Lines are mysterious. They are drawn by the hand, they are seen by the eye, they appear in the world. Lines are what the hands draw, what the eyes see, and what the page represents. Lines form forms. Simple regular visual/spatial forms like dots, lines, and containers, have meanings that are readily apparent in context. They are used in the service of clear communication, to self and others, notably in diagrams and gesture. They are used to organize, indeed to diagram, the world. Other, messy sketchy lines are used for exploration and discovery.
The eye generates them by connecting the dots, creating the continuous contours that allow us to discern objects in the camouflage of shadows and occlusion. The natural world provides them, the plane of the earth as it meets the sky and the perpendiculars of the things that grow from it. The hand draws them on paper and in the air to represent other things, concrete and abstract. The designer constructs them, connecting buildings and towns along streets, books and dishes on shelves. We travel on them as we go from place to place. Are all these lines, real or virtual, in the world or in the mind, connected?
Lines on paper. Let’s begin with the abstract, with lines that represent, lines that flow from the pen held by the hand. The simplest line is just a dot, a point, hardly there at all. Next, a line, a point extended in one dimension. After that, lines with bends and turns, zig-zags and swirls, arrows and writing. Lines that catch their tails, that close, form shapes, simple forms like circles and squares and more complex forms like contours of animals or trees. Lines create meaning by creating recognizable forms like ducks and rabbits, wives and mothers-in-law. They also create meaning by forming shadows, words, sketches, and diagrams.
Diagrams are constructed from lines. Typically, diagrams are meant to simplify a more complex state of affairs to inform or influence or instruct. A frequent kind of diagram is based in forms that bear physical resemblance to what they are intended to represent. Maps are a prototype for this kind of diagram, but also other diagrams, for example, those designed to show the crucial parts of the heart or an engine, to show how the heart pumps or an engine works, to show how to assemble a heart or an engine. Yet, such depictions in diagrams are not typically designed to be realistic renderings but rather diagrammatic renderings; that is, they may omit or exaggerate or reorganize physical appearance and structure, and they may add information, verbal, symbolic, and visual in the service of informing or instructing. Part of what makes them diagrams and not simple depictions is the addition of simple forms, notably, dots, lines, and arrows that organize, label, integrate, explain, extend, and otherwise add to the depictive information about appearances of parts and wholes. Other frequent kinds of diagrams, notably charts and graphs, don’t generally bear physical similarities to what they are meant to represent, relying primarily on simple visual forms and spatial relations, and of course language and symbols, to show data and relationships.
Commonly, these simple visual forms, dots, lines, and blobs, and spatial relations,
center, up/down, left/right, carry meanings that are readily understood in context. The
meanings seem to derive from their geometric and gestalt properties
Journeys can be one-way, relationships can be asymmetric. For that, asymmetric
lines are needed, and arrows serve that need nicely. Arrows are asymmetric lines, and
have a basis in the experienced world: arrows shot from a bow fly in the direction
indicated; arrows form in the mud in the direction of erosion. Arrows change the
meaning of lines. When asked to describe a diagram of a mechanical system without
arrows, people give structural descriptions; they list the parts and their spatial relations.
When asked to describe a diagram of the same systems with arrows, people provide
functional descriptions; they give a step-by-step description of behavior, process,
causality of the system
Often a broader perspective is needed, two dimensions, not a single one. Not at or
to, but in. Not simple dots, but containers. The cells of tables or the bars in graphs or
circles on graphs or maps contain and represent many entities, those that hold the
properties defined by the cells: the cars manufactured in India in 1998, the number of
spectators at soccer games in Brazil in 2004. The variations that characterize each of
the cars and each of the spectators is irrelevant; all that matters is their numbers;
similarly, their exact locations and the exact time of the year are irrelevant. They are
represented as featureless numbers by simple containers, cells, bars, and circles. This
third distinction, container, is also made in language, signified by the preposition in
Why these regular, almost perfect forms; why not blobs of uncertain shape? After
all, we don’t know the exact shapes, so why is a perfect idealized shape used to
represent a shape that might actually be known? Just as “red” represents a range of
shades of red including magenta whereas “magenta” is a more specific shade of red, a
purplish red
Again like linguistic categories, these spatial categories allow inferences, and the
convergences of those inferences are evidence for their meanings, converging with
their geometric and gestalt properties. People interpret bars in graphs as discrete
comparisons, lines as trends; similarly, they produce bars to represent discrete
comparisons and lines to represent trends
Diagrams, maps, charts, and graphs select relevant information and omit irrelevant information. They may exaggerate, even distort, the relevant information for emphasis, for readability. Overall, their goal is clear and unambiguous communication. These simple spatial forms, and others like them, are their units of meaning, like morphemes, of a visual/spatial vocabulary for communication. They can be combined systematically, like rules of syntax, to form genres of diagrams, sketch maps, circuit diagrams, architectural plans.
Sketches are a very different case of lines on paper. They use lines, the lines may form
shapes, but they are typically uncertain, tentative, unclear. They represent ideas, but
amorphous ideas, ideas that are not yet fully formed. Their very lack of certainty
creates ambiguity, allowing many interpretations, not a single clear one. Perhaps for
that reason, messy lines in sketches encourage exploration and discovery, they promote
new ideas. Messy sketches are used productively by artists, designers, and architects,
especially experienced ones, to explore a domain with impunity, and to generate new
ideas
Now the caveats. Of course, messy lines aren’t always ambiguous, and ambiguity isn’t always productive. Similarly, orderly lines do not always convey a clear message.
Lines are what the hand draws and what the eye sees, a magical convergence. The world on the retina is pixels, dots, representing light of varying brightness and hue. The brain connects the dots, forming lines and shapes that constitute the uncountable number of things we recognize. Designers sketch lines, first messy tentative ones that allow interpretation and reinterpretation, evolving into orderly forceful lines that can convey myriad ideas with clarity.
Acknowledgements. The following grants facilitated the research and/or preparation of the manuscript: National Science Foundation HHC 0905417, IIS-0725223, IIS0855995, and REC 0440103, the Stanford Regional Visualization and Analysis Center, and Office of Naval Research NOOO14-PP-1-O649, N000140110717, and N000140210534.