Traversing Space:
Point/Line/Plane/Vector

Homage to Deleuze and Guattari

POINT
When I began hiking the main Tararua Range, the weather was mild– the kind of day that makes you want to walk. Past the gate, the first stretch was up through a cattle pasture, fields that appear simple solid green grass until you try to cross them, then it’s tussock to tussock, cow flops to meadows that are actually bogs. A herd of young steers ran out in front of me, making a muted thundering when they all hit their stride. The stile at the end, one of those inflection points that is always a brown muddy soup, marked the entrance to the range itself, and the path rose fast when I left the pasture behind. As I gained elevation, the temperature dropped, the rain thickened, and the wind began to push me around. This section of the Tararua Range has five Department of Conservation huts (each a different style, age, and comfort level) every eight kilometers or so. My plan was to get to the second one — Te Matawai– that first day, but by 2:30 the rain was intense and the winds pushed even harder, so when I got to Waiopehu, the first hut, I called it a day. The next morning brought no relief. The rain continued so the trail was a stream, and the wind rattled the windows of this well-built but unheated shelter. I spent most of the day reading while seated at the table looking out a bank of windows at an opaque white wall. I was fairly certain below me was the flatland I had hiked out of the day before, but for all I knew, it was the moon or the Arctic. I was inert and immobile, a walker without a path.

POINT-LINE
In his essay “Walking,” Thoreau describes going to see two panoramas (the Imax of the 19th century). The first was of the Rhine River; its castles and ruins were the sites of stories that had stirred him in his youth. Then he saw the Mississippi panorama, depicting stories yet untold. In pairing these, he gestured toward what he considered the heroic age of young America which was building out from Eastern shores to become a transcontinent. Using the idea of the West to signal openness and freedom typifies the rhetoric of his essay, but the way he describes his experience of the paintings also is telling. On the Rhine, he “floated along under the spell of enchantment, as if [he] had been transported to an heroic age.” On the Mississippi he “worked [his] way up,” “gazed,” and “looked” into rivers and an emerging history, an heroic age in the making. Although one is passive, the other active, both are experiences of space as point-line. Thoreau was already inclined to such a narrative as it was the mode of his early book, A Week on the Concord and the Merrimack, which describes a trip with his brother in an unwieldy boat, seeing his familiar Concord and environs from an unfamiliar perspective. Although a river unfolds like a ribbon, bending back on itself, forming within its banks differential currents and lateral complexities, it remains a line, with the boat a point. Perhaps unwittingly, Thoreau’s digression regarding the river panoramas recapitulates the phenomenology of the essay’s subject– walking –which in the frame he initially articulates is a point following a line.

I spent four days paddling the Whanganui river from Whakahoro Landing to the city of Wanganui (spellings alternate between “w” and “wh”). It was locomotion through a combination of river current, piloting, and arm strength (my tramping legs got a rest). The landscape unrolled slowly, with a perspective more distantly specular than the hiking trail because of the openness of the water as opposed to the confinement of the deep dark woods. Piloting the canoe engages the senses in ways at least superficially different from walking. A distant roar could be wind, a waterfall, tributary stream, or rapids that demand alert and instantaneous actions. You hear and feel changes in the current, even as you see stories both old and new unreeling down the line. But this is not to dismiss walking as less sensory intensive. There your ears hear subtle transformation of landscapes (shifting wind on ridge tops) as well as register altitude gradations concomitantly felt in feet and legs. In both, the information is navigational–the ribbon of the water or the worn path of the trail unwind in a line that commands a following.

