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By Root 442 0

behaviors of complex systems that interest us are not understandable at the level of elementary particles or ten-dimensional strings. Even if these elements make up all of reality, they are the wrong vocabulary for explaining complexity. It would be like answering the question, “Why is the logistic map chaotic?” with the answer, “Because xt+1 = R xt (1 − xt).” The explanation for chaos is, in some sense, embedded in the equation, just as the behavior of the immune system would in some sense be embedded in a Grand Unified Theory of physics. But not in the sense that constitutes human understanding—the ultimate goal of science. Physicists Jim Crutchfield, Doyne Farmer, Norman Packard, and Robert Shaw voiced this view very well: “[T]he hope that physics could be complete with an increasingly detailed understanding of fundamental physical forces and constituents is unfounded. The interaction of components on one scale can lead to complex global behavior on a larger scale that in general cannot be deduced from knowledge of the individual components.” Or, as Albert Einstein supposedly quipped, “Gravitation is not responsible for people falling in love.”

So if fundamendal physics is not to be a unified theory for complex systems, what, if anything, is? Most complex systems researchers would probably say that a unified theory of complexity is not a meaningful goal at this point. The science of physics, being over two thousand years old, is conceptually way ahead in that it has identified two main kinds of “stuff”—mass and energy—which Einstein unified with E = mc2. It also has identified the four basic forces in nature, and has unified at least three of them. Mass, energy, and force, and the elementary particles that give rise to them, are the building blocks of theories in physics.

As for complex systems, we don’t even know what corresponds to the elemental “stuff” or to a basic “force”; a unified theory doesn’t mean much until you figure out what the conceptual components or building blocks of that theory should be.

Deborah Gordon, the ecologist and entomologist voiced this opinion:

Recently, ideas about complexity, self-organization, and emergence—when the whole is greater than the sum of its parts—have come into fashion as alternatives for metaphors of control. But such explanations offer only smoke and mirrors, functioning merely to provide names for what we can’t explain; they elicit for me the same dissatisfaction I feel when a physicist says that a particle’s behavior is caused by the equivalence of two terms in an equation. Perhaps there can be a general theory of complex systems, but it is clear we don’t have one yet. A better route to understanding the dynamics of apparently self-organizing systems is to focus on the details of specific systems. This will reveal whether there are general laws. . . . The hope that general principles will explain the regulation of all the diverse complex dynamical systems that we find in nature can lead to ignoring anything that doesn’t fit a pre-existing model. When we learn more about the specifics of such systems, we will see where analogies between them are useful and where they break down.

Of course there are many general principles that are not very useful, for example, “all complex systems exhibit emergent properties,” because, as Gordon says, they “provide names for what we can’t explain.” This is, I think, what I was trying to say in the statement of mine that Horgan quoted. I think Gordon is correct in her implication that no single set of useful principles is going to apply to all complex systems.

It might be better to scale back and talk of common rather than general principles: those that provide new insight into—or new conceptualizations of—the workings of a set of systems or phenomena that would be very difficult to glean by studying these systems or phenomena separately, and trying to make analogies after the fact.

The discovery of common principles might be part of a feedback cycle in complexity research: knowledge about specific complex systems is synthesized