To see why it makes sense to sequence existence before creation, creation before interaction, and interaction before existence, as in a ring,
is made somewhat easier to understand by considering the required implications that must occur when regarding various metaphorical situations,
more commonly known as "thought experiments" in the physics literature.
However, before presenting various such representative scenarios, it is helpful to point out that, in a purely mathematical sense,
among three nodes (the modal concepts), that it is really only possible to form two distinct types of sequenced -- or directed -- rings between them.
This is evident when drawing those nodes as three labeled dots in a graph, and showing that there are only two ways in which they can be connected together with arrows between them to form a ring.
The ring (a triangle graph) either "flows" one way or the other; clockwise or counterclockwise, and rearranging the nodes are just symmetric variations of these two directions.
Therefore, to be a ring, Axiom II can really only take two forms: either its E --> I --> C --> E..., or its C --> I --> E --> C...
The question of about being 'arbitrary' is then only to show which of these two basic ring types is the necessarily preferred form.
To start with, imagine that there are two billiard balls in an otherwise completely empty universe.
Insofar as those balls "exist" within a space, we can define their static relations -- and the "space" that encloses them itself --
mathematically by considering the size of the balls and the distance between them as two possible units of measure in proportion to each other.
However, as long as there is some distance between them, ie, that those two balls are not exactly touching one another,
then it is fair to say that they are 'not interacting'.
To have any notion of interaction -- a transfer of force or some other character between them -- those two billiard balls, at some point, must actually touch.
The notion of other types of forces (electric, magnetic or otherwise) are merely asserting that the space is not actually empty,
as stated in the premise (it is pervaded by "fields") and that those fields are actually a form of touching between those two balls.
In light this, it is simpler to consider that the notion of simple touching as an event is directly equivalent to the notion of interaction.
In effect, this metaphorical system has only three states: separated, touching, and overlapping,
and yet this immediately reduces to just two when observing that the notion of overlapping --
two balls occupying at least some of the same space --
is directly forbidden simply because it contradicts the premise of the model in the first place.
The notion of 'overlapping' means that there is at least somewhat 'less' than two complete balls (ie, their union or intersection).
Thus, it would seem to be the case that there are, in this hypothetical universe, really only two states:
'interacting' (as touching) and 'non-interacting' (as not touching, or separated by at least some distance between them).
Initially, at first glance, it would seem fairly obvious that, if anything, this is a direct example that existence precedes interaction --
you must have the notion of their being billiard balls 1st, before you can consider them as touching ('doing') 2nd.
This precept that 'being is before doing' is a consistent absolute and underlying assumption of both science (in the form of the scientific method) and spirituality
(in the form of the practices of introspection and meditation) the world over.
Yet it is this very precept that overlooks an important truth.
What is it that moves those two balls into coming into touching in the first place?
In some basic sense, existence must go 'beyond' or 'outside' of itself in order for there to be interaction.
Interaction is fundamentally more than existence, since the very premise of the precept as considered so far is that
'there is existence' and then 'the existing things interact'.
The question is: what adds that 'more'?
Where does the 'more' that transcends existence into interaction come from?
In our imaginary scenario, the interaction only 'occurs' when they touch, and this moment or event is fairly unique.
Touching spheres is a characteristically distinct relation of sizes and positions and, (by symmetry conditions), has exactly and only one state.
If the notion of pure existence is going to be established as explicitly and exactly prior to interaction,
then these two concepts cannot in all cases be defined as co-occurring -- ie, we cannot posit that they were "always touching" in the first place.
In other words, there has to be a moment 'before' the event of touching where the two spheres are fully separated from one another in space (by at least some non-zero and arbitrary distance).
Yet this concept of 'beforeness' (time) is in addition to the concept of 'beingness' (space).
In other words, we "have" the billiard balls and then we "add" motion and we "get" interaction.
Yet this addition -- this additional concept of time and motion -- is strictly more than was initially presented in the metaphorical scenario in the first place:
all that was asked so far is that 1) we imagine two billiard balls in an otherwise empty space,
and then 2) that we consider what we must do -- the required implications -- that must occur while we imaging them interacting.
