Three Types of Symmetry

Past 6 months brought a lot of travel, relocation to a new city & country, new job…  now let’s try to get back into good habits like writing.

From 101 Things I Learned in Architecture School I finally understood the appeal of asymmetrical architecture and why is it so beloved by modern architects. This appreciation resonated with a 900 year old echo when we visited Angkor Wat.

1. Static symmetry

The most basic type of symmetry is the one we all imagine when one mentions “symmetry”. Invariance of shapes (or systems) under certain transformations (rotation, reflection, scaling) is deeply appealing to us. Like the layout of the Angkor Wat complex.

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2. Symmetry, broken

The breaking of symmetry is however a quintessential physical mechanism that gives rise, among others, to replicating complex patterns balancing on the edge of chaos (aka “life”).

The breaking of symmetry between past and future gives rise to the arrow of time. And where is time there are stories – such as the The Battle of Kurukshetra. Static symmetry of the army formations is ultimately broken to be able to tell the story of the big battle.

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3. Dynamic balance – the symmetry of asymetry

Finally, we arrive at the least obvious form of symmetry – the dynamical balance.

From 101 Things I Learned in Architecture School:

Balance is inherent in a symmetrical composition, but asymmetrical com-
positions can be either balanced or unbalanced. Consequently, asymmetry tends to
require a more complex and sophisticated understanding of wholeness.

An example – a dancer is in dynamic balance, yet the posture is not symmetrical in the static sense.

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A spinning dancer is in dynamical balance. To keep with the Angkor Wat theme I could have showed a picture of dancing Apsaras. I found this optical illusion however extra interesting, because in addition to dynamical balance it demonstrates a dynamical clockwise/anti-clockwise symmetry in rotation.

This concept too hasn’t been unknown to the builders of Angkor Wat in the 11th century. My favourite bas relief is The Churning of Ocean of Milk.

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It shows 92 gods and 88 demons fighting for the elixir of immortality and a snake caught up in the middle. The gods hold the tail, the demons hold the head, while the snake coils itself around Mt. Mandala. Each time the gods and demons pull from their sides, the mountain turns and the ocean churns.

There is a lot of static (translational) symmetry in the repeating figures. The symmetry is also broken (the head and tail of the world-snake, gods and demons, 92 vs. 88). But ultimately there is a dynamical balance, at least for the moment.

And to close the circle (another symmetry), my new “home” town is famous for its own version of a building in a dynamic equilibrium, that is inspired by dancers: The Dancing House.

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