ABSTRACT
Everything that is simple is merely imaginary; is not “true.” What is real and what is true, however, is neither simple nor is it reducible
to simplicity. Friedrich Nietzsche
1.1 The Opening Scenario
Because the terms complex and complexity are so widely used in everyday language, when an object is described as being complex or a system is said to exhibit complexity, most of us have an intuitive feeling
that we understand what is meant. Yet, if put to the test and called upon to give a rigorous elucidation of what we believe we understand, we soon realize how difficult it is to furnish a meaningful account. In such a situation, we find ourselves in the same kind of dilemma experienced by St. Augustine when he confronted the problem of defining time. In the end he could do no better than to admit [1] that “if nobody asks me, I know; but if I were desirous to explain it to one that should ask me, plainly I know not ” Both time and complexity are rather fuzzy, abstract concepts and our comprehension of them is largely independent of reason. This implies that our grasp of their meaning is founded on shifting sands because any intuitive understanding of the world around us can change quite profoundly as our insights into natural phenomena become ever more penetrating. In the words of the quantum theoretician Holland [2], intuition “is a function of history and not eternally frozen. The notion that a body persists in a state of uniform motion unless acted upon by a resultant force would be counter intuitive to Aristotle but natural for Galileo. [Similarly,] quantum phenomena require the creation of quantum intuition.”
