Phillip Jeffries’s Magic 8-Ball and The Geometry of Twin Peaks

Where it all began — Twin Peaks and 8

Rhombuses, rings, spheres, 8s—all kinds of geometric shapes are part of the Twin Peaks Universe and represent agencies possibly acting alongside lodge entities and humans. The polymorphic 8 specifically represents some sort of god or “living map,” confirmed in Part 17 (1+7) when Phillip Jeffries pipes out the Owl/Judy/Twin Peaks symbol that shifts into an 8 with a dark ball inside of it. The 8 turns around like a key in a lock, then disappears.

It’s the last thing Cooper sees before his “unofficial” story ends; a finale; theophany; a living hieroglyph for the show and an ideogram for the long-lost David Bowie. Let’s analyze the math behind this charismatic shape who gets exactly 48 seconds of uncut screen time. We’ll plug it into the socket of art history to review Erwin Panofsky’s 1934 notion of “disguised symbolism,” and I’ll suggest that the Owl-8-Ball is a disguised symbol whose beating referent may be invisible to us but can be enacted by constructing a 4D perspective and by studying Native American symbology, Renaissance angels, and The Secret History of Twin Peaks.

Sometimes My Arms Bend Back

Twin Peaks blends geometric shapes with pop stars and angels, as does Fra Angelico (1395-1455), the Dominican monk-artist known for his visionary dreams and advanced understanding of mathematics.

Angelico is featured in the essay The Geometry of Angels (1998), where Ralph Abraham teams up with William Irwin Thompson to analyze one of his visionary paintings from 1435. It’s the Annunciation. The angel Gabriel faces Mary and informs her that she’s pregnant with a god. His wings create a series of ellipses, and if we “pull” the 2D ellipses into 3D spheres, Abraham wonders if the wings could represent Dante’s 3-sphere universe—two intersecting onion-like worlds—an image that was on everyone’s mind at the time. Divine Comedy was the Twin Peaks of the day, as Twin Peaks is the Divine Comedy of our day. (TP scholars like Frank Boulègue and Eileen Mykkels have written brilliantly about the show’s connections to Dante, and get this: Dante’s own theology has been referred to as “Twin Peaks.” See The Twin Peaks of Dante’s Theology in the Paradiso. It’s interesting that the circle of hell #8, Malebolge, for “deceivers,” is where lousy magicians have to “walk backwards around the circumference of their circle for all eternity.”)

In the context of Renaissance math and linear perspective, Abraham adds:

the flapping wings generate a family of toroids.

Each wing represents a circle. By stretching out the wings and flapping them, the angel carves out the tori of the cosmic three-sphere. As two spatial dimensions plus movement makes three dimensions, the flight of angels may be seen as a construction of the world, and a means of navigating between the Ball of Heaven and the Ball of Earth.

What a vision! This is really exciting because that “family of toroids” creates a Hopf map; a topological shape not uncovered in mathematics until the 1930s! You can create your own Hopf map here. Essentially, it’s a series of rings that show how a 4D sphere (aka 3-sphere, hypersphere, or “real” sphere) can be mapped by a collection of 2D ellipses. One interesting property of this shape is that each ring or “fiber” is linked with the others exactly once.

Physicist Roger Penrose marked the Hopf fibration “an element of the architecture of our world,” and mathematician Eric Weinstein said to Joe Rogan “it’s the most important object in the entire universe.” It’s also called a “principal bundle,” what the universe and everything “is based around,” a shape not really understood until the 1970s according to Weinstein, yet Fra Angelico painted one in 1435 disguised as some angel wings!?

Rodney: How can that be?

This isn’t the first time an artistic vision predicted a scientific discovery. See Leonard Shlain’s book Art and Physics or Jonah Lehrer’s Proust was a Neuroscientist. Dante also pre-cognized the 3-sphere in the 14th century with his comedy. Check out Dante and the 3-sphere by Mark Peterson, and read more about fibration history here.

