# What is Complexity?

Complexity Science is a relatively new approach to understanding the systems in our lives. Complex systems and complexity science deal with systems that cannot be easily/perfectly predicted (such as the movement of the planets or the weather) or simplified down to a probability (such as flipping a coin or describing the behavior of gas molecules in a room).

A Map showing the Economic Complexity of Ireland. (From TurbulenceAhead.com)

## Simply Put… There are Multiple Definitions

In Complexity: A Guided Tour, Dr. Melanie Mitchell writes about trying to define complexity:

In 2004 I organized a panel discussion on complexity at the Santa Fe Institute’s annual Complex Systems Summer School… The panel consisted of some of the most prominent members of the SFI faculty … all well-known scientists in fields such as physics, computer science, biology, economics, and decision theory… The first question was, “How do you define complexity?”… Each panel member then proceeded to give a different definition of the term… If the faculty of the Santa Fe Institute – the most famous institution in the world devoted to research on complex systems – could not agree on what was meant by complexity, then how can there even begin to be a science of complexity? … The answer is that there is not yet a single science of complexity but rather several different sciences of complexity with different notions of what complexity means.

Mitchell goes on to discuss several ways in which different experts define complexity including:

• size
• entropy
• algorithmic information content
• logical depth
• thermodynamic depth
• computational capacity
• statistical complexity
• fractal dimension
• degree of hierarchy

## Complexity as it Relates to Economics or Systems of Agents

In the examples cited by Dr. Mitchell, complexity is a way to describe a single object or system.  But in a system, complexity isn’t just how difficult it is to reconstruct or describe the system.  What really makes a system complex is it’s behavior.

When we talk about complexity as it relates to economics and systems, complexity is a result of several interacting players (or agents) with relatively simple rules. The resultant behavior of the system as a whole or of individual agents over time cannot be described by probabilistic models or determinate functions alone. As Dr. Steven Phelan wrote in an article for Emergence:

Complexity science posits simple causes for complex effects. At the core of complexity science is the assumption that complexity in the world arises from simple rules… Unlike traditional science, generative rules do not predict an out- come for every state of the world. Instead, generative rules use feedback and learning algorithms to enable the agent to adapt to its environment over time. The application of these generative rules to a large population of agents leads to emergent behavior that may bear some resemblance to real-world phenomena. Finding a set of generative rules that can mimic real-world behavior may help scientists predict, control, or explain hith- erto unfathomable systems (such as the stock market).

### Requirements of Complex System Agents

Complex systems are made of multiple individual pieces, normally referred to as agents.  What makes the system complex is the qualities and behaviors exhibited by the agents.  Professor John Hiles of the Naval Postgraduate School teaches the following during lessons about Complex Adaptive Systems in multi-agent simulations, and the same applies to all complex systems. In order to exhibit complex behavior, system agents must contain the following qualities:

• It must have at least one input. This could be an awareness of it’s environment, such as the ability to hear, for example.  Or, it might be some way to input other information, such as an ethernet cable to a network interface card or computer.
• It must have some decision engine. This engine may use one or several methods to provide a decision on what action the agent will or will not do. It may consider the agent’s input in some cases, but maybe not all of the time.  Some of it’s possible decisions must use it’s input, however.  For example, a car driver decides to slow down when a car in front of him gets too close, or when he sees that he is at his destination.  Or, the driver may decide to make a left turn for a reason unrelated to his senses/inputs. The decision doesn’t have to be some sort of “intelligence”, it could simply be the direct result of an input, e.g. a billiard ball will move if hit with another billiard ball.  While the ball doesn’t have a little man inside deciding what to do when it is hit, it does have a hard-wired decision from physics: when it is hit, it will move in a direction depending on where it was hit, how hard, and other factors. So, the input is translated by physics (the decision engine) into an action, in this case, movement.
• It’s actions must have some impact on or provide input to other agents. For example, a driver who stops in traffic has an impact on drivers behind him, who may or may not decide to slow down, stop, go around, or do nothing.  If drivers behind him do nothing then they crash into him because he occupies a place where they cannot be without crashing.

## Scale Matters

Without all of those three qualities, the agents in the system will not behave with complexity. In almost any system, humans have these qualities.  Ants have these qualities.  Birds (Boids) have these qualities. When it comes down to it, almost everything in the universe has these qualities at a certain level, but it depends on the scale you are looking at. For example:

• A balloon filled with a gas. Each gas particle has inputs (e.g. temperature, other molecules hitting it). Each has a physics decision engine. The molecules have an impact on one another in that they can run into each other and no two molecules can occupy the same spot in space. If you were trying to predict the path of each molecule as it travels at around 1100 miles per hour (Calder, 1), it would be a very complicated problem as each molecule collided with others and the walls of the balloon and exchanged energy, etc.  However on a different scale, such as the scale of looking at the system/balloon as a whole, the behavior is very easy and simple to predict with a couple of equations, and is a direct result of the temperature of the system.

Ultimately, all of the experts are probably correct. It depends on which scale you look at whatever it is you are looking at. Most people would agree that the possible measurements of complexity listed above usually don’t apply to the same system, but many of them might come into play in the same system at different scales.

For example, take a balloon filled with a gas, either air from your lungs or helium.  Each molecule of gas is an individual agent in the system, which means there are millions of agents. However, the balloon as a whole can be described in aggregate very accurately with simple equations.

## Complexity Science is a Budding Discipline

I am certainly not an expert on Complexity Science. I am a bit removed from the sub-culture and academic side of complexity studies because of my current profession. But what I have gathered from reading those who claim to be experts is that the science is still forming. I think on of the key reasons that it is still budding is that many people still have problems defining exactly what it is we are all talking about.

It may be that complexity is “in the eye of the beholder” or that there is some concrete or definite way to describe it. Or maybe everything is complex to a certain degree. I think if we can get a handle on how to describe and define complexity we can then begin to further understand it and, more importantly, spread those discoveries to other people, industries, and sciences.