The Fork-and-Knife Illusion

Recently while dining out, the first author was fooling around with her silverware and placed her knife between the tines of her fork. With the knife in the middle of the fork, the reflective knife looks strikingly transparent (Figure 1). Extended observation of the knife can lead to a bistable percept in which reflective and transparent appearance alternate, though not all observers report this. Moving the knife up and down slowly yields a dynamic effect in which the knife becomes transparent as it descends into position between the tines (see Supplemental Movie). With even a slight tilt to the knife, the illusion is lost. Likewise if the knife is offset from the midline of the fork, the effect is weakened considerably. It can be strengthened, however, by lowering the knife further so that the tines’ reflected images align with the real tines extending above the knife’s occluding upper contour.

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Figure 1.

Top: A reflective knife appears transparent when placed between the tines of a fork. Bottom left (misaligned configuration): A dichroic beam splitter permits simultaneous observation of the reflected and transmitted images of the fork’s tines. Bottom right (aligned configuration): By positioning the beam splitter correctly, the reflected tines coincide with the transmitted ones, yielding a physically ambiguous stimulus.

Given the simplicity of the effect, it is worth considering whether it is an illusion at all. In Mirrors in Mind (1998), Gregory offers a taxonomy of illusions including two hierarchical levels. He categorizes illusions as physical, physiological, or two varieties of cognitive (knowledge or rule-based), and within these categories classifies illusions as ambiguity, distortion, paradox, or fictions. Within this framework, we suggest that the current illusion is an example of a physical ambiguity. In Figure 1, we demonstrate this ambiguity by using a dichroic beam splitter to simultaneously present both reflected and transmitted images of the fork’s tines. By misaligning the beam splitter, we can see these two sets of tines in different colors (Figure 1, bottom left) and by orienting the beam splitter correctly we can make them coincident (Figure 1, bottom right). The close agreement between these images means that the visual system can interpret the scene vis-à-vis a transparent or reflective knife.

Besides this basic ambiguity, there are specific stimulus features that affect the illusion’s strength. Although multiple cues contribute to perceived transparency (see Kingdom, 2008 and Gerbino, 2015), here the presence of X-junctions obeying Metelli’s rules for transparency (Metelli, 1974) are an important cue supporting the effect. These junctions are disrupted when the knife is tilted (nullifying the effect), but preserved in other configurations that include observable reflections of background elements on the knife’s surface (see Figure 2A and C). The persistence of the transparent percept under these conditions is commensurate with observations made by Grieco and Roncato (2005), who demonstrated that specific contrast relationships between surfaces and outline contours support perceived transparency in flat images. Such critical stimulus features can even overcome inferences based on perceptual experience, as demonstrated by Kanisza’s paradoxical transparency images (reprinted in Gerbino, 2020), in which common opaque objects (including a knife!) appear transparent in illustrations that include stimulus structure favoring transparency. Although now transparent plastic knives are readily available, the dominance of perceived transparency in our illusion also demonstrates that stimulus structure can induce percepts that either contradict experience, or are at least less likely.

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Figure 2.

We attempted to weaken the strength of the illusion by introducing elements that provided cues to reflectance. Upper left: Visibly reflected text does not disrupt the transparent percept much. Upper right: A textured background that is not visible in the reflected knife also does not disrupt perceived transparency. Lower left: Large reflected elements (chessboard squares) do not disrupt perceived transparency. Lower right: A larger hand mirror yields a weaker effect, possibly due to the conspicuous misalignment of large background elements (the napkin’s edges).

We examined additional variations of this illusion to determine what factors might strengthen or weaken the illusion when the critical X-junctions were preserved. The strongest disruption of the illusion resulted from using a larger hand mirror, which made it easy to observe large-scale misaligned contours elsewhere on the reflective surface (Figure 2D). We also observed that a dull, scratched knife was more effective than a shiny one. This result is interesting because as Gregory (1998) observes, mirrored surfaces are less visible when they are free from blemishes—a phenomenon we thought would favor perceived transparency. However, a shiny knife makes it possible to see strong specularities along contours in the reflected image that are inconsistent with the appearance of those contours on the real fork, weakening the effect. Considered together, these observations suggest that the ambiguous appearance of the fork (supported by X-junctions that photometrically support transparency) is critical to the illusion and requires a certain amount of counter-evidence (possibly defined by ambiguous vs. unambiguous surface area) to be overcome.

This illusion is not without precedent, but also has unique features that distinguish it from previous reports. Wardle and Carlson (2015) observed illusory transparency when viewing distant mountains, which also depended on Metelli’s (1974) rules for perceptual transparency. An optical configuration similar to ours is also used in mirror box therapy designed to alleviate sensations in phantom limbs (Ramachandran & Rogers-Ramachandran, 1996) and in a popular science museum exhibit called The Divided Self (Gregory, 1998). In both cases, the reflected image formed by a plane mirror that the observer sits beside is experienced as being an image of the limb attached to that side of the body, implying a transparent window rather than a mirror. A closely related predecessor of our illusion are practical effects used in the movie Star Wars: A New Hope to induce perceived transparency beneath a wheeled vehicle traveling over sand, yielding a vehicle that appears to hover over the ground plane rather than roll. Our simple illusory effect thus is an example of how stimulus structure can lead to intriguing percepts, with a novel emphasis on the appearance of surface material properties.