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OP-ED: The philosophy of mathematics

  • Published at 02:42 am September 21st, 2021
Mathematics
Photo: Roman Mager

It can teach us much about life itself

What is mathematics? We attempt to comprehend, but the definitions unfortunately further confound. They frustrate by glancing off the edges of a subject as infinite and indefinable as the discipline they seek with little success to give shape and form to.

Conventional wisdom informs us that mathematics is the study of the measurement, relationships, and properties of quantities and sets, using numbers and symbols, and that arithmetic, algebra, and geometry are illustrative of its manifestations. Further description declares it to be the study of the science of numbers, quantities, geometry and forms.

Interestingly, much of the effort to create a workable understanding of this one word is constructed around the two concepts described in the preceding sentences. This is the first anomaly, for if mathematics is clarity, then the definitions which attach to it are nothing but abstruse. Let us, therefore, attempt to capture our understanding.

Mathematics is empirical, a set of precepts formulated over the millennia of systematically recorded human experience. The same results obtained, without variation, from ceaseless experiment culminated in a series of “laws” tentatively agreed to and eventually etched in stone in the manner of a compact between Man and God.

Empirical? By that logic, the study of any subject in the universe of academia and the classroom could be an extension of the mathematical principle as long as the study is organized along the lines of the criteria established by the definitions. Substitute “numbers, quantities, geometry and forms” with “words and phrases” and transfer to the disciplines of Literature, Theology, and History is seamless. 

The principles of mathematics therefore represent the DNA, the building blocks, of the pursuit of all knowledge and intellect. Mathematics is philosophy, for it theoretically contains the tools to comprehend the entire gamut of human experience. 

Perhaps Sir Isaac may have done well to include a postscript at the end of the glorious peroration of his magnum opus which lies in state in the main hall of Trinity College, namely, that the principles of the Principia Mathematica may be applied with easy variation to any mode and manner of the human quest for truth.

And if philosophy is the quest for truth of life and existence as we experience and otherwise seek to know, then there is little to distinguish between mathematics and philosophy. Perhaps, even, they are merely two sides of the same coin. But computation on a scale of one to nine proves inadequate when contemplating existence possessed of a purported beginning and end. 

Let us remove the obstacle by including the concept of zero and, for argument’s sake, referring to its “opposite” as infinity.

Human thought is linear, as is philosophy. Plot the linear march of the meaning of existence from zero to infinity, and discover how uncannily similar they are. 0 + 0 = 0, 0 X 0 = 0, 0 – 0 = 0, and 0 / 0 = 0. 

By what magic do I arrive at the same result, irrespective of the process of calculation applied? Or is it a compulsion, ordained by the urge for meaning? We can apply the same anomaly to infinity. Add, subtract, multiply, and divide using infinity on both sides of each application, and you will be left with infinity.

Mathematics starts from zero and ends at infinity. But it can also start at zero and end at zero. And, not to forget, it may start at infinity and end at zero. Zero and infinity have the same properties. We do not know what infinity is, we can only guess based on a carefully-crafted conjecture. But without zero, which in itself is infinite, we cannot attempt to define.

A study of the sciences of geometry and forms, you say? If you start moving from one point and keep going, say, east, you will eventually return to the point of commencement. This is the principle of the universe, whose action we just described and which mimics the perfection of the circle and efficiency of the sphere. Is it a coincidence that the billions of planets and stars which spin endlessly in the infinite night are spherical?

We presume that life and action and activity are circular because of the urge to imitate the perfection demonstrated by the universe. Evidence supports, from the golden orb of our sun to a drop of water to the perfectly round shape cast on the ground by sunlight refracting through the layers of leaves of the towering tree. The circle is embedded in our construct and unerringly betrays its indispensability to human existence.

Dear reader. Take a moment to align yourself. Centre yourself, albeit precariously, and follow the radius till the point of commencement is reached. Contemplate for a moment the perfection that you stand in the middle of, and look within you. In a universe of conjecture and precarious precepts and hearsay that we inhabit, create the tiny space in and around you for your personal permanence and truth.

Your infinity is eminently comprehensible, and lies within easy reach.

Sumit Basu is a freelance contributor who writes from India.

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