Share |

The Unpredictable Nature of Dynamic Systems

Can unpredictability of events be harnessed for real-world applications?
The butterfly effect: small differences in initial conditions have a large impact on how events unfold.

Although general system theory explains how interdependent components work together to make the system more than its subsequent parts (Bertalanffy, 1972), chaos theory explains how tiny variations in initial conditions can have major influence on unfolding events within the system (Capra, 1996; Gleick, 2008) that make prediction a risky, if not impossible process. This essay will explore the nature of chaos theory in systems to discover how the unpredictability of events can be harnessed for real-world applications.

Science discovers a complex world

The ideas of interconnectedness and chaos in nature are recent discoveries in scientific and academic philosophies that have traditionally viewed reality as clockwork; however, these ideas are hardly new to humanity. Regardless, traditional science has attempted to identify and explain the predictable, while dismissing irregularities as errors in measurement, until some started to notice universal patterns in irregularities. Gleick (2008) tells how the US government in the 1980s attempted to implement Von Newman’s vision that small modifications in variables could allow humans to control the weather. However, the weather control experiments failed because even the most complex forecasting systems could produce a predictability window of only three days, with seven day forecasts being useless.

The reasons for the failed experiment could be found in Lorenz’s observations while running computerized weather simulations in 1961. Lorenz expected to be able to predict the behavior of his weather simulation by entering the same variables. However, minute differences caused by computer rounding errors caused random behavior that produced unpredictable results in different trajectories that appeared to start with the same initial conditions. In other words, Lorentz found that small differences in initial conditions had a large impact on how events unfolded. This “sensitive dependence on initial conditions” (Gleick, 2008, p. 23) would become known as the Butterfly Effect and served as the foundation of chaos theory.

Like most revolutionary scientific discoveries, Lorentz’s observations were hardly original, but his unique contribution was that the same kind of sensitivity to small changes can affect even simple systems. Chaos theory helps to show how chance appears in a deterministic world; that predictability requires perfect knowledge of the universe and exact laws of nature. Even in the unlikely case that natural laws become clear, humanity will not likely ever know the state of the entire universe (Strogatz, 2008). As stated by Lorentz, (1963) “any physical system that behaves non-periodically is unpredictable” (Gleick, 2008, p. 18).

Interaction between order and randomness

Unpredictability of a system does not mean the absence of order as the name of chaos theory implies; it means something more like yin and yang: a confusing interaction between order and randomness. The natural shape of chaos takes the form of strange attractors: “strange” meaning the complex geometry of unpredictability; “attractor” meaning the system’s long-term mode of behavior, the point to which a system returns after a disturbance, like homeostasis or equilibrium. The order found in chaos makes it possible to harness chaos for real-world applications (Strogatz, 2008; Gleick, 2008).

The unpredictable behavior in dynamical systems presents a paradox in chaos theory: unpredictability that follows deterministic laws. Strogatz (2008) calls this “deterministic predictability” (p. 13). Deterministic means that the present determines the future and that the laws of nature determine what will happen next, with only one possible future resulting from current conditions. This shifts the focus from laws of nature to consequences of laws “and “finding clever ways to infer consequences” (p. 16).

Capra (1996) says that chaos theory does not make predictions impossible, but it does put predictability in the “qualitative features of the system’s behavior rather than the precise values of its variables at a particular time” (p. 134). This shift from quantity to quality became a key feature of systems thinking. “Conventional math deals with quantities and formulas and objective calculations, while dynamical systems theory deals with quality and pattern” that depends on the perspective of the observer and the horizon of predictability.

Predictability window

From the perspective of traditional science and humanity, Haley’s comet, eclipses, the solar system all seem deterministic, predictable, because they have long predictability windows. However, determinism plus periodicity determines the horizon of predictability, what Lorentz (Lorentz, 1963) called deterministic non-periodic flow. This horizon of predictability is different depending on the system. The horizon of predictability for electricity is milliseconds, weather is a few days, and the solar system is five million years (Strogatz, 2008). Since humans exist within the predictability horizon they can use Newtonian physics to track and predict events. However, Newtonian mechanics leads to generalizations about predictability that chaos theory disproves by explaining that even the most accurate measurements cannot predict outside of predictability windows (Strogatz, 2008; Gleick, 2008).

Viewing the real world through chaos

The concepts of chaos theory helped to explain why the government’s weather control experiments failed. As a dynamical system with high sensitivity to initial conditions and a short predictability window, general patterns of weather can be assumed but the weather cannot be predicted. While people might be able to change the weather, Lorenz asserted, it would be impossible to determine what weather would have done otherwise or if the changes were for better or worse.

