From Quadrivium to... Trivium

New from www.woodenbooks.com

Beauty for Truth's Sake was about the four liberal arts known collectively as the Quadrivium. I wanted it to be as practically helpful as possible to people working to reintegrate wisdom and a sense of beauty and the sacred back into education. On this blog and on the main site where the book is listed I continue to place material to supplement what is in the book. One of the resources I recommended is a series of little paperbacks published by Wooden Books on topics such as Harmony, Sacred Geometry, Astronomy, etc. Now the publisher has rolled all these little books into one impressive textbook, the cover of which is reproduced on the right. I thought you'd like to know!

So that is the Quadrivium. But that is only four of the seven liberal arts. Maybe now we should turn our attention to the remaining three, the Trivium of grammar, logic and rhetoric. According to Hugh of Saint Victor, summarizing the tradition in the high Middle Ages, "Grammar is the knowledge of how to speak without error; dialectic is clear-sighted argument which separates the true from the false; rhetoric is the discipline of persuading to every suitable thing." The Quadrivium is about mathematical symbols and geometry (numbers and shapes), while the Trivium is about verbal symbols and the arts of language. The interest of educators in the Trivium and in the Classical Curriculum generally was fuelled by a famous essay of Dorothy Sayers called "The Lost Arts of Learning". (There is also a classic textbook on the subject by Sister Miriam Joseph). It is widely agreed that the skills of speaking, thinking, remembering, communicating and debating are endangered by a culture of instant electronic social networking, images and sound-bites. Yet if we cannot think for ourselves, what becomes of our freedom?

Look and Learn

Classical Montage by Angus McBride

For a boy like me, growing up in England in the 1960s as part of the middle class, Look and Learn is a phrase to conjure with. It evokes whole worlds of imagination and knowledge. Look and Learn was a weekly educational magazine that was carefully built up over the years into a bound set of encyclopedias, each issue full of wonderfully informative and interesting stories and pictures. (This picture is used by kind permission.) Many of these educational treasures have since been reprinted in a limited number of volumes, but the whole archive is available on a web-site for the use of teachers and parents in the 21st century. Do go there and explore - I highly recommend it.

And while I am looking back, I may as well mention the other magazine I received each week - the Eagle, with its very English space-hero Dan Dare being the main attraction. The artwork and tone of the whole thing beat most other comics into the ground, and the artist Frank Hampson won all kinds of awards from the comic art community. There is a Dan Dare web-site where you can see a lot of what went on in this splended series.

In space no one can hear you sing...

The old idea of the "music of the spheres" seems to be coming back into fashion. Astronomers at the University of Sheffield have managed to record for the first time the "eerie musical harmonies" produced by the magnetic field in the outer atmosphere of the sun. They found that huge magnetic loops coiling away from the outer layer of the sun's atmosphere, known as coronal loops, vibrate like strings on a musical instrument.

Other astronomers have done the same for a much more distant and larger star, KIC 11026764, nicknamed Gemma, about 3,100 trillion miles away from the Earth. "Essentially stars resonate like a huge musical instrument," said Dr Bill Chaplin. "Stars make sounds naturally but we can't hear this as it is has to travel through space. Like a musical instrument, stars are not uniformly solid all the way to their core, so the sound gets trapped inside the outer layers and oscillates around inside. This makes the star vibrate causing it to expand and contract. We can detect this visually because the star gets brighter and dimmer and so we can reconstruct the sounds produced from these vibrations."

The scientists at the Large Hadron Collider (where high-energy collisions of subatomic particles result in temperatures of ten trillion degrees) have also turned their readings of the energies released by particle collisions into sound, and are planning to stage a concert of the resulting music.

All of this is very reminiscent of Pythagoras and the search for cosmic harmonies that started off the history of science in the first place. But silence is coming back into fashion too. A successful film (Into Great Silence) and TV series (The Big Silence) have transfixed viewers with the deep, meditative silence of prayer. A record featuring two minutes of complete silence is tipped to rise to the top of the music charts this weekend, for Remembrance Sunday. The director general of the Royal British Legion said "we felt the UK public would recognise the poignancy of silence and its clear association with remembrance." In his recent exhortation, Verbum Domini, the Pope emphasizes the important role of silence in the Liturgy. "The word, in fact, can only be spoken and heard in silence, outward and inward." Thus people must be "educated in the value of silence."  "Rediscovering the centrality of God’s word in the life of the Church also means rediscovering a sense of recollection and inner repose.... Only in silence can the word of God find a home in us, as it did in Mary, woman of the word and, inseparably, woman of silence."

The silence of space is due to the fact that sound cannot travel through a vacuum. But sound is just a particular vibration, and the whole universe is made of vibrations of various sorts, so the music of creation is everywhere. Composers and musicians simply "tune in" to some deep harmonies in nature and filter out the dissonance. That seems to be the message of a sweet modern fairy-tale of a movie, August Rush, mentioned in the sidebar. But everything takes place against a background of silence, which - a bit like the "vacuum" of space - is anything but empty, but rather full of potential energy. By listening to silence we still the unnecessary turmoil of our minds and hearts, allowing the meaning of creation to sound forth.

To affirm the material

In my book I write about 'poetic knowledge' and the importance of imagination as a vehicle of truth. One of the key figures in the English Romantic movement - worth more than a brief mention - is William Blake, who died in 1827. He was influenced by, among other things, Jacob Boehme’s and Emmanuel Swedenborg’s astonishing visions of inner worlds and the “new Church” of the Spirit; but also by his friend Thomas Taylor’s powerful translations of the works of Plato. Blake worked as an engraver and painter, designing visionary images that are nearly always striking, if not startling. He was also a poet and a prophet, expressing his prophetic inspiration through a vast and obscure mythology. These mythological writings represent the triumph of human freedom and the liberation of human energies by means of a cosmic war that rages from Eden through America and Albion to the end of the world.

