Complexity

Stephen White
28 April 2014




Complexity
By Stephen White, Arizona State University

Melanie Mitchell defines a complex system as a system in which large networks, with relatively small components with no central control and simple rules of operation give rise to complex collective behavior, sophisticated information processing, and adaptation through learning or evolution (Mitchell, 2009 p. 13). By this definition, complex systems are all around us in our day to day routines from insect colonies to modern cities like New York. Furthermore, these systems self-organize and adapt to the environment. The ability to adapt through learning or evolution is a key factor in natural selection and it seems to apply here as well. Although these systems use simple agents or components, they can be extremely difficult to measure. In addition, the scientific community has not developed a standard way to measure complexity. To illustrate, Mitchell states "many different methods have been purposed, however, none have been universally accepted by scientist" (Mitchell, 2009 p.13). One method used to measure complexity can be achieved through the use of fractal geometry and Fibonacci numbers. Fractal geometry deals with measuring nature such as coast lines and mountains. Below is an image of a superconductor magnetic fractal. The patterns repeat themselves through a process of fractal geometry. Fibonacci numbers are similar with patterns of repeating number sequences in mathematics and appears in nature on a regular basis. For example, Arthur Benjamin, in his TED talk "The Magic of Fibonacci Numbers", states "The number of petals on a flower is typically a Fibonacci number, or the number of spirals on a sunflower or a pineapple tends to be a Fibonacci number as well"(Benjamin 2013). These are complex patterns made of simple components with a mathematical function. Figure 2 below illustrates the simple pattern in a pineapple. As you can see, the elements in complex systems are a relatively simple pattern of numbers. In this paper, I will attempt to break down the complexity of these networks and their relationship with science and collective decision making through simple rules and self-organization.

The relationship between scientific knowledge and the decision making from a complex systems perspective can be explained through the methods we use to measure complexity. Social insects demonstrate this well. To illustrate, ants, wasps, bees, and termites all build complex nests with no central control. In addition, chemical reactions can bring the colonies together to achieve a higher goal, such as the nest. For example, ants lay chemical trails for fellow ants which can lead them to food or a nest. For instance, Guy Theraulaz, in his article "The Origin of Nest Complexity in Social Insects", states "a mechanism commonly used by social insects to organize and coordinate their building activities relies on templates: The blueprint of the nest already exists in the environment under the form of physical or chemical heterogeneities" (Theraulaz 1998 p.16). The blueprints for the nests are internally coded in the insects and require little decision making if any at all. Figure 3 shows the different layers and chambers inside a termite nest. The nests are large and very complex even though the colony lacks central control. Scientists still do not fully understand how these systems work, but new research is constantly being conducted with new results. Physical and Life sciences has experienced a dramatic change in the way we look at nature in the last century. For instance, Warren Weaver, in his article "Science Complexity" states " Physical science before 1900 was concerned with two-variable problems of simplicity; whereas the Life sciences, in which these problems of simplicity are not so often significant, had not yet become highly quantitative or analytical in character" (Weaver, 1948 p.537). Science has come a long way in how we deal with simplicity and its relationship with complexity. Furthermore, decision making appears to be quite complex in these relatively simple organisms.

The biosphere we live in has been altered through the collective decision making and long-term impacts by society as a whole. We have crossed several of the planetary thresholds are navigating into uncharted territory, so to speak. For example, Jonathan Rockstrom, in the article "A Safe Operating System for Planetary Boundaries", states "Many subsystems of Earth react in a nonlinear, often abrupt, way, and are particularly sensitive around threshold levels of certain key variables; If these thresholds are crossed, then important subsystems, such as a monsoon system, could shift into a new state, often with deleterious or potentially even disastrous consequences for humans" (Rockstrom 2009). Most people seem to be aware of climate change and the greenhouse effect. However, these are not the most severe problems we face today with regards to the planetary boundaries. The rate of biodiversity loss, or extinction rate, is currently rising at an alarming rate. In addition, the Nitrogen cycle in the atmosphere, which is the amount of N2 removed from the atmosphere for human and animal use, has surpassed the planetary boundary of 35 to currently 121 million tons per year (Rockstrom, 2009). Scientist are concerned with planetary boundaries in which the threshold or "tipping point" has already been surpassed. J. M. Anderies, in his article "The topology of non-linear global carbon dynamics: from tipping points to planetary boundaries", states "Increasing human pressure on ecosystems coupled with global change has raised concerns about human societies approaching boundaries or 'tipping points' that, once crossed, may induce fundamental shifts in Earth System dynamics" (Anderies, et al, 2013). It might be too late for some issues such as climate change, and the impacts of previous decisions are just now being observed and we are past the tipping point. Timothy M. Lenton, in the article "Earths Tipping Points", defines a tipping point as: "a critical threshold at which the future state of a system can be qualitatively altered by a small change in forcing" (Lenton, 2011). This shows that the planet, or biosphere, is sensitive to initial conditions and our decisions will have a much greater impact 20-40 years down the road. If we look at complexity in human societies, more specifically our government systems, we see large and small political systems. The uncertainty factor and the role of political leaders, can affect their ability to make crucial decisions for the country. In a free, democratic society, we make decisions both independently and on a larger, more collectivistic level. Both are necessary for smooth order in a chaotic universe. How we should or should not make decisions, both individually and collectively, about how we interact with the planetary system has become a major issue in society today. However, when the central decision makers get too powerful, devastating consequences can and will occur. This reminds me of one of my favorite quotes from Jefferson, "A government big enough to give you everything you want, is big enough to take away everything you have" Thomas Jefferson.





References
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