Intro/FAQ ⎜ Episode 1 ⎜ Episode 2 ⎜ Episode 3 ⎜ Episode 4 ⎜ Episode 5 ⎜ Episode 6 ⎜ Episode 7 ⎜ Episode 8 ⎜ Episode 9 ⎜ Episode 10 ⎜ Episode 11 ⎜ Episode 12 ⎜ Episode 13 ⎜ Episode 14 ⎜ Episode 15 ⎜ Episode 16 ⎜ Episode 17 ⎜ Episode 18 ⎜ Episode 19 ⎜ Episode 20 ⎜ Episode 21 ⎜ Episode 22 ⎜ Episode 23
[Editor’s Note: This is the fourteenth in a series of 23 essays summarizing and evaluating Book of Mormon-related evidence from a Bayesian statistical perspective. See the FAQ at the end of the introductory episode for details on methodology.]
It seems unlikely that an authentic Book of Mormon should have so many anachronisms—or that a fabricated book could correspond so well to Mesoamerican culture.
In this episode we take a bite that’s probably too large to be reasonably chewed, looking at what we might possibly conclude from decades of archaeological research on the Book of Mormon. Building on a previous Bayesian analysis conducted by Bruce and Brian Dale, I form a more conservative estimate of the state of the archaeological literature, particularly in terms of a proposed Mesoamerican setting. After weighing the proposed correspondences against the anachronisms identified by critics, I estimate the probability of a fabricated Book of Mormon at p = 1.25 x 10-28, which would itself represent a critical strike in favor of the Book of Mormon.
However, since we’re being nice, I chose to severely handicap my analysis in favor of the critics. When I give the critics the severe benefit of the doubt, it’s possible to construe the evidence as weighing against Book of Mormon, with odds of around 9,000 to 1. Though this is as strong as any of the negative evidence we’ve considered so far, it’s likely not a strong basis on which to reject the Book of Mormon.
Evidence Score = -4 (decreases the probability of an authentic Book of Mormon by four orders of magnitude)
You, our ardent skeptic, are shaking out the last of the mental cobwebs that had begun to clutter your mind. You’ve been reading for most of the day, its light having long succumbed to the dark of the New England winter. You put down the book almost gratefully. You’d be lying if you said the book wasn’t interesting, but it was most definitely exhausting. You move across the room to your straw mattress and eagerly lay yourself down. Sleep comes quickly, but as it overtakes you, you find a few particular verses, the last you had read that day, echoing through your mind:
And we began to build buildings, and to repair the walls of the city, yea, even the walls of the city of Lehi-Nephi, and the city of Shilom.
And we began to till the ground, yea, even with all manner of seeds, with seeds of corn, and of wheat, and of barley, and with neas, and with sheum, and with seeds of all manner of fruits; and we did begin to multiply and prosper in the land.
This tale had become much more than the minor family drama it had been a few chapters previously. This is an epic of nations, ones that built large public works, that warred with each other, and that left their mark on the land. What’s more, the book makes strong claims about how those people lived: the foods they ate, the crops they planted, how they organized their government, their military technology—surely if these claims were true, such marks would stand through the centuries, their walls and their cities standing as tall as those of the ancient Romans or the pyramids of Egypt.
Yet the civilization the book describes sounds nothing like the savage tribes that you knew still wandered the plains of the Americas. Surely these stories, stirring as they were, were little more than idle fantasy.
You hold on to those fantasies, their threads as thick as ropes, as you sink into the depths of a vivid dream. In that dream you see yourself rising from your bed. You continue to rise—to the ceiling, above your sod roof, and into the air until the whole of your small farm is in view. You rise faster and faster, until you can look up and see the curve of the earth and the glow of the already-set sun. The sight mesmerizes you, to the point that you barely notice your ascent beginning to slow. As you reach your apex your eyes can reach the edges of the continent, and as you fall you notice that your trajectory isn’t taking you where you started. You move far and inexorably to the south and to the west, and as you fall the landscape changes from forests to grassland to dense jungle.
The jungles looked untouched by human hands, but as you continue your fall the layer of jungle seems to melt away, revealing a breathtaking network of cities and roads, a civilization of ages past that, in its way, seems more grand and more lively than the heart of Rome or the bustling streets of London. The vision moves freely through time as well as space, and you watch these nations rise and fall in tides of war and famine and destruction. Soon the smell of sulfur and smoke fills the air as volcanos spew a sea of ash into the sky below you, and panic claws at your mind as it continues to rise, too high, too fast—engulfing you in a sea of inky blackness. That panic shakes you awake, and you feel your lungs hacking on the clean New England air of your own cabin.
