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Experimental data

There is a myth that there are no experimental data for complexity. This is related with the fact that the tasks of experiments in complexity are different than in the usual sciences. E.g. in particles one knows the macroscopic behavior and has to look for experiments to probe the micro. In complex systems one usually knows both the macro and the micro but the intermediate scales connecting between them are not understood.

The experimental characterization of the collective objects relevant at various scales including their (conditional and unconditional) probability distributions and time (auto-)correlations is a very well defined objective. As with all Complexity, the only problem is that it does not fall within one of the classical disciplines.

The myth of irreproducibility is not more justified than accusing classical mechanics of irreproducibility just because in real life one cannot reproduce dice throwing experiments.

The Laws of Complexity

The archetype of finding 'the basic laws' of a science is to find a small group of basic dynamical principles from which 'all' the phenomenology of the field can be explained. For instance, the chemical properties of the atoms can be (in principle) deduced from the quantum electromagnetic interactions between electrons and nuclei. Pauling earned his Nobel prize for putting forward this program.

In the case of Complexity the rules of the game are completely changed: BOTH the macroscopic phenomenology of the collective objects AND the 'elementary' properties of the 'simple' objects are known. The challenge is to deduce one from the other WITHOUT introducing new natural laws !

In this sense finding the 'laws of complexity' has to be preceded by a better understanding of what are we really looking for.

In the meantime, one can concentrate on producing uniform criteria by which to decide in generic situations which objects are to be considered 'elementary' and which collectives are to be considered (and to which degree) as emergent objects.

These criteria should be standardized together with the search for other regularities (power laws, scaling, critical slowing down etc).

Theory and Complexity

Here there are 2 levels at which theorists can function in the context of Complexity:

the long range level with its hope for a 'grand theoretical synthesis' providing the 'laws of complexity emergence' (modulo the doubts above).

the level at which we act now: applying the tools which we have described above: thermodynamics, statistical mechanics, scaling, multiscale, clusters, universality, graph theory, game theory, discrete dynamics, microscopic simulation, informatics etc.

The use of these methods (especially by somebody else) often reminds one of the saying: 'when carrying a hammer, a lot of things look like nails'. This might caution us to keep looking for simplicity even when carrying complexity.

Next: Conclusions and Recommendations
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