This review investigates the potential of non-orientable topology as a fundamental framework for understanding the Poincaré conjecture and its implications across various scientific disciplines. Integrating insights from Dokuchaev (2020), Rapoport, Christianto, Chandra, Smarandache (under review), and other pioneering works, this article explores the theoretical foundations linking non-orientable spaces to resolving the Poincaré conjecture and its broader implications in theoretical physics, geology, cosmology, and biology.

Systems theory offers a language in which one might formulate a metaphysics (or more specifically an ontology) of problems. This proposal is based upon a conception of systems theory shared by vonBertalanffy, Wiener, Boulding, Rapoport, Ashby, Klir, and others,and expressed succinctly by Bunge, who considered game theory, information theory, feedback control theory, and the like to be attempts to construct an "exact and scientific metaphysics." Our prevailing conceptions of "problems" are concretized yet also fragmented, and in fact dissolved, by (...) the standard reductionist model of science, which cannot provide a general framework for analysis. The idea of a "systems theory," however, suggests the possibility of an abstract and coherent account of the origin and essence of problems. Such an account would constitute a secular theodicy. (shrink)