Limited Wish

by Lawrence, Mark

  All this while Halligan kept talking, his back to the audience, facing three great whiteboards almost entirely covered in close-packed mathematics. I hunted for the start, squinting to bring the cramped notation into focus.

  ‘Alright?’ John asked, crouching down on the steps beside me.

  I didn’t answer. I tuned him out. I tuned Halligan out. I sat with my knees wedged against the back of the next row and stared. Mathematics is its own language. The language of everything. It doesn’t need someone to explain it. It explains itself and leaves almost no room for ambiguity.

  I was always good at maths but it wasn’t until I started to take the stuff seriously that I began to see the beauty of it. A good mathematical proof is a gem. It sparkles in the same way, and like a diamond it’s impervious to time. It takes and multiplies the light of understanding, refracting it through many facets.

  The shadows on the flat screen of a shadow play are projections from more complex objects. Our three-dimensional hands can cast a variety of two-dimensional shadows to delight the audience. In the same way there are fabulous beasts that swim in the seas of mathematics. Multidimensional behemoths of incredible beauty that even the best of minds struggle to glimpse. The equations we battle with, the proofs that we use to nibble at the edges of such wonders: these are the shadows cast by those we hunt. And on Halligan’s three boards were a dozen or more fragmented shadows, each struggling to assert itself, each a hint at the magnificent tiger he had by the tail. The edge of an ear there, a hint at a whisker here, and in the middle of it, a glimmer, just a glimmer mind, of an eye. A watching eye.

  ‘Nick?’ John shook my arm. ‘Nick, are you all right?’

  I waved him away. It was happening again, the thing that had taken possession of me that night I mended my father’s proof and nailed his name to it forever. Somehow I was drifting free of the Nick wedged at the end of a crowded row. The discomfort, the aches, the sweat – none of it registered any more. The equations scrawled across the boards, the statements, corollaries, all of them began to lift free, becoming detached from the blue marker ink that tied them to the surface. They began to take on shape and form, floating clear of their surroundings like the glowing pieces of some vast celestial watch reduced to its components. I rotated them this way, that way, searching for the means to fit the teeth of one equation into those of the next so that one might turn the other.

  ‘That’s not right.’ It couldn’t be right. Deep in the middle board was a piece that would never fit. Unsuited to the task. A cog with no teeth.

  ‘Beg pardon?’

  I became aware that I must have spoken, and loudly too. Halligan had turned from his scribbling and strode across the intervening floor so that he now glared at me from less than five yards away. An awed silence reigned in the theatre, the sort of silence that follows the intake of breath on every side. All eyes aimed my way. Everyone waited, fascinated, horrified, eager. All of them knowing that Halligan would destroy me. None of them knowing quite how he would do it.

  ‘Those paths are homotopic in C. In equation 86. The existence of the first homotopy follows from the continuity of the f-functions,’ I said.

  Halligan’s glare narrowed. He was younger than I expected. Maybe thirty, with thin dark hair and a puffy inelegant body stuffed awkwardly into a cheap suit. He had a moustache of the sort you get when you’re too distracted to shave. If it weren’t for the intensity of his pale blue stare he might have been comical. ‘Nonsense.’

  He returned to the equation in question and jabbed at it fiercely with his marker pen. ‘Nonsense. The homotopy follows from the compactness established in . . .’

  He had started to see it. I could tell.

  ‘But . . .’ He added a term. Crossed it out.

  Somewhere at the back of the hall a small gasp, sharp in the hush. Then an older man’s voice, some learned professor perhaps. ‘He might have a point, David.’

  Halligan spun back towards the audience, teeth bared. I knew what gripped him. That same horror that had taken hold of my father. The understanding that the beautiful edifice you have laboured so hard to create is falling apart in your hands and that even as you try to shore it up you are creating still more damage. He didn’t see the packed benches before him. He didn’t care that we were watching, or what we thought of his failure. He just saw that golden palace of ideas collapsing one room after another.

  ‘It can be fixed,’ I said.