In keeping with the spirit of these works, Blake was a radical in social thought, and a heretic in religious belief. He raged against the “dark, satanic mills” of the Industrial Revolution that were destroying Nature and the traditions of human craftsmanship, and against “Newton’s sleep”, the Rationalism that he believed was destroying the life of the Imagination. Interestingly, despite Blake's heretical tendences, in the biography that G.K. Chesterton published in 1910 he presents Blake and St Thomas Aquinas as warriors fighting in the same war, and even on the same side. Chesterton contrasts two types of mysticism, that of Christendom and that of Orientalism. The latter is the mysticism of oversimplification, of the dissolution of many into one. But Blake, he argues, “was on the side of historic Christianity on the fundamental question on which it confronts the East; the idea that personality is the glory of the universe and not its shame”.

So Blake’s heathen mysticism was on the side of Christendom against the Orient. And thus Blake and St Thomas are agreed that “the highest dogma of the spiritual is to affirm the material”. Aquinas confirms Blake’s fundamental intuition that things are more real, not less real, than they appear to us. “And there is an upper world of what the Schoolman called Fruition, or Fulfilment, in which all this relative relativity becomes actuality; in which the trees burst into flower or the rockets into flame”.

The Pope on the Pavement

When Pope Benedict XVI visited the United Kingdom in September, one of the most striking images was of him sitting side by side with the Archbishop of Canterbury, trading polite speeches, on the Cosmati Pavement of Westminster Abbey. That pavement is worthy of some attention, especially if, like me, you are interested in the symbolic meaning of geometrial forms and their role in the great cathedrals of Christendom. (The following notes are abridged from the official website description. But PLEASE WATCH this excellent documentary about the pavement. Bear in mind that the image I have chosen is just a detail.)

The pavement was laid down in 1268 by order of King Henry III who had started re-building St Edward the Confessor’s Abbey in the new Gothic style in 1245. The workmen came from Rome, with a man called Odoricus at their head. It is 24 feet 10 inches (7 metres 58 centimetres) square, with dimensions calculated in Roman feet, and consists of geometrical patterns built up from pieces of stone of different colours and sizes cut into a variety of shapes: triangles, squares, circles, rectangles and many others. The basic layout is a four-fold symmetry, but in detail the variations are endless. No two roundels are the same. Of the four "orbiting" roundels one is circular, one hexagonal, one heptagonal and one octagonal. The infill patterns are all different.

The inscriptions that accompanied the design, now damaged, read in part: "If the reader wisely considers all that is laid down, he will find here the end of the primum mobile" and "The spherical globe here shows the archetypal macrocosm."

The round stone at the centre contains colours representing the four elements. It is on this stone that every king or queen of England was crowned. [See also here.]

A dance of light

Following on from my previous post (The Sea, the Sea), it is worth noting that G.K. Chesterton had a very different and less sympathetic impression of Impressionism. To quote Fr Aidan Nichols' brilliant study, G.K. Chesterton, Theologian:

At the Slade Chesterton also acquired an extremely hostile attitude to the painterly mode called Impressionism, a hostility that not only later defined much of his attitude to art at large but was formative for the development of his realism in metaphysics. Consider his 1907 novel, The Man Who Was Thursday. As Gabriel Syme, fleeing from the agents of Sunday, dives into a patch of woodland, the play of light and shade on the leaves causes him to muse:

Was not everything, after all, like this bewildering woodland, this dance of dark and light? Everything only a glimpse, the glimpse always unforeseen, and always forgotten. For Gabriel Syme had found in the heart of that sunsplashed wood what many modern painters had found there. He had found the thing the modern people called Impressionism, which is another name for that final scepticism which can find no floor to the universe.

'The identification of Impressionism as a symptom of cultural and, especially, epistemological decadence also finds expression in, for example, his 1910 study of William Blake. Seeking to express how for Blake lucidity and decisiveness of outline were the chief desiderata in draftsmanship, Chesterton risks the anachronism of writing that “the thing he hated most in art was the thing which we now call Impressionism — the substitution of atmosphere for shape, the sacrifice of form to tint, the cloudland of the mere colorist.” 

I think Chesterton had a point - there are tendencies of that sort in Impressionism, although I see in several of the impressionists a very different spirit, and Claude Monet (one of whose pictures is reproduced above) I would even call a mystical realist, which is something very different from a sceptic. As for Blake, Chesterton's study of him will be the subject of a future post.

The Sea, the Sea

Golden Wave, by Piers Browne

What is it about the seaside? Is there anyone who does not feel liberated and uplifted by standing on the shore and looking out to sea? Feet planted on the rocks, gazing at the living waters, breathing the charged air, seeing the horizon-line where the sea meets the sky... just add a bonfire, or stars overhead, and all the archetypal elements are represented - as though we were present at the creation of the world. Piers Browne's paintings at Art Jericho in September captured this experience, and particularly the beautiful radiance of light on the ocean; evoking not just the origins of the mundane world but somehow the promise of paradise on earth. I suspect this is the effect that Monet was seeking in his exploration of waterlilies and haystacks and the canals of Venice - the intuition of an eternal heaven glimpsed in the transient effects of sunshine on air and water.

Are women more beautiful than men?

In ancient thought, it was often assumed that the male of our species is more beautiful than the female. Certainly this was the assumption in Greece, and Plato’s dialogues reflect a virtual cult of male beauty. However, I think I have theological proof to confirm my longstanding suspicion that woman are more beautiful than men. See what you make of it.

According to John Paul II’s theology of the body, discussed in the latest issue of Second Spring, the real source and meaning of gender lies in the Trinity. The Trinity is love, which means self-gift. Love includes within it both activity and receptivity, and it is an act that necessarily involves three Persons. We might say the Father is the divine nature as Giver, the Son is that same divine nature as Receiver (and then, as Receiver, in turn a Giver, since he is the perfect image of the Father), and the Holy Spirit is the divine nature as Gift. (John Paul II names the Holy Spirit in his encyclical Dominum et Vivificantem “Person-Gift”.) Thus the Spirit is Gift, both given and received, and unites Father and Son in the act of giving.

