Can Shards be harmed or splintered through conventional means?

[Scion of the Mists]

5 minutes ago, Angsos said:

At the risk of making things more complicated, why would Rayse be afraid of Sazed if they both have infinite power? Is it that having two shards Sazed's mind is expanded twice as much, allowing him access to twice the power?

They both have infinite power.  Harmony has more power.  Those statements aren't contradictions (there are different types of infinity).  

Brandon has said that "Harmony is vastly more powerful than Odium."  

[Fanghur Rahl he/him]

That’s the problem; no matter how you twist and turn it, you still end up claiming, directly or indirectly, that one infinitely powerful Shard has more raw power than another infinitely powerful Shard, which is a contradiction in terms (as I understand it, the different types of infinities simply do not apply in this usage, since we’re talking raw power). By far the simplest way of looking at it it is to conclude that the Shards are unfathomably powerful by human standards, but not infinitely powerful. Under that assumption, all the internal inconsistencies and contrivances dissolve.

Edited September 10, 2018 by Fanghur Rahl

[Jace21 he/him]

Why do differently sized infinities not apply here? 

Its been a while since I was in school but if I remember correctly, there are mathmatical proofs where two things are each shown to be infinite but one is also proven to be larger than the other.

I see no reason why this cant be the case. When perceived by finite beings, as all non-Shards are, every Shard is equally powerful, that is, infinitely so. There is nothing they can't do.

Only when the Shards interact with each other does the amount of their power - "size of their infinity" - become relevant.

[Fanghur Rahl he/him]

1 hour ago, Jace21 said:

Why do differently sized infinities not apply here? 

Its been a while since I was in school but if I remember correctly, there are mathmatical proofs where two things are each shown to be infinite but one is also proven to be larger than the other.

I see no reason why this cant be the case. When perceived by finite beings, as all non-Shards are, every Shard is equally powerful, that is, infinitely so. There is nothing they can't do.

Only when the Shards interact with each other does the amount of their power - "size of their infinity" - become relevant.

Admittedly, I’m far from an expert on calculus, but as I understand it, whether or not one infinity is ‘larger’ than another is entirely dependent on how you choose to analyze it; on which so-called ‘measure’ you use. But it’s only a mathematical notion, not something with any kind of actual referent in reality. For example, if two universes are spatially and temporally infinite, then regardless of whatever mathematical hocus pocus someone tries to play, neither is objectively ‘bigger’ or ‘older’ than the other.

Like I said, I know very little about how calculus works, but I have listen to lectures by actual physicists that I’ve said something relatively similar to this in relation to the multiverse; maybe I’m misremembering, but that’s my understanding anyway. 

[Fezzik]

If you take the infinite numbers above zero, and compare them to the infinite numbers on either side of zero, they are both infinite and unfathomable to the human mind, but one is twice as big as the other.

[Fanghur Rahl he/him]

38 minutes ago, John203 said:

If you take the infinite numbers above zero, and compare them to the infinite numbers on either side of zero, they are both infinite and unfathomable to the human mind, but one is twice as big as the other.

Are they? Or is that just what your intuition would tell you? Because as I had this exact thing explained to me once, technically it isn’t twice as large, regardless of what common sense would suggest, because it’s simply undefined. 

Again, I’m just going on what I’ve been told, for all I know I’m completely wrong about this whole thing. I’m certainly not dogmatic about it or anything.

[Wreith he/him]

30 minutes ago, Fanghur Rahl said:

Are they? Or is that just what your intuition would tell you? Because as I had this exact thing explained to me once, technically it isn’t twice as large, regardless of what common sense would suggest, because it’s simply undefined. 

Again, I’m just going on what I’ve been told, for all I know I’m completely wrong about this whole thing. I’m certainly not dogmatic about it or anything.

My understanding is as follows:
logically (2*infinity) > infinity, but the distinction is taken as meaningless in most mathematics because with sets of the same order there just isn't enough of a difference.

