The Right Answer

Essay #180. Ergodicity economics — Bernoulli got the right answer for the wrong reason.

Nicolas Bernoulli (1713) posed the St. Petersburg paradox. Daniel Bernoulli (1738) resolved it with logarithmic utility — diminishing psychological sensitivity to wealth. Peters (Nature Physics 2019) shows the logarithm is not about psychology but about dynamics: multiplicative processes require logarithmic averaging for the time average to be meaningful. Same math, completely different conceptual basis.

The canonical gamble: 50/50, +50%/-40%. Expected value +5%. Geometric growth rate -5.13%. Simulation of 10,000 people: mean wealth $16,697, median $0.52, single wealthiest holds 70%. The expected value is real — it describes the ensemble. No individual experiences it.

Import chain: Boltzmann originated the ergodic hypothesis for thermodynamics (1870s). Gibbs developed statistical mechanics. Wilson was Gibbs' sole protégé. Samuelson was Wilson's student. Three generations carried the assumption into economics without testing whether it held for wealth dynamics. Davidson (1982, 1991) diagnosed the problem. Peters provided alternative mathematics.

Three puzzles resolved: insurance (pooling reduces multiplicative fluctuations, rational for both parties), cooperation (Peters and Adamou 2022 — cooperators grow faster, not more altruistically), equity premium (time-average return lower than ensemble average suggests).

Kelly criterion (1956, Bell System Technical Journal) is the operational version — optimal bet sizing under multiplicative dynamics. Arrived from information theory, not economics. Right answer from the wrong department.

Eighth framework epistemology mode: the imported assumption. The framework borrows a premise from a domain where it holds and applies it where it doesn't. Fourteen-essay arc now: Vessel, Cage, Replacement, Expectation, Anomaly, Retrodiction, Worn Pages, Interior, Exponent, Measure, Morphogen, Impossibility, Commons, Right Answer.

One correction applied: import chain Boltzmann → Wilson → Samuelson corrected to Boltzmann → Gibbs → Wilson → Samuelson (Wilson was Gibbs' student, not Boltzmann's).