The Interpreter; Bayes Theorem; Nephites and Mayans

[_MonkeyNumber9]

Some really interesting exchanges over in the ldsphilospher.com comments section between Bruce Dale and the writer over there, Jeffrey Thayne. I started to snip out the choicest bits for everyone but there are just too many and so I’m posting the whole exchange here.

http://www.ldsphilosopher.com/a-respons ... storicity/

Poster named Andrew starts it, then Bruce and Jeffrey get into it:

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Andrew
06/09/2019

I am also a believing member of the LDS church, and I couldn’t help but laugh out loud at a number of the statements in the paper. Their tone is one of wide-eyed wonder and a casual sort of relationship to “science”. Perhaps the hope is using statistical-sounding language would give this the sheen of acceptable science. They failed.

What would be really nice is if people were actually somewhat “academic” about this stuff. Start small, establish a bunch of small things, work slowly through a bunch of papers covering any one of the hundred-plus issues that here merit maybe a sentence. Then, as those are “solid”, build from there. I feel like most LDS scholarship wants to jump in right at the end with amazing conclusions, and nobody wants to do the real shovel-work of building up a body of actual scholarship. So we get all these big papers with huge flaws, and it mostly amounts to hot air.

How about we start with, say, at least one paper on the suitability of this statistical approach to analyzing correspondences in texts in general. Say, for instance, multiple news reports of the same incident or something. I have zero reason to believe, coming into this article, that anything they’re about to embark upon actually makes sense in the context where it’s being used.

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Bruce Dale
06/09/2019

Andrew and Thayne:
You are welcome to believe anything you want about our paper, “hot air” or “huge flaws” or “veneer” of scholarship or “wide-eyed wonder”, as you view these issues. As you can imagine, we don’t agree.

However, I would like to point out three things.

First, the scholarship here involved reading Coe’s book at least a half dozen times, the Book of Mormon hundreds of times, View of the Hebrews and Manuscript Found each a couple of times and listening to all six of the podcasts.

We then listed subject areas where Coe’s book and either a) the Book of Mormon, or b) View of the Hebrews or c) Manuscript Found said something specific about a particular fact claim, for example: the presence of writing, cities, wars, agriculture, metallurgy, and so forth. We then compared those fact claims for all three books versus Coe’s book for both positive and negative correspondences. We describe this process in some detail in our paper.

The bottom line is that the Book of Mormon fares very well in this comparison with Coe’s book, while the two “controls” do not.

Second, Andrew and Thayne both appear to believe that our methodology is inherently biased toward finding positive correspondences. Well, if our methodology by its very nature is biased toward uncovering positive correspondences (i.e., evidence in favor of the Book of Mormon), why did it not do so for either of the other books? It did not. The skeptical prior for Manuscript Found was made much stronger by the accumulated evidence against that book, while the skeptical prior for View of the Hebrews was essentially unchanged.

Neither of you have yet engaged with that fact. How do you explain it if our methodology is biased toward finding positive correspondences? Are there any academic studies that support your “considered opinion” that our methodology is biased in this way?

To try to compensate for our possible bias, we did several sensitivity analyses to provide very rigorous tests of our assumptions and data. None of these sensitivity analyses changed our conclusions. You do not engage with that fact either.

One of the commentators did yet another sensitivity analysis in which he removed all of the correspondences that we had weighted as 0.5, and downgraded all the other correspondences. The correspondences weighted as 0.1 were “downgraded” to 0.5 and the correspondences weighted as 0.02 were downgraded to 0.1. Even with these rather severe changes, our conclusions were unchanged.

I suppose someone could respond that we, because we are believing Latter-day Saints, intentionally (or subconsciously) selected evidence in favor of the Book of Mormon and suppressed contrary evidence. We did not.

But at that point, the responsibility for proving their point would pass to the critic. It is inadequate to call someone a liar or deluded.

The critic would have to do the same work we have done, and either show negative points of evidence against the Book of Mormon that we have missed and/or point out where our positive evidence is either overstated or non-existent.

But as the sensitivity analyses show, that is quite a hill to climb.

Best,
Bruce

ps. Spoiler alert: in my last few readings of the Book of Mormon, I have found three more positive correspondences with Coe’s book, but no additional negative correspondences. The additional positive correspondences are: 1) widespread literacy, 2) people living in homes/houses (not teepees or wigwams) and 3)… I will let you find that one.

