Classical neo-Darwinian explanations do not fully account for changes in biological forms, and new theories have emerged, primarily in maths and physics, that offer new approaches to the problem of the origin of life and phenomena of order in evolution. This volume focuses on the role of closure at various hierarchical levels as the catalyst between self-organization and selection. Participants addressed special areas of the closure problem such as autopoiesis and autocatalysis and function and selection, and semiosis. Presentations on physical (...) and mathematical modelling are included. The book seeks to clarify the role closure plays in explaining the emergence, development and evolution of structurally stable systems at the thermodynamic, chemical and biochemical, biological, psychological and cultural levels. (shrink)

The desire to understand the mathematics of living systems is increasing. The widely held presupposition that the mathematics developed for modeling of physical systems as continuous functions can be extended to the discrete chemical reactions of genetic systems is viewed with skepticism. The skepticism is grounded in the issue of scientific invariance and the role of the International System of Units in representing the realities of the apodictic sciences. Various formal logics contribute to the theories of biochemistry and molecular biology (...) and genetics. Various paths of extension are invoked in these formal logics in order to express the information of biological apodicticism. Symbolizing the appropriate notations for invariant relations and for biological extensions of relations is fundamental to the exact generating functions of discrete algebraic biology. Aspects of philosophical perspectives of the relation scientific number systems are contrasted. The deep distinction between physical motion and biological motion is expressed in terms the roles of Aristotelian causes. The interior motion within perplex numbers is contrasted with the exterior motion of physical systems. The need for a new mathematics for biology is suggested. (shrink)