Ripheus23

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...

OK, so this is the process that I'm working with for the Keyscape:

• Key the chaotic hypoplex to an arbitrary aleph-number (higher than aleph.24 = the transfinite ocean).
• Key 23 of the elements of the economic transet to 23 of the elements of the transfinite ocean.
• List the 23 isoset elements in an order. Starting from 0, add 1 to the transcardinal rank of the isoset if the second listed element is cardinally/ordinally greater than the first element. If it less than the first, keep the transcardinal rank at 0. Continue, increasing by 1 for every successor on the list higher than its predecessor, and subtracting 1 in case the successor is lower, unless the subtraction would = -1. If you choose to place the chaos transet's element earlier in the computation, match it against its predecessor aleph-number according to the preceding rules. Otherwise match the last of the 23 elements to the chaotic transet's element. The maximum increase possible will be from 0 to 24.
• Anytime the isoset's transcardinal rank is computed, the isoarchic numbers are keyed to the economic transet's elements one-to-one (e.g. if the transcardinal rank = 14, the isoarchy is reciprocally keyed to aleph.14). If and only if the isorank = a prime number, the elements of the isoarchic transet are keyed to the corresponding element in the Venn transet (the set of Venn diagrams with n regions, where n = the given prime number; for example, a 3-Vennplex is a geometry whose surfaces include 3 integrated circles, 3 integrated spheres, 3 integrated choronal spheres, etc.).

Since aleph.19 is unkeyed in the economic transet, all aleph-numbers in the cardinal staircase, subscripted by 19, are unkeyed to the isoarchic transet (the aleph-rift). However, the aleph-number which is subscripted 19 at the 26th iteration of the aleph-glyph, is one of the aleph-numbers keyed to the transet of sin. Since the rift-transet is a form of "nothingness," when Apollyon uncreates the Form of Evil, It does so in part by keying the rift-element of the transet of sin, to the antiset. (The Form of Evil is uniquely keyed to two other aleph-numbers, though which I haven't decided yet. 0■ which would be thematically similiar to zero-sharp (http://cantorsattic.info/Constructible_universe#Sharps) is another candidate at least for a symbol for one of the elements in the transet of sin.)

There is also a different process that keys 6 of each of the chaotic and the isoarchic transets' elements, to one of the 4 square-transet elements. This is how the Final Power is created (at least in the abstract).

The action-theory of the economies

So, I was working on the model of the cosmos for the story and was semi-accidentally straddling the divide between a multiverse and a multiplane, or even a multiplanar multiverse. I hedged my bets by coding the universes and the planes as economies and deminomies, but the model clearly required 3 or more universes besides the number I'd already assigned to the plot, which struck a wrong chord with me. To revise this situation, I now stipulate the following: the 24-multiverse does not contain only 3-dimensional universes. Instead of the three 24-dimensional universes being in a separate plane, I now am having it that 3 of the 24 universes themselves are 24-dimensional. Well, actually, I have it that 5 of them are (I'll get into the reason for this in a little while) but so the point is, 4 are always 24-dimensional and 1 of them is constantly changing. I.e. two each of the finite and infinite universes (8 per type total) are 24-dimensional, and the 5th 24-dimensional universe is a different one of each of the indefinite universes at a given time. That is, those universes are constantly fluctuating between 5- and 24-dimensional space, regardless of whether they know it.

So, then, the physics of the system is that all the objective graphs of moral information theory constitute dynamical objects in empirical (phenomenal) space. Because we get a 5-dimensional graph at the end of the basic series, it's presumed that the physical cosmos is 5-dimensional as such. But in principle, there is an n-dimensional set of hyperfractal graphs in deontic logic, so when the "computer of the multiverse" traces all the graphs, besides the 5-dimensional objects that it puts in the 24 universes, it also puts an infinite-dimensional object in its own demi-universe/demiplane/deminomy. For further reasons, there's an aleph.24-dimensional object in deminomic space, so besides the antiplane of Apollyon, we have 2 "higher planes of existence."

