Wednesday, March 17, 2010

Zen Uncertainty

Zen Uncertainty: Attempts to understand uncertainty are mere illusions; there is only suffering.
-- WARNING: Physics Envy May Be Hazardous To Your Wealth!
Should we give up? No, there's plenty we can do to make the suffering more bearable. Lo and Mueller give an uncertainty taxonomy of five levels in their 'Physics Envy' paper:
  1. Complete Certainty: the idealized deterministic world
  2. Risk without Uncertainty: an honest casino
  3. Fully Reducible Uncertainty: the odds in the honest casino are not posted, we have to learn them from limited experience
  4. Partially Reducible Uncertainty: we're not quite sure which game at the casino we're playing so we have to learn that as well as the odds based on limited experience
  5. Irreducible Uncertainty: we're not even sure if we're in the casino, we might be outside splashing around in the fountain...
At the bottom of the decent we find level infinity, Zen Uncertainty.

Section 2 of the paper provides a nice historical overview of the early work of Paul A. Samuelson, who single-handedly brought statistical mechanics to the economists, and they have never been the same since. Samuelson acknowledged the deep connection between his work and physics:
Perhaps most relevant of all for the genesis of Foundations, Edwin Bidwell Wil- son (1879–1964) was at Harvard. Wilson was the great Willard Gibbs’s last (and, essentially only) protege at Yale. He was a mathematician, a mathematical physicist, a mathematical statistician, a mathematical economist, a polymath who had done first-class work in many fields of the natural and social sciences. I was perhaps his only disciple . . . I was vaccinated early to understand that economics and physics could share the same formal mathematical theorems (Euler’s theorem on homogeneous functions, Weierstrass’s theorems on constrained maxima, Jacobi determinant identities underlying Le Chatelier reactions, etc.), while still not resting on the same empirical foundations and certainties.
Related to this theme, there's an interesting recent article over on Mobjectivist site about using ideas from physics to model income distributions.

Lo and Mueller propose to operationalize their uncertainty taxonomy with a 2-D checklist (table). The levels provide the columns across the top, and there is a row for each business component of the activity being evaluated, here's their description:
The idea of an uncertainty checklist is straightforward: it is organized as a table whose columns correspond to the five levels of uncertainty of Section 3, and whose rows correspond to all the business components of the activity under consideration. Each entry consists of all aspects of that business component falling into the particular level of uncertainty, and ideally, the individuals and policies responsible for addressing their proper execution and potential failings.
This seems like an idea that could be adapted and combined with best practices for model validation (and checklist sorts of approaches) in helping to define what sorts of uncertainties we are operating under when we make decisions using science-based decision support products.

Their final paragraph echos Lindzen's sentiments about climate science:
While physicists have historically been inspired by mathematical elegance and driven by pure logic, they also rely on the ongoing dialogue between theoretical ideals and experimental evidence. This rational, incremental, and sometimes painstaking debate between idealized quantitative models and harsh empirical realities has led to many breakthroughs in physics, and provides a clear guide for the role and limitations of quantitative methods in financial markets, and the future of finance.
-- WARNING: Physics Envy May Be Hazardous To Your Wealth!

1 comment:

  1. Thanks, I read through the paper. It started out kind of weak, but got better when they started discussing Bayesian degrees of belief on page 12. I still am not sure if their distinction between "risk" and "uncertainty" mirrors the distinction between "frequentists" and "Bayesians".

    I think some of the real physics envy is in people looking for critical phenomena and new states of matter or behavior as opposed to seeking more ordinary explanations to what they observe, like entropic disorder.

    Which reminds me -- I saw no mention of entropy at all.

    Also only a slight nod to John Maynard Keynes, who did much on probability theory, and had to influence Samuelson. And then Boltzmann and his contemporaries were the original econophycists as they suggested applying statistical mechanics arguments to the social sciences first.

    The inconsistent part of their presentation is their discussion of irreducible uncertainty combined with their frequent insistence that they could explain certain parts of the economy.