In the medieval Western world, the universe was widely believed to operate on the basis of the design and subsequent will of its Creator. Its operation was observed and recorded, but the cause and effect of those observations was thought to be the work of a Divine Mover, God.
According to Ptolemy, the principle authority at the time on the movement and arrangement of the heavens, the celestial bodies traveled in spheres which emanated concentrically around the earth. These spheres rotated according to Divine prescription, making a heavenly sound as they moved in relation to each other – the “music of the spheres.”
But then along came Copernicus (and others like Kepler and Galileo) who posited that the rotation of heavenly bodies – in particular the planets – could be explained through the use of formulae which represented physical laws. Moreover, their observations challenged the notion that the earth was the center of the universe and placed the orbits of the planets around the sun instead. Further work led to the discovery of forces (like gravity) that operated on the planets causing them to travel their courses in predictable ways.
A paradigm shift in theories of causation
This work began to break down the paradigm of theological causation according to the unpredictable and changing whim of the Creator and replace it with a mechanical view governed by the predictable operation of natural laws which could be described mathematically. This paradigm expanded rapidly to encompass non-celestial structures. For example, the English physician William Harvey was able to describe the operation of the human circulatory system using these principles. Soon other phenomena were added to the list of those explained through the operation of natural law. In fact, these phenomena became the rule, and the unexplained exceptions were treated as instances of yet undiscovered operational laws.
This structure, which found full flower in the Western Enlightenment, operated quite well even in the setting of complicated systems. The laws were deterministic. Given a set of conditions, the application of a defined force, and a specified system, the outcome was entirely predictable and explained in whole by the principles involved. Experiment after experiment bore this out. However, there was another paradigm beginning to appear just around the corner.
As we said, this deterministic application of natural law to a pre-defined set of circumstances had a particular, repeatable result. The set of circumstances could even contain many elements – a condition known as “complicated” – and the outcome would remain deterministic. An example of a complicated system is the workings of a watch or clock. Many gears of calculated sizes are mounted in specific relation to each other. If the locations, radii, and number of teeth in the gears are known, then we can calculate the rotation of any or all of the gears from any specified rotation of a single gear. The result is determined by the arrangement and specifications. That is the nature of complicated systems. But some sets of circumstances seemed to cause the principles to break down.
Two kinds of complexity
The creature lurking in the background was complexity, a condition over and against complicatedness. In complex situations, the deterministic action of natural laws seemed to break down. We now recognize two kinds of complexity – physical and adaptive.
In a physically complex system, there is movement by the system from one state to another. This is controlled by a set of rules which define the possibilities. From a given state there is a limited set of possible movements to a subsequent state. An easy to understand example of a physically complex system is a game of chess. The beginning state of the game is defined by the rules, as are the movements of the pieces. Only legal moves – those defined by the rules – are possible. But the rules do not say which of the possible legal moves a player must make. This means that the next state of the system is not determined by the rules in the way that principles determine the processes of a complicated system. The choice of an allowable chess move is up to the player.
It is the resulting unpredictability that makes the game interesting. In 1972 Bobby Fischer and Boris Spassky were locked in a struggle for the world chess title. As the sixth game opened, they were tied 2 ½ to 2 ½. Chess players study patterns and attempt to predict what their opponent will do in a given situation and how they might best respond. Playing the white pieces, Fischer opened with an allowable, but extremely rare, move of his Queen Bishop Pawn. This caught Spassky off guard and his response was weak. Fischer continued his line by ceding control of the center of the board – something chess players are reluctant to do. Although he eventually transitioned to a familiar pattern (Queen’s Gambit Declined) of play, Fischer had damaged Spassky’s response enough to eventually secure the win and the lead in the match. Both players moved completely within the rules of chess, but Fischer had used the unpredictability of his moves to gain the advantage. This is a classic example of the physically complex system.
The unpredictability of agents
The other kind of complexity is found in complex adaptive systems. Complex adaptive systems are made up of large numbers of components called “agents” that interact with each other in unpredictable and uncontrolled ways. This results in system behavior that changes and adapts to changes in its environment. Examples of this kind of complexity are embodied in the stock market, biological populations, and the weather. Efforts to understand it are the subject of complexity theory, systems science, and even chaos theory.
The significance of all this for systems engineering is that we must understand that grasping new complexity involves a paradigm shift away from the thinking that sufficed to deal with complicated, deterministic systems. We must be more disciplined, paying more attention to the integrative natures of systems. Our tools and methods must provide us the rigor for understanding the difficult-to-predict emergent behavior of large, complex systems. It is no longer enough to look at snapshots of systems frozen in time. We must understand the dynamics of real complexity if we are to solve real world problems.
