Imagine a young, cocky dabbler who frivolously decides one day, without any previous experience, to become expert in origami, the Japanese tradition of paper-folding. It all seems so simple: some force applied to paper, a little aligning here, some pulling there, and what originally was a square sheet, for some larval time a maze of pleats and creases, then fleetingly a richly decorated cocoon, unfolds by the yank of a nimble finger into a sculpture to gracefully fill all three dimensions. Thus, he reckons, he would be able to make real whatever fanciful motif he has in mind.
And so he begins, with what feels like the most natural, downhill way: he holds the paper mid-air and gropes for edges and corners, with the success and elegance of a soft-pawed kitten. Mid-air origami, he soon realizes, is futile – at least for the optimistic timescales he had in mind. So he tries to apply pressure with a tabletop as support. Now at least individual folds prove enduring and the fumbling process of trial and error resumes, catalyzed by this dramatic increase in probability for edges to firmly align.
Wastepaper rapidly accumulates: though individual folds may endure, any attempt at three-dimensionality is certain to collapse, unless, he discovers, he starts with the big folds and proceeds to progressively smaller ones in a hierarchical manner. He has an inkling of why this could be: awkwardly groping as he is, the fewer options he has to try, the more likely he is of success. So if the big decisions that make the most difference are made first, he can look forward to fewer potential folds to track in his memory. Thus the likelihood that his random actions would by sheer accident produce stable arrangements is no longer negligible. Is it so that the difference between a complex origami sculpture, and the shriveled embarrassments of which he has loads, is to be found in the hierarchical origin stories underlying them?
The now-humbled-but-ever-as-animated dabbler accepts to examine the contents of an aging origami master’s collection of his own wastepaper baskets, with all errors and successes preserved for posterity. It is an overwhelming sight of paper-on-paper. Only through peering eyes do successful sculptures emerge from an undifferentiated backdrop of failures. Undoing these sculptures into their original squares sheets textured with indentations, he wonders how to extract a set of procedural rules to fold anything he wants. Assuming that the old master must too have uncovered the hierarchy-principle to constrain his own blind fumbling, he finds that the sheets invariably have some creases that would be awkward to make after having made others – a spatial hierarchy testifying to a hierarchical history.
This gives the young man an idea. He folds himself a pocket (fumblingly and hierarchically, of course). Then he returns to his table and flattens the master’s old figures by re-using old creases, from bigger to smaller ones, to store them in his pocket, to return to them at a later date.
Why did he do this? Because, he conjectured, much like the origami figures around him, his understanding of them must too develop hierarchically for it to be ordered and stable. In other words, to master origami, he must start by studying the general, critical folds that make the most difference, before step by step mastering the finer, more specific creases, because his knowledge is an origami figure like any other. His studying procedure should be organized according to the same principle as the object of his study, by consistently seeking out the hierarchies that must be there somewhere, buried deep down in the complexity they uphold.