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I’d argue Shards have functionally infinite investiture, but not in actuality.
How? Investiture changes form between matter and energy and vice versa. Thus, a Shard can call upon their Investiture in an eternal cycle (though there are limits to this).
The Vessels are also limited in output. That’s largely why, imo, Rayse was able to be killed by Nightblood. Nightblood exceeded the output and the Vessel was divorced from the Shard
Autonomy’s Avatars are able to use the latent power around the cosmere Bavadin is unable to because her mind cannot focus everywhere as no Vessel is truly omnipresent.
I would argue something similar but slightly different:
- The investiture (power) of a Shard is infinite BUT
- The application of the power by means of the Vessel is finite because even though they have access to infinite power they must still decide how to apply it and decisions take a finite amount of time
Cultivation was able to kill Rayse with Nightblood because she was able to hide Nightblood close to where Rayse’s foresight was limited by Renarin. The chess match Shards are playing against each other requires their time and focus in order to pull off their Shardic feats. Rayse’s plans were going wrong all around him and he was scrambling to put pieces back in place, not realizing that by visiting Taravangian, he was exposing himself to a hidden threat.
This is always how I understood it.
To our best understanding Adonalsium was truly infinite. Dividing infinity by anything is still infinity.
However, the vessels that have taken up these shards are practically infinitesimal by comparison so massively limit the rate at which the power can be used until they're all basically equally limited. They'll never run out of investiture even using it to create matter which isn't destroyed and doesn't flow back into them.
As for splinters and slivers and other invested beings, I think there are two ways to think about them. The first is as you described, infinite energy with an ever smaller power output. Or like a balloon that's been filled with a limited supply of investiture from the shard. Things like Spren I personally believe are a mix. They're each a balloon of investiture directly Connected to Honor's investiture, however, that connection isn't always outputting investiture. In fact it rarely is (except for when a high storm passes over in the cognitive realm) instead if they use/lose a lot of investiture quickly they need to gain investiture from a different source to be able to recover.
Interesting idea. I have nothing to back this up, but I always that that "infinite" was relative. It's not ACTUALLY infinite, but compared to any usage understandable or usable by man it's basically infinite. Sorta like how the universe is infinitely large.
Edit: A second thought. Can anything truely be infinite that has a measurable substance? I think investiture exists in the third realm (not cognitive) right? So that would be that realm is infinite to the 16th power large. We know investiture has to take up some sort of space because of it's limitation on how much can fit into stones. I suppose that's another assumption though.
Edit: A third thought. You got me rolling lol it can't be infinite because of Ruin v Preservation in Mistborn. Preservation gives up his investiture to make Humans and that makes him permanently weaker than Ruin. If they were both true infinite that couldn't happen.
There are different sizes of infinite.
Edit: The sentence above is correct. The sentence below is incorrect. I confidently misremembered information that I had not used in years. See further down the comment chain for more information. I am sorry for spreading misinformation.
Infinity is larger than the same infinity minus 1.
The way I see it, the power itself can be infinite, it's more a question of how much can a being draw at one time. It's like having a straw vs having an industrial pipeline, both pull from the same infinity source but one can pull a *lot* more at any given time. It also explains the ruin-preservation power difference, if preservation was diverting even 1% of their portion of power to humanity then it would give Ruin that tiny advantage, which over time would add up significantly.
Mathematically, it’s actually not, which is important… to mathematicians.
From a function storytelling perspective, it certainly is. Infinity being greater than infinity - 1 is basically the entire Shard level plot of Mistborn.
Edit: I am just wrong here. My explanation here seems intuitive, but this intuition simply does not apply to infinities, which are even weirder than I remembered. I had learned the proper way to conceptualize infinities years ago from videos with real mathematicians, but years of not using that information led to me confidently misremembering the information. I am sorry.
If you have a set of all numbers, that set is infinite.
If you have a set of all numbers except the number 32, that set is infinite.
The first set is the sum of the second set plus the number 32. Thus, empirically, the first set is larger than the second. This isn't a mathematical equation because you can't do simple equations with infinity, but we can make empirical statements about the sizes of different infinities.
This whole argument rests on the presumption that infinity is in fact countable at all. A set requires that you can define its contents.
It’s not just big, it doesn’t end. You actually can’t have a set of all numbers, because it’s infinite.
It doesn’t really matter in the context of this discussion because the Shards can be infinite while their Vessels are a finite manifestation of them in the Cosmere.
Edit: I am just plain wrong. I confidently misremembered something that I had learned years ago. See the comments below for accurate information! I am sorry for spreading misinformation.
It doesn't. I'm not counting. I defined the set as all numbers. That is a valid set.
So far as I am aware, it is entirely valid to do set theory with infinity, and I have watched videos of professional mathematicians explaining exactly this concept.
Take the set of all positive integers. Now, take the set of all positive integers that are odd. You now have an infinite set of even numbers. The first set contains the entirety of the second set by definition along with other numbers. Thus, the first set is larger.
No counting is required here. It is empirically evident.
