Arriving at an Icosahedron

A creative-process detective story about the scandal of abstract thought, the many half-ways an idea travels into the physical world, and a new project for sale.

“Let no one ignorant of geometry enter here,” read the inscription above Plato’s academy, supposedly.

That always struck me as strange, as I never much associated Socrates or Plato with geometry. But I’ve been thinking about it more lately.

The most obvious part of the physical world is space. It’s easier to imagine it in two dimensions, but truer to experience to imagine it in three. But where the mental and physical meet is no neat seam. There are jagged gaps, errors, surprises and tragic turns we should have seen coming.

Life takes place within space, and imagining it correctly would save a lot of heartache. Space is the obvious place to begin a meaningful dialogue with physical reality. And geometry is a straightforward - at least at first - way to understand the distances and relationships in space.

Entering here

There’s a difficulty to bringing an idea into the physical world. Materials need to be considered, tested, and reconsidered. Space and time test any idea, test the maker. There’s a power to anything that passes that test into the physical world, no matter how trivial. Even a critic must respond.

Bringing an idea into the physical world is different from the difficulty of putting an idea into the social world.

If the idea bypasses the consensus-making of the social world on its way to the physical world, that’s one sign that it may be art. In that way, art is upsetting at the outset - no one asked me first!

An idea in the eye

One idea behind Forget This Good Thing is that meaningful coincidences can be engineered within a work of literature to make it unpredictable, highly personal and unexpectedly significant.

This is an idea that my collaborator Matthew Dublin went to great lengths to put into action, and to make instantly accessible in the app. The execution of the idea involves user action and randomization, along with an intuitive interface and thousands of original aphorisms. And in its original, digital form, it works beautifully.

An idea for the hand

This idea, as realized in the app, had its social coming out last fall. After a truly delightful event for Forget This Good Thing at Iffy Books in Philadelphia last October, Matt and I started to talk about more ways to bring the idea deeper into the physical world.

We’re still discussing and experimenting with all kinds of things involving optics, alternative physical publishing systems, solar-powered displays and so on. But one of our first ideas to slide through the many tests to the physical world involved geometry - a subject with which I have a personal, contentious history.

Geometry, a personal take

Geometry wasn’t my idea of a good time, at first.

When I was fifteen and very depressed, I failed geometry in high school. A varsity athlete, I barely passed gym and almost flunked out of school. Though nearly expelled, I was clever and amiable enough to collect my share of gentleman’s D-minuses. The geometry teacher, however, was immune to my charms. That May, I was on the edge of failing the final quarter of the year, which meant I’d fail the class no matter what I did on the final exam. I asked the teacher if I should just skip the test, and he wouldn’t tell me. So I sat down for the weekend and read the geometry book. I got an eighty-something on the final, but I’d failed that last quarter, so I had to do some summer school.

So I got more geometry than I’d bargained for.

Geometry, a well-earned sneer

I live in a large, American city in the first half of the 21st century - all I see are rectangles. It’s the opposite of inspiring. In midtown, geometry can seem like the abandonment of the imagination and the suppression of the human mind. Geometry can seem like the fabric that conceals reality, like the veil thrown up between a person and their own living humanity.

Geometry, a mystical take

So what was Plato on about? I think geometry was something completely different, even scandalous, to people two dozen centuries before. They passed more of their time in nature, where there are almost no straight lines, right angles, or perfect circles. Outside the manufactured environment, there would have been clues, occasional glimpses - the unyielding line in an unearthed crystal, or a long hair pulled taut, a hemispherical bubble on the surface of water.

That these forms would take root at all in the mind is a peculiarity deep inside the mystery of what it is to be a human being. It’s an itch we may continue scratching forever.

But to the early philosophers, geometry may have shown a way into abstract thinking, which sits apart from the physical world. These shapes - circle, square and equilateral triangle - are visible ways to reimagine space according to principles of symmetry and regularity. The power of abstract thinking is easily lost to people who live in abstract worlds of money and power and real estate and so on.

