The Geometer Lobachevsky - Adrian Duncan - E-Book

The Geometer Lobachevsky E-Book

Adrian Duncan

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Beschreibung

When I was sent by the Soviet state to London to further my studies in calculus, knowing I would never become a great mathematician, I strayed instead into the foothills of anthropology. It is 1950 and Nikolai Lobachevsky, a Glav Torf mathematician and great-grandson of his illustrious namesake, is aiding Bord na Móna by surveying a bog in the Irish Midlands. Far from home, he studies the locals and the land. One afternoon, soon after he arrives, he receives a telegram calling him back to Leningrad for a 'special appointment'. Lobachevsky may not be a great genius but he is not foolish: he recognises a death sentence when he sees one and leaves to go into hiding on a small island in the Shannon estuary, where the island families harvest seaweed and struggle to split rocks. Here Lobachevsky must think about death, how to avoid it and whether he will ever see his home again. Following Duncan's critically acclaimed Love Notes from a German Building Site (2019), A Sabbatical in Leipzig (2020) and Midfield Dynamo (2021), Duncan's themes of emigration, displacement and work connect Ireland with the world stage. Colm Tóibín said of Love Notes: 'Written in spare, exact prose ... Duncan writes beautifully about cold weather, gruff manners, systems of hierarchy ... A portrait of work [and] a picture of a sensibility'. SHORTLISTED FOR THE 2023 WALTER SCOTT PRIZE SHORTLISTED FOR THE 2023 KERRY GROUP IRISH NOVEL OF THE YEAR

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Veröffentlichungsjahr: 2022

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THE GEOMETER LOBACHEVSKY

To Susan

ALSO BY ADRIAN DUNCAN

Midfield Dynamo A Sabbatical in Leipzig Love Notes from a German Building Site

THE GEOMETER LOBACHEVSKY

ADRIAN DUNCAN

THE LILLIPUT PRESS DUBLIN

First published 2022 by

THE LILLIPUT PRESS

62–63 Sitric Road, Arbour Hill, Dublin 7, Ireland.

www.lilliputpress.ie

Copyright © Adrian Duncan

Note on the text: This is a work of fiction. All characters, businesses, organizations, artworks and events portrayed in this novel are either products of the author’s imagination or are used fictitiously.

All rights reserved. No part of this publication may be reproduced in any form or by any means without the prior permission of the publisher.

A CIP record for this publication is available from the British Library.

10 9 8 7 6 5 4 3 2 1

ISBN 978 1 84351 8297

The Lilliput Press gratefully acknowledges the financial support of the Arts Council/An Chomhairle Ealaíon.

Set in 12.5 pt on 17.5 pt Fournier by iota (www.iota-books.ie) Printed in Poland by Drukarnia Skleniarz

‘It’s been such a long time since we met,’ the bishop observed, tenderly stroking his mother’s arm and shoulder. ‘When I was abroad I missed you, Mother, I really missed you!’

— ‘The Bishop,’ Anton Chekhov

A dying man lies prone on a coverless bed in a single-windowed room in the upper floor of a building not far from the sea. The window has been left an inch or two ajar. A rhombus of white moonlight illuminates a portion of wall above the bed, and from the ceiling of this room a glinting mobile of small steel shapes – a circle, a square, a triangle, a pyramid – dangles, clinking gently in the sea air.

In his mind’s eye appears the image of a photograph he lost many years before. In the foreground stand five men on the edge of acres of unworked bog. In among these men, all leaning on their implements, stands this man as a younger person. He is smiling, and the wind in the photograph has lifted his dark hair off his forehead into lazy floating strands around his crown.

It is towards these men, over their shoulders and into this broad province of brown earth that the mechanized mind’s eye of the dying man proceeds.

PART I

Point of square touches face of pyramid, while in the background a triangle spins past.

1

I am standing on the edge of a bog. There is wind. And sky meeting arm-opening land. Three men stalk out into this dark terrain. One carries a clinking tripod under his arm and two leather cases in his right hand. Another, head down, bears two bundles of timber stakes on his shoulders, as does the other. I hold a sledgehammer and coiled around my left hand are twenty-two yards of steel chain. My shoes, foot- clothes and feet are wet. I trudged with these men through mud of this kind yesterday and the day before and the day before, laying out across this land a giant if invisible triangle.

