From Complexity to Perplexity
Can science achieve a unified theory of complex systems?by John
Horgan, senior writer
Champagne and big ideas are bubbling at the Museum of Indian
Arts and Culture in Santa Fe, N.M. The museum is hosting a dinner for the
Santa Fe Institute, where complex people ponder complex things. Some of
the institute's brightest luminaries are there, including Murray
Gell-Mann, Nobel laureate and co-discoverer of quarks, with his
permanently skeptical squint; artificial-life proselytizer Christopher G.
Langton, clad in his uniform of jeans, clodhoppers, leather vest and
silver bracelet; the ruddy-faced nonlinear economist W. Brian Arthur, who
has recently been taking calls from the White House; and world-class
intellectual riffer Stuart A. Kauffman, whose demeanor is at once cherubic
and darkly brooding. Mingling with these scientific pioneers are various
"friends of the institute," ranging from mega-philanthropist George Soros
to the best-selling novelist Cormac McCarthy.
the Santa Fe Institute, some researchers have their doubts
Before everyone tucks into the filet mignon, David Liddle, a computer
entrepreneur who chairs the board of trustees, reviews the institute's
accomplishments. "There is a lot to be proud of," he says. There certainly
is, at least from a public-relations standpoint. The institute is not
large: it supports only six full-time researchers in Santa Fe; 50
"external faculty" members work elsewhere. Nevertheless, in the decade
since its founding, the institute has enjoyed much favorable attention
from the press, including Scientific American, and has been
celebrated in several popular books. It has become renowned as a leading
center of complexity studies, a place where scientists impatient with the
stodgy, reductionist science of the past are creating a "new, unified way
of thinking about nature, human social behavior, life and the universe
itself" (as one book jacket put it).
What Liddle does not say is that even some scientists associated with
the institute are beginning to fret over the gap between such rhetoric and
reality. Take Jack D. Cowan, a mathematical biologist from the University
of Chicago who helped to found the institute and remains on its board.
Cowan is no scientific prude; he has explored the neurochemical processes
underlying the baroque visual patterns evoked by LSD. But some Santa Fe
theorists exhibit too high a "mouth-to-brain ratio" for his taste. "There
has been tremendous hype," he grumbles.
Cowan finds some work at Santa Fe interesting and important, but he
deplores the tendency of research there "to degenerate into computer
hacking." Too many simulators also suffer from what Cowan calls the
reminiscence syndrome. "They say, 'Look, isn't this reminiscent of a
biological or physical phenomenon!' They jump in right away as if it's a
decent model for the phenomenon, and usually of course it's just got some
accidental features that make it look like something." The major discovery
to emerge from the institute thus far, Cowan suggests, is that "it's very
hard to do science on complex systems."
Some residents blame the media for the exaggerated claims associated
with the institute. "Ninety percent of it came from journalists," Arthur
asserts. Yet the economist cannot help but play the evangelist. "If Darwin
had had a computer on his desk," he exclaims, "who knows what he could
have discovered!" What indeed: Charles Darwin might have discovered a
great deal about computers and very little about nature.
The grandest claim of Santa Fe'ers is that they may be able to
construct a "unified theory" of complex systems. John H. Holland, a
computer scientist with joint appointments at the University of Michigan
and the Santa Fe Institute, spelled out this breathtakingly ambitious
vision in a lecture two years ago: "Many of our most troubling long-range
problems-trade balances, sustainability, AIDS, genetic defects, mental
health, computer viruses-center on certain systems of extraordinary
complexity. The systems that host these problems-economies, ecologies,
immune systems, embryos, nervous systems, computer networks-appear to be
as diverse as the problems. Despite appearances, however, the systems do
share significant characteristics, so much so that we group them under a
single classification at the Santa Fe Institute, calling them complex
adaptive systems [CAS]. This is more than terminology. It signals our
intuition that there are general principles that govern all CAS behavior,
principles that point to ways of solving the attendant problems." Holland,
it should be said, is considered to be one of the more modest
Some workers now disavow the goal of a unified theory. "I don't even
know what that would mean," says Melanie Mitchell, a former student of
Holland's who is now at the SFI. "At some level you can say all complex
systems are aspects of the same underlying principles, but I don't think
that will be very useful." Stripped of this vision of unification,
however, the Santa Fe Institute loses much of its luster. It becomes just
another place where researchers are using computers and other tools to
address problems in their respective fields. Aren't all scientists doing
Scientists familiar with the history of other would-be unified theories
[see box on pages 108 and 109] are not sanguine about the prospects
for their brethren at Santa Fe. One doubter is Herbert A. Simon of
Carnegie Mellon University, a Nobel laureate in economics who has also
contributed to artificial intelligence and sociobiology. "Most of the
people who talk about these great theories have been infected with
mathematics," he says. "I think you'll see a bust on the notion of
unification." Rolf Landauer of IBM, who has spent his career exploring the
links between physics, computation and information, agrees. He accuses
complexologists of seeking a "magic criterion" that will help them unravel
all the messy intricacies of nature. "It doesn't exist," Landauer says.
