In the mid-fifteen-hundreds, a Swedish peasant named Nils lived on an island called Iggön in the Baltic Sea. He was known to his neighbors as Rich Nils, apparently because of the plenitude of fish in the waters near his home and, even more lucrative, the seals that showed up to hunt them. There was one rock in particular where seals liked to haul themselves out of the ocean to rest and bask in the sun. Nils, for his part, liked to visit this rock with his harpoon.

Eventually, though, Nils noticed that the seals had begun gathering on a lower part of the rock, rather than on the high point, as they once did. It seemed that the water level no longer gave them access to the very top. This was a troubling development for Rich Nils’s income: the high point now obstructed the path of his harpoon when he approached the rock from the shore. Nils used fire to weaken the rock, chipping away at it until he’d not only removed the high point but also lowered the over-all height of the rock, so that seals would be able to rest on it even when the sea reached its lowest level of the year.

Some hundred and eighty years later, the Swedish physicist and mathematician Anders Celsius went looking for Rich Nils’s rock. Celsius was known for his obsession with quantifying the world around him; he tried to calculate the distance between the Earth and the sun, was involved in the long quest to use meridian measurements to determine the size and shape of the Earth, and famously proposed a new scale for gauging temperature. Now he was once again in search of a way to measure what had previously been unmeasurable.

By the early seventeen-hundreds, an emerging consensus held that the level of the Baltic Sea was sinking. Shallow harbors became more so, until they had to be abandoned; offshore islands grew land bridges until they became one with the mainland. To many people of the era, this phenomenon made perfect sense. The Biblical great flood, after all, had covered the world with water. It stood to reason that, all these years later, such a huge volume would still be draining away, ever so gradually. Frustratingly, though, there was no scientific marker that could be used to track these changes, no way to know how quickly the land and the water were separating.

That’s when Celsius realized that seal rocks, valuable pieces of real estate that were regularly described in official documents—tax declarations, inheritance papers, bills of sale—could offer some insight: they were fixed points against which to measure change. Sure enough, he found records of several rocks whose loss of use, and therefore value, was declared after the sea dropped so low that seals became unable to swim to them. It was even possible to identify a specific rock with a chiselled top and a taxation record going back to Nils’s sons.

Between Nils’s time and Celsius’s sketch of the rock, in 1743, the water level had dropped nearly eight feet. Nils’s island was gradually becoming part of the mainland; today, it is a peninsula. In 2012, the scholar Martin Ekman located the rock that made Nils rich; by then, it was no longer in the sea at all. It stood in a young forest, surrounded by trees.

Mountains, oddly, are the reason most of us have learned to think of the level of the sea as a stable point, a baseline, an unmoving benchmark against which one might reasonably measure the height of great peaks. We confidently assert that Mt. Rainier rises 14,411 feet above sea level, without stopping to ask ourselves what exactly we mean: what sea, and where and when, and in what state of weather? The oceans, we know, are never at rest; they’re pulled to and fro by the moon (in the Bay of Fundy, a single tidal change can lower the water by more than fifty-three feet), the wind, the atmospheric pressure, and the considerable gravity exerted by glaciers and landmasses. Even changes in a sea’s temperature can affect its water level, by causing molecules of water to draw closer to, or farther away from, one another. More profoundly, oceans have risen and fallen by hundreds of feet alongside ancient changes in the Earth’s glaciation (in the process allowing people to cross land bridges to the Americas and Australia and what are now the islands of the United Kingdom), and they are currently pushing, at a fairly rapid clip, over seawalls and into cities.

Given this history, it would seem ludicrous to take mean sea level—something “as ephemeral as a fleeting ray of sunshine on a wintery afternoon,” as the Australian geologist Rhodes W. Fairbridge wrote in 1961—to be a standard of stability. How on earth, we might wonder, did we come to treat the sea as a synonym for solidity?

The answer, the environmental historian Wilko Graf von Hardenberg writes, in “Sea Level: A History,” is the same as it is for most of our reference points. Like the metre, the minute, or the meridian that runs through Greenwich, England, “sea level” is best thought of as a social and historical construct, the result of an inherently arbitrary decision taken by generations of people doing their best to make sense of a strange and chaotic world. Von Hardenberg’s history is a story not of the way sea level has changed over time but, rather, of the ways in which humans have understood, and made use of, sea level as a concept, a marker of where we stand in the world.

