Liturgical science? Here is a Way of Beauty replay of an article first published in April 2010. I included this example as part of my class in architecture and traditional proportion recently, to illustrate the fact that modern science does not invalidate the traditional approach to number, rather it reinforces it......
In the Canticle of Daniel, chanted on Lauds Sunday Week 1and all feast days in the Divine Office, all of creation is called to give praise to God. The frosts hail and snow, wind and rain and all the other inanimate aspects of creation listed in this canticle do not give praise to God literally, but through their beauty they direct our praise to God. The cosmos is made for us. Through it, we perceive the Creator. In this sense the whole of Creation is ordered liturgically, in that it directs us to God and we give Him thanks, praise and glory. That thanks and praise of man is expressed most perfectly in the liturgy.
Well it seems that we could modify this canticle in accordance with the discoveries of particle physics, perhaps adding the line: ‘Oh you multiplets of hadronic particles, give praise to the Lord. To Him be highest glory and praise forever.’
In excellent his book, Modern Physics and Ancient Faith, describing the consistency between the Faith and the discoveries of science, Stephen M Barr describes the scientific investigation of a grouping of sub-atomic particles which he refers to as a ‘multiplet’ of ‘hadronic particles’. He describes how when different properties, called ‘flavours’ of ‘SU(3) symmetry’, of nine of these particles were plotted mathematically, then they produced a patterned arrangement that looked like a triangle with the tip missing.
‘Without knowing anything about SU(3) symmetry, one could guess just from the shape of the multiplet diagram that there should be a tenth kind of particle with properties that allow it to be placed down at the bottom to complete the triangle pattern. This is not just a matter of aesthetics, the SU(3) symmetries require it. It can be shown from the SU(3) that the multiplets can only come in certain sizes….On the basis of SU(3) symmetry Murray Gell-Man predicted in 1962 that there must exist a particle with the right properties to fill out this decuplet. Shortly thereafter, the new particle, called the Ωˉ was indeed discovered.’
This result would have been of no surprise to anyone who had undergone an education in beauty based upon the quadrivium, - the ‘four ways’ - the higher part of the education of the seven liberal arts of education in the middle-ages. The shape that Murray Gell-Man’s work completed was the triangular arrangement of 10 points known as the tectractys. As described in my previous articles for the New Liturgical Movement, this is the triangular arrangement of the number 10 in a series of 1:2:3:4. 1, 2, 3 and 4 are the first four numbers that symbolize the creation of the cosmos in three dimensions generated from the unity of God; and notes produced by plucking strings of these relative lengths we can construct the three fundamental harmonies of the musical scale. The importance of this in the Christian tradition is indicated by the fact that Raphael’s School of Athens fresco, which is in the Vatican, portrays Pythagoras the Greek philosopher whose ideas were the basis of these ideas of harmony and order. He is portrayed looking at a chalkboard with a diagram of the tectractys and X, the Latin number 10. (Above it on the chalkboard is the diagram which is a geometric construction of the musical harmonies.
The idea that the tectractys might be governing the arrangements of properties of these sub-atomic particles does not prove that it is a correct theorem (although I do find it intriguing!). Nor, even, is knowledge of the tectractys necessary to see the missing dot in this case. As Barr points out, it is obvious once you look at the incomplete graph. But it is obvious only once one works on the assumption that nature is ordered symmetrically. Once Gellman did this, his intuition gave him the missing point. This intuitive leap is the first step in any creative process. We come up first with an idea of what we think it might be, and then test it with reason.
I do not have a deep knowledge of particle physics, but I doubt that the traditional quadrivium contains the full range of symmetries that one is likely to see and would need to use as a research particle physicist. Nevertheless, I would maintain that the traditional education in the quadrivium would enable the research scientist to be more creative in his work. A traditional education in beauty, which is what this is, trains the mind to work in conformity to the divine order, to which, in turn, the natural order conforms. Such a mind is open to inspiration from the Creator, and is more likely to make the necessary intuitive leap when placed with an array of data. The mind that habitually looks to the divine symmetry is more likely to see the natural symmetry.
Physicist A. Zee put it this: ‘Symmetries have played an increasingly central role in our understanding of the physical world. From rotational symmetry physicists went on to formulate ever more abstruse symmetries…fundamental physicists are sustained by the faith that the ultimate design is suffused with symmetries.Contemporary physics would not have been possible without symmetries to guide us…Learning from Einstein, physicists impose symmetry and see that a unified conception of the physical world may be possible. They hear symmetries whispered in their ears. As physics moves further away from everyday experience and closer to the mind of the Ultimate Designer, our minds are trained away from their familiar moorings…The point to appreciate is that contemporary theories, such as grand unification or superstring, have such rich and intricate mathematical structures that physicists must martial the full force of symmetry to construct them. They cannot be dreamed up out of the blue, nor can they be constructed by laboriously fitting one experimental fact after another. These theories are dictated by Symmetry.’
And what has this to do with the liturgy? I quote from my article on the quadrivium, The Way of Beauty, which appeared on the New Liturgical Movement website in September:
‘The traditional quadrivium is essentially the study of pattern, harmony, symmetry and order in nature and mathematics, viewed as a reflection of the Divine Order. When we perceive something that reflects this order, we call it beautiful. For the Christian this is the source, along with Tradition, that provides the model upon which the rhythms and cycles of the liturgy are based. Christian culture, like classical culture before it, was also patterned after this cosmic order; this order which provides the unifying principle that runs through every traditional discipline. Literature, art, music, architecture, philosophy –all of creation and potentially all human activity- are bound together by this common harmony and receive their fullest meaning in the liturgy…When we apprehend beauty we do so intuitively. So an education that improves our ability to apprehend beauty develops also our intuition. All creativity is at source an intuitive process. This means that professionals in any field including business and science would benefit from an education in beauty because it would develop their creativity. Furthermore, the creativity that an education in beauty stimulates will generate not just more ideas, but better ideas. Better because they are more in harmony with the natural order. The recognition of beauty moves us to love what we see. So such an education would tend to develop also, therefore, our capacity to love and leave us more inclined to the serve God and our fellow man. The end result for the individual who follows this path is joy.’
When the person is habitually ordering his life liturgically, he will tap into this creative force, for he will be inspired by the Creator. Meanwhile all those multiplets of hadronic particles in the cosmos will be giving praise to the Lord.
 For more details of the quadrivium read the following articles written by me for the New Liturgical Movement website: Cosmic Liturgy and the Mind of God; On Number; Harmony and Proportion; The Way of Beauty at Thomas More College of Liberal Arts
 A Zee: Fearful Symmetry, the Search for Beauty in Modern Physics (New York, Macmillan, 1986) p281. Quoted by Stephen M Barr in A Student Guide to Natural Science (Delaware, ISI Books, 1986) p71.