started happening long before there were any humans doing
mathematics (which refutes Wittgenstein's suggestion that mathematics is an
anthropological phenomenon). Many of the discoveries were concerned with what is
possible, either absolutely or under certain conditions, or for a particular
sort of construction-kit.
Other discoveries, closer to what are conventionally thought of as mathematical
discoveries, are concerned with limitations on what is
possible, i.e. necessary truths.
Some discoveries are concerned with probabilities derived from statistical
learning, but I think the relative importance of statistical learning in biology
has been vastly over-rated because of misinterpretations of evidence. (To be
discussed elsewhere.) In particular the important discovery that something is
possible does not require collection of statistics: A single instance suffices.
And no amount of statistical evidence can show that something is impossible.
For human evolution, a particularly important subclass of mathematical
discoveries has been unwitting discovery and use of mathematical structures in
the environment, a discovery process that starts in human children before they
are aware of what they are doing, and in some species before uses of
language for communication have developed. Examples are discussed in the
"Toddler Theorems" document (Note 15).
7 Varieties of Derived Construction Kit
Evolution and its products use the fundamental construction kit of physics and
chemistry to produce derived construction kits, with new powers. including
concrete, abstract and hybrid construction kits. DCKs may differ (a) at
different evolutionary stages within a lineage, (b) across lineages (e.g. in
different coexisting organisms such as plants, insects, vertebrates, etc.), and
(c) during development of individuals that start from a single cell and develop
mechanisms that support different kinds of growth, development and learning,
providing new mechanisms for processing information, at different stages of
development, discussed briefly in Section 5. There is also
variety in construction kits produced by cultures or ecosystems, illustrated by
human languages, applied sciences as in bioengineering, notations for logic, the
theory of computation and computer systems engineering. All new cases build on
what was previously available. Sometimes separately evolved DCKs are combined,
for instance in symbiosis, sexual reproduction, and individual creative
learning.
What sort of kit makes it possible for a young child to acquire competence in
use of any one of the thousands of different human languages (whether spoken or
signed) in the first few years of life? There is evidence that children do not
merely learn an existing language: they construct languages that are new
for them, constrained by the need to communicate with conspecifics (as shown
dramatically by Nicaraguan deaf children who developed a sign language going
beyond what their teachers understood [Senghas, 2005]. In any case, if
human languages had to be learnt from expert users, there could be no human
language, since originally there were no expert users to learn from. (A
recurring theme in this paper concerns acquisition of mathematical competences.)
There are also languages that might have developed but have not (yet).
The evolutionary trajectories leading to human spoken language capabilities may
have gone from internal languages through collaborative actions then signed
communication, then spoken communication, as argued in Sloman, [2008].
If language acquisition were solely, or mainly, a matter of learning from
language users, human language as we know it could never have existed, since
initially there was nothing to learn, and the process could not get started.
This argument applies to many competences thought to be based entirely on
learning from experts. So AI systems based on data-mining in samples of expert
behaviours will never produce AI systems with human competences - only subsets
at best.
The history of computing since the earliest calculators demonstrates some of the
kinds of change that can arise when new construction kits are developed. The
technological changes were not merely changes of size, speed and memory
capacity: there have been profound qualitative changes, in part because
development of new layers of virtual machinery produced new types of mechanism,
including new sorts of mutually interacting causal loops linking virtual machine
control states with portions of external environments, for instance use of GPS
in navigation using a "satnav" device.
Some of the new powers, states and processes include semantic contents referring
to non-physical structures and processes, e.g. mathematical problems, rules of
games, and mental contents including past or possible future mental contents and
contents of other minds. So the machines cannot be fully described in the
language of the FCK even though they are fully implemented in physical
reality. (See note on ontologies p. pageref.)
We now understand some of the key components and modes of composition providing
platforms on which human-designed layers of computation can be
constructed, including subsystems closely but not rigidly coupled to the
environment (e.g. using video cameras and propulsion by propellers, when
coping with a cross-wind).
Several different sorts of "basic" abstract construction kits suffice to
generate the forms of (discrete) computation so far studied. Those basic types
include Turing machines, Post's production systems, Church's Lambda Calculus,
and several more, each capable of generating the others. There has been an
enormous amount of research in computer science, and computer systems
engineering, on forms of computation that can be built from such
components.20
One interpretation of the Church-Turing thesis is that these construction kits
generate all possible forms of information-processing - a claim I question. It
is not obvious that those discrete mechanisms suffice for all biological forms
of information-processing. In contrast, use of a wholly or partly chemical basis
allows forms of computation that include both discrete and continuous mechanisms
that were essential for some forms of biological assembly and
information-processing. In some cases the assembly processes (including
continuous changes such as folding, twisting, coming together, moving apart),
seem to be self-controlling because partial structures constrain later
possibilities. But the ability to form and release chemical bonds also provides
discrete control. Ganti, [2003] shows how a chemical construction-kit
supports forms of
biological information-processing that don't depend only on external energy
sources (a fact that's also true of battery-powered computers), and also
supports growth and reproduction using internal mechanisms, which human-made
computers cannot do (yet).
There may be many different sorts of construction-kit that allow different sorts
of information-processing to be supported, including some that we
don't yet understand. In particular, the physical/chemical mechanisms that
support the construction of both physical structures and information-processing
mechanisms in living organisms may have abilities not available in digital
computers.21
7.1 A new type of research project
Most biological processes and associated materials and mechanisms are not well
understood, though knowledge is increasing rapidly. As far as I know, very few
of the derived construction kits have been identified and studied, and I am not
aware of any systematic attempt to identify features of the FCK that explain the
possibility of evolved biological DCKs. Researchers in fundamental physics or
cosmology do not normally attempt to ensure that their theories explain the many
materials and process types that have been explored by natural selection and its
products, in addition to known facts about physics and chemistry.
Schroedinger () pointed out that a theory of
the physical basis of life should explain such phenomena, though he could not
have appreciated some of the requirements for sophisticated forms
of information-processing, because, at the time he wrote, scientists and
engineers had not learnt what we now know.
Curiously, although he mentioned the need to explain the occurrence of
metamorphosis in organisms the example he mentioned was the transformation from
a tadpole to a frog. He could have mentioned more spectacular examples, such as
the transformation from a caterpillar to a butterfly via an
intermediate stage as a chemical soup in an outer case, from which the
butterfly later emerges.22
Penrose, [1994] attempted to show how features of quantum physics explain
obscure features of human consciousness, especially mathematical consciousness,
but ignores all the intermediate products of biological evolution on which
animal mental functions build. Human mathematics, at least the ancient
mathematics done before the advent of modern algebra and logic, seems to build
on animal abilities, for instance abilities to see various types of affordance.
The use of diagrams and spatial models by Penrose could be an example of that.
It seems to be unlikely that there are very abstract human mathematical
abilities that somehow grow directly out of quantum mechanical aspects of the
FCK, without depending on the layers of perceptual, planning, and reasoning
competences produced by billions of years of evolution. (I have not yet fully
understood his claims, however.)
20th century biologists understood some of the achievements of the FCK in
meeting physical and chemical requirements of various forms of life, though they
used different terminology from mine, e.g. Haldane.23 However, the task can
never be finished, since the process of construction of new derived construction
kits may continue indefinitely, producing new kits with components and modes of
composition that allow production of more complex types of structure and
more complex forms of behaviour in organisms.
