Hierarchy Part 1: Prologue and Introduction

wastepaper origamist

The Parable of the Wastepaper Origamist

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.


Poised on flux

“The most incomprehensible thing about the Universe is that it is comprehensible.”


Quite possibly you too have walked across an abandoned university campus, numb from a last-minute revision-session in the library, with a quivering kind of wonder at the contrast between the physical reality surrounding you, and the cerebral strives in abstract-land that left your mind in such a somber state.

3 hours ago you watched highlighters run down the shiny coat of a lavish new textbook and ballpoint jottings connect revision-note marginalia. A frustrated feeling of trying to unify, to compress, to make inevitable. Of trying to extract an essence, as if the text contained some glistening liquid that could be pipetted, encapsulated, and implanted in your brain so that, if perturbed, it instantly would release an orderly avalanche of inferences. But instead: crammed across your pain threshold, waiting to escape once exams are over and done with.

An hour later you sat hunched over a laptop screen, with crumbly impressions from slides and bullet-points drifting behind tired eyelids, looking for a place to embed, but evading your grasp.

Finally: practice problems. The most soul-crushing part surely, one of burrowing desperately into the fabric of reality, where mathematical truths and physical laws are somehow encoded, in a metaphysical format currently unavailable to your wearily groping mind.

Absurd, isn’t it? The concept of “understanding”? How incompatible this imagery seems with the campus square reality in which you are presently immersed! Because, while at some level you could intuit a carved-up structure to the scenery around you, and while you could imagine labels hovering above each item as if by a Google Glass identification-app, you know that the wind that just swept past was not the work of a differential equation, the attendant chilliness not the act of a correlation. Similarly you know that the corrosive gas of oxygen now caressing your lung interior is flowing in a stochastic whirl fundamentally without pattern, marching towards disorder with thermodynamic resolve. And isn’t your aching head just a dark, skin-draped skeletal case filled with fatty meat, continuous with this plodding dynamic with neither mind nor meaning?

Zoom in enough, and you will find yourself in a pixelated cosmos of uncaring flux, of perpetual change of state, one that owes this unremarkable subset of you no promise of being understandable, explainable, or mastered whatsoever. So what are all our young minds actually doing, itching as we are for that elusive experience of “understanding” to obtain, clearly restricted by the flux but equally so utterly, painfully removed from it?

The following sections review a series of concepts from the discipline known as “complexity science” to explain how this reality can lend itself so readily to textbook subheadings, learning objectives, and practice problems, and why it is so neatly analyzable into “systems”. Why the perceived reality is one of a fizzing, spectral, kaleidoscopic mosaic precariously poised on flux, that makes us perfectly able to treat something as complex as a cell as a particle in biology, or humans as particles in economics, with predictive impunity and without inferential backlash. Why our reality has contours when nothing says it must.

Now try, for a moment, imagining the opposite – of a reality where all matter were organized as symmetrical assemblages and structureless contraptions, widgets arbitrarily tinkered together. Would “understanding” make any kind of sense in such an environment?

Such a simple thought experiment led a man in the next section towards fascinating conclusions. They may be qualitative and untestable, but they are bound to tickle your intellect.


About lovisasundin

I study psychology and computing science in Glasgow but am originally from Sweden. I like drawing and popular science. Please don't hesitate to contact me at lovisafsundin@gmail.com
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