Ripheus23
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Let's start with Wit's little sermon about gobbledygook names and people being ripped apart. I would've just stuck with, "He's talking about Adonalsium," but I noticed some stuff people were saying about how BAM's name is the most complex name for an Unmade. Also, the imprisoning of BAM seems to thematically resonate with the Shattering, like it was morally similar in the eyes of those involved. So maybe Wit was talking about Adonalsium AND the Unmade. But I was also rereading that section of book 2, where Pattern is incredulous at Shallan's explanation for why Nohadon got that name, since it was supposed to be more symmetrical than his original name. Given all that, why didn't they just change his original name to be more symmetrical without being an effectively different name? But note the first syllables of the first name: "Ba"; then the next one is Noh-adon, maybe, like "ado," or if it's No-hadon, still, you've got "hado." Ba-hado-... you catch my drift. So, random guess, the Hierocrats didn't like that Nohadon bonded an Unmade and retconned his name and stuff on account of that. Because of that bond, and because of BAM's apparently key role in the Rosharan magical ecology, his Cognitive Shadow/Spiritual remnant became imprinted on BAM's aura, transmitted into Dalinar's dreams later. Worse theory: BAM is "Unity," no less, and though we were presuming that the Unmade really were direct or indirect servants of Odium by the by, BAM actually wasn't. She was able to set up the whole False Desolation without tipping the Heralds or anyone else off in advance, at least no one in a position of power who could have thwarted her. Also we find out that Odium's tone became integrated into Roshar's when BAM was imprisoned. Odium wants the humans more for his future war, he was the god of the humans first, yadayadayada so it never looks like the Shards physically fight each other during their millennial world building/unbuilding projects, even Ruin vs. Vin was a very unusual event, so I could see the way that Odium fought Honor was by infecting the moral cognition of people on Roshar, especially that of the humans. Then BAM's imprisonment was able to represent a distinct victory for Odium, in part in terms of his prioritizing humans over singers. So anyway, BAM was, as an Unmade, under Odium's power, but we see in Sja-anat that this doesn't translate to outright servitude all the time. And so Odium saw a "we" in his own will, and the will of the humans (the Radiants, incl. Melishi) who imprisoned her, so that when she was able to reach out to Dalinar during the confrontation in book 3, she portrayed herself as "Unity." (Weakness: why "killed you" then, not "banished you" or something? unless BAM became a deadeye inside the gemstone, on account of her bond with the entire singer people being negated? and the honorspren are surprised when Maya speaks, e.g. when deadeyes speak, it tends to be surprising...) Sidenote: Ishar's mad grasp One of the WOR epigraphs suggests that it is contingent that the number of Bondsmiths is only three at most, and that those who wanted the number to be more were considered menacing. What if there are various unusual spren, like Cusicesh, who at some point were involved in attempts to generate Bondsmiths without using the natural/known godspren? Alternatively, of course, it could be that the menace was in the idea of multiple people bonding one godspren, but otherwise, I do wonder if Ishar, who was the one who compelled the foundation of the Radiants under exacting strictures, had some sense that unique spren could be "manufactured" in the relevant manner, and if this then has anything to do with his dire experiments. In this vein, BAM and other Unmade might have been such irregular spren, formed in some prior phase of history (maybe even before the singers knew Honor and Cultivation, unless Adonalsium's Shattering predated the establishment of religion, and hence religious spren, on Roshar?). Also, this might be why Odium thinks Rosharan humans are especially suited to its plot: an army of Bondsmiths would pose an extraordinarily powerful danger compared to armies composed mainly of other apex-type magic-users in other systems. I at first thought maybe it was because of the Dawnshards, because it seemed weird that they'd use those to break Adonalsium, but then Odium wasn't using them to attack the other Shards (at least, I don't know that that's been indicated clearly or not), and if for some reason they were concentrated in the Rosharan system, IDK... So instead, I thought maybe Odium was trying to figure out how to create new Dawnshards, using the magical ecology that Adonalsium had graced Roshar and its solar system with. If you think about it, Honor and Cultivation usurped Adonalsium, in the Rosharan system. One wonders whether Odium ever feels like the other Shards are being preposterously self-righteous in overseeing the religious affairs of various worlds, including worlds like Roshar. Granted, in the Nalthis case for example, the local Shard isn't clearly recognized by the religious majorities of her world, so until we learn more about why Adonalsium's Shattering took place, it remains that accusing the Shards of being merely power-hungry is not necessary. However, at the time Rayse and Odium in parallel even now could've easily lied to themselves about the other Shards to motivate the decision to attack. It remains that Roshar's religious history, in the form of its spren no less, seems to have been peculiar for Adonalsium to have established as it did, so even the Honor/Cultivation godspren don't seem to be the only possible original such "unique" spren, sufficient in order to the Bondsmiths.
