Notes and Confidences
A book that argues for calibrated confidence owes its reader a map of its own. Not every sentence in these chapters carries the same weight, and this is the ledger of which is which: what is theorem, what is well-evidenced, what is contested, and what is analogy doing honest work under its own name.
Chapters 1 and 2 stand on classical test theory and elementary probability; the loss-function reading of averages is standard decision theory, the central limit theorem is a theorem, and Stevens’ scale taxonomy is the standard account, argued at its edges. Chapter 3 is signal detection theory, consensus science since Green and Swets. Chapter 4’s reliability and attenuation results are textbook psychometrics; the brain-training autopsy rests on the 2016 United States FTC settlement, the 2014 scientists’ consensus letter, and the comprehensive 2016 review by Simons and colleagues. Chapter 5’s diffusion model is among the best-supported models in psychology; the EZ shortcut is from Wagenmakers, van der Maas and Grasman, 2007, with its assumptions stated where it appears.
Chapter 6 is a theorem plus the natural-frequencies program of Gigerenzer, which is well replicated; the silent-launch example is an illustration of the machinery, not a measurement. Chapter 7 is Pearl’s framework, mathematically rigorous, with a live and productive rivalry with the potential-outcomes school noted behind its door; the kidney-stone table is the published one, Charig and colleagues, 1986. Chapter 8: proper scoring rules are theorems; the forecasting results are Tetlock’s decades-long empirical program; Darwin’s golden rule is from his autobiography. Chapter 9: Shannon’s results are theorems, and the matched filter is provably optimal for a known signal in Gaussian noise; attention-as-channel is an analogy, load-bearing but an analogy, and should be audited as one. Chapter 10: the two-generals result, the Byzantine bounds, and the FLP theorem are proofs; the security of proof-of-work is an engineering claim, economic and conditional, exactly as scoped in the text.
Chapters 11 and 12 are theorems, presented at walking pace; the dismissal of the Lucas-Penrose argument reflects the majority position among logicians, and the extension of these results to human operators in Chapter 16 is a structural analogy, labeled as such where it occurs. Chapter 13’s predictive-processing framework is productive, prominent, and contested; the tickle result and sensory substitution are solid experimental findings; the free energy principle is marked in the text with the doubt it has earned. Chapter 14 is accurate at the level it operates on, and the question it declines to settle, whether deep compression amounts to understanding, is genuinely open, with serious people on both sides. Chapter 15’s ergodicity point is formally correct and increasingly accepted; the product conclusions drawn from it are the author’s extrapolation. Chapter 16 rests on the judgment-and-noise literature; the captain is a portrait, not a dataset. Chapter 17 is a method, and its verdict is deliberately a shape rather than a prediction. Chapter 18 is a protocol, and makes no claims at all.
Where this book compresses, and it compresses everywhere, the compression was audited: once by its author, who caught some of it, and once from outside, which caught more. The reader now knows the exchange rate.