Friday, January 29, 2010


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.)

Tuesday, January 19, 2010

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 Secret Fire (or if you are in America, The Power of the Ring – that change of title was not my idea!), 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.

Sunday, January 17, 2010

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.

The question, of course, is what makes it possible for music to convey a sense of the sacred in the way that Benedict avers. And the answer should be sought first in our perception of time. Because we are mortal, and because all religion responds to mortality, our intimations of the sacred arise from our experience of the tension between the mortal existence of humankind and the eternal life of God. In revealed religion, God’s time stands in contrast to the earthly time of days and years and the corporeal time of pulse and respiration. A creator God who stands outside nature also stands outside time itself. Eternity is incommensurate with natural time. God made the world ex nihilo before time existed and he will bring it to an end....
Music unfolds in time. The rhythms of the music of all cultures arise from the natural rhythms of respiration and pulse. Unique to the tonal music of the West, however, is its capacity to create a perception of time on two distinct levels, that is, the natural time of systole and diastole, and the plastic time of tonal events. The coincidence or conflict of durational and tonal rhythm, that is, between metronome time and the pace of tonal motion, gives composers the tools to depict higher orders of time. That is what makes possible the sacred in music, for our perception of the sacred involves a transformation in our perception of time....
Music cannot represent eternity—no human artifice can—but it can direct the mind’s ear to the border line at which eternity breaks into temporality.... Tonality—the system in which the horizontal unfolding of melody in time integrates with vertical consonance—has the unique capacity to generate a sense of the future. Once musicians discovered how to link musical rhythm to the resolution of dissonance into consonance, Western music acquired a teleology. Every tonal work has a goal, the resolution of tonal tension in the return to the tonic by way of a final cadence from the dominant....
Western composers abandoned teleology in music at the same time they turned away from Christianity. Tonality enabled music to create deep expectations about the future. With the abandonment of tonality, listeners lost their map of the musical future, and found themselves trapped in a sort of Blind Man’s Bluff of a perpetual musical present. Churchgoers shunned twentieth-century composers as resolutely as they had embraced Bach or Mozart. As in other venues, churchgoers turned to popular music, the last bastion of the old tonality.
 I wonder if tonality, "the system in which the horizontal unfolding of melody in time integrates with vertical consonance", has a particular affinity with Gothic architecture, which perhaps does something similar in space.

Just a thought.

Tuesday, January 5, 2010

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.

Friday, January 1, 2010

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):

Thus the unity that lies beyond the created world is the ultimate principle of every number: "God is the creator and the inventor even of number." Therefore "every number participates in unity - that is, in God.... Even if you begin counting with two, you at least take one two as your starting point." Thus it is true, on the one hand, that the transcendental unity "cannot be added, in a natural way, to another, as can the number one"; it is not affected by number at all.... On the other hand, this unity is so immanent in every number that one must speak, with Pseudo-Dionysius, of a "multiplication of God".
Of course, this is a misleading expression - but so is any talk of "number" in relation to God, even "Trinity" if this is understood as "numbering" God in some way. (As Timothy McDermott puts it on p. 70 of his "Concise Translation" of St Thomas's Summa, "In God the three is not counted by the ones. Number that counts quantity arises from division of a continuum, exists only in material things, and can be applied to God only metaphorically".) Balthasar goes on:

At this point the whole theory of unity returns to the simple scheme of an analogy of being between God and the world: to the absolute transcendence of God and his immanence in created being. God is, on the one hand, "beyond unity"; on the other hand "unity, as the cause of numbers, includes all numbers in itself in a unitary way, just as the centre or point contains the straight lines of the circle."
Thus as Balthasar concludes, we cannot "grasp the Trinity conceptually", because number is only a "sign". Maximus says the numerical unit "does not express a reality but points in a direction" (p. 113). In a sense, I think, one can say this of all the forms and realities of the world, which indicate God not by expressing him but by pointing towards him.

The human being is said in Genesis to be made in the image and likeness of God. The unity of anything, which makes it identically itself, its oneness, is a mark of its participation in being, the mark of the Creator. But the first and foremost way in which we bear God’s likeness is in not simply in being, but in being “I”. Not only are we “one” in ourselves, but we are the centre of our world in the something of the same way that God is the centre of all worlds. Each of us looks out at such a world, and everything appears to revolve around us. I am a consciousness, and that means that I can say “I”. This is a resemblance to the Creator, who is the One around whom everything revolves. For those who have eyes to see, my very selfhood is a proof of God.

In our notation, the resemblance between the first of numbers and the symbol for the self are virtually identical: “I” = “1”. It is a vertical stroke, which describes the creation, the making of something other than God yet dependent on God. Each depicts an axis or radius linking myself, or the thing in question, to its transcendent Source.

See also earlier posts "The Beauty of Mathematics" and "Sacred Geometry".