The Shape of Space: Topology and Trajectory

This paper discusses ‘the shape of space’, in terms of search algorithms and traversal operators. It is pointed out that it is the combination of traversal operators and representation that gives rise to a fitness landscape. This provides an intuitive background to recent discussions on the formal limitations on search algorithms. Dynamic and random remapping of space via base changes—applying multiple heuristics to a given search problem—is proposed as a pragmatic means for probing a cost function from many views. New algorithms based on dynamic representation are introduced, and are demonstrated on a range of standard cost functions.