Explained: Linear and nonlinear systems
Spend some time browsing around the web site of MIT’s Computer Science and Artificial Intelligence Laboratory, and you’ll find hundreds if not thousands of documents with titles like “On Modeling Nonlinear Shape-and-Texture Appearance Manifolds” and “Non-linear Drawing systems,” or, on the contrary, titles like “Packrat Parsing: Simple, Powerful, Lazy, Linear Time” and “Linear-Time-Encodable and List-Decodable Codes.”The distinction between linear and nonlinear phenomena is everywhere in the sciences and engineering. But what exactly does it mean?Suppose that, without much effort, you can toss a tennis ball at about 20 miles per hour. Now suppose that you’re riding a bicycle at 10 miles per hour and toss a tennis ball straight ahead. The ball will travel forward at 30 miles per hour. Linearity is, essentially, the idea that combining two inputs — like the velocity of your arm and the velocity of the bike — will yield the sum of their respective...