It isn’t, and the person above you is correct. Infinity is not a number, so trying to treat it like one doesn’t always make sense. There are different sizes of infinite sets, but the two you describe are equivalent.
To be specific, any subset of a countable infinite is by definition a countable infinite and is therefore equivalent. To find a larger infinite, you need a higher cardinality and an uncountable set.
This can get you started, but this is actually pretty complicated. If you have not studied set theory it’s probably not going to make sense.
https://en.m.wikipedia.org/wiki/Countable_set#:~:text=Georg%20Cantor%20showed%20that%20not,is%20said%20to%20be%20uncountable.
Your “odds and even” example is even specifically addressed…
“This view works well for countably infinite sets and was the prevailing assumption before Georg Cantor's work. For example, there are infinitely many odd integers, infinitely many even integers, and also infinitely many integers overall. We can consider all these sets to have the same "size" because we can arrange things such that, for every integer, there is a distinct even integer”
You have to get into truly uncountable infinities before infinite cardinality matters.
I can… but not very well in a Reddit post. If you really want to know you are best going down the wiki rabbit hole. I know that “formal” part of the wiki I linked looks scary, but it really does explain it pretty well.
This is the critical part to understand
- A to be shown as countable is one-to-one mapped (injection) to another set B then A is proved as countable if B is one-to-one mapped to the set of natural numbers. For example, the set of positive rational numbers can easily be one-to-one mapped to the set of natural number pairs (2-tuples) because
p/q
Since the set of natural number pairs is one-to-one mapped (actually one-to-one correspondence or bijection) to the set of natural numbers as shown above, the positive rational number set is proved as countable.
-
Basically, if I can write a function that returns the value of one set from the value of another, in ANY WAY, those two sets are equivalently infinite. Because all positive integers can be mapped to all integers using p/2=q these two sets are equivalent.
You have to find a set that can’t be mapped. The classic example is real numbers. There exists no continuous function to map all integers to all real numbers. The set of real numbers is said to be uncountable infinite.
This doesn’t get into cardinality - which is its own thing.
The cardinality of a set is n (A) = x, where x is the number of elements of a set A. The cardinality of an infinite set is n (A) = ∞ as the number of elements is unlimited in it.
This article gets into it well -
https://www.cantorsparadise.com/why-some-infinities-are-larger-than-others-fc26863b872f?gi=a288af6baf64#:~:text=Even%20though%20there%20are%20an,are%20not%20equal%20in%20size.
—-
Edit to add add-
The other piece here is you are still thinking of infinity as a number. Saying “one contains the other” is meaningful when talking about finite sets, much less so when talking about infinite sets. You can divide infinite by two- it’s still infinite (this is essentially what you are doing to map evens to integers). You can add infinity to itself, it’s still the same size - infinite.
It’s NOT a number. You can’t treat it like one, and once you do, you can prove some really stupid things, so don’t.
Thank you very much! That was a perfect refresher.
I honestly think what happened is that I watched videos about this topic years ago, assimilated the information and then didn't use it for years. Then, unfortunately, confidently misremembered the correct conclusion. Classic human foible, and I am sorry for having fallen into this trap.
I will go edit my incorrect comments and apologize to the others that I was speaking with! Have a nice day!
I am sorry for spreading misinformation! I fell victim to a faulty memory. I learned about how to conceptualize infinities years ago, but then let that knowledge languish until it atrophied and I confidently misremembered the information that I used to have. I have re-learned the correct interpretation thanks to a helpful redditor below. My apologies.
I see your point, but in this context I disagree. Infinity minus 1 does not equal infinite anymore. In this case investiture is energy (or fuel) in it's most basic sense. That's atleast how I personally view it. If you have an infinite amount of gas and use some, is it still infinite? Seems more philosophy than science. But even so, I feel like you reaffirm my point in that infinite is relative because you are comparing two amounts. Is infinite still infinitely larger than infinite minus 1? What about the two compared to zero? I just feels like it falls apart when you apply a specific usable substance against the logic.
Infinity - 1 is still infinity. Things get weird and unintuitive when you’re dealing with infinities.
Think about an infinite string of houses. You bulldoze the first. There are still infinite houses left, even though you’ve subtracted one.
But then at what point is it no longer infinite? Because Preservation has access to less investiture than Ruin. I agree with your logic, I just don't believe is applies to investiture in the cosmere.
Infinity minus 1 is still infinity. That is an axiom of math, not something open for debate. And some infinities are larger than others. But they're all still infinite.
https://en.m.wikipedia.org/wiki/Aleph_number
Your claim that infinite minus 1 is not infinite anymore is exactly opposite to how infinity works.
You are thinking of infinity as a number. It isn't. Two minus one is no longer two. Infinity minus one is still infinity.
Think about a bunch of grapes. You eat one. You are still left with a bunch of grapes because "a bunch of grapes" is not a number. It is a concept. We can mathematically alter concepts, but we can't do simple calculations with them.
Infinity is the concept of never-ending. Basically, math gets weird when dealing with infinity because infinity is not a number.
