The Interpreter; Bayes Theorem; Nephites and Mayans

[_honorentheos]

The reference to books highlights another aspect of the Dales' cherry picking style. Often they point to a subject in The Maya and/or the Book of Mormon and describe it as pertaining only to the elite. This includes the use of certain types of script, the use of cocoa, or other cultural practices but as a device for explaining why the Book of Mormon was silent on a subject. Yet their Book of Mormon reference that supports correspondence on the presence of books relies on The Book of Mormon describing multiple records of people. It doesn't matter that the Book of Mormon also typically describes these as being in the custody of a specific person usually descended from Nephi or otherwise of an elite status chosen for the specific task of maintaining the records. This is evidence of a specific, detailed and unusual degree of knowledge on the part of Smith regarding Mayan practices when it comes to the subject of writing and keeping books. They also flip and claim that there are elite practice parallels at other times where it seems convenient such as claiming the use of an elite or prestige language is evidence for the Book of Mormon because the Maya had Ch'olti'an and the Book of Mormon describes the Nephite record keepers as using Egyptian or Reformed Egyptian.

The language issue is one that irks on many levels. They note the presence of writing among the Maya is a specific, detail, and unusual hit for Smith because he couldn't have possibly guessed this while attempting to make a story up about migrating Hebrews by observing Native American tribes. They also pick and choose how to use the Book of Mormon specifically describing the use of two languages for spoken and written communication: Hebrew and Egyptian. The Brass Plates were written in Egyptian, the plates of Nephi in Hebrew using Egyptian characters, and the records of the Nephite people are in reformed Egyptian. Mormon specifically says that if there was room on the plates he would have written in Hebrew which was their spoken language, though he says they have modified the Hebrew over time to the point no other people on the planet would know their language. On it's face, the Book of Mormon tells us that whatever the language looked like, Mormon writing in the 4th c. CE recognized it as a form of Hebrew. How likely is this person, if assumed to be real, to make that claim? It seems odd. But OTOH, how likely is it an author writing in the 19th c. would make that claim if they were imagining a Hebrew diaspora? Whatever the likelihood, it is orders of magnitude higher. Add to that the question of how someone who claimed to have a copy of written text but didn't want to have their claims fact checked might attempt to disguise their work as beyond anyone else's ability to read and the comparative likelihood between the Book of Mormon being the product of an authentic contemporary 4th c. CE Maya native or a 19th c. author doing exactly what is described in the Book of Mormon seem ridiculously disparate.

[_Dr Exiled]

The reference to books highlights another aspect of the Dales' cherry picking style. Often they point to a subject in The Maya and/or the Book of Mormon and describe it as pertaining only to the elite. This includes the use of certain types of script, the use of cocoa, or other cultural practices but as a device for explaining why the Book of Mormon was silent on a subject. Yet their Book of Mormon reference that supports correspondence on the presence of books relies on The Book of Mormon describing multiple records of people. It doesn't matter that the Book of Mormon also typically describes these as being in the custody of a specific person usually descended from Nephi or otherwise of an elite status chosen for the specific task of maintaining the records. This is evidence of a specific, detailed and unusual degree of knowledge on the part of Smith regarding Mayan practices when it comes to the subject of writing and keeping books. They also flip and claim that there are elite practice parallels at other times where it seems convenient such as claiming the use of an elite or prestige language is evidence for the Book of Mormon because the Maya had Ch'olti'an and the Book of Mormon describes the Nephite record keepers as using Egyptian or Reformed Egyptian.

