A complicated way to defeat Odium ("for now"), with greater ramifications

[Ripheus23]

This theory worked better in my head when

Spoiler

Rayse still held Odium

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...)

[TruthwatcherDan]

I understood some of those words! 

[EmulatonStromenkiin]

7 hours ago, Ripheus23 said:

This theory worked better in my head when

  Reveal hidden contents

Rayse still held Odium

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...)

I was under the impression that ruin and preservation created a planet because when aligned their intent could be create, as opposed to harmony or disharmony.

I expect that it would be completely possible for other shards to create planets, and I think that they could probably do it with only one shard, albeit with ramifications of being almost reduced to the Stormfather-level power. Black holes should require a significantly less power investment, as they just require mass condensed to a single point, regardless of how much mass. If you do it like in the center of a star, that would be a rather effective way to gain mass. I do want to see the effects of Tri-shard ascension, just because of conflicting intents. It is possible that any intent beyond the state of double will have to end up being harmony or balance, or risk destroying the shard collective.

[WandererNearby]

I have a question about your terminology. The term powerset in my math background was always defined as: "the set of all possible subsets including the set itself and the empty set". So, how do you have a powerset of a cardinal number? If you're referring to the set of that number, the power set is just the empty set and the set of the number. 

Edited April 8, 2022 by DougTheRug
clarity

[Returned]

I've also been thinking that the only real solution to Odium is to combine it with another Shard. There is some evidence that Odium itself was averse to this, not just Rayse, but who knows if Taravangian could overwhelm that with some other aim.

As for planet-generation... maybe? The setup makes some sense, and Investing enough in a planet pins Shards there for quite a while. But would Odium/War fall for this? Being trapped on Roshar is what happened to Odium, and what they've spent millennia trying to escape. Why would they immediately do effectively the same thing? And even if it did happen, there would need to be something to bind Odium/War to the planet so that they couldn't immediately destroy it and leave. Further, I agree that it seems like a stretch (given what we know now) that the back half of SA will involve a totally novel planet with its own geography, people, cultures, possibly magic, etc. mainly as a stalling tactic to draw out the conflict against Odium further. But we'll see, Brandon does well with surprises.

[nehalem]

I think the problem is that Harmony has trouble acting because his 2 shards are opposed to each.

Honor and Odium are not really directly opposed to each other.  The fact that their combination is called War should be a hint that combining the 2 won't lead to inaction.

If anything I would think it would lead to more action.

[Ripheus23]

24 minutes ago, DougTheRug said:

I have a question about your terminology. The term powerset in my math background was always defined as: "the set of all possible subsets including the set itself and the empty set". So, how do you have a powerset of a cardinal number? If you're referring to the set of that number, the power set is just the empty set and the set of the number. 

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:

 

Quote

 

Consider the following subset of X:

A={x∈X∣x∉F(x)}

This subset cannot be in the range of F. For if A=F(a), for some a, then

a∈F(a) iff a∈A iff a∉F(a)

 

 

[Returned]

24 minutes ago, nehalem said:

I think the problem is that Harmony has trouble acting because his 2 shards are opposed to each.

Honor and Odium are not really directly opposed to each other.  The fact that their combination is called War should be a hint that combining the 2 won't lead to inaction.

If anything I would think it would lead to more action.

My feeling is that it's not inaction but rather the kind of action the Shard engages in. Odium has spent thousands of years in a campaign to destroy the other Shards, leaving himself as the unchallenged and unchangeable deity in all of the Cosmere. That forces the Shards into deadly conflicts with one another, whatever the others may wish. War may not be focused on the destruction of all other Shards in the way that Odium has been which could end the deadly conflict that has been playing out so far.

Aside from Autonomy and Odium, the Shards seem mostly content to exist and operate within their respective domains. If War is similar then things might be more action-packed for Roshar but quiet in the rest of the Cosmere. If War is still interested in taking out other Shards then things might be worse everywhere.

[LewsTherinTelescope]

On 4/7/2022 at 9:50 PM, Ripheus23 said:

and their joint power was required

I don't know if this is because of power limits as much as Intent limits (neither ruining nor preserving is creating something new). After all, the Well of Ascension, relatively small compared to the full Shard, was capable of moving the entire planet with plenty of power to spare.

On 4/7/2022 at 9:50 PM, Ripheus23 said:

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.

I don't see any reason to think this is the case?

On 4/7/2022 at 9:50 PM, Ripheus23 said:

besides keeping their magic systems sufficiently distinguishable on-world

Considering the only magic system we know much of so far is of both, accessed via spren of the merged powers, they don't seem very split to me...

On 4/7/2022 at 9:50 PM, Ripheus23 said:

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.

I have no idea how this would happen but that would be wild.

[Leuthie]

On 4/8/2022 at 7:44 AM, nehalem said:

I think the problem is that Harmony has trouble acting because his 2 shards are opposed to each.

Honor and Odium are not really directly opposed to each other.  The fact that their combination is called War should be a hint that combining the 2 won't lead to inaction.

If anything I would think it would lead to more action.

This is a big topic, but it pertains to this conversation. The fact that the Shards he holds have opposing Intents isn't want impedes Sazed's ability to act. Sazed defining the combination as Harmony is the major issue. Trying to hold to a harmonious Intent with the two opposing shards presents a extreme limiting of his actions. He's done this by design. Holding Ruin and Preservation could result in him being completely unhindered. All things could fit his two Intents: actions of destruction, acts of creation, acts of protection. Instead, he's put a box on himself, requiring all entropic actions to lead to acts of preservation and all preserving acts to support acts of ruin. Someone more unhinged could define the new situation as Disharmony, or refuse to see the Shards as a combination at all.

Sazed has seen too many poor uses of power to allow himself such freedom.

[LewsTherinTelescope]

17 hours ago, Leuthie said:

The fact that the Shards he holds have opposing Intents isn't want impedes Sazed's ability to act.

It's what we're told is the cause.

Quote

ericth

Could Sazed take down Rayse since he has two shards?

Brandon Sanderson

Rayse is VERY scared of Sazed. However, given Sazed is a composite of two diametrically opposed shards, he finds it very difficult to act.

Words of Radiance Los Angeles signing (March 5, 2014)

 

17 hours ago, Leuthie said:

Instead, he's put a box on himself, requiring all entropic actions to lead to acts of preservation and all preserving acts to support acts of ruin.

I don't know that this is really a decision he's made. If he just goes around Ruining stuff, I can't imagine the Shard of Preservation would be happy with him, and I can't imagine the Shard of Ruin would like it if he just stopped everything from changing. We do know that Harmony is not the only combination of the two you can Ascend to, but given that the implication is that that would be a result of being unable to control the two, I don't know that he'd really have an easier time getting things done, if he's actively warring against himself.

[clowncarcrash]

It's a cool premise, but I don't think its in the cards. I don't think an opposite shard is in play in the Rosharian system, and Odium is stuck in the system in the medium term. 

 

Maybe if Odium wins your theory could come into play if he goes elsewhere. Like if Part 2 relies on us tricking Odium to pick up Mercy or something.