How Golden is the Golden Section?

23 07 2010

Whenever I talk about proportion and harmony in art and architecture, many assume that I am referring to the proportion known as the Golden Section (often indicated by the Greek letter Φ). When I started to investigate these things, I assumed that the Golden Section was important too. However, to my surprise, my investigations lead me to believe that although it was known to past societies and cultures, it was not as important as we assume today. In fact, the idea that it was used by the ancient Greeks, the medievals or masters of the High Renaissance is, as far as I can work out, largely a myth. I have described before, herehere and here, how important symbolic number, proportion and harmony (expressed numerically or geometrically) was for artists and architects in the Christian tradition and how they were seen as a manifestation of the cosmic liturgy. But it seems that the Golden Section, Φ, isn’t part of that tradition. Most of the books that I read justify their argument with a diagram, like the one shown left. In the diagram a grid placed over a copy of Leonardo’s self portrait drawing. This grid, to my knowledge, is not taken from information given by Leonardo himself in regard to this drawing, but is a modern superimposition. To me it looks like an array different rectangles, no doubt all relating to to Φ is some way, but otherwise arbitrarily chosen until their combination coincides with the main features of the drawing…and not very well at that. The eyes, the mouth, the tip of the nose, the chin (which is hidden) do not coincide with the lines drawn. This is typical. When you look at it, given the margin of error that required to make it fit, you could justify just about any proportion you chose to apply.

My feeling is that the modern obsession with Φ results from a modern, neo-pagan worldview in which the natural world is seen as the ideal of beauty. This is in contrast with the tradition Christian view that the world, although good and beautiful, is fallen and points us to something greater. The Christian interest has always focussed more on what the created world ought to be, rather than what it is; and to what it points us to, that is the ultimate standard of Beauty, God.

If we assume that I am right and that the use of Φ in the past has been exaggerated in modern accounts of art history. Does this mean that it shouldn’t be used today? In my opinion, not at all! However, if we do decide to use it, it should be done so with discernment. We need to consider what precisely we feel that it symbolises and how it relates to the rest of the Christian tradition of harmonious proportion. If we consider it, for example, as a symbol of a fallen, imperfect world, then it should not be used in isolation, but should always be used in conjunction with other proportions that allow it, to use a musical terminology, to resolve to a more perfect harmony.

In the longer article, here, I describe my reasons for these assertions. My mind is not closed on this matter, however. If readers can come up with accounts contemporary to the artists and architects that demonstrate that it was used intentionally by them, I would very happily change my opinion!




7 responses

24 07 2010
Tom Bree

Hello David,

Good to hear from you and great to see you talking about geometry.

There are certainly those who almost make a religion out of the Golden Section claiming to see it almost everywhere in humanly produced objects.

Of course within Creation it can quite undisputably be seen all over the place as it is a mathematical ratio that is fundamental to the natural world and it’s miraculous and beautiful capacity to grow and thus manifest forth its hidden potential (God be praised).

As you will know there is a tradition of secrecy surrounding the ‘Five-fold’. I assume you’ve heard of the term “Sub Rosa”. Anything spoken ‘Sub Rosa’ (usually below an image of a rose on the ceiling of the room in which the ‘sub rosa’ things were being spoken about) was to be kept secret and not spoken about beyond the confines of that ‘hidden’ space.

The primary manifestation of the five-fold in our Roman Catholic tradition can be seen via Our Lady the Blessed Virgin and the associating of her with the five-fold rose which could be looked upon as a European Christian version of the Pentagram. Everytime you pray the ‘Rosary’ you are handling a string of beads that are arranged in a fivefold configuration and those beads that mark out the division points between the Decads are known as the ‘mystery beads’.

The rose and Venus-(Goddess and planet) have long been associated with one another as they embody the same five-fold geometry via the golden section. The 5 sepals of the rose straight forwardly speak of the ‘five-foldness’ of Phi. Along with this, and as I’m sure you know, we here on planet earth also have a ‘five-fold’ relationship with the planet Venus due to the fact that Venus’ orbital period is 224.7 of our Earth days and when 224.7 is multiplied by Phi we get 363.5 which is a close enough approximation to our orbit for a pentagram relationship to be clear to see. This is an astronomical fact that has been known by many cultures throughout history.

There has long been a close symbolic connection between Venus and the rose and Our Lady the Blessed Virgin. This can be seen through her titles ‘Stella Matutina’ (i.e. Venus the Morning Star) and ‘Rosa Mystica’. Cardinal Newman speaks of these two Marian titles as the ‘above’ and the ‘below’ of Mary in his meditations on the Litany of Loretto (see his meditation on ‘Stella Matutina’ – it’s on the web).

Of course Venus is Venus whereas Mary is Mary………they are not the same figure or at least not in outward terms though the whole point of ‘symbolism’ (‘sym’ – together…’bol’ – to throw) is to marry together the outward form with its archetypal principle and thus both Mary and Venus are outward embodiments of Divine Love and Wisdom although outwardly one is a pre Christian Roman Goddess whereas the other is Our Lady.

