Chapter 4

VERSE SPACE

In previous chapters, we proposed that resonance phenomena in the brain underlie our ability to enjoy works of art. In Chapter 2, we attempted to demonstrate that in poetic works of art, the imagistic space is structured into strict symmetrical series, where the symmetry connecting these series can be either symmetry of repetition or inversion symmetry. More complex forms of symmetry than those we have seen may exist in the imagistic space of verse.

The “resonance” hypothesis of art perception explains the presence of symmetrical relationships. However, resonance cannot exist outside symmetrical relationships. It follows that if a work of art aims to create a resonant state, then its artistic space's orderliness (symmetrization) must achieve a high degree.

It should be noted that many, if not consciously recognized, at least sensed this internal orderliness of artistic space.

Go, seek another slave!
But over poets your power is weak,
That he should criminally mix his sacred rights
With mud because of you
What makes his words touch hearts?
Is it thanks to just a loud phrase?
His soul's harmony with the world –
That is the essence of this secret power.
When nature spins life's thread
And time's spindle turns,
It cares not whether the thread runs smooth
Or the fiber has snags.
Who gives, while straightening the spinning wheel,
Both momentum and smoothness to the wheel?
Who brings into the wretched noise of discord
The harmony and beauty of a chord?
Who aligns the storm with turmoil of feelings?
Who twins sadness with sunset by the river?
By whose will does the flowering plant
Drop petals on lovers?
Who crowns heroic deeds? Who protects
The gods beneath Olympian groves?
What is this? Human might,
Openly manifest in the poet.

            Goethe, “Faust”

Goethe clearly contrasts the “wretched noise of discord” with a chord – ordered noise.^[37] Presumably, the orderliness of artistic space must have been recognized in the period when art first emerged – the period reflected in ancient myths.

Here is what A. F. Losev writes about this: “Everything stable, everything formed and ordered, everything structural and organized was perceived by the Greeks as coming either directly from Apollo or established by him, depending directly on him”.^[38]

Thus, the formedness and structuredness of artistic space was felt so strongly that it was perceived as the source of order in the world generally. One might suppose that, for instance, the space of verse must have its own specific geometry, with its own theorems, axioms, etc. Naturally, we are not attempting to develop a geometry of verse space for the simple reason that we still poorly understand this space – we know almost nothing about it. But we will try to demonstrate the existence of a geometry of verse's imagistic space.

Since we aim only to demonstrate rather than fully investigate the problem, we will limit ourselves to analyzing a very short text – two lines by Marina Tsvetaeva (1920):

Love, love: both in convulsions and in coffin
I'll grow alert, be charmed, confused, dash forth...

If we identify the semantic series of words here, the following groups emerge:

1. love, be charmed, confused

2. grow alert, dash forth

3. convulsions, coffin

Is it not true that the first group of words evokes the image of a coquettish schoolgirl and seems taken from a cheap romance? So let us call it the “schoolgirl series”. The second group of words, saturated with indomitable movement, evokes the image of a steed full of distrust and energy. Let us call it the “steed series”. The third group of words is the death series.

The “schoolgirl series” is saturated with the seme of artificiality, falseness. The “steed series” is inversely symmetric, breathing natural freedom and tension. And the death series is inversely symmetric to both the “steed series” and “schoolgirl series”, as it acts like an equation sign between these series, where the seme of artificiality and the seme of naturalness merge in death. But that is not all. Convulsions are a natural movement filled with the highest degree of tension. The highest degree of tension inevitably leads to the destruction of the one who strains, to death. The “death series” proves a natural continuation of the “steed series”.

But the “death series” also proves a natural continuation of the “schoolgirl series”, since the seme of falseness, artificiality, which intensely saturates the “schoolgirl series”, itself enters the “death series” (look at the word “falseness” surrounded by words from the “death series”: falseness, convulsions, coffin).

CONCLUSIONS

1. Three semantic series, each inversely symmetric to the other two, combine into a geometrically regular pattern (ornament), filling the entire imagistic (we consider only the imagistic) space of the verse.

2. There are poems in which the imagistic space is constrained by more than two semantic series.

3. We can hypothesize that each semantic series in such a poem is symmetric to all other series.

It may be worth noting that for the objects connected by point symmetry relationships, of which inversion symmetry is a special case, the concept of “congruence” exists. “A is congruent to B” means that the plane or space can be transformed in such a way that A and B will coincide, merge, become the same. For example, the right and left edges of this page are symmetric, opposite, but if the page is folded in half lengthwise, the left and right edges will coincide and become the same.

Applied to language, congruence appears to manifest in the following way: one can always find a hierarchical metalevel of language (in Bertrand Russell's sense of hierarchical levels) at which the seme-identifiers of inversely symmetric series cease to be perceived as opposed to each other and become the same.