Language of the Universe: Mathematics

Language of the Universe: Mathematics

Mathematics is the language of the universe“. You might have heard this a lot of times from a lot of people. Did you ever think what does it mean? and How is it justified? In this article let us do an analysis of this special language of the universe called Maths.

We live in an age of huge technological and scientific advancements. Today we can do a lot of things which we did not even think about a few years ago. We can land rovers on Mars, we can accelerate tiniest of all particles to unbelievable speeds and smash them.

But there is one single subject which is the reason behind all these things, it is none other than Mathematics. It is shocking that mathematics is so efficient in explaining our physical world and that is why it is called the language of the Universe. Throughout this blog, you will wonder how mathematics is inherently present everywhere in nature. So, let us first start with the subject of mathematics itself. Then we will see some shocking presence of mathematics in nature. We will try to justify that math is the language of the universe

What is Mathematics?

Mathematics is the science that deals with the quantity, shape logic and arrangement. Math is all around us and in everything we do. At the basic level, math is number and counting. Then comes Algebra and some operations which are used to ease the counting and there is number theory that deals with relations between numbers.

Then there is a field called Geometry that is used to describe shapes and the world around us. There is Calculus which is used to track continuous changes around us and was first applied to build the orbits of planets by Newton. Another major part of math is Probability whose application can be seen in predicting the position of an electron. Like that math has been used in everything right from an electron to planets and universe. So, the doubt is whether maths is just used to describe the world or is the world itself is math?

'Many physicists say that Math is used to describe the reality but I go beyond and say that it is the reality' - Max Tegmark (Physicist, MIT) Click To Tweet

Since the beginning of recorded history, mathematical discovery has been at the forefront of every civilized society. The needs of math arose based on the wants of society. The more complex a society, the more complex the mathematical needs. Primitive tribes needed little more than the ability to count but also relied on math to calculate the position of the sun and the physics of hunting.

Origin of Mathematics

Mathematics is numbers and counting at its core and is believed to be inherently present in our brains. Even before we formally named numbers as “one”, “two”, etc, we had the concept of quantity.

Modern research on our ancestral animals suggests that hunter-gatherers would also have this concept of numbers and quantity.

Mathematics: Language of the Universe

Tallying systems are considered the first kind of abstract number system. The first known system with place value was the Mesopotamian base 60 system (ca. 3400 BC) and the earliest known base 10 system dates to 3100 BC in Egypt.

Arabic numerals, Eastern Arabic numerals, Roman numerals, Bengali–Assamese numerals, Malayalam numerals, Thai numerals, Chinese numerals
Arabic numerals, Eastern Arabic numerals, Roman numerals, Bengali–Assamese numerals, Malayalam numerals, Thai numerals, Chinese numerals (Credits: Wikipedia)

The current numbers i.e 0-9 are called Hindu-Arabic numerals. These numbers were first developed in India in around 500 AD and were later modified into Arabic numerals.

Abacus, one of the first tools for counting was invented around 1200 BC. in China. It was used in many ancient civilizations, including Persia and Egypt.

It is believed that Mathematics as an organized science came into existence during the classical Greek period of 600 BC to 300 BC. It was in this period when Algebra came into existence and the first treatise of Algebra was written by Diophantus. The Pythagorean theorem also came into existence in 525 BC which is in this period.

From that point, Mathematics developed with other branches of science into an ocean. Many new branches of mathematics came into existence to analyze, explain, describe, and even predict the physical phenomenon happening around us.

Anyhow the subject has a long history and if you want to go through it, here is a pretty good resource.

Let us move to the main topic

Inherent presence of Math in the Universe

Mathematics gave us a lot of patterns, series, and constants. So, let me first take you through a few things in nature which are so much connected with these mathematical things that it will shock you. These things will definitely make you say “Math is the language of the universe”

The Fibonacci Series

There are a lot of flowers on the planet and you see them every now and then but did you observe any pattern in the number of petals in these flowers? Yes, there is a pattern, first, have a look at the image below.

