Goldenrods bloom with geometrical extravagance. Up close, the panicle, or flowering top, of the plant is composed of racemes, long stems with upturned yellow flowers. I waded into a field and plucked a modest goldenrod panicle, which comprised twenty-three racemes. I counted twenty-eight flower heads on one raceme and forty-nine on another. So any given panicle might contain between five hundred and a thousand flower heads. But then each flower head is composite, too, containing somewhere between two and sixty disc florets, surrounded by a handful of ray florets. My little goldenrod panicle had flower heads composed of six to eight florets, bringing our total to somewhere between three and eight thousand diminutive flowers on a single panicle. Even if there are only two goldenrod plants per square foot, an acre of the stuff could contain a half-billion flowers.

This is absurd prodigality. Why does a plant need so many flowers?