First Principles as Maximum Compression: An Information-Theoretic Formalization of Aristotelian Reasoning, Muskian Strategy, and the Cognitive Structure of Breakthrough Innovation

Aristotle's "first principles" (archai) and Elon Musk's widely cited "first principles thinking" are treated in popular discourse as a reasoning heuristic: decompose problems to their most basic truths and reason up from there. This paper provides the first formal account of what first principles actually are, using the Adaptive Compression Advantage Theory (ACAT; Murata, 2026). First principles are maximum-compression gists: representations that achieve the highest possible ratio of explanatory scope to representational size. First principles thinking is the cognitive operation of compressing domain knowledge to its R(D)-optimal representation — the point on the rate-distortion curve where further compression would introduce intolerable distortion, and any less compression would retain unnecessary redundancy. This formalization explains why first principles thinking is rare (it requires extreme α in the relevant domain), why it transfers across domains (the compression operation is domain-general even though its products are domain-specific), why it is the engine of breakthrough innovation (maximum-compression gists reveal structural possibilities invisible at higher redundancy levels), and why most people cannot do it even when instructed (the instruction "think from first principles" is itself a gist that most recipients lack the compression function to decompress into practice). Keywords: first principles, ACAT, compression, Aristotle, Musk, innovation, rate-distortion theory, archai