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Take the set {a, b, c}. {} (as zero) is appended off the bat, then we have {a}, {b}, {c}, {a, b}, {a, c}, {b, c}, and then the copyset {a, b, c}. So the powerset of 3 is 8 (letting {a, b, c} = {0, 1, 2}, the von Neumann ordinal 3). For infinite cardinals, the problem is infinitely more difficult. For example, one subset of ℕ (the set of all natural numbers) would be every even n, another would be every odd n, another is the set of all squares of n, all cubes of n, all the n starting from 1 instead of 0, all the n starting from 2 instead of 1, all the n with the exception of various random n, say 17 and 23 and 42, etc. It is impossible by rote to list all permutations of n as defined vs. all n criteria, so we have no hope of identifying the powerset of ℕ by rote. All we have is the general rule that this powerset is larger than ℕ (is size-equivalent to ℝ, the set of all real numbers). This general rule is not an axiom, but a theorem, something to do with a generic function from the base to the powerset that is demonstrably not one-to-one; the Stanford Encyclopedia of Philosophy article on type theory reports the theorem like so:
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This theory worked better in my head when since he was the one who was averse to picking up more Shards, not his Shard's own quasi-personality/Intent/w/e. But maybe Rayse has left an imprint of his own aversion, on his Shard, so IDK. Anyway, the gist of the idea is that Team Honor will somehow learn that if one of these divine beings holds two Shards, this changes that being's will, at least eventually possibly leading to a stasis threat (as with Harmony). So to defeat Odium, Dalinar will compel him to take up the remnants of the Shard of Honor, forming a di-Shard (of War?) that will be tempered to relative inactivity. There's a more intriguing possibility woven into that possibility, though. IIRC, Ruin and Preservation were the only Shards to form their own planet relatively ex nihilo (this is a universe with pre-existent substance, though, so no absolute ex nihilo creation except unknowably, perhaps, by the God Beyond), and their joint power was required. Given the role of the Set in all this, what I suspect is that when we get to the deep mathematics of Shardhood, we will be told that each individual Shard has power equal to some transfinite cardinal ℵ, but a di-Shard has power equal to (ℵ to the power of ℵ), which is equal to the powerset of ℵ, which is always a larger transfinite cardinal. So the di-Shardic power level is significantly greater than the mono-Shardic one. Anyway, I'm supposing that individual di-Shards have the same "let's make a planet out of thin air" power that paired Shards seem like they might as such, too. (I can only imagine what the interplay between the Cognitive Realm and set-theoretic forcing might be: forcing is a technique that allows you to create versions of set theory that compute powersets differently from each other, including by forcing powersets to be drastically larger than their bases; so if people forced the powerset of the Shards' individual power to be even greater than it already is...?) So a further assumption: this is relevant to the proposed interdict on paired Shards. For some reason, creating new planets rather than Investing in older ones is problematic. Here, then, might be a reason for Honor and Cultivation to see themselves as acting in the spirit of the interdict, despite clearly being paired: besides keeping their magic systems sufficiently distinguishable on-world, they also did not imitate Ruin and Preservation, here. Ditto for Devotion and Dominion. At any rate, vs. Odium, I'm guessing that Team Honor could force Odium to take up Honor and become War, and then trigger War to create a new planet 'out of nothing,' an act which will severely drain War's power, thus at least temporarily defeating him. That would be an epic subversion of final-battles-with-an-evil-god tropes all across the board, as far as I know (as long as such a plotline hasn't been done before...). One problem I have with this idea, though, is that it seems like it would set the stage for a story set on this newly minted planet, yet we've no indication that the back-half SA will involve travel to a currently hypothetical/unnamed realm, much less any other Cosmere novel yet outlined for us is expected to include such a journey. If it goes through, though, I would anticipate other Shards debating the merits of pairing/merging. Perhaps mass production of planets will be a plot point in the final Mistborn sequence? And then the risks and prospects of tri-Shardic Ascension, etc. It's not clear to me whether Adonalsium exnihilated the entire Cosmere or if it too Invested in some pre-existent worlds, but if a tri-Shard's power level was equal to the powerset of the powerset of a single Shard, then if a di-Shard can 'easily' manifest a planet, I would expect a tri-Shard to be capable of 'easily' manifesting at least either much larger planets (like gas giants) or even stars of various sizes/types. (Eventually, we would have to consider what it would take to form decent-sized black holes; Investiture can already be condensed such as to produce phenomena similar in abstract nature to the kind of spatial warping involved in gravitational singularities, so...)
