The history of science and culture is filled with stories of how many of the greatest scientific and artistic discoveries occurred while the creator was not thinking about what he was working on, not consciously anyway - the daydreaming mode solved the problem for him, and the answer appeared suddenly as a stroke of insight.

Across a range of inferences involving not just language but mathematics, logic problems, and spatial reasoning, sleep has been shown to enhance the formation and understanding of abstract relations, so much so that people often wake having solved a problem that was unsolvable the night before.

Critical thinking is not something you do once with an issue and then drop it. It requires that we update our knowledge as new information comes in. Time spent evaluating claims is not just time well spent. It should be considered part of an implicit bargain we've all made.

One of the most important tools in critical thinking about numbers is to grant yourself permission to generate wrong answers to mathematical problems you encounter. Deliberately wrong answers!