  What fascinates us about animal behavior is its richness and complexity, but
understanding behavior and its neural basis requires a simpler description.
Traditionally, simplification has been imposed by training animals to engage in
a limited set of behaviors, by hand scoring behaviors into discrete classes, or
by limiting the sensory experience of the organism. An alternative is to ask
whether we can search through the dynamics of natural behaviors to find
explicit evidence that these behaviors are simpler than they might have been.
We review two mathematical approaches to simplification, dimensionality
reduction and the maximum entropy method, and we draw on examples from
different levels of biological organization, from the crawling behavior of C.
elegans to the control of smooth pursuit eye movements in primates, and from
the coding of natural scenes by networks of neurons in the retina to the rules
of English spelling. In each case, we argue that the explicit search for
simplicity uncovers new and unexpected features of the biological system, and
that the evidence for simplification gives us a language with which to phrase
new questions for the next generation of experiments. The fact that similar
mathematical structures succeed in taming the complexity of very different
biological systems hints that there is something more general to be discovered.
