How Pythagoras's ideas predicted the existence sub atomic particles 2,500 years ago. And how Christianity has bridged the gap between ancient Greece the particle accelerator.

In a recent posting of my conversation with Brandon Vaidyanathan on Science, Art and the Sacred I described the process of the discovery of a quark by Murrey Gell-Mann in the early 1960s and how the creative process used evoked the ideas of Pythagoras centuries earlier. I thought it would be worth talking about this a little more.

In the book of Prophet Daniel, the Septuagint translation has a Canticle sung by the three young men who were thrown into the fiery furnace by King Nebuchadnezzar the Babylon. God saved them from death in the flames and they sang a song of praise to the Creator of all. The song of the three young men is chanted regularly in the Divine Office and in it each aspect of Creation is depicted as praising God. In turn. 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 reflection on the beauty and order of Creationit, men through centuries, Christian and non-Christian, have seen a sign of a divine Creator and are moved to worship Him. This impulse is called by St Thomas Aquinas the virtue of religion. Man’s reason is weak and it is only through Revelation that we have been able to know who that God is and how to worship Him authentically. That form of worship is passed down to us through God’s Church today, and includes the Canticle of Daniel described above.

In this sense, therefore, we can think of the whole of Creation as being ordered liturgically, in that it directs us to God and thanks, praise and glory that is due to Him.

This Canticle predates Christianity and comes from a time when the detail of material facts known about the cosmos was far less that it is today. It is thought by some that modern advances in natural science serve to undermine this instinct for awe and wonder. However, when the advances in scientific knowledge are viewed with the eyes of faith, they only serve, it seems to me, to reinforce the sense that it is ordered and beautiful. So for me, as one who studied physics at university, the awareness of scientific description of the universe increases my faith and the belief in a Creator who made it all.

Perhaps we could revise are create a new canticle based in which we urge all the newly discovered galaxies, stars, black holes and at the other end of scale of size, molecules, atoms and sub-atomic particles, such as quarks, to give praise to the Lord.

For those who doubt that there is a connection between the old and new way of analysing and describing the universe, I would like to draw your attention to the story of the discovery ot a sub-atomic particle by Murray Gell-Mann.

In 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’ - of the seven liberal arts of education in the middle-ages. ((For more details of the quadrivium read my book, The Way of Beauty. The shape that Murray Gell-Man’s work completed was the triangular arrangement of 10 points known as the tectractys. 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.

Pythagoras ideas were the basis of pre Christian ideas of harmony and order in the cosmos and which were subsequently integrated into Christian thought by figures such as Augustine and Boethius as described by Benedict XVI in his book, The Spirit of the Liturgy. The thought of these pre-Christian classical philosophers, particularly with the thought of Aristotle, became, when integrated with Christian Revelation, the basis of the modern scientific method.

In the Raphael fresco, Pythagoras 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, again see my book the Way of Beauty for a deeper description of this.

The idea that the tectractys might be governing the arrangements of properties of these sub-atomic particles does not prove that Pythagoras’s ideas were correct (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, most people would suggest it when they look at the incomplete graph. But it is obvious only once one works on the assumption that nature is ordered symmetrically, and as Barr points out, the fact that we see the symmetry in nature seems to be part of human nature.

In regard to the discovery of the sub-atomic particle, once Gellman adopted this assumption of the symmetry of the physical world, his intuition gave him the missing point.

This intuitive leap - an educated guess - is always the first step in any creative process and in order to make such a leap we need a natural sense, in any sitution, of what is needed to complete the pattern. This is the 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, (it is a long time since I studied it university and I wasn’t the greatest student even then) 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 for it would stimulate in us that mode of looking that engenders creativity. 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.

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.’ ((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.))

Such a mind, one that is in tune with symmetry, and is open, futher, to inspiration from the Creator, 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. This is supernatural creativity and it is open to all of us if we seek to cooperate with God’s grace.

And what has this to do with the liturgy?

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 and bringing our ideas into reality through for example, the creation of the fine arts and crafts, will enhance our ability to be creative. 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 and with the common good. 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 highest activity of all is the worship of God in the sacred liturgy, and the end result for the individual who follows this path well and sincerely 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.

Therefore, I feel moved, creatively, to promote myself as the poet laureate of sub atomic physics, by suggesting an addition to the Canticle of Daniel:

‘Oh you multiplets of hadronic particles, give praise to the Lord. To Him be highest glory and praise forever.’