HPRgument Blog — February 9, 2010 7:46 pm

Applied Math Democracy

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The other day, my girlfriend (who’s not a math fan) sent me a link to a new New York Times post by Steven Strogatz, an applied math professor at Cornell who is writing a blog that will, over the next few weeks, give readers a quick tutorial on math, “from pre-school to grad school.”  Strogatz starts slowly; his first piece (linked above) was a brief explanation of why numbers are useful, and just yesterday he released a new post, a nuanced lesson in grade school arithmetic.  (For anyone who’s interested, he posts every Monday and will have about 15 entries in all.)

As Strogatz noted in his first column, there are some very intelligent people out there who shudder at the mere mention of mathematics.  It seems that one can self-purportedly “hate” math more than one can have such strongly negative feelings towards other subjects.  A lot of people hate math, and a lot of people, I’m sure, dislike history.  But how many people would say they “hate” history?  Indeed, there is also a tendency to write off math as more broadly inapplicable than other subject areas, and I know plenty of fellow students who grudgingly must find a quantitative reasoning class to fulfill a gen ed requirement and consider the whole exercise a waste of time.

And that’s a shame, because math is one of the most important subjects that a responsible, voting member of this republic can master.

First of all, let me qualify that claim.  I don’t think that much of what is learned in math class is directly applicable in the lives of most Americans.  (As my former soccer coach once said, “When you go to the cash register, they don’t say, ‘That’ll be 3x + 4y dollars.’”)  But one could say the same thing for much of what is learned in any class.  The primary reason for education is not to teach us things that will help us directly in our day-to-day lives; rather, it is to instill in us a way of looking at the world that will equip us to creatively analyze choices we face throughout our lives, be them at work, among friends or family, or in the voting booth.  Indeed, the reason that public education exists at all is so that citizens of a democracy can perform exceptionally well on that last decision set.

In the end, we want to live in a society where people can listen to politicians or read the news and sort out the facts from the spin to make an informed decision; we also want to live in a society that produces policymakers capable of taking new and creative approaches to the problems they encounter.  Math, I argue, gives citizens the tools to do this more effectively than other subjects.

First, math requires creative and focused thinking.  Sooner or later in math class, we reach a problem that the old “plug-and-chug” method can’t solve, and we must approach it from a different angle. In humanities classes, we often define our own questions, formulate our own theses, and find evidence that supports our claims.  Policymakers, however, often do not choose the problems they encounter, and it can’t hurt to have leaders who are trained in creative problem solving.

Second, math is reliant on logic to a greater extent than most other subjects.  Of course, logic is vital to any academic pursuit, but if you make an illogical claim on a math problem, you simply get it wrong; if you present an illogical argument in a history essay, you might escape with a B-. It goes without saying that having a logical electorate and policymakers is preferable to the alternative.

Finally, and most of all, math depends on precision–precision in calculations and, more importantly, precision in language.  There’s a lot of dishonesty inherent in the political process, and most of it is not a result of politicians knowingly telling outright untruths.  Some of it, of course, is that politicians lie, and some of it is that politicians take advantage of the massive tracts of gray area that any issue entails.  But even more of it, I think, is that people are too casual in listening to what other people are actually saying.

Here’s a particularly trivial example:  Remember that 60 Minutes interview with Game Change-author John Heilemann in January?  Heilemann made several claims about Palin’s aptitude to be President, and among them was this juicy tidbit: “[Palin] still didn’t really understand why there was a North Korea and a South Korea.”

This launched a cable-news media frenzy.  Lawrence O’Donnell said, “She didn‘t know North and South Korea are two separate countries.”  Chris Matthews said, “[She doesn't] understand there’s two Koreas.”  And Bill O’Reilly, interviewing Sarah Palin on his program asked, “Is this guy lying? He says you don’t know the difference between North and South Korea.”

O’Donnell, Matthews, and O’Reilly (and countless others) clearly didn’t understand what Heilemann actually said.  He wasn’t saying that Palin didn’t know that North and South Korea were two different countries, only that she didn’t understand the history of why this division came about.  Obviously, it’s concerning that a nominee for Vice-President of the United States doesn’t understand the Korean War, but what’s more concerning is that America’s media couldn’t even understand what Heilemann was actually telling them!

I’m not saying that math is necessary to being an intelligent, informed voter and a productive member of society.  Indeed, creativity, logic, and precision of language are necessary in any academic subject.  Still, these tools are especially emphasized in mathematics, and understanding this makes math more applicable than most people realize.

Maybe calculus should be a requirement for voting?

Photo credit: akirsa on flickr.

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  • Jeffrey Kalmus

    Jeremy, thanks so much for enunciating what are more or less my life plans. I’m a math major but don’t plan on becoming a mathematician, so solving problems like “Prove that the ring R[[t]] of formal real power series is a unique factorization domain” (on my homework!) isn’t going to get me very far in life.

