I'm interested in the "phenomenology" of knowing, and from this perspective, the mind/body duality falls away because I believe we all experience cognition as a physical activity. (And for this reason, it is hubris to claim that it's unique to humans, as Carrie points out.) Indeed, if I haven't slept well, my thoughts are slow as mud. When I'm struggling to solve a problem (technical or not), I am acutely aware of the bits of information I'm shuffling around. I can close my eyes and see them as puzzle pieces, and when I finally fit them together into a bigger picture, there is a shiver of understanding that registers as a bodily sensation. It's the same way that a complex piece of music like a 4-part Bach fugue can transcend its individual components and stir the emotions.
I've also found that when such understandings are revealed, I habitually tend to assume that the map is the territory, that these now-apparent (Platonic) truths were somehow hidden within the objects under study all along. This common perception of "embedded meanings" leads to a narrative of form/content duality that can be found in science as much as in art (with scientific laws being the content of natural forms). Furthermore, this duality implies an opposition between our questioning minds and their subjects. Thus, seeking knowledge can have an alienating effect -- in order to understand how something works, we have to objectify it, to regard it as separate from ourselves.
However, there is an alternative. As Deborah suggests, we could posit that there is no duality, that the form of an object simply is, that it carries no inherent meaning, that we can look at an object without seeking to know it. But if we do choose to reach for knowledge, we can view that "content" as intrinsic to us viewers, not to the object itself, thereby preserving the object's integrity.
In other words, sense-making is a conscious act. Science proceeds under the assumption that all phenomena can be explained rationally, that nature is knowable even if it is not currently fully known. This does not mean, however, that scientists are constantly being scientific. When I gaze at the night sky, I find myself flitting back and forth between two modes of looking: zooming in to pick out individual stars and constellations, and zooming out to take in the entire sky with wonder. Both of these approaches -- the analytic and the holistic -- can co-exist without contradiction, enriching each other.