Relative Power and Weakening from Lerasium

[The One Who Connects he/him]

Forewarning... this thread serves multiple purposes. (Unless I get persuaded to split them up later, you never know)

As anyone who took an interest in the mechanics of Allomancy would know, someone who burns Lerasium becomes a powerful Mistborn. But that power weakens across the generations up to a point. This point, at which average Allomantic power will not get any weaker, has been reached by Era 2. This thread is designed to serve both as a chart comparing the relative power of Allomancers over the generations, and as a mathematical discussion of the weakening of average Allomantic power as it drifts away from Lerasium.

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Maths Tab

Originally, I speculated that the power loss between generations was a steady, even decline each generation. This presented several problems, and one of them led to that equation (y=mx+b) being scrapped. The issue with that equation is that the decline does not stop and level out like it has on Scadrial. Now, I am considering an exponential decay equation, as the slope will even out eventually. If someone has a different base formula that works as well, please suggest it.

Now, onto the other important markers on the final graph. As the power weakens over the generations, it seemed logical to figure out how many generations had passed from Lerasium to Wax/Wayne. The Lord Ruler died in 1022 FE. I assumed he needed a year to set everything up and select the original Allomancers after using the Well. The Empire fell a year before the Well refilled (1024 total), hence 1022 yrs of Final Empire. Sazed ascends shortly after Vin's death in 1025 FE. Assuming that since Wax is part of the weakest generation, we only need the time gap to his birth date, which is 299 PC. This makes the total time-gap from Lerasium to Wax roughly 1324 years.

I leave people to theorize while I read up on exponential decay and come up with an equation that I can easily explain and/or understand.

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Power Level Chart

To be added, formatted and updated later

Base Rules for now:

• Era 1(Vin) is stronger than Era 2(Wax/Wayne)
• Era 2 Flaring may be stronger than Era 1 Baseline
• Duralumin Burn beats Lerasium Baseline (Elend)
• Elend with Duralumin is more or less The Lord Ruler Baseline
• Both a Spiked individual and a Savant can pierce a Coppercloud, while Flaring cannot.

Assumptions: (Until Brandon says yes or no on the subject)

• Savant Baseline is stronger than Flaring (hasn't been expressly confirmed yet)
• Mist-Fueled Elend/Marsh equates to Mistpoint
• Mistpoint is the strongest that an Allomancer can be

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Source Tab

Since I cannot use superscript, things that are sourced to a WoB will have the number in parentheses.

Spoiler

1. Weakening from Lerasium

Quote

Question

Mistings got weaker since Lerasium; will it continue to get weaker?

Brandon Sanderson

They’re pretty much at the point where it’s as weak as it’s gonna get.

2. Baseline vs Flaring, Lack of Proper Canonization

Quote

Question

Question about Feruchemy and Allomancy… what does it take to match Allomantic pewter?

Brandon Sanderson

He imagines that baseline pewter doubles strength, flaring triples. He wouldn’t imagine someone burning pewter and lifting a car. Hasn’t thought about speed and healing. He’s admitting he hasn’t canonized these things.

3. Elend vs TLR Soothing, Max Savant Strength

Quote

BRANDON SANDERSON (paraphrased)

I continued to ask about the Lord Ruler and his Allomantic strength. There's an upper bound to the amount of power you can get from being a savant. Brandon said that, obviously, the Lord Ruler wasn't using duralumin and Elend could only get that powerful in Soothing using duralumin.

4. Savanthood and Copperclouds

Quote

Brandon Sanderson

That’s the scale of what we call savant. Wax can do more with less. It’s not just skill, the burning for long, using for so long, will actually adapt your soul to the power.

Question

So can bronze savants pierce Copperclouds?

Brandon Sanderson

Yes, a bronze savant should be able to pierce Copperclouds. It depends on the strengths of the Coppercloud and the strength of the savant, but yes.

5. Going from a Burn to a Flare

Quote

Question

Is the level of burning [in Allomancy] a continuous distribution, can I burn 0.1 level of steel all the way up to flaring? Or is it just I burn or I flare?

