Inheritance of Alomantic Abilities vs The 16%

[NinjaMeTimbers]

I just finished rereading Mistborn in preparation for the new book, and there is still one thing about the book I haven't been able to figure out. If Allomancy is inherited, then where does the 16% of those who go out into the mists come from? Obviously it can't be explained with genetics and inheritance, since suppose a group of unexposed people go out into the mists together. 16% of them become Mistings. But now supposed that they didn't go out, but that the ones who in the first scenario were unaffected by the mists went out. Then still 16% would fall sick, when none of them would have in the first scenario. And then if the original 16% from the first scenario went out into the mists together, only 16% of them would fall sick and become Mistings, rather than all of them like what happened in the first scenario. So now we have a completely different section of the population who become Allomancers than in the first scenario. Therefore there is no way that this is some unlocking of an inherited power. So the only explanation I can see is that the mists actually grant Allomancy to 16% of the population, rather than unlocking some hidden potential that was already there.

...So has Brandon said anything about this? Or does someone have a different explanation?

[happyman]

I don't know the full answer, but I can say some things. Firstly, I'd say that everybody on Scandrial has some affinity for the metallic arts, simply by virtue of their creation. In their "default" state, however, they couldn't reach those powers without at least (a) an infusion of Lerasium, bringing them closer to preservation or ( the mists snapping them. Because the infusion of Lerasium was inheritable, the nobility were much more likely to snap than the commoners, and the mists weren't in snapping-mode, thus making it essentially only inheritable for the duration of the final empire. With the snapping-mists, the natural affinities were brought out with much more difficulty, often manifesting talents that their ancestors had held latently, but which had never manifested before. I don't know much more than this, though, and your question still has merit.

[DariusJenai]

The mists merely Snap those members of the population that have the potential. So, if a group of people that had never been out in the mists all went out together, approximately 16% of them would Snap. But if the 84% that wouldn't have Snapped went out into the mists, then none would snap.

So, about 16% of the population had the genetic potential for Allomancy. That 16% is what Snapped in the mists. If somehow they were able to know in advance what 16% were going to Snap, then they could achieve a 100% success rate in the mists.

Your second scenario assumes that the mist always Snaps 16% of any group, rather than simply allowing for the 16% of the random population that had the genetic potential to have Snapped in the mists.

A far better question to be asked is:

If Atium isn't considered one of the 16 Basic Metals, but still has the potential for Mistings, then why wouldn't a perfect, divine system have snapped 18%? (16 Basic Metals, plus Atium and Malatium. We'll ignore Lerasium, since apparently anyone can use it).

[ulyssessword]

The mists merely Snap those members of the population that have the potential. So, if a group of people that had never been out in the mists all went out together, approximately 16% of them would Snap. But if the 84% that wouldn't have Snapped went out into the mists, then none would snap.

I don't think that this is correct. The main fact that made mistsickness notable as unnatural was that it was exactly 16% of any given group. There was no random variation at all, in any group, which means that the 16% must have been chosen when they entered the Mists, not at birth. (HoA ch. 21)

[NinjaMeTimbers]

I don't think that this is correct. The main fact that made mistsickness notable as unnatural was that it was exactly 16% of any given group. There was no random variation at all, in any group, which means that the 16% must have been chosen when they entered the Mists, not at birth. (HoA ch. 21)

Yes, this is what I was getting at. 16% with no random variation. Therefore it can't be simply those that have potential.

If Atium isn't considered one of the 16 Basic Metals, but still has the potential for Mistings, then why wouldn't a perfect, divine system have snapped 18%? (16 Basic Metals, plus Atium and Malatium. We'll ignore Lerasium, since apparently anyone can use it).

I agree, this is another really good question, and why was it 1/16 of those who fell sick who got atium, rather than 1/18?... Someone should ask Brandon.

Edited November 9, 2011 by NinjaMeTimbers

[discipleofhoid]

Yes, this is what I was getting at. 16% with no random variation. Therefore it can't be simply those that have potential.

I agree, this is another really good question, and why was it 1/16 of those who fell sick who got atium, rather than 1/18?... Someone should ask Brandon.

From the annotations:

What is going on here is that the mists are awakening the Allomantic potential inside of people. It’s very rough on a person for that to come out, and can cause death. Preservation set this all up before he gave his consciousness to imprison Ruin, so it’s not a perfect system. It’s like a machine left behind by its creator. The catalyst is the return of the power to the Well of Ascension. As soon as that power becomes full, it sets the mists to begin Snapping those who have the potential for Allomancy buried within them.

