# The Lincoln Index

Suppose you've written a book with a colleague, and it has just come back from the typesetter. You and your co-author now independently proof-read it, and you find ten mistakes, and your colleague finds ten as well. But they aren't the same ten - in fact, only seven of the errors were ones that you both spotted.

The first thought might be 'thank goodness two of us did the proof-reading, since two heads have proved to be better than one'. However there is an ingenious device called the Lincoln Index that predicts that in this example, there are some errors that neither of you spotted.

Let's suppose that the number of errors found by the first proof-reader is E1 and the number found by the second proof-reader is E2, and that you found S mistakes in common. The Lincoln Index is used to estimate the total number of errors in the book, and is calculated as follows:

L = (E1 x E2)/S

In this case L = (10 x 10) / 7 , which is just over 14. So since the proof-readers only found 13 between them (the first found ten, the second found another three that the first didn't), this would suggest that one error has sneaked through into print. Nobody likes to discover errata in a book, but I suppose we can all live with a single error making it through to the printed version. But what if both proof-readers find ten errors, of which only one is in common? Now the estimate of the number of errors is (10 x 10)/1 = 100, of which only 19 have been found, meaning 81 have escaped the net. Now that's serious, and means the book will probably be riddled with errors and the proof-readers should find another job.

This is all very relevant to me at the moment, as copies of 'More Maths for Mums & Dads' are beginning to filter into people's homes, and yesterday I received an email headed 'ERRATA'. Thankfully, the two 'errors' picked up were more queries about completeness rather than mistakes. However, my informal estimate for the Lincoln Index for the book is that there might be two or three typos or other errors that have crept through. I've already found one (a missing apostrophe). Over the coming weeks, let's see how many more come out of the woodwork. If they are no worse than missing apostrophes I'll be very relieved.