All axioms are random in the respect they require a degree of spontaneity, with this "spontaneity" observing an inherent "disconnect" in relations. I may observe a vaccum state with particles emerge and disappear spontaneously.

However, randomness does not mean "disorder". While the formation of the axiom may effectively be spontaneous for a variety of reasons

a. Axiom A may variate into Axiom B by standard entropy/negentropy.

b. Axiom A may variate into Axiom B because Axiom B is an approximation of Axiom A in light of Axiom C. Axiom A is an approximation of some other axiom in light of Axiom C. Axiom A reversibly is an approximation of Axiom B and/or C. etc.

c. etc.

; the axiom results in further axioms; necessitating an inherent order where the axiom as "spontaneous" maintains corresponding axioms to which it connects and seperates from. All continuums inherently are "rational" as the composition of the continuum, as an axiom in itself, is composed of and composes further axioms.

Going back to the vacuum state example, that while the particles may emerge and disappear spontanously, this observes a fundamental repitition of "order":

A. Particle A is still of the same class as a specific point of origin as an axiom of reality.

B. The movement of the particles, through a wave, always necessitates a repitition of linear movement founded on Particle A moving through a basic Point X to Point Y foundational dichotomy known as "time".

C. The Emergence and Dissappearance of Particle A observe a foundational alternation within the particle itself necessitating a basic circularity or isomomorphism.

What we deep fundamentally as "irrational" fundamentally is an absence of connection or a cessation in the continuum. In these respects "spontaneity" and "randomness" are irrational relative to the observer, but because they always contain a constant repitition of a "continuum" they are never truly irrational. There is no true irrational in light of space being the foundation axiom of all "being".

## The Impossibility of Randomness

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