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Visual semiotics and space cognition: on the dynamics of

two-dimensional representations of space and

actionWolfgang Wildgen

11th Early Fall School of Semiotics“SEMIOTICS AND GENRE”September 10-16, 2005, Sozopol, Bulgaria

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The distinction between picture and text involves a set of basic semiotic challenges. First, pictures are linked in their production to the motricity of hands, in their receipt by the eye and the visual cortex. Language in its basic form, spoken language, is linked in its production to the motricity of the human vocal apparatus (from the vocal cords to the lips) and in its perception to the ear and the auditory cortex. The dynamics of these four subsystems and moreover the coordination of the pairs of subsystems in production and reception define the base line of any comparison of picture and text.

Part I: Picture versus text

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At least two levels that must be separated: the evolutionary basic distinction between

a mode of manual/visual and a mode of phonetic/auditory communication,

the application of manually based techniques to materials (with color or luminosity differences) and media (canvas, paper, glass, etc.) applying specific instruments (crayon, paint-brush, chisel etc.) is basic for products of the visual arts. This applies also to writing. As a consequence, pictures refer to a highly developed culture of materials, techniques and media

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The linearity of language? A first confrontation with pictures

Unidirectional process

Dependence on past or future steps of the process

Garden path and reanalysis

Major deviations of the unidirectional linearity of language.

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Fractal patterns(between d=0 und d=2

Cantor-set (d < 1)

Sierpinki-triangle (d < 2)

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From one dimensional language to two-dimensional pictures

SilenceLanguage ends Language starts

Virtual dynamics of “silence” in communication

dynamics of corners

dynamics of sub-squares

Rotational dynamics (45o)

Virtual dynamics of a square (diagonal, horizontal/perpendicular and spiral force-lines).

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Historical mandalas as a demonstration of the multiplicity of dynamical and symmetrical structures in a circular space

The flat structure of the atom “gold”

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Steady increase in the number of corners (and therefore of implicit dynamic fields) with d (dimension) two end points in a line segment four corners in a square eight corners in a cube sixteen corners in a four-dimensional

cube 32, 64, 128 … corners if we increase

further the dimensionality of the cube

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Implicit force-fields and the organization of content

In producing a picture these force-fields are relevant.

A strong preference is given to rectangular frames which are near to the ideal (the square) but introduce a basic asymmetry.

If we take the painting the “Last Supper” of Leonardo da Vinci (cf. Wildgen 2002, 2004b and 2004a: chapter 6), the prominent table of the supper fills the basic horizontal line and Christ marks the intersection with a vertical line of symmetry.

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Part II: Geometry and Dynamics in the Art of Leonardo da Vinci

Leonardo da Vinci was born in 1452 in Vinci near Florence. He made the first steps of his career in Florence, where he worked under Verrocchio, became master in his workshop and in 1477 independent master. In 1482 Leonardo asked Ludovico Sforza in Milan for an employment. He stayed in Milan until 1499, when Milan was taken by the French troupes. Leonardo left Milan and returned to Florence. In 1506 Leonardo was invited to Milan by the French governor, Charles d’ Amboise, and worked there until 1513. He left Milan because of the pestilence and went to Rome and left Rome invited by François I, king of France, together with his pupils Melzi and Salai. From 1516 until his death in 1519 Leonardo lived in the Castel Cloux near Amboise in France.

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The two basic pillars of Leonardo’s semiotics of art are:

1. (linear, of color, vanishing); we shall deal with it under the topic of geometry.

2. Dynamics (force, weight, counterpoise, balance, movement, percussion, etc.).

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“Last Supper” by Leonardo da Vinci (Milan)

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Force-fields in the “Last Supper”

..\Eigene Dateien\Präsentationen\Narrative Struktur und visuelle Interpretation.ppt

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As this example shows, all three force fields we analyzed in the case of a void frame are used to organize specific contents (surfaces, figures, persons in space) in Leonardo’s mural painting. The head (ear) of Jesus is at the center of all force fields. The sub-centers of the groups of apostles lie in the intersections between the horizontal axis and the symmetric spiral which end at Jesus’ head (ear). The rectangle of the whole mural painting breaks the symmetry of the (ideal) square.

The perspective generates a subdivision of the background space into three equal zones. In the central zone are situated: Jesus, John (at the right of Jesus), and Thomas, James Major (at the left of Jesus); Judas is already outside of this field although he has the second position at the right of Jesus. Peter and Philip are at the intersections of these fields. [1]

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Basic content complexes organized in Leonardo’s painting The table in the fore-ground. The perspective of the dining room, the

windows, the landscape visible through the window, the subdivision of the background into three equal sub-fields.

