Marcus du Sautoy, Simonyi Professor for the Public Understanding of Science (having succeeded Richard Dawkins in the Chair), is currently presenting a series of TV programmes about mathematics and nature entitled ‘The Code’. Viewers could be forgiven for believing that what he is presenting is a mainstream view of mathematics rather than peddling his own peculiar brand of atheistic metaphysics. Since no appropriate caveats have been employed by the BBC, we feel it necessary to make a few of our own.
Firstly, Du Sautoy’s view that, as the Pythagoreans expressed it, ‘Number is everything’ is of very ancient pedigree; but, nothwithstanding, it is undemonstrable (which should be anathema to a mathematician) and a faith-based religious concept. Secondly, philosophers of mathematics and informed students of mathematics know that there is, to date, no satisfactory understanding of the relationship, if any, between mathematics and reality; to suggest that there is a relationship, and what such a relationship might be, is an act of faith. And thirdly, it is very unfortunate for scientists to be working with mathematics as though mathematics itself is the original reality to which the physical world ‘must’ conform through such things as ‘laws’; science has been hideously corrupted in the last 80 years because of this.
Some Christians might be heartened to see and hear Du Sautoy suggesting that numbers are at the root of all reality, that this is in some way all grist to the mill of Intelligent Design. Not so fast: Du Sautoy is an avowed atheist (who not very wittily gives his religion as ‘Arsenal’) who by his own admission is trying a more ‘softly softly’ approach than Richard ‘The Rottweiler’ Dawkins (whom all can see is a bigoted fanatic) and is not appealing to design, or even apparent design, but to some mysterious entity he calls ‘The Code’. A code at the very least implies information content, but The Code (as a proper noun and with the definite article) suggests something unique and powerful. Thus Du Sautoy:
…underlying everything that surrounds us, from the natural world to the cities we live in, there is a hidden code that explains why things look and behave they way they do.
[This hidden code (‘The Code’)] has the power to unlock the laws that govern the universe.
The Code is the truth of the universe, and its numbers dictate the way the world must be.
So, this hidden code, this entity that Du Sautoy calls ‘The Code’, has total and complete explanatory power, is identical to Absolute Truth, can lead us into All Truth, and is completely deterministic. This is unquestionably a religious position. And it is none other than the old heresy of Pythagoras, the pagan Greek philosopher, re-worked by gnostics, Kabbalists, Freemasons, Rosicrucians, Illuminists, and now, it appears, New Atheists. What a wheeze if they can pull this one off!
Most people know very little about Pythagoras and the Pythagoreans other than the Pythagorean Theorem of the triangle, which was attributed to Pythagoras, but was most certainly known and used for well over 1000 years before Pythagoras lived. Pity. Bertrand Russell, the twentieth century mathematician and philosopher, whilst unsympathetic to Pythagoras, stated,
I do not know of any other man who has been as influential as he was in the sphere of thought.
Not someone we should have forgotten about, then.
Pythagoras and his followers believed that all relations could be reduced to number relations, that mathematics (holos) is the real reality, while the world (cosmos) is a construct of our minds. The Pythagorean ontology was that ‘The Essence of Being Is Number’, number being understood to be ‘that which prior to all things subsists…by which and from which all things are coordinated, and remain connumerated in an indissoluble order.’ (Christians will notice a usurpation of the divine Logos therein). The Pythagorean philosophy was dominated by the ideal that numbers were not merely symbols of reality, but were the final substance of real things.
Aristotle fleshes this out in his Metaphysics, where he states that the Pythagoreans
…believed that the principles of mathematics were also the principles of all things that be. Now, since the principles of mathematics are numbers, and they thought they found in numbers, more than in fire and earth and water, similarities with things that are and that become (they judged, for example, that justice was a particular property of numbers, the soul and mind another, opportunity another, and similarly, so to say, anything else), and since furthermore they saw expressed by numbers the properties and the ratios of harmony, since finally everything in nature appeared to them to be similar to numbers, and numbers appeared to be first among all there is in nature, they thought that the elements of numbers were the elements of all that there is, and that the whole world was harmony and number.
Jetting around the world, the place Du Sautoy starts the programme is Chartres cathedral, the first of the great French Gothic cathedrals. The association is not lost on us. In the Middle Ages the cathedral school at Chartres was the centre for revival and development of Pythagorean ideas, and there is even a sculpture of Pythagoras in the cathedral. The cathedral was built on the site of a Druid temple, the crypt beneath the cathedral being a dolmenic chamber. Diodorus Siculus, writing in 36 BC, describes how these Druids followed Pythagorean teachings, and it is today one of the main centres for those interested in the Knights Templar, Freemasonry, the Lost Ark, the Holy Grail, bloodlines and all that baggage. The cathedral contains a mass of Masonic, gnostic, pagan, astrological and Pythagorean symbols. In Dan Brown’s The Da Vinci Code, his fictional character Robert Langdon lectures on the pagan symbolism of Chartres cathedral. Starting the TV series here is a dead giveaway.