In the creation, Woman is brought to Man precisely as “gift”, crowning the gift of creation in general, which has been made for him. Woman is brought to man not just as wife but as friend, sister and eventually mother as well, all rolled into one in a way that will never again be the case until the advent of the Virgin Mary, who will form with her Son the new beginning of the human race. (In fact the original gift of Woman could be said to include – obscurely and distantly – the gift of Christ himself, who will descend from her in the fullness of time.) Here in this moment of creation Adam represents the Son, the Receiver of the Father’s Gift, and Eve the Holy Spirit, or that which the Father gives. (Perhaps this is why St Maximilian Kolbe describes Mary, the Second Eve, as a "quasi-incarnation" of the Holy Spirit.) She is the breath of life, the living essence of the man, taken out of him and returned in the one form in which he can find himself in his own solitude – that is, in the form of another person to whom he can give himself.

The nature of Woman, then, the deepest meaning of her gender, is to be Gift for Man, to manifest the Spirit, just as the deepest nature of Man is to be the Receiver of the Gift, and to manifest the Son to her. Thus femininity in its totality, at its deepest level, is the essence of humanity made visible to itself as the definitive beauty and glory of creation. (Similarly the essence of masculinity consists in the loving response to this gift which awakens Woman to her own self.)

Adam and Eve fresco by Masolino da Panicale, 1424.

Lost Tools of Learning

I thought readers might like to know about an article by Brad Birzer (author of a good book on Christopher Dawson) over on the "Imaginative Conservative" blog concerning the importance of the Liberal Arts revival for the future of Western civilization: What Might Help Hold Us Together. Also recommended is The End of Literature by Ben Lockerd.

Barbara J. Elliott writes on the same blog. In her The Power of Beauty, she says:

Art has the twin functions of reflecting a culture and shaping it. The problem that contemporary artists face is a difficult one: how to express meaning to a world which has become culturally over-stimulated by the spectacular, hyper-sexualized, dumbed-down by inanity, and increasingly antagonistic to manifestations of Christianity. Some of the artists who are here this week struggle to believe that the vocation as an artist – especially a Christian artist – has any meaning or value at all. They are at the edge of redefining and creating anew with moral imagination a vision of the True, the Good and the Beautiful that has been all but exterminated in Western culture.

She goes on to analyse the defects and influence of modernism in the arts, and calls for a "second culture". I get nervous when words like "conservative" are used as labels, so it is worth mentioning that these guys are in the tradition of Russell Kirk, Christopher Dawson and T.S. Eliot.

Images of heaven

We live in an age of images, in which photography and photoshop, CGI and advertising, surround and enfold us in an inescapable cascade of pictures and fragments of pictures, sometimes to the extent of seeming to create a whole artificial world. The elderly are often dependent on the TV that serves as a companion and tranquillizer, the young live their lives through the computer screen on their phone or laptop. The word "icon" now signifies for most people something purely secular - a tiny image that opens up into an application, or else the trademark appearance of some celebrity. Paradoxically, in this Age of the Image, we have lost the ability to read images - to see through them into their meaning. Instead we go through them to other images, and are caught in an endless chain of distraction. To read images we must appreciate symbolism. The image signifies something ultimately real yet invisible, something grasped by intuition or intellect using the image as a support. We need a revival of "mystagogy". This is something church architects and artists have rediscovered, and as a result many new churches may be easier to pray in than some built in the last generation. Matthew Alderman writes about this in "Heaven Made Manifest" from Antiphon magazine ("The crucifixion is just a symbol, but symbols still have meaning, especially in this age so starved of symbol, sign, and iconography"). The symbolism of the Christian temple is analysed in great detail by Jean Hani in a book of that title. The leader of the new movement in church architecture is Duncan Stroik, who directs the Institute for Sacred Architecture at Notre Dame and its brilliant journal. Take a look, also, at Liturgical Environs by Steven J. Schloeder. The beacons are lit...

Photo of Westminster Cathedral by Rose-Marie Caldecott.

In praise of tradition

The word tradition derives from trans- "over" and dare "to give".  In every traditional society or civilization, a process takes place that can be called a “handing over” of the stories, the knowledge, the accumulated wisdom of one generation to the next. It is a handing over which makes each new generation into a source of wisdom for the one that will follow. What is handed over is a “gift”. It is not simply a bundle of property whose title deed is being transferred to the next generation. Rather, it carries within it something of the giver. Its transmission is an act of love. Thus the gift of tradition involves and transforms the interiority of both the giver and the recipient.

Tradition in the sense I am describing is of the highest value because it is not something we simply manufacture, nor something cooked up by our parents, but something our parents themselves have received with gratitude and respect. Its origin is what makes it sacred.  Some kind of revelation of truth, or what is believed to be a revelation, forms the seed of every great tradition. Tradition is venerated because of this. The moment we suspect that our tradition is based on a lie is the moment it loses its authority over us. Thus tradition is based on the act of faith. I adhere not simply because it has been handed down to me, but because I believe it is “true” (even if I cannot directly verify its truth for myself).

The receptivity proper to love makes possible the transmission of tradition from one generation to the next. And when that spirit is present, tradition is never felt like a dead weight on the present. Only a tradition that has lost this spirit can become a deadening force.

Photograph of the Vatican Library by Br Lawrence Lew OP, used with permission.