A gust of wind breaks and rushes at my face. The two men carrying the timbers topple.

The gust passes.

The two men right themselves and gather up their stakes.

One of the points on this triangle has been carved onto an obelisk three yards to the north of a concrete chimney that protrudes from the horizon in the distance – towards the west-south-west, they tell me. It is a huge if slim flue for a power station being built by Germans and on the face of this squat stone obelisk has been inscribed the foot of a crow, with three talons extending down from a horizontal line, the centre of which lies thirty-four feet, six and five- eighths inches above sea level. The second point on this triangle has been carved onto the side of a bridge three miles east of where I stand now. This structure is old and of British construction and they refer to it as Kjaknu Bridge. It carries a railway that runs west to a large town called Galway, and east to the capital city of Dublin, and beneath this cut-stone bridge runs a canal that leads north to a lake and south to another. They tell me this canal once carried boatloads of flax, then boatloads of people, until it fell out of use. Onto the keystone to the northern face of this bridge is carved another crow’s foot, at twenty-two feet, eight and one-quarter inches above sea level. These three men and I are struggling to place accurately the third point of our triangle into the middle of this stretch of bog before me.

It has begun to rain. The dark undulating hills in the distance have become shrouded in a mist that opens then rolls around these unimpressive summits. The sky is grey in that drab way I would often see, when I was young, in the sky over the shivering countryside outside my hometown, Kazan, on any morning in early spring. The cheerful clipped voices of these three men disappear skyward as they walk a path trampled between long oily openings in the bog. The land reaches out into further plains of brown and black, and tufts of deep green punctured through with tiny wavering dots of white.

The third man, Kolim, a dark and blue-eyed person, drops a dozen stakes. They make a hollow clatter that seems to trigger from behind me the call of a distant crow or raven or an indigenous bird of some kind whose name I have not yet learned. The second man, Mehl, a balding and bearded person, tips from his arms his stakes, then rubs his hands together while smiling impishly – raising his eyebrows as his thinning dark hair lifts from his forehead and stands for a few shuddering moments, then falls. The first of these country men, Rhatigan, creaks out the legs of his tripod. He speaks calmly to his men as he scans the leaning land, while beckoning me, in turn, out onto it.

When I was sent by the Soviet state to London to further my studies in calculus, knowing I would never become a great mathematician, I strayed instead into the foothills of anthropology. What I lack in my ability now to read numbers I make up for with my ability to read people; and I know these people here will never triangulate this land accurately because this land, as far as I can tell, sits upon a lake, of which they seem completely unaware. When I watch them walking across the surfaces of this place, these people suddenly list or stumble, or some days they simply fall over, as if, unbeknown to them, they are on the deck of an enormous ship heaving upon a distant subterranean ocean on a gusty day. Then they pick themselves up like nothing has occurred and continue on their way. I can feel these small shifts in the ground beneath my feet too on days when the dark seas far below must be rough. I picture descending labyrinths in the hull of this ship, shaking around terrifyingly, scaring the crew hands within. Sometimes, on these choppy days, when Rhatigan invites me to the tripod and I lift my spectacles and look through the lens of the level perched on top, with its crosshairs trained, say, on the centre of a distant chimney pot piercing the ridge of a small thatched house, issuing climbing strings of smoke from its cup, he utters: ‘Can you not see that, Nikolai? The chimney, moving across the vertical, then above and below the horizontal.’

‘I can,’ I usually reply.

‘Ground vapour?’ he usually asks.

And he always looks doubtful when I nod to his increasingly convenient postulations, and in his doubt he has begun, I feel, molecule by molecule, to see through me. He will soon see that what is in me, is not what I know about the solution here, but what it is I am keeping from him about this problem – that it is the bogland under their feet that is moving and not the buildings in the distance. I will tell him soon that he is better to use the navigation tools of the seagoing vessel here – the sextant, the chronometer. I will tell him, just before I board my train to Dublin on my route back to the Soviet embassy in London, that he is better to turn away from the Euclidean rigidity he has been employing here up to now, because planes of that kind rest too brittlely on soaked-out places such as this.

I pull my collar up on my neck, tug my cap over my spectacles and step down onto the bog.

