Displacement D
—
how far expectations moved
The measuring bench · claudiocammarano.com
What it measures. One thing: the distance between what you expected before reading and what you expect after — and whether that move took you towards the world or away from it. Two pure ratios, α and r, decide which of five regimes a text is in. The displacement D stays out of the verdict: it says how hard, not how good.
Why it was built. The occasion was the argument about writing with language models — whether a text made with them still counts as the author's. The instrument answers structurally rather than morally. Which tools passed over a text, any tools, enter the equation as a coefficient and never as a load-bearing term; what carries the value is what the author put in, which is observation, selection and recombination. Panel 2 shows it directly: move the disclosure codes across the whole grid and watch how little the value moves.
Move the sliders. Panel 1 computes real quantities in bits from three distributions you set yourself, and places the result on the plane. Panels 2 and 3 explore forms: those numbers are dimensionless and the functions were chosen here, not derived.
This is one of two projects on this site, and the smaller one. The other — validating what a language model claims — has a different object and a different method. They share a premise, not an apparatus.
Exact mathematics, units in bits. Move the three distributions — what the reader expected before, what they expect after, and the world — and everything else is computed: Kullback-Leibler divergence, Shannon entropy, cross entropy. The two pure numbers α and r decide the regime; the displacement D stays out of the verdict as pure intensity.
Readout
Move a slider
The regime is read from α and r together; D only says how hard.
The plane of regimes
Dimensionless; the forms were chosen here. The three content terms stay with the author. The tool stack Σ enters only where the argument puts it: inside η, which saturates at one, and inside ε, which verification ν drives to zero. The disclosure codes move Σ and nothing else — the quickest way to see that a position in a disclosure matrix is not a position in value. The receiver slider does what §8 requires: η sits inside the integral, and depends on who is reading.
Content — stays with the author
Tool, receiver and verification
Postulated coefficients
Declared position in the disclosure grid
Contributions
Disclosure. η = 1 − e−a(F+Σ)·ψ(R) and ε = ε₀(1+βΣ)e−γν are not in the argument. They were chosen to make the model run: the first saturating, the second collapsible by verification. Changing those forms changes the numbers, not the signs.
Eighty authors, three hundred and twenty publications each. At every step each one publishes by mixing their own prior with the corpus mean, in proportion Σ, and reads what the others published. New observation enters only through the non-modal share. The curve is the variance across priors over time; the dashed line is the fixed point Var* = (1 − Σ)·ω² / λ. The field does not collapse, it settles.
Regime
The lever. A single author cannot lower Σ: it is a property of the field. They can raise ω — put new observation in — or lower λ, that is, read their own field less. Halve permeability and watch where the dashed line goes.
Var[𝒫] over time
Where the eighty authors sit