Jin's Map

The Projection

Chapter 31: Jin's Map

The email arrived on a Wednesday. The subject line said DEM complete -- tributary survey 2026, and the attachment was a zip file, 214 megabytes, containing the digital elevation model that Jin had built from the survey data, the same data that Silas had used to draw the contour lines on the vellum, the same angles and distances and elevations from the same stations in the same valley, the data flowing into two channels, two representations, two projections of the same terrain.

Silas opened the file. The DEM appeared on the laptop screen as a shaded relief image, the terrain rendered in grey tones, the high points light and the low points dark, the slopes catching a simulated light source from the northwest, the digital sun casting digital shadows across the digital terrain, the illusion of three dimensions produced by the mathematics of shading, the algorithm doing what a painter's eye did -- reading the light, placing the shadow, creating the impression of depth on a flat surface.

The valley was there. The creek was there. The ridges were there. The saddle was there. The terrain was recognizable, the shape correct, the proportions faithful, the digital representation reproducing the analog landscape with the fidelity that the data permitted, the fidelity that was a function of the number of data points and the accuracy of each point and the algorithm's method of interpolating between the points.

The algorithm's interpolation was different from Silas's interpolation. The algorithm used a method called kriging -- a geostatistical technique that estimated the elevation at unsampled points based on the spatial correlation of the sampled points, the method computing a weighted average of the known values, the weights determined by the distance between the known point and the unknown point and by the statistical structure of the data, the structure described by a mathematical function called a variogram that Silas understood in principle but could not compute by hand, the computation requiring the processing power that Jin's laptop provided and that Silas's pencil did not.

Silas's interpolation was different. Silas's interpolation used judgment. Silas's interpolation used the knowledge that thirty-eight years of looking at terrain had deposited in his mind, the knowledge that said: this slope is convex because the rock is resistant and the erosion is slow. This slope is concave because the rock is weak and the erosion is fast. The contour line bends here because there is a gully that the station data did not capture but that the eye saw from the ridge, the eye recording what the instrument missed, the human observation supplementing the mechanical measurement. Silas's interpolation was not a computation. It was a judgment. It was the act of a mind that had seen enough terrain to know what the terrain did between the measured points, the same way a reader who had read enough sentences could complete a sentence that ended in the middle, the pattern recognized, the rest supplied, the interpolation drawing on the accumulated evidence of a lifetime of observation.

The two interpolations -- the algorithmic and the judgmental -- produced different contour lines. The differences were small. In most places the contour lines agreed, the digital contour and the hand-drawn contour following the same path within the width of the pen line, the agreement close enough that a reader comparing the two maps would see one map, not two. But in some places the contour lines diverged, the digital contour following a path that the hand-drawn contour did not follow, the algorithm reading the data one way and the judgment reading it another, the two representations disagreeing about what the terrain did between the measured points.

Jin called that afternoon. Silas answered the phone in the study, the phone on the desk beside the legal pad and the field notebook and the stack of computation sheets, the instruments of the analog practice arrayed beside the laptop that displayed the digital result, the two technologies coexisting on the desk the way they coexisted in the profession, the old and the new, the hand and the machine, the judgment and the algorithm.

"Did you look at it," Jin said.

"I looked at it."

"What do you think."

Silas looked at the screen. The DEM was still there, the grey terrain, the simulated shadows, the digital valley.

"It's good work," he said. "The model is clean. The drainage is correct. The saddle is in the right place. The ridge lines are plausible."

"Plausible," Jin said. The word was a question. The word said: plausible is not accurate. Plausible is not correct. Plausible is the word a cartographer uses when the representation is acceptable but not authoritative, when the map looks right but might not be right, when the terrain on the page could be the terrain on the ground but the surveyor is not certain.

"There are disagreements," Silas said. "Between your contour lines and mine."

"I know. I overlaid them. I registered your scan to the DEM and I computed the differences. The RMS difference is 2.4 feet. The maximum difference is 11.7 feet, on the east ridge, near station seventeen."

"Station seventeen is the cliff."

"Yes. The cliff is where the disagreement is largest. The algorithm does not handle cliffs well. The kriging assumes spatial continuity -- it assumes the terrain changes gradually between the data points. The cliff violates the assumption. The cliff is a discontinuity, a place where the terrain changes abruptly, and the algorithm cannot represent the abrupt change because the algorithm's mathematics require smoothness, require the gradual transition that the variogram describes."

