The Interpreter; Bayes Theorem; Nephites and Mayans

[_Lemmie]

How does a person tell the difference between being skeptical a million to one vs a billion to one? That difference matters in sophistry not decision making. Somewhere in between two minor pieces of evidence lies the entire range of realistic human doubt and certainty.

Well said, Gadianton, well said. There is ample use for mathematical analysis, but there is an all too human reason for the book title, "Lies, Damn Lies, and Statistics."

[_Physics Guy]

Well said, Gadianton, well said.

Yeah, my reaction above lacked warmth. That last post by Gadianton is probably the most important thing anyone has said in this thread.

[_Lemmie]

One of the authors replying to honorentheos:

Brian Dale
on May 17, 2019 at 7:56 pm said:

Hi Honorentheos,

You said “To continue by using the language analogy, it doesn’t make sense to cap the likelihood an authentic Mayan would describe the language they spoke as Hebrew at 1 in 50.” It is interesting that you choose to object to the likelihood cap. It was a deliberate decision on my part to discretize the allowable likelihoods (for simplicity) and limit the maximum allowable to 50.

The purpose of the limit was actually to avoid “running up the score” too much on the credulous side. In other words, a cap on the maximum allowable strength of any one piece of evidence is beneficial to the prior as it effectively “decelerates” the amount that the evidence can change our beliefs. Since the prior was highly skeptical, the cap benefits the skeptical hypothesis.

If we remove the cap on the evidence then that would apply to the credulous evidence as well. The end result would be even worse for the skeptical hypothesis.

Oh my. I didn't think it could get any worse, but now the author is stating they chose the numerical value which they subjectively assigned to various outcomes, with the intent that the statistical effect of the data on the results would be numerically limited.

We are out of the realm of even statistics here, let alone Bayesian analysis. This is so wrong, it is not even wrong*.


*"Not even wrong" is a pejorative applied to purported scientific arguments that are perceived to be based on invalid reasoning or speculative premises that can neither be proven correct nor falsified and thus cannot be discussed in a rigorous, scientific sense.

wiki

[_Physics Guy]

with the intent that the statistical effect of the data on the results would be numerically limited.

But this is the obvious effect of a cap on LRs. It limits the possible effect of data on the results. It's explicitly saying, "We're going to pretend that knock-down disproof of our hypothesis is nothing more than a modest weight on the scale against it."

It's just a flesh wound!

It's obviously stupid but at least they realize what they're doing. That's something. Or does that just make it even worse?

I'm losing track. This is weird terrain.

[_Lemmie]

with the intent that the statistical effect of the data on the results would be numerically limited.

But this is the obvious effect of a cap on LRs. It limits the possible effect of data on the results. It's explicitly saying, "We're going to pretend that knock-down disproof of our hypothesis is nothing more than a modest weight on the scale against it."

It's just a flesh wound!

It's obviously stupid but at least they realize what they're doing. That's something. Or does that just make it even worse?

I'm losing track. This is weird terrain.

You're not kidding! Me too. Weirder and weirder.

[_Res Ipsa]

This sounds like ad hoc rationalization.

[_honorentheos]

One of the authors replying to honorentheos:

Brian Dale
on May 17, 2019 at 7:56 pm said:

Hi Honorentheos,

You said “To continue by using the language analogy, it doesn’t make sense to cap the likelihood an authentic Mayan would describe the language they spoke as Hebrew at 1 in 50.” It is interesting that you choose to object to the likelihood cap. It was a deliberate decision on my part to discretize the allowable likelihoods (for simplicity) and limit the maximum allowable to 50.

The purpose of the limit was actually to avoid “running up the score” too much on the credulous side. In other words, a cap on the maximum allowable strength of any one piece of evidence is beneficial to the prior as it effectively “decelerates” the amount that the evidence can change our beliefs. Since the prior was highly skeptical, the cap benefits the skeptical hypothesis.

If we remove the cap on the evidence then that would apply to the credulous evidence as well. The end result would be even worse for the skeptical hypothesis.

Oh my. I didn't think it could get any worse, but now the author is stating they chose the numerical value which they subjectively assigned to various outcomes, with the intent that the statistical effect of the data on the results would be numerically limited.

We are out of the realm of even statistics here, let alone Bayesian analysis. This is so wrong, it is not even wrong*.


