In Theory

How Complex Wholes Emerge From Simple Parts

By John Rennie

December 20, 2018

Throughout nature, throngs of relatively simple elements can self-organize into behaviors that seem unexpectedly complex. Scientists are beginning to understand why and how these phenomena emerge without a central organizing entity.

Lottie Kingslake for Quanta Magazine

You could spend a lifetime studying an individual water molecule and never deduce the precise hardness or slipperiness of ice. Watch a lone ant under a microscope for as long as you like, and you still couldn’t predict that thousands of them might collaboratively build bridges with their bodies to span gaps. Scrutinize the birds in a flock or the fish in a school and you wouldn’t find one that’s orchestrating the movements of all the others.

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.

Our latest In Theory video on emergence explains more about how throngs of simple parts can self-organize into a more extraordinary whole:

How do extraordinarily complex emergent phenomena — like ants assembling themselves into living bridges, or tiny water and air molecules forming into swirling hurricanes — spontaneously arise from systems of much simpler elements? The answer often depends on a transition in the interplay between the elements that resembles a phase change.

Video: How do extraordinarily complex emergent phenomena — like ants assembling themselves into living bridges, or tiny water and air molecules forming into swirling hurricanes — spontaneously arise from systems of much simpler elements? The answer often depends on a transition in the interplay between the elements that resembles a phase change.

Directed by Emily Driscoll and animated by Lottie Kingslake for Quanta Magazine

Spooky as emergence can seem, a formal understanding of it might be within reach. Some researchers are looking for universal rules that would describe emergent phenomena in any system. Statistical procedures like renormalization can identify precisely when and how collective phenomena start to become more significant.

As a scientific concept, emergence has its critics, who find it too slippery and too uninformative to be useful. But if nothing else, emergence helps to illustrate why scientists find hierarchies of physical laws and processes operating at different scales throughout nature.

We hope you enjoyed this third episode from season two of Quanta’s In Theory video series. The previous installment described physicists’ efforts to exploit a “holographic duality” in their quest to develop a quantum theory of gravity — that is, to reinterpret gravity in terms of particles that fit within quantum mechanics. Season two launched in August with a video about a mysterious mathematical pattern that’s turning up all over math, physics and biology.

January 28, 2019, update: Episode four, about turbulent flows, is now available here.

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