I would take this to mean that 1/16th of people have the potential for allomancy - the examples I have seen where it was exactly 1/16 of the people taken our in the mist that became sick dealt with large groups of people. The larger the sample group the closer the statistic will be to the correct value. I would say that these were large enough sample groups that the sample matched the correct value.

As for the 1/16th thing when Preservation set his plan up he replaced two of the less accessible temporal metals in the scheme. I can't find the quote on that right at the moment but it is in the annotations or Brandonotholagy.

[ulyssessword]

I would take this to mean that 1/16th of people have the potential for allomancy - the examples I have seen where it was exactly 1/16 of the people taken our in the mist that became sick dealt with large groups of people. The larger the sample group the closer the statistic will be to the correct value. I would say that these were large enough sample groups that the sample matched the correct value.

No again, the only way for it to logically work is for it to be decided when the group enters the mist. The numbers are remarked as being too exact for probability, larger groups would actually decrease the odds of an exact match if mistsickness vulnerability was determined at birth.

As an example, think of flipping coins. If you flip two coins, the chance of exactly one being heads is 50%. If you flip four coins, the chance of exactly two being heads is 37.5%, if you flip 100 coins, the chance of exactly 50 being heads is 8%. They had exact records, so the chances get worse and worse with a larger group, not better. Vulnerability to mistsickness must have been determined when the group entered the mist, nothing else fits the evidence unless the world is much, much more deterministic (no free will) than portrayed.

[discipleofhoid]

No again, the only way for it to logically work is for it to be decided when the group enters the mist. The numbers are remarked as being too exact for probability, larger groups would actually decrease the odds of an exact match if mistsickness vulnerability was determined at birth.

As an example, think of flipping coins. If you flip two coins, the chance of exactly one being heads is 50%. If you flip four coins, the chance of exactly two being heads is 37.5%, if you flip 100 coins, the chance of exactly 50 being heads is 8%. They had exact records, so the chances get worse and worse with a larger group, not better. Vulnerability to mistsickness must have been determined when the group entered the mist, nothing else fits the evidence unless the world is much, much more deterministic (no free will) than portrayed.

The coin flip scenario doesn't really match this situation. In the coin flip each coin has a 50% chance of being either heads or tails. In this situation each person is or isn't able to perform allomancy -- no chance involved at the individual level. At the world wide level 16% of people can perform allomancy. So the closer you get to the worldwide population the better match you should see.

A better example is is you have a bag of 32 marbles 2 of which are red and you pull 8 randomly. If you then pull 1 from those 8 red probabilities might you see? well either 1/4, 1/8 or 0 depending on how many reds you pulled the first time. If you repeat the experiment with a pulling 16 randomly the first time from the second set you would then have a 1/16,1/8, or 0 chance of the final marble being red. If you just pull 1 marble from the 32 then the chance is 1/16. Note that this is the probobility of the second pull the overall probability does not change. So as your sample size gets closer to the original group size your probability gets closer to the overall group probability as well.

Now that I look that over I am not sure I did the probability right. It has been a few years since my discrete mathematics course. But I still think the point is valid. If I slaughtered the math let me know.

Edited to remove bad math

Edited November 9, 2011 by discipleofhoid

[Wispsy]

havent rly made up my mind on this one, but i think what he is getting at is for a genetically passed on ability that has been cultivated in the nobles and culled in the skaa is a little too evenly distributed for all of these people to have naturally been passed down their allomantic powers and hundreds of thousands of people just happen to go out into the mists at the right time with the right group. especially since he has been dead for thousands of years so not really able to influence and pick and choose every person to the right time/place.

so because there should be more snapping in some populations and less in others which their isnt he is saying that they didnt necessarily have any significant allomantic power before entering the mists, however as the group entered them 16% where chosen and invested with that little extra preservation and snapped into their power there and then, not at their birth thru their descendants.

well thats what i thought he was saying anyway but shards are powerful in ways we do not yet understand right, could be anything! xD

[navi_syl]

havent rly made up my mind on this one, but i think what he is getting at is for a genetically passed on ability that has been cultivated in the nobles and culled in the skaa is a little too evenly distributed for all of these people to have naturally been passed down their allomantic powers and hundreds of thousands of people just happen to go out into the mists at the right time with the right group. especially since he has been dead for thousands of years so not really able to influence and pick and choose every person to the right time/place.

so because there should be more snapping in some populations and less in others which their isnt he is saying that they didnt necessarily have any significant allomantic power before entering the mists, however as the group entered them 16% where chosen and invested with that little extra preservation and snapped into their power there and then, not at their birth thru their descendants.

well thats what i thought he was saying anyway but shards are powerful in ways we do not yet understand right, could be anything! xD

The nobility would have a greater than 1/16 chance of snapping because their ancestors burned lerasium. The skaa have the 1/16 chance genetically because that probablitity was present when preservation initially set it up. Elend's army was mostly Skaa so the stat that we see is the 1/16. Most skaa hadn't been forced to snap before the mists started snapping people. Yes Elend brought a few noble men, but since they were mainly already allomancers they were not included in the stat.