Brandon Sanderson

The more skilled you are, the more you have the ability to moderate that. For most people it is burn or flare. But you can kind of burn up to a flare, does that make sense? Going below is really hard.

Question

Can you push a flare?

Brandon Sanderson

Yes.

 

Final Notes

• Credit goes to Robardin for creating the original list that spawned this idea.
• I'm sorry Jondesu, but they're still just called Power levels for now.

[Oversleep]

This ain't so simple. See:

Allomancers are routinely slaughtered so it would weaken the blood overall.

[The One Who Connects he/him]

18 hours ago, Oversleep said:

This ain't so simple. See: [Link]

Allomancers are routinely slaughtered so it would weaken the blood overall.

Despite having participated in that topic in the past, I had forgotten that point. It would put a slight damper on the whole natural decay concept, but that's how life works. It.. could still work out smoothly, but it would either need a lot of assumptions, or take a lot of questions just to satisfy my own curiosity.

The general concept that the maths tab was based on is that as a "natural" system, Allomancy would, over time, try to revert back to its natural pre-Lerasium state. As an assumption, it implies that Wax/Wayne's era is largely similar in Allomantic strength to Alendi's time. Regardless of the man-made bumps it took along the way, that should still hold, if a bit quicker than letting nature take its course. Does that assumption seem reasonable to you?

Either way, I apologize for not being as clear in the starting post. Proofreading is apparently not my strong point

[dgenio8]

In the math department, you need to take into account some population genetics theory instead of simple exponential decay. Unless you assume the power wants to get weaker every generation, what is happening is that allomancy is a multigenetic phenotype (trait) with multiple positions in the genome being important for it. As most of the population does not have it, most couple with allomancer will be of allomancer and non-allomancer... Given recombination in the genome, the number o allomantic alleles decrease in each progeny.

Now, assuming no advantage of being allomancer (or even slighter disadvantage as some will be killed), the expectation is that the power will be diluted. I can try to post some formulas for it later

 

Sorry if I have been to technical, I can explain better latter.

[The One Who Connects he/him]

1 hour ago, dgenio8 said:

Unless you assume the power wants to get weaker every generation, what is happening is that Allomancy is a multigenetic phenotype (trait) with multiple positions in the genome being important for it.

It's.. kind of a mix actually. I implied that the Lerasium's "boost" was an unnatural input in the system, and the system is trying to rectify itself. I based this upon the fact that the reappearance of Mistings only happened after about 300 years into the Final Empire. (I cannot remember where I heard this from) But I'm not too surprised that it had a genetic component, but as that would be almost impossible to easily keep track of, I want to avoid involving it too heavily unless necessary.

My choice of exponential decay is because the parent function graphs out nicely with the few limits that were known at the time. Polygene and QTL is a bit beyond freshman year biology, but it can't hurt to learn. I swear I'm gonna get a degree just off of what I have to learn about different subjects.

1 hour ago, dgenio8 said:

Sorry if I have been to technical, I can explain better latter.

It's no problem, gives me things to learn about. If you want to explain your idea in more detail, by all means do so.

[QuantumSpren]

Remember that in southern Scadrial allomancy seems much rarer.

[The One Who Connects he/him]

1 minute ago, QuantumSpren said:

Remember that in southern Scadrial Allomancy seems much rarer.

Indeed it is. Brandon has said that due to the lack of Lerasium input, Mistings are rarer, and Mistborn almost unheard of. In my opinion, the prevalence of Mistings/Twinborn in the Elendel Basin is largely due to Mistborn Spook having over a dozen children. He/they helped keep the Allomancy genes more prevalent.

[QuantumSpren]

Just now, The One Who Connects said:

Indeed it is. Brandon has said that due to the lack of Lerasium input, Mistings are rarer, and Mistborn almost unheard of. In my opinion, the prevalence of Mistings/Twinborn in the Elendel Basin is largely due to Mistborn Spook having over a dozen children. He/they helped keep the Allomancy genes more prevalent.

I hadn't thought about that, that would make a lot of sense.

[Oversleep]

Don't credit Spook so much - Elendel is counting now... I'm not sure... 5 million people? That's 340 years since Katacendre, I doubt Spook's heritage could significantly influence population like that.

