# Line theory

What is a line?

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Consider the following examples:

A line of text, in English, to be read left to right. In Mandarin , top to bottom.
A trail though the forest, leading us through, presumably, safe passage.
Footprints, showing where one before us had been.
A vein, which is not too different from
a root
a wire
a pipe
An arrow, indicting that there is something that way —————>
<————————or this way.

These examples demonstrate that line is spatial. Lines inherently imply movement. Left, right, up, down. They ask to be followed.

Line is also related to memory and imagination. How else could we trace the path from where we were to where we are? How else could we say where something will be as based solely on where it is? The trajectory of a baseball serves as an example. The line that defines the movement from the pitcher’s hand toward the catcher’s mitt is something the batter must be able to visualize. The line of the ball away from the bat is something the outfielder must be able to imagine.

A fence is also a line, but it is different from the above examples. The proper function of the fence is not to lead, but to define. “Delineate”. A fence indicates a boundary. A really effective fence defends the boundary, more than just defining it. It keeps things that ought be outside the boundary out and things that ought be in the boundary in. Thus, a fence keeps solid the concept of a territory, which is a shape.

It is important the consider that when we think of a territory, we think of it from above, which is a way of flattening space into a shape. A fence, when confronted directly, is just a barrier. It says nothing about the other side except that you do not belong there. (Lines, then, are an inherent aspect of the concept of transgression.)

A line, then, has the power to define inside and outside, but only in two dimensions. In three dimensions, there are no lines, but surfaces. A surface, however, is defined in relation the the space it occupies. There is not, in nature, a clear distinction between the two sides of a surface. In purely physical terms, it is hard to pinpoint the spot where a surface changes into another surface. One can become infinitely more precise in defining the division.

I’m reminded of Zeno’s paradox about the arrow. Before an arrow can reach its target, it must reach the halfway point between its starting point and the target. Before that, it must reach the halfway point between its starting point and that halfway point. Then the halfway point between that halfway point. The space between where the arrow is and where it will be is infinitely divisible, so one could say the arrow must travel to an infinite number of points before it can possibly reach its target. The paradox is that it must travel to these infinite points before reaching the target (and thus should be infinitely stuck in space) and yet we know from observation that the arrow does, in fact, reach the target.

One can resolve the problem by pointing out that the points do not actually exist in physical space. They exist solely in the mind, as a way of measuring space. If points don’t exist, the connection between the points does not exist in nature, which means that lines do not exist in nature.

To say the thing that is being measured does not exist and yet the system of measurement is functional is paradoxical. What is being measured is not space, the perception of being contingent of the nature of perception. We are already aware that different organisms perceive space in different ways, and that the nature of space itself becomes foreign to our Newtonian-oriented minds when measured at a quantum scale.

I’m not trying to be tricky or esoteric or trying to undermine your experience (the opposite, actually). This is only to say that lines are not a construct of nature, but of our nature. The distinction between the two sides of a surface is very applicable to and a natural consequence of the nature of our experience of space. But if such an object existed in nature where the distinction between its surfaces was completely exact and identifiable, this object could serve as the perfect blade, capable of slicing a diamond like butter.

Of course, these divisions in surfaces, or planes more properly called, are perfect in digital modeling programs. These programs, however, create mathematical constructions, not physical reality. Perceivable, like the physical world, but not of the physical world. A digitally constructed object is not composed of any matter. It can only be made to look as if it is composed out of matter.

Here, in this digital landscape, the line that divides two planes is identifiable. The two points that define the line are called vectors, and all vectors are defined by their relative distances between other vectors.

A precise division in space is one way to understand a line, and is perhaps the most intuitive understanding of a line. When one sets out to draw, for example, a nude model (to give a very artsy example), one benefits from determining where the model’s body ends and empty space begins. The mind does this rather naturally. Moving around the model, we see the lines that define where the model’s body is in space change. The only form this rule does not apply to is a perfect sphere. A drawing of the contour of this sphere will always be, simply, a circle. A cube is more complex, but still pretty predictable, and there are certain positions from which one could stand, looking at a cube, that would be perceived as the same flat contour of a square. When looking at a complex form such as a human body, for example, contours continuously change as you move around the model or if the model moves (the model will move unless the model is dead). Thus, the artist chooses one position from which to draw the model, tracing the contours as lines on a 2D surface. If the artist has skill, s/he will be able to use these lines to create the illusion of the form that is before him/herself.

If someone isn’t an artist, s/he can still draw a body in such a way that it is intelligible. This drawing is called a stick figure. Notice the word “stick” instead of “line”. We conceive of the line in this drawing as a stick, a form in space, and we use these sticks to create the illusion of a torso, two arms, and legs. Usually we privilege the face by making it out of a circle with lines inside to indicate the eyes and mouth, a clear indication of how much humans rely on the face for information. Still, this simple drawing is very clear and understandable, if not as elaborated as the artist’s drawing.

In order to create the impression of form in two dimensions, all we need do is use lines to clearly indicate an inside and an outside, like a fence.

There is, of course, another form of drawing, as evidenced best by the drawings of Seraut, that eschews the use of lines and focuses on light, called tone to the 2D artist. Tone refers to the relative lightness or darkness perceived by the eye then recorded on the surface. Tonal drawing is no more nor less observational than line drawing. The difference is that tonal drawing focuses on how the world is perceived and linear drawing focuses on how it is conceived. (This distinction is very simplistic. For example, many artists who focus on line are well aware how to use line to convey an impression of tone. For present purposes, let’s keep things simple.)

Tonal drawings are not “drawings without lines”. They are drawings that rely on the viewer’s impulse to take visual impressions and transform it into spatial information. This is to say, a tonal drawing relies on the fact that you see lines even where none are explicitly presented.

