The study of models and the understanding of reality

Abstract

If we consider modeling as an abstraction from reality that help us to understand and work with it, then mathematical modeling is so ancient that cannot accurately state a specific date on which such practice began. According to Schichl [1], the use of numbers to refer to bones, which can be considered as a mathematical representation of something real, dates from years before the Christian age. Actually, every culture has developed some sort of mathematical knowledge to account for daily life problems, because mathematics is at the base of all human relationships with the natural world and the social construction that allows us to live in community. Examples of this are the optimal use of available space -that requires at least an intuitive understanding of geometry and can be as complex as the most sophisticated architecture-, the distribution of resources such as food, land or materials, the distribution of time and the recording of history through the calendar, and the management of social interactions through the established rules of the market. For natural scientist, the language of mathematics has been crucial to develop useful models for specific problems and, from the study of those models, the creation (or development) of theories. Physicists, for instance, understand the word through models and theories that are supported on the mathematical relation among the measurable quantities related with the studied phenomena. This mathematical rule aim to predict future behaviors of the described system under the right conditions. When new data is found that may compromise the validity of previous models and theories, it is required to build a working explanation inside the accepted models or theories that can account for such data. If such explanation cannot be reached, some sort of change is made on the models so that the new model or theory is enriched with the currently available information. That way, a new and more solid way to understand natural reality emerges. The new model can be explored to find new predictions, new insights about the reality it represents. It is noticeable that the world has not suffer any changes, but the model we use to understand it does. Many scientists believe that a model is a simplified version of something real. Under this perspective, the model is just a representation of reality, not reality itself. Under the process of refinement that models are constantly subjected to, a better model that delivers a more accurate representation of reality is found. The mathematical rules in the model can be understood as a manifestation of the presence of mathematics inside reality, so when a more comprehensive mathematical representation of the world is found, a better understanding of nature is achieved. DOI: https://doi.org/10.18359/rfcb.5835