Declination

The Projection

Chapter 5: Declination

The storm came from the northwest on the third day, not suddenly but with the slow, deliberate approach of weather systems in the Brooks Range, where the terrain funneled wind and moisture through the valleys like water through a pipe and the barometric pressure dropped with a steadiness that you could track on the altimeter of the Brunton compass if you watched it, which Silas did, noting the descent from 30.12 inches at six in the morning to 29.87 by ten, a drop that indicated a front moving in, a shift from the high pressure that had given them two days of clear skies to the low pressure that would bring rain and wind and the particular grey light that made surveying difficult because the overcast eliminated shadows and the landscape went flat, every ridge and every valley the same shade of grey-green, the topography hidden not by darkness but by the absence of contrast.

By noon the clouds were on the ridges. By two the rain began, a thin, cold rain that was not heavy but was persistent, the kind of rain that found every gap in your clothing and every crack in your resolve and settled in for hours or days, indifferent to your schedule, indifferent to your manifest, indifferent to the stations you had planned to set and the angles you had planned to measure. The rain was the terrain's answer to the survey, its way of saying: not today.

They retreated to the tent. Silas zipped the vestibule closed and sat on his sleeping bag with the field notebook open on his knees, reviewing the data from the first two days. Six stations set, from the camp to a point approximately one mile up the tributary. Twenty-three theodolite observations, forty-one GPS positions, twelve compass bearings. The data was consistent. The theodolite and GPS positions agreed to within ten centimeters at every station, which was well within the accuracy he needed for a 1:24,000 map with twenty-foot contour intervals. The survey was progressing on schedule.

The schedule did not account for storms. Schedules never accounted for storms. You planned the work and the weather modified the plan and you adapted, which was the first lesson of fieldwork and the one that most office-based scientists found hardest to accept. The field was not a laboratory. You could not control the variables. You could only observe them and adjust.

Jin sat cross-legged at the other end of the tent, his back against his duffel bag, reading something on his phone. The phone had no signal — they were two hundred miles from the nearest cell tower — but Jin had loaded it with books before the trip, and Silas had seen the titles when Jin scrolled through them: technical manuals on GIS, a history of cartography, two novels. The novels surprised him. He had not expected a GIS specialist to read fiction.

"What are you reading," Silas said.

"Endurance," Jin said. "The Shackleton book."

"The Lansing one."

"Yes."

"Good book."

"Have you read it."

"Margot gave it to me. Twenty years ago, maybe. She said I should read it because Shackleton was a man who made maps of where not to go."

He had not meant to mention Margot. The name came out the way a compass needle swings to magnetic north — not by choice but by the pull of an invisible field, the field that oriented everything he thought and said and did toward a point that was not true north but was, nevertheless, the direction the needle pointed.

Jin looked up from the phone. He did not ask who Margot was. He either knew already — Ruth might have told him, or he had heard it in the office, the way such things were heard — or he sensed that the name was not an invitation to inquiry. Either way, he said nothing, and the silence that followed was not uncomfortable but charged, the way the air before a storm is charged, carrying the potential for something that has not yet happened.

"The rain might last two days," Silas said. "Maybe three. The forecast — what we had before we lost signal — showed a trough stalling over the range."

"So we wait."

"We wait. And we work."

"Work how."

"We reduce the data. Compute the positions from the theodolite angles. Check them against the GPS. Plot the stations on the quad sheet. Start sketching the contour lines."

"Sketching. Before we've surveyed the whole tributary."

"Preliminary sketches. Based on what we've measured so far and what we can infer from the terrain we've seen. The sketches will change as we get more data. But starting early helps me understand the drainage — where the contour lines will crowd together, where they'll spread apart, where the terrain will be hard to map and where it'll be easy."

He opened the notebook to the station data and began the computations. The mathematics of a theodolite traverse were not complex — plane trigonometry, mostly, the sine and cosine of measured angles multiplied by measured distances to compute the northing and easting of each station relative to the baseline. He did the calculations with a mechanical pencil on the waterproof pages of the notebook, writing the numbers in columns, checking each step, carrying the results forward from station to station the way you carry a remainder in long division, each station's position depending on the previous station's position, the errors accumulating as the traverse extended upstream.

This was the weakness of a traverse: the accumulation of error. Each measurement had a small uncertainty — a few seconds of arc in the angle, a few millimeters in the distance — and these uncertainties propagated through the computations, growing with each station, so that the last station in the traverse had a larger position uncertainty than the first. The cure was a closure — connecting the last station back to a known point, so that the accumulated error could be measured and distributed among the stations. Without a closure, the traverse was open, and the position of the last station was uncertain by an amount that depended on the number of stations, the quality of the measurements, and luck.

