Emergence is the word used to describe what happens when a system becomes more than the combination of its pieces. A set of rules, group of animals, or collection of objects can develop special properties that none of the single pieces possess. The exact cause of this transformation is impossible to pin down, and yet it happens each branch of science. From the wisdom of crowds to fluid dynamics - we call it emergence.
It can be difficult to discuss emergence, because it is defined in many different ways. It's called 'self-organization,' or 'bottom-up organization,' generally when dealing with sociological things. When it comes to physics, its more often called 'downward causation.' In pop psychology, it's often called 'the wisdom of crowds'. Emergence can manifest in many different ways, but it always manifests as a new property, held by a group of objects but none of the individual parts, when no larger control is imposed on the group.
Emergence In Biology
One of the most basic creatures ever to drag itself over the earth is the amoeba. It's a boneless, brainless, and sexless sack of goo, meandering along the forest floor, looking for something to osmose. But when the weather is right, and the conditions are right, single cells get together and form something new. A slime mold is grouping of these cells, that begins to work as a single creature.
The slime mold covers more ground than its original cells, can leave colonies of cells in choice locations, and has been shown to find their way through complicated structures. Single cells that manage no more than slowly moving alone can, through no overall organizing force, trace a path through a maze from one food substance to another.
Another emergent biological structure is the brain (and if its insulting to compare the human brain to slime, consider how rarely a brain in a jar finds its way through a maze). Individual neurons, and whole sections of the brain, do not have the properties of the interconnected brain as a whole. When one part of the brain is affected, people report massive swings in cognitive and physical ability, mood, personality, and sometimes total loss of function.
Emergence In Sociology
The holders of those brains are also parts of systems which have emergent properties, though the size of ants brains in the first place is not impressive. Ant colonies maintain an impressive level of organization. Their foraging patterns, nest layout, and labor force are all highly efficient. And although humans may call one ant a 'queen,' she's really just another worker; one whose task happens to be having a lot of babies. There are ants intended to keep her fed and healthy, but no organization structure under her. At any time, 25% of ants are workers clearing out their den, 25% are on defense, while 50% are looking for food. That ratio doesn't change, and yet it's rare that any ant have special work designations, and when an ant dies no other ant is automatically converted. Ants doing certain jobs, though, produce certain scents. As they move through the nest of ants, they encounter other ants and smell them. When they encounter too many of the same workers in a short stretch of time, they automatically assign themselves to less well-represented tasks. This simple signalling system keeps an even labor force no matter what happens to the colony.
The scent markers also help ants solve the problem of efficient foraging. At each promising site, ants leave scent markers. These attract and guide other ants. As more ants come by the site, leaving more scent markers, ants not only come up with a map of the best food sites, but with the most efficient way between them. Although the markers are a way of influencing behavior, the ants don't use them strategically. They just leave them, and the bulk motion of the ant colony reinforces the best pathways.
This doesn't only happen with ants. People in cities select certain neighborhoods based on the density and 'type' of people they find in those neighborhoods. This is why there are quiet family places, rich enclaves, poor areas, student quarters and shopping streets. Although there are factors and programs that can change neighborhoods over time, they also grow up organically and independently, without any central planning.
Emergence In Physics
Emergence in physics and mathematics is often used in a slightly different sense than biological systems. In physics, going from the micro to the macro doesn't necessarily result in great organization, but it does introduce new properties, often ushering in a new structure with it.
A single atom, or two, or three, of water flowing through a pipe and into a lake will flush through and head in any direction, and there's no predicting it. Even billions of atoms, when allowed to trickle through one or two at a time, will not result in any predictable behavior. When a certain flow is attained, though, suddenly there will be certain, predictable dynamics that emerge as well. Fluid dynamics are, in many ways, an emergent property of a random group of atoms.
Many different aspects of physics can be seen as emergence from groups of particles. Temperature, pressure, volume in air, and friction are all properties that are intrinsic to substances. At the same time, none of these properties are really there in single atoms or molecules. Atoms have a volume in and of themselves, true, but groups of atoms have volume and pressure that are kept up beyond the radius of the atoms themselves. Not all the atoms in a pool of water are striking you when you dive in, and yet they all add up to pressure that keeps you afloat.
In some ways, emergence can be reduced even to one of the properties of shape. Most people have played with a Mobius Strip, a strip of paper that can be twisted and turned into a loop that technically only has one side. Imagine doing that with a strip of toilet paper. No single square of the paper makes the strip into a one-sided paper. Each one has two sides. And yet when they're put together in a certain way, another property emerges. Almost anything can be more than the sum of its parts.
Image: Still from Video of Slime Mold Growing Across the US, Andy Adamatzky and Jeff Jones
Image 2: David Benbennick