That idea is familiar to computer scientists and computer systems engineers
since thousands of new sorts of computational construction kit (new programming
languages, new operating systems, new virtual machines) have been developed from
old ones in the last half century, making possible new kinds of computing system
that could not previously be built from the original computing machinery,
without introducing new intermediate layers, including new virtual machines that
are able to detect and record their own operations, a capability that is often
essential for debugging and extending computing systems.
Sloman, [2013a] discusses the importance of virtual machinery in extending
what information-processing systems can do, and the properties they can have.
7.2 Construction-kits for biological information-processing
Applying the ideas from previous sections, we can speculate that the earliest
evolved DCKs supported evolution of new physical/chemical mechanisms, soon
followed by information-processing mechanisms used to gain benefits of selecting
between available competences and tuning them - on the basis of results of
perception, learning, motive formation, planning, and decision making. In some
organisms, mathematical discovery processes, enabled production of competences
used in generic understanding of sensory information, synthesis of separate
information fragments into coherent wholes, and control systems using mechanisms
for motive generation, plan construction, control of behaviour, and prediction.
Many of evolution's mathematical discoveries were "compiled" into designs
producing useful behaviours, e.g. use of negative feedback loops controlling
temperature, osmotic pressure and other states, use of geometric constraints by
bees whose cooperative behaviours produce hexagonal cells in honeycombs, and use
of new ontologies for separating situations requiring different behaviours.
Later still, construction kits used by evolution produced meta-cognitive
mechanisms enabling individuals to notice and reflect on their own mathematical
discoveries (enabling some of them to notice and remove flaws in their
reasoning). In some cases those meta-cognitive capabilities allowed individuals
to communicate their discoveries to others, discuss them, and organise them into
complex highly structured bodies of shared knowledge, such as Euclid's
Elements (Note 1). I don't think anyone knows how long all of
this took, what the detailed evolutionary changes were, and how mechanisms of
perception, motivation, intention formation, reasoning and planning
evolved. Explaining how that could happen, and what it tells us about the nature
of mathematics and biological/evolutionary foundations for mathematical
knowledge is a long term goal of the Meta-Morphogenesis project.24
Many of these naturally occurring mathematical abilities have not yet been
replicated in Artificial Intelligence systems or robots, unlike logical,
arithmetical, and algebraic competences. Examples of topological reasoning about
equivalence classes of closed curves not yet modelled in computers (as far as I
know) are referenced in Note 21. Even the ability to reason about
alternative ways of putting a shirt on a child (Note 10) is still
lacking. It is not clear whether the difficulty of replicating such mathematical
reasoning processes is due to the need for a kind of construction-kit that
digital computers (e.g. Turing machines) cannot support, or due to our lack of
imagination in using computers to replicate some of the products of biological
evolution - or a mixture! Perhaps there are important forms of representation
or types of information-processing architecture still waiting to be discovered
by AI researchers. Alternatively the gaps may be connected with properties of
chemistry-based information-processing mechanisms combining discrete and
continuous interactions, or other physical properties that cannot be replicated
exactly (or even approximately) in familiar forms of computation. (This topic
requires more detailed mathematical analysis. Compare Penrose, [1994].)
7.3 Representational blind spots of many scientists
Although I am not a physicist or mathematician and cannot follow
all the details of writings of physicists, I think it is clear that most of the
debates regarding what should go into a fundamental theory of matter ignore most
of the biological demands on such a theory.
For example, presentations on dynamics of physical systems
make deep use of branches of mathematics
concerned with numerical values, and the ways in which different measurable
or hypothesized
physical values do or do not co-vary, as expressed in (probabilistic or
non-probabilistic) differential equations of various sorts. But the biological
functions of complex physiological structures, especially structures that change
in complexity, don't necessarily have those forms.
Biological mechanisms include: digestive mechanisms, mechanisms for transporting
chemicals, mechanisms for detecting and repairing damage or infection,
mechanisms for storing re-usable information about an extended structured
environment, mechanisms for creating, storing and using complex percepts,
thoughts, questions, values, preferences, desires, intentions and plans,
including plans for cooperative behaviours, and mechanisms that transform
themselves into new mechanisms with new structures and functions.
Forms of mathematics used by physicists are not necessarily useful
for studying such biological
mechanisms. Logic, grammars and map-like representations
are sometimes more appropriate, though I think little is actually known about
the variety of forms of representation (i.e. encodings of information) used in
human and animal minds and brains. We may need entirely new forms of mathematics
for biology, and therefore for specifying what physicists need to explain.
Many physicists, engineers and mathematicians who move into neuroscience assume
that states and processes in brains need to be expressed as collections of
numerical measures and their derivatives plus equations linking them, a form of
representation that well supported by widely used tools such as Matlab, but is
not necessarily best suited for the majority of mental contents, and probably
not even well suited for chemical processes where structures form and interact
with multiple changing geometrical and topological relationships - one of the
reasons for the invention of symbolic chemical notations (now being extended in
computer models of changing interacting molecular structures).
7.4 Representing rewards, preferences, values
It is often assumed that all intelligent decision making uses positive or
negative scalar reward or utility values that are comparable across options
[Luce and Raiffa, 1957]. But careful attention to consumer magazines, political
debates, and the varieties of indecision that face humans in real life shows
that reality is far more complex. For example, many preferences are expressed in
rules about how to choose between certain options. Furthermore preferences can
be highly sensitive to changes in context. A crude example is the change in
preference for type of car after having children. Analysis of examples in
consumer reports led to the conclusion that "better" is a complex,
polymorphic, logical concept with a rich structure that cannot be reduced to use
of comparisons of numerical values [Sloman, 1969,Sloman, 1970]. Instead of a
linear reward or utility metric, choices for intelligent individuals, or for
natural selection, involve a complex partial ordering network, with
"annotated" links between nodes (e.g. "better" qualified by conditions:
"better for", "better if"...). In the Birmingham CogAff project
[Sloman, 2003], those ideas later informed computational
models of simple agents with complex choices to be made under varying
conditions, but the project merely scratched the surface, as reported in
[Beaudoin and Sloman, 1993,Beaudoin, 1994,Wright et al, 1996,Wright, 1977]. Most AI/Cognitive Science
models use much shallower notions of motivation.
Despite all the sophistication of modern psychology and neuroscience, I don't
believe they currently have the conceptual resources required to describe
either functions of brains in dealing with these matters, including
forms of development and learning required, or the mechanisms implementing those
functions. In particular, we lack deep explanatory theories about human
mechanisms that led to: mathematical discoveries over thousands of years,
including mechanisms producing conjectures, proofs, counter-examples,
proof-revisions, new scientific theories, new works of art and new styles of
art. In part that's because models considered so far lack sufficiently rich
forms of information-processing (computation), and sufficiently deep
methodologies for identifying what needs to be explained. There are other
unexplained phenomena concerned with artistic creation and enjoyment, but that
will not be pursued here.
8 Computational/Information-processing construction-kits
Since the mid 20th century we have been learning about abstract
construction-kits whose products are machines that can be used for increasingly
complex tasks. Such construction kits include programming languages, operating
systems, software development tools and environments, and network-technology
that allows ever more complex information-processing machines to be constructed
by combining simpler ones. A crucial, but poorly understood, feature
of that history is the growing use of construction-kits based on virtual
machinery, mentioned in Section 2.
A complete account of the role of construction kits in biological evolution
would need to include an explanation of how the fundamental construction kit
(FCK) provided by the physical universe could be used by evolution to produce an
increasing variety of types of virtual machinery as well as increasingly varied
physical structures and mechanisms.