Visualizing the Invisible

As a 4D sphere (space + time), the Hopf fibration models the “foundation” for the 4D world. Humans are at least four-dimensional beings with a “long self“, even if we feel locked in 3D and the fleeting present moment. 4D is invisible to us. We can’t see it with our eyes, but we can fantasize. Mathematician Nico Belmonte, describing the image above: “You are probably now thinking ‘but what does a 4D sphere actually look like?’ You can’t really see it, but here we use a stereographical projection to show some points of a 4D sphere into 3D space.”

In Art Meets Mathematics in the Fourth Dimension, Steven Lipscomb tells the story of the “quest to imagine the elusive 3-sphere.” Gustave Doré tried in the 1830s, Edwin Abbott Abbott tries with Flatland (1884), and in 1917, Albert Einstein visualized the universe as a 3-sphere (without the aid of Planet Hopf) describing the image as “the place where the reader’s imagination boggles. Nobody can imagine this thing.”

Annunciations

Fra Angelico can. In this version of the Annunciation, he added sand to the paint so that in candlelight the fibers/wings sparkle like star fields. In this version, a black-and-white figure living above the world offers a golden orb that floats down to Mary and Gabriel, reminiscent of the annunciations in Part 8. I’m also reminded of the fictional sophons from The Three-Body Problem—a family of proton-sized supercomputers capable of opening/unfolding and infolding dimensionally—sent to earth by aliens.

(Side note: Giant owls are literal aliens according to Mark Frost. Grays to be exact. Owls = Aliens. In The Secret History, adolescent Margaret, Carl, and someone else get abducted by aliens disguised as large owls. It feels like they went missing for days. Carl: “I’ve already been places.” Margaret: “The owls are not what they seem.” Yet we know that in many cases alien abductions and their “probes” are really symptoms of repressed sexual trauma, “false memories,” as explored in films like Mysterious Skin and FWWM. See also The Science-Fictionalization of Trauma.)

In this version, a tiny angel dressed in red expels people from Eden, while the Father, disguised as black-and-white art, watches over his mystical insemination. Mary looks like a giant, her hands are pronounced, and more flat shapes hang in the air.

What’s noteworthy about Fra Angelico’s Annunciations—besides the embedded Hopf bundles—is that angel and human mirror each other, arms crossed like they’re both dead, or, like they’re both holding invisible babies. The liturgical hand gesture can also signify mourning and baptism.

Lynchian Angels

The 8 in Twin Peaks resembles a double torus and a graphic cross-section of a Horn(e) torus. Tori, with their donut forms and mushroom cloud-like ascending/descending currents, also appear in Alex’s Grey’s paintings of our subtle and causal bodies. Grey calls one a “guardian angel,” “toroidal ball of spiritual light,” and “Mobius Sphere.” Is it the With?

Astrophysicists point out that our sun also has a large toroidal field surrounding it  that is itself embedded inside a larger torus encompassing our galaxy. Some cosmologists go as far as to claim that the spinning 4D torus, symbolized by a 2D figure 8 or ∞, represents “the fundamental form of balanced energy flow found in sustainable systems at all scales, from micro-atomic to macro-galactic.”

Candie: There were tori everywhere!

Designer Jois Pon envisions more practical applications with his Torii Pods, always motivated by the natural flow of things. Philosopher Peter Sloterdjik also has a lot to say about tori and “biunities” and “sphereologies” in his book, Bubbles (2011), the first volume in his Spheres trilogy. Sloterdjik:

All births are twin births; no one comes into the world unaccompanied or unattached.

Further, to describe the feeling of “being-in-the-world,” Sloterjik uses Thomas Aquinas’s idea of angels—that they [we] are “not like physical creatures in space but that they created out of themselves the space that they illuminate and animate with their essence”(2017:190). It’s like what Maurice Merleau-Ponty says in The Primacy of Perception (1964:5): “The body is not in space, it inhabits or haunts space.

It applies itself to space like a hand to an instrument, and when we wish to move about we do not move the body as we move an object. We transport it without instruments as if by magic.

What this all means is that angels create three-dimensional space by beating their wings, and in a sense so do humans. Let’s project this analysis of the Hopf map in Gabriel’s wings onto the Owl-8-Ball in Part 17. Will we get a series of nested ellipses (or chevrons) that create a Hawk’s map? Will we find out that the “owls” create the 3-worlds of Twin Peaks by beating their wings?