However, the technical metaphysics of the story allow us to redefine these 3 demiplanes as deminomies proper. The trick is to assert that the economies are action-theoretic sets.

The Trinity creates the world, as the Test,* by "asking questions" which require an objective world in order for their answers to be given forth. I.e. the Trinity assigns a deontic algebra or aretaic calculus to a simultaneously created universe. Since it is only agents inside these universes that can solve the "algebra problems" of God given to their world, each phenomenal set is "closed off" transcendentally from the others, if not rendered impenetrable. Now the 5-dimensional graph is the outcome of the basic series, which is a set of deontic graphs that correspond to logical operators/constants in moral information theory. But these are all sets that we have living experience with; by contrast, the n-dimensional fractal series (referred to as the Lachesis aleph-forest) is a graph of arbitrarily more complex possible sets of deontic operators, concepts without content. Accordingly, the aleph-forest does not have any particular moral word-problems posed inside of itself as such, and therefore forms not a full economy but only a deminomy (the demiplane of Apollyon, then, is better rendered as the antinomy of Apollyon). It is traversable but invariant (except in relation to the keying dynamic).

*[Since the Trinity is the Game, the Joke, and the Test, a common saying is, "The problems on the Test are based on games where each move is telling or getting a joke, or jokes about games and those who play them."]

Now it is possible to (sort of) explain the actual programming of the system using the aleph-numbers. The aleph-forest corresponds to aleph-zero. In the aleph.24-dimensional deminomy, the power of the numbers aleph.1 through aleph.24 are accessible for keying (with the seleplex artifexium). However, the design of the artifexium only allows 23 of the 24 to be keyed to higher aleph-numbers. So the artifexium gives us 23 aleph-numbers to program with, in addition to those from aleph.1 through aleph.24, minus aleph.19 (this causes a phenomenon known as the aleph-rift, in which all aleph.19-like numbers* are inaccessible).

*[In addition to aleph.0, aleph.1, aleph.2, etc., there are aleph.(aleph.0), aleph.(aleph.1), aleph.(aleph.2), and so on. So, there's an {aleph. ... (aleph.19)}, in an infinite staircase against the surrounding manifold of the aleph-staircase. None of these numbers can be among those keyed for by the other elements of the Key-set.]

The chaotic hypoplex gives as an always-changing set of keyed aleph-numbers, with one element. This structure comes from the isocrystal arrays, since these channel the energy that keys aleph-zero to other arbitrarily higher aleph-numbers. So let's say that gives us something like aleph.x.

Now, I don't want just the staircase aleph-numbers to be in use, so the artifexium deminomy* doesn't just key aleph.1 to, say, aleph. ... (aleph.1762) or so on. Rather, there are many other levels of levels of aleph-numbers, I believe, and in this transfinite ocean many of the keyed-for aleph-numbers are to be located. However, I haven't come up with any specific examples so far. IDK enough about "Mahlo cardinals," for instance, to know whether they would be a good candidate for the plot (aesthetically or logically), here. But just suppose that some of those kinds of aleph-numbers are involved.

*[This one is aleph.24-dimensional, on the assumption that there is enough of a thematic jump (from the 24 economies to aleph.24 itself) to allow for all the aleph-numbers higher than aleph.24, to make up the sea of the Keyscape.]