8.1 Infinite, or potentially infinite, generative power
A construction kit implicitly specifies a large, in some cases infinite, set of
possibilities, though as an instance of the kit is constructed each addition of
a new component or feature changes the set of possibilities accessible in
later steps of that construction process.
For example, as you construct a sentence or phrase in a language, at each state
in the construction there are alternative possible additions (not necessarily at
the end) and each of those additions will alter the set of possible further
additions consistent with the vocabulary and grammar of the language.
When use of language is embedded in a larger activity, such as composing a poem,
that context can modify the constraints that are relevant.
Chemistry does something like that for types of molecule, types of process
involving molecular changes, and types of structure made of multiple molecules.
Quantum mechanics added important constraints to 19th century chemistry,
including both the possibility of highly stable structures (resistant to thermal
buffeting) and also locks and keys as in catalysis. All of that is essential for
life as we know it, and also for forms of information-processing produced by
evolution (mostly not yet charted).
Research in fundamental physics is a search for the construction kit that has
the generative power to accommodate all the possible forms of matter, structure,
process, causation, that exist in our universe. However, physicists generally
seek only to ensure that their construction kits are capable of accounting for
phenomena observed in the physical sciences. Normally they do not assemble
features of living matter, or processes of evolution, development, or learning,
found in living organisms and try to ensure that their fundamental theories can
account for those features also. There are notable exceptions mentioned above,
such as Schrödinger and Penrose, but most physicists who discuss physics and
life (in my experience) ignore most of the details of life, including the
variety of forms it can take, the variety of environments coped with, the
different ways in which individual organisms cope, the ways in which products of
evolution become more complex and more diverse over time, and the many kinds of
information-processing and control in individuals, in colonies (e.g. ant
colonies), societies, and ecosystems.
One of the issues some physicists have discussed is whether the formation of
life from non-living matter requires violation of the second law of
thermodynamics, because evolution increases the amount of order or structure in
the physical matter on the planet. The standard answer is that the second law of
thermodynamics is applicable only to closed systems, and the earth is not a
closed system, since it is constantly affected by solar and other forms of
radiation, asteroid impacts, and other external influences. Some of the ways in
which pre-existing dispositions can harness external sources of energy to
increase local structure are discussed in a collection of thoughts on entropy,
evolution, and construction-kits:
http://www.cs.bham.ac.uk/research/projects/cogaff/misc/entropy-evolution.html
If cosmologists and other theoretical physicists attempted to take note of a
wide range of biological phenomena (including the phenomena discussed here in
connection with the Meta-Morphogenesis project) I suspect that they would find
considerable explanatory gaps between current physical theories and the
diversity of phenomena of life - not because there is something about life that
goes beyond what science can explain, but because we do not yet have a
sufficiently rich theory of the constitution of the universe (or the Fundamental
Construct Kit). In part that could be a consequence of the forms of mathematics
known to physicists. (The challenge of
Anderson, [1972] is also relevant: see Section 11, below.)
If that is true it may take many years of research to find out what's missing
from current physics. Collecting phenomena that need to be explained, and trying
as hard as possible to construct detailed explanations of those phenomena
is one way to make progress: it may help us to pin-point gaps in our theories
and stimulate development of new more powerful theories, in something like the
profound ways in which our understanding of possible forms of computation has
been extended by unending attempts to put computation to new uses. Collecting
examples of such challenges helps us assemble tests to be passed by future
proposed theories: collections of possibilities that a deep physical theory
needs to be able to explain.
Perhaps the most tendentious proposal here is that an expanded physical theory,
instead of being expressed mainly in terms of equations relating measures may
need a formalism better suited to specification of a construction kit, perhaps
sharing features of grammars, programming languages, partial orderings,
topological relationships, architectural specifications, and the structural
descriptions in chemistry - all of which will need to make use of appropriate
kinds of mathematics for drawing out implications of the theories, including
explanations of possibilities, both observed and unobserved, including possible
future forms of intelligence. Theories of utility measures may need to be
replaced, or enhanced with new theories of how benefits, evaluations,
comparisons and preferences, can be expressed. We must also avoid assuming
optimality. Evolution produces designs as diverse as microbes, cockroaches,
elephants and orchids, none of which is optimal or rational in any simple sense,
yet many of them survive and sometimes proliferate, because they are lucky, at
least for a while. Likewise human decision making.
9 Types and levels of explanation of possibilities
Suppose someone uses a meccano kit to construct a toy crane, with a jib that can
be moved up and down by turning a handle, and a rotating platform on a fixed
base, that allows the direction of the jib to be changed. What's the difference
between explaining how that is possible and how it was done? First of all, if
nobody actually builds such a crane then there is no actual crane-building to be
explained: yet, insofar as the meccano kit makes such cranes possible it
makes sense to ask how it is possible. This has several types of answer,
including answers at different levels of abstraction, with varying generality
and economy of specification. The last feature may be relevant to modes of
specification of constructions either in a genome or in a learnt or invented
specification for a solution to a type of problem.
More generally, the question "How is it possible to create X using construction
kit Y?" or, simply, "How is X possible?" has several types of answer,
including answers at different levels of abstraction, with varying generality.
I'll assume that a particular construction kit is referred to either explicitly
or implicitly. The following is not intended to be an exhaustive survey of the
possible types of answer: merely as a first experimental foray, preparing the
ground for future work:
1 Structural conformity:
The first type of answer, structural conformity (grammaticality)
merely identifies the parts and relationships
between parts that are supported by the kit, showing that a crane of the sort in
question could be composed of such parts arranged in such relationships. An
architect's drawings for a building, specifying materials, components, and their
spatial and functional relations would provide such an explanation of how a
proposed building is possible, including, perhaps, answering questions about how
the construction would make the building resistant to very high winds, or to
earthquakes up to a specified strength. This can be compared with showing that a
sentence is acceptable in a language with a well-defined grammar, by
showing how the sentence would be parsed (analysed) in accordance with the
grammar of that language. A parse tree (or graph) also shows how the sentence
can be built up piecemeal from words and other grammatical units, by assembling
various sub-structures and, using them to build larger structures. Compare using
a chemical diagram to show how a collection of atoms can make up a particular
molecule, e.g. the ring structure of C6H6 (Benzene).
Some structures are specified in terms of piece-wise relations, where the whole
structure cannot possibly exist, because the relations cannot hold
simultaneously, e.g. X is above Y, Y is above Z, Z is above X. It is
possible to depict such objects, e.g. in pictures of impossible objects by
Reutersvard, Escher, Penrose, and others. Some logicians and computer scientists
have attempted to design languages in which specifications of impossible
entities are necessarily syntactically ill-formed. This leads to impoverished
languages with restricted practical uses, e.g. strongly typed programming
languages. For some purposes less restricted languages, needing greater care in
use, are preferable, including human languages [Sloman, 1971].
2 Process possibility:
The second type of answer demonstrates constructability by
describing a sequence of spatial trajectories by which such a collection of
parts could be assembled. This may include processes of assembly of temporary
supports to hold parts in place before the connections have been made that make
them self-supporting or before the final supporting structures have been built
(as often happens in large engineering projects, such as bridge construction).
Many different possible trajectories can lead to the same result. Describing (or
demonstrating) any such trajectory explains both how that construction process
is possible, and how the end result is possible. There may be several different
routes to the same end result.