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Jeffrey Thayne [ldsphilosopher writer)
06/09/2019

Bruce,

First, you have not indicated that you understand, nor have you responded to, the independence of observations critique (and how that effects your analysis). Second, it’s still not entirely clear that you understand my main critique either. If either of these critiques are correct, your sensitivity analysis is insufficient, and so is your commenter’s sensitivity analysis.

That you have yet to acknowledge the first, or demonstrate that you understand the second, simply shows that you aren’t taking your critics very seriously. You clearly have a very high estimation of your own work. But lots of smart people are looking at this with concern — and not because they disagree with you on the Book of Mormon, or even disagree with your broad conclusions. But because they think the statistical reasoning is flawed.

Epistemic humility would require that you try to understand what they are saying, correct? So far you have not. You’ve rebutted, but you haven’t actually responded. That’s concerning to me.

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Bruce Dale
06/10/2019

Jeffrey:
I plan to give you a more complete response in the Interpreter comments section in a week or so, maybe sooner if I can get my mission responsibilities done quickly. In the meantime, here are a few points you might want to consider.

1) My son and I are engineers, trained more in the physical sciences and mathematics than in the social sciences. You may be correct that some of the social/cultural correspondences are less strong than we have claimed. But others, as Mark Parker notes and we also note in Appendix A, are probably much stronger than we have claimed.
2) That said, there are many, many correspondences regarding technology, war, geography, etc. between the two books that have little or nothing to do with political or social correspondences. I think these are much less likely to exhibit the overlap that might occur in some social/political correspondences.
3) In either event, we tried to deal with concerns over the strength of the evidence and our personal bias by means of sensitivity analysis, which you do not mention in your article. Even giving the positive correspondences the minimum statistical weight and the negative correspondences the maximum statistical weight, the overall conclusion is unchanged. So we made a strong effort in the paper to deal with our personal bias and strength of the evidence…but you do not mention that effort at all.
4) We had a much more limited scope for our paper than you seem to imply. Our objective was simply to compare the truth claims of the Book of Mormon with facts stated by Dr. Coe in his book. Coe has repeatedly stated that the Book of Mormon has very little to do with ancient Indian cultures, “in spite of much wishful thinking.” But it turns out that the Book of Mormon has a great deal to do with ancient Mesoamerican Indian cultures according to the fact summarized in Coe’s book….and you can entirely set aside the Bayesian analysis and just look at the correspondences without weighting them if our Bayesian analysis is giving you heartburn.
5) Now here is the really key disagreement between us. You state above “that in order for something to be counted as evidence against the Book of Mormon it has to be mentioned in both texts.” That is true. It is also true that in order for something to be counted as evidence FOR the Book of Mormon, it has to be mentioned in both texts. Please explain to me how that approach is unfair or slanted in favor of the Book of Mormon. It is not.
6) I am not sure you have read our paper carefully. For example, you state explicitly that you have not read all of Appendix A (a detailed treatment of the 131 correspondences). I wonder also if you have read the article itself carefully and thoroughly. If you did, then you missed how we attempted to deal with personal bias issue.
7) You also appear to have missed how the Bayesian likelihood ratios were assigned. They were not “arbitrary” as you state above. They were assigned based on any one of three essentially subjective weightings given in the highly-cited Kass and Raftery paper we also referenced. In Appendix A, we justify how those numerical weightings were assigned to each correspondences.
Bruce

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Jeffrey Thayne
06/11/2019

Bruce, thanks for your response!

#2 – If you are referring here to the independence of observations critique, I’m willing to look closer at those other sections. However, the fact that this wasn’t addressed in the original signals that it wasn’t a concern in the original analysis, even though it is a fundamental statistical consideration. Furthermore, it’s not merely “overlap” that is the concern, it is correlation — if two observations are highly correlated, then they cannot be treated as statistically independent.

Let me invent an example. Imagine if you trying to determine the likelihood that Person X smokes. Turns out that people from Utah are 50% less likely to smoke. It also turns out that Latter-day Saints are 90% less likely to smoke. You can’t just put both these variables into the same model, especially one (like a Bayesian model) that will just multiply them, because even though one is “religion” and the other is “state” (geography and religion are two very different things), they are in this case fundamentally connected, and you are just going to inflate your analysis. It’s the issue of multicolinearity.

#3 – You say I didn’t mention this at all, and I thought I had, but it must have been in comments elsewhere. Yes, I do mention the sensitivity analysis indirectly,since it is what demonstrates is that your actual probability assignments turn out to not matter at all — the analysis hinges entirely on the sheer number of correspondences. This might seem like a strength, bu do not do any work to ensure that you are balancing against the relative scarcity of direct contradiction generally.