I don't know if the concept of a transet is valid, since I've kind of just made it up to have the endgame plot go through, but pursuing this concept's application further, let's say, then, that the square transet (for the forms of metafinity) can be keyed for by Apollyon, to the antithetic transet, because Apollyon's power of destruction crucially relies on a theorem in Trinitarian doctrine according to which a transcendental function known as romantic ideality causes essential energy to continuously flow into the physical substance of the world. Since romantic injustice is identified as one of the three final offenses (and thus "part of" the tri-fold Form of Evil), it is via romantic sin that Apollyon is able to block the flow of energy, thus eroding and dissolving the cosmos. (Basically, think of the Form of Destruction, as the Big Bad, using the Form of Evil, as another Big Bad, as itself a weapon.) Now, romantic ideality is constituted, in part, by a special relationship involving the square transet, namely it is possible for one person to be romantically keyed to another person in four different ways, namely the metafinite ones. (So, you'd only be in love with one of the four for a finite time, another you'd indefinitely be attracted to, a third you'd feel eternal heartbreak because of and a fourth, well...) So part of Apollyon's interaction with the romantic injustice of the Form of Evil, allows for the image of romantic love to be counterpointed to the "music" of the antithetic transet (the four Forms of Nothingness).

[The Form of Evil has the transet of sin for itself. This set's three elements can be variously keyed to one specific aleph-number, namely aleph. ... (aleph.19), where the number of "aleph" marks in the staircase is 26, for the 26 quasi-permutations of the final offenses. I.e. it alone (save for Apollyon in the end) accesses the power of the aleph-rift.]

Of course, it is NOT by trying to destroy the entire cosmos, that Apollyon brings about the ultimate apocalypse of transcreation, but by quasi-destroying the Form of Evil. So the erosion-of-substance problem is less a problem for the world of Ripheus than it is the IRL parallel to the spiritual effect of romantic injustice. That is, there is sin in the real world (our world) that = romantic injustice, and the spiritual ramifications of this sin being committed relate to a phenomenon of entropy and accelerated expansion of space in our physical universe.

Cantor's Deck and the Platonic isoplexes

How does the magic dice game work? I've decided that each time the Advocate and Opponent roll the dice, there is at least one card game going on somewhere else in the multiverse, as is named Cantor's Deck. Two players each pick either the Advocate or Opponent cards, and then they get a hand of cards each with a picture of dice on it. There are another Advocate and Opponent card apiece hidden in the rest of the deck. A winning hand is known as Cantor's Hand. The dice depicted in the pictures do not have symbols for whole numbers on them but for aleph-numbers.

Now, an isoplex is a geometry with an infinite-dimensional (aleph.0-dimensional) and infinite number of facets/sides/w/e you want to call them, each with the same number of surface iterations. Now an n-isoplex therefore has n facets.

Consider a 1-isoplex. In this case, each facet of the structure has 1 angle/side/face/w/e, throughout an infinite number of higher rational-numbered dimensions. But a 10-dimensional object enclosed with only 1 point is a degenerate geometry, and in the 11th, and so on and on, up, and down to the zeroth dimension this is so; so these phenomena are also known as isocrystal singularities.

(I haven't thought of a zero-isoplex except by name, but it sounds like it would have some crazy mathematical function.)

On the other hand, some isoplexes might have what I am calling "obgenerate geometries." For example, the 6-isoplex has 6 angles in the 0th and 1st dimensions, which is an overabundance, so to say. (IDK if this is mathematically possible but it seems like it might be.) So there is a range of isoplectic crystals in which they harmonize and endure; otherwise they quickly (almost instantaneously) explode or collapse. These are ones within a certain range of ratios between the isocrystal's obgenerate and degenerate geometries (its obset and deset, as they say). And it just so happens that it is the Platonic solids that correspond to the n-isoplexes that exist within the "island of stability," here. (So 6-isoplexes are stable, for example, as long as their 3-dimensional state is cubic and not hexahedral.)

One aspect of the arrangement is that the aleph-numbers of the Platonic dice are keyed to 2 aleph-numbers in a special transet. This and the dynamic of the isocrystals were an ancient (24,000,000-year old) phenomenon that helped the Host of Ripheus build the Keyscape.

The trick of the Keyscape with respect to the isocrystals is that Ripheus' Host engineered a different artifact to harness the unstable ones. This was a 23-dimensional fractal object that focused the energy flowing through the unstable isocrystals before it was lost to the dissolution of the gems.

