Complex Adaptive Systems: Computational Models of Social Life (Ch3: pp. 35-43)

Complex Adaptive Systems: Computational Models of Social Life (Ch3: pp. 35-43)ModelingModels as MapsA More Formal Approach to ModelingBreaking Down the Formal ModelModeling Complex SystemsModeling Modeling


For every Complex problem, there is a solution that is simple, neat and wrong.

— H. L. Mencken

Things should be made as simple as possible — but no simpler.

— Albert Einstein

Nothing is built on stone; all is built in sand. But we must build as if the sand were stone.

— Jorge Luis Borges


Models as Maps


A More Formal Approach to Modeling

Breaking Down the Formal Model

The success of a particular mode is tied to its ability to capture the behavior of the real world.

Put another way (equations)...

The model "coincides" with the real world if

The requirement that the maps between the model and the real world must be commutative in this way is known as a homomorphism. Thus, the goal of modeling under this view is to find a set of equivalence classes and a transition function that results in a useful homomorphism.

A model requires choices of both the equivalence classes and the transition function, and the art of modeling lies in judicious choices of both.

This continual chasing of the "ideal" model results in a Schumperterian cycle of scientific creative destruction. Modelers attempt to reduce the world to a fundamental set of elements (equivalence classes) and laws (transition functions), and on this basis they hope to better understand and predict key aspects of the world. The ever present quest for refining old, and discovering new, ways to represent the world drives the process of scientific creative destruction.


Modeling Complex Systems


Each time we move to a new level, we are confronted with a new world that requires new models. Moreover, creating a theory about how these new levels arise from existing ones, namely understanding the function , becomes important. We would like to be able to develop a theory that helps us understand how states of the world (composed of lower-level entities and interaction rules) are transformed into higher-level entities.


Modeling Modeling

Regardless of the system or methodology, our goal is to employ high quality models. Thus, we apply the same standards of simplicity and elegance to our computational models that we do to our mathematical ones. Models need to be judged by what they eliminate as much as by what they include—like stone carving, the art is in removing what you do not need. Even though a computational model may require thousands of lines of code, if done well it can still embody the simplicity and elegance that is demonstrated in a mathematical model existing in only a few equations.

Having an explicit awareness of the issues surrounding quality modeling is important if we want to work on the frontiers of science. This awareness disciplines our efforts as we explore new problems and employ novel techniques. Creating a model is much like trying to solve a brain teaser. Finding such solutions is often an extremely difficult task involving a combination of theory, practice, and a bit of art. Yet, once discovered, the answer has strong intuitive appeal and appears all too obvious.

Notes by Matthew R. DeVerna