the 10-16 theorem

[rags]

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?

Possible....but the "10" theme is overpowering on Roshar. 10 heralds, 10 orders of Radiants, 10 essences, 10 Silver Kigndoms, 10 princedoms of Alethkar. Its not just limited to the magic system like in Mistborn.

[Commander Spoonface]

Or perhaps it's simply this: Humans like round numbers. We always have. In nearly all cultures on earth, you'll find relevance attached to (usually) the numbers 2,3,4,7, and 10, and their respective multiples. I admit that the relevance of 16 being attached to Preservation is not explained by this, but many examples are.

As for Roshar, I see this as correlation without causation. Almost any of those instances could be the cause of some or all of the others, or they could all be the cause of another, external factor. So ten is not necessarily a special number, it's just that once there was 10 of one thing, and in emulation or as a result, now there are 10 of many different things.

[Aeshdan]

Possible....but the "10" theme is overpowering on Roshar. 10 heralds, 10 orders of Radiants, 10 essences, 10 Silver Kigndoms, 10 princedoms of Alethkar. Its not just limited to the magic system like in Mistborn.

The Ten Essences, ten heralds, and ten radiant orders are all directly part of the magic system, and I think the ten kingdoms might follow from the Heralds.

[Squigy]

I would just like to point out that in WB the 4 types of Biochromatic Constructs... in Mistborn there are 4 categories of metals, each with 4 metals... and 2 God metals [the square root of 4(or each counts as 2 since they can be alloyed with any of the other metals or are just that powerfull)]. Perhaps the rule of 16 is not as solid as we assume. Correct me if I'm wrong, but didn't we just get the rule of 16 form one man's theory in MB:HoA? After all this would follow similarly to how discovery goes IRL, we used to think that protons were a fundamental constiguite of matter, that is until 1968 when the quark was confirmed through deep inelastic scatter.

So might it be a rule of 10-4 or 10-4x4/10-4²?

For all we know the 16 shards may eventually be arranged into 4 categories too.

Now concerning AonDor, there ARE other ways of tapping into the Dor, Shu-Dereth has their "monks" (also character based through engravings on their bones) and that one foreign nobleman, if I remember correctly from Jindo(I lent my copy to my cousin or I would look up his name) tapped into the Dor through his "martial dance" and began to glow similarly to an elantrian. So for all we know there are 16 different ways of harnessing the Dor.

As I was typing this I realized something...

Say there are only 4 ways of harnessing the Dor: A (AonDor), B (Shu-Dereth's way), C (the Jindo way), and D (some way yet to be seen)

combine them in every combination and you get 15 different ways: A, B, C, D, AB, AC, AD, BC, BD, CD, ABC, BCD, CDA, DAB, ABCD. THEN we assume there is an alternative to combining them into the last one, call it ABCD' (maybe using them as a single power as opposed to 4 separate powers at once in that case call ABCD' E instead).

Now it satisfies the rule of 4x4/16 side of the 10-4² rule for Domination and Devotion opposing each other.

This may even give some insight as to the nature of the other ways of using The Dor, both A and B use symbols and their practitioners undergo some transformation in order to use it becoming Dominated by The Dor(powered by by the same shard?) maybe C & D both require somatic components to access The Dor which is innate in their users needing only discipline through training in the motions, Devoting themselves to The Dor.

We may even see a repeat of the internal/external powers theme from MB A & D are external while B & C are internal

here is A crude diagram of my theory.

I apologize, this came out WAY longer than I was expecting it to.

Edited August 7, 2012 by HighprinceTruserOfHouseAan

[Aeshdan]

I would just like to point out that in WB the 4 types of Biochromatic Constructs... in Mistborn there are 4 categories of metals, each with 4 metals... and 2 God metals [the square root of 4(or each counts as 2 since they can be alloyed with any of the other metals or are just that powerfull)]. Perhaps the rule of 16 is not as solid as we assume. Correct me if I'm wrong, but didn't we just get the rule of 16 form one man's theory in MB:HoA?

I'm afraid you are wrong on several particulars of Allomancy. First, there are sixteen ordinary metals that have Allomantic properties.Second, each God metal has either sixteen or thirty-two alloys (either 1 or 2 for each metal, Brandon has hinted at two).

The rule of sixteen is confirmed by Brandon himself.

Also, as I pointed out above, I have reason to believe there are five kinds of BioChromatic entity, not four.

As I was typing this I realized something...

Say there are only 4 ways of harnessing the Dor: A (AonDor), B (Shu-Dereth's way), C (the Jindo way), and D (some way yet to be seen)

combine them in every combination and you get 15 different ways: A, B, C, D, AB, AC, AD, BC, BD, CD, ABC, BCD, CDA, DAB, ABCD. THEN we assume there is an alternative to combining them into the last one, call it ABCD' (maybe using them as a single power as opposed to 4 separate powers at once in that case call ABCD' E instead).

