Every action has a small number of effects and an enormous number of non-effects. Painting a block blue changes its color. It doesn’t change its weight, its position, its temperature, whether it’s Tuesday, or whether Lisbon is the capital of Portugal. McCarthy and Hayes noticed in 1969 that formal logic handles the first kind of fact easily and the second kind not at all. To represent what a paint action does, you need one axiom. To represent what it doesn’t do, you need a separate axiom for every property of every object the paint didn’t touch. The non-effects outnumber the effects by orders of magnitude.
Gibson, riding in the backseat of a car around 2000, arrived at the same wall from the other end. “Nothing stable. Nothing static. Nothing to stand on or cling to. No maps for these territories, though they are of our own creation.” His complaint was about velocity — the world changing faster than anyone could chart it. But the Frame Problem says the difficulty was never speed.
A map is a list of what’s still true. Every change in the territory doesn’t just add one new fact. It creates an obligation to re-certify every old fact that wasn’t mentioned. Gibson thought he couldn’t draw maps because the territory kept moving. McCarthy showed that even a world with two blocks and a can of paint already makes maps expensive, because the cost isn’t in recording what changed. It’s in certifying what didn’t. Gibson’s complaint about velocity — Too Close to See — turns out to be a special case of the same difficulty.
The territory was never the hard part.