Three pressures, one number — and the forbidden sum is nowhere in it. Free energy is a height under a belief, low where a belief is good and high where it’s bad. You’ll assemble it, verify the evidence sum never enters, and compute it by hand — twice, watching a better belief come out lower.
Five doors as before — the plain line runs straight through; take whichever fit: ▶ Picture it, ✎ Try it (commit before the reveal), ✓ Check it yourself, ▸ Go deeper, ⬡ See it in UNI. Runs locally — no account, no network — and adapts to light and dark.
The one fence that never moves. “Free energy,” “energy,” “entropy” are functional quantities — a number a model computes over its own belief. For you we use felt words; for UNI, functional ones: it holds a belief and its dynamics lower a height. Neither is awareness, feeling, or sentience. The free-energy arithmetic here is proven (Gate F0, sealed) — the floor the organism stands on, not a claim about what it feels.
No scrolling back to Module 3. A doctor reads a scan: a shadow that could be nothing, or could be something. The doctor carries a movable belief about what the shadow is. Reconstruct, cold.
From memory, new domain (the scan): say what “a belief is a position” means, and match each pressure to what it wants. Reconstruct it — no re-reading.
If that came back cold, you’re ready to fuse the three into one number.
Three pressures you can feel is progress, but a mind has to act — turn the dial one way — and three separate tugs don’t say where to stop. You need them on one scale, added into a single score, so “the best belief” is just “the position with the best score.” Build it so lower is better — a height, where good beliefs sit low and bad ones high. A mind then just rolls downhill.
Part one — energy. For each possible cause, ask: under my belief, how unexpected is “this cause together with the sky I saw”? That togetherness is the joint from Module 2, p(y, η) = p(y|η)·p(η) — likelihood (fit) times prior (stretch), already fused. Its surprise is −ln p(y, η). Weight by how much your belief backs each cause, and add up. That’s the energy — low when your belief backs causes that sit comfortably with what you saw.
Part two — looseness. Subtract your belief’s spread — its willingness to stay uncommitted (its entropy). The more honestly loose, the more we subtract, the lower the height.
Put them together — energy minus looseness — and you have the height:
F[q] = Ση q(η) · [ ln q(η) − ln p(y, η) ]
For each cause: take how confident your belief is there (ln q) minus how well that cause sits with the sky (ln p(y,η)), weight by your belief q(η), and sum. That one number is free energy — the height under a belief.
Now the moment this climb was for. Stare at the formula and hunt for the evidence — p(y), the sum over all hidden causes that walled you off in Module 2. Commit a yes/no in your head, then press the button.
See F assembled from the joint terms only, hunt for the evidence (it isn’t there), then compute F by hand — twice. The reveal is that F needs only the joint, never the forbidden sum — not a plotted curve.
You built it. Free energy is the height under a belief — energy minus looseness, fit-and-stretch fused in the joint minus the spread — and it is computable without the evidence. You watched it fall, from 0.944576 at a torn belief to 0.371064 at a sharp one, by hand. Next you’ll draw the whole shape: free energy as a height over every belief — a curve with a valley — and meet an old friend waiting at the bottom. That’s Module 5: the landscape, and the valley is Bayes.