This may even give some insight as to the nature of the other ways of using The Dor, both A and B use symbols and their practitioners undergo some transformation in order to use it becoming Dominated by The Dor(powered by by the same shard?) maybe C & D both require somatic components to access The Dor which is innate in their users needing only discipline through training in the motions, Devoting themselves to The Dor.

While you are probably correct in there being four ways to access the Dor, (there is a fourth confirmed magic system on Sel, but we don't know which Shard fuels it), it is about as certain as it's possible to be that Devotion is behind AonDor and Dominion behind Dakhor, and that undoes your balance.

Finally, this half of your post seems to argue for my theory while the first half argues against it.

[Vortaan]

I'm afraid you are wrong on several particulars of Allomancy. First, there are sixteen ordinary metals that have Allomantic properties.Second, each God metal has either sixteen or thirty-two alloys (either 1 or 2 for each metal, Brandon has hinted at two).

The rule of sixteen is confirmed by Brandon himself.

Also, as I pointed out above, I have reason to believe there are five kinds of BioChromatic entity, not four.

Wouldn't the fifth category be Spontaneous Biochromatic Manifestation in a Non-biological host? Not sure how such a thing could occur, but... Nightshade is arguably alive. If he became unAwakened, it's concievable, maybe, that he could Return? Seems to fit the requirements a bit more than just normal people, as he would still require Breath to survive.

[Squigy]

I'm afraid you are wrong on several particulars of Allomancy. First, there are sixteen ordinary metals that have Allomantic properties.Second, each God metal has either sixteen or thirty-two alloys (either 1 or 2 for each metal, Brandon has hinted at two).

That's what I was saying. The way I describe the Alomantic/Feruchemical/Hemalurgic metals is 4 sets {[(wheels/squares)pure, w/Lerasium, w/Atium, w/both God metals] hey, there's 64 metals} of 4 sets (quadrents) of 2 metals and their alloys, plus 2 pure God metals and the alloy of the 2 God metals together. 67 metals total.

The rule of sixteen is confirmed by Brandon himself.

I was not aware of this and would much appreciate it if someone could direct me towards the source so that I may enlighten myself as to more "Word of God" information to support further theories I hypothesize.

Also, as I pointed out above, I have reason to believe there are five kinds of BioChromatic entity, not four.

In regards to that statement, if a Lifeless were created in such a way as to take in around 3.5x10³ breaths, would they be sentient, and if so, would that be a Returned, or a 6th type of BioChromatic entity. I say the count should be 4 or 10 with more to be discovered yet, but not 5, just my deduction.

While you are probably correct in there being four ways to access the Dor, (there is a fourth confirmed magic system on Sel, but we don't know which Shard fuels it), it is about as certain as it's possible to be that Devotion is behind AonDor and Dominion behind Dakhor, and that undoes your balance.

There is not enough evidence to draw conclusions as to the actual sources of the Dor, or weather the Dor comes from only one shard or both, but I have stated my prediction and stand by it.

Once again, if Word of God has countered my statement, I wish to view the source, material, not that I don't trust y'all, I just want to have records for when I discuss this stuff IRL

And my post was meant to support your hypothesis completely, I just thought of an alternate version of it and thought I would mention it.

Wouldn't the fifth category be Spontaneous Biochromatic Manifestation in a Non-biological host? Not sure how such a thing could occur, but... Nightshade is arguably alive. If he became unAwakened, it's concievable, maybe, that he could Return? Seems to fit the requirements a bit more than just normal people, as he would still require Breath to survive.

I like the sound of that. So now we have:

1) Returned

2) Lifless

3) Awakened objects

4) Greater Awakened Objects

5) Artificial Returned

6) Returned Objects

7) Humans

8) animals and plants

9) Returned Animals and plants

10) spontaneous manifestation of non-phisical constructs of breath

I approve this list.

Edited August 7, 2012 by HighprinceTruserOfHouseAan

[CabbageHead]

While you are probably correct in there being four ways to access the Dor, (there is a fourth confirmed magic system on Sel, but we don't know which Shard fuels it)

Doh. There goes another nascent suspicion in my mind before it had fully formed. I was just thinking about whether the number of magic systems on a planet was related to the number of resident shards. Scadrial, 2 shards, 1 system based on Preservation, 1 on Ruin, one a mix of both. Nalthis, 1 shard, 1 magic system. And until you said that, Sel, 2 shards, 3 known systems. If there was a system for every combination of local shards, we could have 7 magic systems on Roshar. I wonder if the 4th unknown confirmed magic system on Sel is something that falls outside of the shards? Lightweaving was supposedly around before the shattering of Adonalsium.