    Beyond the rigorous and creative problem solving that math teaches, its individual fields have important lessons for our thoughts and our democracy. Algebra, the study of mathematical structures, contains mathematics’ most beautiful results and reminds us that that there can be order in the universe and in our polity. We can’t quite treat citizens as algebraic elements, but algebra can inspire those who know it to look for beautiful, elegant, simple solutions to daunting problems. Analysis, the backbone of calculus, has quite a different lesson–its proofs tend to be constructions of approximations, with the lesson that really, really, close is in fact good enough, and that we need not find the perfect solution.

  • Max Novendstern

    I’ll say that (a) I like this post — a lot, and (b) I totally disagree with it.

    I really like it when people ask the question, Is this thing X good for our democracy? Are big banks efficient or are they systemically high risk? That’s a questions we hear a lot. But the Brandeis question, the Progressivist question, Are big banks good for our democracy — we never hear that.

    Is math good for our democracy? I’ve literally never heard that. Kudos.

    On the other hand, I’m not sure I really buy the conclusion. Democracy is not anything like algebra. It’s a whole lot less elegant. Problems solving is important for policy, and precision is important for media players, but the main traits of governance are probably creativity, persuasiveness, tenacity, public-spiritedness, and then, at some final level, an ironic respect for the opposition’s right to oppose you — math teaches us none of that. Maybe we should be saying that math is good for technocratic authoritarian states, where answers are said to be perfect and people legally are bound to follow them.

  • Jeffrey Kalmus

    True, math doesn’t teach “an ironic respect for the opposition’s right to oppose you,” and it may not teach public spiritedness (although the group problem solving involved could achieve this), but it does teach creativity, persuasiveness, and tenacity. Better, it teaches creativity within bounds, as you’re only given a limited set of assumptions and can assume no more–and it’s always a goal to solve a problem with minimal assumptions. Policymakers certainly work under constraints, and this is in a sense analogous. A well-written mathematical argument is incredibly persuasive and nearly impossible to dispute. And if you don’t think that math teaches tenacity, go to the Lev dining hall at 5 or 6am the day before physics 16 (basically a math class) problem sets are due .

  • Jeremy Patashnik

    Max, you’re right that math certainly doesn’t teach you everything needed to be a good policymaker or citizen. (Though I strongly disagree that math does not teach two of the things you claim: creativity and tenacity. Mathematicians must possess both of these traits to an extraordinary degree.)

    So you’re right that a mathematician would probably make a lousy politician (for reasons you state), but I claim that a politician (or a regular citizen) who has some math training will be more effective than one who does not.

    As Jeff points out in his first post, math gives you techniques for analyzing problems you encounter. His example from calculus, I think, is especially applicable to governance: that “really, really close is in fact good enough.” (Or for governance, maybe we should just say “sort of close is in fact good enough.”) Another useful technique from calculus: the idea that we needn’t approach a problem all at once; let’s slice it into smaller pieces and tackle them one at a time and see if we can’t find a more efficient way of doing things.

    Above all, I can’t stress enough how underappreciated precision of language is in society. Look at all the court cases that arise because laws are worded ambiguously! And just in general, think how much smoother things would run if someone could craft a sentence so that they conveyed exactly what they intended to, and then a second person could hear that sentence and understand exactly what that first person was trying to say. It seems trivial, but mathematicians go to tremendous lengths to ensure that their definitions and statements are logical, and if others did the same, things would just work better.

  • Cathy Sun

    Hey Jeremy, I really agree with what you wrote about math education and its ability to impart an appreciation for precision and logic. It’s not just that Americans need to understand the immensity of the difference between million and trillion, but that they measure the results of governance by the numbers and with full understanding of how measuring occurs. In that sense, I suspect, not only math, but economics and statistics, should be included in any civics course…

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  • Shambhavi

    Hi Jeremy, you’ve got a good article there. I’m doing my post grad in Economics, which perhaps may resound in my bias towards math. Surely in dynamic optimization we study voting functions, on how people’s mindsets change (or become bias to a party) seeing the change in observable variables such as unemployment and inflation over a period of time. Of course I don’t claim that every individual should be equipped with the calculus jargon, but what I do know is that it is in the tendency of every person to optimize. I think math can simply help in quantifying what we observe everyday around us. I was also reading your article on the defense of Ec-10. I think here in India as well, we have such a structure of our course, and one person even commented that in real life indifference curves don’t exist. That in fact is also true. So why do we do it then? Simply, to quantify, filter our minds and to bring some sense out of the chaos. So I agree with you, a politician having some math training will be more efficient. And a politician being a game theory specialist would even be a star.

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