Projection and Invariance in Scientific Explanation

Abstract

Any representational enterprise must omit variation in order to function. NASA still uses Newtonian mechanics, though Einstein superseded Newton, and the standard picture of scientific progress cannot explain how. A description that omitted nothing would be identical to its subject and would explain nothing. This paper argues that omission is not a defect but the central structural feature of any enterprise that builds representations from incomplete information. The key concept is projection: a principled mapping from underlying complexity to a descriptive space that partitions states into equivalence classes, omits within-class variation, and makes patterns visible that would otherwise be lost. Projection is simultaneously revelatory and constitutive: it makes genuine invariants tractably accessible while bringing into being the concepts through which they become expressible. The paper distinguishes vertical cases, in which earlier projections survive as limiting cases of more refined successors with recoverable omission, from horizontal cases, in which omission is constitutive, and invariants are accessible only at the level of the projection that defines them. The framework accounts for persistent pluralism in mature sciences, treats the renormalization group as a systematic implementation of the invariant-tracking criterion, and defends a level-relative realism on which higher-level projections reveal genuine structural features of the world. The deepest claim is an inversion of the standard picture: perspectival structure is not a concession to complexity but the condition for invariant detection. A world rich in invariants cannot be exhausted by a single projection.