Angelico, like Lynch, celebrates the enumerative, ‘decorative’ and ‘flat’ as a way of expressing the spiritual and symbolic. Not everything has to be naturalistic. At first, the intangible 8 is flat and empty, then a shadowy ball rendered in 3D appears in the bottom right corner. BOB? Laura? Earth? The whole construction slowly rotates 180 degrees, and then the ball travels downward to return almost to starting positions, but not quite. This place represents a specific date: February 23rd, 1989, the day Laura died.

Without any geometrical analysis, the floating 8 delivers a layered message. Keith Gow zooms way out and realized, after experiencing Part 17, that,

Watching Twin Peaks is an infinity symbol. Before The Return it was a golden circle: you’d watch Twin Peaks/FWWM/Twin Peaks/FWWM/TP, and on and on. Now the two circles of the original series & The Return both begin & end with FWWM; joined in the middle. An infinity symbol.

Redditor SpclAgntDickCooper describes another aspect of it:

I interpreted the “8” to be an infinity symbol, and the “ball” inside of it a marker for a location in (Interdimensional? Infinite?) time/space. Basically, it was sort of a map of the entire infinite TP multiverse. Jeffries was using it to set whatever Lodge teleportation mechanism to the proper coordinates so Coop could travel to where/when he needed to go.

That sounds so much like Lost.

Meredith S. Fitzgerald, from welcometotwinpeaks:

But after sleeping I think this infinity sign may be an indication of infinite outcomes when trying to confront Judy — but you will always be caught in a loop because evil is always there…ugh need more coffee.

But it isn’t an infinity symbol, is it? It’s an 8, like the one we see on the Palmer House, on Gersten’s door, on Jeffries’s door at the Dutchman’s, on Freddie Sykes jail cell, on the #6 telephone pole, in Part 8 (!), Part 18, on the unseen floor above the Philadelphia offices, and on the Fireman’s ceiling above Andy in Part 14.

That circular screen, by the way, may reference the first narrative film ever, Edwin Porter’s Life of an American Fireman (1902). It’s about a Fireman who has a precognitive dream that takes the form of a circular projection, a “film within a film,” mise en abyme. Watch it here. Recall the wall in Room #8 moves aside like a curtain to reveal a cinema room that looks like it’s from the Fireman’s fortress. The arch shape is also found in the Glass Box and the alcove in Laura’s bedroom, as Lou Ming spotted in Find Laura.

Disguised Symbolism

In the spirit of enigmatic messages, the Owl-8-Ball is on point for Jeffries, whose previous hits include “Hell God Baby Damn No!“ and “Ring the ring.” Panofsky’s notion of “disguised symbolism” (1934) suggests meanings are embedded and masked more than they are “hidden.” We just have to swipe past the first couple of “necessary but not sufficient” ideas to get to deeper, better ones. Lynch: the deeper the dive, the bigger the fish.

Sometimes it’s not the symbol or word itself so much as the way it’s delivered that points to a new meaning. For example, “E-lec-tric-ity” all stretched out like that calls up the Captain Beefheart song “Electricity.” Maybe Cooper needs to remember that song in order to go “in.” Or maybe there is something about the lyrics to that song next to the ceiling fan blades. What’s striking is that as soon as Phillip Gerard says this magic word, Cooper freezes. His story stops—like Chet Desmond’s, in a sense—and all we can hear, as we drift into his sleeping face, is the whooshing fan. Then we see the fan—the original mask. Then the front door of 708.

Panofsky:

The supreme charm of the picture—and this applies to the creations of Jan van Eyck [and David Lynch] in general—is essentially based on the fact that the spectator is not irritated by a mass of complicated hieroglyphs, but is allowed to abandon himself to the quiet fascination of what I might call a transfigured reality.

