Wednesday, June 13, 2007

Mathematical Politics: Part 8

Complex Adaptive Systems
The Santa Fe institute is an affiliation of largely male academics seeking to the spread the theoretical net as widely as possible - especially into the domain of human society and complex systems in general. The theoretical holy grail is to write equations encompassing all that goes on under the sun and thus arrive at a preordained order which once captured means that theoreticians can retire declaring their work to be done. The universe is then a museum piece embodied in a few equations we can muse over, knowing that if we crank their handles they will churn out the answers. They will thereby encode all secrets and mysteries, thus making them no longer secrets and mysteries.

Thank God that’s not true. Even granted that physics contains catchall equations, those equations are very general and not specific. Moreover, our current physics, with its appeal to the absolute randomness of quantum fluctuation suggests that endless novelty is encoded into physical processes. As Sir John Polkinghorne points out in his book “Exploring Reality” the chaotic tumbling of the asteroid Hyperion is maintained by the underlying perturbations of quantum fluctuations. The motion of Hyperion is forever novel.
John Holland is and was a pioneer in the field of genetic algorithms. His work (amongst that of others) has revealed a close connection between learning systems and evolution. Both processes ring the changes and lock in successful dynamic structures when they find them. These structures select themselves because they have the adaptable qualities needed for self-maintenance in the face of the buffetings of a world in restless change. In evolution those structures are phenotypes adapted to their ecological niche; in learning systems they are algorithms encoding successful models of the world thereby allowing their host organism to anticipate aspects of that world.

In his book “Complexity”, Mitchell Waldrop tells of John Holland’s lecture to the Santa Fe institute. He describes how the theoreticians listening to Holland’s lecture were gob smacked as Holland delivered a home truth – there aren’t any final equations (apart, perhaps from some very general physical constraints) because reality is exploring the huge space of possibility and is therefore delivering endless novelty. That endless novelty can’t be captured in a specific way in some catchall theory. In fact there is really only one thing that can cope with it – learning systems like human beings – or as Holland calls them “complex adaptive systems”. These are systems that are themselves so complex that they have the potential to generate an endless novelty, a novelty that matches or perhaps even exceeds their surroundings. Thus, these systems are either capable of anticipating environmental novelty or else at least able learn from it when it crops up. There are no systems of equations capturing everything there is to know about complex adaptive systems or the environments they are matched to cope with. Therefore it follows that apart from God Himself there is only one system with a chance of understanding something as complex as human beings with all their chaotic foibles, and that is another human being.

To be continued.....

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