986.070 Buildings on Earths Surface

986.071 In the practical fortress and temple building of the earliest known Mesopotamians, Egyptians, and Greeks their cubes and omnirectilinear blocks seemed readily to fill allspace as they were assembled into fortress or temple walls with plumb bobs, water-and-bubble levels, straightedges, and right-triangle tools. No other form they knewother than the cubeseemed to fill allspace as demonstrated in practical masonry; wherefore they assumed this to be scientifically demonstrated proof of the generalizability of their mathematically abstracted plane- and solid-geometry system and its XYZ coordination.

986.072 Because of the relatively diminutive size of humans in respect to the size of our planet, world-around society as yet spontaneously cerebrates only in terms of our immediate world’s seeming to demonstrate itself to be a flat plane base, all of the perpendiculars of whichsuch as trees and humans and human-built local structuresappear to be rising from the Earth parallel to one anotherergo, their ends point in only two possible directions, “up or “down.” …It’s “a wide, wide world,” and “the four corners of the Earth.”

986.073 It was easy and probably unavoidable for humanity to make the self-deceptive blunders of assuming that a cube held its shape naturally, and not because the stone-cutters or wood-cutters had chosen quite arbitrarily to make it in this relatively simple form. Human’s thought readily acceptedand as yet doesthe contradictory abstract state “solid.” The human eye gave no hint of the energetic structuring of the atomic microcosm nor of the omnidynamic, celestial-interpositioning transformations of both macro- and micro-Universe.

986.074 Prior to steel-framed or steel-reinforced-concrete construction methods, humans’ buildings that were constructed only of masonry could not be safely built to a height of over 20 storiesapproximately 200 feet high. Such a masonry building was Chicago’s turn-of-the-20th-century world-record Monadnock Building, whose base covered a small but whole city block. It is not until we reach a height of 100 storiesapproximately 1000 feet highthat two exactly vertical square columns, each with base edges of 250 feet, built with exactly vertical walls, and touching one another only along one of each of their base edges, will show a one-inch space between them. The rate their vertical walls part from one another is only \sfrac{1}{100} of an inch for each foot of height.

986.075 Masons’ and carpenters’ linear measuring devices are usually graduated only to \sfrac{1}{16}th of an inch, and never finer than \sfrac{1}{32}nd of an inch. Thus differentials of a thousandth of an inch are undetectable and are altogether inadvertently overlooked; ergo, they get inadvertently filled-in, or cross-joined, never to have been known to exist even on the part of the most skilled and conscientious of building craftsmen, whose human eyes cannot see intervals of less than \sfrac{1}{100}th of an inch.

986.076 If two exactly-vertical-walled city skyscrapers are built side by side, not until they are two and one-half miles high (the height of Mount Fuji) will there be a space of one foot between the tops of their two adjacent walls. (See Fig. 986.076.) Of course, the farther apart the centers of their adjacent bases, the more rapidly will the tops of such high towers veer away from one another:

The twin towers of New York’s Verrazano Bridge are 693 feet high …soaring as high as a 70-story skyscraper …set almost a mile from each other, the two towers, though seemingly parallel, are an inch and five-eighths farther apart at their summits than at their bases because of the Earth’s curvature[^37]

986.077 It is easy to understand how humans happened to think it “illogical” to have to consider that all the perpendiculars to a sphere are radii of that sphereergo, never parallel to one another. Our humans-in-Universe scale is inherently self-deceptiveergo, difficult to cope with rigorously.