I wanted to talk a bit more about Goethe, but in a more relative way. In his experiments, Goethe saw more merit in the visual and conceptual understanding of natural phenomena than in the exact numbers, figures, and calculations that constitute how these phenomena are measured. While Newton felt he needed to relate numbers and the exact degree of refraction to the spectrum of colors, Goethe chose to comment on the colors themselves - how the spectrum went from red to dark purple, how blue and yellow came together to form green, how magenta or pink started to form at both ends, etc. I think Goethe's approach makes more sense because I think that one must mention the basic observations involved in a given phenomena before he or she delves into the specifics of the phenomena. As an example, saying that the acceleration due to gravity is 9.8 m/s/s means nothing if one doesn't know what the Law of Gravity is.
As another example of this, I thought of TV shows that teach scientific concepts to laypeople like NOVA. As far as I've seen, shows like NOVA tent to take an approach like that of Goethe's when relating scientific knowledge, as they tend to stray away from the exact calculations and equations that so into the topic being discussed. When I watch a show like NOVA, I don't see rigid, completely left-brained individuals discussing the specifics of scientific concepts, I see eloquent speakers like Michio Kaku and Neil deGrasse Tyson relay ideas using creative metaphors and examples to relate scientific ideas to laypeople, comparing wormholes in apples to wormholes in space or visualizing a relativistic clock that accounts for movement. It is ideas like this that Goethe would approve of, and an ideology that I have come to favor. It seems that scientific understanding has very little to do with numbers, after all.