Complexity: An Emerging Trend in Social Sciences
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Complexity: An Emerging Trend
in Social Sciences
J. STEPHEN LANSING
Abstract
The social sciences have had a good run with linear models, in which effects are proportionate to their causes. Nearly all of our theoretical models, in fields as diverse
as microeconomics and evolutionary game theory, are equilibrium theories, which
examine the properties of various fixed points and analyze the conditions under
which they are selected. In contrast, “complexity” uses different mathematical tools
to investigate nonlinear processes. But linear models have the advantages of simplicity and power. Is there a real need to import the theoretical apparatus of “complexity” into the social sciences? Or might it be merely the latest example of Fashionable
Nonsense?
As it turns out, one need not seek very far to discover nonlinear dynamics in the social
world. And if more than one attractor exists, the resulting variation in dynamical
behavior will be mistaken for noise if one assumes linearity. In the past two or three
decades, interest in complexity has burgeoned across the social sciences. Under the
banner of complexity, researchers have investigated questions as dissimilar as the
causes of the Maya collapse, the spread of disease, the origins of syntax, the structural
properties of cities, and the evolution of culture. Presently, the mathematical tools
needed to analyze complexity present an entry barrier for many social scientists. But
generation time in graduate schools is short, and the physicists who have taken the
lead in the application of complexity to social science are beginning to have their
elbows jostled by social scientists with a new set of skills. As for the likely impact,
it is still early days. But one change that is already visible on the horizon has to do
with history, which plays no role in equilibrium analysis, but is intrinsic to many of
the questions and methods developed to study complex systems.
INTRODUCTION
The social sciences have had a good run with linear models, in which effects
are proportionate to their causes. Nearly all of our theoretical models, in
fields as diverse as microeconomics and evolutionary game theory, are
equilibrium theories, which examine the properties of various fixed points
and analyze the conditions under which they are selected. In contrast,
“complexity” uses different mathematical tools to investigate nonlinear
Emerging Trends in the Social and Behavioral Sciences. Edited by Robert Scott and Stephen Kosslyn.
© 2015 John Wiley & Sons, Inc. ISBN 978-1-118-90077-2.
1
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EMERGING TRENDS IN THE SOCIAL AND BEHAVIORAL SCIENCES
processes. Nonlinear phenomena are well known in physics, and are
ubiquitous in living systems. Consequently, as Stanislaw Ulam is said to
have quipped, the term nonlinear science is like calling zoology “the study of
non-elephant animals.”
Still, linear models have the advantages of simplicity and power. Moreover,
they may be well suited to the social sciences, which are mostly concerned
with the purposive behavior of rational agents and institutions. Further, there
is as yet no mathematical definition of complexity, nor is there a theory of
what causes it to arise. So, is there a real need to import the theoretical apparatus of “complexity” into the social sciences? Or might it be merely the latest
example of Fashionable Nonsense (Sokal & Bricmont, 1999), a sexy import from
physics that has at most a tangential relevance to the Geisteswissenschaften?
COMPLEXITY IN PHYSICS AND BIOLOGY
To address this question, it may be helpful to begin with a brief overview
of the origins and meaning of “complexity” in the natural sciences. In 1948,
Warren Weaver distinguished two forms of complexity: “disorganized
complexity”, which can be analyzed with probability theory and statistical
mechanics, and “organized complexity” which requires “dealing simultaneously with a sizable number of factors which are interrelated into an organic
whole” (Weaver, 1948). In another seminal paper, “More is Different,” Philip
Anderson argued in 1972 that understanding complexity involves a concept
of emergent properties: “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. Psychology is not applied biology
nor is biology applied chemistry” (Anderson, 1972). Anderson concluded
by quoting Karl Marx’s observation that over time, quantitative differences
become qualitative differences. Four years later, Robert May observed that
“the very simplest nonlinear difference equations can possess an extraordinarily rich spectrum of dynamical behavior, from stable points, through
cascades of stable cycles, to a regime in which the behavior (although fully
deterministic) is in many respects ‘chaotic’, or indistinguishable from the
sample function of a random process” (May, 1976). May’s now-canonical
example was the logistic equation. It is a good place to begin, because it
demonstrates how both linear and nonlinear patterns can emerge from a
simple equation for population growth, in which x is the population and r is
its intrinsic growth rate:
xnext = rx(1 − x)
For most values of r, the equation is linear: increase in x is proportionate to
the increase in r. But at r = 3.44949, the population begins to oscillate between
Complexity: An Emerging Trend in Social Sciences
3
1.0
0.8
0.6
x
0.4
0.2
0.0
2.4
2.6
2.8
3.0
3.2
r
3.4
3.6
3.8
4.0
Figure 1 The logistic map, showing linear, cyclical and chaotic behavior at
different values of the intrinsic growth rate, r. Source: Creative Commons.
http://en.wikipedia.org/wiki/File:Logistic_Bifurcation_map_High_Resolution.png#
filelinks
two values (Figure 1). Between 3.44949 and 3.54409 it oscillates between four
values, after which slight increases lead to oscillations between 8, 16, 32, and
so on. At 3.56995, regular oscillations begin to be replaced by chaotic fluctuations. At these growth rates, tiny differences in the initial population yield all
possible ending populations within a given range. Even more surprisingly,
between 3.56995 and 3.82843 several islands of stability appear (Figure 1).
Thus, merely varying the growth rate in the simplest possible equation for
population growth generates linear, oscillatory, or chaotic behavior. In the
language of complexity, or more specifically of nonlinear dynamics, each of
these is called a regime, or attractor. As long as the growth rate is less than
3.44949, the behavior is linear. But if the growth rate happens to fall in the
chaotic regime, prediction is impossible, even if all the parameters are exactly
known (May, 1976, p. 466).
This simple example allows us to make three observations. First, one need
not seek very far to discover nonlinear processes. Second, linear or equilibrium models will not explain nonlinear systems. And third, less obviously, if
more than one attractor or regime exists, the resulting variation in dynamical
behavior will be mistaken for noise if one assumes linearity. The last point is
particularly important for social science, and we will return to it below. But
before doing so, two practical questions will be addressed. First, how relevant are the mathematics of nonlinear dynamics to real-world phenomena?
Second, what kinds of insights or explanations are possible if more than one
attractor exists, or if a particular system does not settle down into a single,
stable equilibrium?
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EMERGING TRENDS IN THE SOCIAL AND BEHAVIORAL SCIENCES
COMPLEX SYSTEMS
To address these questions, it is useful to distinguish between complex
systems and complex adaptive systems. A good example of the former
is self-organized criticality (SOC), for which the canonical example is not
an equation, but an experiment often performed by toddlers at the beach
(Bak, Tang, & Wiesenfeld, 1987). Take a flat surface, dribble grains of sand
on it until it becomes a pile, and observe the occasional avalanches that
occur as the sides grow steep. As the grains of sand continue to fall, the
avalanches continue, so that the steepness of the sides of the pile remains
constant. At this point, the sandpile has reached its attractor, where the size
of the avalanches (the number of grains of sand that move) is inversely
related to their frequency. This system has several interesting features,
notably that it is self-organizing and produces a robust pattern of emergent,
scale-invariant behavior. Many social and cultural phenomena exhibit
identical patterns, where the size of events such as earthquakes is inversely
related to their frequency. SOC spontaneously generates scale-free networks,
in which the degree distribution of nodes (how many connections they
possess to other nodes) is inversely related to their frequency. Thus, SOC
is governed by a single attractor that produces a characteristic signature,
which can be easily detected for a large swath of phenomena, from sandpiles
to stock markets, citation networks, the World Wide Web, and financial
markets.
