Symmetry

Leonardo Da Vinci, based on the works of an architect known as Vitruvius, after his detailed study of anatomy, conceived The Vitruvian Man, which is probably the greatest symbol of proportion pertaining to the human body, also felt that the workings of the human body were analogous to the workings of nature and The Vitruvian Man was to serve as evidence to prove this, apart from other things. Perhaps he was looking for a greater, cosmic truth. Da Vinci may have had an extraordinary thirst for knowledge and an unmatched curiosity, but it doesn't take a genius to search for patterns in nature and space. Man’s curiosity has led to many things, a natural extension being the identification of the many forms of symmetry.

Yes, there is tremendous beauty in symmetry. But I seem to like asymmetry as much, if not more. Symmetry gives a sense of harmony and an aesthetic feeling which always seems to seem to trigger sentiments of ‘well being’, equilibrium and balance. Perhaps there is meaning beyond symmetry than it first seems and perhaps there are lessons to be learnt by reading between the lines, or in patterns, images, music, structures, monuments, buildings, sculptures and anything else which can possibly be imparted the word ‘symmetric’ at some point.

The Whole Tone scale in music. Each note is separated by a whole tone or two semitones.

The Taj Mahal

Why is Symmetry so commonplace? I am inclined to take a Socratic view of things, i.e. I will answer this question with another question in the hope that I may convince myself along with you with a logical, lucid reasoning. Why should this text be left aligned and not center aligned, or aligned in some other manner? It is of course easier to do than create a bizarre sense of alignment. But the question lies in why any other form of alignment is bizarre in the first place; everything cannot be misconstrued as convenient. It is due to convention and custom. This could be extended to a lot of fields in the sciences and arts where ‘unconventional’ ways are becoming increasingly commonplace. Assuming there is no logical choice, almost anything could have found its place to being ‘accepted’ or ‘modernist avant-garde’; what is accepted is just a random choice in a chaotic world where there is neither an obvious answer or a single one, carried forward by generations, who create stigma, stereotype and justification, and make these randomly selected answers naively commonplace. I will call this interpretation a Randomist view.

There are languages which are written from right to left such as Urdu, Arabic and Hebrew. According to Dictionary.com, both Arabic and Hebrew came from the Proto-Canaanite alphabet, which was written from right to left. Proto-Canaanite was also sometimes written in a hybrid form called boustrophedon in which the directions of the lines alternate. One line is written right to left, and the next line is written from left to right. Chinese and Japanese were written vertically at a point, till the languages adopted the English way. Another example can be religious customs and superstitions, but I doubt it will add ‘sanctity’ to this argument, as religion is too sensitive a subject for too many. The nihilist in me has come forth.

The common belief is that aesthetics and the symmetry of something go hand in hand. But there seems to be a distinct ambiguity in this line of thinking. For instance, the harmony of colour on a canvas is quite integral to the art connoisseur. But what is harmony of colour? This is a question which has no single, obvious answer. The Randomist view should work here. There is certainly no analytical reasoning in art as I know it, as it deals with aesthetics. There may be analytical interpretations, but that explains the perception of only one group of people. Harmony of colour is achieved in different ways for different people.  Now, if everyone has a unique line of thinking, an ‘accepted’ thought could only be reached by varied reasoning to explain the same thing. Total individuality is impossible, different schools of thoughts are a more plausible idea. Each of these schools of thoughts are born from a different Randomist view, even though it is perceived to be a Non-Randomist view for one group and a Randomist view for another, thus rendering asymmetry as acceptable as symmetry. Picasso brought about a revolution of sorts with his Cubism phase, and it was possibly a revolution because asymmetry was more common in art.

