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Impossible trident

The impossible trident, also known as the blivet, devil's fork, or poiuyt, is a two-dimensional optical illusion that depicts a three-dimensional object with three cylindrical prongs at one end that appear to merge into a single rectangular bar, which then splits into only two prongs at the opposite end, resulting in a geometrically impossible structure that cannot exist in Euclidean three-dimensional space.^[1]^[2] This figure was first described and published by American psychologist D. H. Schuster in 1964, who encountered it as an ambiguous advertisement in an aviation journal and named it a "three-stick clevis," highlighting its perceptual ambiguity. Schuster's short article in The American Journal of Psychology marked its formal introduction to scientific literature, where he noted its capacity to confound viewers' expectations of spatial consistency. The illusion gained wider popularity in the 1960s through features in Mad Magazine, which used a variant called "poiuyt" to symbolize nonsensical or absurd concepts, and it later appeared in Scientific American in 1970, further embedding it in popular and academic discussions of visual perception.^[1] The illusion arises from the brain's tendency to interpret two-dimensional line drawings as coherent three-dimensional forms, despite inherent contradictions in the prong connections and depth cues; for instance, the central prong seems to attach inconsistently to the bar, violating principles of projective geometry while exploiting isometric projections that mimic realistic perspective in local segments.^[3]^[2] Cognitive psychologists attribute its persistence to "cognitively impenetrable" visual processing modules that prioritize holistic object recognition over detailed geometric verification, as explored in studies of perceptual organization and impossible figures.^[2] Variants, such as impossible columns inspired by the trident, have been created by artists like Shigeo Fukuda in 1985, demonstrating its influence on optical art and design.^[3]^[4]

Description

Visual Characteristics

The impossible trident is depicted as a three-dimensional object that appears to have three cylindrical prongs at one end that merge into a central rectangular handle or bar, which then splits into only two prongs at the opposite end.^[1] This configuration creates a visually coherent form in two dimensions, where the prongs seem to fork and merge without interruption.^[5] Key visual features include the continuous, curving lines that suggest seamless connectivity between the prongs, often rendered with consistent line thickness to imply uniform material and structure.^[6] Subtle variations in line weight or occasional light shading may be employed in some renderings to accentuate perceived depth and three-dimensionality, enhancing the object's apparent solidity.^[7] Common depictions of the impossible trident consist of simple black-and-white line drawings, emphasizing outline contours over filled areas to highlight the paradoxical form.^[5] These are frequently presented in various scales and orientations, such as rotated views or enlarged proportions, and are typically produced as static 2D illustrations in print media or digital formats for clarity and impact.^[3] As an example of an impossible object, the trident's design exploits two-dimensional representation to evoke a three-dimensional form that defies physical realization.^[1]

Geometric Impossibility

The impossible trident embodies a core structural contradiction: its three prongs at the fork end imply three distinct cylindrical extensions emanating from a central point, yet these appear to converge into only two cylinders at the handle end, breaching the requirement for continuous connectivity in a single, coherent three-dimensional object within Euclidean geometry.^[2] This impossibility stems from the depicted merging and twisting of edges, particularly the middle prong, which shifts from appearing behind the side prongs at the top to in front at the bottom; such a configuration defies consistent orthographic projection from a 3D manifold, as it would necessitate non-manifold intersections or abrupt depth discontinuities not permissible in physical space.^[8] Attempts to realize the trident in three dimensions, whether through physical wire construction or digital modeling in software like CAD tools, invariably fail due to mismatched vertex incidences—the three prongs demand three corresponding attachment points at the handle, but only two are available, resulting in an unconnectable graph where edges cannot pair without artificial gaps or overlaps. In basic topological terms, the object's edge graph violates embedding rules in \mathbb{R}^3, as the degree sequences and connectivity at each end cannot reconcile without self-intersection.^[9]

