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    In library science there’s the study of reference interviews, where the librarian has to go from “what the user is asking” to “what the user actually needs”. It’s like answering XY problems as a formalized discipline. There’s a lot we could learn from librarians!

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      People asking about 0.0000…1 often receive answers from tier 5, but ought to get answers from tier 4, or even tier 3, if you wanted to get into nonstandard analysis à la Robinson.

      I quite strongly disagree with this. Students that are meant to be learning about standard analysis should be taught standard analysis. Nonstandard analysis is an advanced topic. A seventeen-year-old in their first year of university trying to learn basic analysis is just going to be confused if you say ‘well there is a 0.0000…1 but only if you use Robinson arithmetic’. They need to be told ‘no there’s no such thing as that, because this is how we define real numbers’. Because really there isn’t. ‘Nonstandard real numbers’ aren’t real numbers, they’re something totally different and unrelated.

      Part of the problem with online discussion forums and Q&A websites is that you lack context. As a tutor I know what courses a student has done before, I’ve talked to the student before, I can see on their page which previous questions they’ve got right and which they’ve misunderstood. I can use that information to tailor my response. If they’re a bright student that clearly understands the material, then I can go into some more advanced details. If they ask ‘but what about 0.0000…001’ I can decide whether that’s the curious question of someone that’s grasped the basics, or the flailing attempts at understanding from someone that needs to focus on the basics.

      On StackOverflow, all you get is the question. That’s part of why StackOverflow has multiple answers. You can make up for the lack of context by answering questions from different possible contexts. One person can answer ‘no, there is no smallest positive real number because [blah blah blah]’ and someone else can answer ‘in nonstandard real arithmetic [blah blah blah].’ You can have tier 1, 2, 3, 4 and 5 answers to the same question. I don’t think that makes the ‘lower tier’ answers worse or the ‘higher tier’ answers better. This post’s attitude that any answer that just says ‘no that’s incorrect’ is bad. Sometimes people are just incorrect, even if their ideas can with a bit of tweaking lead to interesting different insights. But they’re not studying that different area, they’re studying the one they’re asking about, and in that area they are incorrect and want to be corrected so they can understand the area they’re trying to study.

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        they’re something totally different and unrelated.

        With the hyperreals, the transfer principle means one gets to keep many theorems from the real numbers. Saying they’re completely unrelated is disingenuous.

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        I like this! Sometimes, it feels like answers on StackOverflow would’ve been better off not having been posted at all. If you’re not willing to give a question some thought and try to understand what’s being asked, what’s the point of answering?

        I see answers from the lower tiers occur on many Q&A platforms that give points or benefits to those who answer questions (like the Piazza platform in uni). Low-tier responses require the least thought, but provide an amount of value (via karma, extra credit in a class, etc) that’s “worth it”. However, responses like this, as the author writes, are not all that helpful.

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          I love this.

          Also related: The emotional reasons people make these mistakes:

          1. Dog piling is fun. Playing the wise master to a newbie is fun. See also: Most IRC channels. Both are more satisfying and less work than the article’s suggestion.

          2. Often, finding the correct position on the proposed ladder will unmask your own ignorance – or at least the limits of your “expert” knowledge. There can be real depth in a “dumb” newbie question. Acknowledging that flips the power dynamic people want to act out. That’s how they perceive it, anyway.

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            I like the topic,

            the blog’s author, clearly is very analytical. And tries to ‘normalize/categorize’ questions, almost like a ‘librarian’ only instead of books, he is thinking about the interactive information discovery (eg questions on stack overflow). ( I liked hwayne’s observation, below, about the library science)

            I often thought about it as well, but could not come with a useful mental model.

            One difficulty I see in forums like stock exchange, is that slightly ambiguous questions (or open-ended topics) create N different possibilities of how to understand the question. Out of those possibilities, several responders will assume some overlapping contextual subsets. Then, they will use those contextual subsets to answer the question, and will do that ‘concurrently’.

            So we will then have several answers, that are, perhaps correct within the assumed context. As long as the answers are consistent with the question, and the assume context – to me, as a reader, all of those answers are useful and valuable source of knowledge.

            In summary, I agree with the author, that constructive answers (he calls them ‘upper tier’ in his classification), are useful sources of information, even if the question is not perfectly formulated.