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Have You Ever Thought That an Equation Is a Model Too?

I had a bit difficulty last year on wrapping up the ‘model’ concept in my head. I somewhat understand it yet could not explain it to a child. I don’t understand it well enough, according to Albert Einstein or Richard Feynman.

Here’s my best attempt to explain it to you. Until I published this article.

A model is a representation of a real-world system.

According to Kaplan or at least that’s what I’ve been told in class, the statement regarding model goes like this: “Any system A is a model of a system B if the study of A is useful for the understanding of B without regard to any direct or indirect causal connection between A and B.”

It implies that system A and system B share some common traits and at least resembling same patterns or sequences in both systems. It could be anything basically, a pilot project that is waiting to be upscaled is the model of the end product. A lab experiment to understand why some chemicals in liquid and others are solid. School A can also become a model of school B. Playing flight simulator to understand being a real pilot.

Life simulation in the matrix would be a model of the previous’ life trend. It’s not useful to understand the current situation. It is designed for research so it doesn’t matter… I guess.

No Patrick, Talking in the Sims is not the same as in real life
Figure 1: An Answer for Patrick

Back to the topic, a model is one of our ways to expand our understanding of the world phenomena and filling in gaps between well-established subjects. By saying this and that are similar, then we can try something on this to predict on that.

This is why an equation is a model too. For example, time equals to distance divided by speed (or velocity). To reduce travelling time, we can either reduce the distance or increasing the transport speed (or velocity).

If a model could be represented as a mathematical equation, then why bother to call it a model instead of an equation?

Apparently, it’s not always the case. Some variables would share a categorical type of trait. Colour. Species. Preferences. There are understandings that do not need calculation at all. Our skeleton for example. We would have 206 bones when we reach adulthood that could not be swapped. Each has its own distinct name. Where and what bones broken could help doctors to understand what kind of accident that happened to the victim and what kind of treatment they need.

More often than not, a model holds multiple equations. Making it more complex and more unpredictable compared to a single equation. While equations are often associated with the well-established field, a model is created to sail between known and unknown.

Model is a broad concept. It is a term that uses comparison to understand the real world. I am a believer that analogy and metaphor is also a model that we used in our daily life to make abstract things easier to understand.

Photo by Roman Mager on Unsplash