What is Chaos Theory?

Chaos theory began as a field of physics and mathematics dealing with the structures of turbulence and the self-similar forms of fractal geometry. This is not very descriptive. As it is popularly understood, chaos deals with unpredictable complex systems. Chaos theory stems, in part, from the work of Edward Lorenz of MIT, a meteorologist, who simulated weather patterns on a computer. Working with a computer having limited memory, after viewing a particular pattern, he wanted to recover the data and started the program again, except he put in the values rounded off to 3 places instead of the original 6. He was surprised to find a completely different result on his computer than he had before, and it looked like this when printed out:

In chaos theory, "The Butterfly Effect" refers to the discovery that in a chaotic system such as the global weather, tiny perturbations in the system may sometimes lead to major changes in the overall system. It is theoretically possible that a slight rise in temperature in the ocean off the cost of Peru will create tiny changes in the air flow that would eventually lead to different weather in North America and Europe. In most cases the slight change would make no difference whatsoever, but when the system is unpredictable at a certain stage, the future may unfold quite differently, depending upon what little difference occurred. 

Chaos theory is reminiscent of Gestalt theory; a whole is greater than the sum of its parts. It is also similar to systems theory, for chaos theory is only concerned with systems.  The application of chaos theory to management depicts organizations as complex and unpredictable because of the relations among constituents of a system. 

Many writers seem to regard chaos as disorder. Perhaps it is a bad name, because chaos makes you think of anarchy, mobs, randomness, a mess and out of control.  So what is the real meaning of chaos theory?

Let's consider the discovery of Edward Lorenz in more detail. What Lorenz was trying to do, as a meteorologist, was to predict weather patterns by simulating them in a computer. He put in some equations but his computer was slow and klunky, because this was 1961 before Dell was manufacturing slick, powerful cheap computers. He kept a continuous simulation running on his  simple computer that would output 24 hours worth of his simulation for every minute as a line of text on a roll of paper. 

...Line by line, the winds and temperatures in Lorenz's printouts seemed to behave in a recognizable earthly way. They matched his cherished intuition about the weather, his sense that it repeated itself, displaying familiar patterns over time, pressure rising and falling, the airstream swinging north and south.  (James Gleick)

One day in the winter of 1961, wanting to examine one sequence at greater length, Lorenz took a shortcut. Instead of starting the whole run over, he started midway through. To give the machine its initial conditions, he typed the numbers straight from the earlier printout. Then he walked down the hall to get away from the noise and drink a cup of coffee. When he returned an hour later, he saw something unexpected, something that planted a seed for a new science.

He looked at one set of numbers, then back at the other. He might as well have chosen two random weathers out of a hat. His first thought was that another vacuum tube had gone bad (Andrews, 1996).

What was the difference?  According to Andrews, in the computer's memory, six decimal places were stored: .506127. On the printout to save space, just three appeared: .506. Lorenz had entered the shorter, rounded-off numbers, assuming that the difference-one part in a thousand-was unimportant. As Andrews put it, 

A small numerical error was like a small puff of wind - surely the small puffs faded or canceled each other out before they could change important, large-scale features of the weather. Yet in Lorenz's particular system of equations, small errors proved catastrophic.

The theory is concerned with natural processes expressed in terms of mathematical formulas, calculations that were virtually impossible without computers. In differential calculus, chaotic systems are represented by nonlinear differential equations, which deal with natural phenomena such as water turbulence, friction, or financial markets.  Unlike linear equations which behave predictably, chaotic systems are represented by nonlinear differential equations that change abruptly or discontinuously. In a nonlinear equation, a small change in one variable can have a disproportional, sometimes catastrophic effect on other variables.  The nonlinear equations reveal breaks, loops, recursions and all kinds of turbulence (Briggs & Peat, 1990). 

Characteristics of a chaotic system are as follows: 

Sensitivity to Initial Conditions.  As in the case of Lorenz's work, a complex system reacts to different variables at the outset in unpredictable ways.  Even starting with the same, exact or slightly different variables in a model will not result in the same outcomes, if the system is complex. 

Time Irreversibility. In a complex system, there is never the same context twice. Thus, a college, business, or team with essentially identical personnel and similar characteristics will never perform exactly the same as another (or itself). An analogy often used to explain this is, "You never step in the same river twice," meaning the system is never exactly the same.  The water you cross is different than a moment ago or a few moments later.  In fact, with time the river may meander, dry up, or become a flood.  As applied to management, a strategy or decision will never be made twice with the same context. 

