Relation and Non-Relation

From one point of view it seems that there are only two fundamental bases for coming up with models of reality:

1) Everything is connected
2) Everything is disconnected

Every particular model of reality takes these two bases and combines them in various ways that can range from very simple to incredibly complicated. For example: probabilistic and statistical models quantify basis two, by introducing the idea of uncertainty, which is very closely related to non-relation (e.g. how do the ways in which things are not connected or non-related matter). Deterministic models quantify basis one, because they indicate the way in which objects are related to one another (or are connected).

The problem is that in reality the number of ways in which things are (1) or (2) is an unmeasurable quantity, so any particular model will be an imperfect realization of what is actually going on. This leads me to wonder if there is not an additional "orthogonal" basis that is independent of relation or non-relation that also describes reality in a completely consistent sense. Something that is neither connectedness or disconnectedness. What if we define this third basis as all aspects of a system that are not quantifiable from within a subjectivity?

Could we treat this third component of model building as the unknown unknowns (meta-unknowns)? These unknown unknowns could be incorporated in a Bayesian framework as the joint uncertainty in the model and the uncertainty itself. Or in this case, the joint distribution of parameters and the residual of the model. This joint distribution would give us an idea about how much information (connectedness and disconnectedness) our model is missing as a whole, and could provide a natural metric for testing model level hypothesis, such as how good is our model doing.

This could also lead to a series of Meta-Bayesian questions about uncertainty in model modeling.

"Black then white are all i see in my infancy.
red and yellow then came to be, reaching out to me.
lets me see.
as below, so above and beyond, I imagine
drawn beyond the lines of reason.
Push the envelope. Watch it bend.

Over thinking, over analyzing separates the body from the mind.
Withering my intuition, missing opportunities and I must
Feed my will to feel my moment drawing way outside the lines.

Black then white are all i see in my infancy.
red and yellow then came to be, reaching out to me.
lets me see there is so much more and
beckons me to look thru to these infinite possibilities.
as below, so above and beyond, I imagine
drawn outside the lines of reason.
Push the envelope. Watch it bend.

over thinking, over analyzing separates the body from the mind.
Withering my intuition leaving opportunities behind.
Feed my will to feel this moment urging me to cross the line.
Reaching out to embrace the random.
Reaching out to embrace whatever may come.

I embrace my desire to
I embrace my desire to
feel the rhythm, to feel connected enough to step aside and weep like a widow
to feel inspired to fathom the power, to witness the beauty,
to bathe in the fountain,
to swing on the spiral
to swing on the spiral
to swing on the spiral of our divinity and still be a human.

With my feet upon the ground I move myeslf between the sounds and open wide to suck it in.
I feel it move across my skin.
I'm reaching up and reaching out. I'm reaching for the random or what ever will bewilder me.
what ever will bewilder me.
And following our will and wind we may just go where no one's been.
We'll ride the spiral to the end and may just go where no one's been.
Spiral out. Keep going.
Spiral out. Keep going.
Spiral out. Keep going.
Spiral out. Keep going.
Spiral out. Keep going."

-Lateralus, by Tool

Everything is connected. Except when it is not.

To Grok (...or a post scriptum on the previous post)

Once a person internalizes a unifying theme (symbol, idea, connection, pattern, symmetry, invariance, isomorphism, etc...) underlying a set of objects, or an ensemble of objects, the self of that person molds itself into the unifying theme. But, that is an incomplete picture. For there is also randomness or variation that is always outside of any particular internalization's ability to also internalize. Even if there were a theme that could explain all observed variation in existence, as soon as a person internalized it, there would exist variation that could not be explained by the internalization, merely because there was an agent that was internalizing it. Or in other words, as soon as a self attaches itself to a model of reality, from its subjective point of view new variation comes into existence, even though from an external observer there would not exist any new variation. What is this new variation?

One word: choice