Archive of Our Own

Quick intro.

In the words “Power” and “Principality”, I'm not consciously cribbing notes from Tolkien or Judaeo-Christian teaching, nor quite from the political arena, but they're all influences subconsciously.

(N)PCs scale enormously in power here, but the scaling isn't easy to define, which is made the worse by the syncretic structure of their functions.  Prima facie... it's like going from fine-tuned differences of just how many fingers you have available to count on to the comparisons/contrasts of Traveller and 3e/4e GURPS tech levels' differences (and types), and then on to Kardashёv types (and as with the movie “Cast away  ”, one might possess advanced knowledge and/or power, but be unable to do anything technological or otherwise with it, which is the case in some D&D worlds with low background magic-energy resources [see 1e & 3e D&D “Manual of the planes ”] and throughout The Ice [world-ponds and rare oases aside]: an electrical lamp is a paperweight when the electricity is out).

Speaking of The Ice: when I wrote this, it was targeted at my own story/game-world of “Icewall”, but that doesn't affect the thrust of scaling characters' powers.  Just treat those references as being a setting that you're not familiar with (basically one where a weird Bermuda Triangle-like effect suppresses tech at flashlight-level complexity or above) and move along to the generalities or the next point (though if the idea sounds interesting, you can find the Icewall world-book .pdf on my Google drive).

I'll stick to the general anime/manga ranking method for this one: assume ranks (F), D, C, B, A, S.  You can add AA / AAA or A+ to this, but the principle remains the same.

The general expansion principle beyond that is essentially looking at the differences between the scaling effects of, for example, {10 + 10 + ...} vs. {10 * 10 * ...} vs. {10 ^ 10 ^ ...} vs. {10 ↑↑ 10 ↑↑ ...} vs. etc., and using that as a scaling framework within which one can account for the enormously disparate {bits of accessible data, W/y energy thoughput, effective Kardashёv Type, and Classic Traveller Tech Level equivalent} for a given supermutant and a civilization thereof.
  In some ways, one can say that a linear foot is meaningfully of the same measure (and contains the same aleph null of rational coordinates, or the same beth one of irrational coordinates) as a square foot or a cubic foot, and in other ways (in a deeper mathematical sense, not just the obvious everyday sense), that there's a meaningful and significant difference between them.  You can choose either, for an appropriate context.  For our purposes here, dealing with supermutant gradation, I'm applying the latter path.

Zeroeth tier: non-ranked  ^{Get to the point ▼  Contents ▲}

Life of any kind, or even just the very existence of non-living material, is miraculous — grok some chemistry or physics, or meditate (religiously or philosophically), and you'll be amazed — but let's face it: your average paramecium isn't exactly operating on the same level as your average house cat or human.  This means that there are clearly levels that would fall far short of typical storybook or game characters' capabilities (whether average, or super-powered, or challenged by innumerable slings and arrows).

For argument's sake, I'll simply place them at Kardashёv Type ε (in the sense of (1/ℵ_α =: ε_α) > 0 and [watch the smoke and mirrors behind the curtain] ε_α² ≝ 0, rather than in the sense of (ε₀ := ω↑↑ω) ≫ ℵ_n).

This isn't an accurate rating, just evocative.  Technically, the Kardashёv civilization typing is a logarithmic scale, so paramecia and such might be Type -1 or -2 or something, but I'm going to pull artistic liberty here and just proclaim them to be ε by fiat in order to drive home the relative insignificance of their power levels, knowledge base, etc. (“-1 or -2” just doesn't feel as if it has quite the same impact as ε).

0: Micros' takeaway points

They exist, they use tooth and claw (or some equivalent).  That's about it.

≪10⁶ Wh/d (i.e.: ≪K 0) (where 10^-4 W = K -1).

In this sense, consider K ε as representing a power/etc. level that's asymptotically close to |0|, rather than the more accurate equivalence of K 0+.

Effectively what would be Classic Traveller TL ε (with same clause as K ε).

First tier: ranks F-A  ^{Get to the point ▼  Contents ▲}

Your average human being, or at least the range that one might expect people to fall into.  A small child might struggle with a 10 pound weight, and adult can typically lift and carry 100 pounds (within a factor or so, more or less), and heavy-weight lifters might well reach 1,000 pounds (squat, bench press, or dead lift; perhaps half of this for snatch, or clean and jerk).

The average Ants in “The Colony  ” would rate their own special Rank F, they're that low-statted — but hey, they're better off than the (N)PCs of Creeks and Crawdads (I can't tell if the game .pdf [or the Never cry Crawdad! module .pdf] is legitimately free or not [sorry: I don't wish to risk copyright problems, so you'll have to search for those yourself], so I'll link only the definitely-free Impact System revision), who'd legitimately earn a Rank F-.  <sigh> Those poor Ants and Crawdads.
  NB 29 May 2023:  If you're wondering about the Ants and Crawdads being here at all, but not linked, that's because the Ants' WIP [involving their equivalent of Batman or Spidey] is still collecting electronic dust in my notes, but the Crawdads' fic [The silence of the Clams] will be uploaded sometime this year, or possibly early 2024, depending upon my rate of writing — which is going more slowly than scheduled due to my working on a year-long 24/7 overall AO3 traffic study, in follow-up to my already extant tutorial / study Analyzing AO3 reader traffic flow (re. one's own fics' reader traffic).
  NB 08 Apr 2024:  That year-long study (re. the background half-hourly reader-traffic patterns across all of AO3) is now done and I can now return to my previous deferred-2023-now-2024 projected writing schedule; that fic is absolutely still on the list, though the sequence and immediate length of the list have changed a few times, so here's a brief gloss of the Crawdad language in the meantime.

