Travelling optimally across Asimov’s The Caves of Steel

Abstract

In his famous novel The Caves of Steel, Isaac Asimov imagined a public transportation system based on a series of parallel moving walkways accelerating pedestrians progressively toward a high-speed central lane which continuously carries the crowds of the gigantic cities of our future Earth. In this paper, it is shown that the user of this system would face an interesting optimization problem, namely the design of the path which would minimize the travel time from one place to another. This problem is solved with the classical techniques of Lagrangian mechanics.