Lines That Cut Twice

The idea: line

A line is a mark longer than it is wide, the path of a point in motion. Lines can be actual, drawn or cut, or implied, where the eye joins separate edges, points or gaps into a path that is not there.

In a notan: Nothing in a notan is drawn, so every line is an edge: the place where one value stops and another begins. Each cut makes its line twice, once as the rim of the hole and once, mirrored, as the rim of the piece, so a line that leans one way inside the sheet leans the other way beyond it. A shape can be so thin that it reads as a line: a slit is a line of ground cut into the paper, and a strip left standing between two holes is a line of paper. And lines can be implied, as when a row of small holes reads as one dotted path.

A notan has no pencil. Its lines are made by cutting, and a cut produces two lines at once: the rim of the hole, where the sheet gives way to the ground, and the rim of the piece, which folds out over an edge and lies beyond it as a mirror image. Paul Klee called lines like these passive: lines that result from areas, as their edges, not from a point going for a walk. Almost every line in a notan is passive in this sense, and learning to see them is learning to see the design.

Look for three kinds. The first is the edge itself. The second is a shape so thin it behaves as a line: a slit of ground, or a strip of paper left standing. The third is implied, not cut at all: a row of small holes, or two edges that point at each other across a gap, and the eye fills the gap. Horizontals rest, verticals stand, diagonals move, curves slow the eye and zigzags hurry it. The fold adds a twist, because a mirror reverses every diagonal: a line that climbs toward the edge inside the sheet comes back down beyond it, and the two make a chevron whose point sits on the edge.

Art history

Line has been the first lesson of design for more than a century: Arthur Wesley Dow put it first of his three elements, and at the Bauhaus both Klee and Wassily Kandinsky wrote books that begin with the point and the line. Cut paper has its own history of line. In Chinese jianzhi, recognized by UNESCO as intangible cultural heritage in 2009, a design whose lines are the paper itself must keep every line joined to the rest, or it falls apart in the hand. Each work below finds line without a pencil.

• Paul Klee Pedagogical Sketchbook, 1925

  Compiled from Klee’s teaching at the Bauhaus, the book opens with a line going for a walk for its own sake, then separates active lines from passive ones, which are only the result of active planes, the edges of areas. A notan is built almost entirely of passive lines: look at any edge and ask which areas made it.

• Lucio Fontana Spatial Concept ‘Waiting’, 1960 Tate, London

  Fontana cut straight through the canvas with a blade, and that single cut is what the picture is about. It is a line made by taking material away, and it shows the dark space behind the painting. A slit in a notan is the same kind of line: not a mark on the paper, but a gap that lets the ground through.

• Piet Mondrian Composition 10 in Black and White, 1915 Kröller-Müller Museum, Otterlo

  Mondrian built this painting from short horizontal and vertical marks, after drawings of the sea and its breakwaters on the Dutch coast. The marks are short, yet the eye reads the rhythm of waves, the upright of a breakwater and an oval that holds the whole field. Separate marks, placed well, become a path.

• Lotte Reiniger The Adventures of Prince Achmed, 1926

  The oldest surviving animated feature film was made from black silhouettes, cut by hand and jointed with wire so they could move frame by frame. The lift of a hand or the arch of a horse’s neck is told by the cut edge alone, exactly the situation of every piece in a notan.

Design today

Designers still draw with edges. Paul Rand’s eight-bar logo for IBM, from 1972, runs horizontal stripes through three heavy capitals, so your eye assembles letters that the stripes only imply. Harry Beck’s diagram of the London Underground, first printed in 1933, lets its lines run only horizontally, vertically or at 45 degrees, a constraint that makes it quick to read. The Pen in Studio Notan snaps to the same 45-degree steps.

Where a line is literally a cut, it has a job to do. Packaging designers draw a dieline, the path a steel die follows to cut a box from a flat sheet, and stencil lettering leaves small bridges so the middles of letters such as O and A do not fall out. The cut lines file Studio Notan exports for a laser cutter or cutting plotter is a drawing made only of lines like these.

Warm-up

On a small sheet of black paper, cut five kinds of narrow sliver in from the edges with scissors, without drawing first: one straight, one curved, one zigzag, one that tapers to a point, and a row of three short ones. Lay the sheet on white paper and flip each sliver over the edge it came from, so it lies beside its slit like a reflection. Which line looks fastest? Which looks calm? Which pairs make a shape that points?

In the studio

Make it in Studio Notan, where every cut can be moved, refolded and undone.

