by Charles Baum
matter, energy, forces, and motions in almost every human experience.
The power of these laws lies in their universality. Each law can be ex-
pressed as an equation that applies to an infinite number of events,
from the interactions of atoms to the formation of galaxies. Armed
with these laws, scientists and engineers confidently analyze almost any
physical system, from steam engines to stars.
So sweeping and inclusive are these natural laws that some schol-
ars of the late nineteenth century suggested that the entire theoretical
framework of science had been deduced. All that remained to be dis-
covered were relatively minor details, like filling in the few remaining
gaps in a stamp collection. Though this turned out not to be the case—
modern physics research has revealed new phenomena at the relativis-
tic scales of the very small, the very fast, and the very massive—the
classic laws do indeed still hold sway in our everyday lives.
Yet in spite of centuries of labor by many thousands of scientists,
we do not fully understand one of nature’s most transforming phe-
nomena—the emergence of complexity. Systems as a whole do tend to
become more disordered with time, but at the local scale of a cell, an
ant colony, or your conscious brain, remarkable complexity emerges.
In the 1970s, the Russian-born chemist Ilya Prigogine recognized that
these so-called complex emergent systems arise when energy flows
through a collection of many interacting particles. The arms of spiral
galaxies, the rings of Saturn, hurricanes, rainbows, sand dunes, life,
consciousness, cities, and symphonies all are ordered structures that
emerge when many interacting particles, or “agents”—be they mol-
THE MISSING LAW
13
ecules, stars, cells, or people—are subjected to a flow of energy. In the
jargon of thermodynamics, the formation of patterns in these systems
helps to speed up the dissipation of energy as mandated by the second
law. Scientists and nonscientists alike tend to value the surprising or-
der and novelty of such emergent systems.
The recognition and description of such emergent systems pro-
vides a foundation for origin-of-life research, for life is the quintessen-
tial emergent phenomenon. From lifeless molecules emerged the first
living cell. If we can understand the principles governing such systems,
we may be able to apply those insights to our experimental programs.
DESCRIBING EMERGENT SYSTEMS
If you want to enunciate a law that characterizes emergent systems,
then the first step is to examine everyday examples. You can observe
emergent behavior in countless systems all around us, including the
interactions of atoms, or of automobiles, or of ants. This universal
tendency for systems to display increased order when lots of objects
interact, while fully consistent with the first and second laws of ther-
modynamics, is not addressed explicitly in either of those laws. We
have yet to discover if all emergent systems possess a unifying math-
ematical behavior, though our present ignorance should not seem too
unsettling. It took more than a half-century for each of the first two
laws of thermodynamics—describing the behavior of energy and en-
tropy, respectively—to develop from qualitative ideas into quantita-
tive laws. I suspect that a mathematical formulation of emergence will
be discovered much sooner than that, perhaps within the next decade
or two.
Scientists have already identified key aspects of the problem. Many
familiar natural systems lie close to equilibrium—that is, they are stable
and unchanging—and thus they do not display emergent behavior.
Water gradually cooled to below the freezing point equilibrates to be-
come a clear chunk of ice. Water gradually heated above the boiling
point similarly equilibrates by converting to steam. For centuries, sci-
entists have documented such equilibrium processes in countless care-
fully controlled scientific studies.
Away from equilibrium, dramatically different behavior occurs.
Rapidly boiling water, for example, displays complex, turbulent con-
vection. Water flowing downhill in the gravitational gradient of a river
14
GENESIS
valley interacts with sediments to produce the emergent landform pat-
terns of braided streams, meandering rivers, sandbars, and deltas.
These patterns arise as energetic water moves.
Emergent systems seem to share this common characteristic: They
arise away from equilibrium when energy flows through a collection of
many interacting particles. Such systems of agents tend spontaneously
to become more ordered and to display new, often surprising behav-
iors. And as patterns arise, energy is dissipated more efficiently, in ac-
cord with the second law of thermodynamics. Ultimately, the resulting
behavior appears to be much more than the sum of the parts.
Emergent patterns in water and sand may seem a far cry from liv-
ing organisms, but for scientists studying life’s origins there’s a big pay-
off in understanding such simple systems: Of all known emergent
phenomena, none is more dramatic than life, so studies of simpler
emergence can provide a conceptual basis, a jumping-off point, for
origin-of-life research.
QUANTIFYING THE COMPLEXITY OF
EMERGENT SYSTEMS
Even though emergent systems surround us, a rigorous definition
(much less a precise mathematical formulation) remains elusive. If we
are to discover a natural law that describes the behavior of emergent
systems, then we must first identify the essential properties of such
systems. But what characteristics distinguish emergent systems from
other less interesting collections of interacting objects?
