More about Uncertainty

Last Friday, Burhan Turksen – from the engineering department at UofT - Alaleh Azad and I discussed uncertainty over a wonderful lunch on Baldwin Street. This morning, looking back on the blogs already posted, I see that uncertainty is indeed the reoccurring, underlying theme in decision-making. It warrants a closer look.

So, in theory and practice, what is uncertainty? Chaos theory begins to inform the answer.

We travel through space and we travel through time. The first determines where we go – to the office, to the grocery store, to the cottage, to Mars. The second determines what we become – humans, thinkers, mothers, fathers, Canadians, bankers, soccer players.

The Certain Journey
The journey through space is reversible, predictable, and – barring any obstacles - linear. The classical Newtonian laws that govern it are well understood - simple, invariant, and universal. Each point remains constant in the geometry of space, and we move around among them. Gravity drives the journey. Mathematics calculates it. Science measures it. Technology enhances it. In principle, certainty prevails.

The Uncertain Journey
It is the second journey – our evolutionary trip through time - that is complicated and uncertain. It is irreversible, beyond our ability to predict, and hard to calculate and measure. It is governed by laws that are not simple, invariant and universal. It occurs concurrently at many levels of description – quantum, molecular, and the macro levels that we can see. Different laws hold at different levels.

At the quantum level the journey is a puzzle. Quantum particles can be in different states and different places at the same time. Their behavior is deterministic but unpredictable. The laws that govern this level defy the classical laws of physics. Instead, Schrodinger’s equation and Heisenberg's uncertainty principle seem to hold.

We observe the molecular level through microscopes. Chemical, electromagnetic and genetic descriptions suffice.

At the macro level the journey is governed by thermodynamic laws. Not the Second Law which describes the devolution of closed systems, but the General Law - discovered by Nobel laureate Ilya Prigogine - which describes the evolution of open systems over time.

From Chaos to Certainty
Chaos theory is the offspring of the General Law, and the self-organizing principles derived from the theory point to the role of structure – physical and symbolic - in reducing uncertainty. We build fences, skyscrapers, belief systems, norms, legal systems, languages and mathematical formulas in order to produce a degree of certainty in a complex, confusing world.

What are these principles of self-organization? And how do they act to reduce uncertainty?