We have a sense that the status quo tends to persist because we observe signs of stability, such as repetitive patterns, even in very complex systems. Yet reliance on patterns that should yield predictable outcomes causes problems in our everyday experience. When we look for order, we do not always find it. Unfortunately the simple concept of cause and effect that we learn as a child does not serve us well in the real world. As we get older, we start talking about things like "extenuating circumstances", "unforeseen results", and "accidents". (Highly paid consultants use fancy language like: "Outcomes that are not input determinant.") The reality (that even many adults do not understand) is that our world is not typically made up of simple linear relationships where one cause leads directly to a predictable effect. Frequently we are dealing with systems in which an input rarely causes the same direct effect consistently time after time. A single input may filter through many decision points in a complex system causing one of many different possible results that are hard to predict. Even if a subsystem or group of subsystems appears orderly, the introduction of a new force, often from the intersection with other subsystems, can result in relationships so complex that total disorder appears to take over. Frequently it seems that we live in a world of random events. Other times we can, after the fact, trace through a chain of relationships to explain a series of causes and effects. But this exercise seems fruitless since it isn't likely that the same chain of events would ever be repeated in a billion years. How does one cope with chaos?
 |
Fortunately the situation is not hopeless. What appears random, may not be -- we simply don't understand the complexity or haven't identified the pattern yet. In other cases, what starts out as truly random won't remain that way for long. In the absence of any new outside force, chaos does not persist.
The Theory of Stability rests on the axiom that: "Energy seeks to cure an imbalance". This simply means that energy is that property in the universe which causes an imbalance to push toward balance. Energy can perform work because it wants to move. Starlight wants to radiate outward. Heat wants to radiate outward. Water under mechanical pressure wants to spray outward. This desire of energy to cure an imbalance subsumes Aristotle's statement that "Nature abhors a vacuum". By curing imbalance, energy seeks to increase stability.
Another way to restate the concept of imbalance is to be specific about the direction in which energy wants to move. "All energy attempts to distribute itself to the level of maximum entropy". The concept of entropy typically confuses people. Entropy is a measure of unavailable energy. Thus energy wants to move in the direction of diffusion and depletion. Entropy serves as a measure of how close a system is to equilibrium. Although entropy cannot be measured directly, the degree of entropy can be observed in a system. In the physical world, entropy can be derived from measurable properties such as temperature, pressure, volume, and specific heat. If the system being considered is an information system, the level of entropy can be derived from how relevant the information is and who controls it, or how widely it is disseminated. In a social system, we talk about the level of entropy as a catalyst for social change. In essence, entropy represents the removal of potential. Potential is a measure of the energy that can create work; and work is defined as a force applied across a distance. Thus, as entropy increases, potential decreases. Like water running down a hill, all complex systems seek the level of least potential, or the level of maximum entropy. When there is less potential, less work can be performed, so there is less opportunity for change. A decrease in change or the rate of change means an increase in stability. Therefore, the degree of equilibrium in a system increases as entropy increases; and the state of greatest equilibrium corresponds to the state of greatest entropy. In other words, the point of complete equilibrium (the point of maximum entropy) is the preferred or most stable state. If 'stability' and 'entropy' have equivalent meaning, it follows that when an isolated system achieves a configuration of maximum stability, it can no longer change because any change would require a decrease in entropy. A decrease in entropy requires an infusion of energy. And by definition, there is no way to introduce additional energy into an isolated system. Thus we see the evolution toward stability is a one way street.
The Theory of Stability can be stated very simply as: "Every closed system tends to evolve toward stability". Finding various levels of stability is what allows the human race, as well as all life on earth, to cope, adapt, and survive.
To understand the Theory of Stability, we must first make sure we agree on the definition of the word stability. For the purpose of this theory, stable does not mean static and unchanging. Unchanging may, in some cases, be the ultimate level of stability; but systems seek various levels of intermediate stability on their journey toward maximum entropy. Stable means operating over time, or existing at any moment in time, within a limited range of change, or in a known or familiar manner. Thus, a pendulum swinging back and forth is stable. A planet continuously orbiting the sun is stable. A pendulum on a clock sitting on a planet spinning on its axis and orbiting the sun is stable (at least temporarily). When the clock winds down and the pendulum stops swinging, it will be at a new level of stability.
As an example, the physiology of the human brain is structured around a dependence on familiar patterns or known experiences. The brain is constantly receiving millions of information inputs from sight, sound, taste, touch, smell, etc. It couldn't function efficiently if it couldn't group inputs and categorize them according to some system of priority. The brain defines a range of normal experience and then focuses on the events that are outside of this normal range. In other words, the brain seems to categorize according to some level of expectation or prediction. For example, in a landscape that is expected to be motionless, many details may be missed by a brain that is too busy with other tasks to care about every item in a stable environment. But any motion will command immediate attention because it stands out and is not expected. Since things that are out of the ordinary may constitute a threat to survival, we are programmed through heredity to devote extra attention to unforeseen events. This implies that even though we live in an extremely complex world, most events fall within an acceptable range of stability or predictability so that the brain can differentiate the special events that constitute exceptions.
