Complexity

Could “Complexity Theory” be an oxymoron? Melanie Mitchell in her book “Complexity: A Guided Tour” talks of “the sciences of complexity”, and this might indicate a lack of integration to the field. Indeed, John Bragin in a review of the book for the Journal of Artificial Societies and Social Simulation notes the lack of broad agreement on necessary and sufficient fundamentals within the field, shown by great variability in the course materials for its study at different educational institutions, and the absence of widely accepted and recognised textbooks. Perhaps complexity is just complicatedness, and general theories will forever elude us – complexity might inhabit the interstices of various theories, shot through so completely with contingency and local uniqueness as to evade generalization into any sort of global paradigm. This reminds us of the saying that the Devil (or God, depending on one’s theology) is in the details.

An interesting turning-around of complexity is made by Cohen and Stewart in their book “The Collapse of Chaos” – they indicate that one of the tasks of complexity theory is to explain high-level simplicities, which make the world to some extent navigable for creatures like ourselves; in many ways we do not experience an overwhelming explosion of complexity; they coin the term “simplexity” to indicate this aspect of reality.

Darwinian evolution, the theory of natural selection, seems to be a well-established and relatively simple, at least in its basic outlines, kind of complexity theory, and is often considered in the literature of complexity theory. (For now, here and elsewhere, I take Darwinism, the theory of natural selection, and its concomitants as given and assumed, rather than something I need argue for or about as such.)

[bridging laws]

Why isn’t there just fundamental physics? As Per Bak asks in his ground-breaking book “How Nature Works” –

“How can the universe start with a few types of elementary particles at the big
bang, and end up with life, history, economics, and literature? The question is
screaming out to be answered but it is seldom even asked. Why did the big
bang not form a simple gas of particles, or condense into one big crystal?”

I’ve already used the term “level”. The idea of levels is often invoked to explain higher orders of complexity, and here the related concepts of emergence and hierarchy are relevant. Levels are a fascinating aspect of reality, but should not be taken to dispel all mystery. Rather, I think levels are part of what is to be explained, and not a thorough explanation. We must always bear in mind that levels is very much a metaphor. Often, levels seem bound up with grain and resolution, micro- and macro-, fundamental physics often dealing with the very small, chemistry with full atoms and molecules, biology with biochemistry and larger entities, and so on. However, this is not always the case, for example, the astrophysics of gravity deals with some vast objects.

We often think of there as being a kind of hierarchy of sciences, which would be something like – physics, chemistry, biology, psychology, sociology, to put it in a rudimentary form. I’ve appropriated this diagram from the web to illustrate the idea, but it’s probably familiar –

Each higher science is more limited in its applicability to reality, for example, physics would apply across the universe, but biology only to restricted situations. This interpretation of the narrowing towards the pinnacle of the triangle may be more proper than its suggestiveness for our inclinations to think of superiority and “the higher the fewer”. Personally, I would not count Mathematics as a science, nor put Arts at the pinnacle (the understanding of the arts, aesthetics, maybe).

This article will consider what we might call “Actually Existing Complexity”, complexity as it arises in the physical world. My article Maximization pays more attention to complexity in its mathematical, informational, algorithmic form, as something measurable.

The field of complexity could clearly be quite vast. It is difficult to follow my own path whilst still accurately showing the field, especially as the field is not settled, so I will try to indicate, as I go along, that wider field. My own path here will be to explore some fundamental ideas rooted in the thermodynamics of non-equilibrium systems as pioneered by Ilya Prigogine, and then attempt to unify these ideas with a consideration of complexity as involving some sort of circularity, utilizing ideas from Wiener, Kauffman, Edelman, and Maturana and Varela. The two movements are thus –

1 Thermodynamics – Prigogine

2 Cybernetics – Wiener

I’m hoping to move from Prigogine’s ideas of the thermodynamics of non-equilibrium open systems, via the idea of imbalance, to the idea of something separating off and forming a boundary. I’m then going to try to drive forward the idea of boundary, and circular processes within the boundary, in tandem, and I hope they can be seen as two sides of the same coin.

_____________BELOW HERE UNDER CONSTRUCTION______________

The Prehistory of Complexity Theory

1. General System Theory                      founded by Ludwig von Bertalanffy
2. Cybernetics                                            founded by Norbert Wiener

Complexity Theory could be regarded as the modern equivalent of the search for the philosopher’s stone, and has its precursors in systems theory and cybernetics (we might also add here dialectics, which I deal with in an independent article, and holism, gestalt, …, perhaps even going back to the hermetic and alchemical traditions …)

Both General System Theory and Cybernetics took as imperative the desirability of identifying similar patterns (Bertalanffy talks of “isomorphic laws”) which occur within different specialized sciences. It is here that we encounter an idea which vertically cuts downwards through our idea of levels: similar laws may be identified at different levels within our hierarchy. This indicates a deep integrity to the levels, a similarity between them, with “systems” as the potentially unifying concept.

It was noticed, with the development of science in the nineteenth century, that the findings of thermodynamics and of evolutionary theory seemed to be in contradiction; thermodynamics indicated an inescapable winding-down of organization to a state of disorganization and randomness, whereas evolutionary theory indicated tendencies to complexification, and increasing sophistication and internal differentiation. The theory of open systems goes some way to resolving this contradiction.