Throughout most of human history, maps offered no fixed elevations. For one thing, these were difficult to measure, although a method of doing so through arduous triangulation had been known since antiquity. For another, people recognized that what mattered wasn’t how high a point was in absolute terms but how high it was in relation to other points from which one might need to carry a load or build a bridge or pump water. Mountain summits, von Hardenberg notes, were of less interest to mapmakers than geographical features such as caves and passes, which were more relevant to people’s everyday lives. Elevation was sometimes expressed as the amount of time it would take a person to climb to a destination, or as the distance from whatever baseline was locally known and useful: the surface of a nearby lake, the door of a certain church. There’s little evidence that anyone was thinking about the abstraction of average water levels, since what one needed to be prepared for were the extremes: low water in which boats might founder, high water that might flood ill-placed settlements. People sometimes marked these extremes with rocks that could stand as warnings for a future that was in danger of forgetting the past. We know them now as tsunami stones and hunger stones. A famous one in the Elbe, commemorating a terrible drought, is carved with the words “If you see me, then weep.”

After Celsius published his calculations for the slowly dropping water of the Baltic, the scholars of Europe began arguing over their meaning. The great-flood faction contended that the erosive effects of so much draining water could help explain how coasts and mountains and river valleys formed. But critics of the diluvian theory, who believed the level of the sea to be fundamentally stable, asked why similar evidence of falling seas couldn’t be found everywhere. To some, the sea seemed too large, too immutable, to do something so meek as disappear. “It is certain that the surface of the ocean cannot sink,” a scientist wrote in 1810. “This the equilibrium of the sea will not by any means admit of.”

The debate went on for decades. In the eighteen-thirties, the geologist Charles Lyell travelled from Britain to Sweden to study the question, visiting, among other sites, a rock on which Celsius had marked the sea level a century earlier. Celsius’s mark now sat eighty-six centimetres above the water, but Lyell calculated that the rate of change was significantly different in different parts of the Baltic, leading him to argue that the true reason for the disappearing ports and seal rocks was not a drop in the water but a lifting of the land. (Lyell turned out to be right: the Scandinavian peninsula was, and still is, rising relative to the sea, as a result of the phenomenon known as “postglacial uplift”—the slow bounce-back of land that was long compressed by the great weight of earlier glaciers.)

The era was, the mathematician John Playfair observed, a destabilizing one—literally so for people wondering what, if any, part of their world might stay dependably in place. “The imagination naturally feels less difficulty in conceiving that an unstable fluid like the sea, which changes its level twice every day, has undergone a permanent depression in its surface, than that the land, the terra firma itself, has admitted of an equal elevation,” he wrote.

The stakes were large, in part because the controversy was tied to a much bigger one. As scientists tried to make sense of dinosaur and mastodon bones and the stark geological evidence of immense, long-ago perturbations in the Earth’s lands and waters, different schools of thought emerged. One group concluded that a past shaped by huge, Biblical catastrophes had given way to a calmer present wherein the rules of life and geology now operated very differently. (In the words of Georges Cuvier, a leading proponent of this theory, “Nature has changed course, and none of the agents she employs today would have been sufficient to produce her former works.”) But Lyell and his cohort maintained that the world was essentially uniform—the same basic processes that had shaped the seas, the continents, and the life that inhabited them were still in effect.

“He may still have a chance if we can just get him past this all-you-can-eat buffet.”

Cartoon by Paul Noth

Lyell’s view that the present is the key to understanding the past eventually won out. But so did his theory of a sea whose global level was stable over time. The scientists and mapmakers of Europe, now in agreement that sea level was a metric worth standardizing, began debating which exact point would provide a shared reference for use in measuring mountains and—especially in the colonies over which their governments were working to strengthen their control—for use in drawing new maps and boundaries and in designing roads and ports and bridges. The quest to find a mean sea level for the whole world was part and parcel of the quest to make the world governable. And thus, von Hardenberg writes, did our idea of sea level as a benchmark emerge from a very specific time and place, becoming intertwined with the colonial project and “a long-held perception of holocenic stability.”

In short order, the search for a universal metric of sea level began to founder on the shores of reality. Automated tidal gauges made it easier to collect reams of new data (previously, records were limited by the number of people willing to go out and measure the sea at regular intervals, braving storms and cold and darkness), but they, too, could prove less than reliable. Von Hardenberg recounts the story of the engineer Auguste Bouchayer, who found that fifty years of records of the Mediterranean’s levels at Marseille had been compromised because the gauge’s warden and his wife, for fear of its getting broken, had been cutting off the gauge from the movement of the sea whenever the weather was bad. “Our bases are precarious!” Bouchayer lamented.

