It should be pointed out at the start that there are some stories in life for which the ending is not well understood unless you know the beginning. But the beginning may not seem relevant until you know the ending. It is like landing a ship on a foreign shore. If you knew in advance that you had landed on an island, there would be no need to explore the entire shoreline. But the only way you can be certain that you have landed on an island, is if you do walk the shoreline and end up back where you started. Thus, even though you have ended where you began, you have acquired something in the process. In other words, there is a certain tediousness to acquiring knowledge one piece at a time. You need to pick a beginning, make a journey, and continue until you come to a natural end. But it isn't until the journey is completed that you can understand which of the details are important. Even then, sometimes the details themselves are not as important as the way in which they come together, like the brush strokes of an artist coming together to create a new picture. This is mentioned now to forewarn you that although this discourse may wander and not always seem directly relevant, what is revealed should eventually tie together in a comprehensive package of understanding for you.
A large part of mankind's successful survival and continued growth over thousands of years comes from an ability to observe or experience specific phenomenon and then generalize into concepts. As the concepts are refined, they become theories. And as the theories are tested over time, they lead to fundamental rules: rules in the form of "universal truths" that explain the operation of the cosmos, the universe, and most importantly our planet, the environmental corner of the universe we all inhabit. Correct behavior, that is behavior which is in harmony with one's environment, is essential to survival. Understanding the operation of one's environment leads to an ability to predict. Correct prediction is the single most important element to correct behavior and thus, survival and success. The same rules that explain the physical operation of the universe around us become the foundation for the behavioral rules we use to interact with our environment. We learn to use these rules to govern our own behavior because their predictive abilities are at the heart of our understanding of cause and effect. Once we master the concept that events have consequences and behavior has consequences, we understand that if we can influence the event or change the behavior, we can affect the resulting consequences and improve the chances of survival and even the quality of life.
A familiar example is the law of gravity. Even though we still do not know exactly what gravity is, we can develop rules about its force and effect. Children are able to observe things fall to the ground and develop a general understanding of the principle of gravity. The logical extension of many observations allows people who have never actually fallen off a cliff to still predict what might happen if they were to fall off a cliff. Even young children will tend to be cautious in high places once they understand the consequences of falling. Children also understand that it can hurt when a heavy object falls on them. We didn't need Sir Isaac Newton to develop the Law of Gravity to assure the survival of the human race. Many primitive aborigine people in the world today have never heard of Newton, but they understand the effects of gravity very well. They have internalized certain rules of behavior that protect them from the adverse effects of gravity. However, moving from an intuitive concept to a formal theory with rules has definite advantages. Sir Isaac Newton enjoys a prominent place in history books because of the important contribution he made to our thought process. Formal theories allow us to predict future results and manipulate the world we live in. If you want to fire a space craft from earth and land on a planet that has a different orbit and different rotation, a complete and clear understanding of the law of gravity (as well as other physical forces) is essential.
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Most people tend to live by a random collection of personal experiences (fire is hot, knives are sharp) and aphorisms or old wives tales such as, "Look before your leap", or "A bird in the hand is worth two in the bush". These behavioral fragments are combined with a disjoint collection of formal schooling and perhaps wrapped in a moral or religious behavior code. But few people have a comprehensive tool or framework to assist them with the complicated issues and problems found in their daily environment. The Nomothetic Theorem presents a useful framework for the analysis of complex systems.
The progression from an intuitive concept to a formal theory with axioms, conclusions, and rules is a significant break through step; but, when it comes to complex systems, it is a step that most people in the world have not taken. It is perhaps because people have relatively few nomothetic principles or "universal truths" that are sufficiently broad to be useful in their daily lives that we sometimes see people engage in apparently irrational or inefficient behavior. The belief structure that people operate under can have a major impact on people's direction in life and ultimately society's ability to cope and the degree of success or survival of the human race. People's view of the world is colored with the perspective of different explanations. Where rational explanations are missing, people tend to turn toward superstition or religion for guidance. We can expect to see different attitudes and different results depending on whether people draw from religious faith, personal or anecdotal experience, scientific logic, or some other guiding principles. For example, if a person has a string of misfortunes do they look toward God or do they consider the Law of Averages? Will they give up because they think God is punishing them or fate is against them? Or will they persist because they believe the statistical odds favor their success, or because science says they are pursuing an achievable goal, or because they think God favors them, or because of some other belief structure?
