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The Uses and Abuses of Math

February 8, 2006

Ever since his State of the Union speech, President Bush has been pushing increased government funding to improve science education, with better mathematics preparation as its foundation. While his claims that there is a shortage of workers in those fields and that more government is necessary to fix the problem are hardly convincing (See Lew Rockwell's article yesterday), the long line of international comparisons that have found Americans' mathematics mastery woefully inadequate would seem to establish our general innumeracy as a fact.

However, less clear than our innumeracy is whether we really want to overcome it. The fact that we frequently use mathematics to intentionally fool ourselves and others argues against that conclusion. When we systematically abuse numbers to distort reality, it is no surprise that we handle mathematics poorly.One of today's most obvious misleading number games is grade inflation.

Teachers have accommodated student desires for higher grades to the point that the median GPA of graduating seniors has risen about a full grade point since it was about 2.2 in 1965. At some elite schools almost everyone gets As and Bs today, and who is valedictorian has become how many 4.0 students will share that title.

High schools have gone even further, making it possible to get better than a 4.0. Many make advanced placement or community college courses worth an extra grade point. These and other policies (e.g., statewide comparisons crafted to show that, as in Lake Woebegone, all children are above normal) have, however, thrown away much of the useful information grades once contained.

Price inflation is another form of ego-building by manipulating comparison numbers. If I want to brag that I make more than my father ever did, the effects of inflation can overwhelm every other difference and make it so. On the other hand, older Americans use it to prove how much better things used to be. ("I remember when bread was a nickel...") Politicians are also handy at such abuse when it suits their purposes.

Competitive inflation also occurs in other dimensions. We regularly cheat on the new in "new and improved." For example, books and new car models come out well before the year starts (e.g., the 2007 model introduced during this year's Super Bowl), while magazines arrive with dates two weeks into the future. Statistics and percentages are subject to the same abuse. "Giving it 100%" was once going all out, but that has been replaced with giving it 150%, 200%, and even 1000%. I'm 1000000% sure there is something wrong with this inflated hyperbole. Similarly, statistics are routinely manipulated to make insignificant changes look significant. Instead of saying some drug increases the probability of some cancer from one in ten million to two in ten million, reports scream that it doubles your risk.

We cheat on clothing sizes. Adults want to feel be thinner, so what was a given size dress years ago is now a smaller size. Parents, however, want their children to be "ahead of the curve," so some companies cut infant sizes smaller, so everybody can have children that are ahead of their peers.

Everywhere you turn, people "cheat" to make today's results look better than yesterday's. This is particularly true in competitive sports, where we often judge quality by numbers (e.g., baseball statistics). We have changed rules to favor the offense in sports, so that more points get scored. We have tuned track surfaces with steel springs to make sprinters faster and have designed more flexible poles so pole-vaulters go higher. It is also prevalent in politics, where so many numbers are essentially made up (especially when governments suppress markets and the information they generate) and comparisons are generated to mislead rather than honestly inform.

It is time we were honest with ourselves about our innumeracy. While we understand that better mathematics skills are important and that we would like to handle numbers more deftly, most of us are unwilling to put in the time and effort to do so. And in many cases we simply do not want to "do it right," because that would force us to trade in some of the self-delusions we want to keep for the reality we are often desperate to deny. Besides, even if we were serious about getting a better handle on the use of mathematics, as in so many other areas, history hardly points to the government as the agency we would rely on to get the desired results.

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