The language issue is one that irks on many levels. They note the presence of writing among the Maya is a specific, detail, and unusual hit for Smith because he couldn't have possibly guessed this while attempting to make a story up about migrating Hebrews by observing Native American tribes. They also pick and choose how to use the Book of Mormon specifically describing the use of two languages for spoken and written communication: Hebrew and Egyptian. The Brass Plates were written in Egyptian, the plates of Nephi in Hebrew using Egyptian characters, and the records of the Nephite people are in reformed Egyptian. Mormon specifically says that if there was room on the plates he would have written in Hebrew which was their spoken language, though he says they have modified the Hebrew over time to the point no other people on the planet would know their language. On it's face, the Book of Mormon tells us that whatever the language looked like, Mormon writing in the 4th c. CE recognized it as a form of Hebrew. How likely is this person, if assumed to be real, to make that claim? It seems odd. But On the other hand, how likely is it an author writing in the 19th c. would make that claim if they were imagining a Hebrew diaspora? Whatever the likelihood, it is orders of magnitude higher. Add to that the question of how someone who claimed to have a copy of written text but didn't want to have their claims fact checked might attempt to disguise their work as beyond anyone else's ability to read and the comparative likelihood between the Book of Mormon being the product of an authentic contemporary 4th c. CE Maya native or a 19th c. author doing exactly what is described in the Book of Mormon seem ridiculously disparate.

I think Brant's recent attempt to minimize the language issue is troubling. Mormon 9:32-33 clearly intimates that the people are speaking some bastardized form of hebrew at the time Joseph Smith has his Moroni character writing this chapter. Also, one of the purposes Joseph Smith had his Nephi character go back to jerusalem and kill laban was to get the brass plates to aid in preserving the language. 1 Nephi 3:19. But of course, move the goal posts or change the meaning of words, etc., etc.

[_Res Ipsa]

Yet another problem. The questions that should be asked are:

Presuming the Book of Mormon is fictional, what is the likelihood that it mentions X in the way that it does?
Presuming the Book of Mormon is historical, what is the likelihood that it mentions X in the way that it does?

In their appendix, the Dale’s quote from The Maya, but they generally don’t quote the relevant portions of the Book of Mormon. Instead, they interpret what it says. This conceals from the reader the “in the way that it does” part of the necessary information. It also allows them to interpret the evidence to fit their theory before they even start their analysis.

Their justification is that the Book of Mormon is free so anyone wants to check their work can get a copy and do so. But the reader shouldn’t be required to do that.

[_Gadianton]

Res Ipsa,

I had dropped this point but picking it up again for one last try. It's actually a branch off the greater limb lemmie introduced at the very beginning of this thread. Maybe it's just a twig but --

Previously I'd said:

If the Dales describe a world consistent with how medical testing works, then we'd expect a mix of ratios that come up 50.

You replied,

I don't think we can show how the Dales' reasoning is consistent with any given numerator and denominator. The paper doesn't show a single example of them assigning values to the two components of the LR.

Well, yes and no. We can work backwards, unlike the Dales who merely asserted backwards. We know given Lemmie's criticism that the denominator should approach zero, but we've also been generous to consider the fact that dales reasoning is inconsistent, and that they contradict themselves in the case of misses and leave open the possibility that Coe was wrong. For instance, on iron they say "their use could yet be undiscovered", meaning Coe could be wrong.

Previously I said that all their examples that tally to 50 seem to be high numerator / low den examples of definitive Book of Mormon statements: Book of Mormon def. says horses, steel, iron, goats etc. It's a single kind of way to get to 50.

You suggested another way a "50" could be obtained:

The question is not whether it is likely that Smith would mention turkeys in the Book of Mormon. The question is whether we would expect the omission of turkeys to be more likely in a historical Book of Mormon than in a fictional Book of Mormon. The odds might be low for both, but that’s not what matters — it’s the ratio of the two.

I'm not certain on the wording, but I'm pretty sure about the basic point you're making. My point about a "mix of ratios" is 1) the reason why you do likelihood ratios in the first place is it's hard to visualize how false positives affect a test result. 2) if you see a pattern emerge in your data, especially when consciously working backwards, it's a huge red flag for cherry picking. Your words essentially say to me "The odds in numerator and denominator could both be low and till have a high ratio, and the dales consciously rule these out". Even though they mistakenly assigning low odds to jaguars, in their own universe, they defy the whole point of doing a medical test where the ratio could reveal an unexpected result.

