Geoscience Reference
In-Depth Information
essence, simple algorithms are used to describe simple systems while longer and
more sophisticated algorithms are necessary for complicated systems. These mea-
sures also often focus on entropy, or the amount of order versus randomness in a
system.
Computational complexity and information theory provide measures of how
complicated a system is, but not necessarily how 'complex' the system is in the way
meant by most researchers in complexity science interested in deterministic or
aggregate complexity because it does not distinguish between systems that are
merely complicated and those that exhibit processual elements such as feedback or
emergence (Gilbert, 1995; Reitsma, 2003; Perry, this volume). Algorithmic complex-
ity is useful to complexity researchers, however, because it provides straightforward
measures of how complicated a system will be to represent or how diffi cult it is to
solve a problem. In particular, these measures identify problems that cannot be
solved analytically, but instead must be approximated . Information-theoretic mea-
sures such as entropy are also useful because they assess the degree of order in a
system; as discussed below, complexity research is very interested in systems that
move between randomness and order (Phillips, 2003). More broadly, however, the
use of algorithmic complexity by geographers employing complexity approaches
has been limited (Manson, 2001; O'Sullivan, 2004).
Deterministic complexity
Deterministic complexity is comprised of approaches that describe the underlying
dynamics of a system that determine its state and trajectory of evolution. Systems
can have both negative feedback, whereby changes in the state of the system tend
to diminish over time, and positive feedback, where system dynamics make changes
self-reinforcing. For example, in the case of climate change, warming of the tropical
oceans will generate more cloud cover that will refl ect incoming solar radiation and
thereby dampen the warming effects of anthropogenic greenhouse gas emissions,
while melting of the polar ice caps is a positive feedback that will accelerate global
warming by increasing the amount of solar radiation absorbed at high latitudes
(Rind, 1999; Schneider, 2004). Deterministic complexity provides a framework for
understanding and predicting the dynamics of the climate and other systems by
deriving equations to describe the behaviour of and relationships among their com-
ponent parts and examining how feedback among these equations (and thereby the
system components they describe) affects the system overall. This area of complexity
is also concerned with understanding how feedback can make the system sensitive
to small perturbations, as detailed below (Malanson et al., 1990).
Deterministic complexity takes its name from the idea that a few key variables
in a small set of equations can describe a system. The deterministic aspect
stems from the way in which system behaviour is 'determined' by the equations
and their initial values. To capture animal population dynamics, for example, we
can look to a population growth model developed in 1838 by Pierre François
Verhult:
X
t+1
=
α
X
t
(1
−
X
t
)
(5.1)
This equation predicts the future size of a population
X
t+1
as a function of the present
population size
X
t
(measured on a scale of zero to one) and a rate of growth
α
that