As the coughing subsides and you again begin to fall asleep, one question reverberates in your mind. Could peoples like the ones described in this book have actually existed? And if so, how could this Joseph have guessed so much about them?
Here we come to what may be the primary battleground of Book of Mormon apologetics. The Book of Mormon posits the existence of entire civilizations living somewhere on the American continents, and makes dozens upon dozens of claims about how those people lived—their religious practices, their agricultural activities, their material culture, their methods of warfare, their migration patterns—the potential fodder for a deep analysis is endless, and has fueled decades worth of archaeological activity and speculation. For faithful scholars those claims represent opportunities to place Lehi and his descendants into a concrete and authentic place and time in history. For critics, those same claims are a machine gun of potential silver bullets against the truth of the Book of Mormon and the church that proclaims it.
There’s no way that I could hope to analyze—or even adequately summarize—even a fraction of the research that’s been done on this topic, either for or against. That task would be further complicated by the mountain of shoddy scholarship that has accumulated over the years, on all sides. But what I will do is attempt to judge the overall picture from a bird’s eye view. Could the parallels we observe between the Book of Mormon and the ancient inhabitants of America appear by chance? Are the various purported anachronisms in the text proof that the book is a fraud? We turn to Bayes to help give us an answer.
This analysis is going to be a bit unique, as it’s not clear at first glance whether the archaeological evidence represents positive evidence for or negative evidence against the Book of Mormon. Scholars on either side would likely claim the ground for their own side. Thankfully, with Bayesian analysis we don’t really have to pick—we can consult the evidence for both sides and let the chips fall as they may.
Though the Book of Mormon was not meant as an anthropological summary of Jaredite, Nephite, or Lamanite culture, the book is full of specific descriptions and telling details regarding the various peoples accounted for in its pages, as mentioned above. Each of these details, if true, could be expected to leave a mark on history, and to correspond (or not) to the living patterns of real people who lived in the Americas between 3000 BC and 429 AD.
Since the beginning of the Book of Mormon’s modern history, it’s claims regarding native peoples of the Americas have been roundly criticized. The criticisms of yesteryear look very different than the criticisms being made today, but the critics’ point has taken the same general form in every era—that there is no evidence that a particular native group in the Americas had all of the characteristics ascribed to them in the Book of Mormon. Back when the major comparator was the First Nation groups of the central United States, that lack of evidence concerned claims about writing and large-scale populations. Now that the most serious contenders are certain factions of Olmec and Maya in southern Mexico and Guatemala, those claims have focused on the lack of metallurgy and to the absence of domesticated animals, such as sheep and goats. We also can’t forget that perennial favorite, the current (and surprisingly complicated) scientific consensus that modern horses did not exist in the Western hemisphere prior to Columbus. If the Nephites existed as described in the Book of Mormon, archaeologists should have uncovered convincing evidence of all these things, or so the argument goes.
This evidence is countered by the work of a number of faithful scholars who, over time, have uncovered a number of interesting correspondences between the Book of Mormon and the native societies of the Americas—in particular, the peoples who inhabited a limited portion of Mesoamerica. Though others have tried to place the Book of Mormon in places as varied as the Great Lakes area, the Baja peninsula, or Malaysia, there is, at the moment, a clear frontrunner among the church’s credentialed scholars (and that frontrunner is not the Heartland of the United States—see here and here and here for detailed explanations as to why). John Sorenson, a well-respected archaeologist who founded the BYU anthropology department, spent the majority of his life formulating and researching his model of Book of Mormon lands. This model been supplemented by the research of other noted, respected, and well-credential archaeologists such as Brant Gardner, Richard Hauck, and Mark Wright, among various others. In his magnum opus, Mormon’s Codex, Sorenson outlines 420 different correspondences between the Book of Mormon and Mesoamerican culture, demography, and archaeology. Though not all of those correspondences enjoy wide consensus among even faithful scholars, one gets the general sense that there are more correspondences than there should be for a book written by Joseph Smith in the early nineteenth century.
There are two hypotheses that we’ll be taking a look at in this episode:
Book of Mormon peoples resided in Mesoamerica during the times suggested in the book and participated in the culture of the Olmec and Maya—The archaeological evidence requires that we get a bit more specific than “Book of Mormon peoples existed.” It’s not possible to know if the information in the book is accurate unless we pick something to compare it to, and the best model we have to work with is that put forward by Sorenson. In that case, the parallels we see between the Book of Mormon and Olmec or Mayan cultures would be there because the Nephites, Lamanites, and Jaredites helped put them there. Anachronisms, on the other hand, would occur because we’ve either failed to understand or failed to find evidence for those particular claims within the book.
