by Tim Robinson
To find myself in such a landscape, or series of interlocking landscapes, was, it turned out, to be the business of many years, and has been done principally through mapping and writing. The maps are published under the imprint of Folding Landscapes, the little publishing concern run by my partner and myself, since 1984, in Roundstone, Connemara. The maps produced so far are of the Aran Islands (1976 and 1984) and the Burren (1977); work on Connemara is (endlessly?) ongoing.
I approached mapping as an art-form particularly suited to ordering large amounts of fact into an expressive whole. My education had been in maths and physics, but my ‘formation’ was that of an artist working in abstract and ‘environmental’ modes in the London of the late 1960s, while my draughtsmanship was the residue of a period as a freelance technical illustrator. So I came to the practice of cartography largely ignorant of its specific techniques, theories and received ideas, not to say deeply suspicious of its technological and organizational structures that distance the drawer of the map ever farther from the place to be drawn, alienating the hand from the foot. For me, making a map was to be a one-to-one encounter between a person and a terrain, a commitment unlimitable in terms of time and effort, an existential project of knowing a place. The map itself could hardly then be more than an interim report on the progress of its own making.
However, from the start I found myself in collaboration with a traditional cartography. These marginal areas of Ireland were last mapped in detail by the Ordnance Survey in the 1890s and the eighty-year-old six-inch sheets proved to be the ideal basis for my own work, for they lent it a skeletal correctitude of topography but were singularly short of flesh of their own. In the Burren it was the hope of finding some of the many unrecorded prehistoric sites that had me quartering the blanks on the old maps. In Aran and in Irish-speaking south Connemara the Ordnance Survey placenames, few and far between, had to be discarded as they were anglicized garblings that smelled of centuries of cultural imperialism; it became my duty and pleasure to enquire out their original Irish forms and still vivid meanings, a quest that led me into labyrinths of folklore and local history.
When it came to drawing my first maps, I restricted myself to black, and to linear techniques, the better to represent the interweaving of various aspects of the territory. A coloured map, I felt, could easily fall apart, visually and conceptually, into superimposed but otherwise separate layers. In devising symbols for different terrains such as rocky shore, sand-dunes, craggy hillside and blanket bog, I looked for visual equivalents of their feel underfoot, the internationally standardized ornaments being unknown in practice and a priori unacceptable to me; even the term ‘ornament’, with its connotations of superficiality and redundancy, was quite inappropriate for these textures that were to be the very substance and ground of the drawing. Off-the-peg tints and rulings were out of the question too; in any case I found that by consciously positioning even the minutest specks and flecks (done with a 0.1 mm nib, for reduction 3:2) I could create subliminal clearances around the larger marks such as the dots of townland boundary lines, which enhanced their clarity and compensated for the absence of colour contrasts. It was of course axiomatic that the cardinal features of the territory in question would suggest the layout and presentation of the sheet; I was not in the business of carving up the continuity of the earth’s surface into standard portions. For instance I could choose to show the detail of Aran’s majestic range of Atlantic cliffs in a seagull’s-eye perspective in a way that would have been impossible and irrelevant in the case of the anfractuous shores of Connemara.
In all these choices I was trying to preserve the texture of immediate experience. I had a formula to guide me and whip me on through the thickets of difficulties I encountered: while walking this land, I am the pen on the paper; while drawing this map, my pen is myself walking the land. The purpose of this identification was to short circuit the polarities of objectivity and subjectivity, and help me keep faith with reality.
Some of the more puritanical ordinances of my early practice have been relaxed now, as I revel in the latitudinarian spaces of Connemara. But my basic orientation is the same: a map is a sustained attempt upon an unattainable goal, the complete comprehension by an individual of a tract of space that will be individualized into a place by that attempt. A banal little inequality, etched into me by the cartographical experience, asserts that unattainability. If t is some linear measure of the sheet within which one is to express oneself, T the corresponding measure of the territory one would express, and m a suitable measure of the richness of detail one’s pen can make lucid, then M, the measure of reality these chosen means can grasp, is forever limited thus:
M < mt/T
7
A Connemara Fractal
My intention is to spin a few threads of ideas out of my experience of making a map – the map of Connemara – and tie them to some specific features of that map, in the hope that they will lead off into wider territories of thought.
I’m not very interested in maps from the technical point of view, so I will be brief on how I went about producing this one, and move on to the more interesting questions of what is it like to make a map – insofar as I can untangle my memories of the process – and why maps are, finally, so unsatisfactory. For if cartography is not necessarily more helpless than other modes of representation in the face of the world, it has its own characteristic failings, which the blanks on a map, essential to its legibility as they are, reveal with disconcerting candour.
