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.

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".