The Octorillas and Cuccos of “Sonic's Redemption ” would qualify for this tier (though not all cuccos are Cuccos¹).  The Octorillas are sophont, though only slightly sapient; the Cuccos are somewhat more sapient (their corrals and husbandry techniques showing some sophistication as tools in their own right), though only somewhere between 0 and 1 in sophonce.  Both are fully sentient, but neither has any super powers.  I suppose put them each as F+ (even though the Crawdads might, and the Ants apparently do, have a slightly more advanced overall physical setting and clear social interaction than the Octorillas and Cuccos have).
  By a similar token, one might be forced then to place Wil Huygens' Trolls (see Meat Pies) into something like a D- rank (note that minus sign: they're a D-minus; I can't quite say that they're up to snuff as a full D, just that they're better than an F+ [F-plus]).

Your average peasant, John Q. Public, etc. — such as TMNT's Casey Jones (if I remember correctly, anyway) or the Mystery Men (again: IIRC) — are Rank D: not remarkably good at anything, not remarkably bad at anything.

Friday (a Deku Scrub of “Sonic's Redemption”) has mystical knowledge (though I'm not sure of just how much), and has applied it shamanically (at least pharmacologically, and possibly spiritually/Jungian archetypally), but hasn't yet demonstrated any actual magical powers per se, hence is at least Rank C (possibly higher, of course, just not lower).

Deathclaw (Mr. Fluffykins, of “Deathclaw: the tale of Mister Fluffykins ”) is probably Rank C in raw power and fighting, or just maybe Rank B (by now, at least — he was at the end of his rope when he met Peach, and likely ranked as an overall D or F at the time).  This is in an absolute sense (using the F...A scale relative to typical humans), since his current Awakened state would qualify him as Rank S relative to other cats, based upon his ability to speak and read Common.  Some cats can use doorknobs and toilets (I had one who'd learned both, and another who'd figured out only the toilet, but each of them was completely self-taught); while such skills are fairly remarkable (given the low rate of their occurrence), they aren't S-rank level.

Robin Hood, though an older reference, would likely qualify as Rank A (or a strong B at the very least).

Batman is Rank A (or arguably A+, for a finer-tuned distinction).

None is superhuman.

The overall civilization of Creeks and Crawdads probably stands at about the level of your average kindergarten class... minus the teacher.

The Ants' civilization is operating at perhaps 1^st (just maybe 2^nd) grade level... also minus the teacher (but worse: the Ants are being run by someone who might as well be Angelica, of Rugrats).

<sigh> Those poor Ants and Crawdads.

1: F-A takeaway points

People have cars and computers, or something of an equivalent level; ~30 kWh/d.  Nukes and such (or equivalent) exist; civ. ~10¹³⁺ bits data & ~10¹⁰-10¹¹+ kWh/d ≈ 10¹³-10¹⁷ W/y (these being broad orders of magnitude and using rather varying sources of information about power demands).

Individually, people are estimated at a 100 W throughput (10² W → K -0.4 ≈ K 0); by daily use of items at our command (though pretty much only “first world” usage) 30 kW ~K 0.

All stand at around Kardashёv Type 0.

Individuals might be trained in skills of any Classic TL, but won't have any innate powers as such; an everyday citizen could be expected to have Classic TL 6-9 (depending upon the type of tech. in question) at their immediate disposal.  Their civilization could reach Classic TL 8-10+.  Clearly, these assume something like 20c-21c Earth, and would presumably be higher or lower at other points in time.

Second tier: S-rank Supers  ^{Get to the point ▼  Contents ▲}

Your average superhuman.

Superman, Thor, Wonder Woman, Dr. Strange, Hulk, Spider-Man, Dark Phoenix, Hercules, and anyone else who can do things — even a single something (even if just barely) — that absolutely positively can't be performed by an unaided, unaltered, non-mutated, non-magical, non-psionic, non-cybernetic, non-whatever-else ordinary everyday human, no matter how incredibly buffed up that human's stat.s are, is at least Rank S (or possibly on the teetering edge of S-, if you somehow need such a thing).  No, that doesn't mean that birds and fish are Supers.

How many “S” ranks are there?  I mean, not all divine-cyber-psionic-super-mutant-mages are born equal.  Doesn't matter specifically, but let's say that there are at least 3 (I'm comfortable with 5, too, but that's irrelevant).  I don't know whom you care to rank where, but Doctor Manhattan (perhaps?), Q, and The Beyonder (and Dr. Doom, for a little while there...) are really way out in a class of their own: Rank SSS or Rank SSSSS, given the ranking system so far.

In order to keep it easy to read, I'll use subscripts here: S₃ or Rank S₅.

A normal human is roughly equivalent in level to the state that they're shown as being in “Fantastic planet  ” (or as described in “Battlefield Earth ” [the pulp sci-fi book's description, not the craptastic movie depiction])...: kitty-pets (or verminous shitty-pests, depending — particularly if viewed from something like the perspective that one might imagine of Titans in “Shingeki no Kyojin ”), essentially; not precisely far-far beneath the level of power and intellect of a Super (hold onto your objection 'til after you've read tier three for contrast), but not exactly on an even footing either.

Strictly, a zombie wouldn't fall into the F...A tier since they're somehow defying death if they're undead (a real zombie then — not simply a rage-zombie that's a living being with some virus).  On the other hand, if that's the only condition that applies (and the attendant facts that they can certainly take a world of punishment from environmental to starvation and keep on ticking), then they aren't very far from normal people either (call them... “living impaired, plus perq.s”).  I'll call them S-, but I couldn't really fault anyone for dropping them to something like A+ (this wouldn't be accurate to me, given the details here and the ranking method so far, but... ehh).

