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    I find the “if you can’t explain it to a child” analogy more and more problematic the more I think about it. The question here is, explain for what purpose? The most dangerous thing is not lack of understanding, it’s illusion of understanding. You can easily explain the basic idea behind RSA to a novice (even a literal child). Explaining it in enough detail to implement it correctly is a different story.

    Until you really understand something, you can’t know what is irrelevant and can be ignored. You can miss things that turn out very relevant, and when it comes to applications exposed to the Internet, consequences can be quite serious.

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      Often the more we internalize knowledge and behaviors the less we can verbalize them.

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        This is a good point which I agree with and expand on in the article.

        I think the “explain to a child” is widely misunderstood. It’s not that everything is simple. It’s being self-aware enough and being able to understand a random kid enough to simplify into common simple terms along maybe a million different axes, depending on the situation and the kid. That requires a much deeper understanding than simply being able to do something by rote.

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          Explain to a random kid or a bright kid? IMO ‘explain to a kid’ is just meant to mean you could explain it from first principles, the ‘kid’ representing someone with no existing background/domain knowledge.

          I don’t think it means you should be able to explain it to literally anyone and have them understand it.

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            I guess a correct version should be “if you can’t teach it to a novice given enough time, you don’t really understand it”. For many things, a short explanation is going to be useless even if it’s not lying by omission. One can easily explain basics of calculus to an actual child. A derivative shows how fast a function is growing, like with speed and acceleration. Now what? It doesn’t give one nearly enough information to start using it. Maybe it gives some motivation to study it further, but no more than that.

            As of verbalizing, I have a feeling that verbalizing may not really be enough. At this moment I can tell the formal definition of a limit offhand, not even because I remember the words, but because it’s obvious how to say “as the item number grows, the item gets closer to a certain value” with quantifiers. However, I remember it well that when I first encountered that definition in high school times, it was absolutely confusing to me. What has changed? Did I get more comfortable with quantifiers? Or better at following definitions with multiple levels of recursion? No idea. My attempts to explain things to novices are routinely met with a blank stare no matter what analogies I employ, until they actively try to understand it themselves and explore counterexamples and implications.