The Golden Circle

In chapter 4 of my book I talk about a rectangle inscribed within a circle. Naturally there are an indefinite number of such figures. Take the diagram on the right, kindly produced by Michael Schneider. Look at the outermost circle, and the largest rectangle that lies inside it, touching its circumference at A, B and C. You could move points A and B nearer to the left-hand end of the horizontal diameter of the large circle, or else push them further apart towards the two ends of the vertical diameter, producing an ever-thinner oblong shape. Halfway between these  extremes the rectangle would become a square. But the shape Michael has drawn is a Golden Rectangle, so we can call the whole figure a Golden Circle ("Golden" because of the presence of the Rectangle). The G.R. is famous for being the "most beautiful" of rectangles, possessing the peculiar property that its sides are in the ratio of 1 to Phi (1.618...), so that if you cut off a square portion what remains is a smaller Golden Rectangle - and so forth, forming a logarithmic spiral, as in the following image.

When I wrote the book I was intending to use the Golden Circle as a way of exploring the relationship between Pi and Phi, but I never got around to it. My reason for being intrigued is simple. What we learn from Simone Weil - and what she learned from the Greeks - is that geometry is full of theological meaning. We have forgotten how to make those connections. It is not that we can prove the Trinity or the Incarnation with diagrams, but that the mathematical world is full of analogies that echo theological and spiritual truth. You might even say that mathematical necessities are a portrait of divine freedom, since in God freedom and necessity coincide. The beauties of geometry and arithmetic are a world of metaphors and help to raise our minds towards the contemplation of divine truth. My book only touches on this, but a much fuller and richer account is given by Vance G. Morgan of Providence College in his book Weaving the World: Simone Weil on Science, Mathematics and Love, reviewed here.

Analogy

The use of analogy is fundamental for human thought and language, and in particular for theology. Derived from the Greek analogia "proportion" (ana- "upon, according to" + logos "meaning" or "word"), it refers to the way we compare one thing with another on the basis of some likeness or similarity. It is more complicated than a simile, which happens when I straightforwardly compare one thing to another ("God is like a light"). It is also more complicated than a metaphor, which is when in poetic language I simply assume the similarity in the way I describe something ("God is a light for my eyes and a path for my feet").

An analogy is built out of similes and metaphors - it extends them not just to things but to relationships between things. If a simile is like a ratio (A : B), an analogy is a ratio of ratios (A:B : C:D, or "the relationship of A to B is like the relationship of C to D"). So to form an analogy we might say, for example, "Clay is to the potter as the world is to God". But "analogy" is also used more generally to cover all the ways we compare things that are similar to each other in some respect but not others. Everything we say about God relies on metaphor and analogy, because the words we use necessarily come from the things we can see and touch.*

So God-talk has to be taken with a pinch of salt. When we talk about God we mustn't take ourselves too literally. There is an analogy here with the problem of "graven images", or the temptation to mistake the image for what it represents. But what if God talks about God? In Jesus, we believe, God spoke as a man. Just as the Incarnation gave a justification for icons, so it gave a justification for saying certain things about God and believing them to be true. Philosophy and mysticism were possible before Christ - but now there is also theology. The things in the world were always "like" God in certain ways, not just as signs of his presence and activity but as expressions of his nature, or natural symbols of him. But now they can also be sacraments and sacramentals.

All of this perhaps serves as background to the use in my book of geometrical and mathematical "analogies" to the Trinity. Thomas Aquinas was perfectly clear on the fact that the Trinity cannot be proved by anything in nature - nevertheless, once we know by revelation that God is triune, we can see traces or impressions of the Trinity everywhere. So, for example, all things (1) subsist, (2) have a definite form, and (3) are ordered to an end (echoing Father, Son and Spirit). Following Simone Weil, I wanted to show that fundamental numbers and shapes also "echo" the Trinity in this way. There is no attempted proof here, just an intellectual intuition or an aid to contemplation, but the point is that knowledge of the Trinity enables us to appreciate the beauty of creation by seeing in its ordered harmony a meaning that we could not know before. Mathematics, in its own way (and you won't hear this said too often!), is a picture of love.

* There is much talk in theology about the "analogy of being", or attempts to compare the existence of God and that of the world. For an interesting discussion of that topic go here.

The photograph is by Tom Bree and is used by kind permission.

Exploring patterns

If you enjoy geometrical patterns or colouring or even if you are contructing a tiling system for your kitchen or bathroom, you might want to look at this site from Altair Design. Teachers and parents might like to look too, to see some activities to get kids painlessly interested in geometry. Explore the site - it has a huge variety of patterns that you can colour online, a competition you can enter, and a gallery of the best examples done by other people. The middle button at the top gives you some history and context for the site.

I also recently stumbled on some nice tiling patterns based on Escher's drawings in the Alhambra (one of which is shown in the picture). If you go to the page via the link, click on the individual patterns and you'll open up some spectacular PDFs.

Symmetry

Symmetry is one element of beauty, and in the book I describe how a physicist attempted to locate all particles on a grid consisting of the most symmetrical object conceivable – and failed. Does this failure disprove the coinherence of beauty and truth? Hardly. For in fact a slight departure from symmetry can be even more beautiful. This is true at many levels. In the early moments of the big bang, if matter and antimatter had been exactly balanced the universe would have destroyed itself. I recently read of some research into the shape of the neutron, which at present appears perfectly symmetrical, having an electric charge (or more precisely “electric dipole moment”) of zero. Researchers hope to find some slight asymmetry in order to explain the excess of matter over antimatter which enables us to exist. Zero is the most symmetrical of numbers but not the most beautiful, and existence is always a departure from it. The pattern of human love has been described by Angelo Scola in terms of “asymmetrical reciprocity”. Thus a theologian might say that the tension of asymmetry runs right the way through creation, from top to bottom, as the mark of the Creator, and is only resolved by the Trinity in a way that eternally preserves difference within unity.