Edit: The information above is correct, but the information in brackets below is not. I unfortunately misremembered information that I learned years ago. I have since re-learned how to properly conceptualize infinites thanks to a helpful member of this community. I am sorry for spreading misinformation.
[We can make statements that are objectively accurate according to the laws of logic, like infinity divided by 2 is objectively smaller than the same infinity before you divided it, but still infinite.]
[Think about every number that exists. This is an infinite amount of numbers. Now, delete all of the odd numbers. You still have an infinite amount of even numbers, but this is objectively lacking numbers that the previous infinity contained and therefore it is a smaller infinity.]
You're both right and wrong. I am NOT thinking of infinite as a number, that's what I'm explaining poorly. I'm saying I believe Sanderson's use of the word infinite is NOT the mathematical meaning. Instead I believe he is approaching it like when people refer to the universe as infinite in size. More of a relative comparison. I could be wrong. But I personally believe that the quantitative amount of investiture the shards hold will become relevant in phase 2 which is the point I was disagreeing with OP. Still might not be explaining well though :/
I understand that people use "infinite" colloquially to just mean "more than I can imagine." However, Brandon has based his entire system as much as he can on actual scientific principles. He has gone out of his way to try to break or bend as few of the laws of thermodynamics as possible. He bent over backward to portray a somewhat scientifically reasonable version of magically altering time. I see no reason to assume that Brandon is using "infinite" colloquially instead of accurately.
That said, about the universe being infinite:
So far as we understand, the question of whether the universe is infinite is currently unsolved. The observable universe is definitely finite. However, our measurements and calculations show that spacetime is expanding from every point simultaneously, and that seems an awful lot like infinite expansion. You would never be able to find an end or an edge of spacetime because the expansion isn't relative to any single location. Even moving faster than light would not outpace the expansion due to the fact that you, yourself, are a collection of points from which spacetime evenly expands. So no matter how far or how fast you go, there is always more spacetime.
There are arguments against that logic, and there is the possibility that something could interrupt or halt the expansion somehow. Spacetime might somehow hit a limiter that we don't yet know. So we don't know if the universe is actually infinite or not.
Adonalsium, and subsequently his shards, did not originate investiture.
Since investiture predates shards, then ... shards do not contain infinite investiture. Arguably they could even contain no investiture, apparently not unlike allomancers.
But just like an allomancer can nonetheless *use* investiture, a shard's "great power" is to use investiture on such a scale as no other thing in the Cosmere, short of rolling back to Adonalsium's time.
The investiture itself is infinite, and is also everywhere. It's seemingly a fifth force: gravity, electromagnetism, weak and strong nuclear, and investiture. There's likely a GUT in the Cosmere's scientific future - a grand unified theory.
The splintering of a shard will also leave each piece less potent, and whatever piece is nonintelligent is even less capable of using investiture, instead running on automatic, obeying leftover Intent or whatever the original shard (and the person merged with it) had.
Hum, like Jupiter warps space-time more than an asteroid, and therefore has more gravitational pull. Honor warps the "investiure field" more than the Stormfather does, and therefore has more power.
Good example!
Arguably, intelligent splinters, like Stormfather, have little power because they can't initiate its use beyond the rote implementations they represent. For example, Stormfather could likely destroy mountains, kill armies, but his job is creating, maintaining, and moving an invested hurricane around. It complains and struggles when pushed to do otherwise, and only goes above and beyond when Bonded and Commanded (I hope I got the terms right).
Good example!
Arguably, intelligent splinters, like Stormfather, have little power because they can't initiate its use beyond the rote implementations they represent. For example, Stormfather could likely destroy mountains, kill armies, but his job is creating, maintaining, and moving an invested hurricane around. It complains and struggles, and only goes above and beyond when Bonded and Commanded (I hope I got the terms right).
so, kinda no
we don’t know what adonalium or the shards are exactly, but we do know that every single piece of investiture in the cosmere is keyed to and comprises a shard of adonalsium, and that all investiture in the cosmere prior to the shattering was part of big a. the only potential non-adonalsium investiture in the cosmere is the aethers, but it’s in-universe unconfirmed and contested if they’re actually separate or not. it’s also been said directly by brandon that shards contain infinite (either functionally or literally) investiture
and investiture isn’t a fifth force, brandon has said it’s a 3rd type of…thing? idk, basically in the cosmere e=mc^2 would have to be adapted to include investiture, as investiture is a third form for stuff to be, like matter and energy
I think it's infinite like it's a faucet that never runs out, but it can only channel so much at once. It's a really big faucet, but it's still got limits, but the source will never empty.
The way I see it, they are all tapping the same unlimited source, it's just a question of what volume they can move at any given time. Things like spren would be like someone sticking a straw into a river and sucking out as much water as they can, while a shard would be like a major pipeline, diverting thousands of gallons.
Where it is said Shards have infinite Investiture? Because it contradicts some things we know about Investiture.
For example it was said that amout of Investiture in cosmere is fixed and cannot be destroyes or created. It can only change either to difffetent forms of investitire or matter/energy and back. That would not make sense if there is infinite supply of Investiture.
IMHO idea that Shards have infinite Investiture is wrong.
