The Meaning of Symmetry

If an object shaped like this one 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 in some way:

 

So while there are a lot of symmetrical things in the natural world, there are also plenty that are not symmetrical.

 

Why are some things symmetrical but not others?

Things that are symmetrical are that way because the forces that have affected their design or their evolution are equal across their planes of symmetry. Things that are not symmetrical have been affected by unequal forces.

This might make sense if we first look at an abstract definition of symmetry. This is actually a complicated subject that I won’t go into in detail, but I will touch on it just a bit to mention the parts that I will consider here and the parts that I’ll leave out.

In mathematics, an object is symmetrical if its shape is unchanged when a transformation of some type acts upon it. So, for instance, if you flip or mirror the object that is one kind of transformation. Other kinds could be if you rotate it, or if you move all parts of it from one part of space to another.

For the most part, what I am interested in here is what we usually mean when we talk about symmetry, which is mirror or reflectional symmetry – is there a plane (or several planes) across which you could mirror the object and still have it appear the same. There are three types of reflectional symmetry that I want to consider – spherical, radial, and bilateral.

The simplest and most symmetrical object is a sphere.

 A sphere is symmetrical about all planes that run through its center point. So you could say that a perfect sphere has an infinite number of planes of symmetry. Any plane, at any angle in 3D space, that passes through the center of the sphere is a plane of symmetry.

Spheres are common in nature of course -- stars, planets and moons for example, at least in their overall shape. Although less common, some living things are also spherical, such as certain protozoa, like this Acrosphaera radiolarian,

and some viruses, like the one that causes our old nemesis Covid.

 Although these are not perfect spheres, they are close enough for our purposes. They are essentially spherical in their development, and the parts that deviate from spherical are more or less randomly and evenly distributed on their surfaces.

We also have plenty of human-made objects that are spherical, such as balls and bearings and these things:

Going back to the earlier statement about why things are symmetrical -- that equal forces have acted on the object during its development -- we can see that all of these spherical 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. And again, we get both living things and non-living things that are spherically symmetrical.

A more restrictive type of reflectional symmetry is radial symmetry – where there is one axis (a line) that runs through the center of the shape, and only planes that include this line are planes of symmetry.

That would be things like the planet Saturn: 

Or the ripples in still water:

Any plane that goes through the central axis of one of these forms is a plane of symmetry, but any plane that does not include that line does not work. Generally, radially symmetric things have a different top and bottom side. This occurs in non-living, natural objects like Saturn or in things like a hurricane or those ripples in the pond.

We also see radial symmetry in lots of living things, such as the Enterobacteria phage T4 virus:

Or a sea urchin:

Sea urchins and the virus are actually not completely radially symmetric as there are instead several axes of symmetry around their center but not an infinite number of axes. But its close enough for this discussion.

In these organisms, 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.

Similarly for the ripples in the pond, there is gravity and surface tension that create different conditions at therefore different forms on the up side and the down side, but around the perimeter all the forces are the same, so we get a radially symmetrical form.

Most plants, on the other hand, are kind of in between on radial symmetry.

Plants, generally, are living things that remain in one place. 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 portion of the plant is affected by sunlight, wind, other plants, and so on in a different and sustained way over its life-span, and that results in different branching patterns.

But these differences affect each individual plant uniquely – because plant seeds spread widely and germinate in varied conditions and at varied orientations, there would be no advantage to a mutation in plant DNA that created a “sun facing” side and a “shade facing” side – the plant might easily end up growing with the wrong side facing the sun and since it is not mobile, it would not be able to turn itself around.

 So plants are an interesting compromise between symmetry and asymmetry. In terms of their DNA (I am guessing) their developmental plan is for a radially symmetrical shape – the DNA of plants causes them to develop with an up side and a down side, but otherwise all directions are the same – there is no inherent tendency for limbs on one side or the other to grow more or less.

But once a plant begins to grow, it is predisposed to vary its individual development based on the local environment and orientation unique to that plant, and so each plant end ups asymmetrical in its own unique way.

Now the third type of reflectional symmetry is bilateral symmetry, where the shape has a top and bottom that are different and a front and back that are different, but the two sides are mirror images of each other. This is where things get interesting.

With animals, the three planes of body development are called the frontal, the transverse, and the sagittal planes. When we say that an animal is bilaterally symmetrical, we mean that it is symmetrical about the sagittal plane only. About the other two planes, it is not symmetrical.

Many different animals are bilaterally symmetric – not just large mammals. There is a whole infrakingdom of animals classified as “bilateria’ that follow this basic body plan.

There are developmental reasons for this in the DNA of animals – but what I want to emphasize is the reason that the DNA has evolved that way.

Animals live on a planet with gravity and a surface (therefore a different top and bottom), and animals have evolved to move around. They have evolved to have a head that leads the way when they move, and a tail end that brings up the rear -- because the front and rear are exposed to different conditions and functional requirements.

