Science In Real Life

A very important notion in physics is symmetry, although perhaps not in the form we are most accustomed to seeing around us. Biology as well possesses symmetry, and it is here that we are faced with some of the symmetries that we already countenance from day to day. Chemistry, in the form of molecular structure, also embodies fundamental notions of symmetry that help construct the world around us. Doubtless the entire natural world relies at its very core on various forms of symmetry.

Even though we hear the word frequently, most people don’t know that symmetry in physics reaches deep into the structure of the Universe. First, though, let’s start with an ordinary square, with some Cartesian axes included:

(Image Credit: SiRL)

Gee, this is one symmetrical figure – it has matching pieces on either side of each axis. However, those are not the only ones, since we can also use a diagonal line through the center. It so happens that squares have what we call bilateral symmetry. Just like your face, if we imagine flipping it across that line, it would come out the same. Kids these days (all the cool ones doing science, anyway) call that a reflection, which is a particular example of a very general thing called a transformation. Like it or not, anything you can do to an object, from lifting it up to causing a nuclear explosion, is a transformation. Move that square to the left and you have transformed its position by whatever distance you used. Notice that its essential properties, the things that make it a blue square, are unchanged.

Once you accept that any system can be characterized by a handful of parameters and equations that relate them, it is intuitive to see that any transformation which leaves those equations unchanged must correspond to some constant quantity of the system. Physicist and mathematician Emmy Noether was, in 1915, the first to realize this brilliantly elegant result that has since transformed all of physics. Quite simply, all of the basic conservation laws in physics (like energy and angular momentum) have with this law a simple operational manifestation. Rounding out this idea’s impressive list of accomplishments is a hefty contribution to the development of modern particle physics. Seeing conservation laws in particle interactions led to symmetries led to new predictions, et cetera.

Turning up the complexity a notch, the idea of broken symmetry has found use on the frontiers of physics. Unlike the four forces we have today, early in the Universe (it is suspected) there was just one. Very dramatic expansion and cooling broke that symmetry. When, in particular, the electromagnetic force separated, particles acquired mass. Xanadu the Universe might no longer be, but thanks to the Higgs boson we can form life as we know it. Yes, that Higgs boson. Zounds! You didn’t know, I’ll bet, that all of that stress and agita over the LHC was to find out what kind of broken universe we live in. Xanax might help.

Well, of course physics doesn’t have a monopoly on symmetry. Vases and visages both have it, but first the biology. Ubiquitous throughout the plant and animal kingdoms on Earth, various forms of symmetry dominate the landscape. Truly rare is the ambulatory creature that does not exhibit bilateral symmetry of its entire body. Some of your favorite fruits have spherical symmetry, although here I am comparing apples to oranges. Radial symmetry attracts adherents among a lot of the flora, and bilateral symmetry brands their branches. Questions then arise about why it is so common.

Postulating reasons to explain why evolution zigged instead of zagged is a risky proposition, but we can see there are several advantages that follow from symmetry. On the fauna side, the balance of bilateralization allows for faster locomotion, as well as the centralization of a nervous system. Next, for plants, having such a simple blueprint as radial symmetry is very efficient from a resource management perspective. Moving nutrients through the organism becomes easier, and even the very genetic construction of the plant is simplified. Ludicrously long strings of DNA would be required to build an asymmetric ficus; the ficus with the short genome is less at risk from transcription errors and other harmful mutations (this goes for the animals too).

Kindly zoom in further, and we will see that (a)symmetry is at work at the biochemical level as well. Just like people, organic molecules can be right- or left-handed, and while the lab can synthesize both it seems that life on Earth has chosen one form or the other for each of the common proteins and amino acids. I don’t know if chivalry is dead, but chirality is alive and kicking.

Humans have a massive predilection for symmetry, motivated no doubt by the symmetry of the human form. Guess if you have to, but try to think of the last asymmetric object you saw – I bet you can’t clearly picture it. From Kiev to Carolina, the devices and objects with which we surround ourselves are overwhelmingly symmetrical. Either it’s biology or culture or some mix of the two, but something about symmetry activates very old pathways in our brains that tell us that is how things are supposed to be.

Dubious you would be if I told you this essay covered everything there is to know about symmetry, and rightly so. Come what may, however, you now have a basic idea of how thoroughly the concept pervades our lives. Balance is everywhere. And now it’s here too.