Canticle Sunheart Utilization Rate vs Birthrate?

[Duxredux]

Something I've been wondering that I'm sure the Dragonsteel team considered is what is the actual birthrate compared to power usage needed to sustain Beacon and Union? A day on Canticle is about 10 standard hours. Rebeke's mother sacrificed herself I think in the last cycle or two and they barely had enough juice to do one more cycle before they were out of power. That means that had what, 30-40 hours max from their last new Sunheart to their city of less than 135 people to run out of juice? If we assume that 1 Sunheart can sustain a population of 150 people for 40 hours, that means that they would need... 219 Sunhearts to last a year.  How in the world do they have geriatrics who have lived their whole lives on Canticle? Some basic math taken from Coppermind measurements:

1 Sunheart is at least 200 BEUs.

1 Canticle day = 10 hours.

Assuming traveling approximately at ground level at the perimeter (which we know they aren't, but this makes the math simple) 1 day = 628 miles traveled

Average human gestation period = 672 Canticle days (422,230 miles traveled)

Early female age of fertility (12-18 years old, yes there's earlier cases but even 12 seems really young for most societies and especially for this brand of Threnodite prudishness) = 10512  to 15768 Canticle days (6,604,884 to 9,907,327 miles traveled)

The Sunheart utilization rate at least defines the minimum death rate to sustain the cities, and we know that Union at least generally takes up the equator and so will take the longest route to circumnavigate the planet. I'm not quite sure where to look for a baseline to calculate the death rate, or power expenditure to fly a city that far, but that still seems pretty high. 

I'm assuming the overall population of Canticle is at a sustainable level or that it isn't dramatically decreasing, otherwise I'm not sure if The Cinder King would have the luxury to blow Sunhearts on making Charred. So a few options: the power consumption is with the necessary bounds to not significantly increase the death rate (which says something about how much 200 BEUs worth of Investiture can get you and let you travel) or it implies that their birth rate can match the death rate. There doesn't seem to be any specific protection of women in childbearing years which I think is necessary for any population faced with a high death rate. So... what do we think is going on here? A few ideas and options, though it won't be an exhaustive list.

 

• My first thought is that perhaps the Threnodites of Canticle have the same accelerated growth cycle experience by the plants - though not sure how that works on a cognitive level, nor why the Investiture necessary to produce that kind of mass gain doesn't also sustain their dietary needs. That doesn't explain their perception of Nomad's age though, but it could explain that they actually have an accelerated birth rate that can balance the death rate.
• 200 BEUs is a lot of power and Beacon is grossly oversized, but that doesn't seem that likely.
• They have alternative power sources, but I don't think I saw anything that implied anything that could supplement the Sunhearts enough to cover the power demands.
• Union can't support itself, The Cinder King is trading for power in addition to his other toys. Not sure how this worked before the Scadrians showed up (assuming the Threnodites were here first).

Thoughts? A look at this seems like it will either reveal something weird with the birth rate or how much power the Sunhearts are actually supplying as a look at how much 200+ BEUs will get you.

[A Simple Pilgrim]

The numbers don't make sense on the face of it: Beacon had 50 ships with 150 people on them. Every ship needs a sun heart to keep going. A group of 150 people would struggle to have more than 4-5 children per year. Let's assume the population is stable, not growing or decreasing, so 5 deaths per year. Let's say all 5 get turned into sun hearts. 

Some basic math later and, you get that each sun heart has to last 10 years in order to keep beacon running as it is. The text instead makes it sound like they only last months. If every sun heart lasts 3 months, then they need 200* sunhearts a year to keep beacon running. That is obviously impossible on a population of 150. 

The only way to reconcile this is that beacon hasn't been regenerating sunhearts for years during their situation with the cinder king, or that they had lost many sun hearts in the process of opposing him. Then they instead of dropping ships to conserve energy, spread the energy of their remaining sun hearts through everything in order to keep it running, and that's why they ran out of power all at the same time. The 200 BEU sun heart they gave Nomad was actually already heavily drained, not anywhere near full. 

One of the only things that support this interpretation is that the Charred creation spear, which Nomad I believe thought had about 2000 BEU in it. As charred are made from modified sun hearts, that means a new floor could be put at 2000 BEU, and the one that Nomad had was only at 10% capacity. If you want to be extra about I you can even assume that the modification process makes the sunheart lose some energy, and thus a normal sunheart holds thousands of BEU. The few hundred on the depleted ones that beacon had left would only last a few months, but a normal full one could last a decade. 

Dux, where did you find the part that Rebecca's mother had died only a few days ago. I was under the impression it was longer than that, but I could be wrong. 

