Five Questions on Complexity: Responses

From this perspective, one can see the recent history of complex systems as two sides of the same coin. The first side was the discovery that simple systems can appear random (and high dimensional), even when consisting only of low-dimensional, but nonlinear coupled components (aka “deterministic chaos”). Despite our intuitively negative reaction to unpredictability, deterministic chaos was great news at the time. Could much of the randomness that we see around us in the natural world be, underneath, hidden away, simple nonlinear dynamical systems? If so, we might be able to extract the hidden simplicity—states and dynamic—from a few, or even one, variable. Answering this question led to the introduction of the idea of reconstructing “Geometry from a Times Series” by Norman Packard, myself, Doyne Farmer, and Rob Shaw in 1979. By the mid-1980s that idea had spawned much work on nonlinear time series analysis, which provided an important push against the then-dominant focus on linear, stationary, independent, identically distributed processes.