Nobel Prize–winning economist Ken Arrow had a succinct, almost poetic, way to describe technological advances: “The process of innovation is, virtually by definition, filled with uncertainty; it is a journey of exploration into a strange land.” Indeed, this mysterious terrain can be viewed as a mountainous landscape with soaring peaks and deep valleys, the summits corresponding to breakthrough inventions, the chasms representing dismal failures. We have recently charted this landscape in quantitative terms, drawing on more than 200 years of U.S. patent office data.

A version of this article appeared in the September 2001 issue of Harvard Business Review.