Topology and Life Redux: Robert Rosen’s Relational Diagrams of Living Systems

Abstract

Algebraic/topological descriptions of living processes are indispensable to the understanding of both biological and cognitive functions. This paper presents a fundamental algebraic description of living/cognitive processes and exposes its inherent ambiguity. Since ambiguity is forbidden to computation, no computational description can lend insight to inherently ambiguous processes. The impredicativity of these models is not a flaw, but is, rather, their strength. It enables us to reason with ambiguous mathematical representations of ambiguous natural processes. The noncomputability of these structures means computerized simulacra of them are uninformative of their key properties. This leads to the question of how we should reason about them. That question is answered in this paper by presenting an example of such reasoning, the demonstration of a topological strategy for understanding how the fundamental structure can form itself from within itself.

Overcoming the Newtonian paradigm: The unfinished project of theoretical biology from a Schellingian perspective

“…These provide the entailments to model living organisms with semantic elements that depend entirely on the context created by the circle of self reference associated with the reflexivity of anticipatory systems (Rosen, 2000, 135f.). Such models involve necessary ambiguities and cannot be simulated on a computer, and this is what makes them indispensible for understanding biological and cognitive functions (Louie & Kercel, 2007).…”

Relational Biology of Symbiosis

“…This paper is a sequel to a continuing sequence of papers on relational biology published in this journal: Louie (2006), Louie and Kercel (2007), and Louie (2008). I shall draw upon notation and results from these earlier papers.…”

Functional Entailment and Immanent Causation in Relational Biology

“…I shall now concentrate on the alligation of Aristotle's causation in Rosen's relational biology. [The following diagrams (1)-(15) and their discussions have been presented in detail in a recent paper published in this journal (Louie and Kercel 2007). They are précised here to make the present paper self-contained.…”

“…17 of EL. I have also recently published two papers on the subject in this journal (Louie 2006, Louie andKercel 2007). Details may be found therein.…”