[fyodor]

There is a pretty helpful discussion in this annotation.

http://www.brandonsanderson.com/annotation/345/Mistborn-3-Chapter-Seventy

He makes the point that most of these people did not have sufficient strength to be snapped outside intervention from the mists. I would kind of infer the larger point that a larger share of the population has allomantic abilities than is commonly believed but their abilities are never awakened because regular snapping efforts don't work.

So ability is genetic and the nobility because of its Lerasium infusion has a larger percentage of people that are strong enough to be Snapped with the more traditional physical abuse. However, the ability is still floating around in the larger population (also inherited) and is awakened by the mists.

Edited November 9, 2011 by fyodor

[darniil]

If Atium isn't considered one of the 16 Basic Metals, but still has the potential for Mistings, then why wouldn't a perfect, divine system have snapped 18%? (16 Basic Metals, plus Atium and Malatium. We'll ignore Lerasium, since apparently anyone can use it).

I asked Brandon about this at his Eagle Eye Books signing during Dragon*Con 2010. (Although you worded it much better than I did at the time.)

Essentially, Brandon said that Preservation wanted the number 16 to be noticeable in a multitude of places. This would make it easier for humanity to realize that something specific / unusual / planned was going on. Brandon didn't say why Preservation chose 16 over 18 (or more, due to other atium alloys), just that Preservation wanted the number 16 to be noticed.

My guess is because, in a different world, it would have been pointless trying to figure out why these two guys over here (aluminum and duralumin mistings) couldn't do anything, even though they both obviously Snapped during the Allomantic Aptitude Testing Procedure. (And because it would be too confusing if every atium-alloy misting were also added in to the mix.)

[Wispsy]

that explanation works pretty well xD

still one might expect a little variation in how many pop up in different areas, but then as well as that preservation could have easily just set it up to pick the top 16% or summit every time it finds a load of ppl inside it, alot of them too weak to have normally snapped, with a few even weaker ones that might have been picked in a different group.

[NinjaMeTimbers]

The coin flip scenario doesn't really match this situation. In the coin flip each coin has a 50% chance of being either heads or tails. In this situation each person is or isn't able to perform allomancy -- no chance involved at the individual level. At the world wide level 16% of people can perform allomancy. So the closer you get to the worldwide population the better match you should see.

A better example is is you have a bag of 32 marbles 2 of which are red and you pull 8 randomly. If you then pull 1 from those 8 red probabilities might you see? well either 1/4, 1/8 or 0 depending on how many reds you pulled the first time. If you repeat the experiment with a pulling 16 randomly the first time from the second set you would then have a 1/16,1/8, or 0 chance of the final marble being red. If you just pull 1 marble from the 32 then the chance is 1/16. Note that this is the probobility of the second pull the overall probability does not change. So as your sample size gets closer to the original group size your probability gets closer to the overall group probability as well.

Now that I look that over I am not sure I did the probability right. It has been a few years since my discrete mathematics course. But I still think the point is valid. If I slaughtered the math let me know.

Edited to remove bad math

No, ulyssessword was correct. If we are assuming all Allomancy is inherited, and that 16% of the whole world's population have the potential to become an Allomancer, then individually, each person has a 16/100 chance of becoming an Allomancer. If you randomly take 100 people, the chances of exactly 16 people being Allomancers is nCr(100,16)*(16/100)^16 * (84/100)^84 = 10.8%. If we take this to a larger group, of say 1000 people, the chances of exactly 160 of them being Allomancers is nCr(1000,160) * (16/100)^160 * (84/100)^840 = 3.4%. So therefore, like Elend commented, it was very strange that they were getting EXACTLY 16% to the person.

So I'm thinking that since part of Preservation is inside of everyone, everyone has the potential to be an Allomancer by mist snapping, but only some people, through inheritance, can be "natural" Allomancers. The mists just pick 16% of a given group who goes out into the mists together and snap them, whether these be the 16% with the largest preservation to ruin ratio, or if it's just completely random, I don't know.