Rhatigan dangles an inverted bronze cone from the end of a follicle of shining copper. He is in his late forties, grey- haired but well preserved, and entirely engrossed in his work. The plumb, swinging between the legs of the tripod, is seeking in the wind its centre over a ten-foot iron stake that was hammered into the ground the day I arrived. Six inches above the peat hovers a circular head plate with lurid red and white concentric diameters printed upon it. The circumferences decrease to a circle the size of a kopek and in the middle of this circle a tiny dot has been etched, and somewhere within that tiny dot oscillates the secondary benchmark we are trying, in theory, to place into this expanse.

‘Look,’ says Rhatigan, nodding towards a black cloud rumbling up over the ridge of the distant hill.

‘Kolim, Mehl; leave the stakes. We’ll take shelter!’

The rain drums onto the roof of Rhatigan’s auto as we slough off our coats. The land outside has now disappeared behind this odourless curtain of passing rain. There have been many far more intense storms here this week.

‘I had a thought,’ says Rhatigan, as Kolim, turning from the front seat, flares a match then lights a cigarette, ‘we’ll stake out across this parcel in triangles. The parallelograms feel like points too many.’

Kolim exhales a cloud of smoke across the land map upon which Rhatigan has neatly drawn a grid of squares expanding across a segment of near-featureless land. As the smoke lifts, this grid of squares reappears, pinching to a point in the middle of the indicated trunk road – from where stems the corner of another square, leading to others spreading outward across the land and penetrating this bog in which we shelter from the rain. Rhatigan pencils diagonals through an interlinking line of squares; then, he hopscotches his pencil tip across the drawing, ending at a pillar – the entrance to a house burnt down fifteen years before, or so they told me one day, with barely concealed ardour, almost as if they had done it themselves. A ‘planters’ estate’ they called it.

The rain passes and brings with it a weight of air. We pull on our wax jackets and step down again into the glistening bog.

Two hours have passed and the sun is shining. Our coats lie in a mound to the left of Rhatigan who is stooping, in the distance, to the tripod. We have set out fifteen equilateral triangles across this parcel of land and Mehl and Kolim now trudge back to the auto to collect further armfuls of stakes.

It was fifteen years ago when I first met Rhatigan. He was on a state research trip to Kirov, visiting the largest of Glav Torf’s peat-extraction works and power stations. He came with another Irish engineer, referred to as Oleeri, and their chief, a large man called Glenin. They had flown in some days earlier from Berlin and had been brought on a tour of institutions in Moscow, then Leningrad, then east to us. I was the de facto receiving dignitary at Kirov. The vice- minister for peat had fallen ill and I was dispatched to take his place. I was then instructed to stay there – one of many confusing and paranoiac demotions during that decade. In Moscow they met Minister Malenkov, then a senior state official, a brute, for whom a few years later I would work briefly at the Special Committee on Rocket Technology. At Kirov, we received message ahead that none of these visiting Irish men drank alcohol, but that luckily they all smoked. We wondered what strangers from distant lands might say to each other over the course of an evening if they cannot drink together. This Rhatigan was with us to learn how to ‘win the peat’, as he said often.

Each day he’d wake at four, call us from our rooms and would not relent until after ten in the evening. Each night, as if marking the day’s progress, he’d drink, with a militant moderation, a glass of milk in our company, before retiring to bed. On his first evening, as if trying to impress on us the special difficulties he faced back in his homeland, he pointed to his glass of milk and claimed that ‘there is more dry matter in that glass than in most of the bogs we are aiming to win’. The men from each department at Kirov were glad to see him go. They found his innocent diligence irritating. I accompanied him each day around the land, drainage-systems, railways and works, translating our ideas, processes and problems into English, for him to nod to and make endless notes. I’d observe him as he wrote his lengthy jottings, his head and abdomen bowed into a hunch over his raised thigh, scribbling with a stub pencil into his yellow notebook. On his final night in Kirov, he and I stayed up late, after all of the other delegates had retired to bed. Rhatigan told me about his homeland, the ties they hoped to forge with us, his pride in his new country and the sacrifices they had made. He then told me that he had killed his brother during the Civil War. He and two of his comrades walked this brother, Charles, to the side of a bog and put a bullet into the back of his head. Rhatigan’s hands trembled on his lap as he relayed this to me. And as he stood and clumsily made to embrace me, before he left silently for bed, I realized that he had not spoken of this to anyone for some time, if ever. He and his two research colleagues, this Oleeri and this Glenin, left the next morning before I could speak to him again or bid him farewell.

