Ripheus23

Dr. Atatan

One subsetting of the story is supposed to be a "school for magic" kind of scenario. Actually, there are two examples of the trope at play, but anyway, the one I'm talking about is supposed to fit the profile more normally than the other. Now I'll confess, I'm actually only aware of the following examples in the genre: Harry Potter, scenes from The Magicians and Patrick Rothfuss' Kvothe books, maybe scenes from the tower of the Aes Sedai in The Wheel of Time, and maybe some film or TV (or even videogame) examples I'm not clearly remembering right now. I feel like this is probably a short list (especially considering, IDK, anime and manga?) so I'm not sure if the following "personal touch" on the genre is original or not:

• The main antagonist is a professor.

He's not like Voldemort, then, a troubled student. I guess you could say he's like a combination of Voldemort and Dolores Umbridge or something, or that's the closest approximation, or whatever. However, there's more to it, like, it's not just that there happens to be a smart evil wizard (with or without state sanction) who poses obstacles for the students. It's rather that he's not a powerful wizard so much at all himself, and his primary negative activity is to try to influence his students into doing evil with magic.

And so more precisely, it's not even that this "Dr. Atatan" (working moniker) is getting his students to place curses on others or cast dark spells or what. Rather, the class he teaches has to do with "preparing for the advent of the Final Power." The idea is: we all know it'll happen one day, so what can we do to get ready for it? And Atatan has an evil idea, maybe he doesn't think it is, but it is.

In order for his idea to serve for some foreshadowing, I am (tentatively) setting it to this: just as it is later described, how Armirex attempts to interpose the concepts of evil and nothingness using a default in his moral logic, so it is that Atatan is misapplying the principles of the deontic operators---or, seeks to apply them in a warped way. The idea is that sometimes people try to impose obligations but doing supererogatory things. Like, you do someone a major "favor" so they feel "obligated" to you accordingly. Now, on a technical level, it's already wrong---you can't deduce an obligation from a supererogation like that, in pure logical space---but it is more substantively wrong, too. I.e. it (A) conflicts with the autonomy of those on whom the "obligations" are imposed (their responsibility for which obligations they are under), (B) often involves overlooking the fact that what "seems" beyond the call of duty, as far as generosity or whatever goes, is really what we owe under the circumstances anyway, and (C) often involves getting others to feel "obligated" to do something that is itself wrong (think of crime bosses leaning on civilians, say, or the matter of Satanic temptation in general (so to speak)).

Now, Atatan would then be trying to convince his students to prepare to use the Final Power so that the power of supererogation directly computes the power of obligation, contrary to the above, or resulting in this. In essence, he'd be trying to corrupt the concept of supererogation itself (a fairly malevolent act, I suspect...). This has a theoretical-apocalyptic relevance: the normal ratio of good operators to the evil operator is 2:1 (there is only one operator for evil, the prohibition operator, but two for good---for obligation and supererogation). More importantly, in Morettian space (the space of all possible deontic graphs of n dimensions), all the operators above the first four (obligated, prohibited, permitted differently, permitted indifferently) are in the class of supererogation (since the principle of construction for the supererogation operator simpliciter is equivalent to the principle of construction for the ascending sequence of graphs), which makes the ratio of good to evil infinite. So, the Form of Evil has a vested interest in trying to subvert the concept of supererogation, and its metaphysical influence on Atatan contributes to his deluded plan.

As it turns out, Atatan has access to a "Simon chair." These are named in honor (or memory...) of a man named Simon [something or other] who was uniquely tortured by both Lawclest Damnite and Vyrian Armirex. The symmetry of their sin was that Damnite tortured people to cause magic to happen, whereas Armirex used magic to cause people to be tortured. So that, in some way, was what Simon went through (it was by this act that the two Fallen Artificers determined that compounding their powers, against Apollyon, would be of great worth: so not only did they torment Apollyon physically and magically, but they used the direction-of-force (magic-to-pain) to fuel the other one (pain-to-magic). Since one of the final offenses (the set-codex of the Form of Evil) is recursive disgrace, or a wrongful concept of punishment, Armirex to some extent channeled the power of the Form of Evil to torture his victims. [Which would contribute to his later knowledge of how to use the power of the Form of Evil + the Keyscape, to silence Apollyon.] Simon chairs, then, are designed to channel the same energy, for the reasons of Armirex and Damnite together.