Book of Mormon peoples were fabricated by Joseph Smith—According to this hypothesis, any potential correspondence between the Book of Mormon and Mesoamerican cultures are there due to chance, either because those features exist in a number of different cultures worldwide, or because Mesoamerican culture happens to share a number of features with the cultures available to Joseph as he was writing the book, namely biblical culture, American culture, or common assumptions about America’s Indigenous peoples more generally. Anachronisms would be there because Joseph Smith and his ideas are a poor fit for ancient Mesoamerica.
PH—Prior Probability of a Mesoamerican Setting—Our prior probability for this hypothesis, as always, is based on the evidence we’ve considered in previous episodes. Here’s a summary of those analyses so far:
As you can see, the tables have now turned, with the probability now favoring authenticity at p = 1—2.3 x 10-10.
PA—Prior Probability of a Fabricated Setting—That leaves the remainder for the prior probability of a fabricated Book of Mormon, namely p = 2.3 x 10-10.
To calculate our consequent probabilities, or the probabilities of observing the archaeological evidence we do under each hypothesis, we’re going to be piggybacking on the shoulders of the work done by Bruce and Brian Dale. Bruce Dale is an amateur researcher holding a PhD in chemical engineering, and Brian Dale is biomedical engineer who, in the course of his work, has made extensive use of Bayesian statistics. Together, they use a form of Bayesian analysis to look at many of the correspondences between the Book of Mormon and Mesoamerican culture, as well as the proposed anachronisms, and estimate the likelihood of seeing each.
Their entire article is worth a read, as lengthy as it is, and there’s much that’s commendable about what they did. First off, rather than work off of Sorenson’s expansive list of correspondences, they limited the analysis only to those correspondences and anachronisms that could be found in The Maya, an academic textbook in its ninth edition written by Michael Coe, an acclaimed archaeologist openly hostile to the claims of the Book of Mormon. They also included additional anachronisms from interviews with Coe and other sources. In doing so, they weren’t specifically trying to situate the Book of Mormon in a Mesoamerican or any other geographical context, but instead attempted to refute Coe’s claims that “99% of the details in the Book of Mormon are false,” using the details from his own scholarship.
Their methodology is relatively straightforward, following the process used by secular statisticians when attempting to quantify evidence for scientific theories more generally. The Dales made judgments about whether a correspondence can be specified between the Book of Mormon and Mesoamerican culture (i.e., the correspondence is specific), whether those specifics include notable details beyond a vague description (I.e., the correspondence is detailed), and whether those details would or would not be common to many ancient societies or to Joseph’s own preconceptions (I.e., the correspondence is unusual). They then assigned rough probabilities for observing that correspondence in each case—p = .5 for ones where a correspondence can be specified, p = .1 for correspondences that included notable details, and p = .02, or 1 in 50, for ones that were specific, detailed, and unusual. These probabilities were offset with inverse values for any identified anachronisms, multiplying the overall probability by 2, 10, and 50 for anachronisms where the discrepancies between the Book of Mormon and Mesoamerican society were specific, detailed, and unusual. Multiplying all of these together results in an overarching estimate of the probability of the Book of Mormon being a nineteenth-century fabrication. All told, they identify a total of 131 correspondences and 18 anachronisms, resulting in an overall probability of 1.03 x 10-111, and that’s starting with the prior probability weighted heavily against the Book of Mormon. (They’ve since identified 25 additional correspondences based on material from others of Coe’s works, which they plan to put forward in a future paper.)
Interestingly, they also did the same analysis for two other nineteenth-century works purportedly discussing the populations of ancient America: Solomon Spaulding’s Manuscript Found and Ethan Smith’s A View of the Hebrews, which, as we’ve seen, are among the sources that Joseph was purportedly plagiarizing from when writing the Book of Mormon. If it was so easy for Joseph to have hit on so many correspondences, one might expect similar correspondences from these other attempts. But that’s not what we see—in both books we see as many or more anachronisms as we do hits, with Manuscript Found failing the test dramatically (favoring fabrication at 7.47 x 1029 to 1), and the probability being about even for A View of the Hebrews (p = .0156). The Book of Mormon performs much, much better than we’d expect from something produced by a non-expert (or even an expert!) in the early nineteenth century.
