Space That Changes Sides

The idea: space

Space is the area around, between and within the parts of an artwork. Positive space is the area the subject occupies and negative space is the area around it; on a flat surface, artists also create an illusion of depth.

In a notan: A notan has three spaces, not two: the sheet, the holes cut in it, and the ground all around. The holes are negative space inside the sheet, yet the same areas reappear outside it as positive pieces, so negative and positive are never fixed; they trade places at every edge. The ground between two pieces, or between a piece and the sheet, can harden into a shape of its own, and a good notan makes those in-between spaces as deliberate as the cuts. The flip also claims new space. Every fold sends paper out beyond the edge, so the design grows into the ground around it, and the margin you leave becomes part of the composition.

Beginners see objects; designers also see the spaces between them. Psychologists call the object the figure and everything around it the ground, and the eye tends to hold one reading at a time: a vase that is also two faces works because its outline could belong to either side, and the eye gives it to one side at a time. A notan is a machine for making such outlines. Every cut is negative space inside the sheet and the very same area as positive space outside it. When a cut touches the edge, hole and piece meet along the edge as one symmetrical shape in two values, and the space around it, the sheet on one side and the ground on the other, becomes the contested figure.

The fold also changes how much space a design occupies. A piece lands as far outside the edge as its hole sits inside, so a cut near the middle of the sheet sends paper far out into the ground, and a cut near the edge keeps it close. The empty ground is therefore part of the composition. Too little, and the pieces crowd the frame; too much, and they drift apart and stop belonging to the sheet. Japanese has a word for this charged interval between things: ma.

Art history

The works below treat empty space as a material. A Chinese court painter lets bare silk stand for air and distance; a Danish psychologist shows that the eye cannot hold both readings of a border at once; a British sculptor casts the air inside a room as a solid. Each makes you notice a space you would normally look straight through, as every hole in a notan does.

• Ma Yuan Walking on a Mountain Path in Spring, Southern Song dynasty, late 1100s to early 1200s National Palace Museum, Taipei

  On this small album leaf of silk, a scholar and a boy carrying a wrapped zither walk beneath willows in one corner, and much of the rest is left open, with a poem inscribed at the upper right. Ma Yuan pushed his subjects to one side so often that he came to be called “One-Corner Ma.” The open space is not leftover: it is the space the scholar is walking into.

• Edgar Rubin Synsoplevede Figurer (Visually Experienced Figures), 1915

  In this doctoral thesis the Danish psychologist studied how the eye decides which of two areas is the figure. His best-known illustration can be seen as a vase or as two faces in profile, but not both at once. Where two areas share a border, he observed, the border seems to shape only one of them, which helps explain why a notan flickers as the eye changes its mind.

• Rachel Whiteread Ghost, 1990 National Gallery of Art, Washington

  Whiteread cast in plaster the inside of a living room in a Victorian house in north London, and assembled the casts into a block: the room’s empty space, made solid. The fireplace and the baseboards appear as reversed shapes in its sides. It is the hole turned into the piece, the move a notan makes with every cut.

Design today

The best-known figure-ground mark in design hides in plain sight. In the FedEx logotype, designed by Lindon Leader at Landor Associates in 1994, the space between the capital E and the lowercase x forms an arrow pointing forward; once seen, it cannot be unseen. In type, the enclosed spaces inside letters such as o and e are called counters, and good letterspacing balances the areas of space between letters by eye rather than setting equal distances, because equal distances look uneven.

Architects and interface designers treat empty space as something built, not left over. A courtyard or a page margin is designed as carefully as the walls or the text, and white space on an app screen is what lets a single button be found. When you share a notan from Studio Notan, the preview card sets the sheet and its pieces in the middle of a field of your ground color: the space around the design travels with it.

Warm-up

Show a picture that can be read two ways, such as the vase that is also two faces. Ask learners to say out loud the moment it flips for them. Then, on black paper, cut half a vase from the edge of a square, its flat side on the edge, and glue the cut piece flipped beside its hole on white paper. Where are the faces now? Point to the figure, then to the ground, then try to see it the other way.