But then there's the problem of Sazed's comment, I forget where in the book, that noblemen are all unaffected by the mist... So how does that fit in...?

[discipleofhoid]

No, ulyssessword was correct. If we are assuming all Allomancy is inherited, and that 16% of the whole world's population have the potential to become an Allomancer, then individually, each person has a 16/100 chance of becoming an Allomancer. If you randomly take 100 people, the chances of exactly 16 people being Allomancers is nCr(100,16)*(16/100)^16 * (84/100)^84 = 10.8%. If we take this to a larger group, of say 1000 people, the chances of exactly 160 of them being Allomancers is nCr(1000,160) * (16/100)^160 * (84/100)^840 = 3.4%. So therefore, like Elend commented, it was very strange that they were getting EXACTLY 16% to the person.

So I'm thinking that since part of Preservation is inside of everyone, everyone has the potential to be an Allomancer by mist snapping, but only some people, through inheritance, can be "natural" Allomancers. The mists just pick 16% of a given group who goes out into the mists together and snap them, whether these be the 16% with the largest preservation to ruin ratio, or if it's just completely random, I don't know.

But then there's the problem of Sazed's comment, I forget where in the book, that noblemen are all unaffected by the mist... So how does that fit in...?

I am still lost as to how the jump from 1/16 of the worlds population are able to become allomancers to everyone has a 1/16 chance of becoming an allomancer works. Those don't seem to be the same thing to me. Also could you explain where my analogy with the marbles was wrong? I think I worked that math out right but am unsure.

In any case according to the annotations people are either born with the ability or not. 1/16 of Skaa were unsnapped allomancers. He makes the point that most these traits were buried to deeply for anything but the mists to bring them out. This is in the annotations and is cannon so I imagine the math would have to work out with that fact somehow. Brandon is usually careful about that kind of thing.

[ulyssessword]

I am still lost as to how the jump from 1/16 of the worlds population are able to become allomancers to everyone has a 1/16 chance of becoming an allomancer works. Those don't seem to be the same thing to me. Also could you explain where my analogy with the marbles was wrong? I think I worked that math out right but am unsure.

I always assumed that 100% of the population could become allomancers, but only 16% did, and I don't think that it is directly contradicted anywhere.

As for the marbles vs. coins, in order for the "marbles" system to work, it would need to be a significant part of the population. I believe that the largest groups we saw were in the tens of thousands out of millions of people. The marbles example tends to correct for any deviation by warping probability in to maintain a certain level.

Also, it is 16%, not 1/16.

[discipleofhoid]

I always assumed that 100% of the population could become allomancers, but only 16% did, and I don't think that it is directly contradicted anywhere.

As for the marbles vs. coins, in order for the "marbles" system to work, it would need to be a significant part of the population. I believe that the largest groups we saw were in the tens of thousands out of millions of people. The marbles example tends to correct for any deviation by warping probability in to maintain a certain level.

Also, it is 16%, not 1/16.

Don't know why I had the 1 in 16 stuck in my head, it is 16%. And rereading it this does happen with groups of 100 as well as the large groups. Huh.

In any case the part about not everyone being able to become allomancers comes from the following annotation(italics added):

What is going on here is that the mists are awakening the Allomantic potential inside of people. It’s very rough on a person for that to come out, and can cause death. Preservation set this all up before he gave his consciousness to imprison Ruin, so it’s not a perfect system. It’s like a machine left behind by its creator. The catalyst is the return of the power to the Well of Ascension. As soon as that power becomes full, it sets the mists to begin Snapping those who have the potential for Allomancy buried within them.

Many of these people won’t be very strong Allomancers. Their abilities were buried too deeply to have come out without the mists’ intervention. Others will have a more typical level of power; they might have Snapped earlier, had they gone through enough anguish to bring the power out.

My idea on this is that Allomantic potential is a little like a supersaturated solution. You can suspend a great deal of something like sugar in a liquid when it is hot, then cool it down and the sugar remains suspended. Drop one bit of sugar in there as a catalyst, however, and the rest will fall out as a precipitate.

And you know rereading that never mind I could use that to support either way of looking at the subject.

Edited November 10, 2011 by discipleofhoid

[NinjaMeTimbers]

I am still lost as to how the jump from 1/16 of the worlds population are able to become allomancers to everyone has a 1/16 chance of becoming an allomancer works. Those don't seem to be the same thing to me. Also could you explain where my analogy with the marbles was wrong? I think I worked that math out right but am unsure.

