For my present purpose I am going to refer to complexity as a subjective measure.  To understand why this is a reasonable position we need to look a little deeper at complexity. 

A number of scientists and mathematicians have recognized the problem for some time.  Shannon developed the concept of the information entropy in a message, which describes the amount of uncertainty in the next symbol of a message.  If one were to completely describe an entity then the entropy content of that description (a message) might be a way to represent the amount of complexity.  There are two flaws with this.  The first flaw is that for any given description you do not know if there is another description with less information entropy.  The solution is, of course, to define the amount of complexity as that message with the least information entropy that describes the object.  Unfortunately, we cannot know if we have found the description with the lowest entropy.  The second flaw is that a message implies a message understander.  You cannot encode a description of something into a message unless you know what the receiver can understand.  As the understanding capability of the receiver increases the necessary information content of the message will decrease.

Another approach has come from the computer scientists.  How complex something is can be determined by the length of the shortest algorithm that can predict the behavior of the system.  How do we know we have the shortest algorithm? We can't know.  We also have to have something or someone to execute the algorithm and this affects how we can encode an algorithm.

Rather surprisingly this reveals the most essential thing about complexity that we need to understand.  It is in the eye (or should I say mind) of the beholder.  I don't care if the dictionary cannot adequately define the word.  I don't care if a bunch of people are making a living writing about what the word does or does not mean.  I know exactly what I mean when I look at entity A and at entity B and say that A is more complex B.  I also recognize that another person may very well say the opposite.  Furthermore that other person may explain something about A to me and all of the sudden I realize A is not complex at all.  I just didn't see the pattern before. 

For thousands of years humanity had been observing the motion of the planets and found their movement to be exceedingly complex.  Then Tycho Brahe, followed by Nicolaus Copernicus, followed by Galileo Galilei, and finally followed by Isaac Newton who put the finishing touch on the simple description of the motion of the planets.  Then along came Albert Einstein who showed that it really was not quite that simple.  But, Einstein wrought a more encompassing description of nature that gives a beautifully simple view of what was previously complex.  Of course, you have to understand the mathematics to appreciate it.  To some that is exceedingly complex.  Once again, complexity is in the mind of the beholder.

We need to bring one more recent actor on the stage of complexity - "The Science of Complexity." In this case the mathematicians and scientists are talking about a specific type of complex behavior - behavior of systems that exhibit chaotic dynamics.  Some systems have some outcome parameters that are extremely sensitive to an initial state or input parameters.  The sensitivity is so great that a minute change in some initial condition will result in unpredictable behavior in some outcome parameter at some later time.  Refinement in measurement will not make the unpredictability go away.

Contrary to its name the Science of Complexity is not really all that hard to understand.  That is good because we will need it later, but for now the fact that chaotic dynamics can cause organization failure need only be a footnote.  It is not the common cause.  We can safely ignore it for now. 

The fundamental aspect of complexity that we will be concerned with is interdependence.  I will give a formal definition later.  For now let's consider some examples.

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