Of course kids need to learn algebra.
Don’t Let Economists and Politicians Hack Your Math
By Edward Frenkel|Posted Friday, Feb. 8, 2013, at 2:14 PM ET
Imagine a world in which it is possible for an elite group of hackers to install a “backdoor” not on a personal computer but on the entire U.S. economy. Imagine that they can use it to cryptically raise taxes and slash social benefits at will. Such a scenario may sound far-fetched, but replace “backdoor” with the Consumer Price Index (CPI), and you get a pretty accurate picture of how this arcane economics statistic has been used.
Tax brackets, Social Security, Medicare, and various indexed payments, together affecting tens of millions of Americans, are pegged to the CPI as a measure of inflation. The fiscal cliff deal that the White House and Congress reached a month ago was almost derailed by a proposal to change the formula for the CPI, which Matthew Yglesias characterized as “a sneaky plan to cut Social Security and raise taxes by changing how inflation is calculated.” That plan was scrapped at the last minute. But what most people don’t realize is that something similar had already happened in the past. A new book, The Physics of Wall Street by James Weatherall, tells that story: In 1996, five economists, known as the Boskin Commission, were tasked with saving the government $1 trillion. They observed that if the CPI were lowered by 1.1 percent, then a $1 trillion could indeed be saved over the coming decade. So what did they do? They proposed a way to alter the formula that would lower the CPI by exactly that amount!
This raises a question: Is economics being used as science or as after-the-fact justification, much like economic statistics were manipulated in the Soviet Union? More importantly, is anyone paying attention? Are we willing to give government agents a free hand to keep changing this all-important formula whenever it suits their political needs, simply because they think we won’t get the math?
Ironically, in a recent op-ed in the New York Times, social scientist Andrew Hacker suggested eliminating algebra from the school curriculum as an “onerous stumbling block,” and instead teaching students “how the Consumer Price Index is computed.” What seems to be completely lost on Hacker and authors of similar proposals is that the calculation of the CPI, as well as other evidence-based statistics, is in fact a difficult mathematical problem, which requires deep knowledge of all major branches of mathematics including … advanced algebra.
Whether we like it or not, calculating CPI necessarily involves some abstract, arcane body of math. If there were only one item being consumed, then we could easily measure inflation by dividing the unit price of this item today by the unit price a year ago. But if there are two or more items, then knowing their prices is not sufficient. We also need to know the levels of consumption today and a year ago; economists call these “baskets.” Of course, we can easily find a typical consumer’s expenditure today by multiplying today’s consumption levels by the current prices and adding them up. But to what number from a year ago should we compare it? If the consumption levels were static, we would compute last year’s expenditure by multiplying the same consumption levels by last year’s prices and adding them up. We would then be able to measure inflation by dividing this year’s expenditure by last year’s. But consumption tends to change—in part because our tastes change, but also in response to price variations. The inflation index must account for this, so we have to find a way to compare the baskets today and a year ago. This turns out to be a hard mathematical problem that has perplexed economists for more than a century and still hasn’t been completely solved. But even to begin talking about this problem, we need a language that would enable us to operate with symbolic quantities representing baskets and prices—and that’s the language of algebra!
In fact, we need much more than that. As Weatherall explains in his book, to implement a true cost-of-living index, one actually has to use the so-called “gauge theory.” This mathematics is at the foundation of a unified physical theory of three forces of nature: electromagnetism, the strong nuclear force, and the weak nuclear force. (Many Nobel Prizes have been awarded for the development of this unified theory; it was also used to predict the Higgs boson, the elusive elementary particle recently discovered at the Large Hadron Collider under Geneva.) The fact that gauge theory also underlies economics was a groundbreaking discovery made by the economist Pia Malaney and mathematical physicist Eric Weinstein around the time of the Boskin Commission. Malaney, who was at the time an economics Ph.D. student at Harvard, tried to convey the importance of this theory for the index problem to the Harvard professor Dale Jorgenson, one of the members of the Boskin Commission, but to no avail. In fact, Jorgenson responded by throwing her out of his office. Only recently, George Soros’ Institute for New Economic Thinking finally gave Malaney and Weinstein long overdue recognition and is supporting their research. But their work still remains largely ignored by economists.
So that’s where we find ourselves today: Politicians are still eager to exploit backdoor mathematical formulas for their political needs, economists are still willing to play along, and no one seems to care about finding a scientifically sound solution to the inflation index problem using adequate mathematics. And the public—well, very few people are paying attention. And if we follow Hacker’s prescriptions and further dumb down our math education, there won’t be anyone left to understand what’s happening behind closed doors.
Irrespective of one’s political orientation, one thing should be clear: In this brave new world, in which formulas and equations play a much bigger role than ever before, our ignorance of mathematics is being abused by the powers that be, and this will continue until we start taking math seriously for what it is: a powerful weapon that can be used for good and for ill.
Alas, instead of recognizing this new reality, we keep giving forum to paragons of mathematical illiteracy.
In his book, Weatherall made an admirable effort to start a serious conversation about the need for a new mathematical theory of the CPI. But guess who reviewed this book in the New York Review of Books? Andrew “we don’t need no algebra” Hacker! There is nothing wrong with healthy debate; it can only be encouraged. But something is wrong when an opinionated individual who has demonstrated total ignorance of a subject matter gets called on over and over again as an expert on that subject.
We have to break this vicious circle. As Richard Feynman eloquently said, “People who wish to analyze nature without using mathematics must settle for a reduced understanding.” Now is the time not to reduce math curriculum at schools, but to expand it, taking advantage of new tools in education: computers, iPads, the wider dissemination of knowledge through the Internet. Kids become computer literate much earlier these days, and they can now learn mathematical concepts faster and more efficiently than any previous generation. But they have to be pointed in the right direction by teachers who inspire them to think big. This can only be achieved if math is not treated as a chore and teachers are not forced to spend countless hours in preparation for standardized tests. Math professionals also have a role to play: Schools should invite them to help teachers unlock the infinite possibilities of mathematics to students, to show how a mathematical formula can be useful in the real world and also be elegant and beautiful, like a painting, a poem, or a piece of music.
Working together, we should implement the 21st century version of the Second Amendment: Everyone shall have the right to bear “mathematical arms”—to possess mathematical knowledge and tools needed to protect us from arbitrary decisions by the powerful few in the increasingly math-driven world. So that the next time someone wants to alter a formula that affects us all, we won’t be afraid to ask: “Wait a minute, what does this formula mean and why are you changing it?”