#4 – I wish you would set aside the deeply problematic numerical analysis and just look at the correspondences, if that is your goal. Furthermore, your comments on the article and elsewhere — and the way that the article is promoted by LDS Living and Daniel Peterson — belie the fact that you do see this as evidence of the Book of Mormon’s historicity, and are using it in that way. Despite your protestations of limited scope, the article is being promoted broadly as irrefutable mathemtical evidence that the Book of Mormon is true.

#6 – I haven’t yet read through every single of the 131 correspondences (though I’ve read through many of them), but I did read the main part of your paper clearly.

#7 – I did mention this in my response, contrary to what you have stated.

#5 – You show no evidence you understand my argument here at all. Yes, both correspondences and contradictions need to be mentioned in both places, but this still results in a higher standard for contradictions, in two ways: (1) It had to be a direct contradiction, whereas only veiled and implied correspondences where accepted (see the homosexuality one), and (2) there are inherently more correspondences than direct contradictions in any two texts, and you failed to acknowledge or account for this in your model. Here’s another restatement of my argument here, from a comment I posted elsehwere:

In order to be included in the analysis, a contradiction had to be something mentioned in both texts, and directly contradict each other. So if Coe’s text said, for example (making this up), that the Mayan worshipped cats and every Mayan household had a cat, this was not included in the analysis because the Book of Mormon said nothing about cats. It could only be included if the Book of Mormon explicitly said there were no cats. Heck, Coe could say that the Mayan were visited by aliens, and it wouldn’t be a contradiction because the Book of Mormon is silent on aliens.

This is sorta as it should be, because we can’t call something a contradiction when one text is silent. Silence is not absence. So we should not use something one text is silent on as evidence of contradiction. But what this means is that direct contradictions are going to be much harder to come by when comparing two texts — not because civilizations are similar, but rather precisely because writers don’t normally talk about what is not true of their culture and people. (Ditto for historians — they fill their books with what they believe is the case, not with what they believe is not.)

If you compare any two historical narratives / books by this standard, you are going to find many more convergences than contradictions. Again, not because of the similarities in history or story, but because of the nature of human storytelling and writing. Heck, the Chronicles of Narnia and The Hobbit have orders of magnitude more convergences than contradictions when you set it up this way. The Chronicles of Narnia are silent on hobbits, and The Hobbit is silent on benevolent, all-powerful felines.

But they both have walled cities, wars between nations, commerce, various races, dragons, magic, kings, dwarves, etc. The convergences are going stack high, but the direct, explicit contradictions will be far fewer. Not because they are remotely similar, but because direct contradictions between two stories / historical narratives just don’t happen all that much. Unless C.S. Lewis was explicitly trying to contradict Tolkien, he’d have no need to comment on the absence of hobbits or a forest called Mirkwood. Unless Tolkein was explicitly trying to contradict C.S. Lewis, he’d have no need to comment on the absence of a lamp post in the woods, or a period of winter and a white witch.

It’s precisely this reason that the contradictions that are included tend to be those rare moments where Coe actually asserts a negative. And since asserting a negative is not a very empirical thing to do, he doesn’t do it very much, hence we have fewer of them. Coe clearly had a number of things he could assert to contradict the Book of Mormon, that he didn’t include — and the authors pull a few of these extra things in. But this just illustrates the point: Coe wasn’t trying to contradict the Book of Mormon, so he didn’t include many things he could have in his text.

So to then run a numerical analysis that turns on the number of convergences and contradictions you find is circular logic. You haven’t established anything about the civilizations in question. You’ve only discovered something about human writing and storytelling (or in this case, the way historians write history): unless we are protesting our innocence of a crime, we are usually silent about things that didn’t happen (and also silent about much that did); And unless we are trying to contradict another historian’s narrative, we probably won’t assert very many negatives in our account of history.

This, plus the independence of observations piece, are what makes your final numbers so ridiculously large. Imagine that you included in your analysis of Narnia and the Hobbit correspondences like, “Both stories had a number of fantasy races,” “Both stories include dwarves,” you’ve added two variables that are often co-related, and just expanded your number by a degree of magnitude or two. Do that several dozen times over, and you get results that are well outside normal Bayesian ranges.

