Monday: additional complexity blogging …

In what is hopefully the last journal before I start composing the full report, notes from Towards a theory of everything? – Grand challenges in complexity and informatics, David G Green and David Newth, from Volume 8 of Complexity.org.uk, 2000, p1 – 12:

1. p2: among the very first questions in complexity theory … is how things organise themselves
2. p2: how do large-scale phenomena emerge from the simple components?
3. p2: this issue led to the idea of “holism”(A Koestler, 1967, The Ghost in the Machine, Hutchinson, London), in which objects are regarded not only as discrete entities but also as building blocks within larger structures.
4. p2: one [mechanism identified] is the role of connectivity in a system, which determines whether sets of objects are isolated or a fully connected system
5. p2: one of the most important principles is that global phenomena can emerge out of local interactions and processes. For instance, P Hogewerg and B Hesper (1983, The ontogeny of the interaction structure in bumblebee colonies: a MIRROR model, Behav. Ecol. Sociobiol. 12, 271-283) showed that the scoial organisation of bumblebees emerges as a natural consequence of the interactions between simple properties of bumblebee behaviour and of their environment. [JE - then goes on to say how the ideas behind this can be abstracted to cellular automata]
6. p2 – 3: H Haken (1978, Synergetics, Springer-Verlag, Berlin) … pointed out that in many emergent and self-organizing processes, phase changes (from local to global behaviour) occur at a well-defined critical value of some order parameter. For example, water freezes at a fixed temperature … These properties are now known to be closely related to issues of connectivity.
7. p3: … the issue of identification is still unclear (1995, JH Holland, Hidden Order: how adaptation builds complexity, University of Michigan Press, Ann Arbor). Sometimes, what we may see as an emergent property of a system is apparent only when an assemblage is considered in a larger context.
8. p3: many aspects of complexity can be traced back to issues arising from connectivity. Interactions, state changes, neighbourhoods and many other phenomena all define links or connections between objects.
9. p3: [JDE - NB note that the following has been proposed by the article author himself -- how may citations for each article?] DG Green ({1993, Emergent behaviour in biological systems. Complexity International, 1. http://www.csu.edu.au/ci/vol1/, 39 citations }, {1994, Connectiivity and the evolution of biological systms. J. Biological System 2(1), p91-103, 18 citations }) proved the following theorems:
1. Theorem 1: the patterns of dependencies in matrix models, dynamical systems, cellular automata, semigroups and partially ordered sets are all isomorphic (def’n) to directed graphs (def’n)
2. Theorem 2: in any automaton or array of automata, the state space forms a directed graph
10. p3 (continuing from bullet 9/ above): the implication is that virtually any complex system inherits properties of graphs. The most important of these properties is that, starting from a set of isolated nodes, a phase change in connectivity occurs in any random graph as edges are added to the system (P Erdos and A Renyi, 1960, On the evolution of random graphs. Mat. Kutato. Int. Kozl. 5, 17 – 61). This features of graphs is therefore responsible for many kinds of criticality. DG Green (note article author, 1995, Evolution in Complex Systems. Complexity Internation Volume 2, http://www.csu.edu.ac/ci/vol2) conectures that connectivity underlies all criticality.
11. p3: several authors (e.g. CG Langton 1990, Computation at the edge of chaos: phase transition and emergent computation. Physica D, 42 (1-3):12 – 37) have proposed that maximum system adaptability lies on the “edge of chaos”. An alternative model (note same author, DG Green 1994 Connectivity and the evolution of biological systems. J. Biological Systems 2 (1), 91 – 103) suggests that systems flip-flop across a “chaotic edge” associated with a phase chanage in their structure or behaviour.
1. p4: In the edge-of-chaos model, complex systems evolve to lie near or at the critical point, between chaotic and ordered … In the phase shift model [JDE -- i.e. the author Green's -- see bullet 10/ above], external stimuli flips the system across the chaotic edge into a phase where variation predominates.
12. p5: … an interesting conjecture (originally ascribed to ecologist Bruce Patten, 1975 (Ecosystem linearization: an evolutionary design problem, American Naturalist, 109, 529 – 539) ) is whether the large-scale dynamics of ecosystems are esseentially linear. Natural selection, Patten (1975) proposed, tends to either eliminate non-linear processes or else nullify their effects. He based his hypothesis on the experiences of engineers, who find that linear systems are reliable and desirable, whereas systems with non-linear behaviour are not.
1. [JDE: however, an interesting point here: do we try to apply linear relationships because we know more about them?]
2. [JDE from a little further down p6] These ideas raise an important general question: is the linear behaviour observed in complex systems real? Or does it reflect the way we model them? It can be impossible to decide, from the data alone, what sort of model best decribes a process. Unless they are guided by a theory theat demands a particular sort of model, scientists analyzing data tend to look for the simplext equation that fits their observations: the simples model is usually a straight line. This tendency to use linear models in increasd bevause the range of observeations is often limited. Shorts segments of most continuous functions look like straight lines — the shorted the interval, the better the approximation. We often exploit this fact in interpolation. Similarly, scientists observing nature rarely see a process operate over its whole range; sometimes the range of observations is quite restricted. Finally the last point in important because feedback, and external constraints, act to keep a process within a limited range of values, so that the porcess tehds to look linear.

Dang .. that’s as far as I’ve got. Still have a few pages to read, but have gleaned some interesting references: searching Physica D for Chris Langton is quite interesting.