The Two Cultures

The phrase was made famous by C.P. Snow’s Rede Lecture of 1959, in Cambridge, England, which was viciously attacked by the critic F.R. Leavis in 1962 and later, more moderately, by Lionel Trilling in America, generating a major controversy in academic circles concerning the relationship of arts and sciences. (See C.P. Snow, The Two Cultures, with an Introduction by Stefan Collini, Cambridge University Press, 1998.) The controversy recalled a famous exchange in the 1880s between T.H. Huxley and Matthew Arnold. Snow, like Huxley before him, took the side of the scientists against the men of letters. Not being able to describe the Second Law of Thermodynamics, he thought, was equivalent to confessing that one had not read a work by Shakespeare. His critics argued that the contrast drawn between the two cultures was crude and misleading, that his celebration of consumerism and the industrial revolution showed him to be a rabid philistine, and so forth.

When Snow and Leavis were writing, the English education system forced children to choose between the humanities and the sciences as early as the age of fourteen. As Stefan Collini points out in his

The Alhambra

In their early period of rapid expansion the Arabs took over the Middle East, acquiring and preserving much of the ancient learning. They also developed it, picking up in many ways the intellectual torch of the Greeks. There was a brief shining moment some centuries later when Europe was able peacefully to absorb the knowledge of the then vastly superior Islamic civilization, through translations made in Toledo and the efforts of adventurers like Adelard of Bath. This transmission, as much or more than the redicovery of ancient learning in Italy, lay the foundations of the Renaissance and the rise of modern science. The story is told by historian Bettany Hughes in her accessible TV history documentary about the Moors in Spain - part of a larger series of excellent history programmes. Readers may like to see this clip about the Alhambra Palace in Granada, one of the wonders of the world, in the second half of which she talks about the legacy of Pythagoras and the geometrical principles that made possible this stunning architectural achievement.

Essence of Beauty

Traditionally, truth, goodness and beauty are properties of all being, of everything that exists, in one degree or another. Truth is being as known - the correspondence and coherence of the idea and the reality. Goodness is being as willed - acting in accordance with the fullness of that which is. What, then, is beauty? Beauty is being as enjoyed, as rejoiced in – that which, when seen, pleases. This is why Etienne Gilson can say that man is a creature “who knows other beings as true, who loves them as good, and who enjoys them as beautiful” (The Unity of Philosophical Experience, p. 255).

The association of beauty with joy is important to reflect upon. What is this joy that beauty gives? It is surely the feeling we get of liberation. “For the experiences which should be produced by that which is really beautiful are wonder, and sweet amazement, and desire, and a pleasant fluttering of the wings of the soul” (Plotinus, Ennead 1:6). Beauty liberates or expands us beyond the boundaries of the self.

At the level of eros, we recognize that there are two main ways to expand the self by uniting it with a desired beauty. The feminine way is to receive the beautiful into ourselves. The masculine way is to project or inject the self into the beautiful. At the spiritual level we do both, and both ways are rooted in God, who both receives himself and gives himself in the three Persons.

In order to recognize something as beautiful, there has already to be some connection with it, some element of recognition, as well as an inclination to affirm if not unite ourselves with it. In that sense, beauty cannot be separated from truth and goodness, and from the faculties of knowledge and will. There is something in us by which we judge the beautiful to be such, and this means that we have the essence of beauty already within ourselves, even though it is also beyond us.

Image: Stars in the Water, by Rosie Caldecott

The I of the Beholder

May is such a lovely month in Oxford, with the blossom coming out everywhere. But many people remain convinced that it is purely subjective - that "beauty is in the eye of the beholder". The architect Christopher Alexander developed an empirical test that points in another direction. He calls it the "Mirror of the Self". Subjects who disagree when asked which of two objects are most “beautiful” will suddenly show a remarkable degree of agreement when asked instead, “Which of these two objects would you prefer to spend eternity with?” or “Which would you prefer to offer to God?” or "Which is the best picture of your whole self?" The reason is, surely, that the question causes us to give the object our full attention, so that we start to respond to it as a whole and with our entire selves. When forced to focus in this way, observers quickly come to agree on which object they prefer, on which is the more wholesome and nourishing to their humanity.

What Alexander has proposed is nothing less than an extension of scientific method in which the self is used as a measuring instrument. This escapes the Cartesian paradigm based on the elimination of the self of the observer. What it points towards is that “science of qualities” prophesied by Goethe, based on the accurate observation of inner feeling in relation to the parts of the world. It is complicated by the fact that in order to judge the objective value in things we have at the same time to refine (that is, educate) the instrument with which we measure, the faculty of discernment itself. His test is also a method by which to teach people to discriminate between what they have been taught (by fashion or ideology or habit) to like, and what truly moves, attracts, and inspires them at a deeper level. These are not always, or even usually, the same thing.

"Our apparent liking for fashions, post-modern images, and modernist shapes and fantasies is an aberration, a whimsical and temporary liking at best, which has no permanence and no lasting value. It is wholeness in the structure that we really like in the long run, and that establishes in us a deep sense of calmness and permanent connection."

Christopher Alexander’s most influential book was A Pattern Language (1977), but the Mirror of the Self test can be found in The Phenomenon of Life, the first of a four-book series called The Nature of Order.

[Image: Garden in Shoreham, by Samuel Palmer, from Wikimedia Commons.]

Help in teaching math

I have come across a number of books and websites that math teachers may find helpful - or, come to that, teachers of other subjects who want to build bridges for their students to the mathematical aspects of their own topics. There are the classics, such as Constance Reid's From Zero to Infinity: What Makes Numbers Interesting, and H.E. Huntley's The Divine Proportion: A Study in Mathematical Beauty. Several others are mentioned in my bibliography, including Michael S. Schneider's and Clifford A. Pickover's. These books are full of exercises, drawings, puzzles and anecdotes. One book that isn't in my Bibliography because I only just heard about it is Alex's Adventures in Numberland, by Alex Bellos, but it looks fun. Another is 50 Mathematical Ideas You Really Need to Know by Tony Crilly - highly recommended by several readers.

