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RHETORIC AND SYMMETRY: 
A NEGLECTED LINKAGE
 

JOSÉ LUIS CAIVANO


Architect, researcher (b. Junín, Buenos Aires province, Argentina, 1958).

Address: Facultad de Arquitectura - SICyT, Ciudad Universitaria Pab. 3 piso 4, 1428 Buenos Aires, Argentina; 

E-mail: jcaivano@fadu.uba.ar

Fields of interest: visual semiotics, color theory, light perception, morphology.

Publications

(1990) Visual texture as a semiotic system, Semiotica 80 (3/4), 239-252; 

(1991) Cesia: a system of visual signs complementing color, Color Research and Application 16 (4), 258-268; 

(1993) Semiotics and reality, Semiotica 97 (3/4), 231-238; 

(1994a) Color and sound: physical and psychophysical relations, Color Research and Application 19 (2), 126-133; 

(1994b) Appearance (cesia): construction of scales by means of spinning disks, Color Research and Application 19 (5), 351-362; 

(1994c) Towards an order system for visual texture, Languages of Design 2 (1), 59-84; 

(1995b) Sistemas de orden del color, Buenos Aires: SICyT-FADU-UBA; 

(1996a) Spatial semiosis in architecture: descriptive and generative analysis (in collab.), Semiotica 110 (1/2), 127-144; 

(1996b) Cesia: its relation to color in terms of the trichromatic theory, Die Farbe 42 (1/3). 12. 

(1998) Color and semiotics: A two-way street, Color Research and Application 23 (6), 390-401; 

(1999) La representación del mundo visual en la fotografía y pos-fotografía, Visio 4 (1), 37-42.
 
 

Abstract: Rhetorical figures are a deviation, a conceptual or formal transgression produced in a statement with the aim of bringing the receptor of the message to a meaning that is beyond the literal meaning. Usually, the field of rhetoric has been poetics, or the figurative language; however, these operations extend across all kind of languages, including visual images: painting, architecture, photography, advertisement, etc. The argument of this paper is that rhetorical figures are generally produced on the basis of symmetry rules. Sometimes, these rules constitute the rhetorical operations themselves; in other cases, they act as a kind of zero degree, against which the rhetorical operations can be perceived. 
 
 

Rhetorical figures can be defined as a deviation, a conceptual or formal transgression produced in a statement with the aim of bringing the receptor of the message to a meaning that is beyond the literal meaning. Usually, it is considered that the field of rhetoric is poetics, or the figurative language; however, these operations are extended across all kinds of discourses and languages. For rhetorical operations to be perceived as such, it is necessary the existence of rules or norms of enunciation, from which rhetorical operations constitute creative alterations or contraventions. 

Rhetorical operations also appear in visual images, insofar as the observer possess incorporated rules or norms that can be transformed or broken to produce a message with a non-conventional meaning. Artistic images, painting, architecture, photography, caricature, advertisement, and various other genres of visual production rely mostly in the rhetorical use of visual signs. 

The argument of this paper is that rhetorical figures are generally produced on the basis of symmetry rules. Sometimes, these rules constitute the rhetorical operations themselves; in other cases, they act as a kind of zero degree, against which the rhetorical operations, being a transformation or a breaking of those rules, can be perceived. 

The connection between symmetry and rhetoric, however, cannot be found among the ancients. In his Rhetoric, for instance, Aristotle (350 b.C.) does not mention symmetry at all. The ancient rhetoric was exclusively confined to verbal language, while the classical conception of symmetry was limited to the field of geometry and some of its applications (architecture, the description of nature, including the human body, etc.). Close to these terms is the definition of symmetry by Vitruvius (i.43b.C.-14a.C. [1914: 14]): 

a proper agreement between the members of the work itself, and relation between the different parts and the whole general scheme, in accordance with a certain part selected as standard. Thus in the human body there is a kind of symmetrical harmony between forearm, foot, palm, finger, and other small parts; and so it is with perfect buildings. In the case of temples, symmetry may be calculated from the thickness of a column, from a triglyph, or even from a module . . . 

It is probably for being applied to different domains that both notions, rhetoric and symmetry, did not meet in a common field during the classical antiquity. 

Even when the ancient rhetoric was conceived as the art of persuasion by means of the attractive speech, we can also note that the beauty of poetry basically relies on the use of rhetoric figures: rhyme, metaphor, comparison, antithesis, etc. Already here we can postulate a direct relation to the visual arts, because the use of symmetry with all its variations in art, architecture, and music follows the same purpose: to attract the senses, to create a beautiful visual "discourse". 