Silas worked the numbers. Jin watched for a while, then took out his own notebook and began computing the same positions independently, using the GPS coordinates as a check. They worked in silence, the rain drumming on the tent fabric, the sound steady and monotonous and somehow productive, as if the rain were doing its own work — eroding, depositing, reshaping the valley in increments too small to see but real, measurable, the geology of the present tense.

After an hour Silas looked up. "What do you get for station four."

Jin checked his notebook. "67.4218 north, 150.1847 west. Elevation 2,194 feet."

Silas checked his own numbers. "67.4218 north, 150.1846 west. Elevation 2,191 feet."

"That's three feet of elevation difference."

"The GPS gives orthometric height. The theodolite gives height above the baseline datum. The difference is the geoid undulation — the difference between the ellipsoid the GPS uses and the actual shape of the earth at this location. Three feet is about right for the geoid model in this area."

"So both are correct."

"Both are correct in their own reference frame. The question is which reference frame you want the map to use. I use mean sea level, which is the traditional datum for elevation. The GPS uses the WGS84 ellipsoid. They're different surfaces. The elevations are different numbers for the same point."

Jin wrote this down. Silas watched him write it and thought about the layers of abstraction that separated the number in the notebook from the actual height of the ground — the ellipsoid, the geoid, the datum, the projection, the scale, the contour interval. Each layer was a simplification, a reduction, a choice to represent one thing and ignore another. The ground was real. The number was a symbol. Between them was a chain of mathematical transformations that turned a physical location into a position on a map, and every link in the chain introduced a small distortion, a small loss, a small sacrifice of truth for the sake of representation.

This was what projection meant. Not just the cartographic projection — the Mercator or Lambert or UTM that flattened the curved earth onto a flat page — but the entire process of mapping, the entire act of turning the world into a representation of the world. Every map was a projection. Every representation was a projection. Every attempt to capture something real in a medium that was not real — paper, canvas, language, memory — was a projection, and every projection sacrificed something to preserve something else.

Margot's paintings were projections. She had never used that word, but she had understood the concept intuitively, the way artists understood things that scientists had to learn formally. She knew that the painting was not the mountain. She knew that the color on the canvas was not the color of the sky. She knew that the texture of the brushstroke was not the texture of the rock. But she also knew that the painting could achieve a truth that the mountain, standing there in its massive indifference, could not achieve on its own — a truth of selection, of emphasis, of human attention focused on a landscape that did not ask for attention and did not need it.

What did her paintings preserve. Color. Light. Atmosphere. The feeling of standing in a place at a particular time and looking at a particular thing with particular eyes. Her eyes.

What did they sacrifice. Dimension. Scale. Measurement. The precise distance from the viewer to the mountain, the exact elevation of the ridge, the true bearing of the river.

What did his maps preserve. Shape. Distance. Elevation. The geometric truth of the terrain, the relationships between points, the angle of slope, the direction of drainage.

What did they sacrifice. Color. Light. Atmosphere. The feeling of standing in the place. Everything that made the place a place and not a position.

Between them, Margot and Silas had mapped the territory. Between them, they had preserved everything. Apart, each preserved half and sacrificed the other half, and the halves were not interchangeable, could not be combined after the fact, because the painter was dead and the cartographer was sixty-three and sitting in a tent in the rain with a field notebook and the growing awareness that the map he was making would be the last one and that the last map would be, like every map, incomplete.

The rain intensified. The tent fabric bellied inward under the weight of water running down from the ridgeline above the camp. Silas adjusted the guy lines from inside, tightening them until the fabric was taut, and the drumming became louder, sharper, the sound of rain on a tight surface, a sound he had heard in tents for nearly four decades, in the Brooks Range and the Alaska Range and the Wrangells and the Chugach and the coast ranges of Southeast Alaska and the treeless tundra of the North Slope, in every kind of terrain the state contained, which was every kind of terrain there was, because Alaska compressed the full range of the earth's geography into a single state — glaciers and volcanoes, tundra and rainforest, desert and swamp, mountains that reached twenty thousand feet and plains that extended to the horizon without a single feature to break the line.

He had mapped much of it. Not all — no one could map all of Alaska, not in a lifetime, not in ten lifetimes — but enough to understand that the state was, in cartographic terms, a problem without a solution. Too big for a single map. Too varied for a single projection. Too complex for a single scale. Every map of Alaska was a compromise, a series of decisions about what to show and what to hide, and the decisions were never satisfactory because the territory exceeded the capacity of any representation, the way a life exceeded the capacity of any biography, the way a marriage exceeded the capacity of any account.

