Intro      Writing       Les mots et les noms       The unspeakable Other       Painting       Mathematics       The Thing Itself       Bibliography

Mathematics

Both language and painting can ultimately be said to fail in representing the thing itself because they are always already a part of our culture, and indissociable from the 'busy automatically-connecting mind' (SL, 199). They are constructing an order out of chaos, not representing one. Nevertheless, the text suggests that an inherent order might exist: 'Human cognition has been called 'order from noise': or it may be, contrariwise, the patterning of the world with a constructed map, crystallised in the genes, repeating laws already informing the growing mind.' (SL, 287) Marcus, looking at an ant colony on a youth camp, considers the same question: 'He did not know whether he was watching seething chaos or incomprehensible order.' (SL, 233) On return from the camp, he has what is later called an 'ant-vision of God' (SL, 289):

Everything could be recalled, envisaged, as repeated ovals... White ants' pupae piled in layers, sheep's rumps trotting, the weaving glossy segments of Ruth's plait, thorax and abdomen, white faces turned up to Gideon's firelit brilliance... There was a God, he suddenly knew, a God of overflowing order and intricacy, ovals and ants... a God of fine bristles in dark corridors, of segments and interlocking threads and forms, of force taking shape, innumerable shapes. (SL, 239)

The recurrent ovals are related not to perception, a heightened awareness of ovals, but to a God of order and shapes. Here, once more, is posited the possibility of a language established by divine right, but this time the language is mathematical: geometry. Rather than a chaos to be carved up into sections by human cognition, we find an intrinsic 'overflowing order'. The reliability of geometry as a language was implied earlier with reference to Wittgenstein: 'He spoke of a mathematics of colour, Wittgenstein, a Farbmathematik: one knew saturated red or yellow, once experienced, as one knew the nature of a circle or the square on the hypotenuse.' (SL, 96) The comparison appeals to the authority of geometry: a circle, it assumes, is in no way open to interpretation, in the way two people might argue about the exact shade meant by the word 'turquoise'.

The chapter, 'A Tree, Of Many, One' describes another vision in more detail. Marcus rests under an elm tree in a field, trying to stave off an asthma attack and keep at bay the terrifying mathematical visions that habitually come in its wake. To keep calm, he considers the tree:

He looked up at the crown again, thinking initially of it as amorphose ... he began to see an outer geometry.
Carefully contemplated, the growth of leaves from twigs, twigs from limbs, limbs from bole, showed to a geometric eye a persisting regularity in all this gnarled idiosyncrasy. The leaves grew out of the twigs in alternate ranks, at 180° from each other, and the twigs too could be mapped — given broken ends, scars, variations in girth, blemishes — as growing out of the branches on a regular spiral at the same angle. Marcus stared and mapped, stared and mapped, learning the tree. He took out a notebook and made a sketch of the principle of the spiral ... Geometry he saw. (SL, 291-2)

Unlike any statement I might make about the tree, this geometry is intrinsic to it: the leaves do grow in alternate ranks, at 180°, and this can be checked and measured on the tree; the twigs do grow in a spiral, and this too can be verified. Although it is shown 'to a geometric eye' rather than being instantly observable, it is no less reliable. The geometry is thus intrinsic to the referent, the elm tree under which Marcus rests. It is not, however, identical to it: this particular instance of elm tree has twigs with 'broken ends, scars, variations in girth, blemishes'. Moreover, the 'principle of the spiral' can also be applied to other elm trees, thus making it a signified. Unlike language, where the signified could not exist without the signifier, the geometry of the tree does not require Marcus's sketch or a mathematical formula; it is pre-existent. Unlike language, the signified — the geometric principle — can be exactly represented; no matter how complex the formula required, it is possible for it to be written down.

Mathematical language thus seems to come the closest to representing the thing itself, and the title of the chapter, 'A Tree, of Many, One', taken from the fourth stanza of Wordsworth's 'Immortality' Ode, supports this. The ode sets up an opposition between Edenic descriptions of a lost, childhood paradise and adult regret at its loss, offering the child's acquisition of custom and culture as the intermediary stage. The tree and the field 'speak of something that is gone' (Ode, 54), and are associated with 'the visionary gleam' (Ode, 57) and 'the glory and the dream' (Ode, 58): they become symbols for the idealisation of the presymbolic state. In Byatt's chapter, 'A Tree, Of Many, One', the tree is again a vision, but this time of the intrinsic geometrical order of things. By implication, this geometric order is the presymbolic ideal state.

The title also associates the tree with truth and representation. When Frederica and Raphael are discussing the meaning of the banyan tree in Raphael's novel, Raphael says it symbolises

'Error because it is a multiple tree — truth is One, like the Tree of Life...'
'In the Mallarmé lecture you said that we can't reproduce — le bois intrinsèque et dense des arbres.' [said Frederica] (SL, 257).

There have been many trees mentioned in this essay, most of which also appear in the novel: the linguistic example of the signifier tree as opposed to the signified, 'a tree', which appears repeatedly in linguistic textbooks, including Saussure's Course in General Linguistics; my referent tree through the window, whose branches now rustle in gusting rain, and which remains graspable for me because I am here, now, and elusive to you, because it is ineluctably outside these words; Mallarme's 'bois intrinsèque et dense des arbres' [1] (SL, 257), forever irreproducible now that words have unfitted themselves from objects; the chestnut tree that provoked in Sartre 'a shock of another kind' (SL, 201) to that suffered when painters ceased to imitate apples; the olive trees that may stand for themselves but will always also mean 'the Mount of Olives, the Garden of Gethsemane' (SL, 8); the cypresses that will always mean death; and the tree in the field. The tree that is One, truth, is the vision of geometrical order.

1 'dense, intrinsic wood of the trees'