Making the Path of Least Resistance

Back when Dwight Eisenhower was president of Columbia University, he was asked how the university should arrange the sidewalks to best interconnect the campus buildings. He responded that they should first plant grass seed, let the grass grow, see where the grass became worn by people’s footsteps, and install the sidewalks in the most worn patches. The Percepts and Concepts Laboratory (directed by Chancellor’s professor Robert Goldstone, also director of the Cognitive Science Program) at Indiana University has put Eisenhower’s proposal to the empirical test, asking what kinds of trails people will spontaneously form when they are motivated to take advantage of the trails left by their predecessors. Early trail blazers through a jungle use machetes to make slow progress in building paths – progress that is capitalized on and extended by later trekkers, who may then widen the trail, then later put stones down, gravel, asphalt, and eventually an eight-lane highway.

In the article “Self-organized Trail Systems in Groups of Humans” (appearing in the July/August issue of the journal Complexity, available at, Robert Goldstone and Michael Roberts report the results of a group experiment in which people collectively travel among random destinations in a virtual world. As they step on a location, they change their environment, making it easier for subsequent walkers to step on the same location. In this way, a trail left by a walker often leads other walkers to follow the same trail, thereby reinforcing and extending the trail.

The trails that our experimental groups of participants created are compromises between people going directly to their destinations, and taking paths of least effort. The trail network that completely connects a set of destinations using the minimal amount of total trail length is called a Minimal Steiner Tree. While soap films reliably create Minimal Steiner Trees, our human collectives did not. However, their paths did deviate away from bee-line paths to destinations, in the direction of Minimal Steiner Trees.

We modeled our results by adapting a model from biophysics (Helbing, Keltsch, & Molnár, 1997) that is based on Brownian motion within a field potential, and has been applied to ant trails. This model, which assumes that travelers’ steps are a compromise between going where they want to go and where others have gone before, did a good job of reproducing the trails that our groups formed. The growth of our collectively produced trails offers the promise of revealing principles about how future progress is achieved by exploiting and extending prior innovations. Our experiments and simulations also provide a rigorous way of following the poet Antonio Machado’s exhortation: “Traveler, there is no path. Paths are made by walking.”

Goldstone, R. L., & Roberts, M. E. (2006). Self-organized trail systems in groups of humans. Complexity, 15, 43-50.

Helbing, D., Keltsch, J., & Molnár, P. (1997). Modeling the evolution of human trail systems. Nature, vol. 388, 47-50.