The Interpreter; Bayes Theorem; Nephites and Mayans

[_Gadianton]

Dog, I’m also on the road. To decrease the chances of road rage I’m barely looking in on this issue.

I liked analytics clarification. Of course in a real medical test top and bottom we wouldn’t expect to add to one, but someone explain a scenario where horses would be say, .98 top and .02 bottom, and steel would be .098 top and .002 bottom.

My point was it seems to me the way dales are describing each issue, it seems like top and bottom need to add to one. Medical test isn’t the right model; if Book of Mormon is right, coe is wrong. its 98% likely Book of Mormon Book of Mormon is wrong about horses because there is a 2% chance coe is wrong about horses. If there were only a 1 % chance coe was wrong about horses, then it would be that much worse for the Book of Mormon: 99%.

What dales want seems to be a giant dartboard based on coes book.

Anyway, if analytics can explain the potential horse / steel disparity I mentioned above, then I’m thinking about it wrong.

[_DrW]

Here's a possible title for a rebuttal article: Dr. Dale's Epic Fail: How an Engineer Used Bayesian Statistics to Delude Himself and Others about the Book of Mormon.

Exiled,

Nice title, indeed. It would be great to see a such an article exposing the Drs. Dales' Disaster posted where younger Mormons with doubts might see it, such as over on the Zelph on the Shelf website.

[_Dr Exiled]

You know, in principle his idea isn't bad. A random idea that could be fun would be to setup a crowd sourced Mormonism model that calculates the strength of different hypothesis. I'm thinking something like this. You let people enter pure data. Things that appear in the book, or other things related to Mormonism in general, and also historical facts sourced separate from sources like Coe. Then from that people can start creating a separate list of hypothesis or questions. Then from there coming up with probability calculations. Essentially crowd source a Bayes network that constantly adjusts based on the body of research. People can continuously add and update data if its accuracy is disputed. We break down data points based on objectivity or subjectivity. Like, does the Book of Mormon actually describe a decentralized government or not? Seems there are arguments in both directions. And then calculate different results depending on which things they want to compare. This would be a major undertaking but would be pretty interesting to see the results. Common sense suggests that the model would overwhelmingly show the church is not true.

Here's another idea. We could setup a website that is a kind of Quiz. Titled something like, "Do I believe in the Book of Mormon?" Then start asking questions.

1) Do you think the Book of Mormon has to be literal history in order to be a "true" book? Yes or no.

2) Do you think the Book of Mormon could contain pieces of accurate history even if the narrative if fictional? Yes or no.

Then start giving them different bullet points and have them score them.

3) The word "steel" appears in the Book of Mormon five separate times. Such as in 2 Nephi 5:15 which reads, "And I did teach my people to build buildings, and to work in all manner of wood, and of iron, and of copper, and of brass, and of steel, and of gold, and of silver, and of precious ores, which were in great abundance." How important do you think the presence of steel in ancient America is, as evidence in favor of the Book of Mormon? Irrelevant. Barely worth mentioning. Substantial. Strong. Very strong. The question could also include off to the side a quite from Guns, Germs, Steel about the significance of steel in terms of societal impact.

And then you just keep going down the list of things. But try to decouple and reduce the scope of each element as much as possible. You could have several questions related to just one thing, like horses. Horses vs. Tapir. Elephants. Curelom. Various plants. Trinitarian theology. Polygamy. Isaiah. KJV. Each type of metal mentioned. Yada yada.

Then at the end they hit the "score myself" button. How many TBMs are rattled with the results, "You are totally an atheist and don't at all believe in the Book of Mormon. Based on your answers, it is a trillion times more likely that you're a closet homosexual than the Book of Mormon is true."

What you then do is before scoring their results you ask them to state their belief level. Then this whole endeavor becomes a science experiment to assess cognitive dissonance. From our study, it turns out 80% of self-described "believing" Mormons actually secretly don't believe in the Book of Mormon at all but don't realize this about themselves because they are completely and totally ignorant about what is actually contained in this book.

I like this idea. Those over at interpreter are always straining to make the Book of Mormon appear objectively "true." (In reality they are trying to appear to be an "authority" and then gaslight everyone into believing their "paradigm" This article is more of the same misuse of science to bear their testimony). Your proposal might bring some objectivity or maybe rationality, like they claim to want, by forcing the participants to honestly look at the evidence and not just trust their leaders.