Sophie's choice in the Ripheus story

This is extremely relevant to an issue having to do with the ecographic nature of the Form of Evil. Now as it stands, the intuition one is "supposed" to get from the case is that Sophie will feel guilty no matter what she does. This might be because she will never know if she subconsciously chose the one child over the other for some reason, and so she will feel guilt about the quality of her love for the child she didn't choose, or something along these lines.

But let's suppose she knows she's not choosing one over the other due to some deficit of love for either, or whatever. Should she still feel guilty? One might think she should feel guilty because she has brought about the death of a child she loves. But I think that this is a terrible thing, to think that she should be made to feel guilt on top of everything else under the circumstances.

Now, as far as Ripheus and his world go, the issue is generally over whether there are objective moral dilemmas at all. Of course there are subjective dilemmas where one doesn't know what to do. The existence of objective dilemmas involves a denial of something called "agglomeration" in deontic logic. Roughly, the idea is that from, "You ought to do x," and, "You ought to do ~x," you can infer, "You ought to do (x and ~x)," which means, "You ought to make it true that x and true that ~x," or, "You ought to make it true that (x and ~x)," which is a contradiction.

There is an argument over agglomeration so the deeper logical defense of the proposition, in the Ripheus setting, is this: in imperative logic, +A and +B = +(A and B). Any two commands can be represented as one command to do two things. Since erotetic logic encodes for the transcendental deduction of deontic logic from imperative logic, the imperative agglomeration carries over into the deontic context.

As far as Sophie goes, the issue adverts to this: Sophie actually doesn't know that what she says will decide which child will be killed. Not only could the Nazi kill the opposite child (to spite the mother somehow, suppose), or both regardless, or one a little later, or by sheer random free will neither, but even if he accords with the mother's "choice," this is by his actual choice. So yes, it is perversely unsympathetic towards her, to attribute a "moral remainder" or "moral residue" to her as if nevertheless these arithmetical or chemical analogies didn't have to follow the laws of division or admixture in turn. [And so the ultimate way the Form of Evil tries to warp a person is by infecting their sense of responsibility so that they begin to think of their inactions as negatively morally charged, due to irrevocable dilemmas, which starts to physically and spiritually subvert the person's free will from within itself. The negative charge hypothesis converts into a misalignment of the fundamental concepts of good and evil in a person's logical reasoning, namely it only goes through if the concept of evil is the basis of the concept of good, which is false. Therefore, this amounts to an interposition of the concept of evil and the concept of inaction such that evil seems to "exist as nonexistence," so to speak. Again, Armirex was not spinning his plan out of nothingness(!)...]

Tardigrade-monads

Microscopic lifeforms that manifest in the indefinite-sized universes. They are the "natural prey" of the leviathan hydrae, a set of prion-like pathogens that are also Dirge-shadows. When a tardigrade-monad effectively fights a leviathan hydra, or whenever else a leviathan hydra is dissolved, the hydra releases a small wave of energy that can damage cells around it. Extensive exposure to these waves causes a skin condition known as Apophis syndrome, in which skin cells become highly sensitive to exposure to red light and are electrically charged in an abnormal manner. Long-term untreated Apophis syndrome has a massive chance of fatality.

The Dirge-shadows

The six classes of sincrystal, which are objects that if broken, melted, etc. release a burst of Apollyon's pure destructive power. Each is associated with a different ecographic style (metroarchic, economic, deminomic, metrometric, ecometric, and ecoarchic).

