Opposites And Complexity

Today, I have something that I think is really profound. I have been giving some thought to the nature of opposites. I mean things which are opposite from one another, like night and day. My conclusion is that opposition, or the concept of opposites, could be a powerful tool for measuring complexity and also reveals much about what we have to learn about the nature of the universe.

Opposites are not something to which most people usually give much thought. So, let's do a quick review of what opposites are. We often confuse opposites and pairs. Day and night, male and female, matter and antimatter, salt and pepper. The most fundamental opposite is, of course, negative and positive electric charges.

These are opposites, but they are also pairs. My definition is that pairs are the simplest and most fundamental type of opposite. We will deal mainly with more complex opposites here.

The true definition of a set of opposites involves the reflection of a mirror. When you look in a mirror, you see yourself as you really look with the exception that your left side is the right side of your mirror image, and vice versa. In other words, you and your mirror image are opposites.

Opposition, in my definition, does not mean completely different. Opposition is actually a relationship between two entities. They are not unrelated at all, but are the reverse permutations of the same thing.

Two things that have absolutely nothing to do with each other are not opposites. Consider the following statement: "Mangoes are the opposite of lacrosse". It just sounds nonsensical because the two have nothing to do with each other. Mangoes are tropical fruit, while lacrosse is a native American Indian sport.

To be a meaningful concept, opposition must be concise. The vast majority of words in the dictionary have nothing to do with most of the other words in the dictionary. So, having nothing to do with something cannot be the defintion of opposite. Such a defintion would be so broad as to be meaningless.

Have you ever wondered if the systems of measurement that we use are failing to keep up with advances in science and technology? I have described what a tremendous benefit it would be if we were able to put a number on complexity, to quantify it, instead of describing it in the vague and subjective ways we do at present. Complexity is the total amount of information in a given system. Instead of describing something as "much more complex" or "a little bit less complex" than something else, we could be precise about it and say that this is 2.35 times as complex as that.

The reason we have not yet gotten to that point is that complexity cannot be measured in the traditional ways. It is not possible to quantify it with a ruler, a clock, a thermometer or, a voltmeter.

To get the great benefits that measurement of complexity would bring, we must come up with some creative ways of measuring it. I have already described how the complexity of a dynamic system (meaning in motion) could possibly be measured by keeping track of the coincidences that occur in the system. It is also true that is is sometimes possible to measure complexity directly, by counting the number of levels involved. If a system can be broken down into a formula, or a number of formulae, it also serves as a direct measurement of the system's complexity.

Some other ways of measuring complexity that I have thought of include the Sameness Index. We know that all people are different, but they are more the same than they are different. The Sameness Index is simply the population of the world divided by the number of entries in a comprehensive encyclopedia and dictionary, after eliminating redundancies. The total number of entries represent how different we are, but in comparison with the world's population, we might be 100 times more the same than we are different.

A creative way of measuring the complexity of the human body, in comparison with the background environment of inanimate matter, is to look at a medical library. We know that the more complex a dynamic (moving) system is, the more likely something will go wrong. So, my reasoning is that the total number of diseases, ailments and, injuries which can afflict human beings, including the variations of each, can be used as an effective measurement of the complexity of the human body.

Now, back to the concept of opposites. Opposition is a very useful concept for the measure of complexity. To undertake such a measurement, we would first define two opposites within the system to be measured. This method would be useful whether the system is static or dynamic and the opposites do not have to actually exist, as long as we can be certain of what they would be if they did exist.

The reasoning behind this opposites method is the fact that the more complex a given system is, the more different from one another will be the opposites produced within that system. So, if we can put a measurement on how different the opposites are from one another, we can effectively measure the complexity of the system. Since opposition is a mathematical concept, that should not be too difficult to do.

This concept is analogous to measuring the diameter of a circle. The opposites are represented by diametrically opposite points on the circle while the complexity of the system is represented by the size of the circle. In a simple system, a small circle, the opposites must be close together, or similar to one another. In a complex system, the opposites are far apart, or dissimilar.

Let's consider a simple example. Suppose there is a program, or other system, which generates random strings of letters. The opposite of the string "ABCD" can only be "DCBA". We know that in a simple system, a pair of opposites as defined by the system cannot be very different from one another. In this system, the two opposite strings of letters are exactly the same except that they are reverse permutations of each other. Therefore, this system is simple. It takes a complex system to produce opposites which are very different from each other.

Another simple system is a line of numbers starting at zero and proceeding as positive numbers in one direction and negative numbers in the other direction. The opposite of 241 can only be -241. The two numbers are the same except for the sign in front of them. Therefore, the system in which they are defined as opposites must be simple and it is.

As stated previously, the simplest of systems are those in which the system revolves around a pair, which are also considered as opposites. The fundamental negative and positive charges are such a simple system, as is the rotation of the earth producing night and day.

The important thing about measurement of complexity is whether the measurement proves useful. The accuracy of measurements such as these depends on the accuracy of our definition of the system itself that we are trying to measure. If we do not get this definition perfect when we deal with very complex systems, then our measurement of the complexity of the system cannot be expected to be perfect. But a wondeful thing about measurement of complexity is that it can still be very useful, without being perfect.

There are a couple of ground rules that I came up with concerning measurement of complexity using opposites. The first is that if a number is attached to an object, the number must be considered before the object. If we have 5 pies, the opposite of that would be -5 pies. We would not go into trying to determine the opposite of a pie.

Another ground rule also concerns numbers. If we have both negative and positive numbers in the system, the opposite of a positive number is a negative number. If there are no negative numbers in the system, the opposite of a number is it's reciprocal.

Now, for the part that I consider as really profound. We can see that in simple systems, every entity has an opposite, whether or not it actually exists. Since complex systems are only combinations of simple systems, that can only mean that any entity in a complex system must also have an opposite. Thus, everything in the universe has an opposite.

To determine opposition, which is a mathematical concept, we must completely understand the system. At this point, we cannot identify the opposite of a rock simply because we do not completely understand the universe. By the way, the opposite of a rock which I am referring to is not an identical rock made of antimatter. Matter and antimatter are opposites at the sub-atomic level, but there must be an opposite of a rock whether it is made of matter or antimatter.

To define what this opposite of a rock is, whether or not it actually exists, we would have to understand everything about the universe. To thoroughly understand something means to understand not just what exists, but what does not exist, meaning what could possibly exist but doesn't.