Phase Space in Extremistan?

A series of accidents ...

• A recent Black Swan presentation where I tried to make a connection between Nassim Taleb's Mediocristan/Extremistan idea and several other attempts to categorize the known/unknowable - Kant's phenomena/noumena thing, Castaneda's tonal/nagual concept, etc.
• A slide in that presentation noting that "gray swans" are products of non-linear chaos.
• A dusty clipping from the June 1994 issue of The Economist offering the best explanation I've ever read of the term "phase space".

...leading me to wonder if phase space is part of Extremistan.

Aside 1 - Is synergy a black swan? Maybe.

Aside 2 - What is phase space? It is a mathematical view of action in the "real" world. Consider the example of the pendulum described in the Economist article. The pendulum swings back and forth; its position and velocity constantly changing. In the real world the action of the pendulum is an arc. In phase space, the action is represented by a two-dimensional chart showing changes in position and velocity. An ideal pendulum with no friction would appear as a circle in phase space.

Non-linear chaos refers to fluctuating phenomena that appear disorderly in the real world but display order in phase space. As the article notes, "populations of animals, bubbling pots on a stove or measles epidemics" are all examples of non-linear chaos.

Patterns traversed in phase space are sometimes called "strange attractors" (one assumes because the behavior of systems is strangely attracted to these patterns). The picture below is a two dimensional view of the three-dimensional Lorenz attractor.

It describes the chaotic behavior of weather patterns - leading to the so-called butterfly effect meaning (more or less) that a butterfly flapping its wings in Africa can cause a hurricane in Florida. There is order here - constrained by the strange attractor. But within that order is infinite disorder.

Strange.

So, returning to my original question - Is phase space in Extremistan?

Extremistan is supposed to be the real reality underlying the man-made view of Mediocristan.

So, where does phase space belong?

Which is more real - the confused real world, or phase space which reveals the underlying order in the real world?

Is phase space real?

Does one peer through/past the behavior of the world of appearance to the underlying truth of phase space?

I suppose Taleb might say it doesn't matter. In the real world, the swans are definitely black. In phase space, they are gray. In the real world, you don't know the swans are coming. In phase space, you might know they are coming but you can't know when or where.