Plato claimed that the regular solids are the building blocks of all matter. His views, commonly referred to as the geometric atomistic model, had enormous impact on human thought despite the fact that four of the five Platonic solids can not fill space without gaps. In this paper we quantify these gaps, showing that the errors in Plato’s estimates were quite small. We also develop a mean field approximation to convex honeycombs using a generalized version of Plato’s idea. This approximation (...) not only admits to view convex mosaics in$$d=3$$d=3dimensions as a continuum but we also find that it is quite accurate, showing that Plato’s geometric intuition may have been remarkable. (shrink)

The article examines how Hegel’s negative view of Byzantium is different from the Enlightenment’s critique and especially from Voltaire’s criticism of medieval history. In order to account for the Hegelian specificity of interpretation an effort is made to translate the chapter on Byzantium from the Philosophy of History in terms of the analysis of the Phenomenology of the Spirit and, more precisely, on the basis of the chapters on sensible certitude and on the domination and servitude. Considering that for Hegel (...) every philosophical school possesses an autonomous value, one has to wonder why the Byzantine moment of the Spirit is destined to stagnation. The question about Hegel’s Neoplatonism, especially his affiliation with Proclus’s system, shows how the distance separating the Hegelian system from the Proclusian one explains the inadequacy of the latter as to drawing the consequences from the Byzantine spiritual stagnation. (shrink)