By Gordon Rugg
So what do wireframe Necker cubes have to do with enigmatic facial beauty, Rothko paintings, Sudoku, and video games? The answer is: Quite a lot.
In this article I’ll look at the deep structure of some popular passtimes, and consider some of the implications. This is the first in a short series of articles about the deep structures of desire.
The enigmatic female smile has a long history in art and film, with the Mona Lisa as a classic example. The image below shows a modern example of an enigmatic smile. So what is it that makes the smile enigmatic, rather than standard-issue?
A key feature of this image is that it’s not symmetrical. This becomes more obvious if we take the left half of the image and mirror-image it into a new version of the face. The image below shows the result: A woman staring back at the camera, with her mouth unsmiling.
When we apply the same process to the other side of the original face, we see something very different. We now see a woman starting back at the camera, with the corners of her mouth raised in a slight smile.
This mirror-imaged face is also narrower than the other mirror-imaged face. The blank space on the left in the image above makes this easier to see. The image below shows the three faces next to each other.
When we see the three together, we also see a hint of something else. The eyes in the central image and the image on the right have a faint smile, but the cheek muscles don’t appear to be flexing the way that they would in a smile. So, the image appears to be sending out two sets of mixed signals. The first set involve the asymmetry in the mouth; the second set involves the contrast between slightly smiling eyes and unsmiling cheek muscles.
The bigger picture
Asymmetry in faces is something that artists and scientists have known about for a long time. The short version is that symmetrical faces tend to be viewed as more attractive than asymmetrical faces. This isn’t just a human issue; the same preference for symmetry is widely distributed in the animal kingdom, and has been documented in e.g. bees.
However, there’s more going on in the images above than just asymmetry. The face itself appears to be symmetrical; it’s the expression that is asymmetrical, with the two sides of the face showing different expressions.
This is where Necker shifts come in. In brief, a Necker shift occurs when you suddenly realise that there’s a completely different way of making sense of the same object or situation. It’s named after the Necker cube, which is the wireframe cube shown in the left of the banner image for this article. You can see a Necker cube as either coming out of the page, or going into the page, but you can only perceive it in one of these ways at a time.
I’ve blogged previously about how this maps onto humour, where the punchline is the point at which the audience sees the Necker shift onto a completely different explanation for the build-up. In the same article, I’ve looked at how it also maps onto some aspects of horror, where the audience suddenly sees a frighteningly different way of perceiving the same situation.
In the original asymmetric image of the woman’s face, one side of the face is definitely unsmiling, and the other side is definitely smiling. This sets up the image for Necker shifts between viewing the face as unsmiling, and viewing it as smiling.
Why would a photographer want to do this, if it was done deliberately? One possibility is that it’s a deliberate use of the Necker shift as a way to add interest to the image, since the viewer’s mind will be perpetually shifting between the unsmiling and the smiling interpretation. I’ve blogged here about how this principle can be used in architecture with geometric designs, and here about how it can be applied to some forms of abstract art, where the viewer can switch between different parsings of the same scene.
So, in brief, we can use the Necker shift to define one type of enigmatic smile; the type where a face can be parsed in two different ways, because different parts of the face are sending out different signals. In the image above, each side of the mouth is sending out a signal which is clear and unambiguous on its own, but which is completely different from the signal being sent out by the other side of the mouth.
This is different from the type of enigmatic smile where the viewer doesn’t see enough information to be able to parse the expression unambiguously. Again, this is about not being able to parse something, but with the “not enough information” type, there’s a different reason for not being able to parse it.
At a deeper level, this shows us the same underlying mechanism at work in several settings that are usually treated as completely separate, namely portraiture, architecture, horror and humour.
It’s also possible to see another set of underlying mechanisms that are common to a broader range of settings. Two repeated themes implicitly present through the discussion above are interestingness and the absence of threat.
The portraiture and architecture examples above involve Necker shifts being used to add ongoing interest to an artefact, so that an image or an area of tiling or whatever will continue to be interesting to look at for more than just an initial few seconds. The presence of Necker shifts in humour and some forms of horror is usually structurally different, because it’s intended to be used for a one-off sudden punchline or shock, rather than as an ongoing effect.
So what happens when we start looking for non-threatening problems with more than one possible solution, in other fields? The answer is that they start cropping up in a lot of places. Crosswords and Sudoku are two widespread passtimes that involve a non-threatening activity where there’s an extremely large set of possible solutions, and where the player has to solve the problem of whittling this set down to the one final correct solution. As with the “conflicting but clear signals” type of enigmatic smile, both crosswords and Sudoku involve a closed set of possible answers. Crosswords involve only words; Sudoku involves only numbers. There’s a similar underlying structure in problem-solving video games, which involve closed worlds with closed sets of options.
I’ve blogged previously about ways of measuring the complexity of games. Being able to measure their complexity opens up a fascinating set of possibilities that relate to work by e.g. Ramachandran and Hirstein on “sweet spots” for desire. With this approach, it should be possible to help someone find their individual sweet spot for the complexity of a game, or design, or whatever, and then to use this knowledge to find games, designs etc that are particularly likely to appeal to them. It should also be possible to produce some objective values for preferred complexity values across a population, so that we can design public spaces to be more attractive to more people.
In the next couple of articles, I’ll go further into the issues of attractiveness, ugliness, and threat, and of ways to represent them.
Notes, references and links
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There’s more about the theory behind this article in my latest book:
Blind Spot, by Gordon Rugg with Joseph D’Agnese: http://www.amazon.co.uk/Blind-Spot-Gordon-Rugg/dp/0062097903
You might also find our website useful: http://www.hydeandrugg.com/