Picasso's
'Factory, Horta de Ebbo', 1909 (oil on canvas)

The lack of symmetry is an intriguing thought, just as stated in The Chaos Theory. A double pendulum is bound to produce chaotic motion starkly different from a single pendulum. The fluttering of wings by a butterfly in South America causing a tornado in North America, popularly known as the Butterfly Effect, if true, seems to point at abject failure on the part of anyone who searches for answers to explain dynamic systems, including the one called existence, including me, for I fail to accept anything beyond reason. If I didn’t understand something even after numerous attempts I would most properly find myself in a state of inebriation at a later point of that day. But we humans cannot afford to give up. And explaining the dynamics of the world isn’t enough. We can dismiss the gravest of issues like extinction of species or global warming and talk about the latest reality show. We can complicate or simplify anything, even something like religion. Atheists probably die in hordes in a war based on religious sentiments. A goose is probably better off. Do geese see God? 

Symmetry is quite a topic to write about, and the inspiration behind it was a bed sheet. Yes, a bed sheet. It had symmetrical designs on it and those designs were what my gaze fell on, first thing in the morning. It was the commencement of a rather dull day, a day which most likely had nothing in store for me, and I was lazing on my bed, with my face on the bed. It got me thinking about symmetry, and everyone’s deliberate or unconscious obsession with symmetry. I didn’t seem to give a rat’s ass about whether something should be symmetric or not. Even a rat’s ass is probably symmetric.

Apart from rat’s asses, symmetry can also be found in human emotions: humans prefer a reciprocatory relationship. In case of equals, one would generally be treated how one treats others. People are quick to make note of anyone who breaks the symmetric barriers of qualities, skill and emotion. A genius in any field is most certainly creating an imbalance in talent, which is probably made up by denizens of those not nearly as gifted or hard working. A hundred beggars and a rich man’s average income will be closer to the per capita income, which is quite obvious.  There is a dreamy air about these obvious things. Light and darkness, life and death, fire and water. They are all contrary forces which are also interdependent. These are some manifestations of the Yin-Yang, as it is known in Chinese philosophy.

Yin-Yang

One can find a lot of patterns in day to day life. It all just depends on the extent to which one searches. My friend, after reading The Hitchhiker’s Guide to the Galaxy, told me that it stated the number 42 to be the “Answer to The Ultimate Question of Life, the Universe, and Everything". I hadn’t read the book, but the idea was fascinating and preposterous at the same time. The idea must have led people to search for occurrences of the number and extol the number with praise every time it made an appearance anywhere, rendering it a ‘famous’ number. If the number was any other one, it would still be ‘famous’. Things get more mysterious when it comes to the golden ratio, discovered probably by Euclid. Great masters have dedicated stupendous levels of brainstorming on it. It finds a place in the arts, music, architecture, nature and the sciences. More popularly, it makes a mark even in the apple logo. We humans, in our quest for answers, have reached only the tip of the iceberg and there is a tremendous possibility that our search for everything ends up being a futile exercise. Alternatively, we could extol anything to divinity and create justification for a random answer and bask in the satisfaction of at least having an answer, the Randomist view working here again.

The apple logo's conformity with the golden ratio 

After a rudimentary study of symmetry, my opinion is that there are a tremendous number of phenomena and organisms in nature which conform to some form of near symmetry and not perfect symmetry. In fact, many animals are approximately mirror-symmetric, though their internal organs are often arranged asymmetrically. Symmetry is also hard wired in our genes and springs to life when we look for a mate. The general consensus is that a physically attractive face is one which has near perfect symmetry, not perfect symmetry: the flaws are integral, but they must be as unnoticeable as possible. The leaning of The Leaning Tower of Pisa was a miscalculation, an accidental occurrence. But as the name suggests, that is what the monument is known by.

A computer generated symmetric picture of Scarlett Johannson

The Leaning Tower of Pisa

I must admit that I've been purposely unstructured at various points of this article. But at a certain point in this article, there lies symmetry within asymmetry. I will not state its location. One may call it asymmetry within symmetry as a result of it coming under a Randomist View. I guess I'm generating supremely poetic arguments to explain supremely useless things. But then again, it has become sufficiently lucid to me that the internal dissonance of being can produce the most harmonious conclusions of existence. Ah! The geese!