Of course I can afford this attitude of disinterest in certain aspects of cartography because a lot of the mechanical part of the task has been done for me. Connemara, like the rest of Ireland, was very carefully surveyed in the 1830s and again in the 1890s, by the Ordnance Survey, which is in origins and ethos a section of the army. Indeed it took an army of men, lugging theodolites and chains, to measure all the ins and outs of shoreline and bog and mountain, and there would have been no point in, and indeed no possibility of, one person redoing all that. So the basic topography, in its three dimensions of lengths and breadths and heights, was already available to me. Later I was to discover that this tale of three dimensions is entirely inadequate, not just to the subjective dimensions, the ones that pass through the heart of the cartographer, but even to the objective reality of landscape. But before enmeshing myself in the theory of dimensions, I will mention a few practicalities of the business. Although that Victorian mapping was quite accurate enough for my needs, it is ninety years out of date so far as concerns roads and paths and buildings. So what I did was to take the six-inch OS maps, which break up Connemara into about thirty sheets, and walk or cycle every road and track I could find, marking in the ones that were not on the old maps and noting all the buildings and anything else that had changed since 1898. This sometimes involved a very rudimentary sort of surveying; I had a little compass, and I quickly learned to judge distances of a hundred or two hundred yards by eye. However, I soon found that most new features could be accurately located on the old maps by reference to things that had not changed, or of which traces remained; I could usually see where in the pattern of the old field-walls the new bungalow was set, for instance. It was simple enough, but it took me a total of several years of walking to cover the ground, and some of that was a wearisome struggle against wind and rain and cold. I started when we were still living in the Aran Islands, and I used to come across to Connemara for a month or so at a time, usually in early spring or in the autumn, and stay in a b&b or with friends in some particular area, and work out from there each day; setting off on my bike, leaving it by the roadside while I followed some endless bog road up the mountainside, coming down again, cycling on a bit, discovering another bog road, tramping to the end of that and back again, and so on, and cycling home again at the end of the day. The wind, it seemed, was invariably against me. Sometimes the rain held me up for days; I’d go out whenever it looked about to slacken, hoping it would stop by the time I reached the point it had for
ced me to give up at the day before, and so I often spent hours sheltering under hedges or crouched behind a boulder on a desolate shore while wind and rain reduced my OS maps to pulp. Once in Cill Chiaráin I got so fed up waiting for a clearance that I went out to map the village itself in teeming rain, with my map, my pen and my two hands in a clear plastic bag; I remember people peering out at me, amazed, from the shelter of doorways. That was the topographical experience – much of it a penance. But in this way I got the feeling of the place, its obdurate reality, into my bones. I comforted myself for the loneliness, the cold and the exhaustion I often felt, with the idea that it was necessary, this endurance test, to prepare me for doing the actual drawing of the map. For finally those six-inch OS maps scribbled all over with notes and amendments had to be traced, and the tracings reduced photographically, and all the bits stuck together to make a skeleton map of the area, and then a sheet of transparent film spread over that so that I could use it as a guide to an entirely new drawing of the whole. Thus the drawing of the map took place at a few removes – of time and place and mood – from the exploration of the terrain. And I used to hope that the intensity of my physical experience of Connemara would burn through all these layers of methodological tracing-paper into the final drawing, making it not just a factual record, but an expression of a feeling or a lot of contradictory feelings about the place. Perhaps if I vividly remembered walking along a certain shinglebank, I would be able to put some echo of my footsteps into the dots representing it on my map. However, I have come to think that, if this process transmits anything of the terrain itself, it is not my limited, personal and changeable responses to it, but the objective ground of the possibility of that subjectivity. It is the inexhaustibly densely structured nature of reality itself that I would like to image, however feebly, however smoothed out and generalized, in the texture of the map.
It follows that it seemed to me necessary to go everywhere and see everything, before I had the right to represent anything on my drawing. That was and is my guiding instinct, however little I really understand it, and by and large I have stuck to it. There is scarcely anything on the map I haven’t set eyes on for myself. And of course this insistence on the primacy of personal experience led to many discoveries that otherwise would not have been made, and to many meetings with the people of the countryside. As I was particularly interested in the things that are not well shown on the official maps, such as placenames and archaeological sites, and those that hardly show at all on most maps, like local history and folklore, it was essential for me to meet the people of Connemara, for much of this material is not to be turned up in libraries however deep you dig. Also, since I dislike making appointments, my method of rambling along and greeting people on the road or on the shore, or calling in at cottages or indeed factories and hotels, as and when I reached them, suited me, and although it was not always efficient in terms of information-gathering, it put the people in their context; I talked to turf-cutters out in the bogs, to fishermen on the quays, or to Bean a’ Tí over the breakfast-table, where their conversation was in its natural surroundings, comfortable, immediate, alive.