Vampires, Werewolves, Wendigo (the usual type, not the variation that Warbotdorf [a later alias of Robotnik] refers to in “Seize the Deity  ”)... I'll skip the rant about monsters with human faces (narcissists); the parallels to World of Darkness's Wyrm's draining abuse, all-consuming rage, and mind-blotting need to consume and destroy are apt but off-topic.  Taken as metaphors, vampires and such are still just humans, hence F...A; treated as literal super-powerful beings within a game or a story though, they're S₁ or higher (usually not higher, but it could happen: consider an antediluvian or even just a methuselah of VtM, or Akasha of Anne Rice's “Queen of the Damned  ” — hell, consider Imhotep of [the 1999 version of] “The Mummy  ” [the good one, with Brendan Fraser]).

The city of Ankh-Morpork (Terry Pratchett's Discworld series) could qualify as merely Tier 1 (F...A), or even merely 0 (∷ paramecia), though I can't rule out Tier 2 (Supers and Powers), based upon >>> SPOILER ALERT >>> the events of “Reaper Man ” (the book with the snow globes and the shopping carts). <<< END OF SPOILER <<<

The seemingly-living corporate embodiments in the movie >>> SPOILER ALERT >>> “Branded  ” (you might recall something from it about a red heifer?) <<< END OF SPOILER <<< possibly qualify for S₁ or S₂, in some ill-definable paranormal sense.

WHFRPG Gods and some D&D Gods would probably(?) be Rank S₁, or Rank S₂ at most.

If we assume 5 ranks in the S tier, then Superman might be S₃ or higher (for the general degree of each power, not the scope of his powers).

I'm less familiar with Wonder Woman (outside of the '70s live action TV show and '70s/'80s cartoons), but her divinely-gifted powers are greater than his, by canon.  Whether they're sufficiently greater to place her up a rank I leave to your discretion.

The Fylgjur of “Nyjötnar Saga ” are a bit iffy (I'm only as far as the barest outline and some worldbuilding): I haven't really developed that story very much yet, so I don't have a good handle on all of the details, but if their Fylgjur more or less approximate the norm, then they have some capability beyond everyday people's, but not really on the level of a comic book character.  Let's give them a placeholder of S- for now.

The Ant Queen of “The Colony  ” I'll place as S₁ by way of her ability to pump out gene-tailored kids.  Moreover, they're not simply GMO, but can include flight and fire-breathing (dragons that are still in paper-note form, awaiting transcription), T-virus-like hulking brutes, and a few other mutant superpowers.  Yeah, I'd say that this counts.

The Augments and Cybers of “Sonic's Redemption ” would fit in here as Tier 2 Supers — as long as you'd consider the Six Million Dollar Man or Daleks as being something along the lines of super powered characters.

Kaonashi might qualify for Rank S₁ (footnote in Afterword of .pdf of “Seize the Deity  ”), though I'm not so sure of Caïssa (footnote in Epilogue of .pdf of “Seize the Deity  ”), as would the Great Deku Tree that I never name explicitly (it's world-building background in the back of my head) as being the source of protection (illusory terrain, ghost sound, various vermin and predatory plants throughout the outskirts) that keeps the Deku Scrubs' ancestral lands safe from exploitation.

Other beings — such as Icewall-Titans (something like Dune mélange-induced Greek gods or ST:TOS Apollo / Charlie X) or Icewall-Cthulhu, and some D&D Gods — would fall someplace around Rank S₃...₅.

Icewall's world-trees that seed the plane with mountainous seeds shot like volcanic cousins to the [movie/TV-version] Klendathu (of “Starship troopers ”) are K1 in power, though not canonically named as being intelligent or not (perhaps a huge store of information genetically, but with a K0- consciousness {sapience, sentience, sophonce} on par with what a character might normally expect of a worm or a tree).  Though their [lack of] volitional awareness wouldn't rank them as a Power, the sheer scope of their natural abilities (even if only in a general ecological niche fashion) places them here in the same sense as worms, house cats, and non-super humans are all in the same ballpark in contrast to prokaryotes or Supers.

Each additional S rank leaves the prior ones in the dust to the extent that each F...A rank does the same within the F...A tier.  Clearly though, there's a huge difference between the F...A tier and the S tier.

Zelda's a Goddess (herein an autonomous avatar) and [in my story-world] Peach is O̅kami.  They're Powers.  That puts them someplace in the S tier (I think...?), and I'd guess Rank S₂ - Rank S₃, since I just don't see them as falling into “merely” Rank S₁.

Their incarnate powers don't seem to be much to speak of, but we know that the canon of the real [video game] Hyrule shows Din, Farore, and Nayru as having created that world.  That's some reasonably vast power compared to your average superhero.  Hylia might have the same level or not, I don't know (could be higher than theirs, could be lower).

We've seen Peach pull off her little auto-reincarnation feat within this story-verse, and discussed some of the implications thereof regarding disincarnated O̅kami powers (see “Seize the Deity  ” .pdf ► DELETED scene ► footnote).  Those are some serious abilities.

Sonic and Tails — neither of whom will stay dead, short of a nova — pretty much qualify for S tier.  I'd say Rank S₁, but presumably(?) not Rank S₂.  Tails's current INT is S₁ on its own, and might combine with everything else to boost him to S₂.

