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.

Fractals

Fractals are infinitely complex and beautiful patterns produced through the repetition of a simple formula or shape, patterns which often appear rough or chaotic and which can be found everywhere in nature (the surface of the sea, the edge of a cloud, the dancing flames in a wood fire). I have written about them briefly before.

What appeals to us in such patterns, perhaps, is the combination of simplicity and complexity. They allow our minds scope to expand, and our imaginations to take off in the direction of the infinite, but at the same time to rest in a unity. It is similar to the reason we love science. Scientists are seeking the simple secret at the heart of the complex - the formula or combination of universal laws that governs all of reality and explains why it works or appears the way it does.

Something similar is happening in art, when the artist seeks unity of concept or meaning or mood in a complex scene or sight or landscape.

Not all beauty is produced by these "recursive algorithms" or the repetition of self-similarity at different scales of magnitude. Sometimes a pattern is just there in the thing and does not repeat itself. But beauty always has something to do with order, which means the finding of a unity of form in something complex - a balance between the Many and the One. The finding of unity gives us joy (which is why we call it beautiful) because it enables us to recognise the Self in the Other, outside ourselves. It causes us to expand our boundaries to include the other thing as grasped and understood, or at least as situated in a relationship to us. Fractal patterns are a version of that experience. We sense the unity, but because it is expressing itself as never-ending complexity, it never gets boring.

Therefore all beauty, including fractal beauty, reminds us of God, who is both infinitely simple (in himself, as pure love) and yet infinitely complex (in what he contains and creates).

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.

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.