Balancing the Flip

The idea: balance

Balance is the arrangement of visual weight in a work so that it feels stable. It may be symmetrical, with matching halves; asymmetrical, with unlike parts of equal weight; or radial, arranged around a center.

In a notan: Every cut in a notan moves weight. The hole takes paper out of the sheet, and the piece lays the same shape down outside it, beyond the edge it folded over. So a notan’s balance is never settled inside the sheet: pieces folded only to the right make the whole design lean right, however centered the holes are. Each flip is itself a perfect symmetry, a hole and its mirror image across one edge. Those small symmetries can be arranged into a larger one, with matching cuts on opposite edges; into radial balance, with cuts on all four edges turning around the center; or into asymmetrical balance, where one large piece on one side is answered by several smaller ones on the other.

Balance is the sense that a picture is steady: that it will not tip, slide or fall out of its frame. We judge it with the same instinct we use on a seesaw. Large shapes weigh more than small ones, dark shapes on a light ground more than pale ones, and a shape far from the center pulls harder than the same shape near it, as a child at the end of a seesaw outweighs one near the middle. Artists balance pictures in three main ways: symmetrically, with matching halves; asymmetrically, with different shapes of equal pull; and radially, with parts turning around a center.

A notan adds a twist no painting has: its weight is not fixed inside the frame. Each cut removes paper from the sheet and lays a mirrored piece outside it, so every choice of fold edge is also a choice about balance. A design with all its pieces folded up grows a crown; one with pieces on every side spreads like a flower. In this activity you make a few cuts, then refold and resize them to explore all three kinds of balance.

Art history

Arthur Wesley Dow counted symmetry among his five principles of composition, and noted, after Okakura Kakuzo’s The Book of Tea, that Japanese art shaped by Zen avoided it as uninteresting. The works below show both habits, and a third: the radial designs that appear when paper is folded several times before it is cut.

• Unknown papercutter Round paper-cut with paired horses, 386–581 (Northern Dynasties)

  One of the oldest paper-cuts known, found in 1959 in a tomb at Astana, near Turpan in Xinjiang, China. One small set of cuts repeats around the circle as a ring of horses standing back to back, the mark of paper folded before it was cut. Folding is how paper makes radial balance; a notan’s flip is the same idea with a single fold for each piece.

• Tawaraya Sōtatsu Wind God and Thunder God, early 1600s Kennin-ji, Kyoto; kept at the Kyoto National Museum

  A pair of two-panel folding screens on gold leaf. The thunder god appears at the far left edge and the wind god at the far right, with a wide field of empty gold between them. The gods differ in color, pose and gesture, yet they weigh about the same, so the center holds still. This is near-symmetry: balance without an exact match.

• James McNeill Whistler Arrangement in Grey and Black No. 1, 1871 Musée d’Orsay, Paris

  Known everywhere as Whistler’s Mother. She sits in profile right of center, a large dark shape against a gray wall; a dark curtain at the far left answers her, and a framed print fills the wall between. Whistler called it an arrangement, and it works like one: unequal dark shapes placed until they hold still, a balance shaped by his study of Japanese art.

• Piet Mondrian Composition with Red, Blue and Yellow, 1930 Kunsthaus Zürich

  A large red square fills the upper right. A small blue square at the lower left and a small yellow one at the lower right answer it, helped by heavy black lines pushed off-center. A small, intense shape far from the middle can balance a large one: the seesaw rule, in paint.

Design today

Designers have argued about symmetry for a century. In Die neue Typographie (1928), Jan Tschichold called for asymmetrical layouts, with blocks of type of different sizes balanced against open space, in place of the centered title pages of traditional books. Later he turned back to centered, classical typography, and from 1947 to 1949 he reworked the page design of Penguin Books in that manner. Designers still choose between the two: a centered, symmetrical layout feels formal and calm, as on a wedding invitation, while an asymmetrical one feels active and modern.

Swiss designers of the 1950s and 1960s made asymmetry systematic by building layouts on grids, so that unequal parts still line up. Josef Müller-Brockmann, whose concert posters for the Tonhalle in Zürich began in 1950, set shapes and type off-center on such grids, and his book Grid Systems in Graphic Design (1981) is still taught. On the web the same choice appears as a centered landing page or a left-aligned grid. Either way, designers judge the result as you will here: by squinting at the whole layout and asking whether it leans.

Warm-up

Paper seesaw, ten minutes. Give each learner a white sheet with a light pencil line down the middle and a set of black paper shapes, one large and several small. First arrange them as mirror images on either side of the line. Then put the large shape on one side and balance it with small ones on the other. Talk about what moved the balance: size, number, or distance from the line. A shape near the edge pulls harder than the same shape near the middle.