Ruru's gotta be at least Rank S- (S-minus), simply based upon her spell-like abilities.  (Yeah, this technically opens the question of everyone with any magic, psionics, chi, etc. as qualifying for S tier, but let's skip the pedantry; for now, just assume that alchemists and wizards learn things and hence don't qualify for more than A+ as-is, but also that how and how much wizards do what they do is beyond human bodies' natural capabilities just as much as sorcerers' innate control, and thus qualify them as S- or better — a warlock's pact-granted-powers would be hand-me-down sorcery on par with Doc Oc's cyber-powered super-strength (or Spidey's, since that came from a bite rather than au naturel [and let's face it: Iron Man is just Tony in a flying tank, but it still sort of fits into the S ranks]).  A spell-like ability that simply does otherwise normal F...A things would qualify as S₁ in its magical nature and complete lack of necessity for the normal human approach, even if not in its scope of being merely an F...A result.
  Much like Iron Man and Doc Oc, I'd say that The Mask and Juggernaut probably sit somewhere in this tier, though whether S₁ or some higher rank I'll leave for the reader's discretion (this applies particularly to Juggernaut, who showed greater power and skill than I think that I actually give him credit for, whereas The Mask is more obviously capable of pulling off some serious shit).

Amy too (Amy Wong, the AI of “I am Legion ”), by dint of being essentially a liquid metal Terminator: S- to S₁.  Her INT skews things a bit, since I suspect it of being at least on par with Tails's, which might bring her to a total of S₁...S₂.
  Come to that though, Amelia (the other Amy, of “In for an Amy, in for a Pond  ”) would probably qualify as well, by being a Time Lady.

Peach specifically stated (obliquely) in the epilogue of “Seize the Deity  ” that Shīfù Lǎorén, the Immortal Wombat, is a Power — and she wasn't guessing or being polite.  We know [from the Afterword in the .pdf] that he's immortal (can be killed, but won't simply die on his own), and that he's of an insanely high OCC-level (at 15 levels each of everything combined into one style, ~465 per Ninjas & Superspies, but with an actual canonic effective level of about 1,200).  Yeah: he's some kind of S tier, minimum, whether literally or de facto super.

Daemon (the ReBoot character whom I used for “I am Legion”) I'm not sure of — she might be multi-S, and she might be next-level (hell, bookmark her for now as being S_ω).

The Avatars in Charmed (original 1998 TV series) are probably at her level.

The Gaian of “Sonic's Redemption” is somewhat spread across the tiers.

• In terms of power that it can muster, or intellectual capability, it's pretty much dead in the water: tier 0 or tier 1; it's arguably on par with a sequoia or armillaria ostoyae (other than that its components can move).

• Given its integration of organisms over unnamed vast distances to form its being, that's a super power of some kind: tier 2.

• In light of its purely zooic nature, it might reasonably fall into the bottommost ecological niche of tier 3: Principalities (see next tier-entry).

“It” (i.e.: Morgoth, of “When the paladins come marching in ”) probably lies somewhere within the above-outlined S_n range, but I don't have a bead on just where.

All are superhuman in one way or another, and/or have access to laws of nature other than those that are commonly perceived (e.g.: they can perform “supernatural”-seeming feats through magic, psionics, chi), but none is truly supernatural in the sense of decreeing new laws of nature as such.  At truly staggering ranks, the wishes, loyalties, and hatreds of F...A ranks are as irrelevant to them as an ant's agreement or objection might be to your drinking a glass of water or going shopping (note that this doesn't mean that a superhero wouldn't bind themselves to non-Super law, only that they choose to do so by their own honor, whereas a super-villain feels no more bound to it than a non-Super villain, and is less constrained to do so).

One could argue that modern Earth nations stand at this level, or at least at the very bottom threshold thereof.

2: Supers' takeaway points

People run around with über-tech coursing through them as much as we've had mitochondria for billions of years and give it no thought.  Tailored worlds and walk-through stargates exist; civ. ~10¹³-10¹⁵ bits data & ~10¹⁶-10²⁶ W/y.

Kardashёv Type ~I-II?  (Clearly not invariably, since our heroes usually don't exhibit full K1 power levels, so take these with some latitude as an approximate upper limit.)

Individuals might reasonably possess personal powers (GMO/mutant, psionic, nano, etc.) on the order of Classic TL 9-20 (variance due to type of tech. in question), whether typical or atypical of their civilization; an everyday citizen probably would have fairly unquestioned access to Classic TL 10-17 (depending upon the type of tech. in question).  Their civilization overall could reach Classic TL 25+.

Third tier: next-level incomprehensible  ^{Get to the point ▼  Contents ▲}

Your average god-like entity, and I don't mean Greek Gods, I'm thinking cosmic-level shit here.

What about beings on the scale of Moorcock's gods of Law and Chaos, since they're more or less my conception of Negent (and similar entities) — except that they seemed to be a bit limited in their potentia in contrast to what Negent is (then again, maybe they were more interactive than he, and operated under essentially the same constraints as he, hence it's simply more apparent with them)?  They're clearly not F...A, but I wouldn't class them in the S tier and call it a day.  The same might(?) be said for Discworld's Azrael or Adventure Time's Prismo (and others) — and arguably [the essentially Platonic ideal conceptual entity] Darkseid [and the New Gods in general] (his [and their] true form(s) on Apokolips, not his [and their] mere manifestations across the DC multiverse): these entities don't show their hands, so I can't really say shit, but I'm not sure that they're operating at anything less than T3 R3 (and honestly, I can't rule out T4).