He and Margot had been married for thirty-three years. He sometimes thought of those years as a traverse — a chain of stations extending through time, each station connected to the previous one by the measured angles and distances of shared experience, the chain growing longer and the accumulated error growing larger with each year, the early stations (the wedding, the first house, the first field season together) known precisely and the later stations (the diagnosis, the treatment, the hospital, the death) known less precisely, blurred by the distortion of grief, which was a kind of error that no instrument could measure and no computation could correct.

The traverse of a marriage. The baseline of a commitment. The backsight of memory.

He closed the notebook. He was doing it again, turning everything into a surveying metaphor, which was either a sign of professional deformation or a sign that the metaphors were real, that surveying was not just a method of measuring the ground but a way of understanding all measurement, all representation, all the ways that human beings tried to capture the world and hold it still long enough to draw a line around it.

"Silas," Jin said.

"Yes."

"Can I ask about the compass."

"What about it."

"The declination. You said it's twenty degrees east in this area. But the declination printed on the quad sheet says nineteen degrees. The sheet is from 1957. Has the declination changed."

"Yes. The magnetic pole moves. It's drifted westward since 1957. The current declination for this area is about twenty point four degrees east. The quad sheet gives the 1957 declination and the annual rate of change, so you can compute the current declination."

"And if you don't correct for it."

"If you don't correct, your bearing is off by the amount of the error. If you're using the 1957 declination instead of the current one, you're off by about one point four degrees. Over a mile, that puts you about forty meters from where you intended to be."

"Forty meters."

"Enough to be in the wrong drainage. Enough to miss a camp. Enough to get lost."

"Has anyone ever gotten lost because of declination."

"Many people. The history of exploration is full of people who followed the compass without correcting for declination and ended up somewhere they didn't intend to be. The compass always tells the truth. It always points to the magnetic pole. The error is in the assumption — the assumption that where the compass points is where you want to go."

Jin thought about this. Silas could see him working through the implications, fitting the idea into his understanding of navigation and measurement and the relationship between instruments and the reality they measured.

"So the compass is accurate but the user is wrong," Jin said.

"The compass is accurate for what it measures. The user is wrong about what it measures. The user thinks the compass points north. The compass points to the magnetic pole. The difference is the declination. If you know the declination, you can correct. If you don't know it, you can't."

"And the declination changes."

"Everything changes. The magnetic pole moves. The ground subsides. The rivers shift their channels. The benchmarks sink. The datum adjusts. Nothing stays fixed. The work of surveying is the work of measuring things that move and pretending, for the purposes of the map, that they don't."

"That sounds dishonest."

"It sounds practical. The map is a snapshot. It represents the terrain at a particular moment in time. The terrain will change after the map is published. The rivers will move. The glaciers will retreat. The coastline will erode. The map will become inaccurate. But it will still be useful, because the rate of change is slow relative to the human need for navigation, and a map that is slightly wrong is better than no map at all."

"And the projection."

"What about the projection."

"You said no projection preserves everything. What does UTM preserve."

"Shape. UTM is a conformal projection. It preserves the shape of small features. Angles measured on the ground are the same as angles measured on the map. But it distorts area. A square on the ground becomes a slightly rectangular figure on the map, wider in the east-west direction than in the north-south direction, and the distortion increases as you move away from the central meridian of the zone."

"So a UTM map lies about area."

"It lies about area to tell the truth about shape. Every projection makes that kind of trade. Mercator preserves direction but distorts area. Lambert conformal conic preserves shape but distorts distance. Equal-area projections preserve area but distort shape. You can't have everything. You choose what matters."

"What matters to you."

Silas looked at Jin. The question was not about cartography. Or it was about cartography in the way that all questions, asked in a tent in the rain in the Brooks Range, were about cartography — about the way you represented the world, the choices you made, the sacrifices you accepted.

"Shape," Silas said. "Shape matters to me. If the map gets the shape right, you can understand the terrain. You can see the ridges and the valleys and the drainages. You can see how the water flows. You can see where the steep ground is and where the flat ground is. Shape is the story. Area and distance and direction are details. Important details, but details. The shape is the thing."

"Margot would have said color," he did not say. Margot would have said: what matters is the light. What matters is the way the light falls on the ridge at four in the afternoon in August, the gold on the south-facing slope and the blue shadow on the north-facing slope, the way the colors shift as the sun moves, the way the mountain changes without moving. That is what matters. That is what I paint.

And she would have been right. And he would have been right. And between them they would have been more right than either one alone, and this was the thing about marriage that the metaphors could not capture, the thing about partnership that the projections could not preserve — the way two partial truths, held together, made a truth that was not partial, not complete, but sufficient. Present. Real.

He opened the notebook. He looked at the numbers. He closed the notebook.

