Calderis he/him Posted September 26, 2018 Posted September 26, 2018 5 minutes ago, HSuperLee said: I've seen this theory in other places across the Shard, but it seems a little weird to me. This part isn't theory, this is stuff straight from Brandon. Spoilered for length. Spoiler Quote Questioner How far does Sazed's power actually extend? Brandon Sanderson It is mostly limited to his immediate sphere of influence, so the planet. Questioner But doesn't he move stars at the end? Brandon Sanderson No, he moved the planet. His solar system, he can definitely have influence on the solar system. But none of the other planets around Scadrial are inhabited. source 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 As far as how Rashek was able to look outward... We don't know enough about the Shards honestly to answer that. It's possible, and Rashek got hints. Quote Phantine How cosmere-aware was the Lord Ruler? If a Returned waltzed into Kredik Shaw, would he have any idea what was going on? Or at least be able to recognize, "Hey that guy seems Endowmenty." Brandon Sanderson Aware enough to know he wasn't alone, but not so aware that he'd know specifics. He didn't hold the power long enough to explore outward very far. source But we know that other shards are aware of Harmony, even Odium despite being trapped, and that things (presumably Trell) are blocking Harmony's ability to do this. What those methods are though, and how they work? I can't even attempt to answer.
HSuperLee Posted September 26, 2018 Posted September 26, 2018 Huh. Well alright then. I guess as weird as it is, if that's what Sanderson says, that's how it is. I'm going to do the old reliable thing and blame it on Connection.
Fanghur Rahl he/him Posted September 26, 2018 Author Posted September 26, 2018 (edited) 7 hours ago, Juanaton said: 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. So how does the concept of ‘measures’ fit into it? The way I heard it described by physicists Alan Guth, Max Tegmark, and Sean Carroll, many physicists now think that a multiverse exists, either in the sense of one spacetime that is spatially infinite or the sense of a potentially infinite ‘sea’ of discrete spacetimes (or both). But they said that the problem with it is that in either case predictions are difficult because in an infinite universe, anything physically possible, regardless of how unlikely it is, will occur an infinite number of times, and we don’t know how to meaningfully talk about one thing being any more ‘likely’ than another in this framework. And they said we currently lack the correct ‘measure’ to accurately make useful predictions based on it. Is this just something completely unrelated to ‘infinity’ in the context of this discussion? Or are you just using different terminology? Because that’s why I previously was under the impression that whether one infinity is ‘larger’ than another just depends on the parameters you choose to analyze it by. I’m guessing based on what you said that I’ve misunderstood their point? Edited September 26, 2018 by Fanghur Rahl
Solant he/him Posted October 1, 2018 Posted October 1, 2018 On 9/25/2018 at 11:38 PM, 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. This is the explanation I am most comfortable with, due to the Shard of Solant's Vessels limited capacity for math. Here's my analogy. Ruin, Preservation, and Harmony all have infinite amounts of money in the bank. Ruin can withdraw $500 at a time from his bank, while Preservation can only withdraw $450. Harmony has accounts in both banks, and therefore can withdraw both $500 and $450. Who has the most money? I'm being facetious, of course, but this is what makes the most sense to me. 2
Fanghur Rahl he/him Posted October 1, 2018 Author Posted October 1, 2018 (edited) 4 hours ago, Solant said: This is the explanation I am most comfortable with, due to the Shard of Solant's Vessels limited capacity for math. Here's my analogy. Ruin, Preservation, and Harmony all have infinite amounts of money in the bank. Ruin can withdraw $500 at a time from his bank, while Preservation can only withdraw $450. Harmony has accounts in both banks, and therefore can withdraw both $500 and $450. Who has the most money? I'm being facetious, of course, but this is what makes the most sense to me. That’s actually a pretty good way of thinking about it. Have you been reading Brian Greene? Edited October 1, 2018 by Fanghur Rahl
Helwar he/him Posted October 5, 2018 Posted October 5, 2018 On 10/1/2018 at 6:01 AM, Solant said: This is the explanation I am most comfortable with, due to the Shard of Solant's Vessels limited capacity for math. Here's my analogy. Ruin, Preservation, and Harmony all have infinite amounts of money in the bank. Ruin can withdraw $500 at a time from his bank, while Preservation can only withdraw $450. Harmony has accounts in both banks, and therefore can withdraw both $500 and $450. Who has the most money? I'm being facetious, of course, but this is what makes the most sense to me. This is similar to how I explained to some friends some time ago. All shards have an infinite tank of water. Water never, ever runs out. But some have a garden hose, and Sazed has a firefighter water cannon. Or more precisely, two water hoses but they are entangled together and they are quite hard to aim. As per the difference in power between Preservation and Ruin, when both have an infinite of a similar magnitude, the small differences are what count. If Preservation invested more (his hose was a liiiiiiiiiiiiiiiiiiiiiittle smaller), he would have eventually lost against Ruin. Using the Atium sent the investiture back to the system, and way from the planet, so temporally, Ruin lost some measure of grip on the planet. Just a tiny bit, but enough.
Juanaton he/him Posted October 5, 2018 Posted October 5, 2018 On 9/26/2018 at 6:05 AM, Fanghur Rahl said: So how does the concept of ‘measures’ fit into it? The way I heard it described by physicists Alan Guth, Max Tegmark, and Sean Carroll, many physicists now think that a multiverse exists, either in the sense of one spacetime that is spatially infinite or the sense of a potentially infinite ‘sea’ of discrete spacetimes (or both). But they said that the problem with it is that in either case predictions are difficult because in an infinite universe, anything physically possible, regardless of how unlikely it is, will occur an infinite number of times, and we don’t know how to meaningfully talk about one thing being any more ‘likely’ than another in this framework. And they said we currently lack the correct ‘measure’ to accurately make useful predictions based on it. Is this just something completely unrelated to ‘infinity’ in the context of this discussion? Or are you just using different terminology? Because that’s why I previously was under the impression that whether one infinity is ‘larger’ than another just depends on the parameters you choose to analyze it by. I’m guessing based on what you said that I’ve misunderstood their point? I'm a math professor so i just have to point out that physicists are weird. But also, that's a completely different discussion than what we are having. They are talking about making predictions of likelihood (probabilities) in infinite systems, while we are/were talking about the way infinities can have different sizes.
Ripheus23 Posted October 12, 2018 Posted October 12, 2018 I think "Investiture" is both a substance and an attribute. As an attribute, all Shards have it to the same infinite degree. As a substance, each Shard originally had 1/16th of the finite amount of it in the Cosmere. Imagine a space of possible temperatures. Let's say each original Shard could increase the Investiture-temperature in 1/16th the locations in the Cosmere. But wherever they can increase the temperature, they can keep pushing it towards being infinite-degrees Kelsier [Kelvin]
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