The five-fold and Phi are, in Christian terms, also associated with ‘Incarnation’ and inevitably so because of the many golden section relationships that exist within the human body. How could Christ our Lord have died for us if he had not become Incarnated through a human form? How could Our Lady the Blessed Virgin have brought forth the Word made flesh if there was no corporeal womb to allow foetal development?

This world is beautiful though imperfect. Its imperfection is just a fact of existence but it’s beauty is a primary path by which we are in a position to move closer in proximity to He who brought it forth. It is through Creation that we are in a position to come to know the Creator and thus everytime we as Geometers draw the mathematical ratios that the Creator used (and perpetually uses in his great and beautiful Work) we are emulating Him in the act of Creation. If the golden ratio is good enough for the Creator then it’s good enough for us.

I don’t know how much value is there in getting too wrapped up in Art History and about who did what and when they did it and how conscious they were of whether they were doing it etc…….. Art History has its place but ‘Art Now’ is far more fundamental in helping us to move closer to God.

Geometry is first and foremost a study of eternal laws that ‘Are’, presumably always have Been’ and, God willing, always will Be and this is why it can used as such a profound form of prayerful meditation by which we enter into ‘Relationship’ with He who Is, always has Been and always will Be.

Golden section and the five-fold are traditionally a hidden knowledge and this is why it is not so commonly seen up front and ‘in your face’ as it were within Christian art though it is most definitely there in places and very notably so within the 14th century Lady chapel at Wells Cathedral which I’ve just recently done an analysis of – it’s Fibonacci-tastic!!! (forgive my overly technical terminology 😉

The more usual expression of fiveness in Christian art is via the quincunx whether it be Christ surrounded by the Evangelists, the five wounds as seen in the form of the speared Heart of Christ surrounded by the two hands and two feet as well as many other quincunx arrangements. The four-fold division of Christ’s garments followed by the drawing of lots for the seamless (undividable) coat can be looked upon as quincunxial in it’s symbolic nature.

The fourness of the square implies the cross and the cross implies a centre…a fifth point – the ‘Quintessence’-(fifth essence) where the vertical and horizontal lines meet one another and thus the ‘Divine’ and the ‘human’ enter into relationship with one another through Christ. This fifth point is centrally located in the quincunx but in the pentagram it is traditionally seen as the pentagram point that points upwards to heaven whereas the downward pointing pentagram speaks of spirit descending into form (don’t believe those heavy metal teeshirts that you see in Camden Lock – that’s a very recent interpretation of the pentagram pushed into popular culture by a crazy American hippy who was pushing the ideas of a shady Victorian occultist)-(For a very old upturned Roman Catholic pentagram check out the 13th century north rose window at Notre Dame in Amiens)

I hope that all is going well for you in the States

Yours in Christ

Tom Bree

24 07 2010

Hi Tom, great to hear from you! This is a lot of stuff, which I need to read through. But the general points in my article still hold: I am satisfied that five-fold symmetry was used occasionally, but this makes the Golden Section incidental to the process, not deliberately sought. As regards hidden knowledge…if it is hidden and not documented, how do we know that it really existed and is not some modern invention? As regards modern analysis of building, the argument I made in the longer article still needs to be answered I think – the error range is too great for the analysis to be a reliable source of information that the analysis reveals that the Golden Section was used intentionally. Your analysis that it was Fibonaccian – would come under this too – there are alternative proportions that predated the Fibonacci series and which were expressly linked to Christian tradition (and so not hidden knowledge) eg Boethius’s Fourth of Four. Anyway, we shall continue to correspond I’m sure.

24 07 2010
Tom Bree

p.s. The 5th month is the month of Our Lady and the 10th month is the month of her Rosary. It isn’t expressly stated that this is for for reasons of sacred number but it is certainly an appropriate relationship to be the case.

(by the way October became the month of the Rosary just after it moved from being the 8th month of the year to the 10th month)

25 07 2010

Hi Tom, a couple of additional points. My understanding is that the Church wouldn’t recognise ‘hidden’ knowledge in the sense that you seem to be describing these things. There has never been part of the Church that is a cognoscienti who have been designated as worthy of a greater knowledge than the rest of the masses. It is a public religion. The ideas of secret knowledge preserved for the few is called gnosticism, which is heretical. So if it was a secret knowledge then it wasn’t part of the Catholic tradition.

That doesn’t rule out the possibility of it having been part of the tradition in the past but through accidents of time we have just no record of it nowadays, of course. But in order to be convinced it fell into this status I would need some reliable records of artists or architects of the time using it (which is what we have for these other proportions). Also, Fibonacci published his series in 1202, or thereabouts, I wonder when was Wells Cathedral built? It as after this but it was some time before the Fibonacci series was widely known an given any significance in relation to the Golden Section wasn’t it?

