The 8 x 8 Grid
In the article Excellence, Decency and Badness we split the Cartesian plane into vertical segments, each of which represents a classical level. It would perhaps be more pertinent to split them into static levels according to the amount of classical or romantic quality in the patterns of that level, whichever is lower. This way the higher levels retain a stronger moral superiority over the lower ones and the model is consequently better suited for moral evaluation. If we then proceed to split the grid vertically into clusters we can define sixteen slots per quadrant. The resulting model allows us to sum patterns of static value as vectors.
A Venn diagram of the result would look something like the following one that was drawn assuming that each slot contains precisely one pattern. The elements of the sets (the dots) are "quanta of quality" and set membership indicates whether the quanta are classical or romantic, and mystical, normative, objective or subjective. The coordinate of the slot is determined by counting the dots.
Some slots in the following diagram have nonstandard names. For some reason I'm unable to edit the text with the editor with which I created the file and hex editor doesn't reveal anything I know how to edit. The standard names are presented later in this article.
Note that the slots of the above Venn diagram are not ordered like the slots of the grid. I couldn't find a way arrange them like that in a two-dimensional Venn diagram. The Venn diagram is just a formal abstraction of the way in which the Cartesian plane has been divided into slots. The meaning of the split can be approached by way of reading a lengthy explanation that covers each slot one at a time.
What are these slots? Do they correspond with something remotely familiar or are they completely theoretical? I'd find the slots to be Sinns in the senses Frege meant when he spoke of Bedeutung and Sinn. These slots are like the sensor of a digital video camera that records abstract, not tangible (ie. visible) information of Sinns. Or one might want to think of them as some kind of an origin-centric oscilloscope that however displays a low-resolution rasterized image so that the contents of the pixels are references to Sinns and the meaning of the reference is determined according to the pixel's X and Y coordinates. Or maybe it's a radar screen but rectangular instead of circular. These are just metaphors. These correct non-metaphorical description, to my best knowledge, is that the slots are a projection of Sinns on a Cartesian coordinate system.
This 8 x 8 Grid is based on the assumption that patterns can be excellent or flawed. If they are excellent, classical quality and romantic quality manifest in equal amounts within patterns of the same level. If they are flawed there is a disparity between these amounts. The amounts are measured in quanta of quality which is a hypothetical theoretical construct. In practice: excellent inorganic patterns have one classical quantum and one romantic quantum whereas excellent intellectual patterns have four classical quanta and four romantic quanta.
Patterns, that are flawed, are either decent or bad. They are decent if they have an excess of classical quanta and bad if they have an excess of romantic quanta.
Let us denote the absolute value of the X coordinate of a pattern by x and the absolute value of the Y coordinate of said pattern by y. The value of an excellent pattern equals 2y. The value of a decent pattern equals 2y - ⌊x/2⌋. The value of a bad pattern equals x - y. This is always a negative number as the definition of badness includes the notion that x < y. The core idea is that goodness increases upon approaching the excellence axis while withdrawing from the origin whereas badness increases upon withdrawing from the excellence axis while remaining on the quadrant.
We can use the language of the Metaphysics of Quality in order to formulate descriptions of what each of these slots are like. We already have descriptions of the excellent slots. These are the descriptions of the levels themselves. After all, it'd make sense to suppose that when Pirsig described the four levels in Lila, and when I described the levels on the other quadrants, we both tried to do so in terms of what would be an ideal manifestation of that level. An ideal manifestation of any level would, unless otherwise noted, be an excellent pattern of that level. Although it's possible to infer also descriptions of flawed patterns from the descriptions that have so far been presented, I will proceed by assuming all of the excellent slots to have already been explained and none of the flawed slots to have been explained.
We will name the slots as they are named in the grid below. These names are supposed to be quite straightforward to understand for someone who is already familiar with the levels. We will also experiment with other names later. The naming of the slots isn't completely uniform throughout this wiki for now but should suffice in eliminating ambiguity.
Let me make a remark about the lingo we're going to use. Two patterns of the same quadrant belong to the same classical level if their classical portion has the same amount of quanta. They belong to the same romantic level if their romantic portion has the same amount of quanta. This means romantic levels are different from romantic clusters. The static level of a pattern is determined by checking which one is lower, the amount of classical quanta or romantic quanta, and by assigning the level according to the lower value. Defining the lingo this way seems to maximize expressivity while minimizing redundancy.
Furthermore, from now on we will replace the concepts of "romantic quality" and "classical quality" with the concepts of "actual quality" and "potential quality". The latter are more descriptive of the way these notions are used to construct the meanings of the slots of the grid.