Research inside Emergent Systems

I'd like to give an example to suggest that the fact that a given system may lie far beyond the phase change does not mean we should lose all hope in our traditional means of understanding, explanation and prediction:

Consider an analogy with the game of chess. Current computer chess programs use extremely sophisticated but nevertheless brute-force approaches to `simulate' the game and make predictions. Human grand-masters use a wonderfully subtle combination of pattern-matching, generalisation, comparison and analogy-making with some look-ahead to `understand' the game and make their predictions. The branching factor of simulations is so high that humans are currently far superior at determining such elusive concepts as positional advantage. I would posit that chess lies on the emergent side of the phase boundary, so that solution by simulation is ultimately the best approach. However, human expertise and understanding seem to achieve an astonishing amount in the face of the above information paradox.

This highlights the fact that my result only states we can do no better than a simulation by using our understanding. A sufficiently sophisticated combination of approaches may be the brain's best bet for prediction in complex systems. The brain itself, of course, is an extremely complex system, which I would suggest lies far beyond the phase change - this clearly has important ramifications for artificial intelligence.

Let us now look at the direct study of emergence. There are two alternative view-points from which we could approach emergent complex systems.

Firstly there is the possibility of performing a limited characterisation on the space of emergent systems. Although the boundaries of any such classification in complex system space will be very imprecise, many important systems may fall nicely into such a scheme.

Secondly, given that we know a particular system evolves to a particular type of emergent state under some interesting conditions (or perhaps under most conditions), we may be interested in the behaviour of the system on that emergent state.

1. By virtue of its emergent nature, the interesting, coherent parts of its emergent states will usually be composed of ever changing subsets of the actors which comprise the complex system. Is the split between co-organised and apparently separated actors ergodic? Perhaps we can apply statistical physics techniques to some sub-system.

2. We would like to know the structural stability of the emergent state under external perturbations.

3. The emergent state may exhibit interesting dynamics, e.g. self-organised critical phenomena such as power-law scaling in its structure or constituents.

4. How robust is the emergent state to changes in the underlying rules (interaction stability)?

5. What happens if we allow the system itself to evolve by modification of its own rules?