The rain fell. It fell all afternoon and all evening and all through the night that was not a night, and the creek rose, the water turning grey with silt, the current strengthening, the sound of the water changing from a murmur to a rush to a steady roar that filled the valley and drowned out the rain and made the tent seem very small and the mountains very large and the instruments, in their cases in the vestibule, very precise and very futile and very necessary.

They did not leave the tent. They computed and checked and plotted and sketched and ate freeze-dried meals and drank tea and said little, because the rain and the work filled the space that conversation would have occupied, and the silence between them was the silence of two people doing the same work in the same small space, a functional silence, a productive silence, the silence of a survey party waiting for the weather to clear so the measurements could resume.

Silas slept badly. He lay in his bag and listened to the rain and the creek and thought about the traverse extending upstream through the valley, station by station, point by point, the chain of measurements growing longer, the accumulated uncertainty growing larger, and he thought about the closure that would come at the end, when the traverse reached the headwaters and looped back to a known point and the accumulated error could be measured and distributed and the positions adjusted and the map drawn with confidence.

But there would be no loop in this traverse. The tributary ran from its mouth to its headwaters in a single line, and the traverse would follow it, and at the end there would be no closure, no known point to connect back to, just the headwaters and the saddle and the sky beyond the saddle and the next drainage over the ridge, unmapped, unmeasured, unknown. The traverse would be open. The error would be unresolved.

He lay in the dark that was not dark and thought about open traverses and unresolved errors and the particular kind of loss that came from reaching the end of a line and finding that the end did not connect to the beginning, that the circuit was not closed, that the measurements could not be reconciled because there was no final benchmark against which to check them.

The rain fell. The creek rose. The night, such as it was, passed.

In the morning the rain had eased to a drizzle. The clouds were still on the ridges but lifting. The creek was high and brown and fast, running over the lower bench, the water carrying branches and tundra and the grey silt of glacial till that it had picked up somewhere in the headwaters where the permafrost was thawing and the ground was giving up its frozen sediment to the stream, the way the past gave up its sediment to the present, slowly, continuously, in increments too small to notice until the water changed color and the channel shifted and the gravel bar where you had landed your plane was underwater and the camp you had made was threatened by a river that had been tame two days ago and was not tame now.

They moved the tent. They carried the equipment cases to higher ground, above the willows, to a flat area of tundra where the ground was firm and the water could not reach. The work was wet and cold and they did it without speaking, the urgency of the situation replacing the need for words with the need for action, and when the camp was relocated and the equipment was safe they stood on the tundra and looked down at the creek, which was running where the tent had been, and Silas thought: the map does not show this. The map shows the creek in its normal channel, at its normal level, in its normal season. The map does not show the creek in flood. The map does not show the creek eating the gravel bar. The map does not show the creek reminding you that you are a visitor and the creek is not.

"How long until we can work," Jin said.

"When the water drops. Two days, maybe. Depends on the rain."

"Two days."

"The field teaches patience. The field teaches you that your schedule is not the terrain's schedule. The terrain has its own schedule and it does not consult you."

Jin looked at the creek. He looked at the mountains. He looked at the sky.

"Two days," he said again, and this time it was not a question but an acceptance, and Silas heard in it the sound of a young man learning the first hard lesson of the field, which was that the landscape did not care about your plan and that the plan, no matter how carefully prepared, was always subordinate to the conditions, always subject to revision, always at the mercy of the weather and the terrain and the river and the ten thousand variables that no manifest could list and no schedule could accommodate.

They went back to the tent. The rain continued. Silas opened the notebook and began writing.

He wrote about the storm. He wrote about the creek rising. He wrote about moving the camp. He wrote the observations that the numbers could not contain — the color of the water, the sound of the rain, the smell of the wet tundra, the feeling of standing on the bank of a creek that was running where his tent had been ten minutes ago, the feeling of being small and precise and temporary in a landscape that was large and rough and permanent.

He wrote these things because Margot would have wanted him to. Because Margot, who had kept her own field journals, had always said that the observations between the data were the ones that mattered, the ones that told the truth about the place, the ones that no instrument could measure and no algorithm could compute. He wrote them for her, knowing she would never read them, knowing that writing for the dead was a kind of open traverse — a line extending into a territory that had no closure, no benchmark, no known point to connect back to.

He wrote until the pencil needed sharpening. He sharpened it with the knife he carried in his pocket, the same knife he had carried for thirty years, the blade worn thin from thirty years of sharpening pencils and cutting flagging tape and slicing cheese and performing the thousand small tasks that a knife performed in the field. He sharpened the pencil and wrote more.

The rain fell. The creek ran. The declination between where he pointed and where he intended to go was, as it had always been, the angle of loss.