[Spoolofwhool]

56 minutes ago, Oversleep said:

Don't credit Spook so much - Elendel is counting now... I'm not sure... 5 million people? That's 340 years since Katacendre, I doubt Spook's heritage could significantly influence population like that.

True. Still, it's mainly the noble families which trace to him, so they're probably the ones who feel his heritage the most, as noted by Wax in AoL.

 

[The One Who Connects he/him]

27 minutes ago, Oversleep said:

Don't credit Spook so much - Elendel is counting now... I'm not sure... 5 million people? That's 340 years since Catacendre, I doubt Spook's heritage could significantly influence population like that.

I don't mean to imply that he is the sole source, but having a Mistborn with 12 kids is a good starting place. On the subject of 5 million people however, I noticed that the Elendel map is measured in miles. It is about 7.5 "mile squares" across. A circle with a diameter of 7.5 miles has an area of 44.178 square miles. That means that the city has an area of roughly 44 sq mi, counting the canals and the Field of Rebirth. A city that small cannot easily have a population that large without quite tall buildings.

5,000,000 people / 44.178 sq mi = 113,178.5 people per square mile

For reference, Manhattan had an estimated population density of 72,033.2 in 2015, and Manhattan is a vastly different city than Elendel. If Elendel could manage with the same population density, it would have a population of roughly 3.182 million people. It would still be a lot of people for Spook's bloodline to have any meaningful effect on, but anything is possible.

[Savanorn he/him]

Hold on, presuming Spook to be noble, and presuming nobles prefer to breed amongst themselves (as was historical) it's also possible his blood could be effecting two different populations differently; the greater Elendel/basin and the noble houses. Do we know if nobles as of Era 2 are notably more likely to be Allomancers? Or was this lost post catacendre due to crossbreeding?  

 

 

[dgenio8]

I don't think we need to assume Spook has many children, or that the nobles tend to breed amongst themselves (although I would argue that is probably the case). Even if Spook is the only Mistborn alive after the Katacendre, other Mistings have survived.

Now, the genetics part. This might sound pedantic for the ones with the a Biology degree, but I guess some of you don't have it so to put everyone in the same level fro this discussion:

- Some traits, like your height, are not defined by one gene. They have many genes interacting to define how tall you are (for more details search fro QTLs). A simplistic way to imagining it is to think of only ones and zeros. If each gene can only be a one or a zero, you would sum up  the number for all the genes and get a value that is then linearly related with your height. On top of that, instead of 1s and 0s the genes could have any number in between, which would increase a lot the possibilities.

- Human are diploid, which means we have two copies of each gene, one from the mother and one from the father. However, remember that the parents are diploid also, so they have two copies. If one has  a copy with all the good genes and another with bad genes, you don't get either one or the other (my life would be so simpler...). Because we have a process called recombination, we you're parent's gametes (sperm and ovule) are generated the DNA from their two copies get entangled and mix. In this way every gamete is unique because it get's not only just one copy of you parent's DNA (in a process called meiosis) but also the combination of genes in this gamete did not necessarily existed in you parent's copies.

- On top of all that theirs mutation and selection...

Now, let's assume Allomancy is genetic, with a large set of genes been related to it. A Mistborn would have all the Allomantic genes on the best configuration possible. Now, for some wild theory... The difference between Mistborns and Mistings would be like a threshold thing... If you have enough on the genes in good enough configurations you're a Mistborn, otherwise you are a Misting. The type of Misting, on the other hand, is harder... Do we have evidence for Coinshots to have Coinshots kids? If not, maybe that's the part that is not genetic (magic ).

After the Katacendre, several individuals with Allomancy survived (Spook and all the other Mistings/Mistborns). They started as a very small population and it expands, so the contribution of this initial pool of Allomancer's is very important. They did not breed with complete outsiders, and I believed that even the non-Allomantic people would have some good Allomantic genes.

Besides all that, the time since the Katacendre was small. 340 years means roughly 9 human generations... Without any pressure, is normal that the Allomantic power is still very present...

