Why Should We Approximate the Future?

Imagine that you are a foreseer, and you predict that a calamity is drawing near, and you know how to prevent it. Would you rather stand up and prevent it, or would you only watch how your surroundings collapse and become the only survivor? What would you do if you already knew how everyone is going to behave and react to certain messages? Would you always seek to implement the easiest, cheapest, and most sustainable solution to a problem?

Mathematics has established different abstract objects and methods that can be applied to represent our surroundings, whose main purpose is to describe its dynamics and make predictions about future behavior. That is modeling: the art of establishing a mathematical description of a situation that enables you to predict future behavior. More generally, a model enables you to capture the essences (relevant information) of your problem and represent it.

What if, through using this technique, we can become foreseers? However, it is important to mention that not all the models are 100% accurate because assumptions are made to approximate the solution, because it would be impossible to consider everything. Even though problems can be difficult to handle, models can give you enough accuracy to describe your situation, hence, the results are valid. There are models to models, with each having a balance between accuracy and complexity. Normally, more accuracy implies more complexity to the model, but a simple model can give the same needed results as a complex model.

For example, you do not need Einstein’s theory of relativity to describe the motion of particles when their speed is much smaller than the speed of light. By knowing how things are going to beh

ave in the future, one has the knowledge to make better decisions and solve problems, and it enables you to optimize or make a heuristic search for the best processes.

In a nutshell, modeling enables you to make educated guesses; it gives you an idea of how things work; it gives you a starting point for solving a problem.

Want to learn more about models? Check out this video from Dr. Richard Feymann as he explains quantum mechanics and states that even though models are not accurate, they give you a good idea of how a system works. I bet you already made models without perceiving it, but you have not gotten the most of it.

Find more about the power of modeling on the next story.