SYSTEMS: SOME THEORY
Kevin O’Shea March 2004
System theory emerged in the late 20th century as a study of the emergent properties of phenomena. The whole is
more than the sum of its parts. There are properties that are emergent from the whole system, not from particular
parts of the system. These properties only manifest themselves at an integrated, systemic level.
Systems may be closed, or open.
In a closed system, entropy increases until there is even distribution, and eventually inertia. See the second law
of thermodynamics (Clausius, 1850).
In open systems, there is an increase of organisation and information. An open system is not a compound, it is
more like a functional family. There is complexity in it. The degree of complexity in a system can be indicated
either by the length of non-recursive computer code needed to describe it, or by the number of significant
connections/interactions that occur in it (synergy).
This complexity is the outcome of an ongoing process, called ‘complexification’. It is a non-zero-sum process. A
dynamic is going on, and is getting more complex results all the time. It is a process of interaction between the
system and its environment. It is not a continuous process. It is an instance of what is called ‘punctuated
exchange’ (Gould).
From the exchanges with the environment, there arises both order and disorder, that is, there are in the whole
system some events that are predictable, and some events that are stochastic. This means that the process of
complexification (which comes from a certain amount of disorder and stochastic events) goes hand in hand with a
process of decomplexification (which comes from a certain amount of order and predictable events). From the
process of complexification, arises ‘emergence’ of the new. From the process of decomplexification, arises
‘reversion’ to the situation of a closed system. In simpler terms, some events push the system over the edge into
something different, while other events hold it back into something very much the same as ever. An open system
is said to be ‘plastic’ in so far as its conditions include both order and freedom. It is on the cusp between order
and freedom that emergence occurs.
The universe as a whole is considered to be a closed system. Earlier, most parts of it were also considered to be
closed mini-systems. Feynmann once said, about electrons, if you’ve seen one, you’ve seen them all. Now the
mood is the opposite. Much of material nature is made of systems that seem to be heterogeneous, and perpetually
changing. Their ‘system-history’ (or evolution) seems to matter more than their ‘nature’ (at their origin).
Many of these are self-organising, complex, open systems. They are purely material self-organising systems, with
their own active complexity. [ They are not linked to a contributing/controlling consciousness, as the explanation
of their openness.] They are purely material self-organising systems, with their own active complexity. The
variables found in their processes are too many for study without computers. One of the problems now is the
number of variables in such complexity systems: there are too many.
There is a desire to work out the informational rules for the complex-evolution of such systems. This has
happened slowly, over the last half-century.
It begins in the 50’s with von Neumann. He wanted to understand how information-bits were used according to
pre-set computational rules. This was called ‘cybernetics’. The aim was practical, to produce a machine of a
new kind, open for all information, but pre-set for a determined kind of result.
This led him, and others, to work on mimicking biological processes in non-living, artificial systems. It
amounted to a mathematics of ‘living’ and a translation of it into non-living materials.
This led him, and others again, to want to create ‘learning machines’, where their own output functions would be
reintroduced into the system as input functions. ‘Feedback’ machines.
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This has led, finally, to the realisation of the possibility of ‘cellular automata’ (CA): computational systems that
are so like life-processes that they can reproduce themselves, and ‘thrive or die’. A CA is represented on a grid
of equal squares on a lattice. The lattice is often taken to be 2-dimensional.
This connects with different work such as that of James Conway (The Game of Life – 1970). He saw that state
transitions depended on another 8 neighbours of the cell… It also links with the work of Stephen Wolfram who
pondered a CA on a 1-dimensional lattice, with 2 colours (black and white). He and others then have classified
four types of system:
- 1)Those with a limit-point attractor, that as a result die quickly.
- 2)Those with a multi-point attractor, that as a result oscillate between several states:
3)some then behave like chaotic systems,
but not dependent on initial conditions of the system,
and not random,
and so exhibiting a kind of intrinsic ‘chaos’
4)others act on the edge between ‘oscillation’ and ‘intrinsic chaos’.
and as a result, are actively complexifying and ‘emergent’.
The major interest has been in these last. Through them, there is scientific expression of the insight that in nature
there is an intrinsic energy for novelty. 1
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It is useful to contrast this final position with ‘chaos theory’. There was once a received view, that nature was a machine,
and obeyed mechanical laws, formulated for example in the deterministic equations of Newton. I must admit it is hard to
imagine surprises in this model, and harder still to imagine how (or even why) God might act in a special way in that kind of
universe. Laplace said that if he could be given the position and velocity of every particle, he could predict, completely, the
entire future history of the universe!
Quantum theory has demonstrated the need for probabilities, not certainties, in very small systems. It actually explains some
well known phenomena: for example, the randomness of radioactive decay.
But nowadays random behaviour has been observed in very many systems in nature, to which quantum theory does not
apply: they are too large for that. Some examples: movement of dust particles, weather patterns, the flow of a mountain
stream, the roll of a dice, the drip of a tap, irregular beating of the heart, movement from laminar to fluid motion (e.g. in an
aeroplane when turbulence is encountered.)