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While trying to resolve the Continuum Hypothesis, I accidentally solved an entirely different, and arguably much more important, set of problems, namely the question of justifying the axioms of set theory: the ZFC axioms firstly, and arbitrarily many axioms of higher infinity besides. This is how I did so. (Btw, I happen to wonder how far Brandon Sanderson will take his set-theoretic Easter eggs. There happens to be a form of set theory interwoven with graph theory, which seems relevant to the notion of Spiritwebs. So will these eggs manifest most strongly in stories/substories involving the Cognitive Realm, or is there, after all, a mathematical side to the Spiritual Realm too? And if so, will it be a form of set theory that constitutes this Spiritual aspect? Supposing it is a form of set theory, will Sanderson (obliquely or not) bring up, say, the intricate doctrines of large cardinals? (Will he bring these up even if his set-theoretic Easter eggs reach their apex in the Cognitive Realm only?))
Preamble: the choice between set, type, and category theory as a foundation of mathematics
I am choosing set theory as my foundation of mathematics. It is said that category theory and type theory go together very well, in the end, even such as to say that categories are effectively reducible to types. However, in light of the historical fact that set theory won out over type theory, but has not won out over category theory, I am going to assume the following: a term refers to a set if the referent has elements; it refers to a type if the referent has tokens; and it refers to a category if the referent has elements and tokens. That being said, typology adverts more to the logical sphere, whereas elementhood is more distinctly mathematical. So a category is mathematical inasmuch as it has elements. Nothing seems to have actually been gained, then, in providing a foundation of mathematics in category theory instead of set theory.
The fundamental understanding of set theory's internal justification
In the pure theory of knowledge, there is a problem, the problem of the regress of reasoning, with four "mathematical" solutions: either the regress ends in self-justified axioms (foundationalism), the regress forms loops (coherentism), the regress is infinite (infinitism), or the problem is unsolved (skepticism, which corresponds to J0 in justification logic). Coincidentally, the elementhood relation can be sequenced in all four of these same ways, viz. there are well-founded sets, looping sets, infinite descending elementhood chains, and then the empty set-theoretic object, that which has no elements. My fundamental claim will, then, be that well-founded, looping, and descending sets are all justifiable modulo the positive solutions to the regress of reasoning. By implication, then, although descending sets are justifiable somehow, it is not permissible to axiomatize this justification. Justification by inference from axioms is per se nota well-founded justification, so that only the well-founded sets are justifiable in terms of the axiomatic method as such. And although I have a model of a justified descending set, my focus for the remainder of this discourse will be the axiomatic hierarchy. This is because it is modulo that hierarchy, that solutions to various other problems of set-theoretic justification with which I am familiar, have appeared.
