SCIENCE · INVESTIGATE AND EXPLAIN

Diagnose clock disagreement without averaging away an open system

A radiometric age is conditional on isotope retention and the geological event represented by closure. If daughter escapes after accumulating, a simple daughter/parent calculation can underestimate elapsed time. A younger apparent age need not mean radioactive decay slowed or reversed.

Learning outcome: Compare no loss with several daughter-loss fractions at a fixed true time. Close the retained-plus-escaped inventory and explain why the age difference is not itself the time of a heating event. Propose one independent observation that could discriminate loss from inheritance.

Starting recap

Distinguish present position, relative event order, numerical age and duration. Preserve calibrated ranges, clock assumptions and missing observations instead of forcing one history.

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

Try

At 200 Myr, parent 25 and produced daughter 75 remain before loss. Losing half the daughter leaves 37.5; apparent age 100 log₂(2.5)≈132.193 Myr, while the unperturbed comparator remains 200 Myr.

Open the experiment

Predict

What will selective daughter loss do to a naive closed-system age?

Your prediction and reason

Experiment

Compare no loss with several daughter-loss fractions at a fixed true time. Close the retained-plus-escaped inventory and explain why the age difference is not itself the time of a heating event. Propose one independent observation that could discriminate loss from inheritance.

Test the closed-system assumption against selective daughter loss

Worked teaching model · synthetic values · Fictional clock starts with100 parent units, no daughter, half-life100 Myr. At measurement a fraction b of radiogenic daughter escapes instantaneously; parent remains. Apparent closed-system age uses retained D/P. Comparator retains its daughter and records true elapsed time. No actual mineral closure temperature is supplied.

True elapsed time before loss: 200 Myr Fraction of radiogenic daughter lost: 0.5 fraction

Reset keeps your prediction, captures and practice history.

Selective daughter loss makes this simple clock appear younger without reversing radioactive decay.

A discordant clock comparison diagnoses failure of a shared interpretation, not a unique thermal event. Parent gain, inherited daughter or different closure histories require different models; averaging discordant ages can conceal the problem.

Complete conditional quantities
Quantity	Value	Unit
Present parent	25	count units
Daughter before loss	75	count units
Daughter retained	37.50000	count units
Daughter escaped	37.50000	count units
Apparent closed-system age	132.1928	Myr
Unperturbed comparator age	200	Myr
Remaining parent plus daughter	62.50000	count units

These are invented observation packets and calculations, not mapped field records or laboratory isotope measurements. Retain the source assumptions and first reasoning separately from public feedback.

Selective daughter loss makes this simple clock appear younger without reversing radioactive decay.

Observation to attach to a capture

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

Understand

1. Define the time interpretation

2. Connect observations, mechanism and assumptions

The fictional clock begins with 100 parent units and no daughter, half-life 100 Myr. After time t, surviving parent is 100×2^(−t/100) and produced daughter is 100−P. An instantaneous event then removes fraction f of daughter without changing parent. Retained daughter is(1−f)(100−P).

The naive closed-system age is 100 log₂(1+Dretained/P). An independently stipulated comparator retains its daughter and reports the true elapsed time. Comparing them reveals a failure of the shared closed-system interpretation, but not a unique geological cause.

Actual clocks can differ in closure behavior, inherited components or parent mobility. Averages of incompatible ages can conceal those mechanisms. Before reporting a geological event age, connect mineral context, analytical uncertainty and a tested retention model; no actual thermal history is supplied by these sliders.

3. Reconstruct the worked packet

At 200 Myr, parent 25 and produced daughter 75 remain before loss. Losing half the daughter leaves 37.5; apparent age 100 log₂(2.5)≈132.193 Myr, while the unperturbed comparator remains 200 Myr.

4. Predict and investigate

Predict first: What will selective daughter loss do to a naive closed-system age?

5. Test a changed case

Apply the evidence to a changed case

At 100 Myr with half the daughter lost, find retained parent/daughter and apparent age.

Retain the chronology, calculations and assumptions before opening public feedback.

Compare a worked response

Parent 50 and retained daughter 25 give apparent age 100 log₂(1.5)≈58.4963 Myr. Remaining inventory 75 plus escaped 25 returns the initial 100 units.

6. Retain a defensible observation notebook

Preserve the original prediction, complete observations/relationships, calculations, uncertainty convention and rejected alternative. All sections and isotope packets here are invented instructional cases, not actual mapped outcrops or measured isotope analyses. Public practice is not independent reasoning review or supervised field competence.

Method and mechanism reference, checked 30 October 2026. Original prose, diagrams, numerical packets and exercises.

Apply

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

At 100 Myr with half the daughter lost, find retained parent/daughter and apparent age.

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: Separate clock slope from initial composition using an isochron Next: Separate active deposition rate from whole-section apparent rate

Save a science backup or import one

Science work is stored locally in this browser, separately from mathematics and AI. It does not sync automatically. Use this science-only backup; this checkout's older all-subject export does not include science.

A legacy file is available only when the complete snapshot fits the 36 MB limit. For larger snapshots, prepare a complete file set below; never discard notebooks to make a smaller file.

Choose a science backup (maximum 36 MB)

Matching imported notebook drafts replace their current drafts. Omitted lessons and known first attempts remain. Export your current work first if you want to retain both drafts.

Complete file sets and course backups

A file set can hold more work than one science file. Keep its manifest and every part together. Each file is limited to 36 MB. This format needs this version of LearnAI or a compatible newer version; older versions can use only the legacy single-file backup above.

Export scope

The set includes every saved science course and global continuation at this moment. Later edits need a new export. A conflicting tab exports its own visible work, which may differ from saved work in another tab.

Choose the manifest and all parts together

0 file(s) selected. File order and filenames do not determine identity. Missing, changed or conflicting parts block the entire restore; no good part is applied by itself.

Science storage: loading. No account or remote computation is required.