Aren't We Squares

Paperfolding types being generally nice, as a group we tend to be inclusive and tolerant about what gets counted as origami so long as scissors are not much in evidence. Nevertheless the question of the limits of origami keeps coming up and even nice people can have strong opinions about this. (So it’s good there are no scissors around.) I don’t want to jump straight into this maelstrom but do want to describe a case that I think points to where the edge, or one edge, of this field is.

Suppose you wanted to make an origami human hand, from say a square or a rectangle. There are already a few simple and nice solutions to this, so there’s little point to actually inventing a new one. But one conceivable way to do it would be to take an indefinitely long strip of paper, roll it out to the first fingertip, fold, roll it back to the palm, fold, out to the next fingertip, fold, back to the palm, and so on. What you get is effectively the same as what you’d get if you drew a hand with a pen on paper, without lifting the pen; only instead of ink you’ve now used a paper strip. The strip can be thick or thin, the principle is the same. This would not be happily called origami, exactly because it is like continuous-pen drawing; it has only the elements of continuity and change-of-direction in common with origami, but does not use the pre-existing two-dimensionality of the paper in any way except as filler.

What this shows, I think, is that there’s a potential problem with paper strips of indefinite length--a medium by the way that I’ve been making a lot of use of lately. You can slip into this easily enough by saying What’s wrong after all with a rectangle; or by thinking, an indefinite strip is just a series of squares joined end to end, and if I treat each unit in the usual origami manner why should anyone complain. But you might be relying on one-dimensionality for the underlying architecture without noticing it, and the more you do this the farther you’re getting from what makes origami distinctive. It’s two-dimensionality in the end that has to be respected, made something of.

Indefinite strips are a gray area.