Taylor begins the discussion of complexity examining the work of two artists.
Chuck Close?/Andrew Crumey
Both utilize structures, in the creation of their art work, that are self-reflexive and fold in upon themselves. Painting for Close and writing for Crumey.
Close's body of work is characterized by a high level of realism. Taylor gleans to points from Close's work that serve to establish ground work for his definitions of complexity.
1.Close systematizes his art so that the process structures the whole or the resultant portrait. Authorship is downplayed.
2. Individual discreet/heterogeneous “atoms” of the picture combine to form a coherent whole.
Taylor begins the discussion of complexity by illustrating how the perceived noise of Chuck Close's work resolves itself into a coherent message.
Drawing on the work of Serres and his essay “The Origin of Language: Biology, Information Theory, and Thermodynamics” Taylor asserts some interesting properties of biological systems (cells/organisms etc.)
Biological systems are not in equilibrium rather they are constantly in flux, and it is necessary to maintain this imbalance. Utilizing a vague analogy, Taylor cites Serres who states that systems mobilize information and produce noise. In the thermodynamic sense this could be considered a by product of the energy utilized to mobilize any given information. Perhaps this is describing the system in terms of conservation of energy.
Serres is inspired by Atlan in his work. Atlan postulates that as an organism can be considered a communications system, noise can be construed as “transmission between substructures but with ambiguity or equivocation”. The conclusion being drawn that an increase in ambiguity results in an increase in structure or order. Noise can be construed as destructive, in this situation. However if the system can somehow appropriate this noise, utilize it for generating structures, or mitigating internal conditions it would be considered “complex” by Atlan
Atlan's Criteria for a Complex System
1. “composed of a great number of parts interconnected in multiple ways”
2. “emergent phenomenon whose occurence cannot be acurrately predicted”
3. “processes at work in living organisms ' produce an evolution apparently oriented toward more complexity'”
Negentropic: A system that is capable of maintaining constant its own internal entropy level
Monotheistic structure has in some ways shaped our understanding of systems. Simplicity is more godly then complexity.
The etymology of the word complexity derives from the Latin to entwine combined with the root to fold.
Complexity can be understood in computational terms: “According to Chaitin, 'The complexity of something is the size of the smallest program which computes it or a complete description of it. Simpler things require smaller programs.” Something that is incompressible in this sense would be random, or the algorithm for describing it would include or be an instance of the very thing it was describing.
Information is equated to difference, difference increases through multiple connections between discreet parts of a system. These connections are understood to be connection between parts and connections between part and whole. Therefore information increases with an increase in connections between parts.
Taylor cites Ludwig von Bertalanffy call for an approach to systems that moves beyond mechanistic and atomistic understanding. General systems theory seeks to understand natural phenomenon through its organization. General systems theory seeks “'Developing unifying principles running 'vertically' through the universe of the individual sciences' von Bertalanffy concludes”. Complexity theory is similar in the sense that it seeks to describe the behaviors and properties of highly diverse systems across an wide array of phenomenon.
Generally Taylor cites some properties of complex systems The final property leads us into the next area, Taylor's investigation of the concept of emergence
“7. Emergence occurs in a narrow possibility space lying between conditions that are too ordered and too disordered. This boundary or margin is 'the edge of chaos,' which is always far from equilibrium.”
Taylor defines feedback in a system. Negative feedback tends to have a governing or mitigating effect, dragging the system towards equilibrium Positive feedback increases information and operational speed, in a highly interconnected system positive feedback results in effects that are disproportionate to their causes.
Basically a system or grid of cells, where each cell carries an algorithm or instruction set dictating its behavior based on the behavior of its neighbor cells over time. Though von Neumann, the first to propose this concept, never created a self-replicating machine, a computer program: John Conway's “Game of Life” illustrated the principles of cellular automata nicely.
Moreover through the research of Chris Langton and Stephen Wolfram cellular automata could be classified by four typical behaviors:
1. rigid structures that do not change
2. oscillating patters that change periodically
3. chaotic activity that exhibits no stability
4. patterns that are neither too structured nor too disordered, which emerge, develop, divide and recombine.
It is this last behavior that is particularly interesting. Understanding this in terms of phase transitions of a solid to a liquid to a gas. This last state occurs in the interstitial region between a highly ordered and highly chaotic state. Ordered enough to stay coherent as a system but disordered enough to produce surprising results.
In describing emergence and the behaviors of an emergent system, Taylor cites an experiment envisioned by Stuart Kaufman whereby 1000 light bulbs (N) are connected via a discreet number of inputs (K) and at random bulbs are assigned one of the possible boolean functions (on|off).
Between a static state cycle (K=1) and chaos (K=4||5) lies a “spontaneous emergence of self-sustaining webs” The notion of order arising from randomness or “order for free”.
The evolution of a system whereby a community of discreet interrelated units reach a super critical state as a result of their interactions. This self organized system displays a number of properties common to complex systems. The system develops to a tipping point where individual reactions can have disproportionate, catastrophic effects.
In an interesting note Taylor discusses the methods understanding these events, following the arrow of time it is impossible to predict the exact interaction that will lead to the catastrophe, but the event can be understood by reversing the arrow of time. “Life is understood backwards, but must be lived forwards” Randomness and law are not polar opposites.
The point at which a system follows one of two outcome paths during the process of developing. In the thermodynamic sense as a system moves further and further away from thermodynamic equilibrium more and more choices or bifurcation points are encountered. This increases the information and can lead to chaos. In a complex system order can arise from decisions where the consequences of one or another option are not known apriori.
Taylor cites the swarming of insects, and the behaviors of both schools of fish and flocks of birds as classical examples of the principles of cellular automata. These are complex systems. Behavior that is a result of the interactions of units as distinct from the action of an individual unit.
Allelomimesis : “In allelomimetic behavior, the conduct o each individual is influenced by the activity of its neighbors.”
Taylor asserts some properties of a network. Drawing inspiration from Millonas' connectionists models related to the the study of neural networks. Neworks consist of discreet nodes the connections between which are mediated by connections. The dynamics of the network represent the intereactions of the nodes based on the rules governing their interactions. Learning represents a progressive establishment of connection strengths. This in turn describes the progression of the dynamics. The network is decentered, and distributed, local relations dictate global dynamics.
Emergent self-organizing systems act as a whole but do not totalize. Because there is room within this organized system for aleatory events as a direct result of "irreducible unpredictability". Emergent phenomena can be discreet parts of larger more complex emergent systems. Complex emergence systems are adaptive, when there is sufficient incentive the system should adapt. There should be significant randomness withing the system to allow for a suitably varied response.
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