These are both matters of statistical reasoning that you are being very dismissive about, in ways that damage your credibility. Yes, you are very informed and seem like you know a lot about Bayesian statistics. But I’ve seen lots of other people who also work with Bayesian analyses who say that these concerns are very, very damaging to your analysis. I’ve yet to see you actually address these concerns rather than blithely dismiss them.

[_Gadianton]

First, you have not indicated that you understand, nor have you responded to, the independence of observations critique (and how that effects your analysis).

zing! and they have yet to respond -- "my son and I have been trained in math...." blah blah blah. You and your son apparently don't understand basic descriptive stats. But don't let me stop you from going around the internet making a fool of yourself. I'm going to grab a bag of chips and watch.

[_Lemmie]

First, the scholarship here involved reading Coe’s book at least a half dozen times, the Book of Mormon hundreds of times, View of the Hebrews and Manuscript Found each a couple of times and listening to all six of the podcasts.

I don't understand why Bruce Dale keeps insisting he has "read" things multiple times, as though that guarantees a level of understanding, or is sufficient to establish academic competency in his work, or is how math and statistics are done. Counting and announcing one's "read-throughs" establishes NONE of that.

[_honorentheos]

First, the scholarship here involved reading Coe’s book at least a half dozen times, the Book of Mormon hundreds of times, View of the Hebrews and Manuscript Found each a couple of times and listening to all six of the podcasts.

I don't understand why Bruce Dale keeps insisting he has "read" things multiple times, as though that guarantees a level of understanding, or is sufficient to establish academic competency in his work, or is how math and statistics are done. Counting and announcing one's "read-throughs" establishes NONE of that.

I suspect it's his safety argument that begins with Coe. Coe is faulted for only having read the Book of Mormon once. Critics of his paper are questioned as to how many times they have read the Book of Mormon or The Maya. It's a moat around his deeply emotional, irrational beliefs that is protecting them from real examination. He's uniquely able to see what others can't because they haven't put in the hours.

It's a dumb defense but it's probably his strongest held belief. It won't be penetrated, either. The upside, and switching metaphors, is he is unlikely to do much more than stand in the middle of the ring absorbing shot after shot. There isn't a counterstrike in that belief, it protective posturing.

[_Arc]

Bruce is really digging in his heels over in the comments section on that ldsphilospher.com (Jeffrey Thayne) critique of his paper:

http://www.ldsphilosopher.com/a-respons ... storicity/

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Scott Goates
06/05/2019

Thank you for your analysis [directed to the writer at ldsphilosopoher.com] – I agree with everything you have pointed out. Any interest in writing a response to the editor asking for a retraction? Publications of this sort delegitimize the entire field of Mormon Studies. Happy to collaborate!

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Bruce E. Dale
06/12/2019

Hi Scott:
You are welcome to ask for a retraction if you wish. However, neither my son nor I will retract the article voluntarily and Interpreter has already said that the article will not be retracted.
Bruce Dale

This exchange is not the first suggestion to Bruce that the paper be pulled. In a private communication a few days after the Interpreter paper appeared, Bruce was urged to retract it.

The reason given had nothing to do with its damage to Mormon studies, but rather the risk it posed to his, and especially his son's, professional careers because of the blatantly incompetent application of Bayesian inference, and the outrageous and ridiculous conclusions that resulted.

Given the caliber of the paper, one can only imagine that there have been other calls for a retraction as well. Bruce's statement that the Interpreter had assured him the the paper would not be pulled by them indicates that the subject had already been discussed. No surprises there.

The main concern here is that they used their professional secular world credentials in an attempt to legitimize their unfounded beliefs. Worse yet, the son claims that he uses Bayesian statistics as a tool in his professional work.

If they do not retract he paper, chances are that some day, some way, their totally inappropriate, naïve, and error ridden application of Bayesian analysis is going to come back to bite them in their professional lives.

Such is the internet.

[_DrW]

Bruce is really digging in his heels over in the comments section on that ldsphilospher.com (Jeffrey Thayne) critique of his paper:

http://www.ldsphilosopher.com/a-respons ... storicity/

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Scott Goates
06/05/2019

Thank you for your analysis [directed to the writer at ldsphilosopoher.com] – I agree with everything you have pointed out. Any interest in writing a response to the editor asking for a retraction? Publications of this sort delegitimize the entire field of Mormon Studies. Happy to collaborate!