Justification values
Frege proposed that truth is not a predicate of an assertion, but is the reference of that assertion (if it is otherwise factually correct). This is the notion of truth values. Likewise, in my theory of set theory(!), there are justification values. Truth-theoretically, the values are made to coincide with 0 and 1 on the numerical side of things, with fuzzy logic usually also having every other real number between 0 and 1 as a possible "degree of truth." There is no such bracketing required for the doctrine of justification values, and this allows us to formulate the initial axiom of infinity in a novel way, one that wears its justification on its sleeve. This is to have that axiom be, "The assertion that the initial level of infinity exists, has a justification value equivalent to that level." More concisely, have j(S) be the justification function, which takes sentential inputs S and outputs the degree of justification S has. So say: ∃S(j(S) = ω), with the very S in question being ∃ω, so that j(∃ω) = ω.
This happens to turn the entire question of justifying any axiom of infinity on its head. If every higher infinity makes possible a higher infinite degree of justification, it follows that the stronger and stronger axioms of infinity are all the more justified than the lower ones, down to the axiom of ω. Not that the initial principle is therefore unjustified: it too is infinitely adequate to the question of its own existence, of course, here.
Specific justifications of large-cardinal axioms
The above might not be good enough to "explain" the justification of specific large-cardinal axioms, however. Granting that this is so, I would say that we can intrinsically justify, in a Gödelian way, at least some of these axioms, not by analysis of the iterative concept of sets, but by analyzing the concept of justification itself. In other words, replace ZFC's standard background logic with a justification logic. Then you open the door (as far as I know) to at least the following axioms:
The model-theoretic characterization: every set theory of a certain form has an initial worldly cardinal assigned to it. ZFC with justification logic is such a theory. So there is a justification-theoretic worldly cardinal (and it is justifiable to assert that this cardinal exists).
The proof-theoretic characterization: every set theory of a certain form has a proof-theoretic ordinal assigned to it. Sometimes, to "identify" this ordinal, one has to imagine a much taller, but still countable, ordinal, that figures in what is called a "collapsing function," this function being the one through which the "identification" of the proof-theoretic number is given. Those much taller countable ordinals can be "shadows" of genuine large cardinals. ZFC with justification logic is a theory such that those shadows and their counterpart large cardinals figure in its proof-theoretic analysis. So there is an (otherwise uncharacterized) justification-theoretic large cardinal.
The infinitary-logic characterization: some standard large cardinal axioms can be formulated in terms of infinitary logic. ZFC can be assigned an infinitary justification logic for its background. So there are large-cardinal characterizations available modulo this assignment. These inherit the intrinsic justification of the logic (again), such that it is sufficiently justifiable to assert that these (they are called "weakly compact" and "strongly compact") cardinals exist. Bonus points: when you introduce strongly compact cardinals, for example, you get some other types of large cardinals below the initial strongly compact one, and you get a sizable amount of those types, too. (You don't get these with the worldly cardinals, and although it is "probable" that the proof-theoretic mirror cardinalities are much greater than the smallest model-theoretic ones, I could tell you nothing about the interim between the mirrors and the worldlies, whereas I could at least attest to measurable and inaccessible cardinals in light of the strongly compact ones.)
From what I can tell, you can do a lot more with this justificatory template. I've "rambled" long enough for now, though, so I'll leave it to the interested reader (if there are any) to ask me about that "lot more," or to go seeking for it themselves.
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I had to change my physics idea significantly due to considerations regarding infinitary logic. The idea is that the laws of physics are infinite conjunctions under an ℒ(κ,λ)-structure that shifts over time, with major cosmological processes constituted by those shifts. For example, at t = 0, let the infinitary logic of a given universe be ℒ(0,0). Over the interval t(0 to 1), the structure shifts to ℒ(ω,ω), which corresponds to the initial expansion, the Big Bang. Further major shifts in expansion dynamics result from further increases in ℒ(κ,λ), so that the accelerated expansion, for instance, is a consequence of these dynamics.
The model has two grounds: an empirical observation and a major prediction. The first involves the idea that perception of a standard continuum results from existing in a dimensionality that succeeds the cardinality of that continuum, much like "complete" perception of a two-dimensional structure results from existence in three dimensions. Assuming that the cardinality of a continuum is aleph-1, then we assume that ℒ(κ,λ) here has aleph-2 for κ (which is the variable for time's dimensionality in the system), such that we perceive time as continuous (of cardinality aleph-1).
