The Meaning of Symmetry

If an object shaped like the one shown above were discovered in outer space, it would be proof of extraterrestrial life.

Regardless of its size or material, and whether or not it looks like something we can identify, just the shape would be convincing evidence of life. Intuitively, just by looking at this shape, many people would agree. But why? The answer is in the meaning of symmetry.

Symmetry is a natural phenomenon -- Lots of things, both living and not, are symmetrical.

But then lots of other natural things are not symmetrical:

Things in nature that are symmetrical are that way because the forces affecting them are equal across their axes of symmetry. Those that are asymmetrical are affected by unequal forces.

The simplest and most symmetrical object is a sphere. It is symmetrical about all axes, and is common in nature -- stars, planets and moons for example. Although less common, some living things are also spherical, such as certain protozoa and some viruses. All of these objects exist in an environment that is essentially uniform on all sides, or they move through their environment in a way that exposes all sides of their shape to uniform forces.

The next step up is radially symmetric forms -- things like the planet Saturn: 

The top and bottom are the same here, but the rings define a "middle" that is not there in a simple sphere.

Then there are radially symmetric forms with a different top and bottom side, like a sea urchin:

Sea urchins are actually not completely radially symmetric as there are instead five axes of symmetry around their center. But close enough for this discussion.

In this organism, the top is not the same as the bottom. That is important, and is a result of the fact that it lives on Earth and is subject to gravity and to the effect of a "land" versus a "sea" side to its existence. As the sea urchin moves slowly (with no preferred direction) across the ocean floor, that difference of top vs. bottom is the critical one for its development. But all sides are acted upon equally by the environment, so they are radially symmetrical.

Most plants (usually these are living things that remain in one place) are not symmetrical. But they do have a clear top and bottom -- a root side and a leaf side. The branches or shoots are usually not radially symmetrical, but they are kind of similar on all sides in a way that the top side and the bottom side are not. That makes sense, because like the sea urchin, plants experience gravity and the effect of land vs. air. Unlike sea urchins, though, they do not move around and so each side is uniquely affected by sunlight, wind, other plants, and so on and that results in different branching patterns.

Almost all animals are bilaterally symmetric -- they have a top and bottom that are different, and a front and back that are also different. But they have two sides that are essentially identical:

Animals are bilaterally symmetric because like plants they live on a planet with gravity and a surface (therefore a different top and bottom), but unlike plants they move around. Most importantly, they have a head that leads the way when they move, and a tail end that brings up the rear -- so the front and rear are exposed to different conditions and functional requirements. The two sides, on the other hand, are exposed to varying but unpredictable influences due to movement. Over a long period of time, variation in the forces acting on the two sides of an animal essentially "cancel out" and can be considered to be equal.

Obviously living things are shaped by their environments differently than a moon or a rock is. Much of the shape of living things is determined by their DNA, which is the result of many years of evolution in ancestral organisms. A rock, on the other hand, is shaped purely by forces acting on that specific chuck of matter. But the end result is the same -- when forces from the surrounding environment are equal due to a homogeneous environment or due to the cancelling-out effect of motion, then things are symmetrical. When forces are unequal, then there is asymmetry.

Other than animals, the only things in the world (and perhaps the universe) that are bilaterally symmetric are a few type of molecules, and objects that are made by animals -- generally, but not exclusively, by human beings.

Although molecules are interesting, the focus here is on visible objects. And it is intriguing that while there are natural phenomena that have a top and a bottom and a basic radial symmetry (such as ripples in a pond, the funnel of a tornado, or the cone of a volcano) the only shapes that have bilateral symmetry are living things or objects made by living things (and usually intelligent ones at that).

The essential, common feature of both natural (living) and fabricated bilaterally symmetrical objects is that they embody intention. They have a front end and a back end, and the front is meant to point somewhere. Rocks, clouds, hurricanes, and planets may move around, but they do not intend to move nor did someone create them for the purpose of moving or facing them in a certain direction. All animals, as well as arrowheads, TVs, cars, and desks do have this intention inherent in them.

That is why if we did find an object out in space like the one shown at the beginning of this post, it would be evidence of life beyond our planet. Either it would be a living thing (or the remains of one) or it would be an object created by a living thing with the intention of some directionality in its use.

Here on Earth, it is interesting that most objects made by animals other than human beings are not bilaterally symmetric. Bird nests, wasp nests, beaver dams, and the like are either radially symmetric or they are asymmetric.

One notable exception are the nests of Bower Birds:

These nests (really more like mating platforms) are among the most fantastical of animal creations. Their purpose is to attract a female bower bird for mating. Some of these bowers have a directional intent (a preferred direction of approach, and a particular orientation to the bird's body) that causes them to have bilateral rather than radial symmetry.

The reason that animal-made objects are not usually bilaterally symmetric is that they are almost always fixed in place. Usually they are nests, sometimes barriers, but they are not objects to be carried around or thrown. By contrast, most human-made objects are mobile -- our weapons, furniture, vehicles, toys, and jewelry. As is the case with the difference between mobile animals versus fixed plant organisms, the mobile variety has bilateral symmetry while the fixed object is asymmetric.

Given these facts, consider the oddity of symmetrical buildings:

Petit Trianon, Versailles, France, 1768

Why would any building be symmetrical? It certainly does not move around. Although buildings usually have a front and rear (which are different) why would the two sides be identical? They are exposed to different conditions of sun and wind as well as usually different surrounding vegetation or topography. Yet throughout human history and in many cultures there are symmetrical buildings.

Not all buildings are symmetrical, of course:

Urban vernacular architecture, where each new piece of construction must fit around existing built conditions, often is not.

And architecture of the Modern Movement, with its emphasis on exterior expression of the building's interior functions, is also often asymmetrical:

Bauhaus, Dessau, Germany, 1925

But many free-standing buildings, both vernacular and those designed by architects, are bilaterally symmetric:

Batak House, Sumatra, Indonesia

Capitol Building, Washington, D.C., 1800

In some cases, such as the Capitol Building shown above, the interior layout of rooms is not symmetrical -- the exterior is, therefore, forced into an unnatural symmetry that responds neither to the interior structure nor to the exterior environment.

Why do it, then? Perhaps the same intuition that would infer extraterrestrial life from a bilaterally symmetric object influences the human desire to create symmetrical structures -- they demonstrate intentionality rather than an organic response to stimuli, and that intentionality is emotionally appealing to human beings even if it is illogical.