Yes/No (2011)

by Erik Demaine, Martin Demaine, and Sarah Stengle

The Yes/No print consists of the crease pattern (top) and 3D folded form (bottom) of a folding design.

This print was first exhibited in the “Measure for Measure” show at Central Booking in Brooklyn, New York, February 2011–April 2011, together with The Circle series of curved-crease sculpture.

This collaborative art piece, Yes/No, combines the mathematics of computational origami with ideas from book art, combining words with an image in the form of a folded paper structure. The piece consists of hand-inked paper that looks unrecognizable when unfolded, but when folded forms the three-dimensional form of one word while the print simultaneously comes together to form the word's antonym. In short, if you look down on the folded word “yes”, you see the image of “no”, and vice versa. The completed folded structure simply negates itself by embodying an intentionally mixed message.

Origins

We met Sarah Stengle in the summer of 2009 in Banff at BRIDGES, a conference about the connections between mathematics, music, art, architecture, and culture. Erik gave a talk about how we enjoy working on projects across both mathematics and art, with new mathematical theorems and unsolved problems inspiring new artwork, and the challenge of creating art inspiring new mathematical questions. Central to this spirit is collaboration, both the extensive father-son collaboration, as well as collaboration with hundreds of other mathematicians and artists.

Sarah was intrigued by this concept of collaboration. Given her expertise in book art, and our expertise in approaching origami mathematically, we decided to collaborate on a book project that involved folding. Over the next several months, we discussed via email various ideas centered on making a textual object as a subset of book art. A desired quality was to produce something new and spontaneous, and several ideas evolved through this brainstorming. We discussed flipbooks, book furniture, construction toys, blown glass (we are both glassblowers, Sarah casts glass), and new fonts. In the end we went back to our original thought of incorporating origami, as it seemed the most natural for us. What followed were several conversations in which we raised the possibility of folding words out of text. Sarah suggested that it would be wonderful to fold words that said one thing, and were printed with another message entirely. In short, an object would convey an emotional state of being conflicted, while being grounded in mathematics.

One of our first ideas was the concept of folding one word into another, representing the transformation and uncertainty of ideas. For example, the text “yes” could be printed on the paper and fold into a printed “no”, or vice versa, representing the uncertainty of decision or the making of a decision. We experimented with different foldings, but lacked a general mathematical principle for designing the folds, making it difficult to find a design with the elegance that we felt the idea required. We looked at existing origami fonts, and agreed that it would be far more interesting to fold entire words rather than single letters. So although we had this idea early on, we needed the right mathematics before we could turn it into a reality.

In summer 2010, we published a paper, together with an MIT graduate student and origami expert Jason Ku, about how to fold origami “mazes”—orthogonal vertical walls protruding at equal heights from a rectangular floor—efficiently from a rectangle of paper just a small factor larger than the floor. Also that summer, we realized that we could use these orthogonal mazes to write letters, and designed a font to “write” a desired message by folding a rectangle of paper. The result is a computer algorithm that transforms any text into a crease pattern which folds into a 3D version of that text. In some sense, the crease pattern encodes a secret message that can be deciphered by folding, which is often quite a challenge. You can experiment yourself with creating such crease patterns using an online web application, but be warned that the folding is quite difficult.

Coming Together

The maze-folding mathematical algorithm, and the font design project, in turn inspired us to come back to our concept with Sarah of folding one word into another. One idea is to print a crease pattern on top of text onto a sheet of paper, and the crease pattern folds a 3D realization of different text, and renders the original text no longer legible. Thus the artwork could be in two states: the simple unfolded state where the printed text is legible, and the complex folded state where only the 3D text is legible. This piece could represent the difficulty in making up one's mind.

To add somewhat to the mystery, we opted for a different approach: print pieces of letters and a crease pattern onto a sheet of paper so that, by folding, both the printed text and the 3D text become simultaneously visible. In this way, the unfolded sheet is again a puzzle—both the printed text and 3D text require some thought to read—but by folding, they simultaneously come into view.

Our first piece in this series is called Yes/No, and it represents coming to understand both sides of a decision simultaneously. We go from confusion in seeing neither the Yes nor the No, to confusion in seeing both Yes and No, not knowing what the answer is. Perhaps there never is one right answer. The print is from elephant hide paper, a strong archival paper that can withstand robotic scoring and retains it shape well when folded.

The Yes/No handout lets you try folding the crease pattern.

Handout

Accompanying the piece is an 8.5" × 11" handout encouraging you to try folding the form. Feel free to print it out and challenge yourself.

Details

Material: Elephant hide paper.
Dimensions: 24.4" × 27.6"
Limited edition of 50

Series

This piece is part a series of prints mixing folded and inked messages. Our second piece is Science/Art (2011).

Last updated May 7, 2014 by Erik Demaine.