Everything connects

In practical terms, what can a university do to encourage the sense that "everything connects", that the individual disciplines concern aspects of a "whole", that the meaning of those disciplines depends on that which transcends them? In many cases it is not possible to redesign the curriculum. Nevertheless, it must be possible to do things within existing structures that will move things gradually in the right direction. We spoke, for example, of the importance of allowing opportunities for students to acquire first-hand experience of nature, whether through gardening or field trips, and also of other cultures

Transmodernism

Are we being modern, postmodern or premodern when we seek to recover and integrate the "lost wisdom" of the ancient world within the contemporary university? In discussing the point among the faculty of the University of St Thomas in Houston after the Earth Day lecture recently, we came up with the term "transmodern". It contains echoes of the "transcendent", and the prefix trans- suggests we are looking "across" the modern world, as well as beyond it, to find the elements of our synthesis. The goal is not to impose a Catholic or theological vision on all the disciplines, but to foster a deeper conversation within and between disciplines against a theological "horizon". That is, theology serves as a placeholder for the truth that lies beyond all of us.

We need in each case to seek within our own discipline for the direction in which truth lies, even if we never lay hold of it entirely. To give up the search or aspiration for truth would be to abdicate our reason. As McIntyre argues in God, Philosophy, Universities, there has to be the "conception of a whole to which each discipline contributes as a part" and towards which it is reaching by its own methods. It is in the search that we will find some convergence with other disciplines, or some opening towards them, some basis for conversation. And it is when we assume that we have attained all important truth within our own field, or alternatively when we have decided that truth is unobtainable, that we become closed off to one another. At that point the university (like the universe) fragments into a myriad shards.

Once again I want to recommend the Pope's lecture to La Sapienza University, before talking next time about some practicalities that came up during our discussion in Houston.

A veiled presence

While in Houston I took the opportunity to visit the Rothko Chapel right across the road from the Byzantine Fresco Chapel Museum, near the University of St Thomas and the Menil Gallery. Both chapels use modern materials to create an appropriate space to serve the art within. The Byzantine frescoes from the Church of Cyprus show Christ Pantokrator and the Blessed Virgin, with angels.They are displayed in a glass chapel at the heart of the structure and evoke a sense of the sacred in the traditional manner of sacred art. The Rothko Chapel is equally effective in a very

Creation and the University

I am currently in Houston to give the Earth Day Lecture at the University of St Thomas. I want to thank the staff, faculty and students, Sister Damien Savino FSE, the John Paul II Forum, and the Basilian fathers, for being so kind and gracious to me. Our discussions around the lecture focused largely on the question of how to implement the educational approach that my book tries to introduce and explore, and I hope to report more on these discussions in the weeks to come. One place where an approach like this is already being tried very successfully is Thomas More College in NH, where David Clayton has developed a "Way of Beauty" programme within the main curriculum of the College - this can be viewed here (make sure to follow the link from the main curriculum page to the Way of Beauty). David has also started an excellent Blog that you will enjoy.

My lecture was partly about the problems caused by specialization. Our knowledge has increased exponentially, yet as knowers we are increasingly fragmented. We seem to know more and more about less and less. But what is still possible for each of us to discover is how everything connects together. We might not know anything except our own field in great detail, but we can put a broken world back together, and that is the task of the new educators.  The role of philosophy is especially important in this, as John Paul II emphasized in Fides et Ratio, and Pope Benedict also explained in his wonderful lecture for La Sapienza University in 2008 about the university, the liberal arts, and the search for truth and wisdom.

The transcript of the Lecture plus ongoing discussion of the book and the visit from John Hittinger's JPII Forum blog can be found here, here, here and here.

Cosmology of the Sacraments

Sandro Magister's excellent website has reproduced one of the Pope's Easter homilies where he talks of the symbolism of the four sacramental elements (which correspond I suppose to the ancient "natural" elements of water, earth, fire and air). The Pope goes on to develop the link between oil and the priesthood. The whole thing is fascinating. Here is an extract:

There are four elements in creation on which the world of sacraments is built: water, bread, wine and olive oil. Water, as the basic element and fundamental condition of all life, is the essential sign of the act in which, through baptism, we become Christians and are born to new life. While water is the vital element everywhere, and thus represents the shared access of all people to rebirth as Christians, the other three elements belong to the culture of the Mediterranean region. In other words, they point towards the concrete historical environment in which Christianity emerged. God acted in a clearly defined place on the earth, he truly made history with men. On the one hand, these three elements are gifts of creation, and on the other, they also indicate the locality of the history of God with us. They are a synthesis between creation and history: gifts of God that always connect us to those parts of the world where God chose to act with us in historical time, where he chose to become one of us.

 Photo of Port Meadow by Rosie Caldecott

Beauty on the Cross

For Christians, the place to look for answers to all the important questions is the Cross of Christ.  In that Cross, read in the light of faith and tradition, we can find the keys to unlock the doors of the world.  And what we see there is not a distant world of Platonic archetypes, but the Archetype of archetypes wedded to the world, and allowing itself to be crushed by the world in order to transform it.

The figure on the Cross, covered in blood and spittle, has been made repulsive by torment. What we see, nevertheless, is the supreme work of art. We see a divine act that takes existing matter, the matter of history and prophecy, and weaves it into a new design, a fulfilment that could not have been expected or predicted but, seen by those who have the eyes and ears for it, is perfect, as though no stroke of the pen, no flick of paint, no note or chord, could be changed without diminishment. We see on the Cross an image that transforms the way we view the world. The Passion of Christ the Logos changes the world and remakes it, creating something new of it, bringing life out of death.

This is an extract from Beauty for Truth's Sake.  
The image is borrowed from Vultus Christi.

