Shape-Shifter

by Pauline Melville

  One hazy day in August, Jane Cole took her sandwiches and went to sit on the grass of a nearby park during her lunch-break. The park was nearly empty. On a day like this when the sky was glazed, Jane could allow herself to look up. Overhead an aeroplane flew low, making the sound of cloth ripping slowly and unevenly. Another, more distant and at right angles to it, flew in a higher plane, two grey sharks lazing in a muggy sky. Idly, Jane began to work out their relative speeds. Then she turned and noticed a man looking at her from about twenty feet away. There was something odd about his position. With his left hand he held onto the slender trunk of a sapling recently planted by the council, his feet tucked into the base so that he leaned out at an angle. Suddenly he let himself swing gracefully round, anti-clockwise, swapping hands mid-swing so that he grasped the tree with his right hand, ending up at the same angle on the other side. He raised his hat to her.

  Immediately, Jane gathered her things and set off to walk back to the salon. As she passed the man she saw that he had a pale and beautifully symmetrical face, the face of an aesthete with a long aquiline nose and eyes set slightly too close together. An elegant gaberdine raincoat hung on a slender body. His gaze was mocking and inquisitive. He smiled as she went by. Three riffs of a Miles Davis number she had heard once on the radio and tried to put out of her head, started up again in her brain.

  That afternoon, to her great satisfaction, Jane Cole got by on the following phrases:

  ‘Oh what a shame.’

  ‘The same rinse as last time.’

  ‘Good afternoon.’

  ‘Is that drier too hot for you?’

  ‘I know. I know.’

  ‘That’s all right.’

  ‘Fancy.’

  The same evening, a huge red sun sank behind the outline of the rooftops opposite leaving a pinky-grey dusk. Jane looked from her window to see if the chip shop on the corner was still open.

  There he was again.

  This time he executed the same peculiar swing round the, lamp-post on the other side of the street but did not seem to be looking in her direction. Jane frowned. Behind the greasy rectangle of light that was the chip shop window she could see the misty figures beginning to pack up for the night. Either she went now or she missed her supper. She ran down the lino-covered stairs. As she stepped into the street, the man twirled and waved his hat. At that moment she felt a pricking in the toe of her right foot as if she had a stone in her shoe. She hobbled to the shop and bought her cod and chips. By the time she left, the whole of her right foot was pricking painfully as if the shoe was filled with thistles. She came to a halt. In the light of the street-lamp she could see the concern in his eyes:

  ‘May I be of assistance?’

  The man appeared so genuinely concerned, so anxious to help, that she let him take her arm along the street. Now she could not even put the foot on the ground for the sharp jabbing pains. She leaned on him as they climbed the stairs. At the front door of her flat she hesitated. The man whipped out a card from his pocket:

  ‘Let me present myself,’ he said. The card read:

  J.F. WIDDERSHINS

  GEOMETER

  AND

  MAKER OF DIVIDERS

  AND POLYHEDRAL SUNDIALS

  The pain was now so acute that she was powerless to do anything but turn the key in the lock and let them in. He took her weight and helped her over to the divan bed by the window. Jane had done nothing since she moved in to make the flat more homely. The bed sagged under a coverlet whose pattern had wilted and faded. There was a tiny Belling stove in the corner next to the sink, two ugly wooden armchairs and a table with a blue and white chequered formica top. He fetched the stool for her leg.

  ‘I think we’d better take a look at that leg,’ he said. He bent over, his shiny chestnut hair glinting in the fading light. Jane felt safe with him, grateful for his presence. With long, tapering fingers he deftly undid the laces of her ankle-boot and gently removed it. Then, with the utmost delicacy, he began to roll down the white knee sock:

  ‘Ah!’ he said as he did so. ‘A classically beautiful leg if I may say so.’

  Jane stared at her leg. From just below the indentation left by the elasticated top of the sock, her leg no longer consisted of flesh and blood. Instead, she found herself looking at the most dazzlingly intricate, three-dimensional network of geometrical shapes. The leg was transparent. Beneath it she could see the yellow plastic seat of the stool. It seemed to have been drawn in mid-air with the finest of pencils. The diagrammatic leg retained the same outline as before and she could distinguish the toe-nails now transformed into a complex of polygons. The main parts of the foot and leg, however, were made up of a web of delicately interconnecting geometric forms, tessellations, cub-octahedrons, star-pentagons, rhombic faces (which revolved), cones, triangles and the cubic lattices of crystallography. Shocked and fascinated, Jane stayed dumb.

