← Back to article

Equation 13 · Every Test Changed the Scene and Kept the Chair Red

What does this equation mean?

CAI\mathrm{CAI}

Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.

This mathematical expression combines the displayed quantities; its precise role follows from the surrounding article text. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

Read it piece by piece

How to interpret it

Read this expression with the definitions, units, and assumptions supplied by the article.

What the article says around this equation

State in advance what each outcome would mean, so the test can be graded rather than argued with after the fact. To make the arithmetic concrete — using invented placeholder numbers only, to illustrate what the ratio means, not anything measured — suppose CfC’s Urban Patio baseline stayed at its published 67.5% while its measured CAI\mathrm{CAI} under the recolor intervention came back at 61%. That would give RRR(CfC)\mathrm{RRR}(\mathrm{CfC}) ≈\approx 0.90 : high, and hard to explain without the network actually tracking the target’s identity rather than its color. Suppose instead the same baseline of 67.5% paired with a measured CAI\mathrm{CAI} of 9%, most of those trials converging on the red decoy…
Read the full surrounding passage
State in advance what each outcome would mean, so the test can be graded rather than argued with after the fact. To make the arithmetic concrete — using invented placeholder numbers only, to illustrate what the ratio means, not anything measured — suppose CfC’s Urban Patio baseline stayed at its published 67.5% while its measured CAI\mathrm{CAI} under the recolor intervention came back at 61%. That would give RRR(CfC)\mathrm{RRR}(\mathrm{CfC}) ≈\approx 0.90 : high, and hard to explain without the network actually tracking the target’s identity rather than its color. Suppose instead the same baseline of 67.5% paired with a measured CAI\mathrm{CAI} of 9%, most of those trials converging on the red decoy instead of the recolored true target. That would give RRR(CfC)\mathrm{RRR}(\mathrm{CfC}) ≈\approx 0.13 : a near-total collapse, exactly what a shift-stable color detector predicts once its one reliable cue is handed to the wrong object. Both numbers are fictional. They exist only to show what a high ratio and a low ratio would look like once real trials replace them; the actual test has not been run, by this article, by the paper’s own authors, or by anyone identified in a targeted search of the citing literature.

Read the equation in its article →

Sources cited in the article section

These citations give research context. Read each source to check which claims it supports.

Return to Every Test Changed the Scene and Kept the Chair Red

See this formula across 2 published contexts →

Browse the mathematical compendium →