What limits Shard power is how much Investiture they can effectively control at a time. They are limited by Vessel ability to control powers they got by holding Shard power. They have more Investiture than they can control and given that Investiture cannot be destroyed they can "recycle it" somehow and use again. That gives them technically Infinite supply of Investiture but total amount of their Investiture is still fixed. And it would have similar result as your proposed limited throughtput.
I always had it in my head as the shards where like hoses hooked up to the ocean. Each shard has 1 hose all pulling from infinity water. Harmony has 2 hoses so can pull more out faster compared to other shards.
It's infinite in the sense that it can't really be destroyed. There's basically a large well of investiture somewhere in the spiritual realm, maybe. So yes, the Shards do expend it when they do stuff, but once that investiture is expended, it kinda flows back to that big well. So it is essentially infinite in that it can never be destroyed, just recycled.
So when a Shard invests a planet or person, that investiture stays with that person or planet instead of recycling back to their well of investiture which is why you have situations where Ruin is stronger than Preservation because Preservation is more invested in the humans of Scadrial and the planet as a whole
I think the output of investiture really is unlimited, but control of said investiture is finite. We saw this when Rin took control of Ruin and Harmony, she could do things that were incredibly powerful, but she had no idea how to control it so people wouldn’t die.
Surprised that noone has brought up dawnshards yet.
Shards do have infinite investiture but most of it is in the spiritual realm which is why there are no investiture black holes/crazy time dilation forming in the physical/cognitive realms.
Shards can only draw upon their infinite investiture at a finite rate which is limited by the vessel and their alignment with their Intent and the Intent of the action they are trying to inact.
This is why the dawnshards exist. They provide supercharged Intent which allowed Adonalsium (and shards of they ever got hold of a dawnshard) to channel and command shardic levels of investiture. Shards are still very very powerful but we have seen that they are still heavily nerfed by their Intent in most cases. Dawnshards would bypass this "Intent cap".
investiture is described as infinite in shards but as others have pointed out, i believe that its *functionally* infinite, not truly
haven’t read far enough to see if others have mentioned this part, but brandon has explained why shards can’t access all of the investiture that they contain: its because they’re mortal. a shard is a mortal mind expanded to be god-like. but that’s the key part, god-*like*. mortals are still mortal, and even if the being is something immortal or immortal adjacent, it’s still not a god. we don’t know for sure what adonalsium was, but my money is on the idea that adonalsium *was* the shards, not a being that held them or whatever. adonalsium was birthed from an incomprehensibly large mass of investiture coalescing and gaining sentience, and thus could fully understand and control all of its body and mind, whereas a shard holder is limited to using only the investiture they are consciously aware of
all 16 shards are spread throughout the entire cosmere. there’s ruin on roshar and odium on taldain and devotion on scadrial, but no shard could ever consciously control all of that investiture, their minds simply aren’t large enough to do so. adonalsium however, if i’m correct, would have been able to, since it *was* that investiture and was built to make use of it fully and properly
my guess is that adonalsium was born when, in the moments after the big bang, all investiture existed in a much smaller, more confined area, and in those conditions that investiture became sentient and awoke as what we know as big a
It's like a pipe connected to the ocean
Yeah, there's functionally an infinite amount, from a small to a pretty large scale, but you're limited by the output of the pipe, which would be things like the Vessel itself, the shard's intent, and the limited focus and willpower of the vessel to actually put out that much power.
Over long enough timescales, infinity can seem less large, but it's still infinite.
just like how the water cycle works, investiture is constantly switching between itself, matter, and energy.
and when you break apart a large pipe into smaller ones you get less output, especially if they're coming from the same place, since there's more physical pipe and less open space
Nearly right. Their power is cyclically infinite, in that it forms a closed system and never ordinarily is permanently removed from said cycle. Also, I think that with enough power you could make a False Shard, Ascend to the Spiritual Realm, and start your own cycle, and I think that's the purpose of Canticle and it's sun.
I once heard of a religion where priest with metal eyes said a sliver of infinity is still infinity. A really cool girl with an earring proved that false like a lie detector on Maury.
That makes sense. I'd say the "basically" infinite Investiture has to be funneled through a Vessel that, though dramatically expanded, still has limits on what it can use **at a given time**. Investiture that is expended eventually gets back to the Shard that sent it out via the Spiritual Realm.
We know that Preservation was weaker than Ruin because Leras had invested more of his essence in humans. The only thing that could be "weaker" would be the Investiture that was available to be funneled through the Vessel. So Leras had Invested humans with, say, 0.0000001% of the Investiture he could channel. Maybe Leras could channel a Googleplex of BEUs (Breath Equivalent Units). But it's not **INFINITE.** Because the expanded Vessel is still limited.
Remember, neither Leras nor Ati could create a world on their own. If their Investiture were truly infinite, they could each create worlds as they wished. Especially when they were new to their Shards and the Intent hadn't changed their souls yet.
The only thing that could be limited if the Investiture were basically infinite in both cases (Preservation and Ruin) would be the Vessel. Maybe the Investiture the Vessel could use is limited by their unconscious limits of perception.
