Saturday, December 15, 2012

Wrong Mathematics in a Jack Reacher Novel

Lee Child is the author of the popular Jack Reacher thriller novels. He's probably going to get a lot more attention soon, now that the first Jack Reacher movie is headed for release next week.

Five years ago, I discussed some mathematics in Bad Luck and Trouble. I complained that suddenly, a new characteristic of Reacher was unveiled: he was a gifted mental calculator who could determine the primality of numbers quickly, and he was interested in properties like 'square root of n equals sum of n's base-10 digits'.

Now, in the new Reacher novel, A Wanted Man, Child returns to this numerological interest of his main character. First, Reacher is thinking about automorphic numbers: these are positive integers n such that n2 ends in the same base-10 digits as n.

Then (on page 64), Reacher is thinking about 81, and he "muse[s] about how one divided by 81 expressed as a decimal came out as .0123456789, which then recurred literally forever, 0123456789 over and over and over again..."

The problem? That's not the decimal expansion of 1/81. It's actually 0.012345679012345679012345679012345679012345679012345679012345679 ..., where the period of the expansion is 012345679 and not 0123456789. The "8" is missing! The reason for this is not so surprising, and generalizes easily to the expansion of 1/(n - 1)2 in base n.

A savant like Reacher, who can determine the closest prime to a randomly-chosen 6-digit number in a matter of a few seconds, would not have made such a silly mistake. Maybe Lee Child needs a mathematical consultant for his next novel. Hey, I'm available.

11 comments:

Eamon Knight said...

....or even just give the author a calculator that displays at least 12 digits?

RBH said...

Reacher would just head-butt a mathematician who presumed to contradict him. :)

Bayesian Bouffant, FCD said...

You need to make a road trip and blog about this place:
Museum of Mathematics at Madison Square Park

William said...

I checked the book while in a bookstore, and found the relevant passage (on page 72), where the period of the expansion was given correctly as 012345679 (not 0123456789). The book I saw on sale was the UK paperback edition published by Bantam Press.

Takis Konstantopoulos said...

When I was young, I had read a book by Arthur Koestler, in Greek translation. whose title, in Greek, was "the Zero and the Infinity". (Later, I realized that the English title was "Darkness at Noon" and that the Greek title was a copy of the French one, "Le Zéro et l'Infini").

In the preface of the book, probably written by a Greek translator--I can't remember, it was stated that infinity is the result of the division of zero by zero. I was appalled.

Jeffrey Shallit said...

Good to know, William. My copy is the hardback published in New York by the Delacorte Press.

Bayesian Bouffant, FCD said...

So they dumbed it down for the American market?

Steve Watson said...

Sounds like the Delacorte editor "corrected" their edition.

Anonymous said...

In either the first or second Reacher book, he was figuring out how many days he'd been alive. He was 36 at the time, so it was 36 x 365 + the # of days since his b-day + 12 for leap days. Excuse me - TWELVE leap days? At 36 years the highest # of leap days would be 10, but it's more likely 9.

Then in 61 Hours, it was stated that a Boeing 737 could hold 36,000 pounds total, about 16 tons. Sorry, 36,000 pounds is 18 tons. Nowhere was it stated he was talking about metric tons.

Where are the editors? If I can catch it, they should too.

Anonymous said...

His thoughts about automorphic numbers are incorrect too. Reacher thinks that 76 and 25 are the only automorphic numbers below 100, completely forgetting 5 and 6.

KL11 said...

He's ba-a-a-ck! In PERSONAL, Child explains that the force (which is mass times velocity squared) of Reacher's kick can be increased fourfold by increasing his footspeed by 20%.

Hmmm. Increasing by 20% is multiplying by 1.2. Squaring 1.2 gives 1.44. So, that looks to me like a 44% increase.