Absolutely straight lines or an absolutely flat plane would, theoretically, continue outwardly to infinity. Intellectual comprehension occurs when patterns of experience return upon themselves in all directions. The difference between infinity and finity is governed by the taking of angular sinuses, like pieces of pie, out of surface areas a round a point in an absolute plane. This is the way lamp shades and skirts are made. Joining the sinused fan-ends together makes a cone; if two cones are made and their open, ergo infinitely trending, edges are brought together, a finite system results. It has two polar points and an equator. These are inherent and primary characteristics of all finite systems. Man has employed the convention of subdividing the unity of encirclement around a point into 360 degrees, formed by the sum of the radial segmentations around a point in an absolute plane. If we call 360 degrees “unity,” I may state my discovery of the law of systems as follows: if we subtract the sum of the convergent angles around all the vertexes of any system from the numbers of vertexes times 360 degrees, the difference will always be 720 degrees, which is exactly two times unity; this is to say that the difference between infinity and finity is always exactly 2. This law explains many of the previously uncomprehended aspects of topology [Fig. 8]. Its philosophic implications are startling.

The compressively interprecessional cooperative and accommodative functionings of all structural systems are locally persistent constellations of resultant force-vectors, which are always angularly shunted, and regeneratively re-shunted, inwards of the system’s tangential lines, i.e., at resultant angles less than 180 degrees in respect to the direction of origin of the generative force. In the high and low tide cooperative precessional functionings of tension vs. compression I saw that there are times when each are at half tide, or equally prominent in their system relationships. I saw that the exterior of the equatorial compressional island rim atoll of the wire wheel must be cross-sectionally in tension a s also must be its hub island’s girth. I also saw that all these tension vs. compression patterning relationships are completely reversible, and are entirely reversed as when we considered the compressively spoked “artillery wheel” vs. “the tensional spoked wire wheel.”

I followed through with consideration of these differentiable, yet complementarily reversible, functions of structural systems as possibly disclosing the minimum, or fundamental set of differentiability of non-redundant, precessionally regenerative structural systems.

Employing that concept as an hypothetical verity or working premise for further probing, I observed that whereas there existed a limit to slenderness ratio as already noted of a compression member’s girth diameter in respect to its longitudinal axis length, no such limit slenderness ratio characterized tensional dominated structural components. Astronomical magnitudes of structural system coherence are accomplished by tensionally dominated structural functions of zero slenderness ratio, i.e. by gravitational functioning. I also noted that compressionally dominated structural components tend toward contour transformation in which the radius of curvature steadily decreases under axial loading, that is the cigar shaped column forces tend toward “squash-” or “banana”-like bending of their contours [Fig. 11]. This tending of compressionally loaded systems toward arcs of lessening radius was in direct contrast to the contour transformation trending of tensionally dominated structural components which always tend toward arcs of ever increasing radius of axial profile. For instance, the coil of rope tends toward “straightening out” when terminally tensed, but never attains absolute straightness [Fig. 9]; instead, it progresses toward ever-greater radius of locally-spiralling but overall-orbital arcing which must eventually cycle back upon itself [Fig. 12]. Tensionally dominated patterning is inevitable self-closing, ergo finite.

It is seen also that, whereas compressionally dominated functions of structural systems are inherently self-diminutive in overall aspect, tensionally dominated structural functionings are inherently self-enlarging in overall involvement. Therefore the sum of all the inter-active force relationship of universe must continually accelerate their inter-transforming, in such a manner as to ever result in more remotely and locally multiplied islanded compressional functions–comprehensively cohered by ever-enlarging finite patternings of the tensional functions. The universe mast be a comprehencively finite integrity, permitting only a locally-islanded infinitude of observer-considered-and-regenerated differentiating discovery [Fig. 13]. This is to say that we have herein discovered a workable man-awareness of a complete reversal of presently accepted cosmology and of general a priori conceptioning regarding the general patterning scheme of universe which, heretofore, has always conceived only of locally finite experiences as omnidirectionally surrounded by seemingly unthinkable infinity.

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