Issue 15

Is Britain's coastline infinite?

By Edward Platt

I know nothing about fractals, except for what a friend of mine once said to me when he was trying to elucidate their mysterious beauty: ‘Britain is fractal,’ he said. ‘It’s a finite area bounded by an infinite perimeter.’

My friend was no mathematician either, but he was fascinated by the work of Benoit Mandelbrot, the mathematician known as ‘the father of fractals,’ and particularly by an essay he wrote in 1967. The first part of the title - How Long is the Coastline of Britain? - raised a seemingly simple question. The second part - Statistical Self-Similarity and Fractional Dimension – reminded us that we were not in realms where simplicity prevails. Yet the answer was one of those beguiling and irreducibly mysterious propositions that transcend the constraints of an esoteric discipline and enter popular culture: the coastline of Britain can’t be measured, Mandelbrot said, because the coastline of Britain is infinite.

He redefined the idea when he coined the word ‘fractal’ seven years later. Imagine looking down on Britain’s coastline from a balloon. Then imagine looking at the ground beneath your feet as you walk along the cliff: the shapes are the same, and remain the same, no matter how tightly you zoom in. Fractals consist of identical or ‘self-similar’ forms, endlessly repeating, which means that you will never get a definitive figure for the length of the coast, because the measurement will keep increasing in inverse proportion to the scale.

The objection seems obvious: the coastline of Britain isn’t infinite, you might say. You can walk round it – it will take a while, but you will get back to where you started in the end. And you can measure it as you go: Wikipedia says the coastline of Britain is 12,429 kilometres long. Yet Wikipedia also acknowledges the ‘coastline paradox’ which says that the coastline of a landmass does not have a well-defined length, partly because ‘the measured length of a stretch of coastline depends on the scale of measurement,’ and partly because there is no consensus about which features should be included: should you measure every headland, rock and stone? And how far does the land extend in a village like Blakeney, in Norfolk, where the sea retreats at low tide every day to reveal an in-between world of marshes and creeks?

Besides, the coastline isn’t fixed: it’s changing so fast that by the time you got back to the place you started, you would have to set out again. The outline of Britain that we are used to seeing on a map is as familiar as a well-loved face: it is hard to imagine the squat, elfin figure, its brow tilted backwards, its waist swollen by the bulbous growth of Wales, its rounded backside nestling in the curve of the Low Countries, taking any other shape. Yet it only emerged 8,000 years ago.

At the end of the last Ice Age, 20,000 years ago, Britain was not an island: a landmass called Doggerland joined the entire east coast, from Scotland to the Isle of Wight, to continental Europe. And Doggerland was not an isolated corner of the continent: according to the archaeologists who have begun to map the lost world using the data collected by oil companies prospecting beneath the waters of the North Sea, it was its heartland, and its disappearance would have been hugely traumatic for the tribes of hunter-gatherers who regarded it as their home. The last part of Doggerland to be submerged was Dogger Bank, the high ground in the centre of the plain, which is now the North Sea shoal referred to in the nightly prose-poem of the shipping forecast. It was swamped in around 6100 BCE, when a subterranean landslide off the coast of Norway sent a wave ten metres high crashing across it: the force of the water was so great that many of Doggerland’s estimated population of 5,000 hunter-gatherers would have been dismembered, one geologist said. In the northeast, the wave travelled 25 miles inland, and further south, the marshes that used to stretch to France became the English Channel. As the waters of the North Sea reached the Atlantic, Britain became what Shakespeare called ‘this precious stone set in the silver sea / Which serves it in the office of a wall, / Or as a moat defensive to a house.’

There has never been a repeat of the Stone Age tsunami triggered by the Storrega Slides, but there have been other occasions when the sea has set about the land, and redesigned its outline with the peremptoriness of a topiarist reshaping a hedge. In 1287, a storm swept away the Suffolk port of Dunwich, and remade the coast of Kent so drastically that the town of Rye, which used to sit on the edge of a semi-circular bay that formed a perfect harbour, found its access to the sea barred by the newly-created expanse of Romney Marsh. And the sea is no less destructive when it works more slowly: Dunwich has been rebuilt many times since 1287, but nothing can protect the land on which it stands. Twelve parish churches have fallen into the sea, and the ruins that lie beneath the waters of the bay cover a far greater area than the existing village on the rapidly retreating cliff.

During the Victorian era, Dunwich became a place of mournful pilgrimage - poets like Walter Swinburne were drawn to it, because its constantly re-enacted demise seemed to dramatise the futility of all human endeavours. Not all the inhabitants of the east coast are quite so fatalistic. While I was in Dunwich last summer, I went to see a man called Peter Boggis, East Anglia’s King Canute, whose family owns and farms the land in Easton Bavents, half a mile to the north of the busy resort of Southwold, and five miles north of Dunwich.

Boggis' grandfather had bought the land in Easton Bavents in 1925, and in 1934 - when Boggis was three years old - his family moved into a house on the cliff. Even when they went on holiday, they didn’t go very far: they used to rent out their house for the summer, and relocate to a caravan on the beach. Yet all the time the sea was eating away their land: 160 metres had been lost since World War II, and in 2002, as the cliff continued to advance towards to Boggis’ grandfather’s house, where he lives with his second wife, he decided to construct his own defences.