In the studio

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

1. Name the three spaces. Open the studio and cut any shape from the middle of the sheet. Point to the sheet, the hole and the piece. Notice that the ground shows in two places, inside the hole and all around the sheet. Is the hole part of the sheet, or part of the world around it?
2. Make a reversal at the edge. With the Pen, draw half a vase against the right edge: start with a click on the edge, where the Pen snaps, work down the profile with clicks and short drags, finish on the edge and close the path. Fold it over the right edge. Hole and piece meet as a whole vase in two values, and the sheet on one side and the ground on the other become two faces looking at each other. Adjust the profile with Points until you can switch between vase and faces at will.
3. Draw where you want the paper to land. With Ellipse, drag out a circle on the ground a little above the sheet. Because it is mostly outside the sheet, the studio mirrors it onto the sheet and opens the chooser with the up arrow ready. Press it: the hole opens inside the sheet and the piece lands exactly where you drew. See Flipping for how it chooses the edge.
4. Shape the space between. Plan two or three more pieces the same way so they land close together outside one edge. Now look at the ground between them rather than at the pieces. Move the cuts with Move, watching the pieces move in mirror image, until the in-between space is a clear shape of its own: a channel, a diamond, a star.
5. Change the fold, change the space. Select a cut and click the arrow on another side of its selection box to send its piece over a different edge. The same hole now claims space in a new direction. Try all four edges for one cut and keep the one that gives the whole design the best balance of full and empty ground.
6. Set the margin. In the Paper section of the Controls tab, try a different width and height, or turn the sheet with the rotate button. Your cuts stay where they are while the edges move, so pieces fold from new places and the spaces between them open or close. Stop when the ground around the design feels charged: not crowded, not empty.
7. Test it on someone else. Show the design to a partner, on your screen or through an ‘Only view’ link from Share, and ask what shape they see first. If they name a space you meant as ground, you have made a reversal; if they name only the pieces, strengthen the in-between shapes and try again.

With paper and paint: Two Colors Trade Places

On screen, a color is a setting you can change at any moment. On paper you paint it, and the two colors become two real layers: the ground lies underneath, the sheet sits on top, and in side light every cut edge casts a thin shadow that tells the eye which is which. Cutting two painted squares at once gives you the same shapes in opposite colors, so you can test Rubin’s question with your own eyes: when two areas share a border, which one does the border belong to? Loose paper also teaches the value of empty ground. You can slide a sheet across its ground and watch the margin open and close, but once the glue is down the decision is made.

1. Paint the grounds and the sheets in two colors far apart in value; here they are blue and yellow. Paint one ground blue and the other yellow, edge to edge, in flat, even coats. Paint both sides of one square blue and both sides of the other yellow, letting the first side dry before you turn it over, so that holes, pieces and sheet use only two colors. Keep every coat smooth, so the only differences left are color and shape.
2. Let everything dry flat. Paint that looks dry on top can leave the paper damp beneath, and damp paper tears under scissors and smears under glue. Once the sheets are dry to the touch, press any that curl under a heavy book, between clean sheets of paper so that no paint transfers.
3. Cut two at once. Stack the squares with their edges matched and clip them together at two corners. On the top square, draw half a vase against one edge, its flat side on the edge, and cut through both layers, so that the two half vases match exactly.
4. Lay out, but do not glue. Set the blue square on the yellow ground and the yellow square on the blue ground. Turn each half vase over the edge it came from, so that hole and piece meet along the edge as one whole vase, half blue and half yellow.
5. Look for the reversal. Step back. In each version, do you see the vase first, or the two faces made by the sheet on one side and the ground on the other? Ask someone who has not watched you. Then look closely at a cut edge in light from a lamp or window: the thickness of the paper casts a thin shadow that tells the eye which layer lies on top. Does the reversal survive it?
6. Plan two pieces from where they will land. On scrap paper laid against another edge of the top square, sketch two small shapes placed so that the space between them makes a shape of its own: a channel, a diamond, a star. Draw their mirror images inside the square, as far in from the edge as the sketches sit outside it, clip the squares together again and cut through both, starting each shape with a short knife slit on its outline, since a snip started inside it would split the piece. Turn the pieces out and look at the painted ground between them.
7. Set the margin, then glue. Slide each square around its ground until the empty space feels charged, not crowded and not empty, and trim the ground with the knife against the metal ruler if it is too big. Glue the square first, then each piece. Glue is the one decision you cannot take back.
8. Compare the two versions side by side. The shapes are identical; only the colors traded places. Which color read as the figure in each, and did the figure follow the color or the shape?

Take care: Let each coat dry right through before you turn the paper over, cut or glue; choose paints with the ACMI AP seal, and rinse brushes before the paint dries in them. Two layers need sharp scissors and steady pressure, and any knife work happens on a self-healing mat, away from your body, with an adult doing it for younger learners.

Take it further

Look for the same reversal in the world: the gap between two buildings against the sky, the space inside a letter, the arrow in the FedEx logo. Photograph one, bring it into the studio with Trace a photo, and use Invert to swap which side of the split becomes the front. Which version makes the in-between space read as the figure?

Reflect

• In your design, which spaces did you plan and which appeared on their own?
• When you drew a shape outside the sheet first, how did it change the way you thought about the hole it made?
• Is the ground around your sheet part of the artwork? What would change if you cropped it away?
• How is Whiteread’s cast of a room like a piece folded out of your sheet?

What to look for

• The learner can point to the sheet, the holes and the ground, and say which reads as figure in each part of the design.
• At least one space between cuts reads as a shape in its own right.
• At least one piece was placed by drawing it outside the sheet first.
• The empty ground around the pieces is balanced: the design neither crowds the frame nor falls apart.
• Two painted versions with the colors swapped are compared, and the learner can say which area reads as figure in each.