My idea of having a great time: smoking sheesha in Egypt, wearing my favourite T-shirt (ThinkGeek.com). The print on the shirt consists of the first 4,493 digits of the number Pi in the shape of the symbol itself. In my view, the number Pi, not the number 42 as some have proposed, symbolises the ultimate truth of the universe. Let me explain why.
On the way 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 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 dilemma’s? Can we improve our understanding of Shakespeare by expressing his prose in formal language?
I tend to agree with Professor Martin Seldon, played by John Hurt in the same movie:
“Since man is incapable of reconciling mind and matter he turns to confer some kind of entity on ideas because he can not bear the notion that the purely abstract only exists in our brain.”
With this in mind, why does the number Pi reflects the ultimate truth about the universe?
Pi is an irrational and transcendental number and the digits of which it is composed comprise an infinite array of random numbers. Even after calculating billions of digits, there does not seem to be any pattern in the arrangement of the digits. It is this lack of any pattern, the absence of logic, that illustrates the structure of the universe itself.
Pi is an artificial structure of our mind, not something existing in reality. Nature doesn’t care about perimeters and diameters, although it might seem that the ubiquitous nature of Pi seems to suggest differently.
Pi is an important number in physics and is included in many formulas. This implies to me that there is something inherently random in the structure of reality.
However, we perceive our environment in discrete terms. Common sense mathematics does not include irrational numbers such as Pi. We think in whole numbers and fractions. This is reflected in the fact that in ancient cultures, Pi was perceived to be a fracture, such as 22/7. This is the value that I use in my own calculations as it is accurate enough for almost all computations.
But the number Pi is ubiquitous in mathematics and physics. We rely on an irrational numbers such as Pi and e in much of our modeling of reality. What does this say about the structure of reality? I do not have an answer on this, but for me, the existence of irrational numbers shows the great divide between common sense and our scientific description of the world.