Maybe we should simply assume direct hyperoperation as the key at this point (e.g.: humans being additively more powerful, Supers multiplicatively so, and Principalities exponential), rather than which value is being hyperoperated on.  This will get a little ad hoc, so please bear with me.

A Principality (Void, Kallistṓ, Entropy, and Negent - all of “I am Legion ”) would qualify for the Sⁿ tier (at that point, does the exact value of the |n|-Rank really matter all that much, in overall scale?).  Technically, the S₁, S₂, etc. ranks fall within the Sⁿ tier, in that they'd all be factors of S¹ — and by that same token, F...A ranks would be infinitesimal fractions of S¹.  Assume here that any significant Sⁿ refers to magnitudes of S (i.e.: n>1) — much like the differences between a point and a line segment, and an area, and a volume (though only somewhat, since a figure of n-dimensions [regardless of measure] always has the same number of DIM 0 points, as far as I know [ZFC² aside, anyway]) — such that:

If we do this, then the Principalities can be ranked roughly like superheroes and average people.

If we further assume either the actual layout above or one extremely similar, then Negent and the others would probably be something like Rank S^1...5.  There's always the chance that there are other, hidden Principalities (such as one that arranges filigreed patterns, rather than emptiness, randomness, blended equilibrium, or polarizations — assuming that this weren't a subtle play by Tào, and that Tào isn't simply a Principality of great skill and delicacy), and their power could go off-scale, but for now we'll simply assume that at least these four are fairly closely balanced.  Perhaps there are huge asymmetries, but only in dissimilar ways, much as with S tier: Brainiac's intelligence vs. Dormammu's magic vs. Saitama's punch — each is vastly qualified within their field of expertise, but how does one compare and contrast between them?  Q and The Beyonder might (just barely) fall into this tier, rather than the standard S tier (Dr. Manhattan not so much, but this same “not so much” arguably applies perfectly to Principalities, so... yeah).

Primordium, named in the prologue of “What evil lurks ” (Link's sidequel adventures to my main Zelda series) might fall into any tier above F...A.

Whether it's a Power, a Principality, or something wholly other on even footing with Tào (“I am Legion ”) or something, I don't know, but it's definitely capable beyond merely human levels.  I described it as chaos that strode the lands in darkness (with the deliberate lack of narrative cohesiveness regarding Primordium's logical place as an actor in history, given the inherent self-contradictory nature of Icewall), a thing which in turn found [life / goodness / something referred to indirectly] to be a brittle burr and consumed itself with a non-specific intense yearning [to destroy utterly this brittle burr], apparently capable of “...stoking the currents that flowed across eternity, plucking the threads that guided all things, searching for the weak spot to harry...”.  The reader is [meant to be] led to believe [correctly] that it proceeds to do so through indirect means, not by clashing headlong with existence itself or any god-like beings, but by subverting life into malformed creatures of chaos and evil (active malevolence, rather than “mere” callous indifference) — such as Kandarian Demons (and presumably beings of the Cthulhu cycle, and/or Warhammer's Chaos Gods' minions [to include Malice and the Horned Rat and the various Skaven ideologies, and lesser-known examples such as Hashut or Necoho as described by Richard Jones]).

To cause or create such beings is at least super-level (I'd argue Principality, but wouldn't be able to prove that).  I don't have a good handle on Primordium yet, and I probably won't develop it as a detailed NPC, but I conceive it as being Principality-like (if you were to view Void vs. Chaos and Negent vs. Entropy as diametrically opposed edges of a tetrahedron, then picture Primordium as being like a disc that's radial to Void's and Chaos's fulcrum: not really on the others' axes, yet not exactly orthogonal to them all, just perpetually tangential to the one axis while maintaining a complicated and variable relationship with the other axis — in this fashion, Primordium parallels Moorcock's Singularity to an extent, insofar as they each wish to cause their respective opposite number's “otherness” to cease existing).  That it should expect world-unmaking results from driving some putz like Link crazy indicates either rather poor judgment at the least or vast insight indeed.

If its power level is that high (more to the point: assuming that it's not too low to consider), then its being off of the game board (so to speak) leaves me wondering as to its nature.  Logically its actions must fall within its own purview or that of some [other?] Principality, unless these actions are completely cloaked from their awareness and/or operate at a level above their ability to comprehend.  I think that it's safe to assume that the cloaking example isn't the case, but the comprehension level doesn't make sense either.  I really don't see Primordium as a Tào-like entity, much less anything on a level with Ayn Sof or Ohr Ayn Sof.

Perhaps its actions introduce what the [other?] Principalities would view as minor imperfections in the weave, nagging loose threads that must surely derive from their various actions (and perhaps those of Tào), and surely not some agency unknown.

In any of these cases, you'll note the pronoun “it”.  This isn't an issue of uncertainty or coy ambiguity or physical hermaphroditism or fluid identity or PC neutrality or anything: Primordium is sexless and genderless.  Some of its actions could potentially be described as masc./fem. in some way or other, but should not be ascribed to masculinity or femininity or whatever-else-inity as such.  It simply is an “it” — a living, thinking “it”, but very much an “it”.

Worth noting is that Primordium's existence lying outside of the Negent “pantheon” implies a multi-dimensionality to the “real” history of Icewall (that is: each different sequence of events and origins could be considered to be true, regardless of the sequences' mutually exclusive natures).  As well, Primordium's existence also implies that there could be some sort of thriving ecologically diverse set of “pantheons” at any given tier, not necessarily interactive, but present.

