Does This Make Sense?

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?”

13 thoughts on “Does This Make Sense?

  1. My older daughter is a great mathematician with an innate understanding of very complex concepts. Unfortunately, she’s a terrible arithmetician, so folks like Mr. Garabedian drove her out of math. Oh well, that’s life, what can you do?

    Jon Murphy wrote: “some chaotic theory and claim … that their model/theory … provides an outcome contrary to what might seem logical.”

    Of course lots of people work with complexity and chaos theory, but just in case I’m one of those you’re referring to, those outcomes seem logical to me and others even if they seem contrary to what’s logical to you.

    Jon Murphy wrote: “Does it make sense that the world is so chaotic that there are no such things as trade-offs?”

    Again, just in case you’re referring to something I’ve written, just to be clear, there are, of course, trade-offs even in a chaotic system, it’s just that the trade-offs are different than would be expected in a simple, linear and/or equilibrium system. One example of this is fluid dynamics. All of the theories and predictions that work with laminar flow (pre-chaotic flow) break down utterly and completely once the flows become turbulent. And to the extent that my studies of physical systems and economics overlaps, economic activity and trade seems to have more than a little in common with fluid flow. And I’m not the only one. The Santa Fe Institute is an economics research organization that specializes in what they call “complexity economics and nonequilibrium economics” and they think that fluid mechanics has a fair amount in common with economics and trade.

    And in case you think Santa Fe Institute is totally fringe, note that one of its founders was nobel prize winner Kenneth Arrow who Don Boudreaux refers to regularly for his work in public choice theory.


      • Ron H.,

        Off the top of my head, I don’t think economic theory explains bubbles and other economics crises very well. Yet it would be trivial to create a chaotic system that would very definitely have periods of stability and bubbles.


        • Bret: there are lots of economic explanations for bubbles and crises. The Keynesians blame animal spirits. The Austrians blame malinvestment caused by market interventions. The Monetarists look toward monetary policy.

          Economists spend a good amount of time looking for explanations on why things are out of equilibrium, why bubbles and economic crises happen. In fact, most of our models have an error term in then to account for the unpredictable. In fact, if you want to sum up macroeconomic analysis simply, it is this: the study of why economies deviate from growth patters and how long it takes them to return to equilibrium.


          • Jon Murphy wrote: “… and how long it takes them to return to equilibrium.”

            They will never return to equilibrium. There is no equilibrium to return to. There is, at best, brief periods of time with relative stability when enough bits of the system pull far enough away from strange attractors, but those still aren’t equilibrium periods. And the larger the system becomes, the less stable it will become.


              • I agree with that. Substitute “destructive periods of rapid change” for bubbles. There is no equilibrium, but there are destructive periods of rapid change.


            • Equilibrium doesn’t mean a set price. The whole point of the price system is to vary to respond to different information on relative demand/supply. But it does mean, for lack of a better term, a “natural” price.

              Think of it like this: the thermostat of a home is set at 70. When the temp >70, the furnace turns off. When the temp is <70, the heat turns on. When the temp is right at 70, the furnace does nothing. There is the feedback loop to keep the temp around 70. There is some deviation, of course, but it hovers around there. If the temp plummeted to, say, 60, then there would obviously be something wrong with the feedback mechanism You'd know there is some kind of problem with the thermostat because the temperature is deviating greater than normal from the natural level. That's the same thing as a bubble forming (or popping) in the economy.

              So, the only way to know if a bubble is forming (or popping) in an economy is to have some kind of equilibrium. In other words, to know you have a deviation from the norm, you need to have a norm. Therefore, your complaint that economics is not good at explaining bubbles, and that there are no such thing as equilibrium are incompatible.


              • Now take your thermostat and modify it so that it changes the set point chaotically and unpredictability due to feedbacks from countless other system subcomponents. Then I’d agree with the model and such a model would have periods of relative stability and destructive periods of rapid change (perhaps the house would get so hot it would burn down, for example).

                Perhaps, system wide, the best you can do is let the system be and tolerate the destructive periods.

                But, perhaps not.


        • Bret

          Jon beat me to it. I personally favor the Austrian business cycle explanation – along with the “greater fool”: theory.

          Yet it would be trivial to create a chaotic system that would very definitely have periods of stability and bubbles.

          Could you elaborate on that?


    • Wait…if your daughter is good with the mathematics intuition, then how would have Mr. Garabedian driven her away from mathematics given he teaches mathematics intuition?


      • She would’ve aced his class with a calculator. She’s terrible at simple things like addition, subtraction, multiplication, and other arithmetic. She’s the only person I know who can multiply 9 and 8 and come up with 63. And unfortunately, no matter how intuitive the math is, if you can’t add without making mistakes, you’ll have a hard time on the tests.

        In college stats, she taught all her friends. But she was able to use a calculator. Without it, she would’ve failed miserably.


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