  ‘Well, well,’ said Widdershins, kneeling to inspect the mathematical limb more closely. ‘No wonder the shoe and sock were painful – all those acute angles. Has the pain abated somewhat?’

  Jane nodded. Widdershins regarded her quizzically:

  ‘You seem surprised. Why is that?’ he asked.

  Jane searched for the vocabulary she had jettisoned. It failed to arrive:

  ‘Dunno really,’ she said.

  ‘Come, come.’ His tone was mildly reproving. ‘You are one of us. I think you have always known that there is nothing real except mathematics. May I help myself to one of your chips?’

  Jane still held the warm, greasy packet of fish and chips to her chest. She opened it and he took one, pulling up one of the armchairs to sit beside her in the evening light:

  ‘I am a pure mathematician. A classicist. The pure mathematician is the only one in direct contact with reality. The reality of pure mathematics lies outside us. The area of a circle is πr2 not because our minds are shaped one way or another but because it is so, because mathematical reality is built that way. A man who could give a convincing account of mathematical reality would solve the most difficult problems of metaphysics. If he included physical reality in his account, he would have solved them all.’

  Widdershins fell into a deep musing, the soggy chip dangling from between his fingers. Jane Cole looked out of the window to check that the street was still there. Nothing had changed. A fat dog waddled by. Widdershin’s presence unexpectedly soothed her, his manner was calming and the sight of her leg, far from disturbing her, only seemed to re-affirm something she had known, albeit hazily, since she was a young child. Besides, the leg was astoundingly beautiful. She altered the position of her foot. Immediately, the complex pattern of forms shifted in the manner of a kaleidoscope.

  ‘Ahhhhhh,’ said Widdershins, opening his eyes and observing the leg once more. ‘The exquisite double helix. And look! Kepler’s stella octangula.’

  He pulled out a handkerchief and wiped his hands fastidiously with it: ‘I wonder if I might ask a favour of you. Do you think I might call on another acquaintance of mine to come and have a look at this?’

  ‘Certainly,’ said Jane, beginning to enjoy the attention.

  Widdershins moved swiftly to lift up the wonky sash window. He leaned out and gave a melodious whistle. Straightaway, a figure detached itself from the shadows of the building opposite and came leaping across the road. Jane heard footsteps bounding up the stairs two at a time. Into the room burst a tall, gangly young man with a shock of yellow hair. He wore a black and red check lumberjacket shirt of brushed cotton and black jeans. Holding up his arms like a singer acknowledging cheers he gave an extravagant off-centre bow and announced himself:

  ‘Hoodlum. Rock and roller. Anarcho-syndicalist and collector of irrational numbers, OK? What’s going on then? Do I smell chips or do I not smell chips?’

  He came over to grab some chips from the packet proffered by Jane. She smelt the sweat as he reached out his arm.

  ‘Whoop de doop doop doop! What have we here?’ he crowed a
s he spotted the leg.’

  ‘I thought you might be interested,’ said Widdershins modestly.

  Jane fixed her hair back from her eyes. Events this far beyond her control allowed her a delicious irresponsibility. She waggled her toes and watched the ensuing transformation of the geometrical pattern. Hoodlum goggled at the permutating shank. It was getting dark. He walked round the leg to view it from another angle.

  ‘I can fuck that leg up,’ said Hoodlum suddenly.

  ‘I think not,’ said Widdershins, on the defensive.

  ‘I can fuck it up numerically.’

  Widdershins frowned. ‘How?’

  ‘See that little square.’ He pointed to a tiny perfect square just below the little toe. ‘Measure it,’ he challenged Widdershins. Widdershins took out a pair of dividers and a tape from his pocket.

  ‘One centimetre each side,’ he said.

  ‘Gotcha!’ yelled Hoodlum. ‘Look at the leg numerically for a minute.’

  Jane regarded Hoodlum with amazement. The whites of his eyes, white as school milk, bulged and the dark centres were spinning. Immediately, she experienced a tingling in her leg. She looked down and flinched. The leg appeared to be swarming with ants. On closer inspection she saw that it was a seething mass of miniature numerals and tiny black multiplication, addition and minus signs all marching in file through the density of her leg and turning over with incredible rapidity.