This means that their behaviour is unpredictable in the long term, though perhaps not in the very short term. It is not because
we don’t have the technology to do the prediction, but because the systems are intrinsically unpredictable.
These systems are not necessarily complex in themselves: they can be simple, with few components. They can be systems
that follow deterministic laws.
The randomness that they exhibit is only apparently random (in the ordinary use of that word). There is an order in the
randomness. It is of a kind different from the usual. It has a discernible geometric form.
This seeming lack of order, which is a different sort of order, is called ‘chaos’. Again, it is not ‘chaotic’ in the ordinary
sense of the word.
It comes about, for example, when small uncertainties in the initial conditions of the system are exponentially amplified. But
that is not the only explanation.
Let us look at it more closely.
We are talking broadly about ‘dynamical systems’. We try to describe their state (information about them), and then try to
describe the evolution of that state over time. This is done by expressing an equation, or a ‘dynamic’. It is graphed by using
a moving point in what is called state space.
When we do this, we find there are actually two kinds of system: non-chaotic ones, and chaotic ones.
For a non-chaotic system, the moving point describes a simple curve (a spiral, a circle, a period, etc...). This allows
prediction of long-term behaviour. This picture is called an ‘attractor’ because the system can with relative ease be nudged
back into it.
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It is still very difficult to express the character of these systems. This comes from a peculiarity in scientific
theory. Many theories can be expressed both in a local and in a global form. Newton’s laws (and their
differential equations) are expressed in a local form: they are true at individual (local) points of the motion.
Lagrange’s mechanics (with contributions to the functional that are added up for continuously varying time) are
expressed in a global form: they are true at all points of the variation.
Joseph-Louis Lagrange conceived mechanical systems in a different way from Newton. He invented a
mathematical concept called a ‘functional’, and realised that it was to be either maximised or minimised. The
evolution of a mechanical system made this happen. In fact, this was the meaning of a mechanical system. As a
result, a calculus of variations could be set up, from which equations of motion could be derived. They agree
with Newton’s laws of motion. But they show, at a global level, why Newton’s laws are and must be true at their
own local level. There are many theories that can be expressed in either local or global form.
This recalls the conviction of many scientists that scientific theories are often underdetermined by empiric data,
at least by ‘local’ empiric data. Such theories do not end up being in contradiction (or competition) with one
another: but they are often not measurable by one another’s points of view, or reducible to another systemic
model.
Another aspect of theory is known as ‘generalisation’. Michael Heller has shown that most new theories identify
older theories as true in one particular field or set of situations, one of the many and diverse such fields or sets
that the new theory expresses more ‘generally’.
But attractors are of finite size. You can’t have an exponentially diverging orbit forever. The attractor must then at some
stage fold back and over on to itself.
For a chaotic system, the attractor is stretched and folded back on itself: it is called ‘mixing’. as a result of the doubling,
bifurcation cascades occur. The periodic points get very dense, and the whole system is very sensitive. Its behaviour is not
‘regular’ in the sense above, but seemingly random. Some kind of example of this: the shuffling of a pack of cards,
repeatedly, and quickly.
We have to admit there is at present no universally agreed mathematics to express this.
Mathematically, the strange attractor is a fractal. More and more detail is revealed as it is amplified. As it moves smaller
and then larger, in microscopic patterns, it discloses a beautiful microscopic structure or order. [It is a bit like a baker
making dough by kneading it.]
One way of talking about it is this. You could imagine the space between order and chaos as a continuum. At the heart of
the continuum there is a complexity. If we could use imagination further, we could think of the continuum as a phase
transition (between say ice and air) and we could think of the complexity as the liquid phase of H2O.
It is suggested nowadays that evolution takes a system to this point of complexity, to the ‘liquid phase’. Sometimes it is
called the ‘edge of chaos’. Sometimes it is called a ‘broken symmetry’. What happens there – at the onset of chaos – is an
increase in the possibility of universal computation of the system. The system then becomes an IGUS – an information
gathering and using system. It has a depth of its own......
l.
Some ‘practical’ thoughts:
1. Small, gradual changes in causes do not always give rise to small, gradual changes in effects.
2. Deterministic rules of behaviour do not always give rise to completely predictable events.
3. All real-world truths are not always the logical outcome of following a set of rules.
4. Complicated systems cannot always be understood by breaking them down into simpler parts.
5. Surprising behaviour does not always arise from complicated, hard to understand interactions among a system’s
component parts.
The main difference between chaos thinking and the new complexity thinking, is the lack of dependency of the complex
system on initial conditions. It is an intrinsic complexity.
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SYSTEMS IN AN EVOLUTIONARY WORLD
In present biology and genetics, the genome is looked on as a complex distributive system. It is no longer a
matter of finding out how many genes are present in the genome. It is a matter of learning how they function.
They function as a complex open system (not one by one). All ecosystems are interactive distributed complexity
systems. Gene expression is affected by the cytoplasm and the ‘environment’, and they seem to from an
integrated whole, and work as a system. Evolution itself could be seen as such a system. In fact, this approach
invites a refinement of the definition of evolution itself.
