the 10-16 theorem

[Aeshdan he/him]

Alright, so my theory is that when complementary Shards are on the same world, then all complementary shards produce "16"-based magics, while when no complements are present, "10"-based magics are created.

How this theory plays out in the books:

Mistborn: This is the obvious one. Ruin and Preservation are perfect complements, and they produced three 16-systems.

Warbreaker: Endowment is the only shard on her planet, so she cannot have a complement. Awakening has the Ten Heightenings, and there are five forms of BioChromatic entity (Vasher missed Spontaneous Sentient BioChromatic Manifestations In a Living Host in his explanation).

Stormlight: There are three 10-based systems here (Surgebinding, Voidbinding, and ?Lifebinding?), and the general consensus is that Honor, Odium, and Cultivation are non-complementary.

Alcatraz: Rutabaga.

[Chaos he/him]

I saw this idea in a previous thread, and I really like it. But how do you explain Elantris? Devotion and Dominion are certainly complementary, but there are lot more than sixteen Aons.

there are five forms of BioChromatic entity (Vasher missed Spontaneous Sentient BioChromatic Manifestations In a Living Host in his explanation).

Can you explain this fifth BioChromatic entity for me? We haven't seen this in the book, I'm pretty sure...

[lyssie95 she/her]

Dunno about warbreaker, but as for Elantris there are a lot of aons we don't know yet. It could be a multiple of 16... and if you throw in the god metals you can make more sets of 16 in allomancy, so the theory *could* fit, there is just no way of proving it right/wrong using elantris until we know the real number of aons.

[Commander Spoonface he/him]

I declare this theory to be Exceptionally Shiny.

This explains elegantly why there appear to be two numerical systems.

On the subject of Aons:

If I remember correctly, the most basic Aon has four lines, correct? Perhaps that in of itself is a reflection of the law of 16.

[Voidus]

Actually the basic Aon (Aon Aon I'm assuming you mean?) Is two lines and a dot.

Aon Rao does have the four cities though so that's something. We don't really know enough about the Aons to speculate too much though, the whole system seems to be quite a bit more open then any other system, but perhaps the Aons fall into 16 categories? entirely speculation but the lack of organisation and limitations to the elantrian magic systems gets to me sometimes, I'm too used to all of the other rigidly scientific systems

[Chaos he/him]

Dunno about warbreaker, but as for Elantris there are a lot of aons we don't know yet. It could be a multiple of 16... and if you throw in the god metals you can make more sets of 16 in allomancy, so the theory *could* fit, there is just no way of proving it right/wrong using elantris until we know the real number of aons.

My worry is that technically, there are an infinite amount of Aons, right? You can add modifiers to any base Aon and it is a "different" Aon that has a different effect. Just as there effectively infinite Commands, there'd be infinite Aons.

I declare this theory to be Exceptionally Shiny.

This explains elegantly why there appear to be two numerical systems.

On the subject of Aons:

If I remember correctly, the most basic Aon has four lines, correct? Perhaps that in of itself is a reflection of the law of 16.

Two actually (that isn't the best image, but whatever), but that comment about four makes a compelling case.

By the way, Reader, my favorite part of this theory is the comment about the Ten Heightenings. I don't think anyone picked up on the significance of the "ten" there before you, and that's seriously cool. I just wish the Selian magics would conform to this scheme; I wouldn't hesitate to espouse it if they did.

[Zas678 he/him]

Other people have picked up on the Ten Heightenings before, I'm pretty sure.

I think.

But I'm tired and don't want to dig it up now.

[Aeshdan he/him]

Can you explain this fifth BioChromatic entity for me? We haven't seen this in the book, I'm pretty sure...

Ordinary people!

[Aradel he/him]

Meaning ordinary Nalthians born with a single breath (which makes up the biochromatic part), but I'm not sure about spontanious. Pregnancy usually doesn't happen without... well you know what I'm talking about.

I can still see it counting as a fifth entity, Vasher just didn't think to add them because he's never seen someone born without a breath.

[Chaos he/him]

More importantly, the four BioChromatic entities require Breath to even exist. If Breath was not present in those entities, they would die or cease to be Awakened. This is very different from people, who can give away their Breath and reasonably be expected to live. The lack of Breath isn't immediately deadly.

[Odium's_Shard]

But it is immediately Dull.

[Commander Spoonface he/him]

More importantly, the four BioChromatic entities require Breath to even exist. If Breath was not present in those entities, they would die or cease to be Awakened. This is very different from people, who can give away their Breath and reasonably be expected to live. The lack of Breath isn't immediately deadly.

