The Stone Man and Maths

Received a fantastic email from a reader recently, one making a few points about how Andy’s dismissal of TSM as an ineffective alien invasion would actually be very, very wrong if things had gone a different way … here it is in its entirety. MAJOR SPOILER ALERTS if you haven’t read the book!

“Luke,

First off, I just basically inhaled The Stone Man and The Black Room on

my kindle over a few days. TSM was recommended to me after I read The

Martian by the Amazon AI and the reviews persuaded me and your devil’s

trick of including a bit of the next book at the end worked. I’ll rate

and review on Amazon, of course, but what really struck me reading them

back-to-back was the development of the writing between the two. TBR was

a much richer book, I felt, with themes threading through it and I felt

genuine empathy with the characters. Both were absolutely gripping and I

couldn’t put them down – thanks for the immense pleasure I got from both

of them.

However, I couldn’t help but pick up on something in TSM which I am

certain has been raised before (unless I was reading too fast and

misunderstood; entirely possible given how excited I was). As I

understand it, the Stone Men intend to take their target, extract the

body part, split it into two and create two new stone men. The

characters seemed pretty casual about this not being an invasion since

the population would grow and this would always be a relatively small

harvest compared with the population. I feel like the characters were

wrong about this because of exponential growth.

First visit: 1 stone man creates 2 more (we now have three)

Second visit: 3 stone men create 2 more each (OK, one failed, but let’s

just go with the ideal model) – we now have six new stone men, making a

total of 9

Third visit: Each of the 9 stone men make two more, so that’s 27

Fourth visit: 27 x 3 = 81

So you can see from the pattern that the number of stone men (in the

ideal scenario as far as they are concerned) trebles each visit. This

needs a little table:

Visit Total Stone Men After

1 3

2 3×3=9

3 3x3x3=27

4 3x3x3x3=81

5 3x3x3x3x3=243

…

n 3^n (three to the power n)

The problem with exponential growth is that it is fucking fast. It

starts off looking OK, but then it cuntifies. So at the end of visit 10

there will be 3x3x3x3x3x3x3x3x3x3 = 59 049 Stone Men. This is still

pretty small compared to the population of the UK, but how about after

15 visits?

3^15 = 14.3 million. That’s a big chunk.

18 visits? – 387 million. We’ve run out of British people. 20 visits

wipes out half the world’s population.

Anyway, I’m a maths teacher and I go back to work tomorrow. My holiday

has obviously been too long so I feel the need to explain maths to

whoever, including an author who probably heard this all already or

thought of it himself. So apologies if this wasted good writing time.

Anyway, I bloody loved the books. Keep it up.”

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