Complexity

Abstract

C onsider a single molecule of water. Many of its properties, such as bond lengths, bond angles, and energy levels, can be calculated from quantum mechanics, the appropriate theory at the atomic scale of matter. Add 10 further molecules of water, and you’ve got a liquid, which is described by hydrodynamics—an altogether different ball game than quantum mechanics. Eddies and vortices don’t exist at the level of a single molecule. Decrease the temperature, and the liquid freezes. Now you can push the rear side of a block of ice and the front side moves instantaneously along with it. Rigidity is hardly a property of a fluid or a gas. A very large number of water molecules thus constitute an “object” so rich that it needs a different theory at different temperatures! In the early 1970s, Phil Anderson, a Nobel Laureate and member of the SFI Science Board, coined the slogan “More is different” (Science, 177:393–396, 1972). Emergence points to the fact that new properties come to dominate a system’s behavior as we increase its degrees of freedom or as we tune a parameter to break a symmetry. There are different mechanisms for emergence. Yet they all depend on the fairly obvious fact that the components of a system interact. Increasing the number of interactions, or emphasizing certain interactions over others (breaking symmetry), triggers feedback loops among the components, giving rise to collective behavior. Components that are locked into such behavior can be treated together as a new unit. While the composition of a system has remained the same, its internal boundaries—which suggest how to parse a system into “parts”— have been redrawn from within. This forces a change in the way we describe that system and how we must think about it. For example, we do not think of the air over the U.S. as a flowing gas, but we think of it in terms of cold and warm fronts or huge vortices such as hurricanes. Those who emphasize the global view of a system say that “the whole is more than the sum of its parts,” where the “more” refers to properties deriving from WALTER FONTANA AND SUSAN BALLATI