History

Early Appearances

The earliest documented appearance of the impossible trident traces back to an advertisement in an aviation journal, which D. H. Schuster, an American psychologist, noticed in 1964 and described as depicting a novel ambiguous figure resembling a "three-stick clevis" used in mechanical contexts.^[5]^[10] This figure, presented without explicit recognition of its impossibility, served as a practical illustration in the ad, highlighting Schuster's observation of its perceptual ambiguity in a technical setting. Shortly thereafter, an anonymously contributed version of the figure, labeled as a "hole location gauge," appeared in the June 1964 issue of Analog Science Fiction and Fact magazine, where it was shared as a humorous puzzle with the caption noting that "it can't be drawn as shown."^[5] This publication framed the image lightly, as an intriguing gauge or tool that defied straightforward replication, appealing to the magazine's readership interested in science and speculative concepts.^[5] In December 1964, Schuster formally documented the figure in a short article titled "A New Ambiguous Figure: A Three-Stick Clevis" in The American Journal of Psychology, where he sketched it himself and described its perceptual effects without assigning a specific name beyond the mechanical term "clevis." His contribution emphasized the figure's novelty as an optical ambiguity, drawing directly from the aviation ad he had encountered earlier that year.^[10] Prior to 1964, no confirmed antecedents of the impossible trident exist in optical illusion literature, though earlier works on ambiguous figures like the Necker cube (1832) explored related perceptual reversals without producing this specific form.^[5] The figure later evolved into popular names such as the "blivet."^[5]

Popularization and Naming

The impossible trident gained significant public attention shortly after its initial depiction through a prominent feature in Mad magazine issue #93, published in March 1965, where artist Norman Mingo illustrated the figure on the cover with mascot Alfred E. Neuman balancing it on his finger under the caption "Introducing 'The Mad Poiuyt'".^[11] This satirical presentation introduced the playful name "poiuyt"—a nonsensical term derived from the top row of typewriter keys—and markedly boosted awareness of the optical illusion among a wide audience.^[12] The term "blivet" emerged in 1967 through a satirical article by Harold Baldwin titled "Building Better Blivets" in Worm Runner's Digest, a humorous scientific periodical, where he outlined mock "construction rules" for variations of the figure, thereby popularizing the name and inspiring further playful explorations.^[13] Building on this, American artist and optical designer Roger Hayward contributed to the nomenclature in December 1968 with his article "Blivets—Research and Development" in the same publication, presenting additional impossible figures and interpretations that reinforced the blivet as a staple of visual paradox literature.^[14] By the early 1970s, the figure had entered academic discourse under names like "impossible fork" and "devil's tuning fork," with the latter coined in a 1975 Perception journal article by Brooks Masterton and John M. Kennedy, who analyzed its construction and perceptual effects.^[13] This scholarly attention facilitated its inclusion in psychology texts throughout the decade, such as Masterton and Kennedy's own work, and later in reference works like Andrew M. Colman's A Dictionary of Psychology (2009), which defined the "impossible trident" as a classic example of an undecipherable figure.

Psychological Mechanisms

Perceptual Interpretation

The human visual system interprets the impossible trident as a coherent three-dimensional object through ambiguous line junctions, where lines meet at corners that allow for multiple conflicting depth interpretations. At the "fork" end of the figure, the junctions suggest occlusion, with one prong appearing to pass behind others, creating the illusion of a solid structure despite the overall inconsistency. This ambiguity arises because local line arrangements follow rules of three-dimensional projection that are valid in isolation but fail globally, leading the perceptual system to assign depth relations that cannot coexist.^[7] The figure exploits depth cues such as linear perspective and interposition to imply solidity and recession, with converging lines at the handle end suggesting distance and overlapping elements indicating foreground occlusion. However, these cues are applied inconsistently—for instance, the prongs appear to emerge without corresponding occlusion shadows or perspective foreshortening—yet the visual system initially integrates them to construct a plausible volumetric form. Shading, if present in variants, further reinforces the perception of cylindrical surfaces, though it contradicts the branching geometry elsewhere.^[7] Gestalt principles of closure and continuity play a central role, as the brain tends to complete incomplete contours and perceive smooth, uninterrupted paths across the figure, unifying disparate lines into a single impossible shape. Closure fills in implied gaps at junctions to form enclosed prongs, while continuity favors flowing lines over abrupt breaks, overriding the detection of contradictions until focused attention reveals the anomaly. This low-level grouping mechanism prioritizes a simple, holistic interpretation over detailed scrutiny.^[7] Experimental studies demonstrate that viewers initially perceive the trident as a possible object, with early visual processing treating it similarly to real figures, only registering impossibility during later analysis. In one study, participants responded to the two-pronged trident with increased right-lateralized parietal activity for the impossible variant, indicating delayed conflict detection in spatial processing.^[15] Similarly, adults often reproduce or describe such figures as three-dimensional until instructed to examine junctions closely, highlighting the robustness of initial perceptual coherence.^[16]