All emergent systems display the rather subjective characteristic of
“complexity” —a property that thus far lacks a precise quantitative defi-
nition. In a colloquial sense, a complex system has an intricate or pat-
terned structure, as in a complex piece of machinery or a Bach fugue.
“Complexity” may also refer to information content: An advanced text-
book contains more detailed information, and is thus more complex,
than an elementary one. In this sense, the interactions of ants in an ant
colony or neurons in the human brain are vastly more complex than
the behavior of a pile of sand or a box of Cheerios.
Such complexity is the hallmark of every emergent system. What
scientists hope to find, therefore, is an equation that relates the proper-
ties of a system on the one hand (its temperature or pressure, for ex-
ample, expressed in numbers), to the resultant complexity of the
THE MISSING LAW
15
system (also expressed as a number) on the other. Such an equation
would in fact be the missing “law of emergence.” But before that is
possible we need an unambiguous, quantitative definition of the com-
plexity of a physical system. How to proceed?
A small band of scientists, many of them associated with the Santa
Fe Institut
e in New Mexico, have thought long and hard about com-
plex systems and ways to model them mathematically. But their efforts
yield surprisingly diverse (some would say divergent) views on how to
approach the subject.
John Holland, an ace at computer algorithms and a revered
founder of the field of emergence, models emergent systems as com-
puter programs with a fixed set of operating instructions. He suspects
that any emergent phenomenon, including sand ripples, ant colonies,
the conscious brain, and more, can be reduced to a set of selection
rules. Holland and his followers have made great strides in mimicking
natural phenomena with a few lines of computer code. Indeed, for
Holland and his followers the complexity of a system is closely related
to the minimum number of lines of computer code required to mimic
that system’s behavior.
A delightful example of this approach is BOIDS, a simple program
written by California programmer Craig Reynolds that duplicates the
movements of flocking birds, schooling fish, swarming insects, and
other collective animal behaviors with astonishing accuracy. (To check
it out on the Internet, just Google “BOIDS.”) Lest you think that this
effort is idle play, remember that computer programmers of video
games and Hollywood special effects have made a bundle on this type
of simulated emergent behavior. Think of BOIDS the next time you
watch dinosaur herds on the run in Jurassic Park, swarming locusts in
The Mummy, or schools of fish in Finding Nemo.
Physicist Stephen Wolfram, a mathematical prodigy who made
millions in his twenties from the elegant, indispensable computer pack-
age Mathematica, provides a complementary vision of emergent com-
plexity from simple rules. Like Holland, Wolfram was captivated by
the power of simple instructions to generate complex visual patterns.
Sensing a new paradigm for the description and analysis of the natural
world, he has spent the past 20 years developing what he calls “a new
kind of science” (NKS for short). A mammoth tome by that title pub-
lished in 2002 and an elaborate Web site (www.wolframscience.com)
illustrate some of the stunning ways whereby geometric complexity
16
GENESIS
may arise from simple rules. Perhaps, Wolfram argues, the complex
evolution of the physical universe and all it contains can be modeled as
a set of sequential instructions.
Many other ways to view complex systems have been proposed.
The late Danish physicist Per Bak described complex systems in terms
of a mathematical characteristic called “self-criticality.” These systems
evolve by repeatedly achieving a critical point at which they falter and
regroup, like a growing pile of sand that avalanches over and over again
as new grains are added. Santa Fe theorist Stuart Kauffman proposes
another tack, focusing on the emergence of chemical complexity via
competitive “autocatalytic networks,” by which collections of chemi-
cal compounds catalyze their own formation. And Nobel laureate
Murray Gell-Mann, who also works at the Santa Fe Institute, has re-
cently introduced a new parameter he calls “nonextensive entropy”—
a measure of the intrinsic complexity of a system—as a path to
understanding complex systems.
All these approaches and more inform the search for a law of emer-
gence; all provide a glimpse of the answer. Yet each seems too abstract
to apply to benchtop chemical experiments on the origin of life. An
experimentalist needs to decide on the nitty-gritty details: What should
be the starting chemicals at what concentrations; how acidic or basic
the solution; what run temperatures, pressures, and times? Is there any
way that the ideas of emergence can help?
A classic scientific approach to discovering general principles and
laws is to examine the behavior of specific systems. The study of simple
systems that display emergent behavior may well point to physical fac-
tors that lead to patterning in much more complex systems, including
life. We can hope that observations of specific systems will eventually
point to more general rules.
