What does nonlinearity mean? In its simplest explication, it is a curved line. In Riemann-Lobachevsky geometry, all straight lines are actually curved.2 Nature pro- duces no straight lines, while human technologies are mostly based on organizing their products in linear orders—straight lines, fixed corners, etc. Likewise the meth- odologies of the social sciences are built upon the notion of linearity—turning com- plex nonlinear phenomena into artificially “measured” entities (Michell, 1999). By forcing the nonlinear into a process of linearized “measurement” operations creates an irreversible loss of the relevant features of the phenomena.
We assume that the relation between “ugly” and “beautiful” is that of polar mutually exclusive opposites that—if put on a linear scale—can even be turned into quantified indexes (Fig. 8.2b—an equivalent of a rating scale). Yet such quan- tification of a linear scale is an epistemological impasse (Wagoner & Valsiner, 2005) as it inadequately represents the nonlinearity of the phenomena (e.g., Fig. 8.2a) that it is supposed to “measure.” Most objects we seemingly easily rate on a linear fixed scale (like Fig. 8.2b) are complex multifaceted wholes, the Gestalt qualities that vanish in the act of superimposition of the subjective linear order (rat- ing scale). In the example in Fig. 8.2, this vanishing act is exemplified by the inher- ent ambivalence in the scene—the Biblical personage of Judith after killing Holofernes by cutting off his head, now, is depicted carrying it into the public domain of the viewers of the painting. Her just finished act is deeply ambiguous—
she is a murderer, a schemer who purposefully went to the enemy general
2 Since every straight line can be viewed as a part of an infinitely large circle—where both ends of the straight-looking line eventually meet.
130
Holofernes seducing him so as to kill him. At the same time, she is a hero—a woman whose assassination act saves her people from being slaughtered by the troops of Holofernes. The depiction of Judith by the artist does not fail to display her bodily beauty together with the holding of her trophy—Holofernes’ head—in her hands.
The realistic process involved in the relating with the object of evaluation differs from the superimposition of the linear order onto the nonlinear phenomenon (as depicted in Fig. 8.2a). It is the adjustment of the psychological system to the nonlinear nature of the object—curvilinearization of the perceiving and appreciating mind—that leads to the self to create its own experience through the catalytic
Fig. 8.2 Linear order superimposed on complex processes and its curvilinearization. (a) An object of evaluation (Giorlamo da Capri, 1540–50 Judith with the head of Holofernes. Vienna, Kunsthistorische Museum), (b) Regular assumption of a linear binary opposite in evaluation (a or b), (c) Curvilinearization of the opposition (from a or b to bringing a and b to linking with each other) and emergence of the relation of tension
J. Valsiner
conditions of the object that is the “target” of evaluation. The flexibility of my psyche is being modulated by myself under the conditions of the scene I am experiencing.
The psychological tension (Fig. 8.2c) that curvilinearization of the psyche brings with it is temporary—it either escalates to a breaking point (and arrives at dialectical synthesis—Valsiner, 2015; Vygotsky, 1971) or de-escalates to a non-tensional state of quasi-linearity.
I posit that this tension is crucial. The dynamics of linearization <> curvilinear- ization of the structure of the human psyche can be seen as the basic principle of human mind. We become trapped into the insoluble web that unites “love” and
“hate” at times (curvilinearized state) in some relation (toward a displeasing politi- cal figure or abusive parent) while being completely linear in the relation to subjec- tively trivial details of daily life (linearization).
An alternative possibility is to see mutually linked opposites as two sides of a Möbius loop—permanently turning into one another (Fig. 8.3). Here the two are permanently together—each + vector is immediately opposed by its counter-vector (−) while their positions on the loop itself fluctuate between front and back posi- tions at every turn of the loop. “Love” turns into “hate” in temporal dominance only to be followed by a next reversal of the dominance relations. This depicts the eternal maintenance of a fixed ambivalence relationship without any possibility of break- down or breakthrough (synthesis). The tension continues in the eternal cyclicity of reversals of the dominance of opposites.
The Basic Tension: Between Linearity and Spirality I posit (Valsiner, 2019) a very general abstract tension between two orders of any form—linear and spiral (helical). Triskeleon (Fig. 8.4a) is the maximum case of curvilinearity. It is a graphic abstraction of the closing of two-dimensional space and opening of the third dimen- sion at the eyes of the spirals (in contrast with the right side, Fig. 8.4b) where the linear abstraction from the center point can expand in two dimensions in all three linear directions, but there is no opening to the third.
This tension is triggered by the settings we are in—the conditions for our activities. We introduce linearity into our human-made natural environments by architectural straight lines—which vanish as the building becomes a ruin and the
Fig. 8.3 Unity of opposites in perpetual dynamics of regular place change (Möbius strip with forces added)
132
natural growth takes over. We reproduce curvilinearity in ornamenting spaces of symbolic kinds—such as ceilings of tombs of burial chambers (Fig. 8.5).
The tensions of social living—unity of openness and closedness—are encoded into the forms of environmental decorations during our lives, at the entrance into the
“other” world, and in our imagination of the latter.
Ornamentation of any kind is human encoding of meanings into the periphery of our action fields. But what is the “action field” for a dead Egyptian pharaoh whose ceiling of the tomb in which the casket with his embalmed dead body is located under many wrappings? It encodes a generalized and abstracted catalytic orienta- tion for entrance into afterlife.
Ornaments are of catalytic value for our meaning construction acting within our environments (Valsiner, 2019). We create them as decorations (of something—our clothing, our life environments), but while being that, they become catalysts that are present in our agentive actions and provide their meaningful context.