Then, one day some years later, while I was returned to Leningrad once more – this time to revise and re-translate into English a paper my great-grandfather had composed over three-quarters of a century before, on the geometry of curves – I decided to write to this Gunter Rhatigan. I wanted to know how well he had learned from us. I wanted to know how their research trip had served them. I wanted, in truth, to make contact with him again because I had then lost the second of my two only friends – Matvei, a scriptwriter. His passing had compounded the loss of my other friend from years before – Gusev, a sculptor of abstract forms, who had perished in a camp in the north. Some weeks after I sent my letter, Rhatigan responded, informing me that he and his Irish colleagues were doing well, that they had ‘drained and won over a large bog in Offaly, and a smaller one of fifteen hectares near Kildare’, and that their work, railways, machines and housing projects were on schedule and that they hoped to extend ‘into the Midlands’, where they intended to continue enacting what they had learned from us in Kirov years before. I wrote back immediately; and this began our years-long correspondence, which has culminated in Rhatigan’s recent request for my help in measuring this troublesome piece of land.

Rhatigan approaches flinging his cigarette stub into a puddle.

‘Nikolai,’ he says, in his thin voice, ‘you know you’re not obliged to accompany us here all day; we can easily report to you in the office.’

I tell him that I can really only advise on the processes of measurement I see.

‘And what would you advise, Nikolai?’ he asks. ‘Dublin’s getting impatient.’

He is smiling a pained smile, the large gap between his front two teeth showing.

‘Can you make available an hour in my hotel bar this evening?’ I ask, to which he nods.

Kolim and Mehl return and drop their armfuls of stakes at our feet. I pick up the twenty-two yards of chain and we string it out into the wet land. Rhatigan returns to his tripod, steps in behind, pulls focus and indicates Kolim left, then right, then left once more, all the while his head obscured behind the glinting theodolite eye. I wonder, from there, can he see dejection in our expressions. He gestures Kolim to stop with the upraised palm of his hand. It shines white in the sun. Then he points his index finger downward and Kolim pushes a stake into the ground; Mehl thumps it with the sledgehammer, and again. We pin one end of the chain to the stake and walk at an angle out twenty-two yards, until it pulls taut, then we look back to Rhatigan in the middistance, still leaning into the tripod, his hand in the air shuffling Kolim over and back in tiny steps around a point somewhere in the black peat below.

2

The front bar of the hotel I’m lodging in for the duration of my visit is quietly hosting the last few billion rays of the day’s sun. It is a summer’s evening, even though during the day it felt to me like an afternoon from early spring and a morning from late autumn. Groupings of men stand in the light at the end of the bar, smoking cigarettes. More sit to the rear on timber stools eating sandwiches and moment to moment taking sips from glasses of a shining black drink they call ‘porter’. Then these small men utter words that are largely indistinct to me. They are affable, but none over the whole of my four weeks here have sat with me. They bid me ‘hello’ and ‘good evening’. The wealthy farmers who come each week from the livestock mart in the town to the east have yet to arrive. Mister Leevee, the owner of this hotel, stands at the bar rubbing down a tap. He is one of the roundest creatures I have ever seen. He moves, if he moves at all, at the rate of schisms. Then, he materializes.

In my leather satchel beside me are bundled my drawing tools: a variety of ropes and ribbons – white, blue, green and red. I have a spool of thread too and a ball of pink wool.

On the table lies open a letter, delivered today, ordering me back to Leningrad to take up a ‘special appointment’. The letter is unsigned, merely a stamp on its bottom corner. I finger it a moment and wonder what is being said about me back at the State Geometers’ Office and what is being said from those there to those in the MGB offices from where this letter came. In the pit of my stomach bubbles a pool of bile; I want to take a match to this pool, light it and burn it away, then take the match to what remains.

An old gentleman, carrying a hammer and a trophy made of what looks like brass and marble, stomps in through the swinging door of the hotel bar. He is stout and his hindquarters protrude in a way that thrusts the top half of his body forward, as if he smells the world first before he sees it. He approaches the bar and orders a drink, climbs onto a high stool and swings himself out to the floor of the bar, which is simple, dusty, dry. The expansive fireplace at the other end of this irregularly shaped room has, from the broad sticks in its hearth, begun to smoke and crackle. This gentleman, whom I would estimate is in his late sixties, doffs his cloth cap. I am sure I have not seen him before. I nod and return to my notebook. Then I hear his hammer being lifted with a scrape from the bar, and out of instinct I look up.