The prediction the theory makes is that at some point in the future, there will be another major shift. The equation I assigned to the shifts picks out aleph-4 as the value for κ resulting from the next shift. Consequently, empirical consciousness should change accordingly, then. So if we survive to that day, we could receive predictive evidence for the model from specifics of cognitive changes at that time.
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I just finished The Last Druid, and though I enjoyed it and think it works, thematically, for the most part, I do wonder if it could've been more... epic? For example, the final duel was way less intense than the one in The Wishsong of Shannara or The Gypsy Morph. Thoughts? Thanks!
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Well one prediction came true, one book earlier than I expected, another seems to have been falsified, and my theory about Adonalsium being like a city got some minor evidence behind it, haven't read DAWNSHARD to double-check but yeah, overall, couldn't have asked for a better RHYTHM OF WAR, except maybe he could've used commas when using the word "though," more often.
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I don't doubt that the long-term consequences of Autonomy's actions will lead to crisis events, but how deliberately diabolical these would be...?
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Everyone knows that Sanderson books are too short, especially Stormlight books. What to do about it? A: origami coding. Fold the pages to line up parts of words for more content. B: invisible ink in the margins/spacing. Possibly include magnifying glass with purchase and blacklight for the ink directly. C: invent an alternative English that can be read two ways, so that after reading the actual text in original English, you can start over with second English. In fact, you can do this multiple times, maybe indefinitely, and once translations are brought in... D: coat the paper in mild hallucinogens so readers add their own books to the books while reading. E: start a forum for people to transcribe hallucinations, both chemically induced and meditatively realized.
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Then there's Hoid, Hoid, and Hoid
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I have a notion of free will as involving the structure of time, such that we don't always or even perhaps mostly make choices "moment by moment." Free will ranges over entire line-segments (of the timeline), sometimes, consolidating our actions over periods of time. So once a word's meaning is learned, the chain of thought behind that learning gets consolidated, so it doesn't manifest as a "decision" to know what words mean, each time we use a word. I guess, to a degree, that decision has already been partly made, by the time we learn the word. But then think of those moments when you say a word over and over again and its meaning seems to sort of dissipate? I wonder if that's relevant to what I'm saying... In my model, I guess this appears at the erotetic level. Here, thought has an assertion function, but also a question function. The question function is the one that allows us to directly keep ascending the staircase of recursion (always taking itself as an input...).
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On the tip o' my tongue for some years now
Ripheus23 replied to Ripheus23's topic in Cosmere Discussion
Two things, though. Well, three even, but anyway, first, Odium isn't actually "Passion." That's a complex lie of his. The Dawnchant description of Odium was of something that drained all emotion, leaving a void. Second, supposing Sanderson was inspired enough by any of this to incorporate it into the Shards, it had to have been going back some years, before the planes got these mechanisms tagged to them? Third, but this is just me, I always preferred yugoloths over baatezu and tanarii, on a conceptual level. I mean, I held strongly to that "neutral good is most good, neutral evil is most evil" notion (I started out as chaotic good but then found out it wasn't "pure" good, so I switched to neutral good, etc.). I feel like Odium's evil is great enough to be the closest in the cosmere (of the Shards we've seen) to pure evil. Now granted, the yugoloths also have a major hub in Gehenna, it's where their lord is after all, but otherwise, the yugoloths supposedly originating in Hades also pushes me in the Odium:Hades direction. -
The concept of True Words
This was a concept I liked a lot in fantasy, but couldn't reconcile with the way the concept was executed. My take on it was to suppose a moral codex where each kind of good action corresponded to a letter, so that performing a sequence of good actions meant "spelling out a word" and then forming "sentences" and so on. Anyway, someone with a name in the language of good actions would have that for their True Name, and a True Word would be a word for a thing in this language.