The problems of complexity begin with the term itself. Complexologists
have struggled to distinguish their field from a closely related
pop-science movement, chaos. When all the fuss was over, chaos turned out
to refer to a restricted set of phenomena that evolve in predictably
unpredictable ways. Various attempts have been made to provide an equally
precise definition of complexity. The most widely touted definition
involves "the edge of chaos." The basic idea is that nothing novel can
emerge from systems with high degrees of order and stability, such as
crystals. On the other hand, completely chaotic systems, such as turbulent
fluids or heated gases, are too formless. Truly complex
things-amoebae, bond traders and the like-appear at the border between
rigid order and randomness.
Most popular accounts credit the idea to Christopher Langton and his
co-worker Norman H. Packard (who coined the phrase). In experiments with
cellular automata, they concluded that a system's computational
capacity-that is, its ability to store and process information-peaks in a
narrow regime between highly periodic and chaotic behavior. But
cellular-automaton investigations by two other SFI researchers, James P.
Crutchfield and Mitchell, did not support the conclusions of Packard and
Langton. Crutchfield and Mitchell also question whether "anything like a
drive toward universal-computational capabilities is an important force in
the evolution of biological organisms." Mitchell complains that in
response to these criticisms, proponents of the edge of chaos keep
changing their definition. "It's a moving target," she says.
Other definitions of complexity have been proposed-at least 31,
according to a list compiled several years ago by Seth Lloyd of the
Massachusetts Institute of Technology, a physicist and Santa Fe adjunct.
Most involve concepts such as entropy, randomness and information-which
themselves have proved to be notoriously slippery terms. All definitions
have drawbacks. For example, algorithmic informational complexity,
proposed by IBM mathematician Gregory J. Chaitin, holds that the
complexity of a system can be represented by the shortest computer program
describing it. But according to this criterion, a text created by a team
of typing monkeys is more complex-because it is more random-than
The Poetry of Artificial Life
Such problems highlight the awkward fact that complexity exists, in
some murky sense, in the eye of the beholder. At various times,
researchers have debated whether complexity has become so meaningless that
it should be abandoned, but they invariably conclude that the term has too
much public-relations value. Complexologists often employ "interesting" as
a synonym for "complex." But what government agency would supply funds for
research on a "unified theory of interesting things"? (The Santa Fe
Institute, incidentally, will receive about half its $5-million 1995
budget from the federal government and the rest from private benefactors.)
Complexologists may disagree on what they are studying, but most concur
on how they should study it: with computers. This faith in computers is
epitomized by artificial life, a subfield of complexity that has attracted
much attention in its own right. Artificial life is the philosophical heir
of artificial intelligence, which preceded it by several decades. Whereas
artificial-intelligence researchers seek to understand the mind by
mimicking it on a computer, proponents of artificial life hope to gain
insights into a broad range of biological phenomena. And just as
artificial intelligence has generated more portentous rhetoric than
tangible results, so has artificial life.
As Langton proclaimed in the inaugural issue of the journal
Artificial Life last year, "Artificial life will teach us much
about biology-much that we could not have learned by studying the natural
products of biology alone-but artificial life will ultimately reach beyond
biology, into a realm we do not yet have a name for, but which must
include culture and our technology in an extended view of nature."
Langton has promulgated a view known as "strong a-life." If a
programmer creates a world of "molecules" that-by following rules such as
those of chemistry-spontaneously organize themselves into entities that
eat, reproduce and evolve, Langton would consider those entities to be
alive "even if it's in a computer." Inevitably, artificial life has
begotten artificial societies. Joshua M. Epstein, a political scientist
who shuttles between Santa Fe and the Brookings Institution in Washington,
D.C., declares that computer simulations of warfare, trade and other
social phenomena will "fundamentally change the way social science is
Artificial life-and the entire field of complexity-seems to be based on
a seductive syllogism: There are simple sets of mathematical rules that
when followed by a computer give rise to extremely complicated patterns.
The world also contains many extremely complicated patterns. Conclusion:
Simple rules underlie many extremely complicated phenomena in the world.
With the help of powerful computers, scientists can root those rules out.
This syllogism was refuted in a brilliant paper published in
Science last year. The authors, led by philosopher Naomi Oreskes of
Dartmouth College, warn that "verification and validation of numerical
models of natural systems is impossible." The only propositions that can
be verified-that is, proved true-are those concerning "closed" systems,
based on pure mathematics and logic. Natural systems are open: our
knowledge of them is always partial, approximate, at best.