*"Not even wrong" is a pejorative applied to purported scientific arguments that are perceived to be based on invalid reasoning or speculative premises that can neither be proven correct nor falsified and thus cannot be discussed in a rigorous, scientific sense.

wiki

Hi Lemmie -

Thanks for pointing this out. I had not gone back to check if there were replies to prior comments and it seemed like the defense of the paper wanted to focus on nitpicking the bones of old claims the Nephites fit in a Mesoamerican context. Claims I personally think beastie devastatingly took done years ago. And frankly those are boring arguments that don't add anything to the discussion. People who want to believe in the Book of Mormon are going to find reasons to believe in that theory, and those who want to find it in North America will find it there. Where they won't find it is in the broader, non-LDS archeological record but you can't convince them of that as we've seen going on decades of debate.

But in the context of this paper, I'm wondering if this leads to a chance to help illustrate what's so crazy about their approach? and I'm hoping you, Physics Guy, Water Dog, Res, Gad or whomever wouldn't mind pointing out any errors in this proposed reply before I post it over at The Interpreter?

Hi Dr. Dale,

Thank you for the response. I’m sure there is a sense on your and your father’s parts that constraining the likelihood ratios was an act of generosity. Perhaps it is, perhaps it’s just another of multiple issues with the selection and application of the methodology used. I think this may provide an opportunity to explore that question if you’re willing.

Let’s take the governor off, so to speak, and have the maths done out in the open in the comments. Perhaps for the sake of transparency we can treat this one question as one where we are interested in comparing two hypotheses. Because that's how it's supposed to be done, as you know. Anyway, hypotheses:

H1) The Book of Mormon was authored by a person or people in the 19th c. CE attempting to create a believable origin story for the Native Americans relying on common myths and beliefs of their time with limited access to reliable prehistory of the Americas.

and

H2) The Book of Mormon is the result of the translated, compiled history of multiple authors initially completed around the 4th c. CE by a person living within a Mayan culturally influenced or influencing society.

We also need to acknowledge we are working with the data set in regards to identifying the language of the Maya per your methodology. It’s a bit choppy right out of the gate for that reason given the data (D) is limited to what Coe has to say, but you did do H1 a favor of sorts: You ACTUALLY reviewed two documents that were penned in the 19th c. CE that made similar attempts to what H1 hypothesizes was the aim of the Book of Mormon. Of those (View of the Hebrews and Manuscript Found), View of the Hebrews describes the people as speaking Hebrew while the other goes for a different Old World language but not Hebrew. Given our data set, we must assume the probability for an author attempting to describe the original parents of the Native Americans speaking Hebrew is 1 in 2 or (p1)=0.5.

We could change H1 and H2 to expand the language question to those of old world origin, which would truly be running up the score against the Book of Mormon (View of the Hebrews = Hebrew; MF = Latin, Book of Mormon = Hebrew & Egyptian) if we really wanted to make Dr. Coe’s point with prejudice. It would give us a p1 of 1.0 and that would be catastrophic for your aims. But let’s stick with the Hebrew for now.

Our data set on the other side is The Maya. Does the Maya describe the Mayan peoples speaking Hebrew or provide reasonable evidence that the language they spoke has Hebrew or Egyptian roots? No. It’s speaks of Proto-Mayan with the language branch graphic showing how modern Mayan languages arose out of it but that’s it. That’s (p2)=0. No Hebrew, no Egyptian. Our data set tells us there is no instance, and therefore zero probability, of a Mayan claiming to speak Hebrew, Egyptian, or claim Mayan languages have their roots in those languages which is what the Book of Mormon claims. (And anyone who put their pen down right here is spot on in doing so.)

For those still thinking we need to do the maths and anxiously holding their pens to the ready, we’ll keep going I guess.

Lacking any outside data or objective means of determining probabilities, our p1(19th c. author claiming Old World Language) = 0.5.
Realistically, our p2(Ancient Mayan Author) = 0.0. It’s impossible that an ancient Mayan would claim to have spoken languages they never encountered or heard of and isn’t attested in our chosen data set of Coe’s book. Maybe it’s possible in the same way there is a set of infinite monkeys typing on infinite typewriters could compose the works of Shakespeare but that’s not the intent of this exercise and doesn’t change much anyway. But looking ahead, we’re going to need to make some calculation here otherwise we’ll implode the universe by trying to divide by zero. So let’s assume the author of the Book of Mormon was authentically Mayan per H2, but they are our lone person making this statement. So given the population in the Classic period was around 22 million, we’ll say 1 in 22,000,000 or p2(0.0000000454545)