Understanding this helps one understand the great innovation of DaVinci: sfumato, meaning “smokey” or “fume-like”. The Mona Lisa is culturally prized for its ambiguity. People romanticize her expression. What makes (or, I guess, made) this painting so important was that, instead of clearly indicating the model’s expression, DaVinci made certain points on her face (the corners of her mouth and eyes) “smokey”. Unclear. Basically, your mind’s impulse to “read” her face, and DaVinci’s clever way of denying your mind the necessary information to do so, makes her expression ambiguous. Ambiguity, when used in proper relation to clarity, is dynamic. This has the consequence of enticing your imagination. Your mind will see the expression it chooses to see, because it desperately wants to do so and there are no lines to stop it.

When line is present and contours are clearly rendered, the mind is given everything it needs to clearly “read” the space. Such linear drawing is exemplified by schematic or diagrammatic drawing. No ambiguity should ever be present in a diagram.

I keep saying “read” because the process of using line to convey meaning is the foundation for both the artist and the writer. For the writer, the line becomes a letter.

I don’t think this connection is superficial. Obviously, the lines the writer uses (in Western Languages) work together to create characters that convey sounds. This is phonetic writing. The sound the letter conveys will, of course, depend on what a given culture has agreed upon. This is the cause for difference in accents. Within the same language, however, regardless of accent we all agree that certain combinations of specific sounds create recognizable words. We start basic with kids. C-A-T= cat. (Non-phonetic writing, for example, Japanese Kanji is pretty much iconic drawing. Hito, for example, looks rather like a stick figure. Such abstraction, however, becomes more complex in relation to the concept being conveyed. For a basic example, the name of a day of the week is something far removed from what presents itself to observation. Still, any Kanji character has an iconic quality for those familiar with the language.)

Becoming literate is not necessary for speaking. In a way, the two processes of writing and speaking are inherently different. One need not be able to recognize the written word “cat” in order to say it. One only needs to hear it said enough and to apprehend the connection between the noise and the concept (then the concept and the object. Or, I’d venture to guess, the connection between the concept and the object precedes the connection between the sound and the concept. I can’t speak about this with authority).

I’m not sure how line plays into speaking. I think lines are the basis of logic. An argument establishes vectors in the form of premises and a conclusion. A story establishes vectors in the form of subjects and predicates. The straightness of the line between these vectors establishes the clarity of the story or the validity of the argument (are you following my line of thought?). But, then again, one need not speak clearly or logically in order to speak.

You learn to recognize a letter by drawing it. Your capacity to read and your capacity to write are thus inherently connected. The same applies to drawing (with line), seeing as they are fundamentally the same process. Just as when you read, most of your looking is composed of active, unconscious guessing. Taking advantage of this fact is the birth of illusion. A magic trick works by proving your guessing wrong. A drawing works by proving your guessing right.

The implication is that if you know how to understand a drawing, you know how to draw. You might think you don’t, for reasons we need not go into here, but you do know how to draw. The stick figure is evidence of that. Maybe you think the stick figure inadequate in some way. I’d argue it is completely adequate in conveying the level of information you are trying to convey (a nameable concept: “human body” or “hito”). An artist, who might be highly prized for possessing skills beyond a normal person, simply has other levels of information he wishes to convey. The level of attention he pays to that which he tries to convey determines the form the drawing takes.

The artist might wish to convey a likeness, depth, or movement. The drawing will convey these things. When it comes to the body, the matter is not one of ability but of elaboration. If one wishes to draw a recognizable body, a stick figure is very effective. If one chooses to see the body as being composed of muscle and bone, one will create a drawing that describes these muscles and bones.

Of course, you might point out that drawing is not as easy as I’m making it seem. Even if you start drawing anatomy, this does not mean you will draw it “well”. To respond to this, I’d like to bring up the example, again, of the fence. When you accidentally encounter a fence in a landscape, you have no knowledge of the entirety of its boundary. I’ve already pointed out that you conceive the territory contained inside the fence as a shape, seen from above. This is made clear by looking at a map. But if you don’t have a map, you do not have a mental construct of the shape of the territory. The only way to develop this construct is to walk around the territory, following the fence. If the shape is a simple square, you need not walk around the fence much before you can form a clear picture in your mind of what it looks like from above. If the shape is complex, walking around the fence once probably wont be enough. The first walk around will give you a general idea, but you might need to walk around several times before you develop an acceptable image. Even then, the image of the shape only exists in imagination. The adequacy of the image is determined through testing.

The more complex the information the drawing is intended to record, the more you have play a drawing guessing game. You will draw a line, thinking it conveys information adequately, then you will draw more lines to realize your first line needs amending. You will realize that drawing involves a lot of imagination, even when you are drawing what you are looking at. Imagination is, after all, the ability of the mind to create an image. You realize, in drawing, how mistaken or inadequate that original image was. Or, you feel satisfied that the image was adequate. Maybe the image you construct records exactly what you saw as important (such explains the anatomy of such artists as Alice Neel.)

Someone who has drawn many maps doesn’t get as tired or as frustrated as someone who has just begun drawing maps. A veteran is also aware of all the things it takes to not draw a map, and he stops doing those things.

All things considered, I’m not trying to sell the reader on the idea s/he should develop his/her drawing ability. I am explicitly stating that the reader, insofar as s/he can understand what a drawing conveys, can draw. The metaphor of literacy is relevant. Insofar the meaning of a word has no inherent connection to the object it describes, but is an agreed upon construct, we see it as an intuitive means of describing experience and conveying information. Like a word, a line is nowhere to be found in nature. Yet, in simply perceiving, the use of line is so intuitive, the meaning is so fundamental, it is almost pointless to meditate on the question.