[Oversleep]

2 hours ago, dgenio8 said:

he type of Misting, on the other hand, is harder... Do we have evidence for Coinshots to have Coinshots kids? If not, maybe that's the part that is not genetic (magic ).

IIRC there is a WoB that the type of Misting is kind of random, so you don't get a line of Coinshots or Soothers.

[The One Who Connects he/him]

4 hours ago, dgenio8 said:

Now, let's assume Allomancy is genetic, with a large set of genes been related to it. A Mistborn would have all the Allomantic genes on the best configuration possible. Now, for some wild theory... The difference between Mistborn and Mistings would be like a threshold thing... If you have enough on the genes in good enough configurations you're a Mistborn, otherwise you are a Misting. The type of Misting, on the other hand, is harder... Do we have evidence for Coinshots to have Coinshots kids? If not, maybe that's the part that is not genetic (magic ).

Quoth Brandon, Misting type is determined at birth. I believe it is still largely random as Oversleep says, otherwise the Era 1 Nobility's political habit of hiding who had what powers would seem somewhat out of place if they knew. On a side note, I'm looking into combination and permutation again because genetic recombination is a bit beyond me for now

[cometaryorbit]

On 1/11/2017 at 8:27 PM, Oversleep said:

Don't credit Spook so much - Elendel is counting now... I'm not sure... 5 million people? That's 340 years since Katacendre, I doubt Spook's heritage could significantly influence population like that.

Depends how many kids they tended to have, and how bad infant mortality is/was on Scadrial. I'd assume given the generally Edenic environment, disease is pretty rare, so it's probably quite low. (Hmmm... given Sazed altering the population, I wonder if Scadrians have no genetic disorders?)

On the other hand, if infant mortality was that low, I'd expect a much larger population - especially since generation times seem short.

Wax is 16th Lord Ladrian; Breeze was 1st, so 15 generations.

Spook had 'over a dozen children'. Say 15. If each generation had 3 surviving children on average, there would be "just" ~6570 direct descendants of Spook in the 15th generation, but if it was 4 (doubling each generation) then ~491,500 - almost 1/20 of the world's population. And that's not including people in the immediately older & younger generations.

[cometaryorbit]

On 1/12/2017 at 4:07 AM, dgenio8 said:

Besides all that, the time since the Katacendre was small. 340 years means roughly 9 human generations... Without any pressure, is normal that the Allomantic power is still very present...

The 15 generations between Breeze and Wax does seem like a lot, but 9 in 340 years implies a generation time of ~38 years. That's really high, especially in a lower tech culture; it would take very unusual circumstances to get that in a human population, and I don't think you could get that high in a growing population, barring really advanced medical technology or magic to extend fertility into later years. 25-30 seems more likely, which would imply ~11-14 generations in 340 years.

[cometaryorbit]

On 1/11/2017 at 9:40 PM, The One Who Connects said:

A city that small cannot easily have a population that large without quite tall buildings.

5,000,000 people / 44.178 sq mi = 113,178.5 people per square mile

Ancient Rome supposedly had a higher population density than that (I've seen 125,000/square mile quoted, based on a population of 1 million and 8 square miles in the city itself - those are probably rounded numbers though). The Romans had multi-story buildings - at one point tenement heights were limited by law to 70 feet, so they had the technology to build at least that high - but not as good as Elendel's.

[The One Who Connects he/him]

17 hours ago, cometaryorbit said:

Wax is 16th Lord Ladrian; Breeze was 1st, so 15 generations.

Thank you for this little snippet. No idea how I missed this before, but that may very well make dgenio8's population genetics concept easier for me to handle.

17 hours ago, cometaryorbit said:

Ancient Rome supposedly had a higher population density than that (I've seen 125,000/square mile quoted, based on a population of 1 million and 8 square miles in the city itself - those are probably rounded numbers though). The Romans had multi-story buildings - at one point tenement heights were limited by law to 70 feet, so they had the technology to build at least that high - but not as good as Elendel's.

I decided to look into this. r/AskHistorians has a fascinating collection of info on the subject. It appears that I have underestimated both Rome and Elendel.