I recently read through Alma 2, but didn’t get very far when I ran into verse 19.
"And it came to pass that the Nephites did pursue the Amlicites all that day, and did slay them with much slaughter, insomuch that there were slain of the Amlicites twelve thousand five hundred thirty and two souls; and there were slain of the Nephites six thousand five hundred sixty and two souls."
Normally I would have read Alma 2:19 without much interest. If you read the Book of Mormon like I do, your brain skips of the words with numbers in them to the more interesting parts. This time, I wrote the number down. 19,094 people died meant a lot more to me than there were slain of the Amlicites twelve thousand five hundred thirty and two souls; and there were slain of the Nephites six thousand five hundred sixty and two souls.
That’s a lot of people. Then I wondered what percentage of Nephites that could be. How big is the typical Nephite capital in your mind? Is there a way to estimate the population of Zarahemla before the war?
It turns out there is a way. My numbers suggest Zarahemla had a population between 80,000 and 150,000 in 86 B.C.
Disclaimer: If you're not into math, this will get very boring very fast and I’d suggest skipping to the So What? section.
Here’s the word problem:
The year is 86 B.C. Alma the Younger, Chief Judge in Zarahemla, is challenged in an open election by a dude desiring to be king, Amlici. The people vote and Amlici loses. Those who voted for Amlici get together and crown him king of the Amlicites. His first order of business is to kill those who didn't vote for him. War ensues. After 12,532 Amlicites and 6,562 Nephites are killed in the battle, the Amlicites retreat. Given the above, estimate the population of Zarahemla before the Amlicite war.
In order to make the math possible, I've made the following assumptions.
- Only men and every man voted in the election of 86 BC.
- Only men and every man from Zarahemla fought in the war.
- Only men are included in the numbers of the dead given in Alma 2:19
- There are as many women as men in pre-war Zarahemla.
- Every woman is married, and W% of men are married
- Every married man has C number of children.
Variables and Likely Bounds
A subscript of i means initial value (prewar) and f means final value (postwar)
Ni = initial population of Nephites
Nf = Ni - 6562 = post war population of the Nephites
Ai = population of Amlicites before the war
Af = Ai - 12532 = post war population of Amlicites
D = total number of dead = 12,532 + 6,562 = 19,094
Mi = initial male population of Zarahemla
Mf = post war male population of Zarahemla = initial population minus those that died = Mi - D
Ri = Ni / Ai = the ratio of Nephites to Amlicites before the war. Given my assumptions, Ni is the number who vote against Amlici. A is the number that votes for Amlici. Given my assumptions, Ri to be greater than 1 since the Nephites won the election. In other words, just one vote in favor of the Nephites to tip a 50/50 election. We also know that R has to be small enough that the Amlicites think they can win a war. So, if the election had gone 75/25 for the Nephites, the Amlicites probably wouldn't have picked a fight. I think the highest R could be is 1.5, or 60/40. I don't think they'd pick a fight against the Nephites if there were more than three Nephites for every two Amlicites. So, 1 < Ri < 1.5.
Rf = Nf / Af = The number of Nephites per Amlicite at the moment the Amlicites retreat (Alma 2:18). How many enemies per soldier will cause an army to retreat? My guess is at least 2, but maybe as many as 4. So, 2 < Rf <4.
W = percentage of men in Zarahemla who are married. The number of women in Zarahemla would then be M * W. \
C = number of non-fighting children per married Nephite or Amlicite male. Does 2.5 kids per married family make sense?
Z = total pre-war population = Men + Women + Children
Z = Mi + Mi*W + Mi*W*C = [W*(C+1)+1] * Mi
The Algebra
Mi = Ai + Ni
and
Ri = Ni / Ai
so
Mi = Ai + (Ai *Ri ) = Ai*(Ri +1)
Do the same algebra for Mf
Mf = Af + (Af *Rf ) = Af*(Rf + 1)
There are now two equations for Mf - Mi.
Mf - Mi = D
Mf - Mi = [Af*(Rf + 1)] - [Ai*(Ri +1)]
Set them equal to each other
D = [Af*(Rf + 1)] - [Ai*(Ri +1)]
Af can be put in terms of Ai (Af = Ai - 12,532), so substitute it.
[(Ai -12,532)*(Rf +1)] - [Ai *(Ri +1)] = D
Put in 19,094 for D:
[(Ai -12,532)*(Rf +1)] - [Ai *(Ri +1)] = 19,094
Multiply out and simplify, solving for Ai:
[Ai*Rf+Ai*1 - 12,532*Rf - 12,532*1] - [Ai*Ri + Ai] = 19,094
Ai*Rf + Ai - 12,532*Rf - 12,532 - Ai*Ri - Ai = 19,094
Ai*Rf + Ai - Ai*Ri - Ai = 19094 + 12,532*Rf + 12,532
Ai * (Rf + 1 - Ri -1) = 12,532*RF + 31,626
Ai= (12,532*Rf+ 31,626) / (Rf - Ri)
Expand the equation for total pre-war population (Z):
Z = [W*(C+1)+1] * Mi
Z = [W*(C+1)+1] * (Ri +1) * Ai
Z = [W*(C+1)+1] * (Ri +1) * (12,532*Rf+ 31,626) / (Rf - Ri)
Plug the final equation for Z into a spreadsheet, and voila! You’ve got yourself an estimated population.
So What?
Apart from illustrating that some of us like to play with numbers and spreadsheets more than others, what does the above tell us? Why does it matter what the population was?
The answer is that it gives us a hint of context. The scriptures are full of context clues that casual reading misses. When Alma later takes some missionaries of to Antionum to visit the Zoramites, he lists off a few friends whose names I always used to skip over. If you look at who he’s talking about in chapter 31, you realize Alma is opening up the Antionum Zone with a powerhouse of super-missionaries. Glazing over the context means the story is not as rich.
The context clue verse 19 gives is that Zarahemla was a big place. In my mind, I always assumed the cities in the Book of Mormon were small, agrarian villages with some minor institutions in place. A pre-electricity population of 100k in a city means we’re dealing with much more than a mesoamerican Boonyville. Complex economic, political, and social systems would have been required to keep Zarahemla running smoothly. This is the city Alma the Younger is running as chief judge. The four sons of Mosiah turned down a kingship of Zarahemla in favor of a 14 year mission to their hostile enemies. The size of Zarahemla matters because the city is a character in many of the stories in the middle of the Book of Mormon. Missing the context means we miss some of the richness of those stories.