Similarly, “Malice” (an entirely different one, my own of “The Devil is in the details ”) — and the other hosts of such kind — must logically lie within the Sⁿ range or higher, but could arguably be below it.  For now, let's just say no more than S^ω.

Why “no more than ”?  Because Malice is perhaps an ultimate expression of iterated power sets, and as such cannot exceed these bounds.  Whatever Tào (et alios) might be or be capable of, any upper bounds thereon aren't limited by such bounds as might apply to Malice.

3: Cosmics' takeaway points

Laws of nature are malleable to Principalities.  Their decision that something operate a certain way is as much a given for them as picking up a glass of water is for most of us (that is: we “choose” to hold it a certain way subconsciously, to move it through a certain path to our mouths, etc. — but we give it hardly any thought at all while a much larger [and still insignificant, though unparsimoniously so] portion of our awareness and being is dedicated to watching TV or replying to an e-mail).  They basically are supernatural forces unto themselves.

Here we can see another clear distinction between individual capabilities and those of the associated civilization.  Just as your average human on Earth doesn't wield the same power as an entire nation, the Æsir as a whole wield far greater power than any single Áss.  Where any Áss alone might stand at K1 or command K2, the Æsir civilization operates somewhere rather above this (let's say ~K3?) — see the Icewall .pdf technical appendix for a detailed description of the dimensional engineering involved with their star, which is also their computing source.  A similar comparison would not be inapt were we to draw such for Kryptonian technologies, though they eschew magic (and psionics).  The same could likely be said of the Vanir psionic technologies.

Spacetime and massenergy are by whim to these beings; civ. >10²⁶-10¹²⁰⁺ bits data (and this extrapolates only as far as K3 & K4) & ~10³⁶-10⁵⁶ W/y (noting that our observable universe produces something on the order of ~10⁴⁵ W).  With K4 being the defined maximum within a given universe, I suppose that a being on a multiverse scale (e.g.: Negent, per his own testimony) would presumably weigh in at K5 (minimum).

Kardashёv Type ~III-V?

Individuals can be presumed to possess individual powers (sheer ability, though defining this as scientific or magical or zooic [psionics, bio-E, chi, etc.] is probably folly) on the order of Classic TL >27, whether typical or atypical of their civilization.  Their civilization overall should be taken as Classic TL 31(+), if there's any difference between individual and collective potentia.

Fourth tier: a (Super's Super)'s Super  ^{Get to the point ▼  Contents ▲}

Negent referred to other entities or tiers, though he didn't assert that they're definitely real.  Tào would presumably qualify for the S↑^pk (Knuth's up-arrow notation) tier.  Again, just assume that n>1, though in this case “n” is “p”.  By way of a quick intro./refresher, if /p/ here refers not to the single-arrow's exponentiation value (after all: just how might we meaningfully raise a non-numeric arrow to an exponent?), but instead to how many arrows are intended (such that S↑²k = S↑↑k = k-many “S”s in an iterated exponentiation of S^S^...; a power tower [of S] of the order k) then:

This first table [above] isn't meant to show how quickly the values of 2↑ⁿ4 grow, since those are specific to only the number |2|, and the “values” of S_n and Sⁿ aren't exactly numeric things (seriously: how might one really evaluate S_n = S+S+..., or Sⁿ = S*S*..., or S↑²n = S^S^...?).  It's meant only to give you a feel of how the up-arrow operator functions.  You're familiar with how addition just keeps adding things, and most people can follow the principle of multiplication in general; most people's grasp of things tends to drop off around exponentiation (and even if familiar with something, we all forget things sometimes).  That gives you the next operator {∃, I, Δ, +, *, ^, ↑↑}.
  As a greatly-belated note, I should mention that this is only the direction that I chose (and there's some good material on extending ↑↑ at Wolfram MathWorld and in a fascinating thread on negatives and fractions [e.g. 8↑↑-3 = log₈(8↑↑-2) = log₈(log₈(0)), or (-3)↑↑3 = ⁻²⁷√(-3), or 2↑↑0.5 = 2↑↑(1/2) ≈ 1.458781816] on 知乎 | Zhīhū), and it's just to construct a rapidly increasing scale of power; one could always find a more mathematically satisfying alternative such as powerlog (a^ln(b) = b^ln(a)) courtesy of Zach Star.
  NB:  If you're really itching to play with ↑↑, then you can use Wolfram Alpha, but must break down your up-arrow notation into the expanded power tower (e.g.: 2↑↑16), which is unfortunate, I know, but it's not as fast as Robert Munafo's Hypercalc (which, by way of a logarithm adjustment method, instantly spits out far larger answers in the blink of an eye 🙂, e.g.: 2^2^2^...^2 = 2↑↑4,096 [for which it gives 8188 PT (19727.780405607016) as its answer] where you've doubled your twos via copy-and-paste so that this string is 2^12 = 4,096 twos long, though it does bog down if you double those to 2↑↑8,182... ask me how I know).  For a fair comparison, Wolfram Alpha takes 6 seconds to compute a string of {2^2^2^...^2 = 2↑↑16 = 16 twos and 15 carets}, which it displays as 10^{1010101010101010101010^19727.78040560677} or 10^(10^(10^(10^(10^(10^(10^(10^(10^(10^(10^(10^19727.78040560677))))))))))), while Hypercalc spits out the same {2^2^2^...^2 = 2↑↑16 = 16 twos and 15 carets} input's answer as 12 PT (19727.780405607016) instantly — and bonus: unlike Wolfram Alpha, Hypercalc's Wayback backup does work 🙂... however, it's important to note that unlike Wolfram Alpha, it thinks that -1^0.5 = 6.12323399573677 * 10^-17. 😑
  I should also add that there's something on Desmos looks capable of doing an extremely nested towers thing, but I just don't have the patience to fiddle with (and it looks more like it maps the towering, rather than calculating it).

