How Many Socks Make a Pair? Surprisingly Interesting Everyday Maths, Rob Eastaway (2008)
I’ve been returning to this book with pleasure and profit for over a year now: it doesn’t just interest, it informs and enlightens too. Unlike Ian Stewart’s The Mathematics of Life (2011), which promised much and delivered little, it seems simple but points to the profound. Maths is like that: it’s a mansion with many rooms or a mountain with gentle slopes and sheer cliffs or an ocean with shallows and abysses. Infinitely many rooms, in fact, infinitely high cliffs, and infinitely deep abysses. Maths is wider than the world because it is the foundation for all actual and possible worlds and is perhaps, at the most fundamental level, the substance of all actual and possible worlds. Some of the topics introduced here, like fractals, probability, and the Fibonacci sequence, lead on to very difficult and important mathematics, but both intelligent children and amateur adults should be able to take the first steps towards the peaks, where problems wait that are still challenging and defeating professional mathematics. It’s a book that has a P, please, Rob: it discusses puzzles, paradoxes, pranks, playfulness, penney ante, Pythagoras’ theorem, and Pascal’s triangle. Plus the palindromic performativity of 196 – or rather, the non-palindromic. If you reverse and add a number like 59 or 382, you soon arrive at a palindrome, or a number that reads the same in both directions.
Despite being a lot smaller than 382, 89 takes longer, requiring 24 reversals-and-additions. 1,186,060,307,891,929,990, on the other hand, takes 281 rev-adds. And 196? It hasn’t produced a palindrome yet, despite having a lot of computer time and power thrown at it: Eastaway notes that “it is the smallest of many numbers that are now thought to be ‘unpalindromable’” (pg. 101). In base ten, anyway: in other bases, 196 quickly produces a palindrome. That’s not something noted here, but it would be a much longer book if it stopped to follow every thread. In fact, it would be infinitely long, like the book in Jorge Luis Borges’ story “The Book of Sand” (“El libro de arena”), or would take infinitely long to write. But that’s one of the things I like about this book: it doesn’t lay down the law, it leads you down the lane and then gives you the chance to explore further for yourself. You can expand and adapt the maths here to your heart’s content and for once the hyperbole on the back-cover isn’t misleading: “a witty book that provokes the imagination” is the quote from The Times, while the London Maths Society said that it “exudes a friendly charm that is hard to resist.” I agree and I wish more young males were reading books like this and looking at less porn. But porn, like everything else, is under the sway of Mathematica, the Magistra Mundi, or Mistress of the World, and if you’re like me How Many Socks…? may even make you feel guilty about neglecting the Mistress. I know that I should put more effort into understanding some of the topics it covers, like “Calculating without a calculator” in chapter 2. But maths is like a endless box of chocolates: there’s also something else to sample. To taste the magic, try this book.