In some cases a complex object has type 1 possibility although not type 2. For
example, from a construction kit containing several rings it is possible to
assemble a pile of three rings, but not possible to assemble a chain
of three rings even though each of the parts of the chain is exactly like the
parts of the pile.
3 Process Abstraction: Some possibilities are described at a level of
abstraction that ignores detailed routes through space, and covers many
possible alternatives. For example, instead of specifying precise trajectories
for parts as they are assembled, an explanation can specify the initial and
final state of each trajectory, where each state-pair may be shared by a vast,
or even infinite collection, of different possible trajectories producing the
same end state, e.g. in a continuous space.
In some cases the possible trajectories for a moved component are all
continuously deformable into one another (i.e. they are topologically
equivalent): for example the many spatial routes by which a cup could be moved
from a location where it rests on a table to a location where it rests on a
saucer on the table, without leaving the volume of space above the table. Those
trajectories form a continuum of possibilities that is too rich to be captured
by a parametrised equation for a line, with a number of variables. If
trajectories include passing through holes, or leaving and entering the room via
different doors or windows then the different possible trajectories will not all
be continuously deformable into one another: there are different equivalence
classes of trajectories sharing common start and end states, for example, the
different ways of threading a shoe lace with the same end result.
The ability to abstract away from detailed differences between trajectories
sharing start and end points, thereby implicitly recognizing invariant features
of an infinite collection of possibilities, is an important aspect of animal
intelligence that I don't think has been generally understood. Many researchers
assume that intelligence involves finding optimal solutions. So they
design mechanisms that search using an optimisation process, ignoring the
possibility of mechanisms that can find sets of possible solutions (e.g. routes)
initially considered as a class of equivalent options, leaving questions
about optimal assembly to be settled later, if needed. These remarks are closely
related to the origins of abilities to reason about geometry and
topology.25
4 Grouping:
Another form of abstraction is related to the difference between
1 and 2. If there is a sub-sequence of assembly processes, whose order
makes no difference to the end result, they can be grouped to form an unordered
"composite" move, containing an unordered set of moves. If N components are
moved from initial to final states in a sequence of N moves, and it makes no
difference in what order they are moved, merely specifying the set of N
possibilities without regard for order collapses N factorial sets of possible
sequences into one composite move. If N is 15, that will collapse 479001600
different sequences into one.
Sometimes a subset of moves can be made in parallel. E.g. someone with two hands
can move two or more objects at a time, in transferring a collection of items
from one place to another. Parallelism is particularly important in many
biological processes where different processes occurring in parallel constrain
one another so as to ensure that instead of all the possible states that could
occur by moving or assembling components separately, only those end states occur
that are consistent with parallel constructions. In more complex cases the end
state may depend on the relative speeds of sub-processes and also continuously
changing spatial relationships.
This is important in epigenesis, since all forms of development from a single
cell to a multi-celled structure depend on many mutually constraining processes
occurring in parallel.
For some construction kits certain constructs made of a collection of
sub-assemblies may require different sub-assemblies to be constructed in
parallel, if completing some too soon may make the required final configuration
unachievable. For example, rings being completed before being joined could
prevent formation of a chain.
5 Iterative or recursive abstraction: Some process types involve
unspecified numbers of parts or steps, although each instance of the type has a
definite number, for example a process of moving chairs by repeatedly carrying a
chair to the next room until there are no chairs left to be carried, or building
a tower from a collection of bricks, where the number of bricks can be varied. A
specification that abstracts from the number can use a notion like "repeat
until", or a recursive specification: a very old idea in mathematics, such as
Euclid's algorithm for finding the highest common factor of two numbers.
Production of such a generic specification can demonstrate a large variety of
possibilities inherent in a construction-kit in an extremely powerful and
economical way. Many new forms of abstraction of this type have been discovered
by computer scientists developing programming languages, for operating not only
on numbers but many other structures, e.g. trees and graphs.
Evolution may also have "discovered" many cases, long before humans
existed, by taking advantage of mathematical structures inherent in the
construction-kits available and the trajectories by which parts can be assembled
into larger wholes. This may be one of the ways in which evolution produced
powerful new genomes, and re-usable genome components that allowed many
different biological assembly processes to result from a single discovery, or a
few discoveries, at a high enough level of abstraction.
Some related abstractions may have resulted from parametrisation: processes by
which details are removed from specifications in genomes and left to be
provided by the context of development of individual organisms, including the
physical or social environment. (See Section 5 on
epigenesis.)
6 Self-assembly:
If, unlike construction of a toy meccano crane or a sentence or a
sorting process, the process to be explained is a self-assembly process, like
many biological processes, then the explanation of how the assembly is possible
will not merely have to specify trajectories through space by which the parts
become assembled, but also
-
What causes each of the movements (e.g. what manipulators are required)
-
Where the energy required comes from (an internal store, or external supply?)
- Whether the process involves pre-specified information about required steps or
required end states, and if so what mechanisms can use that information to
control the assembly process.
- How that prior information structure (e.g. specification of a goal
state to be
achieved, or plan specifying actions to be taken) came to exist, e.g. whether it
was in the genome as a result of previous evolutionary transitions, or whether
it was constructed by some planning or problem-solving mechanism in an
individual, or whether it was provided by a communication from an external
source.
- How these abilities can be acquired or improved by learning
or reasoning processes, or random variation (if they can).
7 Use of explicit intentions and plans: None of the explanation-types
above presupposes that the possibility being explained has ever been represented
explicitly by the machines or organisms involved. Explaining the possibility of
some structure or process that results from intentions or plans would require
specifying pre-existing information about the end state and in some cases also
intermediate states, namely information that existed before the process began -
information that can be used to control the process (e.g. intentions,
instructions, or sub-goals, and preferences that help with selections between
options). It seems that some of the reproductive mechanisms that depend on
parental care make use of mechanisms that generate intentions and possibly also
plans in carers, for instance intentions to bring food to an infant, intentions
to build nests, intentions to carry an infant to a new nest, and many more. Use
of intentions that can be carried out in multiple ways selected according to
circumstances rather than automatically triggered reflexes could cover a far
wider variety of cases, but would require provision of greater intelligence in
individuals.
Sometimes an explanation of possibility prior to construction is important for
engineering projects where something new is proposed and critics believe that
the object in question could not exist, or could not be brought into existence
using available known materials and techniques. The designer might answer
sceptical critics by combining answers of any of the above types, depending on
the reasons for the scepticism.
Concluding comment on explanations of possibilities:
Those are all examples of components of explanations of assembly processes,
including self-assembly. In biological reproduction, growth, repair,
development, and learning there are far more subdivisions to be considered, some
of them already studied piecemeal in a variety of disciplines. In the case of
human development, and to a lesser extent development in other species, there
are many additional sub-cases involving construction kits both for creating
information structures and creating information-processing mechanisms of many
kinds, including perception, learning, motive formation, motive comparison,
intention formation, plan construction, plan execution, language use, and many
more. A subset of cases, with further references can be found in
Sloman, [2006].
The different answers to "How is it possible to construct this type of object"
may be correct as far as they go, though some provide more detail than others.
More subtle cases of explanations of possibility include differences between
reproduction via egg-laying and reproduction via parturition, especially when
followed by caring for young. The latter allows a parent's influence to continue
during development, as does teaching of younger individuals by older ones. This
also allows development of cultures suited to different environments.
To conclude this rather messy section: the investigation of different types of
generality in modes of explanation for possibilities supported by a construction
kit is also relevant to modes of specification of new designs based on the kit.