Regardless of where the rules of behavior originate from, their success depends on whether the behavior successfully integrates with the environment. Ultimately, success depends on correct pattern recognition. As long as we understand that the sun always rises in the east, for most purposes it is less important to know whether it is because the earth is spinning, the sun rotates around the earth, or the earth rotates around the sun. We may think the god Apollo is pulling the sun behind his chariot as he flies across the sky. The answer to why the sun rises in the east is initially less important than merely recognizing the pattern. Knowing why is only useful if it improves the accuracy of prediction. Knowing there is a summer and winter is more important than knowing why. But we seek to know the answer why so that we can improve our predictive abilities. We want an explanation for eclipses, and we want to be able to navigate dependably by the stars. As we observe more patterns, eventually all these patterns come together into a workable model that serves as an explanation. But regardless of the explanation, the predictive ability of the model is all that matters. Survival depends on successful pattern recognition which is at the heart of prediction.
Just think about how people's attitudes have changed as science has brought new understanding and theories to the field of medicine and disease. People learned from experience to shun the sick because that minimized the transmission of disease. Although people may not have known why illness occurred, those who survived learned successful behavior patterns based on cleanliness and avoidance. But many people also engaged in useless behavior. When plagues swept the land, people made sacrifices to the gods out of fear and cast blame wherever it seemed most appropriate. Now we understand how most common diseases are communicated, and doctors know how to effectively cure many illnesses. People's attitudes have generally changed from fear to constructive care.
There are still many things in our universe that people have trouble explaining and dealing with. When we suddenly find a new tool that allows us to get a better grip on a problem, we want to run through the streets, like Archimedes, shouting Eureka! There is comfort knowing that we can finally put a little more order and understanding into our lives. The exciting process of discovery is the giant step that goes from knowing we have a need, to actually finding the right tool to solve the problem.
A theory is simply a tool of understanding that should enhance one's ability to deal more effectively with the world. People's perception of usefulness will affect whether or not they choose to adopt a theory. But if the theory represents a universal truth, it should apply equally to everyone regardless of whether they embrace it or not. When a theory is first developed, it needs to survive repeated tests both in scope and over time in order for confidence to be gained in its usefulness. The validity, and thus the usefulness, of any theory ultimately depends on the degree to which it is shown to be universally true.
I mention all this because the theory that I am going to present to you may seem intuitively obvious. That is good! It implies that we are dealing with basic principles of the universe. However, a sense of familiarity is not the same as having a valid universal truth and a clearly defined foundation from which we can make useful predictions. The Nomothetic Theorem has been developed from observations, and the reorganization of existing knowledge. Importantly, the perspective afforded by different time scales plays a significant role. It is hoped that describing a formal theory will provide a useful tool to explain many diverse complex systems such as: physical and mechanical systems, social systems, biological systems, information systems, economic systems, or any other complex system or group of systems.
The Nomothetic Theorem
The Nomothetic Theorem acknowledges that our universe exists in the context of a balance between opposing forces that struggle against each other. It is therefore fitting that the theorem itself is a dualism. It consists of two theories that are themselves interdependent as polar opposites. The Nomothetic Theorem says every complex system experiences continuous random motion; and every complex system, when not influenced by any outside force, will move toward increasing levels of stability. Thus, we have the Theory of Volatility and the Theory of Stability.
Much of the world's knowledge is very old. The strength of the Nomothetic Theorem is that it does not contradict that wisdom which has stood the test of time. The new ideas being presented to you are, in many cases, simply a new perspective that reorganizes many of the very old truths.
The Chinese speak of the harmony between the opposing forces of Yin and Yang. Just as you cannot have darkness without light, good without evil, up without down, you cannot have stability without volatility. Therefore, the Nomothetic Theorem encompasses the Theory of Stability and the Theory of Volatility. Let us begin with the Theory of Stability.