Intelligence operates at the boundary between knowing-that and knowing-how, expanding knowledge through structured iteration. Omega knowledge (propositional understanding of natural phenomena) and lambda knowledge (prescriptive techniques for manipulating the world) iterate together—theoretical insights generate new techniques, practical experimentation reveals new principles. Knowledge advances through paradigm shifts that reframe what counts as a problem and solution. It grows through bold conjectures subjected to severe refutation; at its core, knowledge consists of good explanations—hard to vary accounts that have survived criticism. Language models accelerate these processes, compressing vast propositional knowledge into systems that generate prescriptive outputs while enabling rapid iteration between conjecture and test.