Now, their analysis has faced a fair bit of criticism (some of it by me; you can take a look at the comments section of their article for some of the thoughts I had at the time), and despite their best efforts, I don’t think the Dales’ analysis is nearly as conservative as it needs to be. Of all the criticisms that have been made, the three that I think stick are:
1) Many of their correspondences are not statistically independent. By multiplying the probabilities of each correspondence together, they’re assuming that the probability of one correspondence appearing is independent of each of the others. But some of the correspondences are clearly related to each other such as the appearance of big cities and the appearance of city walls—a big city would be much more likely to have a wall than a small city, making the correspondences interdependent.
2) They count a number of parallels that the Book of Mormon and Mesoamerica share with the peoples described in the Bible. The Dales assume that Joseph would have modeled the Nephites and Lamanites on the Indigenous peoples of the Northeastern U.S., rather than on the bronze-age Israelite society that appears in the Bible. As such, they count many correspondences that would be unusual among the Indigenous peoples of Joseph’s day, when they wouldn’t have been at all unusual in a biblical setting. If he was an author writing about how Indigenous peoples are descended from a migration of Israelites, he could easily have based them on Israelites than on those Indigenous peoples.
3) They include several correspondences available within A View of the Hebrews. A conservative analysis would exclude any of these correspondences, since they could be explained (however poorly) by contact with that book.
Thankfully, now that they’ve done all the heavily lifting, it would easy enough to go back through the Dales’ analysis and see what happens when some of these issues are corrected, which is exactly what I needed to do before providing my estimates of consequent probability.
A Bayesian Reanalysis
What I did was go through each of the 131 correspondences proposed by the Dales, doing my best to account for each of the three shortcomings I note above. I combined several sets of correspondences that seemed related enough to be interdependent, and I removed correspondences that aligned with what could be found in either the King James Bible or in A View of the Hebrews. I also took another look at their judgments of whether a correspondence was specific, detailed, and unusual, adjusting them as I felt necessary. Note that I brought over the anachronisms they identified, giving them the same weight as in the Dale’s analysis. (I didn’t take into account potential interdependence between those anachronisms, though I could’ve—the presence of iron, steel, copper, brass, silver, and gold would all likely be inter-related, for example.) You can find my point-by-point analysis in an appendix at the end of this episode.
The result was a much more conservative number of correspondences, ones that I feel are much more supportable and independent from each other, and that can’t be explained through biblical or other forms of plagiarism. I note a total of 48 correspondences, organized according to the same general categories as in the Dales’ analysis: Political, Social, Religious, Military, Geographic, and Miscellaneous. You can see each of them in the table below, along with the reference number from the Appendix of the Dales’ analysis, where you can read about the original correspondence in more detail.
|Dale Reference #||Type||Correspondence||Weight|
|1.01||Political||City States with Suzerain||0.02|
|1.06||Political||City of Lamanai||0.02|
|1.16||Political||Foreigners Take Over||0.1|
|1.17||Political||City Administrative Zone||0.5|
|1.18||Political||Separate Records for Reigns of Kings||0.1|
|1.19||Political||Native Leaders Incorporated||0.5|
|1.22||Political||King, King-Elect, Captain Structure||0.5|
|1.26||Political||“Seating” With Political Power||0.1|
|1.31||Political||Hidden Knowledge for Rulers||0.5|
|2.01||Social||Ancient Cultural Origin||0.5|
|2.02||Social||Interchange of Elite Ideas||0.5|
|2.05||Social||Pockets of Language Areas||0.1|
|2.07||Social||Settlement by Seafarers||0.1|
|2.08||Social||Olmec and Mayan Decline||0.02|
|2.11||Social||Egyptian Cultural Correspondence||0.5|
|2.25||Social||Lineage Histories Kept by Priests||0.1|
|2.27||Social||Sacred or Prestige Language||0.5|
|2.28||Social||Repopulating Abandoned Cities||0.5|
|2.30||Social||Fascination with Ancient Culture||0.5|
|3.02||Religious||Strong Christian Elements||0.1|
|3.03||Religious||Change in Cultic Traditions||0.1|
|3.12||Religious||Opposition in All Things||0.02|
|3.16||Religious||Combining Priestly and Political Roles||0.5|
|3.18||Religious||Calendars Kept by Priests||0.5|
|4.01||Military||Extreme Cruelty and Cannibalism||0.1|
|4.04||Military||Thick Clothing as Armor||0.02|
