John Hagel claims our views are “shifting from a Gaussian world to a Paretian world.” This will alter our understanding of probability and help us create more effective strategies (via John Robb).

“These are two very different ways of viewing the world, with some events following a Gaussian distribution (classic example: the heights of individual human beings) and other events following a Pareto distribution (classic examples: frequency of word use, size of human settlements, distribution of Internet traffic and intensity of earthquakes).”

The Gaussian Bell Curve usually describes patterns without interacting parts. The Paretian graph describes complex systems through Power Law which is P(k) ~ k^−γ.

“While on the surface Paretian worlds appear much more complex and unpredictable than the seductive simplicity of the Gaussian world, deep structural forces are at work shaping Paretian worlds…. The problem is that most of our analytical tools are designed to understand Gaussian worlds. These same tools seriously miss, or even distort, the dynamics of Paretian worlds. We need an entirely new analytical tool kit for the Paretian world.”

A reductionist approach is helpful. We study the individual parts and their operations. Simple interactions accumulate and produce the complex order that would otherwise mystify us.

In a Paretian world, surface events can become a distraction, diverting attention from the deep structures molding these surface events. Surfaces are extraordinarily complex and rapidly evolving while the deep structures display more simplicity and stability. These deep structures are profoundly historical in nature – they evolve through positive feedback loops and path dependence. Snapshots become misleading and understanding requires a dynamic view of the landscape.

Here’s an analogy: Say there is a ball rolling on the ground. Movement starts with F=ma and is countered by friction and gravity.

A photograph is misleading as it hides motion. We lose knowledge of mass, direction, velocity, etc. We are led further astray if the viewer inserts his feelings as if he was interpreting art. The results are absurd if he uses it as a substitute for science.

Likewise, we need better tools to understand politics, economics and other aspects of society. Understanding Power Law helps us start.