In the universe, the human brain is the most evolved complex system we know. Its complexity is of such a large
order of magnitude that is it almost infinite (see Aristotle: anima est quodammodo omnia). It is a system that is
physical (neuronal – the brain) and that is also spiritual (the mind/soul). Both aspects are very integral to the
whole brain-mind system.
Some have then theorised that the spiritual dimension is the product of the neuronal activity. Mind is then what
the brain does. Brain is the noun, mind is the verb. Character change, and personality change, are then basically
and purely physical. The re-organisation of the neurons embodies and ‘creates’ what we call spirit. Spirit is the
functional outcome of the working of the biological system. This means that the brain works ‘bottom up’. This
means that the spiritual is the environment and the outcome of the brain system. This is, philosophically, a form
of reductive materialism or physicalism.
There is more evidence available than the data on which the above is based. It is agreed that a system will not
complexify unless there is in it some measure of order and freedom. But human experience suggests that the
brain tends to complexify – even in the arrangement of the neurons - when the spiritual state or condition of the
entire system (i.e. of the whole person) includes order and freedom. That spiritual state seems to have an
influence on the actual physical organisation of the neurons. This implies that the spiritual dimension is not just
the environment of the physical system. Usually we speak of an environment as something distinct and different
from the reality we are interested in, and surrounding it and containing it. The spiritual is much more than that
for the brain. The spiritual is integral to the whole mind-brain system itself. We are dealing with a true,
integrated, meaningful system: mind-brain. The complexity that emerges from it as a system emerges from the
whole of it. This means that there is a ‘top-down’ causation at work as well as a ‘bottom up’ one. The spiritual
dimension can be the true cause of a result that is ‘felt’ in the material dimension. There is a hylomorphic
resonance of one dimension in the other. In fact, this goes both ways: the echoing is mutual, from spirit to flesh,
and from flesh to spirit.
The spiritual, here, acts much like what Teilhard called the noosphere: it is a communication system that is an
aura around and in the physical system, and that draws the latter into itself. [As Aquinas said, the body is in the
soul, more than the soul is in the body.] It seems to make emerge some unexpected (from a physical point of
view) directions of the large and integrated system. It seems to do so to make a certain elegance and beauty
emerge (as Dirac once put it).
SYSTEM IN THE PRESENT MOMENT OF HUMAN EVOLUTION
The 20th century represents only 100 years out of the 4 million years of humanity’s existence, but it has hosted
20% of all the human years ever lived. Human life expectancy has doubled in the last century and may soon
extend beyond the known limits of approximately 120 years. [The potential for disasters has also never been
greater.]
Humans – especially present human beings - have inherited much. This is the ever-increasing commonweal of all
humanity, passed on through a mode of linguistic replication called education. But we are at a totally new stage
in human evolution.
Human evolution can now bypass the simple dynamics of genetics. Natural selection – differential reproduction
and survival – operates on a supposed background of random genetic drift. Human evolution can now, for the
first time in human history, due to new technologies, allow for intentional culturally-acquired adaptations and
their transmission. The values and intentions of humans can now be the driving force in the future evolution of
the planet. This is biocultural evolution. Now, in this human cultural evolution, selection will operate on the
background of intentional adaptation. The phenotype will direct the genotype. This opens up a radically new and
accelerating kind of creativity.
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Humans have changed. In one way, they have changed very little. We are biologically and psychologically
identical to our ancestors 100 or 10,000 years ago. But there is little in the collective patterns of human
behaviour now – and in the future - that empirically resembles the past. The human nature that is encoded over
millenia in our genes, is present, but it is like a leash that keeps us back from wandering too far away from our
inheritance. From a scientific point of view, it does not dictate where we will go. [Obviously, for some, there
will be ideological considerations that will dictate that it will not change.] But the leash is also getting different
(could it be elastic?) [If all you have is a hammer, every problem looks like a nail.] There is now a horizon of
complexity beyond which we cannot see. We cannot see how to integrate it into our past, or better, we cannot see
how to integrate our past into where we will go.
There are moral questions here. An ethic could be conceived that is based on this level of complexification. But
how do you spell out the details?
In fact, one of the most significant emergences (echoings) is religious experience. There is a real possibility of a
comprehension of God within the dance of this living system. The relation of this new religious awareness to the
kind of religious awareness we have had in the past, is a new question for all of us. Perhaps it is a new kind of
experience….
Teilhard:
In a world which has become conscious of its own self
And provides its own motive force,
What is most vitally necessary to the thinking earth is a faith –
And a great faith – and even more faith.
To know that we are not prisoners.
To know that there is a way out,
That there is air, and light, and love,
Somewhere, beyond the reach of all death.
To know this, to know that it is neither an illusion nor a fairy story. –
That, if we are not to perish smothered in the very stuff of our being,
That is what we must all costs secure.
And it is there that we find what I may well be so bold as to call the evolutionary role of religions.
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