The distinction becomes meaningful when you have infinity of one order compared to infinity of another order
{-1.1...,-1,...,-.1,...,0,...,.1,...,1,...,1.1}> {...,-2,-1,0,1,2,...}
real infinity > cardinal infinity
infinity^infinity > infinity

infinity to the infinite power is still technically just infinity, but it's a much more meaningful difference at the higher order.

^ That just to try and help make the point that infinities can be different.

 

With respect to shard power, I easily accept that the power of 2 shards is greater than the power of one shard despite both being infinite.
And...you know...WoB

Edited September 10, 2018 by Wreith

[Fanghur Rahl he/him]

Well, regardless, I still say that it makes it needlessly complicated to think of them like that, even if I granted that I’m wrong and it’s possible to meaningfully describe them as infinite. But I guess that’s just my personal opinion.

[Jace21 he/him]

It is quite deep, but Brandon does seem to like putting obscure math thongs in the Cosmere.

Like has already been said though, the different orders/sizes of infinity are only relvant for Shard v Shard confrontation, to us mere mortals they are all infinitely powerful when we are not, so the specifics dont matter.

[goody153]

I would say no as well. Even the nightblood case since Nightblood is basically a drop in the bucket to what the shards are. Even the Well of Ascension from Mistborn wasn't affecting preservation at all.

Ruin doesn't even get affected when Scadrial was being demolished into pieces and Scadrial is made up of his essence so even physical wouldn't work. 

It has to be work of another shard to bring another shard down(even if that shard was himself/herself)

On 9/11/2018 at 2:03 AM, Angsos said:

At the risk of making things more complicated, why would Rayse be afraid of Sazed if they both have infinite power? Is it that having two shards Sazed's mind is expanded twice as much, allowing him access to twice the power?

They can only cover so much because even their enhanced minds could only grasp so much of the scope of their power. Sazed kinda has double scope considering that he is both Ruin and Preservation. So his mind covers twice as much as Odium would. 

It just means that Harmony has reign over investiture of Ruin and Preservation. While Rayse has reign over Odium alone. So Harmony kinda covers twice as much influence as Odium would. 

And we know that while everything is made up of investiture of another shard. It doesn't mean that something is always from another shard (in the case of Roshar even if Ruin was situated in Scadrial and was not aware of it. It might be possible that some spren from Roshar like decayspren might be his. Or maybe other spren in roshar might be of Autonomy or Ambition)

Edited September 12, 2018 by goody153

[Fanghur Rahl he/him]

6 hours ago, Jace21 said:

It is quite deep, but Brandon does seem to like putting obscure math thongs in the Cosmere.

Like has already been said though, the different orders/sizes of infinity are only relvant for Shard v Shard confrontation, to us mere mortals they are all infinitely powerful when we are not, so the specifics dont matter.

Well the other problem I have with it is that it seems pretty clear that a Shard only has access to as much Investiture as their expanded mind directly encompasses, which presumably corresponds to a volume of space roughly as large as a solar system, since we’ve never seen a Shard directly influence anything beyond its own solar system. But even if you want to extend that several orders of magnitude, you still ultimately end up with having an infinite amount of Investiture either crammed into or at least connected to a space of finite volume. And Brandon has on more than one occasion compared investiture to energy and thermodynamics in terms of the rules governing its behaviour (minus the supernatural component of course). 

[HSuperLee]

The way I'm interpreting the WoB about Shards and infinite power is not that Shards have access to an infinite energy source, but more that any investiture they expend eventually returns to them and can be reused.

In the case of Ruin and Preservation, if we think about Ruin's power like a boomerang, he threw it, and Preservation caught it in a cage. Now, it's a weird supernatural boomerang, so it's still moving around inside the cage, either being Atium, or pure energy in the Pits, but it can't return to Ruin. So, the goal was to find the Atium, and unlock the cage so he had access to the investiture again.

Or, that's how I interpreted it, at least.

