Complex Systems

The study of Complex Systems is considered by many to be a new scientific field, and is distinguished by being a discipline that has applications within many separate areas of scientific study. The study of Neural Networks, Traffic Patterns, Artificial Intelligence, Social Systems, and many other scientific areas can all be considered to fall within the realm of Complex Systems, and can be studied from this new perspective. The advent of more capable computer systems has allowed these systems to be simulated and modeled with far greater ease, and new understanding of computer modeling approaches has allowed the fledgling science to be studied as never before. The preliminary focus of this paper will be to provide a general overview of the science of Complex Systems, including terminology, definitions, history, and examples. I will attempt to look at some of the most important trends in different areas of research, and give a general overview of research methods that have been used in parallel with computer modeling. Also, I will further define the areas of the science that concern themselves with computer modeling and simulation, and I will attempt to make it clear why the science only came into its own when the proper modeling and simulation tools were finally available. In addition, although there seems to be general agreement between different authors and institutes regarding the generalities of the study, there are some differences in terminology and methodology. I have attempted in this paper to bring as many elements together as possible, as far as the scope of the subject is concerned, without losing focus by studying Complex System techniques that are bound to one particular area of scientific study, unless that area is that of computer modeling. 1. THE SCIENCE OF COMPLEXITY The science of Complex Systems has been described by the New England Complex Systems Institute at MIT (NESCI) as “a new field of science studying how parts of a system give rise to the collective behaviors of the system, and how the system interacts with its environment. Complex systems have multiple interacting components whose collective behavior cannot be simply inferred from the behavior of components. The recognition that understanding the parts cannot explain collective behavior has led to various new concepts and methodologies that are affecting all fields of science and engineering, and are being applied to technology, business and even social policy” (NECSI website). This collective approach is a relatively new strategy within science in general, as research techniques in the past have typically been reductionist, or geared toward breaking objects apart in order to understand them. Scientists that study Complex Systems maintain that these systems have key components and comprehensible properties in common, even though these systems exist in separate branches of science (Lamper, Website). A fundamental reason why this field of study has only recently been explored has to do with the availability of proper tools to study and simulate these systems. The human mind has difficulty keeping track of “many and arbitrary interacting objects or events – we can typically remember seven independent pieces of information at once” (Bar-Yam, xii). The computer is useful as a tool in areas where the human brain is not as useful: it is able to remember and precisely simulate the interaction of a large number of elements. Just as it would be impossible to underestimate the role of the microscope when studying Biology, the role of the computer has been essential for the study of Complex Systems. The science has been around for years, as evidenced by the work of Vemuri in his book, Modeling of Complex Systems, from 1978. However, the science has attempted to use other tools like mathematics, number theory, statistics, to understand different varieties of Complex Systems, and it is not until the computer became a viable research tool that a more complete study of these systems was possible (Bar-Yam, xiii). Some of the best-known examples of Complex Systems are systems we interact with everyday: The weather, the stock market, traffic on the road to work, etc. The vast complexities of humanities’ interaction with the world, of the individual to society, the permutations of the brain, and the interactions and behavior of an ant colony are all examples of systems with different levels of complexity. 1.1 What is a Complex System? The NECSI website describes a Complex System as having “multiple interacting components whose collective behavior cannot be simply inferred from the behavior of components. The recognition that understanding the parts cannot explain collective behavior has led to various new concepts and methodologies that are affecting all fields of science and engineering, and are being applied to technology, business and even social policy” (NECSI website). A Complex System is a system which has these properties: • It has more than a few and less than too many parts/elements. • These parts/elements are heterogeneous, and must interact in a non-linear fashion. • It has a definite purpose, objective, function. • It does not operate in equilibrium i.e. it is adaptive, dynamic, and always changing. • It has collective behavior that cannot be inferred from its parts/elements (Cilliers, 5). This definition is by no means complete. The field of study is new enough so that scientists will expound upon the properties of a Complex System, but are unwilling to commit to very many specific laws that define these systems. The rules above are ones that were universally described in the research materials used, but for further clarification, Paul Cilliers’ complete list of properties are included in Appendix I of this study (CSCS Website). What they essentially state is that a Complex System is a system that cannot easily be explained in a mathematical fashion, and contains too many elements for a formal description of behavior to be presented. 