[_Lemmie]

Another underlying issue seems to be the Mayan assumption.

They are not only asserting that if the Book of Mormon matches Coe's Mayan facts, it is true, but that it is true, AND set in Mayan times.

[_Physics Guy]

Its 98% likely Book of Mormon Book of Mormon is wrong about horses because there is a 2% chance Coe is wrong about horses.

That's not quite how it works.

According to the Dales, they assume that Coe is 100% right about Mesoamerican history, so they're assuming that the chance of horses in Book of Mormon times is 0%. The 2% chance that appears in the analysis is: IF we grant that the Book of Mormon is a genuine ancient history of Mesoamerica, then there's still a 2% chance (according to the Dales) that it might describe horses. How could that be, if there were no horses and the Book is authentic? Well, maybe "horses" meant tapirs. Or maybe Moroni wasn't only smoking tobacco. Whatever: 2% fudge factor because Dales. The chance that an authentic Book of Mormon would mention horses, even though there were no horses, is set at 2%.

The question that has to be 98% if that one was 2% is, "How likely would it be that an authentic Book of Mormon would not have mentioned horses?" That's a counterfactual question, since whether the Book of Mormon is fake or authentic, in fact it does mention horses. Apart from being counterfactual, though, this question is just not the question that you need to ask in Bayesian inference.

The Bayesian question that represents the flip side of the 2% "true Book mentions horses" is: "How likely would it be that a fake Book of Mormon would mention horses?" That certainly doesn't have to be 98% just because the other answer was 2%. These two probabilities are as unrelated as the probabilities of Batman and Spiderman dying. Just as Batman is in the DC universe and Spiderman in the Marvel universe, the 2% chance of mentioning horses is in the universe where the Book of Mormon is authentic. The other chance is the one in the universe where the Book of Mormon is fake.

The probabilities of horses in the two different true-Book and fake-Book universes are unrelated to each other, but of course both are related to the larger question of whether the Book of Mormon is likely to be true or fake, given that it mentions horses. Pinning down just how they both feed into that larger question is Bayesian inference.

[_honorentheos]

Another underlying issue seems to be the Mayan assumption.

They are not only asserting that if the Book of Mormon matches Coe's Mayan facts, it is true, but that it is true, AND set in Mayan times.

It's possibly worse than that. They are asserting if a correspondence in Coe dates to the classic period, which would be later than the majority of Book of Mormon timeframe, it can be treated as if it were likely at any earlier point in Maya history that overlaps Book of Mormon times because it could have been present but not developed or widespread enough to become culturally dispersed. Yeah.

So the assertion is if there is even the most tenuous overlap between Coe and something stated in the Book of Mormon, it is true that Smith was accurately describing the Maya even if Coe would not agree with the timeframe, details, or degree of overlap.

[_Res Ipsa]

Dog, I’m also on the road. To decrease the chances of road rage I’m barely looking in on this issue.

I liked analytics clarification. Of course in a real medical test top and bottom we wouldn’t expect to add to one, but someone explain a scenario where horses would be say, .98 top and .02 bottom, and steel would be .098 top and .002 bottom.

My point was it seems to me the way dales are describing each issue, it seems like top and bottom need to add to one. Medical test isn’t the right model; if Book of Mormon is right, coe is wrong. its 98% likely Book of Mormon Book of Mormon is wrong about horses because there is a 2% chance coe is wrong about horses. If there were only a 1 % chance coe was wrong about horses, then it would be that much worse for the Book of Mormon: 99%.

What dales want seems to be a giant dartboard based on coes book.

Anyway, if analytics can explain the potential horse / steel disparity I mentioned above, then I’m thinking about it wrong.

The same thing confused me! I think my confusion arose from the way the Dales talk about the statistics. Although the foundation for their analysis is the likelihood ratios, they talk about the statistics as if only probabilities are involved. I kept thinking that their likelihood ratios had to add to one even though I knew they didn't have to. When Analytics posted what the actual likelihood questions should look like, it kind of clicked into place.

A big part of this problem is that the Dales don't actually compute the likelihood ratios. They claim that it's just boring math. But it's not. How you decide on what the numerator and denominator should be is a critical part of the analysis. But the Dale's just hand wave it away, apparently on the basis that it's "just subjective." But they don't disclose even that assumption.

