He writes the following:
Between technical and popular science writing is what I call “integrative science,” a process that blends data, theory and narrative. Without all three of these metaphorical legs, the seat on which the enterprise of science rests would collapse. Attempts to determine which of the three legs has the greatest value is on par with debating whether π or r2 is the most important factor in computing the area of a circle.
Which is more important in calculating the area of a circle? I say r2. It's interesting that there is a constant, but the way in which the area of the circle grows when you increase the radius (namely, twice as fast) is more important to me. I may only be saying this, though, because I don't have to actually calculate the area of a circle. The people who made the circular table I'm sitting at certainly care about π to tell them how much raw material they will need.
The "twice as fast" statement there is a bit vague, but I mean it in the sense that if one increases the radius of a circle by some small fraction ε (as usual, ε2 = 0), one increases its area by the fraction 2ε. That is,
π(r(1+ε))2 = π(r2 + 2εr2+ ε2r2) = (πr2)(1+2ε)
where the last equality assumes ε2 = 0. For the most part this is how I think of derivatives -- at least simple ones like this -- in my head. The ε2 = 0 idea is the sort of thing one might see in the proposed "wiki of mathematical tricks" of Tao and Gowers (the real meat of the discussion is actually in the comments on those posts), although perhaps at a slightly lower level than they're aiming at.