1.1.1 Definitions What do we mean when we discuss a Complex System, or a highly non-linear complex heterogeneous system? The first important distinctions to make are between simple, complex, and complicated systems. These distinctions are often a function of our distance from the system, because a hidden complexity in a system can be masked by a simple presentation, and a complex system can exist “below” the level in which we are interested. For example, a complex traffic pattern might be a system we are interested in studying, while the occupants of the vehicles that compose the pattern are not interesting to us. We may also be interested in the flight patterns of a large flock of Canadian Geese, but we may not be interested in the color patterns of their feathers. Our frame of reference, known as our frame in Complex System language, is the level of complexity we are currently interested in studying. A simple system is one that can typically be understood by explaining the properties of a single element/part, or the interactions of a few elements/parts. Simple systems have long been the domain of traditional scientific investigation, and explain the properties of mysteries like the motion of the Earth around the Sun, or a nuclear chain reaction. A complicated system is actually a simple system, but it is disguised as something more complex. The classic example of this is the Brownian motion of gas in a vacuum. Even though many molecules make up the gas, the overall properties of the gas are explained by conventional laws of Thermodynamics. It is a system with many moving parts, but little complexity (Cilliers, 3). The fundamental rule that distinguishes these systems is called emergence. An emergent property is a property that exists in a group of elements in a Complex System, but does not exist in each individual element. The previous example of a gas under pressure describes this concept well: The gas has properties like pressure and temperature, which are properties that the separate molecules do not possess. Complex Systems possess different degrees of emergence, both local and global. The gas properties of pressure and temperature are examples of local emergence, with just a small number of elements exhibiting the same properties as a large number of elements in a similar situation. A Complex System is distinguished by its display of global emergence, or properties that are present only in the entire system, and not in the elements or groups of elements. The classic example is the human brain, in which a neuron or a group of neurons can “remember” specific memory patterns. If neurons are removed from this group, the whole system may lose its ability to remember any memory patterns. This is not true with a gas, in which elements are interchangeable and removable, and the removal of a part will not change the attributes of the whole (Bar-Yam, 10). It is not yet clear how dramatic this distinction is, and just as it may be gradual shift from local to global emergence, it may also be a slow change from a complicated to a complex system. An analysis of traffic patterns in New York City street grid may only be a complicated system, but the addition of a Broadway street that breaks up the grid pattern and a Knicks game at Madison Square Garden may make the traffic pattern a Complex System. A true Complex System may possess both global emergent complexity and global emergent simplicity, which means that collections of simple objects can possess complex emergent properties and collections of complex objects can possess simple emergent properties (Bar-Yam, 293). The fundamental building block in a Complex System is known as an agent. Previously this has been referred to as an element or part, but a Complex System usually has elements that can be distinguished by having specific roles and attributes, and so agent is more appropriate. Agents can be very simple constructs, like the molecules in Brownian motion, but more typically has a complicated strategy and many attributes, with varying rules of both linear and non-linear interaction (Axelrod, 4). This generally means that for any given action upon it, an agent will exhibit behavior, and sometimes this behavior will be out of proportion to the action. For example, a free gas molecule will always exhibit a linear response to an action upon it. In a Complex System, it is possible that an agent will exhibit no reaction when action is taken on it the first time, and then exhibit a reaction that is twice the magnitude of the action the second time it is acted upon (NECSI website). The agents can be categorized into specific types. For example, in the free gas molecule scenario, some of the molecules could be Nitrogen, and some water vapor, and they