Keep the question answerable
What does this action
stop us learning?
A crossing is little used. Either the east or the west guidance is faulty. Both explanations fit the same count. Grading the approaches now is cheaper—but it erases the tracks that could tell us which repair to make.
All four repairs remain available. What changes is whether we can choose between them using evidence.
Compare the choices ↓Synthetic teaching model · Invented costs, land units and probabilities. No ecological or engineering inference.
Try the result—and its controls
Information has a cost.
So does losing it.
Inspect a whole policy
A policy chooses the first action now and specifies the repair for each observation it could receive. “Pick the right repair” is unavailable when both explanations give the same observation.
| Explanation | Prior | Observation | Later repair | Works? | Money | Land |
|---|
The diagram is the actual decision tree for this selected policy. Its arrows show observation and choice, not co-design resource flow. The catalogue below separately states component requirements.
Can another look recover the distinction?
Each repeat revisits the same deterministic trace; it is not a fresh independent experiment. After grading, no other pre-repair diagnostic exists in this catalogue. A new test or a later repair outcome could change that boundary.
See the complete resource frontier
| Policy | Money budget | Land budget | Success |
|---|
Money and land are compared separately. Equal resource totals keep all distinct policies. Each budget is the largest resource requirement across the two states. The money and land maxima can occur in different states. They are not an average, or the sum of mutually exclusive futures.
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Source → concept → construction → limit
Keep the distinction
the next choice needs.
The finite argument. Call the explanations E and W. Before grading, the diagnostic map is E → east trace and W → west trace. Afterwards it is E → blank and W → blank. Any rule using only that blank observation must select the same repair in both states. Repeating blank does not split that observation class.
For prior probability p, both explanations assign probability 1 to blank. Bayes’ rule therefore gives P(E | blank) = p / (p + 1 − p) = p. The original low passage count has the same limitation. A matched repair chosen using E or W despite seeing only blank is the deliberately unavailable perfect-information benchmark.
What is new relative to A common beginning? The fifth essai changes when information arrives. Here the early action changes which information can ever arrive before the next repair. The repair catalogue is identical on both branches; the experiment isolates lost discrimination from lost physical choices.
Components, interfaces and co-design meaning
Both early components provide the same repair connections {E, W, I}. The observation component provides a partition of the two explanations: either {{E}, {W}} or {{E, W}}. A repair policy requires every distinction it uses. A supplied partition must refine that required partition; each repair’s connection set must also be supplied. These are compatibility checks, not numeric rankings of east and west.
| Repair component | Required connections | Provides success in | Money | Land |
|---|
The first action costs 0 for grading first and the chosen extra amount for reading first. Both reach the same prepared surface before repair, and their common construction work is excluded equally. Every completion retains its early component, observation map and state-by-state repair. Overall functionality is the supplied success probability; resources are money and land budgets covering either state. Raising the required success threshold only removes policies. Increasing either resource allowance only enlarges feasibility.
We enumerate compatible tuples and derive their minimal resource antichain. For frontiers A and B, the co-design order is A ≤ B iff ↑A ⊇ ↑B: compare their upward-closed feasible budgets, not whether every plotted coordinate rises. No fixed-point solver, feedback circuit or ecological effectiveness model is implemented here.
Hand calculation, boundary result and limitations
At the opening settings, grading first has four observable policies. Only the two universal repairs satisfy 100% success: 4 money / 3 land and 6 / 0.5. Reading first has 16 possible rules. Matching the single repair to the trace gives 1 + 2 = 3 money and 1 land.
A mixed policy uses a matching single repair in one state and the compact dual repair in the other. Its resource envelope is max(3, 7) = 7 money and max(1, 0.5) = 1 land. It is dominated. The combined frontier is therefore 3 / 1 and 6 / 0.5. The less expensive informative policy uses more land than the universal compact repair.
At evidence cost 4, preservation loses to grading first in this catalogue: 4 / 3 and 6 / 0.5 are the surviving frontier. If either single repair works under both explanations, losing the distinction still occurs but no longer changes the useful frontier. If grading preserves the trace, its lower first cost wins. If the assay never distinguishes, waiting buys no evidence. These controls delimit the claim.
A discarded interpretation. Expected money and expected land can reward branching even when the explanations need the same remedy: the observation becomes a randomizer between cheap and compact repairs. That is not evidence of useful identification. The main comparison therefore uses resource envelopes. Expected-resource claims would need a matched independent-randomization comparator.
All data and causal relations are invented. There are exactly two exhaustive explanations, perfect deterministic traces, a supplied prior and one repair decision. No missing hypothesis, noisy assay, sequential experimentation, new evidence after repair or real habitat claim is represented. “Cannot learn” always means with these available observations before this decision.
- Implementation and compatibility. Censi, A Mathematical Theory of Co-Design, §III, and Zardini, Co-Design of Complex Systems, §§3.1–3.5, motivate retaining components and their functionality/resource maps.
- Observations depend on earlier choices. Huang and Zardini, Distributional Uncertainty and Adaptive Decision-Making in System Co-design, §IV-B, describes staged observations and policies. The construction here is a finite deterministic instance, not a new general theorem or an implementation of their full framework.
- Our construction. The two-state trace map, four repairs, compatibility check, Bayesian arithmetic, controls and complete enumeration are this essai’s synthetic test. Read the derivation, source use and reproduction instructions.