Mathematics can be used and presented in a manner that distorts the underlying truth or at least the underlying likelihood of a truth.

A mathematician seated at a table, working on mathematical equations

A mathematician seated at a table, working on mathematical equations

YAWWWNNNNN, who cares – Charles Seife does and tells us why you should care too in this book, “Proofiness: How You’re Being Fooled By The Numbers“.

Seife’s position is that bad math is more than being hoodwinked into buying oatmeal (see Quaker Oatmeal cholesterol numbers); bad numbers disenfranchise voters and erodes the democratic rights of Americans.

A Bad Math Field Guide

Be warned, this is a heavily American-focused book in which about half is dedicated to the challenges of the US voting systems.  If you can get past this bias, some interesting terminology and underhanded methods are exposed.  Here are a few:

  • Truthful numbers: come from good measurement that is reproducible and objective
  • Potemkin* numbers: derived from nonsensical or a non-genuine measurement
  • Disestimation: taking a number too literally without considering the uncertainties in its measurement
  • Fruit packing: Presentation of accurate numbers in a manner that deceives through the wrong context.  Techniques include cherry-picking, apples to oranges and apple polishing.
  • Cherry picking: Selection of data that supports an argument while underplaying or ignoring data that does not.
  • Comparing apples to oranges: ensuring the underlying unit of measurement is consistent when comparing two or more populations.
  • Apple-polishing: data is touched up so they appear more favourable (this was the Quaker Oatmeal trick).
  • Randumbness: because humans are exceptional at discerning patterns we also suffer from randumbness, insisting there is order where there is only chaos.
  • Prosecutors Fallacy**: Presenting a probability incompletely and leading to a false data assumption.

* Named for Prince Potemkin who convinced the empress of Russia that the Crimea was populated by constructing villages that were only convincing when viewed from a distance – such as a passing royal carriage.  An example of a Potemkin number was Joe McCarthy’s famous claim of 205 communists in the State Department.

** This one is worth a blog on its own so for more, read:’s_fallacy.

Take Your Field Guide With You to Work

These are important concepts for not only a citizen to consider when looking at dubious polling information but in the business or public policy world as well.  If there is a shortcoming in Seife’s book, this is it.  In my opinion he over focuses on the bad use of numbers in the public arena without touching on how CEO’s, CFOs, Boards and government-Ministers may also be hoodwinked.

Individuals being asked to make decisions based on numbers need to be able to cut through the packaging techniques discussed above.  This is becoming more important as our society moves to a 144 character Twitter attention span and public policy needs to be distilled down to a simple infographic.  As well, while developing a dashboard for a business is valuable, be sure that it is not filled with polished, cherry picked, Potemkin numbers based on a disestimation

Disenfranchising a few Million

Returning to the book, Seife has some advise for the US when it comes to the United States census.  Written into the constitution, once-every-decade process of counting all American citizens costs about $6.5 Billion dollars.  For this expenditure, it is estimate that the census misses about 2% of the United States population and double counts about 1%.  While these numbers would in theory cancel each other out (more or less), the impact is that there about 10 million US voters not accounted for in the census.

This error rate can be mitigated through techniques known as statistical sampling which will smooth out the distortions.  The result would be generally more people counted in poorer, racial minority areas who don’t like to fill in census forms or talk to government officials.  The ‘result of the result’ would be these people would then have more politicians to vote for (larger representation) and to send to Washington.

So far sounds good except that poor, non-white folks tend to vote for the Democrats which is why there is another perspective: only a count – counts. This being America, the counting challenge has generated a lot of legal attention and two population numbers.  One used by everyone who needs precise data to estimate everyday population trends and another used to reapportion the House of Representative seats.  After numerous legal battles, millions of Americans are disenfranchised because only a more error prone enumeration technique is permitted (see pages 185-198 for a more thorough explanation and also some very impressive legal gymnastics by the Supreme Court).

A Math Journey with a Curmudgeon

Seife sees himself as unbiased journalist although his leftiness tends to negate this somewhat.  He distrusts political polls, NASA, fluffy articles in scientific journals and the social sciences.  In other words, reading Proofiness is like visiting with a self-indulgent, opinionated curmudgeon – who is also brilliant and often right.  If you use numbers to make decisions in your day to day life, I would encourage you to take your ‘Proofiness-Field Guide’ with you.