Honestly, at this time in Nalthis's history, most people aren't very familiar with how BioChroma works, and even Vasher may not know exactly how it works. Consider that Kelsier was one of the most experienced allomancers alive during his time, but there was still no way he could know about the temporal metals.

Perhaps there is another way to use breaths, maybe involving the Tears of Edgli... Or maybe several more.

[Chaos he/him]

Honestly, at this time in Nalthis's history, most people aren't very familiar with how BioChroma works, and even Vasher may not know exactly how it works. Consider that Kelsier was one of the most experienced allomancers alive during his time, but there was still no way he could know about the temporal metals.

Perhaps there is another way to use breaths, maybe involving the Tears of Edgli... Or maybe several more.

Yes, of course. This is certainly a possibility. But I'm pretty sure Vasher, even without knowing anything about Endowment, in his centuries of life, probably thought about Breath in humans, and decided it did not fit with his schema, and kept it this way because it was conceptually easier. That doesn't mean he's right in everything, but I'm going to trust Vasher until shown otherwise.

[Commander Spoonface he/him]

Yes, of course. This is certainly a possibility. But I'm pretty sure Vasher, even without knowing anything about Endowment, in his centuries of life, probably thought about Breath in humans, and decided it did not fit with his schema, and kept it this way because it was conceptually easier. That doesn't mean he's right in everything, but I'm going to trust Vasher until shown otherwise.

That is a fair point. Of course, that brings the number of Chromatic majiggers down to four, which abides by the law of 16.

Speaking of 16, why is it that there are 16 Shards? Is it because all the shards combined compliment each other?

Perhaps this is a viable theory: 16 is an Adnolasium related number, and therefore appears in the way a shard interacts with the world. 10 is a number related to the shardworlds themselves, and therefore appears in the way the world interacts with the shard.

...

...

Okay, that didn't make any sense.

So, here's how that fits with what we know of numbers in the cosmere.

The reason that Allomantic metals are grouped into groups of 4, 8, and 16 is because those metals were present before they had Allomantic properties. Preservation "selected" metals in 16-based groups to work with allomancy. Not saying it was a conscious process, but whatever.

The reason there are ten essences on Roshar is that those essences existed on Roshar before, and that soulcasting does not actually add properties, just changes between those ten.

There are ten heightenings, I believe, because those properties existed already in humans, and are accessed by Breaths...

Okay, it doesn't work with that last one. I think this is more of a starting place, anyway.

[Ironeyes he/him]

I can still see it counting as a fifth entity, Vasher just didn't think to add them because he's never seen someone born without a breath.

I had assumed that Vasher's four categories were just in-world explanations that don't actually have to do with how the magic intrinsically works. Therefore it wouldn't matter.

[Aeshdan he/him]

Meaning ordinary Nalthians born with a single breath (which makes up the biochromatic part), but I'm not sure about spontanious. Pregnancy usually doesn't happen without... well you know what I'm talking about.

I can still see it counting as a fifth entity, Vasher just didn't think to add them because he's never seen someone born without a breath.

The Investiture is spontaneous in that it does not require an Awakener to Command it.

[Commander Spoonface he/him]

The Investiture is spontaneous in that it does not require an Awakener to Command it.

Perhaps Endowment is an awakener? Or somesuch? That would make sense if the humans on Nalthis were created by Endowment.

[Windrunner he/him]

I had assumed that Vasher's four categories were just in-world explanations that don't actually have to do with how the magic intrinsically works. Therefore it wouldn't matter.

Well, just because it's in-world doesn't mean we can totally discount it. The people are bound to get stuff right sometimes. I think that Vasher's categories have a sort of innate symmetry in them, so I don't particularly like adding a fifth. After all, it doesn't really fit with the others. it's impossible to Awaken something already alive, so there can't be an opposite to this one. The others just seem to fit together in my opinion. I could be wrong though.

Perhaps Endowment is an awakener? Or somesuch? That would make sense if the humans on Nalthis were created by Endowment.

I don't think Endowment would be an Awakener any more than any other Shard is. They all have the ability to make humans, and since Breath is part of the spiritual aspect of these people, they're not really all that different from any other people in the cosmere, other then the fact that they can choose to give a part of their spiritual aspect away.

