The treatment of a fracture is not difficult, and is almost any practitioner’s job.
Hippocrates, Fractures
A YEAR AFTER FINISHING the job in Antarctica I flew out to West Africa to learn about the work of my friend Stephen, a paediatrician. He was carrying out some research on malnutrition, and running a back-country clinic near the Gambia’s border with Senegal. The clinic lay to one side of a small village community and did basic, vital work as well as research: minor injuries, treatment of infections, pregnancy care, nutritional advice. There were no X-ray facilities and few drugs. Every morning as I ate breakfast I’d watch a queue lengthen from the clinic’s front door along a shaded walkway and out into the surrounding trees. I had little experience of rural tropical medicine then, but hoped to learn.
It was April, the hottest month of the year, and the temperature climbed over 40°C. In the hottest part of the day it was impossible to work: I’d lie still in a hammock strung between two trees. The wind that came scorching out of the Sahara was like a furnace blast, warming the skin rather than cooling it. Within a year my skin had passed through a hundred degrees of heat – from the fifties below zero in Antarctica to the forties above. Vultures sat panting in the dust, wings outstretched to cool themselves, the way I’d seen penguins do when Antarctic temperatures approached the melting point of ice.
The sun fell so swiftly that there was little sense of an evening, but when the day’s clinical work was done, and the temperature became more bearable, I’d take a walk through the village. Though at times it felt remote – there was no phone signal after 5 p.m., and the internet connection was vestigial – there were hints of the wider world. One of the village’s earthen huts housed a bakery: when flour arrived from the coast you’d see smoke from its chimney, and know that there’d be French baguettes on sale. There was a small shop run by a Mauritanian pedlar, who sold lanterns and buckets made in China. Those goods were imported by Lebanese merchants who’d been settled for a century on the Atlantic coast. As he worked, the pedlar listened to the BBC World Service in Arabic.
If there was time I’d continue on towards the river, beneath a spreading mango tree, down an avenue of baobabs and through thickets of man-high yellow reeds. Beyond the reeds there were squared ridges of dry-baked soil – rice paddies in the wet season – then some mudflats and, in the distance, the brown slick of the river. I’d been brought up with the reliable rivers of northern Europe, but this was something altogether different: briny and unpredictable, an oily wallow of mud, fed by the fickle rains of the Saharan fringe. Lungfish flopped into holes at my approach, breathing heavily. It seemed a land where categories were unstable, and the unexpected was routine.
‘GEOMETRY’ MEANS ‘measurement of the earth’, and as a science it has its origins in ancient Egypt. It was used to calculate the land available for agriculture as the water level rose and fell in the fertile Nile delta. One of its foundational texts is Euclid’s Elements, written in Alexandria around 300 BCE – said to be the most influential textbook ever written, second only to the Bible in terms of the number of editions that have been printed. It starts with defining terms (‘a line is a breadthless length’, ‘a boundary is an extremity of any thing’) and goes on to postulate various axioms (‘the whole is greater than the part’, ‘all right angles are equal to one another’). From these definitions and axioms it constructs a whole mathematical world, then tames it. Proofs tumble from its pages. One of the most famous of its proofs shows how the two basal angles of an isosceles triangle must always be equal. In the Middle Ages, scholars gave this proof the name ‘Bridge of Asses’, because students who struggled with it were unlikely to progress.
At school I always enjoyed mathematics; I liked its absence of words, the way it encouraged visualisation of the infinite, and its reliable delivery of neat conclusions – at my level at least. There was pleasure in mastering each new technique: now the circumference of a circle, now the length of a hypotenuse, now the gradient of a curve. Calculus was particularly satisfying – a kind of arithmetical magic. That a string of letters and numbers could be transformed into a sweeping parabola was an unexpected delight.
I learned that one inventor of calculus was Isaac Newton and that for him transformation was a universal, elemental process: everything in flux that could be measured and portrayed in algebraic form he termed a ‘fluent’. His mathematics summoned a world of ceaselessly changing rivers of numbers. He invented calculus to describe the rate of change of each fluent, which he called ‘fluxion’.
The word algebra is Arabic, al-jabr, which means ‘bonesetting’. Although there are hints of algebra in ancient Greek texts such as Euclid’s Elements, and even in the writings of the Greek physician Galen, the algebra that we know today was invented in ninth-century Baghdad. The mathematics of algebra was named for bonesetting because it pulls apart two sides of an equation, balances them, then resolves them to find solutions – just as a broken bone could be pulled apart in traction and then made to heal. In southern Spain, thanks to the legacy of the Arabs, bonesetters and barber surgeons were known until modern times as algebristas.
