The Truth About Pi

Smoking sheesha in Luxor, Egypt

Smoking sheesha in Luxor, Egypt

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?

To be or not to be

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.

The end of magic?

discoverieI have recently purchased a facsimile copy of Reginald Scott’s The Discoverie of Witchcraft (originally published in 1584). This is an important book in the history of Western civilisation as it is the first ever book in which methods for creating magic are explained. This might seem an overstatement, as magic is nowadays a trivialised from of theatre which barely has any influence on the way we think.

Scott’s book is important because it was the first time somebody openly challenged the belief in witchcraft and supernatural powers by exposing conjuring methods. The book contains some interesting magic; there are pictures of trick knives that make it seem like you are cutting your nose or finger. The picture on the left shows a contraption used to create the illusion of somebody’s head being severed. There is also a description of a Magic Colouring Book, which is still used in children’s magic shows and many other tricks still performed by contemporary magicians.

The book was published in the Renaissance, a period which heralded Western culture as we know it today. Although many people see the renaissance as a period where Europe emerged from the Dark Ages, some do not see this as a positive development. Dutch historian Johan Huizinga, for example, questioned whether the renaissance was a positive change and argued that it was a period of decline from the High Middle Ages, destroying much that was important.

One of the important cultural phenomena that was destroyed was the sense of magic commonplace in humanity. The Discoverie of Witchcraft illustrates helped this development by dispelling magic as tricks. It might seem strange for an engineer/philosopher like myself to argue that dispelling a belief in magic would not be a good thing. Magic is, however, more than a simplistic belief in supernatural forces that control our lives.

Read more about the end of magic in: Perspectives on Magic: A book about scientific views of conjuring

Read more about the end of magic in: Perspectives on Magic: A book about scientific views of conjuring

Magicians have been part of human civilisation for as long as there are records—and possibly as long as human culture exists. There are many anthropological accounts of medicine men and shamans using conjuring skills as part of their healing and rituals. Most magic history books interpret this use of sleight of hand as an attempt by the shaman to obtain power mischievously. But there is much more to magic than one person gaining power over others. Magic is a means to understand our position in nature. Although some might argue that magic has been wiped from contemporary culture, it has never actually disappeared from our psyche.

Simple acts, such as writing your name on a wall are in fact magical. To some this is a simple act of vandalism, but that is not the real motivation for people to do this. Writing your name on a wall makes the wall becomes an extension of yourself and you become part of the wall. It is a way to exert our self onto the world. This is I think the deeper psychological reason for the popularity of tagging. Tagging is a way to impart part of your self onto the environment in which you live. This is in essence an act of magic because it is a way to connect the inner world (psychology) with physical reality. There is no rational reason to write your name on a wall

There are many more examples of non-rational behaviour; why do we prefer one brand over another? Why we choose one political party or football team over another? When analysing motivations in every day choices we see that people often cross the horizon of reason and this is the realm of magical thinking. Magic, as a psychological force, is still alive and kicking in a hyper-modern world.


Read more about the future of magic in my book Perspectives on Magic.

The illusiveness of fairness

Fairness is a concept which is used often to justify a point of view when discussing the distribution of goods or benefits – “it should be done fairly”. But what does this mean, what is fair and what is not fair? Most people seem to have a very strong sense whether something is fair or not, but what is this based on? As a philosopher, I do not take common sense for granted and decided to research this claim.

I was initially surprised to find that none of the philosophical dictionaries and encyclopaedias I have access to contain a lemma on fairness (besides references to John Rawls’ concept of Justice as Fairness). Searching the scholar section of Google provided some starting points. Unfortunately academic publishers charge exorbitant amounts to read journal articles and I refuse to pay for research which is essentially funded through taxes. So I started from scratch.

The common sense point of view of fairness is a sense of equality. Our sense of fairness is cultivated at a very early age: I remember having fights with my sister over who should get the largest piece of cake and even using a measuring tape to support our point of view.

Fairness as an absolute equality, such as in the cake problem, is a strange concept. If we apply this childish view of the world to adult problems, everybody would be paid exactly the same salary; would live in the same kind of house, wear the same clothes …

In most cases references to fairness lead to equal suffering between all parties – i.e. the preferred solution is usually the one that takes away from one party.