Making a historical summary of the development of rhetoric, Áron Kibédi Varga (2000) classifies three civilizations and three kinds of rhetoric: the oral civilization and rhetoric, the written civilization and rhetoric, and the media civilization and rhetoric, including in this last category all the sensory representations involved in mass media communication, and also architecture. As some authors rightly point out (Zunzunegui 1992: 93-94, Group µ 1996: 5, among others), it is Roland Barthes the first scholar to have applied the categories of rhetoric to the visual image, mainly to advertisement, in his pioneering article on rhetoric of the image (1964). Later on, Jacques Durand (1970) made an analysis and inventory of the traditional rhetoric figures in the advertisement image, and defined rhetoric as an instrument for creativity. 

However, in the literature about symmetry, rhetoric, or semiotics, it is next to impossible to find a direct or explicit connection between rhetoric and symmetry. More or less closer approaches, but considerably distant from the point, could be the one by Durand (1970 [1972: 110-115]), when proposing a formal scheme for rhetoric, in the fashion of logic, or the one by the Group µ (1992 [1993: 231]), when defining rhetoric almost as a geometrical operation, as the ruled transformation of the elements of a statement. The closest connection I was able to find was in an article by Winfried Nöth (1999: 145), where he says: 

In the syntagmatic dimension of verbal language, symmetry is the underlying principle of textual and poetic repetition. Any recurrence both in the plane of expression and in the plane of content of the text represents an occurrence of translatory symmetry, inasmuch as an invariable element of the content or the expression is repeated. Bilateral and antisymmetrical forms of textual recurrence appear in the antithesis and in other oppositive figures of language . . . (my translation) 

Nevertheless, we should note that Nöth remains within the limits of verbal language and does not reach to make a transposition to the visual images. 

Some non-direct connections between rhetoric and symmetry can be made by means of a reasoning with a transitive character. For instance, Johann Sebastian Bach has been considered by some scholars as the master in the art of musical rhetoric, and, at the same time, the symmetrical aspects of his music (the structure of his fugues, canons, and all the polyphonic devices) have been profusely analyzed and emphasized by others. I would like to highlight that both groups are referring to the same aspects of Bach’s works. A transitive relation can also be found in the following: rhetoric operations are considered to be an instrument of creativity (see, for instance, Durand 1970 [1972: 110-112)]; and, similarly, operations of symmetry and symmetry breaking are considered the main elements of creativity and production of beauty in art (see, for instance, Nöth 1999: 148). 

On the other hand, the concept of dissymmetry, as an imperfect symmetry, with little deviations from perfect geometric symmetry, does not seem to me very far from the concept of rhetoric. Dissymmetry results more attractive than perfect symmetry. According to Pasteur, the Universe is a dissymmetric system and life is a function of this dissymmetry (in Walcerz 1995: 522). 

Among the present notions of symmetry, we can find a kind of gradation: perfect symmetry, dissymmetry (an intermediate state), antisymmetry (another intermediate state having both the similar and the opposite as characteristics), and asymmetry (as the case opposed to symmetry, its negation). Dénes Nagy (1998) makes a comparison with color: white (in one of the extremes), chromatic colors (in the middle, where we can also include gray colors and their mixtures or gradations with the chromatic colors), and black (in the other extreme, as a negation of color). Obviously, in both cases, color and symmetry, the most interesting aspects for art and the creative production are found in the middle, in the gradations, in the possibility of variation. This holds true also for other fields, because, as Collier (1996) rightly points out, it is the breaking of symmetry (producing the intermediate cases in the previous classification) what generates information. 

The breaking of symmetry, in most cases, could be taken as an example of rhetoric operation. However, as the Group µ remark, 

even when the syntagmatic rules of a statement have been identified, any variation in its orderly elements should not necessarily be considered as a break, because it can perfectly be a difference that brings information. . . We will only talk of a deviation when the effective content of a given position does not result as it is expected to be. (1992 [1993: 286]) 
The transgression of a regularity is not sufficient to speak of rhetoric, it is necessary that the redundancy is not destroyed to the point that the nature of the occurrence expected in this position cannot be determined. (1992 [1993: 291], my translation) 

Summing up, and stressing again the point of this paper, I think that at the present time it is easier to make a connection between rhetoric and symmetry by resorting to some modern conceptions of both terms, where they are related to operations, basically, operations of repetition and transformation or ruled variation. In this way, symmetry is explained by operations of translation, rotation, specular reflection, and dilation. Rhetoric figures also rely on operations of adjunction, suppression, substitution, and permutation. Even not being possible to find a one-to-one equivalence between the four main rhetorical operations and the four basic operations of symmetry, they usually interact one with another; for instance, a substitution of an element for another can be performed over a translatory pattern, a permutation between two elements can be performed over a dilatatory symmetry, and so on. 

The principles of art and poetry closely concur with the principles of rhetoric, which in turn closely concur with the principles of symmetry. The full paper will present arguments and examples to demonstrate the relation between rhetoric and symmetry, which has been almost totally neglected during the 2,000 years in which both concepts have evolved. 

(References are available on request.)
 
 

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