Finding economical forms of abstraction may have many benefits, including
reducing search spaces when trying to find a new design and also providing a
generic design that covers a broad range of applications tailored to detailed
requirements. Of particular relevance in a biological context is the need for
designs that can be adjusted over time, e.g. during growth of an organism, or
shared across species with slightly different physical features or environments.
Many of the points made here are also related to changes in types of computer
programming language and software design specification languages. Evolution may
have been us to important ideas. That these levels of abstraction are possible
is a metaphysical feature of the universe, implied by the generality of the FCK.
10 Alan Turing's Construction kits
Turing, [1936] showed that a rather simple sort of machine, now known as a
Turing machine, could be used to specify an infinite set of constructions with
surprisingly rich mathematical features. The set of possibilities was infinite,
because a Turing machine is defined to have an infinite (or indefinitely
extendable) linear "tape" divided into discrete locations in
which symbols can be inserted.
A feature of a Turing machine that is not in most other construction kits
is that it can be set up and then started after which it will modify initial
structures and build new ones, possibly indefinitely, though in some cases the
machine will eventually halt.
Another type of construction kit with related properties is Conway's Game of
Life,26 a
construction kit that creates changing patterns in 2D regular arrays. Stephen
Wolfram has written a great deal about the diversity of constructions that can
be explored using such cellular automata. Neither a Turing machine nor a Conway
game has any external sensors: once started they run according to their stored
rules and the current (changing) state of the tape or grid-cells. In principle
either of them could be attached to external sensors that could produce changes
to the tape of a turing machine or the states of some of the cells in the Life
array. However any such extension would significantly alter the powers of the
machine, and theorems about what such a machine could or could not do would
change.
Modern computers use a variant of the Turing machine idea where each computer
has a finite memory but with the advantage of much more direct access between
the central computer mechanism and the locations in the memory. (A von Neumann
architecture.) Increasingly, computers have also been provided with a variety of
external interfaces connected to sensors or motors so that while running they
can acquire information (from keyboards, buttons, joy-sticks, mice, electronic
piano keyboards, or network connections) and can also send signals to external
devices. Theorems about disconnected Turing machines may not apply to machines
with rich two-way interfaces to an external environment.
Turing machines and Game of Life machines can be described as as
"self-propelling" because once set up they can be left to run according to the
general instructions they have and the initial configuration on the tape or in
the array. But they are not really self-propelling: they have to be implemented
in physical machines with an external power supply. In contrast,
Ganti, [2003] shows how the use of chemistry as a construction kit provides
"self-propulsion" for living things, though every now and again the chemicals need
to be replenished. A battery driven computer is a bit like that, but someone
else has to make the battery.
Living things make and maintain themselves, at least after being given a
kick-start by their parent or parents. They do need constant, or at least
frequent, external inputs, but, for the simplest organisms, those are only
chemicals in the environment, and energy either from chemicals or heat-energy
via radiation, conduction or convection. John McCarthy pointed out in a
conversation that some animals also use externally supplied mechanical energy,
e.g. rising air currents used by birds. Unlike pollen-grains, spores, etc.
propagated by wind or water, the birds use internal information-processing
mechanisms to control how the wind energy is used, as does a human piloting a
glider.
10.1 Beyond Turing machines: chemistry
Turing also explored other sorts of construction kits, including types of neural
nets and extended versions of Turing machines with "oracles" added. Shortly
before his death (in 1954), he published Turing, [1952] in which he
explored a type of pattern-forming construction kit in which two chemical
substances can diffuse through the body of an expanding organism and interact
strongly wherever they meet. He showed that that sort of construction kit could
generate many of the types of surface physical structure observed on plants and
animals. I have been trying to show how that can be seen as a very simple
example of something far more general.
One of the important differences between types of construction kit mentioned
above is the difference between kits supporting only discrete changes (e.g. to a
first approximation lego and meccano (ignoring variable length strings and
variable angle joints) and kits supporting continuous variation, e.g. plasticine
and mud (ignoring, for now, the discreteness at the molecular level).
One of the implications of such differences is how they affect
abilities to search for solutions to problems. If only big changes in design are
possible the precise change needed to solve a problem may be inaccessible (as I
am sure many who have played with construction kits will have noticed). On the
other hand if the kit allows arbitrarily small changes it will, in principle,
permit exhaustive searches in some sub-spaces. The exhaustiveness comes at the
cost of a very much larger (infinite, or potentially infinite!) search-space.
That feature could be useless, unless
the space of requirements has a structure that allows approximate solutions to
be useful. In that case a mixture of big jumps to get close to a good solution,
followed by small jumps to home in on a (locally) optimal solution can be very
fruitful: a technique that has been used by Artificial Intelligence researchers,
called "simulated annealing".27
A recently published book Wagner, [2014] claims that the structure of the
search space generated by the molecules making up the genome increases the
chance of useful, approximate, solutions to important problems to be found with
relatively little searching (compared with other search spaces), after
which small random changes allow improvements to be found. I have not yet read
the book but it seems to illustrate the importance for evolution of the types of
construction-kit available.28
I have not yet had time to check whether the book discusses uses of abstraction
and the evolution of mathematical and meta-mathematical competences discussed
here. Nevertheless, it seems to be an (unwitting) contribution to the
Meta-Morphogenesis project.
10.2 Using properties of a construction-kit to explain possibilities
A formal axiomatic system can be seen as an abstract construction kit with
axioms and rules that support construction of proofs, ending in theorems. The
theorems are formulae that can occur at the end of a proof using only axioms and
inference rules in the system. The kit explains the possibility of some theorems
based on the axioms and rules. The non-theorems of an axiomatic system are
formulae for which no such proof exists. Proving that something is a
non-theorem can be difficult, and requires a proof in a meta-system.
Likewise, a physical construction kit can be used to demonstrate that some
complex physical objects can occur at the end of a construction process. In some
cases there are objects that are describable but cannot occur in a construction
using that kit: e.g. an object whose outer boundary is a surface that is
everywhere curved, cannot be produced in a construction based on Lego bricks or
a Meccano set, though one could occur in a construction based on plasticene, or
soap-film.
10.3 Bounded and unbounded construction kits
A rectangular grid of squares combined with the single digit numbers, 0,1,..,9
(strictly numerals representing numbers) allows construction of a set of
configurations in which numbers are inserted into the squares subject to various
constraints, e.g. whether some squares can be left blank, or whether certain
pairs of numbers can be adjacent, whether the same number can occur in more than
one square. For a given grid and a given set of constraints here will be a
finite set of possible configurations (although it may be a very large set).
If, in addition to insertion of a number, the "construction kit" allows extra
empty rows or columns to be added to the grid, no matter how large it is, then
the set of possible configurations becomes infinite.
Many types of infinite construction kits have been investigated by
mathematicians, logicians, linguists, computer scientists, musicians and other
artists.
Analysis of chemistry-based construction kits for information-processing systems
would range over a far larger class of possible systems than Turing machines (or
digital computers), because of the mixture of discrete and continuous changes
possible when molecules interact, e.g. moving together, moving apart, folding,
twisting, but also locking and unlocking - using catalysts [Kauffman, 1995]. I
don't know whether anyone has a deep theory of the scope and limits of
chemistry-based information-processing.
