The Interpreter; Bayes Theorem; Nephites and Mayans

[_Gadianton]

Not to get off the main topic; I've finally got a break I can pay a little more attention, and I've opened my infamous Baye's spreadsheet, that helps me remember concepts -- for some reason, it only gets opened in the context of Mopologetics...other than that and Christian apologists calculating the odds of the empty tomb, I just don't see anyone use it.

Anyway, Dr W. "Again, if they had just stopped and thought about what they had done, and perhaps asked themselves if this were such a sure thing, why no one else had come up with this kind of (apparently) ironclad demonstration"

I was going to say the same thing. Nobody stopped and thought -- doesn't this seem a little too easy? Heck, Wyatt knows this board is going to eat his Journal alive over it, he had to have been thinking "well, here goes nothing!" when he pushed the button to put in online. The poor authors probably had no idea what they were walking into. Did Wyatt really press the mathematician reviewers? "Hey guys, thanks for the glowering feedback as always, but seriously, can you just make sure there aren't basic errors that are going to come back and bite us on this one? Normally we don't publish stuff that's falsifiable, but this paper depends on some pretty clear-cut technical material that could be easily shown to be wrong if incorrect."

They do realize the point of critical feedback is to help themselves, not anyone else, right? Or maybe they just don't care. Maybe Lou Midgley being the first to respond, falling over himself in ignorant praise, is all that they're looking for?

[_DrW]

Just noticed that someone identified as "Mr. Blanco" copied my initial post on this thread and, with a few changes to the text, posted it over in the Interpreter comments section. This was done without my knowledge and certainly without permission.

Whoever did that obviously reads this board. To that individual, I would just say that we strongly condemn plagiarism on this board for good reason. (DCP, was that you?).

To anyone who might think that I am also "Mr. Blanco", I would invite you to read my initial post on this thread and compare it to the one posted by "Mr. Blanco" over in the interpreter comments. You will see that the changes (deletions) that were made certainly took the edge off. I suppose this was done to prevent it from being taken down.

If the individual who did this feels that I am being a bit too sensitive about the plagiarism, anonymous as it may be, you are invited to PM me and we can talk about it in private.

(And yes, even you, Dr. Dan)

[_Physics Guy]

I have to clarify: I have not actually read this article. I have only been raising general issues that could be problems with an article like this, in the hope that someone else would do the grunt work of reading the paper and seeing what problems are actually there.

If these guys have been talking about likelihood ratios, then my second potential problem of normalization is not relevant. The normalization factor will be the same for both P(A) and P(B), so it will cancel out in the likelihood ratio. So if the paper is all about ratios, then my second potential problem is really completely irrelevant. It should not be considered as another weight on the scale against this paper. It should instead be completely discounted.

There may remain a serious issue related to it, if the probability that a genuine historical record should screw up a basic fact of Mayan society was artificially limited in this paper to no lower than 2%. If these guys have done that kind of thing, then that is a real problem. As my discussion of normalization mentioned, the probability of basic screw-ups like that should be way lower than 2%. Even the 0.1% that I assumed arbitrarily for the sake of example was generous. I mean, how likely is it that a contemporary American historian should describe the presidency as a hereditary office? How likely is it that an American state would make its governorship hereditary and have the anomaly persist for several generations? That's the sort of scenario we'd be considering, I think, if were to suppose that some of the discrepancies between Mayan society and the Book of Mormon were nonetheless compatible with historical authenticity. Assigning a probability of 2% to such errors is way too lenient.

[_Lemmie]

If we give these authors the benefit of the doubt that they understand the basic math, "B" means the basket of evidence that we actually have. Thus, P(B|A) means, "What is the probability we'd see this basket of evidence if the book is historical?" Likewise, P(B|~A) means, "What is the probability we'd see this basket of evidence if the book isn't historical?"

That's not how they defined those two terms at all. I used their definitions, very specifically. And i don't blame you for not following, its not really a logical argument they are making.

[_Gadianton]

3- How can you possibly conclude that a true book mentioning "excellent workmanship" (point 6.18) is 50 times more likely than a false book mentioning it? This is totally made up.

