Q: Why do we use modeling in math if it is useless?
A:
“With great power comes great responsibility”
Sometimes when we do stuff, it was not necessary, because we could have approached it in a simpler manner.
The same applies to mathematical modeling. It sometimes is not necessary, because there would be more open, effective ways to solve the problem. This is quite subjective to how useless/useful things can be to different people. I will stick with usefulness as how effective it achieves our end goal; in this case, to capture the thing we try to model with reasonable accuracy.
Modeling then still stands. Do remember that math is based on pattern, regularity, structure, and all else relatable. The heart of math is not stochastic i.e random. Because of this structure, we were able to replicate how things may evolve, and we may be able replicate the past in the future, which is forecasting, and is mostly the goal of modeling.
Now some may argue about the study of randomness, such as chaos theory or stochastic processes. However, the theories and the applications of them are still based upon some basis. When we argue about how stock prices walk randomly, we can still explain though they walk randomly, but still tends to revert to certain values. Moreover, modeling stock price, though the stock zigzags all over, is based upon a certain fact that the returns are normally distributed: if you plot a histogram of the percent changes in stock price, it approaches a structure, which is why we model.
We obviously do not model if it’s useless. You know how we got the weather forecasts on TV so that you know your picnic or hangout with friends won’t be possibly ruined? It’s called Numerical Weather Prediction (NWP). It’s very accurate.
We model because it has proven itself to work, and that means it’s useful.
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