1. Open the studio. On the Controls tab, leave ‘Flipping’ on ‘Each shape’, so every cut asks for its direction as soon as you finish it. Keep the black sheet and white ground a new design starts with: two values show a line most clearly.
2. Make a slit. Choose the Pen and click a point on the right edge of the sheet; the Pen snaps to the edge. Click a second point deep inside the sheet, a third back on the edge a little below the first, and close the path on the first point. In the chooser, press the right arrow. The thin wedge becomes a line of white in the sheet and a line of black beyond it.
3. Vary the line’s quality. Make three more slits: one straight and even, pressing Shift after its first click so the Pen keeps to 45-degree steps; one curved, by pressing and dragging as you place a point; and one freehand, a long, narrow loop drawn in one stroke with the Draw tool. Before you draw, set the Drawing slider toward ‘Accurate’ to keep the wobble of your hand, or toward ‘Smooth’ to calm it.
4. Make a strip, the opposite kind of line. With the Rectangle tool, draw a tall rectangle and fold it over the bottom edge, then draw a second beside it, leaving a narrow band of paper between them, and fold it the same way. The band is a line of paper, not of ground. Which pulls your eye harder, the white slit or the black strip?
5. Build an implied line. Drag out a small circle with the Ellipse tool low on the left side, pressing Shift once the drag has begun, and fold it over the top edge. Select it with Move; in Transform on the Controls tab, set a small move right and up (up is a negative vertical move), set Copies to 5 and press ‘Apply’. The row of holes reads as one dotted line, and above the sheet the pieces make a second one leaning the other way.
6. Press Replay, beside the zoom control, and watch each piece fold out, oldest first. Every fold draws its line a second time.
7. From the ‘File’ menu, save ‘Cut lines, SVG’ and open it. It keeps only the paths a blade would follow, a clear way to see what your lines really are.

With paper and paint: Brush Line, Blade Line

A brush line is a mark. It has a width, and the width records your hand: it swells as you press, thins as you lift and breaks into dry flecks as the brush runs out. A cut is an edge. It has no width of its own and no soft end, because the blade is either in the paper or it is not. Painting lines and then cutting them on one sheet puts Klee’s active and passive lines side by side in your hands. Painting the lines first also follows Arthur Wesley Dow, who put line first: in Composition he preferred Japanese brushes, ink and paper for exercises in line drawing and in notan. And paper keeps an order the screen does not. The ink must dry before a blade can follow it, and a line once cut stays cut.

1. Practice on scrap. Dip the brush in ink and stroke off the extra on the rim of the dish. Paint lines slow and fast, press down and lift up, then paint one long line without reloading until the brush runs dry and the line breaks into flecks. Notice that a brush line has a width, and that the width changes with every movement of your hand.
2. Paint the sheet. On the watercolor paper, paint five lines, each starting on an edge of the sheet and running no more than halfway in: a straight line, a curve, a zigzag, a line you press hard at the edge and lift as it travels so that it tapers to a point, and a row of five dots. Give each line its own part of the sheet.
3. Let the ink dry completely, about 20 minutes, until no part of it shines. Wet paper drags and tears under a blade, and wet ink smears onto fingers and onto the ground.
4. Cut three of the lines out of the sheet: the curve, the zigzag and the taper. Cut along both sides of each stroke, from the edge to its tip, so that it comes free as a sliver. Where the ink feathered into the paper or the brush ran dry, you must decide where the edge really is. A brush can fade out; a cut cannot.
5. Make one more line with the blade alone. On a part of the edge with no paint, cut a straight sliver as narrow as you can manage, with the knife against the metal ruler or with scissors. This line was never a mark. It began as an edge.
6. Glue the sheet in the middle of the black ground, and leave the straight line and the row of dots painted and uncut. Turn each sliver over, white back up, and glue it beside its slit, mirrored across the edge it started from.
7. Compare near and far. From across the room, the black slits and the painted lines look alike. Up close, the painted line has a soft edge where the ink soaked into the paper, and a width that swelled and thinned with your hand; the slit has a clean edge and a width you had to cut twice. Beyond the edge, each white strip keeps the shape of a brush stroke but none of its ink: the fold copies an edge, never a mark.

Take care: Cover the table, wear old clothes and choose inks and paints with the ACMI AP seal; india ink stains and dries permanently, so rinse the brush in water as soon as you finish, and give younger learners washable tempera. Cut on a self-healing mat, away from your body, with the hand that holds the ruler well clear of the blade’s path; younger learners use scissors, and an adult handles any knife.

Take it further

Bring in a photograph full of strong lines, such as power cables or a staircase, with Trace a photo, and see which of its lines survive as edges. Or give the back a bright color, so the mirrored lines outside the sheet shout while the slits inside stay quiet, and notice how a change of value changes which line leads.

Reflect

• Which of your lines did you actually cut, and which did the viewer’s eye make on its own?
• How did the fold change the direction of your diagonal lines, and did the mirrored lines help your journey or fight it?
• Where did a slit of ground feel stronger than a strip of paper, and why do you think that was?
• If you had one more cut, where would you put it to make the path clearer?

What to look for

• The design contains a slit that reads as a line of ground and a strip that reads as a line of paper.
• At least one line is implied by separate holes or by edges that point at each other.
• The learner can point to the two lines each cut makes, the rim of the hole and the rim of the piece.
• On the painted sheet, brush lines and cut lines sit side by side, and the learner can say how a painted line’s width and edge differ from a cut’s.
• A viewer tracing the design with a finger follows the intended path.