In another life, he thought, he’d have been a geographer. The drawing of maps, sinuous treks, modelling landforms would have filled his days. He was born in a valley, not in Canada but in a village called Llangattock – in the south of Wales – as ruggedly Welsh a landscape as you could ever hope to find, as Welsh as his surname, which was Bowen, and though he left with his family as an infant, the misty hills and the ever-changing light had become a part of him and stayed with him always thereafter.

Vaughan remembered better Walton-on-Thames, the market town south of London where his mother, a reverend’s sudden widow, had found work teaching schoolchildren religious education. The transplant of the Welsh valley family to an English suburb succeeded, but not without rendering the Bowen brothers conspicuous. Their mother said things that were funny to English ears. She said ‘daro’ if she dropped something and what sounded like ‘dew dew’ for ‘well, well’. Vaughan did not speak like this. His accent was his own. He only mumbled and blushed when he started primary and promptly learned that he was fatherless. The English boys meant no harm by it – might their Welsh counterparts have been crueller? The boys in Walton simply meant to ask what it was like, but Vaughan had no way of answering. He’d never thought to consider it. Several of the older boys almost envied him and half regretted not being fatherless themselves – they fantasised fathers who had swollen up from the sting of a bee, sleepwalked off a cliff or been struck down by a Rolls-Royce. As if the glamour of such a passing might set a son apart.

No old man, they said, to give them a clip on the ear or worse.

Certainly Mrs Bowen knew how to hold a classroom, and at home she could tell off for two. She had four young sons to feed and clothe and she expressed her love in never-ending instructions: ‘Ych a fi, go and wash your hands! Pass me your coats! Fetch some mint and apples from the garden!’ She made every shilling of her salary go as far as possible.

With little money for toys, Vaughan and his brothers spent their free hours rambling about the town and outlying fields. He thrived on the fragrant air which smelled of recent rain and of grass crushed underfoot. In his memory, sunlight accompanied him across the browning grass beside the railway station as he walked parallel to the tracks. More so than his brothers he’d delighted in treading the same ground that carried these tracks for miles. The first time out here – sixty-something years ago, back when his life was only a life and not yet a story – an exiting train chugged past him bound for London. Full of sudden wonder, he stopped near the tracks and waited for the next one to pass. Presently he heard a clanking of rods and felt the air start to shudder and caught sight of the growing train fogging the air with its white puffs of smoke. He could taste the train – it tasted of smoke and hot metal and his own dry mouth.

He would have happily stood there all day until he ran out of trains to spot but he recalled then that he had a mother and dinner and a bath to be returning to.

In retrospect, it had been the beginning of everything: his whole life he could trace to that encounter with trains – so startling and stimulating. From that moment on he’d begun to catalogue data, classify, subdivide. Many an afternoon and weekend, he stood near the station and consigned all the passing trains’ names and numbers, wheels and sizes to a little notepad, and the thrill never waned as the familiar, delicious smoke approached and the platform became the scene of a minutely timed drama. ‘Union Castle,’ he wrote in biro under ‘Name’ and the date – 16/4/61 – along with the locomotive’s number, 35002, and its wheel arrangement, 4–6–2, while brakes groaned and a whistle flared and passengers clambered down or boarded.

He was also learning to dissect space and time, in railway stops and timetables.

Sometimes, for a treat, when family tickets were going cheap, his mother took her boys on a day trip to Southampton. ‘Hurry up,’ she’d shout as they ran with their bags along the platform, ‘or we’ll lose the train.’ They ran with heavier bags in the summer, when the Pembroke Coast Express transported the Bowens from Paddington to Swansea, to the hill overlooking Mumbles Bay where the grandparents lived. As they rode, all along the track quarter-mile posts reared up and whipped past, and from his window seat Vaughan counted the seconds between the posts to gauge the speed.

He’d hardly told anyone before Anu – Anu Sharma-Niwa, his psychologist in Calgary – that one of the reasons he’d gone on to study medicine in Edinburgh was so he could thunder up and down the coast aboard the Flying Scotsman. The journey always swift and sleek. Now that was what he called a train! He’d catch the 10 a.m. out of King’s Cross, with only the one stop in Newcastle. Sitting back, absorbing the steady hum of the diesel electric engine, watching the world roll by at 100 miles an hour.

