Numbers don’t lie, but they tell a lot of half-truths. We have been raised to think that numbers represent absolute fact, that in a math class there is one and only one correct answer. But less emphasis is put on the fact that in the real world numbers don’t convey any information without units, or some other frame of reference. The blurring of the line between the number and the quantity has left us vulnerable to the ways in which statistics can deceive us. By poorly defining or incorrectly defining numbers, contemporary audiences can be manipulated into thinking opinions are fact.
Charles Seife’s forthcoming book Proofiness: The Dark Arts of Mathematical Deception (out next month on Viking) lays bare, in remarkable clarity, the many trappings of trusting numbers a bit too much. While people are usually adept at recognizing numbers that are blatantly false, such as “85% of statistics are false or misleading”, more subtle manufactured numbers can have a dramatic effect on public opinion. Seife’s most oft-cited example of this phenomenon is the 205 suspected communists Joe McCarthy claimed were working in the US State Department, effectively sparking the Red Scare. While his list was never released, the unverifiable “205 communists” were enough to make an obscure junior senator from Wisconsin one of the most divisive politicians of the twentieth century.
Numbers don’t have to be manufactured to be misleading. One of the most common misunderstandings concerns the precision of a measurement. This problem is dealt with by significant figures, a concept that’s the bane of high school physics students nationwide (not to mention, playful fodder for another of Randy Munroe’s comics). Whenever you assign a quantity to something in the physical world, that number will only be as precise as your method of measurement allows. If I measure a table by comparing it to my wingspan, I can say it’s about six feet long, but if I use a tape measure I can acquire a more precise measurement of 6 feet 5.5 inches. Now, most people will accept 6’5.5" as the absolute length of the table, but using more sophisticated measuring devices I will always be able to make more precise measurements to smaller fractions of an inch (until I get to the subatomic scale, and quantum physics messes everything up). However, we’re hard wired to believe that the numbers we hear in everyday life were measured with infinite precision, and that can lead to complications. I always remember this from a lesson my physics teacher told me in the eleventh grade, “If you go to the Grand Canyon one year on a family vacation, and the tour guide says it’s 17 million years old, when you go back a year later, the tour guide won’t say it’s seventeen million and one.” We can’t possibly hope to know the age of the Grand Canyon that precisely because of the methods used to determine its age.
Most of the time, believing that a measurement is more precise than it actually is isn’t really a problem. But, in 2000, the US Government certified that George Bush had 2,912,790 votes in Florida while Al Gore had 2,912,253 (And to be bi-partisan, the state of Minnesota claimed Al Franken received 1,212,431 votes in 2008 to Norm Coleman’s 1,212,206). However, the methods for tabulating votes will always be prone to human and mechanical error (For a complete discussion, check out Seife’s book). There is no way anyone could know, down to the vote, how many any of these four candidates had. As far as anyone can say for certain, both races ended in a tie, and no amount of recounts will change that.
A recount is an attempt to eliminate a systematic error, or problems with the process of collecting data. Lost votes and misinterpreted ballots will lead to imprecise vote totals, but another type of systematic error is more common today. Visiting ESPN’s SportsNation produces a perfect example of systematic error almost daily. It seems that people in New England believe Tom Brady to be a more legendary quarterback than Brett Favre. Asking a group that is largely comprised of New England Patriot fans will introduce a systematic error biasing Brady. While internet polls may create something easy news stories, they are plagued by systematic errors. How else do you think Stephen Colbert almost got a part of the International Space Station named after him?
The Internet has opened up a whole new forum for mathematical misleading. Even bogus mathematical falsehoods like The Timecube and the “50 million” 2012 websites that Dr. Neil deGrasse Tyson playfully debunked in an informal chat during a star party this year’s World Science Festival can gain traction. And, with no offense meant towards Dr. Tyson, the 50 million figure holds about as much weight as McCarthy’s 205 communists. But Tyson’s other points in this video are what’s important. “I could just tell you it’s all bunk,” he says, “but then you wouldn’t be empowered to understand why… It’s my duty as an educator to empower you to think, so that you can think accurate thoughts…Science literacy is…how is your brain wired for inquiry. What is the next question you ask when someone wants to sell you something.”
Michael J Kennelly is a Senior Physics Major at Columbia University, where he holds a I.I. Rabi Scholarship. He has completed research internships at Columbia, Rutgers University, The Princeton Plasma Physics Laboratories, and The Large Hadron Collider at CERN. He currently is making up numbers for the World Science Festival.