Strange Attractors.  Attractors in chaos theory are like the influence of gravity, sets of values in the "phase space" to which a system migrates over time, also called islands of stability (possible states of a dynamical system).  In a formula an attractor can be a single fixed point, a collection of points, a complex orbit, or an infinite number of points. While it is less clear how these are represented in a social organization, there is the belief that any organization has "attractors" that cause the behavior of the organization to alter over time, depending upon which social, economical, or other forces drive the system at a given point and how they interact.

Fractal Forms. A fractal is any curve or surface that is independent of scale. Any segment, if magnified in scale, appears identical to the whole curve. In the management analogy, it is assumed that different levels of organization resemble others, like a fractal in the managerial hierarchy. A form of social structures can be examined in relation to characteristics of the whole system at the macro and micro levels.

Bifurcation. Bifurcation is the sudden appearance of qualitatively different solutions to the equations for a nonlinear system as a parameter is varied. In an organization, two different patterns (groups) can emerge to address an issue differently, as complexity increases.  This is often recommended as a source of creativity.

The appeal of chaos theory is the view that organizations are complex adaptive systems that have behaviors similar to those found in nature--different stages of stability and chaos. Rather than control an organization, a manager is prompted to take advantage of its complexity.  Theorists in management and social organization now believe that organizations are also non-linear dynamic systems, having the same characteristics as natural phenomena  (Stacey, 1996).  The organization is often seen as complex adaptive system comprised of the formal and shadow systems, and in this way the analogy is made between chaos in natural systems and the social organization.  Similarly, the long-term behavior of the organization is unpredictable, akin to the inability to predict hurricanes far into the future.  Stacey addresses this issue by stating that managers much learn how to manage the anxiety that accompanies being on the edge of chaos, employing a nearly mystical concept of "creative destruction."  Stacey ends with optimism, believing that although long term outcomes are impossible to predict, dealing effectively with change and challenge on a daily basis will ultimately result in success. 

It is obvious from mathematicians and scientists who study natural phenomena, such as hurricanes, cardiac patterns, or friction, the mathematics on a computer can show a chaotic pattern.  As Dennard (1996) said: "What good is a science of chaos, if it doesn't tell us how to overcome chaos and complexity?' Isn't that what management is about?' (p. 495).  In the final analysis, this is precisely the most important question.  If a manager cannot control anything or force a system into some form of order, is management possible?  Is a manager necessary? 

Except in specific cases, such as world monetary flows and heart arrhythmia that can be easily represented numerically, it is difficult to prove that social systems have the same traits.  Nonetheless, as a metaphor or an analogy, chaos theory is often used as a way to conceptualize management theory and other social systems.  Therefore, the efficient manager will plan for and expect constant change in the environment. His or her goals become not a set of results but a series of contingency scenarios to which he or she can react in the short term at some later date in the future.

The same principle applies to human society. Tiny changes in one person's state of mind can, on occasions, lead to major changes in society as a whole. Or simple acts can lead to unintended consequences. 

Example 1:

Back in the early 1980s, IBM was the dominant company in the world and mainly concerned with mainframe computers. It decided that there might be a market for personal computers, since there were good sales of  Apple, Atari, Commodore, and other small companies. Before they could produce their own PC, they needed a new disk operating system (DOS) because the one they had was designed for the large mainframe computers. In search of a DOS  they ended up in negotiations with Bill Gates, who had a small company claiming to have a DOS system.  Actually, he did not but he knew someone who did and bought the rights immediately for a few thousand dollars. He made a deal with IBM to get a royalty on every disk operating system (DOS) sold. Believing that PCs would not amount to much, IBM made the deal. You know the rest of the story, with Microsoft becoming one of the biggest companies in the world and IBM suffering huge losses and its place in the firmament as a big, powerful company. 

Example 2:

Theresa LePore decided to make the typeface on ballots larger for Palm Beach voters in the US Presidential election, because many of her residents were older and had difficulty seeing small print. She did not notice that it now took two pages instead of one that could confuse voters about which button to push when they voted.

As a result 19,120 voters punched holes for both Pat Buchanan and Al Gore, and their ballots had to be thrown out. Another 3,407 people appeared to vote for Pat Buchanan, which he himself found most surprising , expecting only a couple of hundred votes. Ms. LePore's new design caused about 22,000 votes for Al Gore to not be counted. If they had, Florida would have gone to Gore, he would have been President, and the U.S. Supreme Court would not have selected Bush.  Gore would have likely signed the "Kyoto Protocol on Global Warming," probably not declared Iraq part of an "axis of evil" and probably would have not invaded Iraq. Of course, other things would certainly have happened that we cannot imagine. 

