Indexing the archive…
Your Universe of Digital Possibilities
Two squares of one photograph from NASA’s archive — the same window, the same grays, the same spectrum to a percent. One is the camera’s; the other had its finest phases shuffled. Pick the camera’s, twelve times. Then a scanline counts the steps between neighbouring pixels, and the world’s edges turn out to live where the spectrum cannot see.
Take every step between horizontally neighbouring pixels and ask how heavy its tails are: the fourth moment over the square of the second, less the Gaussian’s three. A photograph steps gently almost everywhere and leaps at its edges, so the steps pile into a sharp peak with long tails (κ̂ ≫ 0). A field with the same spectrum but shuffled phases has nowhere to keep an edge; its steps fall into a bell.
The exact central interval for K, the count of wins in n independent plays at win probability p — computed from the rules alone, before a single play. A record inside it is the rules working; a record outside it happens one time in twenty, and the band says so in advance. When the chance of each play is fixed before it is played but differs from play to play, the same band comes from the Poisson-binomial sum.
A forgery can match everything the standard analysis measures — the histogram exactly, the power spectrum to a percent — and still be empty of world. Second-order statistics carry a texture’s loudness, not its geometry; natural images are sparse and heavy-tailed in their derivatives, and that is where the photograph lives (Field 1987; Ruderman & Bialek 1994). The Noise and The Skin synthesise texture; this fake is a photograph’s own shuffle, the surrogate move of The Wire and The Drift. The Phase recovers phase from magnitudes; here the magnitudes are kept and the phases lost.