Self-Organization: The Invisible Conductor

A new cutting-edge science is emerging to answer a question faced by many scientific fields: How do systems governed by simple rules produce complex emergent behavior? This new science, sometimes called the science of complexity or self-organization, is directly relevant to problems in physics, biology, mathematics, and computer science. Emergent behavior can be found in many systems, from ant colonies to human societies. The behavior of these systems is often chaotic, despite the apparent order of the emergent patterns. Fractal geometry, an example of emergence in mathematics, shows that infinitely complex patterns can emerge from simple rules that are iterated. A better understanding of emergent behavior in self-organizing systems will be essential to the progress of science in the 21st century.

Emergence is the central phenomenon of self-organizing systems. In order to be described as self-organizing, a system must satisfy two primary conditions: organization and lack of coordination. Obviously, if a system has no observable organization (structure or behavior that is not the result of random chance), it cannot be self-organizing. On the other hand, a system whose organization is the direct result of a single entity (e.g. the conductor of an orchestra) is not self-organizing either. Only when a system has high-level organization that emerges from the aggregation of simpler, low-level interactions can it be called a self-organizing system. The term emergence refers to the process by which the rules that govern a self-organizing system produce its apparent organization.

Countless examples of emergence exists in natural and human systems. A flock of birds can have complex patterns of behavior that seem to be centrally coordinated, but each bird is following a simple set of rules with only local knowledge. Similarly, a colony of ants is capable of performing many complex tasks with apparently intelligent organization, but each ant is extremely limited in its intelligence. On a much larger scale, self-organizing systems can be found in human societies. From small social groups to cities and nations, human behavior naturally leads to organization on many levels. Although many of these groups have leaders, their formation is not solely the result of one person's actions, nor can they be controlled by any one member. The presdent of a country has a lot of influence, but he is unable to change the self-organizing structure of society except through the most extreme measures. The resiliency of self-organizing systems is what makes them so common in nature and society.

Perhaps the most interesting property of self-organizing systems is their unpredictability. Even if the low-level interactions are entirely understood, the emergent behavior can be chaotic. This is the domain of chaos theory, which studies the behavior of systems that are highly sensitive to initial conditions. This idea is commonly known as the “butterfly effect”, a term coined by Edward Lorenz. Lorenz was a pioneer of chaos theory, and defined the mathematical concept called a Lorenz attractor. He plotted the values of three variables as a set of equations were iterated, each mapping the current values to the next value of a variable. In many cases, the changes in the values appeared to be regular, but Lorenz would eventually discover (by accident) that slight variations in the initial values of the three variables lead to drastically different outcomes. This idea is in contrast to the philisophical traditions of determinism, which can be traced back to Laplace. Laplace stated that if someone knew the precise position and momentum of every particle in the universe, they would be able to predict the future by deterministically applying the laws of physics. Although this is not contradicted by chaos theory, it is missing the other side of the idea: that the future can never be predicted in reality because the universe can only be observed with finite precision. The same is true for any system that has emergent behavior. This is why the weather and the stock market are so hard to predict. The sensitivity of these systems to variations in initial conditions makes their behavior highly unpredictabable beyond a certain point.

Another important field of mathematics, fractal geometry, shows that simple rules can produce emergent patterns of infinite complexity. Fractals, first studied rigorously by Benoit Mandelbrot, are shapes that have the property of self-similarity and can be generated by infinitely iterating a certain rule. They exists throughout the natural world, from mountain ranges to river systems and from tree branches to blood vessels. The abundance of fractals in living systems may be due to the fact that they can be encoded consisely by a set of simple rules. However, fractals have recently been incorporated into antennae design and other technologies, which suggests that fractals have some inherent benefit other than the fact that they can be procedurally generated. Although not all self-organizing systems have fractal structure, all fractals can be said to be self-organizing in the sense that they are high-level patterns that arise from simple rules. The key concept is that fractals are not only very complex, they are infinitely complex. The implication of this finding is that the behavior of self-organizing systems is not limited by the simplicity of the rules that govern it.

One of the most important challenges in modern science is the understanding of emergent behavior in self-organizing systems. It is directly relevant to nearly every branch of science, and it has profound implications to philosophy. Even the Earth itself could be thought of as a self-organizing system, in which we are merely particles interacting on the lowest of levels. It would seem, then, that for the future of our planet, anything is possible.