Suppose four bugs at the corners of a 2-by-1 rectangle start chasing each other at speed 1. Bug 1 chases bug 2, bug 2 chases bug 3, and so on. What happens next will surprise you. As we follow the bugs to their eventual collision at the center, we will encounter the biggest numbers you´ve probably ever seen and confront some fundamental questions about what it means to try to understand our world through mathematics.