IBM defines a system as an abstract medium that stores information.
For a great deal of time now, I have been fascinated with the notion of “systems” and systems theory. This is because systems theory establishes a framework that enables one to conceptualize and formulate a belief about a particular domain. For instance, in ecology, systems theory allows ecologists to formulate new beliefs about the ecosystem. In the domain of anthropology, systems theory is used to conceptualize government, legal, and economic systems.
Generally speaking, a system is defined by first defining objects that exist within the system and then defining primitive operations that modify the state of said objects. For example, in the domain of computer science, computing machines are defined as data (ones and zeros) and primitive instructions that manipulate the data. Complex behavior can be extrapolated by stringing together many different operations.
For instance, consider a system where we define the objects as bodies where each body has a notion of size and movement. Then, let us define a simple rule (the operation) that dictates how they should interact and affect each other. Let such a rule be that each body causes a change of movement on the bodies surrounding it so that the amount of change is proportional to the size of the source body and inversely proportional to the distance of the destination body. In other words, the larger and closer the body is, the more movement it imparts on its neighbors.
Now let us observe the course of this little system. The initial state of the system has a sparse arrangement of bodies with relatively little movement. In the next moment, the rule we defined starts to orchestrate movement, and at some point, bodies start clustering to form a planet with an orbiting moon. As more planets are formed, many bodies cluster into a large central body, gravitationally binding the planets with it, and with that, a solar system is born.
At polynomially many operations, solar systems come together to form galaxies. At an exponential number of operations, the little system, like the waves of a violent sea storm, is in a state of constant undulation as galaxies repeatedly form and collapse. Evidently, with only two simple specifications, we were able to coax the behavior of nature.
In conclusion, complexity theory provides us with a vehicle to reason about and model the complexities of the world around us. By defining objects and their interactions within a system, we can witness the emergence of intricate patterns and behaviors that mirror those found in nature. From the smallest particles to the grandest cosmic structures, the principles of complexity theory offer a unifying framework for exploring the fascinating phenomena that shape our universe.