Mathematical Truth

young Andy kayaking

Biology and boats require knowledge of tipping points. Photo courtesy Andy Stahl

By Andy Stahl
Forest Magazine, Fall 2008

I was introduced to “tipping points” while sea kayaking in Washington’s Puget Sound. Against the advice of my more-experienced partner, I stood up in my kayak to climb onto a concrete sea wall. In the blink of an eye, I was upended in the water.

My partner understood the physics of our boats—the mathematical relationship that determines how far my center of gravity can stray from the boat’s mid-point axis without irreversible results. But I ignored her advice, choosing to rely on my youthful sense of balance. She was right; I was all wet.

In the summer of 1984, in a coastal Maine lobster shack, population biologist Russell Lande scrawled several equations on a buttery napkin to answer my question: “Would protecting 5 percent of the spotted owl’s old-growth forest habitat, as the U.S. Forest Service proposed, ensure the owl’s survival?” His equations said “no”—much more forest would have to be saved.

Pointing a lobster claw at one indecipherable equation, Lande told me, “There’s a tipping point here; spotted owls won’t decline proportionally as habitat is lost.” He explained that well before all old growth is logged, the spotted owl’s population would crash. We can’t tell exactly when that point will be reached, he said, but we do know that by the time it arrives, it will be too late to prevent the spotted owl’s extinction.

Lande explained that the spotted owl’s tipping point is inherent in this species’ biology (and many others, too). Young spotted owls must find old-growth forest territory at a rate greater than mature owls die to sustain the population. The number of young produced and their ability to establish themselves is related to the number of suitable nesting areas spread throughout the landscape—more owl territories mean more young owls born and an easier time for each owl to find a home. As habitat is lost to logging or fire, fewer young owls are born, and each one that hatches faces a tougher task finding a place to live. There is also a lag effect—the spotted owl will continue to decline even after habitat loss is halted.

The spotted owl’s biology is much like our planet’s climate. Each functions according to mathematical truths. We may not have precise data or know in detail all the mathematical relationships that link our atmosphere with the earth’s vegetation and oceans. But we understand the arithmetic principles well enough to make accurate predictions.

These forecasts show that our planet faces tipping points that make the spotted owl’s crisis pale in comparison. The world’s great ice sheets are melting, which will result in dramatic sea level increases. Amazon rain forests are converting to savannah. Each is a predictable consequence of increases in carbon dioxide from fossil fuel burning. These consequences are based on mathematics, not speculation, ideology or politics. We know what will happen even if we don’t know precisely when it will happen.

The spotted owl’s tipping point catalyzed a revolution in national forest policy away from logging ancient forests and toward their protection. Thoughtful scientists and forest managers understood the canary-in-the-coal-mine warning implicit in the spotted owl’s population collapse.

Now more than ever, we need to elect people to office who understand our planet’s tipping points. We need to take the actions demanded by the mathematics of climate science to save our planet’s habitability—stop worldwide deforestation, cease building coal-fired power plants and ensure that through the marketplace, carbon-based energy pays the full environmental cost of its use. We must do so because the mathematics of climate change is as irrefutable as a kayak’s tipping point.