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Necker cube

Necker cube is a physics topic covered in the lgStudy science library. This page brings together a partial reference excerpt, illustrations, worked examples, real-world applications and a short study plan, so you can understand Necker cube rather than just read about it. In short: The Necker cube is an optical illusion that was first published as a rhomboid in 1832 by Swiss crystallographer Louis Albert Necker. It is a simple, wire-frame, two-dimensional drawing of a translucent cube with no visual cues as to its orientation, so it can be interpreted to have either the lower-left or the upper-right square as its front side.

Necker cube — main illustration
Necker cube — illustration

Key takeaways

  • Necker cube belongs to physics; place it in that map before memorising details.
  • Learn the definition first, then one example that makes the definition concrete.
  • Connect Necker cube to a quantity you can measure, compute or draw — that is where exam questions come from.
  • Reproduce the core statement of Necker cube from memory before moving on to harder problems.

Reference excerpt

The Necker cube is an optical illusion that was first published as a rhomboid in 1832 by Swiss crystallographer Louis Albert Necker. It is a simple, wire-frame, two-dimensional drawing of a translucent cube with no visual cues as to its orientation, so it can be interpreted to have either the lower-left or the upper-right square as its front side.

Ambiguity

The Necker cube is an ambiguous drawing. Each part of the picture is ambiguous by itself, yet the human visual system picks an interpretation of each part that makes the whole consistent. The Necker cube is sometimes used to test computer models of the human visual system to see whether they can arrive at consistent interpretations of the image the same way humans do.

Humans do not usually see an inconsistent interpretation of the cube. A cube whose edges cross in an inconsistent way is an example of an impossible object, specifically an impossible cube. With the cube on the left, most people see the lower-left face as being in front most of the time. This is possibly because people view objects from above, with the top side visible, far more often than from below, with the bottom visible, so the brain "prefers" the interpretation that the cube is viewed from above. There is evidence that by focusing on different parts of the figure, one can force a more stable perception of the cube. The intersection of the two faces that are parallel to the observer forms a rectangle, and the lines that converge on the square form a "y-junction" at the two diagonally opposite sides. If an observer focuses on the upper "y-junction" the lower left face will appear to be in front. The upper right face will appear to be in front if the eyes focus on the lower junction. Blinking while being on the second perception will probably cause you to switch to the first one.

It is possible to cause the switch to occur by focusing on different parts of the cube. If one sees the first interpretation on the right it is possible to cause a switch to the second by focusing on the base of the cube until the switch occurs to the second interpretation. Similarly, if one is viewing the second interpretation, focusing on the left side of the cube may cause a switch to the first. The orientation of the Necker cube can also be altered by shifting the observer's point of view. When seen from apparent above, one face tends to be seen closer; and in contrast, when seen from a subjective viewpoint that is below, a different face comes to the fore. The Necker cube has shed light on the human visual system. The phenomenon has served as evidence of the human brain being a neural network with two distinct equally possible interchangeable stable states. Sidney Bradford, blind from the age of ten months but regaining his sight following an operation at age 52, did not perceive the ambiguity that normal-sighted observers do, but rather perceived only a flat image. During the 1970s, undergraduates in the Psychology Department of City University, London, were provided with assignments to measure their Introversion-Extroversion orientations by the time it took for them to switch between the Front and Back perceptions of the Necker Cube.

References in academia and popular culture The Necker cube is discussed to such extent in Robert J. Sawyer's 1998 science fiction novel Factoring Humanity that "Necker" becomes a verb, meaning to impel one's brain to switch from one perspective or perception to another. The Necker cube is also used to illustrate how vampires in Peter Watts' science fiction novels Blindsight (2006) and Echopraxia (2014) have superior pattern recognition skills. One of the pieces of evidence is that vampires can see both interpretations of the Necker Cube simultaneously, which sets them apart from baseline humanity. Cultural critic Benjamin Kirbach uses the figure of the Necker cube as the basis for what he calls neckerology. Kirbach draws on concepts ranging from object-oriented ontology, speculative realism, and new materialism to show that even the average everyday objects we encounter only ever appear to us through partial aspects and profiles (what phenomenologists call "adumbration"). Like a Necker cube, these aspects and profiles can only become perceptible through the occlusion of other aspects and profiles that remain hidden from view. Kirbach also reveals that Necker himself, whose full name is Louis Albert Necker de Saussure, is the first-cousin once-removed of renowned linguist Ferdinand de Saussure. The latter Saussure's division of the linguistic sign into signifier versus signified—what he called a "two-sided psychological entity [une entité psychique à deux faces]"—is perhaps not unlike the perpetual push-and-pull of a Necker cube. "[B]y dividing it into signifier and signified," Kirbach writes, "we might say that Saussure himself 'neckerized' the sign".

See also Ambigram Binocular rivalry Multistable perception Pareidolia Rhombille tiling Schroeder stairs Spinning Dancer

References

Further reading Einhäuser, Wolfgang; Stout, James; Koch, Christof; Carter, Olivia Louise (March 2008). "Pupil dilation reflects perceptual selection and predicts subsequent stability in perceptual rivalry". PNAS. 105 (5): 1704–9. doi:10.1073/pnas.0707727105. PMC 2234208. PMID 18250340.

External links

History of the cube and a Java applet

Illustrations

Necker cube illustration
Necker cube illustration
Necker cube illustration
Necker cube: Necker cube (left) and impossible cube (right)
Necker cube (left) and impossible cube (right)
Necker cube: Adding an intermediate blue bar object going "down from the top" (left) or "up from the bottom" (right) shows how the image can change its perspective simply by changing which face (front or back) appears behind the bar.
Adding an intermediate blue bar object going "down from the top" (left) or "up from the bottom" (right) shows how the image can change its perspective simply by changing which face (front or back) appears behind the bar.

Worked examples

Example 1 — a first encounter with Necker cube

Start with the simplest possible case. Write down what Necker cube claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In physics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Necker cube before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Necker cube ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Necker cube

In research
Necker cube appears in physics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry
Engineering practice reuses Necker cube in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom
Necker cube is common in secondary-school and first-year university syllabi. It links to neighbouring topics 1832 introductions, Cubes, Impossible objects, so understanding it makes those chapters shorter.
In everyday life
Look for Necker cube outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

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How to study Necker cube in 20 minutes

  1. Read the reference excerpt below once, without taking notes.
  2. Close the page and write down what Necker cube means in your own words.
  3. Compare your version with the excerpt and mark what you missed.
  4. Work through the three examples above with pen and paper.
  5. Explain Necker cube out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Necker cube in simple terms?

The Necker cube is an optical illusion that was first published as a rhomboid in 1832 by Swiss crystallographer Louis Albert Necker. It is a simple, wire-frame, two-dimensional drawing of a translucent cube with no visual cues as to its orientation, so it can be interpreted to have either the lower…

Why does Necker cube matter?

Because it connects several physics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Necker cube?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Necker cube.

Tags

  • 1832 introductions
  • Cubes
  • Impossible objects
  • Optical illusions

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