Motivated by the relation between particle shape and packing, we measure the volume fraction ϕ occupied by the Platonic solids which are a class of polyhedrons with congruent sides, vertices, and dihedral angles. Tetrahedron-, cube-, octahedron-, dodecahedron-, and icosahedron-shaped plastic dice were fluidized or mechanically vibrated to find stable random loose packing ϕ(rlp)=0.51,0.54,0.52,0...

The concept of micelles was first proposed in 1913 by McBain and has rationalized numerous experimental results of the self-aggregation of surfactants. It is generally agreed that the aggregation number (Nagg) for spherical micelles has no exact value and a certain distribution. However, our studies of calix[4]arene surfactants showed that they were monodisperse with a defined Nagg whose values...

We present a geometric theory of the performance of robot manipulators, applicable to systems with constraints, which may be non-holonomic. The performance is quanti ed by a geometrical object, the induced metric tensor, from which scalars may be constructed by invariant tensor operations to give performance measures. The measures thus de ned depend on the metric structure of con guration and w...

The recognition that cognition is situated is a major advance over the essentially Platonic approach of earlier AI. We are starting to realise that the knowledge we express isn't a poorer expression of deeper (implicitly archetypal) knowledge. Rather knowledge is created for specific single use purposes and the knowledge created is shaped by its purpose in the world and the concerns of its crea...

In this paper, we enumerate the parameter matrices of all perfect $2$-colorings of the Platonic graphs consisting of the tetrahedral graph, the cubical graph, the octahedral graph, the dodecahedral graph, and  the icosahedral graph.

cognitive mode. Indeed Socrates asserts that as the levels of cognition are ascended, with the character of "clearness" and "precision," so do their objects "...partake of truth and reality." Unfortunately, just as the "Good" itself was left unexplained as a causal principle in the sun eikon, so is that unhypothetical first principle also left unexplained here, in the divided line. Most importa...

INTRODUCTION Ideas of reference (IOR), paranoia and social anxiety are features of schizophrenia-spectrum disorders, which appear to be conceptually related; however, the precise nature of these relationships is unclear. These relationships may be partially explained by perceived intentionality (PI), a social-cognitive bias for perceiving other people's actions during unpleasant situations as b...

We consider the N-vortex problem on sphere assuming that all vortices have equal strength. develop a theoretical framework to analyse solutions of equations motion with prescribed symmetries. Our construction relies discrete reduction system by twisted subgroups full symmetry group rotates and permutes vortices. approach formalises extends ideas outlined previously Tokieda (C R Acad Sci, Paris ...

Philosophical prose has a long-standing tradition in both Eastern and Western cultures. With the emergence of Zen Platonic dialogues, writers throughout history have used non-fiction to portray nuances human experience. This approach capacity bring ideas life facilitate new ways thinking about world around us. Following these traditions, this experimental piece provides an autobiographical rete...