Number of Petals and Fibonacci Series
Number of petals in different flowers

Did you have a look at that image? Did you observe any pattern there? If you are a mathematician then you would have noticed it. Yes, it is the famous Fibonacci Series.

What is the Fibonacci Series?
Fibonacci Series is a series that takes 1 and 1 as its first two elements and then the next term is obtained by adding the last two terms. So the series is 1, 1, 2, 3, 5, 8, 13, 21, 34, 55… This series was firsst given by famous mathematician Leonardo Fibonacci

But why? why is the number of petals in this series? what is the reason? Though there are theories which explain this. Sadly, we still don’t have a perfect answer. This can be something beyond human understanding, for now just accept it that it is somehow embedded in nature.

Now, you might think that this can be a coincidence, and for those who do, let me show a few more places where Fibonacci Series is present.

  1. The spirals in the scales of a pine cone are in the Fibonacci series. Adding up to the mystery, the number of spirals counted in one direction will be the adjacent Fibonacci number of the number of spirals counted in the other direction.
  2. The same thing happens with the spirals formed by seeds on a sunflower head.
  3. The number of spirals on the head of Romanesco broccoli is a Fibonacci number.
  4. It is also observed that many plants have a pattern in their leaf alignment and this pattern is again a Fibonacci series. Starting from any leaf, after one, two, three, or five turns of the spiral there is always a leaf aligned with the first, and, depending on the species, this will be the second, the third, the fifth, the eighth or the thirteenth leaf.
Arrangement of leaves on a stem. Credits: The Fibonacci sequence in phyllotaxis – Laura Resta (Degree Thesis in biomathematics)
Arrangement of leaves on a stem. Credits: The Fibonacci sequence in phyllotaxis – Laura Resta (Degree Thesis in biomathematics)

Now, let us see a ratio that is everywhere in the world.

The Golden Ratio (ɸ)

First, let us understand what the golden ratio is, and then we will move to its presence in nature.

What is the golden ratio?
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.
In simple terms, consider a line and dive it into two parts. Let the length of the longer part be “a” and the length of the shorter part be “b” and if a/b is equal to (a+b)/a then both would be equal to the golden ratio which is 1.618… and is denoted by phi(ɸ)

How do we obtain the golden ratio
How do we obtain the golden ratio

As we divide every adjacent pair of Fibonacci series, the quotient approaches the golden ratio.

Now, this number 1.618… is literally found at a lot of places right from molecular DNA to huge black holes. Let us list a few of them.

  1. The DNA molecule measures 34 angstroms long by 21 angstroms wide for each full cycle of its double helix spiral. These numbers, 34 and 21, are numbers in the Fibonacci series, and their ratio 1.6190476 closely approximates Phi, 1.6180339.
  2. When women are at their most fertile, between the ages of 16 and 20, the ratio of length to width of a uterus is 1.6 – a very good approximation to the golden ratio.
  3. The golden ratio is precisely the point where a black hole’s modified heat changes from positive to negative, and it is part of the equation for the lower bound on black hole entropy. The golden ratio even relates to the loop quantum gravity parameter to black hole entropy. The related equations can be seen below.
1. Black Hole Heat changes, 2.Loop Quantum gravity 3. Black hole entropy equations
1. Blackhole Heat changes, 2.Loop Quantum gravity 3. Blackhole entropy (Credits Quantum Gravity Research)

And there are a lot of things which have this number 1.6 in it, isn’t it shocking that there is this number everywhere? Are you convinced that the universe speaks in mathematics? No, let us see more

Let us see another interesting geometrical thing which is seen everywhere in nature.

The Golden Spiral

This section is more or less related to the golden ratio only as the golden spiral itself comes from the golden ratio. First, let us know about the golden spiral.