Connections between Meta-Morphogenesis and entropy are discussed in a related
work-in-progress document on issues involving entropy
changes in evolutionary trajectories:
http://www.cs.bham.ac.uk/research/projects/cogaff/misc/entropy-evolution.html
11 Conclusion: Construction kits for Meta-Morphogenesis
A useful survey of previous attempts to show how life and its products relate to
the physical world is in Keller, [2008,Keller, [2009], which concluded that attempts
so far have not been successful. Keller ends with the suggestion that the
traditional theory of dynamical systems is inadequate for dealing with
constructive processes and needs to be expanded to include "objects, their
internal properties, their construction, and their dynamics" i.e. a theory of
"Constructive dynamical systems". This paper outlines a project to do
that and more: including branching layers of new derived construction kits
produced by evolution, development and other processes. The physical world
clearly provides a very powerful (chemistry-based) fundamental construction kit
that, together with natural selection processes and processes within individuals
as they develop, produced an enormous variety of organisms on this planet, based
on additional derived construction kits (DCKs), including concrete, abstract and
hybrid construction kits, and most, recently, new sorts of construction kit used
as toys or engineering resources.
The idea of a construction kit is offered as a new unifying concept for
philosophy of mathematics, philosophy of science, philosophy of biology,
philosophy of mind and metaphysics. The aim is to explain how it is possible for
minds to exist in a material world and to be produced by natural selection and
its products. The idea is still at an early stage of development and there are
probably many more distinctions to be made, and a need for a more formal,
mathematical presentation of properties of and relationships between
construction kits, including the ways in which new derived construction kits can
be related to their predecessors and their successors. The many new types of
computer-based virtual machinery produced by human engineers since around
1950 provide examples of non-reductive supervenience (as explained in
Sloman, [2013a]). They are also useful as relatively simple examples to be
compared with far more complex products of evolution.
In Esfeld et al, [in press] a distinction is made between two "principled" options for
the relationship between the basic constituents of the world and their
consequences. In the "Humean" option there is nothing but the distribution of
structures and processes over space and time, though there may be some
empirically discernible patterns in that distribution. The second option is
"modal realism", or "dispositionalism", according to which there is
something about the primitive stuff and its role in space-time that constrains
what can and cannot exist, and what types of process can or cannot occur. This
paper supports a "multi-layer" version of the modal realist option
(developing ideas in Sloman, [1962,Sloman, [1996a,Sloman, [2013a]).
I suspect that a more complete development of this form of modal realism can
contribute to answering the problem posed in Anderson's famous paper
[Anderson, 1972], namely how we should understand the relationships between
different levels of complexity in the universe (or in scientific theories). The
reductionist alternative claims that when the physics of elementary particles
(or some other fundamental physical level) has been fully understood, everything
else in the universe can be explained in terms of mathematically derivable
consequences of the basic physics. Anderson contrasts this with the
anti-reductionist view that different levels of complexity in the universe
require "entirely new laws, concepts and generalisations" so that, for
example, biology is not applied chemistry and psychology is not applied biology.
He writes: "Surely there are more levels of organization between human ethology
and DNA than there are between DNA and quantum electrodynamics, and each level
can require a whole new conceptual structure". However, the structural levels
are not merely in the concepts used by scientists, but actually in the world.
We still have much to learn about the powers of the fundamental construction kit
(FCK), including: (i) the details of how those powers came to be used for life
on earth, (ii) which sorts of derived construction kit (DCK) were required in
order to make more complex life forms possible, (iii) how those construction
kits support "blind" mathematical discovery by evolution, mathematical
competences in humans and other animals and eventually meta-mathematical
competences, then meta-meta-mathematical competences, at least in humans, (iv)
what possibilities the FCK has that have not yet been realised, (v) whether
and how some version of the FCK could be used to extend the intelligence of
current robots, and (vi) whether currently used Turing-equivalent forms of
computation have at least the same information-processing potentialities (e.g.
abilities to support all the biological information-processing mechanisms and
architectures), and (vii) if those forms of computation lack the potential, then
how are biological forms of information-processing different? Don't expect
complete answers soon.
In future, physicists wishing to show the superiority of their theories, should
attempt to demonstrate mathematically and experimentally that they can explain
more of the potential of the FCK to support varieties of construction kit
required for, and produced by, biological evolution than rival theories can.
Will that be cheaper than building bigger better colliders? Will it be harder?29
Endnote
As I was finishing off this paper I came across a letter Turing wrote to W. Ross
Ashby in 1946 urging Ashby to use Turing's ACE computer to implement his ideas
about modelling brains. Turing expressed a view that seems to be
unfashionable among AI researchers at present (2015),
but accords with the aims of this
paper:
It would be very interesting to know whether he had ever considered the question
whether digital computers might be incapable of accurately modelling
brains making deep use of chemical processes. He also wrote in Turing, [1950]
"In the nervous system chemical phenomena are at least as important as
electrical."
But he did not elaborate on the implications of that claim.
References
- [Anderson 1972]
-
Anderson P (1972) More is different. Science, New Series 177(4047):393-396,
URL http://robotics.cs.tamu.edu/dshell/cs689/papers/anderson72more_is_different.pdf
- [Ashby 1952]
-
Ashby WR (1952) Chapman and Hall, London
- [Beaudoin 1994]
-
Beaudoin L (1994) Goal processing in autonomous agents. PhD thesis, School of
Computer Science, The University of Birmingham, Birmingham, UK,
URL http://www.cs.bham.ac.uk/research/projects/cogaff/81-95.html#38
- [Beaudoin and Sloman 1993]
-
Beaudoin L, Sloman A (1993) A study of motive processing and attention. In:
Sloman A, Hogg D, Humphreys G, Partridge D, Ramsay A (eds) Prospects for
Artificial Intelligence, IOS Press, Amsterdam, pp 229-238,
URL http://www.cs.bham.ac.uk/research/projects/cogaff/81-95.html#16
- [Bell 2008]
-
Bell G (2008) Selection The Mechanism of Evolution. OUP, second Edition
- [Braitenberg 1984]
-
Braitenberg V (1984) Vehicles: Experiments in Synthetic Psychology. The MIT
Press, Cambridge, MA
- [Chappell and Sloman 2007]
-
Chappell J, Sloman A (2007) Natural and artificial meta-configured altricial
information-processing systems. International Journal of Unconventional
Computing 3(3):211-239,
URL http://www.cs.bham.ac.uk/research/projects/cogaff/07.html#717
- [Coates et al 2014]
-
Coates J, Umm-E-Aiman, Charrier B (2014) Understanding "green"
multicellularity: do seaweeds hold the key? Frontiers in Plant Science Doi:
10.3389/fpls.2014.00737
- [Esfeld et al in press]
-
Esfeld M, Lazarovici D, Lam V, Hubert M (in press) The Physics and Metaphysics
of Primitive Stuff. British Journal for the Philosophy of Science
URL http://arxiv.org/abs/1411.7545
- [Ganti 2003]
-
Ganti T (2003) The Principles of Life. OUP, New York, Eds. Eörs
Szathmáry & James Griesemer, Translation of the 1971 Hungarian edition
- [Gibson 1966]
-
Gibson JJ (1966) The Senses Considered as Perceptual Systems. Houghton
Mifflin, Boston
- [Gibson 1979]
-
Gibson JJ (1979) The Ecological Approach to Visual Perception. Houghton
Mifflin, Boston, MA
- [Hameroff and Penrose 2014]
-
Hameroff S, Penrose R (2014) Consciousness in the universe: A review of the
`orch or' theory. Physics of Life Reviews 11(1):39 - 78,
DOI http://dx.doi.org/10.1016/j.plrev.2013.08.002
- [Jablonka and Lamb 2005]
-
Jablonka E, Lamb MJ (2005) Evolution in Four Dimensions: Genetic, Epigenetic,
Behavioral, and Symbolic Variation in the History of Life. MIT Press,
Cambridge MA
- [Kant 1781]
-
Kant I (1781) Critique of Pure Reason. Macmillan, London, translated (1929) by
Norman Kemp Smith
- [Karmiloff-Smith 1992]
-
Karmiloff-Smith A (1992) Beyond Modularity: A Developmental Perspective on
Cognitive Science. MIT Press, Cambridge, MA
- [Kauffman 1995]
-
Kauffman S (1995) At home in the universe: The search for laws of complexity.
