An Irrational Phenomenon

“In nature, nothing is perfect and everything is perfect. Trees can be contoured, bent in weird ways and they will still be beautiful.” quoted Alice Walker. How do we really define 'perfection'? Is perfection only restricted to beauty, or is it also about efficiency and functionality? Something could be imperfectly perfect but also perfectly imperfect. Overall, the word 'perfect' is extremely subjective. Wabi Sabi, a Japanese concept, delves into finding beauty in imperfections. I could perceive the current climate as imperfect but an alien watching from far away who would potentially want to invade our Earth might perceive climate change to be in its favour and thus, perfect.

Ironically, entropy influences most of the universal activities. But the true charm lies where entropy embodies itself so perfectly that it gives rise to everything we see around us- and everything we don't. Humans will find perfect patterns in randomly arranged clouds and marvel at a well-groomed field of flowers without hesitation. This innate response is because we see certain patterns in nature- one singular pattern that fits all beautiful beings- the Fibonacci sequence which unfolds in numbers like 0, 1, 1, 2, 3, 5, 8, 13, 21, and so on. When consecutive pairs of these numbers are divided, they approach the Golden Ratio—approximately 1.6180339887. This irrational number represented by phi, is magical in a way because of its ability to appear almost everywhere. It is a random number and for some, insignificant, but in its absence, the universe may not exist.

In about 300 BCE, Acharya Pingala who was a poet and a mathematician wrote about a pattern of short and long syllables in the lines of Sanskrit poetry which deciphered a sequence of numbers called matrameru. This sequence was named "Fibonacci sequence" about 1500 years later by the Italian Mathematician Leonardo Bonacci.

Since I have already created this intrigue about finding this sequence anywhere and you probably don't see the sequence floating around you right now, let me get to the point. All sorts of naturally occurring spirals that can be found have this sequence embedded in themselves. Most seed heads, pinecones, fruits and vegetables have spirals of some kind. If you count the diagonally arranged spirals of a pinecone one at a time covering all the diagonal lines and note the number of the outgrowths in each line, you will obtain the Fibonacci sequence. Many seed heads, pinecones, seashells, fruits, and vegetables exhibit some form of spiral arrangement. If you count the diagonally arranged spirals on a pinecone, taking note of the number of outgrowths in each line, you will find that they follow the Fibonacci sequence. This also applies to the seedheads of a sunflower, the arrangement of cauliflower and pineapple. The intricate webs spun by a spider, the terrifying hurricanes and storms, and our very own galaxy, the Milky Way also express the sequence.

Some plants express this sequence in their growth points (Phyllotaxis). In huge trees, the first number could be obtained from the main trunk. This trunk will then give rise to one or two branches representing the second number. These branches will give rise to another few branches- the third number and so on. The number of petals on a particular flower is found in the Fibonacci sequence too- Lillies have 3 petals, roses have five, and delphiniums have eight- all numbers constituting the Fibonacci Sequence.

Interestingly, we find this golden sequence in social arrangements too- A honeybee colony consists of a queen, a few drones and several workers. The female bees (queens and workers) have two parents: a drone and a queen. Drones, on the other hand, hatch from unfertilized eggs. This means they have only one parent. Therefore, Fibonacci numbers express a drone's family tree in that he has one parent, two grandparents, three great-grandparents and so forth.

We like to believe that human beings are the greatest creation of nature and it would be catastrophic if we didn't embody the sequence. Leonardo da Vinci's 'Mona Lisa' is mysterious yet so beautiful due to this very sequence. Faces, both human and nonhuman, abound with examples of the Golden Ratio. The mouth and nose are each positioned at golden sections of the distance between the eyes and the bottom of the chin. Similar proportions can be seen from the side, and even the eye and ear itself (which follows along a spiral). The more closely our proportions adhere to the golden ratio, the more "attractive" those traits are perceived. The most "beautiful" smiles are those in which central incisors are 1.618 wider than the lateral incisors, which are 1.618 wider than canines, and so on. Looking at the length of our fingers, each section — from the tip of the base to the wrist — is larger than the preceding one by roughly the golden ratio. The DNA molecule measures 34 angstroms long by 21 angstroms wide for each full cycle of its double helix spiral. These numbers, 34 and 21, are numbers in the Fibonacci series, and their ratio of 1.6190476 closely approximates Phi, 1.6180339.

Speaking of DNA, since we find the sequence so abundantly in nature, the cause could be linked to phylogenetics. The number in itself, is known to favour traits that improve survival and reproduction. Patterns that follow the Fibonacci Sequence often provide advantages in resource allocation, space optimization and reproductive success, thus being naturally selected. One such example is that of a hawk- when a hawk approaches its prey, the sharpest view it obtains is at an angle to their direction of flight- this angle equals the Fibonacci spiral's pitch- a pitch that could have developed due to natural selection. Proportions of hormone transport and distribution such as Auxin in plants can create Fibonacci-like patterns. In phyllotaxis, leaf or flower primordia often position themselves in a spiral-like pattern around the shoot apex when the Auxin concentrations reach a threshold. This positioning follows the golden angle which corresponds to the Fibonacci Sequence. This placement is such that there is maximum optimization of space and resources- getting access to sunlight and gases. The meristem, or the growth tissue is regulated by genes and can produce Fibonacci-like patterns due to mechanical and biochemical interactions.

The Fibonacci sequence is an omnipresent and enigmatic phenomenon that contributes its benefits wherever it appears. While the cause of its widespread occurrence remains a mystery, we understand that its influence is undeniably significant.