Edited September 14, 2018 by HSuperLee

[Jace21 he/him]

On 9/11/2018 at 2:41 AM, Fanghur Rahl said:

Well the other problem I have with it is that it seems pretty clear that a Shard only has access to as much Investiture as their expanded mind directly encompasses, which presumably corresponds to a volume of space roughly as large as a solar system, since we’ve never seen a Shard directly influence anything beyond its own solar system. But even if you want to extend that several orders of magnitude, you still ultimately end up with having an infinite amount of Investiture either crammed into or at least connected to a space of finite volume. And Brandon has on more than one occasion compared investiture to energy and thermodynamics in terms of the rules governing its behaviour (minus the supernatural component of course). 

The problem with this, and the issue I have with the comparisons to Thermodynamics is that in the cosmere you cant "minus the supernatural component". The three realms idea, particularly the Spiritual, are inextricably linked with Investiture and its part of what makes creating a "unified theory of the cosmere" impossible with the information we have.

Infinite investiture isnt "crammed" anywhere, the bulk of a shards power is in the spiritual realm which is independent of location. So really what we have is infinite power being directed by a mind that can only focus on 1 solar system (that we have seen so far). Which is more reasonable.

12 minutes ago, HSuperLee said:

The way I'm interpreting the WoB about Shards and infinite power is not that Shards have access to an infinite energy shource, but more that any investiture they expend eventually returns to them and can be reused.

Thats definitely one way to interpret the WoB and may well turn out to be correct. We use infinity to mean a lot if things nowadays so we may be overthinking this with respect to the technical definition.

[Calderis he/him]

The issue of infinite power only really matters when we start discussing the Shards beyond the Vessels sphere of influence, and most of this only came to light due to recent revelations about Autonomy's Avatars. 

The cyclical explanation makes sense when referring to power expenditure, and is certainly true with the information we've been given. We've been told directly with Allomancy that expended power returns to Preservation and that atium returned to be reformed in the pits. 

Where it gets murky is when we start discussing what Jace just mentioned. 

14 minutes ago, Jace21 said:

So really what we have is infinite power being directed by a mind that can only focus on 1 solar system (that we have seen so far). Which is more reasonable.

And this what I believe is the case, due to WoBs like this one. 

Quote

Overlord Jebus [PENDING REVIEW]

Is all Investiture in the cosmere associated with a Shard?

Brandon Sanderson [PENDING REVIEW]

Yes, well, okay. So this is a complicated one. *pauses* So, Investiture predates the Shattering of Adonalsium, all Investiture was from Adonalsium, all Investiture got assigned to one of the 16 Shards when Adonalsium was Shattered. Some of the Investiture was not on Yolen but location is irrelevant. So Investiture is related to Shards even on planets where none of the Shards are inhabiting. 

Overlord Jebus [PENDING REVIEW]

Are they aware of that Investiture?

Brandon Sanderson [PENDING REVIEW]

That's part of the whole seeing into the infinite, being beyond even the power of a Shard. So, technically you could make the argument that Harmony could feel the sense of Preservation on every world in the cosmere, right? Because the building blocks of all life and creation are these things.

Overlord Jebus [PENDING REVIEW]

So the Shard of Preservation embodies all preservation in the cosmere?

Brandon Sanderson [PENDING REVIEW]

Yes but he just can't do that, right? Like, he's not infinite. The Vessels are not, even if their minds are enormously expanded by holding a Shard, they are not infinite. The Connection is all there in the Spiritual Realm

source

 

[Fanghur Rahl he/him]

Yeah, I much prefer that interpretation, personally, just because it leads to far fewer potential plot holes. In the whole of forever, there has to my knowledge never been a single concept of a truly omnipotent deity that actually cares about and interacts with the universe that doesn’t inevitably self-destruct under even trivial logical scrutiny (even Sazed says essentially this in Hero of Ages). 

BTW, Brandon was the one who has on several occasions likened Investiture to thermodynamic laws, I’m just going on his own words here. I see Investiture as essentially being ‘spiritual energy’.

