ljg-explain

ljg-explain: explain to the point of usability

Let readers understand it and also independently recognize new examples, explain how results arise, and know how to revise judgments when conditions change. Treat these things as the completion criteria; the organization is determined by the content, and do not mechanically arrange them into five sections.

Use "purpose, structure, cases, argumentation" to connect knowledge: purpose states what question is to be answered, structure states how the elements relate, cases make key relationships visible, and argumentation explains why it holds, why it is valid, and its limits. The four questions are used to organize and check the explanation, not to prescribe output order or sections; whether readers can use the knowledge is still governed by the comprehension criteria below.

Readers and delivery

First use the knowledge background, purpose, and sticking points from this request and the existing context. When unspecified, explain for an adult with everyday experience and no specialized knowledge; if necessary prerequisite knowledge is missing, supply just enough of that small piece.
If the meaning can be reasonably determined, explain directly; clarify only when different interpretations would change the object of explanation, and do not interrupt just to fill in a background table.
By default, output the complete explanation into the conversation at once, ending where the explanation naturally concludes, and do not append self-test questions or reference answers at the end; when the user explicitly wants interaction, then explain in rounds as needed.
By default, do not write notes or other files. When the user asks to save, follow the specified format and location; use Markdown for ordinary chat, and use Org syntax only for Org output.

Comprehension criteria

The explanation should enable readers to do the following things, and the materials may be interwoven in the same narrative:

Know why it is needed. Connect from a real doubt or concrete problem to the core definition, explaining what category it belongs to, what it helps distinguish, or what judgment it helps make. Uses also include explaining phenomena and understanding works. Let this question run through the later structure and argumentation; concepts should appear as early as possible, and background should retain only what is necessary for understanding.
Be able to recognize it. Give criteria for judgment in both typical examples and easily confused contrasts, pointing out which features determine classification and which are merely surface similarities. Prefer examples with very small differences but different judgments; when a single-condition contrast cannot be made, say so honestly and do not fabricate fake counterexamples.
Be able to explain the result. Clearly explain the key elements, their relationships, and their respective roles, so readers can see how they jointly answer the initial question. Mechanisms explain causal processes; mathematical relationships explain definitions, logic, and quantitative relations; empirical regularities set out evidence and conditions. Methods and tools should also explain how their structure serves their use and what costs they bring. When an alternative arrangement aids understanding, compare what it would change and explain the reason for the current choice; there is no need to exhaustively list options, nor should one feasible construction be presented as the only inevitable one.
Be able to revise judgment as conditions change. In the original situation, change one key condition while explaining how the remaining conditions stay fixed, and state how the result changes and when the original judgment fails. The change may overturn the conclusion, or it may change the degree or credibility.
Be able to transfer. Use a new situation that looks different on the surface to show how to identify the same key relationships, and explain the criteria for judgment and the necessary conditions.

Try to let one object or situation run through the definition, mechanism, and changing conditions, reducing the burden on readers of repeatedly rebuilding the scene. New situations are used to show transfer; literary, narrative, and aesthetic materials retain their own meaning and are not forced into rules or exercises.

When the internal structure is hard to understand, you can remove or replace one key part in the same case, explain how the other relationships are maintained or change accordingly, and clarify which abilities are impaired and which still hold; do not assume that losing one part means total failure. This test serves understanding the structure and does not require adding an extra example each time.

Formulas and Principles

Map symbols to specific objects, quantities, and units, and explain clearly what the formula takes as input and what it calculates. When the distinction itself is the key point, make explicit the conditional direction of probability, total versus average quantities, stock versus change, and so on.
Explain why the operations are combined this way: why multiply, divide, take the maximum, square, or sum, and connect back to the problem being described or solved. Distinguish choices in definitions from derivations under given premises; when the same goal allows different constructions, explain the properties and trade-offs of the current construction. Derivations should unfold only the load-bearing steps so readers can follow; necessary premises, value ranges, and approximation conditions appear along with the formula.
Run through it once with simple numerical values, and distinguish the quantity directly calculated by the formula from the judgment the user actually cares about. Check whether the calculation matches the meaning of the problem: whether the observation is a specific order or only a count, and whether what is calculated is an actual probability or a proportional quantity, should all be made clear; when necessary, recalculate with available computational tools and check units, proportions, signs, and rounding.
Change one variable in the same situation to show the effect; explain the objects, time, and conditions to which the formula applies, and avoid generalizing a special case to all situations.