So, now what does the Book of Mormon say? Does it describe the people speaking Hebrew? I’ve argued yes and that the last instance of this claim is from Mormon showing this extends to the very end of claimed Nephite history. There are those here who say the language used shows the language has evolved from Hebrew to something that a native Hebrew speaker wouldn’t understand. Ok. But it’s still Hebrew. It’s not proto-Mayan, no one outside of the LDS world is finding proto-Native American languages have roots in the middle east, it’s derived from Hebrew and Mormon knew it was Hebrew if claiming it was so evolved no one else in the world could understand their language. (Which, by the way, is another of those points that one should ask, “How likely is a native Mayan who never saw the Old World to say this compared to an author in the 19th c. attempting to write a story about biblical migrations to the Americas? But that is a digression…)

Moving on and working with the definition for the Law of Likelihood, “within the framework of a statistical model, a particular set of data supports one statistical hypothesis better than another if the likelihood of the first hypothesis, on the data, exceeds the likelihood of the second hypothesis” we can say without doing the maths that yes, our data set supports H1 being more likely than H2. But by how much?

Here we have many, many problems that are inherent with your approach which has treated the Bayesian inference like so many rolls of a dice. We aren’t rolling dice numerous times. We’re looking at the Book of Mormon, comparing it to The Maya, and either finding a hit or a miss. How does one go about determining the results obtained in the analysis other than either a binary 1 or 0? I think so long as we’re stuck with your method, we’re stuck with that one attempt and the binary result.

So, looking at the Maya and finding Hebrew was not spoken, we obtain 1 from 1 attempt. The Maya matches itself. Who would have thought? Looking to the Book of Mormon for the claim they spoke Hebrew we find they did, which is a miss compared to the data in what should be an increasingly obviously farcical exercise. Playing along, we obtain a zero from one attempt.

Plugging in the numbers, we have this for our likelihood ratio or LR:

p1 = 0.5
p2 = 0.0000000454545
D1 = 1
D2 = 0

LR = (0.5^1*(1-0.5)^0) / (0.0000000454545^1*(1-0.0000000454545)^0) = (0.5/0.0000000454545) = 11,000,0011

Based on this one single item, the likelihood ration for H1 over H2 when it comes to the author claiming the Mayans spoke Hebrew is essentially 11 million to one.

[_honorentheos]

In hindsight, to be consistent should P1 be 0.67 if we treat the Book of Mormon as valid under H2 as a source for showing an ancient Mayan might claim they spoke Hebrew? Meaning, to be consistent we would also need to consider that the Book of Mormon is a 19th c. attempt under H1, and it's either p1 = 0.5 and p2 = 0.0, or p1 = 0.67 if we allow p2 to = 0.0000000454545 to keep it equal? I mean, it all seems like kids playing at being adults to me anyway. I'm just wondering if there is a need to treat both sides equally which makes intuitive sense but wonder how easily that would be challenged?

[_Dr Exiled]

Honor:

I like it but the glaring problem with your analysis from the TBM perspective is that you don't give Joseph the break that you should give him. So, of course your results don't align with historicity. Proper TBM emphasis on Joseph's prophetic mission should always infect the analysis. This is a war in case you didn't realize.

[_honorentheos]

To keep goofing around with the math like a Dale:

Cont –

Since you argue that this would be more likely to benefit the “credulous” evidence, let’s start with 1.1 then, and see.
Let’s start with the same process, same hypotheses.

H1) The Book of Mormon was authored by a person or people in the 19th c. CE attempting to create a believable origin story for the Native Americans relying on common myths and beliefs of their time with limited access to reliable prehistory of the Americas.

and

H2) The Book of Mormon is the result of the translated, compiled history of multiple authors initially completed around the 4th c. CE by a person living within a Mayan culturally influenced or influencing society.

The data we are considering from The Maya was that, “It was clear that there had never been (an ‘Old Empire’). In it’s stead, Mayanists proposed a more Balkanized model, in which each ‘city state’ was essentially independent of all the others;…the distance from the capital to the polity’s borders seldom exceeding a day’s march.”

Our job, once again, is to consider if “within the framework of a statistical model, a particular set of data supports one statistical hypothesis better than another if the likelihood of the first hypothesis, on the data, exceeds the likelihood of the second hypothesis”.

