Darko Sarenac

Department of Philosophy
Colorado State University

http://lamar.colostate.edu/~darko/

Friday, September 18

12:00-1:30 pm

Fractals as a Panacea of Spatial Reasoning?

Abstract:

In this talk, I discuss the connection between some of my (earlier) work

on the spatial logic for reasoning about the objects of standard metric

topological spaces, and a particular class of objects in fractal geometry.

Fractal geometry has been labelled `the geometry of the real world' by

its proponents. The thought is that the broken, imperfect, irregular but

self similar objects of fractal geometry resemble the real space with its

complex features a lot closer than the idealized spheres, cubes, and other

perfect entities of the Euclidean geometry. In this work, I found a strange

coincidence: the logic of standard metric spaces, conceived completely

independently of any fractal considerations ended up using fractals and

fractal considerations in some of its deepest formal constructions. Thus

while the logic was designed to fit the products of perfectly symmetric

world of standard topological spaces and entities, it was at the end better

suited to the real world of uneven entities that thread the fine line of

Euclidean order and chaos(in its recent technical sense). While I provide

no deep theoretical explanation of this phenomenon, a variety of

intriguing pictures, intuitions, suggestions, and a number of theoretical

puzzles are offered. The hope is that we can leave with a deeper

understanding of the role of fractals in formal spatial reasoning, but more

specifically and importantly, the role of fractal objects and constructions in

reasoning about everyday objects.

Key words: Modal Logic, Logic of Space, Spatial Reasoning, Fractals,

Topology, Metric Spaces