Going Over The Top

When an athlete swings upside down atop a 7-meter pendulum, it may seem like a feat of strength, courage, or technique. A new study suggests it is something more fundamental: a striking demonstration of how intelligence emerges from the interaction of brain, body, and environment.

In a paper published in the Journal of Nonlinear Science, Harvard researchers use mathematics, physics, and control theory to analyze kiiking, an extreme sport invented in Estonia in which athletes pump a giant swing until they complete a full rotation.

At one level, the problem appears straightforward. The athlete repeatedly stands and squats to inject energy into the swing. Yet this simple action inspires a question that reaches far beyond sport, touching neuroscience, robotics, biology, and human performance: How does an organism learn to exploit the dynamics of its environment to achieve a goal?

“The athlete is not imposing motion on the world,” said L. Mahadevan, the Lola England de Valpine Professor of Applied Mathematics, Organismic and Evolutionary Biology, and Physics, and senior author of the study. “Instead, the athlete is learning to cooperate with the world’s dynamics.”

For decades, scientists viewed movement as a command-and-control problem in which the brain computes movement and the body executes it. Modern theories of embodied cognition instead suggest that behavior emerges from the interaction of neural control, biophysics, and the physical environment.

Kiiking offers an unusually clean example of this principle. The athlete’s objective is simple: invert the swing. Yet success depends on understanding, either consciously or intuitively, the natural dynamics of an active pendulum many times taller than the athlete. The athlete cannot simply generate more force. Energy must be supplied in the right amount at precisely the right moments. Too early or too late, and the effort is largely wasted.

Every child who learns to pump a playground swing discovers this principle through trial and error: some movements amplify the motion while others do not. The mathematics developed in the study explains why.

The optimal strategy is to stand near the bottom of the trajectory, where the swing is moving fastest, and squat near the turning points, where it moves most slowly. These movements alter the effective length of the pendulum and transfer energy into the system with maximum efficiency. 

Lead author Petur Bryde says, “What appears externally as a simple rhythmic motion is an elegant solution to a complex control problem involving timing, force production, gravity, inertia, and aerodynamic drag.”

Most of the energy that raises the athlete does not come directly from muscular effort. Instead, the athlete contributes a modicum of metabolic energy during each cycle while exploiting the accumulated (and larger) energy already stored in the pendulum’s motion. Thus, the athlete does not so much overcome gravity as negotiate with it.

This principle extends far beyond kiiking. Birds exploit air currents, fish exploit vortices, and human walkers exploit the passive dynamics of their limbs and tendons. In each case, successful behavior depends on leveraging the structure of the environment rather than fighting it.

Beyond its relevance to an unusual sport, the study highlights a broader scientific challenge: understanding intelligence as a property of the system. Whether learning to walk, fly, swim, or manipulate tools, organisms solve problems not through computation alone but by exploiting the structure of their bodies and environments. Kiiking provides a transparent example of this process. The athlete, the swing, and gravity become a single dynamical system—and it is that system, not the brain alone, that discovers how to fly upside down.

Ian Davenport also contributed to the study, which was supported by the Simons Foundation and the Henri Seydoux Fund.