  I stood, slowly, not wanting to lose sight of the floating glory that had been revealed to me, the thing of many moving parts, the thing that the equations on the board were mere shadows of. People cleared from my path without needing John to announce my leukaemia this time. Halligan stood immobile, incapable of movement. I passed him, took a red marker, and started to write.

  They say that when you learn to type you reach a point where you no longer give any thought to the motion of your hands. You see the paper, imagine the words, and somehow your fingers flicker and the words appear. In the Cockcroft lecture theatre that day I kept my eyes firmly on the shapes I saw rotating slowly in the air. Even as I watched they were fading, their truths growing more elusive. My hands moved and truth appeared on the boards . . . but I gave no thought to the mechanics that put it there. And when at last there was nothing left before me but the board and my ink-stained hands I saw that I had added a river of red entwining Halligan’s blue, one supporting the other like the twin strands of a DNA helix.

  Nobody in that room understood what I’d done except for Halligan, who was standing in amazement, running his hands around my additions as if they were braille and he might absorb their meaning through the tips of his fingers. Maybe one or two of the lecturers in the audience had caught an edge of the meaning, but the rest were silent simply because Halligan was silent.

  ‘This . . .’ Halligan tore his eyes from the board, ‘. . . is not possible.’

  ‘It’s rather wonderful though, isn’t it?’ I took two more steps back to admire it.

  We were two explorers who had advanced further into the unknown than any before us, delving into a realm very few could ever see, discovering and claiming new territory that the human race would own forever after.

  Halligan glanced at me and I could see a smile starting to take possession of his face. ‘Who are you?’

  ‘Nicholas Hayes.’

  He furrowed his brow even as his grin spread. ‘I mean . . . who the hell are you?’ He waved an arm at the boards. There were tears in his eyes. ‘This . . . This is incredible.’ In the next moment he had my shoulder in a vice-like grip and those pale blue eyes of his bored into mine. ‘You’re working with me now. You have to.’

  And I nodded. ‘OK.’

  June 1986, Cambridge

  ‘Who’s Demus?’ Helen asked.

  ‘Who?’ I looked up, hauled from my memories of that first trip to Cambridge and back into Helen’s cramped little room wallpapered with gig posters and smelling somehow of sandalwood and flowers rather than the odour of stale coffee and old socks that haunted my digs.

  ‘Demus,’ she said. ‘The fact he died at forty stopped your friend John getting his nose out of joint over you getting famous all of a sudden.’ She was sitting cross-legged on her bed, watching me with more interest and more caution than before. ‘I didn’t understand that bit. You said he was your “future self”. Is he someone you thought you might end up like if you weren’t careful?’

  ‘Something like that.’ I wasn’t sure how I’d let that slip out or what else I’d said. I’d been lost in the retelling, sure, but there was more to it than that. Somehow I’d found myself sufficiently comfortable with a complete stranger to let myself fall into honesty. And that just didn’t happen, not to Nick Hayes, awkward in my own skin and wearing sixteen years as poorly as most boys do. Definitely not with a pretty girl that I’d just met.

  I looked at Helen then. Really looked. Took in her dark eyes, the line of her cheekbone, her small, determined mouth, and suddenly I kne
w.

  ‘I’ve seen you before!’

  ‘We go to the same university in the same small city,’ she said.

  ‘I didn’t finish my story.’ I adjusted the towel across my lap, too amazed by her to feel silly. ‘The strangest thing about the day John and I came down to see Halligan was that what went on in the lecture hall wasn’t the strangest thing to happen to us.’

  Helen smiled and watched me. ‘So what was this incredible event that put your moment of glory into the shade?’

  ‘You were.’

  And I fell back into telling my tale of that winter’s day four months earlier.

  February 1986, Cambridge

  Professor Halligan had wrung every detail out of me, from my telephone number and address down to my mother’s maiden name, and sworn that he would have me as a fully fledged student at Trinity College within the week. Finally, and with great reluctance, he let me go. I think if he had had free rein he would have had me imprisoned in a cellar and set me to work immediately.