Sand piles have a single attractor. The possibility that real-world CS might
contain more than one attractor was demonstrated by the discovery of
alternate stable states in Dutch lakes. For decades, excess fertilizer flowed
into the lakes, triggering algae blooms and eutrophication. But reducing
the amount of fertilizer entering the lakes was not enough to restore them
to clarity. It turned out that alternate stable states or attractors existed, one
turbid and the other clear. In ecology, such alternate stable states or attractors
are called regimes. The effects of nutrient flows depended on which regime
a lake was in, so generalizing across all lakes obscured these differences.
But once the existence of alternate regimes was recognized, a simple intervention was sufficient to restore the lakes to health. Temporarily removing
the fish allowed sediment to settle and zooplankton populations to increase,
whereupon water clarity could be improved by reducing the amount of
fertilizer flowing into the lakes (Attayde, Van Nes, Araujo, Corso, & Scheffer,
2010). The comparative study of such processes by ecologists produced
new theoretical insights into transitions between attractors. As a dynamical
system approaches the boundary between alternate attractors, it will exhibit
certain generic properties. These telltale signs have by now been observed
in many natural systems (Scheffer et al., 2009). This phenomenon has yet to
Complexity: An Emerging Trend in Social Sciences
5
be conclusively demonstrated for social phenomena, but it has triggered a
lot of interest, because of the potential relevance for understanding critical
transitions in social systems.
COMPLEX ADAPTIVE SYSTEMS: HIDDEN ORDER
As we have just seen, CS are simply aggregates of interacting elements. If the
elements are agents, in other words if they exhibit purposive or goal-seeking
behavior, then they form a CAS. CASs are ubiquitous in living systems, and
we are beginning to notice them in the social world. Is a given social system
composed of adaptive agents, and does it produce emergent behaviors that
arise from their aggregate behavior? What might such emergent behaviors
look like? When do quantitative differences turn into qualitative transformations? Similar to the logistic equation for populations described earlier, even
the simplest examples of CASs can contain surprises. To see this, we can turn
the logistic equation into an evolving CAS by adding a single environmental
parameter, so that growth is affected by something in the environment. The
resulting model, created in 1992, helped trigger a revolution in the environmental sciences.
The model is called Daisyworld (Lovelock, 1992), and the environmental
variable is temperature. Daisyworld is an imaginary planet orbiting a star
similar to the Sun and at the same orbital distance as the Earth. The surface
of Daisyworld is fertile earth sown uniformly with daisy seeds. The daisies
vary in color, and daisies of similar color grow together in patches. As sunshine falls on Daisyworld, the model tracks changes in the growth rate of each
variety of daisy, and changes in the amount of the planet’s surface covered
by different-colored daisies.
The simplest version of this model contains only two varieties of daisies,
white and black. Black daisies absorb more heat than bare earth, while whites
reflect sunshine. Clumps of same-colored daisies create a local microclimate
for themselves, slightly warmer (if they are black) or cooler (if white) than
the mean temperature of the planet.
Both black and white daisies grow fastest and at the same rate when
their local effective temperature (the temperature within their microclimate)
is 22.5 ∘ C, and they respond identically, with a decline in growth rate, as
the temperature deviates from this ideal. Consequently, at a given average planetary temperature, black and white daisies experience different
microclimates and therefore different growth rates.
If the daisies cover a sufficiently large area of the surface of Daisyworld,
their color affects not only their own microclimate but also the albedo or
reflectance of the planet as a whole. As with our own sun, the luminosity
of Daisyworld’s star is assumed to have gradually increased. A simulation
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EMERGING TRENDS IN THE SOCIAL AND BEHAVIORAL SCIENCES
70
Mean temperature (°)
2
2
30
2
1
1
1
1
2
−10
0.75
0.95
1.15
Luminosity
1.35
1.55
Figure 2 Simulated temperature regulation on Daisyworld. As the luminosity of
its aging sun increases from 0.75 to 1.5 times the average value, the temperature
of a bare planet would steadily rise (line 2). In contrast, the temperature of
Daisyworld stabilizes close to 22.5 ∘ C with daisies present (line 1).
of life on Daisyworld begins in the past with a cooler sun. This enables the
black daisies to spread until they warm the planet. Later on, as the sun grows
hotter, the white daisies grow faster than black ones, cooling the planet.
So over the history of Daisyworld, the warming sun gradually changes the
proportion of white and black daisies, creating the global phenomenon of
temperature regulation: The planet’s temperature is held near the optimum
by and for the daisies, as shown in Figure 2.
Imagine that a team of astronauts and planners is sent to investigate Daisyworld. They would have plenty of time to study the only living things on
the planet, and they would almost certainly conclude that the daisies had
evolved to grow best at the normal temperature of the planet, 22.5 ∘ C. But
this conclusion would invert the actual state of affairs. The daisies did not
adapt to the temperature of the planet; instead, they adapted the planet to suit
themselves (Saunders, 1994). A Daisyworld without daisies would track the
increase in the sun’s luminance (line 2), rather than stabilizing near the ideal
temperature for daisies (line 1). Only when the sun’s luminosity becomes
too hot for the daisies to control will the daisy’s former role in temperature
stabilization become apparent.
Lacking this understanding, planners hoping to exploit Daisyworld’s
economic potential for the interstellar flower trade would fail to appreciate
the possible consequences of different harvesting techniques. While selective
flower harvests would cause small, probably unnoticeable tremors in planetary temperature, clear-cutting large contiguous patches of daisies would
create momentary changes in the planet’s albedo that could quickly become
permanent, causing temperature regulation to fail and daisy populations to
crash.
Complexity: An Emerging Trend in Social Sciences
7
The Daisyworld model soon became the canonical example of a selforganizing, self-regulating environmental system. As an example of a CAS,
it has several interesting features. The biology is as simple as its creator,
James Lovelock, could make it. The model shows how small-scale local
adaptations can produce an emergent global structure; and it also shows
why such global structures can easily fade from view, becoming noticeable
only when the system as a whole has been pushed to its limits. But is
Daisyworld simply a mathematical curiosity? Does it have any relevance to
the social sciences?
Something very similar to the Daisyworld catastrophe occurred in the 1980s
in the rice terraces of Bali. Because this case has been discussed extensively
elsewhere,1 here I provide only a summary highlighting the parallel with the
imaginary failure of temperature regulation on Daisyworld. In the 1970s, the
Asian Development Bank became involved in an effort to boost rice production in Indonesia. The bank’s consultants learned that on Bali, local groups of
farmers synchronize their irrigation schedules. In most regions, these schedules produced two rice harvests of native Balinese rice per year. The consultants saw two ways to improve harvests. The first was to encourage the
farmers to grow higher yielding “Green Revolution” rice varieties, which
produce more grain than native Balinese rice. The second recommendation
took advantage of another feature of the new rice: it grows faster than native
rice. Consequently, the farmers could plant more frequently. The Ministry of
Agriculture adopted both recommendations, and competitions were created
to reward the farmers who produced the best harvests. By 1977, 70% of the
southern Balinese “rice bowl” was planted with Green Revolution rice, and
soon after, planting native rice was forbidden.