An absolutist concept of fairness can also lead to some extreme consequences. The Old Testament concept of “an eye for an eye” (Exodus 21:23-27) is a very well known example of absolute fairness. This is one of the arguments that Christian apologetics use to justify the death penalty. This bizarre ritual is, for many reasons outside the scope of this article, a very irrational punishment. The eye for an eye concept leads to situations such as we currently see in the middle east and is a slippery slope that should be avoided.

Absolute fairness is an artificial concept, which does not take the realities of life into consideration, e.g. we don’t all need or deserve the same piece of cake. It is a dangerous concept which can lead to unwanted consequences.

This leads to the next concept: relative fairness. For the cake problem this means that one child should get a larger piece because he or she is more hungry than the other or has behaved better. This relative concept comes much closer to the common sense concept of fairness which is used in every day life.

We accept that doctors are paid more than taxi drivers. Doctors save our lives, while taxi divers perform a much less critical function in society. Western society is, when it comes to distribution of wealth, basically a meritocracy in which everybody is rewarded on their merit.

Although merit is not the primary driver, it is a guiding principle in determinations of fairness. But is consideration of merit by itself sufficient to have a fair determination? Who determines who has how much merit? Is merit our individual contribution to society or to a business or is merit based on our personal needs? How much merit warrants one person getting a piece of cake twice as big as the other?

Another determinant in distribution problems can be need. The most hungry people need to most or best food. Need, beyond primal necessity, is not a very practical concept to use. Need is a concept which can be used only in situations where survival or health of people is at stake. Health care is an example where need has preference over merit.

If we want to use fairness as a determinant in solving a wealth distribution problem, we effectively shift the question. The discussion shifts from fairness to merit (being good) or need (being more hungry) and possibly other considerations I have not yet explored.

It seems that fairness is an utterly useless concept when trying to determine the distribution of goods. We can not use it to determine who gets which size of cake because it either leads to a blanket absolute equality or a series of further questions. The answer of these further questions (what is merit? what is need?) depends on our philosophical (or political) orientation.

My conclusion is that fairness should not be used as a determinant in wealth distribution problems and the word should be reserved for its original meaning, e.g. “free of spots and stains“.

The limits of Dawkinism: Whereof one cannot speak, thereof one must be silent

I have been reading Richard Dawkins‘ book, The God Delusion. Although I largely agree with his atheist point of view, I think he stretches his argument a bit too far as he does not seem to acknowledge that there is a limit to what we can achieve with reason, a horizon across which rational thinking can not take us.

His view can be summarised by Wittgenstein’s famous proposition: Whereof one cannot speak, thereof one must be silent. Dawkins places the limits of knowledge at the limits of reason. His view of religion, which lies largely outside the limits of reason, is directly derived to this assumption. I would, however, like to argue that the limits of knowledge are not formed by the limits of reason.

One of his arguments is that there is a negative correlation between religiosity and intelligence, e.g. the higher the IQ, the less likely somebody is religious. This seems to give the impression that religious people are generally less smart than atheists, thereby labelling most of the world population as dumb.

The reason for this correlation is, however, that measurement of IQ is totally biased towards rational thinking. Tendencies towards religion or spirituality in general are not part of an IQ test. This does not explain the correlation, but shows the limitations of comparing religiosity and intelligence.

Religion should be considered as a Vehicle for Meaning. Rational thinking can not provide us with meaning to life and religion is for a lot of people a way to deal with the vacuum.

Religion is not my preferred way if providing meaning to life; I choose an existentialist point of view—flying in a metaphysical hot air balloon. This attitude is, however, only possible after deep and complex rational thinking. Most people do, however, not have the energy or capability to live this way and religion is an ‘easy’ way out.

Dawkins does not seem to consider the provision of an answer to meaning to life questions. He places a very high burden on the rational abilities of people. The creation versus evolution question is an example of this.

Dawkins might reply that this is all very well, but the provision of truth has primacy over providing meaning. This is philosophically very slippery ground. Science is based on presuppositions, as much as religion is. Science is only confirmed by its own rules, it is a self fulfilling prophecy—the same can be said for religion.

I think truth is not important, if absolute truth does exists, we will not be able to find it. Knowledge is more important than truth and knowledge is nothing more than that which is able to provide the outcomes we desire. Both religion and science are very capable of doing this.

