There's bound to be someone in the audience to which the thing that is actually obvious is not in fact obvious, so the lengthy description will probably help someone at some point. And there's less work required in skipping over a boring bit than there is in figuring out the page of reasoning that should replace an overconfident "clearly".
The trouble is that what actually happens is that you read a somewhat dense article and suddenly you come across a lengthy passage that seems to be saying something obvious. The natural assumption is that really it's as dense as what went before so you must have missed something, so you read it more and more carefully and eventually conclude that no, it really was just saying something obvious.
I'm not convinced. The lengthy description of the obvious causes you to waste a load of time for no benefit. The concise description of the obscure will also take some time to figure out, but at least it was time well spent!
There is that. In practice what I do at that point is go off and look at the web for other explanations of the same thing. If even that doesn't help then you were likely doomed before you started...
More than that; the effort required to work through the concise description will do a far better job of lodging the understanding in your mind, than skimming lightly over the paragraphs muttering "yes, yes, yes" to yourself.
A colleague has observed that, from a perspective of 25 years on, it's the really craply lectured stuff that he can now remember well; the brilliant crystal-clear lectures have descended into a kind of "oh I remember understanding that" kind of state. I think I've found the same (to a lesser degree).
What isn't nice is inadequate and concise descriptions, or ones where the author is trying to conceal their dodginesss of grip by blurring what they say.
Also, an article can be read at the pace of your understanding. I'm not sure what my answer would be in a lecture, but I think it might switch. Wasting 100s of hours of time explaining something dull and trivial v's than leaving people with something to puzzle out in their own time, especially if they can ask you questions on it, is not so clear cut.
Conciseness around subtle points is a disaster in a lecture - you can't pause the lecture to take as long as you like to figure it out. Worse, if you don't get it, the rest of the lecture might be incomprehensible even if actually all follows in relatively simple ways from the subtle bit: the point where I start taking things on trust tends to be the point that I look track, IME.
I have to say, I think an incomprehensible bearded man killing my parents would be worst. You're not reeling from the explanation of banach-tarski, are you?
I'm not sure. It shouldn't be worse, but somehow a long explanation tends to lead you astray and get you concentrating on the details. If it said "and so, blah de blah" and then had two paragraphs in brackets saying "this is fairly obvious, but consider, etc", or even presented as a lemma elsewhere, it works ok, but if you just plunge in you often lose your place entirely.
I have to say, I think an incomprehensible bearded man killing my parents would be worst.
But only in a mathematically inclined article, not in real life. So although it would be bizarre to find such a description in the middle of, say, a proof of the fundamental theorem of algebra, it wouldn't really be that terrible.
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(Er, I seem to have become an owl. Sorry.)
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A colleague has observed that, from a perspective of 25 years on, it's the really craply lectured stuff that he can now remember well; the brilliant crystal-clear lectures have descended into a kind of "oh I remember understanding that" kind of state. I think I've found the same (to a lesser degree).
What isn't nice is inadequate and concise descriptions, or ones where the author is trying to conceal their dodginesss of grip by blurring what they say.
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I'm not sure. It shouldn't be worse, but somehow a long explanation tends to lead you astray and get you concentrating on the details. If it said "and so, blah de blah" and then had two paragraphs in brackets saying "this is fairly obvious, but consider, etc", or even presented as a lemma elsewhere, it works ok, but if you just plunge in you often lose your place entirely.
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But only in a mathematically inclined article, not in real life. So although it would be bizarre to find such a description in the middle of, say, a proof of the fundamental theorem of algebra, it wouldn't really be that terrible.
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