If the United Nations population wonks are correct, and they usually are, a baby born on Halloween, of all days, will tip the population meter to seven billion souls. The world is already doing a poor enough job of feeding those mouths. How will we ever sustain a population that is headed to 10.1 billion by the end of the century—the equivalent of adding two new Chinas to the planet?

Any self-respecting ecologist will tell you that populations don’t grow indefinitely, and the faster they grow, the more likely it is that a crash is around the corner. The world population has grown incredibly fast for the past 100 years or so. That growth is beginning to level off, fortunately, but even so, we are in an increasingly precarious position. Even the human population held steady at seven billion, rising standards of living in countries such as China and India alone would be enough to keep ecologists awake at night.

If we think we can innovate ourselves out of this mess, Geoffrey West, professor at the Santa Fe Institute, painted a sobering picture at the Compass Summit conference this week in Rancho Palos Verdes, Calif.

Innovation, of course, is the reason that doomsayers like Malthus have been wrong so far. As the human population rises, a new cycle of innovation always appears to increase the available resources and enlarge the human petri dish, making further growth sustainable—until the next round of innovation is needed. The discovery of infectious diseases and antibiotics, the Green Revolution, and fossil fuels are just a few of the big advances that have keep the human engine going. But West points out an alarming pattern: the cycle of innovation needs to increase in frequency as the size of the population increases. The bigger we grow, the faster we must innovate to keep pace.

"Unbounded, exponential growth requires accelerating cycles of innovation to avoid collapse," says West. "If you want continuous growth, you actually have to have continuous innovation. But there’s a catch. The period of time you have to go from one cycle to another gets shorter."

"This is what we’ve been doing," says West. "We’ve been going faster and faster. Is this sustainable? Obviously it isn’t. Eventually you’d have to have an equivalent of an Information Technology revolution or an industrial revolution every year."

That is a pretty high bar, even for the current innovation-crazy century. Innovation alone is probably not going to keep the human race from avoiding—or at least postponing—the fate of all quickly growing populations.

An answer to this conundrum isn’t forthcoming (if I had one, I’d tell you). But it seems rational to avail ourselves of any and all appropriate remedies—carbon reductions, efficiency programs, birth control, energy policies, agriculture research and aid, and so forth. Innovation deserves a place at the top of a To Do list for saving the planet. But we need everything else on the list, too.