Finally on the overall point, I don't think there's any indication whatsoever that Canticle had accelerated aging or birth rates. In fact as I don't even remember seeing any kids. They probably do have tons of kids though, the puritans historically rejected sex in many ways, but definitely not for reproduction. That's how the early puritan settlers had some of the highest population growth rates in the world at that time, once married women had tons of kids. We even see 'an' example of this with Rebecca having a brother and a sister at the start. Brandon's stories usually don't have that many siblings despite being set in historical periods where everyone should have like 5-6 siblings. 

 

*It's interesting that despite two different approaches to calculating how many sunhearts are needed, we came up with similar numbers. That means the impression that Brandon gave was consistent. 

[Sophrosyne]

Chiming in to mention that there was a child in there actually sever children mention int the text. a little girl points at the Night Brigade ship, she calls it a "new star", and another kid is in the arms of Contemplation when Zellion save them near the end. I only remember this cause it was odd to. Brandon hasn't mentioned kids too often in his books but he differently did in this one.

The book implies Rebeke's mom died recently but not in the last few days, She's grieving still (you never get over that though) But she talks about her mom like that was a distant thing and even the greater good, the next one to dies, aren't acting like that's imitate until they start burning lots of fuel for all the crazy plans.

[Duxredux]

On 11/5/2023 at 9:00 AM, A Simple Pilgrim said:

Dux, where did you find the part that Rebecca's mother had died only a few days ago. I was under the impression it was longer than that, but I could be wrong. 

I was lazy and didn't want to look it up. It's not a few days, but it's on the scale of weeks, not months. She died 2 weeks previous to Rebeke picking up Nomad.

Spoiler

"This one here," she said, resting her hand on the housing, "was my mother. Two weeks ago. We left her for the sun, then recovered her sunheart on the next rotation. Her body vaporized by the heat, her soul condensed into this stone."

Now... I'm not sure if that's 2 Earth weeks (24x14 = 336 hours) or 2 Canticle weeks (10*14 = 140 hours). That can make a bit difference, and that puts it in a range of 26 - 62 Sunhearts to sustain 135-150 people an Earth year (earth year = 24*365=8760. That's substantially better, but that's still between 17% - 46% of the population needing to be replaced every year to maintain equilibrium, assuming that Sunheart conversion account for 100% of the deaths on Canticle. That's better than 146% replacement rate, and much more plausible, but still...

To maximize the utilization of a single Sunheart then we would assume that Rebeke's mother was the only person sacrificed 2 weeks previous to their 10-20 hours of running out of power. However the sunheart from Rebeke's mother is powering her personal cycle, it's not powering the rest of the Beacon ships. How many people did they have to sacrifice to get less than 3 weeks of power? I assume that if it came to it, they would slot Rebeke's mother's sunheart into the rest of the Beacon ships, so I think the maximum runtime that a sunheart can produce is still given by this 2-3 week window for all of Beacon. The rest of their historical stores don't really matter, it's the time from their last refueling with brand new sunheart(s) to running out of power for the population they're sustaining. Adding any sunhearts to the equation just reduces the efficiency of each sunheart and correspondingly increases the necessary death rate. 

On 11/5/2023 at 9:00 AM, A Simple Pilgrim said:

Brandon's stories usually don't have that many siblings despite being set in historical periods where everyone should have like 5-6 siblings. 

I think the justification for this is that Cosmere humans often have innate Investiture and so have less diseases and lower mortality rates. The Demographic Transition Model (DTM) is based on birth rates and death rates:

1. DTM 1 is characterized by high birth rates and high death rates. Population growth is low.
2. DTM 2 is characterized by high birth rates and decreasing death rates. Population growth is high.
3. DTM 3 is characterized by decreasing birth rates and low death rates. Population growth is slows.
4. DTM 4 is characterized by low birth rates and low death rates. Population stabilizes and growth nears zero as the land approaches carrying capacity.

Generally advances in medicine and technology kick off DTM 2 and 3 as death rates are reduced as food production increases with technology and medical and sanitation practices reduce mortality rates. The Cosmere breaks this as death rates for diseases are lower by nature of humanity's innate Investiture making them hardier and faster healing. It breaks it even more when people have magic that utterly upend earth technology development rates, like Roshar having access to Soulcasters after the various desolations. DTM 2 and 3 are colonial periods where people are still having high birth rates to counteract the death rate and it takes overcrowding and saturation of the local land's carrying capacity for birth rates to start to decrease. In other words, the high birth rate we expect in a colonial historical period on is not to sustain colonization, the high birth rate is a carry over from when death rates were so high and more and more hands were needed to sustain life. Cosmere worlds naturally have lower death rates, so the birth rates may not be at a preexisting high state to kick off colonization at a rate that was seen on Earth, despite in many ways mirroring historical Earth time periods. 

 

At any rate, Canticle still seems unsustainable without something going on. Innate resistance to disease provides zero reduction to death rate by solar immolation, so I would expect the birth rate to be at least as high as the death rate prior to discovering that sunhearts could be recharged. If that's the case, I would expect more social pressure to protect those capable of childrearing.