Semiotic Seams: Fractal Dynamics of Re-entry

This essay concerns fractal geometry as a bridge between the imaginary and the real, mind and matter, conscious and unconscious. The logic rests upon Jung’s theory of number as the most primitive archetype of order for linking observers with the observed. Whereas Jung focused upon natural numbers as the foundation for order that is already conscious, I offer fractal geometry, with its endlessly recursive iteration on the complex number plane, as the underpinning for a dynamic unconscious destined never to become fully conscious. Everywhere in nature, fractal separatrices articulate a paradoxical zone of bounded infinity that both separates and connects nature’s edges. By occupying the “space between” dimensions and levels of existence, fractal boundaries exemplify reentry dynamics of Varela’s autonomous systems, as well as Hofstadter’s ever-elusive “tangled hierarchy” where brain and mind are most entwined. At this second-order, cybernetic frontier, the horizon of observers observing the observation process remains infinitely complex and ever receding from view. I suggest that the property of self-similarity, by which the pattern of the whole permeates fractal parts at different scales, represents the semiotic sign of identity in nature.