• The Typhon. Metroarchic.
• Flamesand. Used for one of the Sinkorosst (the planar bindings on the Typhon). Appears as a thin layer of red sand in some desert regions. When grains of flamesand are melted together into glass, this is considered "destroying" them, so melting them is what brings forth the wave of Apollyon's energy. Metrometric.
• The leviathan hydrae ["Apophis particulates"]. Microscopic sub-living things. Ecometric.
• Sinstone in general. Economic.
• The Void of Threnody. Deminomic.
• The Shield. Held by Ripheus. A literal hand-held shield. Uniquely weakest of the Dirge-shadows, it cannot be destroyed by anything save the Final Power, and even if it could be destroyed, it would release the weakest wave of Apollyon's energy. [Legends suggest a number of obscure origins for the Shield, namely it is commonly, and mistakenly, judged to be a sincrystal construct admixed with something else [ore from the Labyrinth, petrified wood from the aleph-forest, ceramic from objects in Cantor's house, compacted unicorn-horn dust, ortholithic [Form of Adventure-like] matter, residue deposited by tardigrade-monads, exotic metrometric crystal, the "bones" of the Form of Fear, etc. or perhaps even some combination of any or all of the above.]

The Unicorn Archons

A faction among in the ecometers who are devoted to protecting the pegasus seraph.

What is wrong with Armirex's reasoning

There's more to the problem than just, "Let's replace the concept of evil with the concept of nothingness." Armirex sort of already BELIEVES the privation-of-being theory of evil, in that he defines evil not as "the opposite of" but as "the absence of" the good. However, the fundamental principle of the concept of difference in itself is, "Absences and opposites are different differences." And the true concept of evil is not "not good" but "anti-good."

So, in deontic logic, the operators OBLIGATED (Ob), PERMITTED, (Pm), FORBIDDEN (Fr), and so on, all have interrelations. For example, you might say that something is obligated, Ob(x), just in case it is not permitted to not do it, ~Pm(~x). [Although, to be sure, such a negative relational definition would make goodness itself into a form of nothingness...] The fundamental semantics for the deontic operators are grounded in the simple interfunctions of the deontic syntax in general and the syntax of basic propositional logic in the operators AND, NOT, and OR. So, something is obligated if and only if there is a reason to do it, Ob(x); if there is no reason to do something, and no reason not to, that thing is indifferently permitted ~Ob(x) & ~Ob(~x) = Pm(x); something might have a reason to or to not do it inside itself, which is differentially permitted*, Ob(x \/ ~x); something might have a reason to not do it, Ob(~x) = Fr(x). And there's a fifth "simple" formula (relying only on the simplest interchanges of the basic logical operators), here, which I won't spell out but it corresponds to something being "supererogated," beyond the call of duty/an act of grace. AFAIK these are the only 5 moral descriptions of an action that can be constructed from simple logical forms as such.

So, in Armirex's mind, since evil is nothingness, somehow, he doesn't draw the distinction between the two spheres of permission as he should, and thence neither is his identification of moral negation (Fr(x)) is compromised, too. Wherefore, in a way, you could say his attempt to destroy the Form of Evil by fusing it with the Form of Nothingness, also amounts to attempting to fuse the Form of Evil with the Form of Permission.

The supercolor superparenthesis

﴿...﴾ 

are parenthetical glyphs used in a number of exotic functions in higher transet theory. It was eventually determined that superparentheticals have a chromatic index, but only for the four colors red, blue, green, and yellow. The only other glyphs known to cartoglyphers to have a chromatic index are the isoset semiosis (the "musical" transet).

... A special mapping relating to Apollyon is that taking the Apollyon glyphset to the power of the first musical number, equals the Apollyon number with a glyphdex of ♪_♪ which would be one of the only known cases of a musical number functioning as a glyphdex (or of a chromatic index being emphasized at all).

۞ꙮ

꙲

ﷺ

...other cool symbols I found ...