Physics guy did a great explanation of the horse example. Here's my lesser than great stab at steel.

If the Book of Mormon were fiction, what is the likelihood that it would say the following about steel? .098
If the Book of Mormon were history, what is the likelihood that it would say the following about steel? .002

The numbers don't have to sum to 1 because we are dealing with likelihood ratios and not probability. Any combination of numbers between 0 and 1 could have been used by the Dales as long as the ratio is 50.

I don't think Analytics was actually trying to estimate the likelihood. I think he was just illustrating the point that the numbers don't have to add up to one. My original example almost did, but only because I'd tried 98 and 2 out for yuks and it happened by equal 49.

[_Res Ipsa]

Thanks for posting the blog excerpts. To me, they highlight the fact that the Dale's have not given serious thought to how evidence actually works. They are convinced that the number of "evidences" is what matters. That's just flat out wrong.

Evidence can be defined something like this: A is evidence of B if and only if A increases the probability that B is true. That increase can be minuscule or it can be determinative. When analyzing evidence, the side with the most instances of evidence doesn't necessarily win. One piece of determinative evidence can outweigh many instances of contrary evidence. Probably the best practical example is the freeing of death row prisoners by the innocence project. All of these prisoners were convicted under an evidence standard of beyond reasonable doubt. But one single piece of evidence, DNA, overcomes all of the prosecution's evidence at trial and results in the prisoners being freed.

The Dales hide the qualitative dimension of evidence by arbitrarily imposing a limit of 50 -- one piece of evidence can never be more than 50 times stronger than its opposite. The effect of this limit can be shown using the horse example:

Start with the denominator. If the Book of Mormon is history, how likely is it that it would mention horses in the manner it does? Coe says horses were extinct at the relevant time, so that has to be taken as absolutely true under the terms of the Dales' analysis. What does the Book of Mormon say about horses?

Horses associated with travel and chariots

Alma 18:9-10
And they said unto him: Behold, he is feeding thy horses. Now the king had commanded his servants, previous to the time of the watering of their flocks, that they should prepare his horses and chariots, and conduct him forth to the land of Nephi...Now when king Lamoni heard that Ammon was preparing his horses and his chariots he was more astonished...
Alma 18:12
And it came to pass that when Ammon had made ready the horses and the chariots for the king and his servants...
Alma 20:6
Now when Lamoni had heard this he caused that his servants should make ready his horses and his chariots.
3 Nephi 3:22
And it came to pass in the *seventeenth year, in the latter end of the year, the proclamation of Lachoneus had gone forth throughout all the face of the land, and they had taken their horses, and their chariots, and their cattle, and all their flocks, and their herds, and their grain, and all their substance, and did march forth by thousands and by tens of thousands, until they had all gone forth to the place which had been appointed that they should gather themselves together, to defend themselves against their enemies.
(It should be noted that we are not told if these chariots served a purpose in riding, or if they were for transport of goods, or if they had a ceremonial function. One assumes some sort of practicality or ritual use in war, since they brought chariots to the siege in 3 Nephi.)

Horse mentioned in quotes of Old World scripture

[Omitted]

Wild horses

1 Nephi 18:25
And it came to pass that we did find upon the land of promise, as we journeyed in the wilderness, that there were beasts in the forests of every kind, both the cow and the ox, and the ass and the horse, and the goat and the wild goat, and all manner of wild animals, which were for the use of men.

Verses in the Book of Mormon that talk about "horses", Fairmormon, https://www.fairmormon.org/answers/Book ... 2horses.22

Likelihood values can range from 0 to 1. What is the likelihood that a historical Book of Mormon would have said all this about horses? Zero or something extremely close to it. .002 is not close to zero. Put 10 zeros in front of the 2. Or 100. It would be reasonable to assign a value for this single piece of evidence that would change the bottom line of the Dales's analysis from the Book of Mormon is historical to an unimaginable degree of certainty to no change from the prior probability.

Now, the numerator: If the Book of Mormon is fiction, how likely is it that the Book of Mormon would mention horses in the way it does? Smith was actually trying to write a history of a migration of jews to the Americas and the events thereafter. Given what he was attempting to do, including horses would not be surprising. Smith was aware of horses being present in the old world and in North America. They were important in his part of the world for transportation. It is not surprising at all that he would include horses in his account. Say something in the range of .25 to .5.

