By Alina Ostrovsky
Life is a “domain” of a certain span of time that starts ticking from the year in which we were born, beginning from a certain numerical value on the x-axis. At the same time, within that “domain”, it harbours a “range” of experiences of increasing growth on the plain of the y-axis, which can be conceptualised on a spectrum much more abstract than the way the x-axis can be thought of. On our path towards growth, we discover our passion, forming our life’s ambitions, which, in turn, create a sense of purpose in us. Throughout the “domain” of our life’s span, we are after, what seems to be, a never-ending pursuit of what makes sense. When we lose our grasp of sense, we are thrown into a dark realm of confusion empowered by its inconsistencies.
A gateway to reason and logic
Yet the study of mathematics builds our understanding of what “makes sense” by sharpening our sense of reason, which is a tool that can guide us towards the right path of “decision making”. Although maths stands on the basis of hypothetical thinking alone, its applications to real life in the ‘realm of reason’ will never disappoint. Therefore, it can be posited, “Mathematics is the purest of the arts [based upon the contingency of] asking simple and elegant questions about our imaginary (hypothetical) creations [in which the asking party gets to] craft satisfying and beautiful explanations”. We, just like expert mathematicians, are in the constant pursuit of building a network of explanations regarding the experiences we face that will serve to give us the wisdom with regard to finding solutions to our life-related problems. Maths is just one portal through which those ‘explanations’ can be reached.
An art form
Still, in which sense does it mean for maths to be the “purest of the arts”? Is it “artful” in the study of it or “art” in the tangible sense of the word? Believe it or not, aside from maths being a science, its mechanisms can satisfy the conditions of making art. Maths, thought-of as science in terms of its ‘cosmological’ capacities, excavates what’s already known about the universe and still is unknown, only waiting to be discovered. Art, however, standing on its own, is defined as being “a skill in performance acquired by experience, study, or observation”, standing on the basis of a certain “system of rules or methods of performing particular actions”, as Doctor Patterson said.
Doris Schattschneider put what’s stated to be art in the application of its maths most comprehensively. She explains that “art is an illusion [in which mathematical] transformations are important”. Those transformations come in three forms: isometries, similarities, and affine transformations. Isometry can be simply understood as “transformations” of certain entities of equal dimensions—it is a line or an object being drawn or sculpted in uniform lengths, respectively. “Similarities” is another form of maintaining perfect symmetry, which is what brings out the essence of art. Symmetry is what helps a certain artwork to be what we perceive to be beautiful. Lastly, affine transformations preserve shapes to be exactly parallel to each other in a way that they are twisted from the perspective of different angles. This specific type of transformation allows artists to create “images with purposeful distortions” if not intentioned to be ‘exactly’ paralleled, whose “projections can represent three (or higher)-dimensional forms on two-dimensional picture surfaces, even curved ones”.
A philosophical dimension
The principles of maths can be also thought-of philosophically. Maths is a study of smooth congruency—its logic comfortably resonates inside your head. It is extremely patient with you, guiding you towards the truth of its solution. It highlights its human-calculated discrepancies. You have the freedom and its permission to make mistakes, and, most importantly, learn from your mistakes. By learning from your mistakes, it redirects you back into the caresses of its rightness. In the process, it redeems you from your wrongness. Maths is candid with you in the way that you ‘stand to be corrected’ by it. This way, you can play no tricks with it, which means, as Maria Popova harshly put it, “Lying cannot serve as an instrument of thought!” It crumbles on the basis of denial altogether. As we come into agreement with that statement, she continues: “Now, is not this statement usually considered to be a moral principle? And yet, without it, we cannot have any satisfactory mathematical system, nor any satisfactory system of thought—indeed we cannot even play a game properly with contradictory rules…”
Pervasive nature of maths
With this understanding, wouldn’t it mean that based on mathematical principles of ‘morality’, which trains our thinking, it can further construct a good-functioning government, working in benefit of all individuals? Or wouldn’t it mean that knowledge of maths would help shape the operations of our politics in such a way that would exclude its corruptions, embezzlement, and bribery that are all meant to be in favor of self-interest? What about a nation’s economics? If we were religiously following the balanced-out equations that it presents, such a thing as inequality should be non-existent. Maths is the great equalizer! The only problem here is our flawed human nature that is outside the ‘realm of Mathematics’—it just naturally demolishes the pillars on which maths stands. For these reasons, the Greek philosopher Dutton has rightly remarked that “gossip, flattery, slander, deceit—all speak for a slovenly mind that has not been trained by Mathematics, which altogether make up the evil of humanity.” Nonetheless, the study of mathematics shapes people into being individuals that contribute to their societies. According to Dr. Thomaskutty and Dr. George,
“The mental power one gets from learning Mathematics is the acquisition on the art of proper thinking and effective reasoning. The study of mathematics imbibes in the individual values like honesty, truthfulness, open-mindedness, objectivity, self-confidence, self-reliance, patience, willpower, and orderly habits like concentration, punctuality, neatness and hard-work, etc.”
Legacy of Ramanujan
One of the most aspired mathematicians known to modern history is Srinivasa Ramanujan. He was a humble Hindu mathematician born in British India, 1887. Despite all the odds running against him in making his genius known, he still had managed to make it into Cambridge University in England even though his relatives thought it to be a morbid sin to step foot out of the outskirts of India’s shores. In his mathematical career at Cambridge University, Ramanujan was pulling mathematical formulas and their calculations out of his brilliant mind like effortlessly pulling bunnies out of a magician’s hat.
Ramanujan attributed his success of performing those mathematical stunts to this basic, but wholehearted, belief: “An equation for me has no meaning unless it expresses a thought of God”. In other words, maths is a spiritual entity for him. Yet not many mathematicians chose to view it so. In fact, Professor Hardy, the person who discovered him, was a committed atheist. Hardy was only persuaded by proof, which oftentimes stifled the originality of Ramanujan’s work because his theorems predicated on what Ramanujan was convinced to be “divine intuition”. Yet Mathematicians of Hardy’s type “were willing to take nothing of faith…[They have been after a drive] to create a firm and logical ground on which to base Mathematics [in order] for it to be a great replacement for Religion and Classical Philosophy. But [that approach to Maths] fails. Mathematical systems, Godel later showed, have to depend on certain ‘givens’ (one might say ‘gifts’), which cannot be proven within [the mathematical] system. Those givens just have to be believed and accepted, otherwise, the whole stunningly complex cathedral of higher mathematics could never even begin to be constructed”.
So can the inclusion and the ‘belief in’ those “givens” be another way of believing in ‘hope’? When we are up against a very convoluted problem that we don’t think can bear a solution, can we just trust that those “givens” will help us work our way out of those problems? By trust, I mean, hope. They work miracles in maths. They construct “mathematical cathedrals”! Why are we short-selling the power of those “givens” in our life, or, in more applicative language, the power of our hope?
So let’s pick ourselves up by the bootstraps, grab a pencil to write with and a paper to write on, and start solving some equations. It will do marvels to our intellectual life, to our character, and to our spiritual thinking.
Featured Image Source: Pexels
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