….

Thermodynamic disequilibrium within open systems (Prigogine) means that boundaries can develop.

Prigogine seems to regard asymmetry as the cosmic aspect of disequilibrium.

boundary, closure, insulation initially for us an enclosing membrane. Note also Volk’s idea of borders and pores, one of his metapatterns.

“the concept of an autonomous agent is inherently a non equilibrium concept” Kauffman

The thermodynamics of open systems, perhaps differences within far-from-equilibrium states, means that insulation / closure / boundary can occur. This allows for the development of forms of circular causation, re-entrance, etc. It means that systems can develop which are closed to energy / matter in brute form, but open to information (though there is always an energy cost to information). [or closed to information but open to energy / matter?]

feedback, or something like it, is central to complexity, control, and emergence.

We might need a general term  – circularity, circular causation, cyclicity, loops, recursion – to subsume more specific forms, including but not restricted to feedback, negative and positive. Negative feedback has great importance. Modulation, mentioned by John Holland, may be a middling form.

There is something about catalysis (including enzymes) which makes it important as a building block for the circular processes, including autocatalysis, which are in turn important at a higher level. Not being used up in a process is similar to the “weight” of information in control.

As an aside, I am utterly against any attempt to take the concept of circular causation in a mystical direction, as if it involves some sort of time travel; formulations like “self-causing cause” invite such speculation. The circular causation I consider here is completely compatible with our usual intuitions about causality and time.

autocatalysis – Kauffman

re-entrance – Edelman

operational closure – Maturana and Varela

Kauffman talks of circuits a lot – I’m still analysing his work, but as yet he doesn’t seem to put the notion of circularity centre-stage, which would make it easier for me. However, his circuits implicitly involve circularity. Here it may seem that I am resorting to an argument from etymology. However, it is clear that he is not thinking of a circuit that begins and ends in a battery, but of a self-sustaining network.

Deacon, in his paper “Emergence: The Hole at the Wheel’s Hub” uses an image I have independently used, that of the Ouroboros –

“The image of a snake biting its own tail (ouroboros) is an ancient sign for
the mysterious. Circularity is also the key to unlocking the mystery of the
apparent time-reversed causality of self-organizing and teleological processes.”

Prigogine –

“Although the effects of “nonlinear” reactions (the presence
of the reaction product) have a feedback action on their
“cause” and are comparatively rare in the inorganic world,
molecular biology has discovered that they are virtually the
rule as far as living systems are concerned. Autocatalysis (the
presence of X accelerates its own synthesis), autoinhibition
(the presence of X blocks a catalysis needed to synthesize it),
and crosscatalysis (two products belonging to two different reaction
chains activate each other’s synthesis) provide the classical
regulation mechanism guaranteeing the coherence of the
metabolic function.”

Circularity seems often assumed by the most advanced thinkers, implicit, and thus never quite given its full recognition. It is an invisible thread, crochet, or knitting.

Recursion seems to underlie nonlinearity, a key concept of chaos and complexity theory, and both recursion and nonlinearity seem based on some form of cyclicity.

Ellis makes a useful distinction between two forms of control / feedback – the lower form of homeostasis and the higher form of the explicit setting of values and goals. Homeostasis can also be thought of in terms of convergence rather than divergence, using the notion of an attractor. Bertalanffy argues quite persuasively against any subsumption of homeostasis to negative feedback on the reasonable grounds that homeostasis can occur at low levels of organic behaviour, whereas negative feedback is dependent on differentiation of function, especially into a control hierarchy, a sort of specialization which he would regard as a kind of mechanization. Equifinality, also stressed by Bertalanffy, seems related to homeostasis.

[logic gates, neurons, neuronal groups, discrete, continuous, complex]

You can’t really have information without closure. You would just have cause and effect.

Circular causation and downward causation are two aspects of the same process.

The blocking of complete interaction means we can have triggers and filters (see Koestler). This opens the way for control, especially negative feedback. The energy utilized is not causative in the normal sense. The concept of constraint is important here.

We have a duality of closure and circularity.

Two conditions for levels and emergence are closure and circular causation. Circular causation might cause closure, or conversely closure might cause circular causation. Each causes the other. It would be difficult to assign priority.

The circularity carves out its circular pathways, and in doing so, excludes a lot of outside interference. Or – circularity IS the lessening of outside interference / influence.

from Maturana and Varela – The Tree of Knowledge –

Bateson, a cyberneticist who could be regarded as a middle link between Wiener, and Maturana and Varela, talks of living processes as being tautological, and I believe this can be seen as an aspect of cyclicity. Something else which may be relevant is the idea of self-reference.

Chaos Theory is connected to Complexity, but antichaos with its dampening effects might be the most relevant aspect of this, at least as regards levels, emergence, and downward causation. Whereas chaos theory describes situations which display extreme sensitivity to initial conditions, biological systems and other stable systems show the opposite – which Bertalanffy calls “equifinality” – a tendency, even with outside perturbations, from different starting points, to lead to the same end state. Nowadays, such insights are usually expressed with the language of “attractors”, chaos having its strange attractors. We might provisionally align things thus –

negative feedback : positive feedback :: antichaos : chaos

though a third term, closed thermodynamic system, has the attractor of thermodynamic equilibrium.