Chaos theory provides an interesting perspective into real-world applications that seems to counter conventional wisdom. For example, Capitalist economics is often criticized for its short-term focus, projecting forecasts on quarterly and annual clocks. Regardless of the knowledge and experience that goes into the forecasts, business leaders typically find themselves having to explain each quarter why performance did not meet projections while they adjust the next quarter forecasts to current variables. Seen from the perspective of dynamical systems theory, business leaders learn quickly that events cannot be predicted; they can only be explained--giving rise to the power of public relations. Chaos theory seems to be saying that the short--if even existent--predictability window in a dynamic competitive environment would require shorter projections and faster adjustments if the organization is to adapt successfully to and influence dynamically interacting factors in its internal and external environments.

The short predictability window in economics also seems to bring into question long-term forecasts, like annual forecasts in capitalist economies and the five year plans that are the hallmark of Marxist governments. The capitalist has little influence over a dynamic free market, and must continuously adapt to survive. This proposes a counter-intuitive business strategy that might de-emphasize long-term strategic planning to refocus resources on developing flexible organizations and operations with redundant processes that allow the organization to more quickly respond the environment. On the other end of the economic spectrum, the Marxist government generally has to impose restrictive controls on people and processes in order to progress towards its long-term forecast; but chaos seems to find its way into the most controlled systems or even be caused by the control mechanisms imposed by the government.

As the science of change (Strogatz, 2008), chaos theory also poses some interesting questions for global warming politics. When viewed through a political lens, global warming politics makes sense as a tool for driving societal change to consolidating global power for facilitating sustainable societal development (United Nations, 2002). However, chaos theory also implies some interesting questions about global warming science. With the predictability window of weather being about three days and seven day forecasts being “worthless”, of what value are the 100 to 1,000 year forecasts that fuel global warming politics? Lorenz agrees that people may be able to influence the weather (Strogatz, 2008; Gleick, 2008), and chaos theory would explain how small changes in current conditions can have large consequences. However, as Lorenz’s predictability argument implies, how is it possible to determine whether the results are different from what they would have been otherwise, and if the consequences are good or bad compared to other possible outcomes?

Climate change happens; it always has and will likely continue in the foreseeable future regardless of human efforts to control the dynamic system by controlling interconnected subsystems, including political structures. Even if humans somehow develop methods for controlling the weather, what would be the consequences of stabilizing the environment? As Capra points out, the earth (Capra, 1996) is a dynamic living open system in which the interaction of subsystems generates and support life. Mars and the moon serve as examples of planets with stable climates.

Conclusion

This essay looked at key concepts in chaos theory to explore how understanding the nature of dynamic systems can help to harness unpredictability for real-world applications. Even the smallest variables have random and unpredictable consequences in simple systems; consequences are amplified as systems increase in complexity. However, unpredictability does not mean absence of order. Unpredictability follows deterministic laws that allow chaos to be harnessed for those who can shift from quantitative reasoning to being able to recognize quality and patterns in a system's behavior. Deterministic predictability offers ways to infer consequences, but not to predict events.

Chaos theory provides lessons for and suggests practices that can be applied in the real world. This essay focused on how chaos theory implies that short-term tactical planning might be a more effective survival strategy than long-term strategic planning for business and governments who might otherwise be inclined to focus on long-term strategic planning, and how predictability windows suggest questions about that value of long-term weather forecasts and human efforts to stabilize the climate.

In conclusion, chaos theory shows that the smallest variables can significantly influence unfolding events in dynamically interacting components and subsystems, making predictions virtually impossible beyond predictability windows. In other words, while consequences may be inferred and can be explained, they cannot be predicted.

Works Cited

Bertalanffy, L. V. (1969). General system theory. New York: George Braziller, Inc.

Capra, F. (1996). The web of life. New York: Anchor Books.

Gleick, J. (2008). Chaos: Making a new science (Second ed.). New York: Penguin Books Ltd.

Lorentz, E. N. (1963). Deterministic nonperiodic flow. Journal of the Atmoshperic Sciences , 20, 131-141.

Strogatz, S. (2008). Chaos. Chatilly: The Teaching Company.

United Nations (2002). Agenda 21: The United Nations programme of action from Rio. Retrieved September 23, 2009, from Division for Sustainable Development: http://www.un.org/esa/dsd/agenda21/