Example 3: 
 

On the Titanic, the crew had no binoculars, which could be used to see approaching icebergs. Captain Edward Smith also canceled the scheduled life boat exercise for passengers.  In addition to the overweening attitude that the ship was unsinkable, these two small factors contributed to the deaths of 1500 people after the ship struck ice. Captain Smith also refused to reduce his speed after there were warnings of ice in the channels. When it was evident that the ship would sink, neither the passengers nor the crew knew exactly what to do. They did not know which boats to get into, and the crew did not know that it was possible to lower the boats with people already in them. In fact, there were not enough life boats for everyone on board. Captain Smith's decision to cancel the life boat drill caused massive loss of life. A little thing with big repercussions.

From a social perspective the most important concept may be that complex and unpredictable results can and will occur in systems that are sensitive to their initial conditions. The generator of unpredictability in complex systems is what Lorenz calls "sensitivity to initial conditions" or "the butterfly effect." The concept means that with a complex, nonlinear system, very (infinitely) small changes in the starting conditions of a system may result in dramatically different outputs for that system. 

We know that all organizations of human beings are systems, that there is always change, and today there is rapid technological change and globalization. We must all be flexible, willing to learn new things, willing to question our assumptions all the time, and to recognize that we are blinded by our own prejudices and biases. Things that worked in the past may not work in the future, so you have to keep on learning and experimenting.  Even if you don't change, everything else and most other people will, so they will change you environment so much that you will be forced to react. 

As you consider yourself, your life, your family and friends, and your place of work, do not fall prey to illusions and be on guard to your own biases and prejudices. Be aware of the impermanence of existence and the different interpretations of reality. You nor I can know everything, or even know most things for sure, because each mind is different, each person has different experiences, and we are all subject to false interpretations. 

People with schizophrenia have chemical differences in their brains that create extraordinary delusions. They hear voices, feel compelled to follow the orders of unspoken masters, and are often extremely paranoid. Nonetheless, what they hear, see, and feel is real to them, because reality is created by the brain. Free of chemical imbalances, your brain is only better by degrees because you do not always see and hear things clearly, nor always pay attention, or concentrate.  You forget, filter, and distort data, which alters your view of reality. 

That finishes our tour of systems theory and Gestalt laws. We can try to summarize as follows:

• The parts of a system communicate with one another.
• The system has an environment with which at least one of its parts communicates.
• The system is always changing.
• The behavior of the system cannot be predicted from the behaviors of its parts. 
• All systems have similar characteristics. 
• Many managers still see organizations as "machines" that can be wound up with rules and procedures. It is not possible for the manager to control what happens to the system. 
• An organization near death (one traumatized by fear and anxiety) will be stagnate and certain sub-systems will wither.
• If there is too much top-down control, creativity and productivity will be stymied. 
• A system as a whole works differently than its parts. 
• Parts alone cannot do what the system can do (a motor with no truck, a movie with no plot, a body without a heart, an individual without a team).
• Effective organizations (individuals) have networks communicate with others). 
• Each part does something special, and the sum of the parts make a whole.
• One of the lessons of systems theory is that there is no preferred observer, and a lesson from Gestalt psychology is that your perception as an observer may be wrong.
• Gestalt psychology teaches us that we cannot see reality objectively, and our mental models of the world are deeply ingrained with personal assumptions, even mental images that influence how we understand the world and how we take action---we may be wrong!
• Working with others should make you aware that they have different mental models and that you must build a common vision or shared picture of the world and your goals.
• Nothing is stable, things are always changing.
• The effects of some behavior on an organization are not predictable. 
• The relationships between elements in a complex system are short-range, but the information that passes through a system is likely to be altered or modified in some way.
• A small stimulus may cause a large effect, or no effect at all. 
• Energy and information are constant inputs and outputs of any system crossing the boundaries. Therefore, every system is in a constant state of flux, trying to achieve equilibrium. 
• Parts cannot contain the whole.
• No element in a system can totally control a system, except in the most dire circumstances.  If it can, then, then it portends death (starvation for a human, running out of money for a business). 
• Any organization is complex, and the components of the system make the system complex.
• A system is adaptive, so the organization will change.
• The future is unpredictable. 
• You can forecast the future by erecting several potential plans, or scenarios, so it is possible to plan for different possibilities but you will not know for sure which one might appear.