The examples in this chapter demonstrate one of the most important ideas in complexity science: emergence. An emergent property is a characteristic of a system that results from the interaction of its components, not from their properties.
To clarify what emergence is, it helps to consider what it isn’t. For example, a brick wall is hard because bricks and mortar are hard, so that’s not an emergent property. As another example, some rigid structures are built from flexible components, so that seems like a kind of emergence. But it is at best a weak kind, because structural properties follow from well understood laws of mechanics.
In contrast, the segregation we see in Schelling’s model is an emergent property because it is not caused by racist agents. Even when the agents are only mildly xenophobic, the outcome of the system is substantially different from the intention of the agent’s decisions.
The distribution of wealth in Sugarscape might be an emergent property, but it is a weak example because we could reasonably predict it based on the distributions of vision, metabolism, and lifespan. The wave behavior we saw in the last example might be a stronger example, since the wave displays a capability — diagonal movement — that the agents do not have.
Emergent properties are surprising: it is hard to predict the behavior of the system even if we know all the rules. That difficulty is not an accident; in fact, it may be the defining characteristic of emergence.
As Wolfram discusses in A New Kind of Science, conventional science is based on the axiom that if you know the rules that govern a system, you can predict its behavior. What we call “laws” are often computational shortcuts that allow us to predict the outcome of a system without building or observing it.
But many cellular automatons are computationally irreducible, which means that there are no shortcuts. The only way to get the outcome is to implement the system.
The same may be true of complex systems in general. For physical systems with more than a few components, there is usually no model that yields an analytic solution. Numerical methods provide a kind of computational shortcut, but there is still a qualitative difference.
Analytic solutions often provide a constant-time algorithm for prediction; that is, the run time of the computation does not depend on
t, the time scale of prediction. But numerical methods, simulation, analog computation, and similar methods take time proportional to
t. And for many systems, there is a bound on
t beyond which we can’t compute reliable predictions at all.
These observations suggest that emergent properties are fundamentally unpredictable, and that for complex systems we should not expect to find natural laws in the form of computational shortcuts.
To some people, “emergence” is another name for ignorance; by this reckoning, a property is emergent if we don’t have a reductionist explanation for it, but if we come to understand it better in the future, it would no longer be emergent.
The status of emergent properties is a topic of debate, so it is appropriate to be skeptical. When we see an apparently emergent property, we should not assume that there can never be a reductionist explanation. But neither should we assume that there has to be one.
The examples in this book and the principle of computational equivalence give good reasons to believe that at least some emergent properties can never be “explained” by a classical reductionist model.