Author: Navya Nair
From: Trivandrum, India
Like it or love it (or hate it), it’s pretty safe to say that mathematics is one of, if not the most integral tool that has brought mankind as far as it’s come. It has endowed us with the power to measure the immeasurable, predict existences, and see the invisible, all with astonishing accuracy.
(Photo by Martin Mariani from Pexels)
But beyond just strokes on paper, there are plenty of real-world examples of math in nature. Take, for example, the Fibonacci sequence (a set of numbers where each one is the sum of the two before it) which makes a unique spiral that ‘coincidentally’ is the same shape as hurricanes and the spirals on animal shells.
Many notable scientists have asserted that the entire universe is inherently mathematical in nature. Now, you might think this is absurd - how could, say, a flower possibly be mathematical, right? But if I asked you to explain what a rose was, yes, you could tell me that it smells fragrant, that it’s red, but at its core, it’s still matter made of elementary particles; particles that have only mathematical qualities (such as charge and mass).
What psyched up many ancient philosophers to declare math as the “language with which God has written the universe” is its seeming omnipresence and “unreasonable effectiveness”, as Nobel laureate Eugene Wigner put it in his 1960 paper. Can you blame them? Once you start looking for mathematical patterns around you, you realize they’re everywhere.
Not only that, but time and time again, whether it be predictions about the existence of radio waves or of the properties of gravity, mathematical deductions have been spot on. Hypotheses drawn from mathematical calculations have been proven experimentally decades later. Equations and inferences formed centuries ago are as faithful today as when they were made. This is a testament to the idea that the mathematical model we’ve created over generations is, at the very least, a working one.
But here’s the thing - just because we find patterns in things and our model seems to work, can we confidently claim that our universe and everything we see around us is fundamentally mathematical? In short, can we declare math as a matter of discovery rather than invention? This is a common approach, especially amongst the scientific community, but it has its flaws.
The problem with axioms
For starters, mathematics relies on certain axioms that we have no choice but to accept at face value. Without them, we’d never find any answers to our questions. As physicist Richard Feynman rightly explained in this interview clip, “You have to be in some framework where you’re allowing things to be true. Otherwise, you’ll be perpetually asking why.” However, the consequence of this is that nothing can ever wholly be explained due to the intervention of some fundamental assumptions that form the basis of our conclusions.
Let me explain. An example of one of the mathematical axioms is this - “things which are equal to the same thing are equal to one another”. This might seem fairly straightforward to most of us. In fact, it’s one of the first concepts we are implicitly taught while learning math. But if we stop to think about it, these so-called “truths” are only assumptions we made thousands of years ago to try and keep our thoughts in order while problem-solving. There’s no real way of proving their accuracy. As Feynman said, a framework of underlying rules is necessary, but the result is that no matter how elegant of an equation we create, at the end of the day, it is based on a series of assumptions rather than proven absolutes.
Math and reality
On its own, mathematics isn’t enough to reveal the secrets of the universe. Here’s an example - let’s say you calculate the trajectory of an object thrown in the air. If you worked out the math, i.e. you used Newton’s equations of motion, you’d end up with two answers. But are there really two answers? No, in actuality there is only one because there is only one object and one trajectory, but mathematics doesn’t tell us that. The point to be made here is that although mathematics will take us far, in vacuum, it cannot possibly give us all the answers.
Another point to be made is that the fundamental nature of math is very human. It is a human ability to be able to categorize objects as similar or same, and by extension, count ‘one’, ‘two’, ‘three’. The British mathematician Michael Atiyah once pointed out that if we were jellyfish living in the depths of the pacific ocean, where there’s nothing to count, our mathematics would be based on continuous quantities rather than the natural numbers we swear by. I bring up this point to highlight that math likely looks the way it does because of the way humans perceive information, meaning it couldn’t exist independent of the human mind.
The map is not the territory
“The map is not the territory, the word is not the thing it describes” - Alfred Korzybski
So you could say math is like a man-made map that we’ve drawn up (based on our perspective) to try and decipher the complexity of the universe. There isn’t anything inherently wrong with reducing complexity, but there are certain consequences of doing so, all of which Korzybski discusses in his 1931 paper on mathematical semantics. He discusses the limitations to every “map”: the map could have mistakes without us realizing it, errors in interpretation of the map, and most importantly, the map in and of itself is a reduction of its real counterpart and therefore does not communicate all the information on what it’s modeling.
Long story short, we have to allow the possibility of mathematics not being the same as the natural phenomena it’s trying to explain. Rather, it’s how we choose to interpret said phenomena.
My conclusion
Despite its shortcomings, mathematics is the powerful lens through which we observe our universe. It’s currently the strongest tool we have to try and decipher the universe we’re in. What’s important is that we don’t get whisked away in the elegance of an equation, and instead frequently touch base with reality, reminding ourselves that the model is not the phenomena.
About the Author: Navya Nair
Navya is a rising junior in high school from Trivandrum, India. She enjoys learning new things and problem-solving. She is passionate about all the sciences, but am particularly interested in physics.
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