The two sides of an animal, on the other hand, are exposed to varying but unpredictable influences due to movement. Any genetic mutation that would cause one side of an animal to be different from the other will generally not provide a survival advantage, because for an organism on the move the two sides are, over time, essentially the same. Any side to side environmental differences cancel out over the life of the organism and a genetic difference from one side to the other would not be an advantage.

So going back to the general principle, then, an animal is bilaterally symmetrical because it is only across that sagittal plane that the forces affecting development are equal. Across the other two planes, the factors that have affected the evolution of that animal are consistently different and some mutations in DNA that create differences across the transverse and frontal planes have been beneficial to the survival of the animal’s ancestors – therefore the animal is asymmetrical across those two planes.

So far, then, we have looked at natural objects of two kinds – those that are living and those that are created by some non-living natural process, like a planet, a rock, or ripples in a pond. 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 or a moon, 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.

 Of all these examples of symmetry in the natural world, bilateral symmetry is especially interesting.

As we have seen, there are examples in nature of non-living spherical symmetry (like planets) and non-living radial symmetry (like ripples in a pond, or a hurricane, or a volcanic mountain, or the planet Saturn). But it is extremely rare to find a non-living bilaterally symmetrical object – except for the trillions of objects created by humans.

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

We will look at a couple of exceptions later, but 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, fish hooks, TVs, cars, and desks do have this intention inherent in them. Either they intentionally point themselves somewhere, or someone made them with the intention of pointing in a certain direction.

That is why if we did find an object out in space like this one, 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 symmetrical.

Bird nests, wasp nests, beaver dams, and the like are either radially symmetrical or they are asymmetrical. So finding a bilaterally symmetrical object out in space that is clearly fabricated and not “natural” would probably be evidence of intelligent life.

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 radially symmetrical or completely asymmetrical.

This is kind of a digression, but one notable exception to this sub-rule about things made by non-human life 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. 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.

Throughout all these examples, symmetry is the result of how forces either equal or unequal affect the development of an object -- and bilateral symmetry in particular indicates an intention for the object or the being to face a certain direction.

And by implication, then, that bilateral symmetry implies life – either because the object itself is or was alive, or because the object was created by a living thing (and probably an intelligent living thing at that).

Now for some exceptions to these rules. I don’t think these invalidate the general concepts, but like almost everything there is no absolute and sometimes the exceptions are as interesting as the rule itself.

Starting with the very small, the first exception that I find to the general rule about bilateral symmetry is the molecule of ethanol, which is the intoxicating ingredient in alcoholic drinks.

Another is propene (not propane, but a different hydrocarbon gas), as seen here.

There may be some others as well. These molecules are bilaterally symmetrical, but not because of the general rule that I have been discussing. They are not subject to similar influences on the sides and dissimilar influences front and back or top and bottom. They are this way just because of the way that atomic forces work and how certain atoms happened to stick together when certain energy was available. 

A much larger but similar exception is certain wind-eroded rocks, like this one in the White Desert of Egypt.

This rock is pretty much bilaterally symmetrical, but it is not alive or made by a living thing. It is the result of steady wind erosion with the wind coming consistently from one direction. So it meets the general rule about why it is symmetrical but not the conclusion about that implying life.

Most wind-eroded rocks, though, are not symmetrical in this way because the wind direction is not so consistent. So again, this one is the exception and the fact that it is called the Rabbit Rock and that it is a tourist destination is an indication of how rare this type of rock is.

There are also some exceptions in the other direction – that is, living things that should (by the rule) be bilaterally symmetrical but that are not. One is the flounder:

And another is the Fiddler Crab:

The Fiddler Crab is interesting because only the males have the asymmetry – one large pincer that is used to attract a mate, and the smaller one for feeding. But both the males and the females look alike when they are juveniles. The asymmetry develops only as the males mature. As with several other evolutionary oddities, sexual selection causes otherwise logical rules to break.

In a similar way, perhaps, the flounder starts out in its development as a typically-oriented fish that is bilaterally symmetrical:

But as it develops, one eye migrates to the other side of its body and the body itself morphs somewhat to lie flat on the bottom:

So here the fish is starting from one kind of bilateral symmetry (like all other fish) and in the course of its juvenile development it morphs into almost bilateral symmetry around a different body axis.

Now to the final interesting exception, and the thing that got me thinking about this subject -- the oddity of symmetrical buildings which are, of course, made by people.

Why would any building be bilaterally symmetrical? It certainly does not move around. Although buildings usually have a top and bottom and a front and rear (which are different for good reasons) why would the two sides be identical? They are exposed to different conditions of sun and wind as well as usually different surrounding vegetation, topography, or other human-made conditions like roads or other building. 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:

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

In some cases, such as the Capitol Building shown here,

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 especially for a formal structure that intentionality is emotionally appealing to human beings even if it is illogical.

Another possibility is that our brains have evolved to respond to symmetry for the very reasons discussed here -- it is a signal of life and of intention. Our brains seek out symmetry because it is a signal that we are looking at another living creature (which may be helpful or harmful) or that we have found an object created by intelligence (and that may be good to know about). Our instict to seek symmetry may therefore lead to a desire to create symmetry even where it does not need to exist.