Entropy characterizes the uncertainty pertaining to a set of possible outcomes for a given event, and may be usefully applied to simply cases of organismal uncertainty (Smaldino, 2013). However, learning in complex environments often consists of integrating and organizing information into semantic networks and action sequences (Hawkins and Blakeslee, 2005; Hills et al., 2012). Evidence of learning might therefore be reflected not by the predictability of individual state-action pairings, but by other metrics that can better characterize the integration of complex schematic information. Behavioral scientists often characterize learning as a decrease in the time needed to solve a repeatedly presented problem, such as navigating a maze. From a computational perspective, such an idea may correspond to Bennett’s (1988) concept of logical depth, in which the complexity of an algorithm is characterized by the time it takes to compute. Such an approach has some advantage over entropy approaches, because although learning really does imply less variation in behavior in some scenarios – as in the movement of a rodent searching for a hidden platform in murky water (D’Hooge and De Deyn, 2001), for example – in other scenarios the opposite is true. Given a complex, open-ended problem to solve, an expert may have more variation in her behavioral output than a novice, both because she is better able to see subtle nuances in the stimuli and because she can draw on a wider range of options for behavior.
An abstraction of organismal learning and behavior has been used to highlight a feature of learning in real organisms. In some regards, this is old news. Psychologists have long known that increased knowledge brings with it an increased awareness of the vast array of things one does not know (Kruger and Dunning, 1999). Bertrand Russell is well known for his quip that “One of the painful things about our time is that those who feel certainty are stupid, and those with any imagination and understanding are filled with doubt and indecision” (Russell, 1951). However, there is something more subtle at play here. Learning can change behavioral patterns. Yet learning is itself based on previous behavioral patterns. So every time an individual learns, and that learning affects future behaviors, she potentially creates new uncertainties – new opportunities for learning.