Tuesday, July 31, 2012

Should we allow professors to advocate innumeracy?

When I think about energy and energy policy, I almost immediately find myself immersed in numbers.  At a macro level, it seems to me that it's almost impossible to avoid that.  If nothing else, the numbers are so big that you have to do simple scale calculations just to be sure that you're not making some really stupid blunder.  For example, does the US grow enough corn to replace all of its gasoline usage with ethanol?  Tom Murphy's Do the Math is filled with that type of scale calculation, and Tom punches holes in a lot of the proposals for how we can meet future energy needs cleanly and affordably.

Last Saturday the New York Times ran an opinion piece titled "Is Algebra Necessary?" by Andrew Hacker, an emeritus professor of political science.  Dr. Hacker's basic position is that we keep too many people from succeeding in high school and college because of our silly infatuation (my adjective and noun, not his) with making people learn high school algebra.  To quote one of his statements, "But there’s no evidence that being able to prove (x² + y²)² = (x² - y²)² + (2xy)² leads to more credible political opinions or social analysis."  I claim that's not true, that there are a lot of non-credible political opinions held by  people who didn't do the math.  And even worse, if they can't do the math, they have no way to determine that their position is unsupportable.

A commonly heard statement about the US Social Security system is that over the next few decades, we will move from the current situation with about three workers per retiree to having only two workers per retiree, so it must follow that the system is insolvent.  If that's so, I tend to ask, then how did we move from having 16 workers per retiree in the early days of SS, to the current three workers per retiree, but the system continues to roll along?  And accumulated a $2.7 trillion dollar surplus in the Social Security trust fund?  Yes, we raised the tax rates to reflect more generous per-retiree benefits.  But if you can't explain how worker productivity increases allowed a 5:1 decrease in the ratio of workers to retirees over the past 80 years, then you're not competent to have an opinion on the subject [1].  And you can't make that explanation without understanding how exponential functions work.  And now you're back to algebra.

I admit to a bias on this topic.  I was an applied mathematician before I was any of the other things I did in my career(s), and it's how I think about a lot of things in the world.  Mathematical models aren't the only way to think about the world [2], but there are a lot of topics, including political opinions and social analysis, where there are questions that you can't answer without math.  However, I'm willing to meet Dr. Hacker half-way.  At one point he writes, "Yes, young people should learn to read and write and do long division, whether they want to or not. But there is no reason to force them to grasp vectorial angles and discontinuous functions."  I'll offer the alternative, "Yes, young people should learn to read and write [3] and do long division, whether they want to or not.  But there is no reason to force them to grasp Shakespeare and Chaucer or why England and France fought the Hundred Years War."

[1]  It's perfectly reasonable to develop a model and derive numbers and show that the productivity gains needed to allow the continued decrease in the worker-to-retiree ratio are unlikely to occur.  I wrote an argument that suggested that energy supplies are a key to that discussion here.

[2]  And I cheerfully acknowledge the wisdom in George Box's statement that all models are wrong but some are useful.  I'll also point out that a non-mathematical chain of reasoning can be just as wrong, and for many of the same reasons

[3]  I'd go at least a step farther than the minimum writing typically required in high school.  I want everyone to have to pass a real composition class; one where you write something almost every day and someone critiques it.  Such a class is, of course, a hell of a lot more work to teach than literature appreciation.  But probably more broadly useful than literature, too.  The composition class I took in high school as an option (well done, Ms. Morgan) was enormously more valuable, over the course of my life, than the literature classes I had to take in college that masqueraded under the name "English Composition."

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