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Whom watcheth the watchethmen
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On the tip o' my tongue for some years now
Ripheus23 replied to Ripheus23's topic in Cosmere Discussion
If any of this was an indication of anything, that leaves three more evil (from our POV, or whatever) Shards, one for a prison-plane, one for some floating volcanoes or what IIRC, but where one of the ultimate fiend-lords dwells, and one for another battle-plane. Preservation, maybe. -
For some reason, the 16/17 thing about the Shards has always subtly reminded me of something, but I couldn't figure it out. The closest was thinking that the 16 might be relevant to a personality test. However, within the last few days, I finally remembered. The Outer Planes from D&D. I don't know what state the D&D cosmologies are at today, but while I was growing up, they were still roughly at the, "Sixteen Outer Planes surrounding a seventeeth," stage. Now, the logic behind them is morally slanted, plus only really requires nine examples, but let's imagine that there's a vague possible mapping from the Outer Planes to the Shards, with the 17th Shard being the neutral "center." Here are my guesses: Odium: The Gray Wastes (from Wikipedia: "Here, all emotion and compassion is drained away, until only hopelessness, selfishness and apathy remain"). Dominion: Baator Ruin: The Abyss Mechanus: Preservation (Wiki: "This clockwork plane is the ultimate in order") Having a heck of a time with Cultivation, maybe Arcadia, the Beastlands, or Arborea Honor: Ysgard ("The eternal battleground where true heroes prove their valor": Tranquiline Halls much? though this depends on how much of the TH mythos is Honor's) Devotion: Elysium Autonomy: Limbo Ambition: Pandemonium Endowment: Bytopia (only "link": the term "BioChromatic Breath") EDIT: Possible extra Shards Ingenuity/Wisdom and Grief = have neutral planar counterparts? Also if Honor is not Ysgard, he's Celestia, maybe.
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The key to defeating Odium is to arrange a marriage for him... ... to Taravangian. The Stormfather again officiates, hence the title.
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OMG Knights of Honor's Truth Knife of Heaven's Treasure Knowledge of Hope Knowledge of Wind Ketek of Highstorms House of Worldsingers
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Mwahahaha Knowledge of Wailing Tentacles, Keep of Worrisome Turtles, Kiln of Weaponized Terebinths. King of Wriggling Teetotalers. Knights of Whistling Tomatoes.
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"Since ZFC provides us with the resources to construct ultrapowers, we can construct inner models using mice."
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I will square the circle, even if it is impossible.
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Kelp of Wiggles. Krill of Whales. Knurl of Whirls. Kerfluffle of Whiplash. EDIT: Kettle of Worms, Kaleidoscope of Wishes, Kiosk of Windows, Keel of Wolves, Knell of Wilting, Knee of Wit, Koala of Width, Knife of Worship, Karaoke of Wealth.
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Sanderson also uses the phrase "one-to-one correspondence" periodically (in WoBs). In set theory, the word "cardinality" was originally read off the notion of suits and ranks in decks of cards (the example being 4 suits X 13 ranks giving you a "set with a cardinality of 52"). 1-to-1 correspondence ends up being crucial to defining "different sizes of infinite cardinalities." I wonder if there's anything about the Physical-Cognitive interface that suggests you could get a lot of indirect magical power from thinking about infinite sets. My guess is that there is, that the Set are either on to the problem or know (part of) its solution, etc.
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Kiss of Wonder
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"The souls of the lepidoptera finalitas contain prophecies. Think of them like flying fortune cakes..." "Be gentle! Heed the lepidoptera..."
And they said:
"Hither! Purple whispers creep! The noose is loose! Kitten and a kaboose!"
"There are 9.23 grams of marmalade dried to the base of Mrs. Losensky's blue ceramic bucket..."
"I woke up one morning to find that my nose had detached itself from my face and been transformed into a hideous, lavender-scented aardvark..."
"Apollyon likes bloody omelets..."
"There seem to be a few problems with the argument: it is too long and only quotes The Minstrel of Lettuce..."
"The quotient of a positive shirt and a negative shirt is a set of four-legged pants..."
"Good grief, it looks like I missed the coronation of my skeleton's last remarks..."
"What a mighty! I! What!"
"My nephews never believed that I used the abacus for firewood to power my mitten-crinkling machine..."
"Tsk. As if YOU had ever shaken hands with the Form of Handshakes..."