On What Mary Could Not Have Known

Working notes toward the knowledge argument · the lab notebook, first pages

1 · The room

Consider a scientist who has lived her whole life inside a single sealed room. Everything in it is achromatic: gray walls, gray instruments, a monochrome monitor through which she studies the world outside. She has never seen a color. She has, however, read everything. She knows the physics of electromagnetic radiation between 380 and 750 nanometers. She knows the reflectance function of every surface, the absorption curves of the three cone classes, the opponent recoding in the retina, the cortical maps beyond it. If a physical fact bears on color vision, it is in her library, and she has mastered it. The question the room poses is simple to state and has kept philosophers busy since 1982: when she finally steps outside and sees a red tomato, does she learn anything new?

2 · The library

Everything in this laboratory is built on the room side of that door. A spectrum arrives here as thirty-eight numbers on a ten-nanometer grid. A color is a linear functional applied to those numbers. A match between two colors is an equation; a mismatch is a distance; an appearance under a different lamp is a matrix acting on a vector. The instruments in the library do what the scientist does: they reason about color without ever experiencing it. It turns out an enormous amount can be known this way, more than the tooling of the field has bothered to compute. You can prove two surfaces will remain distinguishable under every lamp in a family. You can construct the exact light that defeats a palette. You can enumerate the infinite crowd of spectra hiding behind a single color and measure the width of that crowd at every wavelength. None of this requires seeing anything at all.