The Battle of el Samir

Explain a plot badly:

"An Odium-Sephiroth hybrid uses a Ruin-Worm of the World's End hybrid to attack a Dark One-Morgoth hybrid." --- explanation of the Riphean endgame

1. The Preface to This Resistance
2. The Axioms of Paradise
3. Reason's Trinities
4. A Tower of Fire Defy
5. In the Days of Ascension
6. Seven Fallen
7. Of Their Dominion
8. Will Always Be
9. Alas! the Broken
10. Herald the End
11. Ask Why This Should Be
12. For the Sake of Three Things
13. Nothing Instead
14. The Darkness Not
15. To Heaven to Go
16. To Take a Stand
17. Wherefore Apollyon et Ripheus...

[Hypothetical list of titles for the series. OTOH I'm not sure I've come up with 17 books' worth of material, even in principle. I.e. the demiplane of Apollyon is book 1, 2 through 4 are the Precentor trilogy, 5 through 7 are the Septatheon trilogy, 8 through 10 are the Keyscape trilogy, 10 and 11 are the evil schoolteacher duology, the Dirge-shadow known as the Void of Threnody storyline is somewhere in the next set [IDK if I've mentioned the Dirge-shadows yet here?], as well as the conclusion to Bassilfastion's quest and the buildup to the awakening of Apollyon (that latter is at the end of 16).]

"For the Sake of Three Things": the unholy trinity of the final offenses. Three interlocking (perichoretic) sins, whose personification is the so-called Form of Evil.

"The evil of corruption is negating the essence of goodness in something; the evil of destruction is negating the existence of goodness as something." "But it is possible to think of destroying the properties that make something good without replacing them with other properties that would be evil; the evil is all in the destruction of the good properties, not their replacement or lack thereof. So would not Apollyon be the actual Form of Evil?"

I was reading a book about logic and apparently I misremembered the symbol for possibility in standard modal logic. The square is used for necessity, whereas a diamond is used for possibility. :/

Gödel coordinates

It is possible to use transets and operations thereon to represent an equation that maps onto the set of an ecograph's indices. For example, to represent the index of reduction, you take 0 [not the integer zero, but the use of the classical symbol of zero to represent a special transet function [related to the concept of integral zero]] to the power of 0 as many times as a reduction takes place. For example, the Form of Adventure's index of reduction is 1, so it is assigned the transet of 0 alone, whereas Apollyon's index of reduction is 3 so it has 0^(0^0).

For historical reasons, these are referred to as Gödel coordinates.

The color transet

Part of cartoglyphy, the theory of the color transet is that there are glyphic variations on the known semiotics of the transets grounded not in differences in iterations of shapes but also on variations in the colors used to draw the glyphs in physical space. Whether physical reality is intrinsically "greater" than the sphere of the aleph-numbers and their transets, is not known, so the theory of the color transet remains unproven in general [although there are some applications related to coloring problems in mathematics, that testify to a possible chromatic index for aleph-numbers; see also aleph-color.

• Aleph-color. The theoretical aleph-number whose internal determination of symbolic use involves colors. The idea is that colors are, in some strict sense, numbers, just like integers or fractions or irrational decimals, or whatever; see also Dorothy's staircase.
• Dorothy's staircase. Also known as Cantor's rainbow. Assuming that aleph-color is an n-aleph.n indexed transfinite number, it is possible to represent an exotic staircase using the transfinite variable z, and the transet of 0, in relation to the indeterminate glyphset for aleph-color. A large amount of contemporary staircase theory concerns attempts to prove the existence of Cantor's rainbow in such a way that the numerical index of aleph-color becomes apparent in the process. See also Munsell color sphinx.
• Munsell color sphinx. A bizarre ecometric (possibly metrometric) lifeform with the appearance of a sphinx whose head is not an ornamented human's but a physical-matter copy of the Munsell color solid. They can be found in the ecometric realm guarding mysterious staircase-demiplanes believed to be possible physical incarnations of Cantor's rainbow.

The Lay of Vyrian

Wherefore the preface to this resistance

is true,

the Axioms of Paradise

and reason's trinities

a tower of fire defy;

and in the Days of Ascension,

seven fallen are denied.