Stable does not mean fixed, although sometimes that may be the case. An important element of stability is predictability. But predictable does not mean simply repetitious. Predictable means operating within a limited range or in a manner that allows us to forecast the next location, the next formation, or next event. Thus, stability means order and dependability. Stability implies a "balance" of the forces acting on a system. An airplane flying at 550 mph across country is not static, but it can be stable. When aerodynamic lift is in balance with gravitational forces, and engine thrust is in balance with drag, the airplane can be thought of as stable. From this example we can perhaps understand that stability does not mean unchanging. The airplane is very dynamic. But we can predict where it will be. And we can depend on our prediction. A stable system can therefore include change. In fact, constant change can itself be a form of stability.
Physics provides an example for the concept of stability with the law of Conservation of Momentum. If the amount of something remains unchanged during a physical process, we say that the quantity is conserved. Inertia (resistance to change) is a property of all objects of mass. Momentum is defined as inertia in motion. The product of the mass of an object and its velocity is momentum.
momentum = mass x velocity
When one billiard ball has a head-on collision with another billiard ball, the momentum of the first ball is passed on to the second ball. The relative motion of the balls has changed (first they are moving together, then they are moving apart), but the total momentum (the quantity mv) is conserved. It is therefore possible to say the system as a whole is stable even though some of its components are changed. There is a direct linear relationship as the momentum passes from one ball to the next.
Chaos is composed of multiple components seeming to move in a non-relational manner. The Theory of Stability says the majority of the components will tend to offset or neutralize each other. Therefore any net change to the whole system will tend to be small. And over time, the net changes themselves will tend to neutralize each other. There is a tendency for complex systems to evolve toward stability.
 |
There are two important parts to the statement made in the above paragraph. 1) If we take a snapshot view, the majority of components will be neutralized by an offsetting force. In other words, at any one instant in time, we only need to focus on the net imbalance of the system to understand the result and make an accurate prediction. 2) When we look at the system over time, the net imbalances will themselves tend toward stability.
The next concept to understand is "drift". As we said above, stability does not mean unchanging. The net change to the system over time is called "drift". Drift can be thought of as the average result of the net imbalance of all forces on a system. We tend to think in a linear fashion. But just as complex systems can be multi-dimensional, drift can also be multi-dimensional. However, most practical applications don't have to be complex to be useful. Continuing with our example of an airplane, if the plane is stable, the drift may be west to east across country. If there is a wind from the north, the drift may be pushed southeast across country. If the plane is planning to land, the drift may be southeast and descending. As we shall see later in the Theory of Volatility, stable systems are subject to volatility (such as clear air turbulence) and to "events" (such as an engine failure). Volatility does not cause a lasting change to drift. But "events" do change drift.
 |
Once we understand the Theory of Stability, several useful rules can be constructed.
- Outside random interference to an otherwise closed system will delay the evolution toward stability. Corollary: The correct application of influence to a chaotic system may speed its progress toward stability. Example: Whether we are dealing with international politics or children squabbling on the playground, interference by an outside party may confuse the situation by shifting the balance of power and delay any settlement. On the other hand, if an outside party can correctly identify the issues in a dispute and apply appropriate pressure, a lasting settlement may be imposed more rapidly than what would naturally evolve.
- In a closed system, the evolution toward stability is a one-way street. In other words, entropy (the degree of equilibrium) can only increase. It cannot decrease without the introduction of a new force from the outside. Therefore, in a closed system, often the best method to deal with chaos is to wait. Over time, chaos will evolve into a recognizable level of stability. Example: A spectacular aerobatic maneuver often seen at airshows is called the lumpshovack (polish for "headache"). As the plane tumbles end over end and wing over wing in a random manner, the preferred recovery technique is for the pilot to release all controls and wait until the plane settles into a recognizable position (such as a spiral dive). The pilot then performs a standard recovery from that attitude.
- On its voyage to increasing levels of stability, a system may be temporarily destabilized by internal events. The level of stability of a system may be temporarily influenced by the level of stability of its subsystems. Example: Contaminants in the fuel tank of an automobile may periodically clog the fuel pump or injector nozzles. The instability of the fuel mixture affects the stability of the fuel system which affects the stability of the engine system which in turn affects the dependability of the entire automobile. If a change is not made to the subsystem, stability for the automobile may eventually mean sitting in one place.
The Theory of Stability appears to be very simple, and it is. But its effects are far reaching and can only be properly applied alongside an understanding of the Theory of Volatility. Therefore, before I expand on the applications of the Theory of Stability, let us consider the role of volatility in complex systems.