Having served for a long time under Ostrogothic kings, then removed from office, Cassiodorus (vith century) designed his writings for the members of the famous monastery that he founded at Vivarium. In his monumental Expositio Psalmorum, meant for the novices, he wanted to give his readers not only an exegesis of the biblical text, but rudiments of Liberal Arts too, especially of dialectics and logic. This paper intends to show Cassiodorus’ conception of an orthodox study of dialectics, and his pedagogical (...) devices. Then is considered the way in which Cassiodorus applies in his commentary categorical and hypothetical syllogistics. Finally, special attention is given to Cassiodorus’ rigorous demonstration about the famous Three Chapters controversy. In the dialectical passages of the Expositio appears the artificial cha­racter of this attempt to reconcile secular culture and biblical exegesis. The best in Cassiodo­rus’ enterprise is his enthusiasm. (shrink)

A geometrical model is proposed that describes the emergence of a primordium at the shoot apex in Dicotyledons. It is based on recent fundamental results on plant morphogenesis, viz.: – the emergence is preceded by the reorganization of the microtubules of the cortical cytoskeleton, leading to a new orientation of the synthesis of the cell wall microfibrils; – the resulting global stress is related to the general orientation of the cell growth.

Plant morphogenesis exhibits numerous bifurcations with particular angle values such as 41°, 53°, which, in lower plants, can be measured in the thallus, and, in higher plants, in the ribs of the leaves. An interpretation of these angles is attempted. Since they characterize the functioning of a morphogenetic field, a formalism was constructed suitable for the study of living systems. The mathematical tool devised here, named the Arithmetical Relator, combines Geometry and Arithmetic, and assumes that a general system results from (...) the interaction between an internal cyclic structure and an environment to which this structure is adapted. The formalism described therefore takes into account partial self-reference and changes in the level of organization. Within this framework, the particular values of the ramification angles are extreme for slight shifts in the internal structure. A pattern of the relations between the genome, the cell and the organ is suggested. (shrink)

A geometrical model of the emergence of a primordium at the shoot apex in dicotyledons is proposed. It is based on recent fundamental results on plant morphogenesis, i.e.:- the emergence is preceded by the reorganization of the microtubules of the cortical cytoskeleton, leading to a new orientation of the synthesis of the cell wall microfibrils; - the resulting global stress is related to the general orientation of the cell growth. So the model sums up the continuous interactions linking the microtubules, (...) the microfibrils and the cell growth axis. (shrink)