“Modern preconceptions have it that simply by applying our brains and concentrating hard enough on a problem (e.g. a crossword clue), we should be able to see the solution. This is the “Hare brain” approach.
The book says that there are two types of solution moments. Yes, one is when we sit down and just think hard. But there is another solution moment which comes seemingly out of nowhere, when we’ve been staring out the window, or having a shower, going for a walk. This is the tortoise mind approach. This is a result of a) having done the hare brain thinking in the first place and b) just relaxing your frontal lobes, and letting the rest of your brain “background render” the solution.