The arrangement of 12 apostles (grouped by 4 x 3) on both sides of Jesus.

The gestures (body poses) and glances of Jesus and his apostles superimpose a further dynamical structure.

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The geometrical scheme is that of a pyramid with the angel on the second (visible) side of it. The front side has on its vertex the face of the Virgin, on its edges, the Jesus-baby at the right and St. John Baptist as baby on the left (above the base-line of Jesus and the angel).

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Mary

Angel

Jesus

John

hold protect

point

blessadore

The pyramid in the “Virgin in the Rocks”.

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The hand gestures alone define five different force-lines and all four persons have different gaze-lines involving different angles of the head. All these forces imply some narrative context, i.e., Leonardo tries to concentrate a complex story in the static configuration of

one painting. Drawing-study for the pointing gesture of the angel

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The semiotics of a figural composition

A sketch for the Epiphany

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The triangle is asymmetric as the right side is the line between the gaze of Mary and Jesus which point to the face of a kneeing Magus. This is the central force-line inscribed into the triangle.

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Levels of semiotic analysis:

-  The space (time) of the scene depicted (perspective, light/shadow, outfit of the scenario).- The thematic persons. These constitute a relational schema which is represented by their relative positions in space, the static relations and the movements (e.g., the relative movement of the head in relation to the trunk, the gestures of the hands, the directions of gaze).- A narrative content related to a known episode. The scene may be identified as one moment resulting from a series of prior events and having specific (known) consequences

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Part III: Dimensional transitions, symmetry, and transformations

An architecture (3-space) is represented in an illusionist painting (trompe l’œil), but one can neither enter the room nor move before it without destroying the illusion.

A sculpture is represented in a mural painting; one part may be sculpted, the other painted. In a proper position against the wall, it may be difficult to grasp the difference between 3-space and 2-space.

A text describes a landscape, a building, a person either directly or as represented in a painting.

A sentence contains an action scenario (in 3-space + time) in its valence structure, e.g., “Eve gives Adam an apple in the garden Eden”. The action in 3-space + time is flattened to a sentence with verb and case assignments/linear order.

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Compression of information

The technique of perspective (rediscovered in the Renaissance) codes artificially for the third dimension; gestures, glances, frozen actions code for the temporal dimension.

The technique of valence patterns (control of NPs), case assignment, etc., codes for the spatial parameters and allows their flattening into a sequence of verb (V) + subject (S) + object (O), etc. (in different orders dependent on the type of langue: SVO, SOV, VSO, etc.).

All the non-spatial or non-temporal dimensions are coded for by attributes/shape modifications/colors in a painting or by lexical differentiations in a sentence.

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Symmetry and chaos-controllers as guarantees for semiotic stability

Group operation on a triangular star:

•Identity (translation)

•Rotation (120°)

•Mirroring on an axis

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Hexagonal symmetry in a snow flake

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Spatial symmetry in language (rare)

S A T O R

A R E P O

T E N E T

O P E R A

R O T A S

The sower (sator), called Arepo

directs (tenet)

The carriage (the wheels =rotas)

with care (opera)

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Leyton‘s generative geometry and the semiotics of pictures

„GENERATIVE GEOMETRY: A geometric object is one from which the transfor mations are recoverable; i.e. a geometric object is a memory store.”

The regularity of the base space is the presupposition for the generation of “information” on deformations, asymmetries inscribed into the (pre-informative) space.

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Translation

Rotation

Translation

The generation of a square and a rod via group operations

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Generation of complexity

By a multiplication of basic types, By an intersection or blending of

different entities, e.g. curved (sphere) and straight (cube).

By an approximation of living forms (plants, animals, humans) in their geometry.

By the addition of decorative patterns

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Example from architecture: the townhall in Bremen

Decorative elements

Renaissance transformation of a gothic town hall

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New geometrical devices in the 20th century

Opera in Sidney, 1957-1973, and the spherical geometry which underlies its construction

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Conclusions

Dimensionality fixes the basic geometry and dynamics which govern the organization of forms.

Symmetries restrict possible constructions and thus contribute to the stability of the result.

Capacities for meaning generation are created by possible deviations from the symplest and most symmetric forms (Leyton‘s axiom).

Natural semiosis is a process of memory generation and exploits systematically the geometry and dynamics of underlying forms.

Decorative elements are inserted into the basic geometric and dynamic structure and profit from its memory function.

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End of the presentation

For further materials on the topic, cf. http://www.fb10.uni-bremen.de/homepages/

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