The Maths Behind The Errors In The Maths Behind

I recently had a flurry of correspondence with translators of The Maths Behind (available wherever etc., but also soon in Swedish and Korean): embarrassingly, they had caught several mistakes in the book. These things happen; we try to put them right and move on.

However, it got me wondering: can I use the translators' corrections to get a sense of how many errors there are in the whole book?

Of course I can, or else I wouldn't be writing about it!

Let's suppose there are $n$ errors in the book, and that the translators each have a fixed probability of finding each error. We'll call Mr. Svensson of Sweden's - probability $p_s$, and Ms. Kim of Korea's probability $p_k$.

Mr Svensson found 8 errors, and Ms Kim found 15; only two were common to both.

We then have (assuming independence):

  • $n p_s = 8$
  • $n p_k = 15$
  • $n p_s p_k = 2$

Eliminating $n p_s$ from the first and third equations gives $p_k = \frac{1}{4}$; similarly, $p_s = \frac{2}{15}$ and $n$, horrifyingly, is 60. (I've found at least a couple of others, but suppose there must be another 40-odd lying around).

Of course, there's scope for improving the model - perhaps modelling the number of errors found by each as some kind of distribution to find reasonable ranges for $n$, perhaps giving the whole thing to Sam Hartburn to read and find all of them.

If you have better ideas (or if you've spotted a misprint!), I'd love to hear about it in the comments below.

Colin

Colin is a Weymouth maths tutor, author of several Maths For Dummies books and A-level maths guides. He started Flying Colours Maths in 2008. He lives with an espresso pot and nothing to prove.

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3 comments on “The Maths Behind The Errors In The Maths Behind

  • Barney

    Equation at top of page 28 should the (x – mu) be squared?
    Page 120 the maze algorithm: the third blob from the middle needs moving further in (I think we discussed this at Jam many moons ago). Great algorithm but picture didn’t quite tally with description at this point.
    David mentioned the inverse square law was down as an inverse cube law on one page but I can’t immediately see what page that was,.
    And in the interests of focussing on the positive, the book was fab and I’m visiting Giant’s Causeway in a couple of weeks so will think of you when I get there!

    • Colin

      Thanks, Barney! *scribbles notes*

      • Barney

        Just occurred to me also that the assumptions of “fixed probability of finding an error” and “each party finds errors independently” are most unlikely to hold as some errors will be subtle and others glaring.

        Not sure about a better model but perhaps there could be n subtle errors and m glaring errors, with the probability of finding a glaring error = twice that of finding a subtle one?

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