Emergence

One of the most important concepts that most people don't understand, but which is needed to understand things in many fields ranging from physics to psychology to economics, is emergence.

Emergence refers to situations in which a system can be analyzed on two levels: as the action of a bunch of small individual components, each acting according to its own simple rules of behavior; and as a large system which evidences patterns and complexities of behavior which do not seem to be directly related to the behaviors of the smaller components, and cannot be readily predicted from an analysis thereof. Classical examples of emergence are fish (and bird) schooling, the stock market, automotive traffic patterns, hydrodynamics, insect colony behavior, and the mind. There's an excellent summary of emergence in the Wikipedia article.

By its nature we like to imagine things are built up by an understandable and predictable progression from small to large. A building made of Legos behaves in a way you can understand from the patterns of individual Legos. Put more chocolate chips in your cookie dough and the cookies have predictably more chips each.

But for every example where macrobehavior is easily predicted from microbehavior, there's one we like to ignore where it isn't. And not recognizing how emergence works, or even that it happens, is the source of many of the logical fallacies and mistakes of understanding made by people, even well-informed and literate ones. Not just in the areas of science or philosophy but also in politics and economics (you can't regulate markets without understanding the ways they do, and do not, regulate themselves, for instance). Everyone should familiarize themselves with the concept.