Abstract thinking is nothing less than a wholly independent means of evaluating and reimagining the world of our immediate experience. It’s a stop upon the obvious and the seemingly inevitable. It’s a private place of unlimited possibility. It’s still a marvel to those who forgo the term miracle.

Plywood, zip ties and PVC pipe

In July of 2012, geometry mattered to me again. I had access to more time, space and energy than I may ever have again in my life. I built a pyramid.

The idea came to me after I’d finished a big project, a short film, another hard thing to bring into the world. I wanted to do something different. I came up with a plan to build a pyramid, with a PVC-pipe frame, plywood skin, and zip ties stitching it all together. On paper, I figured out the design and calculated the materials using the Pythagorean theorem. I had a back yard at the time. I bought the materials and borrowed a circular saw. Other than that, I only needed a tape measure, a drill, a chalk line and a pencil. I set to work, starting with the frame.

"Let no one ignorant of geometry enter here," haunted me that first day. The PVC frame didn’t come together as promised by the calculations in my yellow notebook. Maybe my math was fine, but the pipes were the wrong lengths and the angled PVC segments didn’t fit. I’d screwed up, and forgotten to factor in the third dimension, and failed calculate the angles based on the diagonal of the pyramid’s square base.

I sat down in the heat with the notebook and went back to work, then re-cut the pipes. It took three sweaty days to get the idea into reality. In the end, I was happy with how it came out. Though steeper than the one I’d drawn up, it was graceful and symmetrical, with an 8’X8’ base and twelve-foot-high faces.

For a few months, my friends and I would hang out in the pyramid, drinking beer and talking. It was great. Then my neighbors asked me to take it down for a party they wanted to throw. Then some workers that the landlord hired took all the materials. But it was fun while it lasted.

Coincidence capture

Forget This Good Thing is designed as an oracle. Its design draws on a host of past models of prophecy and augury.

The earliest oracles consisted of reading the twists of sheep entrails, or counting the cracks in an overheated ox-bone or the number and direction of birds visible from a temple window at dawn. The point is that certain very important things, like the outcomes of wars or marriages or the founding of towns, are entirely unknowable. One way to inquire about them is to ask a question of other such unpredictable phenomena.

There have been attempts to capture this process in a physical tool, like Tarot Cards, and the I-Ching. More recently, Brian Eno tried to harness the force of coincidence in his Oblique Strategies, which works as a deck of cards or as an app.

When making a list of contemporary American forms of divination, the most iconic ones are probably the flipped coin and the Magic 8 Ball. In the inky depths of the Magic 8 Ball is an icosahedron - a 20-sided object, each side a triangle of equal size, with an answer inscribed on it.

With twenty sides, there are twenty possible answers, though the Magic 8 Ball only offers up three - ten Yeses, five Nos and five Maybes. Oblique Strategies has 120 cards in a deck, and the I-Ching has 64 hexagrams, which can give you as many as 4,096 answers to your question, depending on how you use it. What they all attempt to do is to take the cosmic tendency towards randomness and put it to work in a fixed context where meaning can be inferred.

A book you need a garage for

Forget This Good Thing has 2,400 original aphorisms that can appear based on a built-in random number generator. All 2,400 aphorisms are equally likely to come up at any given time. What would that look like physically?

The app was designed as a reaction against the structure of a book, where one page follows another. There are workarounds, like in the Choose-Your-Own-Adventure series. But all the pages come out of a single spine, where sequence is built in.

If it were to be a book, Forget This Good Thing might resemble a dandelion puff, with 2,400 individual spokes coming out of the center, each with a small page. The pages would have to be laminated so as not to be destroyed in its handling and storage. It could be hung from the ceiling, two feet from the floor, making all the aphorisms equally accessible, if not equally convenient.

Brian Eno saw randomness in a deck of cards. But a deck of 2,400 cards is too big to shuffle.