Venom Crystals and the Meaning of Life

Venom Crystals and the Meaning of LifeI am currently writing an essay on futility and its relation to the meaning of life, based on a paper by William Joske.1. Joske argues that philosophy is a dangerous activity because almost all flavours of thinking lead to the conclusion that life is futile. No rational philosophical or scientific theory has been able to work out the purpose of Life. Joske writes about life in general, not our individual lives.

Many years ago in one of my first encounters with the Internet I downloaded a philosophical gen created by Kevin Solway, called Venom Crystals, a collection of quotes from Eastern and European philosophy. Reading Joske’s paper, I realised that philosophy is indeed a Venom Crystal. We are hypnotised by its beauty, but the content is poisonous. The more deeply we think about life, the universe and everything, the more we come to realise that life is futile. We do not seem to have any rational justification to think that life has meaning.

This does, however, not imply that we are forced to accept a non-rational system – such as religion – in order to provide meaning to life. Plato writes in his famous myth of the cave that a philosopher is somebody who is able to crawl out of the cave and stare into the bright sun. A philosopher is somebody who is able to accept the meaningless of life. Douglas Adams describes the problem thus:2

“You know,” said Arthur thoughtfully, “all this explains a lot of things. All through my life I’ve had this strange unaccountable feeling that something was going on in the world, something big, even sinister, and no one would tell me what it was.” “No,” said the old man, “that’s just perfectly normal paranoia. Everyone in the Universe has that.”

“Everyone?” said Arthur. “Well, if everyone has that perhaps it means something! Perhaps somewhere outside the Universe we know …”

“Maybe. Who cares?” said Slartibartfast before Arthur got too excited. “Perhaps I’m old and tired,” he continued, “but I always think that the chances of finding out what really is going on are so absurdly remote that the only thing to do is to say hang the sense of it and just keep yourself occupied.”

What Slartibartfast is saying here is very profound indeed. He has an existentialist attitude in that he believes that the likelihood of determining the meaning of life are ‘absurdly remote’. His conclusion is that he should focus on the coastlines; in other words actually lead our lives in a constructive way, instead of wasting it by trying to find its meaning.

By the way, if the chances of finding out the meaning of life are absurdly remote, then the Infinite improbability Drive would be a good way to find that answer, but that is another story …


  1. W.D. Joske, ‘Philosophy and the Meaning of Life’ Australasian Journal of Philosophy (1974), 52:93-104 

  2. Douglas Admas (1979) Hitchhiker’s Guide to the Galaxy

The Validity of Religious Experiences

The Blues Brothers having a religious experience

The Blues Brothers having a religious experience

The question of the epistemology of religious experience deals with the issue whether information obtained through religious experiences can be considered valid knowledge. For a brief introduction into different forms of religious experience, see my paper on that subject.

Information obtained through religious experiences, which I shall further refer to as Revelation, is not considered valid knowledge in contemporary society mainly because the information obtained through revelation can not be verified. Religious experience is thus a very personal experience and unique knowledge, only available to the person receiving the revelation. The receiver of the information is the only one who is able to interpret the revelation and communicates it as thus to the wider world.

In pre-industrial society power was vested in the intermediaries between the transcendent and the immanent. The Latin word Pontifex (priest) illustrates this beautifully as it also means ‘bridge’. The priest as bridge builder between the material and the spiritual worlds.

Knowledge gained through revelation is unique and invests power into the person receiving that knowledge as they are the only ones capable of interpreting the information. Knowledge in this sense is esoteric, only available to a small group of people.

Empirical philosophy has, in combination with rationalism, revolutionised human knowledge of the material world. This combination has been an important and powerful tool. Where does this leave revelation? Can we simply say that revelation is not relevant and that religious experiences are mere delusions?

Because revelation is always esoteric knowledge, every experience is interpreted different, depending on the cultural and psychological dispositions of the person receiving the revelation. An important question to be asked is why a Hindu does not receive revelations concerning Jesus Christ or any other cross cultural experiences?

Religious experiences are particular and esoteric. In a society where knowledge is available to anyone through empiricism (although this is not completely true as we do not all have a particle accelerator in our backyard) the Pontifex has lost his power over society as the sole interpreter of knowledge.

The consequence of this, however, is that we have thrown the baby with the bathwater by ignoring religious experience as a valid source of knowledge.

I believe that religious experience can be a valid source of information to make decisions about non material things. It can people guidance about their life, which can have a very profound impact on their lives in the ‘real’ world. Religious experiences also have an effect on how we interpret the material world which shapes our world views.