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Strange Attractors and Paths Untrodden

Experiments with chaos + information spaces

Mar 14, 2018 · 6 min read

The following is adapted from Episode 4 of Artist in the Archive. You can listen to the whole thing .

In the 1950s, the mathematician and meteorologist Edward Lorenz was thinking about weather. Lorenz was experimenting with statistical forecasting, but he found that his simulations didn’t match the messy, wet, reality of real world. So Lorenz set out to develop a non-linear model that would match the unpredictability of nature.

In 1963, he published a paper titled “” in Journal of the Atmospheric Sciences, which laid down the foundations for an entire branch of mathematics called chaos theory. Chaotic systems are interesting in that they start off quite predictable. After a certain amount of time, though, they start to behave in a way which, for a lot of intents and purposes, resembles randomness. One of the things that defines a chaotic system is that it’s particularly sensitive to initial conditions. That is, the state of the system when it starts has a huge effect on how it will behave long into the future. This idea — that these extraordinarily elaborate mathematical structures could be so dependent on minute changes to their state right at the beginning — gave rise a famous term that Lorenz coined: .

Lorenz’s model, popularly called the Lorenz Attractor, is a set of three simple differential equations. There are three constants, called sigma, rho and beta which define those delicate initial conditions that we just spoke about. By changing the values of these numbers, the system can output a vast menagerie of strange geometries, from tight spirals to messy tangles of loops and curls. Set to very particular values — ρ=28, σ=10, β=8/3, the Lorenz Attractor outputs a structure which, anyone would have to admit, looks an awful lot like a butterfly.

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The Lorenz Attractor

It’s when we watch that butterfly emerge, though, by setting the system free to animate over time, that we get a real sense of the beauty of the Lorenz Attractor, we see how it lives through long periods of regularity, where we start to recognize a pattern, only to — seemingly at random — switch course or change direction.

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We’re taught in high school that math exists inside cartesian coordinates — x, y & z. But the fact is that math doesn’t care about or for our made up axes; indeed we can set up a Lorenz attractor inside of any space we can imagine. Real world space, or computational space or emotional space or flavour space or whatever we want.

I want you to imagine for a second that the room you’re in, or the bus or the subway car, is filled with words. Every word in the english language, floating in space. Over there by the door is a cluster of fruit words, pear and apple and orange and kumquat. Right under your chair are all of the synonyms for love. Above your head are hope and dreams and imagination. Proper nouns are here as well, in dense clusters. The Presidents are near the window, just beside all of the countries and states and provinces and cities. There’s New York, in the center of it all (hey, I didn’t write the algorithm) If you look back at the cluster of fruits by the door, you’ll see that apple is closest to New York, drawn to it by so many pop-cultural references.

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A trip through a small slice of word space

As an experiment, I thought I’d build the attractor in this word space, and see if the path of the butterfly could be used to generate a series of words that might resemble some kind of geometric poetry. So I used a corpus of 3 million english language words and their relationships to create a 3 dimensional map of language. I let the attractor do its thing inside of this gigantic word cloud, and recorded the results. Now remember, these attractors are very sensitive to initial conditions, so making small changes really affects the structure of the attractor, and thus the kind of so-called poem that is generated.

Here’s a short poem that came from a Lorenz attractor roaming in word space, which I’ve edited a tiny bit to make it a little more readable:

this dynamic ride itself sounds this variable declaration;
this online spell it sounds this online location.
The ranks of beauty, one is beauty and the beauty attribute is one.
imported of its export.
Review and export.
Of the export, imported of export, and the export of its obstacles matches the symbolic to itself.

Supply the sustainable caring.
Supply the placement.
The caring of the review.
Supply the rank and the rank of the symbolic, to supply match supply.
Works. Ranks.
Reply the export. Reply obstacles.
Reply the obstacles, the obstacles symbolic. Warring obstacles.

This variable.
Variable spell imported of this variable talks.
Yes. Younger. Younger genius.

Of classification and this competitive supply.
Classification: This competitive, competitive spell.

Reply the symbolic reporting. Reply the specialty.
The reporting of the translation.
Fly the travel and the objection of the ranking.
To match fly. Work spheres.
Supply the demand. Supply motives. Feeling. Proceeding. Classification.
Supply these announcements.
These announcements competitive.
Warring statements.

It’s tempting to think of this text as a poem, to consider this computational system that I’ve created as some kind of a robotic poet, but that’s not really my intent. I think of these texts instead as a sort of linguistic scaffolding, a set of generative walkways which might help us to explore this vast and confusing space of language, aided by the strange mechanics of chaos.

So what does this all have to do with the Library?

Let’s push all of those words out of the room. Usher them out the doors, sweep them down the drain, push them out of the windows. Let’s instead fill the room with everything that the library holds. All of the maps and manuscripts and objects and interviews and of course books. So many books. Let’s put the tweets in there too, and the websites and the animated GIFs.

Like our words, these library things are organized by their relationships. That big, messy ball in the center is the civil war. Off in the corners are a lot of the things that we’ve discovered in the podcast. . . .

I’ve been thinking a lot about how humans navigate this space. Through the web site, or in person, in one of the Library’s reading rooms. If we plotted one person’s course through this space, it would most often show up as a densely tangled knot, occupying just one tiny mote in this vast galaxy of information. Nothing like those elegant sweeps of the Lorenz Attractor.

This is the problem with large archives, with any data space of significant size: they can easily facilitate linear search, but they don’t do much for the messy, wet, real world process of discovery. If you don’t know exactly what you’re looking for, you’re confined to curated galleries and, led along roped off pathways, not allowed to really get into the mess of the archive at all.

Now, I was born in 1975. I got my first computer when I was nine. When I went to university, in 1993, I taught internet classes in the library. There were two words that I would use a lot, back then, 25 years ago, that are rarely used at all again when we talk about the internet. Those words are ‘hyper’ and ‘surf’

The term hyper comes from mathematics. It refers to a an extension, a generalization, a kind of radical opening. The word surfing comes, well… from surfing. To surf the web was to be carried off by the force of curiosity, not quite sure where you were headed.

So far in my residency I’ve made abstract maps and and . I’ve put together artists names into and I’ve turned the Lorenz attractor into a vehicle for exploring text.

All of these endeavors have been trying to do the same thing — to bring ‘hyper’ back. To bring ‘surfing back’. To find nonlinear avenues through this building and amongst all of the wonderful things that it holds.

Strange paths, heretofore untrodden.

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