Impossible Trident



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What is wrong with the figure that Alfred E. Newman is balancing on his finger? How many prongs can you count? Where exactly is that middle prong located?

So What is Going On?

Among the most famous as well as the most interesting of all impossible figures is the impossible trident. The outline of the middle prong merges into the outline of the two outer prongs. In addition, the middle prong appears to drop to a level lower than the two outer prongs. The paradox is quite powerful, because within it are various impossibility sources.

Cover up parts of the figure. If you cover the top half, you will find that the bottom part of the figure is entirely possible. In this case, you interpret the foreground figure as being built of flat faces constituting two rectangular prongs.

Now look at only the bottom half of the figure. You interpret this figure as built of curved surfaces constituting three separate cylindrical lines.

The two parts that are joined in this figure have different interpretations of their shapes when they are perceived separately. Furthermore, when you join the two parts, surfaces that have one interpretation (part of the foreground figure), get a different interpretation (part of the background). The figure therefore violates the basic distinction between the background and an element of the object.

When you look at this figure, you first calculate contours or outlines, and from this you try to perceive the boundary of the shape. Your visual system's confusion occurs because several contours of this figure are ambiguous (they are outlined in red): The same outline can be seen as belonging to either one of two objects or interpretations. For example, this figure makes use of the fact that a cylinder can be represented by a pair of lines, while a rectangular bar requires three lines. The illusion is constructed by completing each pair of lines to make a cylinder at one end, and each triplet to make a square bar at the other end.

This ambiguity makes the figure violate another basic distinction, that between flat and curved surfaces, where a flat strip twists into a cylindrical surface. The two outer edges can also be interpreted as either the straight edge of a rectangular surface, or as the "slide-off" edge of a cylindrical surface. The figure, furthermore, gives contradictory cues for the depth estimation for the position of the middle prong.

Although this figure does have multiple impossibility sources, the first thing that you notice, however, is the counting paradox. This suggests that your visual system compares different regions by counting. This may be one of the few figures that reveals that your visual system also counts. The other impossibility sources may not be so apparent.

Consistently, when the impossible trident has more than 7 or 8 columns the impossibility of the figure no longer apparent even though the other contradictions are still present.

What happens to your perception of the figure's impossibility when the figure is longer or shorter?

These examples show how your brain builds up a symbolic representation of depth. Small details are used to build up an explicit depth description for local parts of the scene. In general, the overall consistency of the figure is not treated as so important. Since you cannot attend to the entire figure at once, you must compare the different parts before you realize that it is impossible.

When the figure is long, it can be perceived as a three-dimensional object locally, but its impossibility is not perceived immediately. This is because the contradictory clues are too separated.

When the figure is medium in length, the figure is easily interpreted as a three-dimensional object, and its impossibility is quickly perceived.

If the prongs are very short, the two different interpretations are both trying to fit within the same local area. There is no consistent interpretation and the illusion breaks.

Several early books and published papers on impossible figures have erroneously stated that there are different classes of impossible figures: those that can be built as three-dimensional objects and those that cannot. The impossible trident was grouped into the second category, because the apparent irresolvable conflict between the background and the foreground. It turns out, however, that all impossible figures can be constructed as three-dimensional objects seen from a single vantage point.

This is a three-dimensional model of the impossible trident or disappearing column made by Japanese artist Shigeo Fukuda in 1985. You can see three cylindrical columns at the top and two rectangular columns at the bottom. Only from one critical angle does the illusion work.

History of the Impossible Trident

This illustration at the top of the page was taken from the March 1965 cover of MAD Magazine by artist Norman Mingo. MAD introduced the figure as the MAD "Poiuyt." (Look at your keyboard to see how MAD came up with this name!)

Other names for this figure have included:

"The Devils Fork,"

"Three Stick Clevis,"

"Widgit,"

"Blivit,"

"Impossible Columnade,"

"Trichotometric Indicator Support," and

the "Triple Encabulator Tuned Manifold."

It turns out that MAD magazine bought the figure from a contributor who claimed that it was original, but the management soon found out to their embarrassment that the figure had been previously published.

No one knows who first designed this figure, although it first began to surface simultaneously in several popular engineering, aviation, and science-fiction publications in May and June of 1964. D. H. Schuster published an article that same year in the American Journal of Psychology that first brought the figure's importance to the psychological community. There has also been a claim that it was first originated by an MIT engineer in the mid 1950's, but there has never been any substantiation to this claim.

Over the years it has re-appeared in countless forms and adaptations.. For example, Stanford psychologist Roger Shepard cleverly used the concept as the basis of an impossible elephant.

Swedish artist Oscar Reutersvärd's mastery of such figures has led him to draw thousands of variations on this theme.