  John, distinctly unimpressed at having been left to cool his heels in a small mathematical library, hauled me off immediately with most un-John-like talk of missing the train and being late.

  I hadn’t realised how long I’d spent with Halligan. The best of the day had gone and it had been a pretty raw slice of February to start with. A wintry sun watched us with a red eye as John force-marched us up the long road to the station. My breath puffed out white ahead of me. All the shadows seemed to point my way, bare trees reaching.

  The girl came running straight at us. I saw her from a way off, heard her footsteps ringing on the pavement. The few people in her way had the sense to move aside quickly. She didn’t look like someone that was going to stop. John said something and in that moment she crashed into me. One second she had been fifty yards off and the next almost knocked me to the ground.

  ‘Nick!’ She grabbed me by the forearms. ‘Help me!’

  Even through her terror, even if she hadn’t used my name, I would have known that she knew me.

  ‘How?’ But I could see it before the word was out of my mouth. Something was coming after her, along the same path she’d taken. It was as if she had left copies of herself strewn behind her, but made of glass or water so that all you could see of them were outlines and a blurring to give away their shape. And they weren’t frozen in place where she shed them but chasing her down with the same desperate speed. Dozens of them. Something else was rushing on behind them, right at the back, something that looked like a miniature tornado, again glassy and hard to see, a distortion in the dying light, but full of fury and motion.

  ‘Keep them off me!’ the girl panted, hunting in a pocket and dragging out an oversized key. She stumbled past me towards the front steps of the next townhouse.

  I stood there with the first of the ghosts racing towards me and the girl climbing the steps to my left. It wasn’t the ghosts that left me speechless, or even the silent nightmare of the tornado behind them. It was something about the girl. Something familiar and strange at the same time. As if I’d known her all my life and just misplaced her name. More than that, though, there was something between us I couldn’t explain, but that was as real as my skin: the knowledge that it really didn’t matter what was coming down the road behind her. I was going to stand in front of it regardless.

  I heard the key fumble in the lock as the first ghost reached me. I stepped into its path and it slammed into me. It hit like a wave of icy water, taking the air from my lungs. The next hit and the next, each one jolting into me before I could start to fall. A series of blows that set my mind ringing like a hammered bell, shattering a million images free from memories that couldn’t have been mine.

  I heard the girl drag the door open. I didn’t have time to look, but from the flat blue light that flooded out across the street I knew that whatever lay behind that door it wasn’t what anyone would have expected.

  ‘Thank you.’

  The door slammed shut with a noise that could have been the full stop at the end of the world. And I was left facing the tornado that was less of a windstorm and more of a swirling wound in the stuff of the universe . . .

  June 1986, Cambridge

  ‘And?’ Helen prompted after I had fallen silent.

  I blinked. I’d been so lost in my story that I’d almost forgotten where I was or that I had an audience.

  ‘And when John picked me up off the street everything was back to normal. The girl was gone and the rest of it he hadn’t seen, just me jerking around as if I were having an epileptic fit.’

  ‘So . . . don’t you think you might have been? Having some kind of fit, I mean.’

  ‘Well. I guess . . .’ I waved the idea away. ‘Anyway, that’s not the point. The point is that when I first saw you today you seemed very familiar to me. And now I know why. That girl who asked me to save her four months ago. It was you!’

  CHAPTER 3

  ‘Those trousers should be dry by now.’ Helen stood to retrieve them from outside the window.

  ‘Thanks again, for saving my bacon.’ I felt rather foolish now, unloading my unbelievable true stories on her. She probably thought I was mad. If she didn’t then she had a severe overdose of gullibility.

  ‘Not a problem.’ She tossed me my trousers, then passed over my socks and shoe. ‘Apparently you saved mine first.’

  ‘It wasn’t you?’

  Helen shook her head.

  It had looked like her. Different hair and clothes but the same eyes, mouth, nose. Even in that brief moment the girl’s face had imprinted itself on my mind. Though how it already seemed familiar was another puzzle to add to my growing store. ‘You don’t have a sister?’

  ‘I do.’

