Complexity

The Limits of Reductionism

Classical science and engineering have successfully used a reductionist methodology, that is, separating and simplifying phenomena in order to predict their future. This approach has been applied in a variety of domains. Nevertheless, in recent decades, the limits of reductionism have become evident in phenomena where interactions are relevant. Since reductionism separates, it has to ignore interactions. If interactions are relevant, reductionism is not suitable for studying complex phenomena.

[Page 135]There are plenty of phenomena that are better described from a nonreductionist or “complex” perspective. For example, insect swarms, flocks of birds, schools of fish, herds of animals, and human crowds exhibit a behavior at the group level that cannot be determined or predicted from individual behaviors or rules. Each animal makes local decisions depending on the behavior of its neighbors, thus interacting with them. Without interactions—that is, with reductionism—the collective behavior cannot be described. Through interactions, the group behavior can be well understood. This also applies to cells, brains, markets, cities, ecosystems, and biospheres.

In complex systems, having the “laws” of a system, plus initial and boundary conditions, are not enough to make a priori predictions. Since interactions generate novel information that is not present in initial or boundary conditions, predictability is limited. This is also known as computational irreducibility; that is, there is no shortcut to determine the future state of a system other than actually computing it.

Since classical (nonquantum mechanical) science and (versions of) philosophy assume that the world is predictable in principle, and relevant interactions limit predictability, many people have argued that a paradigm shift is required, and several novel proposals have been put forward in recent years.

The Complexity of “Complexity”

There is a broad variety of definitions of complexity, depending on the context in which the term is used. For example, the complexity of a string of bits—a sequence of zeroes and ones—can be described in terms of how easy it is to produce or compress that string. In this view, a simple string (e.g., “010101010101”) would be easily produced or compressed, as opposed to a more “random” one (e.g., “011010010000”). However, some people make a distinction between complexity and randomness, placing complexity as a balance between “ordered” and “chaotic” dynamics.

...