Penguin Books, London
- [Keller 2008]
-
Keller EF (2008) Organisms, Machines, and Thunderstorms: A History of
Self-Organization, Part One. Historical Studies in the Natural Sciences,
38(1 (Winter)):45-75,
URL http://www.jstor.org/stable/10.1525/hsns.2008.38.1.45
- [Keller 2009]
-
Keller EF (2009) Organisms, Machines, and Thunderstorms: A History of
Self-Organization, Part Two. Complexity, Emergence, and Stable Attractors.
Historical Studies in the Natural Sciences 39(1 (Winter)):1-31,
URL http://www.jstor.org/stable/10.1525/hsns.2009.39.1.1
- [Laird et al 1987]
-
Laird J, Newell A, Rosenbloom P (1987) SOAR: An architecture for general
intelligence. Artificial Intelligence 33:1-64
- [Lakatos 1980]
-
Lakatos I (1980) Falsification and the methodology of scientific research
programmes. In: Worrall J, Currie G (eds) Philosophical papers, Vol I,
Cambridge University Press, Cambridge, pp 8-101
- [Luce and Raiffa 1957]
-
Luce RD, Raiffa H (1957) John Wiley and Sons, Inc.; Chapman and Hall, New York;
London
- [McCarthy 1979]
-
McCarthy J (1979) Ascribing mental qualities to machines. In: Ringle M (ed)
Philosophical Perspectives in Artificial Intelligence, Humanities Press,
Atlantic Highlands, NJ, pp 161-195,
http://www-formal.stanford.edu/jmc/ascribing/ascribing.html
- [Minsky 1987]
-
Minsky ML (1987) The Society of Mind. William Heinemann Ltd., London
- [Minsky 2006]
-
Minsky ML (2006) The Emotion Machine. Pantheon, New York
- [Penrose 1994]
-
Penrose R (1994) Shadows of the mind: A Search for the Missing Science of
Consciousness. OUP, Oxford
- [Popper 1934]
-
Popper K (1934) The logic of scientific discovery. Routledge, London
- [Powers 1973]
-
Powers WT (1973) Behavior, the Control of Perception. Aldine de Gruyter, New
York
- [Schrödinger 1944]
-
Schrödinger E (1944) What is life? CUP, Cambridge
- [Senghas 2005]
-
Senghas A (2005) Language Emergence: Clues from a New Bedouin Sign Language.
Current Biology 15(12):R463-R465,
URL http://dx.doi.org/10.1016/j.cub.2005.06.018
- [Sloman 1962]
-
Sloman A (1962) Knowing and Understanding: Relations between meaning and
truth, meaning and necessary truth, meaning and synthetic necessary truth.
PhD thesis, Oxford University,
http://www.cs.bham.ac.uk/research/projects/cogaff/07.html#706
- [Sloman 1969]
-
Sloman A (1969) How to derive "better" from "is". American Phil Quarterly
6:43-52,
URL http://www.cs.bham.ac.uk/research/cogaff/papers.html#1969-02
- [Sloman 1970]
-
Sloman A (1970) "Ought" and "better". Mind LXXIX(315):385-394,
URL http://www.cs.bham.ac.uk/research/projects/cogaff/05.html#200508
- [Sloman 1971]
-
Sloman A (1971) Tarski, Frege and the Liar Paradox. Philosophy
46(176):133-147,
http://www.cs.bham.ac.uk/research/projects/cogaff/03.html#200304
- [Sloman 1978]
-
Sloman A (1978) The Computer Revolution in Philosophy. Harvester Press (and
Humanities Press), Hassocks, Sussex,
URL http://www.cs.bham.ac.uk/research/cogaff/62-80.html#crp
- [Sloman 1983]
-
Sloman A (1983) Image interpretation: The way ahead? In: Braddick O, Sleigh A
(eds) Physical and Biological Processing of Images (Proceedings of an
international symposium organised by The Rank Prize Funds, London, 1982.),
Springer-Verlag, Berlin, pp 380-401,
URL http://www.cs.bham.ac.uk/research/projects/cogaff/06.html#0604
- [Sloman 1993]
-
Sloman A (1993) The mind as a control system. In: Hookway C, Peterson D (eds)
Philosophy and the Cognitive Sciences, Cambridge University Press, Cambridge,
UK, pp 69-110,
URL http://www.cs.bham.ac.uk/research/projects/cogaff/81-95.html#18
- [Sloman 1996a]
-
Sloman A (1996a) Actual possibilities. In: Aiello L, Shapiro S
(eds) Principles of Knowledge Representation and Reasoning: Proc. 5th Int.
Conf. (KR `96), Morgan Kaufmann Publishers, Boston, MA, pp 627-638,
URL http://www.cs.bham.ac.uk/research/cogaff/96-99.html#15
- [Sloman 1996b]
-
Sloman A (1996b) Beyond turing equivalence. In: Millican P, Clark
A (eds) Machines and Thought: The Legacy of Alan Turing (vol I), The
Clarendon Press, Oxford, pp 179-219,
URL http://www.cs.bham.ac.uk/research/projects/cogaff/96-99.html#1,
(Presented at Turing90 Colloquium, Sussex University, April 1990
- [Sloman 1996c]
-
Sloman A (1996c) The SimAgent TOOLKIT - for Philosophers and
Engineers (And Some Biologists, Psychologists and Social Scientists).
Http://www.cs.bham.ac.uk/research/projects/poplog/packages/simagent.html
- [Sloman 2000]
-
Sloman A (2000) Interacting trajectories in design space and niche space: A
philosopher speculates about evolution. In: MSchoenauer et al (ed)
Parallel Problem Solving from Nature - PPSN VI, Springer-Verlag, Berlin,
Lecture Notes in Computer Science, No 1917, pp 3-16,
URL http://www.cs.bham.ac.uk/research/projects/cogaff/00-02.html#62
- [Sloman 2003]
-
Sloman A (2003) The Cognition and Affect Project: Architectures,
Architecture-Schemas, And The New Science of Mind. Tech. rep., School of
Computer Science, University of Birmingham, Birmingham, UK,
URL http://www.cs.bham.ac.uk/research/projects/cogaff/03.html#200307,
(Revised August 2008)
- [Sloman 2006]
-
Sloman A (2006) Requirements for a Fully Deliberative Architecture (Or
component of an architecture). Research Note COSY-DP-0604, School of
Computer Science, University of Birmingham, Birmingham, UK,
URL http://www.cs.bham.ac.uk/research/projects/cogaff/misc/fully-deliberative.html
- [Sloman 2008]
-
Sloman A (2008) Evolution of minds and languages. What evolved first and
develops first in children: Languages for communicating, or languages for
thinking (Generalised Languages: GLs)?
URL http://www.cs.bham.ac.uk/research/projects/cosy/papers/#pr0702
- [Sloman 2009]
-
Sloman A (2009) Architecture-Based Motivation vs Reward-Based Motivation.