Of their dominion

"was" an end.

Will always be until the end.

But alas! the broken come

To seal all light in the dimension of sin,

Or else to herald the end of all that there is;

and why ask why this should be?

If all is denied for the sake of three things?

But if darkness is nothing instead,

how would the darkness not come to an end?

To heaven to go,

to take a stand,

to sing the song of silence,

to pass the Test:

"Wherefore Apollyon et Ripheus*"...

*[pronounced "Rif-ae-es" to rhyme with "Test"]

_____________________________________

"Although Armirex used the power of the Form of Evil to silence Apollyon at the terminus of the Last War, the Artificer later came to believe he had sinned in doing so [to use Evil's Form at all], and so sought to atone for his sin by awakening Apollyon at the end of time..."

π_π is the spheration index, the cardinality of the set of hosothetic functions (functions converting rectilinear matter into spherical matter).

↑_↑

^↑↑_↑

↑_↺

^↑↑_↺

^↺↑_↑

^↺↑_↺

↺_↑

… and so on, these are the “ascension numbers,” the transcardinal rank of the set of standard ascension functions in aleph-space.

♥ = an operator, so used in transfinite arithmetic as in e.g. ℵ₀ ♥ ℵ₀ ♥ ℵ₀ = _▲▲_▲ [the transet of the triangular functions of reality]. The heart transet is the set of heart operations, symbolized ͜♥, which has the unique properties that it cannot be x in either x_x or ^xx_x and no aleph-number can have ͜♥ as its exponent, and indeed the heart transet only appears in functions in which the heart operator appears.

Now, there also the “magic numbers,” symbolized m and q. These are similar to x and z. They are like magic variables in the aleph-numbers.

There’s also the use of integer numerals like 0, 1, 2, and 4 to symbolize special aleph-numbers. And so on and on. Anyway, to give an example of what this all “adds up to” in the story, let’s assert an aleph-heart operation:

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.

Cool picture I found 

The music transet

♪_♪

^♪♪_♪

♪_♫

♫_♪

^♪♫_♪

^♫♪_♪

^♪♫_♫

And so on, I think there are ten plays on the theme possible. These are the transets of the Keyscape, also known as the Key-set. They are ecometric functions, or nomographical manifolds, in which the basic operation of the transet’s elements is represented by the single note to its own degree, then according to the staircase axiom in single form, and so on and on. They are ecometric because they are, if you will, economic questions existent at all deminomic and economic locations. So, in other words, the Key-set is a special set of ten questions on the Test, each involving the theme of aleph-24. Or, in game-theoretic metagraphics, it is a phenomenon of the power of the Game, in which one has aleph-24 options available at any time and must make aleph-24 decisions over all the sum of agent-time.

_______________________________________

With those in mind, some other weird symbols for magical aleph-numbers:

♪_{Ø♯ = ???}

▲_{▲ = the Gearscape transet}

^▲א_{▲ = the absolute transet}

Ø_{○ = the zero-actuated transet}

_{□_{○ =} ○_{□} = equivalence of possible actuality and actual possibility}

A_{Ω = the transet of Apollyon}

_{é = the elohim number}

L_{λ = the Lernean number (hydra index)}

{C_s, C_C} = the Cocytus numbers

π_{π = ??? (not pi as we know it...)}

{↑_x,↑_↑, ^↑↑_↑, ^x↑_x, ^↑↑_x, ^x↑_{↑ ... "the ascended numbers" (also "the inference numbers" and "the iteration transets) ...?}}

_{ψφψφψφψφψφψφψφψφψφψφ …} א_{+ (the transequent order of questions and answers)}

The "sigma-actuation diagram"...

I have read that some cardinal numbers are ordinals/some ordinals are cardinals, maybe all are both, so I should have to redefine the "transcardinal rank" and "transordinate magnitude" notions in "transet theory."

________________________________________________

But with respect to a topic I am more familiar with...

