Having had zero experience of pop-ups till last week, common prudence would suggest not wagging my tongue on this subject at all. But Prudence, Dear, you’ve never really stopped me before, and my tongue hasn’t wagged for a good few months now. It seems to me that thinking about pop-ups sheds a little light on the nature of origami too; so here goes.
Some of the magic of both of these ways of manipulating paper is the same: you start with a flat surface, perform a simple action or series of actions and Presto! have a three-dimensional form, or a shape otherwise of visual interest.
Moreover—manifestly in pop-ups, but implicitly in origami, the process is reversible. You close the book and the form tucks itself away; or you unfold your glorious insect (heavens no!) and get back the original square. —It suddenly strikes me that this unfoldability may be at the core of the origami rules, don’t cut, don’t glue; and possibly at the heart of the feeling people sometimes have (only reinforced by the choice of a flimsy material like paper) that the formed origami object isn’t quite an object, but an ‘object-in-becoming’, on the verge of existence. For the hand in origami can always be withdrawn; no final decisions have been made. What’s done can be undone. No cuts, no glue: that means also, no commitment: nothing’s been sliced away & thrown to the trash, or joined in a union which no man may pull asunder. --No doubt too, that accounts for the appeal origami has for some of us terminal procrastinators. Grow up, they keep telling us.
Pop-ups, of course, do use cuts and do use glue; liberal amounts of both. I was struck by this when I tried to make a pop-up that combined an origami element with other effects: how different the feeling is, when you take up the scissors. Integrity is lost; and one feels quite the sinner, violating that membrane.
The brain too is differently tasked. Pop-ups when done by the masters can show great cleverness or intelligence, but the genius, one feels, is distributed across the page, and is combinatoric: parts keyed & notched together to form some rich, total, tandem effect, from an economy of movement on the part of the viewer/reader. In origami, by contrast, the intelligence is sequential, and is distributed more in time than in space: your result has a long history of folds behind it, not the simultaneity which is the hallmark of the pop-up. One long event in time, giving rise to a single object in space; as opposed to one short event in time, and a multiplicity of interacting objects in space.
Also, though it seems stupidly obvious now, I just hadn’t thought of it before: Most origami models are created through compaction of the initial material. Things end up smaller than the square or rectangle you started out with. There may or may not be a stage of enlargement, when you open the folded-up thing part-ways, pull at the base of the boat to create a glorious hull, open out some flaps to reveal a fine and sturdy box. If so, and only for that stage, origami exists in the condition of the pop-up, with its expanding surprise. But the pop-up lives in that state always, which is the opposite of origami: a form emerges from the stretching of the bundled-up thing, from the unfolding of it. [A pop up invariably starts from the flattened state, but what each of its parts is trying to do when it opens is achieve an even more flattened state (a thinner one), only it runs into obstacles with other parts each trying to do the same—and the result is a 3-D form.]
It’s been proposed that much origami, which has a final stage in which it moves from the two-dimensional to the three-dimensional, can work as a pop-up if the sides are suitably glued to an openable surface. That is no doubt true, but it seems to me you won’t often get the best of both worlds by this marriage. From the origami side it is a little like those compendiums of “climax” themes in classical music: you are given the memorable high points, but without any of the build-up that grants them richness or depth. The creation history, the fold-sequence, isn't what opens to your view except for its ultimate stages. And from the pop-up side, the same 3D form more or less can be made with a lot less bother if you allow yourself a few cuts, as pop-ups typically do; so you might well wonder, why the person has gone to all that trouble. The integrity of origami is a little wasted here.
Closer to my heart is origami designed in advance to function as a pop-up, or to pass through different interesting stages via simple, global moves--pulls, pushes, twists, flexes of a whole surface into a cylinder. The tessellations folks are doing a lot of things of this vein nowadays, although (strangely, to me) the potential for pop-up applications is not being sufficiently explored. Thank goodness, then, for Jeremy Shafer, who hasbeen mining this seam-line now for some time.
Meanwhile, still far behind, here is my first trembling contribution. The flower is straight & simple origami, from a square; the leaf action, in many ways more interesting, is not.
[Video removed; see this post for more advanced developments of this idea. --S.]
Hope you enjoy.