The need to define terms, especially at the outset, is keen throughout science; but the peculiarities of ideonomy are such that what elsewhere would be a mere need here becomes an absolute necessity.
Let this not give rise to a misimpression: within ideonomy the same problems and limitations that beset the definition of terms and concepts in other fields are no less stubbornly present, and the grail of definitions that are perfect and absolute will always remain elusive (although revolutionary advances in this direction are indeed possible and will certainly occur).
Also, because ideonomy is in its infancy many of its terms and concepts should only be defined tentatively, ambiguously, polysemously, open-endedly, mutably, multiply, even contradictorily; and they should be redefined repeatedly. For definitions of divisions this is especially appropriate.
So path, in the sense of the present division, might variously, imperfectly, but hopefully suggestively be defined as:
l [Structured, ordered, continuous, simple, unique, self-identical, consequential, useful, exclusive, &VC] connection between. two [points, loci, regions, poles, things, boundaries, limits, events, actors, attractors, nodes, configurations, 2 states, levels, holes, subsets, neighborhoods, values, &vc];
2 The continuous series of [positions or configurations] assumed in any [motion or process of change] by any [Moving or varying system;
3 [Way, course, track, or channel] traversed, traversable, traceable, retraceable, or usable] by something.
The most elaborate definition of path I can offer at the moment is that produced by concatenating as many forms of oppositeness as I can think of that might characterize its range of possibilities in a multidimensional space, and by letting it be understood that-whatever a path is- it is some sort of structure, entity, or set of possibilities in this stupendous abstract space (for which I apologize to readers):
4 {[Retraceable <-> unretraceable] [persistent <-> instantaneous] [Actual <-> postulated] [Directed <-> undirected] [Unidirectional <-> bi-directional] [Commutative <-> noncommutative] [Positively defined <-> negatively defined] [Spatial <-> temporal] [Associative <-> nonassociative] [Distributive <-> nondistributive] [Transitive <-> intransitive] [Geometric <-> topological] [Past <-> Present <-> Future] [Two-ended <-> multi-ended] [Symmetric <-> asymmetric] [invariant <-> changing] [Finished <-> developing] [Homogenous <-> heterogeneous] [Uniform <-> nonuniform]} {[Breadthless line <-> area <-> volume <-> field] [locus <-> thing <-> operation <-> function] [Continuous series <-> series of (two or more) (points, loci, or referents]} {CONNECTION, NEXUS,COURSE, ROUTE, TRACK}
Actually I can already see that my elephantine 'definition' is inexcusably incomplete.
A simple reason why I am devoting a chapter to paths is that I think readers will turn out to be surprised by the degree of interest and importance they actually have. Another reason is that I have found empirically in the course of my ideonomic investigations- rather to my own surprise-that certain ideogenetic formulas that refer to paths are unusually successful, productive, and powerful. The subject can therefore attest to the feasibility of ideonomy and to its ultimate creative potential.
There are fields and phenomena in connection with which the importance of paths is already well-known. EXAMPLES ARE: physics (the path of an elementary particle), operations research (CPM or the critical path method, used in detailed project planning and control), astronautics and military science (the trajectories of rockets and shells), hydrology (river meanders), astronomy (precise orbital paths of celestial bodies - e.g. their sensitive ties and projections backward and forward in time), oceanography (paths of currents and eddies), mathematics (asymptotic path for a meromorphic function, the paths of Markov processes or projective geometry), archaeology (trade routes), meteorology (jet streams), musicology (the path of a theme through a symphonic fabric), biology (the cellular or bodily path of a genomic communication, path of migrating caribou, or path of a windborne pollen grain), sociology (a rumor's path), and chemistry (a reaction path).
There are other fields and phenomena possessed of paths, or to which the concept of a path applies, but whereof the relevance of paths remains undiscovered, unimagined, or undeveloped. Here ideonomy may serve as a corrective through the richness of its vision and the novelty of its methods, and through what is perhaps its greatest insight: that phenomena and methods for treating phenomena are essentially universal.