Cognitive Biases Involved

The perception of the impossible trident involves top-down processing, where prior expectations of familiar three-pronged objects bias viewers toward interpreting the figure as a coherent, three-dimensional structure, overriding low-level geometric inconsistencies. This conceptual-driven influence relies on knowledge of tridents as everyday tools, leading the brain to fill in ambiguities and impose unity on the drawing despite its inherent contradictions.^[17] Confirmation bias further sustains the illusion, as observers tend to overlook or downplay the paradoxical elements—such as the mismatch between the three prongs at one end and two at the other—to preserve the perception of a single, valid viewpoint. In experimental tasks involving possible and impossible objects, exposure to plausible figures increases the likelihood of classifying ambiguous or impossible ones as "possible," demonstrating how preconceived notions favor confirmatory interpretations over disconfirming evidence.^[18] Similar cognitive challenges appear in other impossible figures, like the Penrose triangle, where attempts at mental rotation fail to reconcile the depicted geometry with real-world spatial rules, highlighting a broader failure in visualizing non-Euclidean forms from multiple angles. Neuroscientific evidence from fMRI studies reveals that impossible objects, including trident-like figures, activate object recognition areas in the ventral visual stream, such as the lateral occipital complex (LOC), in a manner comparable to possible objects, indicating that the brain constructs coherent representations without resolving the underlying paradox. This activation persists even when participants are aware of the impossibility, suggesting that higher-level cognitive processes, rather than early sensory analysis, account for the sustained illusion.^[19]

Structural Variations

Structural variations of the impossible trident maintain the core optical illusion of conflicting prong counts and depth cues while introducing modifications to enhance or alter the perceptual effect. Basic alterations often involve adjusting prong lengths, such as drawing the middle line shorter than the outer ones in tutorials to create the diverging prongs.^[20] Adding design elements, such as shifting the middle prong from the background at the handle to the foreground at the fork, amplifies the depth ambiguity central to the illusion.^[8] In modern realizations, 3D-printed models post-2010 attempt partial constructions of the trident, often building segments separately—such as the handle and prongs in distinct planes—to achieve the illusion from a single viewpoint without full connectivity. A notable example is a 2023 STL model designed for 3D printing, which constructs the object as interlocking but non-impossible parts when viewed obliquely, demonstrating how digital fabrication can approximate the 2D drawing in physical space while revealing inconsistencies upon rotation.^[21] Animated versions of the trident rotate the figure to expose the geometric contradiction, transitioning from a seemingly coherent 3D form to disjointed elements that highlight the perceptual error. These animations typically employ simple 360-degree spins to show how the prongs fail to align in three dimensions, reinforcing the illusion's reliance on static, orthographic projection.^[2] Drawing tutorials for variations focus on step-by-step line placement to control illusion strength, beginning with the rectangular handle formed by two parallel lines connected by perpendicular bars, then extending three diverging lines for the prongs with precise overlaps at the junction to create the ambiguous merge. Emphasizing even spacing and subtle curves at the fork end ensures the cylindrical illusion, while variations might elongate specific lines or add subtle asymmetries to test perceptual thresholds without resolving the core impossibility.^[20] Artist Shigeo Fukuda created an impossible columnade inspired by the trident in 1985, using similar principles of conflicting depth cues in architectural forms.^[3]

Analogous Impossible Objects

The Penrose triangle, introduced by psychiatrist Lionel Penrose and mathematician Roger Penrose in their 1958 paper, represents the foundational impossible object in the genre of optical illusions. This figure consists of three rectangular bars arranged in a triangular formation, where the edges appear to connect seamlessly from certain viewpoints but reveal inconsistencies when viewed holistically, preventing its construction in Euclidean three-dimensional space.^[22] The core principle of edge inconsistency in the Penrose triangle—where local perspectives align but global geometry fails—underpins many subsequent impossible figures.^[23] Examples of perspective paradoxes include the impossible cube and the impossible staircase, both of which manipulate depth cues to create spatial contradictions. The impossible cube depicts a wireframe cube with lines that suggest multiple incompatible vanishing points, making it appear three-dimensional while violating rules of projective geometry.^[24] Similarly, the Penrose stairs, also originating from the 1958 Penrose publication, illustrate a closed loop of steps that seems to rise indefinitely in a square configuration, exploiting ambiguous directional flow to confound motion perception.^[25] Multi-pronged impossible objects include fractal-like variants of the fork, such as the Devil's Gatling Gun, which features circular arrays of subdivided prongs mimicking a Cantor set after two levels of subdivision, and the Devil's Comb, which introduces three levels of branching for heightened complexity in the handle-to-prong transition.^[26] These evolutions build on earlier work by artist Oscar Reutersvärd in the late 1950s and were further developed by Cameron Browne in 2007.^[26]^[27] Historical parallels to these figures emerged in the 1950s and 1960s through M.C. Escher's lithographs, which popularized paradoxical geometries and influenced later developments in impossible objects. Works such as Belvedere (1958) and Ascending and Descending (1960) depict impossible architectures with inconsistent perspectives, drawing directly from Penrose's ideas to explore perceptual impossibilities in art.^[28] Escher's contributions during this era fostered a cultural fascination with such objects, bridging mathematical rigor and visual artistry.^[29]

