Science, Art and Geometrical Imagination

From the geocentric, closed world model of Antiquity to the wraparound universe models of relativistic cosmology, the parallel history of space representations in science and art illustrates the fundamental role of geometric imagination in innovative findings. Through the analysis of works of various artists and scientists like Plato, Durer, Kepler, Escher, Grisey or the present author, it is shown how the process of creation in science and in the arts rests on aesthetical principles such as symmetry, regular polyhedra, laws of harmonic proportion, tessellations, group theory, etc., as well as beauty, conciseness and emotional approach of the world.Comment: 22 pages, 28 figures, invited talk at the IAU Symposium 260 "The Role of Astronomy in Society and Culture", UNESCO, 19-23 January 2009, Paris, Proceedings to be publishe

Alberti and Ficino

Leon Battista Alberti and Marsilio Ficino, though separated by twenty-nine years in age, had a close relationship as mentor and pupil. Concepts which can be found in Alberti’s De pictura (1435) and De re aedificatoria (1450) are infused in Ficino’s De amore (1469). The concepts include Alberti’s theories of armonia, lineamenti, concinnitas, ornamento, and the pyramid of light in the theory of vision. In both Alberti and Ficino, harmonies shared by the body and music are manifestations of the harmonies of the soul. Beauty in body and matter is determined by beauty in mind (mens), that part of mind directed toward intellectus divinus, and beauty is made manifest in mind by the lineamenti, the lines in the mind which are distinguished from matter. Beauty is the internal perfection of the intellectus divinus, which is the good, which is a perfect harmony called concinnitas. Ornament is not beauty, but rather a physical complement to beauty

The Good, the Bad, and the Ugly: Does Plato Make Room for Negative Forms in His Ontology?

Plato seems to countenance both positive and negative Forms, that is to say, both good and bad ones. He may not say so outright, but he invokes both and rejects neither. The apparent finality of this impression creates a lack of direct interest in the subject: Plato scholars do not give negative Forms much thought except as the prospect relates to something else they happen to be doing. Yet when they do give the matter any thought, typically for the sake of a prior concern, they try either to support the textual evidence or to contradict it, indicating that the evidence does not stand on its own. The purpose of this paper is to determine why they tend to affirm or deny the obvious, how they try to confirm or dispute it, and what this says about Plato’s position. The strategic vehicle is a comparative case study. The confirmation comes from Debra Nails (2013), who needs to embrace negative Forms to demonstrate that the unhypothetical first principle of the all is not identical to the Form of the good, something she cannot do unless Plato recognizes negative Forms. The contradiction comes from Holger Thesleff (2013), who needs to reject negative (Ideal) Forms because the defining feature of his (Ideal) Forms is the possession of positive intrinsic value, which cannot be predicated of anything negative. Despite defending opposite views, or perhaps because of this, they jointly make up for any lack of interest in the scholarly community. I appreciate both yet side with Thesleff