The Planck Length - 03/29/09

The Planck length is the physical boundary between what we know and what we do not. Under 1.6 x 10 ^-35 meters, the boundaries of four dimensional space time melt into a quantum foam—space and time become indistinguishable and subject to the mysterious, largely unknown force of quantum gravity. On these small scales, the work of Galileo, Newton, and Einstein is irrelevant.

Understanding quantum gravity presents a unique challenge: our measuring tools are too blunt to measure the foam without permanently changing it. This is the premise of Heisenberg's uncertainty principle. Measuring the quantum world from three dimensional space is like using a nuclear reaction to illuminate a dark room to ascertain it's size. The energy of the reaction will, for a split second, illuminate the room, just before incinerating it. By using the wrong instrument, the "light" becomes an active force in changing and shaping a new state of the universe. There was a dark room before the reaction. After the reaction, there is a hole in the ground. We still have no idea of the room's size and never will. Any quantity related to the house becomes irrelevant—it's gone.

This speaks to the importance of having the right tools when it comes to quantifying and measuring a system. I'm concerned that financial economics as an institution has built policy on top of theories stemming from blunt, broad, general assumptions on how the world works. Assumptions like the rational agent and the wealth maximizing firm make for an elegant mathematical framework but leave out the details on what's being maximized. Is it money? Reputation? Likelihood of survival?

Placing faith in the idea that intricate mathematics makes right is a recipe for disaster. "Complexity," Michael Lewis deftly explains, "is not intelligence." A second order differential equation that models options prices (read Black-Scholes) and assumes risk is the historical variability of returns may look elegant, but it can still be wrong. What about other components of risk?

I came across a great line once, "the devil is in the details. If you don't go after that devil, he'll come after you." The collapse of LTCM showed that when a risk assessment overlooks some details (e.g. asset covariance, credit liquidity, and tight coupling), the devil returns to take money, shatter reputations, and destroy companies. The jury is still out on the current crisis, but I am sure we'll find that large financial institutions placed enormous bets on the back of risk measurements derived from crude and incomplete theories. The damage to the system—the world economy—by relying on blunt risk profiles has finally been felt.

Financial economic policy, executed responsibily, is a powerful force for good in the world—a force that allocates capital to those who can best use it, while also lifting people from poverty. Responsible execution going forward will require economists and financial engineers to realize their work must be propelled by empirical fact over tradition. To that end, the details—the devil—must be addressed by digging deeper, exploring the core assumptions of financial economic theory, and making changes where necessary. This is the successful path that physics has followed by going beyond the visible structure, beyond the molecule, down into the atom, right up against the boundary, the Planck length, of what is knowable and what is not.

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