[Jace21 he/him]

On 9/14/2018 at 9:50 AM, Fanghur Rahl said:

Yeah, I much prefer that interpretation, personally, just because it leads to far fewer potential plot holes. In the whole of forever, there has to my knowledge never been a single concept of a truly omnipotent deity that actually cares about and interacts with the universe that doesn’t inevitably self-destruct under even trivial logical scrutiny (even Sazed says essentially this in Hero of Ages).

Those types of deities could certainly exist, the logic required to back it up just requires faith to work, also acknowledged in HoA. But Brandon has also stated on several occassions that Shards are not that kind of deity.

I see it this way, Shards have sufficient power to do anything under normal circumstances, with two main exceptions:

1. They have to be able to consciously perceive/direct it. As many have pointed out in this thread, Shards minds are expanded, but not infinite, limiting their capacity to wield the power.

2. If directly opposed by another Shard (or any sufficiently large amount of investiture) their actions can be limited, as we see in Mistborn. The success/failure of the intended action is then reliant on raw power.

Whether the amount of power refers to available amount of limited (but huge) power (cyclical theory) or the "size of different infinities" idea actually doesnt really change the end result either way. 

On 9/14/2018 at 9:50 AM, Fanghur Rahl said:

BTW, Brandon was the one who has on several occasions likened Investiture to thermodynamic laws, I’m just going on his own words here. I see Investiture as essentially being ‘spiritual energy’.

Oh I know, and I think it is the best real life analogue. It just makes it sound like you can easily plug investiture into the existing rules/laws of Thermodynamics and sadly that is not that case.

Edited September 15, 2018 by Jace21

[Ripheus23]

Well if a physical person can take up a Shard in the first place, who knows?

[+Mistbreaker]

Personally, I think the one with the highest odds of accomplishing this would have actually been the Lord Ruler if he had killed Vin in Final Empire. My logic goes as follow:

After getting rid of Vin and the rebellion, it wouldn't be long before his next opportunity to pick up the power at the Well of Ascension. Also, we know from a WoB (can't remember which) that the first time Rashek held the power he was able to reach out into the Cosmere far enough to figure out his people weren't alone in the universe but due to all the things he need to course-correct in Scadrial he didn't have the time to look very far. But if he could have endured the thousand year wait to become a sliver again, I suspect he would have tried a lot harder to learn more of the other Shardworlds, world hopping and most likely a way to finish off Ruin once and for all. 

So, let's say that in this alternate timeline where TLR lived to hold the power another day, he learned through his temporary near omniscience that it would be too difficult for him under his circumstances to take over another Shard. He would then try to look for a way to kill Ruin with more conventional means and that's when he learns of Nightblood in Nalthis. With his rapidly expanding mind he plots his new plan and discovers what he needs to do to get to Nalthis and back and how to better connect the magic systems of Biochroma and Allomancy through Duralumin Feruchemy, as it has been confirmed that can also change one's Spiritual connection to a planet, which can help worldhoppers with magic systems.

Once he gets there, he overpowers Vasher and takes the blade that can cut through all three realms. Then, he would need to find a way to coerce Susebron into giving him his massive amount of breaths. Once the mighty Lord Ruler gets a massive power boost as he gets to the 10th heightening he returns to the place of the Well of Ascension with Nightblood in tow.

Now, this is the key part to make any of this scenario even remotely plausible. We know Ruin is trapped in the well. Not weak of course but his powers are contained, maybe even to the point he would be unable to directly fight back against Rashek although I am not so sure about that point. Regardless, now that the Lord Ruler has both Nightblood and treasure trove of breaths, right before striking at the restrained Ruin with Nightblood, he could compound on his Duralumin, which would ensure Nightblood would eat through all 50,000+ breaths at once in a single, shattering blow against Ruin.

Now, would this actually work? I am not entirely sure, but it is the most plausible scenario I can think of. What do you guys think?