On the river, following the point-line is staying within a laminar flow. Drifting off the line even for a moment takes you into the slack of a backwater or head-on into a turbulent flow from which only chance will extricate you. Walking, particularly footpaths, tends to minimize such vortical or non-linear disturbances. Paths are usually there to lead you through. Long-distance hiking is the willing subjection to the tyranny of the point-line, though at times, like on the water, there are counter-currents. All hikers resist, complaining about track lay-out where designers inevitably and for seemingly no reason swing through difficult terrain or arbitrarily go over every hilltop no matter how difficult the climb or unappealing the vista. In addition, pathways themselves can produce turbulence or resistance, something Christopher Alexander’s landscape design tries to exploit. In laying out walkways, particularly for college campuses, Alexander tries to build in the possibility of an eddy forming in the flow of students, a place where the path compresses and releases in such a way that some of those following it are ejected into a calm space, one for chance encounters and possibly quiet conversation outside the restricted choreography of academic intercourse. Alexander’s point-line becomes vector, a way out of simple directedness.

POINT-LINE/PLANE
Ideally, the point-line form of being is one of constant orientation. Hiking the Appalachian Trail can be almost completely a point-line affair. In good weather, the trail itself is worn and usually obvious. That line is supplemented by the white rectangular blazes appearing with regularity throughout. Junctions might have supplemental signage or just a clear white blaze indicating the proper choice. The Te Araroa aspires to such a state and often succeeds by a visible track and strategically placed orange triangles. Because it is a trail fairly recently cobbled together via a number of already existing trails, such signage can be inconsistent or even absent. This is compounded by what seems a general reluctance to nail the plastic triangles to tree ferns, small bush, or on any pines in a tree plantation (nails in stump timber completely devalues the lumber). Consequently, navigation is more complicated. I find I rely heavily on PDF maps supplied by the Te Araroa Trust and a New Zealand topo/GPS smartphone app. As a result, my experience of point-line becomes point-line/plane. I position myself as a pulsing blue dot on a screen at the same moment that I stand firmly (or slip uncertainly) on a terrestrial path. The representational plane supplements the point-line function; however, at that navigational moment, it is only tangentially planar. On the screen, the topography surrounding the line is inconsequential. The only information of significance is confirmation that I am indeed standing where I am supposed to be, moving along the line I need to follow. The plane becomes significant when the line is misread or unreadable.

As is well-documented, Thoreau sometimes made his living as a surveyor, rendering the landholdings of his neighbors onto gridded paper, representing through points and lines a plane or a plat. There cairns, spikes, or blazed trees don’t mark a way through but instead are the metes and bounds of properly surveyed land. Representing space as planar, perhaps a map laid out on a table or the ichnographic vision of GPS or google maps, is a form of mastery, a Cartesian leverage. Conversely, seeing the world from a point-line is phenomenologically distinct and at least in part embraces uncertainty. It is according to Ezra Pound “Periplum” which he characterizes in this way: “not as land looks on a map/ but as sea bord seen by men sailing.” A point-line makes a way, a point-line/plane makes a difference. This is not to say that the experience of space is a simple duality–point-line or plane–only to note those are dominant modes that can help us understand how it is that we come to walk in the world, or how it is that we world when we walk.