"And my contour lines."

"Your contour lines show the cliff. Your contour lines compress at station seventeen, the spacing tight, the lines close together, the cliff represented by the crowding of the lines, the visual convention that says: here the terrain is steep. Here the slope exceeds the contour interval. Here the map is struggling to keep up with the ground."

"The hachure marks," Silas said.

"Yes. You drew hachure marks on the cliff face. Short lines perpendicular to the contour lines, pointing downslope. The hachure marks say: this is a cliff. This is not a steep slope. This is a vertical or near-vertical surface, a surface that the contour lines cannot represent at this interval, a surface that requires the supplementary symbol, the annotation, the cartographer's admission that the standard representation has failed and the terrain requires special treatment."

"The algorithm does not draw hachure marks."

"The algorithm does not know what hachure marks are. The algorithm knows elevation values at grid points. The algorithm computes contour lines by connecting points of equal elevation. The algorithm does not know that a cliff is different from a steep slope. The algorithm does not know that the terrain's story changes at station seventeen, that the quartzite gives way to the schist and the resistance changes and the erosion accelerates and the slope becomes a face and the face becomes a cliff. The algorithm has data. The algorithm does not have knowledge."

Silas was quiet. He looked at the screen. He looked at the cliff on the DEM, the place where the simulated shadow was darkest, the digital slope steepest, the grey tones compressing from light to dark in a narrow band. The cliff was there. The cliff was represented. But the cliff was smoothed, the abrupt transition averaged, the discontinuity interpolated into a continuity, the algorithm's mathematics imposing their assumptions on the terrain, the terrain made to conform to the model rather than the model conforming to the terrain.

"Your mother would understand this," Silas said.

Jin was quiet for a moment. The phone carried the silence between them, the silence of Anchorage and the silence of Fairbanks connected by the satellite relay, the signal traveling from Jin's phone to the tower to the satellite to the tower to Silas's phone, the conversation routed through space, through twenty thousand kilometers of vacuum, the words traveling the same path that the GPS signals traveled, the same satellites, the same electromagnetic spectrum, the words and the positions using the same infrastructure, the same physics, the same speed of light.

"What do you mean," Jin said.

"The algorithm and the hand-drawn map disagree about the cliff. The algorithm smooths it. The hand-drawn map shows it. The disagreement is about how to represent a discontinuity -- a place where the terrain changes abruptly, where the gradual becomes the sudden, where the rules that apply on one side do not apply on the other."

"Yes."

"Your mother's paintings and her database. Her painting of a landscape and the GIS representation of the same landscape. They would disagree about the same thing. The GIS would smooth the transitions. The painting would show the abruptness. The GIS would average the colors. The painting would preserve the contrast. The GIS and the painting would disagree about how to represent the moment when the light changes, the moment when the shadow arrives, the moment when the green of the spruce becomes the gold of the birch -- the boundary, the edge, the place where one thing ends and another begins."

"She would say the boundary is where the painting lives," Jin said. "She says that. She says the interesting work happens at the edges, at the transitions, at the places where one color meets another and the meeting is not smooth, is not averaged, is not interpolated but is sharp, is sudden, is a line."

"A contour line."

"A contour line. A boundary. A place where the elevation changes and the change is marked and the mark says: here is the transition. Here is the edge. Here the terrain is different from what it was a moment ago, a step ago, a foot ago."

Silas thought about Margot's paintings. The boundaries in the paintings -- the boundary between the ice and the moraine in the glacier painting, the boundary between the tundra and the bare canvas in the unfinished painting. The boundaries were sharp. The boundaries were deliberate. Margot had painted the boundaries with precision, the edge of the ice defined by a line of white against the grey of the moraine, the edge of the tundra defined by the last brushstroke against the cream of the canvas. The boundaries were where the painting made its argument, where the representation asserted itself, where the painter said: this is what I see. This is where one thing ends and another begins. This is the contour line of the visual world.

"The algorithm is not wrong," Silas said. "The algorithm is doing what it was designed to do. The algorithm is interpolating between the known points using a mathematically defensible method. The algorithm's contour lines are consistent with the data. The algorithm's representation is valid."

"But."

