Guidelines & Plotlines.

Marc A. Reynolds, Minor Third Series: Harmonics, 2011.

The line of Culture

In algebra, a line is defined by the equation of any two terms, each of which is the product of a constant and the first power of a variable. It might be expressed by the formula ax + by = 0, where a and b are constants, and x and y variables. Plotting the possible values of the two variables by means of Cartesian co-ordinates, the result is a line that is perfectly straight. Other, more complex algebraic functions yield figures of the kind mathematicians call curves. For example, the equation y2 = 4ax generates a parabola. Equations of this kind are called non-linear, even though the curves they specify are composed of lines. It seems as though the quality of straightness has become somehow fundamental to the recognition of lines as lines, not just in the specialized field of mathematics but much more widely. Yet there is no reason, intrinsic to the line itself, why it should be straight. We have already encountered plenty of instances where it is not. Thus our question becomes a historical one: how and why did the line become straight? 

In Western societies, straight lines are ubiquitous. We see them everywhere, even when they do not really exist. Indeed the straight line has emerged as a virtual icon of modernity, an index of the triumph of rational, purposeful design over the vicissitudes of the natural world. The relentlessly dichotomizing dialectic of modern thought has, at one time or another, associated straightness with mind as against matter, with rational thought as against sensory perception, with intellect as against intuition, with science as against traditional knowledge, with male as against female, with civilization as against primitiveness, and – on the most general level – with culture as against nature. It is not difficult to find examples of every one of these associations. 

Thus we suppose that protean matter, being the physical stuff it is, has a texture revealed to close inspection as a mass of almost chaotically tangled threads. We saw in Chapter 2 that the word ‘tissue’ – applied to the materials of living things – carries a similar connotation. This is the stuff we feel with our senses. But we imagine that, in the formation of interior mental representations of the material world, the shapes of things are projected onto the surface of the mind – much as in perspective drawing they are projected onto the picture plane – along straight lines modelled on rectilinear rays of light. And if the lines along which light travels are straight, then so are the ways of enlightenment. The man of reason, wrote Le Corbusier, the supreme architect of rectilinearity in modern urban design, ‘walks in a straight line because he has a goal and knows where he is going, he has made up his mind to reach some particular place and goes straight to it’ (Le Corbusier 1924: 274). As he walks, so he thinks, proceeding without hesitation or deviation from point to point. What Ong calls the ‘sparsely linear’ logic of the modern analytic intellect has often been compared in this vein with the more circuitous, mytho-poetic intuitions attributed to people in ‘traditional’ societies, and above all to those without writing of any kind (Ong 1982: 40). Through this comparison, ‘thinking straight’ comes to be regarded as characteristic of literate science as against oral tradition. Moreover, since the straight line can be specified by numerical values, it becomes an index of quantitative rather than qualitative knowledge. ‘Its function’, as Billeter notes, ‘is to separate, to define, to order, to measure, to express number and proportion’ (Billeter 1990: 47). (...) 

Guidelines and plotlines 

In earlier chapters, following de Certeau, I have shown how the modern maker or author envisions himself as though he were confronting a blank surface, like an empty page or a wasteland, upon which he intends to impose an assembly of his own design. The straight line is implicated in this vision in two quite distinct ways: first, in the constitution of the surface itself; secondly, in the construction of the assembly to be laid upon it. For the first,imagine a rigid line that is progressively displaced along its entire length, in a direction orthogonal to it. As it moves, it sweeps or rolls out the surface of a plane (Klee 1961: 112–13). For the second, imagine that the plane is marked with points, and that these points are joined up to form a diagram. This, in a nutshell, is the relation between our two manifestations of the straight line. One is intrinsic to the plane, as its constitutive element; the other is extrinsic, in that its erasure would still leave the plane intact. In what follows, and for reasons that will become evident as we proceed, I shall call lines of the first kind guidelines, and those of the second plotlines. A few familiar examples will help to clarify the distinction. 

In the assembly line of modern manufacture, the surface upon which the assembly takes shape is literally rolled out in the movement of the conveyor belt. On the surface of this belt, components are joined together in the construction, piece by piece, of the final product. Here, the unrolling line of the belt is a guideline; the joints of the construction are plotlines. However, the first assembly line, as Ong has pointed out, ‘was not one that produced stoves or shoes or weaponry, but one which produced the printed book’ (Ong 1982: 118). In printing it is the job of the compositor to assemble the blocks of type on a composing stick before placing them in the galley. The line of assembled type is a plotline, but the straight, raised edges of the composing stick and the galley, against which the type rests, are guidelines. Of course, on the printed page, neither guidelines nor plotlines are visible as such. On the modern musical score, however, we can see both. Here the five parallel lines of the ruled stave are guidelines that establish a space, arrayed on the dimensions of pitch and tempo, on which the values of individual notes can be plotted. The ligatures connecting successive notes into phrases are then plotlines. ‘Musical notation’, as Kandinsky observed, ‘is nothing other than different combinations of points and lines’; however it should be added that the lines, respectively, forming the stave and joining the notes are of an entirely different character and significance (Kandinsky 1982: 618–19). 

Next, imagine a modern scientific graph. The lines of the graph, drawn with a ruler, connect points, each of which has been plotted by means of co-ordinates on the surface of the page. To facilitate this, the page itself is ruled with fine lines in two parallel sets, running respectively horizontally and vertically. These are guidelines that effectively establish the page as a two-dimensional space. And the lines connecting the points of the graph are plotlines. When graphs are reproduced in published texts, the original guidelines usually vanish, such that the plotlines figure against a plain white back- ground. It is as though they had been swallowed up by the very surface they have brought into being. All that remain are the straight lines marking the axes of co-ordinates. Yet they are still followed implicitly when we ‘read’ the graph, running our eyes or fingers either up or across to reach each point. It is rather the same with a cartographic map. Here the ruled lines of latitude and longitude are guidelines that enable the navigator to plot a course from one location to another. 

T. Ingold, Lines: a brief history. London; New York: Routledge, 2007, pp.152-153 & 155-156.