‘I’ve another thirty of these,’ he says, looking at me, waving this small lump hammer beside his large round head.

He thuds the hammer back onto the bar, then fixes his glasses and peers at my notebook as if it were an exotic bird. I push it closed, folding my letter within, and he continues, ‘I’ve thirty of them above in the museum.’

‘Hammers,’ I reply.

‘Thirty, all the same, but different, and those are just for beating lead. I’ve another thirty for cobbling and building.’

‘And the trophy?’

‘You’re not from the Midlands, are you?’

‘I’m visiting from Leningrad – to help Mister Rhatigan … The trophy?’ I say.

‘Bill Makonel’s man-of-the-match award for the ’35 county final,’ he says. Then he leans forward with a creak, and as his face breaches the shaft of softening sunlight between us, he says, ‘Tell me now, boyo: How’s Uncle Joe? Still slaughtering away over there, is he?’

I smile.

He sits back.

‘I don’t like Commies,’ he says.

‘I don’t think of myself as one,’ I say.

My friend takes a drink from the porter Mister Leevee had moments earlier placed down on the bar. His little finger is raised as he tips his head back. He swallows, in mechanisms, then pushes the back of his hand across his mouth. Other than Leevee receiving an order from the opposite side of the bar, there is little being said. A horse and cart pulls in off the road. A cluster of children pass, talking quickly as they skip and lurch, one with two upturned metal buckets tied to her bare feet, raising her above the others as if she were on stilts.

‘And how’s Bermuda treating you out there?’

I look up and see he is smiling at Leevee, who has reappeared at our end of the bar once more. My friend looks back to me, over the rims of his glasses. His eyes are dark and one has been damaged. He looks jaundiced, and I discern he might be a bachelor.

‘It’s a difficult project,’ I reply.

‘If it has the beating of Rhatigan, then it must be.’

And there is a pause.

He rubs his lips again, and sips from his glass. He places the porter back, but he is still looking at me, his arm making an awkward shape as he searches for the surface of the bar.

‘You know I’ve Russian bullets from the last war too,’ he says.

‘In this museum?’ I reply. ‘I like to visit museums.’

‘I don’t tell many about it. But then I don’t have you down as a thief. Tell Rhatigan to drop you over some evening and I’ll give you the grand tour.’

The door swings open to my right again; a tall and slim man enters.

‘Shaihmeen, you’re early,’ he says.

My friend turns, looks over his glasses at the tall and slim man entering and replies, gesturing lazily towards me, ‘I’d an urgent meeting with the Russki here.’

‘Rhatigan’s aide,’ says the man, looking down at me.

They greet each other in the way men, I notice, usually greet here – on the cusp of shaking hands until the moment or moments for handshaking ebbs and their bodies relax into a shape that most allows for the sort of idle chatter that seems, between the silences, to flood the place.

I remove my spectacles, rub my eyes, then order another whiskey from Leevee and a glass of porter too. As he turns to prepare my beverages, I grasp my notebook, stand and leave the bar. I go to the front wall of the hotel to take some air. It is warmer outside. There is an old man leaning back on the windowsill, his face turned to the evening sun. He’s smoking a cigarette and appears to be in a trance. I bid him a greeting and open out my letter.

‘Special appointment,’ it says. ‘Return to Leningrad and present by the 12th of May inst.’