At first, rice harvests improved. But a year or two later, Balinese agricultural and irrigation workers began to report “chaos in water scheduling”
and “explosions of pest populations.” At the time, planners dismissed these
occurrences as coincidence, and recommended higher doses of pesticides.
However, the parallel with Daisyworld offers an alternative explanation for
the harvest decline (Lansing & Fox, 2011). On Daisyworld, the growth of
the flowers was driven by a single environmental parameter: temperature. A
model of Balinese farming as a CAS requires two environmental parameters,
water and pests.
Traditionally, Balinese rice farmers manage their fields collectively in
organizations called subak. Because irrigation depends on seasonal rainfall,
each subak’s choice of an irrigation schedule affects the availability of water
for their neighbors downstream. The timing of irrigation can also be used
to control rice pests such as rats, insects, and insect-borne diseases. This is
1. Perfect Order: Recognizing Complexity in Bali. Princeton University Press, 2006. Julian Steward Prize,
American Anthropological Association. Lansing and de Vet (2012)
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EMERGING TRENDS IN THE SOCIAL AND BEHAVIORAL SCIENCES
accomplished by synchronizing rice harvests and then briefly flooding the
fields, thus depriving the pests of their habitat. The larger the area that is
encompassed by the post-harvest flooding, the fewer the pests. But if too
many subaks try to flood their fields at the same time, there will not be
enough water to go around.
To test the ability of the subaks to discover effective solutions to this
trade-off between pest control and water shortages, we constructed a
forward-in-time simulation model (Lansing & Kremer, 1993).
By simple trial and error, each subak seeks to discover an irrigation schedule that minimizes losses due to pests or water shortages. A patchwork of
synchronized irrigation schedules soon emerges in the model, as groups
of subaks adopt identical cropping schedules. As this occurs, rice harvests
improve because water shortages and pest damage are reduced for the entire
watershed. When the key environmental parameters are stabilized, variation
in harvests declines because these benefits spread across the entire system.
Conceptually, the model is similar to Daisyworld, except that the flowers of
Daisyworld adapt to a single environmental parameter (temperature), while
the Balinese farmers adapt to two (pest infestations and water availability).
As with Daisyworld, it is an example of a self-organizing CAS, in which the
agents are subaks.2
Meanwhile, in Bali, the Green Revolution inadvertently created an experimental test of this model. The farmers were told to plant as often as possible,
and set aside their traditional system of synchronized planting. This effect
can be replicated in the model by running it backwards, and breaking up
the co-evolved patterns of synchronized planting schedules. In the model,
this produces water shortages and exploding pest populations. When this
actually happened in Bali, consultants for the Asian Development Bank interpreted them as chance misfortunes, and urged the farmers to apply higher
doses of pesticides while continuing to plant as often as possible. But even
very high doses of pesticides proved ineffective. It was only when the farmers spontaneously returned to synchronized planting schemes that harvests
began to recover; a point subsequently acknowledged by the final evaluation
team from the Bank:
Substitution of the “high technology and bureaucratic” solution in the end
proved counterproductive, and was the major factor behind the yield and
cropped area declines experienced between 1982 and 1985 … The cost of the
2. Interestingly, when the subaks along a river settle down into a globally optimal patchwork of irrigation schedules, the correlation between their cropping patterns resembles a collection of nesting Russian
dolls. That is, a patch of subaks following the same irrigation schedule will find itself inside a larger patch
containing several irrigation schedules. If the river system is large enough, these patches in turn may be
embedded in larger ones. At this point, the entire system is at or near its critical point, with correlations
between irrigation schedules at all lengths, resembling an Ising model of spin glasses.
Complexity: An Emerging Trend in Social Sciences
9
lack of appreciation of the merits of the traditional regime has been high.
Project experience highlights the fact that the irrigated rice terraces of Bali
form a complex artificial ecosystem, which has been recognized locally over
centuries.3
ISLANDS OF ORDER
Granting that exotic mathematical models may shed new light on the gardens of Bali and Daisyworld, a skeptic might be forgiven for wondering if
complexity has any broader relevance to social science. In fields such as theoretical ecology, bold claims about the ubiquity of nonlinear systems have
been backed up by many recent empirical studies. But in the social sciences,
empirical studies are just beginning, and they tend to be spearheaded by
physicists and mathematicians rather than social scientists. There are, however, some intriguing results, such as the recent discovery that a great many
properties of cities, from patent production and personal income to crime,
innovation, and the speed at which people walk and talk are power law functions of population size (Bettencourt, Lobo, Helbing, Kühnert, & West, 2007).
There has also been a very productive conversation between mathematicians
and social scientists about the dynamic properties of networks. Still, is there
more to complexity than the piecemeal application of mathematical ideas
about nonlinear dynamics to the social sciences?
This question has recently been addressed by theorists of “complexity economics,” notably Brian Arthur. Arthur argues that complexity offers nothing
less than a new foundation for economics:
Complexity economics builds from the proposition that the economy is not
necessarily in equilibrium: economic agents (firms, consumers, investors)
constantly change their actions and strategies in response to the outcome they
mutually create. This further changes the outcome, which requires them to
adjust afresh. Agents thus live in a world where their beliefs and strategies
are constantly being “tested” for survival within an outcome or “ecology”
these beliefs and strategies together create. Economics has largely avoided
this nonequilibrium view in the past, but if we allow it, we see patterns or
phenomena not visible to equilibrium analysis. These emerge probabilistically,
last for some time and dissipate, and they correspond to complex structures in
other fields.4
Consequently, Arthur concludes, “complexity economics is not a special
case of neoclassical economics. On the contrary, equilibrium economics is
3. Project Performance Audit Report, Bali Irrigation Project in Indonesia; Asian Development Bank
1988.
4. Arthur (2013). For an earlier formuation of these ideas, see Arthur (1999).
10
EMERGING TRENDS IN THE SOCIAL AND BEHAVIORAL SCIENCES
a special case of nonequilibrium and hence complexity economics.” Still, it
may take a rather large push to persuade social scientists to adopt this perspective. Are there really “patterns or phenomena not visible to equilibrium
analysis,” waiting to be discovered?
As before, I offer a simple example. The simplest of all games used by social
scientists to study altruism and pro-social behavior is the “Dictator Game”
(Kahneman, Knetsch, & Thaler, 1986). It is so simple that, strictly speaking, it
is not a game. To play it, a “proposer” determines an allocation (split) of some
endowment, such as a cash prize. The second player, the “responder”, simply receives the remainder of the endowment left by the proposer. In typical
cross-cultural studies, the experimenter gives each proposer the local equivalent of a day’s wage, and explains that they may share as much or as little
as they choose with another player who is present. Players are assured that
the identity of both givers and receivers will not be revealed. For example, a
recent study compared offers in the Dictator Game in 15 societies (Henrich
et al., 2010). Variation in the average generosity of the players, from one society to the next, was interpreted as support for a hypothesis about the need
to trust strangers in larger and more complex societies. To simplify this relationship, the authors constructed a scale of “market integration”: how much
of one’s food is purchased in the market, versus grown at home?
But do whole societies gravitate towards an equilibrium level of prosociality? Or might this assumption obscure the possibility that more than
one attractor exists? To find out, we asked farmers in eight Balinese subaks to
play the Dictator Game. The subaks in this study are located along the Sungi
River in central Bali. Social surveys showed that four upstream subaks were
more satisfied with their harvests, and their subak, than four downstream
subaks. For the Dictator Game, a group of farmers in each subak were
randomly selected as proposers, given the cash equivalent of a day’s wage,
and offered the chance to share as much or as little as they chose to a fellow
member of their subak, selected at random. The identities of both proposers
and recipients were concealed. Results are shown in Figure 3.
