Get the latest tech news

Complex dynamics require complex solutions

The behavior of a high-dimensional dynamical system can, very roughly speaking, be divided into two regimes. The first is what one might call the "effective dynamics" regime, in which the complex, high-dimensional dynamics can be well approximated (in the observables that one particularly cares about, at least) by lower-dimensional effective equations or models that emerge from the more fundamental laws of motion, and are easier to understand and analyze. A classical example is the laws of thermodynamics, which can effectively govern (some of the) macroscopic behavior of a large number of interacting particles, due to mixing effects that greatly simplify the impact of most of the degrees of freedom. Another example from physics is Hooke's law, that asserts that an elastic object, such as a spring, exerts a linear restoring force to push it in the direction of its equilibrium. Similar linear restoring force phenomena can be seen across the sciences (such as climate science, biology, economics, or even political science): not as fundamental laws of nature, but as empirically observable laws that emerge from more fundamental ones. Such effective laws can provide a valuable amount of long-term stability, predictability, and simplification to the dynamical understanding of many real-world complex systems. (1/4)

Get the Android app