Quiet fascination, but also obsessive analysis with profound rewards. Panofsky explains that the reasons artists conceal or “disguise” symbols are: (1) to facilitate a revelation, which is fun and feels good; and (2) as a way to reconcile 2D symbols with 3D naturalism. It’s not “intentional concealment from the viewer.” Nothing is hidden, per se. Everything you need to see is staring you right in the face. It’s like those “pointing out instructions” in Tibetan Buddhism, where the teacher will ask you to stare into your own chaotic mind until you recognize its crystal clear nature. If you can’t recognize it, they’ll point it out to you.

John L. Ward, in Disguised Symbolism as Enactive Symbolism in Van Eyck’s Paintings, notes that artists especially like to use symbols that, when their significance is discovered, appear to enact the meanings they symbolize.

As a quick aside: Leo Steinberg in his book The Sexuality Of Christ uncovers disguised symbols most people miss in Renaissance paintings of Jesus—symbol magic that may inform our interpretations of the 8 in Part 17.

Steinberg focuses on Madonna and Child images that include a “chin-chuck,” where the baby reaches out and touches Mary’s chin. These paintings are everywhere and look innocent enough, but what we must understand is that in 15th-century Europe, touching someone’s chin is how a man chooses a lover. Whaaat? Furthermore, in a different context, it’s what a father does to his daughter. Uh oh. The baby’s hand gesture signals that they are the Lover, the Father, and the Child all at once. Meanwhile…

Artists relied on “Christian sexual hermeneutics” (see Lee Siegel) to tell a layered and mystical story, a circular story. Because Renaissance peasants couldn’t read or understand Latin, paintings and rituals had to function as a distillation of the entire book, as well as sensual supports for revelations.

The brief scene with Gabriel, like the brief scene with Jeffries, doesn’t make much sense rationally, but it does make sense as a celebration of good storytelling. William Irwin Thompson writes in Coming Into Being (1998: 200) that in religious stories, it isn’t the large narrative arcs so much as the brief, spectacular, “exaggerations of the archetypal encounter”—the “wild and wacky stuff”—usually including some kind of numeration, that becomes memorable and therefore religious-making.

I think it’s clear that everything Phillip Jeffries says sticks out of the story—is a “big fish” full of keys, codes, symbols, and symptoms. In his brief time, Bowie speaks iconic images that resonate across the entire show. (Check out THE MANY OCCURRENCES OF THE OWL CAVE SYMBOL IN A SINGLE GIF). He whimpers Ahh, Oh, Oh, Oh like the screaming lady in Part 11; he shakes his head, smiles, and says “Ring… the ring.” He screams bloody murder! Also in The Missing Pieces, Gordon shouts “Hello! Hello!,” the lights flash off and on, and Jeffries looks up and says “February 1989” (jump to Mr. Jackpots and Part 17, “Please be specific…”). I think we should consider all conversations with Jeffries cut up, coded, and shuffled.

More, we get hints that Phillip is speaking in code because he doesn’t know if it’s Cooper or Mr. C in the room. “I found something in Seattle at Judy’s” could be code. His conversations in Season 3 could also be in code for the same reason.

Twists and Turns

Let’s return to the shape itself. There is an undeniable mirroring and doubling that happens all over Twin Peaks. Not just human people but convenience stores, motels, and houses all appear to have doppelgangers. Jeff Jenson noticed that The Duchman’s is a reflection of the motel used by Leland/BOB in FWWM, and wonders if,

Perhaps places on Earth trafficked and corrupted by Black Lodge demons become cloned by the Black Lodge itself or absorbed into its space. What happens when they taint all the earth?

 

In rock art sites across the so-called USA, there’s a bird made out of an hourglass or X-form: two triangles touching peak-to-peak. Coleville artist Joe Fedderson, of a Plateau tribe related to the Chief Joseph Band of Nez Perce, says the “contrapuntal chevrons” represent “The Mother.” (It’s the complete reversal of the diamond-shaped Goddess figurines found across Neolithic Europe, rhombi that also appear momentarily in the 8.)

The hourglass form also lives in Lakota cosmology as a symbol for “kapemni” or twisting, an ideogram that contains,

our entire relationship with the universe—an intertwining of the physical world, philosophy, and religion.