The 42 Traverse is a section of the Te Araroa that follows a mountain-bike path from the beautiful village of Owhango over a small mountain range into the Tongiriro Reserve. The area was extensively logged in the 20th century and now is a protected reserve, regenerating as wild bush. The trail itself is a wide, well-benched gravel surface. The Te Araroa hiking directions describe the point where the trail splits off from the Traverse to descend into the Tongiriro area at a point further north than the end of the Traverse. I started this part of the tramp one afternoon after lunch at the cafe in Owhango, planning to get about half-way and pitch my tent for the evening. The traverse is the epitome of point-line tramping. Near the end of the day, I found a grassy spot next to a small stream to camp. The next morning I resumed my trek, and, not paying careful attention, missed the Te Araroa turnoff. This did not initially trouble me because the guidebook had warned that portion of the trail was poorly marked and it was reasonable to just follow the 42 Traverse to the end. However, when I pulled up the full planar view on my phone, I saw that I would connect with the highway at a very great distance from my destination point which happened to be the only camping accommodation any where near my path. The planar view offered a number of other possible lines to follow, lines that, if navigated properly, would save me many kilometers even if they didn’t make up for my negligence in missing a turn. Now I was in full planar navigation though my map did not have the resolution necessary to make good judgments nor to have confidence in the lines I hoped to follow. The area had once been criss-crossed with logging roads, many of which remain open for ATV travel while others are overgrown and impassable. I spent the afternoon tracking old tracks, some there, some not, following a faint line to its end, backtracking to another, never quite certain where or how I would find my way out. After a good 30+ kilometer day, I found myself trespassing through a school property and finally out onto the highway, only to discover I had another 7 km to the campsite. Of course it then started to rain–not a pleasant day. Clearly I occupied space that day differently from a normal tramping day. The shift from point-line to point-line/plane produced a space fraught with tensions and decisions, stress and anxiety, even as I remained within the confines of the planar striations (not that I wasn’t tempted to strike out through the gorse in hopes of finding another way out). But the addition of the plane view did finally make a difference. What I experienced on the ground was not exactly what was represented on the map, but the combination resulted in (relatively) successful navigation. The doubling of view– sea bord and bird’s eye–worked.

PLANE-VECTOR
As a tramper, my occupation of space almost always follows the point-line/plane model, but clearly there are other forms of walking being. As mentioned earlier, on that same traverse I pitched my tent on a perfect moss bed just off the trail. It was a cool evening, and I had walked a long way, so, as is my wont, I crawled into my tent early, got warm in my sleeping bag and read for a long while. You can imagine my surprise when, in the middle of John McPhee’s travels in Alaska, a gun cracked a short distance from my tent. The sound came from downhill, off the trail. I looked out, straining my ears for other noises, and hearing none, returned to my book though now on alert. Some time later another, louder report echoed around my site, and this time I could hear a rustle in the bush. Soon a middle-aged man in green and camo carrying what looked like a 30-30 bolt action rifle appeared. We spoke a while. He had shot a deer with a silencer on his rifle, then later fired an unsilenced shot to signal his hunting partner. It was then that I saw the man’s hands, both covered with blood to the wrists. Clearly he had brought down his prey. Bidding good evening, he headed down the trail in the direction I had passed earlier that day. Before long I heard the roar of an ATV engine, off down the hill away from the trail. As dusk set in and I grew sleepy, voices came from the other direction (tomorrow’s destination) and soon there appeared my hunting friend with a younger man who appeared to be wearing a backpack. Only as they passed did I realize the straps were the deer’s front legs as he was carrying the gutted animal, still bleeding out. Soon after I heard the ATV start up and drive away, the engine noise fading with the day’s light.

I lay there that night thinking about how those two men and I differently occupied the same space. I was, quite literally, on a linear traverse, but they were following a series of vectors enabled first by their familiarity with the actual plane of the land and their reason for occupying. Long-distance hikers move in an open, free space relative to the places they likely occupy in the workaday world. My job which to varying degrees dictates my position in space and time seems much more structured than my trek down the Te Aroara, but my position on the 42 Traverse was completely linear compared to the hunters (and their prey) as they moved not via point-line but instead plane-vector. The hunters deployed machines (guns, ATVS), positioning sounds (engine noise, shots), topographic features (hills, streams, dense bush), and their own historically constituted understanding of the New Zealand terrain coupled with their time in this particular place. They knew its affordances including the possible vectors of human and animal movement. Their senses were differently tuned to sounds and motions that I could safely ignore or probably didn’t even notice.