The average offer for the entire sample of farmers was 30% with a large variance, at the low end of the scale in cross-cultural studies. Buried within this
variance, however, were contrasting patterns: Farmers in the downstream
subaks were less generous overall, while the most generous farmers of all
were those in the two upstream subaks experiencing water shortages. Thus,
the variance in responses between the two groups appears to be meaningful, suggesting the presence of more than one attractor. This conclusion was
amply supported by a follow-up study. A simple survey of farmer’s opinions revealed that the upstream and downstream groups experience similar social and environmental conditions, but respond to them in different
ways. For example, differences in class and caste exist in all eight subaks, but
Complexity: An Emerging Trend in Social Sciences
11
0.5
Downstream
Upstream
0.45
Offer
0.4
0.35
0.3
0.25
0.2
2
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
3
Subak condition
Figure 3 Offers in the Dictator Game in eight Balinese subaks. Among the
downstream subaks, the worse the condition of one’s subak, the smaller the offer.
The opposite pattern emerged in the upstream subaks: the worse the state of
one’s subak, the more generous the offer. These correlations have opposite
effects, so at the level of the global system of eight subaks there was no
correlation. Source: Lansing et al. (2014b), p. 237.
their effects vary systematically between the two groups. The more successful
upstream subaks flourish in a small but deep basin of attraction. Confident
in their collective ability to meet any challenge, they are exceptionally public spirited. Their neighbors downstream cluster around their own attractor,
revealing that muddling through can also be a steady state, with different
dynamical relationships among state variables than in the upstream group.
Statistically, these differences are highly significant (4 sigma). But they only
become apparent if we allow for the possibility of more than one attractor or
regime (Lansing et al., 2014a).
CONCLUSION: BREAKING THE MEDUSAN MIRROR
In the past two or three decades, interest in complexity has burgeoned across
the social sciences. Under the banner of complexity, physicists and modelers have turned their attention to questions such as the causes of the Maya
collapse (Weiss & Bradley, 2001), the spread of disease (Craft, Volz, Packer,
& Meyers, 2010), the origins of syntax (Ferrer-i-Cancho & Sole, 2001), and
the evolution of culture (Tehrani, Collard, & Shennan, 2010). Presently, the
mathematical tools needed to analyze complexity present an entry barrier
for many social scientists. But generation time in graduate schools is short,
12
EMERGING TRENDS IN THE SOCIAL AND BEHAVIORAL SCIENCES
and the physicists who have taken the lead in the application of complexity
to social science are beginning to have their elbows jostled by social scientists
with a new set of skills.
As for the likely impact, it is still early days. But one change that is already
visible on the horizon has to do with history, which plays no role in equilibrium analysis. Multivariate statistics, the other standard mathematical tool of
the social sciences, can be used to investigate time series, but while it can tell
us how some processes have changed over time, the usual methods will not
tell us how surprised we should be. These weaknesses were the basis for the
critique of positivist social science by the Frankfurt school. The “positivist
dispute” is now largely forgotten, but it left a lasting legacy in the enduring division between positivist versus qualitative and historical approaches
to social science. Complexity has the potential to open a new chapter in this
debate, by reframing the analytical importance of history and change.
The original debate, which came to be known as the positivist dispute, began
in 1961. The German Sociological Association invited Karl Popper to give a
lecture on the logic of the social sciences, and asked Theodor Adorno to offer
a critical response. Popper held forth on the importance of statistical validation for social theory. In response, Adorno argued that it is necessary to imagine alternatives to contemporary social reality: “only through what it is not
will it disclose itself as it is … ” (Adorno, Dahrendorf, Pilot, Albert, Habermas, & Popper, 1976). This led Adorno to a critique of descriptive statistics as
the primary tool for social inquiry. He observed that “a social science that is
both atomistic, and ascends through classification from the atoms to generalities, is the Medusan mirror to a society which is both atomized and organized
according to abstract classificatory principles … ” Adorno’s point was that a
purely descriptive, statistical analysis of society at a given historical moment
is just “scientific mirroring” that “remains a mere duplication.” For Adorno
and other Continental social theorists, the purpose of social science was to
illuminate the driving forces producing historical change.5 And to break the
seal of reification on the existing social order, it was necessary to go beyond
descriptive statistics or equilibrium models to explore historical contingency.
But the mathematical tools needed for this kind of analysis did not exist.
Today, they do.
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Ferrer-i-Cancho, R., & Sole, R. V. (2001). The small world of human language. Proceedings of the Royal Society B: Biological Sciences, 268(1482), 2261–2265.
Henrich, J., Ensminger, J., McElreath, R., Barr, A., Barrett, C., Bolyanatz, A., … Ziker,
J. (2010). Markets, religion, community size and the evolution of fairness and punishment. Science, 327, 1480–1484.
Kahneman, D., Knetsch, J. L., & Thaler, R. H. (1986). Fairness and the assumptions
of economics. The Journal of Business, 59(S4), S285.
Lansing, J. S., Cheong, S. A., Chew, L. Y., Cox, M. P., Ho, M.-H., & Arthawiguna, A.
(2014a). Regime shifts in Balinese Subaks. Current Anthropology, 55(2), 232–239.
Lansing, J. S., Cheong, S. A., Chew, L. Y., Cox, M. P., Ho, M.-H., & Arthawiguna, A.
(2014b). Regime shifts in Balinese Subaks. Current Anthropology, 55(2), 237.
Lansing, J. S., & de Vet, T. A. (2012). The functional significance of Balinese Water
Temples: A reply to critics. Human Ecology, 40(3), 453–467.
Lansing, J. S., & Fox, K. (2011). Niche construction on Bali: The gods of the countryside. Philosophical Transactions of the Royal Society B, 366, 927–934.
Lansing, J. S., & Kremer, J. N. (1993). Emergent properties of Balinese Water Temples.
American Anthropologist, 95(1), 97–114.
Lovelock, J. E. (1992). A numerical model for biodiversity. Philosophical Transactions
of the Royal Society of London B, 338, 365–373.
May, R. M. (1976). Simple mathematical models with very complicated dynamics.
Nature, 261, 459–467.
Saunders, P. T. (1994). Evolution without natural selection: Further implications of
the Daisyworld parable. Journal of Theoretical Biology, 166, 370.
Scheffer, M., Bascompte, J., Brock, W. A., Brovkin, V., Carpenter, S. R., Dakos, V.
… Sugihara, G. (2009). Early-warning signals for critical transitions. Nature, 461,
53–59.
Sokal, A., & Bricmont, J. (1999). Fashionable nonsense: Postmodern intellectuals’ abuse of
science. New York, NY: Picador Press.
Tehrani, J. J., Collard, M., & Shennan, S. J. (2010). The cophylogenies of populations and cultures: Reconstructing the evolution of Iranian tribal craft traditions
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Weaver, W. (1948). Science and complexity. American Scientist, 36(4), 536–44.
Weiss, H., & Bradley, R. S. (2001, January 26). What drives societal collapse? Science,
291(5504), 609–610.