Maybe it could be a massive sphere, like a disco ball, with an aphorism on each tessera. Given that each square or hexagon would need to be around 1.5” at their widest to hold a legible aphorism, the ball would have to be to 8-12 feet in diameter, probably weighing around 200 pounds. To be transported in and out of most buildings, it’d have to be made in sections, taken apart and then reassembled.

This idea, while exciting, would have a very steep test to pass if it was to arrive in the physical world. Maybe someday.

120 sides to every story

Given my limited time, space and money, the gargantuan disco ball would have to wait. The next candidate was, of course, the pentagonal hexecontahedron, with its spherical silhouette and 120 sides. With aphorisms arrayed like letters on an IBM Selectric typeface ball, it would be possible to capture the entire collection of aphorisms on 20 of them.

In a single gallery, these pentagonal hexecontahedrons could hang from the ceiling at varying lengths, creating a dreamlike experience. Or with the aphorisms printed upon the shapes in rubber, in reverse, they could operate like those typeface balls, with each surface being a stamp containing a single aphorism. People visiting the space would be given a notepad and an ink pad, and could take a random wander, publishing their own book of aphorisms as they go.

I went so far as to have a stamp of one of the aphorisms made, the aphorism inscribed inside one of the shape’s diamond pentagons.

But it was impossibly expensive when multiplied by 2,400 aphorisms, or even just by 120.

Maybe someday.

To play is to cheat

As much as I may enjoy operating within abstract spaces, I live in time and space, with very real and often painful limitations on both. And don’t even get me started on money.

Ask any artist in any medium who is actively making things, and they’ll tell you: The limits are part of the game.

So what limits would I accept? Fewer aphorisms would work. If the aphorisms are randomly selected, then an object with fewer aphorisms would follow the spirit and intention of Forget This Good Thing. Maybe one pentagonal hexecontahedron, with its 120 sides, would be enough.

A quick search for the shape online yielded one such object for sale, at $280, without the cost of inscribing the aphorisms.

The other side of the conversation

By this point it seemed I didn’t have an idea, so much as half an idea, maybe half of a half. But I had discovered a tolerable cheat - fewer aphorisms, as long as they were randomly selected, which the app already does.

A founding assumption of Forget This Good Thing is that there is a message in the unintended, accidental and coincidental. Thanksgiving came and went with these impossible geometrical projects stalled out on the page. The next move belonged to unpredictable reality.

One December night, I was out at dinner with my collaborator Matt Dublin. After a big Chinese meal, we walked over the rump of Sunset Park to Fifth Avenue. It was a blustery night, and we ducked in and out of stores to catch a break from the wind. One place we popped into was Five Below, a discount store exulting in what may be the waning days of the Golden Age of Cheap Plastic Crap.

With Christmas coming, I picked up a Transformer for my boy and some headphones for my girl. Matt has two dogs, and browsed the pet section, where he found a perfect thermoplastic icosahedron, for dogs to chew on. Five bucks.

The next day, I cut cardboard into triangles, copied down twenty aphorisms - randomized by the Mac desktop app - onto them, and glued them to the icosahedron. I’ve never had the hands or the patience to be an arts-and-crafts wiz, but it came out okay.

In practice, it worked like the app. And it fulfilled the hope of having a randomized textual experience, distinct from opening a book to an arbitrary page. You could roll the icosahedron like the twenty-sided dice from Dungeons & Dragons and get an answer to any question you posed.

Mocked again by geometry

There may be no deeper basement than the basic regular geometric shapes - circle, square and equilateral triangle - that we choose by which we first endeavor to experience space. To turn our attention to these shapes is to begin to understand the often-frustrated appetite for perfection that defines our lives.

The earliest holy cities often began with a demarcated square, an imposition of this magical ability upon the dirt, the nosy tree roots, the meandering deer paths and the opportunistic scrub.