At least the masters of Chartres tried to ‘Christianize’ some of the ideas and put them to some use in theology, hence as Otto von Simson (The Gothic Cathedral, Harper & Row, New York, 1956) states,
The masters of Chartres, like the…Pythagoreans of all ages, were obsessed with mathematics: it was considered the link between God and the world, the magical tool that would unlock the secrets of both.
David J. Stucki remarks
…from the dawn of Western Civilization and through the Middle Ages the heart of mathematics was strongly tied to religious thought. Eventually, however, the humanism of the Renaissance and the empiricism of the Scientific Revolution began to open the door for the breakdown of this marriage. Scientism, the granting of absolute authority to the empirical and objective, became the mistress of the modern mind. The resulting ‘mathematization’ of science and culture (Howell & Bradley, 2001) had a myriad of consequences. The Church was no longer perceived as having a monopoly on Truth. The success of mathematics in accounting for the structure and behavior of the physical universe ultimately led to a naturalistic version of the Pythagorean ontology that ‘Everything is number.’ The divorce of theology and mathematics in the modern age created the 20th century crisis of ‘Foundationalism’ in mathematical philosophy…[and] epistemological progress in mathematics is devastating to Christian theology under the Pythagorean legacy.
Clearly the Pythagoreans are still around; Du Sautoy for one, but also an increasing number of physicists are being seduced into thinking that ‘the principles of mathematics are also the principles of all things that be’, that somehow mathematics is primary reality.
For example, I. V. Volovich, CERN physicist, in his paper Number theory as the ultimate physical theory concludes that
the fundamental entities of which we consider our Universe to be composed cannot be particles, fields or strings but numbers.
Others have dived into the deep end, for example Vasilios Gardiakos:
That ‘all is number’ will allow us to create what many theologians thought only God was capable of…all can be numerated and computerized…Mathematics is the most basic requirement for existence. It has no mass, dimension and time and yet it can create these and many more phenomena.
The Thales era which brought us science is near the end. It is to be followed by the Pythagorean era with…the realization that ‘all is number’…we will gain the vision that ‘all is mathematics’…This is the point that we begin to perceive our existence as numerical.
The philosophy of mathematics is a contentious issue. It explores, but never resolves (apart from theology), the debates between the Platonists and the Formalists, the Realists and the Nominalists. The Pythagoreans aim to cut through the debate by making both views redundant through asserting a radical third way, which aims to dominate the whole scientific enterprise.
Platonists/Realists believe that mathematical entities exist independently of the human mind, declaring the existence of an abstract and immutable world apart from this material universe in which absolute mathematical truths reside. In this view, mathematicians do not create mathematics but discover it. But if these entities are not part of this universe, how can they be discovered and recognized? The standard answer to that it is by intuition or divine revelation and illumination, which are not attractive to atheists. Christians might be attracted to such a view, in that such entities ‘exist’ in the mind of God, (or somehow in God himself, who is transcendently not part of this universe, and yet immanent within it, though there is an ever-present danger of lapsing into panentheism when applying this to the created universe). St Augustine was generally Platonist in such things.
Formalists/Nominalists on the other hand deny the existence of mathematical entities, making mathematics a construction of the mind (whether the mind of man or the mind of God). In this view, mathematics is a very useful common language and tool that can help us try to make sense of the world, and can lead us into some very fruitful lines of enquiry, but which is nonetheless conventional rather than real. Augustine interestingly had some thoughts along these lines as well, that numbers are the universal language conveyed by God to us as confirmation of the truth.
Whereas Realists and Nominalists are agreed that there are no mathematical entities within this universe, the Pythagoreans assert that mathematical entities are not only within the universe, but actually comprise the universe: this is attractive to reductionist atheists. In summary:
Realism: asserts that mathematical entities exist outside the reality of the universe. The connexion, if any, between these entities and reality is a debatable issue.
Nominalism: asserts that there are no mathematical entities; mathematics is a product of the mind apart from reality.
Pythagoreanism: asserts that there are mathematical entities within the universe, which constitute the whole of reality: all else is a product of the mind.
We will explore the development of these philosophical concepts in subsequent posts, but suffice for now to say that Marcus du Sautoy’s Pythagoreanism (or Neopythagoreanism) is in no way representative of the mathematics or physics community at large, and it is disingenuous that the BBC are promoting what amounts to a religious view under cover of a programme about patterns in the world.
St Augustine had said,
If you see anything at all that has measure, number, and order, do not hesitate to attribute it to God as craftsman.
Just imagine the howls of disapproval, and the threats by the New Atheists, if this TV series had introduced a subtext of Intelligent Design underlying the patterns and numbers highlighted!