A mathematical model is more precise than a verbal (mental) formulation. A mental formulation is more fuzzy as Forrester writes. One author has stated that the human mind cannot imagine the behaviour of a dynamic system with as few as three feedback loops.
Jay Wright Forrester characterizes normal debate and discussion as being dominated by inexact mental models (Wikipedia):
- “The mental model is fuzzy. It is incomplete. It is imprecisely stated. Furthermore, within one individual, a mental model changes with time and even during the flow of a single conversation. The human mind assembles a few relationships to fit the context of a discussion. As the subject shifts so does the model. When only a single topic is being discussed, each participant in a conversation employs a different mental model to interpret the subject. Fundamental assumptions differ but are never brought into the open. Goals are different and are left unstated. It is little wonder that compromise takes so long. And it is not surprising that consensus leads to laws and programs that fail in their objectives or produce new difficulties greater than those that have been relieved.”
A mathematical model can be checked for completeness and consistency. The assumptions in a model can be investigated if they are clearly documented. The model can be tested and compared to observations.
Not all mathematical models are useful. My opinion is that most published economical models are rather dubious. That is the reason why I develop the Economic Circular Flows (ECF) method. The design of a model also enforces the user to consider if the assumptions are realistic descriptions of the real world.
JAY W. FORRESTER discusses how COMPUTER MODELS OF SOCIAL SYSTEMS can be used in the article COUNTERINTUITIVE BEHAVIOR OF SOCIAL SYSTEMS (download the PDF).
- “By contrast to mental models, system dynamics simulation models are explicit about assumptions and how they interrelate. Any concept that can be clearly described in words can be incorporated in a computer model. Constructing a computer model forces clarification of ideas. Unclear and hidden assumptions are exposed so they may be examined and debated.”