Anu, whom he’d found online in 2012 at the collapse of his marriage of thirty-four years, proved a worthy successor to Frank, the doctor who had rescued him from his first breakdown in the seventies. She listened sedulously as Vaughan told her all about the trains and everything else besides, session after session, following which she’d found the words – words unavailable or unthinkable in Frank’s day – to explain that he was a savant and in a career perfectly tailored for him. ‘Autism?’ he’d repeated, seated for the first time in decades on the patient’s side of a desk. Autism: a retarding mental illness that renders children unable to function in society. Or so he’d been taught during his early seventies medical training. How inaccurate those textbooks had been. How misguided.

And so he had discovered in himself this enlightening autism, this savantism, at the age of sixty-three. It clarified so much, fed his self-discovery and confidence.

So that, ten years on from these early sessions with Anu, he could relate everything again to a youngish man named Daniel, corresponding freely with him, sharing all manner of details which had never before left his psychologist’s office, because this Daniel Tammet, aside from being a writer, was also what doctors called an autistic savant. The writer understood things about him that others might not have. Vaughan was excited at the thought of seeing his story put into print. Then, hopefully his ex-wife, with whom he remained on good terms, would come to a clearer idea, on reading it, of the often awkward, silent, confusing man who had loved her as best he could during all those years.

Years that had rolled by at the speed of life.

✲

The day after their rounds of the orthopaedic unit, Vaughan and the American put on gown, gloves and mask and positioned themselves around the operating table. The American observed in silence while Vaughan worked. The older surgeon’s gestures were deft and graceful. His patient had been put at ease with anaesthesia, and between the surgeons and the nurse there was no distracting small talk. The masks and the music – something delicately classical playing low – heightened Vaughan’s absorption in his task.

Head bowed, eyes focused, all his attention went to the slumbering hand in front of him. That morning he’d tended to a young and muscular forearm which for years had lobbed and served and sliced drop shots; in its place now lay a middle-aged thumb hampered by arthritis. Where the incision had been made, he could see past layers of skin and fat to the basal joint. The sight was familiar, blood and bone had never aroused any squeamishness in him; he was fascinated by the body’s intricate networks of nerve, artery and tissue, all those inner parts that go unseen and on which our visible surfaces depend. What things of beauty, of nature’s ingenuity, the violin strings that are the tendons! And the wrist bones shaped like a boat (the scaphoid), a crescent moon (the lunate), a pyramid (the triquetrum) – three among the twenty-seven bones in the human hand. In his mind’s eye, he could picture each one of these small bones in three dimensions, he could visualise their every binding ligament and every muscle, the galvanising sparks and the irrigating scarlet threads.

‘See the joint surface here?’ Vaughan said to the American, as he extracted the bone fragments one by one. ‘That’s the arthritis.’

Minutes later, ‘See here, the cartilage has all worn down.’ Then, addressing the nurse, ‘Give me a little traction, please.’ Then, to the American again, ‘Now I’m opening a channel in the trapezium.’

He was repeating the one he’d just opened in the trapezium in his mind’s eye. Deep into the joint he drilled. Close by, surrounded by forceps and scalpels and scissors, the implant to replace the patient’s lost bone shone bright. It was made of titanium – strong yet light and ductile and practically, most enviably, unbreakable.

The operation took just over an hour and was a complete success. Vaughan peeled off his scrubs and soaped his hands and smiled. He had barely stepped out from the operation room when he saw a woman approach him with a sheet of paper. He nodded when she said something about a schedule, less to signal assent than to cover his confusion. The woman thrust the sheet into his hands, turned on her heels and went back to her office. Only then did he realise she was his medical office assistant of twenty-plus years, and his face burned in embarrassment. He’d tried memorising her hairdo, and the comfortable jumpers she favoured, for all the good it had done him. At least she had been with him long enough to understand. From his earliest days, his memory for faces had been dreadful. He always imagined his assistant sitting attentively behind her desk, or busy with the phone. Without her desk, and walking to boot, he struggled to recognise her.

✲

Sometimes he wondered whether it had been quite the same for his grandfather, this near-illiteracy when it came to reading the expression on a face.

