In philosophy, systems theory, science, and art, emergence is a word that describes that a system is more than the sum-behavior of it’s sub pieces, and in fact can’t be predicted by it’s sub pieces. It’s more!
Emergence is focused on how different levels of complex systems integrate and arise from one another. For instance, the phenomenon of life as studied in biology is commonly perceived as an emergent property of interacting molecules. Molecules are then studied in chemistry, as phenomena that emerge from interactions among elementary particles, Particle physics, can be modeled in gravitational physics.
At each level of phenomena, sub-levels of elements ‘seem’ to generate the top level, but often the mechanism of generation is either completely mysterious or only partially understood. A classic example of an emergent system is a flock of birds. The beautiful patterns that the birds fly in emerge from the birds – probably out of a simple bird-to-bird signaling. But the exact path that the flock takes can not be predicted by any knowledge about the flock itself or the individual birds.
Most phenomena in life, including art, culture, biology, the weather, the economy, the stock market, and evolution itself are all emergent systems
A fun and informative presentation on emergence can be found here.
Much of exact science is based on Reductionism which is opposite in concept to emergence. Emergence is a bottom-up process, while Reductionism is a top-down process ( where the behavior of a system can be reduced to the behavior of it’s subparts ( e.g. a clock). ) Reductionist thinking can usually be modeled with equations. There are no equations for Emergent systems – beyond possibilities and probabilities.