In the studio

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

1. Open the studio and make the sheet square: in the Paper section of the Controls tab, set both the width and the height to 5 inches. On a square, a quarter turn lands every edge on another, which radial balance needs.
2. Draw one shape near the left edge, such as a leaf with the Draw tool or an oval with the Ellipse, and when the chooser opens, press the ← arrow to fold it out over the left edge. With Move, select it and use Align to set it flush against the left edge and centered from top to bottom (a single selected shape always aligns to the sheet). Squint: one piece outside the sheet is enough to make the whole design lean left.
3. Symmetry. Option-drag (Alt-drag) the shape to pull away a copy. With the copy selected, turn on Reflect Y in Transform and press Apply, so it faces the other way. Align it flush against the right edge and centered from top to bottom, then click the arrow beside the right side of its selection box to fold it out over the right edge. The two sides now mirror each other across the center line. Export the artwork as a PNG before you go on.
4. Radial balance. Drag a marquee around both shapes to select them. In Transform, set Rotate to 90, leave the reference point in the center, set Copies to 1 and press Apply. The two shapes sit symmetrically, so the center of their selection is the center of the sheet, and the copies land at the top and bottom. They still fold left and right, so select each new copy and click the arrow beside the side of its box that faces its nearest edge. Now a piece leaves over every edge and the design turns around its center. Export it.
5. Asymmetry. Select one of the four shapes and drag a corner handle with Shift held to make it about twice as large. The design now leans toward it. Rebalance it without shrinking that shape: move, turn, resize or refold the other three, or add a few small cuts on the far side, until the design sits still when you squint. Export this version too.
6. Watch the weight arrive. Press Replay and the flips play again in the order they were made. After each piece lands, ask which way the design leans now. Then cover each half of the screen in turn and compare what each side carries.
7. Compare the three exported versions side by side. Which feels calmest? Which feels most alive? Which would make a good logo?

With paper and paint: Paint, Cut, Then Weigh

In the studio a piece weighs nothing, and Undo takes back any cut. Paper is less forgiving and more honest. A cut cannot be undone, so you test the balance first with loose pieces, sliding them as you would on a seesaw. Paint teaches the other half: the weight you see is not the weight you hold. A small scrap painted dark weighs almost nothing in your hand, yet on a light ground it can balance a much larger pale shape. Mondrian used the same pull when he answered a large red square with small squares of blue and yellow set far from it. Color and value are weight too.

1. Paint first, so the papers can dry while you work in the studio. Cover the table. Paint the front of the square dark and leave its back white. Paint the large sheet, the ground, in the middle color. On a scrap, paint one patch dark and, beside it, one patch pale: white with a little of the middle color. Let everything dry until it no longer feels cool against the back of your hand, then press it flat under the book.
2. Weigh with your eyes. Cut a large circle from the pale patch and a small circle from the dark one. Lay them on the warm-up sheet on either side of its center line. Which side sinks? Slide the small dark circle out toward the edge until the two feel even. Now pick them up: the large one is heavier in your hand, yet on the page the paint has made the small one strong.
3. Plan with templates. Cut one large shape and three or four small ones from scrap cardstock, each with one straight side. Lay the painted square, dark side up, in the middle of the ground. Set each template just outside an edge, its straight side against the edge, where a piece would land. Move them along the edges and from edge to edge, and squint, until the design holds still.
4. Mark the holes. Flip each template over the edge it touches, onto the square, and trace around it with the white pencil, since graphite hardly shows on dark paint. The traced shape is the hole; the place the template came from is where its piece will land.
5. Cut each traced shape out of the square with scissors, starting from the edge. Keep every piece: there will be no other.
6. Flip and test. Turn each piece over its edge, white side up, into its mirrored place on the ground. The pieces show the paper’s white back against the middle ground, and the holes show the ground inside the dark sheet. Stand back and squint. If the design leans, slide the whole sheet with its pieces across the ground, or try one more small shape with a template before you cut it.
7. Glue the sheet down first, then each piece, lining its straight edge up with the edge of its hole, and press the notan under the book until the glue sets. Set it beside your studio versions. Which kind of balance did you make, and what besides size gave each piece its weight?

Take care: Young learners use child-safe scissors; any knife cutting is done by an adult or an older learner on a self-healing mat, with the blade moving away from the body and the other hand behind the metal ruler. Choose washable, non-toxic paints with the ACMI AP seal, cover the table, and let the paint dry fully before cutting or gluing.

Take it further

Take radial balance further. Fold a square of paper in half, in half again and then along the diagonal before you cut, and count how many times each cut repeats. In the studio, try Copies with a turn alone: set the reference point to one corner of a small petal and the copies fan around that corner like a flower. Refold the petals so each piece leaves over its nearest edge, and decide whether the flower still reads as radial once its pieces are scattered to four sides.

Reflect

• Which of your three versions feels calmest, and which feels most alive? Why?
• How did folding a piece over a different edge change the balance, even though its hole did not move?
• In your asymmetrical design, what balanced the large piece: size, number, value, or distance from the center?
• Where do you see symmetrical, asymmetrical or radial balance in the objects around you?

What to look for

• The symmetrical version mirrors exactly across the sheet’s center line.
• The radial version has one piece folded over each of the four edges, arranged around the center.
• In the asymmetrical version, unequal shapes are arranged so that viewers agree the design does not lean.
• The learner can point to the pieces outside the sheet and explain how each one shifts the balance.
• In the paper version, the pieces were tested loose before gluing, and the learner can say what moved the balance: size, value or distance.