About Complex Systems

What are Complex Systems?

Complex systems can be identified by what they do - display organization without a central organizing principle (emergence) and also by how they may or may not be analyzed - decomposing the system and analyzing subparts does not necessarily give a clue as to the behavior of the whole.

A complex system is a system with a large number of elements, building blocks or agents, capable of interacting with each other and with their environment. The interaction between elements may occur only with immediate neighbors or with distant ones; the agents can be all identical or different; they may move in space or occupy fixed positions, and can be in one state or multiple states. The common characteristic of all complex systems is that they display organization without any external organizing principle being applied. In the most elaborate examples the agents can learn from past history and modify their states accordingly. Adaptability and robustness is often the byproduct. Part of the system may be altered and the system may still be able to function.

Complex systems are systems where knowledge of the elementary building blocks - a termite, a neuron - does not even give a glimpse of the behavior of the global system itself; i.e. rich macro dynamical behavior with "simple" elementary building blocks. It is however clear that some complex systems are simpler than others.* Possibly the most unyielding example may be the human brain. At an individual level, we know quite a bit about neurons; however, we are nowhere close to comprehending consciousness. The individual elements in food webs or ecosystems are, in a few cases, relatively well understood. However, this may give no clue as to the robustness and adaptability of the entire system. Possibly the simplest complex example, one arising in theoretical physics, is the celebrated 2D Ising model, a caricature of a magnet, a lattice with elements displaying up-down, black-white behavior. The realm of particles or grains and how they interact with each other is well understood. However, how the multitude of length scales that appear in sand dunes - from centimeters to hundreds of meters - arises from the individual particles is far from obvious.

Examples of complex systems:

• Metabolic pathways
• Ecosystems
• The world-wide web
• The U.S. power grid
• Supply chains
• Propagation of HIV infections
• Transfer of knowledge within organizations
• Evolution of communities and behavior
• Evolution of languages
• The Earth as a system

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Complicated and Complex

What is complex and how does it differ from the merely complicated?

The most elaborate mechanical watches are called très compliqué. They are, as their French name implies, complicated. A Star Caliber Patek Phillipe has 10³ pieces. A Boeing 747-400 has, excluding fasteners, 3x10⁶ parts. In complicated systems parts have to work in unison to accomplish a function. One key defect (in one of the many critical parts) brings the entire system to a halt. This is why redundancy is built into designs when system failure is not an option (e.g. a nuclear submarine).

The stock market, a termite colony, cities, or the human brain, are complex. The number of parts, e.g. the number of termites in a colony, is not the critical issue. The key characteristic is adaptability. The systems respond to external conditions. A food source is obstructed and an ant colony finds a way to go around the object; a few species become extinct and ecosystems manage to adapt.

The boundary between simple and "complex" is subtle. It takes little for a simple system to become anything but simple. A forced pendulum - with gravity being a periodic function of time - is chaotic. In fact one can argue that the driven pendulum contains everything that one needs to know about chaos; the entire dynamical systems textbook by Baker and Gollub (1990) is built around this theme. A double pendulum - a pendulum hanging from another pendulum - is also chaotic. And it does not take much to make billiards chaotic. The trajectories of a hard sphere in circle are regular but in a stadium - a rectangle with two opposing sides being semicircles - are chaotic.

Engineering Complex Systems

The reductionist viewpoint: There are three broad categories of complex systems, Physical and Chemical Systems, Biological Systems, Social Systems and Organizations. It may be argued that physical and chemical systems are the simplest: we know the building blocks quite well. At some level however, one may argue that everything is a physical and chemical system. And therein lies the paradox. How does complex behavior arise from simple building blocks? Physics is driven by simplicity; the harder one looks the simpler it gets. But once one reaches the ultimate simplicity (e.g. Newton's laws), how does one manage to put things back together?

The study of complex systems runs somewhat contrary to the normal (or reductionist) approach followed in physics, chemistry, biology, and economics: The central tenet of these disciplines is that if one understands the elementary building blocks - particles, atoms and molecules, a strand of DNA - we can formulate problems and infer consequences marching upwards in scales. However, it is clear that this approach, though eminently successful since Galileo's times, has limits. Complex systems cannot be understood by studying parts in isolation. The very essence of the system lies in the interaction between parts and the overall behavior that emerges from the interactions. The system must be analyzed as a whole.

Building blocks: The concept of building block brings also its own bit of semantic confusion. Quite rightly many disciplines regard their "elementary building blocks" as complex - no one would label a neuron or an individual in an organization as being "simple." Also it may be difficult to design an experimental methodology, or the key experiments, for studying the elementary block. Or there may be open theoretical questions. Thus, for example, one talks of "complex fluids" in polymer and colloidal science.

In many disciplines the systemic complexity is acknowledged and the building block is isolated and analyzed/studied under well-defined conditions. However, these studies often fail to reveal some of the aspects and properties that will allow the conceptual reconstruction of the global system. Consider the case of biology. One of the grand challenges in this area is the synthesis of the relevant building blocks. Another one is the development of scientific (experimental and theoretical) methodologies for the study of the elementary blocks in action as parts of the system they are part of (for example the attempts to extract evolutionary and functional information from genome sequences, the development of high-throughput techniques, DNA arrays and proteomics, imaging, etc). Given this avalanche of information, the study of the elementary blocks themselves and interactions between building blocks has become difficult and "complex." In fact, in some areas, biology being the prime example, one could argue that new technologies are providing information at a much faster rate than our ability to digest and understand it. How does our ability to simultaneously monitor and observe complex systems at different scales enhance our understanding of these systems? What are the scientific methods that will allow us to understand these systems?

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