The notion of adding time and motion -- change -- to an otherwise static situation -- existence -- is necessary to consider (to imagine) the concept of interaction.
Therefore, we at this point know that there are really two things that are necessary to imagine first before we can even begin to imagine interaction: both existence and motion.
In effect, motion transcends existence to create interaction.
Yet even in this phrasing, the notion of 'to create' is itself a change -- the event of going from non-existing to existing -- and therefore itself a type of motion.
Therefore, insofar as these three concepts (to move, to transcend, to create) are in this context and in this specific way, the same -- ie, as changes,
then really, the metaphor/model so far can be represented by a simple equation: M * E == I
, or "motion and existence equals interaction".
Thus our imagined scenario -- our thought experiment -- must take one of two possible forms:
either we imagine that there were two billiard balls in an otherwise empty space, separated by some unchanging distance,
and then "something causes" them to move toward one another -- some invisible hand or force -- that brings them into contact,
OR instead, if we do not like the idea of this imagined something other coming into the picture,
we can imagine these two billiard balls as infinitely far apart, infinitely far back and time, and thus "created that way"
in a constant velocity of motion towards another, so as to eventually come into contact.
Insofar as the latter picture seems to be the simpler one -- it does not have or require any "mysterious hand" -- it seems best to start with that one,
explicitly because it appears to be more supportive of the premise being considered: that existence precedes interaction.
Unfortunately, with a little thought, it is actually possible to show that these two apparently distinct imagined scenarios are actually and strictly the same as one another.
If we are to assume that the two billiard balls were always already in motion before the singular moment of their interaction, then we must consider how we know they are moving.
To have a notion of motion, we effectively must define it in terms of a basis in position, ie, as changes in position or changes the distance between the two balls.
Yet to establish the notion of distance itself, as a measure of the space between the billiard balls, there is a need to establish a unit of measure -- a relativity or proportion.
The only thing available for this purpose is the diameter of the balls.
But their diameter(s) are an arbitrary measure.
They is not central to the consideration any more than a consideration of what material, what "stuff", the billiard balls happen to be are made of.
If the diameter of the balls themselves is the only basis to establish their metric of distance in space and thus their motion,
and yet this diameter is an arbitrary feature, then there is a question as to on what actual basis the notion of change really rests.
For example, one could attempt to imagine the balls shrinking down to dots until they are equivalent to the concept of mathematically dimensionless points
existing in a separated state, and then later as in an interacting, not separated or 'connected' state.
Such considerations obviate completely the need to define a metric of distance at all: it is a Boolean and has either a value of 1 (separated points) or 0 (a union of "two" points, now really only one point).
Unfortunately, this also has the effect of collapsing the notion of time: the infinitely past becomes strictly equivalent to just 'the moment before', which then leads to 'the moment of', interaction.
In either event, the notion of a change in addition to existence is an intrinsic: what is it that chances the 'one' to a 'zero', in terms of distance, or a 'two' to a 'one', in terms of points?
That 'invisible hand' has returned with a vengeance!
In other words, it simply does not matter if the billiard balls are imagined as having only velocity beforehand, or if there is some sort of acceleration involved,
in either case, the notion of 'motion' must occur after the notion of 'existence' and before the notion of 'contact'.
What does this mean?
However we elect to consider the situation, by whatever methodology we attempt to create an imagined scenario, ANY imagined scenario at all, it is effectively strictly impossible
to imagine the concept of motion, or change, prior to the concept of existence.
This is a rather astounding result!
Yet, in retrospect, a fairly obvious one.
In effect, how could you imagine 'changing' unless you have already imagined a 'something' which changes?
What is surprising is that this truth is now defined in such a way that it is invariant with respect to the process of imagination itself.
It simply does not matter "how" imagination works --
by whatever process, mental, physical or otherwise, we create or consider imagined scenarios in the first place --
or even what, ie, what content, we elect to imagine, consider, or think about.
