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Choose Math.

From the Norwegian newspaper Aftenposten, a short essay in praise of math.

Now, I would not call myself a mathematician by any stretch of the imagination. I struggle with anything calculus-related that's more complicated than basic integrals and differentials. I dropped my linear programming class because the matrix algebra was breaking me; I still couldn't tell you what an eigenvector is without looking it up on Wikipedia. Everything I know about Fourier transforms I learned in my acoustic phonetics class or via pillow talk with my electrical-engineer boyfriend. I cringe when the mathematicians I know lament the dismal state of innumeracy -- and, worse yet, pride in innumeracy -- that so many people exhibit. Somehow it's shameful to be unable to read, but an inability to balance one's checkbook is chuckled over as an all-too-common state of affairs. Compound interest I can remember, but the Chain Rule? Fucking hell, I admit it, I'm a poser.

But Espen Andersen's essay hits on a truth more profound than the Axiom of Choice.
Choose math because it makes you smarter.

Choose math because you will lose less money.

Choose math because you will live in a world of constant change.

Choose math because it doesn't close any doors.
Andersen is talking about math not as a collection of equations and operations, but as a way of life. The math Andersen cares about is the math of Feynman's "different box of tools": a way of thinking critically about problems that lets you decompose difficult constructions into manageable components, evaluate a structure of easy pieces rather than a baffling whole.

Nor does this mode of thinking necessarily require you to remember a laundry-list of equations from a textbook. It's far more useful to understand the relationships between entities, because if you can do that, then you can reconstruct the equations later. If you can think "Okay, I've got two quantities, and one of them is increasing twice as fast as the other," and visualise the relationship between them, congratulations, you understand linear equations and do not need to memorise and regurgitate the Slope-Point Formula, the Slope-Y-Intercept Formula, the Two-Point Formula, the Two-Intercept Formula and all the other permutations of Ax + By + C = 0 that my kid sister's high school algebra teacher tried to force down her throat. Likewise, if you can envision two quantities, one of which is increasing (or decreasing) sometimes faster than the other and sometimes slower -- then recognise that this rate of change itself has a rate of change -- and that you can keep examining how the rate of change is changing until you get to a single constant value1 -- congratulations, you've just discovered differential calculus and recursion. Continuous math and discrete math, delicately coupled in the everyday world of thrown baseballs or traffic on the freeway.

No, I'm not a mathematician. But I try to look at the world through the eyes of one. I know there are math teachers reading this, and I'd like to thank you for the work you do. The more you can encourage your students to choose math, the better we'll all be for it.

1Okay, okay, not if it's a trig function (as one example). You pedant.

Comments

( 3 comments — Leave a comment )
kenshi
Mar. 22nd, 2006 12:11 am (UTC)
I completely agree to the extent that a thorough knowledge of mathematics can be a very valuable tool in dealing with any sort of linear problem you might encounter.

At the same time, reliance on the linearity of methematics and mathematical problem-solving is extremely counter-productive when dealing with any sort of wicked problem. I see this all the time with engineers. Because of their focus on liner problem solving, they are woefully unprepared to deal with any sort of "wickedness" at all.
maradydd
Mar. 22nd, 2006 12:52 am (UTC)
Fundamental to the understanding of math is an understanding of the limits of math.

A good example of this is constraint optimization problems. Describing a problem as an LP and solving that LP may help you to determine a useful real-world solution, but if the constraints you define are irrelevant or incomplete -- say, a production model which fails to take into account fluctuations in the prices of supplies -- the derived solution will be less useful or in fact entirely useless. Nor is a model useful if you're using the wrong hammer: continuing the previous example, if your constraint variables are interacting multiplicatively instead of additively, then you are facing a quadratic programming problem, and linear programming techniques will not help you.

The properties of wicked problems described on that Wikipedia page -- particularly "wicked problems have no stopping rules" and "discrepancies in representing a wicked problem can be explained in numerous ways" -- indicate that while there may certainly be aspects of wicked problems in which mathematical techniques are useful, a respect for the limits of math is crucial.

Hell, there's an entire discipline of math devoted to demonstrating that certain problems are unsolvable using computational techniques available to us, not to mention unsolvable using computational techniques we can only speculate about .
bigby
Mar. 22nd, 2006 05:17 am (UTC)
This starts in preschool if rather than solve the argument you try to get them to think about other perspectives..
( 3 comments — Leave a comment )

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