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As all maths geeks know, the world is divided into 10 kinds of people... those who understand binary code, and those who don’t. As a matter of fact, human beings love dividing things into groups. We’re a classifying species: homo taxonomicus – all librarians at heart. When it comes to books, there are of course many ways to divvy them up beyond the Dewey Decimal System, and sometimes it’s fun to see where one’s own preferences lie. Happy endings versus sad? Realism versus fantasy? Contemporary versus historical? Long versus short? First versus third person narration?

Now, what about convex versus concave books? Not come across that distinction? That’s because I just made it up - but I'd love to know what you think. The way I see it, a concave book is one that reflects light onto itself. It’s a book that takes a particular setting, containing a limited number of people, and explores them thoroughly. It may choose to disrupt this group, perhaps by the device of a Stranger Coming to Town, but the book is all about looking deeper, finding out more, seeing how surface appearances may be deceptive. Concave books thrive in almost all genres. Emma is a concave book. So are Shane, Lord of the Flies, Animal Farm, The Midwich Cuckoos and Murder on the Orient Express. Villages, islands, ships, and other isolated locales are the classic concave settings, and once the plot arrives there it tends not to leave. Concave plots also lend themselves to metaphorical or even allegorical meanings (as with Golding and Orwell). The village is the world writ small.

Convex books, by contrast, reach beyond themselves, reflecting light outwards. Books involving journeys, quests, world-shaking historical events, books conveying a sense of the bustling, multi-faceted nature of life, books that scintillate off to the horizon, are convex books. Great Expectations; War and Peace; The Odyssey; Bonfire of the Vanities; Tom Jones all qualify. They imply the world metonymically (if you like figures of speech).

Some of my favourite books appear in both lists. Thinking it over, however, I realise that all my own books have been concave, to a greater or lesser degree. Perhaps that’s just the way my mind works – although I’d love to think I could write a good convex book too, if I really tried. Can I train myself to do it? I’ve had a book in my head and in notebooks for years now – a convex book, too – which just hasn’t managed to get written, and I’m worried it's because of my ingrained concavity. As to where that comes from, my partner has suggested that a writer’s own life experience may be a factor. If you grow up in a city, you catch glimpses of a hundred new faces every time you walk down the street, and (if you’re that kind of writer) you may wonder about all the stories those faces suggest, stories that weave in and out of each other and off to the edge of the page. If, like me, you grow up in a small town, you see the same faces over and over again – and you wonder what’s going on behind the apparent sameness. The city impresses with its razzle and dazzle; but for us concavers inspiration is more likely to come from a twitching curtain suddenly let fall.