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Bruce E. Dale
06/12/2019

Hi Scott:
You are welcome to ask for a retraction if you wish. However, neither my son nor I will retract the article voluntarily and Interpreter has already said that the article will not be retracted.
Bruce Dale

The Interpreter should take the Dales' paper down. It is a joke. Valid and much deserved criticism will continue, and damage to Mormon studies and the credibility of the Mormon narrative in general will mount.

This paper will become a monumental black eye for what passes as scholarship in Mormondom. It will be worse than the Hamblin - Jenkins debate disaster, because it is published and promoted by what claims to be a journal of Mormon scholarship and faith. As such it is a self-inflicted wound.

This paper is some of the best evidence one could imagine that faith supersedes scholarship in Mormonism. In this case faith is not only unsupported by facts, in this paper, the Dales' unfounded beliefs are directly refuted by the facts.

Religion works best when its truth claims are not falsifiable. Such is not the case here. Dale's claims as to the fantastical odds against the Book of Mormon being anything other than a divinely revealed historically accurate document are readily falsified by simple application of properly executed statistical analysis - the very analysis they claim to have used in the paper.

Anyone at the Interpreter who has the faintest clue regarding statistics or the scientific method in general is strongly encouraged to take some time and review this entire thread.

Please pay special attention to the tutorials on Bayesian methodology provided by "Lemmie", a professor of mathematics. Several other professionals with domain expertise, at least one of them a non-Mormon (nevermo), have also weighed in with valid criticisms of the paper.

Dr. Daniel C. Peterson, an avid reader of this message board and a self-admitted great fan of Lemmie, should exercise a bit of his professed appreciation for science and try to learn a bit from her. Then he should show he actually understands, demonstrate a bit of intellectual honesty and a sliver of courage, and pull the Dales' verdammte paper.

[_Philo Sofee]

Dr. W
Anyone at the Interpreter who has the faintest clue regarding statistics or the scientific method in general is strongly encouraged to take some time and review this entire thread.

Please pay special attention to the tutorials on Bayesian methodology provided by "Lemmie", a professor of mathematics. Several other professionals with domain expertise, at least one of them a non-Mormon (nevermo), have also weighed in with valid criticisms of the paper.

Dr. Daniel C. Peterson, an avid reader of this message board and a self-admitted great fan of Lemmie, should exercise a bit of his professed appreciation for science and try to learn a bit from her. Then he should show he actually understands, demonstrate a bit of intellectual honesty and a sliver of courage, and pull the Dales' verdammte paper.

Apologists love to imagine that they are enlightened by the Holy Ghost in having truth, therefore good folks and honest critics like Honorentheos, Lemmie, Dr. W, Grindael, Gadianton, and Scratch along with hosts of others are seen as being in the dark. The testimony is the thing for Mormon apologists. There is no reason, in their minds, to worry about what any critic thinks, since they were "inspired" to write this, and therefore, it will stand as a bastion of truth, even if other non-enlightened Mormons argue against it. It's an amazing debacle to witness first hand without question. The objections will never be allowed in their peer review process because they do not come to the conclusion that the Holy Ghost has already testified of, therefore, no matter how scientific, it is still not as advanced knowledge as what the Dales, the Peterson's, and Interpreter folks already possess. To their way of thinking, to ever admit an error is to impugn God the Holy Ghost. That just isn't going to happen. This thread deserves, nay NEEDS to be put in the pinned all time classic Hall of Fame threads!!! Shades needs to update that series of threads with this one. This is the singular most powerful response to Mormon apologetics on the Internet so far as I can find. The utter bankruptcy of the Mormon apologetic intellect is complete. And the inability to learn truth is completely demonstrated beyond reasonable doubt in this magnificent effort and thread of so many thoughtful thinkers, and fine teachers.

[_honorentheos]

There were a flurry of posts on The Interpreters comment section over the weekend, and I'm still sorting through them given the non-chronological structure. But I thought this one deserves to be brought forward as soon as I read it.

From Bruce Dale, on June 16th,

Response to Jared, et al, about “exhaustive” Bayesian treatments.

Jared’s point about the need for an “exhaustive” treatment is correct, and we did not address it particularly well in the text of the manuscript. We appreciate the opportunity to better address it now. However, this is also an exceedingly minor point as far as the conclusions of our article are concerned.

For those who may be unfamiliar with Bayesian terminology, “exhaustive” means that the set of hypotheses considered must cover the entire space of possibilities, i.e. be both exhaustive (covers everything) and exclusive (no overlapping). You can think of it in terms of a Venn diagram, there is some space of possibilities and each hypothesis covers some region of that space.

