We carry out the harmonic analysis on four Platonic spherical three-manifolds with different topologies. Starting out from the homotopies (Everitt 2004), we convert them into deck operations, acting on the simply connected three-sphere as the cover, and obtain the corresponding variety of deck groups. For each topology, the three-sphere is tiled into copies of a fundamental domain under the cor...

The debate on television’s "public service"obligations can only make full sense if integrated in the broader context of the debate on the best political model for society. In fact, the classic "public service"rationale is based in a normative conception of good and in a suspicious view of the average citizen that is largely tributary of a Platonic or Elitist approach to the political organizati...

A new class of spatial data structures called discrete global grid systems (DGGS’s) is introduced and the general application classes for it are discussed. DGGS’s based on subdivisions of the platonic solids, called Geodesic DGGS’s, are then introduced. A number of existing and proposed Geodesic DGGS’s are examined by looking at four design choices that must be made in constructing a Geodesic D...

ideas to physical life. In other words, these techniques and exercises help bridge theory and practice. Doctoral nursing students must learn abstract philosophical content as well as the ways in which this content might appear in clinical practice. For example, knowledge of the differences between Platonic and Aristotelian ideas of reality is an important part of their development as scholars. ...

A Platonic map is a regular map M on the sphere S. Following [CMo] we say that M has type {n,m} if it has n-gonal faces and the vertices have valency m; since these parameters determine a Platonic map uniquely, one can unambiguously write M = {n,m}. As one must have 0 ≤ (m − 2)(n − 2) < 4, there are precisely the possibilities M = {n, 2} (dihedron), M = {2,m} (hosohedron), M = {3, 3} (tetrahedr...

Recently the existence of certain SU(2) BPS monopoles with the symmetries of the Platonic solids has been proved. Numerical results in an earlier paper suggest that one of these new monopoles, the tetrahedral 3-monopole, has a remarkable new property, in that the number of zeros of the Higgs field is greater than the topological charge (number of monopoles). As a consequence, zeros of the Higgs...

As the Platonic philosophy of mathematics is increasingly being questioned, computer technology is able to approach Platonic perfection in limited domains. This paper argues for a mathematical philosophy that is both objective and creative. It is objective in that it limits the domain of mathematics to questions that are logically determined by a recursively enumerable sequence of events. This ...

mathematical forms, handling vast numbers of possibilities at once. In some cases it can help to expose the aesthetic beauty and economy, and the insightfulness, of the theoretical structures that physicists like Dirac, Einstein, Feynman, Salam, Weinberg, and others have used to such awesome effect. Careful serial reasoning systematises and economises large parts of the consistency checking pro...