Charles Bailey describes the Lakota X-form as a way to represent a “cosmology of reflection…a spiritual view in which the physical world is dramatically mirrored in the sky and stars directly overhead.” It isn’t flat two-dimensional triangles. We should imagine two tipis, no, two lodges touching peak-to-peak while a Thunderbird flaps its wings.

“The People” live where the two lodges touch.

 

 

Ascending and descending, “intercourse between two worlds,” the Shri Yantra, Merkabah. Lynch: “The deeper you go, the more there is, until you hit pure bliss.”

For Indigenous star knowledge and X-forms presented as dance, check out the troupe Red Sky and their new piece, Trace, “offering a glimpse into our origin as well as our future evolution.”

Visual Puns

The Owl-8-Ball may be part of a visual pun or polysemous joke. For example, sometimes the “U-forms” of Northwest Coast formline designs represent eyebrows, fins, and feet, at the same time. Tsimshian artist Terry Starr says the tails of some creatures also represent wolf cubs. Likewise, a single ovoid eye can become another entity containing more eyes, “double-eyes,” like the creature behind Ben Horne’s desk at the Great Northern. I count 22 eyes in that Heiltsuk water monster, two of them with clear pupils!

Stories within stories, faces within faces, masks, disguises…this is what formline drawings, Renaissance paintings, and Twin Peaks are all about! In his painting Origins/Coalition (2011) Haida artist Lyle Wilson illustrates the evolution of the ovoid: it begins as the eyespots on the wings of big skates, then the eyespots on killer whales, then finally, the more squared eyeholes of the human skull. The 8 in Part 17 likewise goes through a 3-phase transformation, animated here by Disney’s Justin Weber in the style of 1930s Fleischer cartoons. “Who Is Judy?” It’s the owl, then the 8, then the 8 with a ball in it.

 

 

“One and the same.”

Artists still exploit the polymorphic capacity of ancient formline designs, using them to, as Janet Berlo puts it,

play on fundamental philosophical perceptions of structural dualities, the deceptiveness of appearances, mythic processes of transformation, and the paradoxical coexistence of two truths as a single juncture in time and space.

That sounds like what Lynch/Frost are doing with the 8 in Part 17, doesn’t it? More, the 8 could be an example of formline “split representation,” the mirroring or doubling of an image to expose two sides at once. It’s cubist, in a sense: higher-dimensional space mapped onto two-dimensional space. It’s not two balloons; it’s one viewed from two different perspectives.

Not two Coopers; one split in half.

And the lower half evidently has a dark ball inside of it.

Smoke Signals

What are we actually looking at? A spotlight on spewing smoke with animation projected on top? It’s reminiscent of Lynch’s paintings for Wallpaper Magazine in 2010 of circles containing “images of absolute simplicity and spiritual purity.”

It’s a tool. This could be a stretch, but Cooper practices throwing stones as a form of Tibetan lithomancy, so it isn’t too strange that he—or Laura—would practice other forms of divination. The 8 above the circle surrounded by darkness makes a Magic 8-Ball. Turns out the mega-popular fortune-telling device was invented in…1945!

Twin Peaks fans perk up. The 8-Ball dropped alongside Trinity, Little Boy, Fat Man, and David Lynch (b. 1946), and David Bowie (b. 1947).

The original device, the Syco Seer, was more like a fortune-telling dick—a hard cylindrical toy that could be used for fun or for serious divination. Casting (or “throwing”) its icosahedron/20-sided die isn’t too unlike casting the 64 sided I-ching hexagrams.

On the Wings of Love

In un/resolving the endings of Twin Peaks, I wonder if there are ten affirmative, five neutral, and five negative answers, as it is with Magic 8-ball answers.

The billiard ball element was added in the early 1950s in the wake of Dada, assisted readymades, and American streamline toy designs inspired by eugenics. It was also most certainly lifted from the Three Stooges film, You Nazty Spy! (1940). Spoiler: The ball in the film is hollow, and due to sexual jealousy it gets smashed open on someone’s head. Inside the 8-ball, a letter is found revealing the identity of the spy. Whaaaat?

