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Measuring Complexity

Daniel W. McShea

Cosmic Evolution: The Rise of Complexity in Nature. Eric J. Chaisson. xii + 274 pp. Harvard University Press, 2001. $27.95.

The universe seems to be getting more complex. In the first few moments of the Big Bang, 10 to 20 billion years ago, the universe contained only radiation, out of which condensed the elementary particles. As the universe expanded and cooled, these particles assembled to form simple atoms; gravitational attraction among atoms (mainly hydrogen) laid the foundations for galaxies; within galaxies, stars and planetary systems differentiated; and in these, with the emergence of the heavier elements, complex chemical, biological and ultimately cultural entities arose. In each transition, the complexity of the most complex structure in existence seems to have increased: Galaxies are more complex than atoms, stars are more complex than galaxies, and so on.

In presenting the history of complexity in Cosmic Evolution, Eric Chaisson appears to have two main goals. The first is to show that the increases in complexity are consistent with the second law of thermodynamics. The second law, in its statistical-mechanical interpretation, requires that disorder increase in closed systems, which means that complexity—understood, say, as the opposite of disorder—must decrease. However, a complex structure such as a galaxy, a star or an organism is an open system, able to generate and sustain complexity by exporting enough disorder to its surrounding environment to more than make up for its internal gains. In effect, the second law is satisfied because disorder increases in a larger system, one consisting of the complex structure plus its local, external environment. For example, the rise in complexity within a newly ignited star occurs at the cost of a much larger increase in disorder exported to the surrounding space in the form of radiation. In his classic 1944 essay, "What Is Life?," Erwin Schrödinger offered a similar account of the relationship between the second law and the origin and maintenance of complexity in organisms. In effect, Chaisson extends the argument to certain inanimate systems.

Chaisson's second goal is to show that the physical principle producing complexity in these disparate transitions is the same in each case. I understand this principle well enough to explain it only very roughly. Where strong energy gradients are present, conditions are sometimes right for the spontaneous emergence of structures that tend to dissipate the gradient. While the gradient persists, these structures may be stable, maintained in a (near) steady state of high complexity—that is, far from equilibrium in a statistical-mechanical sense—by the flow of energy through them. A classic example is a hurricane, a structure that arises in a thermal gradient between the upper and lower atmospheres. The structure is complex; it is also "dissipative" in that it facilitates the dissipation of the gradient by transferring warm air from the sea surface below to the cold upper atmosphere. Chaisson argues that stars are also complex dissipative structures, dissipating the energy gradients produced in clouds of hydrogen atoms collapsing under gravitational attraction. Organisms too are dissipative entities, complex structures arising and maintained in a kind of gradient between the high-free-energy chemical bonds of their food sources (or sunlight, in the case of photosynthesizers) and the low free energy of their waste products.

To make the case that complexity increases in systems as disparate as stars and organisms, we need an operational definition of complexity sufficiently broad that it can be applied to both. Otherwise, their complexities would not be comparable—that is, not graphable in any meaningful way (to show a trend, for example) on the same set of axes. To his credit, Chaisson provides a definition and then actually uses it. (Many treatments of this sort do not.) He proposes that we measure complexity as energy density, the rate of energy flow through a system per unit mass, or φ m . This quantity, he argues, is likely to be inversely correlated with degree of disorder and therefore positively correlated with complexity. This claim is somewhat problematic, I think (see below), but φ m does have the great virtue of being measurable in real systems. Indeed, Chaisson walks us through calculations of it for an impressive range of systems, including our sun (φ m ~ 2 ergs/sec/gram), the human brain (150,000 ergs/sec/gram) and human civilization (500,000 ergs/sec/gram). And in a fascinating table and a series of graphs, he shows that φ m increases from galaxy to society and therefore also increases over time.

Why is a trend expected in φ m ? My understanding, based on Chaisson's argument, is this: In a far-from-equilibrium system (including the universe as a whole), the dominant dissipative structures will be those that are able to capture the greatest part of the energy flow—that is, those with the highest energy density. Thus φ m should increase as new structures arise (via fluctuations or mutations) and the system discovers faster dissipative routes.

But why should these high-φ m structures be especially complex? The answer may be simply phenomenological; we observe that they are. But the answers typically given, including Chaisson's, imply that nonequilibrium thermodynamic theory has an explanation—that some logic exists whereby complexity is expected. Indeed, a logic may be present in the various technical treatments—I do not know. (Perhaps Chaisson will offer such a logic in his promised longer work, of which this book is only an abstract.) What does seem clear, however, is that no model, analogy or imagery has yet been devised that makes that logic clear to interested readers in other fields.

More worrisome is that in actual systems, complexity (as degree of order) seems to increase with φ m only up to a point, and then it decreases, as Chaisson acknowledges. There are a number of reasons for this. For example, in some cases, as φ m rises past some optimum, the flow of energy starts to tear the system apart, to destroy order. In any event, a consequence is that we do not really know, based solely on φ m values, that a human brain is more complex than the sun. Let me emphasize that despite this and other difficulties, Chaisson's use of φ m —and in particular his attempts to estimate it in real systems—offers a significant advance. Devising operational measures is the central problem in the search for systems-level principles, and Chaisson deserves considerable credit for adopting and applying this one so consistently.

I have other complaints, none of them serious. Difficulties (such as those I've noted) are downplayed. He should have highlighted them instead, to draw the attention of others who might solve them, building on his basic approach. Also, Chaisson is prone to using inflated language. For example, he writes that cosmic evolution "is a story about the awe and majesty of twirling galaxies and shining stars, of redwood trees and buzzing bees, of a Universe that has come to know itself. But it is also a story about our human selves—our origin, our existence, and perhaps our destiny." (Our destiny? As Chaisson points out more than once, the analysis is retrospective, not predictive.) Still, Chaisson's project—the search for unifying patterns of change across the largest temporal and spatial scales—is a worthy one. And the suggestion that the unifying patterns will have something to do with complexity, and even with the second law, is highly plausible. (A similar answer has been proposed by others: In my own field, evolution, similar themes run through the work of Jeffrey S. Wicken, Robert E. Ulanowicz, Daniel R. Brooks, Edward O. Wiley, Stanley N. Salthe and others.) If such principles exist, they will undoubtedly be systems-level principles that are concerned with complexity indirectly, if not directly, and probably with other variables at a similarly high level of abstraction. In other words, Chaisson's theory has the ring of rightness.



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