companion to “the rules are half the physics”

Three experiments, each run twice in worlds that differ by exactly one thing

An AI can ace every test you give it and still not understand the thing it is predicting. The way to tell the difference is to change something and see whether it copes. Each experiment below runs the same setup twice, changing exactly one thing, and puts both runs side by side.

the goal

Build a model that still gets the right answer after the world changes, not one that was only ever memorising how things used to go. Each experiment below scores how close we got.

Every number here comes out of sim/run_all.py. Nothing is drawn to illustrate a point.

experiment 1 · coherence under intervention

Close the streets

the setup

Two AIs learn to drive the same small city. One studied the sensible routes people actually take. The other studied nothing but aimless wandering, strictly worse study material. Now start closing streets and see who still gets home.

the goal

Get from the dot to the square. Closer counts, so we measure how many blocks away it ended up, not just whether it made it. Turn the detour rate up and watch the closed streets pile on in orange.

detour rate view

experiment 2 · the definition-change test

The ruler changes length

the setup

On one announced day the rule for who counts as “severe” is rewritten, so more people get counted. Not one person got sicker. It is lowering the pass mark and then announcing that more students are passing. Both AIs see the new, bigger number.

the goal

Notice the count jumped, and still say correctly that nothing happened to anybody. The dark line is the truth. Stay on it and you win; jump with the count and you have mistaken the measuring stick for the world.

panel

experiment 3 · two clocks

The past does not stay put

the setup

Same business, same rule for when to step in: act if costs look too high. On the left the numbers are final the moment you see them. On the right they are not, bills keep trickling in for months, a big one lands three quarters late, and figures you already acted on get quietly rewritten behind you. That is how regulated data actually arrives.

the goal

Make the right call each quarter, judged against the numbers once they finally settle. Nothing about the business differs between the two panels, so any calls lost on the right were lost purely to bad timing.

panel

Independent replications of the mechanisms, not of anyone's published figures. Experiment 1 follows Vafa et al., Evaluating the World Model Implicit in a Generative Model (NeurIPS 2024) on a 12×12 lattice with count-based models, so the absolute numbers are ours.
Re-run with python3 sim/run_all.py; the figures rebuild from its output.