In modal logic, which is the logic of possibility, actuality, and necessity (and which is a matter of formal logic inasmuch as we speak of the truth of premises necessitating the truth of conclusions in valid sequences), there are some symbols used as "operators," like □ for possibility and ○ for actuality (IIRC). Now there is a general rule,

• From ○x, infer □x.

The reciprocal, so to speak, is,

• From □x, infer ○□x.

And we can imagine infinite strings of these operators unfolding from x according to these rules.

In imperative logic, the operators are for "do" and "don't (do not)." At least, this is the way I approach IL.* So I use + for "do" and ¬ for "don't." Natural language supports prefacing any given imperative sentence, such as, "Be nice," with, "Do," as in, "Do be nice" (archaic, granted), and exclamations like, "Don't do that!" testify to iterated countermands. So, we can say, "Do do that," "Don't not do that," and so on. In a string of IL operators, if there are an even number of ¬ marks, they all cancel out and the overall sequence counts as a command. +¬ = ¬, ¬+ = ¬. (Two pluses plainly make a plus.)

*[Another option is to underline the set of words expressive of the command (the x itself, here), or to expand all imperatives into propositional reports, e.g. to convert, "Go to the store," into, "Act so that it is true that you go to the store." (A propositional report is otherwise usually known, IIRC, as a "that-clause.")]

What happens, then, if we sum the dyadic helix of modality or the IL prefaces? IDK for sure, except in the IL case (an infinite negative command is equivalent to a single positive one). Modalitywise, for the sake of the deep metaphysics (called "metagraphics" in the setting) of the Ripheus story, I am going to assert that the "unpacking" of the actuality operator, from the possibility of x, in an infinite sequence, creates an infinite "surfeit" of virtual actuality(?), which forms the material plenum of transcreation. That is, when the computer of the multiverse runs the possibility-actuality program, it applies aleph-zero to the calculation, extracting an infinite quantity of pure actuality from pure possibility (in light of the use of summation notation intended for the full description of this postulate, I am referring to the dynamic as "sigma-actuation"). The sigma-function for IL equalizes the pure command as a pure positive imperative, and the relationship between IL and modal logic* unifies the three glyphic sequences to forge the crucible of transcreation, if you will.

*[Although it is possible to state conjunction, negation, and disjunction in natural imperative language, it is ungainly to say something like, "If go to the store, go for a walk," in contrast to, "If you want to go to the store, go for a walk." However, the "fi"-operation corresponds to the "if"-operator:

• From A, infer B.

... which in all lexical fairness could just as well be put as, "Infer B from A." This is inference itself as a command, which corresponds to modus ponens simpliciter:

1. If A then B.
2. A.
3. Therefore B.

Accordingly, IL comprises the pure inference function itself, and this, as the if-operation, comprises pure possibility (where, "X is possible," is explained as, "There is a situation A such that if A, then X," which indexes the possibility of X to A). Immanuel Kant confusingly enough states both that necessity is that which is actual because it is possible, as well as if the necessary were a unique concept over and above possibility and actuality; in my system, possibility and actuality are dealt with as the dyad-elements of the modality transet.]

Due to the role of the legend of the 36 Justiciars, in the Ripheus story, I have decided that there will be the ל-numbers (lamedh-numbers), which are an infinite list of cardinal numbers that have the peculiar property that 36 of them (any selected 36) can be keyed together as the so-called "justice transet."

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There was a war long ago, the War of Sin and Hell, the First Ecomachy. (The Second Ecomachy, the Isomachy, was also the Last War.) This was when the Form of Evil attempted to transcreate its own economy. It would do so at a later time by trying to infect the Riphean isocrystal causeways, and through them pollute an entire economy unto itself, but the elder attempt depended on an assault on the deminomies first. What the Form of Evil did was corrupt a precursor of the Platonic dice, an object known variously as Plato's box or Pandora's dice, in order to generate hosotopic waves from the stable isocrystals, and use these to tear off pieces of an already-existent deminomy on the one hand, and Cantor's house on the other, whereafter it tried to ram its own deminomy (a corruption of the Keyscape) into the fragments of the other two.

