What is Complexity? Lecture given by David Krakauer

The lecture explores the concept of complexity, considering it as a scientific discipline and comparing it with fields like physics and biology. The author questions what defines a discipline and suggests that complexity stands out because it is not reductionist: it does not try to explain systems by breaking them down into parts, but rather aims to understand the behavior that emerges from the interaction between those parts.

The science of complexity deals with phenomena that lie between absolute order and total chaos, a space where structure and unpredictability coexist. Here, traditional physics equations are no longer sufficient, and new mathematical tools are needed. On one hand, artificial intelligence offers high predictive power but with little transparency; on the other, complexity science seeks to explain mechanisms, even if with less predictive accuracy.

The author then discusses methods used to study these phenomena, such as models based on autonomous agents or network analysis. These tools help describe real situations, like the evolution of a city or the spread of a disease, even without reducing everything to simple formulas.

Finally, the text reflects on the relationship between mathematics and reality. While in physics equations can describe the world with great precision, in the realm of complexity mathematics loses some of its effectiveness. Nevertheless, some principles, like scaling laws, still manage to provide powerful descriptions even in biological or social domains.