Friedrich Hayek's claim that the price system communicates dispersed knowledge has inspired a productive research program in computer science. Researchers have built Hayek Machines that use price-like signals to solve resource allocation and planning problems in multi-agent systems. This paper argues that such systems, while successful, capture only part of Hayek's project. The Hayek Machine coordinates agents within a given problem space; Hayek's deeper inquiry concerned how problem spaces themselves are constituted. Drawing on Hayek's neglected work in cognitive psychology, particularly The Sensory Order (1952), the paper distinguishes the Hayek Machine (a proven architecture for decentralized coordination) from the Hayek Project (a philosophical inquiry into the recursive co-evolution of minds and institutions). Hayek argued that perception is structured by evolved classificatory systems that differ across individuals, generating the dispersed knowledge that markets coordinate. Institutions shape these classifications even as individual actions reshape institutions. This dual recursion cannot be computationally replicated because it depends on embodied cognition, interpretive judgment, and consequence bearing. The paper concludes that artificial intelligence systems can optimize within inherited categories but cannot meaningfully create new categories, which has significant implications for algorithmic governance and institutional design.