The next table [below] shows some input-n values across the top with each operator's row giving the respective output-entry values and their intermediate k^th-element and iterated sequence steps listed in separate end-columns — I'm skipping some steps, but this isn't meant to be a proof.  It's broken into two pieces in an attempt to make it accessible to people reading on their 'phones; for that same reason, the table is truncated to 5 columns, rather than 8 (for that [and some annotating comments], you can find it in the appendix of the “I am Legion ” .pdf, linked in the summary).
  The numeric results below are irrelevant — they're accurate for the numbers used³, but only meant to demonstrate each operator's rate of change when acting [for the n^th time] on the preceding iteration's value.  It's not properly constructed, since realistically one should take a given value and apply say... ^2 or ↑↑2, etc. (and n here is really the i ^th iteration: f(n) at first, and for next n=f(f(n)), and so on), but the results' rates are easier for 2↑↑ than for ↑↑2 (and while not key to general construction of (N)PC power scales for most purposes, combinatorics are pivotal to my own story-universe's nature, hence strongly inclining me toward 2↑↑), so since this is only illustrative, not an actual math treatise, I opted to cut corners here.  The point isn't the numbers: it's to parallel the rate of power scaling sketched out in earlier subsections: Tier 1 (2+ = F...A) additive power scale of difference (no superpowers), Tier 2 (2* = S_1...5) representing superbeings, etc..
  Don't focus on the numbers, just glance at the differences: the difference between n=3 and n=4, for example, for one operator is nothing like the much larger difference for those same n under any later [higher order] operator.  That's the point.  The {difference between one semi-average person being better or worse at something than the next semi-average person} and the similar {difference between a couple of Supers} isn't the same difference, not simply in the raw amounts of differences, but even in the differences' sheer ratios; i.e.: not only is {d_S4-S3 - d_B-C} > 0 (different in their amounts), but moreover even {d_S4/S3 / d_B/C} > 0 itself is in turn a positive slope.

That second table presents a glimpse of the enormity involved with tier 4 (bottom row, i.e.: ^, or ↑¹).  The first two rows {2∃, 2I} being my own debatable placeholders (as is 2Δ, really), but in this context each one of those two pretty much boils down to meaning “something exists”:

• “2∅” or “2{}”— null, the empty set — isn't shown, but I mention it here for completeness;

• “2∃” shows only that any given k exists at all (existential operator: the actual value of n being irrelevant, so k=1 in all cases), and

• “2I” shows any given entry k to hold the same value as n itself (identity operator: specifically k = n; the count of a set of existing things being the enumerated iteration of acknowledging the presence of one after another, each given its unique number and so establishing cardinality, but only marginally iterated in this sense).

• Its first contextually meaningful row, “2Δ”, is tier 0 (the successor operation: for the successor of n by 2, we find that the value is always k = n+2 [hence the delta “Δ”: the amount of difference between any given n and its k]; specifically: addition occurs as an operator on n, but it's not iterated from one result to the next),

• the second contextually meaningful row, “2+”, is tier 1 (F...A, in which the k^th entry holds the value of 2₁+2₂+2₃+...+2_n = 2*n; multiplication: iterated addition),

• the third contextually meaningful row, “2*”, is tier 2 (Supers: S₁...S₅: 2₁*2₂*2₃*...*2_n = 2^n; exponentiation: iterated multiplication), and

• the fourth contextually meaningful row, “2^”, is tier 3 (cosmic beings: S¹...S⁵: 2₁^2₂^2₃^...^2_n = 2↑²n = 2↑↑n; tetration: iterated exponentiation).

• With the bottom row, “2↑↑”, representing tier 4 (Dreamtime; pentation: iterated tetration), we begin to get a feeling for the sheer scope of power at the 2↑³1...5 range when contrasted against the previous tiers' 1...5 ranges' slopes.

• Failing a deep grasp of mathematics, I would venture that such a construct might be analogous to treating the usual operators as particular instances of {∃ = op⁰, I = op¹, Δ = op², + = op³, * = op⁴, ^ = op⁵, ↑↑ = op⁶} — though subscripts (re-indexed to 1...7?) might be more appropriate than superscripts — but that's too far astray from our purposes here.

This isn't a perfect analogy, of course, just a rough set of scales per operator.  It shows how any given S↑^pk₅ is vastly beyond any lower-p tiers' 5^th elements {7, 10, 32, 2*10^19,728(+) [i.e.: 19,729 digits], 2↑²(2↑²65536)}, which gives us some sense of scale — but it also leaves most of their initial elements equal {3, 2, 2, 2, 2}, and that (i.e.: F ≈ S₁ = S¹ = S↑³1) just isn't the case.  In this, perhaps we should view them as {k ^th element} ordinals rather than as |n = value| cardinals.

Regardless of the specifics above, and whether Tào et al. are real (within my story world's hierarchy), if we follow such a ranking structure, and we rank Tào someplace within this tier, then Tào would be of Rank S↑³1...5.

Following this layout, we can use the up-arrow notation for the other tiers right along with Tào as follows:

• 0 (“ε”, e.g.: paramecia) ∷ Rank S↑^-11...5;

• 1 (average F...A) ≡ Rank S↑⁰1...5;

• 2 (Supers and Powers) = Rank S↑¹1...5;

• 3 (Principalities: Void, Chaos, Entropy, and Negent — and the putative Other) = Rank S↑²1...5;

• 4 (Tào) = Rank S↑³1...5;

• 5 (Ayn Sof, Ohr Ayn Sof — more on them in next entry down) ⇒ ≥Rank S↑⁴1...5.

