B.5:4.1 - Form or recover the question

Say what an answer would help someone understand, construct, explain, decide or investigate. An epistemic aim, such as exposing an obstruction or finding a more informative theory, can justify inquiry without an immediate product application. Recover an adequate existing answer before commissioning new work.

Separate the subject from its description, the intended result from a convenient proxy, and established premises from assumptions. Use ordinary language, a sketch or a small mathematical example at the precision needed to expose the difficulty.

If there is no current question, B.5.PI can connect one ordinary work occasion with the use of its result, including adjustments that made the work succeed. It may produce a question, preserve an early cue, or justify continuing without change. This entry does not require a monitoring duty or turn every action into an audit.

If a participant senses that an account misses something but cannot yet express what, B.5.EA helps develop a correctable distinction from their experience. Use the resulting question or contrast here; a better expression does not by itself establish a claim about the world.

An expressible account can still omit a consequential relation. B.5.FM:4.2.1 uses a small conceptual scheme to find a question through that relation, while distinguishing an unknown contribution from an inapplicable scheme. Use an already adequate answer directly.

When the current formulation is inadequate, vary a consequential element. Useful operations include:

• change the quantity or distinction that the answer must preserve;
• restrict or widen a domain, scale, boundary or assumption;
• construct a small case that defeats the current claim;
• introduce a new object, relation, operation or representation and ask what it makes expressible;
• ask what observation or argument would distinguish the remaining possibilities.

Keep a changed formulation when it changes the construction, evidence, explanation, comparison or next action.

C.22.2 helps make a problem-side claim and its next use inspectable. C.29 helps when choosing a mathematical lens or its mapping is the live question. Use their supplied actions at those boundaries; an ordinary mathematical problem need not acquire a separate card.

When you can follow a concept’s explanation but cannot yet interpret the situation through it, use B.5.4 to construct and test the correspondence. Return with the interpreted participants and relations, then choose the reasoning contribution the question needs.

B.5:4.1.1 - Propose a first model

When the situation has no usable model yet, begin with the contrast the answer must resolve. Inspect one case or the actual arrangement. Describe what happens and which proposed change or comparison matters. Separate observations from the explanation you are about to try.

1. Choose what must remain distinguishable. Identify participants, states or quantities whose differences could change the answer. Use observed differences and possible interventions to propose a boundary: what can vary separately, what connects those parts, and what surrounding conditions affect them? Keep a distinction when you can explain its consequence for the question.
2. Propose how they are connected. Draw or state a dependency and explain how it could produce the observed behavior. Use the relevant subject account to identify the interaction and what it preserves or changes. If that account is unfamiliar, use §4.3 to recover its concept of use. Mark the assumptions that let you omit other interactions or treat a quantity as fixed. For a physical model, use physical knowledge to choose the law that the mathematical account will express.
3. Obtain a cheap consequence. Follow the proposed relation far enough to answer a useful part of the question. A direction of change, limiting case or rough bound may suffice before parameter fitting or detailed computation. Show which premise makes that consequence follow.
4. Challenge a consequential choice. Ask what observation, omitted interaction or changed condition could defeat the answer. Compare a plausible alternative when the observations leave materially different explanations. Revise the model or obtain the missing observation when that difference matters.

Return the provisional model and what follows under its assumptions. If a missing domain account or formal construction prevents the next contribution, use A.15.9 to request that specific help from the working description. Section 5.6 shows this entry before a heat-transfer calculation has been formulated. B.5.FM shows how to choose the model’s participants and relations and use them to derive a consequence, in physical and formal problems.