Fractal Entanglement Between Observer and Observed

Abstract

This article explores paradoxical dynamics embedded in the fabric of existence. The logic of Spencer-Brown, as extended by Francisco Varela, is placed within the historical context of cybernetics. Varela's concept of reentry provides a bridge to fractal geometry through recursive iteration on the complex number plane. Fractals are dynamic process-structures that negotiate spatial and temporal interfaces between various forces and dimensions of existence. This article argues that fractal reentry dynamics provide contradictory foundations by which different levels of nature, including mind and matter, both separate and connect. Finally, natural fractals reveal a new level of reflexivity in science, by which the observer is paradoxically embodied within the observed.

Forest Climax Phenomenon: An Invariance of Scale

“…With the discovery that a set of symbols has been used by nature to encode the information for the construction and maintenance of all living things, fractals-the invariant sets of chaotic systems-serve paradoxical functions as physical boundary keepers, both to separate and connect various subsystems and levels of being [24,[44][45][46]. The key notion of a fractal is that it possesses structures on a hierarchy of scales generated by the reiteration of a mathematical formula [35], which is "a form of feedback, where the answer to the formula recycles into the original formula to generate the next solution" [47].…”

“…The key notion of a fractal is that it possesses structures on a hierarchy of scales generated by the reiteration of a mathematical formula [35], which is "a form of feedback, where the answer to the formula recycles into the original formula to generate the next solution" [47]. Therefore, the complexity of dynamic process-structures is measured by their fractal dimension [24,48]. For instance, the number N(x) of objects with a characteristic linear dimension greater than x can be given by N(x)~x −D , where N(x) is a number measure corresponding to the scale unit x and D is the fractal dimension [8].…”

“…Dynamical criticality explains evolution by reference to the broad internal disposition of a population to evolve in order to stay extant, rather than any actual evolutionary trajectory of populations by capturing the influence that the internal features of populations can have upon the outcomes of evolution [107]. Taking into account the above, I propose the conceptual framework for assessing habitat dynamics at a network-system-trajectory interface ( Table 1): The network, because nature can be viewed in terms of multilevel, multidimensional hierarchies of inter-related event clusters that form a metaheterarchy, or a heterogeneous general hierarchy [24]; the system, because the experience of events can be viewed as a summary of the facts through which the events took place-a fact pattern [108,109]; and the trajectory-an expression of a relation among certain fact patterns in the network [79,110]. Table 1.…”

“…A synthesis of the literature was undertaken within the context of the fractal fragmentation and connectivity of landscape habitats. "Fractals are dynamic process-structures that etch time into space; by illuminating fractals, we self-reflexively illuminate the observer in the observed in nothing short of nature herself" [24]. However, it is necessary to clarify that, contrary to ideal fractals, landscape patterns can be considered fractals only for limited scale intervals; this is due to the dimensionality of successional elements, determined by their regeneration response to disturbance [25].…”