One of the best teachers I ever had was Mr. Garabedian. He was my pre-calculus professor in undergrad. Mr. Garabedian had a strict “no calculators” rule in his class. Not because he was some old hard-ass who was afraid of technology, but just the opposite: he was well aware of how powerful technology was and how easily a relatively cheap calculator could produce the answers to mathematical problems. In his career, he noted that students could become very competent at using calculators (and later Google) to solve math problems. Memorizing formulas was no longer necessary. But this, in turn, lead to students not understanding the reasoning behind the mathematics. A student could determine 4 * 4 = 16, but not explain why. Conversely, students would get a wrong answer supplied by the calculator but not have the ability to know/detect the answer was wrong, or where the error might be. So, his class focused primarily on the intuition aspect of mathematics; the logic behind the framework. I am not a great mathematician; I never have been and never will be. But this method of teaching broke through to me and things that were jumbled messes of numbers and letters suddenly became clear. Knowing the intuition, I’d be able to work through mathematical problems without knowing formulas, and be able to tell when an answer didn’t make sense. Furthermore, this helped me become a better student by knowing when to seek help.
In short, Mr. Garabedian taught me not just math, but to ask the question “does this outcome make sense?”
Asking that question is what separates the thinker from merely the purveyor of science. All too often, I come across someone who is very smart point to some mathematical model or some chaotic theory and claim, with a perfectly straight face, that their model/theory (simply by the virtue of being a model coupled with mathematics) provides an outcome contrary to what might seem logical. This is true not only of economics (which does have its fair share of “sciencism”), but of politics, and business, and sociology, psychology, biology, chemistry, etc. In short, they fail to ask the natural follow up question: does this outcome make sense? Does it make sense than a minimum wage hike of 107% would have no impact on employment margins (regardless of what the model says)? Does it make sense that the world is so chaotic that there are no such things as trade-offs (regardless of what the theory says)? Does it make sense to alienate an entire demographic of voters (regardless what the voting models say)? The list goes on.
To be clear, none of this is to say that mathematics and models aren’t important. They are. But they are just one tool in our toolbox and one must remember that, ultimately, data never speak for themselves and mathematics is, ultimately, a logical field. When confronted with data, no matter how rigorous or precise your model might be, be sure to ask the question “does this make sense?”