THE HERE AND NOW OF PROJECTION

Multicellular organisms have a tactile sense of three spatial dimensions. However, aural and visual perception is essentially two-dimensional requiring subliminal processing of differential stereophonic and stereoscopic data - phase or echo respectively parallax > triangulation - to infer the third spatial dimension. Although well suited to our immediate environment in which tactile and particularly visual examinations tend to correspond, reconstituting the third dimension from two planar observations becomes ever less reliable the greater the disparity between the baseline from one to the other and the distance to the observed target. Consequently, separate observations of distinct properties of a distant or atomic scale target will be inadequate to capture and reconcile all of its dimensional arrangement.

An observer failing to take these shortcomings into proper account may be confounded by the projections that may present of an observational target - for example as the 2d shapes around the circle in the accompanying illustration - and be unable to come to a valid conclusion of their relationship. Yet when expanding the discourse to greater dimensionality these shapes can coalesce to that of the pyramidal top and bottom halves of an octahedron - albeit the illustration can but show a 2d projection: only the red-fringed black edge (vector) of the octahedron (bottom right) is true (real), the red-fringed white edges are imaginary and the solid red edges are foreshortened, meaning they are complex the resultant of real and imaginary component vectors.

Accordingly, what appears as a 3-degree vertex of the diamond shape to the right of the circle, in actuality is a 4-degree vertex from which a fourth edge extends from a coincident vertex of (real) ‘outdegree’ zero to imaginary ‘indegree’ n (4-degree for the present example, similarly regarding its two 2-degree vertices). In other words, this fourth edge, being orthonormal as in the line-of-sight, is imaginary of unknown length between zero and infinite. Now in the example of the octahedron the source for observation of the further part of a complex edge comes from an earlier time than that of the nearer, from which one must conclude that the imaginary component of a complex edge is temporal and meaning that the octahedron’s several imaginary component vectors are not the same and similarly so for all such in any observation regardless from what angle and so are not coincident (edges shown all but parallel for targets at infinite distance and quantum scale).

Only one conclusion follows confirming this presentation’s revelation: time is a 3-d domain in which any reference zero is at spatial infinity while any spatial reference zero is temporally unending. What is observed is real including the real component of a complex aspect of a property, all else imaginable that has been or will be real - i.e. at some other place and/ or time - is imaginary the instant, here and now, an observation is made.