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True complexity
What is "true complexity"? Science in Africa interviewed George Ellis,
professor of Mathematics at the University of Cape Town to find out more
on the subject.
What is true complexity?
True complexity involves the study of real-life processes and goes beyond the
approximations of statistics, and methods such as chaos theory and catastrophe
theory. The systems I call truly complex systems are the systems of molecular
biology, animal and human brains, individual human behaviour, social and
economic systems, digital computer systems, and the biosphere. They are
reflected in associated language systems and symbolic systems.
What makes them complex?
Vast quantities of stored information and hierarchically organised structures
that not only process information, but do so in a purposeful manner. This
purposeful behaviour is achieved through goal-seeking feedback loops. True
complexity is made possible by bio-molecules such as RNA, DNA, and proteins.
These molecules have folding properties and lock-and-key recognition mechanisms.
They underlie all membranes, cells, neurons, and indeed the entire bodily fabric
and nervous system.
Are all complex systems characterised by hierarchies?
Yes, all have hierarchical structures delineating both complexity and
causality. They have different levels of order and descriptive languages, and
usually they have a relational hierarchy at each level of the structural
hierarchy. Each level is determined by a lower level. For instance our behaviour
as human beings can be presented on a scale like this:
Sociology/Economics/Politics< Psychology <Physiology < Cell biology
< Biochemistry < Chemistry < Physics < Particle physics.
The relational hierarchies at each level of complexity may be based on
appearance, structure, function, geographic location, evolutionary history, or
other factors. These categorisations go from the generic to the specific, so
that my dog Freddy can be categorised as Animal - Mammal - Domestic Animal - Dog
- Staffordshire Bull Terrier - Freddy. With each upward step in the hierarchy of
biological order, new properties emerge that were not be present at the simpler
levels of organisation. These properties arise from how the parts are arranged
and interact. The behaviour of any given level of organisation cannot be
explained by breaking it down to its parts.
'Complex systems exhibit purposeful behaviour'. What does this mean?
All living systems use information purposefully to control physical functions
in accord with higher level goals. This is achieved by feedback control systems
that can learn by capturing, storing, recalling, and analysing information. This
information is used to set the system goals through the use of simple or complex
predictive models. It is these capacities that make the difference between
complex systems and those that are merely complicated. Causality in coherent
complex systems can be bottom up, same level, or top down, and in fact all three
operate simultaneously. When higher levels structure lower level interactions in
a top-down action, this affects the nature of causality significantly, because
inter-level feedback loops become possible.
Can you give an example of top-down action?
Well, when you switch on a light switch, electrons systematically flow in
wires leading from a power source to a light bulb, and the room is illuminated.
Here, specification of a higher level state (the switch being on) determines a
family of lower level states (each describing numerous individual electrons
moving in a wire), any one of which may be implemented to obtain the higher
level state -- the light switch being on corresponds to many billions of
alternative detailed electron configurations.
In evolution, to take another example, top-down action is central to two main
themes of molecular biology. First, the development of DNA codings (the
particular sequence of bases in the DNA) happens through an evolutionary
process. This is a classical case of top-down action, because through the
process of adaptation, the environment, along with other causal factors, fixes
the specific DNA coding. We could never predict this coding on the basis of
biochemistry or microphysics alone. Then, in the second central theme of
molecular biology, the organism reads the DNA. This is not a mechanistic
process, but is context-dependent all the way. Positional information determines
which genes do or do not get switched on in each cell, so determining their
developmental fate. Without this feature, organism development in a structured
way would not be possible.
Why are information linkages so important?
They have a key role. Information linkages are the basis of goal choice in
all living systems. In all living cells, plants, and animals there are systems
that automatically, without conscious guidance, maintain homeostasis -- they
keep the structures in equilibrium through multiple feedback systems that fight
intruders (the immune system), they control energy and material flows, breathing
and the function of the heart, body temperature and pressure. They are
maintained through numerous enzymes, anti-bodies, regulatory circuits of all
kinds. Information flow uses very little power, only as much as is required to
get the message to where it is needed. Think of the temperature of the human
body, which is maintained with great accuracy. This came about through
evolution, and is unaffected by individual history. In manufactured artefacts,
the goal may be explicitly stated and controllable, for example the temperature
setting of a thermostat, or the speed of an engine.
Not only are the feedback control systems themselves emergent systems, but
the implied goals are also emergent properties that guide numerous physical,
chemical, and biochemical interactions. They represent distilled information
about the behaviour of the environment in relation to the needs of the organism.
At the higher levels they include the instinctive behaviour of animals.
At the highest levels in animals, important new features arise: namely
explicit behavioural goals. These are either learnt or consciously chosen. It is
in the choice of these goals that explicit information processing comes into
play. Information arrives from the senses and is sorted and either discarded or
stored in long-term and short-term memory. Conscious and unconscious processing
of this information sets up the goal hierarchy (with ethics as the topmost
level) which then controls purposeful action.
How does the organism process this information?
Organisms make computations based on stored variables and structured
information flows, so hidden internal variables affect external behaviour.
Current information is filtered against a relevance pattern. The irrelevant is
discarded; the moderately significant is averaged over and stored in compressed
form; the important is selectively amplified and used in association with
current expectations to assess and revise immediate goals. The relevance pattern
is determined by basic emotional responses which provide the evaluation function
that determines the specifics of neural connections in the brain. In this way
emotional responses underlie the development of rationality. Expectations are
based on causal models that are based on past experience (e.g. how to behave in
a restaurant), which are constantly revised on the basis of newer experience and
information.
At the highest level, the process of analysis and understanding is driven by
the power of symbolic abstraction, codified into language, involving both syntax
and semantics. This underpins other social creations such as specialised roles
in society and the monetary system on the one hand, and higher level
abstractions such as mathematics, physical models, and philosophy on the other -
all encoded in symbolic systems.
How can all this be described mathematically?
There are two approaches. Network mathematics and related network
thermodynamics tackle the problem directly. The other approach is the study of
neural networks, genetic algorithms, and control systems. What is needed are
computer hierarchical models, plus heuristic understanding of interplay of
components, together with mathematical models of specific sub-systems and
networks and physical models of molecular structure and interactions (needing
mathematical models of 3-dimensional structure) that allow this to come into
existence in complex systems.
You have attempted to examine implications of this approach for
ontology…
One can take as given the reality of the everyday world - tables and chairs, and
the people who perceive them - and then assign a reality additionally to each
kind of entity that can have a demonstrable causal effect on that everyday
reality. The problem then is to characterise the various kinds of independent
reality which may exist in this sense. Taking into account the causal efficacy
of all the entities discussed above, I have suggested, as a possible completion
of the proposals by Karl Popper and John Eccles, and of Roger Penrose, four
kinds of worlds as being ontologically real. These are (1) Matter and Forces,
(2) Consciousness, (3) Physical and Biological possibilities, and (4)
Mathematical reality.
These 'worlds' are not different causal levels within the same kind of
existence. They are rather quite different kinds of existence, but related to
each other through causal links. The challenge is to show firstly that each is
indeed ontologically real, and secondly that each is sufficiently and as clearly
different from the others that it should be considered as separate from them. I
suggest that any attempt at a physical description of the real world will be
causally incomplete if it does not take into account these four kinds of
existence.
More information:
Prof George Ellis will be delivering a lecture on this topic at the Sasol
Scifest. More information on his lecture and the Science festival at: www.scifest.org.za
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