A little room to wonder

Models & Explanations

A model preserves selected relationships for a purpose. Check its starting conditions, compare its output with evidence and avoid treating a neat fit as a complete explanation.

What does your model preserve, and what does it leave out?

A wooden tangram set with coloured pieces arranged inside a square frame.
A tangram keeps a fixed set of pieces while changing an arrangement. It illustrates selected constraints; the two numerical machine rules are supplied separately in the article.Nevit Dilmen · Source · CC BY-SA 3.0

Choose a purpose before judging detail

A model represents something through selected features. A route diagram may preserve which stops connect while distorting distances. A scale drawing may preserve lengths while omitting sounds and movement. Detail is useful when it serves the question; extra decoration does not automatically improve an explanation.

State inputs, rules and limits. A model’s output follows from those choices. Applying it outside its intended conditions can fail even when every calculation inside the model is correct.

Worked example: two fictional tile machines

Machine A is defined to output twice its input. Machine B adds four to its input. With input 4, both produce 8: 2 times 4 equals 8 and 4 plus 4 equals 8. One matching result cannot distinguish the two rules.

Try input 5. A predicts 10 and B predicts 9. A supplied fictional observation of 9 would disagree with A on that test and agree with B. It would not prove B is the only possible rule: a third invented rule could also match the two recorded pairs. Keeping the tested inputs visible limits the claim.

A representation and an explanation have different jobs

A table can record input-output pairs without explaining why a real process produces them. A rule can predict a new pair while leaving the underlying mechanism unknown. Say whether your model organises observations, calculates an expected result or proposes a process.

Check a model against observations beyond the ones used to choose it. If it fails, examine both the model conditions and the observation record. Rewriting an inconvenient value without evidence would remove the test rather than improve the explanation.

Use an informative next test

A useful next input is one on which the candidate models predict different outputs. Repeating input 4 may check consistency, but it cannot distinguish these two rules if both still predict 8. The best test depends on what you want to find out.

The machines are paper rules, not devices to build. Record a successful prediction, a mismatch and one omitted feature. You can then revise the model openly without claiming that it ever contained the entire real system.

Only if you feel like trying

Distinguish two paper models

  1. Make a table with inputs 4, 5 and 6, then calculate the output of both supplied rules.
  2. Choose one input that distinguishes the rules. Explain why another result of 8 at input 4 would not do that job.
  3. Invent a third rule matching the supplied pairs 4→8 and 5→9. Find an input where it could differ from B.

Optional paper or spoken reasoning with supplied fictional examples. No personal beliefs, experiences, accounts, purchases or public sharing are required.