on 14 August 2012
I'm not a reader of non-fiction for two reasons: (1) it usually purports to tell the truth when it is merely reporting a version of the truth like, well, fiction; and (2) it is usually less well written than fiction, where style tends to count more. But I'm happy to say that this rare foray into the realm of written reality scored on both fronts: (1) it reported pretty much indisputably factual information with only the odd conjecturable opinion; and (2) it was very well written.
There is much to admire about this book, but the two things that stand out are: (1) it appears to the maths laity (that's me) to be meticulously and comprehensively researched; and (2) the writer, Alex Bellos, is a journalist who graduated university with a double major of maths and philosophy and is therefore a keen amateur and not a professional mathematician. The latter is no doubt core to the book's strengths, because Bellos brings a hobbyists's enthusiasm along with a sympathy for the semi-literacy most of us bring to the maths. I also liked that Bellos does not revert to hyperbolic fan's zeal to inspire the same passion in the reader. Rather, he provides a series of interesting facts and folksy supporting anecdotes to show the development of: (1) different fields--geometry, probability, statistics; (2) concepts--pi, phi, infinity, zero; and (3) tools--logarithms, slide rules, the quincunx; in a way that is mostly understandable and usually entertaining. Along the way, he relates amusing stories involving eccentric people and their often mundane means--origami, sponges, crochet--of giving physical shape to the downright unfathomable.
The book is divided into 12 chapters, numbered 0 to 11. Chapters 0 tells how numbers emerged, evolving from a means of counting items necessary for survival to wholly counter-intuitive abstract concepts. Chapter 1 discusses the evolution of counting and is devoted to the limitations of the base 10 numeral system under which the West operates. Why base 10 when base 12 is measurably superior? Two reasons: (1) we have ten fingers, a pretty obvious observation after someone points it out to you; and (2) the French, who pretty much forced Europe to adopt decimalisation, probably in a fit of pique after losing out to English in the language stakes. Chapter 2 discusses the creation of zero, which contrary to what I thought, was developed in India, and not Arabia, prompting the following conversation with my colleague Peeyush (an Indian):
Me: Know what India invented?
Peeyush: Big hair? Finger cymbals? Corruption?
Me: Nothing. India invented nothing. And why are you so biased against India?
As the book progresses, so does the abstract nature of the subject matter, and the concept of pi provides the perfect bridge between numeracy and philosophy, which had already emerged with the chapter on zero. Chapter Five reinforces the connection, noting, "Algebra lets us see beyond the legerdemain providing a way to go from the concrete to the abstract--from tracking the behaviour of a specific number to tracking the behaviour of any number." But as illustrative of my point as this passage may be, I only included it because it contains the word "legerdemain." At this point, the book also irritated my psoriasis, as it reminded me of two of my education failures: (1) the slide rule; and (2) logarithms. The slide rule exposed my lack of dexterity, which I blame for a lifelong preference for the directionally correct over pinpoint accuracy. Logarithms exposed the limitations of a brain that can memorise useless facts but could not hope to make the abstract concrete in a month of infinite Sundays.
Which would provide a great segue to the book's discussion of infinity if it weren't for intervening chapters on: (1) mathematical puzzles/games-Sudoku, the Rubik's Cube; (2) number sequences--the most fascinating anecdote being the development and applications of The On-Line Encyclopaedia of Integer Sequences, a kind of numerical genome; and (3) the concepts of phi and "the golden ratio" and their relationship to Fibonacci sequences. Concerning "the golden ratio," Bellos notes, "It may sound Orwellian, but some irrational numbers are more irrational than others. And no number is more irrational than the golden ratio." Which means it should be the ultimate kindred spirit but in fact only recalls another bad high school memory and a conversation with my maths teacher:
Me: Look, It's irrational. It can't be a number. It can be a parental demand or a political promise, but numbers behave, darnit!
Mrs Kohl: Wells, stop making this as difficult as yourself. The test is only ten questions. So quit messing around and whip it out.
From here, the book backtracks into another chapter on games, or more accurately gaming, and the evolution of probability theory, which, as any derivatives trader with an ounce of conscience can attest, is the root of the current economic downturn if you don't count Obamacare and high tax rates on corporations and the rich (ok, that was sarcasm). The chapter uses maths to confirm that there are a few clever clogs who can improve gambling odds but the rest of us are easy prey to owners of casinos whose only redeeming quality is that they are as stupid as the rest of us in understanding how probability theory works and must therefore put their faith in the quants they employ, much like the purchasers of derivatives products.
Which flows nicely into another bit of mathematical fiction, statistics and the bell curve. This is yet another concept with which I struggled, this time as a university student in 1974, because the idea of anything normal in a world characterised by Vietnam, Watergate and the Bay City Rollers could only be, in the words of Spiro T. Agnew, "a damnable, palpable lie." It also reminded me of the debates I would have as a portfolio analyst with my quant boss about over-reliance on statistical models to predict the fortunes of industry segments. I was instead a believer in the theory that an industry segment collapses under the weight of too much money chasing it, and all you need for that analysis is a critical mass of Wall Street Journal headlines.
And that brings us to the final chapter, appropriately about infinity, a concept discussed throughout the book--especially in the bits on counting and number sequencing--but thoroughly analysed from a mathematical and philosophical standpoint here. And, face it, infinity is nothing if not a philosophical concept, especially when you consider that it can be mathematically proven that there are different values of infinity. Perhaps even an infinite amount of values of infinity. Yeah, think about it.