So the actual result is not 50, but many orders of magnitude greater than 50.

Stepping back, remember that the Dales put the prior probability of a fictional Book of Mormon at a billion to one. The valuation of the horse issue is 50 to 1. How did they conclude that the horse evidence is 8 orders of magnitude weaker than the totality of everything else we know about the Book of Mormon? Why do they reach that conclusion? They don't explain. They just take extremely strong evidence against the Book of Mormon and dramatically weaken it by putting an artificial limit of 50 on the likelihood ratios. The result is an overwhelming bias that overemphasizes the importance of weak evidence and underemphasizes the importance of strong evidence. That is, in part, what allows them to overwhelm a few, very strong instances of evidence that the Book of Mormon is fiction with many instances of weak evidence that the Book of Mormon is historical.

[_Philo Sofee]

Res Ipsa
Stepping back, remember that the Dales put the prior probability of a fictional Book of Mormon at a billion to one. The valuation of the horse issue is 50 to 1. How did they conclude that the horse evidence is 8 orders of magnitude weaker than the totality of everything else we know about the Book of Mormon? Why do they reach that conclusion? They don't explain. They just take extremely strong evidence against the Book of Mormon and dramatically weaken it by putting an artificial limit of 50 on the likelihood ratios. The result is an overwhelming bias that overemphasizes the importance of weak evidence and underemphasizes the importance of strong evidence. That is, in part, what allows them to overwhelm a few, very strong instances of evidence that the Book of Mormon is fiction with many instances of weak evidence that the Book of Mormon is historical.

And fully 95% of the Mormon readers of Interpreter (almost all 3 of them ) will not realize this is how they incorrectly set it up. Carrier does indeed go into enormous detail in his book Proving History to show this is problematical in historical studies using Bayes Theorem. I confess, I have not read about Bayes and using it for a few years since I am focused on chess now, so I have been absent for the most part in a discussion I started. But the follow through by you experts has been class! What an education we all are receiving, and I, for one, am seriously grateful for the time put into it. I suspect in the up coming years this method will continue to be abused in apologetics, as they really have no choice but do misuse it. It's sad, but I figured it was being misused. Thanks again to all of you who have participated and shared your knowledge and time. It is gratefully received!!! I still want to see how they justify their "historical Jesus" with Bayes when Jesus has been called into question all together, again, with Bayes! That ought to fairly scream at them for attention.

[_honorentheos]

Thanks for posting the blog excerpts. To me, they highlight the fact that the Dale's have not given serious thought to how evidence actually works. They are convinced that the number of "evidences" is what matters. That's just flat out wrong.

Evidence can be defined something like this: A is evidence of B if and only if A increases the probability that B is true. That increase can be minuscule or it can be determinative. When analyzing evidence, the side with the most instances of evidence doesn't necessarily win. One piece of determinative evidence can outweigh many instances of contrary evidence. Probably the best practical example is the freeing of death row prisoners by the innocence project. All of these prisoners were convicted under an evidence standard of beyond reasonable doubt. But one single piece of evidence, DNA, overcomes all of the prosecution's evidence at trial and results in the prisoners being freed.

...

Stepping back, remember that the Dales put the prior probability of a fictional Book of Mormon at a billion to one. The valuation of the horse issue is 50 to 1. How did they conclude that the horse evidence is 8 orders of magnitude weaker than the totality of everything else we know about the Book of Mormon? Why do they reach that conclusion? They don't explain. They just take extremely strong evidence against the Book of Mormon and dramatically weaken it by putting an artificial limit of 50 on the likelihood ratios. The result is an overwhelming bias that overemphasizes the importance of weak evidence and underemphasizes the importance of strong evidence. That is, in part, what allows them to overwhelm a few, very strong instances of evidence that the Book of Mormon is fiction with many instances of weak evidence that the Book of Mormon is historical.

Res,

You should post this on The Interpreter's comments section. Dr. Bruce Dale did come back today to engage with some of the comments. I think your example above or something like it would go a long ways towards moving the conversation beyond the intrenched view that critics are intimidated by the scope of the results and "kicking against the pricks". Not that I'd know the difference, but I really thought you put this quite clearly and understandably.