"But the algorithm does not see the cliff. The algorithm does not know the cliff is there. The algorithm has data points on both sides of the cliff and the algorithm connects them with a smooth curve and the smooth curve does not describe the cliff, does not represent the cliff, does not tell the reader that there is a forty-foot face of quartzite between station sixteen and station eighteen where the terrain does something that the smooth curve cannot express."

"And your contour lines do."

"My contour lines do. Not because my contour lines are better than the algorithm's contour lines. Not because my method is superior to your method. But because I was there. I stood at station seventeen and looked at the cliff and saw the quartzite and saw the face and saw the scree at the base and heard the rockfall in the night and felt the wind off the face and smelled the lichen on the rock. I was there. The algorithm was not."

Jin was quiet again. The satellite carried the silence. The phone hummed with the hum of electronics, the baseline noise of the system, the sound of the signal when the signal carried no words, the sound of the channel open and empty, waiting for content, the way the vellum waited for contour lines, the way the canvas waited for paint.

"So which map is right," Jin said.

Silas looked at the screen. He looked at the DEM. He looked at the cliff, the smooth cliff, the averaged cliff, the cliff that the algorithm had interpolated into a steep slope.

"Both maps are right," he said. "Both maps are wrong. Both maps are projections, and both projections sacrifice something to preserve something else. Your map preserves mathematical consistency. My map preserves observational detail. Your map is reproducible -- anyone with the same data and the same algorithm would produce the same map. My map is not reproducible -- no one else would draw the contour lines exactly as I drew them, because no one else stood where I stood and saw what I saw and knew what I knew. Your map is objective. My map is subjective. Your map is the terrain as the data describes it. My map is the terrain as the surveyor experienced it."

"And the terrain."

"The terrain is what it is. The terrain is the cliff and the slope and the creek and the saddle and the bear that walked upstream and the sparrow that sang every forty seconds and the light at two in the morning and the sound of the rockfall in the night. The terrain is everything. The map is not everything. The map is a selection, a reduction, a choice. The map chooses what to show and what to hide, what to preserve and what to sacrifice. The choice is the projection. The choice is the art."

"The art," Jin said. "You called it art."

Silas paused. He had called it art. He had used the word art in connection with cartography, which was a thing he had never done before, the word belonging to Margot's vocabulary, to the vocabulary of the studio, not the study. But the word was correct. The word described what he meant. The choice of what to show and what to hide, the judgment of what to preserve and what to sacrifice -- this was not science. This was not computation. This was the exercise of judgment informed by experience, the application of the eye's knowledge to the hand's work, the act of making a representation that was not a copy but an interpretation, not a reproduction but a rendering.

"The art," Silas said. "Yes."

The conversation ended. Jin said he would incorporate Silas's observations into the DEM documentation. He would note the cliff. He would note the disagreement. He would include both representations -- the digital and the analog -- in the project archive, the two maps filed together, the algorithm's map and the cartographer's map side by side, the agreement and the disagreement both documented, both preserved, the archive holding both versions of the truth the way the valley held both the bear's survey and the surveyor's survey, the two records incompatible and complementary, each one capturing what the other missed, each one faithful to what it could see and blind to what it could not.

Silas closed the laptop. The DEM disappeared. The screen went dark. The valley was gone -- the digital valley, the simulated valley, the valley of grey tones and shaded relief. The actual valley was three hundred miles to the north, under the August sky, the creek running, the ridges standing, the cliff standing, the terrain being itself, undisturbed by the representations that had been made of it, undisturbed by the contour lines and the grid points and the algorithms and the hachure marks and the disagreements about how to show a forty-foot face of quartzite that was, at this moment, the same face it had been in June and would be in September and would be, with insignificant modification, for the next ten thousand years, the cliff indifferent to its representations, the cliff indifferent to the maps, the cliff standing in the valley the way it had always stood, vertical, fractured, real, the thing itself, the territory, the ground truth against which all maps were checked and all maps fell short and all maps, in their different ways, tried to honor.

Silas opened the field notebook. He turned to the page where he had written the addendum to the legend. He read it again. He added a line:

Two maps of the same valley. One drawn by hand, one computed by algorithm. They disagree about the cliff. Both are correct. The cliff does not care.

He closed the notebook. He put the pencil down. He went to the kitchen and made coffee in the French press and stood at the window and looked at the garden and drank the coffee and thought about cliffs and algorithms and the particular, irreducible knowledge that came from standing in the terrain and looking at it with the eyes of a person who had spent a lifetime learning to see.