I can't decide whether I hate this or agree with itpic.twitter.com/hZakziWu0c
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I can't decide whether I hate this or agree with itpic.twitter.com/hZakziWu0c
I don't see why this should be true? It's possible to explain why a result would be surprising or interesting and then prove it. In some cases, "doing your job" could involve just pointing out the surprising thing without a proof, for example:pic.twitter.com/YUE7iCpIXe
I think the idea is that a good exposition doesn't just mention something surprising or even prove it, it gives you a solid intuition for why it is so, thus demystifying it. Yr quote doesn't do this at all; it says true and surprising things w/o explanation.
I don't think all good intuition-building explanations leave the learner feeling de-surprised, but this definitely does happen sometimes.
Although there are exceptions to this, I think that not explaining why something is surprising (when there's some reason it's surprising) generally does people a disservice.
Something I saw a lot in school was that people would think that something that was explained to them was SUPER OBVIOUS and you'd have to be an idiot to miss the conclusion. But after talking to them, their reasoning would be wrong and could often lead to the opposite conclusion.
The actual reason the thing was true would be something relatively subtle, but the seeming obviousness of the conclusion as presented made people think they didn't need to think through the subtleties.
I think this and Sridhar's complaint about "mind-blowing" pop math exposition can both be true, although I'm interested to hear examples of things being "deceptively nonobvious".
You know how "elementary" math textbooks will often say the only pre-requisite is "mathematical rigor"? I think everything that goes into that is really non-obvious for 99% of people, maybe even more like 99.9%?
My engineering classes never tried to engender that kind of rigorous thinking and IMO it showed in, e.g., cases where the professor accidentally asked the wrong question, the equivalent of an HN article being mistitled revealing that no one reads the article before commenting.
In a grad level emag class I took (IIRC, this was 17 years ago), on an exam, the professor meant to ask you to describe the e-field when you have a sphere with constant charge above an infinite metal plane. Instead, he asked about the case where the sphere has constant voltage.
The constant charge problem was the closest problem to pattern match to, so people did that, but the problem was very different. IIRC, only 2 or 3 people didn't get the problem completely wrong (no one fully solved the problem, the computation for the real problem was v. long).
IMO, it's easy to overgeneralize and the way things are usually taught (in school, pop sci, whatever) tends to encourage this. I think one way to fight back against this is to think about why things aren't obvious, what conditions are really necessary for something to hold, etc.
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