[Editor's note: These ideas conjured up by Jacob Bird and Isaac Sanford]
The theory of Cuil details a method of quantifying abstractions from reality. "Abstractions" being the key word, indicating that whatever Cuil is made, expresses itself as a contrast sources from a given situation. This is the accepted premise. It is no stretch to state this mathematically as:
Where "C" is the Cuil level, "n" is the Cuil degree, and "x" is the given situation, or root, or reality.
There comes an issue of expressing C in terms of the observer's new reality experience before another layer is made clear. This is to say that upon entering "n/x," the abstraction must be re-labeled to constitute the new experience, and can be state as follows:
C+1= n/(x/n), the trend continues…
The suggestion being that these layers are not arbitrarily created, but a pre-existing inevitability which an observer makes manifest as it explores. Necessarily, for these layers to exist they must continually bounce off of the increasingly distant reality, being comprised more and more of stacking Cuil layers. I am calling this the "Echo Theory of Cuil," because the effect can be simulated in reality by placing two mirrors facing each other. If this Echo Theory has any validity to it, then the Theory of Cuil becomes something akin to peeling away layers of an onion while stacking an onion-layer house of cards on top of it. Each successive layer of Cuil reveals more about the innate nature of a given moment and situation by layering symbolic abstractions on top of each other.
If zero Cuil is an unreachable, perfect ideal, then why include and surpass it with negatives? An alternative to using the modern system of mathematics (in which the concept of zero is the only innately abstracted integer, presupposing a "something" for which there is a lack instead of representing a truer nothingness) involves never reaching zero. Anything less than 1 becomes a fraction, split further and further from symbolic unity. In this way we would be suggesting that there is only greater or fewer layers of Cuil to a given quantity, as mankind's hyper-realities are really just another form of abstraction from reality.
If the Echo theory holds any logical water, then the inclusion of irrational numbers might be like stating that the observer itself is also a "mirror," and as the observer crosses each threshold into a new Cuil layer, it simultaneously delves deeper into itself.
[Editor's note: For this last bit I haven't reviewed my hypothesis, so I'll leave it to the community to validate as you see fit]