Vaughan’s resemblance to his mother’s father was in no way physical. He remembered a very short man, bow-legged (rickets was his medical opinion later on). It was rather his grandfather’s unusual mind that he’d inherited. A trained surveyor’s feel for geometry. A talented retailer’s head for figures. An eye for minute detail. Not that he understood this for a long time. John Sydenham Richards of Swansea, known in those parts as JSR, or as Papa by his grandchildren, was already an old man when the Bowens spent their summers visiting the grandparents. He was something of a local character, a staunch pillar of the community: he put the Richards into Manning, Martin and Richards, wholesalers formerly of Union Street. ‘Matting, Mats and Rugs’ proclaimed their slogan. They also sold linoleum, Acme wringers, Newmaid suction sweepers, paints and cloths. Inventorying would have been for Richards, the director, what trainspotting and medicine would become for his grandson.

It had never occurred to Vaughan to make these connections until quite recently – until, that is, the day back in the UK when a brother showed him one of their grandfather’s many diaries. He showed him 1939. It was pocket-sized and filled with meticulous, vigorous handwriting. Every page was not only dated but also timed. Vaughan’s brother flipped the pages to July, to the eighteenth, which had separate entries for 8.30 a.m., 9.15 a.m., 12.50 p.m., 3.23 p.m., 3.30 p.m., 4.45 p.m., 6.32 p.m., 6.34 p.m., 6.35 p.m., 6.37 p.m., 6.38 p.m., 6.40 p.m., 7.00 p.m., 7.10 p.m., 7.30 p.m.

On 18 July 1939 their grandfather and his wife May were holidaying in Bergen, Norway.

‘4.45 p.m. Harbour of Bergen. Loads of fish being transferred to a ship for England. All motor cars on Quay appear to be American. Passed customs in shed. Walked along Quay to Hotel Rosenkrants,’ he had written.

‘Keep reading,’ said Vaughan’s brother, his voice almost hushed. ‘Papa counted everything!’

‘Room No 309. Lady’s Gent’s cloakroom. Sitting room. 3 couches. Writing table. 3 tables. 2 armchairs. 2 chairs. 1 writing stool. Telephone. Cabinet. 19 lights. 2 reading lamps. Sewing materials. 3 radiators. 2 twin beds. Bath. Wash up. Lavatory (W.C.). 4 Drinking glasses. 6 towels.’

In the day’s next entry, timed 6.32 p.m., their grandfather had described going up the ‘Floibanen or funicular railway’ where he’d met an Australian tourist and enquired after her name, maiden name, occupation and address. (Mrs Freida Moyle. Miss Freida Walker. Calculator Bookkeeping Machine Expert. 20 Queen Street, Melbourne.) ‘Beautiful view of Bergen,’ he’d jotted down then, just before noting the ticket fare: ‘1.50 Kr each return. 3.00 Kr two persons.’

But for these diaries, passed down to his brother, Vaughan would have known nothing of his grandfather’s inner life – and of how much more than blood they shared.

He thought of his grandfather’s father who had launched the family business in the 1870s. His great-grandfather had left a rural hamlet for Swansea to set up as a wholesale grocer and butter merchant. Between father and enterprising son, the name of Richards had traded proudly in the city for a hundred years. Vaughan liked to think that certain autistic traits – tremendous focus, attention to specifics, imaginative somersaults – had played their part in the family’s flourishing.

His mother had not inherited her father’s strange mind. It seemed to Vaughan that there was more Richards in him than in his grandfather’s eldest daughter. A chatty woman, his mother, always at ease with herself and other people and leery of spending much time alone. It was possible that her son’s inwardness and intense gaze intimidated her. Chatty as she was, she never opened up to him. Or maybe, just maybe, she had, or had tried, and he’d simply not understood.

There were times as a boy he’d wanted her to assuage the distress, the confusion, inside him with a well-chosen sentence. He’d wanted her to make everything clear in his head so that he might breathe more easily. But the times were flat against that; very few people talked about feelings in the fifties, the early sixties. Except perhaps the gossips. Language back then was strictly policed. Always you minded your language, watched your p’s and q’s.

When Vaughan turned nine the distance between mother and son grew miles wider. He became a boarder at a free independent school for fatherless boys in Hertfordshire. Yearround he lodged there till he went up to Edinburgh at eighteen, returning to his family only for the long school holidays.

