Lecture G1 - Randomness and Chaos (2020-04-16)

In this lecture, we introduce stochastic modeling as well as the topic of chaotic behavior in complex systems. The first half of this lecture focuses on stochastic modeling and the distinction between randomness and stochastic modeling, where "stochastic modeling" is the deliberate choice to use randomness in a model to simplify the modeling process. We then transition to discussing chaos (a particularly extreme sensitivity to initial conditions in models), which gives models an appearance of random behavior despite having no randomness within them. We close with an explanation of the so-called "butterfly effect" and an explanation of "strange attractors" frequently captured in the study of chaotic systems.