


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:
 Holland, J. H. (1998). Emergence. Reading, MA: Perseus Books.
 Luce, R. D. (1999). Where is mathematical modeling in psychology headed? Theory & Psychology, 9, 723737.
(Added April 2011)



