Sophie that day, I’d spent the afternoon touring the bookshops. In every single one, I’d picked a book that shared a shelf with Cupid’s Engine, pulled it out, then posted it over the top of the others, so that it dropped with a thunk into the dark, hidden space at the back of the shelf. I’d been doing this for years and usually I chose a Borges to take the fall, if one was available. I’d always thought that he, of all writers, wouldn’t mind it so very much. Anyway, with a single book removed like this, there’s more room on the shelf. I would use this room to create a book-sized gap between Cupid’s Engine and the next book along to the right. It’d become a ritual over time, I suppose. In every bookshop I went to, I’d make a book-sized space, a gap big enough for Andrew Black’s second novel. I don’t know why I started it. Maybe I thought that one of us – Andrew, me, my father – had to publish something. Time’s arrow had to keep making us a past, present and future, and as my father wouldn’t be writing anything else – oh, I don’t know. For years, I made those gaps in every bookshop all over London, even after I became sure that a second Andrew Black book would never come. Recently, I think I’ve come to understand that creating those spaces was less about the giving of room, and more about the recognition of a hole.
I stamped my feet to bring some warmth back and watched the teenagers disappearing into a bar some way up the road. I let out a long sigh that escaped as steam through my collar. Six years ago, Andrew Black sent Sophie Almonds over a cliff, and it was clear that she’d never forgive him for it. The sheer force of her reaction took me by surprise though. And what she’d said about my looking for reassurance from her, that took me by surprise too. Was I really looking for permission to contact him? I didn’t know. When I asked myself that question, I got nothing back but the vague mental image of wading through a patch of brambles. The brambles had no malicious intent as far as I could tell – no hint of Sophie’s raccoon trap – they were just brambles, but it was a dense and thorny tangle nonetheless. And once in, the image seemed to be saying, you might not find it so easy to get yourself back out.
I sucked air in through my collar and fixed my attention on the hypnotic, endless parade of headlights travelling along the road towards me. Before long, a bus rounded the corner at the far end of the street, and I joined the shuffling, rain-glittered queue forming to meet it.
o
Maybe I wasn’t ready to be back inside our empty little flat so soon, maybe I wanted to be out in the world of things a little while longer, or maybe I’d been half planning it all along. Whatever the reason, I got off the bus a couple of stops early that night and struck out on my own to walk the rest of the way home.
My route took me along the edge of Victoria Park, where the wind whipped up great shoals of fallen leaves and sent them tumbling and hissing in racing waves, swirling past my legs as I walked, then spiralling up in tornado spouts, up and up, under the streetlamps. On such a quiet and empty street, the noise was incredible.
As I pushed forward through the leaf storm, head down and blinking, I found myself thinking of a story that Sophie had told me a few months earlier. Almost every time I saw her, Sophie’s little black book would make an appearance, its pages holding the specifics of some new story, a new set of names, dates and technical terms that she’d keep referring back to while telling me something remarkable. Once, she told me about Johann Fust, the shady business partner of Johannes Gutenberg, inventor of the printing press. Apparently, Fust betrayed Gutenberg, got himself arrested for witchcraft, and became – according to some historians – the inspiration for Doctor Faustus. Another time, she told me how a man named Thomas Harvey stole Albert Einstein’s brain, kept it in a beer cooler for thirty years, and studied it by cutting bits off in his spare time. Harvey became drinking buddies with William Burroughs, and Burroughs liked to brag to friends that he could get hold of bits of Einstein’s brain any time he wanted to. There were lots of others too, from how duelling algorithms led to a book about fly DNA going up for sale for $23,698,655.93 on Amazon, to the origin of the word ‘ampersand’ and the brief period where ‘&’ appeared in the alphabet after ‘z’. The story that came back to me on that particular night though, the one I remembered as I made my way home through the swirling, whirling leaves, was about a mathematician named Barbara Shipman.
Shipman was a researcher at the University of Rochester in New York State, and she studied ‘manifolds’, that is, exotic, theoretical shapes described by complex mathematics. Bizarrely, manifolds can be shown to exist in many more dimensions than the three that we are able to perceive. Specifically, Shipman had been working with a six-dimensional shape known as a ‘flag manifold’. How does a three-dimensional human attempt to comprehend a theoretical, six-dimensional shape? Well, she doesn’t. What you need to do is find a way to visualise the shape in a form that the human mind can actually grasp, and this is generally achieved by the detailed study of shadows cast onto a flat surface such as a wall (to the delight of Plato fans everywhere, Sophie had said). Just as a three-dimensional cube might cast a shadow that appears as a two-dimensional square, so a flag manifold can be made to cast its own complex two-dimensional shadow that the human brain is able to comprehend and work with. I imagine that a fair number of mathematicians have calculated and projected the shadow of a flag manifold, but when Barbara Shipman did so, her life as a mathematician collided unexpectedly with another part of who she was – it collided with her life as the daughter of a beekeeper, of all things. Because of this collision, Barbara Shipman saw something in the shadow of the flag manifold that no one else had ever seen before.
You see, while the mathematicians have been studying their manifolds, the beekeepers have been baffled by a mystery of their own. For millennia, they’ve been puzzled by an odd little routine that bee scouts perform when they return to the hive. Known as the waggle dance, this strange performance sees the scout moving through series of loops and figures of eight, while vibrating the back half of its body at various points in the process. This seems to provide the other bees with strikingly accurate directions to the best sources of pollen, though how on earth the scout bee is able to transmit such complex data through such a simple little dance has always been a mystery. A mystery, that is, until Barbara Shipman looked at the shadow of her flag manifold and saw in it not the complex geometry of a theoretical six-dimensional shape, but the familiar waggle dance of her father’s bees.
It’s easy to forget in the midst of day-to-day life, but logical conclusions needn’t always be boring, pedestrian things. Sometimes, a logical conclusion is so wild, so wonderfully bizarre, that only the fact that it is a logical conclusion allows any sane person to imagine it in the first place. The logical conclusion to be drawn from Barbara Shipman’s observations is this: though we as human beings live our lives entirely in the familiar three dimensions, bees do not. Bees are fully aware of, and see and communicate in, six-dimensional space. What does that mean, practically speaking? What does the world look like to a bee? What do we look like, going about our three-dimensional business? It’s impossible to say because the human mind is completely incapable of comprehending the answers to these questions. There are some things out there that we simply cannot understand.
Running my fingers along the cold park railings as I walked on through the leafy night, I imagined Barbara Shipman waking up on the day of her discovery, cleaning her teeth, getting dressed and having her breakfast, all as usual, and then preparing to face what seemed like another ordinary day. The truth is, none of us have the slightest idea what we’re in for when we get up in the morning. A phone rings, a shadow dances across a wall, a plane falls out of the sky, a letter arrives out of the blue and, before we know it, the world is a different place.
I stopped at a windy junction on the lonely road home, the blowing leaves tumbling all around me. Turn left, and I’d be back at the flat in less than five minutes. Carry on along the park-side road, and it’d take me to the red post box opposite the old, boarded-up church at the end of the street.
I unzipped my coat pocket and pulled out Andrew Black’s letter. The hungry wind pulled and tugged at it, but I kept my grip tight.
Take