PATTERNS IN THE SAND
You don’t need a laboratory to observe emergent phenomena. In fact,
you can’t go on a hike without seeing dozens of examples of emer-
gence in action. Among my favorite emergent phenomena are inter-
actions of water and sand, which provide a convenient and compre-
hensible example of structures arising from the energetic interactions
of lots of agents (not to mention a great excuse to spend the day at the
shore). When moving water (or wind, for that matter) flows across a
THE MISSING LAW
17
flat layer of sand, new patterns arise. Periodic sand ripples appear, as
sand grains are sorted by size, shape, and density. The system thus
becomes more orderly and patterned as energy—the flow of wind or
water—dissipates.
My favorite emergent sandy system lies at the base of the fossil-
rich hundred-foot-tall cliffs that border the Chesapeake Bay’s western
shore in Calvert County, Maryland. Fifteen-million-year-old whale
bones, razor-sharp sharks’ teeth, branching bleached corals, and ro-
bust fist-sized clamshells abound in the wash zone, where waves con-
stantly wear away the soft sediments. Walks along those majestic
formations often lead to thoughts about the factors that contribute to
complexity.
At times of unusually low tide, especially near a new moon in the
cold clear winter months, receding waters expose a gently sloping pave-
ment of ancient sediments below the base of the cliff—a formation
called blue marl. Treacherously slippery when wet, this firm flat sur-
face commonly accumulates a thin layer of sand—particles that dis-
play emergent patterns when subjected to the wash of shallow water.
Over the years, I’ve noticed four distinct factors that contribute to the
emergence of complex sand patterning.
Factor 1: The Concentration of Agents
The first obvious factor in achieving a patterned, complex system is
simply the density of sand grains—that is, the number of interacting
particles per square centimeter of the blue marl’s surface. It’s easy to
estimate this number by collecting almost every grain of sand from an
area 10 centimeters square, about the size of a small paper napkin. I
collect the sand in a plastic bag or bottle, take it back to the lab, dry it,
and weigh the sample. Using a microscope, I count out 100 grains from
the sample and then weigh that batch. As it turns out, the total number
of grains per square centimeter is approximately equal to the total
weight of sand from the 100 square-centimeter (10 × 10) area divided
by the weight of 100 sand grains.
I find that with fewer than about 100 sand grains per square centi-
meter, the dusting of particles is too sparse for any noticeable patterns
to emerge. Given the minute size of the average sand grain, typically
less than half a millimeter in diameter, 100 grains per square
centime-
ter provides a sparse coverage over less than 10 percent of the smooth
18
GENESIS
A
B
C
Patterns in sand grains emerge as the concentration of grains increases. At about a thousand grains per square centimeter (A) small, black-topped piles are observed; at a few thousand grains per square centimeter (B) discontinuous bands arise; and
above 10,000 grains per square centimeter (C) continuous ripples cover the surface.
blue marl surface. Increase the sand concentration to about 1,000
grains per square centimeter, however, and an intriguing pattern of
regularly spaced sand piles, each a centimeter or two across, appears
on the hard blue surface. What’s more, a small circle of darker sand
grains typically crowns each little tan pile. Evidently a minimum con-
centration of several hundred grains per square centimeter is required
to initiate patterning in sand.
Increase the sand concentration slightly to a few thousand grains
per square centimeter and you get discontinuous short bands of sand
at right angles to the gentle back-and-forth wave motion of the shal-
low water. As with the mini-sandpiles, each tan band is topped by a
line of darker grains. And as sand concentration exceeds 10,000 grains
per square centimeter, continuous, evenly spaced, black-capped ripples
form across the hard pavement. I’ve seen this classic rippled surface
cover hundreds of square meters of shallow water in patterns so hyp-
notically regular that I hesitated to disturb the symmetry by walking
on it.
THE MISSING LAW
19
And that’s it. Higher concentrations of sand simply provide a
deeper base for the regular ripples. Buried sand grains don’t partici-
pate in the process so no new structures arise beyond the elegant, wave-
like, periodic forms on the surface.
This systematic behavior suggests that the concentration of inter-
acting agents plays a fundamental role in the emergent complexity of a
system. Below a critical threshold, no patterns are seen. As particle con-
centrations increase, so too does complexity, but only to a point. Above
a critical saturation of agents, we find no new behaviors.
Similar observations have been made about other emergent sys-
tems. One ant species— Eciton burchelli, the army ant—stays close to