Whatever I was able to observe seemed pretty unnatural to me, but schoolfellows more sophisticated than I explained that what Stanley and Florence did was the usual thing done by men and women. What I’d seen and heard through the keyhole, the grunting and the outcries and the heavy work of it, fascinated me, and I looked forward to a time when the world of the keyhole would open to me.

  What I wrote a few moments ago about a little box of images, music, words and so on – I know what put that into my mind: it was the memory of Stanley’s cigar boxes. He stored screws, nuts and bolts and other bits of ironmongery in the empty ones and I had several as well in which I kept marbles and string and various treasures of the moment.

  There must be cigar boxes all over the world with bits of people’s lives in them – photographs and postcards from everywhere, letters in all languages in cigar boxes in Mongolian yurts, bedouin tents in the Sahara, Indian huts on the Amazon. I think Stanley smoked La Coronas but that might be a false memory. The scene on the lid that I recall is probably a conflation of several: a gorgeous world of pyramids and palm trees, distant blue skies, balloon ascensions, racing locomotives, fallen pillars, and wheels of commerce and industry presided over by the beautiful goddess of the cigar-box lid. In my more fanciful moments I wonder if cigar boxes glim, and if the scene on the lid is what they’re glimming.

  I have no cigar boxes now, but they live somewhere in my memory, and as I call up one from my years with Stanley and Florence I open it and see, at the top of the several layers of this time-capsule, a broken mother-of-pearl penknife, a postcard from Crystal Cave, a roll of caps from a toy pistol, some Indian-head pennies and a silver dollar, two aggies and a glass shooter, a souvenir ballpoint pen in which a tiny Kong climbs the Empire State Building, a coil of the strong-smelling string called tarred ganja, and a school photograph of Clara Wilson.

  The little black-and-white photograph of Clara, taken when we were both nine, has almost nothing of the real nine-year-old Clara I remember in an empty hayloft in the old barn where the dust-motes danced in the sunlight that came through the cracks in the siding. It was summer, the air was warm and lazy with the drone of cicadas. I see her now with her clear blue eyes, her little smile, and the sunlight backlighting her fair hair. She was from Milwaukee and she was visiting next door. She brought with her distance and enchantment and I can’t remember how, or if, I led up to it but I asked her if she would show me hers if I’d show her mine and she said yes. It’s still there in my mental cigar box, her very gracious yes.

  27

  The Beckoning Other

  ‘Have you fallen asleep?’ said Amaryllis.

  ‘What?’

  ‘I asked you what the words Unnatural practices yes meant to you and you seemed to go into a trance. Are you all right?’

  ‘I’m fine. It was just something from my childhood; I used to think that anything men and women did in bed was an unnatural practice because of something my uncle said one time.’

  ‘Childhoods,’ she said. ‘Everybody has one.’ She leaned back and crossed her arms on her chest. I like the rain; maybe we don’t need to talk, maybe we could just drink and be together and listen to the rain.’

  ‘Whatever you say, Amaryllis.’ So we did that: she arranged herself on the couch with her bare feet tucked under her and I took the chair and footstool opposite. We drank and listened to the rain while I mentally undressed her. I thought of us wide-awake and naked in front of the fire but it was too warm for a fire. Our glasses were empty; I refilled them.

  ‘The rain is putting me to sleep,’ she said. ‘How about some music?’

  ‘Sure, but let’s go up to the studio. I want to see you and the painting together.’

  ‘Have you finished it already?’

  ‘No, it’s still developing but I want to see how it looks to me when you’re standing next to it.’

  The rainlight was wonderful in the studio; the rain on the windows was like the muffled drums of time. I removed the Barbara Strozzi disc from the CD player and put in The Art of Fugue, the recording by Musica Antiqua oln – it seemed right for this particular afternoon. It’s more painterly than the keyboard versions; the colours of the instrumental voices, like the Invisible Man’s bandages, help to reveal what can’t be seen directly.

