Sunday, November 7, 2010
Proofiness by Charles Seife
In skillful hands phony data, bogus statistics, and bad mathematics can make the most fanciful idea, the most outrageous falsehood seem true. They can be used to bludgeon enemies, destroy critics, and to squelch debate. Indeed, some people have become incredibly adept at using fake number to prove falsehoods. They have become masters of proofiness: the art of using bogus mathematical arguments to prove something that you know in your heart is true – even when its not.
Our society is now awash in proofiness. Using a few powerful techniques, thousands of people are crafting mathematical falsehoods to get you to swallow untruths. Advertisers forge numbers to get you to buy their products. Politicians fiddle with data to try to get you to reelect them. Pundits and prophets use phony math to get you to believe predictions that never seem to pan out. Businessmen use bogus numerical arguments to steal your money. Pollsters, pretending to listen to what you have to say, use proofiness to tell you what they want you to believe.
Sometimes people use these techniques to try to convince you of frivolous and absurd things. There's no limit to how absurd proofiness can be. At the same , proofiness has extraordinarily serious consequences. It nullifies elections, crowning victors who are undeserving – both Republican and Democrat. Worse yet, it is used to fix the outcome of future elections; politicians and judges use wrongheaded mathematics to manipulate voting districts and undermine the accuracy of the census that dictates which Americans are represented in Congress. Proofiness is largely responsible for the near destruction of our economy- and for the great sucking sound of more than a trillion dollars vanishing from the treasury. Prosecutors and justices use proofiness to acquit the guilty and convict the innocent – and even put people to death. In short, bad math is undermining our democracy
The threat is coming from both the left and the right. Indeed, proofiness sometimes seems to be the only thing that Republicans and Democrats have in common. Yet it is possible to counteract it. Those who have learned to recognize proofiness can find it almost everywhere, ensnaring the public in a web of transparent falsehoods. To the wary, proofiness becomes a daily source of great amusement – and of the blackest out rage.
[The author provides the following example of a type of proofiness- mathematical deception- called disestimation.]
There's an anecdote about an aging guide at a natural history museum. Every day, the guide gives tours of the exhibit ending with the most spectacular sight in the museum: a skeleton of the fearsome tyrannosaurus rex that towers high over the wide-eyed tour group. One day, a teenager gestures at the skeleton and asks the guide, “How old is it?”
“Sixty-five million and thirty-eight years old,” the guide responds proudly.
“How could you possibly know that?” the teenager shoots back.
“Simple! On the very first day that I started working at the museum, I asked the scientist the very same question. He told me that the skeleton was sixty-five million years old. That was thirty -eight years ago.”
In reality, when the scientist says that the dinosaur skeleton is sixty-five million years old, that number is assumed to be a rough approximation; the measurement error is on the order of tens of hundreds or even millions of years. The museum guide screwed up when he took the sixty-five- million -year figure too literally. He ignored the errors inherent to the measurements of the dinosaur's age. Since the errors in measurement absolutely dwarf the time he spent working at the museum, his figure of 65,000,038 years is ridiculous. The guide trusted the measurement beyond the point where it should be trusted. He committed an act of disestimation.
Very similar acts of disestimation occurred in the judgments which determined the final victors in the electoral contests between George Bush and Al Gore in the Florida Presidential contest of 2000 and in the 2008 Senate contest between Al Franken and Norm Coleman in Minnesota. In consideration of the number of people who voted in each of these elections, the unavoidable flaws in balloting procedures and errors in counting, the margins of victory- a few hundred votes- represented a disestimation of the same order magnitude as the anecdotal case of the museum guide. No system of ballot validation or any number of recounts subsequent to the polling could have vouched for the accuracy of the final count, though weeks, months and millions of dollars were spent in an attempt to do just that. In reality both these elections ended in a tie and should have been decided as provided in the state law of both Florida and Minnesota: a flip of the coin.
The consequences of similar kinds of disestimation used in the U.S. Census- which also involve inherently inaccurate headcounts (more effective sampling techniques have been speciously rejected by the majority of conservative justices on the Supreme Court)- are more severe than in the case of the Florida and Minnesota elections. The Census is used to apportion representation to the U.S. Congress. As a result of inaccuracy in the Census itself, millions of Americans are effectively disenfranchised.
The understanding that real-world numbers come from imperfect measurements can inoculate you against Potemkin (fake- as in IQ tests for one) numbers, disestimation, and fruit-picking – it imparts a skepticism about where numbers come from, whether they are trustworthy, and whether they've been presented in an honest and trustworthy manner. A little mathematical sophistication – and a little practice – allows you to recognize the errors of randumbness, causuistry, and regression to the moon; once you get used to spotting phony patterns and false connections, you'll begin to see them everywhere. You'll see how advertisers pump up their products, how bureaucrats cover their failing projects, and how would-be prophets convince the unwary to believe meaningless predictions. And while mathematical knowledge won't stop businesses from ruining the economy, politicians from stealing elections, and court officers from undermining our court systems, it will prevent malefactors from getting away unobserved.
Randumbness: insisting that there there is order or pattern to events where there is only chaos- creating a pattern where there is none to see, like the gambler who believes his luck is “on a roll”, whereas the odds on each individual roll of the dice are exactly the same.
Causuistry: a specialized form of casuistry where the fault in the argument comes from implying that there is a causal relationship between two things when in fact there isn't any such linkage.; mistaking correlation with cause. Causuistry is particularly common in health and nutrition research, as in the studies that supposedly proved that Nutrasweet caused brain cancer, or that mercury in vaccines causes autism.
Regression to the moon: Regression analysis is a mathematical tool that people use to create lines, curves, formulae or equations that fit a set of data; it quickly extracts a pattern from whatever data you provide it. It's an extremely powerful technique yet it is easy to generate a faux patterns to sets of data that have no real explanatory or predictive value at all. Faux regression analysis predicted that in 2000 Gore would win against George Bush with 56.2 percent of the vote. The prize for regression silliness, though, has to go to the academics who crank out equations or formulae for everything under the sun whether or not there's any quantifiable data available or not, such as a formula for happiness which was gobbled up by the press in 2003.