The Bottleneck Primitive: Statistics as the Study of Information Compression

Every statistical operation is a projection through an information bottleneck, and every statistical result is jointly a property of the data and the bottleneck's geometry. This paper argues that the classical "paradoxes" of statistics — Simpson's paradox, the base rate fallacy, regression to the mean, the misinterpretation of p-values — are all instances of a single error: confusing a property of the compression for a property of the world. The same bottleneck/world confusion is shown to operate in adversarial attacks on AI safety classifiers (where attackers characterize and exploit the defender's projection geometry) and in institutional risk assessment (analyzed through Anthropic's Sabotage Risk Report for Claude Opus 4.6). The contribution is not the information bottleneck concept itself, which has formal precedent in Tishby et al. (2000), but the claim that it constitutes the generative grammar of inferential epistemics — and that recognizing this reveals the analyst's cognitive topology as legibly as it reveals properties of the data.