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Determinism vs Predictability

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Oct. 8th, 2011 | 12:43 pm

Last weekend I was at dinner with some MIT profs and ex-traders, talking about the predictability of the stock market. The usual ideas about the three-body problem, Hofstadter, complex systems, etc, were in the air. In science, some things are deterministic and predictable: the flight of a ball follows a parabola. Other things are deterministic but unpredictable.

The job of traders in markets is to diminish the predictability surplus by capturing alpha in a competitive way. The inherent difficulty arises because the game is reflexive.

Expanding this notion to "computational cosmology" – Nick Bostrom's Simulation Argument – I found myself waking up this morning to a forcefully argued thought experiment in which our current universe arises as the outcome of a dispute between godlike entities who themselves have run out of predictability surplus about what would happen: "i bet you're wrong." "no, i bet you're wrong." "fine, let's find out." "okay, run it."

The interesting part of this argument was that adjacent virtual universes may exist, in which the boundaries between deterministic and predictable fall slightly differently. But our own universe ends up dominant because the determinism / predictability tradeoff attains a local optimum, perhaps maximizing some property, such as information density: this universe maximizes the amount of new information generated per unit of simulation cost. We're a giant random number generator.

Of course, Douglas Adams got there first. The answer is 42.

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