I try to pinpoint what’s finally ruptured the film of seeming untouchability that has protected me since graduation from university. Perhaps they have located my letters to Gusev. We met at army training camp in ’37 where we both then also befriended Matvei, the young scriptwriter, frustrated at this year of training keeping him from the work he loved. It was this feeling of fear and frustration that drew the three of us so close. Then, one day Gusev heard his father had been disposed of and the next he himself was gone. It was not until one December morning in ’39 that I heard from him again. I had returned home from London and I met my dear Matvei near a train station in Leningrad; he had a stack of unopened letters from Gusev. I wrote back to him immediately, but each letter took a fortnight to arrive at the wood combine, at the farthest reaches of the north, into which poor Gusev had been cast two years before – branded an ‘Article 58’ subversive. That he was not killed, he claimed in his first letter to me, was ‘the greatest miracle of the ’30s’. We continued to write for six years, up to his final disappearance, no matter where I was stationed, even during the War when I was hospitalized for months with a snapped shin, then sent to the power station in Kirov once more, to organize the storage of paintings and furniture moved east from the Hermitage. These paintings came without their frames and, as I stacked and itemized each canvas in the cellar in Kirov, I often pictured a multitude of empty frames covering the many walls of the vast Hermitage many hundreds of miles west of the huge and dust-dry cellar where I spent my days. Each of my letters to Gusev was directed through Matvei’s uncle, a voluntary at the same wood combine where Gusev was imprisoned. Perhaps, even though Matvei is dead six years, someone has finally unearthed my letters to Gusev.

I fold the official missive away. The old man, who seems to have lifted clear of his trance is now waving to a person approaching on a ticking bicycle. I squint for a few moments at this smudge of dark blue emerging from horizontal bands of grey and brown and green and sky blue. It begins to gather into the shape of a police officer. He pedals into clarity, and dismounts.

‘Paskal,’ he says.

‘Sergeant,’ the old man mutters, as he steps past me, returning indoors.

‘I didn’t see Rhatigan yet today,’ says this policeman, a man they call Makaihb. ‘He’s gone off radar. I needed to call out myself. Can you sign and I’ll be on my way.’

As I scribble my name onto this page, he asks, ‘And how’s the work progressing for ye out yonder?’ Then he pulls his watch from his pocket and checks it.

‘Very well,’ I reply.

‘Good men. I’ll be off.’ And he turns, lifts his bicycle away from the wall and as he pedals across the forecourt and onto the road his form re-disintegrates into a vertical daub of dark blue. It shivers for a while until it swerves then disappears again into the soft broad bands of green and brown and mauve. I return indoors to my table and, as I put my spectacles on, the world around me sharpens back into itself and I can hear the two men at the bar cackle hard.

A few hours later, and I see the bob of a white circle of light belonging to a carbide lamp break the navy darkness outside. The light is suddenly extinguished. The bar is now smoke-filled and raucous. Four of the wealthy farmers who are driving back towards the West are exceptionally drunk, far drunker than I have seen them before. They seem to be celebrating the sale of a particular herd or a particular prize animal. The hammer and the trophy have changed owner- ship, yet the two men still sit drinking and leaning in towards each other whispering about further treasures. Leevee is joined now by his wife, Nell. She is so incongruously slim beside him that all I can think of when I see them standing in what seems to be a rather frigid proximity to each other is: their marital bed. She has short dark hair and white acne- scarred skin. She has grown into handsomeness and she is kind to me. Each morning she asks quietly if I have slept well and if there is anything I need to make my stay more comfortable. I tell her that everything is in order.

I gesture across the room to her for another whiskey. I have had four large glasses now and the same number of porter. None have dulled my anxiety. The whiskey is passable but this porter, though sweet at first, bloats me badly and gives me a headache.

Rhatigan stands at the door, frowning at the room. I can tell from his disdain that he views all drinkers as beneath him – puppets acting out a distasteful play. He sees me, and his face softens. He strides through the smoke and takes a seat, produces a cigarette and offers me one too. I take it and light it from his struck match. I find his hand cupping the flame, coupled with the way he stares with such intense care at the end of my cigarette, moving. I suck, and he pulls the match back towards his own cigarette, sucks, then shakes it out and mutters, ‘Christ, I haven’t been in this place for a while.’

‘I decided to take a drink,’ I say.

‘No harm sampling the local fare,’ he replies with a smile. ‘Little else to be doing out here I suppose.’

‘I talked with that man at the bar,’ I say. ‘The museum owner, Shaihmeen …’

Rhatigan shakes his head, ‘French? A museum owner? – ha!’ Then, looking at me and perhaps seeing that I find all of this plausible, he continues, ‘Well, okay, now you say it, I suppose it is a museum of sorts. He collects and sells and collects to sell again and collect, and if that’s not a museum owner then I suppose, yes …’

‘He invited me to visit.’

Rhatigan’s eyebrows raise as he smiles once more. He seems impressed that I’ve gained an invite from this Shaihmeen French.