Ripheus23 Posted March 3, 2025 Posted March 3, 2025 (edited) Here's a WoB (for full WoB, see @Treamayne's post below): Quote Each pairing and grouping of Shards will have different sort of augmentations to what they can accomplish, and things like this, because the Shards aren't all-powerful, they're just part of something that once was, if that makes sense. (That's not how math works in infinity, but it is how infinity works in the cosmere.) Interestingly, I've of late found out that this is mostly right. It's basically right if you consider just the most-studied transfinite quantities, the aleph numbers, with which I have no doubt Sanderson is familiar. Because letting A be some aleph number, then A + A = A. And then even A squared = A, although to be sure, A^A > A (this is a case of Cantor's famous/infamous theorem). However, the alephs are the "only" transfinite cardinals only if every set must be well-ordered, and universal well-ordering can be waived by jettisoning or at least compromising the even more infamous Axiom of Choice. So there's a whole subdiscipline that's about exploring relations of cardinals that correspond to sets which aren't well-ordered, e.g. ones called "amorphous." So for a remotely layman-accessible overview of some of the quirky mathematics, here, see this paper. Basically, it goes over the arithmetic of multiplying some sort of choiceless numbers by 3, showing that it's not trivially true (or then not always true!) that some infinite 3X collapses back to just X. (Or, that's how I've been reading this and other such material.) So what if Adonalsium's power level was actually some X such that X/16 doesn't equal X, but some Y, so that then e.g. 4Y (for a tetra-Shard) would be indeed greater than the base Y? I wonder, then, if Sanderson is a little familiar with this stuff, too, but so his WoB is code for, "Infinity in mathematics doesn't usually work the way I'm saying it does in the cosmere, though sometimes there's infinitary math that does resemble cosmere infinity more"? Endnote: see stuff from Jech's great book on the Axiom of Choice and theories where it falters/fails. Endnote 2: a short, nice paper about this stuff. Quote One important consequence of AC is the absorption law of cardinal arithmetic. It states that for any cardinals m and n, if m < or = n and n is infinite, then m + n = n and if m /= 0, m · n = n. This makes it easy to compute the sum and product of any two cardinals. Without AC, this property is no longer true. In this paper, we will first investigate some conditions that make this property hold as well as an instance when such a property cannot be proved in the absence of AC. EDIT: or maybe there could be something like: the aethers, if they predate/are independent on Adonalsium, are this way because their entire power level signature class is a separate form of infinity compared to that of the Origin of Songs. Like, Ado uses well-ordered infinite cardinals but the aethers use amorphous cardinals, or vice versa, etc. Edited March 4, 2025 by Ripheus23 2
Treamayne Posted March 3, 2025 Posted March 3, 2025 1 hour ago, Ripheus23 said: Here's a WoB: Quote Each pairing and grouping of Shards will have different sort of augmentations to what they can accomplish, and things like this, because the Shards aren't all-powerful, they're just part of something that once was, if that makes sense. (That's not how math works in infinity, but it is how infinity works in the cosmere.) Interestingly, I've of late found out that this is mostly right. Here is the full WoB (if you use the copy button on the top-right of the WoB, it will include the link back to the Arcanum entry as well as provide the date(s) and associated data for others to find the source on Arcanum) Please see the Sharder FAQ for more info. Spoiler Questioner My question is about Ruin and Preservation creating life. Is that an example of two individuals having a super team up? Or is there some co-influence, cross-influence that let them do something that would be outside of themselves? Brandon Sanderson Rephrase that for me. Talk around a little bit. Let me see if I'm gonna get the right answer, okay? Questioner Ruin ruins, and Preservation preserves. If they're creating life, well, that takes a little of everything, right? Is that an influence, like Ruin being in proximity to Preservation and vice versa? Would their co-mingling happen... and how would that influence other dual or triple Shards? Brandon Sanderson I get what you're saying. Each of the Shards has certain strengths and weaknesses, and they're capable of certain things and not other things. Some of them can do what was done by Ruin and Preservation on their own. Most cannot. Most combinations of two could; some would need three. So, it really kind of depends on the situation and the Shard. Each pairing and grouping of Shards will have different sort of augmentations to what they can accomplish, and things like this, because the Shards aren't all-powerful, they're just part of something that once was, if that makes sense. (That's not how math works in infinity, but it is how infinity works in the cosmere.) FanX 2024 (Sept. 26, 2024) Hopefully Chaos will find time to chime in, as the post is likely to be in their wheelhouse. 1
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