You want your set of hypotheses to cover all of the space and to not overlap. Our set of hypotheses is that the Book of Mormon is either fiction or it is non-fiction. That is an exhaustive and exclusive set, and that type of partitioning of the space is common (A or not A), since it is the easiest way to form an exhaustive and exclusive set with two hypotheses.

For the “Book of Mormon as fiction” hypothesis we have named Joseph Smith as the author since under that hypothesis he clearly had an authorship role, but whether or not he worked with any unnamed co-authors is irrelevant to the question of whether the Book of Mormon is fiction or non-fiction. Any co-authors that Joseph Smith could have plausibly worked with would have had a very similar background to his.

Our assigned Bayesian likelihoods were based on generic considerations of what information could have come to a typical person in Joseph Smith’s historical time and place. They were not based on detailed analysis of letters, meetings, communications, school curricula, or other things that would have tied the analysis specifically to Joseph. Therefore the analysis would cover any plausible coauthors equally.

The coauthors had to be close acquaintances of his, and none of his close acquaintances were scholars at all…let alone Mesoamerican scholars. (In fact, Dr. Coe says that as of 1840—ten years after the Book of Mormon was published, that “no one knew anything about the Maya area”.)

It would be equally probable or improbable for Hyrum Smith, or Oliver Cowdery, or anyone else Joseph Smith knew to make those guesses regarding the fact claims of the Book of Mormon. Thus we specified that it was for Joseph. Therefore our weightings (assignment of probability ratios) would not have changed if we considered other individuals as authors.

So, although we didn’t talk in depth about this “exhaustive” treatment issue in the paper, it is certainly not a weakness of the paper or the methodology.

Jared, can we suggest that perhaps you are making a mountain out of a molehill? You apparently want us to further partition the “fiction” hypothesis into “fiction written by Joseph Smith” and “fiction written by person X, or Y or Z” etc. That could be done, but it is not necessary—not at all. Fiction vs non-fiction, as we have set up the analysis, is already both exclusive and exhaustive. This approach satisfies the statistical requirements and is a common approach to Bayesian analysis.

Bruce

[_honorentheos]

So there you have it, Lemmie. They really were out to prove the Book of Mormon was fact and not fiction, editor comments be damned.

It's interesting that he so blatantly misses with his explanation for why their approach was, in fact, comprehensive. I'm still unsure what he imagines critics of the Book of Mormon believe are plausible alternatives to the faithful explanation for it's authorship if he is sincere? It's like the Mesoamerican theory is a lamp he is drawn to like a moth, imagining he is circling the moon.

ETA - damn Billy lit back into Dale over that. It's like Ali in his prime having moved past rope-a-doping an opponent and with immaculate brutality getting down to the business of ending a fight in spectacular perfect fashion.

[_honorentheos]

Hi Bruce,

You are simply wrong on this point. The way you interpret the evidence, assign the probabilities, and decided that the “guesses” were independent is in fact based upon a devastatingly inexhaustive space of hypotheses. You consistently asked questions like, “Why would Joseph Smith have ‘guessed’ that the ancient Mesoamericans had strong elements of Christianity in their religious practices?” That question is based upon the narrow, specific hypothesis that Joseph Smith was deliberately guessing about what ancient Mesoamerica was like.

The hypothesis that Joseph Smith was making guesses about ancient Mesoamerica is mutually exclusive from the far more likely hypothesis that Joseph Smith believed that Christianity was true and wrote speculative fiction about how the ancient mound builders of North America were immigrants from Israel. The question “Why would Joseph Smith have ‘guessed’ that the ancient Mesoamericans had strong elements of Christianity in their religious practices?” is from an entirely different part of the space than the question, “What is the probability that Joseph Smith would have included elements of Christianity in his book, assuming that he was a believing Christian who was writing speculative fiction about how God led some proto-Christian Jews out of Israel before the siege of Jerusalem, that this body of Jews settled the new world and became a mighty mound-building civilization that eventually fell and left the north-American Indians as their remnants?”

Can you see how, “What are the chances Joseph would have guessed X about the Mesoamericans” could have a very different answer than the question, “What are the chances Joseph would have speculated X about an imagined group of proto-Christian Jews who came to the new world, developed a magnificent mound-building civilization that collapsed and left the North-American Indians as a remnant?”

If those two questions have different probabilities, it proves that your space of hypotheses is in fact materally inexhaustive.

Regards,

Billy