At a meeting of the American Society of Naturalists in 1960, the noted British ecologist G. Evelyn Hutchinson posed what he called “the paradox of the plankton.” Look at a flask of seawater; it will be filled with diverse species of plankton, all competing for the same vital elements and nutrients. Yet natural selection implies that over time, only one species should occupy an ecological niche, a concept known as competitive exclusion. And what is true of plankton seems to be true of many protozoa, plants, birds, fish and other organisms, too. How can ecosystems routinely have so many competing species that stably coexist?
Ecologists have mulled over this vexing paradox ever since, but they have generally taken comfort in a solution known as … Read the rest
Physics contains equations that describe everything from the stretching of space-time to the flitter of photons. Yet only one set of equations is considered so mathematically challenging that it’s been chosen as one of seven “Millennium Prize Problems” endowed by the Clay Mathematics Institute with a $1 million reward: the Navier-Stokes equations, which describe how fluids flow.
Last month I wrote a story about an important new result related to those equations. If anything, the new work suggests that progress on the Millennium Prize will be even harder than expected. Why are these equations, which describe familiar phenomena such as water flowing through a hose, so much harder to understand mathematically than, say, Einstein’s field equations, which involve stupefying objects like black holes?
The … Read the rest