Ripheus23

So, I was thinking that the Noumenal Artificers in the Ripheus story, resemble the Elohim in the Thomas Covenant series. I was thinking of having a sort of "foil" for the Artificers, then, a mysterious group of magic-wielders comparable in power and organization to the Artificers. These would be like the Insequent in the Covenant setting.

I also had a quasi-entity or object known as the Labyrinth, and some other odds and ends I couldn't define easily. That is, I seemed to need a different set than just {economy, isonomy, antinomy, deminomy}. I had {demiarchy} for the Form of Evil, and {isoarchy} for the Keyscape, and I was fiddling with the notions of ecometry and ecoarchy.

On the basis of all that, I have decided that the prefixes and suffixes anti-, demi-, eco-, iso-, metro-, -archy, -metry, and -nomy, can be put together in various ways to produce the action-theoretic categories or metagraphical functions. Nomo- can also be used but there's a "theorem" that reduces the nomothetic functions to a different one. Without a complete analytical justification for doing so, I have set the list of the categories as follows:

antinomy - deminomy - economy - isonomy - metronomy

demiarchy - ecoarchy - isoarchy - metroarchy

demimetry - ecometry - metrometry

"Theorems":

• Antiarchy reduces to antimetry to antinomy.
• Nomonomy reduces to nomoarchy to nomometry to metronomy.
• Isometry reduces to either isoarchy or isonomy.

The following is a list of kinds of magical beings resulting from the above:

1. The Noumenal Artificers: solutions to the economic function.
2. Apollyon: unique solution to the antinomic function.
3. Septatheon: solutions to the ecoarchic function.
4. The Form of Evil: the unique solution to the demiarchic function.
5. The Form of Adventure: both deminomic and the unique solution to the demimetric function.
6. Cantor's house, the Lachesis aleph-forest, the Advocate and Opponent: deminomic.
7. The Labyrinth: the unique solution to the metronomic function.
8. The Keyscape: unique solution to both the isoarchic and isonomic functions (through the isometry).
9. The Metroarchs: the "foils" of the Artificers. Includes the metroarchic equine.
10. Ecometers: disorganized (independent) lone individuals and clusters who use ecometric power.
11. The Anomalies: metrometric functions.

These entities/beings/structures/w/e all correspond to ecographs, which are metagraphical determinants. Every ecograph has an

• index of reduction
• index of finality
• index of modality
• index of prefixture/suffixture

The first index is of how many nodes in the graph are compacted at an actualized endpoint on the graph. The index of finality is for how many nodes are actual endpoints; the index of modality is for the possible number of endpoints. The prefixture-suffixture index tabulates the action-theoretic categories according to the number of times their prefixes and suffixes appear in the list.

So, for example, the ecograph of the Form of Adventure is

demimetry<----- FOA ----->deminomy

Neither category is reduced to the other, so the index of reduction is 1 (there is 1 node at the endpoints). The index of finality is 2, for the number of actual endpoints. The index of modality is 2. It has a weird P/S index so I'll use Apollyon as an example of that idea first.

So, Apollyon's reduction = 3, finality = 1, modality = 1, and its P/S is (1, 5). The Keyscape has

Keyscape -----> isometry -----> (isoarchy OR isonomy)

So its reduction = 2 (isometry + isoarchy or isometry + isonomy), its finality is 1, its modality is 2, and its P/S = (2,4) or (2,5).

The metrothetic categories admit of a peculiar ecography, namely their P/S indices are counted either by the number of times metro- appears, the number of times -metry appears, or the number of times both metro- and -metry appear. So their P/S numbers are

• Metrometry: (3, 3), (3,6), (6,3), (6,6)
• Metroarchy: 3/6, 4
• Metronomy: 3/6, 5
• Ecometry: 3, 3/6
• Demimetry: 3, 3/6

IDK exactly how to compute the P/S number for the Form of Adventure as a joint demimetric-deminomic entity, but I think it would be something like "((3, 3/6) + (3, 5))," whatever that would mean.

Anyway, the Labyrinth, as defined, has the "power level" I felt it had, in relation to the other entities: e.g. the Hammer of Ilium, which is the only weapon that can break the Typhon, is carved from the stones of the Labyrinth.