  As the voices went over and under, advancing and retreating and passing through themselves, Amaryllis put down her drink and put her hands over her ears. ‘Please stop that awful Klein-bottle music,’ she said, ‘before I throw up.’

  ‘Sorry!’ I said. I removed the Bach and inserted the Barbara Strozzi which was of course much better music for viewing the painting. Why had I put on the other?

  ‘Yes,’ said Amaryllis as Mona Spägele’s voice mingled with the rainlight. ‘That’s more like it.’

  When I replaced Bach on the shelf the painting was not in my field of vision and I wasn’t watching Amaryllis as she took up a position in front of the canvas but I heard the silence that followed. When I turned I saw only the back of the easel but I saw Amaryllis’s face and she had gone deathly pale.

  ‘Amaryllis,’ I said. ‘What is it?’

  She rushed past me and I followed her to the bathroom and held her hair out of the way while she vomited into the toilet. When she’d finished she went to the sink and rinsed her mouth and face.

  ‘Are you all right?’ I said.

  ‘Fine. Too many boilermakers, need a little fresh air.’

  ‘It’s still raining.’

  ‘Fine. Rain’s good. Fresh.’ She went downstairs fast but wobbly, put on her things, slung her shoulder bag, saw me putting on my mac, said, ‘No taxi, need to walk. By self. Don’t come with,’ and lurched off into the wet.

  I went back to the studio, went around the easel to stand in front of the painting. The misty moonlight was gone. There were no Carpathians, no Borgo Pass, no ruined castle. No Amaryllis. Broad daylight, and there was Lenore, all in black, her face pale, her long black hair whipping in the wind. She was standing at the edge of the cliff with the sea behind her. Her right arm was raised as she beckoned me to follow. Was she shaping ‘Yes!’ with her mouth? My hearing, doing its new thing, seemed to shut down so that for a moment the music and the sound of the rain were gone. Then they came back, and with them the silence that Amaryllis left behind her.

  28

  What Now?

  Was I awake or was I glimming? With my right hand I pinched my left arm and it felt solid and real but then every part of me always felt real in glims. I picked up the telephone and dialled 123. ‘At the sound of the third stroke it will be six-thirteen and thirty seconds,’ said a cultured female voice. Pip pip pip. I put down the phone. The woman had spoken in the weary cut-glass tones of someone who really had no time for me. What had happened to the Accurist man who always gave Accurist time in such a strong and manly way? You knew where you were with him; his voice was like a tall building with all the lights on. Trust me, it said, in the day, in the night, in the small and lonely hours, the world is still here. Of course he was only a tape, so even if the world were gone his voice might still come on when you dialled 123.

  I went downstairs. Amaryllis’s puddles were still there. I opened the door, stepped out into the rain, got wet. That didn’t prove anything. Was I passing through myself? Had I already done that and come out on the other side? I went back up to the studio. There she was: Lenore at the cliff’s edge with the sea behind her. I touched the painting, got paint on my finger.

  ‘Not a glim,’ I said. I clapped my hands together, felt myself do it, heard the sound. Had I been sleep-painting? Nothing like this had ever happened before. I looked away from the painting and looked back. Lenore was still there.

  Why had Amaryllis run out of the house like that? Evidently she knew Lenore. Did she know about Lenore and me? She’d left the RCA the year before I arrived – that would have been 1992 but she was probably still in touch with people from the school. Life seemed more and more like a Klein bottle.

&nb
sp; I picked up the phone again and dialled the number for Rail Enquiries.

  29

  Looking at Shapes

  Taking a tolerant view of whatever reality was operative at the time and accepting things pretty much at their face value, I found myself the next day on the 13:01 to Flitwick. I was on my way to see Alan Bennett, the Klein-bottle man.

  The Thameslink trains left not from the usual King’s Cross platforms but from a parallel universe reached by a long corridor from King’s Cross tube station and an escalator of doubtful authenticity. Nevertheless, having committed myself to this expedition I persevered, bought a ticket, and was directed to Platform B. This would-be terminus seemed not quite a proper railway station; it was as if someone with a few trains had decided to squat there and had hacked their way into the system to get arrival and departure times posted on legitimate screens.

