Nietzsche sometimes praises the drive to order—to simplify, organize, and draw clear boundaries—as expressive of a vital “classical” style, or an Apollonian artistic drive to calmly contemplate forms displaying “epic definiteness and clarity.” But he also sometimes harshly criticizes order, as in the pathological dialectics or “logical schematism” that he associates paradigmatically with Socrates. I challenge a tradition that interprets Socratism as an especially one-sided expression of, or restricted form of attention to, the Apollonian: they are more radically disparate. Beyond strengthening the case for this basic point, I develop a distinctive account of what, exactly, distinguishes the Apollonian-classical and Socratic forms of order. To this end, I advance interrelated interpretations of Apollonian-classical simplicity and the “cold” calm that it elicits, by contrast to superficially similar Socratic phenomena. This illuminates Nietzsche's broader ambivalence toward science, in part by clarifying the nature and value of an idealized Apollonian science.