Hier Auszüge aus dem eingereichten Artikel, nicht zur Weiterleitung bestimmt. Den Hinweis auf die DNA-Struktur verdanke ich Dir, lieber Ingo T. :-)

Abstract

Conventional systems theory does not address how systems create content and genuine interiority. Correspondingly, meaning is attributed as semantic content only secondarily from the outside. The present model generates potential content, followed by perspectival meaning generated through the interactions between two or more agencies. The transition of potentials into individually realized interactional coherent dynamics creates the primordial relational elements of meaningful systems. Potential-based interactional meaning generation is described and applied to topics typically reserved for the humanities. Biological content generation, as an affinity-guided self-assembly stabilized and intensified by membranous enclosures and inside-from-outside delineating potentials, has been described in previous publications. The creation of biology-detached eigenworlds in mathematics, ideas, thoughts, music, and art is generally described using the proposed principles of content generation. The physical nature of potentials, mentally idealized as “things,” can be described in trans-individual, general categorical, algebraic, and numeric terms or as realized in individualizing (i.e., personalized) interactions.

Materials and methods

To plot the structure of the proposed model, we start with a conventional xyz diagram, with the x- and y-axes forming a plane, and the z-axis vertically going through this xy-plane. The z-axis shows a constant forward movement according to the progress of time, designated as z(t). A circular movement around the z-axis is displayed on the xy-plane. Its angular rate of rotation in the xy-plane is denoted as ω, r is the constant radius of the helix, and c is the constant rate of advance along the z-axis. Therefore, the speed and radius of motion are set as constants. To derive the corresponding differential equations of the constant forward movement along the z-axis and constant spiraling around it, the conventional method using sine and cosine functions can be replaced with a more elegant form using imaginary numbers. In the latter form, the position on the xy-plane at time t, represented as a complex number, is ζ(t) = x(t)+iy(t) = re^iωt; in the LaTeX display, it is \zeta(t) = r e ^{i \omega t}. The real component of the linear motion on the z-axis at a constant speed is z(t) = c.

In an imaginative shift in perspective and as a tentative thought experiment, this article reinterprets the spatial coordinates x, y, z, and time parameter t from the abovementioned helical motion as describing a “three-dimensional” form of time, with t representing a one-dimensional spatiality. In this conceptual inversion, the xy-plane is a manifold of temporal simultaneity, the z-axis represents a linear temporal progression from the past (negative z) through the present (i.e., the xy-plane at z = 0) to the future (positive z), and t is a spatial parameter. This one-dimensional parameter represents “spatiality as such,” providing an internal homogeneity by implying a uniform spatial context or single spatial dimension along which the system evolves.

In this interpretation,

·      ζ(t) = x(t) + iy(t) represents a position in the temporal simultaneity plane, where x and y are coordinates in a 2 D temporal manifold;

·      t is now a spatial parameter, and ζ(t) describes how the “temporal position” in the simultaneity plane evolves as a function of spatial position t;

·      ζ(t) = re^iωt suggests that the temporal coordinates x, y “spiral” or oscillate in the simultaneity plane as the spatial parameter t advances;

·      r is a measure of the “extent” of temporal variation within the simultaneity plane, and ω determines the rate of this spiraling per unit of spatial parameter t;

·      The z-axis represents the linear temporal progression, and t is a spatial parameter.

After applying this semantic inversion from three-dimensional space to three-dimensional time, two qualitative aspects must be considered. First, as the proposed model’s dynamic elements consist of relating, mutually considering processes, the temporal coordinates x, y “spiraling” or oscillating in the simultaneity plane as the spatial parameter t advances, concern two or more motions in parallel, corresponding to the simultaneity of two or more interaction partners. Hence, the temporal “spiral” metaphorically resembles a DNA double helix in conventional spatial terms (Peyrard 2004). Second, the strange, miraculous z-axis, representing a linear temporal progression with t acting as a spatial parameter, must be redefined according to moment-restricted spatiality and temporality. It loses its inherent, automatically guaranteed continuity in favor of a momentary, punctual form of existence, shaping its future in the form of organizing and providing present enhancers on the level of probability and corresponding probability distributions rather than a linear, mechanical determination. Thus, the punctual, discrete providers of coherent co-occurrence are potential and not yet their realization. The latter occurs in the form of oscillations and spiraling around the z-axis. Consequently, the z-axis, previously assumed to be engaged in continuous linear progression, comprises a series of discontinuous, momentary, punctual re-installments, prompting purely interactional spiraling.