Just looking at my spreadsheet here, and I think we've gone over this point before with Bayes and apologetics. Accounting for the likelihood of seeing the evidence if H is false is possibly the main thing religious belief does wrong as it goes about finding justifications for belief. If I Google "excellent workmanship" 1830 archive.org, the hits pour in. In fact, you can discount anything the Book of Mormon says that would have been natural to write about in 1830. The control texts are ridiculous. They are writing as if, here are a known collection of facts about the ancient Myans, now here is a text by Spaulding that tries to guess what would have been true for the Myans. And now here is a book by Smith that tries to guess at what would have been true for the Myans. We see that Smith did far better than Spaulding and so our method of finding hits fails for the control texts. But that's the wrong control: the right control is the sum of all 1830 influences that would have caused smith or spaulding to create a hit if the Book of Mormon is false (or MS is false).

And so it's not exactly what was pointed out above about all ancient societies having something in common, it's about what we would have expected a 19th century writer to say about the ancient world. The only evidence that would be interesting at all in the least, would be something the Book of Mormon says that would be considered extremely odd for somebody to have said in 1830. I'm open to examples but can't think of any.

Funny enough, Carmack and Skousen are in the ballpark conceptually at least, with the understanding that grammar common to the 19th century is thrown out; if the grammar didn't exist in the 19th century, it's a candidate. It gets past the first filter. But then there is the problem (Lemmie's favorite one) that these bits aren't locked into a specific period. That would be like, okay, Smith said some unusual things that we wouldn't expect a 19th century writer to say about the ancient world, but there is no tight commonality to mesoamerica.

So the "commonality to ancient people" doesn't become important until first, you get past the glaring error of underestimating the likelihood of seeing the evidence if the Book of Mormon is false, given 19th century influence on smith.

Okay, physics guy, forget everything else I've said in this thread up to this point, this is my candidate for the Achilles heel. Please provide your criticism.

(fyi Lemmie, I have to get through the "C" student level discussion first, then I'll come back to your points, which while they may seem easy for you, will take me a little work to understand; i have glimpses, but not all put together)

[_Res Ipsa]

I have to clarify: I have not actually read this article. I have only been raising general issues that could be problems with an article like this, in the hope that someone else would do the grunt work of reading the paper and seeing what problems are actually there.

If these guys have been talking about likelihood ratios, then my second potential problem of normalization is not relevant. The normalization factor will be the same for both P(A) and P(B), so it will cancel out in the likelihood ratio. So if the paper is all about ratios, then my second potential problem is really completely irrelevant. It should not be considered as another weight on the scale against this paper. It should instead be completely discounted.

There may remain a serious issue related to it, if the probability that a genuine historical record should screw up a basic fact of Mayan society was artificially limited in this paper to no lower than 2%. If these guys have done that kind of thing, then that is a real problem. As my discussion of normalization mentioned, the probability of basic screw-ups like that should be way lower than 2%. Even the 0.1% that I assumed arbitrarily for the sake of example was generous. I mean, how likely is it that a contemporary American historian should describe the presidency as a hereditary office? How likely is it that an American state would make its governorship hereditary and have the anomaly persist for several generations? That's the sort of scenario we'd be considering, I think, if were to suppose that some of the discrepancies between Mayan society and the Book of Mormon were nonetheless compatible with historical authenticity. Assigning a probability of 2% to such errors is way too lenient.

The paper's assumption of a symmetry between the effect of a "hit" as opposed to a "miss" is fatal. I played with some numbers for a while. The effect of a "miss" is orders of magnitude greater than the effect of a "hit" when you seriously think through the likelihood of true and false positives. Compound that with another fatal error -- treating each parallel as independent -- and there's really nothing to be salvaged.

[_Physics Guy]

So the "commonality to ancient people" doesn't become important until first, you get past the glaring error of underestimating the likelihood of seeing the evidence if the Book of Mormon is false, given 19th century influence on Smith.

