The Dark Arts of Mathematical Deception


Charles Seife

Penguin Group, 2010, 295 pp.   ISBN 978-0-670-02216-8



Seife is a professor of journalism at New York University and the author of four other books.  In this book he shows how numbers are misused to deceive.     


"Numbers can be a powerful weapon.  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 bludgeon enemies, to destroy, critics, and to squelch debate." (3) 


Proofiness is "the art of using bogus mathematical arguments to prove something that you know in your heart is true--even when it's not." (4)  Bad math is undermining our democracy.  "Understand proofiness and you can uncover many truths that had been obscured by a haze of lies." (5)


"If you want to get people to believe something really, really stupid, just stick a number on it." (7)  "No matter how idiotic, how unbelievable an idea is, numbers can give it credibility." (8)  Just listen to the news; you'll hear things like 'Fifty-eight percent of all the exercise done in America is broadcast on television.'  (MCNBC)  Obviously this is nonsense. (8) 


"Numbers have that power over us, because in its purest form, a number is truth.  Two plus two is always four."  However, in real life, numbers are rarely in their pure form: they are always attached to something. 


"Behind every real world number, there's a measurement.  And because measurements are inherently error-prone … they aren't perfectly reliable.  Even the simple act of counting objects is prone to error…." (10)  "Bad measurements…deceive us into believing a falsehood--sometimes by design.


 One red flag is when a measurement attempts to gauge something that's ill-defined, intelligence, for example.  Sometimes there is no settled-upon way to measure something reliably, for example, pain or happiness.


Whenever there's a big public event, someone has a vested interest in making up a number that makes the crowd look huge-- like the "million man march on Washington." (17)


The natural history tour guide told patrons the dinosaur bones were 65 million and 38 years old.  38 years earlier a paleontologist told him the bones were 65 million years old.  (18)  Nice round numbers signal large measurement errors.  If someone says they paid $20,000 for a car, you might assume it was somewhere between $19000 and $21000.  If they say they paid $20,112 you assume that's the precise amount.  "Disestimation imbues a number with more precision that it deserves, dressing a measurement up as absolute fact instead of presenting it as the error-prone estimate that it really is.  It's a subtle form of proofiness: it makes a number look more truthful than it actually is…." (23)  No one knows which baby will be the 7th billion person living on earth, even though several babies will be celebrated as such.  Our normal body temperature of 98.6 degrees Fahrenheit is simply the conversion of the round number 37 degrees Celsius.  (25)


Fruit-packing (like supermarkets packing fruit with the most delectable pieces visible) presents data in a way that creates a false impression.  Cherry-picking is carefully selecting the data points that support your argument while underplaying or ignoring data that undermine it.  In Al Gore's film "An Inconvenient Truth," the computer simulations show much of Florida and Louisiana being submerged, based on the assumption that melting ice will drive the sea level up by twenty feet.  However, this is a worst possible case scenario.  Most scientists project the oceans will rise two to four feet.  George Bush also cherry-picked data in proving that the No Child Left Behind Act had actually improved test scores. (28-29) 


Another trick is comparing apples to oranges.  This can be quite powerful, making the false seem true and true seem false. This occurs frequently when comparing income and expenses across years, neglecting the changing value of the dollar over those same years.  For example, government officials may say that a particular initiative is getting an increase in funds when the value of the dollar has dropped more than the increase in funds. 


Apple polishing is used to put the finishing touches on data, manipulating them so they appear more favorable than they actually are.  A common technique is to use a graphical representation that truncates the "Y" axis, making small differences look large.  (See graphs on p. 35-36)  Another form is to exploit the term "average."  If 1 person in an organization makes $999,991 and the other 9 each make $1, on the average they each make $100,000.  This could be very deceiving if you were applying for a job!  It would be more accurate to use the median.  When a politician says that the average tax break will be $1000, don't count on getting $1000.


