BOOK REVIEW
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.