Our natural world is complex. This can be encapsulated by the fact that the patterns and dynamics that we observed around us are neither purely regular nor utterly disordered. They seem to perch somewhere between the regimes of regularity and randomness, as if in a state of criticality. This is the perspective conveyed to us by the theory of self-organized criticality, and the aim of this lecture is to make this perspective concrete. In particular, what do we mean by criticality and how does it arise in a self-organized manner? Why is self-organized criticality known to be the first general theory of complex systems with a firm mathematical basis even though there are many theories proposed to describe individual systems? In order to answer these questions, the lecture will delve into the science of self-organized criticality: its theoretical framework, mathematical structure and experimental validation. The lecture will discuss how this intriguing and beautiful theory is able to provide insights and understanding on the underlying mechanisms of diverse complex systems, such as earthquakes, biological evolution, the brain, and the social and economic phenomena of traffic jams, riots and stock market crashes. In addition, the lecture will also evaluate on the inadequacies of the theory, its outstanding issues, recent research progress, as well as the development of related and complementary ideas since its discovery less than thirty years ago.

References:
[1] Per Bak, “How nature works: the science of self-organized criticality”, Springer-Verlag, New York, 1996.
[2] Henrik Jeldtoft Jensen, “Self-organized criticality: emergent complex behavior in physical and biological systems”, Cambridge University Press, 1998.
[3] Per Bak, Chao Tang and Kurt Wiesenfeld, “Self-organized criticality”, Physical Review A 38, 364 (1988).
[4] Per Bak and Kan Chen, “Self-organized criticality”, Scientific American, page 46, January 1991.
[5] Donald L. Turcotte, “Self-organized criticality”, Reports on Progress in Physics 62, 1377 (1999).
[6] Dimitrije Marković and Claudius Gros, “Power laws and self-organized criticality in theory and nature”, arXiv:1310.5527v3.