Vladimir_Nesov comments on Is That Your True Rejection? - Less Wrong
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From my experience, the most productive way to solve a problem on which I'm stuck (that is, hours of looking at it produce no new insight or promising directions of future investigation), is to keep it in the background for long time, while avoiding forgetting it by recalling what's it about and visualizing its different aspects and related conjectures from time to time. And sure enough, in a few days or weeks, triggered by some essentially unrelated cue, a little insight comes, that allows to develop a new line of thought. When there are several such problem in the background, it's more or less efficient.
Inferential distance can make communication a problem worthy of this kind of reflectively intractable insight.