The Theory of Volatility starts with the axiom that: "No one thing can be in two different places at the same time". In the space-time continuum of four dimensions, this is the same as saying: "Every unique point in all four dimensions can only be occupied by one unique thing". One thing cannot be in two places at the same time, nor can two things occupy the same place at the same time. Any violation of this axiom should make us suspect that what appears as one thing is in fact more than one thing. Or what appears to be two different places is in fact the same place. Or what appears to be the same time is in fact two different times. For our purposes, the most interesting aspect of this axiom is the relationship between different places and time. Whether we select two different points relative to one dimension, two dimensions, or three dimensions, the concept that defines the space or distance between the points is dependent on motion; and motion is dependent on time. In a broader sense, dimensional space cannot exist without time, and time is meaningless without motion.
In order to define the distance between any two points, it is necessary to consider what is different from one point to another. Difference comes from change, and change comes from motion. If time did not exist, it would be impossible to witness change, and motion would not exist. Without time and motion, it is impossible to arrive at any concept of distance or size. Distance is a result of change over time. This argument is expressed mathematically in the simple formula:
If motion does not exist, rate equals zero; and therefore the distance equals zero (i.e. distance does not exist because there is no change during any period of time). Likewise, if time does not exist, distance does not exist, and there is no such thing as space.
From the axiom "No one thing can be in two different places at the same time." it can be concluded that time and motion are essential ingredients of our three dimensional space environment. You cannot have one without the other. From this spring board it is easier to leap to the Theory of Volatility which regards motion as omnipresent.
The Theory of Volatility consists of one statement: "All complex systems experience continuous random motion". There is motion! This may seem extremely simplistic; but it has a number of implications, particularly when combined with the Theory of Stability.
Since the forces that cause closed systems to evolve toward stability counteract volatility, the Theory of Volatility, while stating that there is random fluctuation, accepts the fact that there is a limit to the degree of normal fluctuation in a closed system. The outer limits of the normal, random fluctuations define a normal range of volatility. By definition, motion or changes that occur within the normal range of volatility are random. Therefore the Theory of Volatility says, "The next movement from any point within the normal range of volatility is unpredictable." The normal range of volatility contains one (or more) ultimate points of stability. Although the size of the range of volatility may itself change over time, at any moment in time, there is a discrete and measurable range of volatility known as the "normal range of volatility".
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The "norm" is the point of stability that the system is evolving toward and is found within the normal range of volatility. Frequently, but not necessarily, the norm is the mid-point of the normal range of volatility. It is possible for there to be more than one possible point of ultimate stability. In addition to discreet points, stability may be defined by an orbit or a range of oscillation. However, in all cases there will be an accompanying range of volatility. Due to system drift, the point of stability that defines the norm (and its surrounding range) is in fact a trend that is continually evolving over time toward stability (equilibrium or entropy) in direction and degree and dimension.
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Random motion takes on significance when it becomes a deviation from the norm that exceeds the normal range of volatility. An extreme movement beyond the normal range of volatility is called an "event". An event may be caused by something internal to the system or it may be an external force caused, for example, when two systems (or more accurately, subsystems) intersect. The effect of an event is to put pressure on the norm and perhaps ultimately move the norm unless there is an equal and opposite "balancing" event. An event, or a series of events, may change the rate of change of a trending norm or start a new trend. The influence on the norm is a factor of time and degree of deviation. 1) The more recent the event, the more relevant its effect. 2) The more extreme the event, the greater the effect on the norm. 3) The longer an event or series of events persists, the greater the effect on the norm. Events typically cause a change in the normal range of volatility as well as a change in the norm.
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The usefulness of the Nomothetic Theorem comes from its prediction of next point position. Accurate predictions can be built from the theory's rules, specifically: Over time, all points will tend to converge with the norm. However, because of the normal range of volatility, predictions cannot be made that are more accurate than the range of volatility. The greater the deviation from the norm, the higher the probability that a move back toward the norm will occur (unless the deviation is caused by an "event" of such magnitude that it alters the trend of the system, thus changing the norm). The longer a deviation from the norm persists in one direction, the greater the probability that a change in the direction or degree of the trending norm will occur. (In other words, a sustained series of events will cause the norm to converge with the next point rather than the next point returning to the old norm.) Older events help define the range of volatility, but have a decreasing influence on defining the future norm. Events often provoke reactionary events which cause increased volatility. Obviously, an increase in volatility destabilizes the system and makes it harder to predict when and how stability will be restored.
A simple illustration of a system that embodies these principles would be a dog tied to a very heavy weight by a short leash made of an elastic material. Sometimes (more often when first placed there and less often as time goes on) the dog may wander away from the weight by stretching his leash. However, the pull from the leash will eventually encourage the dog to return to the weight and wander less far in the future. Most of the time we can predict that the dog will sit very close to the weight. We can't predict exactly where he will sit because he is allowed a certain range of volatility (defined by the length of the leash); but he will tend to sit close to the weight. It is possible that some event may occur that could cause the dog to run away with such force that the leash is stretched to its limit and the dog actually drags the weight behind him. However, because it takes such a large effort to move the weight, this doesn't happen very often and it typically doesn't last for very long. Once the dog gets tired, the weight will stop moving and the stretched leash will tend to pull the dog back to the weight. The weight will be in a different position that will allow the dog a different predictable limited range of motion. The entire system has drift given to it by the dog's master who moves the weight six feet to the east every morning to prevent the dog from wearing out the grass in one spot.