Astronomy and Music

Two very enjoyable TV series are currently unrolling on the BBC, one on Astronomy and one on Music (two of the seven Liberal Arts, the first being traditionally regarded as the application of Geometry and the second of Arithmetic). They can be watched online, at least in the UK, and the associated websites provide excellent resources for educators. If you can't access them through the BBC, they are available as segments on YouTube. The Wonders of the Solar System by Brian Cox is full of spectacular scenery and special effects, and suitable for all ages. If this doesn't turn your children into astronomers, nothing will! Episode 2 was all about order out of chaos, the "beauty and symmetry that lies at the heart of the universe", and featured spectacular shots of Saturn's ring system. Sacred Music presented by Simon Russell Beale is glorious in a different way. After a recent episode I am a fan of Anton Bruckner, a devout Catholic contemporary of the better-known Brahms. This is the second series already, but presumably the whole thing is available on DVD. Do take advantage of the availability of these programmes if you can. For a better view of the Saturn picture above, go here.

How the World Is Made?

One of the topics in my book is so-called "sacred geometry". I didn't do it justice, of course. It need a lot more, and better, illustrations, but that wasn't an option at the time. So instead, as readers will know, I recommend the work of educator Michael Schneider. He seems to strike the right balance of enthusiasm and sanity, and his book is full of nice pictures and geometical constructions. Unfortunately, sacred geometry and number along with numerology and astrology have become a playground of the New Age. But while this should certainly engender caution, it should not put orthodox Christians off completely. These symbolic systems are part of the great Classical and Medieval civilization and were employed in the writing of Scripture and the building of the great cathedrals. We need to understand them better. The two great modern masters of the subject are Keith Critchlow (who teaches at the Prince's School of Traditional Arts) and John Michell. Shortly before he died, Michell completed How the World is Made, which is recommended by Michael Schneider. The book is illustrated by Michell with full colour images like these, and is published by Inner Traditions in the US and Thames and Hudson in the UK. I hope to review it in Second Spring, where I will try to say why I think the subject is important, even though I have to attach a strong warning, because it is mixed together (as you will see in Michell's book) with a lot of eccentricity and downright anti-Catholic prejudice.

Homeschooling

This blog has become a bit of a jumble - partly because the topic of education is so broad it touches on everything.  I have added a list of relevant links and postings on the left under 'Schooling etc.' There you will find some material on Homeschooling, Unschooling and Primary Schools. I am in touch with a number of small groups of homeschoolers around the U.S. who are trying to develop novel and interesting approaches. Charlotte Osterman's group is working on the question of how to use geometry to foster "poetic knowledge" in children - see the "Holy Geometry Project" under Ideas of what to use with kids in the left-hand column. Meanwhile Katie Kimball and others are working on the idea of Kitchen Stewardship - i.e. looking practically at ways to "balance God's gifts of time, health, earth and money" (on a small budget). I am also speaking with groups thinking radically about the curriculum in primary schools, and how those schools might work more closely with parents, who are - the Church teaches - the first educators of their children, whether they like it or not. And it seems to me this whole discussion must be connected also with attempts to apply John Paul II's Theology of the Body to education, both at home and in school. This offers a holistic approach to building a culture of life on the basis of a new and profound understanding of human nature. More on that another time.

Song of the Angels

“'The angels sing praise to the Creator, and in doing so, they, with Holy Wisdom, bind and heal the created order.' ...It is this song of the angels that we should listen out for, now that the coming of Christ has reunited humanity with the celestial liturgy that Adam heard before the fall."

In this way the Telegraph columnist, Christopher Howse, concludes his very fine piece about the Archbishop of Canterbury's Lent book this year, Lucy Winkett's Our Sound is Our Wound. The book is not all about the Angels (please read the full description), but the remark caught my eye since it connects so directly with the themes of Beauty for Truth's Sake, and with earlier postings on this site, such as this one on Sacred Music, this on the Music of Creation in Tolkien, and this on the Sphere of the Angels.

If this Lent Book is as good as last year's - Timothy Radcliffe's brilliant Why Go to Church? - it will be well worth reading in the weeks ahead. And it certainly sounds so from Mr Howse's description.

Primary education

The question of reforming Catholic education at every level should not be reduced to an ideological battle between Left and Right. It is not a matter of adding some more or different religious instruction or imposing a more rigorous moral code within the school. The defects of Catholic education run deeper than that. We need more effective religious instruction, of course, but we also need holistic educational reform across the board. In our quest for wholeness we should study and learn from what has been done and suggested by the progressive education movement, both here and within other countries and other religious traditions. Whatever we decide to do, it will be governed by our anthropology - what we believe about the human person, and about the child. So what might primary education look like, if shaped by an adequate anthropology? Read on... 


Photo by Rose-Marie Caldecott

Simplexity

The world as a whole is complex, but it is also a unity. It is “simplex”, founded on simple principles. Poets, painters, scientists and mathematicians are all searching for simplexity in their own way. Aesthetic pleasure is very largely the delight we feel in seeing order, meaning and relationship – the beauty that Coleridge called unity in variety. But it has to be an order unforced, seemingly spontaneous, rather than brutally imposed upon the material. The world as a whole is beautiful in just this sense.

Modern science describes the world as to a large extent “self-organizing”, because sophisticated and unpredictable patterns are now thought to emerge spontaneously from the indefinite repetition of simple algorithms. Furthermore they do so without violating the law of entropy. Evolution is then held to account for the refinement of those patterns through the process of selection. None of this - if true - is incompatible with theism (although it makes Intelligent Design look a bit foolish). The Christian God is the principle of existence itself, the creator without whom there would be nothing either simple or complex to admire. (For the compatibility of theistic faith with an up-to-date cosmology see Stephen Barr’s Modern Physics and Ancient Faith, reviewed here.)  If with complexity emerges unpredictability, this merely highlights the possibility of a higher-level order we call providence, governing coincidence and chance. God is the principle of order, and thus the ever-present source of unity as well as diversity.