J. STEPHEN LANSING SHORT BIOGRAPHY
J. Stephen Lansing directs the Complexity Institute at Nanyang Technological University in Singapore. He is also an External Professor at the
Santa Fe Institute, birthplace of complexity theory, an Emeritus Professor of
anthropology at the University of Arizona, and a Senior Research Fellow at
the Stockholm Resilience Centre. Before moving to Arizona in 1998, Lansing
held joint appointments at the University of Michigan in the School of
Natural Resources & Environment and the Department of Anthropology,
and earlier chaired the Anthropology Department of the University of
Southern California.
In the 1980s, Lansing and ecologist James Kremer showed that Balinese
water temple networks can self-organize. Later research showed that over
the centuries, water temple networks expanded to manage the ecology of
rice terraces at the scale of whole watersheds. In 2012, Bali’s water temple
networks were recognized as a UNESCO World Heritage.
As the pieces of the water temple story were falling into place, Lansing
became interested in self-organizing processes elsewhere in the archipelago.
In 2000, he began to work with Indonesian geneticists, linguists, and public
health officials to study the co-evolution of social structure, language change,
and disease resistance on 14 Indonesian islands. Recent publications and
films are available at www.slansing.org.
Complexity: An Emerging Trend in Social Sciences
15
RELATED ESSAYS
Agency as an Explanatory Key: Theoretical Issues (Sociology), Richard Biernacki and Tad Skotnicki
Heterarchy (Archaeology), Carole L. Crumley
Behavioral Economics (Sociology), Guy Hochman and Dan Ariely
From Individual Rationality to Socially Embedded Self-Regulation (Sociology), Siegwart Lindenberg
-
Complexity: An Emerging Trend
in Social Sciences
J. STEPHEN LANSING
Abstract
The social sciences have had a good run with linear models, in which effects are proportionate to their causes. Nearly all of our theoretical models, in fields as diverse
as microeconomics and evolutionary game theory, are equilibrium theories, which
examine the properties of various fixed points and analyze the conditions under
which they are selected. In contrast, “complexity” uses different mathematical tools
to investigate nonlinear processes. But linear models have the advantages of simplicity and power. Is there a real need to import the theoretical apparatus of “complexity” into the social sciences? Or might it be merely the latest example of Fashionable
Nonsense?
As it turns out, one need not seek very far to discover nonlinear dynamics in the social
world. And if more than one attractor exists, the resulting variation in dynamical
behavior will be mistaken for noise if one assumes linearity. In the past two or three
decades, interest in complexity has burgeoned across the social sciences. Under the
banner of complexity, researchers have investigated questions as dissimilar as the
causes of the Maya collapse, the spread of disease, the origins of syntax, the structural
properties of cities, and the evolution of culture. Presently, the mathematical tools
needed to analyze complexity present an entry barrier for many social scientists. But
generation time in graduate schools is short, and the physicists who have taken the
lead in the application of complexity to social science are beginning to have their
elbows jostled by social scientists with a new set of skills. As for the likely impact,
it is still early days. But one change that is already visible on the horizon has to do
with history, which plays no role in equilibrium analysis, but is intrinsic to many of
the questions and methods developed to study complex systems.
INTRODUCTION
The social sciences have had a good run with linear models, in which effects
are proportionate to their causes. Nearly all of our theoretical models, in
fields as diverse as microeconomics and evolutionary game theory, are
equilibrium theories, which examine the properties of various fixed points
and analyze the conditions under which they are selected. In contrast,
“complexity” uses different mathematical tools to investigate nonlinear
Emerging Trends in the Social and Behavioral Sciences. Edited by Robert Scott and Stephen Kosslyn.
© 2015 John Wiley & Sons, Inc. ISBN 978-1-118-90077-2.
1
2
EMERGING TRENDS IN THE SOCIAL AND BEHAVIORAL SCIENCES
processes. Nonlinear phenomena are well known in physics, and are
ubiquitous in living systems. Consequently, as Stanislaw Ulam is said to
have quipped, the term nonlinear science is like calling zoology “the study of
non-elephant animals.”
Still, linear models have the advantages of simplicity and power. Moreover,
they may be well suited to the social sciences, which are mostly concerned
with the purposive behavior of rational agents and institutions. Further, there
is as yet no mathematical definition of complexity, nor is there a theory of
what causes it to arise. So, is there a real need to import the theoretical apparatus of “complexity” into the social sciences? Or might it be merely the latest
example of Fashionable Nonsense (Sokal & Bricmont, 1999), a sexy import from
physics that has at most a tangential relevance to the Geisteswissenschaften?
COMPLEXITY IN PHYSICS AND BIOLOGY
To address this question, it may be helpful to begin with a brief overview
of the origins and meaning of “complexity” in the natural sciences. In 1948,
Warren Weaver distinguished two forms of complexity: “disorganized
complexity”, which can be analyzed with probability theory and statistical
mechanics, and “organized complexity” which requires “dealing simultaneously with a sizable number of factors which are interrelated into an organic
whole” (Weaver, 1948). In another seminal paper, “More is Different,” Philip
Anderson argued in 1972 that understanding complexity involves a concept
of emergent properties: “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. Psychology is not applied biology
nor is biology applied chemistry” (Anderson, 1972). Anderson concluded
by quoting Karl Marx’s observation that over time, quantitative differences
become qualitative differences. Four years later, Robert May observed that
“the very simplest nonlinear difference equations can possess an extraordinarily rich spectrum of dynamical behavior, from stable points, through
cascades of stable cycles, to a regime in which the behavior (although fully
deterministic) is in many respects ‘chaotic’, or indistinguishable from the
sample function of a random process” (May, 1976). May’s now-canonical
example was the logistic equation. It is a good place to begin, because it
demonstrates how both linear and nonlinear patterns can emerge from a
simple equation for population growth, in which x is the population and r is
its intrinsic growth rate:
xnext = rx(1 − x)
For most values of r, the equation is linear: increase in x is proportionate to
the increase in r. But at r = 3.44949, the population begins to oscillate between
Complexity: An Emerging Trend in Social Sciences
3
1.0
0.8
0.6
x
0.4
0.2
0.0
2.4
2.6
2.8
3.0
3.2
r
3.4
3.6
3.8
4.0
Figure 1 The logistic map, showing linear, cyclical and chaotic behavior at
different values of the intrinsic growth rate, r. Source: Creative Commons.
http://en.wikipedia.org/wiki/File:Logistic_Bifurcation_map_High_Resolution.png#
filelinks
two values (Figure 1). Between 3.44949 and 3.54409 it oscillates between four
values, after which slight increases lead to oscillations between 8, 16, 32, and
so on. At 3.56995, regular oscillations begin to be replaced by chaotic fluctuations. At these growth rates, tiny differences in the initial population yield all
possible ending populations within a given range. Even more surprisingly,
between 3.56995 and 3.82843 several islands of stability appear (Figure 1).
Thus, merely varying the growth rate in the simplest possible equation for
population growth generates linear, oscillatory, or chaotic behavior. In the
language of complexity, or more specifically of nonlinear dynamics, each of
these is called a regime, or attractor. As long as the growth rate is less than
3.44949, the behavior is linear. But if the growth rate happens to fall in the
chaotic regime, prediction is impossible, even if all the parameters are exactly
known (May, 1976, p. 466).
