A paper by Aloisius Louie and Stephen Kercel, entitled “Topology and Life Redux: Robert Rosen’s Relational Diagrams of Living Systems”, has been published in the latest issue of the journal Axiomathes. The 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.
There are a number of interesting discussions in the paper. In particular, the “topological strategy” involves utilizing the property of traversibility in graph theory as a means of identifying impredicative loops in relational models.
 Louie, A., Kercel, S. “Topology and Life Redux: Robert Rosen’s Relational Diagrams of Living Systems”. Axiomathes. 17(2):109-136. DOI:10.1007/s10516-007-9014-z
[It is unclear exactly when this paper became available. The Springer email notification announcing the availability of the 17(2) issue of Axiomathes arrived today (11/11/07). Yet the Springer Axiomathes website shows issue 17(2) as dated July 2007, while the same webpage simultaneously lists the issue’s “SpringerLink Date” as 10/30/07. And finally, the same Axiomathes website shows the paper itself as published online on 10/23/07.]