Edited September 25, 2018 by Mistbreaker
spelling mistakes

[Quantus he/him]

On 9/10/2018 at 4:54 PM, Fanghur Rahl said:

Are they? Or is that just what your intuition would tell you? Because as I had this exact thing explained to me once, technically it isn’t twice as large, regardless of what common sense would suggest, because it’s simply undefined. 

Again, I’m just going on what I’ve been told, for all I know I’m completely wrong about this whole thing. I’m certainly not dogmatic about it or anything.

I (accidentally) took this class in college (ie "Philosophy of Mathematics", focused on Set Theory).  It's not technically "Twice as Big" but it's also not "undefined" so much as it is of a higher order of Aleph (which is a set of numbers that they invented just to be able to compare different sets of Infinity). For what it's worth, I found it easier to think of it in terms of Venn Diagrams, you can be sure one is larger than the other if one can be proven* to contain another.

* "Proven" comes down to a oddball mathematical principle of "Countability", so there is an element of Proof vs just Intuition, but I cant promise it actually makes it any easier to understand.  They could prove fairly easily that, for example, all Whole number are larger than all Integers, because you can line them up from the start and see both progress toward infinity together.  By contrast they couldnt prove Fractions for a long time because you couldnt count the set and ever get all the way from "1" to "2". To prove it they had to plot all fractions on a matrix, with one axis on the numerator and another on the denominator, and count in the diagonals...

 

In the case of Shards, they are lesser subsets of the more complete Infinite that was Adonalsium.

Edited September 25, 2018 by Quantus

[Fanghur Rahl he/him]

43 minutes ago, Quantus said:

I (accidentally) took this class in college (ie "Philosophy of Mathematics", focused on Set Theory).  It's not technically "Twice as Big" but it's also not "undefined" so much as it is of a higher order of Aleph (which is a set of numbers that they invented just to be able to compare different sets of Infinity). For what it's worth, I found it easier to think of it in terms of Venn Diagrams, you can be sure one is larger than the other if one can be proven* to contain another.

* "Proven" comes down to a oddball mathematical principle of "Countability", so there is an element of Proof vs just Intuition, but I cant promise it actually makes it any easier to understand.  They could prove fairly easily that, for example, all Whole number are larger than all Integers, because you can line them up from the start and see both progress toward infinity together.  By contrast they couldnt prove Fractions for a long time because you couldnt count the set and ever get all the way from "1" to "2". To prove it they had to plot all fractions on a matrix, with one axis on the numerator and another on the denominator, and count in the diagonals...

 

In the case of Shards, they are lesser subsets of the more complete Infinite that was Adonalsium.

Fair enough. Like I said, my university education was biotechnology and microbiology not advanced calculus, so I’ll take your word for it, though I still question how much realworld (or even fictional world) applicability the concept actually has though. 

[Juanaton he/him]

So I'm a bit late seeing this one...which is sad for me since I'm actually a math professor so I could MAYBE have explained about the sizes of infinities earlier. But better late than never.

The different sizes of infinity ARE really different. However, the size differences DON'T happen where our "common sense" says they should.

The cardinality of the natural numbers (1,2,3,...) and the integers (...,-3,-2,-1,0,1,2,3,...) are the same. There are no more integers than there are natural numbers, even though one way of "counting" them would seem to indicate there are twice as many. To see this, you have to order the integers differently than they are on the number line. If you write down all the integers using the pattern 0,1,-1,2,-2,3,-3,... you can see that you can assign a natural number to every integer and never run out...so those infinities are the same size. In other words, 2*infinity is NOT greater than infinity. In fact, there is even a way to assign a natural number to every possible fraction of integers, so even if you add in every rational number, the infinity hasn't grown at all. These levels of infinity are all the "smallest" type of infinity, and are called "countably infinite."

A truly larger infinity is the cardinality of the real numbers between 0 and 1. No matter what numbering scheme you come up with, there are ALWAYS infinitely many values between 0 and 1 that your numbering system misses. So there are truly more numbers in there than there are counting numbers. Both are infinite, but one is infinitely larger than the other.

