Identify minerals by intersecting independent observations

1. Define the geological question

A mineral is a naturally occurring solid with an ordered internal structure and a characteristic composition or compositional range. A rock can combine several minerals, glass or other constituents. Identification therefore begins with an individual material and a documented observation, not a rock color or a familiar-looking photograph.

2. Build the mechanism and evidence ledger

Hardness describes resistance to scratching; Mohs numbers order reference minerals but do not define equal physical intervals. Cleavage is repeatable breakage along crystallographic planes, unlike an irregular fracture or an external growth face. Color may vary within one mineral. Streak, luster, density and composition can supply additional evidence, but none should be invented when unobserved.

The supplied virtual set contains quartz (hardness 7, no cleavage), a feldspar exemplar (6, two cleavage directions), calcite (3, three non-right directions) and halite (2.5, three right directions). The controls initially conceal cleavage angles. Intersect the retained sets for hardness and cleavage. An unknown observation must leave possibilities open rather than being coded as a negative finding.

One surviving candidate is unique only within this small reference set. Zero survivors can indicate a mixed specimen, a mistaken observation or an incomplete library. A defensible report names the evidence that would discriminate remaining alternatives. Do not scratch, grind, taste, heat or chemically test unknown material; these are supplied observation records.

3. Reconstruct a worked example

Hardness above 5 retains quartz and feldspar. No cleavage then retains quartz alone. Hardness below 5 plus three directions retains both calcite and halite until cleavage angles or other independent evidence are supplied.

4. Predict and investigate

Predict first: Which candidate ambiguities remain if hardness is known but cleavage angles are not?

Compare unknown hardness with below/above 5 while preserving the same cleavage observation. Retain each candidate set and propose one discriminating observation. Deliberately choose an incompatible pair and explain why no match is not proof of a new mineral.

5. Test a changed case

Apply the mechanism to a changed case

Hardness is below 5 and three cleavage directions are observed. An additional record reports right angles. Which supplied candidate remains, and what limit remains?

Retain the calculation, evidence and assumptions before opening public feedback.

Compare a worked response

Halite remains in the supplied set; calcite has non-right cleavage angles. This conditional identification is not certification of an actual specimen or an exhaustive search of all minerals.

6. Retain evidence and its limits

Keep the first prediction, complete ledger, changed case and rejected alternative in the lesson notebook. Supplied observations and bounded CPU models are not actual specimen handling, fieldwork or independently assessed competence. Record source purpose and uncertainty rather than treating public feedback as independent reasoning.

Mechanism and classification reference, checked 30 October 2026. Original teaching prose, numerical packets and questions; no source illustration or exercise is copied.