I've read several books about innovation, and am reading another which I'll review shortly here on the blog, which talk about the importance of combining disparate skills or capabilities when innovating, or holding two diametrically opposing ideas and finding the happy medium. What should be obvious is that one of the most important skills from an innovation perspective is the act and insight of synthesis.
This is a real challenge, because most people are taught to break down problems into smaller, finite pieces and solve the smaller problems. We also work as specialists, with deep understanding of our core capabilities and knowledge, but often with little insights or knowledge beyond our education or jobs. So most people don't use synthesis skills on a regular basis, and are probably prone to avoiding synthesis since synthesis requires introducing a number of new and possibly unknown factors which may simply make the problem larger and more difficult.
Innovation relies on synthesis