Elements of Space (Topic 1 of Orientation)

 

Everyone partakes of space. The following approach to dealing with space starts from experiential basics, steps intuitively, observes the obvious and not so obvious, and proceeds quite productively. 


Although the geometric form structuring GDCode's model has been known since antiquity, it is built here from scratch. The value of doing this will gradually be appreciated, fully so when architectural and subsequent design guidelines are derived. Until then, space is revisited in a kind of primitive way.


To construct the model's form from scratch, elemental building units are drawn from the most common of spatial forms - spheres.
Be they represented by countless celestial bodies, the ubiquitous central force fields of physics, a shiny new ball captivating an infant's attention, or perhaps nebulous souls - spheres are everywhere. Geometrically, spheres are omnidirectional expansions of the dimensionless points that center - and are thus integral to - their surface-manifested essences.


Of all possibilities pertaining to the relative size of spheres, for purposes here they are specified to be of equal size; with regard to their spatial relationships (separated, overlapping, engulfing, etc.) surfaces of neighboring spheres are required to be just contacting.


Much happens in the initial, one-at-a-time assembly of spheres so-specified: with 2 spheres, the line joining their center-points manifests the first dimension; a 3rd sphere placed in mutual contact with the 2 spheres - in what is termed planar nesting - delineates the 2-dimensional plane of an equilateral triangle with lines connecting the 3 spheres center-points.


Into the 3-sphere cluster naturally goes a 4th sphere. Such deep nesting forms the 3rd dimension of space with an underlying tetrahedron - 4 triangles delineated by 6 lines joining 4 center-points. The 4-sphere cluster is the last arrangement in which each sphere contacts all other spheres.


From here, it is tempting to continue deep-nesting, but doing so leads to random disordered growth. Thus future placements require the deliberation explained in Rational Accretion, topic 2 of Orientation.