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I’d argue Shards have functionally infinite investiture, but not in actuality. How? Investiture changes form between matter and energy and vice versa. Thus, a Shard can call upon their Investiture in an eternal cycle (though there are limits to this). The Vessels are also limited in output. That’s largely why, imo, Rayse was able to be killed by Nightblood. Nightblood exceeded the output and the Vessel was divorced from the Shard Autonomy’s Avatars are able to use the latent power around the cosmere Bavadin is unable to because her mind cannot focus everywhere as no Vessel is truly omnipresent.
I would argue something similar but slightly different: - The investiture (power) of a Shard is infinite BUT - The application of the power by means of the Vessel is finite because even though they have access to infinite power they must still decide how to apply it and decisions take a finite amount of time Cultivation was able to kill Rayse with Nightblood because she was able to hide Nightblood close to where Rayse’s foresight was limited by Renarin. The chess match Shards are playing against each other requires their time and focus in order to pull off their Shardic feats. Rayse’s plans were going wrong all around him and he was scrambling to put pieces back in place, not realizing that by visiting Taravangian, he was exposing himself to a hidden threat.
This is always how I understood it. To our best understanding Adonalsium was truly infinite. Dividing infinity by anything is still infinity. However, the vessels that have taken up these shards are practically infinitesimal by comparison so massively limit the rate at which the power can be used until they're all basically equally limited. They'll never run out of investiture even using it to create matter which isn't destroyed and doesn't flow back into them. As for splinters and slivers and other invested beings, I think there are two ways to think about them. The first is as you described, infinite energy with an ever smaller power output. Or like a balloon that's been filled with a limited supply of investiture from the shard. Things like Spren I personally believe are a mix. They're each a balloon of investiture directly Connected to Honor's investiture, however, that connection isn't always outputting investiture. In fact it rarely is (except for when a high storm passes over in the cognitive realm) instead if they use/lose a lot of investiture quickly they need to gain investiture from a different source to be able to recover.
Interesting idea. I have nothing to back this up, but I always that that "infinite" was relative. It's not ACTUALLY infinite, but compared to any usage understandable or usable by man it's basically infinite. Sorta like how the universe is infinitely large. Edit: A second thought. Can anything truely be infinite that has a measurable substance? I think investiture exists in the third realm (not cognitive) right? So that would be that realm is infinite to the 16th power large. We know investiture has to take up some sort of space because of it's limitation on how much can fit into stones. I suppose that's another assumption though. Edit: A third thought. You got me rolling lol it can't be infinite because of Ruin v Preservation in Mistborn. Preservation gives up his investiture to make Humans and that makes him permanently weaker than Ruin. If they were both true infinite that couldn't happen.
There are different sizes of infinite. Edit: The sentence above is correct. The sentence below is incorrect. I confidently misremembered information that I had not used in years. See further down the comment chain for more information. I am sorry for spreading misinformation. Infinity is larger than the same infinity minus 1.
The way I see it, the power itself can be infinite, it's more a question of how much can a being draw at one time. It's like having a straw vs having an industrial pipeline, both pull from the same infinity source but one can pull a *lot* more at any given time. It also explains the ruin-preservation power difference, if preservation was diverting even 1% of their portion of power to humanity then it would give Ruin that tiny advantage, which over time would add up significantly.
Mathematically, it’s actually not, which is important… to mathematicians. From a function storytelling perspective, it certainly is. Infinity being greater than infinity - 1 is basically the entire Shard level plot of Mistborn.
Edit: I am just wrong here. My explanation here seems intuitive, but this intuition simply does not apply to infinities, which are even weirder than I remembered. I had learned the proper way to conceptualize infinities years ago from videos with real mathematicians, but years of not using that information led to me confidently misremembering the information. I am sorry. If you have a set of all numbers, that set is infinite. If you have a set of all numbers except the number 32, that set is infinite. The first set is the sum of the second set plus the number 32. Thus, empirically, the first set is larger than the second. This isn't a mathematical equation because you can't do simple equations with infinity, but we can make empirical statements about the sizes of different infinities.
This whole argument rests on the presumption that infinity is in fact countable at all. A set requires that you can define its contents. It’s not just big, it doesn’t end. You actually can’t have a set of all numbers, because it’s infinite. It doesn’t really matter in the context of this discussion because the Shards can be infinite while their Vessels are a finite manifestation of them in the Cosmere.
Edit: I am just plain wrong. I confidently misremembered something that I had learned years ago. See the comments below for accurate information! I am sorry for spreading misinformation. It doesn't. I'm not counting. I defined the set as all numbers. That is a valid set. So far as I am aware, it is entirely valid to do set theory with infinity, and I have watched videos of professional mathematicians explaining exactly this concept. Take the set of all positive integers. Now, take the set of all positive integers that are odd. You now have an infinite set of even numbers. The first set contains the entirety of the second set by definition along with other numbers. Thus, the first set is larger. No counting is required here. It is empirically evident.
