Maxwell's Demon. Steven Hall

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 it home and burn it, Sophie had said.

      I stared at my name and address on the front of the envelope as it flapped wildly between my fingers, trying to get free. I could feel the edges of the Polaroid picture inside.

       What do you think this is?

       You’re right that this is a hook. What in God’s name makes you think it’s a good idea to bite?

      I reached inside my coat on the other side, and pulled out a second envelope. This one was addressed to Andrew – my reply, already written, stamped and ready to post.

       You shouldn’t respond to this. If you’re asking for my advice, then that’s the advice I have for you. Do not respond to this.

      The wind sent a breaker of leaves roaring past me, skittering and crashing away towards the old church with the post box outside. Stuffing both hands – and both letters – into my coat pockets, I put my head down and made my way after them.

      o

      I stood in front of the post box, for two, three, four minutes.

       Just put it into the slot. It’s just a letter.

      My hand didn’t move.

      ‘Fucking hell.’

      I didn’t want to stand there like an idiot for another five minutes, so I crossed the road, climbed over the old fence and sat myself on the steps of the boarded-up church, Black’s letter in one hand, my reply in the other.

      ‘Fucking hell, Sophie,’ I said.

      That’s another thing I should’ve told you about Sophie Almonds – whenever she gave advice, it was almost always right. The longer I’d known her, the harder it had become to dispute this one simple fact.

      ‘Fucking hell.’

      There were more trees by the church, the fallen leaves even more plentiful, and swarms of them whipped and tumbled as the icy wind threw its weight around the little graveyard.

      I stretched out my arms, holding both envelopes up to the wind and they fluttered and shook violently, trying to get free. It would’ve been the easiest thing in the world to let them go. The leaves were so deep, they’d probably lie forgotten amongst the weathered headstones until they mulched down in the cycle of winter snows and thaws. The thread of this whole story would simply blow away and be gone. Nothing would come next: no answers, no problems, no decisions, no nothing. Turn off the computer – click, and that would be that.

      I held my hands up a little higher. Sophie had done all she could to convince me to let this whole business go, and with the slightest movement, I could do exactly that.

      The entropy of a closed system tends to a maximum, I thought, picturing those coloured plastic letters on the fridge back home. I thought about Imogen, away from home for so long, and about what our marriage might be, or not be, when she came back. I thought about frayed phone cables and crossed lines over empty fields, and about all the silence and all the noise between my father and me. I felt the envelopes in my hand and I thought, ‘clue’ is an old-fashioned word for a ball of twine, promising guidance through the labyrinth. Was Black’s sphere photograph a clue? I thought, of course it’s a hook and beware raccoon traps promising answers. I thought, there is no labyrinth, no grand plan. Only chaos and collapse. Things just fall apart. I thought, ‘I talk to God, but the sky is empty.’

      I closed my eyes, focusing on the thunder of leaves all around me.

       The entropy of a closed system tends to a maximum.