Bakhtiar Ali Khan received his Bachelor's degree in electrical engineering from GIKI Pakistan, followed by a Master’s degree from Jacobs University Germany. He is currently pursuing a doctoral degree in the field of electromagnetics at Concordia. His research interest resides in antenna design for next-generation satellite and space applications. So far, he has published around 10 journal and conference articles.
Math and reality
Is math a figment of our imagination or is it fundamentally ingrained in the universe? Math is sometimes referred to as the language of the universe. To illustrate the idea consider the following images:
The structure of a galaxy and the spiral of a shellfish can be accurately represented by a mathematical function called log. Why is that so? Is the universe speaking in these terms or is it our perception of reality that was laid on mathematical foundation?
Effectiveness of Math
Nobel laureate Eugene P. Wigner puts brilliantly that the unreasonable effectiveness of mathematics in explaining the natural sciences is sufficient evidence for him. Let me put this in perspective. When Johannes Kepler made observation about the plants in the night sky roughly about 400 years ago, those observation were not at all accurate. Yet, Isaac Newton laid down the mathematical foundation of theory of gravitation based on those scanty observations, which was later proved to be not only accurate but was used to put satellites in orbit and man on the moon. To this day, we use this same mathematical model to study the planets, stars and other solar systems.
Another example would be the discovery of the Higgs boson, the elementary particle which was predicated mathematically in 1960’s and observed in 2013.
Sometimes it might seem that a mathematical theory is too abstract and might not even have an immediate application in sight when the theory is put forth. However, the same was true when Einstein laid down the theory of general relativity. But 100 years later, we use the same theory to understand space, time and gravity. The question one might ask is: why is math so effective?
This question is sometimes answered with an argument. Imagine that the universe did not follow the mathematical models we have. This would consequently lead to a change in the universal constants like the speed of light and the gravitational constant. Consequently, the law of conservation of energy would not hold. If that was the case, life or the universe as we know it would not exist at all.
Math and intuition
The observation of the universe can only lead us so far. However, math can lead us beyond. In my engineering career, I have been faced with some problems which challenged my intuition and sometimes, some things would come out to be downright counter intuitive. But my mathematical model would predict it. As uncomfortable as that made me, I would have to disregard my intuition in favour of the math. Given the objectivity of the mathematical model, it would predict all possible and probable solutions. When I was asked why that happens, I find myself saying "I do not know... it just comes out from the math".
I think math and reality (as we know and understand it) are two sides of the same coin. They can be distinguished but cannot be separated. To uncover the mysteries of the universe, we have to speak its language.