 This paper discusses the importance of identifying effective variables in complex systems. It explains why persistent structures, which remain consistent over time and length scales, are suitable variables for studying these systems. The authors demonstrate their theory by applying it to several examples, including the study of market crashes. They show that before a crash occurs, there is a distinct change in the spectrum of the graph Laplacian, as well as a shift in the Fiedler vector's distribution. This suggests that the presence of persistent structures may provide insight into the occurrence of market crashes. This article was authored by Peter Tsongwen-Yen, Kelin Xia, and Su Wenchong.