There may be a temptation to throw it all back at Coe, as they basically follow Coe's objections on misses. But here's the problem: The Dales have gotten themselves into a fork, as apologists tend to do: they can either work backwards and reveal an obvious pattern in their numbers, cherry picking, or they can go to Mark Hoffman levels of creativity and try to come up with a mix of ratios that look more like something you need to work out the math for. can you imagine if they said there is a 99% chance Joseph Smith guessed steel and a 50% chance he guessed horse, but a 2% chance Coe was wrong about steel and a 1% chance he was wrong about horses? i really don't think the human brain is wired to intuitively make a call that there's a 1% chance vs. 2% chance of something, let alone intuitively come up with the kind of odds your example requires. this is where the actual real data from the world of medical tests is helpful. The medical test model is quite simply, a horrible model for what they're trying to do, even if a baysian analysis in general is on the table.

[_Res Ipsa]

I can't’t say whether the Dales consciously excluded evidence with a very low numerator and denominator but a high LR. My point was that they failed to consider things mentioned in Coe but not in the Book of Mormon. That would generate a bunch of examples, perhaps enough to offset the 131 correspondences. The LRs would be low, but the lowest the Dales can assign is 2 using their methodology. The methodology is biased against evidence of fiction and in favor of evidence of fact.

[_Res Ipsa]

There was no Bayesian analysis on the table. They only analyzed a single question: how could Smith have guessed X?

[_Physics Guy]

What's the chance that the Dales started out just trying to refute Coe's statement (that the societies portrayed in the Book of Mormon are nothing like Mayan society), and then got carried away into making a Bayesian claim that the Book of Mormon is almost certainly true?

That might make some sense of Wyatt's assertion that the paper is only about refuting Coe. The current text of the paper seems to have several clear claims that go well beyond that and say the Book of Mormon must be authentic, but perhaps Wyatt was thinking of some earlier version of the paper that was more modest and focused.

It might also explain the bizarre methodology as something that just gradually grew, from initial assumptions that might have made more sense for the more limited study. By the time the authors got excited about how impossibly good a guesser Smith would have to have been to make all those hits, they might have been taking things for granted that no longer applied.

I'm not trying to excuse the Dales, just understand how the heck this could have happened. I'm also not trying to say that the hypothetical original refutation of Coe would have been a good paper. My guess is that it would have been a banal exercise in showing that Book of Mormon geography and Mayan geography both have hills and forests, their peoples both ate food, and stuff like that. It might not have been completely crazy, however. The craziness might have set in later as the thrill of tiny probabilities took hold.

[_Analytics]

Thought some here might find today's reply from Dr. Bruce Dale interesting given the other discussion in this thread.

Hi Billy:
No, the controls do not support your interpretation.

The question we asked is: “Is Dr. Coe correct when he states that 99% of the details in the Book of Mormon are false”?

We show that, according to the details given in his own book, the Book of Mormon fits very well with ancient Mesoamerica but neither View of the Hebrews nor Manuscript Found fit at all with that world as described by Dr. Coe in The Maya....

I got a kick out of Billy's response.

Hi Bruce,

Thanks for the response and for your generous offer to purchase a copy of The Maya. For now I’m going to decline your invitation, because at the moment I’m more interested in understanding your Bayesian reasoning.

So, I’d like to keep my comments focused on the actual arguments you made in the paper. Setting aside whether I think your methodology, selection of evidence, and weighting of evidence was flawed, lets review your methodology to make sure I understand what you are trying to do.

In your paper, you tested the null hypothesis that “the Book of Mormon is a work of fiction” against the converse hypothesis that “the Book of Mormon is fact-based and essentially historical.“ To test this, you used a Bayesian approach. In your words, “In the Bayesian approach, the strength of each piece of evidence is the likelihood ratio, which is the probability of the evidence assuming that the hypothesis is true divided by the probability of the evidence assuming that the hypothesis is false.” (“hypothesis” in this quote is referring to the null hypothesis—that the Book of Mormon is a work of fiction). Thus, likelihood ratios less than one are evidence that the Book of Mormon is historical, and likelihood ratios greater than one are evidence that the Book of Mormon is fictional.

