Gordon Chang maintains (click here) that “China has passed an inflection point” in its ascent to world power, and that bad things are in the offing. I tend to agree . . . although as the great Yogi Berra counsels, making predictions is tough—especially about the future.

Some years back some friends and I—including the aforementioned Mr. Chang—put together a volume (click here) exploring how population decline shapes great-power politics and strategy. The outlook for China was grim at best. Beijing may have relaxed its one-child policy, for instance, but it will have to live with the social and cultural wreckage—not just declining population numbers but the destruction of China’s traditional family system—for decades to come. Gordon projects economic figures that likewise portend ill for China’s world-power standing.

Now, it appears Gordon, unlike many commentators, deploys the mathematical phrase inflection point with precision. He’s not saying China is in freefall, or even that its rise has already come to a halt. He is saying its rise is slowing and could come to a halt—or even go into reverse.

Denizens of wonkdom oftentimes use the phrase interchangeably with maximum or minimum, or sometimes just as shorthand for some significant change of state. It offers a fancy way to indicate that something or some trend has peaked or cratered. What an inflection point really marks, though, is a change in the rate of change from acceleration to deceleration or vice versa. The gradient flips from positive to negative or the reverse—akin to applying the brakes or the accelerator in the automotive context.

So a curve that’s on the rise will keep rising for a time after it passes the inflection point, but its rate of ascent will slow until it reaches zero at the curve’s maximum point. At that point it may plateau, or it could go into decline. It could even resume its upward trajectory if it passes another inflection point. The converse is true of a descending curve or trend. Its descent will slow until it flatlines, bounces back, or reverts to freefall.

Transposing the concept from a math textbook to East Asia, China could still be growing by economic and military measures, and amassing new diplomatic clout to go with its physical power. But at the same time its rate of growth could be decelerating—perhaps to zero. China’s rise could top out or even slip into decline. It would take some serious wisdom and resolve on the part of the Chinese Communist Party leadership to restart the uptrend.

We shouldn’t take too much comfort, though, if China is indeed bumping up against its limits. You might suppose a state undergoing demographic or economic decline would conduct its affairs with caution in order to husband increasingly scarce resources. And you would be right: that does make sense. But my finding from the population-decline study—drawing on demographic catastrophes in classical Greece—was that demographic stresses may have just the opposite effect. A contender could run even more risks than it normally would despite its loss of manpower and other resources.

Far from trying to conserve scarce resources, Athenians—always a venturesome folk—courted greater and greater dangers in their war against Sparta after suffering a plague that claimed the lives of some thirty percent of the populace. That seems perverse—but if it happened before it could happen again. China might embark on an Athenian future, accepting new risks if the leadership believed troubles at home were about to cap its ambitions abroad. Internal woes could give rise to foreign-policy adventurism on a scale hitherto unseen, if China’s rise has gone past an inflection point.

A turbulent ride could await Asia.