A quest for God in irrational numbers

My physicist friends sometimes go crazy with the “magic” of numbers. A recent discussion involved the famous irrational number “pi”. A friend was mesmerized by a YouTube video on what the speaker in the video called “Powell’s Pi Paradox”.

A quest for God in irrational numbers

Representation image (Photo:SNS)

My physicist friends sometimes go crazy with the “magic” of numbers. A recent discussion involved the famous irrational number “pi”. A friend was mesmerized by a YouTube video on what the speaker in the video called “Powell’s Pi Paradox”. The presentation dealt with how the digits in pi after the decimal point differ between its exact value and its various approximations if one continues to extend the value of pi with hundreds of digits.

I got bored after watching about half of it and did not share his excitement. Pi, after all, is just a ratio of two lengths – circumference and diameter of any circle – and all theories and formulas in physics and mathematics do not really care what the exact value of pi is. In any practically useful computation, one can retain the number of digits necessary to get an answer to any desired degree of accuracy. Please do not get me wrong.

I have a PhD in theoretical physics and have been marvelled numerous times by the magic of mathematics. Analytical expressions for pi given by Ramanujan are mind-boggling to me. However, as I have grown older, I realized that our entire universe is full of such magic and mysteries.


It is not just the numbers; think of anything we see around us: the internal organs of a human body, how a baby is born, a thunderstorm, mutation of coronavirus, structure of DNA; it is incredible how intricately the various parts of the puzzle come together. The internet is full of stories about phenomena that science cannot explain.

I realized that everything has been created by God with a certain purpose but we are never going to learn the detailed reasoning and what that purpose is no matter how smart we are or how much we learn. It is a game that God plays with us to see who can come out of this entangled labyrinth of material world and realise that He is the only answer.

I no longer spend time watching the “fantastic” explanations of various phenomena we see in nature. I always try to see if there is any message from God hidden in whatever we are observing. I am fascinated by concepts of “Sacred Geometry” which are based on the premise that God created this universe following a geometric plan. Whether it is crystals, stars, dodecahedrons, beehives, nautilus shells, DNA helix, fractals, spider’s webs, they all have specific geometric appearances.

Therefore, it is no wonder that temples, churches, mosques and many religious structures such as pyramids and tabernacles have unique geometric appearances.

My view, which is the reverse of these concepts, is that if one starts with these geometries and associated numbers and works backwards, there might be clues about God’s plan – kind of like following the “Da Vinci code”. Going back to the number “pi”, God created a geometric figure viz. a circle. Even for a simple parameter like the ratio of its circumference over diameter, we must continue indefinitely if we want to assign a numerical value to it.

All clever methods of calculating pi are just different paths in our effort to reach this unattainable answer. It is the same as the quest for God. If we feel God in our heart, He is very simple – perhaps appearing as a circle of light; but if we want to logically quantify Him it is a never-ending quest taking thousands of reincarnations.

Perhaps evaluation of every irrational number is a metaphor for the search for God. What fascinates me more than pi is the other famous number “e” or the Euler number because its implications are more profound. Unlike pi, e is not a definite ratio; it is a limit of an expression involving some variable n as n becomes infinitely large which means you can continue to iterate with higher and higher values of n to get a more and more accurate estimate of e.

The beauty of this number is that if one raises it by a variable exponent x it can be considered as a function of x and this function can be graphed, differentiated, integrated and expanded as a power series just like any other function of x but with interesting results.

We will denote this function by exp(x), exp being short for “exponential” since such functions are called exponential functions. The most striking aspect of this function is that if we replace x by the imaginary number “ix” we get the following identity, known as the Euler formula: exp(ix) = cos(x) + i sin(x) Where cos and sin are the cosine and sine functions of trigonometry, and i is the so-called imaginary number or square root of negative one. It is called an imaginary number because there is no real number whose square is one.

The significance of this formula cannot be overstated. It provides a bridge between algebra and trigonometry, and it is fair to say that laws of electromagnetic theory and perhaps the entire subject of electrical engineering could not be formulated without this equation. The mathematicians get great joy in the special case of this identity if one replaces x by pi. Since sin (pi) is zero and cos (pi) is minus one it reduces to exp(ipi) = -1; this is known as Euler’s identity.

It has been described as the most beautiful equation in mathematics because it brings together five fundamental numbers together: pi, e, i, 0 and –1. I believe that the significance is much greater. In mathematical language, exp(ix) is a complex number consisting of a real part cos(x) and an imaginary part sin(x). It dawned on me as a metaphor of God being Radha and Krishna together. Most single people hanker for their soulmates.

A soulmate is believed to be just like him/her in every respect with the same common interests, intellectual level and belief systems but of opposite gender. Sometimes they think that they have found their soulmate only to be invariably disappointed later. In my opinion, the concept of a soulmate is a myth. It is really a “reflection” of a person in the opposite gender.

If you are a man your soulmate is a female version of you and vice versa, but it only exists in your imagination and not in real life. In Euler’s formula, cos(x) represents a real person and sin(x) symbolizes his/her imaginary soulmate. Exp(x) represents God and is of course complex.

We know from trigonometry that cos(x) and sin(x) behave very similarly as x changes; one just lags the other by pi/2. Similarly, a person and his/her soulmate behave exactly in the same way but they are not in sync, so to speak. This makes sense because you do not want your soulmate to be in sync with you in every activity; you just want her to be like you.

The imaginary number “i” reminds us that the second part of exp(x) is imaginary just like a soulmate is imaginary. The imaginary soulmate completes us; my soulmate and I together represent the “whole”. I am only a part of God; my soulmate is the missing part. The trigonometric identity where the sum of squares of sine and cosine functions of x, for any value of x is one, symbolizes this; together we make one. There are other irrational numbers in mathematics with similar fascinating implications.

One example is the so-called “Golden Ratio”. There are many articles on the internet on Golden Ratio and its relationship to Fibonacci sequence and Penrose tiles. I will urge the interested readers to read them. My main point is that while all these numbers and their interrelationship are quite fascinating to mathematicians and scientists, these are just manifestations of a divine plot.

(The writer, a physicist who worked in academia and industry, is a Bengali settled in America.)