Connected by Touch

Fairy tales are the fashionable thing in Hollywood and on TV. Every studio seems to be reinventing the classic tales – mostly with dire results. The successful new Tim Kring TV series Touch is much more original. Like the delightful film August Rush (which is based on the idea that people are mystically connected through music), Touch tells us that the world is built on numbers. The credit sequence alone is a work of art, showing a kaleidoscope of images drawn from the natural world and human society with diagrams of symbolic geometry superimposed. The story is built around a father (played by Keifer Sutherland) and his "autistic" son Jake, who won't speak or allow anyone to touch him. But the son has a gift with numbers. Naturally, in order to heighten the excitement, he is supposed to be "the next step in human evolution", and his gift enables him to predict the future, or "see" possible futures in the patterns of numbers he sees all around him. Once the father realizes his son is trying to communicate with him entirely through numbers, he also learns that the boy is detecting examples of human suffering and potentialities for disaster, which by following the clues his son gives him he can begin to avert. He becomes an "invisible knight", doing good to people without their realizing it. Each episode is constructed around several plot threads involving characters in different continents whose stories interweave and are all resolved in the final moments of the episode. Quite often they involve mobile phones or the internet – maybe the first time these aspects of modernity have been fully integrated into a fairy tale.

Apart from its entertainment value, is there anything educational going on here? As I said in Beauty for Truth's Sake, the idea that the world is built of numbers, that numbers are in a sense "God's thoughts", goes back a long way (at least to Pythagoras) and very deep (the foundations of both art and science). The English writer John Michell once said, "The mathematical rules of the universe are visible to men in the form of beauty." It is this intuition, which I believe is valid, that Touch is trying to evoke (or the cynical might say is trying to exploit), along with the sense of providence, meaningful coincidence, and the natural moral order (though without explicit mention of God). I called it a fairy tale, and like all true fairy tales (according to Tolkien) the final resolution takes place through eucatastrophe. For all I know the series may flounder and lose its way later on, but it is off to a great start, and if it sends people off to look into the mysteries of the Golden Ratio or Fibonacci series, or just to explore the wonders of mathematics with writers like Clifford A. Pickover (see The Loom of God), or Michael S. Schneider (see his Constructing the Universe, that in itself is a good thing.

There is a further humane message in the series. It is that human beings are all connected, that we are all in relationship, and that we are meant to cooperate and work together, to help each other without seeking reward. Mathematics, beauty, and love are all connected. Even in prime time.

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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.

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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.

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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

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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.]

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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.)

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The Pope on Beauty

The "way of beauty" is the theme of the Pope's recent address to artists on 21 November 2009 in the Sistine Chapel. In it he writes - quoting both Hans urs von Balthasar and Simone Weil, who are influences on the book on which this blog is based (see left), and building on the Letter to Artists of Pope John Paul II - as follows: "Beauty, whether that of the natural universe or that expressed in art, precisely because it opens up and broadens the horizons of human awareness, pointing us beyond ourselves, bringing us face to face with the abyss of Infinity, can become a path towards the transcendent, towards the ultimate Mystery, towards God.... In this regard, one may speak of a 'via pulchritudinis,' a path of beauty which is at the same time an artistic and aesthetic journey, a journey of faith, of theological enquiry.... Simone Weil wrote in this regard: 'In all that awakens within us the pure and authentic sentiment of beauty, there, truly, is the presence of God. There is a kind of incarnation of God in the world, of which beauty is the sign. Beauty is the experimental proof that incarnation is possible. For this reason all art of the first order is, by its nature, religious.'"

The Pope has also recently spoken very eloquently of the beauty of the medieval cathedrals, one of which, the Cathedral of Orvieto, is featured in the photograph. There he speaks of "a much broader form of reason, in which the heart and reason come together. This is the point. This, I think, is in some way the proof of the truth of Christianity: the heart and reason come together, beauty and truth touch. And to the extent that we are able to live in the beauty of truth, so much more will faith again be able to be creative, in our own time as well, and to express itself in a convincing artistic form."

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The beauty of mathematics

For many of us, “mathematics” and “beauty” sit oddly together. We may remember math as boring or even frightening, but hardly beautiful. Yet math is the key to science, and science dominates our age. And there is another way to look at it.

The single most compelling reason to explore the world of mathematics is that it is beautiful, and pondering its intriguing ideas is great fun…. To study the deep truth of number relationships feeds the spirit as surely as any of the other great human activities of art, music, or literature. -- Calvin Clawson

This quotation is taken from p. 239 of a wonderful book called A Passion for Mathematics: Numbers, Puzzles, Madness, Religion, and the Quest for Reality, by Clifford A. Pickover. It is full of games and quotes and ideas that parents and teachers will find useful to get kids of all ages and all backgrounds interested and involved with maths and geometry. Pickover himself believes that “mathematics is the loom upon which God weaves the fabric of the universe” (p. 53).

Looking back on the maths classes I sat through as a kid, I can't help wishing I had been taught the subject not as a collection of seemingly arbitrary rules and procedures but (1) historically (starting with Pythagoras), (2) aesthetically (in relation to music, painting, architecture), and (3) symbolically (with a view to qualities, meanings, analogies inherent in numbers and shapes) - not to mention (4) playfully.

The religious and secular use of numbers are related, as I tried to show in The Seven Sacraments (Crossroad) as well as in Beauty for Truth’s Sake. The numbers particularly prominent in Christian tradition are 1, 2, 3, 4, 7 10 and 12. One is the source of all other numbers, 2 is the beginning of multiplicity, there are three divine Persons and three theological virtues, four cardinal virtues and four Gospels, seven sacraments as well as seven days of creation, ten commandments, twelve apostles and twelve tribes. And all these numbers are interrelated: 7 is 3 plus 4, 10 is 3 plus 7, 12 is 3 times 4. So in a way the fundamental structural numbers only go as high as 4, and all the others are made up from these. That takes us back to the sacred Tetraktys of the Pythagoreans, whose influence on the Christian tradition has been underestimated.

There is a fascinating article by Karen Kilby called MATHEMATICS, BEAUTY AND THEOLOGY that I recommend to your attention if the subject interests you. (Just follow the link.) And I also want to mention "The Curriculum of Beauty" by David H. Albert and Joyce Reed in Life Learning magazine. Albert writes:

Our children have within themselves, or so I am led to believe by my experience of them, an inner yearning for the beautiful, a potential wonderment and a delicious longing and love and trembling waiting to be empowered on its quest. This yearning is not likely to be fulfilled in a high school hallway or on the shopping mall checkout line. So what if we were to set as our task – as parents and as educators – acquainting our children with the beautiful without and the cultivation of the beautiful – the yearning – within? How might we go about our homeschooling lives differently if we were to conceive of what we are doing as primarily an aesthetic task?

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