We already know The Maya is going to match The Maya. But what about the Book of Mormon? As I’ve noted in these comments, they describe the Lamanites being governed by a single king. They describe the Nephites as being governed by a single king or a chief judge at different points in their history. There are moments when they divide up and we have the City of Zarahemla under King Mosiah, King Noah elsewhere, the people of Ammon, and other splinter groups. But the narrative usually describes these as contentious times, and when they are united they are under central rule. At the end of the Nephite civilization, Mormon is the head of all their armies fighting against a Lamanite king who heads their people. The fighting goes from city to city, land to land, tens of thousands are killed, and it sounds largely like two major peoples are fighting against one another as it’s described in the Book of Mormon.

That’s certainly not an exact match. So how do we go about this one? Understanding that with likelihood ratios the hypotheses can change but the data must hold, I guess we need to change our H’s and evaluate the data to see how likely one H is over the other H.

Hmmm. How about this?

H1) The Book of Mormon describes primarily two peoples who most often lived under a form of central government, in contrast with how The Maya describes Mayan political government.

and

H2) H1) The Book of Mormon primarily matches the description in The Maya describing multiple polities centered on single cities with a king over them who are largely Balkanized, non-centralized peoples primarily united by common ancestry and similar cultures.

This may be more like your dice rolling example. We could go through the Book of Mormon and find every mention of the government and determine if it supports H1 or H2. What we absolutely shouldn’t do is take the lack of a single word and claim that lack of a single word shows the hypothetical author in H2 would have had to have specific, detailed, unusual knowledge of the Mayan people. Good thing no one here did that, right?

Let’s shorthand the discussion for the sake of brevity and this not being a scientific paper but just an exercise in bias confirmation and break it down by books instead. 1 and 2 Nephi? Kings over both. That’s a hit for H1. Jacob? Still the Nephi’s serving as a king over the Nephite people. The Lamanites are not as clear but they are a people. That has to go to H1 as well. The Jarom-Omni books are H1. Nephite people fighting Lamanite people. Mosiah could be said to go for H2 so that three hits for H1, one hit for H2. Alma? Chief judge, King of the Lamanites…definitely a hit for H1. Helaman? H1. 3 Nephi? Hmm. Anarchy could be for H2 so let’s go that direction. That’s five for H1, two for H2. 4 Nephi is unusual as it describes a condition that didn’t exist among the Maya – universal peace and communism. But it also makes the weird claim that after three hundred years they go back to being Lamanites and Nephites because…? I’m excluding this chapter because it doesn’t fit either hypothesis. Mormon, as mentioned above, is a hit for H1 as it described both a king over the Lamanites and Mormon is the leader of the Nephite armies. Ether gets excluded because it is not purported to be in the same period as the Mayans…well, yeah technically since it overlaps with Mosiah it would cover about 100 years but why run up the score? It’s out. Last of all, Moroni. Chapter 9 is the clearest evidence that both the Lamanites and Nephites were considered centralized peoples. That’s also a hit for H1.

So our totals are: 10 attempts if we exclude 4 Nephi and Ether, with Mosiah and 3 Nephi being the only hits for H2 while we have 8 hits for H1.

But what of the probability question? How do we define our (p)s on this question? To be consistent, if we argue that under H1 the probability is based on how our known and assumed 19th c. authors behaved, we could go back to saying it’s a 2 for 3 (Book of Mormon and MF) with p1=0.67. And our H2 Mormon author representing the probability that an authentic Mayan would contradict Coe given the methodology? Still seems like 1 in 22,000,000 or p2(0.0000000454545).

We have this for our probabilities under each hypothesis:

p1 = 0.67
p2 = 0.0000000454545

Since we had ten attempts:
n!=10
x1 = 8
x2 = 2

So, on to the maths:
LR = (0.67^8*(1-0.67)^2) / (0.0000000454545^8*(1-0.0000000454545)^2) = (0.1089*0.33)/ (1.8222798756396637381449446161651e-59*0.999999909) = (0.035937/1.8222797098121950549355444449751e-59) = 1.97209022E57

Based on this one single item, the likelihood ratio for H1 over H2 when it comes to the hypothesis that the Book of Mormon is more likely the result of a 19th c. author attempting to describe Mayan governmental organization compared to an authentic Mayan source is 1.97209022E57 to one.

That looks pretty bad. I think your skeptical prior was way, WAY off.