  ‘Ah—’

  ‘She’s nearly thirty and has red hair.’

  ‘Oh.’

  Helen turned to face the window. Taking the hint, I hurried to dress.

  ‘You do know,’ she said, ‘that the bit of your story that really needs defending isn’t the part where some girl looked rather like me?’

  I zipped my fly. ‘You mean the ghosts chasing her . . .’

  ‘And the tornado.’

  ‘. . . and the tornado.’ I buttoned up and started to pull on my socks. They were still a little damp and smelled of river. ‘I mean, it wasn’t a tornado. It was more of a . . . thing.’

  Helen turned back to watch me tie the lace on my single shoe. ‘A thing.’ She nodded.

  I stood and shrugged apologetically. It wasn’t going how I’d hoped it would. ‘Thanks again.’

  She smiled that unreadable Mona Lisa smile of hers and said nothing.

  I turned to go, limping slightly because of my missing shoe. A moment later I was standing in the hall with Helen’s closed door behind me.

  ‘Shit.’

  I crossed the hall slowly and banged my forehead against the wall, once, twice, three times. Just hard enough to hurt. I could have played that better. I needed the girl to help me understand what had been happening ever since that first day in Cambridge. Nothing had been the same afterwards. Nothing had been right. And things had been pretty fucked up even before she vanished through that door and left me to deal with her ghosts.

  I’d been haunted ever since. And ‘haunted’ is not a word that comes easily to any man of science.

  February 1986, Cambridge

  John had got me to my feet and then, unsteadily, into the station.

  ‘What the hell was that?’ I collapsed onto a platform bench.

  ‘Some kind of fit?’ John asked. ‘Too much exercise too soon? Or overworking your brain showing off to the eggheads?’

  ‘I mean the girl and the things chasing her.’

  ‘Things?’ John slumped down beside me.

  I turned to stare at him. ‘You remember the girl, right?’

  He nodded. ‘The hot girl.’

  ‘And?’

  ‘She was wearing a T-shirt. Which was pretty odd for February, now I think about it.
’

  ‘She was?’ I had had other things to look at.

  ‘Yeah. Words on it. Something about chilli peppers . . .’

  I could tell where John’s attention had been. ‘And?’

  John looked confused, as if ‘hot’ was really all that need be said. ‘Well, she nearly knocked you over.’

  ‘And then?’

  ‘And then you started having some kind of fit and fell over.’

  ‘You saw what was chasing her, yes?’

  Again the frown. ‘No.’ He got back to his feet. ‘Train.’

  ‘Woah.’ In the act of standing John momentarily split into half a dozen Johns. One stayed sitting, one rose before the others, one held out a hand to help me up, one stooped to pick up a five pence piece from the floor. A heartbeat later they reunited with a snap and there was just one John, striding to meet the train, no hand offered.

  I looked down. A dirty five pence piece glinted up at me.

  ‘Come on!’ John called.

  That night wild dreams followed me home and came uninvited into my bedroom. I wrestled with elusive versions of Halligan’s equations, red chasing blue over a thousand boards until the whirlwind came, lifting all the symbols and scattering them like Alice’s deck of Wonderland cards.

  I woke late to an alarm clock that had elevated itself to defcon 2 and found myself tangled in sheets wet with sweat. All the books had been scattered from my shelves, the main light and the bedside lamp both had their bulbs blown, and in the condensation on the window a thousand equations, one overwriting the next, all in impossibly neat script.

  I rolled out of bed with a groan. ‘I’ve seen this film. It’s called Poltergeist . . .’ It wasn’t a film I had any desire to live out.

  D&D was at Simon’s and I’d be late if I took the time to clear up the mess. Ignoring the chaos, I struggled into my clothes. I’d seen ghosts before, though not like this. I’d seen them the first few times Demus got close to me. He’d called them temporal resonances. Echoes in time set off by the supposedly impossible encounter between me and myself, two incarnations of Nicholas Hayes twenty-five years apart and yet together on the same timeline, influencing each other’s lives in a closed loop free from paradox.