It isn’t, and the person above you is correct. Infinity is not a number, so trying to treat it like one doesn’t always make sense. There are different sizes of infinite sets, but the two you describe are equivalent. To be specific, any subset of a countable infinite is by definition a countable infinite and is therefore equivalent. To find a larger infinite, you need a higher cardinality and an uncountable set. This can get you started, but this is actually pretty complicated. If you have not studied set theory it’s probably not going to make sense. https://en.m.wikipedia.org/wiki/Countable_set#:~:text=Georg%20Cantor%20showed%20that%20not,is%20said%20to%20be%20uncountable. Your “odds and even” example is even specifically addressed… “This view works well for countably infinite sets and was the prevailing assumption before Georg Cantor's work. For example, there are infinitely many odd integers, infinitely many even integers, and also infinitely many integers overall. We can consider all these sets to have the same "size" because we can arrange things such that, for every integer, there is a distinct even integer” You have to get into truly uncountable infinities before infinite cardinality matters.
Can you elaborate? Both are infinite, but one contains the other.
I can… but not very well in a Reddit post. If you really want to know you are best going down the wiki rabbit hole. I know that “formal” part of the wiki I linked looks scary, but it really does explain it pretty well. This is the critical part to understand - A to be shown as countable is one-to-one mapped (injection) to another set B then A is proved as countable if B is one-to-one mapped to the set of natural numbers. For example, the set of positive rational numbers can easily be one-to-one mapped to the set of natural number pairs (2-tuples) because p/q Since the set of natural number pairs is one-to-one mapped (actually one-to-one correspondence or bijection) to the set of natural numbers as shown above, the positive rational number set is proved as countable. - Basically, if I can write a function that returns the value of one set from the value of another, in ANY WAY, those two sets are equivalently infinite. Because all positive integers can be mapped to all integers using p/2=q these two sets are equivalent. You have to find a set that can’t be mapped. The classic example is real numbers. There exists no continuous function to map all integers to all real numbers. The set of real numbers is said to be uncountable infinite. This doesn’t get into cardinality - which is its own thing. The cardinality of a set is n (A) = x, where x is the number of elements of a set A. The cardinality of an infinite set is n (A) = ∞ as the number of elements is unlimited in it. This article gets into it well - https://www.cantorsparadise.com/why-some-infinities-are-larger-than-others-fc26863b872f?gi=a288af6baf64#:~:text=Even%20though%20there%20are%20an,are%20not%20equal%20in%20size. —- Edit to add add- The other piece here is you are still thinking of infinity as a number. Saying “one contains the other” is meaningful when talking about finite sets, much less so when talking about infinite sets. You can divide infinite by two- it’s still infinite (this is essentially what you are doing to map evens to integers). You can add infinity to itself, it’s still the same size - infinite. It’s NOT a number. You can’t treat it like one, and once you do, you can prove some really stupid things, so don’t.
Thank you very much! That was a perfect refresher. I honestly think what happened is that I watched videos about this topic years ago, assimilated the information and then didn't use it for years. Then, unfortunately, confidently misremembered the correct conclusion. Classic human foible, and I am sorry for having fallen into this trap. I will go edit my incorrect comments and apologize to the others that I was speaking with! Have a nice day!
I am sorry for spreading misinformation! I fell victim to a faulty memory. I learned about how to conceptualize infinities years ago, but then let that knowledge languish until it atrophied and I confidently misremembered the information that I used to have. I have re-learned the correct interpretation thanks to a helpful redditor below. My apologies.
I see your point, but in this context I disagree. Infinity minus 1 does not equal infinite anymore. In this case investiture is energy (or fuel) in it's most basic sense. That's atleast how I personally view it. If you have an infinite amount of gas and use some, is it still infinite? Seems more philosophy than science. But even so, I feel like you reaffirm my point in that infinite is relative because you are comparing two amounts. Is infinite still infinitely larger than infinite minus 1? What about the two compared to zero? I just feels like it falls apart when you apply a specific usable substance against the logic.
Infinity - 1 is still infinity. Things get weird and unintuitive when you’re dealing with infinities. Think about an infinite string of houses. You bulldoze the first. There are still infinite houses left, even though you’ve subtracted one.
But then at what point is it no longer infinite? Because Preservation has access to less investiture than Ruin. I agree with your logic, I just don't believe is applies to investiture in the cosmere.
Both of them have infinite investiture, but Ruin's infinity is larger.
Infinity minus 1 is still infinity. That is an axiom of math, not something open for debate. And some infinities are larger than others. But they're all still infinite. https://en.m.wikipedia.org/wiki/Aleph_number
Your claim that infinite minus 1 is not infinite anymore is exactly opposite to how infinity works. You are thinking of infinity as a number. It isn't. Two minus one is no longer two. Infinity minus one is still infinity. Think about a bunch of grapes. You eat one. You are still left with a bunch of grapes because "a bunch of grapes" is not a number. It is a concept. We can mathematically alter concepts, but we can't do simple calculations with them. Infinity is the concept of never-ending. Basically, math gets weird when dealing with infinity because infinity is not a number. Edit: The information above is correct, but the information in brackets below is not. I unfortunately misremembered information that I learned years ago. I have since re-learned how to properly conceptualize infinites thanks to a helpful member of this community. I am sorry for spreading misinformation. [We can make statements that are objectively accurate according to the laws of logic, like infinity divided by 2 is objectively smaller than the same infinity before you divided it, but still infinite.] [Think about every number that exists. This is an infinite amount of numbers. Now, delete all of the odd numbers. You still have an infinite amount of even numbers, but this is objectively lacking numbers that the previous infinity contained and therefore it is a smaller infinity.]
