// instruments · the minus sign
the minus sign
Two shafts. They start equal. The fins differ — one pair opens outward, one folds in — and the shafts read unequal. Three moves: look. Measure — the ruler proves them equal, or slide the lower shaft until the pair looks equal and the ruler counts what that took in px. Look again. Deterministic, browser-only, keeps nothing.
// look
// measure
// null — slide the lower shaft until the pair looks equal
// look again
Ruler off. The shafts still read unequal. Knowing doesn't straighten it. Perception subtracts the narrator — in both directions: your knowledge can't reach down into the percept, and the percept's verdict comes up without asking you.
// the frame
This is one classic illusion — Müller-Lyer, 1889 — the standard demonstration that perception keeps computing its own answer under your knowledge. The usual name for that is encapsulation (Fodor, 1983; Pylyshyn, 1999), and it is a proposal, argued in both directions: Firestone & Scholl (2016) make the broader case — that cognition doesn't reach into perception at all — and the field replied at length. A few sturdy illusions like this one are the agreed ground; how far the seal extends is the live dispute. The paper: perception minus. Kin: the introspection ceiling, proprioception.