SCIENCE · INVESTIGATE AND EXPLAIN

Test a model beyond its tuning cases

Distinguish curve fitting from transferable explanation.

Learning outcome: State a fresh test and an assumption that can fail outside the fitted conditions.

Starting recap

A model can fit observations without identifying the physical cause.

All lessons are open directly. Your saved experiments remain when you leave and return.

Try

The exact synthetic rule matches four observed times. A changed surface could produce different motion.

Open the experiment

Predict

Does zero residual guarantee a correct prediction after the surface changes?

Your prediction and reason

Experiment

Find the exact coefficients and record the fit. Then deliberately alter one coefficient to represent a changed mechanism.

Compare a model with observations

Worked teaching model · synthetic values · Four synthetic positions follow y = 2t + 0.5t² exactly. They contain no measurement noise. Matching this curve is not evidence that a real cart follows it.

Linear coefficient: 2 m/s Quadratic coefficient: 0 m/s²

Reset keeps your prediction, captures and practice history.

Calculated values on the same fixed scale
Row	Quantity	Value (m)
1	Observed at 1 s	2.5
2	Predicted at 1 s	2
3	Observed at 2 s	6
4	Predicted at 2 s	4
5	Observed at 3 s	10.5
6	Predicted at 3 s	6
7	Observed at 4 s	16
8	Predicted at 4 s	8

Root mean squared residual: 4.704 m.

Prediction = linear coefficient × t + quadratic coefficient × t². Residual = observation − prediction. Four tuning points are development evidence; reserve another condition to test transfer.

Observation to attach to a capture

Captures preserve recipes and replay their calculated results. They are synthetic model evidence, not physical measurements.

Understand

A perfect fit has a limited claim

Setting the linear coefficient to 2 and the quadratic coefficient to 0.5 matches all four synthetic observations. This demonstrates that the candidate family contains the generating rule. It is not an independent discovery about a physical cart.

The rule predicts position 22.5 metres at 5 seconds: 2 × 5 + 0.5 × 25. That is an extrapolation beyond the four displayed times. Checking this prediction would test the rule farther out, provided the measurement method and physical conditions remain applicable.

A new condition may change the mechanism

Changing the surface could change the acceleration. Using the previous coefficient without checking that assumption can fail. In the lab, changing a coefficient illustrates such a change; it is not a measurement of a new surface.

Keep a distinction between interpolation, extrapolation and transfer to a new condition. Interpolation asks about an input between observed values. Extrapolation extends the range. Transfer changes another aspect of the situation.

Before seeing new evidence, record your prediction and the assumptions needed for it. Then inspect the discrepancy and consider several explanations: measurement bias, an omitted force, a changed initial state or an inappropriate model family. Do not tune against the test and continue calling it untouched evidence.

Apply

Public practice checks a specific claim. It does not establish independent mastery.

Write a prediction for a new time and explain which physical condition must stay unchanged.

Your explanation and limitations

Continue

Completion requires a saved prediction, at least one capture and a reflection. Presence checks do not grade your reasoning.

Skipping retains experiments and awards no mastery.

Previous: Inspect what a model misses Next: Write a procedure someone can repeat

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