One of the ideas mentioned in passing in the post about the Four Quartets is the Unity of Opposites. This refers to a situation where two things often thought of as opposite are necessary for each other to exist, and so are mutually dependent. As noted in that post, one of the epigraphs to the Four Quartets is Heraclitus’s observation that
the way upwards and the way downwards is one and the same.
Note the verb is ‘is’, not ‘are’ – there is one way, and it runs in both directions. The notion of upwards doesn’t make sense without downwards, and vice versa.
Earthsea
I first encountered this idea (without understanding it as such) at about the age of 9 or 10 in the epigraph to Ursula Le Guin‘s A Wizard of Earthsea:
Only in silence the word,
– The Creation of Éa
only in dark the light,
only in dying life:
bright the hawk’s flight
on the empty sky.
(The Creation of Éa is a song of Earthsea, Le Guin’s fictional archipelago.)
At various points in A Wizard of Earthsea one or another of the characters refers to the unity of opposites, for example by saying ‘to light a candle is to cast a shadow‘ and ‘For a word to be spoken, there must be silence. Before, and after.‘
Silence and speech, dark and light, death and life: all are pairs of opposites that co-constitute each other. Le Guin explores this idea throughout all the Books of Earthsea, perhaps most of all the necessity of death for life to have meaning. In the third book of the series, The Farthest Shore, the character Sparrowhawk, greatest mage of his day, says ‘To refuse death is to refuse life‘ and later ‘Only what is mortal bears life … Only in death is there rebirth. The Balance is not a stillness. It is a movement – an eternal becoming.‘
A mathematical analogy
Consider a line extended indefinitely far in both directions, and bend the ends of this line into a circle so that the extremities almost but don’t quite touch each other, as illustrated below:
The circle is ‘missing’ the point right at the very top, because the two ends of the line never quite meet no matter how far out we go in both directions. The circle can be completed by adding a single point, called the point at infinity and denoted ∞ without a + or – prefix.
Adding the point at infinity can be interpreted as unifying the opposites, and the point itself represents their unity.
(As an aside for mathematicians: this is an example of the Alexandroff one-point compactification, and contrasts with the two-point compactification of the real line in which two points at infinity are added, +∞ and -∞, one at each end of the line. My Grandad, an academic mathematician, always used to note that the use of +∞ is to distinguish from the ∞ involved in the one-point compactification and so the + sign is not redundant. The one-point compactification generalises to the stereographic projection between the complex plane and the Riemann sphere, and in fact the diagram above can be regarded as a cross-section through the stereographic projection.)
A deeper metaphor
The Matter with Things is the magnum opus of Iain McGilchrist. There is much more to be said about this book (and his earlier work The Master and his Emissary) both of which are truly magnificent, but at the time of writing this post I haven’t quite finished the first of the two volumes in which it is published and so this will have to wait.
As a brief aside in chapter 15, McGilchrist expresses the mathematical analogy above, and then adds a third dimension by recasting the circle as a spiral:
Although paradox can fruitfully be thought of as two ends of a dipole, another way of expressing the coming together of opposites is not in terms of a straight line, but of a curve, prolonging each end until one comes ‘full circle’. However, it may be not so much a case of coming full circle as ‘full spiral’, so to speak. Not that when you go far enough in one direction you arrive precisely where you started from, but that you arrive at a position superimposed on that from which you started, at the next turn of the spiral.
The Matter with Things, Chapter 15 (p. 607)
McGilchrist goes on to quote from Eliot’s Little Gidding:
We shall not cease from exploration
Little Gidding: V
And the end of all our exploring
Will be to arrive where we started
And know the place for the first time.
and notes in relation to this quotation ‘this is why Eliot says, truly, that over a lifetime one keeps arriving at a fresh understanding of what seem to be the same imponderables, the same words, the same set of circumstances, images or ideas‘.
Let us return now to the epigraph from A Wizard of Earthsea quoted at the start of this post, and its final lines ‘Bright the hawk’s flight / on the empty sky.‘
As with all good poetry this can be interpreted in many different ways: before reading the book as making the most of life in the sure and certain foreknowledge of death; after reading it as a reference to the character Sparrowhawk; even, perhaps as alluding to emptiness and the brightness even a tentative and partial understanding of this can bring to life.
In the light of McGilchrist’s spiral metaphor, it’s hard not to think of an additional layer to this, with the hawk’s flight moving from the two-dimensional opposites in the earlier lines of the epigraph (only in silence the word) into the third dimension of the spiral. Thus I have arrived back at the place where I started from, nearly 40 years later at the time of writing this post, but now from a higher vantage point; and if not quite knowing the place fully, then at least understanding it better.