You're both right and wrong. I am NOT thinking of infinite as a number, that's what I'm explaining poorly. I'm saying I believe Sanderson's use of the word infinite is NOT the mathematical meaning. Instead I believe he is approaching it like when people refer to the universe as infinite in size. More of a relative comparison. I could be wrong. But I personally believe that the quantitative amount of investiture the shards hold will become relevant in phase 2 which is the point I was disagreeing with OP. Still might not be explaining well though :/
I understand that people use "infinite" colloquially to just mean "more than I can imagine." However, Brandon has based his entire system as much as he can on actual scientific principles. He has gone out of his way to try to break or bend as few of the laws of thermodynamics as possible. He bent over backward to portray a somewhat scientifically reasonable version of magically altering time. I see no reason to assume that Brandon is using "infinite" colloquially instead of accurately. That said, about the universe being infinite: So far as we understand, the question of whether the universe is infinite is currently unsolved. The observable universe is definitely finite. However, our measurements and calculations show that spacetime is expanding from every point simultaneously, and that seems an awful lot like infinite expansion. You would never be able to find an end or an edge of spacetime because the expansion isn't relative to any single location. Even moving faster than light would not outpace the expansion due to the fact that you, yourself, are a collection of points from which spacetime evenly expands. So no matter how far or how fast you go, there is always more spacetime. There are arguments against that logic, and there is the possibility that something could interrupt or halt the expansion somehow. Spacetime might somehow hit a limiter that we don't yet know. So we don't know if the universe is actually infinite or not.
Adonalsium, and subsequently his shards, did not originate investiture. Since investiture predates shards, then ... shards do not contain infinite investiture. Arguably they could even contain no investiture, apparently not unlike allomancers. But just like an allomancer can nonetheless *use* investiture, a shard's "great power" is to use investiture on such a scale as no other thing in the Cosmere, short of rolling back to Adonalsium's time. The investiture itself is infinite, and is also everywhere. It's seemingly a fifth force: gravity, electromagnetism, weak and strong nuclear, and investiture. There's likely a GUT in the Cosmere's scientific future - a grand unified theory. The splintering of a shard will also leave each piece less potent, and whatever piece is nonintelligent is even less capable of using investiture, instead running on automatic, obeying leftover Intent or whatever the original shard (and the person merged with it) had.
Hum, like Jupiter warps space-time more than an asteroid, and therefore has more gravitational pull. Honor warps the "investiure field" more than the Stormfather does, and therefore has more power.
Good example! Arguably, intelligent splinters, like Stormfather, have little power because they can't initiate its use beyond the rote implementations they represent. For example, Stormfather could likely destroy mountains, kill armies, but his job is creating, maintaining, and moving an invested hurricane around. It complains and struggles when pushed to do otherwise, and only goes above and beyond when Bonded and Commanded (I hope I got the terms right).
Good example! Arguably, intelligent splinters, like Stormfather, have little power because they can't initiate its use beyond the rote implementations they represent. For example, Stormfather could likely destroy mountains, kill armies, but his job is creating, maintaining, and moving an invested hurricane around. It complains and struggles, and only goes above and beyond when Bonded and Commanded (I hope I got the terms right).
so, kinda no we don’t know what adonalium or the shards are exactly, but we do know that every single piece of investiture in the cosmere is keyed to and comprises a shard of adonalsium, and that all investiture in the cosmere prior to the shattering was part of big a. the only potential non-adonalsium investiture in the cosmere is the aethers, but it’s in-universe unconfirmed and contested if they’re actually separate or not. it’s also been said directly by brandon that shards contain infinite (either functionally or literally) investiture and investiture isn’t a fifth force, brandon has said it’s a 3rd type of…thing? idk, basically in the cosmere e=mc^2 would have to be adapted to include investiture, as investiture is a third form for stuff to be, like matter and energy
I think it's infinite like it's a faucet that never runs out, but it can only channel so much at once. It's a really big faucet, but it's still got limits, but the source will never empty.
The way I see it, they are all tapping the same unlimited source, it's just a question of what volume they can move at any given time. Things like spren would be like someone sticking a straw into a river and sucking out as much water as they can, while a shard would be like a major pipeline, diverting thousands of gallons.