"Like a novel, a model may be convincing-it may ring true if it is
consistent with our experience of the natural world," Oreskes and her
colleagues state. "But just as we may wonder how much the characters in a
novel are drawn from real life and how much is artifice, we might ask the
same of a model: How much is based on observation and measurement of
accessible phenomena, how much is based on informed judgment, and how much
Numerical models work particularly well in astronomy and physics
because objects and forces conform to their mathematical definitions so
precisely. Mathematical theories are less compelling when applied to more
complex phenomena, notably anything in the biological realm. As the
evolutionary biologist Ernst Mayr of Harvard University has pointed out,
each organism is unique; each also changes from moment to moment. That is
why biology has resisted mathematicization.
Langton, surprisingly, seems to accept the possibility that artificial
life might not achieve the rigor of more old-fashioned research. Science,
he suggests, may become less "linear" and more "poetic" in the future.
"Poetry is a very nonlinear use of language, where the meaning is more
than just the sum of the parts," Langton explains. "I just have the
feeling that culturally there's going to be more of something like poetry
in the future of science."
A Critique of Criticality
A-life may already have achieved this goal, according to the
evolutionary biologist John Maynard Smith of the University of Sussex.
Smith, who pioneered the use of mathematics in biology, took an early
interest in work at the Santa Fe Institute and has twice spent a week
visiting there. But he has concluded that artificial life is "basically a
fact-free science." During his last visit, he recalls, "the only time a
fact was mentioned was when I mentioned it, and that was considered to be
in rather bad taste."
Not all complexologists accept that their field is doomed to become
soft. Certainly not Per Bak, a physicist at Brookhaven National Laboratory
who is on the Santa Fe faculty. The owlish, pugnacious Bak bristles with
opinions. He asserts, for example, that particle physics and
condensed-matter physics have passed their peaks. Chaos, too, had pretty
much run its course by 1985, two years before James Gleick's blockbuster
Chaos was published. "That's how things go!" Bak exclaims. "Once
something reaches the masses, it's already over!" (Complexity, of course,
is the exception to Bak's rule.)
Bak and others have developed what some consider to be the leading
candidate for a unified theory of complexity: self-organized criticality.
Bak's paradigmatic system is a sandpile. As one adds sand to the top of
the pile, it "organizes" itself by means of avalanches into what Bak calls
a critical state. If one plots the size and frequency of the avalanches,
the results conform to a power law: the probability of avalanches
decreases as their size increases.
Bak notes that many phenomena-including earthquakes, stock-market
fluctuations, the extinction of species and even human brain waves-display
this pattern. He concludes that "there must be a theory here." Such
a theory could explain why small earthquakes are common and large ones
uncommon, why species persist for millions of years and then vanish, why
stock markets crash and why the human mind can respond so rapidly to
"We can't explain everything about everything, but something about
everything," Bak says. Work on complex systems, he adds, will bring about
a "revolution" in such traditionally soft sciences as economics,
psychology and evolutionary biology. "These things will be made into hard
sciences in the next years in the same way that particle physics and
solid-state physics were made hard sciences."
In his best-seller Earth in the Balance, Vice President Al Gore
said Bak's theory had helped him to understand not only the fragility of
the environment but also "change in my own life." But Sidney R. Nagel of
the University of Chicago asserts that Bak's model does not even provide a
very good description of a sandpile. He and other workers at Chicago found
that their sandpile tended to oscillate between immobility and large-scale
avalanches rather than displaying power-law behavior.
Bak retorts that other sandpile experiments confirm his model.
Nevertheless, the model may be so general and so statistical in nature
that it cannot really illuminate even those systems it describes. After
all, many phenomena can be described by a Gaussian or bell curve. But few
scientists would claim that human intelligence scores and the apparent
luminosity of galaxies must derive from common causes. "If a theory
applies to everything, it may really apply to nothing," remarks the Santa
Fe researcher Crutchfield. "You need not only statistics but also
mechanisms" in a useful theory, he adds.
Another skeptic is Philip W. Anderson, a condensed-matter physicist and
Nobel laureate at Princeton University who is on the SFI's board. In "More
Is Different," an essay published in Science in 1972, Anderson
contended that particle physics and indeed all reductionist approaches
have only a limited ability to explain the world. Reality has a
hierarchical structure, Anderson argued, with each level independent, to
some degree, of the levels above and below. "At each stage, entirely new
laws, concepts and generalizations are necessary, requiring inspiration
and creativity to just as great a degree as in the previous one," Anderson
noted. "Psychology is not applied biology, nor is biology applied
"More is different" became a rallying cry for chaos and complexity.
