Pi Approximation Day: The Esoteric Secrets of the Number π

The number Pi (π) is the most popular irrational number in the world with somewhat of a celebrity status. It is in fact so popular that it has its own holiday. Many people observe Pi Day on March the 14th because writing this date the American way looks like 3.14. This does not make sense for most of the rest of the world and therefore I prefer to celebrate Pi Approximation day on 22 July (22/7 = 3.14).

Why does a number deserve its own holiday? Even though Pi is an irrational number, it is also a practical number because it appears in many equations that describe the physical world. The number Pi is fascinating and has kept many mathematicians busy for more than two thousand years. As an engineer, I used to hit the π button on my calculator many times every day and have a mild fascination with this number. In this article, I share some of my thoughts on this most rational and mystical number.

In the photo below, I am smoking a sheesha pipe in Egypt and wearing my favourite nerdy T-shirt. The number π on the shirt consists of the first 4,493 digits of the number Pi in the shape of the Greek letter itself. The relationship between π and Egypt is not coincidental as many people believe that the design of the Khufu pyramid at Giza reveals that Egyptians of the fourth Dynasty knew about π, long before any other culture did.

The perimeter of the pyramid, divided by its height, is approximately two times Pi. Whether the designers of the Khufu pyramid knew about Pi is doubtful as there is no evidence in any papyrus. Nevertheless, many people are convinced that the geometry of the Great Pyramid hides mystical properties and ancient knowledge. The article discusses

Smoking sheesha in Luxor in my favourite t-shirt in 2008.

Smoking sheesha in Luxor in my favourite t-shirt in 2008.

The Digits of Pi

The Inner Secrets of π?

Pi is an irrational and transcendental number with an infinite array of randomly distributed digits. Unfortunately, it will take an infinitely large T-Shirt to show all digits of Pi. Even after calculating billions of digits, we cannot seem to find any pattern in the arrangement of the digits. The number Pi is an irrational number because it cannot be expressed as a fraction. In other words, you cannot divide two number by each other and get the number Pi. The only way to describe Pi accurately is to use an infinitely long series, for example:

\frac{\pi}{2} = \frac{2}{1} \cdot \frac{2}{3} \cdot \frac{4}{3} \cdot \frac{4}{5} \cdot \frac{6}{5} \cdot \frac{6}{7} \cdot \frac{8}{7} \cdot \frac{8}{9} \ldots

This number being a mathematical constant, it is also one of the most rational tools to understand the universe. If the universe is rational, then why do we need an irrational number to describe it? Does this contradiction mean that Pi hides an inner meaning and that it hides an inner logic that we have yet to discover?

In the novel Contact by Carl Sagan, the heroine Ellie discovers a hidden message in the base-11 representation of Pi. This discovery is not as miraculous as it sounds as there Pi has an infinite number of decimals. Even the complete works of Shakespeare could eventually be found inside the digits of Pi. My birthday appears at the 107,070,083rd decimal digit of Pi. My PIN appears many times in the first million decimals of Pi

The idea that an irrational number helps us to understand the universe can be a worrying thought. Mathematicians have tried for centuries to square the circle. They tried to find a logical to construct Pi using nothing but a ruler and a compass, but they failed miserably. Fully understanding Pi requires us to deal with infinity. What does the fact that we cannot grasp Pi in simple terms tell us about the structure of the universe? Is Pi really a property of the universe, or is it just a construct of our mind?

Pi and the Horizon of Reason

Flying back from Egypt, I watched The Oxford Murders. In this movie, the question whether mathematics is the underlying truth of the world is discussed between the two main characters. Martin, a student, played by Elijah Wood, said:

“Things are organised following a model, a scheme, a logical series. Even the tiny snowflake includes a numerical basis in its structure. Therefore, if we manage to discover the secret meaning of numbers, we will know the secret meaning of reality.”

But is Martin correct? Can all philosophical questions and truths be expressed in mathematics? Will we eventually calculate our way out of ethical dilemmas? Can we improve our understanding of Shakespeare by expressing his prose in mathematics?

2b \vee \neg 2b = Q

To be or not to be, that is the question.

I tend to agree with Professor Martin Seldon, played by John Hurt in the same movie, who said:

“Since man is incapable of reconciling mind and matter he turns to confer some sort of entity on ideas because he cannot bear the notion that the purely abstract only exists in our brain.”

Does the infinite sequence of random numbers mean that Pi is an artificial construct of the human mind and not something that exists in reality? The idea that we need an irrational number to describe reality does not seem to match our perception of the world as a discrete set of things. Our common sense view of the world consists or integers and fractions, not of irrational numbers.

Pi exists on the Horizon of Reason.

Nature doesn’t care about perimeters and diameters, although it might seem that the ubiquitous nature of Pi in physics seems to suggest differently. The existence of irrational numbers seems shows the great divide between common sense and our scientific description of the world. Our common sense concept of the world is most likely wrong, just like almost all our perception of the world is a construction of reality. Perhaps reality is not as discrete and countable as we believe it to be and we are projection our rationality upon the world.

Pi Approximation Day or Pi Day?

The coolest thing about Pi is that it has its own holiday. The American part of the planet celebrates Pi Day on 14 March, which in their notation is 3/14. These two decimals are only a rough approximation of Pi. In 2015 we nudged a bit closer to accuracy because Pi day was on 3/14/15.

A slightly more accurate day to celebrate Pi is 22 July or Pi Approximation day.  On this day, I celebrate the number Pi and its fantastic approximation 22/7 = 3.142 …

Even though Pi has an infinite number of decimals, as an engineer, this simple approximation is good enough for most applications and has been very useful in my professional life. Pi Approximation Day recognises the beauty of mathematics but also shows that the infinite precision demanded by mathematical theory is but a construct of our mind.

Peter Prevos

Social scientist and engineer who dabbles in magic tricks.

1 Response

  1. 19 April 2018

    […] of Pi. In the 1998 film Pi by Darren Aronofsky, the protagonist is driven mad by the idea that a secret pattern in random numbers. The string of numbers that form the decimals of Pi might seem random, but they […]

Leave a Reply

%d bloggers like this: