Towards the end of the essay, Galison sums up several points, which I believe are the answer to your question:
- Science has traditionally been concerned with "things and thoughts" - mechanisms and metaphysics.
- The "bottom-up" view, also known as empiricism, has traditionally looked strictly at things, and required that thoughts emerge from them as an explanation. Thoughts follow things.
- The "top-down" view, also known as idealism, has traditionally looked for patterns, symmetry and connections, leading to theories which then inform the experiments and investigations conducted to pursue them. Things follow thoughts.
- Einstein's innovation may have suggested a way of breaking out of this binary approach because it contains elements of both systems.
Specifically, Einstein saw that there were elements of empiricism, such as EM current induction, that had given rise to superfluous and asymmetrical explanations; the "bottom-up" approach generated scientific flaws. Seeing symmetry elsewhere, Einstein's "top-down" approach generated the idea that there must be a better explanation. The irony was that despite his top-down view leading to superior results, he simultaneously removed the top-down authoritarian aspect of time by eliminating the "master clock" concept from which other times might derive their authenticity.
Galison's point is that innovation can and should arise from a blending, or rejection, of the either/or approach to these problems. We're already past the point, as a culture and in our technology, where one or the other is entirely sufficient. Attempting to "simplify" things by being the champion of one approach or the other is, in fact, causing more complications than allowing the simplicity of nature to make itself apparent. Essentially, nature isn't seeking to conform to artificially-imposed human categories, so the driving force behind breakthroughs is the rejection of these categories as definitive approaches.