  The Thameslink train turned up right on time carrying more emptiness than passengers. It hurried out of London as if it didn’t care where it went; I feared that it might forget Flitwick altogether. Places along the way came and went in a succession of not-herenesses, presenting themselves like a lineup of the usual suspects as the train approached, paused at, then left St Albans, Harpenden, Luton, Leagrave, and Harlington. When a sign said FLITWICK I got off, went up stairs, over a bridge, down stairs and through the life-size model railroad station to the pick-up point where Alan Bennett was waiting in a small red car.

  Imagining backwards from the attenuations of Klein-bottlery to their maker I’d arrrived at someone who looked like Basil Rathbone or Peter Cushing. In this I wasn’t too far off; Bennett might have been Cushing’s younger brother, competent to deal not only with vampires but with strange surfaces as well. He was of middle height, slight in build, had fair hair going grey, and spectacles. His dominant feature was a high domed forehead that looked as if any number of Klein-bottle variations and other topologies might be quietly circulating within. Clearly this kept him in a good humour; he had an easy lightness and brightness about him that made me aware of how heavy and dark I was feeling.

  We exchanged the usual arrival remarks as he drove through Flitwick, pointing out pubs and other landmarks and explaining how it had grown, but I wasn’t taking in what he said because while he spoke I was thinking, Is life like a Klein bottle? Were Amaryllis and I ever going to be together again to pass through ourselves at the point of intersection? If the bottle is broken, does the passing-through carry on without it?

  Bennett’s house was in a modern yellow-brick terrace. His wife, Virginia, had the cheerfully unfazable manner of someone who could deal with Klein bottles and Möbius strips without going round the twist. She gave me a cup of tea while their dog, a King Charles spaniel called Amber, having thumped a welcome with her tail, came over to get acquainted. ‘Actually,’ said Alan when he thanked me for the Glenfiddich I brought, ‘I do have a weakness for whisky.’

  ‘I’m glad,’ I said, ‘because I want to get on the good side of you. I’m hoping you can help me with my Klein-bottle problem.’

  ‘What sort of problem?’

  ‘They trouble me.’

  ‘In what way?’

  ‘I think I might be in one, in a manner of speaking.’

  ‘Looking for a way out?’

  I don’t know; I’m confused. Have you ever thought that life is like a Klein bottle?’

  ‘Not that I can remember. Felix Klein described his bottle as “a one-sided surface that is closed and has no boundary”. An ant on any part of the surface could walk in any direction without ever going over an edge; there are no edges. Does life seem like that to you?’

  I thought of the boundaries and edges in my life; there seemed to be more of them all the time. I grimaced and scratched my head. ‘Not really,’ I said.

  He seemed concerned, rubbed his face a little. I doubt that I can help you with your problem, but let’s go to my workshop and I’ll show you what I do and maybe something will come to you.’

  I finished my tea and we stood up. Virginia nodded encouragement. ‘Ideas come to Alan at all hours of the day and night,’ she said, ‘so you never know.’ Amber smiled reassuringly and expressed with her tail that everything, if it wasn’t already all right, would be all right in the fullness of time. Her life had obviously been different from Queenie’s and she was an optimist.

  I followed Alan to the workshop which was just outside the house and used to be a garage. I’ve had people follow me up to my studio the same way, expecting something out of the ordinary, hoping perhaps to see through my eyes something they’d missed with theirs.

  As soon as we entered the place I recognised it as one of those magic caves found here and there where enthusiasts of divers kinds devote themselves to alchemy or perpetual motion, the esoterica of clockwork, the images of anamorphism, the observation of celestial bodies or the manufacture of ships in bottles – all manner of disciplines not always listed in the yellow pages.

  There were a large lathe and a smaller one and three gas burners whose flames fluttered patiently on standby. Benches and shelves were crowded with tins, bottles, boxes, and various appliances relevant to his work. Several of his non-Kleinian artefacts were on some of the shelves. One of them featured the word CHAOS in glass tubing; when activated by the gravity feed from its little reservoir, blue bubbles went round chaotically inside the glass letters. Nearby stood a small glass fountain patterned on the one invented in antiquity by Hero of Alexandria.