One summer, he returned to an empty house. He was twelve or perhaps thirteen. The holidays hadn’t arrived yet in Walton-on-Thames and he walked to the school where his mother taught. She left the blackboard and told him to wait for her in home economics, where the children were busy baking bread. He was getting tall as well as lean, with a long fringe and bright eyes, and the girls had looked up and smiled as he joined them to knead the dough. No need for him to follow a recipe. Vaughan often assisted his mother in the kitchen. She baked a marvellous teisen lap – sweet and buttery with a hundred raisin eyes. Standing beside her at the counter, he would observe the flour as it snowed. ‘Pass the whisk,’ then ‘pass the spatula,’ she would say and he would pass her the one, and then the other, quick, quick. He’d hear the regular clinking in the mixing bowl. Feel the dip of a spoon. Feel important, like those Sundays when he broke the skin on the rice pudding.

The smell of the bread baking in the classroom. A warm, homely, informal smell. It tortured him, the memory of it, weeks later, as the autumn term loomed. Not even the prospect of riding the railway out of Waterloo could lift his spirits in the slightest. How he despised his school, its cold dorms and colder housemasters (with names like Clotworthy), the plummy voices which droned on and on for what seemed to him like days, the frightening rifle target practice. To say nothing of the awful beatings. And indeed not one word was breathed of any of this during visits home. Only as an adult, nearing thirty, would Vaughan start to articulate what he’d been through, the damage done to him, confiding in a doctor in the Canadian hospital where he worked after immigrating. Until then, he’d supposed the fault lay somehow with him, and felt the ordeal far too shaming in any case to ever mention.

Before this doctor, Frank, he’d dared not address any man by name. ‘Sir’ and ‘Professor’, and later ‘Doctor’ had been the rule: ‘Dr Bowen?’ ‘Yes, Dr Green?’ or ‘Yes, Dr Smith?’ And as for calling his mother by her first name, well, perish the thought!

‘Call me Frank, Vaughan,’ the doctor had said gently. In 1976, if memory served him right. That year, and over the following years, Frank would lead Vaughan out of the darkest caverns in his mind, just as Anu would decades later.

Even now he felt twinges of regret at losing touch with Frank after moving to another city. He had always been bad at looking people up, asking after them. He’d learned of the doctor’s death in 2004 from a years-old obituary republished online. In 2004 he might have thought to call his mother in England with the news. Remember Frank? Dr Frank Coburn? Not a chance. By that time, she was always losing her train of thought.

The memory of mother’s teisen lap. Where had that come from? And why did it have to remind him – of all things – of his boarding school thrashings? Spoons and spatulas. Clotworthy. Frank’s kindly gaze.

Vaughan had always been dexterous – he could pick up and repair a shattered vase, shard by shard, repair a hand bone by bone. But the fragments of a mind – that was something else altogether. So hard to grasp and reassemble.

✲

Of the thousands of patients he’d treated down the years, several had left Vaughan puzzled. In his memory, two – a young woman, and an older man – stood out most sharply.

The young woman had come in one day with a forearm needing surgery. His assistant had recognised her as a recent patient, ushered her into his office and handed him her file. Vaughan proceeded to inspect the young woman’s forearm. According to the file, he had operated on her months before, but there was a problem. She had no scar.

‘Oh, that was my twin,’ the young woman said.

Were the two sisters so identical, Vaughan wondered afterwards, that they had developed the exact same low bone density in the forearms? Or, had the scar on one, throwing off their symmetry, incited the other to undergo her sister’s operation?

The older man – a driver in his fifties – had had his wrist crushed in a collision. The wrist had necessitated a big operation, lasting hours, but no sooner had the man’s anaesthesia worn off than he discharged himself, saying only, ‘I have an urgent flight.’ The sole address he’d left was a box number in a Chinese city. He had no healthcare insurance so Vaughan did not get paid.

Then, one day, eighteen months later, Vaughan’s assistant phoned him. ‘You will never guess what just happened,’ she said. Did he remember the man with the Chinese address? Well, he’d just left a bulging unmarked envelope for him with her, which she’d opened. Inside was the fattest wad of used $20 bills.