Mountains and a moving reference line

Provenance: Constructed RS Learning Lab teaching walkthrough, authored with AI assistance on 2026-09-11. The prediction, correction, and calculations are prepared examples, not a recorded learner or chatbot exchange. The numeric result is a prepared worked construction, not measured evidence.

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Choose and predict before calculating

This extends Which mountain is tallest? with wholly invented coordinates. Open that original walkthrough for real research and its attributed sources. Neither fictional mountain represents Everest or another real mountain.

Question: if the same reference line rises faster, will either height ordering change?

Constructed prediction to inspect: “With a faster reference change, the above-reference numbers will shrink faster. Maybe B will become higher than A.” Make your own prediction before reading the worked table. What would have to change for the ordering to reverse?

Inspect the rules

Copy the mountain block from the Model cards: A has peak 10 and base 0; B has peak 8 and base -6. Both runs start with shared reference L = 0. Each turn adds r to L. Above-reference values are peak minus L, with negative values allowed. Base-to-peak heights remain A = 10 and B = 14. Run three turns with r = 1; reset L to 0 and run three with r = 2.

Only r changes. The peaks and bases do not move. Before the live exchange, use Safety if considering anything beyond these invented values.

Ask for one live check

Here is my invented model: [paste the mountain rule block]. I will compare r = 1 and r = 2 for three turns, resetting L to 0. Propose one hand check of the rules. Do not change assumptions, move the peaks or bases, add physical effects, or calculate both runs for me.

Use the actual response. Compare it with the card. Reject an added rule that shifts a peak with L or treats the line as a real climate forecast. A chatbot response does not establish correctness; follow Reality Check and execute the rules yourself.

Prepared worked result

For the baseline, the first update is L = 0 + 1 = 1. The heights above reference are 10 - 1 = 9 and 8 - 1 = 7. Continue applying the same rule. Reset L to 0 before using r = 2.

Scroll sideways to see all columns.

Hand-check changed turn 2: L = 2 + 2 = 4; A = 10 - 4 = 6; B = 8 - 4 = 4. Check r = 0 separately: L stays 0, leaving A = 10 and B = 8 at every turn.

Correct and interpret

At turn 3, changing r from 1 to 2 lowers each reported above-reference value by 3: A goes from 7 to 4; B goes from 5 to 2. The gap remains 2. Under base-to-peak measurement B remains 14 and A remains 10 in both runs.

Constructed correction: “I predicted that the reported numbers would shrink faster, and they did. I was wrong about a possible reversal: subtracting the same L keeps their gap fixed. B was already taller from base to peak, and that separate ordering also stayed fixed.”

Moving a shared reference cannot change physical heights or reverse ordering under either of these fixed definitions. The example has no erosion, tectonics, climate, or real-world forecast. It illustrates arithmetic under assumptions, not how actual mountains change.

Your unworked variation

Reset and compare r = 1 with r = 3 for three turns. Predict first, make a live AI request, then run and check it yourself. Keep signed values if the line passes a peak. Name what AI contributed and what your checks established. Choose to stop or return to the original research inquiry for a question requiring real evidence.

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Source: labs/change-one-thing/gallery/mountain-reference-line.md