Painted with Numbers: Mathematical Patterns in Nature

Photo by Erol Ahmed on Unsplash

There’s a mathematical order inherent in our universe. Let’s start with rivers. If we measure the length of a river and divide it by the direct route from the start to the end, we’ll get its sinuosity or bendiness.

Mathematicians found that the average sinuosity of every single river in the world is pi. The same mathematical constant used to calculate the mass of an electron and the gentle breathing of a baby helps define how bendy all rivers are. Its digits never end and never show a pattern, but they cannot possibly be random because they represent the inherent order of so many things in nature.

We can observe that a drop of water is a liquid at a smaller scale, but depending on how the molecules are arranged, it could also be a solid or a gas. Only if it’s liquid, though, is it considered wet. Not all water is wet. This specific arrangement of molecules is caused by surface tension that gives it the emergent property of wetness. If we were to arrange water droplets together in a certain way, we could get a waterfall. All waterfalls across the world fall at the same speed because they are all subject to the same acceleration, gravity. The Navier-stokes equation describes how all fluids like the water in a waterfall will move and behave. It also explains everything from how blood flows in our bodies to how we can best simulate water in video games.

We can understand the order of the universe by studying the patterns that emerge from it. Even something as seemingly random as the shape of a tree’s branches has an order. The main trunk will grow until it produces a branch with two growth points, and each stem branches into two. This pattern is repeated for every new stem.

We can model this using the Fibonacci sequence. Each successive number is the sum of the previous two. The average ratio of every two consecutive terms in the sequence gives us a famous constant called a golden ratio. We can find examples of the golden ratio everywhere in nature. The seed pods of a pine cone are in a spiral pattern. If we measure the angle offset between a leaf on a plant stem and the one below it, we’ll find the average value uses the golden ratio. It’s even present in the formation of waves in the ocean.

This mathematical order applies to mammals as well. What makes something alive or dead? The difference between a living bird and a dead one isn’t that we’re adding some secret life juice to it? Its state depends on the specific pattern of its molecules. Many birds use celestial objects like the Sun or stars to navigate their flight path, requiring some trigonometric calculations. But it’s not that they’re calculating these things consciously. Animals do what comes naturally to them. Millions of years of a divine gift helped equip them with the capabilities to survive. Birds solve a trigonometry problem in the same way a waterfall solves the Navier-Stokes equation, or a dog solves object location using visual and chemical signals.

Mathematics is just the language that helps us interpret all this activity. So the question is, can math also help us understand how our brains work? Can we quantify the feeling of meeting someone special for the first time or the feelings we get when we spend time with them? Consciousness is a mathematical pattern. When information is being processed governed by a set of patterns like those found in the branches of a tree or the fluid dynamics of a waterfall, the way it feels is consciousness.

It’s a beautiful emergent phenomenon arising only when molecules are arranged in a particular pattern, just like how wetness emerges only when water molecules are arranged in a certain pattern. Math gives us a framework to reason about what the order behind these patterns could be, and we can use the beauty that’s all around us as our torch in this journey. One that we hold up and follow with the belief that eventually, it might just lead us to the truth.

I know that you need some words to talk. Here, reading will be perfect for you.

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