— Fractal Integration —
One for All
The idea that numbers are also their reciprocals and that the combinations of the values for an integer might indicate its optimum tells us that numbers can be considered atoms having size.
Having elsewhere looked at 5 and 2 with 4 and 8 we want to look at three, but before we look at three, let us cast a glance on the basic integer, 1.
As in everything, One is a special case, being the reciprocal of itself. The positive mean value of 1 is 1, exactly — but from this follows that the deviation is also 1. If so, the domain of one is 0.0 and 2.0. Hidden just out of sight from that statement is the idea that it must be either, not both, and nothing in-between; including itself. We cannot look upon one without looking upon its immediate surroundings.
Center of Centers
If one is either zero or two but not one, for zero the opposite is the case. It, too, has a self-identical deviation, meaning it deviates not from itself at all. Whatever is zero is completely and fully zero and precisely, exactly so, no deviance whatsoever. Zero is orthogonality and perpendicularity fused into one, like wood and air turn into fire.
Zero is Origo.
Zero as Hestia
The difference between one and zero could be stated, then, to be that one can visit zero, but zero does not visit any one.
Zero is like the Greek goddess Hestia, whom both Apollo and Poseidon wanted to marry, but who asked of all-father Zeus that she be allowed to forever remain a virgin, to be given no other place than with the sacred fire of sacrifice, tending to the hearth of and fire of the immortal gods. Where the fire of sacrifice burns, were the flaming spirit of the eternal Integers is present, Hestia, is. Goddess of hearth and home, of the paradigmatic Here, Hestia thus is first among equals, her name preceding even the holy one, the All-Father’s name. All-wise Zeus granted this wish.
Zero precedes Zeus as Hestia the One.
Elaborating further, if zero is never-present outside itself, perhaps not present even there, and if, jumping a bit now, every integer relates to one by exactness, it would seem that just like one is absent from itself, so is every other integer also. Zero is what every Integer is, at heart.
Integers become real by absence. The atoms, the environment, is there, but the center, the whole and exact integer as such — n.0 —, is empty.