What is the Golden Spiral?
A golden spiral is a special case of logarithmic spirals whose growth factor is φ, the golden ratio. That is, a golden spiral gets wider by a factor of φ for every quarter turn it makes.

Approximate and true golden spirals: the green spiral is made from quarter-circles tangent to the interior of each square, while the red spiral is a golden spiral, a special type of logarithmic spiral. Overlapping portions appear yellow (Credits: Wikipedia)

Now, if you observe nature around you, you would have already observed this kind of spiral at a lot of places, let us list down a few (We see a very good approximation of golden spiral but not the exact spiral obviously)

  1. The arms of spiral galaxies form the golden spiral.
  2. Phyllotaxis is connected with the golden ratio because it involves successive leaves or petals being separated by the golden angle forming the golden spiral.
  3. Cyclones, sunflower head, a lot of mollusk shells, several plants and a lot of things form this so-called logarithmic spirals, a few of them are close to golden spiral.

Now, this again is shocking, right? Tell us in the comments about your feelings on this math embedded in nature.

Let us move to another well known constant

The Pi (π)

Pi is a pretty familiar constant used in a lot of calculations across mathematics and appears in a lot of physics equations. First, let us know a bit about pi.

What is pi?
Pi is defined as the ratio of a circle’s circumference to its diameter, and it also has various equivalent definitions. Pi is an irrational number and its value is 3.14159….. As of now, 31.4 trillion digits of pi have been calculated and was done by a google team.

We already know that pi is very much there in circles, in related shapes, and in a lot of physical equations.

Firstly, let me show how this pi pops up strangely everywhere in mathematics itself and then we will move to nature.

(Ramanujan–Sato series)

Isn’t is amazing to see how these different sequences are equal to pi? There are a lot more such sequence, you can have a look here

Now, let us see how pi appears in the physical universe.

  1. It is observed that the ratio of the length of a river from source to mouth and the distance between source and mouth is a little greater than 3. Though it is different for different rivers, the average comes to be 3.14 which is a pretty good approximation of pi. A lot of rivers that flow on slopes have this ratio pretty close to pi.
  2. Take any periodic process right from heartbeat to breathing to waves, pi is encountered everywhere, it is encoded in it.
  3. Pi also shows up in probability, for example, take a white sheet and a needle, draw line with a gap between two equal to the length of the needle. Drop the needle on to the paper, the probability of needle falling at a position such that it crosses a line is 2/(π), What???

If we see look into physics, we find pi in a lot of equations, right from Heisenberg’s uncertainty equation to Einstein’s Field Equation.

This is really astonishing, pi is literally everywhere, but think, why only pi? Why not anything else?

Let us move to the final thing on the list to justify “Mathematics is the language of the universe”

Fractals

A few of you might be familiar with this term especially mathematicians and for those who don’t know about it, let’s see

What is a Fractal?
Fractals are infinitely complex patterns that are self-similar across different scales. They are created by repeating a simple process over and over in an ongoing feedback loop. There is a whole branch of mathematics behind this terms known as fractal geometry.

A Fractal (Source)

Now, you can find fractals everywhere in nature, let us see this as well.

  1. The best example of fractal appearing in nature is a snowflake. Watch the video below to understand fractals and snowflakes
  2. Romanesco Broccoli, which was mentioned above as well is also a very good example of fractal geometry.
  3. Fractals are found in trees in the pattern of branching, they are found in blood vessels, they are found in how rivers branch, etc.

So, fractals are in a lot of places, but how is it possible? Why is nature forming this pattern? There is no certain answer.

Conclusion

We have seen a few mathematical things which are inherently present in the universe right from the tiniest to the gigantic things. This topic is so interesting and shocking, it surprised our team a lot of time while doing the research for the topic. I hope you are convinced in saying that mathematics is the language of the universe

This subject of the connection between Math and the world is becoming more and more interesting as we find new things. Let us wait and search for the answer to why are these numbers and patterns there around us. What is being conveyed through this special language of the universe: Mathematics.

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