To all visitors:
Serendip was born in 1994, and developed forums in 1996. The forums have been and continue to be a place where everyone is invited to make comments, ask questions, and carry on conversations about anything and everything that comes to mind when exploring Serendip. As such, they have been and continue to be an essential part of Serendip's development. At the same time, any developing organism needs periodically to refresh itself. The past remains but is put in boxes to clear the mind for the next part of the future. So have we done, as of today, with Serendip's forums. All past material is still available, by clicking on highlighted years above to access forum archives. And we have, as of today, a blank slate for the next phase of Serendip's development. If you have been here in the past, you're already a part of what Serendip has become so far. Please leave your thoughts as part of the next phase of Serendip's life. And if you're new, please join in as well.
Now, thanks to James Gleick and Benoit Mandelbrot, at least some portion of the educated public has discovered the joys of Chaos Theory and Fractals.
And yet, I daresay 99% of the public still believes in the foundation axiom of Western Civilization -- that rule-based systems are inherently orderly. How long will it be before the public realizes that our civil regulatory mechanism -- the Rule of Law -- is founded on a mathematically disprovable myth?
Other models (notably Girard's) suggest that the Rule of Law generates (down through the ages) a chaotically rising tide of violence, oppression, injustice, corruption, poverty, ignorance, alienation, suffering, and terrorism. We are moving toward a compelling system model of human socio-cultural mechanics that demonstrates this behavior in a mathematically compelling way.
Of course all is not lost. There do exist regulatory mechanisms which work as desired. They are not rule-based of course. They are model-based and rely on higher-order computations (inversion of the system model) to achieve stability. This method amounts to rocket science, since inversion of arbitrary functions amounts to solving implicit functions (i.e. primitive recursive functions). That is, one must have mastered the tools of thought found in Newton's Calculus, since we are obliged, in general to compute the limits of infinite sequences whenever we deal with functional models that are nonlinear in a nontrivial way.
But evolving Western Civilization from the Rule of Law to Model-Based Reasoning seems all but impossible from a political point of view. And yet if we fail to make that leap, there is a growing probability that our culture will collapse in a tragic failure to think our way into the future.