  ‘The exact numerical representation of your geometry,’ said Hoodlum triumphantly to Widdershins. ‘Which means that the diagonal of your one centimetre-sided square is the square root of two. An irrational number. It don’t exist,’ hooted Hoodlum.

  Even in the dim light, Jane could see that Widdershins had gone pale.

  ‘You’ve made a hole in her leg,’ he said in alarm.

  Jane began to feel faint. Where the square had been, just below her little toe, the numbers were falling off into nowhere. Widdershins hurried to the door:

  ‘I’ll have to get Afreet.’ He vanished down the stairs.

  ‘Who’s Afreet?’ she asked.

  ‘A mechanic,’ said Hoodlum. ‘Can I have this fish?’

  He gobbled down the fish before she could reply. Then he leapt into the middle of the room, miming playing the guitar, and sang raucously:

  ‘Goodbyeeee Google-eyeeee.’

  Jane thought he was good-looking. She tried to look vulnerable:

  ‘Do you think I’ll die?’ she asked.

  ‘Fuck knows,’ said Hoodlum.

  Jane chanced another squint at her leg. The numbers were not falling off into nowhere. They were falling onto the floor in a little heap like iron filings.

  ‘I’d like my leg back to normal. I have to stand up all day.’

  ‘All day and all of the night,’ sang Hoodlum.

  Suddenly, Hoodlum was all over her, plastering her face and neck with ecstatic wet kisses.

  ‘Mind my leg,’ she said, enjoying the roughness of his shirt rubbing up against her.

  ‘I can fuck you without touching that leg,’ boasted Hoodlum, which was exactly what he was doing, while she kept an eye on the mounting pile of numbers on the floor next to the stool.

  Two voices could be heard coming up the stairs. Hoodlum got up and did up his jeans:

  Widdershins opened the door, switched on the light and ushered in a short man, not more than three feet high with an enormous head covered in frizzy, electric hair. He carried a tool-bag:

  ‘Right, now.’ His manner was slow and practical. ‘I’m the quantum mechanic. Where’s the trouble?’

  ‘Over here.’ Widdershins gestured elegantly in the direction of Jane. ‘This young lady has developed a hole which is, I’m afraid, beyond repair by classical means.’

  Hoodlum blushed and began to whistle. Afreet went over to the wash-basin and stood on tiptoe to wash his hands. Then he came over to the bed:

  ‘Let’s have a look. No need to get upset, miss,’ he said at the sight of Jane, who was looking a bit rumpled.

  His broad forehead wrinkled as he studied the leg:

  ‘I see what you mean. Well, you’ve been looking at it the wrong way. It’s always the same with you pure mathematicians, if you don’t mind my saying so. Airy-fairy idealists. I’m a nuts and bolts man myself.’

  A pained expression passed over Widdershin’s refined face. Hoodlum scuffed his feet.

  ‘Well, you’ll have to look at it my way. I know you don’t like it, Mr Widdershins, but that’s all there is to it.’

  ‘Hurry up, please,’ said Jane.

  ‘Now I’m not one to be hurried, miss. In fact, I like to take my time and explain things as I go along so everyone’s in the picture.’ As he spoke, Afreet rummaged in his tool-bag. He took out a geiger-counter, a tin box with the word ‘photons’ written on it in felt-tip pen and the parts of what looked like a telescope, which he proceeded to assemble. When he had done this he sat down in the chair next to Jane.

  ‘Now miss, you know that you are nothing but a mass of jigging electrons and sub-atomic particles, don’t you?’ he said, patting her kindly on the hand. Jane nodded doubtfully. Her leg was itching. Afreet continued:

  ‘It’s an ancient idea. Democritus had it in 420 BC. He decided that when you cut an apple, the knife finds out the spaces. between the atoms. Not far wrong. Leibnitz was another one. An atomist.’ Hoodlum gave a loud yawn which Afreet disregarded. ‘Leibnitz would have thought of that table over there as a colony of souls. Sometimes, when I’m feeling a bit romantic, I think of myself as a soul-tailor,’ he added sheepishly.

  Hoodlum, showing major signs of jealousy, let out a loud guffaw. Widdershins shut him up with a glance.

  ‘As I was saying, matter is just a handy way of collecting atomic and sub-atomic events into packages. And now we’re going to examine your leg in that light.’

