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Vladimir_Nesov comments on Open Thread, February 1-14, 2013 - Less Wrong
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I'd guess it's a less systematic variant of the process described here, where the initial impression is sufficient to grasp enough of the problem statement to develop auxiliary ideas helpful for understanding the material on the second reading.
I had another guess: if some task is at the limit of my abilities, then success or failure is mostly governed by chance. Maybe I randomly fail the first time but succeed the second time.