Before I go any farther, I would like to point out that it is also possible to conceive of 1‽ as one jump between objects in the first person, or one observer. Therefore, the cuil value of a statement would be calculated by the number of jumps in observers between two statements.
The calculation for cuil would then be obtained by attributing the initial observer a cuil value of 1, and the final observer a value of N
Think about it this way. You start out with an observation. The final statement has 3 jumps between you and the final observer.
This attributes a cuil value of 4 to the final observer.
A simple delta calculation yeilds the distance between initial and final observers. ‽f-‽i=Delta‽ 4-1=3. As stated before, there are 3 jumps between initial and final observers. The calculation of distance from the initial to final observer is ‽i-‽f. This would yield -3‽. The -3‽ represents the number of abstractions from himself the initial would have to take to reach the level of abstraction of the final. One explanation of 0‽ is that it represents true reality. I would like to consider it as an observer which is in fact the system (the universe, god, the planet, etc). This means that for the 0‽ observer to reach our initial observer, they must move 1 level of abstraction towards the observer. It was also stated that a negative cuil value may represent hyper-reality.
the -3 cuil value between the initial and final observer represents the number of abstractions that the final observer would have to make to reach the level of the initial observer, thereby decreasing their level of abstraction by (in the example), 3‽.
I think that to make meaningful statements about a situation of statements, we must first define some variables. These are by no means complete, but may act as a groundwork for a future entry on the axioms of cuil.
To perform a calculation of a cuil, you must first define the expected reality of the conscious observer. You must also have a defined "true reality" or some meaning for 0‽.
From this, it should be possible to observe abstractions and assign a cuil value based on the relationships between these abstractions.
For something as complex as a statement of reality, and percieved reality, these should ideally be stated sets of equal size. It would b possible to create an infinite set of statements about absolute reality (if such statements were possible… we shall assume that they are). This may cause a branching of cuil into several seperate but related mathematical and philosophical models.
I feel that we should have a name for these sets of information about the real world and the expected world. For now, I will use vector notation <i,j,k>.
As an example, I shall use the following statements.
You see a goldfish. You feed the goldfish. You observe that the goldfish eats the food.
You expected to see no goldfish. You expected to feed the goldfish. You expected the goldfish to not eat the food.
The difference between expectation and reality is <1,0,1>
This is not to say that cuil is the expectation of one observer rated against another, but that it may be possible to do calculations using the concept of a cuil with multiple types of problems.