[Musicspren he/him]

Forgive the mild thread necromancy, but I wanted to mention that Scadrial is not devoid of 10: The Well fills every 1024 years, which means every 2¹⁰ years. Whether that 10 is significant, I don't know (but this is Brandon Sanderson, so what are the odds it isn't to some extent significant). Also, on Nalthis, I don't think we can really count on numerical significance of Heightenings - it's a spectrum varying by each Breath, and the heightenings are generally points at which something becomes complete. Perfect pitch does not "turn on" at the second heightening, it probably just stops improving (I wonder if there are musicians in world who gather Breaths specifically for that...or who give them up to preserve their sanity). The heightenings are probably just convenient points to mark by. With metals, there is iron, there is steel, there could be impure iron or steel, but there is nothing partway between. With Breath there is a scale of practically infinitely small increments (remember that some Breaths are stronger or weaker than others, so they aren't confined to whole number Breath counts). We also don't know what might come above the tenth heightening - no one has ever acquired that many Breaths. There might be other Heightenings with new abilities (drawing color out to the point of transparency, drawing people's Breaths out against their will, domesticating Nightblood, etc.).

[Joe ST he/him]

Scadrial has 10's too, the symbol for AtiumMalatium is the numeral 10. Ten High Noble Houses, ten (of 16) atium beads. There were ten members of Kelsiers crew (a bit of a stretch lol) and some other tens that I've misforgotten

[Aeshdan he/him]

Forgive the mild thread necromancy, but I wanted to mention that Scadrial is not devoid of 10: The Well fills every 1024 years, which means every 2¹⁰ years. Whether that 10 is significant, I don't know (but this is Brandon Sanderson, so what are the odds it isn't to some extent significant). Also, on Nalthis, I don't think we can really count on numerical significance of Heightenings - it's a spectrum varying by each Breath, and the heightenings are generally points at which something becomes complete. Perfect pitch does not "turn on" at the second heightening, it probably just stops improving (I wonder if there are musicians in world who gather Breaths specifically for that...or who give them up to preserve their sanity). The heightenings are probably just convenient points to mark by. With metals, there is iron, there is steel, there could be impure iron or steel, but there is nothing partway between. With Breath there is a scale of practically infinitely small increments (remember that some Breaths are stronger or weaker than others, so they aren't confined to whole number Breath counts). We also don't know what might come above the tenth heightening - no one has ever acquired that many Breaths. There might be other Heightenings with new abilities (drawing color out to the point of transparency, drawing people's Breaths out against their will, domesticating Nightblood, etc.).

I would agree that Mistborn has a lot of tens, but my point was merely that the magic system seems to be 16-based rather than 10-based.

As for your point about the Heightenings: I agree that there could be more Heightenings, but as far as we know there aren't. Also, the fact that some of the Heightenings are culminations of incremental abilities doesn't mean they don't exist.

Perhaps Endowment is an awakener? Or somesuch? That would make sense if the humans on Nalthis were created by Endowment.

But then the Returned wouldn't count as spontaneous either (Endowment-awakening is defined as spontaneous in-world).

Edited May 19, 2012 by Windrunner
Please don't double post. If you wish to quote more then one person you can use the multiquote feature

[Aeshdan he/him]

Scadrial has 10's too, the symbol for AtiumMalatium is the numeral 10. Ten High Noble Houses, ten (of 16) atium beads. There were ten members of Kelsiers crew (a bit of a stretch lol) and some other tens that I've misforgotten

But none of these specifically have to do with the magic.

[Commander Spoonface he/him]

Forgive the mild thread necromancy, but I wanted to mention that Scadrial is not devoid of 10: The Well fills every 1024 years, which means every 2¹⁰ years. Whether that 10 is significant, I don't know (but this is Brandon Sanderson, so what are the odds it isn't to some extent significant).

It's also 16*64, or 4*16^2.

[rags]

I think there is one more possible explanation for this 10-16 problem. The worlds on which 10 seems to be the theme are Nalthis and Roshar, on both worlds we have the presence of splintered shards (or another interpretation is worlds on which Odium has visited.) While unsplintered shards result in the original 16 based theme as is seen on Scadrial.

Sel is still a bit of a problem, but we don't know either way what its number theme is.But if you notice the "map progression" post on Brandon's blog, there are 10 named nations. (I do know thats bit of a long shot but well it was the best I could come up with)

Edited July 31, 2012 by rags

[Thought]

Mistborn: This is the obvious one. Ruin and Preservation are perfect complements, and they produced three 16-systems.

The curious thing here, though, is that it wasn't generally recognized as a 16-system until rather recently. If you recall, people thought there were only 10 metals in the first book (and, thus, for the majority of the existence of mistborn). Perhaps it is just that simple? Magic systems have "ten" abilities that are common knowledge, with the full 16 abilities limited, really, to those who have gained shardic knowledge?