The Bottleneck Primitive: Statistics as the Study of Information Compression

Every statistical operation is a projection through an information bottleneck. Classical paradoxes — Simpson's, base rate fallacy, regression to the mean, p-value misinterpretation — dissolve once the bottleneck is made visible. The same dynamic operates in adversarial AI attacks and institutional risk assessment. The bottleneck primitive constitutes the ur-operation from which statistics derives, revealing the analyst's cognitive topology as legibly as the data's structure.