April 26, 2008

Book: How Long Is A Piece Of String? More hidden mathematics of everyday life

Rob Eastaway & Jeremy Wyndham

"How Long Is A Piece Of String?" is a book about the mathematics that underlies everyday life.  Written by the authors of "Why Do Buses Come In Threes?", it's a quick, interesting read.

Here are the contents:
Chapter 1 - Why Does Monday Come Round So Quickly? 
Chapter 2 - How Do Conmen Get Rich? 
Chapter 3 - What Makes a Hit Single? 
Chapter 4 - Why Won't the Case Fit in the Boot? 
Chapter 5 - Should I Phone a Friend? 
Chapter 6 - Is It Quicker to Take the Stairs? 
Chapter 7 - How Long Is a Piece of String? 
Chapter 8 - Why Do Weather Forecasters Get it Wrong? 
Chapter 9 - Will I Catch Flu Next Winter? 
Chapter 10 - Am I Being Taken for a Ride? 
Chapter 11 - Will I Ever Meet the Perfect Partner? 
Chapter 12 - Is It a Fake? 
Chapter 13 - Will the Underdog Win? 
Chapter 14 - Why Do Karaoke Singers Sound So Bad? 
Chapter 15 - How Can I Be Sure? 
Chapter 16 - Can I Trust What I read in the Papers?

In chapter 12 - "Is It A Fake?  Number tests that can detect the fraudsters" - the authors provide this nugget of information:

Everyone knows that typographical errors (called typos by those in the trade) are sometimes difficult to spot, so a printer might ask two proofreaders to read through independently to look for errors.
Suppose the first reader finds E1 errors and the second finds a different number, E2.  They now compare their results, and discover that some of the errors, a number S, were the same ones.  How many errors might they expect there to be in total? 
There is a way of making a good estimate, known as the Lincoln Index.  This says that the total number of errors in the manuscript will be roughly:
Expected Errors = (E1 * E2) / S
For example, suppose the first reader found fifteen errors and the second twelve, and that ten of the errors were found by both.  The Linoln Index predicts (15 x 12) / 10 = 18 errors in total.  Of these only seventeen have been found so far - ten found by both readers plus five more that only the first reader found and two more than the second found.
It occurs to me that this could be an interesting experiment in bug estimation.

Have two testers spend some time trying to find all the bugs in a piece of code, keeping the list of bugs found hidden from each other.  Then use the Lincoln Index formula to estimate how many have yet to be found.

I'll have to look for an opportunity to try this and see how well it works in the real world.