The Nomothetic Theorem gives us a framework from which to view and measure numerous everyday events that are happening all around us. For example, over the centuries the practice of medicine in the western world has been defined by the Hippocratic oath as well as laws of the sovereign state and ethics and rules of conduct promulgated by medical associations. The practice of medicine has experienced normal volatility that comes with the occasional malpractice suit or technological advance or the promotion of a personality like Dr. Spock, the "baby doctor". But within this range of volatility, society has been in general agreement on the duties of a doctor. Then along came the Karen Ann Quinlan case in the United States where the ethics of disconnecting a patient from life saving support systems became an issue of dissension. This was an "event" (a deviation from the norm) that started to change the norm of medical practice. Next came Dr. Kervorkian, known as "Doctor Death", another "event", that raised more controversy with practices that push even further outside the normal range of volatility. It is one thing to allow a patient to die by not providing extraordinary medical support. It is quite another thing to actually assist in a suicide. What is significant about Dr. Kervorkian is, not only his degree of deviation from the norm, but the fact that he was allowed to persist for so long in spite of feeble legal attempts to contain him. The Nomothetic Theorem causes us to focus on both the degree of the deviation and the persistence of the deviation over time. The Theorem predicts that, to the degree that Dr. Kervorkian (and any other doctor like him) is allowed to persist, the norms of society are going to change and the acceptable duties of a medical practitioner are going to be redefined. That is to say, although assisted suicide is a deviation from the norm, the Theorem predicts that because the deviation was not immediately greeted with great intolerance and punishment, there has not been a return to the norm, and the norm is probably going to change.
A similar situation is the escalating level of violent protest that is occurring at abortion clinics. Peaceful protests and minor skirmishes were within the normal range of volatility. But now we are seeing people murdered simply because they work at a clinic. An event (a significant deviation from the norm) occurred when the TV program 60 Minutes interviewed a Catholic priest who preaches that such murders are not only justified but are in fact demanded by God's teaching. The Nomothetic Theorem does not make any value judgements about what is happening. But the theorem does allow us to understand and predict the trend regarding how this issue will be resolved. The fact that the TV is publicizing this point of view, and the fact that the Catholic church has refused to fully denounce this priest and strip him of his robes and duties tells us an event is taking place that threatens our norms. Pretty soon we need to see some offsetting events that demonstrate that there will be a return to the old norm (such as the strict legal prosecution of people who engage in violence), or we can predict that a new norm is being established for the issues in this controversy and acceptable behavior in similar situations.
As in the above examples, the usefulness of the Theories of Stability and Volatility is that they focus our attention on the degree of deviation from the norm, and the factor of time, as a means of making accurate predictions. Another focus is the degree of volatility as illustrated in the next example.
Consider another example of social relationships. Suppose we have a married couple going along with the normal volatility found in any marriage. But then there is an event. The wife has an extramarital affair and the husband finds out. The husband longs for a return to the old norm. Remembering the old maxim, "What's good for the goose is good for the gander," he thinks an equal offsetting event might balance out the relationship. As a result, the husband also has an extramarital affair. It is possible that this might work, but we have to remember that we are dealing with a complex system. The event may not be equally offsetting and produce the desired result. We do know for sure from the Theory of Volatility that the range of volatility in the relationship has now been dramatically increased. Another name for volatility is risk. The risk in this relationship has now increased, and that means the cost to each participant has gone up. This relationship will eventually evolve to a new norm of stability. But the increased volatility makes it much harder to predict where the future trend of this relationship is going. The wife should have considered the impact her affair would have on the norm. The husband should have realized that by increasing the level of volatility, he probably did more harm than good. He has increased the risk that the new norm may trend even farther away from the old norm.
The universality of the Nomothetic Theorem means that scale should not affect its validity. But that does not mean that we can ignore scale. Stability and volatility are relative to size, distance, and time. What appears to be very stable on one scale may be very volatile on another. Therefore, we must be aware of the scale we are working in.
In physics, the Nomothetic Theorem is consistent with Newton's Laws of Motion. For example his first law says, "A body at rest will remain at rest, and a body in motion will continue to travel at a constant speed in a straight line unless acted on by an outside force". (Where Newton's law identifies stability as an end result, the theory of stability is more concerned with the process of progressing to the end result.) Our solar system has existed long enough to evolve into a stable system. The normal range of volatility is tolerably small. And except for the small deviations that occur within the normal range of volatility, Newton's basic laws of mechanics allow us a high degree of predictability; and Einstein's general theory of relativity allows even more accurate prediction of planetary position. It is only through very gradual evolution, or when a special event comes along, that the "norm", or level of stability, in our solar system will be changed. According to the Nomothetic Theorem, our solar system is constantly seeking to find a greater level of stability. We can have confidence that, within the scale of human life, the sun will continue to rise in the east every morning. But someday, a significant event may realign our solar system (or cause a collapse or disintegration). Within the relatively short span of one human life, the statistical probability of an event upsetting the stability of the system and the planet earth is small. But on an appropriate scale, over millions or billions of years, we can expect that the norm will change. Failing a dramatic change, there will be an evolutionary change. Scientific measurements confirm that the sun is losing millions of tons of mass and will eventually consume itself. The earth's moon is moving away, and the orbits of the planets are wandering. Although ever so slight in some cases, change is all around us.