It's possible to approach Easton Bavents by road, from inland, but Boggis told me to follow the route taken by the lorries that brought in the mud and rubble he used to fortify the cliffs. I crossed the bridge above the river that sometimes floods and turns Southwold into an island, and turned into Pier Avenue, a wide street lined with suburban villas. The pier at the far end offered the traditional working-class sea-side entertainments of arcades, brass bands and ice-creams, which complement the smart restaurants and expensive shops in other parts of the town. Yet once I reached the gate at the end of the pier car park, I left Southwold behind, and entered the Boggis’ domain: I unclipped the rope with the first of many keep out signs, which Boggis had told me to ignore, and climbed the road that ran between the beach and the sheep-dotted heath inland. The road was Boggis’ work as well: he had built and maintained it with the soil and rubble brought in by the first lorries, so he could get others to bring in more. In total, 12,000 lorries trundled along Pier Avenue and along Boggis’ road, and dumped their material on the beach, where Boggis moulded it into a kind of sacrificial wall, which he offered to the sea in place of his family’s land.

By the end of 2005, he had constructed an earthen rampart a kilometre long, and thoroughly enjoyed himself as well: ‘It was all tremendous fun,’ he told me, when I got to his house. His wife was in the kitchen, but we sat in his study, in front of a computer displaying an aerial photograph of the cliff taken just as he had completed his defences. Boggis was 82 years old, with bright blue eyes behind pink-framed glasses and a white beard. He talked in a measured way, placing words on the table with the deliberation of a digger depositing a ton of soil. He must have been a powerful man in his prime, though when we went to the cliff-edge to look down on the remnnants of his sea-wall, I had to take his hand and help him down the short slope on the edge of the field. Yet frailty will not prevent him taking up the fight again, for he wields power through the tools and machines that litter the cliff-top, like suits of armour or discarded exoskeletons that he will don again.

It wasn’t nature that stopped Boggis’s work: it was English Nature, the government quango charged with maintaining the Suffolk cliffs. As his Dahl-like name implies, Boggis is a true English eccentric, devoted to defending the castle that is home, and like most English eccentrics, he wanted his day in court. In the end, the cost of fighting English Nature bankrupted him, and he was forced to abandon his project, but he is counting the years until the order expires, and he can begin again. Should the cliff threaten to collapse in the meantime, he will deploy his final defence - the concrete blocks piled on the summit of his homemade road, beside his first wife’s house, waiting to be tipped onto the beach below.

The comparison with Canute seems apt. Canute was not attempting to demonstrate his power over nature when he tried to hold back the waves: he was trying to show his subjects that even a king cannot defy it. Peter Boggis revels in his fight with English Nature, or English ‘Nazis’ as he calls them, and takes great pride in his engineering prowess, but he knows that the confrontation with nature is much more one-sided: his first wife remembers dancing in the garden of a bungalow that now lies several hundred metres beyond the shore, and Boggis knows that the rest of his family's land will eventually be lost as well.

One of the reasons she had stayed so long was that she wanted to remind people of the state of Britain’s eroding coast: it was absurd that we had resisted invasion over the years, and then let the sea eat away the land, bit by bit, she said to me – a statement that would have seemed hyperbolic, had we not been sitting at a table laid with glass coasters within feet of the cliff. She objected to the fact that the coast at Bacton, four miles north, where a significant proportion of the UK’s gas is brought ashore, is protected, and Happisburgh is not. Yet Happisburgh is another reminder of the inexorable way the landscape changes: 850,000 years ago, the Thames used to flow through the caravan park in the village, and flint tools left by the hunter-gatherers of the species homo antecessor who lived in the adjoining flood plains have been found nearby. The storm that destroyed Bryony Neirop-Reading’s house exposed another remarkable find on the beach - the oldest human footprints ever discovered outside Africa.

I wanted to go back to Happisburgh in the aftermath of the storm, but there is something about the county of Norfolk that always seems to frustrate my plans: when I drove up last summer, my car had broke down on the Norwich ring-road, and after the December storm, my internal engine broke down - I succumbed to one of the coughs and colds that my children had been incubating through the winter months, and instead of walking the Norfolk cliffs, I lay in bed listening to the heavy rain that marked the arrival of yet another winter storm.

The December storm had not been as destructive as its predecessor in 1953: no-one drowned, thanks to improved flood defences and better warning systems, though two people were killed in Scotland, and houses up and down the east coast, from Essex to Hull, were flooded. By the time I resumed my travels round the country, the storms had moved on: the seas were battering the south coast and Wales, and the flood-waters were rising in Somerset, Kent and the Thames Valley. I tried to walk the Thames tow path, from Cookham, Stanley Spenser’s new Jerusalem, to JG Ballard’s Shepperton, via the flooded villages of Datchet and Wraysbury, though the rising waters often forced me to divert my course, and I punted through the flooded lanes of the Somerset Levels, which offered a glimpse of the future of other low-lying counties, such as Norfolk and Suffolk: if sea-levels rise as predicted, then the land beyond the fraying east coast will become a northern European version of the Venice lagoon, with isolated farms and villages scattered across an archipelago of islands, navigable not by road or car but by boat. Doggerland is not the last habitat that we will lose, as the finite area on which we live continues to erode - Byrony Neirop-Reading’s house has gone, and Peter Boggis’ will go one day, and as the coasts retreat and the waters rise, more of us will be left with memories of dancing in gardens that lie beneath the waves.

Edward Platt is an award-winning writer who lives in London. His most recent book was The City of Abraham: A Journey through Hebron. He is currently writing a book about flooding.

Cover image licensed under Wikimedia Commons.