Orienteering in Knowledge Spaces

Gregory Leibon

Coherent Path / Mathematics Department Dartmouth College

Navigation of knowledge spaces (like Wikipedia) depends on one's objective. If one's objective is to try to find something efficiently with regard to the number of nodes visited, then there are well developed network geometries to help one navigate. But if one's goal is discovery of the unknown, then what are good candidates for the geometry? In this talk, we will examine a candidate for such a geometry. This geometry is constructed via a coupling of the notion of a network with directions with an adaptation of the four-point probe from materials testing. This four-point probe geometry shares many of the properties of hyperbolic geometry, wherein the network directions take the place of the sphere at infinity. This enables orienteering of the space with the directions serving as the points on a compass. Real world examples will be presented, and my hope is to make this talk very accessible; in particular, no prior knowledge of hyperbolic geometry is necessary.

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