Where it is said Shards have infinite Investiture? Because it contradicts some things we know about Investiture. For example it was said that amout of Investiture in cosmere is fixed and cannot be destroyes or created. It can only change either to difffetent forms of investitire or matter/energy and back. That would not make sense if there is infinite supply of Investiture. IMHO idea that Shards have infinite Investiture is wrong. What limits Shard power is how much Investiture they can effectively control at a time. They are limited by Vessel ability to control powers they got by holding Shard power. They have more Investiture than they can control and given that Investiture cannot be destroyed they can "recycle it" somehow and use again. That gives them technically Infinite supply of Investiture but total amount of their Investiture is still fixed. And it would have similar result as your proposed limited throughtput.
I always had it in my head as the shards where like hoses hooked up to the ocean. Each shard has 1 hose all pulling from infinity water. Harmony has 2 hoses so can pull more out faster compared to other shards.
It's infinite in the sense that it can't really be destroyed. There's basically a large well of investiture somewhere in the spiritual realm, maybe. So yes, the Shards do expend it when they do stuff, but once that investiture is expended, it kinda flows back to that big well. So it is essentially infinite in that it can never be destroyed, just recycled. So when a Shard invests a planet or person, that investiture stays with that person or planet instead of recycling back to their well of investiture which is why you have situations where Ruin is stronger than Preservation because Preservation is more invested in the humans of Scadrial and the planet as a whole
I think the output of investiture really is unlimited, but control of said investiture is finite. We saw this when Rin took control of Ruin and Harmony, she could do things that were incredibly powerful, but she had no idea how to control it so people wouldn’t die.
Surprised that noone has brought up dawnshards yet. Shards do have infinite investiture but most of it is in the spiritual realm which is why there are no investiture black holes/crazy time dilation forming in the physical/cognitive realms. Shards can only draw upon their infinite investiture at a finite rate which is limited by the vessel and their alignment with their Intent and the Intent of the action they are trying to inact. This is why the dawnshards exist. They provide supercharged Intent which allowed Adonalsium (and shards of they ever got hold of a dawnshard) to channel and command shardic levels of investiture. Shards are still very very powerful but we have seen that they are still heavily nerfed by their Intent in most cases. Dawnshards would bypass this "Intent cap".
investiture is described as infinite in shards but as others have pointed out, i believe that its *functionally* infinite, not truly haven’t read far enough to see if others have mentioned this part, but brandon has explained why shards can’t access all of the investiture that they contain: its because they’re mortal. a shard is a mortal mind expanded to be god-like. but that’s the key part, god-*like*. mortals are still mortal, and even if the being is something immortal or immortal adjacent, it’s still not a god. we don’t know for sure what adonalsium was, but my money is on the idea that adonalsium *was* the shards, not a being that held them or whatever. adonalsium was birthed from an incomprehensibly large mass of investiture coalescing and gaining sentience, and thus could fully understand and control all of its body and mind, whereas a shard holder is limited to using only the investiture they are consciously aware of all 16 shards are spread throughout the entire cosmere. there’s ruin on roshar and odium on taldain and devotion on scadrial, but no shard could ever consciously control all of that investiture, their minds simply aren’t large enough to do so. adonalsium however, if i’m correct, would have been able to, since it *was* that investiture and was built to make use of it fully and properly my guess is that adonalsium was born when, in the moments after the big bang, all investiture existed in a much smaller, more confined area, and in those conditions that investiture became sentient and awoke as what we know as big a
It's like a pipe connected to the ocean Yeah, there's functionally an infinite amount, from a small to a pretty large scale, but you're limited by the output of the pipe, which would be things like the Vessel itself, the shard's intent, and the limited focus and willpower of the vessel to actually put out that much power. Over long enough timescales, infinity can seem less large, but it's still infinite. just like how the water cycle works, investiture is constantly switching between itself, matter, and energy. and when you break apart a large pipe into smaller ones you get less output, especially if they're coming from the same place, since there's more physical pipe and less open space
Nearly right. Their power is cyclically infinite, in that it forms a closed system and never ordinarily is permanently removed from said cycle. Also, I think that with enough power you could make a False Shard, Ascend to the Spiritual Realm, and start your own cycle, and I think that's the purpose of Canticle and it's sun.
I once heard of a religion where priest with metal eyes said a sliver of infinity is still infinity. A really cool girl with an earring proved that false like a lie detector on Maury.
That makes sense. I'd say the "basically" infinite Investiture has to be funneled through a Vessel that, though dramatically expanded, still has limits on what it can use **at a given time**. Investiture that is expended eventually gets back to the Shard that sent it out via the Spiritual Realm. We know that Preservation was weaker than Ruin because Leras had invested more of his essence in humans. The only thing that could be "weaker" would be the Investiture that was available to be funneled through the Vessel. So Leras had Invested humans with, say, 0.0000001% of the Investiture he could channel. Maybe Leras could channel a Googleplex of BEUs (Breath Equivalent Units). But it's not **INFINITE.** Because the expanded Vessel is still limited. Remember, neither Leras nor Ati could create a world on their own. If their Investiture were truly infinite, they could each create worlds as they wished. Especially when they were new to their Shards and the Intent hadn't changed their souls yet. The only thing that could be limited if the Investiture were basically infinite in both cases (Preservation and Ruin) would be the Vessel. Maybe the Investiture the Vessel could use is limited by their unconscious limits of perception.