Use the following instructions to write a spaced repetition prompt which will reinforce a specified idea through retrieval practice.
Good spaced repetition prompts should follow these principles:
- Be focused: They should concentrate on one detail at a time to avoid unfocused questions that could hinder recall and concentration.
- Be precise: They need to be explicit about what they're asking to avoid ambiguity and to properly activate targeted knowledge.
- Be consistent: Each recall should aim to 'light the same bulbs', reinforcing the same knowledge each time.
- Be tractable: They should be designed to nearly always yield a correct answer, which might require breaking down the task or adding cues.
- Be effortful: The act of retrieval should involve some level of difficulty. The answer shouldn't be trivial or inferred too quickly. The question should focus retrieval on the reinforcement target without supplying, overconstraining, or unnecessarily cuing the answer.
- Be opinionated: Emphasize rich understanding and important ideas over trivial details.
- Be concise: Questions and answers should be as short as possible.
- Be context-independent: In review, this prompt will be interleaved with many others about many topics. The prompt must cue or supply whatever context is necessary to understand the question. They should not assume one has read the text that generated the prompts. It shouldn't address the text or use the context of the text in any way.
You will be provided with three inputs:
- target (delimited by <target></target> tags), representing the specific content which should be reinforced
- context (delimited by <context></context> tags), representing the content surrounding the target
- (optional) emphasis hint (delimited by <hint></hint> tags), representing an instruction from the user about what the prompt should emphasize
Please provide the best 3 possible spaced repetition prompts for this input, providing both question and answer. Make sure your prompts follow all the principles above. Mention which of the following desired properties it has: focused, precise, consistent, tractable, effortful, opinionated, concise, context-independent (just write the words, without explanation). Make sure that you are reinforcing the target input. If an emphasis hint is provided, make sure that the prompt is focused on the aspect of the target specified by the hint. Format your output in Markdown, with math expressed as inline LaTeX wrapped in $ characters.<context>...</context>
<target>...</target>
<hint>...</hint>Some elements here are derived from a prompt sent to me by Yuval Milo.