So my map of Connemara is the record of a long walk, an intricate, knotted, itinerary that visits every place within its territory. Some such idea was in my mind when I started, and it was suggested by the extraordinary form of the southern coast of Connemara. It looks so complicated as to be unmappable; it’s a challenge to be unravelled. In an essay I wrote a year or two after starting this map, ‘Setting Foot on the Shores of Connemara’, I said that the distance from Ros a’ Mhíl to Roundstone is only about twenty miles, but that the coastline in between is at least 250 miles long, even as estimated from a small-scale map. My unthought assumption here was that if one estimated its length using a larger-scale map, showing more of its details, one would arrive at a figure a bit bigger than that, a more accurate answer. And, finally, that if one actually measured the coastline with a ruler, going round all the irregularities scrupulously, one would get a more accurate answer still. But this, I was soon to learn, is a naive assumption, and one that short-changes the riches of the natural world. (This question of the length of a coastline is separate from that of the uncertainties and variabilities caused by tides and waves; one can picture the problem as concerned with the edge of an ocean frozen at a moment in time.) When I wrote, I was ignorant of the fact that in the 1960s an American mathematician, Benoit Mandelbrot, had proved that an outline as complex as a coastline does not have a definable length. The idea that one gets a better and better approximation to its length by measuring it in finer and finer detail is false; the series of approximations does not converge to an answer, it just gets bigger and bigger, to infinity.
This disturbing doctrine – disturbing to one who fondly imagined he had walked a coastline with due attention to its quiddity – I first learned of from a newspaper-clipping sent to me out of the blue by an unknown admirer of ‘Setting Foot on the Shores of Connemara’, who I am sure did not realize its implications, its annihilating critique of my essay’s imagery – for such was its effect. A coastline cannot be straightened out, conceptually or experientially, by walking its length; it is not a ‘tangled tightrope’.
A related feature of coastlines, I learned when I went into the matter, is that they look roughly the same at whatever scale one examines them. Think of the coastline of the North Atlantic, as it appears in a small sketch-map: a wriggling line with a few loops off it (Fig. 1). Now think of a bit of that coastline, say part of Ireland, drawn to fill a similar area and with the same degree of inattention to detail: it too is a squiggle with a few loops off it, different in specifics but the same in its general crookedness as the first map. And if then one makes the same sort of casual map of a fraction of that Irish coast, such as Connemara, the result is yet another squiggle with loops. The three drawings are much of a muchness; if they were shuffled, only an inspection of specific shapes could establish which represents the largest sector of coast. Of course some coastlines are more complicated than others. Take part of the south Connemara coast (Fig. 2), and then a bit of it drawn on a larger scale, and then a bit of that enlarged again. Again, at first glance these drawings would look equally convincing if presented in any other order. It is as if the first curve revealed more and more detail the closer it is examined, and that this detail is always similar to the whole. In fact the general characteristics of coastlines are the same, roughly speaking, at all scales, from the whole side of a continent down to the margin of a rockpool.
1. The North Atlantic coast, and two successive fractions of it.
Such shapes are described as ‘self-similar’. A simple geometrical analogy to a coastline can be constructed starting from a jigged line (Fig. 3); smaller jigs are added to each straight bit of the original line, then smaller ones still to each straight bit of the result, and so on to the infinitesimally small, so that it one examined any part of it under a magnifying glass or the most powerful of microscopes, it would look the same, jigs upon jigs for ever. Such an entity is more than a line, which has one dimension, its length, and yet it is not quite an area either, with two dimensions, length and breadth. In fact Mandelbrot showed that it is possible to assign it a dimensionality of one and a half. It may seem absurd to talk of something having 1.5 or 2.7 or 0.3 dimensions, but it turns out that such concepts are not just the dreams or nightmares of mathematicians; indeed fractional dimensionalities are a feature of many natural entities, from curdled milk to coastlines, systems of geological faults, cloud-forms, and even the distribution of the 200 billion galaxies in space. The reason, very hastily stated, is this: mathematically self-similar structures are the result of applying a procedure to a simple initial entity, then applying the same procedure to the result, and so on – an iterative process, as in the example of jigs applied to the results of previous jigs of jigs, etc.; and Nature itself applies its transforming powers again and again to the outcome of previous transformations, thereby bringing into being
forms that are self-similar over a wide range of scales and of a degree of complexity that pre-Mandelbrot geometry cannot model. Mandelbrot called such forms – whether mathematical or natural – ‘fractals’, from the Latin fractus, broken. Conventional geometry would indeed regard such things as broken, confused, tangled, unworthy of the dignity of measure.
2. Part of South Connemara, and two successive fractions of it.
The difficulty of the concept of fractional dimensions is that our everyday idea of a dimension is a possible direction of movement. Thus within the space of a box, we can move an object from side to side, from front to back, and from top to bottom, that is, in three independent dimensions. If the object is to be kept on a tabletop, a plane surface, it can only be moved from left to right, say, or from front to back – two independent dimensions; and if it is strung like a bead on a wire we can only slide it to and fro along that line of one dimension. There is no generalizing that idea to cover fractional dimensions; one cannot have two and a half directions. But there are other ways of conceiving of dimensionality, some of which can be stretched to cover fractals more comfortably. To get a taste of one of these, first note that some ordinary geometrical forms are, in a way, self-similar too. For instance a cube can be divided up into smaller cubes, each of which is similar to the whole but reduced by a certain factor, and then the smaller cubes can be dissected in the same way. Think of a cube with sides of unit length, divided up into little cubes with sides of length 1/b. (Fig. 4 shows the case where b = 4.) The number of little cubes fitting along one side of the big one is b, and the total number N of little cubes making up the big one is b x b x b. That is,