Ironically, Anderson's principle suggests that these antireductionist
efforts may never culminate in a unified theory of complex systems, one
that illuminates everything from immune systems to economies. Anderson
acknowledges as much. "I don't think there is a theory of everything," he
comments. "I think there are basic principles that have very wide
generality," such as quantum mechanics, statistical mechanics,
thermodynamics and symmetry breaking. "But you mustn't give in to the
temptation that when you have a good general principle at one level it's
going to work at all levels."
Anderson favors the view of nature described by the evolutionary
biologist Stephen Jay Gould of Harvard, who emphasizes that life is shaped
less by deterministic laws than by contingent, unpredictable
circumstances. "I guess the prejudice I'm trying to express is a prejudice
in favor of natural history," Anderson says.
Anderson's views flatly contradict those of Stuart Kauffman, one of the
most ambitious of all the artificial lifers. Kauffman has spent decades
trying to show-through elaborate computer simulations-that Darwinian
theory alone cannot account for the origin or subsequent evolution of
Kauffman says he shares the concern of his former teacher John Maynard
Smith about the scientific content of some artificial-life research. "At
some point," he explains, "artificial life drifts off into someplace where
I cannot tell where the boundary is between talking about the
world-I mean, everything out there-and really neat computer games and
art forms and toys." When he does computer simulations, Kauffman
adds, he is "always trying to figure out how something in the world works,
or almost always."
Kauffman's simulations have led him to several conclusions. One is that
when a system of simple chemicals reaches a certain level of complexity or
interconnectedness (which Kauffman has linked both to the edge of chaos
concept and to Bak's self-organized criticality), it undergoes a dramatic
transition, or phase change. The molecules begin spontaneously combining
to create larger molecules of increasing complexity and catalytic
capability. Kauffman has argued that this process of
"autocatalysis"-rather than the fortuitous formation of a molecule with
the ability to replicate and evolve-led to life.
"Obscurantism and Mystification"
Kauffman has also proposed that arrays of interacting genes do not
evolve randomly but converge toward a relatively small number of patterns,
or "attractors," to use a term favored by chaos theorists. This ordering
principle, which Kauffman calls "antichaos," may have played a larger role
than did natural selection in guiding the evolution of life. More
generally, Kauffman thinks his simulations may lead to the discovery of a
"new fundamental force" that counteracts the universal drift toward
disorder required by the second law of thermodynamics.
In a book to be published later this year, At Home in the
Universe, Kauffman asserts that both the origin of life on the earth
and its subsequent evolution were not "vastly improbable" but in some
fundamental sense inevitable; life, perhaps similar to ours, almost
certainly exists elsewhere in the universe. Of course, scientists have
engaged in interminable debates over this question. Many have taken
Kauffman's point of view. Others, like the great French biologist Jacques
Monod, have insisted that life is indeed "vastly improbable." Given our
lack of knowledge of life elsewhere, the issue is entirely a matter of
opinion; all the computer simulations in the world cannot make it less so.
Kauffman's colleague Murray Gell-Mann, moreover, denies that science
needs a new force to account for the emergence of order and complexity. In
his 1994 book, The Quark and the Jaguar, Gell-Mann sketches a
rather conventional-and reductionist-view of nature. The probabilistic
nature of quantum mechanics allows the universe to unfold in an infinite
number of ways, some of which generate conditions conducive to the
appearance of complex phenomena. As for the second law of thermodynamics,
it permits the temporary growth of order in relatively isolated,
energy-driven systems, such as the earth.
"When you look at the world that way, it just falls into place!"
Gell-Mann cries. "You're not tortured by these strange questions anymore!"
He emphasizes that researchers have much to learn about complex systems;
that is why he helped to found the Santa Fe Institute. "What I'm trying to
oppose," he says, "is a certain tendency toward obscurantism and
Maybe complexologists, even if they cannot create a science for the
next millennium, can limn the borders of the knowable. The Santa Fe
Institute seemed to raise that possibility last year when it hosted a
symposium on "the limits of scientific knowledge." For three days, a score
of scientists, mathematicians and philosophers debated whether it might be
possible for science to know what it cannot know. After all, many of the
most profound achievements of 20th-century science-the theory of
relativity, quantum mechanics, Goedel's theorem, chaos theory-prescribe
the limits of knowledge.
Some participants, particularly those associated with the institute,
expressed the hope that as computers grow in power, so will science's
ability to predict, control and understand nature. Others demurred. Roger
N. Shepard, a psychologist at Stanford University, worried that even if we
can capture nature's intricacies on computers, those models might
themselves be so intricate that they elude human understanding. Francisco
Antonio Doria, a Brazilian mathematician, smiled ruefully and murmured,
"We go from complexity to perplexity." Everybody nodded.