This simple example allows us to make three observations. First, one need
not seek very far to discover nonlinear processes. Second, linear or equilibrium models will not explain nonlinear systems. And third, less obviously, if
more than one attractor or regime exists, the resulting variation in dynamical
behavior will be mistaken for noise if one assumes linearity. The last point is
particularly important for social science, and we will return to it below. But
before doing so, two practical questions will be addressed. First, how relevant are the mathematics of nonlinear dynamics to real-world phenomena?
Second, what kinds of insights or explanations are possible if more than one
attractor exists, or if a particular system does not settle down into a single,
stable equilibrium?
4
EMERGING TRENDS IN THE SOCIAL AND BEHAVIORAL SCIENCES
COMPLEX SYSTEMS
To address these questions, it is useful to distinguish between complex
systems and complex adaptive systems. A good example of the former
is self-organized criticality (SOC), for which the canonical example is not
an equation, but an experiment often performed by toddlers at the beach
(Bak, Tang, & Wiesenfeld, 1987). Take a flat surface, dribble grains of sand
on it until it becomes a pile, and observe the occasional avalanches that
occur as the sides grow steep. As the grains of sand continue to fall, the
avalanches continue, so that the steepness of the sides of the pile remains
constant. At this point, the sandpile has reached its attractor, where the size
of the avalanches (the number of grains of sand that move) is inversely
related to their frequency. This system has several interesting features,
notably that it is self-organizing and produces a robust pattern of emergent,
scale-invariant behavior. Many social and cultural phenomena exhibit
identical patterns, where the size of events such as earthquakes is inversely
related to their frequency. SOC spontaneously generates scale-free networks,
in which the degree distribution of nodes (how many connections they
possess to other nodes) is inversely related to their frequency. Thus, SOC
is governed by a single attractor that produces a characteristic signature,
which can be easily detected for a large swath of phenomena, from sandpiles
to stock markets, citation networks, the World Wide Web, and financial
markets.
Sand piles have a single attractor. The possibility that real-world CS might
contain more than one attractor was demonstrated by the discovery of
alternate stable states in Dutch lakes. For decades, excess fertilizer flowed
into the lakes, triggering algae blooms and eutrophication. But reducing
the amount of fertilizer entering the lakes was not enough to restore them
to clarity. It turned out that alternate stable states or attractors existed, one
turbid and the other clear. In ecology, such alternate stable states or attractors
are called regimes. The effects of nutrient flows depended on which regime
a lake was in, so generalizing across all lakes obscured these differences.
But once the existence of alternate regimes was recognized, a simple intervention was sufficient to restore the lakes to health. Temporarily removing
the fish allowed sediment to settle and zooplankton populations to increase,
whereupon water clarity could be improved by reducing the amount of
fertilizer flowing into the lakes (Attayde, Van Nes, Araujo, Corso, & Scheffer,
2010). The comparative study of such processes by ecologists produced
new theoretical insights into transitions between attractors. As a dynamical
system approaches the boundary between alternate attractors, it will exhibit
certain generic properties. These telltale signs have by now been observed
in many natural systems (Scheffer et al., 2009). This phenomenon has yet to
Complexity: An Emerging Trend in Social Sciences
5
be conclusively demonstrated for social phenomena, but it has triggered a
lot of interest, because of the potential relevance for understanding critical
transitions in social systems.
COMPLEX ADAPTIVE SYSTEMS: HIDDEN ORDER
As we have just seen, CS are simply aggregates of interacting elements. If the
elements are agents, in other words if they exhibit purposive or goal-seeking
behavior, then they form a CAS. CASs are ubiquitous in living systems, and
we are beginning to notice them in the social world. Is a given social system
composed of adaptive agents, and does it produce emergent behaviors that
arise from their aggregate behavior? What might such emergent behaviors
look like? When do quantitative differences turn into qualitative transformations? Similar to the logistic equation for populations described earlier, even
the simplest examples of CASs can contain surprises. To see this, we can turn
the logistic equation into an evolving CAS by adding a single environmental
parameter, so that growth is affected by something in the environment. The
resulting model, created in 1992, helped trigger a revolution in the environmental sciences.
The model is called Daisyworld (Lovelock, 1992), and the environmental
variable is temperature. Daisyworld is an imaginary planet orbiting a star
similar to the Sun and at the same orbital distance as the Earth. The surface
of Daisyworld is fertile earth sown uniformly with daisy seeds. The daisies
vary in color, and daisies of similar color grow together in patches. As sunshine falls on Daisyworld, the model tracks changes in the growth rate of each
variety of daisy, and changes in the amount of the planet’s surface covered
by different-colored daisies.
The simplest version of this model contains only two varieties of daisies,
white and black. Black daisies absorb more heat than bare earth, while whites
reflect sunshine. Clumps of same-colored daisies create a local microclimate
for themselves, slightly warmer (if they are black) or cooler (if white) than
the mean temperature of the planet.
Both black and white daisies grow fastest and at the same rate when
their local effective temperature (the temperature within their microclimate)
is 22.5 ∘ C, and they respond identically, with a decline in growth rate, as
the temperature deviates from this ideal. Consequently, at a given average planetary temperature, black and white daisies experience different
microclimates and therefore different growth rates.
If the daisies cover a sufficiently large area of the surface of Daisyworld,
their color affects not only their own microclimate but also the albedo or
reflectance of the planet as a whole. As with our own sun, the luminosity
of Daisyworld’s star is assumed to have gradually increased. A simulation
6
EMERGING TRENDS IN THE SOCIAL AND BEHAVIORAL SCIENCES
70
Mean temperature (°)
2
2
30
2
1
1
1
1
2
−10
0.75
0.95
1.15
Luminosity
1.35
1.55
Figure 2 Simulated temperature regulation on Daisyworld. As the luminosity of
its aging sun increases from 0.75 to 1.5 times the average value, the temperature
of a bare planet would steadily rise (line 2). In contrast, the temperature of
Daisyworld stabilizes close to 22.5 ∘ C with daisies present (line 1).
of life on Daisyworld begins in the past with a cooler sun. This enables the
black daisies to spread until they warm the planet. Later on, as the sun grows
hotter, the white daisies grow faster than black ones, cooling the planet.
So over the history of Daisyworld, the warming sun gradually changes the
proportion of white and black daisies, creating the global phenomenon of
temperature regulation: The planet’s temperature is held near the optimum
by and for the daisies, as shown in Figure 2.
Imagine that a team of astronauts and planners is sent to investigate Daisyworld. They would have plenty of time to study the only living things on
the planet, and they would almost certainly conclude that the daisies had
evolved to grow best at the normal temperature of the planet, 22.5 ∘ C. But
this conclusion would invert the actual state of affairs. The daisies did not
adapt to the temperature of the planet; instead, they adapted the planet to suit
themselves (Saunders, 1994). A Daisyworld without daisies would track the
increase in the sun’s luminance (line 2), rather than stabilizing near the ideal
temperature for daisies (line 1). Only when the sun’s luminosity becomes
too hot for the daisies to control will the daisy’s former role in temperature
stabilization become apparent.
Lacking this understanding, planners hoping to exploit Daisyworld’s
economic potential for the interstellar flower trade would fail to appreciate
the possible consequences of different harvesting techniques. While selective
flower harvests would cause small, probably unnoticeable tremors in planetary temperature, clear-cutting large contiguous patches of daisies would
create momentary changes in the planet’s albedo that could quickly become
permanent, causing temperature regulation to fail and daisy populations to
crash.