may act differently in response to a stimulus. In a more correct example, when analyzing traffic patterns in New York City, some of the agents could be of the “truck” type, and some of the “automobile” type. All of these agents are gathered together to form a population (Axelrod, 4). The entire Complex System will be gathered together in an environment. This is entirely dependent upon how the system is framed by the observer, as mentioned previously. The observer is generally outside the system, just as the environment exists around the system, but the possibility exists that either could exert influence on the system. The Heisenberg Uncertainty Principle is a useful analogy that serves to illustrate this point: By attempting to measure the momentum of an electron, it is necessary to bounce photons off of it, which will change the momentum of the electron and give the observer incorrect results, and also result in a change of state in the electron. The influence that is exerted and received from a Complex System is one of the reasons they are innately difficult to study. In another field of study, an anthropologist studying a hunter-gatherer tribe in South America would find it difficult to study the tribe without becoming a part of the tribe. As a result, Bar-Yam of NECSI presents the following definition: “An observer is a system which, through interactions, retains a representation of another system (the observed system) within it” (NECSI website). 1.1.2 Concepts Some explanation has been given as to the interactions that can be expected to occur in a Complex System, but more definition is needed. Specifically, how can these interactions be characterized, and can any fundamental rules of behavior be determined? The best way to explain this is to classify the different kinds of Complex Systems. 1.1.2.1 Non-Adaptive Complex Systems The Non-Adaptive Complex System (NACS) is a system composed of agents without a choice. They do not change their rules of behavior during the operation of the system. While the objects interact with each other, they follow predictive rules, without exception. They follow the same rules under all conditions of interaction (Casti, website). The “Game of Life” is a good example of such a system. The various agents are placed in a starting position on the game-board, and the simulation starts. Each event after this point is determined by the rules, which decide whether an agent “survives” into the next round, or is eliminated. The agents do not adapt, and the success of the system is determined by the starting locations of the agents. The rules for this game are explained below, in Section 1.1.4. 1.1.2.2 Complex Adaptive Systems The Complex Adaptive System (CAS) is a collection of agents which are in interaction with each other and that have a choice of rule systems which are followed during the interaction (Casti, website). Naturally, a CAS can also contain aspects of a NACS, and can contain agents that do not change their behavior. Similarly, an aspect of a particular CAS may be that the agents only change their behavior at specified moments. What is important is that the possibility exists that the agents will display adaptive behavior. Many researchers maintain that it is this adaptability that makes the system complex, but the field is divided on this issue (Axelrod, 9). 1.1.2.3 Interactions Much of the terminology for a Complex Adaptive System has already been introduced, but there are a few key concepts introduced by Robert Axelrod that characterize the interaction of the agents in such a system: The system is generally composed of a population or a multiple population of agents of varying types, some adaptive, some non-adaptive, all interacting in a concurrent, coevolutionary fashion. The co-evolutionary or co-adaptive process follows a model that is already known in evolution and genetic programming, in which mutation, crossover, extinction, birth, and recombination occurs between populations of agents (see ). Essentially this means that all agents are interacting and surviving based upon their own criteria for success, and slowly evolving based on either learned responses (in the field of Sociology or Anthropology) or based on reproduction (as in the case of genetic algorithms). In fact, it is not always clear if the system is adaptive based on the individual agents or the emergent properties of the system. For example, in the case of a Neural Network, it might be understood that the system is adaptive, and not the agents (Axelrod, 40). The other aspect is that the agents are doing all of this concurrently, which simply stated means “simultaneous occurrence” (Ghosh, 23). Section 1.1.3.4 Paul Cilliers maintains that the set of rules that govern a Complex System can be abstract, or agent and type based, or they can be centralized, or both. This concept is not a surprise, especially within the study of Politics or Economics. It’s important to note that this control can occur at any level in a Complex System (Cilliers, 3). There are many other specific descriptions of agent interaction, but most are specific to the type of Complex System being considered, and would be too numerous to detail here. Many of the terminology here has been used before to describe Complex Systems in a multitude of forms, and it is perhaps for this reason that the field has not agreed on a set standard.