Newsletter on Philosophy and Computers 09(1):10-13,
URL http://www.cs.bham.ac.uk/research/projects/cogaff/misc/architecture-based-motivation.html
- [Sloman 2010]
-
Sloman A (2010) How Virtual Machinery Can Bridge the "Explanatory Gap", In
Natural and Artificial Systems. In: Doncieux S, et al (eds) Proceedings SAB
2010, LNAI 6226, Springer, Heidelberg, pp 13-24,
URL http://www.cs.bham.ac.uk/research/projects/cogaff/10.html#sab
- [Sloman 2011]
-
Sloman A (2011) What's information, for an organism or intelligent machine?
How can a machine or organism mean? In: Dodig-Crnkovic G, Burgin M (eds)
Information and Computation, World Scientific, New Jersey, pp 393-438,
URL http://www.cs.bham.ac.uk/research/projects/cogaff/09.html#905
- [Sloman 2013a]
-
Sloman A (2013a) Virtual Machine Functionalism (The only form of
functionalism worth taking seriously in Philosophy of Mind). Research note,
School of Computer Science, The University of Birmingham,
URL http://www.cs.bham.ac.uk/research/projects/cogaff/misc/vm-functionalism.html
- [Sloman 2013b]
-
Sloman A (2013b) Virtual machinery and evolution of mind (part 3)
meta-morphogenesis: Evolution of information-processing machinery. In: Cooper
SB, van Leeuwen J (eds) Alan Turing - His Work and Impact, Elsevier,
Amsterdam, pp 849-856,
URL http://www.cs.bham.ac.uk/research/projects/cogaff/11.html#1106d
- [Sun 2006]
-
Sun R (2006) The CLARION cognitive architecture: Extending cognitive modeling
to social simulation. In: Sun R (ed) Cognition and Multi-Agent
Interaction, Cambridge University Press, New York, pp 79-99,
http://www.cogsci.rpi.edu/~rsun/sun.clarion2005.pdf
- [Turing 1936]
-
Turing AM (1936) On computable numbers, with an application to the
Entscheidungsproblem. Proc London Math Soc 42(2):230-265,
URL http://www.thocp.net/biographies/papers/turing_oncomputablenumbers_1936.pdf
- [Turing 1950]
-
Turing AM (1950) Computing machinery and intelligence. Mind 59:433-460,
(reprinted in E.A. Feigenbaum and J. Feldman (eds) Computers and
Thought McGraw-Hill, New York, 1963, 11-35)
- [Turing 1952]
-
Turing AM (1952) The Chemical Basis Of Morphogenesis. Phil Trans R Soc London
B 237 237:37-72
- [Waddington 1957]
-
Waddington CH (1957) The Strategy of the Genes. MacMillan
- [Wagner 2014]
-
Wagner A (2014) Arrival of the Fittest: Solving Evolution's Greatest Puzzle.
Published by: Oneworld Publications
- [Wiener 1961]
-
Wiener N (1961) Cybernetics: or Control and Communication in the Animal and the
Machine. The MIT Press, Cambridge, MA, 2nd edition
- [Wright 1977]
-
Wright I (1977) Emotional agents. PhD thesis, School of Computer Science, The
University of Birmingham,
URL http://www.cs.bham.ac.uk/research/projects/cogaff/96-99.html#2
- [Wright et al 1996]
-
Wright I, Sloman A, Beaudoin L (1996) Towards a design-based analysis of
emotional episodes. Philosophy Psychiatry and Psychology 3(2):101-126,
URL http://www.cs.bham.ac.uk/research/projects/cogaff/96-99.html#22
Footnotes:
1
http://www.gutenberg.org/ebooks/21076
2http://plato.stanford.edu/entries/democritus/\#2
http://en.wikipedia.org/wiki/Democritus
3http://www.cs.bham.ac.uk/research/projects/cogaff/crp/chap2.html
4Extended in
http://www.cs.bham.ac.uk/research/projects/cogaff/misc/meta-morphogenesis.html
5
http://www.cs.bham.ac.uk/research/projects/cogaff/misc/explaining-possibility.html
6https://www.youtube.com/watch?v=wcXSpXyZVuY
7See
http://en.wikipedia.org/wiki/Control_theory
http://en.wikipedia.org/wiki/Nonlinear_control
8The role of entropy is discussed briefly in:
http://www.cs.bham.ac.uk/research/projects/cogaff/misc/entropy-evolution.html
9
http://www.theguardian.com/cities/2014/feb/18/slime-mould-rail-road-transport-routes
10Such as putting a shirt on a child:
http://www.cs.bham.ac.uk/research/projects/cogaff/misc/shirt.html
11http://www.it.bton.ac.uk/Research/CIG/Believable\%20Agents/
12http://en.wikipedia.org/wiki/Two-streams_hypothesis
13The BICA society aims to bring together researchers on biologically inspired
cognitive architectures. Some examples are here:
http://bicasociety.org/cogarch/
14The
Birmingham SimAgent toolkit is an example
http://www.cs.bham.ac.uk/research/projects/poplog/packages/simagent.html
15As discussed in connection with
"toddler theorems" in
http://www.cs.bham.ac.uk/research/projects/cogaff/misc/toddler-theorems.html
(Contributions from observant parents and child-minders are welcome.
Deep insights come from individual developmental trajectories
rather than statistical patterns of development across individuals.)
16For more on Kantian vs Humean
causation see the presentations on different sorts of causal reasoning in humans
and other animals, by Chappell and Sloman at the Workshop on Natural and
Artificial Cognition (WONAC, Oxford, 2007):
http://www.cs.bham.ac.uk/research/projects/cogaff/talks/wonac
17http://en.wikipedia.org/wiki/Symbiogenesis
18Some
of them listed in
http://www.cs.bham.ac.uk/research/projects/cogaff/misc/mathstuff.html
19http://www.cs.bham.ac.uk/research/projects/cogaff/misc/meta-morphogenesis.html\#blind-theorem
20For more on this see:
http://en.wikipedia.org/wiki/Church-Turing_thesis
21Examples of human mathematical reasoning in geometry and
topology that have, until now, resisted replication on computers are presented
in
http://www.cs.bham.ac.uk/research/projects/cogaff/misc/torus.html
and
http://www.cs.bham.ac.uk/research/projects/cogaff/misc/triangle-sum.html
22http://en.wikipedia.org/wiki/Pupa
http://en.wikipedia.org/wiki/Holometabolism
23http://en.wikipedia.org/wiki/J.\_B.\_S.\_Haldane
24A draft discussion of evolution of mathematical mechanisms is at
http://www.cs.bham.ac.uk/research/projects/cogaff/misc/befm-sloman.pdf
25Illustrated in these discussion notes:
http://www.cs.bham.ac.uk/research/projects/cogaff/misc/changing-affordances.html
http://www.cs.bham.ac.uk/research/projects/cogaff/misc/triangle-theorem.html
http://www.cs.bham.ac.uk/research/projects/cogaff/misc/torus.html
26http://en.wikipedia.org/wiki/Conway.27s.Game.of.Life
27One of many online explanations is
http://www.theprojectspot.com/tutorial-post/simulated-annealing-algorithm-for-beginners/6
28An interview with the author is online
at
https://www.youtube.com/watch?v=wyQgCMZdv6E
29Here's a cartoon teasing particle physicists:
http://www.smbc-comics.com/?id=3554
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