Complexity: An Emerging Trend in Social Sciences
7
The Daisyworld model soon became the canonical example of a selforganizing, self-regulating environmental system. As an example of a CAS,
it has several interesting features. The biology is as simple as its creator,
James Lovelock, could make it. The model shows how small-scale local
adaptations can produce an emergent global structure; and it also shows
why such global structures can easily fade from view, becoming noticeable
only when the system as a whole has been pushed to its limits. But is
Daisyworld simply a mathematical curiosity? Does it have any relevance to
the social sciences?
Something very similar to the Daisyworld catastrophe occurred in the 1980s
in the rice terraces of Bali. Because this case has been discussed extensively
elsewhere,1 here I provide only a summary highlighting the parallel with the
imaginary failure of temperature regulation on Daisyworld. In the 1970s, the
Asian Development Bank became involved in an effort to boost rice production in Indonesia. The bank’s consultants learned that on Bali, local groups of
farmers synchronize their irrigation schedules. In most regions, these schedules produced two rice harvests of native Balinese rice per year. The consultants saw two ways to improve harvests. The first was to encourage the
farmers to grow higher yielding “Green Revolution” rice varieties, which
produce more grain than native Balinese rice. The second recommendation
took advantage of another feature of the new rice: it grows faster than native
rice. Consequently, the farmers could plant more frequently. The Ministry of
Agriculture adopted both recommendations, and competitions were created
to reward the farmers who produced the best harvests. By 1977, 70% of the
southern Balinese “rice bowl” was planted with Green Revolution rice, and
soon after, planting native rice was forbidden.
At first, rice harvests improved. But a year or two later, Balinese agricultural and irrigation workers began to report “chaos in water scheduling”
and “explosions of pest populations.” At the time, planners dismissed these
occurrences as coincidence, and recommended higher doses of pesticides.
However, the parallel with Daisyworld offers an alternative explanation for
the harvest decline (Lansing & Fox, 2011). On Daisyworld, the growth of
the flowers was driven by a single environmental parameter: temperature. A
model of Balinese farming as a CAS requires two environmental parameters,
water and pests.
Traditionally, Balinese rice farmers manage their fields collectively in
organizations called subak. Because irrigation depends on seasonal rainfall,
each subak’s choice of an irrigation schedule affects the availability of water
for their neighbors downstream. The timing of irrigation can also be used
to control rice pests such as rats, insects, and insect-borne diseases. This is
1. Perfect Order: Recognizing Complexity in Bali. Princeton University Press, 2006. Julian Steward Prize,
American Anthropological Association. Lansing and de Vet (2012)
8
EMERGING TRENDS IN THE SOCIAL AND BEHAVIORAL SCIENCES
accomplished by synchronizing rice harvests and then briefly flooding the
fields, thus depriving the pests of their habitat. The larger the area that is
encompassed by the post-harvest flooding, the fewer the pests. But if too
many subaks try to flood their fields at the same time, there will not be
enough water to go around.
To test the ability of the subaks to discover effective solutions to this
trade-off between pest control and water shortages, we constructed a
forward-in-time simulation model (Lansing & Kremer, 1993).
By simple trial and error, each subak seeks to discover an irrigation schedule that minimizes losses due to pests or water shortages. A patchwork of
synchronized irrigation schedules soon emerges in the model, as groups
of subaks adopt identical cropping schedules. As this occurs, rice harvests
improve because water shortages and pest damage are reduced for the entire
watershed. When the key environmental parameters are stabilized, variation
in harvests declines because these benefits spread across the entire system.
Conceptually, the model is similar to Daisyworld, except that the flowers of
Daisyworld adapt to a single environmental parameter (temperature), while
the Balinese farmers adapt to two (pest infestations and water availability).
As with Daisyworld, it is an example of a self-organizing CAS, in which the
agents are subaks.2
Meanwhile, in Bali, the Green Revolution inadvertently created an experimental test of this model. The farmers were told to plant as often as possible,
and set aside their traditional system of synchronized planting. This effect
can be replicated in the model by running it backwards, and breaking up
the co-evolved patterns of synchronized planting schedules. In the model,
this produces water shortages and exploding pest populations. When this
actually happened in Bali, consultants for the Asian Development Bank interpreted them as chance misfortunes, and urged the farmers to apply higher
doses of pesticides while continuing to plant as often as possible. But even
very high doses of pesticides proved ineffective. It was only when the farmers spontaneously returned to synchronized planting schemes that harvests
began to recover; a point subsequently acknowledged by the final evaluation
team from the Bank:
Substitution of the “high technology and bureaucratic” solution in the end
proved counterproductive, and was the major factor behind the yield and
cropped area declines experienced between 1982 and 1985 … The cost of the
2. Interestingly, when the subaks along a river settle down into a globally optimal patchwork of irrigation schedules, the correlation between their cropping patterns resembles a collection of nesting Russian
dolls. That is, a patch of subaks following the same irrigation schedule will find itself inside a larger patch
containing several irrigation schedules. If the river system is large enough, these patches in turn may be
embedded in larger ones. At this point, the entire system is at or near its critical point, with correlations
between irrigation schedules at all lengths, resembling an Ising model of spin glasses.
Complexity: An Emerging Trend in Social Sciences
9
lack of appreciation of the merits of the traditional regime has been high.
Project experience highlights the fact that the irrigated rice terraces of Bali
form a complex artificial ecosystem, which has been recognized locally over
centuries.3
ISLANDS OF ORDER
Granting that exotic mathematical models may shed new light on the gardens of Bali and Daisyworld, a skeptic might be forgiven for wondering if
complexity has any broader relevance to social science. In fields such as theoretical ecology, bold claims about the ubiquity of nonlinear systems have
been backed up by many recent empirical studies. But in the social sciences,
empirical studies are just beginning, and they tend to be spearheaded by
physicists and mathematicians rather than social scientists. There are, however, some intriguing results, such as the recent discovery that a great many
properties of cities, from patent production and personal income to crime,
innovation, and the speed at which people walk and talk are power law functions of population size (Bettencourt, Lobo, Helbing, Kühnert, & West, 2007).
There has also been a very productive conversation between mathematicians
and social scientists about the dynamic properties of networks. Still, is there
more to complexity than the piecemeal application of mathematical ideas
about nonlinear dynamics to the social sciences?
This question has recently been addressed by theorists of “complexity economics,” notably Brian Arthur. Arthur argues that complexity offers nothing
less than a new foundation for economics:
Complexity economics builds from the proposition that the economy is not
necessarily in equilibrium: economic agents (firms, consumers, investors)
constantly change their actions and strategies in response to the outcome they
mutually create. This further changes the outcome, which requires them to
adjust afresh. Agents thus live in a world where their beliefs and strategies
are constantly being “tested” for survival within an outcome or “ecology”
these beliefs and strategies together create. Economics has largely avoided
this nonequilibrium view in the past, but if we allow it, we see patterns or
phenomena not visible to equilibrium analysis. These emerge probabilistically,
last for some time and dissipate, and they correspond to complex structures in
other fields.4
Consequently, Arthur concludes, “complexity economics is not a special
case of neoclassical economics. On the contrary, equilibrium economics is
3. Project Performance Audit Report, Bali Irrigation Project in Indonesia; Asian Development Bank
1988.
4. Arthur (2013). For an earlier formuation of these ideas, see Arthur (1999).
10
EMERGING TRENDS IN THE SOCIAL AND BEHAVIORAL SCIENCES
a special case of nonequilibrium and hence complexity economics.” Still, it
may take a rather large push to persuade social scientists to adopt this perspective. Are there really “patterns or phenomena not visible to equilibrium
analysis,” waiting to be discovered?