Now, the Platonic dice, when rolled, rotate their correspondent isocrystals. This rotation adjusts the flow of energy in the noumenal domain, so depending on whether the Advocate (good) or the Opponent (evil) has the higher score in their game, at any given time, either of the two aleph-numbers keyed to the Platonic transet can be invoked in the physical domain, either increasing or decreasing the universal probability of good or evil at that time (in the use of magic: i.e. if the Advocate's score is much larger than the Opponent's, a much larger amount of noumenal energy gets cycled through the isocrystals and into morally-correct uses of magic).

The Daykey and the Fifth Nothingness

At one point in the first Critique, Immanuel Kant comes up with another one of his random tables of categories and it has to do with the concept of nothingness. He basically says that this concept is what is common to the four categories he tabulates. Now one character in this story is supposed to be walking by a wall in a weird city one time, and he's supposed to see a message written on it (graffiti, blood, IDK): "Apollyon came to destroy that which does not exist." This is supposed to be super-foreshadowing of the endgame, since I want the "let's destroy the Form of Evil by turning it into the Form of Nothingness" to be the endgame danger, but not to be clearly stated ever beforehand. (Like, the idea that there even is this particular danger is not stated outright before, or that Apollyon could even have Its own ultimate plan.)

So, the meta-form of nothingness that encompasses the four categories, might be thought of the Fifth Nothingness. But actually this is a phrase or title that is supposed to show up at random, another shadow-clue, to point towards the end, because the Form of Destruction might be thought of as the fifth Form of Nothingness in the sense that destruction is that which causes nonexistence. And Apollyon is wielding the essence of the Form of Nothingness itself also, in the endgame. So, the shadow-phrase points towards this event.

It also points towards its explanation in terms of the magic system in the story. So, one way to put the theme of the story is "programming the multiverse using the transfinite numbers." Or, "solving word problems in algebra by using the transfinite numbers." Whichever of those descriptions resonates with you, if either. To "program" the Keyscape, which is what allows physical beings to directly use magic, they had to use the transfinite numbers.

This is defined, first, from the notion of keying one aleph-number to another. The idea is that every aleph-number has a cardinality and an ordinality, and a transcardinality (which, under the definition, can also be called a transordinality). Two sets that differ in cardinal or ordinal rank, can have the same transcardinal rank. Sets of elements with the same transcardinal rank are known as transets. So, there's an economic transet, which is the transcardinal rank of the 24 universes (the "phenomenal economies") together. What the Host of Ripheus did long ago, was to use the seleplex artifexium to key aleph.1 through aleph.24 to arbitrarily "higher" (cardinally or ordinally greater) aleph-numbers, and these 24 arbitrarily indexed sets are all in the same transet. This is known as the isoarchic transet since the elements are all equal in rank and this equality is decided instead of inherent. An instrument known as the Daykey is what the Host of Ripheus used to make that decision (an adjunct to the seleplex artifexium, along with a crystal isoplex array). In turn, the elements of the economic transet are keyed to the elements of the isoarchic transet, establishing the necessary "link."

If you're with me so far: Apollyon has Its own transet. This is the transet of the Form of Nothingness. Now, there are also four forms of the finite-nonfinite difference (finite, indefinite, infinite, absolute), and the Final Power comes from keying the elements of the isoarchy to the angles of the Square of Metafinity (another transet). However, when Vyrian Armirex gives His share in the Final Power to Apollyon, the Destroyer can key Its transet itself, to the entire Square itself as a transet.

One of Apollyon's powers is known as Contradiction. (Unprovable objects, objects defined as absences, empty objects: fictitious, privative, and ur-plenary functions are the other three Forms of Nothingness listed (not in those terms) by Kant.) This is the harshest of the Nothingness-Forms so it becomes the image of the transcreation of all possible evil, simultaneously iterated with the destruction of all that evil, to infinity.

So there's actually a totally different original, and still necessary, reason for Apollyon to have a fourfold tower at Its center...

