Babies, sculpture and bowerbirds: A look at structural coupling

I have tried to make the argument, in some of the things I have written, that mathematics experiments with the ways we are able to ‘see.’  But there is a great deal of complexity in what it means ‘to see.’ ‘Seeing’ and ‘reasoning’ are not easily unraveled.  An infant’s ‘intuitive physics,’ the subject of recent infant cognition research, is also ‘seeing.’

From the point of view of biologist Humberto Maturana and the late Francisco Varela, the nature of the nervous system is understood only within the history of mutually congruent structural changes that happen between systems, or, to make it a little plainer, the interactive history between the cells we identify as a living unit and its containing environment.  They call this history of ‘recurrent interactions’ leading to ‘structural congruence,’ structural coupling. This coupling is how they define cognition, even when there isn’t a nervous system.  And even when there is one, sensory-motor and cognitive processes cannot be easily disentangled, if at all.  In this light, the physicist and the mathematician may be said to experiment as the baby does, spontaneously, but in the presence of a complex history of structural couplings.

One can imagine that the artist experiments with this coupling also, as Alva Noë considers in his piece on Experience and Experiment in Art. Noë looks at the work of artists like Richard Serra. (Photos of some of this work can be found here)

When one first encounters a piece, such as Running Arcs (For John Cage), one is liable to be struck by the scale and the visually inscrutable orientations and distributions of weight. One not only notices these qualities, but one is disturbed by them. One puzzles: what stops these giants from falling over? To wander around or through a piece such as this can cause a loss of balance. In this way the works make us reflect on how we feel, perceptually, in their presence.

And they direct our attention to the complexity of our experience, a complexity we easily overlook. The loss of balance, for example, introduces us to what are strictly non-visual (e.g. vestibular, kinesthetic) components of our ‘visual’ experience.

What I shall argue is that Serra’s work (and also the work of these other artists) enables us to catch ourselves in the act of perceiving and can allow us thus to catch hold of the fact that experience is not a passive interior state, but a mode of active engagement with the world

The weave that the body builds with experience is tight, as is evidenced by cognitive studies like the one showing how body posture can influence our estimations of quantity, reported by Mo Costandi at the Guardian. The study was published here.

According to the mental number line theory, we think of numbers along a horizontal line with small numbers on the left and larger ones to the right. Rather than being specific to certain cultures, this seems to occur universally and may be due to the way in which the brain represents numbers. With this in mind, Anita Eerland and her colleagues hypothesized that secretly making people lean to the left or right would affect their estimations of quantities.

The study shows that the manipulation of body posture influenced the participants’ estimations, even though they were completely unaware of their true posture. How might this work? It is thought that estimating something such as the height of the Eiffel Tower involves a strategy of ‘anchoring and alignment’ – we think of the height of another building and then mentally compare it to the Eiffel Tower. This would involve retrieving information from memory, so leaning to the left may make smaller numbers more accessible than larger ones.

The findings provide further evidence for the embodied cognition hypothesis, the simplest form of which states that the content of the mind is partly determined by the form of the body. We are only just beginning to understand how the body influences mental function, but it now seems quite clear that the influence of the body extends to abstract concepts and – as this new research shows – to complex cognitive processes such as decision-making.

To round out the theme, I find the recent study on how Bowerbirds create illusions in their own sculptures (also reported by Mo Costandi) to be great food for thought.

Male bowerbirds use their intelligence to impress the females, constructing elaborate structures called bowers to attract mates. They are not on master builders, but also accomplished artists. Males of some species decorate their bowers lavishly with flower petals and sparkly manmade objects. The Satin bowerbird even paints the walls of his bower with charcoal or chewed up berries.

Male Great bowerbirds are even more remarkable. Their bowers, which are among the most complex of all, are true marvels of avian architecture. But as well as being builders and artists, males of this species are also magicians – the bowers they build are like a house of illusions, with built-in visual tricks that manipulate females’ perceptions and increase their likelihood of choosing the builder as their mate.

They do so by arranging the objects covering the floor of the court in a particular way, so that they increase in size as the distance from the bower increases. This positive size-distance gradient creates a forced perspective which results in false perceptions of the geometry of the bower, which is visible only to the female when she is standing in the avenue. From her point of view, all of the objects in the court appear to be the same size.

Lest you think it’s not intentional,

Endler and his colleagues manipulated the decorative objects in the bower to reverse the gradient, with the large objects placed closest to the bower and the smaller ones further away, and found that the birds re-arranged the objects to restore the original pattern. This happened very quickly – in all cases, the positive gradient was restored within three days and the pattern was almost identical to the original by two weeks.

There are photos of the structures in Costandi’s blog that are worth seeing. Researchers can’t find reason beyond courtship for these wonderful little experiments with perception.  But whatever the reason, these birds are actively engaging their sense of space, and perspective…..making art and mathematics?

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