[Aminar]

I'm pretty sure the systems are tied to the number of shards. That just means that some of the magic systems are technically the same system. I think the basic formula is (2^# of shards)-1

We'll just have to RAFO.

[lil_literalist]

I like the idea that Humans group things by 10's, while Shards group them by 16's. Even if not everything adds up.

Because the Shards were all part of Adonalsium at one point, they share common characteristics, such as the penchant for the numbers 16 and 10.

[Turos]

Lol! This is interesting stuff

Okay, so picking from just a few portions, here's some stuff to boggle the mind

"Indicate the achievement of the material power."

"Being considered as the "final" number of the emanation, it represents the Incarnation completed, according to Abellio."

"In the Hindu religion, an Avatar is an extraordinary being, the miraculous incarnation of the Divine in a human form, for the well of the humanity. By definition, the Avatar has sixteen particular gifts: the ability to materialize objects at will; qualities of omniscience, omnipresence and omnipotence; the capacity to transmit a pure love current, inexhaustible; the possibility to transcend all conditions of the Karma which appears by his capacity to transform miraculously the life of a person by an act of divine will."

"Sum of the four first odd numbers (1+3+5+7=16) which, by theosophical addition, gives 1+6=7, the sacred number."

And the kicker for the 16-10 thing:

"According to R. Allendy, it represents "the role of the Karma 6 in the cosmic unit 10. This role consists in creating a current of evolution (1 + 6 = 7) but towards two opposite directions, so that, by itself, 16 even number, is unable to choose." As a product of 2 x 8, it is the positive evolution leading to the karmic liberation, or the negative evolution leading to an increasingly tight sequence in the cycles of nature."

I don't know much about these idealisms, but I know numbers play a big role in the world's cultures. Maybe there's some clue to it all in our own world. Ooooooh.... Aaaaaaaaah....

[Kaurne]

My most humble apologies for the thread necromancy.

I'd like to ask firstly if anyone has a link to the hints from Brandon that each god metal has 32 alloys, because that just shot down an idea of mine. If each god metal has 16 alloys, we have 16 'normal' metals, 16 lerasium alloys, 16 atium alloys, and the two god metals. That's 50, or (10^2)/2, which is certainly a much rounder number than what we get if we have two alloys a piece, and fits (loosely) into the number 10 link. Hell, some things do appear to run on 5's (number of Biochromatic entities, number of Knights Radiant oaths) so it fits decently.

Two alloys apiece gives us 16 'normal' metals, 32 lerasium alloys, 32 atium alloys, and 2 god metals, which is 82 metals. A really annoying number.

[NOTE: This is where my wild theorising with no basis in anything one might call evidence begins.]

But wait! Let us say that there is a hypothetical alloy of lerasium and atium that does... something (hey, maybe it makes you a feruchemist ) and that it can be alloyed with all 16 of the 'normal' metals, (perhaps to make them ferings? Hell, this actually makes a little sense) then we get 99 metals.

That's really close. Really, really close, and I've got the feeling I'm missing something.

Maybe this is where the 'final metal' born by the men of red and gold, (as described by Miles in AoL) comes in. Problem is, I've no idea what it could be; we've kind of run out of things to do with our 18 initial metals. I've also no idea what it could do; I have a loose theory about what the lerasatium alloys do, and we're reasonably confident that lerasium alloys make people mistings, but beyond that we haven't a clue, although that does benefit us in the sense that if we need to come up with 47 new powers, 48 doesn't make much of a difference. That isn't counting, of course, that lerasium (and presumably its alloys) have a different, 'primary', function to the one we've seen.

Anyone have any ideas? If we can bring things up to a nice round 100 metals then suddenly everything fits a LOT better.

Edited September 30, 2012 by Kaurne

[Voidus]

I'm not sure about 2 alloys for each god-metal not sure where that came from but there's this.

FIRE ARCADIA

Are there 50 Allomantic Metals?

BRANDON SANDERSON

Nearly. Does Harmony have a metal?

FIRE ARCADIA

Is that an alloy of Lerasium and Atium?

BRANDON SANDERSON

You're along the right lines.

So not 50

EDIT: There's also this and it kind of depends how you interpret the answer.

17TH SHARD

Are there a limited amount of atium and lerasium alloys for each metal?

BRANDON SANDERSON

Hmm, yes…I suppose there would be but there are…

17TH SHARD

More than sixteen?

BRANDON SANDERSON

Yeah, way more than sixteen.

17TH SHARD

Oh wow. Okay. That's fascinating. More than sixteen and less than infinite.

BRANDON SANDERSON

Yes.

So there might not just be 1 atium and 1 Lerasium alloy for each metal either, but it's not necessarily 2

Edited September 30, 2012 by Voidus