Beautiful Mathematics in the Natural World

The Mathematical Order Inherent in Our Universe

There is a mathematical order inherent in our universe that can be observed and studied. Take, for example, a river. If we measure the length of it and divide by the direct route from the start to the end, we will get its synyosity or bendiness. We found that the average sanyasa T of every single River in the world is pi, the same mathematical constant used to calculate the mass of an electron. This suggests that there is a hidden order at play, one that governs the behavior of rivers and other natural phenomena.

The Gentle Breathing of a Baby

The gentle breathing of a baby also helps define how bendy all rivers are. The digits never end and never show a pattern, but they can't possibly be random because they represent the inherent order of so many things in nature. This is a fascinating observation that highlights the complexity and beauty of our universe.

Surface Tension and Wetness

At a smaller scale, we can observe that this drop of water is a liquid, but depending on how the molecules are arranged, it could also be a solid or a gas. Only if it's liquid, though, does it possess the emergent property of wetness. This specific arrangement of molecules caused by surface tension gives it the ability to behave in a certain way. If we were to arrange these 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

The navier-stokes equation describes how all fluids, like the water in this waterfall, will move and behave. It also explains everything from how blood flows in our body to how we can best simulate water in video games. This equation is a fundamental concept in understanding the behavior of fluids and has far-reaching implications for many fields of study.

The Shape of Tree Branches

Even something as seemingly random as the shape of tree branches has order. The main trunk of a tree will grow until it produces a branch, which then branches into two more stems. This pattern is repeated for every new stem, creating a complex and intricate network of branches. We can model this using the Fibonacci sequence, where each successive number is the sum of the previous two.

The Golden Ratio

The Fibonacci sequence gives us a famous constant called the golden ratio. This ratio appears everywhere in nature, from the seed pods of a pine cone to the formation of waves in the ocean. It's a remarkable example of how mathematics can describe and understand the natural world.

Mathematics and Living Things

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, which requires some trigonometric calculations but is not conscious.

Mathematics as a Language

Mathematics is just the language that helps us interpret all this activity. It's the framework we use to reason about what the order behind these patterns could be. We can use beauty, the beauty that's all around us, as our torch in this journey, following it with the belief that eventually it might just lead us to truth.

Hiking and Reflection

As I write this article, I'm here in Portland Oregon, hiking and reflecting on the wonders of our universe. I hope you guys liked the video from the last coding challenge, which was won by Vishal Bhature. He's the badass of the week! And to all those who participated, a big thank you for taking part in this community.

The Video and Holiday Greetings

This video is meant to relax and take a breather. It's not about solving a complex problem or achieving a specific goal; it's just a moment to appreciate the beauty around us. As we move into the holiday season, I want to wish you all happy holidays, with love and appreciation for everything that makes our lives richer.

The Next Hike

For now, I've got to go hike up to a waterfall. It's time to get back out there and explore more of nature's wonders. Thanks for watching!

"WEBVTTKind: captionsLanguage: enthere's a mathematical order inherent in our universe take a look at this River if we measure the length of it and divide by the direct route from the start to the end we'll get its syn yosity or bendiness we found that the average sanyasa T 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 can't possibly be random because they represent the inherent order of so many things in nature at a smaller scale we can observe that this drop of water is a liquid 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 it's this specific arrangement of molecules caused by surface tension that gives it the emergent property of wetness if we were to arrange these 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 this waterfall will move and behave and it also explains everything from how blood flows in our body 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 order the main trunk of a tree will grow until it produces a branch which has 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 and 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 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 and this requires some trigonometric calculations but it's not that they're calculating these things consciously animals simply do what comes natural to them millions of years of natural selection helped equip them with the capabilities to survive in their evolutionary niche birds are solving 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 own brains work can we quantify the feeling of meeting someone special for the first time what's been your favorite trip oh yeah or the feelings you get when you 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 certain pattern just like how wetness arises 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 beauty 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 truth hello world it's Suraj I'm here in Portland Oregon just hiking I hope you guys liked the video the winner of the coding challenge from the last video is Vishal bhature badass of the week and the runner up is set to year no coding challenge this video relax take a breather and happy holidays to you and everybody you love for now I've got to go hike up to a waterfall so thanks for watchingthere's a mathematical order inherent in our universe take a look at this River if we measure the length of it and divide by the direct route from the start to the end we'll get its syn yosity or bendiness we found that the average sanyasa T 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 can't possibly be random because they represent the inherent order of so many things in nature at a smaller scale we can observe that this drop of water is a liquid 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 it's this specific arrangement of molecules caused by surface tension that gives it the emergent property of wetness if we were to arrange these 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 this waterfall will move and behave and it also explains everything from how blood flows in our body 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 order the main trunk of a tree will grow until it produces a branch which has 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 and 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 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 and this requires some trigonometric calculations but it's not that they're calculating these things consciously animals simply do what comes natural to them millions of years of natural selection helped equip them with the capabilities to survive in their evolutionary niche birds are solving 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 own brains work can we quantify the feeling of meeting someone special for the first time what's been your favorite trip oh yeah or the feelings you get when you 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 certain pattern just like how wetness arises 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 beauty 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 truth hello world it's Suraj I'm here in Portland Oregon just hiking I hope you guys liked the video the winner of the coding challenge from the last video is Vishal bhature badass of the week and the runner up is set to year no coding challenge this video relax take a breather and happy holidays to you and everybody you love for now I've got to go hike up to a waterfall so thanks for watching\n"