The Lernean virus

Also the Lernean seraph hydra, the virus-hydra, and the virus-forest. [So, revision: the Scylla and Charybdis numbers are BOTH Cocytus numbers, in fact that's their distinction, is that they are elements of the Cocytan subset of the transet of sin. The Lernean number is the other element of the transet of sin, and is sometimes referred to as the seraphim number.]

Function of the Form of Evil that infects the Lachesis aleph-forest. Generally, the seraph hydra is contained within the Form of Evil itself. This Form does not have its own demiplane but instead has what is known as the hamartic demiarchy, and the virus-hydra is the "monster" that inhabits it. It is a hydra with an infinite number of heads (or, a single being made out of an infinite number of hydrae each with an infinite number of heads). Because the infinity in question is aleph-zero, the hydra is able to quasi-intersect the aleph-zero infinity of the Lachesis demiplane. Because not all of its heads are made of "flesh" but some are plant-like, an infinite subset of its heads are trees that form remote glades in the aleph-forest for unwary travelers to be caught within. The seraphic manifold represents the recursive place of transcendental delusion in all other particular sins.

Now, the Scylla and Charybdis numbers are keyed to cruciform manifolds. That is, in Cantor's staircase, the rift occupies all n-aleph.19 positions, but there is also a line proceeding along all 19-aleph.n positions that forms a slanted cross with the rift. Likewise, because 26 is the number of the permutations of the final offenses*, all numbers crosswise out from 26-aleph.26 form another rift-like structure: this intrinsically stable rift-sequence is the Scylla number. Prior to the Last War, the Charybdis number was constantly oscillating horizontally across the staircases for aleph.1 through aleph.24, but Armirex keyed it to the rift in the Keyscape, which fixed it at the staircase for aleph.19.

*[The final offenses can be committed one, two, or three at a time, in different combinations of consciously and subconsciously/unconsciously. So there are 26 possible orders as such.]

The quadrilateral of the Cocytus numbers (in the grid of the staircases) is geonomically juxtaposed with the semiotic transets* to form what is known as Cantor's house. Legends or jokes have it that this house is built from the trees of the virus-forest, and is the only possible prison for the seraph hydra, should this entity ever emerge from the Form of Evil (hence this "house" is also known as Cantor's durance, with the durance-staircases besides it (or the paradise-durance/Durance of Paradise)).

*[The staircase is the semiotic representation of all aleph-numbers in relation to 2-dimensional space. Because physical space is inherently 5-dimensional, there are three more dimensionalized sets of aleph-numbers, so there are 5 special dimensions to the infinite forms of infinity. These four transets are the semiotic transets, and Cantor's house is an orthotopic manifold constantly being unfolded from the Cocytan quadrilateral via deontic crystallization.]

There is also a hyper-gap between the transet keys for aleph.24 and aleph.26, and this is involved in the nature of the Sea Alone.

C'mon, Dean... I can't hold it all together by myself... And I know you're not the only one who knows how to hold on to this, too, but I don't know anyone else out of all of you who can.

The Cerberus numbers

The elements of the transet of sin. These are specifically the Cocytus number (26-aleph.19, from the rift in Cantor's staircase), the Scylla number, and the Charybdis number. The Cocytus number is associated with the sin of romantic injustice; the Scylla and Charybdis numbers are associated with transcendental delusion and recursive disgrace. [The identification of the Scylla mythopoesis with transcendental delusion is contested by many ethical philosophers, who would rather refer to this sin-number as the Phalaris or Telemachus number, though the similarity between the words 'Telemachus' and 'Temeluchus' and the latter's association with Apollyon have produced further poetical disagreements on this score.]

• Cerberus-dimensional objects. Any physical object whose geometry is proportioned according to the dimensions of the Cerberus numbers. Examples include the Nemean skeleton [a "leonine" n-skeletal entity] and the holocaust-minotaur [a being that compounds the destructive energies released when a sinstone is broken].

