6945 - The geometry of time

N. Lygeros
Translation: Paola Vagioni

One way to approach the geometry of time is through complex analysis. A representation of complex functions may be done by using the dimension of color. This procedure allows the study of objects, which typically need four dimensions. This property can also enrich other cognitive sectors where geometry is necessary. One of those is strategy, which, depending on what it is combined with, can be transformed into geostrategy and topostrategy. In any case, geometry of time can be highlighted with the dimension of color. The implementation of this idea is not difficult, because usually our maps exploit only two space dimensions. We can imagine now better this approach. Usually, color is static, either in the political maps where it only enhances the notion of borders, or the physical maps where it represents the third dimension of space, in other words it operates as an altitude. While the color representation of maps is capable of displaying the dynamic and incorporating the geometry of time. With this approach, we are now in a position to activate this tool in topostrategy and especially in the Voronoi diagrams and the Delaunay triangulation on the Aegean Sea. The idea is not just the coloring of the Voronoi cells, which would have been a simple reproduction of the same mental schema that constitutes the substrate of traditional maps. The coloring is a field equivalent to the one we encounter in dynamic systems and more specifically with the notions of the Julia and Fatou sets. In this way we can interpret for example the Voronoi cells as basins of attraction of the point attractors. In the following phase, the unification of the Voronoi cells that have a common base, such as an island, gives us the possibility to interpret it as a new solid attractor which influences the unified basin of attraction. We understand then that we have at our disposal a radically different picture of the Aegean Sea, which highlights its robustness.