Don’t we all use Twin Peaks as a sort of crystal ball? Isn’t experiencing the show itself a form of scrying magic? We watch a random episode (or investigate a random element) and see something new, like a Christian practicing bibliomancy. We keep finding stories to see against our own, to bring our own story into a sharper focus.

Coordinates

Finally, the 8 appears to Cooper at about the same time the coordinates appear to Mr. C, at the end of their conversation with Phillip. The second episode of Take the Ring focuses on the “arc” of this “energy living inside of a machine,” this character played by mega pop star David Bowie, and argues that Phillip speaks to both Coopers simultaneously through his smoke-signal/Fireman powers. Take the Ring splices together a bit of the two conversations, and noEmbryo simply plays them on top of each other (Thank you, Unable_Courage_5909 for finding that one!)

Example:

(Part 15) Mr. C: So it was someone else who called me?

(Part 17) Jeffries: There may be… someone.  Did you ask me this?

This… is where you’ll find Judy

Not knowing for sure who is who, or when is when, Phillip gives Mr. C the coordinates (literal floating numbers) to the Fireman’s trap and then zaps him back to his car, whereas he gives Cooper a shapeshifting hieroglyphic angel shadow and then zaps him to a specific time and place directly, like a god.

Considering Phillip’s statements may be out of synch, I wonder if the owl symbol was intended for Mr. C and has no direct connection to the 8 it morphs into. There is also a chance the entire story of “Judy” and her coordinates is part of a big ‘five-dimensional’ trap set up by Phillip, Cole, Briggs, The Fireman, Cooper, and Diane. After all, in Part 17, Cole says “Listen to me” in front of three phones and a room full of listening devices.

Nevertheless, the Owl Cave symbol/symptom, “the more or less avatar of Twin Peaks” (Take the Ring) now represents the 8 with a ball in it, multiple timelines, multiple narratives, and Phillip Jeffries. “With infinite outcomes, the story of Phillip Jeffries becomes a perfect metaphor for the story as a whole.”

Conclusions

[Ominous whooshing]

“They sat quietly for hours.” Fra Angelico paints invisible shapes to be ‘seen’ or rather enacted by the viewer’s own imagination, aided by perception’s inclination towards closure and boundary completion (see Finding out about filling-in).

Twin Peaks is full of disguises. The torus and secret agent inside the 8 could be Laura, or BOB, or the stone in “Two birds with one stone.” Maybe it’s the ceiling fan, hissing, whooshing, humming. Clank. It may represent the 1992 film FWWM moving inside the track of The Return. Or maybe the entire 8 is FWWM, and the ball marks the timestamp. The ball could even be that extra little piece that distinguishes the Owl Ring symbol from the Owl Cave symbol.

For today, the figure’s themes settle into the visual cultures of Northern Europe and the Pacific Northwest, where angels are made of mathematics, and tribal designs shapeshift into birds, star charts, and other things. I also think Lynch is telling us, through blatant visual rhyming, that the universe of Twin Peaks is a kind of Magic 8-Ball held in the hands of a David Bowie.

Thompson would call this strange symbol the “fragment” that sticks out of the story “like a fossil skull in the exposed strata of a cliff.” Aldous Huxley would call this mundane yet hallucinogenic imagery “living hieroglyphs that stand in some peculiarly expressive way for the unfathomable mystery of pure being.” Perhaps the 8 or lemniscate (“ribbon”) is an angelic frequency like a mantra, like the Tibetan “A” (“ahh”), the primordial ground, always seen floating on a sphere of light (thigle), used in Tibetan Dream Yoga and in Japanese Shingon Ajikan “Ah-meditation” practice to help the dreamer awaken.

The charismatic 8 above the Lynchian thigle also reads as a symbol for the double torus: two donuts that contain a dark ball. However, when it rotates 180 degrees (turning inward?) by collapsing into a single line, we get the feeling that this 2D geometric vision really represents a 4D torus; a 3-sphere; Hopf map/Hawk’s map for the Dantean 3-worlds of the Twin Peaks Universe.

Then, on top of that, it’s a key “in,” evidently. What do you think?

Jeffries: There it is. You can go in now. Cooper. Remember.

Mike: E-lec-tric-ity