If science interests you, take this awesome trip through the known universe. (The image above, by the way, is a fractal from Wikimedia Commons. For more on fractals see this clip on fractals in Africa.)

Music of Creation in Tolkien

“There's a divinity that shapes our ends, Rough-hew them how we will." (Hamlet V.II.)

Both C.S. Lewis and J.R.R. Tolkien saw the creation of the world as taking place in some way through music. Readers of the Narniad will recall Aslan singing Narnia into being in The Magician’s Nephew. As for Tolkien, he composed a whole “Elvish Book of Genesis” in the form of the Ainulindale, the opening section of the posthumously published Silmarillion, describing the creation of the world by the One God (Illuvatar). In that mythological account – which he believed to be compatible with the creation story in Genesis – God first proposes the world as a musical theme, which he gives to the Angels (the Ainur) to develop and express, much as a composer might give the score to an orchestra – although a jazz analogy might be more appropriate, given the amount of improvisation the players are allowed. One of the Angels, Melkor (Lucifer), tries to force the music in another direction, but his rebellious dissonance is finally integrated within the whole design, much as in the real world evil is at first tolerated and eventually becomes the occasion for a greater good that could not have been anticipated. But this is not yet the creation proper, only the composition of the music “which is over all”. Now God turns the music into light, and shows the Angels the world in a vision in the Void. But even this is not yet the creation. That takes place when music and light become Being through the Word of Iluvatar, “Ea! Let these things be!” God sends into the Void the Flame Imperishable (Holy Spirit) which forms the heart of the world and sustains it in existence.

As I remark in my book The Power of the Ring, drawing on A.K. Coomaraswamy, Fire or “Agni” (in Latin Ignis) is one of the names of God in the ancient liturgical hymns known as the Rg Veda - a spiritual Sun whose rays are the Devas or Angelic Powers (“And sundry sang, they brought to mind the Great Chant, whereby they made the Sun to shine”). Agni is the giver of the Spirit (Breath), a “formal light that is the cause of the being and becoming of all things”. Coomaraswamy sees a connection here with the teachings of Heraclitus. He also points out a linguistic “equivalence of life, light, and sound” in the similar roots of the words for “to shine” and “to sound” – a connection present even in English when we speak of “bright” ideas and “brilliant” sayings.

Tolkien’s mythological construction has deep roots – less, I suspect, from the study of Indian religion than from the implications of philology (he being a seer who, one person rightly said, had gone “inside language”). Also he was theologically better informed than you might think, since one of the great theologians of our age, Louis Bouyer, was a close friend and admirer, according to important research by Michael Devaux. It seems that for Tolkien, the creation is envisaged in three stages - music, light, and being - corresponding in some way to the Father, the Son, and the Spirit. Yet the whole Trinity is involved in every stage, and the Logos or Word, who is the Second Person of the Holy Trinity, can justly be called the order, harmony and meaning of the cosmos, revealed to the Angels but only expressed in creation through the Breath of God.

Illustration shows the 2004 edition illustrated by Ted Nasmith.

Sacred Music

In Beauty for Truth's Sake I introduce the subject of music but for those who wish to go more deeply into it I recommend Jeremy Begbie's Resounding Truth (2007). You may also like to read an article in First Things by David P. Goldman, called "Sacred Music, Sacred Time". Goldman argues that there are objective criteria for achieving a musical form that raises our minds and hearts towards God:

Whether it is Bach or Mozart that we hear in church, we have a sense in either case of what Gloria Dei, the glory of God, means. The mystery of infinite beauty is there and enables us to experience the presence of God more truly and vividly than in many sermons,” wrote Benedict XVI in his book The Spirit of the Liturgy (2000). Simpler music can foster camaraderie among worshipers and even communal joy. Authentically sacred music does more: It inspires awe, even fear.

Catholic Church Architecture

I have just been reviewing the most gorgeous book for the next issue of Second Spring journal (an issue on "theology of the body" that will be out in the spring). It is by Denis McNamara of the Liturgical Institute, and is called Catholic Church Architecture and the Spirit of the Liturgy. Though it looks like a coffee-table book, it is a feast for the mind and heart as well as the eyes, and completely complementary not only to David Clayton's work, mentioned elsewhere on this site, but to the many brilliant books of Scott Hahn (who wrote the Foreword) and the "new wave" of liturgical writers inspired by Ratzinger's The Spirit of the Liturgy to recover symbolism, cosmology, and the principles of sacred tradition.

The key principle is this: “Architecture is the built form of ideas, and church architecture is the built form of theology.” “As go the ideas, so goes the architecture.” No wonder things went off the rails in the 1960s. “We call things beautiful when they reveal their ontological ‘secret’, the invisible spiritual reality of their being as objects of understanding.” What makes this book much more than an exhortation, or a manifesto, or a philosophical treatise, is the precise and careful thinking that has gone into the rules of beauty, which follow in large part from this definition. We may “like” a church that reminds us of a comfy living room or Swiss chalet or an aircraft hanger, but that doesn’t make it “beautiful”; it doesn’t make it look like a “real church”. Thanks to this book, future generations are more likely to have real churches in which to worship.

If this subject interests you, you'll probably also enjoy Jean Hani's The Symbolism of the Christian Temple and Stephen J. Schloeder's Architecture in Communion.

The Mystery of One

Yesterday was the first day of a new decade. The image of two overlapping circles and ten triangles is a geometrical way of representing the interplay between numbers - Ten emerging from One via Two. Thus One is the first number in the Decad. Or is it? In p. 56 of the book I mention that, according to the Pythagorean tradition, One is not a number but the "number beyond number". Saint Maximus the Confessor inherits and explains this tradition, according to this passage by Hans Urs von Balthasar, taken from his book Cosmic Liturgy (pp. 113-14):