The Mathematics of Chaos

Now that we've reviewed the math of particle physics and relativity, we can move on to the math of things we can touch, feel, see, hear and smell.

No, we aren't interested in Newtonian Mechanics at this point. We want to show how chaos theory is a bridge from "simple" systems like atoms to "complex" systems like humans, ecologies, and economies.

Just as patterns in the subatomic world give rise to the mathematics of particle physics, patterns in nature and the cosmos give rise to the mathmatics of complex systems.

A universality has been found in patterns beneath the surface of things like the human heart, weather, internet traffic, the human brain, nature's rhythms, and cosmic expansion.

There is a holism and universality not unlike that found in certain subatomic patterns in the world around us.

Historically, mathematicians and scientists have attemped to deal with the nonlinear patterns of complex systems using standard mathematical structures like transformed differential equations and probability theory. The problem is that complex systems involve patterns that ultimately don't cooperate with such standard approaches.

As was the case in quantum mechanics and relativity theory, a new way of thinking is needed if we are really going to make progress in understanding complex systems. The dramatic increase in computing power in recent years has provided opportunities for such new thinking.

State and phase space, perturbation, fractals, attractors, power laws, cascades, symmetries, topologies, multifractals, and phase transitions are examples of notions which have arisen in the search for patterns in complex systems. If the mathematics underlying those patterns happens to relate to the patterns uncovered in the subatomic world, a metaphysical and scientific revolution of unprecedented power will be unleashed.

A mathematics of reality which begins with the fuzzy patterns in the subatomic world and shows how those patterns, even in principle, can be followed up the chain of reality, could lead us to a picture of human and cosmic reality which is holistic, interconnected and transcendent.

Economic activity, political activity, social activity, intellectual activity and spiritual activity could all be viewed from the perspective of universal patterns emerging into structures of truth beauty and justice. Quite a leap in logic, perhaps, but better than most of the other possibilities.

We have discussed in other blogs, and will discuss in future blogs, how such deep perspective can help us deal with the problems of the day. As a highly complex system, the global economy cries out for holisitc analysis. The tools of complexity science and actuarial science are ready to be combined with those of relativity and quantum mechanics to form an analytical structure for public policy analysis in the twenty first century.

Are we up to the challenge?

Yes we are.

Lee