This anti-geometric tendency is innate to the physical world. It’s what gives the Great Pyramid and the straight avenues boulevards their power. It haunts a maker. The bent pyramid in Saqqara attests to the perfidy of materials and the confounding of physical ambitions. About halfway up the thing, the builders realized that it was simply too steep, they had to complete the second half of this enormous stone structure at a lower grade.

In my own endeavors using prefabricated icosahedrons, I’ve also been confounded. Cutting a straight line in cardboard with scissors is no picnic. Tracing and repeating a shape is harder than it looks. Distortions crop up everywhere. Fitting cardboard to thermoplastic rubber is a science I haven’t mastered, with too much or too little glue.

The result is that the icosahedrons themselves express the tension and frustration of a flawed creature in close contact with a perfect geometric solid.

Half of halfway to a full idea

Even with some glue gobs and some off-kilter triangles, it was a cool object. It looked nice on a shelf. The translucent thermoplastic rubber caught the light nicely. My kids liked it. But what to do with the thing? It was still half an idea. More months passed.

Being a writer or an artist in the digital age is difficult, confusing. Meaningful work flickers in and out of fashion. Money shows up unexpectedly and then is nowhere to be found. It’s fraught with professional, emotional and spiritual traps. As a result, there’s a whole genre of writing around this shared frustration.

Passing time in the genre, I came across the Metalabel project Kickstarter founder Yancey Strickler. It’s a platform (I know, another platform) for limited-edition art objects that’s designed to bring novelty, anticipation and urgency to a digital realm which is lacking in all three.

Maybe it wasn’t the entire other half of the idea. But, in the manner of Zeno’s Paradox, it was a step that spanned half the distance between where I was and a full idea.

Obstacles on the road to reality

That afternoon, norovirus was coming on. I woke in what I thought was a bad mood, but it was my stomach under a different strain. My son threw up repeatedly the night before, and then again in the rental car home from our one-night family getaway. My daughter had it two days before. It was my turn.

To get the kids in the car, rather than risk my boy throwing up in the hotel pool, I’d agreed to stop at Five Below for one cheap toy each. The location we arrived at held the full tapestry of South Brooklyn, with loud teens, Orthodox moms, and old Chinese couples. In the twilight of oncoming nausea, there was a strange quality to the place.

Synchronicity gave me a wink. The store’s limited book section had a pile of Egyptian Books of the Dead, which seemed a charged selection, as I’d been working on an essay that touched on it. But I guess Wallis Budge is out of Copyright, and the Late Kingdom certainly is. So for $5, I grabbed a copy.

I had ulterior motives for making my second trip to Five Below. In the pet section, I found my icosahedrons. five of them, in different colors.

Icosahedrons for fun and profit

Now you can buy an Oracular Icosahedron!

Each one carries the synchronistic properties of the app. The twenty aphorisms on its surfaces are selected randomly by the Forget This Good Thing random number generator, and further randomized when you roll the object.

Made from thermoplastic rubber and locally sourced cardboard, it can be used in fortune-telling and divination. Each of the six in the series is hand-detailed, uniquely botched and completely different from the others. It’s a nice-looking object at about six inches high and about 18 inches around. It’s one of the first physical instantiations of the concepts behind Forget This Good Thing.

Will there be more? Maybe someday.

Extended bibliography

Purchase a first-edition, collectible Oracular Icosahedron!

Tim Speed Levitch holding forth gorgeously on the oppressiveness of rectangles

Stickers for your nearest rectangle!

An account of Forget This Good Thing’s marvelous night in Philadelphia

The first glimmer of the icosahedron concept, back in March of ‘24

Forget This Good Thing – Try it now! – The free app for iPhone and iPad – The free app for Android - Paper book 1 - Paper book 2 - Paper book 3 - All About It - A reintroduction - Its creation - What it can do for you - Why it matters - Thirteen descriptions - The risks - Case study - Case study #2 - The secret history - instagram @forgetthisgood

Make your own icosahedron!