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From my observation, a lot of analytically strong people suck at synthesis. And add to that, they are not even self aware about this. True mastery requires synthesis or what you call integration of different ideas/concepts in a domain.

It is easier to illustrate this using Chess. The game has 3 distinct stages - the opening, the middle game and the end game. Opening and end game stages are mostly technique and uses the analytical part of the brain. The middle game, however, with the pieces all over the board requires synthesis. Often, it is not even clear what one should do.

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