The Loop That Does Not Close: Against the Idea of Substance in Economics

Abstract

Economics speaks of a price level as of a water level, and of a stock of capital as of a quantity of wheat. This paper treats that language as a hypothesis and tests it. If a substance exists, its measure is a state variable; and a magnitude is a state variable only if every closed cycle is free. Two loops are then computed in full, by hand. A three-week promotion loop in which prices and purchases return exactly leaves a chained price index 37.5 per cent higher — the chain drift the statistical institutes measure every year, and which Hulten's 1973 theorem shows cannot be removed without a potential function. Samuelson's own 1966 reswitching example leaves a reversal that no change of numéraire can undo. The two failures share one witness, the loop that does not close, yet the two literatures never cite each other; the paper documents the near-misses and the tactical reasons the bridge was never built. It then proposes Carnot's gesture: not to correct the residue but to type it — an adjustable gauge on one floor, an irreducible sign on the other. Three refutable predictions follow.