Ambiguous Flatness; A "Sufficiently Large" Sphere

[* This part of the reasoning most resembles Physics' "A random fluctuation in nothing" *]
....(Thus revealing that Physics doesn't understand the concept of [NoThing], either....)

Consider a hollow sphere composed of dimensionless, noncoalesceable points.
As in our discussion of its expanding nature, we find that this hollow sphere has no real limitation on its size. In theory, it could go on expanding forever (there are, after all, an infinite number of pionts, all trying to express their actuality/individuality --in only two dimensions, so far).

Now, a sphere has a curved surface, but in the "limit" (despicable concept, but apparently unavoidable) of any very small area of that surface, the curvature of same becomes less and less, the larger the sphere gets.

Imagine a child's marble, and look at one square centimeter of its surface (nearly half the marble): its curvature is obvious.
Imagine a ping-pong ball, and look at one square centimeter of its surface: its curvature is still obvious.
Imagine a weather balloon, look at that same area: the curvature is less obvious.
Imagine a ball the size of a small moon: you begin to see that the larger the sphere we imagine, the flatter will be that one square centimeter area of its surface.
(You might guess: this is why the Earth looks quite flat when standing on it, but spherical when very far from it.)

Now, "in the limit" (nasty phrase, that....), we should see that as the sphere approaches infinite 'surface' area, the curvature of this tiny area under our consideration approaches 'perfectly flat.' How much less curved, then, would be a ten-or-so-piont area of it? These pionts are dimensionless!

Hence, we find it possible to suggest that while formerly, piont-to-piont "contacts" (instances of minimum distance) may have kept them all in place in that two-dimensional "surface" of the expanding sphere, now that the area where they are has become indistinguishable (to them) from "flat," they may be able to escape--to find themselves able to make use of a third dimension for expression of their individuality: that minimum-piont-ness area inside the sphere.

Result? In Tetrahedraverse, an IMPLOSION of pionts into the formerly "empty" interior, which is by this stage quite, quite "large."

 

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