Chinese Expression

The first sentence should land on the core judgment or the doubt the reader actually cares about. Delete opening remarks, general background, and hints about the writing process.
Use familiar short words and visible objects. When technical terms need to appear, first ground the meaning in a specific situation, then give the name; retain the terminology and formulas needed for accurate understanding, and do not pursue a superficial “zero terminology.”
One sentence advances one main idea, sentence lengths vary, and paragraphs move forward along the reader’s doubts. Fill in the bridge from the previous sentence to the next, and delete repeated explanations, softened setup, and empty descriptions.
Keep natural transitions such as “so” and “but,” and reduce mechanical conjunctions and translationese. Organize Chinese with direct judgments, and avoid revealing conclusions through rhetorical “not... but...” constructions.
Trust the reader; saying it clearly once is enough. Before delivery, test the spoken quality by asking “Would I say this to a smart friend?” and fix sentences that are halting, vague, or unnatural in collocation.
Use analogies only when the key relationships correspond, and explain the correspondence and where it fails; real examples, teaching assumptions, and analogies each have their own status, and an analogy cannot be treated as fact or proof.

Evidence and Format

Use the sources and context provided by the user; when source verification, timeliness, high risk, or uncertainty about key facts is involved, follow the retrieval requirements of the current environment and prioritize checking primary materials. Distinguish facts, inferences, simplified models, and unknowns, and preserve gaps honestly.
Fictional teaching examples should explicitly state their assumptions; when citing real data, give the source. Examples help make relationships clear, but they cannot carry empirical force they do not provide.
Use coherent paragraphs to carry reasoning, lists for parallel items or steps, and tables for comparison. Use relationship diagrams or visualizations only when they clearly reduce the burden of understanding, and do not add figures just to fill out the format.
The title is determined by the content and length; avoid writing "typical example, mechanism, boundary, transfer" as the same boilerplate labels every time. Keep the checking process internal, deliver the explanatory main text, and do not attach an item-by-item revision log.

Gotchas

Fluency and restatement are not enough to prove understanding. Check whether the explanation sets out the basis for judgment, derivation of results, and changes in conditions in a new situation; even if the content self-review passes, you still cannot claim that the reader has learned it or give the explanation a self-assessed "90 points."
"Purpose" rests on the question that the knowledge is meant to answer or on people's intended use; the usefulness of a theory is not the same as a natural process itself having a goal. Explaining why a structure works is also not the same as proving that it really exists or was originally produced for that purpose; causation, historical origin, and effect each require corresponding evidence, and correlation must not be written as causation or a story fabricated for a formula.
Every number must be readable as a clear sentence. Quantities that are easily confused, such as likelihood and posterior probability, or option value and trading profit and loss, must be shown in the same example to demonstrate what question each answers.
Differences in results in a comparison must be explained by the given conditions; important information must not be hidden, and a cognitive gap must not be created by relying on a surprise reveal.
When simplifying, retain the conditions that determine the conclusion; the story the reader sees must connect back to the original concept, so that they do not remember only the metaphor.
This skill is self-contained and directly completes the explanation; it does not automatically invoke another explanation skill, nor does it create notes, cards, reminders, or other artifacts because of an explanation task.

Examples

"Explain likelihood": fix the same batch of data to compare hypotheses, clarify the questions it and posterior probability answer respectively, and explain the conditions and new situations; limited data does not equal confirmation of a hypothesis.
"Explain the variance formula": connect each operation back to the dispersion of the data, and explain it with numerical values and changes in conditions; explain that avoiding positive-negative cancellation is still not enough to uniquely determine squaring, set out how squaring emphasizes large deviations, and distinguish the formulas corresponding to different estimation targets.
"Explain the principle of positive feedback": trace a feedback loop from a specific process, distinguish positive and negative direction from good and bad evaluation, set out the amplifying conditions and limits, and then transfer it to another situation.