You then said, “Once we have chosen the likelihood of guessing correctly about each individual fact, we then multiply the likelihoods of guessing right about each of these specific facts. The number obtained by multiplying all the individual likelihoods together is the strength of the total body of evidence that whoever wrote the Book of Mormon was guessing about these fact claims.

“Thus the overall Bayes factor or likelihood ratio is the weighted strength of the evidence, and it tells us how much we should change our prior beliefs based on the new evidence.”

When you applied your methodology to View of the Hebrews, you found 15 positive correspondences and 9 negative correspondences. When you multiplied all of the likelihood ratios together, you came up with “the weighted strength of the evidence” being 0.0156. This means that in aggregate, we have “strong evidence” that the View of the Hebrews “is fact-based and essentially historical.”

This is your methodology and your numbers, including your explicit definition of what the term “strong evidence” means. Right?

[_Lemmie]

After reading Gadianton's last point and looking over the paper again, I really think that the authors did not actually determine what the likelihood ratio should specifically be for the 18 elements B to which they assign a LR = 50.

It should match the wording for the LR calculations < 1:

It is calculated as the probability that the statement is true if whoever wrote the Book of Mormon was guessing divided by the probability that the statement is true if instead the Book of Mormon is fact-based and essentially historical.

And they define the 18 as:

Of those 149 statements of fact in B for which corresponding statements of fact in The Maya existed we found that 131 of them agreed and 18 did not.

and

The Maya defines the facts and the Book of Mormon statements of fact are compared to the actual facts in The Maya.

So the LR should be:

calculated as the probability that the statement is trueFALSE if whoever wrote the Book of Mormon was guessing divided by the probability that the statement is trueFALSE if instead the Book of Mormon is fact-based and essentially historical.

They state:

...the Bayes factor specifically accounts for the possibility that the evidence may have occurred under the other hypotheses. This is accomplished in the denominator of the Bayes factor.

If the P (B is true and from The Maya book, given it came from a true Book of Mormon) is either one or very close to one, then the P (B not true and NOT from The Maya book, given it came from a true Book of Mormon) MUST BE either zero, or very close to zero. (or else the "true" Book of Mormon is filled with "untrue" statements...)

In other words the likelihood ratios for false statements in the Book of Mormon have a denominator close to zero, and to limit the corresponding ratios to 2, 10, and 50 is arbitrary and does not reflect their own set-up.

So bottom line, to use 3 ratios for support of the historical Book of Mormon and then simply assign the inverse of those ratios for non-historical Book of Mormon is WRONG. It assumes the denominators of both ratios are free to range from 0 to 1 and they are not.

By assuming all Coe statements about the Mayan era are true, they force the first denominator to be = 1 or close to 1, and the second denominator to be = 0 or close to 0.

They simply cannot rationally justify limiting the LR ratios to the inverse of each other.

[_Gadianton]

I can't’t say whether the Dales consciously excluded evidence with a very low numerator and denominator but a high LR. My point was that they failed to consider things mentioned in Coe but not in the Book of Mormon

I agree. After failing to consider all the things they should have, or in their view, ruling out things unscientific of them to consider, had they tried to work backwards and assign numbers to the LRs (instead of merely asserting backwards), I think a pattern would have emerged, which could have indicated to them they were cherry-picking their data.

My comment about bayes being on the table meant that in principle, i think a bayes analysis of a historical problem could be appropriate though I'm on the skeptical side in practice, but I'm extremely skeptical of the medical test framework being applied to a historical problem. At best, a real expert might get it to fit, but probably superfluous to what could have been done without it. Of course for the dales, having the veneer of complex equations at work bolsters their credibility with the faithful.

to me why it's such a big deal to try and plug in numbers (even if they are already guilty of working backwards) is that the whole point of doing Bayes in a slippery framework like history is that the results tend to be counter-intuitive as people tend toward confirmation bias. you're supposed to plug some numbers in and say, "gee, I thought after seeing that evidence, I'd have much more certainty than the equation is telling me!" instead it's their rocket fuel to propel bias into the stratosphere.