gwern comments on Use the Try Harder, Luke - Less Wrong
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An excerpt from a likely-never-to-be-finished essay:
--Manuel Blum, "Advice to a Beginning Graduate Student"
Good quote. I guess the lesson there would be to tell yourself "It might just actually be possible for me to do this"?
His brother's hint contained information that he couldn't have gotten by giving the hint to himself. The fact that his brother said this while passing by means that he spotted a low-hanging fruit. If his brother had spent more time looking before giving the hint, this would have indicated a fruit that was a little higher up.
This advice is worth trying, but when you give it to yourself, you can't be sure that there's low hanging fruit left. If someone else gives it to you, you know it's worth looking for, because you know there's something there to find. (The difference is that they, not you, took the time to search for it.)
Again, it's a worthwhile suggestion. I just want to point out that it boils down to "If you're having trouble, check for easier solutions," and that while you can always give this advice to yourself, it will not always help.
The brother could have spent arbitrarily much time on the jigsaw puzzle before Claude started playing with it.
I suppose, but even then he would have to take time to review the state of the puzzle. You would still expect him to take longer to spot complex details, and perhaps he'd examine a piece or two to refresh his memory.
But that isn't my true rejection here.
If you assume that Claude's brother "spent arbitrarily much time" beforehand, the moral of the story becomes significantly less helpful: "If you're having trouble, spend an arbitrarily large amount of time working on the problem."
I don't think that's what it becomes. It remains what it was: 'a solution exists, and oddly enough, reminding yourself of this is useful'.
Not credibly and not with the actual information content that the brother's utterance provides. That leaves the question of whether and in what circumstances it is instrumentally rational to self deceive in the direction of optimism bias (or optimism regarding the relative merit of rechecking the low branches for more fruit instead of climbing higher). Some considerations: