It's a topic we touch upon from time to time as it relates to things like how stock prices behave or how the economy works, but emergence is much more than that. Quanta Magazine's short 3-and-a-half-minute video from their In Theory series provides a taste of what it is and where else it is seen:
Quanta's John Rennie explains the wonderful way complex order comes into being:
Nature is filled with such examples of complex behaviors that arise spontaneously from relatively simple elements. Researchers have even coined the term “emergence” to describe these puzzling manifestations of self-organization, which can seem, at first blush, inexplicable. Where does the extra injection of complex order suddenly come from?
Answers are starting to come into view. One is that these emergent phenomena can be understood only as collective behaviors — there is no way to make sense of them without looking at dozens, hundreds, thousands or more of the contributing elements en masse. These wholes are indeed greater than the sums of their parts.
Another is that even when the elements continue to follow the same rules of individual behavior, external considerations can change the collective outcome of their actions. For instance, ice doesn’t form at zero degrees Celsius because the water molecules suddenly become stickier to one another. Rather, the average kinetic energy of the molecules drops low enough for the repulsive and attractive forces among them to fall into a new, more springy balance. That liquid-to-solid transition is such a useful comparison for scientists studying emergence that they often characterize emergent phenomena as phase changes.
If you have a spare hour and 13 minutes, you can hear economists Don Boudreaux, Mike Munger, and Russ Roberts discuss how emergent orders arise in human activities via an EconTalk podcast!