  ‘I guess you’ve been doing this for a while,’ I said.

  ‘I’ve been in scientific glass-blowing for forty years,’ said Alan. ‘I left school at fifteen and became an apprentice in a local company, and after a couple of years I was designing or redesigning everything they made. I carried on doing that wherever I worked until I took early retirement in 1995. Since then I’ve been in business for myself’

  ‘How did you get started on Klein bottles?’

  ‘Someone showed me one back in my apprentice time and I worked out how to make it – they’re not the easiest things to make – and then I didn’t think anything more about them until probably 1990. I found out from somewhere that Felix Klein said that if his bottle is cut along the correct line it makes two single-twist Möbius strips. So I thought, If a basic Klein bottle cuts to give two single-twist Möbius strips, what shape would cut to give two three-twist or five-twist? Hence the collection.

  ‘I’d got all the way up to design No. 14 before I realised that if you cut the Klein bottle right across the middle in a straight line you get two Möbius strips – I hadn’t recognised that before. The wonderful thing is that if I had known where to cut the Klein bottle I’d never have made designs 1 to 14; this is what interests all the mathematicians, because it’s a research project done purely in a practical way with no mathematical knowledge at all, simply by looking at shapes, redesigning shapes, and the whole lot’s cast in glass and they’ve got it for ever.’

  I tried to think whether I had any for ever in my life. Amaryllis? Doubtful. ‘I’ve stood in front of your display at the Science Museum,’ I said, ‘and been baffled by it. The sheer intricacy of all those comings and goings in the bottles overwhelmed me.’

  ‘If I show them to you one at a time it’ll be easier,’ said Alan. He produced one of those black sample cases used by salesmen, started unwrapping the contents, and set down on the nearest free space the basic Klein bottle, the one that I had by now seen from all angles, animated and still, on the various Internet sites where it was featured. It’s a nice thing to look at – odd but apparently harmless.

  That was No. 1. From there he took me through successive elaborations, each time setting down the example beside the previous one as the glittering array grew in numbers and complexity. As he warmed to his subject his voice took on more and more authority, his eyes grew brighter, and he seemed to grow taller. I watched and listened attentively; being an idea-and-image man, I always look for the idea in the image and the image in the idea – I don’
t care which comes first. As he showed me one after the other I tried (and failed) to send my mind through all the turnings. I was intrigued by various of the vessels but it was No. 15 that rang the bell for me.

  Drawing by Alan Bennett

  ‘This one has five piercings,’ he said.

  ‘Passes through itself five times,’ I said.

  ‘That’s right.’

  The vessel he was showing me was shaped like a tumbler, with the mouth at the top becoming a tube that descended through the body of the vessel. It passed through it once, went round to pass through it again, and went round yet again before returning to the main body. That’s how it is with Amaryllis and me, I thought: there is the vessel of our two selves; from it they coil outward and return, five times piercing the point of intersection. Those words in my mind seemed to have significance but I wasn’t sure what they meant.

  ‘Are any of these helping you with your problem?’ said Alan.

  ‘I don’t know. What you do is art, and art isn’t meant to solve problems, is it.’ I didn’t really want to talk any more, I wanted to go away and think about No. 15 and I wanted to be able to look at it while I thought about it.

  ‘Actually,’ said Alan after a moment’s consideration, ‘I wasn’t thinking of them as art when I made them. When I made the first fourteen I was just trying to work out where to make the cut for two single-twist Möbius strips. No. 15 happened because it was the next thing to do after No. 14, and so on.’

  He showed me the rest of the collection but No. 15 was the one I wanted to get my hands on and I persuaded him to sell it to me. I could feel that this one wanted to be my friend. Maybe it wanted to look at me as much as I wanted to look at it. Questions and hopes of answers had already left my mind; mysteries are the only real satisfaction and this one had agreed to live with me.