The inferno transet

The antiset and the Cerberus numbers together.

Unrelated:

The Alcubierre telescope: a telescope that uses quasi-wormholes to deliver simultaneous instead of delayed transmissions of photographic information about distant objects in space. So, a star seen through an Alcubierre telescope is seen according to its occurrent status, rather than according to the photon traces it has left over the ages.

I know I shouldn't hate people, so I'm trying my hardest not to hate our president right now.

Random terms/phrases

Cantor's staircase. Also the cardinal staircase, the paradise-staircase. Aleph-numbers listed as aleph.0, aleph.1, aleph.2 ... aleph. n, and aleph-aleph.0, aleph-aleph.1, ... aleph-aleph.n, and aleph-aleph...-aleph.n. (This will allow me to one day write a sentence that includes "the rift in Cantor's staircase"...)

• There is (hypothetically) a scene where Ripheus (or whoever) is standing above a hollow pillar, and the interior surface of the pillar appears as fractal accordion-staircases. This is supposed to visually represent Cantor's staircase. (The rift would be a weird distortion, here; we'd probably just have the staircases for aleph.1 through aleph.24 represented, unless the fractals allowed us to represent all of them. Anyway, if there were just the 24, then the 19th would, IDK, look like it was made of obsidian or glowing darkness or something.)

Son of Atropos, the. A poetic/prophetic designation of Ripheus (points towards his sonship under Apollyon).

Ecoarchic isonomy, the. Also the geonomy(?). The total of all economies and deminomies, i.e. all transcreation.

Orthomorph, the. The geometrical designation of the Form of Adventure (Ripheus' cube/tesseract-shaped companion).

The Septatheon and the Sea Alone

There is a theorem in the system that says that some set of agents must always exist. This is either a permanent finite number of agents, or an indefinite number of impermanent ones, or an infinite number of either, or something like that. This is where the Noumenal Artificers "come from": they are (trans)created directly by the ethics-magic, to satisfy the theorem. The Septatheon form from/in the infinite-size economies due to an interplay between the infinite form of the theorem and their own spatial extent. Now, like the Artificers who joined the Host of Ripheus, these entities have the power to directly access the magic of the system in the following way: first, they can access the 7-Vennplex to control the hosotopic waves given off by collapsing 7-isoplex crystals.* This allows them to use the hosotopic waves themselves to access the power of the Lachesis aleph-forest and, through this, aleph-7. Aleph-7 being in the economic transet, it is one of those keyed by the seleplex artifexium to the isoarchy. So the Septatheon are, if you will, "hacking" the Keyscape to reset aleph-7 therefrom. This will allow them to affect the codex of the Keyscape, the "programs" that the "computer" runs. Now only one of the Septatheon at a time can do this, so they're dueling each other over who gets to.

*[Waiving the fact that there are rectilinear Venn diagrams... the explanation is that the curvature of the 7-Vennplex can be "folded around" the curvature of the 7-isoplex collapse-waves. Compared to the stable isocrystals used by the Host of Ripheus, these energies might be referred to as isoplasma.]

... The Sea Alone is a phenomenon resulting from the seleplectic rift. Each of the 24 universes has a physical relationship with one each of the aleph-numbers from aleph.1 through aleph.24, and so one has a physical relationship with aleph.19. This does not mean that the 19 universe is blocked from the Keyscape. However, this does mean that the rift manifests physically in that universe, and this is the Sea Alone.

The purpose of the rift, so to speak, was to block Apollyon from the advent of the Final Power. As stipulated elsewhere, the Broken Ones created by the Form of Evil put a different block on Apollyon's access to the Final Power. The rift prevents the original acquisition, the Broken Ones prevent the acquisition-by-transecration.

So, maybe Ripheus thinks that the rift is the Proof of Default. Like, he thinks he needs to drain the Sea to "fill in" the rift, and if he does so he will have completed the "absolute proof" codex that his Host defaulted on when programming the Keyscape. Something along those lines, I suppose...