[lutusp]

Unlike the earthquake power law graph, the income distribution graph has two tails -- one causes destructive oligarchy, the other demolishes people's incentive to work. Both ends of the graph contain the potential for relatively improbable, but catastrophic, events.

People should remember this when discussing income distribution and public policy -- oligarchy is unfair and dangerous to society, and aggressive income redistribution is ... unfair and dangerous to society. The "sweet spot" is when both groups (the rich and the poor) complain with equal volume. That's why politics is called the art of the possible.

[andrewthesmart]

Sure but the question is how much control is possible; people have been trying to control nonlinear systems since the 18th century without much luck. If society/economy/culture is a dynamical system that generates the power-law income distribution and this system cannot dissipate its "energy" and the exponent reaches some critical value then it will collapse or we'll have some kind of catastrophic phase transition.

I don't think power-law distributions have 2 tails - they have one very long tail.

[lutusp]

> people have been trying to control nonlinear systems since the 18th century without much luck.

Not so. Nonlinear systems are not difficult to control as a rule, with appropriate understanding of servomechanisms. To see how extraordinary such control can be, look at this video:

http://robohub.org/video-throwing-and-catching-an-inverted-p...

> If society/economy/culture is a dynamical system that generates the power-law income distribution and this system cannot dissipate its "energy" and the exponent reaches some critical value then it will collapse or we'll have some kind of catastrophic phase transition.

These things happen, but usually because the system is not fully understood, or there's a reason it isn't being controlled, not because the system is innately uncontrollable. Obviously this moves away from technology and into philosophy, because the question becomes -- not whether the system can be controlled -- but whether such control is consistent with democratic principles.

> I don't think power-law distributions have 2 tails

Of course they do -- for example, any power law rule involving a power that's an even number:

http://i.imgur.com/HU3KZQ7.png

In fact, strictly speaking, all power law distributions have two tails, just not in the same direction:

http://i.imgur.com/tcPYrJW.png

[andrewthesmart]

Well all physical systems are actually nonlinear; linearity is something we use when we can.

I would call those types of nonlinear control toy problems compared with nonlinear systems like the climate or society. But agree that we just don't know the equations or the variables.

I still would argue that at least with many nonlinear systems, they are intrinsically unpredictable the farther into the future you go because of their sensitivity to initial conditions, self-organization and nonlinear internal dynamics.

I'm referring to the statistical long tail: http://en.wikipedia.org/wiki/Long_Tail

For more details:

http://tuvalu.santafe.edu/~aaronc/courses/7000/csci7000-001_...