16 10 2010
Ginny Koumantarakis

Dear Tom Bree
I dont know if you are the same person that was giving a class at Waterperry House – Oxford, on the 3rd October 2010?
I was at Nanpantan House for the Sanskrit Week and saw the flyer advertising the workshop ‘Portraying the Divine’. I was not able to get to Oxford and therefore my correspondence with you.
I am very interested in Geometry and have taught a bit to the children at the School of Philosophy in Durban, South Africa where I live.
I have been an admirer of Keith Kritchlow for many years and was fortunate to meet him 2 years ago on the Island of Samothraki where he gave an afternoon talk.
I would love to correspond with you and find out more about your classes.
If this is all not making sense to you, I have the wrong Tom Bree. Please let me know either way.
Kind regards

23 10 2010
Tom Bree

Hello David,

Good to hear from you and thanks for passing Ginny onto me.

I’m surprised that you should say that there has never been any element of cognoscienti in the church. Are you sure that you’re not talking about more recent Roman Catholic tradition?

In any culture and religion there will inevitably always be a small number of people who have an inclination towards what might be called the ‘Mystical’. Mysticism, much like religion itself, has had a rather rough ride since the enlightenment due to our more recent need to reduce all knowledge to that which is rationally comprehendable. But how can rationality come to know that which transcends it? As Gregory of Nyssa said “Every concept grasped by the mind becomes an obstacle in the quest to those who search”

It is also important not to mix up the gnostic heresy with ‘gnosicism’ itself. This would be similar to being anti-community because of communism.
As I’m sure you know the word gnostic simply means ‘to know’ though the ‘knowing’ that is implied by the word is of an inner sort that from a Roman Catholic perspective would be associated with people like Mother Julian, John of the Cross, Catherine of Sienna, Meister Eckhart, Nicholas of Cusa plus many others.

The gnostic heresey is an example of where ‘gnosticism’ went astray and this ‘straying’ is something that can occur within any area of any religion be it within the sphere of moral, political, doctrinal, mystical or any other activity for that matter. So mystical approaches are not anti Roman Catholic – they are actually an important thread within its fabric.

One of the reasons why mystical paths tend to be more hidden is because they are often misunderstood. A good example here is with the Islamic mystic Al Hallaj who was quite open and public about his experiences of mystical Union. He would say things like “I saw my Lord with the eye of my heart and I said ‘who art thou?’…and he said, ‘thou'”.

A person hearing these words who is on a level of ego will assume that the mystic is also on a level of ego and that they are effectively saying “My ego has turned into God” If this is what a mystic was meaning it would be a great heresy and an absolutely disasterous delusion for that quasi-mystic to be in.
But when mystics say things like this they are expressing the Oneness that they have entered into. Prior to Union there were two – God and the mystic – but with Union there becomes only One…..God…..because the mystic has become dissolved back into God. The mystic has certainly not turned into God.

(By the way The Unitive stage is the third and final stage of Roman Catholic mysticism with the ‘Purgative’ and the ‘Illuminative’ being the first and the second)

As I said before there will always be a small number of people in any culture or religion who are inclined towards a more inward form of Knowing. If a religious institution casts these people out they will not suddenly stop being of this inclination…they will just become prey to dubious New Agey groups that you and I are both rather wary of so it is essential that a religion caters for this sort of approach for the small amount of people within any culture that there will ‘always’ be who are that way inclined.

As to the golden section I would suggest a scholarly book to you which I’ve recently got hold of called Ad Quadratum published by Ashgate ISBN 0 7546 1960 5. It’s coming from an art history angle and shows various examples of pentagonal forms mainly up at east ends of medieval cathedrals/churches. I would dearly love to show you what I’ve been finding in Wells Cathedral in the last couple of months – it goes far beyond what is in the fore mentioned publication. I’m going to start a PhD in relation to it next year so I can’t really put it in a public forum such as this but if you come to the UK anytime I’ll show it to you. By the way, due to my exhuberance I was using incorrect language when I said ‘Fibonacci-tastic’. It’s all Golden section that I’ve found in Wells and a rather startling example of it that I’ve just found in recent weeks.

Lastly, on the subject of written records, the problem with only relying on written records as evidence is they disregard oral tradition. As artists surely we are both aware of the fact that we learn best through copying the example of a master rather than reading about someones process in a book. Have you noticed how Pythagoras didn’t write a single thing down? Or Socrates who felt that Philosophy ceased to be philosophy once it was written down – but he knew nothing -(which is why he was the wisest man in Athens 😉 – On this subject of ‘learned ignorance’ I would strongly recomend Nicholas of Cusa’s magnum opus “On Leaned Ignorance”. It’s one of the greatest examples of maths and mysticism that Christendom has produced.

Yours in Christ


23 10 2010

hi Tom Nice to get your reply. Here are the responses I would make to your points. There always was, and still is mysticism in the Catholic Church, but it is not a secret or hidden knowledge. Catholicism is a public religion. And of course I might have it wrong, and also perhaps we are at cross purposes in the terminology we use, but my understanding is that gnosticism is heretical, full stop. David

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