Our minds are very diligent to look for patterns.  And we can convince ourselves we see them even when they aren't there.  People often draw a straight line through a random scatter of points on a graph.  Further correlations are often interpreted as causal relationships where none exist.  Virtually anything can be correlated with almost anything else.  But they are only correlations.  Casuistry "is the art of making a misleading argument through seemingly sound principles … implying that there is a causal relationship between two things when in fact there isn't any such linkage." (44)  Brain tumors went up as NutraSweet consumption was going up.  But a lot of other things were on the rise too, such as cable TV, Sony Walkmen, and Tom Cruise's career. The increase in government spending correlates with almost everything that increases. 


A change in diagnostic criteria can look just like an epidemic.  Doctors are much more likely to diagnose autism than they were twenty years ago.  (48)


It is often difficult to differentiate the cause from the result.  Researchers are prone to say A causes B when actually B causes A.  If bad health correlates with debt, does the emotional weight of debt cause health to deteriorate or do people get into debt because of the costs of bad health?  "Casuistry stems from our need to link every effect to a cause of some sort.  Anytime we see two things that are correlated in some way, our brains leap to the conclusion that one thing must cause the other.  It's often not so." (53)  "If you take any random collection of data and squint hard enough, you'll see a pattern of some sort.  If you're clever, you can get other people to see the pattern too." (56)


If statistically calculated risks are too high to bear, organizations ignore them, e.g. NASA.  "Minor changes in wording can easily make a huge risk seem worth taking or an insignificant risk seem dangerous.  As a result, we are vulnerable to manipulation. … We are prey to risk mismanagement."  "In NASA's case, it meant billions of dollars."  "Much of our economy revolves around risk--risk and money go hand in hand.  There are entire industries devoted to managing and assessing risk…  And where there's money to be made, there's risk mismanagement.  If you gaze deeply into the center of the ongoing financial crisis, you see risk mismanagement staring back at you.  Risk mismanagement is crippling our economy, and along the way making a small handful of malefactors very, very wealthy." (72-3)  "If you move money around in clever enough ways, you can camouflage risks and make an absolute mint. … The Ken Lays and the Bernie Madoffs of the world are able to make their money by hiding risk and moving it from place to place, deceiving their investors." (80)


You can also take something that's mundane and exaggerate its risks, making it loom large in the public's imagination.  Journalists are particularly fond of this.


"The tragedy of the commons occurs when an individual can take an action that benefits him, yet the negative consequences of that action are diffused--such as when they are divided among a large group of people or when they take a long time to materialize.  In situations like these, people act selfishly, getting as much benefit as they can, but as a consequence, we're all worse off."  [An example is when people cheat their insurance companies or Medicare.]  "When financial gain is divorced from the risks involved in making that gain, very bad things happen.  The subprime mortgage meltdown was a great example of moral hazard in action."  (87)


"All companies that are too big to fail…are swimming in moral hazard.  Once they know that they won't be allowed to collapse, it's almost guaranteed that they will fill their own pockets while passing the consequences of their risky behavior on to the taxpayers." (90) 


"Polls are perhaps the leading source of proofiness in modern society."  "Most of the time…a poll is a factory of authoritative-sounding nonsense." (92-3)  "A poll frees journalists from having to wait for news to happen….  Polls allow a news organization to manufacture its own news.  It's incredibly liberating." (96)  Polls are inherently error-prone.  Random, or statistical, error occurs because a sample does not accurately represent a whole population.  The smaller the sample the bigger the error.  But there are plenty of other errors.  When polls go spectacularly wrong it is almost always systematic error.  When polls depend on a voluntary response, those with strong opinions respond more than others.   Systematic errors can be very subtle, completely invisible.  And people regularly lie to pollsters, making the data almost meaningless. Some people, including pollsters, try to manipulate the outcome of polls.  Wording of survey questions is crucial.  Extremely minor wording changes (both deliberately and unknowingly) can completely reverse the outcome of polls. "Internet polls have no basis in reality whatsoever.  Yet has an Internet poll on its front page every day.  It's not for information; it's for titillation." (120)  "When it comes to polls, I believe that the news media as a whole…regularly act with reckless disregard for the truth." (121)


Several chapters deal with election processes, vote counting, and interpretation.  Chapter 8 deals with propaganda by numbers.  But you get the idea.




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