The terrain we were all traversing also had vectors formed since the volcanic eruptions laid down its soils. Pre-human New Zealand was a land with no mammals (except a particular species of bat), so birds of bewildering variety evolved to occupy various ecological niches. As waves of humans arrived, so did their animals and plants. Rats, opossums, deer, wild pigs, stoats, rabbits, all flourished in an environment with few or no enemies. Introduced plants also flourished, transforming the landscape. There is a lot of finger pointing regarding responsibility for the more invasive varieties. A Kiwi farmer I met blamed the Irish for the introduction of gorse. The Irish tend to get blamed for much in New Zealand it seems, but regardless of who brought it, gorse was a bad idea. This reserve was nearly completely logged off– first of native large trees, then of planted pines (another introduced species). In the last decades the government has set out to restore the area as native bush, a strategy that on the surface is laudable, but raises the question regarding what point in history one chooses to restore. One thing is clear, the gorse is here to stay. The mammals seem to be the primary targets and are aggressively pursued with traps, poisons, and hunters, so the hunters here include both human and chemical (one has to wonder about the cyanide legacy of attempted species eradication). What is important to recognize is that point-lines are drawn, established, and maintained, actions that require effort, diligence, take place in time, but also follow fairly predictable patterns. Plane-vectors unfold dynamically in time through unexpected and unpredictable paths. Gorse might be attractive, sweet smelling and generally docile in Ireland, but it becomes an aggressive, dominant plant on disturbed land in New Zealand. It, like the animals the program seeks to eradicate, thrives on edgelands, places of possibility, quickly occupied by the opportunistic.

VECTOR
I watched a pastoral version of the vectoral play out one day tramping down a road on a ridge not far from Manunui. It had on its right (as I walked south) a narrow verge with, as is common in New Zealand, fencing up to the edge of the road enclosing a pasture. What was striking to me was the narrow shelf of turf just inside the fence before the land dropped off precipitously many meters before leveling off in a field where I could just see in the distance a farmer next to his truck. (The pastures are so steep in New Zealand they fertilize them from airplanes.) A little further down the road, the narrow shelf broadened out to form a plateau of perhaps an acre where about thirty steers were grazing quietly. As I walked toward them I heard the sharp whistle of the farmer and saw two border collies racing up the vertical pasture wall toward the cattle. Alarmed, the cattle began to move about. A number followed along the fence line onto the narrow strip where I stood. The dogs separated and, responding to different whistles, proceeded to draw the group back together. I stood transfixed, not wanting to disturb the operation and fascinated by what was unfolding. The cattle came near me, spooked, split off, some heading back, others trotted down the fence line. Those outlaws were soon headed by one of the dogs, and as the herd regrouped at the apex of the narrow strip and the wider pasture, one steer–spooked, slipped, pushed, had the ground give out beneath him–turned and ran downhill. Then a cascade of cattle descended the declivity, while dogs circled up the remaining few who joined the herd in a rapid descent to the main pasture. Not a profound event, just a morning on the farm for farmer, dog, cow, and turf, but it was a marvelous moment, showing the spontaneity of vectoral traverse.

That brings me back to Thoreau because I have not fairly represented him. His essay “Walking” is a classic celebration of the vectoral. His ideal walking is never on a road, or even crossing roads (though that is something that remains unavoidable for anyone who walks distance). He seeks out huckleberries and wild apples–the denizens of the margins–and celebrates swamps, edgelands, and the aimlessness of wandering. It was in “Walking” that he wrote the often (mis)quoted line: “In wildness is the preservation of the world.” There is much that can (and has) been said about what he means by “wild,” but I would add to it the notion of vectoral walking. Following out a line of flight through a point of intensity, a bifurcation, a moment of possibility, is a form of the wild. Like the tree grown from an apple dropped somewhere by man or beast, it is a wilding. Traversing space through point-line, or positioning and navigating carefully through a planar representation or through sheer familiarity with the space is a form of traverse but also a form of discipline and even subjection. Thoreau’s ideal is a purer resistance. His sauntering follows out unacknowledged internal impulses, a “subtle magnetism” coupled with the “capabilities of the landscape,” the affordances it provides and the dialog it produces to cross the line, escape the plane and follow the vector. It is a traverse without goal, except to express and even live the possibilities of the space, the open, the wild.

T. Hugh Crawford