Is Nature a Mathematician?

A much debated question. Did humans invent mathematics to make sense of the world, or are there underlying codes and patterns in the universe, waiting to be discovered?

I lean towards the latter.

According to neuroscientists, it is human nature to detect patterns in our environment. Experts in pattern creation are called artists. They are also called mathematicians.

"Mathematics is the science of patterns, and nature exploits just about every pattern that there is." - Ian Stewart

Mathematical thinking is an undiscovered sense of patterns and logical connections in nature. This sense allows you to perceive the realities of the universe with a new mathematical perspective. For example, instead of immediately running away from a spider, have you ever tried taking a closer look at their webs? Spiders unknowingly use mathematics in the way they create webs. Apart from the math involved that make webs capable of great elasticity and strength in the structure of the webs, spiders also use different angles to make their webs into iconic shapes.

Something that is very clear is that nature loves mathematics. This might not be super obvious to everyone (yet), but let me help you develop your mathematical thinking sense by sharing with you some of my favourite examples of mathematics in nature.

1. Hexagons - The bees' preferred shape!

A hexagon is a 6-sided polygon and can be seen in basaltic rocks, snowflakes, corals, crystals and insect eyes. In all the irregularities and messiness of the world, why does nature seem to prefer hexagons? An easy way to see this for yourself is using soap bubbles. Bubbles clustered together will always revert to a hexagonal shape.

The most common example of hexagons in nature is honeycombs. I do not believe that the bees sit down together in a meeting and discuss the best shape to use for their hives, so why the hexagon?

The reason is mathematical optimisation. First of all, hexagons fit together perfectly without wasting any space. This is true for other polygons as well, such as triangles and quadrilaterals. However, a hexagon minimises the perimeter for the given area with its 120 degree angles. Even though bees make their honeycombs with circular units, the pull of surface tension in each direction results in the beeswax hardening into hexagonal shapes.

Why does this matter? In the case of a honeycomb, minimising the perimeter means using less beeswax and getting more honey. This is the ultimate business enterprise! Minimising the cost (beeswax) and maximising the profit (honey). How clever is that!

There might be a big difference between honeycombs, insect eyes and volcanic rock, but the overall reason for the hexagonal shape is the same: mathematical optimisation.

2. Fractals - Branches aren't just for trees.

Since I was a child, repeated patterns and shapes in nature fascinated me. It was only much later that I learnt that this type of pattern is called a fractal. Fractals are patterns that are repeated in smaller and smaller versions of themselves. Every branch of a tree, from the trunk to the smallest branch is a scaled version of the previous one. The closer you look at fractals, the more scaled repetitions you will see. A good example of this is the fronds of a fern or Romanesco Broccoli.

Fractals get their name from fractions and fractures — the broken and fragmented shapes in nature. You can see examples of this all around you. Trees, plants, lightning strikes (my personal favourite), mountains and even coastlines are natural fractals. River deltas are fractals that can only really be appreciated from the air. Even though it is uneven, every part of a river delta is a micro version of the greater whole.

It might surprise you to know that the human body also consists of many fractals. Have a look at your eye up close in the mirror. Or the veins on your hands. We are fractal! Even our brains and lungs look like branches of a tree. Fractal geometry allows our lungs, brains and circulatory system to maximise their surface area and therefore optimise us as human beings.

Fractals in nature can often only replicate finitely, but theoretical fractals can be infinite. Artificial Intelligence is capable of creating simulations that model infinite fractals. The Mandelbrot Set can be programmed into basic lines of code that creates an infinite amount of transforming, self-similar patterns. Benoit Mandelbrot coined the term “fractal” and is also the person responsible for discovering the mathematics in the Mandelbrot Set.

3. Transformations - The most obvious mathematics.

Similar to biological transformations where a caterpillar changes into a butterfly, mathematical transformations convert one geometric shape into another. Transformations is probably the most obvious mathematics in the world. Just a look in the mirror will confirm that humans, along with animals, birds, fish and insects are all symmetrical. In a reflection transformation, all the points of an object are reflected or flipped on a line called the axis of symmetry or line of reflection.

Tessellations is a very common transformation that is not only evident in nature, but also much loved by artists such as M.C. Escher, one of the world's most famous graphic artists. Growing up in Africa, I saw natural tessellation often. Many animals use tessellations as part of their camouflage. A zebra’s stripes, a leopard's spots, even the scales on a snake’s skin are all examples of natural tessellations.

The aesthetic side of mathematics can be seen in most flowers. A flower is a universal symbol of beauty. Rotational symmetry plays a big role in this perceived beauty. In flowers, the petals are being rotated 360 degrees around a fixed point without changing its size or shape. You can spin a flower around and around, and it looks pretty much the same.

Sunflowers display another well-known pattern called the Fibonacci sequence. We will look at this in more detail in a future post.

And so much more...

Mathematics reveals hidden patterns that help us understand the world around us. By looking at all the occurrences in which nature exists in near mathematical perfection, it is evident that nature loves mathematics.

“Study the science of art. Study the art of science. Develop your senses – especially learn how to see. Realise that everything connects to everything else.” - Leonardo da Vinci

I listed only a few examples in this post, but many other types of mathematics can be found around us. The spirals on seashells or chameleon tails. The concentric circles in tree trunks. The Fibonacci spiral. But we will leave these for another time.

In the meantime… Next time you are going for a walk or to the beach or just looking outside your window…take notice. Practise your mathematical thinking sense.

Do you think nature is a mathematician?