4: Dreamtime takeaway points

Law and nature don't really apply here anymore.  At this point, it's all Dreamtime manifested.  Every thing implies all other things, so that it's more a question of “where” you are in the plenum than of what “is” or “isn't”.  To “be” is to dream, to dream is to “perceive”, to “perceive” is to manifest as being.

One might conclude that if a being's civilization's K type is arguably one type greater than a being's own, then Principality (= tier three) civilization (∷ tier four?) might well stand at this Dreamtime level.

“Reality” and “unreality” are a meaningless distinction to someone at this tier; even “individuals” (aspects?) ∷ ≫10¹²⁰ bits data & ∷ >10⁶⁶ W/y, insofar as {bits, data, watts, power, or a year} can be said to have any meaning here either.

Kardashёv Type ~VI.

Traveller TL loses meaning by this stage (and might very well have done so before even tier three), but take beings at tier four as Classic TL ≫31.

Fifth tier: to infinity and beyond  ^{Contents ▲}

Ohr Ayn Sof (and even Ayn Sof alone) would normally be taken as infinite, though in the above tier system one could suppose another hyperoperator beyond the up-arrow, but it's more of a notation than an actual operator (then again, aren't they all?).  In this sense, the fifth tier would be a function of {element k = S↑⁴1...5 ⇒ sequence = S↑³i_n-1} and Kardashёv Type >VI.

Aside from the values of k (vast) and the implications of K type VII+ equivalent power / knowledge / perception / etc. (meaningless to me: absolutely aware of everything at once), it's probably safe to assume that these don't actually apply to them.  Perhaps these k values apply to someone in the Icewall food chain, but I'm pretty sure that Ayn Sof and Ohr Ayn Sof are the source of all.  Period.  Full stop.

Do I know this?  Well, no.  Yes, I'm the guy writing it all, but I haven't designed that particular aspect as yet, and I doubt that I ever will.

I suppose that as a tier in itself — whether it applies to any (N)PC or not — tier 5 would simply follow the pattern set forth so far: 5 = S↑⁴n, hence having (N)PCs of Rank S↑⁴1...5.

You want to know where Ayn Sof should logically fall?  <sigh> Let's say that it would have to be something like tier Ω.

TL;DR:  ^{Contents ▲}

So, where does all of that leave us?  It leaves us contemplating a universe from the perspective of a grain of sand.  That's not a statement of insignificance, either — it's multilayered: reality as a fractal, logarithmic scales of scientia and potentia, and able to view at least one tier upward and downward from a given position.

Each tier might see the downward tiers as being like fragile soap bubbles, or mere shadowplay, or ephemeral figments of thought.  Looking upward might be akin to a caveman trying to grasp the workings of a castle, or a Death Star, or the inner mind of Cthulhu.

For simplicity, assume further that within a given tier, someone might personally possess different specific ranks of knowledge vs. perception vs. power vs. etc., command some higher rank of each (such as personal possessions, legal authority, etc.), and yet be part of a civilization that is perhaps at least one full rank higher still (all of this leading to upward of an entire K-typal difference between the individual and the world that they live in).  In this way, the range covered by a rank R within a given tier T might be considered to be equivalent to R = 0.20 ΔT; it's a bit awkward, since although the ranks of each tier progress smoothly, successive tiers progress with the next higher derivative: ΔT₁ < ΔT₂ < etc. (i.e.: a smooth slope per tier, but with each tier's slope being greater than the previous one's).

N.B.:

If the mathematics grabbed you more than the general idea did, and you feel a need to run it into the ground, then you might want to look into things like the Ackermann function, Graham's number, Loader's number, the TREE function (note: TREE(n) ≠ tree(n)), and fast growing hierarchies.
    For a quick intro. to these, try these videos (plus one 6K essay):

• Graham's Number – Numberphile (explaining the basic nature of the question that Graham's number answers),

• What is Graham's Number? (feat. Ron Graham) (explaining the n-cubic question itself),

• Graham's Number Escalates Quickly – Numberphile (expanding on the process to reach it, fleshing out just how insanely large a number we're looking at),

• The Enormous TREE(3) – Numberphile (showing just what the TREE game is),

• TREE(Graham's Number) (extra) – Numberphile (this one in particular looks at the Shannon data entropic limits of the universe),

• TREE vs Graham's Number – Numberphile (expanding on the iteration of f(f(f(...(f(n))...) and introducing {ε₀ = ω↑²ω, ε₁, ε₂, …, ε_ε1, …, ζ₀ and η₀ via Veblen hierarchies of functions, and eventually the Feferman–Schütte ordinal Γ₀});

• Who Can Name the Bigger Number? (Scott Aaronson, 1999; walks through the usual fun and ends with a bang: good old Busy Beavers).

(I hesitate to add this, but some might also like The World's Largest Numbers, Part One, which covers a far more clearly arranged write-up of Bowers's “Infinity Scrapers”, an extremely TL;DR version of which can be found at the array notation entry in the Googolology Wiki.)

Addendum, 15 Jul 2024:  While perhaps unnecessary at this point, if you enjoy materials along the lines of the above few links, then you might also enjoy Quest To Find The Largest Number (CodeParade, 09 Jul 2024), which outlines the usual suspects in a 160 char. (140 byte) SMS limited context, leading to Buchholz's Ordinal.

O ~~~ O