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
Introduction to the book, if it is hard to speak of one simple dividing line between art and science any more, the underlying problem has not gone away. The fragmentation of the disciplines has continued, and we have lost a sense of how of these each fits into the larger cultural whole. This problem afflicts even liberal arts colleges in the United States, and connects with deeper problems that need a spiritual and not just a bureaucratic response. In an article in The New Atlantis called "Human Dignity and Higher Education", Peter Augustine Lawlor writes:

It is no secret that most of our colleges that give lip service to “liberal education” do not deliver it, and what they do teach exaggerates — not moderates — the undignified confusion of our time. They certainly do not give students the impression that there is much — if any — moral or humanistic content (as opposed to method, like critical thinking or analytical reasoning) that they need to know. And so they do not give students the impression that their education is about who they are or what they are supposed to do. Moreover, the permissive and indulgent atmosphere of our colleges extends adolescence far more than it serves as a bridge between childhood and adulthood. Our colleges inculcate habits that are positively antagonistic to the formation of moral virtue, and they often undermine the good habits and confident beliefs that students sometimes bring with them to college in the first place.

 Lawlor praises some of the smaller liberal arts colleges in the US for offering a real education, but he points out that secular institutions tend to be victims of the culture around them - all the more important, then, when choosing a college, to go for one that is explicitly religious in its foundation and ethos (one like Thomas More College, perhaps, shown in the picture). Luigi Giussani's book The Risk of Education: Discovering Our Ultimate Destiny (Crossroad, 2001, reviewed here by Joel Garver) makes a refreshing read on this subject. "Never before," he writes, "has society... had so many tyrannical tools to invade our consciousness. Today, more than ever, society is the sovereign educator or perhaps more correctly, mis-educator. In this climate, the educational crisis appears first as a lack of awareness in which teachers the,selves become unknowing promoters of society's flaws." Giussani goes on (p. 74):

It also appears in a lifeless approach to teaching, in which teachers lack the energy to wage war against a pervasive negativity, choosing traditional, formalistic positions instead of renewing the eternal redeeming Word in the face of the new struggle.

Does a religious commitment belie the term "liberal" by contricting academic freedom? Not necessarily. It all depends on the spirit and the people involved. Faith should be an act that deepens our freedom to love, not one that inculcates fear and suspicion. For Giussani, education is a calling that appeals to all the dimensions of the human spirit, and that is why love is always the key. "To love is first of all a way of conceiving oneself as 'sharing one's life', thus as being ontologically linked to everything" (p. 79). God, the origin of being, is precisely this sharing of life - the ultimate and inexhaustible meaning of life, the world, and history.