Fat-tailed worlds shift proof standards closer to history than physics

Evidence

For Mandelbrot, the failure of many existing statistical techniques in a world of Levy distributions with infinite variances was an incentive, not a deterrent. He relished the challenge of examining situations in which the “causally structural features” of systems “are likely to be very much more hidden by noise” than if the central limit theorem applied. With established analytical approaches failing, one might have to turn, for example, to geometrical investigations and to visual intuition. Standard notions of mathematical rigor might have to be set aside: ”… when one works in a field where the background noise is [Levy-distributed], one must realize that one faces a burden of proof that is closer to that of history and autobiography than to that of physics” (Mandelbrot 1963b, pp. 422 and 433). — Donald MacKenzie, An Engine, Not a Camera, 484

Categorization

• DEEPTHINKING: Mandelbrot’s insistence that infinite-variance worlds demand history-style rather than physics-style proof is a paradigm-level inversion of how economic knowledge is validated — dense and unsettling rather than a casual observation.
• QUESTION: What would ‘history and autobiography’ standards of proof actually look like operationally in quantitative finance?
• XREF: connects to: Theory of history is possible despite the uniqueness of historical facts — Antonio Gramsci, Selections from the Prison Notebooks, 1526

Broader Connections

• Theory of history is possible despite the uniqueness of historical facts #complicates (0.72) — Antonio Gramsci, Selections from the Prison Notebooks, 1526