We have explained from several points of view how every line is an abstraction. Scientifically speaking, a line exists only in the imagination, since it has no depth or width, and thus cannot be visible.
seen consists entirely of surfaces; they may be exceptionally narrow, but they remain surfaces. Pictures, however, are not concerned with mathematical reality but with practical vision, which accepts the convention that even a broad line exists only in the dimension of length. The mathematician, as well, must ultimately accept this convention, since he has to see his figures.
Nonetheless, the draftsman should never forget that a line is an abstraction, primarily the representation of a sensed but invisible boundary between two surfaces. The line thus becomes part of the mental equipment of the draftsman. It is irrelevant that he sometimes sees
surfaces which can, with the best of intentions, only be felt as lines, such as telegraph wires, the highlighted edge of a table, the outlines of roof tiles -- there are endless examples.
In theory every abstraction is reversible, and therefore ambiguous: the mathematical equation (y = X2), the wisdom learned from living (Where there is much light there is also much shadow), and equally so an outline. The ambiguity of the circle in the space which we invoked
earlier can be applied further: for instance, linear perspective is always ambiguous, indicating either space or volume until other elements give it definition.
The moment that the outline is doubled, not too closely, or the line itself gives the illusion of shading and perspective by swelling and diminishing in width, all ambiguity disappears. This is equally true when the line is
drawn not in one continuous stroke, but with numbers of small strokes. Either this produces an illusion of space or volume by implying perspective, or the line, especially if it is drawn with many strokes, is the beginning of surface texture
which separates substance from emptiness and even leads to perspective.
Optical illusion makes one sometimes see a long, horizontal, straight line as though it had a downward curve. The idea of gravity is linked with it quite unconsciously, as though it were a rope which always
sags slightly however tightly it is stretched. This fact was known even in ancient Greece, and with interesting consequences, as the following example shows.
It was for long a scientific puzzle why the broad steps in ancient Greek architecture were not made with exactly
horizontal edges and treads, but showed a slight curve upwards to the center. Practical comparison gives the answer: absolutely straight steps, when they are
very wide, give the impression of curving downwards.
The reason for this is that part of the tread, being above eye level, is not at first visible; only the edge can be seen. Being so long it appears to dip. When the treads are visible the light falls more strongly on them than
of the risers. For the person climbing, the light is strongest ahead of him, and this is generally in the middle of the stairway.
Here arises another phenomenon of optical illusion: a light line on a dark surface seems broader than an equally broad dark line on a light surface.
Light stimulates the retina to spread its effect to a greater or lesser extent over the surrounding darkness.
This makes the visible tread of the step seem to be broader in the middle. If it were absolutely horizontal it would seem to be worn away. For both of these reasons the
steps were given a slight upward curve, imperceptible to the eye, which sees the steps as absolutely straight.
This effect of sagging is even more apparent if the straight lines are punctuated with something resting on them, like a pillar or a figure. Again an upward curve will set this to rights and go unnoticed.
This is an adjustment which only the freehand draftsman can make. The technical draftsman would very soon upset his whole construction if he attempted it. Now you can begin to see why it is that a freehand drawing of architecture can give a better effect of solidity and unity
than an architect's drawing.
Next: Drawing a perfectly straight line