Yeah, this might be the big flaw. As JarMan pointed out, a lot of the coincidences between Nephites and Mayans are simply common features of ancient societies. Ancient societies were a somwhat popular topic in 1830s New England. So a lot of the coincidences between Nephites and Mayans may simply have been memes of 1830s New England—memes that happened to be substantially right.

If anyone wanted to argue that popular culture of 1830s New England was inspired by God, then perhaps the remarkable accuracy with which a bunch of backwoods hicks grasped ancient empires could be impressive as evidence. Or perhaps the accuracy of their historical memes would simply show the value of literacy. Either way, though, it would have nothing to do with the inspiration of Joseph Smith in particular. If you want to show that he was more inspired than his New England neighbors, you have to show that his guesses about Mayans were better than theirs would have been.

Along with this point, I would say, one has to emphasize as well that it's a package deal. If a certain picture of ancient societies was a common meme in 1830s New England, then you can't count each little individual aspect of that picture as a separate guess about the Mayans by Joseph Smith. For him to adopt his contemporary meme wholesale would be just one guess on his part, as a package. It may be surprising that that whole package is as accurate as it is, but that's no reflection on Smith. He doesn't get credit for that, if all he did was go along with the preconceptions of his contemporaries.

[_Physics Guy]

The paper's assumption of a symmetry between the effect of a "hit" as opposed to a "miss" is fatal.

This is what I was thinking. A con artist making stuff up may be guessing 50/50, or even 2/98, but a contemporary describing his own real world is way less likely than 2% to get basic things wrong. This might be a second basic flaw.

[_Res Ipsa]

So the "commonality to ancient people" doesn't become important until first, you get past the glaring error of underestimating the likelihood of seeing the evidence if the Book of Mormon is false, given 19th century influence on Smith.

Yeah, this might be the big flaw. As JarMan pointed out, a lot of the coincidences between Nephites and Mayans are simply common features of ancient societies. Ancient societies were a somwhat popular topic in 1830s New England. So a lot of the coincidences between Nephites and Mayans may simply have been memes of 1830s New England—memes that happened to be substantially right.

If anyone wanted to argue that popular culture of 1830s New England was inspired by God, then perhaps the remarkable accuracy with which a bunch of backwoods hicks grasped ancient empires could be impressive as evidence. Or perhaps the accuracy of their historical memes would simply show the value of literacy. Either way, though, it would have nothing to do with the inspiration of Joseph Smith in particular. If you want to show that he was more inspired than his New England neighbors, you have to show that his guesses about Mayans were better than theirs would have been.

Along with this point, I would say, one has to emphasize as well that it's a package deal. If a certain picture of ancient societies was a common meme in 1830s New England, then you can't count each little individual aspect of that picture as a separate guess about the Mayans by Joseph Smith. For him to adopt his contemporary meme wholesale would be just one guess on his part, as a package. It may be surprising that that whole package is as accurate as it is, but that's no reflection on Smith. He doesn't get credit for that, if all he did was go along with the preconceptions of his contemporaries.

Yep, as Analytics pointed out, we have to look at the basket of hits and misses and ask how likely it is that a history of natives written by someone in that place, time and circumstances would result in a similar pattern of hits and misses, especially as hits and misses are defined by the authors.

One other thing, the authors conclude that the odds of the Book of Mormon not being a history of the Mayans are orders of magnitude less than less than me being killed by a meteorite. That's the kind of fantastical result that should lead an author to go back over the paper to figure out where he screwed up. It's almost as if the purpose of the paper isn't to claim the Book of Mormon is historical, but to attack the usefulness of Bayesian analysis.

[_Res Ipsa]

The paper's assumption of a symmetry between the effect of a "hit" as opposed to a "miss" is fatal.

This is what I was thinking. A con artist making stuff up may be guessing 50/50, or even 2/98, but a contemporary describing his own real world is way less likely than 2% to get basic things wrong. This might be a second basic flaw.

Yeah, it's hard to see the magnitude of the difference without playing with the numbers. Thank whoever you choose for online Bayesian calculators!