Unravelling the Vast Universe
“The universe cannot be read until we have learnt the language and become familiar with the characters in which it is written. It is written in mathematical language, and the letters are triangles, circles, and other geometrical figures, without which means it is humanly impossible to comprehend a single word.”
-Galileo Galilei
Mathematics is the science of creative logic, patterns and their relationships. The essence of mathematics is so much that those beautiful conclusions drawn after solving problems involving a significant amount of intuitive thinking can explain each element of our cosmos. From the smallest particle to the gigantic galaxies, there is hardly any object whose behaviour cannot be explained by simple or complex mathematical equations.
Be it the motion of a particle, the behaviour of electromagnetic waves, the trajectories of planets, or the shapes of galaxies; all can be decoded by mathematics. But mathematics isn’t just restricted to explaining various concepts and theories; it has also been instrumental in several discoveries! Take the example of the planet Neptune. Astronomers had noticed that the observed position of Uranus differed from its predicted position by a significant amount. John Couch Adams and Urbain Jean Joseph independently solved this mystery by using mathematics to predict that the gravity from another planet beyond Uranus affected Uranus’s orbit. They figured out not only where the planet was but also how much mass it had. This mysterious planet was later observed with the help of a telescope and was named Neptune. The prediction of the existence of Higgs Boson and radio waves further illustrates that mathematics is highly versatile in nature.
But, how did the role of mathematics come into the field of astronomical sciences? Astrophysicists define a fictitious sphere concentric to earth, having an arbitrarily large radius, known as the celestial sphere. By applying the concepts of spherical trigonometry on the celestial sphere, ancient astronomers, with the help of their observations, were able to map the positions of celestial objects, predict eclipses, and make a reasonable estimate of the periods of revolution and rotation of the earth and moon. These small discoveries were the stepping stones to unravel the mysteries of the universe, which were very poorly understood until then.
Mathematics, since then, has continued to solve one of the most complicated riddles of the seemingly chaotic universe. People had started realising that mathematics was not meant merely to ease them in daily-life calculations but to further their understandings of their place within the universe. As soon as humankind decided to turn their mathematical wonder towards the sky, spurring advancements in astronomy and technology were not far. The discovery of calculus in the 17th century brought a spark in the field of astronomical mathematics. Since then, mathematics has continued to grow and help us to know our universe much better than before.
But, does it not seem strange how close this relationship of the universe with mathematics is? Is it just fair enough to treat mathematics as the language of the universe? Indeed, this has also puzzled mathematicians and physicists around the globe. The effectiveness of mathematics in simplifying and explaining the fundamental nature of the universe is so much that scientists have started considering that the universe is not just defined by mathematics; rather, the universe in itself is mathematics.
Hey, wait! Let’s stop for a moment and think about this again. If the universe indeed is a mathematical structure, then we would have to convince ourselves with the idea that mathematics is solely sufficient to explain it. But then, one may argue that physical features like the roughness of a cricket ball have no relation with mathematics. So, is our hypothesis wrong?
If we ponder for a while, we may realise that it is not. The roughness of a cricket ball or any object depends on the arrangement of its molecules. Now the arrangement of any number of entities is mathematics. But what about the molecules? If a thing is a mathematical object, then its smallest entity must be a mathematical object too. Well, molecules are made up of atoms which in turn are made of electrons, protons, and neutrons. Let’s take the example of the electron. Ever wondered what an electron is? It is just a mathematical structure with a specified mass, a specified charge, and a spin quantum number (+1/2 or -1/2).
Can we think of something that does not involve the subatomic particles and still argue that we can explain it solely by mathematics? Let’s take the example of space. We can consider space to be made of 3 dimensions. But how did this 3 come into existence? Why isn’t the dimensionality of space 4 or 2 or maybe even 0? Probably because it’s the law of the universe and the law is purely mathematical. We might then conclude that it is not possible to find any example which cannot be explained by mathematics.
Perhaps the most famous theory which describes the idea of considering the universe to be a giant mathematical model is the Mathematical Universe Hypothesis (MUH). The MUH, proposed by Swedish-American physicist Max Tegmark combines all the previous theories on the same subject and presents its idea much more rationally. According to the MUH, “there exists an external physical reality completely independent of us humans,” and this “external physical reality is purely a mathematical structure.”
Tegmark first assumes the existence of an external physical reality, which he vividly describes under his External Reality Hypothesis (ERH). Going by this assumption, he puts forward a simple argument. For the description of such a reality to be complete, it needs to be appropriately defined according to the non-human forms (like aliens), which don’t understand the concepts made by humans. What form of language will they understand then? Of course, it has to be mathematics. Hence this external reality must be a mathematical structure. Therefore, if one believes in this external reality independent of humans, one must also accept that our physical reality is a mathematical structure. Tegmark’s work has been discussed all over the world. It has been appreciated by some and criticised by others.
In a nutshell, we may conclude that the relationship of the universe with mathematics is way too unique and complicated to comprehend. Mathematics is not limited to some trigonometric equations or calculus problems; its true meaning extends beyond that. It is a means by which we can travel through outer space merely by sitting on our desk; it is a means of interacting with the stars that twinkle at night, heavenly bodies that are in constant motion, the black holes which can never be seen or the dark matter which can never be felt. As students of mathematics, we all have had the privilege to understand the awesomely gigantic cosmos lucidly and systematically, which otherwise would have been far too intricate, well beyond the human understanding level.
By Aman Bucha
Batch of 2024