Everything in our life has only mathematical patterns.
Ali KayasporFollowOct 8, 2018 · 8 min read
How can it be that mathematics, being after all a product of human thought which is independent of experience, is so admirably appropriate to the objects of reality?
Albert Einstein…
One evening a few years ago, I was with friends from the college at the backyard of the college, and talking about the relationship between science and mathematics. One of my friends’ friends made a comment, “Science does not explain objects, it just describes them.” That made me utterly surprised because I was pretty sure that mathematics and science were the best languages to explain what is happening in the universe.
That night, I saw that most of the people don’t believe that “Mathematics is the beautiful language of the universe.” In other words, for them, mathematics is not an explanation of the universe and nature. I think that approach is normal for them, because the real mathematics is an abstract concept, not a tangible thing that you can smell, touch or eat. And being an abstract makes mathematics deep and mysterious. However, everybody agrees on that a human being can develop himself anytime. And there is no upper limit to numerical abilities of a human being. First, they discovered the fire to get warm. Then needed a light in their house and they invented electricity and the bulb. When they need to talk to someone who is 10000 miles away, they just invented the Internet. Behind all these inventions, there was mathematics.
Of course, the universe can not speak or think. However, we, the people, can read the universe. Because there are so many scientifically and mathematically inclined people can read the universe and find answers and then describe the universe and nature. We, the normal people, can also use our imagination as an apparatus in order to read the universe, and also nature. If we can read, hence something is written. In order to write, a language is always needed. So, the universe should have a language. The letters are circles, triangles, hexagons, etc… Or this language just contains patterns.
Everything in our life has only mathematical things. For instance, I love watching documentaries about wildlife. The narrators are always telling us many animals have stripes or patterns for the purposes of camouflage. But why do a leopard or a cheetah or a tiger have particular designs? Enigma codebreaker Alan Turing -you can watch the nice movie “The Imitation Game” to see his life- had a mathematical theory about leopard’s spots. He had an idea that the patterns on animals can be explained by mathematics 60 years ago. *1
Stars have patterns. And most of the astrologist believe that our destiny depends on the patterns of the stars. Some of the astrologists thinks that the stars really determine who we are, and the others think that the stars influence our destiny. Yes, a person like me or you can not control his/her life. For that reason, people have been looking in the universe and searching for patterns to reveal their real characters and destiny. And when they find something, it is always about mathematics.
Seasons have patterns. They come and go. And every time they have an influence on nature; the clime change, animals migrate north or south, rain comes, snow melts, earth changes color, etc…Of course, seasons cannot make these miracles things. They can only have mathematical patterns.
All these patterns showing us there is a gap between the human being and the universe. Einstein had been pondered how mathematics does work in science perfectly for years. He had wrestled with this question all the time. He knew that mathematics is the connection or the bridge or the language for that gap. And at this point, being a connection between us and the universe makes mathematics the greatest achievement for the people.
If you also take a look closer at the patterns of our world, you will always reveal the beautiful mathematics. It is 100% true because mathematics is all in our hands. Let me give you some specific examples.
Fibonacci, the golden ratio, spiral, cabbage…
Our universe is filled with spiral designs. Spirals can be found in the shape of DNA double helix, flowers, elephant tusks, sunflowers, hurricanes, draining water, horns of animals, a nautilus shell, a snail shell, a pinecone, a cabbage, a fingerprint, algeas, galaxies. Tons of lifeless and alive things have spiral designs. And they are not random spirals. They have something in common: the ubiquitous constant ratio, the golden ratio! A surprisingly this golden ratio probably is also a property of space-time. *2
All these spirals in the nature tell us there are numbers all around us. Let’s observe numbers of petals of some flowers. When you count the number of petals of flowers in your garden, or the flowers in a botanical garden during your visit, you will get the numbers 3, 5, 8,13, 21, 34, or 55. These numbers are not random numbers. These are very unique numbers and all of them part of Fibonacci sequence, which are series of numbers developed by a 13th century mathematician. You can also get the same numbers if you start with the numbers 1 and 1. And from that point on you keep adding up the last two numbers. 1+1 = 2, 1+2 = 3, 2+3 = 5, 3+5=8 and you keep going like this. You will get the number of the petals of flowers.
Definition: The Fibonacci numbers are the numbers in the following integer sequence, called the Fibonacci sequence, and characterized by the fact that every number after the first two is the sum of the two preceding ones: *3
But, why those Fibonacci numbers are so important. The key is the relationship between progression of growth and the proportion. There is a harmonic proportion is hidden in Fibonacci sequence.
A fact: If you divide one number in the sequence by the previous number, the answers result in or come closer to phi:
For example: 3/5 = 1.6666,
13/8 = 1.6250,
377/233 = 1.61802575,
317811/196418 = 1.618033399
Definition: In mathematics, two quantities are in the golden ratio if their ratio is the same as the ratio of their sum to the larger of the two quantities. *5
These numbers can be demonstrated with the spiral of the florets in a sunflower. The florets in a sunflower head also form two spirals. If you count the clockwise and counterclockwise spirals that reach the outer edge, and you’ll usually find a pair of numbers from the sequence: 34 and 55. If it is a very large sunflower, you will get 89 and 144. *4
These divine spirals don’t only belong to sunflower. They appear a lot in botany. You can find them if you get a pine cone, or a daisy. If you mark the spirals and count them you will always get a number from Fibonacci sequence. And if you count in the other direction, this time you will find an adjacent Fibonacci number.
the Nautilus Shell, the Golden Mean
What makes the nautilus shell so special? Having the Golden Mean makes the Nautilus Shell so special for mathematicians. The Golden Mean is the same with the Golden Ratio. But how do we know that the nautilus shell has the Golden Mean?
First of all, we will start with drawing a small, one unit square. Then we will draw another square which is larger than the previous one. We need to add in a counterclockwise direction. The length of the each square has the value from the Fibonacci sequence; 1, 1, 2, 3, 5, 8, 13, 21, 34, 55 … Then we can draw spirals starting with the smallest one outward through the largest one Then the Golden Mean will appear.
The Fibonacci sequence appears all the time frequently in our nature. Those unconscious flowers, plants, or objects have no idea about mathematics. A divine force is just setting up a little system and, they have been showing us a beautiful mathematical art and fascinating us for thousands of years.
1- https://www.bbcearth.com/blog/?article=the-maths-behind-a-leopards-spots
2- https://www.sajs.co.za/article/view/4033
3- https://en.wikipedia.org/wiki/Fibonacci_number
4- http://www.sciencemag.org/news/2016/05/sunflowers-show-complex-fibonacci-sequences
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