  ‘Couldn’t you put me to sleep with an anaesthetic?’ asked Jane, quailing at the thought.

  ‘’Fraid not, miss. Consciousness is crucial in quantum mechanics. You’ll have to observe your leg. Unless you see it, it won’t be there, so to speak. Even the tiniest electron can’t really be said to exist until there’s an observer, let alone a whopping great leg.’

  Widdershins could no longer contain himself: ‘But surely, at some level quantum physics turns into classical physics?’

  ‘Who said?’ snapped Afreet.

  ‘Surely the world enjoys an independent existence, an objective reality in accordance with certain classical laws which it obeys whether there is anyone to observe them or not?’ said Widdershins.

  ‘It did, Mr Widdershins, until quantum mechanics came along. Now everything’s atoms. Reality is a fuzzy business, Mr Widdershins. I see with my eyes, which are a collection of whirling atoms, through the light, which is a collection of whirling atoms. What do I see? I see you, Mr Widdershins, who are also a collection of whirling atoms. And in all this intermingling of atoms who is to know where anything starts and anything stops. It’s an atomic soup we’re in, Mr Widdershins. And all these quantum limbo states only collapse into one concrete reality when there is a human observer. Like the young lady here. Now then. We have a leg here that is dripping numbers. Do you want me to try and deal with it or not?’

  Jane held her hands over her eyes. Widdershins was unable to leave well alone: ‘Einstein,’ he said loftily, ‘believed that there is a reality which we uncover by our observations. He believed in a substratum of deterministic forces that drive the unpredictable hi-jinks of your electrons. He just happened to die before they were discovered.’

  The mention of the name Einstein seemed to throw Afreet into a frenzy. He stood up and banged his tool-bag on the ground. Hoodlum backed off into a corner.

  ‘Einstein,’ he growled. ‘It was his bloody theory that stopped us finding out about faster-than-light signalling. He didn’t know about the conspiracy of particles – what he called “spooky action at a distance”. He didn’t know about enfolded order – space folding and unfolding. He
didn’t consider the possibility of multiple universes.’ Afreet began to hop up and down:

  ‘LOOK AT THE LEG,’ he roared. ‘LOOK AT THE LEG.’

  Just then, Jane felt the tingling in her leg stop, to be replaced by a sensation of unbearable lightness. She took her hands away from her eyes. Below the knee, her leg had no beginning and no end. She saw clearly the same infinite space, the same dizzying void that she had seen once before on a clear winter’s night, the same spiralling galaxies and pendant heavenly bodies that could be either stars or electrons.

  Afreet appeared to have recovered his equanimity and was fiddling about with the telescope:

  ‘I think I’ve got it. I can see the problem way down one end. It’s a black hole.’ He packed up his telescope. Jane kept her eyes averted from the celestial limb.

  ‘Can you fix it?’ enquired Widdershins, anxiously. ‘Surely you can. After all, as Einst …’ He corrected himself. ‘As somebody said, “God may be subtle, but he’s not malicious”.’ He laughed, nervously.

  ‘That’s not my experience, Mr Widdershins. In my experience God is extremely malicious. And the answer is “No”. I can’t fix it. As you well know, it is the point where all laws cease.’

  Hoodlum let out a whistle, secretly proud of himself for having fucked a woman who contained such lawlessness.

  ‘The best I can do,’ said Afreet, wiping his forehead with a handkerchief, ‘is a Schrodinger’s cat job. And that only has a fifty-fifty chance of success.’

  Widdershins swivelled slowly round on his heels from left to right: ‘It’s not very satisfactory,’ he said.

  ‘It’s the best I can do. She’ll have a fifty per cent chance of living.’

  Turning her head to avoid seeing the vertiginous depth that was her leg, Jane determined to exert some control:

  ‘If I’ve got to take a risk, I want to know the facts,’ she demanded. Patiently, Afreet explained:

  ‘If I don’t do something, in twelve hours’ time all the atoms of which you are comprised will collapse into that black hole. I can set up a condition whereby either that will happen or you will revert to your former self with your former leg. It’s a quantum superposition of two states – alive and dead. You will be both alive and dead at the same time. Only when a human observer comes and looks in the room will you flip definitively into one of the two states. Hopefully, in your case it will be life. Schrodinger designed the experiment for a cat, originally.’