That said, I don't think the differences in cardinality are how we should think about the different comparative power levels of the Shards. Rather, we should be viewing the power levels of the shards like polynomial functions and their comparative power levels as rational functions. If each of the 16 original shards were similarly powerful, we can consider that power to be x for all of them. So their power is limitless, or it's limit is infinity. However, if we then compare the power of one Shard to another, we get the ratio x/x, which is just 1. But if one person (Sazed) picks up TWO Shards, their powers add together since x+x=2x. Now comparing the power of Harmony to another Shard gives the ration 2x/x, which is 2. So Harmony is twice as powerful as a standard Shard, even though both shards (or all three, depending on how you count Harmony), are infinitely powerful.

Edit: and now I look back more carefully and see Quantus did address the cardinality stuff a little bit. Even describing how we were able to establish the countability of the rational numbers. Anyway, I still like my functional analysis of shard powers better than cardinality so there's still that.

Edited September 26, 2018 by Juanaton

[HSuperLee]

I'm personally not prepared to converse on that level of math, but it seems to me you would still hit some trouble when it comes to Leras trapping part of Ruins power so that they were equal. Certainly unless you're subtracting infinite power from an infinite source you can't actually remove enough to make a difference. Is that correct?

[Juanaton he/him]

2 minutes ago, HSuperLee said:

I'm personally not prepared to converse on that level of math, but it seems to me you would still hit some trouble when it comes to Leras trapping part of Ruins power so that they were equal. Certainly unless you're subtracting infinite power from an infinite source you can't actually remove enough to make a difference. Is that correct?

For the rational functions view, if we use x for Ruin's power and x-1 for Preservation's power (post creation of Scadrian humans), the limiting value of the ratio is still 1. However, 1000/999 is a bit more than 1, and 10000000/9999999 is too. So there is still a VERY slight power imbalance that could result in the future victory of Ruin without Leras' plans for dealing with the imbalance.

[Calderis he/him]

@HSuperLee the infinite nature of the Shards is irrelevant in this case, because the Vessels themselves aren't infinite. They are only able to wield the power that they are aware of, which is also why they are limited in scope to the solar system in which they've invested.

So what Leras broke away from Ruin was a significant portion of the power that Ati was capable of wielding in his limited capacity. It should not, in contrast, have been a significant portion of Ruin's investiture as a whole. 

It's confusing, and at least in terms of Shards with a Vessel makes "infinite power" misleading. It does, on the other hand, Make situation like Harmony far more immediately obvious discrepancies. He has access to two pools of investiture within the same sphere of influence, doubling the investiture that is usable to him. 

It's to bad that his opposing intents render him incapable of actually wielding it. 

[HSuperLee]

4 minutes ago, Calderis said:

@HSuperLee the infinite nature of the Shards is irrelevant in this case, because the Vessels themselves aren't infinite. They are only able to wield the power that they are aware of, which is also why they are limited in scope to the solar system in which they've invested.

So what Leras broke away from Ruin was a significant portion of the power that Ati was capable of wielding in his limited capacity. It should not, in contrast, have been a significant portion of Ruin's investiture as a whole. 

It's confusing, and at least in terms of Shards with a Vessel makes "infinite power" misleading. It does, on the other hand, Make situation like Harmony far more immediately obvious discrepancies. He has access to two pools of investiture within the same sphere of influence, doubling the investiture that is usable to him. 

It's to bad that his opposing intents render him incapable of actually wielding it. 

I've seen this theory in other places across the Shard, but it seems a little weird to me. If a Shard's awareness is limited to the solar systems they've invested themselves in (I'm also not sure of the potentially magical connotations of that word right now,) how would Rashek have become aware that there was other life in the Cosmere when he interfaced with a portion of Preservation? I guess maybe he could have been gaining information from Leras's cognitive shadow, but if that's the case, I'd have expected he wouldn't have messed the world up as much as he did.