Nothing groundbreaking by any means, but what this quadrant is meant to point out is that both analytical and intuitive thinking can occur across a variety of different subject matters. Just because I'm trawling a mass of scientific data doesn't mean that I can't think intuitively about it and the problem (top right) and just because I'm creating art doesn't mean I can't be analytical/knowledge-based in my creation of it (bottom left).
This quadrant is, perhaps, a useful reminder that Dionysian and Apollonian modes of thinking can occur in disciplines right from art to science. To reiterate, D&A is a very different distinction from art and science (and please forgive my simplfication of the art-science distinction to an axis - I know it's not that simple). On one extreme, progress in the particular bit of pure maths I studied (JBW*-triples) required some detailed, analytical thinking about the axioms and equations but also intuitively dealing with what these JBW*-triples 'are' (basically squares and rectangles inside each other!). Similarly, Picasso's a good example of an artist who rigorously and analytically developed his knowledge of the subject, (largely) before letting his intuition lead him to cubism.
I'm not sure on this quadrant quite how to represent the thought of D&A raising each other aloft. Obviously this thinking lies somewhere around region of the horizontal axis, but it's not simply about balancing intuition and knowledge. Picasso's cubist innovation wasn't a balancing of his hard-work in developing traditional skills and his intuition; it was a collision of the two producing profound effects. Similarly, dare I say it, the couple of results I proved about JBW*-triples weren't a balancing but a coming together of intuitive thought and knowledge. Perhaps it's something like the following.
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