In any case according to the annotations people are either born with the ability or not. 1/16 of Skaa were unsnapped allomancers. He makes the point that most these traits were buried to deeply for anything but the mists to bring them out. This is in the annotations and is cannon so I imagine the math would have to work out with that fact somehow. Brandon is usually careful about that kind of thing.

If 16% of the worlds population had the potential to become an Allomancer, and you picked one person at complete random, there would be a 16/100 chance that the person you chose had the potential to be an Allomancer. It's not that everyone personally has a 16/100 chance, it's that you have a 16/100 chance of picking a potential Allomancer if you picked someone at random. Since the groups that went into the mist were completely random from the standpoint of Allomantic potential, this would hold for them. The rest of the formula is just a binomial probability formula that you can read about here: http://mathbits.com/mathbits/tisection/statistics2/binomialatmost.htm

But basically, even if you only had a group of 100 people picked at random who went out into the mist, if only 16% of the worlds population could become Allomancers, then the chances that exactly 16 snapped would be at about 10%. So it's already low there, and it just continues to get lower the bigger your group. Which means that inheritance cannot be a valid solution.

[DariusJenai]

I asked Brandon about this at his Eagle Eye Books signing during Dragon*Con 2010. (Although you worded it much better than I did at the time.)

Hmm, I was at D*C 2010. I don't remember that question, although I'm glad to hear it. It's been bugging me since I finished the series.

[darniil]

Hmm, I was at D*C 2010. I don't remember that question, although I'm glad to hear it. It's been bugging me since I finished the series.

This was at Eagle Eye Books, very offsite from the con. http://g.co/maps/6aua5 He was doing a WoK signing there on Sunday of that weekend. I asked him that after his talk, when he was signing books.

[DariusJenai]

Ah, I just got him to sign my copy at the con, so I didn't go to the off-site signing.

[happyman]

discipleofhoid: You are making a mathematical mistake, but it's remarkably subtle. Others have explained it here as well, and done so correctly, but I thought I'd give it a shot as well.

To be rigorous, let's define things carefully. We have two competing hypothesis in this thread. They are:

1. Of the entire population of Scandriel, 16%, chosen randomly and essentially independently and at birth, were potential Allomancers. These are the people the mists snapped.
   
2. Every person on Scandrial was a potential Allomancer, albeit often very weakly. When a group was found by the mists, the mists chose 16% (or as close as they could get) to snap.
   

Which one of these hypothesis is correct?

The remarkable answer is that the second one is far, far better supported than the first. The reason is, mathematically, in what is known as the second moments of the distribution. Basically, both hypothesis state that if you took a large number of people, 16% of them on average would snap. So far so good. However, it is also simple to calculate that for the first hypothesis, the deviation from the average, for any specific group, is also a known distribution. In fact, if the size of the sample (number of people) grows as N, the size of the deviation from the average grows as the square root of N. The percentage of the population that is affected goes as 1 divided by the square root of N, and this last fact is the reason the law of large numbers works. By the second hypothesis, however, the deviation from 16% for each sample in absolute numbers should consistently be as small as possible.

It is this second effect that the book describes. Every group, no matter how large or how small, had 16% of the people (or as close to it as rounding would allow) snap. If hypothesis 1 had been true, it would have been unremarkable; the scribes would have said "Looks like about 15.79% of the population is vulnerable. Huh." But hypothesis 1 is ridiculously unlikely; the technical details are dull and complex, and I'm not inclined to do them just to get an obscenely small number. But it's true.

[NinjaMeTimbers]

So now where does Sazed's remark that nobles are unaffected by the mists come in...? And I think there might've been something about Terrismen not being affected either...

[Wispsy]

So now where does Sazed's remark that nobles are unaffected by the mists come in...? And I think there might've been something about Terrismen not being affected either...

Ye I think when whoever it is that goes to meet the terris people in the pits hears they haven't been affected, but then they have spent a long time having feruchemy bred out of them and were the least likely to gain hereditary lines of allomancy

Can't remember about nobles

[happyman]

So now where does Sazed's remark that nobles are unaffected by the mists come in...? And I think there might've been something about Terrismen not being affected either...

Apparently you can't snap more than once. Anyone who had been tried and hadn't snapped wasn't even considered by the mists, apparently. Once you had been out in the mists and nothing had happened, you could go out in them without trouble for the rest of your life. If you had been nobility and beaten into submission to point where you would have snapped if you could have, the mists apparently didn't even try. I don't know why. Maybe you did snap, but didn't have any actual powers?