This particular post to become a repository of some running thoughts taken from my journal of scattered notes.
Regarding the colloquial “sharing the same space at the same time”, it would seem our physical universe prohibits coincidence. (This, with possible exception to that of blackhole-like conditions and/or quantum effects.) However, in the shelter provided by the abstract, theoretical constructs offer me opportunity to better analyze and more clearly delineate some of my thoughts.
Adding to these as I find necessary, the following represents a philosophical reconciliation of several fundamentals offered before I venture broader ideas. I concede the unconventional and oxymoronic nature of some (e.g., parallel lines). Hopefully a careful parsing will resolve their counterintuitive appearance.
1. A locus exists in the conventional sense unless otherwise specified.
2. While reducing to a singular feature, coincidence exists as a descriptor of intersection.
3. A point is a dimensionless placeholder whose relevance is dependent upon another feature.
4. Three non-colinear points constitute an infinite plane.
5. A line segment, being the locus of all points constituting the shortest distance between any two, may enjoy infinite extension as a straight line.
6. Their relative offset zero, coincident lines are parallel.
7. A singularity, of infinitely distant coincidence, renders the loci of coplanar straight lines parallel. The same, less the infinite constraint, must necessarily coincide elsewhere and as such form an angle between them.
8. Where the locus of a straight line serves as an axis of rotation for a non-coincident point:
a. Any two non-coincident points in the locus of revolution define an orthogonal straight line, albeit not necessarily of coincidence with axis of rotation.
b. Any three non-coincident points in the locus of revolution define an orthogonal plane.
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I should note here, and at least for now, my anecdotal thoughts of negative volume (i.e., negative dimension) and a concept I have of departure velocity, have coalesced to that of the blackhole and the Planck scale(s) respectively.