The Platonic dice

So, I've had an idea for high-level background characters in the Ripheus story, who I am for now referring to as the Advocate and the Opponent. These are two people playing an eternal dice game. This is an avatar of the Game Itself, which is a moral reality, so if the Platonic solids have a metaphysical relationship to the making of fair dice, let's say that the dice the Advocate and Opponent are using are those solids and hence are known as the Platonic dice.

Now, some other miscellaneous phrases:

1. The isoarchic transet. The set of the Key-sets, in which the Key-sets are not ranked except overall against their power-set. The consequence of the isoset function.
2. Isoplectic crystal. A crystal with an infinite number of n-dimensional external facets, each corresponding to one n-simplex, with no n-simplex being reiterated.
3. Seleplex artifexium. A component of the Keyscape. "Seleplex" is short for "selector function x-plex." Made of the three unique icositridimensional crystals located in the 23-dimensional demiplane of the 24-dimensional plenum (in the conjugate infinitely expansive universe thereof), the 23D-demiplane of the aleph.zero-dimensional plenum, and the 23D-demiplane of the aleph.24-dimensional plenum. Allows each aleph-dimensional object for each level of the set aleph.(1 ... 23) in the aleph.24-dimensional plenum, to be keyed to an arbitrary aleph.n number. The 23 keyed numbers are used in the transet computation performed by the Keyscape ("transfinite algebra"). Since which of the aleph.n numbers is keyed for, is decided by free will, they are referred to as "selected" according to the Second Axiom of Choice.
4. Chaotic hypoplex. Always-changing transdimensional crystal keyed by an artifexium function to random aleph.n numbers. When conjoined to the seleplex artifexium, it can be used to change the flow of energy through an isoplectic crystal array, to transpose the noumenal power of the Keyscape into the 24-fold multiverse overall. The day of the Final Power's advent was determined (outside of particular epistemic space) by a computation from the value of the chaotic hypoplex.

OK, so the reason the first Ripheus book is supposed to be called The Axioms of Paradise is because the entire series is supposed to encode an elaborate moral theory, or theory of moral information, into itself. One of the keys to the system is the concept of the final offenses, which are the three ultimate forms of sin. Together, they are the Form of Evil itself because one of them is implicated in all wrongdoing simpliciter and the others, despite being fundamentally inspired by the one, are equivalent in demerit.

So, this maximal evil cannot be perfectly committed by anyone, because rationalistic moral psychology rules it out. It is possible to map "consciously" and "unconsciously" to any junction of the three offenses, so there are 26 ways to consciously or subconsciously commit them at the same time. 9 of these would involve consciously committing the fundamental sin consciously, which is metaphysically impossible otherwise speaking, in conjunction with either the others consciously or unconsciously. So, there are only 17 arrangements that can actually obtain.

Now in the story, the Form of Evil is a given entity or object, a real presence. It is, after all, what Apollyon destroys and then transcreates at the apex of the finale. Before this endgame, though, the Form of Evil tries to break itself into pieces that cannot be simultaneously destroyed, implanting its essence in 26 people who it resurrects from the dead: the Broken Ones. These are not wicked people, to be sure. They are infected but not controlled.

The rules of the game, here, are that unless one of the 9 has been killed, none of the 17 can die. Until one of 9 dies, the advent of the Final Power will be greatly delayed. If any of the 9 die, then any of the 17 can be killed, but until one of them is, the advent of the Final Power will be forestalled. So, some of the quasi-protagonists will unfortunately end up accidentally hastening the apocalypse by killing some of the Broken Ones; or these beings will be inspired to kill themselves, or whatever. Maybe one is killed by others and one commits suicide. IDK but anyway, this situation is a counterpoint to Intuition's plot (Intuition being the Shard-like name for one of the Septatheon) to halt the Final Power, which is one of the highest-level arc questions of the series and the only question with two arc-answers (the problem of Intuition and the problem of the Broken Ones; all the other kinds of crisis are faced only once).