Path and journey

A path is a way trodden out over time by the feet of humans or animals using it with some frequency or, more generally, the course or route along which any object moves, even if the movement is not repeated (as with a boulder rolling down a hill).

The course of action followed by an individual or group may be perceived as a journey over a path. The action may take the form of a time of argument developed through a number of stages. A number of times of argument may intertwine like a network of pathways with varied points of focus.

The surface implicitly defined by any path or journey and the distinction between being on or off the pathway and being on or off that surface.

Descriptions of arguments make frequent use of journey-related terms (e.g. set out to prove, on the way to solving the problem, getting to the next point, arriving at a conclusion, pointing to the next step) including those related to going 'off-track' (e.g. straying from the path or from the line of argument, missing the point, getting lost in an argument or going around in circles). The paths of arguments are also related to movement over a surface (e.g. covering points or ground, getting on or off the subject, going in circles). In philosophy thinking itself has been considered as a path. The motion of a path, and its stages, is central to many schools of religious and spiritual development.

That surfaces as contrasted with other surfaces and other geometrics. Closed surfaces. Topological spaces. The Möbius, strip, Klein bottle and the torus. The relationship between the beginning and the end of the path. Topography, geography and cartography. Catastrophe theory.