Cultural and Educational Significance

Media and Pop Culture References

The impossible trident made its debut in popular media through Mad magazine in March 1965, where it was illustrated by Norman Mingo as part of a cover feature on optical illusions.^[8] This appearance marked an early instance of the figure's use in satirical and humor-driven publications, contributing to its recognition beyond academic circles.^[30] Subsequent uses in comics and magazines have included illusion-themed illustrations and gags, with collections of such cartoons appearing in directories dedicated to optical paradoxes.^[31] For example, the figure has been incorporated into comic strips and single-panel humor exploring themes of visual deception, maintaining its presence in print media focused on mind-bending concepts. In film and animation, the impossible trident has featured in short productions highlighting optical anomalies, such as the 2024 animated film The Chicken The Fox & The Paradox, where characters interact with the shape in a chase sequence.^[32] It has also appeared in educational video segments on illusions, often as a brief visual example in post-2000 content discussing perceptual tricks. During the digital era, the impossible trident has proliferated through stock image libraries, with hundreds of royalty-free photos, vectors, and illustrations available for commercial use on sites like Adobe Stock and Shutterstock.^[33]^[34] This accessibility has facilitated its integration into online graphics and web content. Merchandise featuring the impossible trident includes protective iPhone cases designed for tech enthusiasts and engineers, with listings on Amazon showcasing black-and-white renderings of the illusion since 2023.^[35] These items, such as cases for iPhone 15 models, emphasize the figure's appeal to those interested in geometry and puzzles.^[36]

Applications in Education and Art

The impossible trident serves as a valuable teaching tool in psychology classrooms to demonstrate optical illusions and principles of visual perception, particularly Gestalt theory, which emphasizes how the brain organizes sensory input into coherent wholes despite ambiguities. For instance, in a 2021 cognitive psychology course at Pennsylvania State University, students analyzed the trident to explore how perceptual grouping fails in impossible figures, leading to misinterpretations of spatial relationships.^[37] Such examples highlight its role in fostering discussions on cognitive processes, where learners trace the illusion's ambiguity to the brain's tendency to infer three-dimensional forms from two-dimensional cues.^[5] In educational resources, the impossible trident features prominently in online databases dedicated to optical illusions, aiding instructors and self-learners in studying perceptual mechanisms without requiring advanced equipment. The Illusions Index, an ongoing curated collection, describes the trident as a classic example of an undecidable figure, providing interactive explanations that link it to cognitive science research on how viewers resolve geometric inconsistencies.^[5] This resource supports broader pedagogical goals, such as illustrating the limits of human vision in introductory neuroscience or design courses. Beyond academia, the impossible trident inspires artistic applications, particularly in digital art and body modification, where it embodies themes of perceptual paradox and impossible geometry. Artists incorporate it into vector illustrations and stock graphics for graphic design projects, leveraging its stark lines to create mind-bending visuals that challenge viewers' spatial intuition.^[38] In tattoo culture, the trident appears as a minimalist optical illusion, with examples including forearm designs that provoke ongoing viewer engagement through its inherent ambiguity.^[39] Workshops and tutorials on drawing the impossible trident further bridge education and art, encouraging participants to construct illusions step-by-step to understand perspective and line manipulation. YouTube channels since 2018 offer accessible guides, such as beginner-friendly demonstrations that break down the figure's construction, promoting its use in creative hobbies or informal art classes.^[40] These practices draw from the broader tradition of impossible objects in fine art, akin to M.C. Escher's lithographs, though the trident's simplicity makes it ideal for digital experimentation and personal expression.^[5]