One of the great reassurances of mathematics is that equations work out the same every time. The human way of healing doesn’t fit well into the ethereal perfection of mathematical formulae: it’s different for every individual, and every injury. Mathematics can probe transcendent mysteries such as prime numbers reaching into infinity, or the impossible calculation of negative square roots. The business of human healing is messier, though no less mysterious.
ONE AFTERNOON A BOY of eight was carried into the Gambian clinic having fallen ten feet from a mango tree and injured a leg. He was unable to walk and, sobbing with pain, wouldn’t let anyone examine him. Stephen injected local anaesthetic into the groin at the top of his left leg to numb the thigh, which allowed the boy, eventually, to straighten his hips. His left leg looked shorter than it should have, and his left knee was turned out to one side – both signs suggesting his femur had been fractured. It was a life-threatening injury: femoral fractures can prove fatal either from blood loss within the leg or from pneumonias that set in with immobility. The best way to ease the pain of these fractures is to pull the leg out into traction on a frame called a Thomas splint, which restores the thigh to its normal length and brings the snapped ends of bone together.
Thomas splints are named for a Welsh surgeon called Hugh Owen Thomas, who came from a long line of Anglesey bonesetters – perhaps his ‘innovation’ was simply the adaptation of a family secret. I’d had two of these ‘Thomas splints’ in my clinic in Antarctica and never needed to use them. In the Gambia, where I really needed one, there were none available.
We wrapped the boy’s leg in loose bandages and made a box with pieces of wood lined with crumpled tissue paper – he’d be more comfortable with the leg immobilised, but without the traction of the Thomas splint his leg still looked shorter than it should. The only way to assess his injury thoroughly would be to get an X-ray, which meant a four-hour journey, on dirt roads, to a clinic on the Atlantic coast.
The boy’s father was a solemn old man, stately in his dirty white robe and skull cap. No, he said, the boy wouldn’t go to the coast. He knew someone who had gone there with a fractured leg and had never returned. The boy would come home with him and they’d see a bonesetter in the village.
Some of the nurses began to get angry, accusing the father of child abuse. He was threatened with a call to the police. I tried to explain through interpreters that there was a chance the boy would be crippled, that his leg would shorten and tilt unless it was treated correctly. But with dignity the man simply gathered his boy in his arms and walked off through the trees.
FOR MANY CENTURIES algebra evolved in parallel with geometry, rather than integrated with it. They were thought of as mutually exclusive mathematical systems: geometry was the more distinguished elder cousin, representing the world in concrete terms that were discrete and universally applicable. Algebra was the newcomer, a slippery, Arab-inflected symbolism which, for many in the West, carried a hint of the occult (the philosopher Thomas Hobbes called it ‘a scab of symbols’).
It was Descartes, the philosopher of division between body and mind, who finally unified algebra with geometry. He showed how the two disciplines were part of the same cosmic continuum, that together they could resolve mathematical problems that had previously been insoluble. He plotted geometrical shapes on perpendicular axes that we still call ‘Cartesian coordinates’ in his honour, giving the letter ‘x’ to one axis, and ‘y’ to the other. He had devised a system of mapping shapes of infinite dimensions.
With his division of body and mind, Descartes broke the physical world into parts and processes, heralding the specialisation of science and medicine and unleashing a revolution in thought still reverberating today. And with his fusion of algebra with geometry he paved the way for calculus, for a mathematics of transformation to fit the churning, evolving world.
A WEEK AFTER THE INCIDENT with the boy and the broken leg I drove out with Kalilu, one of the clinic’s nurses, to another village to deliver ‘directly observed’ tuberculosis therapy (‘DOT’). Kalilu wore a neat Islamic beard with no moustache, and wore a black woollen skull cap. His spectacle frames were ornate and golden, and clipped to his nursing uniform he carried a mobile phone. He had a calm air of imperturbability, and told me that he hoped one day to study in the UK. On the drive he told me about the DOT initiative to ensure adequate treatment of TB, and to limit its spread. We roared away from the clinic into the loose, Sahel scrubland, beeping at donkeys and goats that strayed into our path. Baboons loped across the road ahead of us, green vervet monkeys swung up into the trees. There were no road signs, but termite mounds towered along each verge like snow poles. The track was not so much potholed as undulating; sometimes the earth looked scorched, but whether deliberately cleared for agriculture or accidentally ignited by a stray cigarette, Kalilu couldn’t say. We drove past swamps, savannah and rubble-fields of volcanic rocks. The air felt gritty with Sahara-blown sand. The landscape was so beautiful that I didn’t want the journey to end, but suddenly I saw tin and thatched roofs appear through the trees, announced by a tired UNICEF notice: ‘Baby Friendly Community’.
