Axioms of Nature
“The laws of nature are written by the hand of God in the language of Mathematics.” - Galileo Galilei
Mathematics is the systematic application of any circumstance. It is the foundation of all patterns, and the world would not make any progress without it. It’s not hard to optically discern mathematics in nature, whether it’s a simple plant or spiral galaxy, but it may require a more proximate look.
Symmetry is a mathematical formulation that is noticed frequently in our daily lives, from microscopic to macroscopic organisms. Take a moment and observe things around you; look at the mirror; what you observe is the symmetry between the left and right parts of our body. Humans have bilateral symmetry, and that is the primary symmetry in nature. Some symmetries are not very common in nature; for say, bi-radial species combine radial and bilateral symmetries. Comb Jellies are a great example of bilateral symmetries.
Have you ever cogitated how nature has organized itself in patterns? Natural patterns include symmetries, trees, spirals, meanders, waves, etc, and all these patterns have consequential reasons for their use. Mathematics has the ability to illustrate this at different calibres. Even if you have noticed, it adheres to the same basic mathematical rules as human music when a bird sings. The branching pattern of trees was described in the Italian Renaissance by Leonardo da Vinci. He stated that: when a parent branch splits into two or more child branches, the surface areas of the child branches add up to that of the parent branch.
Another topic of our interest is recursion. It is a situation in which the outcome is determined by explaining more minor instances of the same situation. If we visually examine the things around us, we can find many examples of recursion in the natural world because nature is plenary of recursion. From the branching structure of rivers to patterns on an animal’s skin are diverse examples of recursion. Another weird but interesting fact is that peacocks attract mates with repeating patterns in their plumage. Fractals, ferns and Romanesco broccoli are typical examples of self-similar sets.
THE FIBONACCI SEQUENCE
The Fibonacci sequence, portrayed as 0, 1, 1, 2, 3, 5, 8, 13, 21, 34, …, is a sequence in which each number is the sum of its two preceding numbers. This sequence of numbers reflects the order of numerous natural happenings mathematically, the number of petals on a flower, the number of spirals on a sunflower, and there are endless examples of the Fibonacci sequence in nature. One vital role of the sequence is in phyllotaxis (The Study of arrangement of leaves, branches, flowers, or seeds in plants) to highlight regular patterns. Most flowers have three (like lilies and irises), five (parnassia, rose hips) or eight (cosmea), 13 (some daisies), 21 (chicory), 34, 55, or 89 (Asteraceae) number of petals; keeping up with the sequence.
While visualizing the Fibonacci sequence numbers as squares with widths, the shape turns out to be a beautiful spiral, known as the Fibonacci Spiral. After learning the spiral shape, you may start noticing the spiral pattern frequently in nature. On a closer look, this spiral pattern can be seen in flower petals as well as in outer space explorations. One of the best representations of fractal forms in nature is the Roman cauliflower, where each nub is a Fibonacci spiral.
THE GOLDEN RATIO IN NATURE
Nature is a highly organized physical realm bound by mathematics laws. One of the most fundamental ways these laws manifest is through the golden ratio.
The golden ratio denoted by the symbol “phi” and approximately equal to 1.618 is a unique mathematical ratio. It tends to crop up with surprising frequency within the natural world and seems to be everywhere in nature.
The human body represents and exhibits perfect proportionality in terms of the golden ratio. The ratio of a person’s height to the height of their navel is roughly equal to the golden ratio. Take your hand and look at the proportions of your index finger. Each section of your index finger, from the tip to the base of the wrist, is larger than the length of the tip to the finger joint by about the golden ratio. Also, your hand creates a golden section in relation to your arm, as the ratio of your forearm to your hand is also 1.618, The Divine Proportion. The human face is considered attractive if its proportions are close to the golden ratio, i.e. a beautiful person’s face is about 1 ½ times longer than it is wide. Ocean waves are another example of the golden ratio manifesting in nature; the golden spiral can be traced in ocean waves curling forward upon themselves before crashing on the shore.
The mathematical relationship of the golden ratio and the Fibonacci sequence is quite intimate, which can be proved by dividing two consecutive Fibonacci numbers. The golden ratio reveals itself even in the microscopic realm. For example, the DNA molecule measures 34 angstroms long by 21 angstroms wide for each entire cycle of its double helix spiral; these numbers are part of the Fibonacci series, with their ratio tending to “phi”.
Mathematical models help us understand nature in an extraordinary amount of ways. The natural world often displays models, patterns and phenomena we see in mathematics. Sometimes these coincidences force us to think about the base reason behind it, which is still unknown.
By Geetanjali Karma
Batch of 2024