Seven Short Reflections on Symmetry

by James Morris

My favorite palindrome is “Go hang a salami, I’m a lasagna hog.” This sentence reads the same forward and backward. In other words, the two halves of the sentence are mirror images of each other. This kind of symmetry can be found in nature too.

#1 Two halves are better than one
CatOur left and right sides look approximately alike. We are, after all, bilaterally symmetric. Many animals share this trait, including flies and lobsters, frogs and lizards, birds and cats. All of these organisms have distinct heads and tails, as well as fronts and backs. But our left and right sides are very similar to each other.

JellyfishSymmetry is not just a distinctive aspect of many animals; it is actually used to classify them. There are organisms, like sponges, that are irregular in form. They have no planes of symmetry at all. Then there are organisms that display radial symmetry – they have many planes of symmetry around a central axis. Jellyfish and sea anemones are familiar examples. Finally, there are organisms like us that exhibit bilateral symmetry.

We are members of a great group called Bilaterians, reflecting this fundamental and defining aspect of our body plan.

#2 Something fishy
This way of classifying organisms sounds simple, but there are some interesting wrinkles. Take starfish. They display striking five-fold symmetry, with five arms projecting out of a central body. But they are grouped with other organisms showing bilateral symmetry. Why is this?

StarfishIt turns out that starfish go through several developmental stages, starting off as larvae and then undergoing metamorphosis (like insects) into adult sea stars. It’s the larvae that show bilateral symmetry, like us, giving them proud membership in our Bilaterian club.

#3 Only skin deep
InternalAnatomyFrom the outside, we are more or less bilaterally symmetric. But, beneath the surface, we are not. Our heart is on the left; our liver on the right. Our colon ascends on the right, crosses the midline, and descends on the left. And anyone who has had appendicitis knows that the appendix is typically in the lower right of the abdomen.

This is true of most of us. However, there are some individuals who have their heart on the right, not the left. This condition is known as dextrocardia (literally, right-hearted).

And some individuals actually have all of their internal organs completely reversed. This is known as situs inversus and it occurs in about 1 in 10,000 individuals. In these individuals, the heart, stomach, and spleen are on the right (rather than the left), and the liver and gallbladder are on the left (rather than the right). For these people, pain in the lower left of the abdomen may be a sign of appendicitis, not pain in the lower right.

Sometimes, situs inversus is associated with a host of medical problems, but, remarkably, sometimes it doesn’t and these individuals are completely healthy.

#4 Nothing’s perfect
Our left and right sides are similar, but not identical. For many people, one foot is slightly larger than the other. One leg may be a bit longer than the other. Moles and freckles may be distributed randomly on our skin.

Most of us have a dominant hand, preferring to use our right hand or our left hand, but not both. Some people are able to perform tasks equally well with the right and left hands, but these ambidextrous people make up only a small percent of the population and some have become ambidextrous through practice, for example by athletic training and musical performance.

BrainThe two halves of our brain look alike, but they are specialized for different functions. The left side is thought to excel in language, logic, and math, whereas the right side seems to be important for spatial relationships, expressing emotions, and creativity. This dichotomy, however, is likely too simple, with both sides of the brain cooperating for many tasks.

Nevertheless, one task that is thought to localize predominantly to the right side of the brain is the ability to recognize faces. Faces provide another example of imperfect symmetry. Although the two halves of our faces look alike, they are not perfect mirror images of each other. New York-based photographer Alex John Beck recently took photos of people’s faces, and then put two right halves together, and two left halves. The resulting photos are striking.

Want to try it yourself? There is even an app for that.

#5 A look in the mirror
When we consider our left and right halves, they look similar but are not the same. In fact, they are mirror images of each other. What this means is that you can’t superimpose a particular structure from one side onto the other.

HandsTake your hands. If you try to line them up, with palms facing down, your right thumb points to the left, and your left thumb points to the right. No matter how you contort your hands, you simply cannot make one exactly like the other. That’s because they are mirror images of each other.

ScapulasThe same is true of other parts of the body. Your right and left shoulder blades, or scapulas, are also mirror images of each other. You can’t “put” your left shoulder blade on the right; it just doesn’t work. When I teach anatomy and we are examining bones, I commonly ask, “Is that the left or right scapula?” From the various hills and valleys (processes and fossae), you can figure it out, and there is only one “right” answer.

#6 Deep asymmetry
In Greek, the word for “hand” is “chiral.” A chiral molecule is asymmetric, and can’t be superimposed on its mirror image, just like your hand or scapula. It turns out that most of the molecules that make up your body are chiral.

Consider amino acids, the building blocks of proteins. An amino acid has a carbon atom, which is often attached to four different molecules. As a result, this central carbon atom is asymmetric, and the amino acid can’t be superimposed on its mirror image.

AminoAcidsAmino acids therefore come in two forms: there are L forms (left-handed) and D forms (right-handed). Remarkably, even though both forms are equally likely and equally good at doing their job, all of the amino acids that make up the proteins in your body are L amino acids.

And it’s not just you. By far the majority of amino acids that make up the naturally-occurring proteins in all organisms are L. This is one of many pieces of evidence that all life shares a common ancestor.

#7 A broader look
Symmetry is not just a feature of us and our close animal cousins. We see it in all kinds of organisms.

Viburnum TulipDaffodilThistle DandelionMany flowers show radial symmetry, just like jellyfish. Viruses come in many shapes, but one of the most common is an icosahedron, a shape with 20 sides made up of equilateral triangles. The icosahedron is one of five Platonic solids, which speak to symmetry and even beauty in geometry.

Symmetry comes up in many human endeavors as well, from art and architecture, to music and literature. Snowflakes are crystals that show six-fold symmetry. And some say that math and physics are based on layers of symmetries. Perhaps this is why the physicist Philip Anderson once wrote, “It is only slightly overstating the case to say that physics is the study of symmetry.”

It’s simply up to us to find and explore these underlying patterns.

© James Morris and Science Whys, 2016.

8 thoughts on “Seven Short Reflections on Symmetry

  1. Ben

    I find this fairly similar to what you wrote about here. Great article, this is just a bit to add on to it. It is a short video about repeated images and numbers in nature.

  2. James Morris

    Here’s one of the longest palindromes I have every heard: “Doc, note I dissent, a fast never prevents a fatness; I diet on cod.”


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