We slowed as we entered the village. Groups of men sat in the shade and waved to Kalilu as we passed. The women were all working: carrying wood, pounding flour. Children ran from the earthen-walled houses to follow the car, surrounding us as we emerged, shouting ‘What-is-your-name-what-is-your-name.’
‘Just say, “Tubab”,’ said Kalilu. ‘It means “white man”.’
He led me to an earthen-walled house with a corrugated steel door; an old woman sat in the shade outside. Beside her stood a naked boy aged two or three who gazed open-mouthed at my pale skin. We went in and called but there was no answer. Inside there were two rooms: one bare, its walls washed in white, a torn cloth mattress rolled up in one corner. The other room was empty but for a well-made double bed and, on it, a dirty throw. We walked back out, Kalilu calling for his patient. A crowd began to gather, then a young woman in an ankle-length sarong and matching headscarf stepped forward, laughing. She directed us back into the house: our patient had been sleeping under the dirty throw.
The man who emerged from beneath the throw was so thin that each joint and ligament, each vein and tendon, stood out as if he’d been flayed. He acknowledged his audience (spectators were crowding into the room), lit a cigarette stub, and with a groan pulled himself over to the edge of the bed. Kalilu poured the correct dose and combination of anti-tuberculous pills into a cup. No, the patient said, shaking his head. He wouldn’t take them. There were too many, and they made him feel sick. ‘See how thin he is,’ muttered Kalilu to me, tut-tutting. ‘He has refused a test for HIV.’ More of the man’s family began to appear, pushing through the onlookers, raising their voices and pointing. ‘They are telling him not to be stupid,’ Kalilu translated, ‘they are telling him to take the medicine.’ Village elders arrived, and gave more indignant advice. Most onlookers seemed amused, but their voices began to edge with impatience. Still the man sat calmly, smoking and shaking his head as the villagers remonstrated with him.
As with the boy with the broken leg, I knew that having treatment available for a particular medical problem didn’t mean that I knew how to persuade a patient to accept it. And then there were the wider economics of his situation: in nineteenth-century Britain, before anti-TB treatments had been developed, death from the disease was directly linked to the sufferer’s level of poverty. Even with effective drugs available, the link between poverty and TB deaths remains stubbornly robust. To treat the man’s TB effectively, he had to be cured of his poverty and, as a doctor, I didn’t have the first idea how to approach that.
I asked Kalilu what he was saying to the man. He said: ‘I’m telling him the tubab doctor is ordering him to take the medicine.’
The man pointed up at me and said something – everyone laughed.
‘What did he say?’
‘“If the tubab wants me to take them, he can pay me”,’ Kalilu said.
Kalilu shook his head and laughed at the suggestion – though hidden within it was the tacit acknowledgement that money was as necessary as medicine in the cure of this disease. Resistance broke: the crowd looked on silently while one by one the man took the tablets, swigging them down with cola before falling back on the mattress and pulling the throw over his shoulders. The women drifted back to their work, the men to the shade, the children to their games.
IN THE FIRST PHASE of bone healing there’s a flare of inflammation, with clotted blood forming around the broken ends, and the body’s immune system provokes pain and swelling. The blood clot becomes a framework for tough, fibrous cells, and the lining of each bone (the ‘periosteum’) transforms into a tissue that can lay down new cartilage and bone. This new bone grows out in a bulbous mass from each end of the fracture, until they meet one another in the middle to form a bridge of ‘fracture callus’. This process may take days with a small bone or weeks with a large one. How close the broken ends are to one another, and how well aligned, influences the speed of healing.
The new bone to be laid down is spongy and frail; over further weeks it is gradually replaced with layered, stronger, ‘lamellar’ bone. Lamellar bone is then remodelled by specialised cells that streamline the callus outline. Sometimes I see X-rays in which the fracture healing has been perfect – there’s little sign on the image that there’s been any injury at all. At other times lumpy irregularities and thickenings endure, and I’ll be able to turn to a surprised patient and ask ‘So when did you break your ribs?’ Small bones, like the ones in the fingers, may be fully healed by three weeks. A bone like the femur may take twelve.
As I walked back to the car with Kalilu, I saw the boy of the week before, limping along after his friends. ‘Look!’ I said to Kalilu, pointing over to him. ‘There’s that boy with the femoral fracture. But those fractures take six weeks at least.’
Kalilu shrugged. ‘Maybe the bonesetter worked some magic. Maybe you were wrong – the leg wasn’t broken at all.’
We drove back into the bush, which seemed less beautiful on the return journey. Rather than admire the scenery I thought about the economics of health and how much about being a doctor I was yet to learn. Another day working in medicine, another Bridge of Asses I struggled to cross.