As data proliferated, European scholars gathered regularly to define sea level for the Continent. But tides and winds, plus coastal topography and changes in the Earth’s crust, meant that even the averages often differed significantly from place to place. Different countries, even different parts of countries, began adopting their own varied and highly local baselines. France chose, and then abandoned, the mean level of the Atlantic where the Loire River flowed into it. The Belgians, to avoid the need for negative elevation numbers on maps of the coast, settled on the low-water point recorded during spring tide at Ostend. In England, sea level was a hundred feet below a mark on St. John’s Church in Liverpool—until the datum was changed to one averaged at a certain dock at the mouth of the River Mersey, some forty-three feet higher than the previous reference. Today, when British maps refer to mean sea level, they’re actually referring to the average of the water levels that were recorded hourly between 1915 and 1921 at a pier in Newlyn, Cornwall.

But, even as scientists sought to determine the sea’s level, their ongoing studies of the Earth slowly undermined the theory of a stable sea. It was becoming clear that Europe’s glaciers had once been dramatically larger, and had left evidence of their past size in the form of fjords and erratically distributed boulders. Wouldn’t such an enormous unlocking of water—though this history was hidden as water rose to cover it—have affected the level of the oceans as well? Our bases, it seemed, were more precarious than anyone had recognized.

After decades of meetings, the effort to choose a single vertical datum for Europe quietly washed out. But height above sea level had by then become a common measure. It’s just that the specifics of what this meant continued to depend on where you were. In New York City, as late as 1915, officials were using more than ten different reference planes, and it was only in 1929 that the U.S. adopted a shared reference for setting mean sea levels around the country; it was derived from calculations based on twenty-six tidal stations and 106,724 kilometres’ worth of coastline surveying. “Change the frame of reference or the accuracy of an instrument,” von Hardenberg writes, “and even the apparently stable measure of a mountain is revealed as but a snapshot of a specific technological moment.”

The definition of sea level is still far from straightforward. We know that, because of the way the Earth bulges as it spins, the water levels of equatorial seas are some twenty-one kilometres higher than the sea ice at the North Pole. (This bulge also complicates how we think about mountain heights, since the peak of Mt. Chimborazo, rising close to the equator, is actually farther from the center of the planet than is the peak of Mt. Everest.) A gravity anomaly in the Indian Ocean means that a large swath of its waters—an area nearly as large as India itself—has a top level that’s as much as a hundred and six metres lower than the global average. Contemporary systems for determining sea level, which can now incorporate G.P.S. and lidar and satellite altimetry and so on, no longer rely on water levels alone. Nowadays, many measurements of sea level are based not on the top level of the actual ocean but on calculations of where an imaginary sea—one that reflects the differing effects of gravity around the planet but is not beset by wind, tide, or current—would gather, if such a sea existed. This theoretical version of our watery world is known as the geoid.

Our awareness of the complexity of the question has also advanced alongside our technology. We know that relative sea levels (a measure of how the height of the ocean relates to the local elevation of land) are affected, for example, by land subsidence, which humans create by draining swamps, altering the course of rivers, and relentlessly pumping water, oil, and gas from beneath the Earth’s surface. (Parts of California’s Central Valley have fallen by nearly thirty feet as the aquifers beneath them have emptied, and areas of Louisiana, robbed of the Mississippi River sediment that once counteracted erosion, are sinking by as much as three-quarters of an inch per year.) Sea levels are also affected when humans burn fossil fuels, causing the atmosphere, and oceans, to heat up and the world’s immense reserves of ice to melt.

That ice was already thinning in 1940, when the Icelandic geologist Sigurdur Thorarinsson posited that worldwide “glacier shrinkage” could produce a new, modern era of sea-level changes. It’s remarkable just how early people grasped that fossil fuels could change sea levels. In 1959, the American Petroleum Institute was warned that, if the world continued to burn oil, “the ice caps will start melting and the level of the oceans will begin to rise.”

We now know much more about the specifics. The Greenland ice sheet holds enough water to raise the height of the world’s oceans by twenty-three feet; a complete melting of Antarctic ice could lift them by two hundred feet. We know that a number of feedback loops—such as the effect of warmer seawater slipping under ice shelves and glaciers—are speeding the melting, and that rising sea levels are already increasing the danger of hurricanes and storm surges, pushing people out of low-lying homes, and contaminating soil and groundwater with salt. The higher sea levels are also setting the stage for future geopolitical conflicts—much, much larger echoes of the long-ago fuss over seal rocks—as the islands around which territorial boundaries and claims to fishing and mining rights were founded begin to disappear beneath the waves. Once again, our measurements struggle to keep pace with a fluid reality.