As before, I offer a simple example. The simplest of all games used by social
scientists to study altruism and pro-social behavior is the “Dictator Game”
(Kahneman, Knetsch, & Thaler, 1986). It is so simple that, strictly speaking, it
is not a game. To play it, a “proposer” determines an allocation (split) of some
endowment, such as a cash prize. The second player, the “responder”, simply receives the remainder of the endowment left by the proposer. In typical
cross-cultural studies, the experimenter gives each proposer the local equivalent of a day’s wage, and explains that they may share as much or as little
as they choose with another player who is present. Players are assured that
the identity of both givers and receivers will not be revealed. For example, a
recent study compared offers in the Dictator Game in 15 societies (Henrich
et al., 2010). Variation in the average generosity of the players, from one society to the next, was interpreted as support for a hypothesis about the need
to trust strangers in larger and more complex societies. To simplify this relationship, the authors constructed a scale of “market integration”: how much
of one’s food is purchased in the market, versus grown at home?
But do whole societies gravitate towards an equilibrium level of prosociality? Or might this assumption obscure the possibility that more than
one attractor exists? To find out, we asked farmers in eight Balinese subaks to
play the Dictator Game. The subaks in this study are located along the Sungi
River in central Bali. Social surveys showed that four upstream subaks were
more satisfied with their harvests, and their subak, than four downstream
subaks. For the Dictator Game, a group of farmers in each subak were
randomly selected as proposers, given the cash equivalent of a day’s wage,
and offered the chance to share as much or as little as they chose to a fellow
member of their subak, selected at random. The identities of both proposers
and recipients were concealed. Results are shown in Figure 3.
The average offer for the entire sample of farmers was 30% with a large variance, at the low end of the scale in cross-cultural studies. Buried within this
variance, however, were contrasting patterns: Farmers in the downstream
subaks were less generous overall, while the most generous farmers of all
were those in the two upstream subaks experiencing water shortages. Thus,
the variance in responses between the two groups appears to be meaningful, suggesting the presence of more than one attractor. This conclusion was
amply supported by a follow-up study. A simple survey of farmer’s opinions revealed that the upstream and downstream groups experience similar social and environmental conditions, but respond to them in different
ways. For example, differences in class and caste exist in all eight subaks, but
Complexity: An Emerging Trend in Social Sciences
11
0.5
Downstream
Upstream
0.45
Offer
0.4
0.35
0.3
0.25
0.2
2
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
3
Subak condition
Figure 3 Offers in the Dictator Game in eight Balinese subaks. Among the
downstream subaks, the worse the condition of one’s subak, the smaller the offer.
The opposite pattern emerged in the upstream subaks: the worse the state of
one’s subak, the more generous the offer. These correlations have opposite
effects, so at the level of the global system of eight subaks there was no
correlation. Source: Lansing et al. (2014b), p. 237.
their effects vary systematically between the two groups. The more successful
upstream subaks flourish in a small but deep basin of attraction. Confident
in their collective ability to meet any challenge, they are exceptionally public spirited. Their neighbors downstream cluster around their own attractor,
revealing that muddling through can also be a steady state, with different
dynamical relationships among state variables than in the upstream group.
Statistically, these differences are highly significant (4 sigma). But they only
become apparent if we allow for the possibility of more than one attractor or
regime (Lansing et al., 2014a).
CONCLUSION: BREAKING THE MEDUSAN MIRROR
In the past two or three decades, interest in complexity has burgeoned across
the social sciences. Under the banner of complexity, physicists and modelers have turned their attention to questions such as the causes of the Maya
collapse (Weiss & Bradley, 2001), the spread of disease (Craft, Volz, Packer,
& Meyers, 2010), the origins of syntax (Ferrer-i-Cancho & Sole, 2001), and
the evolution of culture (Tehrani, Collard, & Shennan, 2010). Presently, the
mathematical tools needed to analyze complexity present an entry barrier
for many social scientists. But generation time in graduate schools is short,
12
EMERGING TRENDS IN THE SOCIAL AND BEHAVIORAL SCIENCES
and the physicists who have taken the lead in the application of complexity
to social science are beginning to have their elbows jostled by social scientists
with a new set of skills.
As for the likely impact, it is still early days. But one change that is already
visible on the horizon has to do with history, which plays no role in equilibrium analysis. Multivariate statistics, the other standard mathematical tool of
the social sciences, can be used to investigate time series, but while it can tell
us how some processes have changed over time, the usual methods will not
tell us how surprised we should be. These weaknesses were the basis for the
critique of positivist social science by the Frankfurt school. The “positivist
dispute” is now largely forgotten, but it left a lasting legacy in the enduring division between positivist versus qualitative and historical approaches
to social science. Complexity has the potential to open a new chapter in this
debate, by reframing the analytical importance of history and change.
The original debate, which came to be known as the positivist dispute, began
in 1961. The German Sociological Association invited Karl Popper to give a
lecture on the logic of the social sciences, and asked Theodor Adorno to offer
a critical response. Popper held forth on the importance of statistical validation for social theory. In response, Adorno argued that it is necessary to imagine alternatives to contemporary social reality: “only through what it is not
will it disclose itself as it is … ” (Adorno, Dahrendorf, Pilot, Albert, Habermas, & Popper, 1976). This led Adorno to a critique of descriptive statistics as
the primary tool for social inquiry. He observed that “a social science that is
both atomistic, and ascends through classification from the atoms to generalities, is the Medusan mirror to a society which is both atomized and organized
according to abstract classificatory principles … ” Adorno’s point was that a
purely descriptive, statistical analysis of society at a given historical moment
is just “scientific mirroring” that “remains a mere duplication.” For Adorno
and other Continental social theorists, the purpose of social science was to
illuminate the driving forces producing historical change.5 And to break the
seal of reification on the existing social order, it was necessary to go beyond
descriptive statistics or equilibrium models to explore historical contingency.
But the mathematical tools needed for this kind of analysis did not exist.
Today, they do.
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J. STEPHEN LANSING SHORT BIOGRAPHY
J. Stephen Lansing directs the Complexity Institute at Nanyang Technological University in Singapore. He is also an External Professor at the
Santa Fe Institute, birthplace of complexity theory, an Emeritus Professor of
anthropology at the University of Arizona, and a Senior Research Fellow at
the Stockholm Resilience Centre. Before moving to Arizona in 1998, Lansing
held joint appointments at the University of Michigan in the School of
Natural Resources & Environment and the Department of Anthropology,
and earlier chaired the Anthropology Department of the University of
Southern California.
In the 1980s, Lansing and ecologist James Kremer showed that Balinese
water temple networks can self-organize. Later research showed that over
the centuries, water temple networks expanded to manage the ecology of
rice terraces at the scale of whole watersheds. In 2012, Bali’s water temple
networks were recognized as a UNESCO World Heritage.
As the pieces of the water temple story were falling into place, Lansing
became interested in self-organizing processes elsewhere in the archipelago.
In 2000, he began to work with Indonesian geneticists, linguists, and public
health officials to study the co-evolution of social structure, language change,
and disease resistance on 14 Indonesian islands. Recent publications and
films are available at www.slansing.org.
Complexity: An Emerging Trend in Social Sciences
15
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