References

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Impossible Fork -- from Wolfram MathWorld
Schuster, D. H. "A New Ambiguous Figure: A Three-Stick Clevis." Amer. J. Psychol. 77, 673, 1964. Seckel, A. The Art of Optical Illusions. Carlton Books ...
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### Summary of Impossible Trident
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... impossible trident (Schiffman, 1982). At one end there are three prongs, but at the other end there are only two. Such a figure is called an impossible figure.
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Shading in a picture can also give the illusion of depth. It gives information about parts of an object which project or are inset, and gives the impression ...Missing: optical | Show results with:optical
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Impossible trident
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Modeling and animating 3D scenes with possible and impossible objects. See the submission video for the complete animation. previous 3D approaches it is ...
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Hard Cases for a Handle Theory | Jeff Dolven - Cabinet Magazine
... three-stick clevis,” now better known as the “impossible trident.” It is a letter from an Escheresque alphabet, ambiguously two- and three-pronged, the ...<|control11|><|separator|>
[10]
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Jul 23, 2015 · Wikipedia's article on the blivet mentions the figure appearing in a 1964 issue of Analog Science Fiction and Fact but I suspect it goes back ...
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Dec 11, 2018 · Begin by drawing three straight lines connected at right angles. Notice that the lines are of different lengths, the middle line being much ...
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The Impossible Trident by caffinatedprinter | Download free STL model
Rating 5.0 (1) Mar 11, 2023 · Many have said this is a shape that can be drawn but can never be made. Prove them all wrong with your very own impossible object! Tags. tuning ...Missing: partial realizations
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IMPOSSIBLE OBJECTS: A SPECIAL TYPE OF VISUAL ILLUSION
IMPOSSIBLE OBJECTS: A SPECIAL TYPE OF VISUAL ILLUSION. L. S. PENROSE,. L. S. ... First published: February 1958. https://doi.org/10.1111/j.2044-8295.1958 ...Missing: triangle | Show results with:triangle
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Impossible Triangle - The Illusions Index
The Penrose Triangle is an impossible figure (or impossible object or undecidable figure): it depicts an object which could not possibly exist.
[22]
Impossible Cube - The Illusions Index
It's impossible for the Impossible Cube to exist because in order for it to exist rules of Euclidean geometry would have to be violated. For example, parts of ...
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Penrose Stairs - The Illusions Index
It was first published in the British Journal of Psychology in 1958. Shortly afterwards, in 1960, Escher produced his lithograph print Ascending and Descending, ...
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Impossible Constructions: Up and Down. July 1947, Lithograph. Relativity. July 1953, Lithograph. Convex and Concave. March 1955, Lithograph. Belvedere.
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Animated Short Film | The Chicken The Fox & The Paradox - YouTube
May 24, 2024 · A short film inspired by classic cartoons where a clever chicken is chased by a less clever fox across the impossible trident.
[31]
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Find 21 Impossible Trident stock images in HD and millions of other royalty-free stock photos, 3D objects, illustrations and vectors in the Shutterstock ...Missing: Adobe | Show results with:Adobe
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iPhone 15 Impossible Trident Optical Illusion for Inquiring Minds Case
Featuring picture of impossible trident rendered in angled black and white lines, this quirky design is ideal for engineers, architects and those who work with ...
[34]
iPhone 15 Pro Max Impossible Trident Optical Illusion for Inquiring ...
Impossible trident optical illusion artwork will appeal to engineers, draftsmen, drafters and all those with inquisitive, inquiring minds.
[35]
Impossible Trident | Psych 256: Cognitive Psychology, 003, FA21
Sep 7, 2021 · The impossible trident may seem like an illusion that demonstrates the failures of the Gastalt Principles of Organization to perceive things correctly.
[36]
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[37]
My arm will now make people dizzy forever! Impossible Trident done ...
Dec 7, 2020 · Just put your finger on the middle darkened spot. It will break the illusion.Speculation behind the "impossible trident"/"devil's tuning fork" logo[TOMT][Website][late 2010s?] an optical illusion type thing that lets ...More results from www.reddit.comMissing: viral 2010s
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How to Draw Impossible Trident Easy | Optical Illusions Drawings
Dec 30, 2018 · Do you want to learn how to draw an impossible trident or devil fork for beginners. It's super easy art tutorial how to draw optical ...Missing: depth perception