Geoscience Reference
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or global climate with a few simple rules or equations as called for by many com-
plexity approaches. An important drawback of algorithmic complexity, for example,
is the confl ation of data with knowledge or meaning; some systems simply may not
be amenable to representation with bits and bytes in an algorithm. Rates of change
in environmental systems can be represented using mathematically well-understood
non-linear differential equations, for example, but these are diffi cult to solve. As a
result, 'modellers have had to fi nd various ways to approximate them using methods
such as numerical iteration or fi nite difference calculation that provide analytically
tractable solutions' (Mulligan and Wainwright, 2003; Demeritt and Wainwright,
2005, p. 215). A related problem with implementing concepts of deterministic
complexity is fi nding appropriate and measurable variables for use in mathemati-
cally tractable equations. Choosing and defi ning these variables is a diffi cult task
that can result in the omission of important factors. This said, while fewer systems
than hoped for are deterministically complex (Zimmer, 1999), strong examples from
systems ranging from river systems to earthquakes do exist in environmental
geography and cognate fi elds such as ecology, biogeography, and geomorphology
(Phillips, 2003).
Aggregate complexity also poses challenges to encoding real systems into data
and models because it posits that system characteristics emerge 'bottom up' from
interactions among entities at small scales. Translating these straightforward prin-
ciples into a model that can use empirical data or test existing theories is a diffi cult
task because both quantitative models and qualitative theories can quickly become
more complicated (but not more complex in the sense meant in complexity research)
in order to describe real systems (Torrens and O'Sullivan, 2001). For example, a
host of different complexity-based methods are used to examine land change,
including neural networks, cellular automata, and agent-based modelling. As these
approaches have become more common and more sophisticated, however, modellers
are increasingly tempted to capture a large number of features in human-
environment systems. In doing so, they run the risk of moving away from a basic
tenet of complexity science, namely that seemingly complex systems or dynamics
can be generated by a small set of rules, such as transition rules for cellular automata
or simple decision-making strategies of agents (Parker et al., 2003).
Complexity researchers often risk focusing on patterns that they believe signal
the presence of complex processes instead of the complex processes as such. Algo-
rithmic, deterministic, and aggregate complexity all search for hallmark patterns of
complexity such as information-theory measures or fractals. This is because these
patterns can indicate the existence of processes including deterministic chaos, emer-
gence, and self-organised criticality (Goodchild and Mark, 1987; Bak, 1996; Barabási
and Bonabeau, 2003). Patterns associated with complexity do not necessarily indi-
cate the existence of complex processes, however, because many processes may
create a single pattern and a single process may create many patterns. This is the
case for deforestation in many parts of the world, for example, where a single
pattern such as runaway tree felling can be driven by a broad range of social and
economic processes, and a single process, such as infrastructure development, can
result in a range of different deforestation patterns (Geist and Lambin, 2002). It is
also possible to create complex patterns using complex processes that have no cor-
respondence to real-world processes. A growing body of work questions the validity
of using generic complex processes such as self-organised criticality to model systems
