April 30, 2015

Paths


Kbase Thing

Paths are either a non-self-crossing path or a cycle. A path may be spatio-temporally abstract (e.g. links in Graph Theory), spatially-located but intangible (e.g. a latitude line might be used as a path in some system), or fully concrete (such as a road, railroad, sea-lane, cowpath, pipe, blood vessel, fiber, or wire). A path can be anything that is used as a path in some path system. For example, an orange is not a customary path, but it can be a path for ants in a specified ant path system. For any path, there can be a traversal of something moving along the entirety of that path (and a single traversal can cross itself, double back along itself, or go back and forth along some part of a path any number of times). Note that a path does not have to be an individual, because there is nothing in principle to prevent a mathematical set or a collection from being “used as a path” in some path system. For similar reasons, few if any collections or sets can definitively be considered disjoint with Paths.