Geoscience Reference
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related approaches to complexity: algorithmic complexity, deterministic complexity,
and aggregate complexity. Within each of these approaches and the larger fi eld of
complexity research, we can also identify and critically evaluate several areas that
host the latest debates and larger challenges. Among the most pressing are questions
about the novelty of complexity, reconciling simplicity with complexity, under-
standing the balance between equilibrium and change, bridging various disciplinary
divides, and understanding how complexity affects our assessment and use of
spatial, temporal and organisational scale.
Approaches to Complex Systems
Complexity research examines systems. A system is a set of entities connected in a
way that gives the system an overall identity and behaviour. Systems can be of
almost any scale, from atoms bound together in a molecule, to households in an
economy, or the planets of our solar system. Complexity research centers on iden-
tifying the most important system elements and describing relationships among
them. Systems are defi ned in part by these internal elements as well as by their larger
environments. An ecosystem is self-contained in terms of much of its structure and
function, for example, but also has many connections to the larger climatic, geo-
physical, and biotic environment.
Complexity research tends to fall into three broad areas of theory and practice
(Manson, 2001), although many categorisations and defi nitions exist (cf. Byrne,
1998; Cilliers, 1998; Lissack, 2001; Reitsma, 2002). The fi rst kind of complexity
research can be termed algorithmic because it measures the structure of a system in
terms of the computational processes needed to replicate the system. The second
form is deterministic complexity, which explores systems via mathematical
approaches that have become known as non-linear dynamics and chaos theory. The
third form of complexity research examines aggregate complexity, or the manner
in which systems such as ecosystems emerge from the local interactions of individual
elements such as animals or plants.
Algorithmic complexity
Algorithmic complexity encompasses mathematical and computational approaches
that attempt to calculate or characterise how diffi cult it is to represent or model a
system in mathematical or algorithmic terms. The fi eld of computational complexity
theory measures the diffi culty of solving mathematical or computational problems,
particularly with respect to how changes in the size of a system affect the diffi culty
of representing a system. One common problem in environmental geography is
determining the time or computational resources required to calculate all permuta-
tions in a resource allocation situation, such as choosing a set of conservation areas
designed to maximise biodiversity in a given region (Aerts et al., 2003). For prob-
lems of moderate size, say involving the allocation of 100 areas of interest (e.g.,
represented as a 10
10 raster grid or 100 discrete regions) there are billions of
different ways of ordering the permutations of suitable areas. Solving this problem
in a Geographic Information System or spatial model is very diffi cult without
recourse to approximation or heuristics. A related subfi eld of mathematics, informa-
tion theory, quantifi es the 'complexity' of a system as the shortest algorithm that
can reliably describe the system and reproduce its behaviour (Chaitin, 1992). In
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