As for the multi-polar world stability and the mechanism to protect it from a new hegemony. On a purely psychoevidence level, it seems an unlikely scenario that will be substituted by a world with a new hegemony. What kind of mechanism can that be?

Will we see a relatively long period of oscillation between multi-polar conditions with world hegemonies, until there are no polars left?

]]>Here’s a toy example. Pick some function of one variable that behaves chaotically when iterated. Call it f. Now consider a two-dimensional system that evolves according to g(x,y) = (f(x), y/2). The dynamics of this system are as follows: wherever you start, you converge exponentially towards the subset defined by y=0, but the way you move around that subset is unpredictable.

This sort of behaviour is quite common in “real” systems: there’s an attracting subset that almost all orbits converge toward; once you get near it, your motion is predictable in that it stays near the attractor but unpredictable in that you can quickly find yourself anywhere in the attractor.

]]>A cyclic attractor (eg. x1 -> x2 -> x3 -> x1) would be contained within one of the buckets within the partition.

Isn’t ‘chaotic attractor’ an oxymoron? If it is chaotic, how can one predict with very high confidence that it will continue (or not continue) doing anything?

]]>