Nonlinearity

In a linear model, the whole is exactly equal to the sum of its parts (Luce, 1999).  New and surprising phenomena will not emerge from a linear model of data, because if you have knowledge of each of the parts, you can predict exactly the behavior of the whole.  In contrast, if a model is nonlinear, then the whole is more than the sum of the parts.  That is, nonlinearity is a prerequisite of emergence (Holland, 1998).

References:

1. Holland, J. H. (1998). Emergence. Reading, MA: Perseus Books.
2. Luce, R. D. (1999). Where is mathematical modeling in psychology headed? Theory & Psychology, 9, 723-737.

(Added April 2011)