In all situations, change (event) comes after being (thing/existence) -- and that this is an intrinsic to the process; not just the of imagination, but to the very notion of "process" itself.
At first this result seems to be consistent with the very premise being considered --
that being (stuff) is before doing (change) --
and yet what has actually been identified here is that the notion of 'that which transcends existence' is actually and inherently of three kinds, not one:
- 1; There is the change associated with the event of imagination
itself (ie, as "creation", that which is "before the beginning", or rather more simply,
the establishment of the mental visual of two billiard balls in an empty space in the first place).
- 2; There is the change associated with the motion of those billiard balls, to go from simply statically existing separately, to moving towards one another (the invisible hand), or
alternately, to transition from 1 to 0 (itself also the same transition as from 2 to 1).
- 3; There is the notion of the event of interaction itself, the moment of touching or the union of two points (ie, somewhere on the surface of each billiard ball or mathematically).
All three of these concepts are properly considered as concepts which transcend, or go beyond/outside, the concept of existence.
If we consider what has happened when we try to imagine interaction, or in effect, what must happen, we find that the required
description of our scenario is:
1st there is imagination of matter (the billiard balls in space -- necessarily included for completeness),
2nd there is the imagination of motion (as established above), and then, only then, is there any possibility at all of there being
3rd, the imagination of interaction.
Thus 'change' comes after
'being' (thing/existence) and yet before 'interaction',
or more simply, "Existence precedes Change which precedes Interaction".
The key insight is that for every kind of being, that there are actually two
kinds of doing (change and event), not just one.
Not only is it the case that at two things are needed to have an interaction, but that for every being there are two kinds of doing.
In effect, our equation above must be expressed as "assert(M * E --> I)"
and that the operators or symbols of "assert" (as the verb 'to imagine' or 'to create'), "*" (add and/or multiply), and "-->" (equality, transform, isomorphism, etc) must in themselves be accounted for.
While these three kinds of operator concept are not identical,
as they cannot be conflated insofar as they have different roles of action,
they are also ultimately the same,
in the sense that they are of the same 'type': 'that which transcends existence' (all that is around the central 'E' symbol).
The notion of interaction depends not just on the notion of existence, but also on the notion of change, and that this notion of change must also occur after the notion of existance.
Insofar as the type of the concept of change is the same type as the concept of creation itself,
then therefore, the actual pattern fundamentally observed is: Omniscient (existence) --> Transcendent (change/motion) --> Immanent (interaction/event).
And yet this does not quite go far enough as it does not include or account for the event of imagination itself -- a 'kind' or 'type' of change itself.
The basic premise or process behind this 'thought experiment' in the first place is to exactly notice and carefully describe all of the necessary things that must occur when electing to imagine interaction.
To have an event of imagination, there is effectively
1st a self -- some subjective basis, mind, or person making a choice and then later engaged in the action -- of
2nd creating an imagined scenario, in which
3rd an event of interaction is (potentially/metaphorically/symbolically/actually) perceived.
Considered in terms of concept types -- the roles that each aspect plays with respect to the other two -- this situation would need to be modeled as "Self Imagines Thing",
or more fully "Self (a person exists) Imagines (a choice event; creates) Thing (an internal content of mind, a perception)".
Insofar as the notion of perception is strictly a concept of interaction, then at this level the metaphor is still modeled by Axiom II as:
Omniscient (the observer) --> Transcendent (to imagine, to create) --> Immanent (the subjective perception of two billiard balls interacting)".
Only in this way is that 'invisible hand' -- our own as 'the imagineer', the change which initiates -- fully accounted for.
Insofar as both levels of consideration end up requiring same result in terms of flow,
and moreover that the notion of change is strictly isomorphic to the notion of creation (ie, an event of novelty),
it seems that there is actually a rather strong bias that selects which Axiom II flow, of the two available, is the preferred one.
This impression is even further strengthened when it is also considered that the very process used to establish or determine that something exists,
a measurement of its properties (note that the concept of measurement is inherently an interaction) also establishes a basis for the idea
that interaction precedes existence.