|4.06||Military||Societies Destroyed by Warfare||0.02|
|5.01||Geographic||Highlands and Lowlands||0.1|
|5.02||Geographic||Volcanic Activity and Earthquakes||0.02|
|5.03||Geographic||Periods of Drought||0.02|
|5.06||Geographic||Powerful Highland Culture||0.02|
|5.08||Geographic||Deforestation and Regrowth||0.1|
|6.01||Miscellaneous||Millions of Inhabitants||0.02|
|6.13||Miscellaneous||Houses with Gardens||0.5|
|6.16||Miscellaneous||Buildings of Cement||0.02|
|6.19||Miscellaneous||Goods Shipped by Sea||0.1|
|6.20||Miscellaneous||Books in Stone Boxes||0.02|
|N1.06||Neg-Maya||Refined Gold and Silver||10|
Though the number of correspondences was trimmed dramatically from what the Dales proposed, the overall conclusion isn’t all that different. Multiplying all the values together for the positive correspondences gives us an estimated probability of observing them at 2.5 x 10-47. When combined with the 18 anachronisms from the original analysis (which, when multiplied, give us an offsetting value of 5.0 x 1018), the total probability of a fabricated Book of Mormon stands at p = 1.25 x 10-28—a far cry from the Dales’ estimate, but still exceptionally unlikely (strong enough, in fact, for the archaeological evidence to represent a critical strike in the Book of Mormon’s favor).
But the Dales didn’t stop at producing that estimate. They also, in responsible fashion, conducted a number of sensitivity analyses to make sure that their conclusion would hold, even if they were horribly, horribly wrong about the number or strength of their identified correspondences and anachronisms. I applied those same sensitivity analyses to the results of my reanalyzed correspondences.
First, we could assume that the Dales were wrong about the strength of the identified anachronisms. Perhaps the identification of things like sheep, swine, and wheat really do each represent specific, detailed, and unusual evidence against authenticity, and we just can’t see why that would be. If so, we could alter the analysis such that each of the 18 anachronisms receive a maximum strength of 50 against the Book of Mormon (which would change the offsetting value to 3.8 x 1030). Doing so would alter things somewhat, but wouldn’t be enough to overturn our overall conclusion. Under those conditions, the probability of a fabricated Book of Mormon is still a prohibitive p = 9.54 x 10-17.
Second, we could assume that we’ve accumulated too many positive correspondences, and that a significant number (say, half) are completely invalid. If we do that, and assume that there are half as many positive correspondences as what I was able to identify, each with the same relative probabilities (i.e., 8 at a strength of .02 instead of 16, 7 at a strength of .1 instead of 14, and 9 at .5 instead of 18), the value for the positive evidence is reduced by quite a bit to 5.0 x 10-24, though still not by enough to alter our conclusion. Since in this scenario the values for the negative evidence remain the same (5.0 x 1018), that would leave the overall probability at a still-troublesome p = .000025.
Third, and lastly, we could assume that we’re wrong about the strength of our evidence, and that none of them represent detailed or unusual correspondences in the way that we believe them to be. If so, we could assign all of our correspondences the weakest weight possible, changing the probability of each to .5. If we do that, it turns out that our conclusions do change. The overall value for the positive evidence gets pushed down all the way to 3.55 x 10-15. When offset by the value for the negative evidence (5.0 x 1018), this means that the evidence would instead favor fabrication, at 17,764 to 1 (or 8,882 to 1 if you don’t count the DNA evidence, which we’ve already examined in a previous episode).
So that leaves us with a bit of a pickle. Depending on how one interprets the evidence and how badly one wants to handicap the Book of Mormon, we get a broad set of estimates encompassing more than 30 orders magnitude. To me, this situation captures pretty well the state of Book of Mormon archaeology—each side brings interesting and valid arguments to the table, and though the faithful position is surprisingly strong, there are enough points of contention that precision is essentially impossible. In that context, it seems reasonable to allow the critics the full benefit of the doubt, particularly since we’re committed to taking an a fortiori approach. We’re going to be using the third and most stringent sensitivity analysis as the basis for our estimates, which will mean using the final value for our positive evidence as our consequent probability estimate, at p = 3.55 x 10-15, as we indicate below.
CH—Consequent Probability of a Mesoamerican Setting—If we assume that the Book of Mormon took place somewhere in Mesoamerica, then anachronisms are something that need to be dealt with, and the Dales’ analysis provides us with a useful summary of those anachronisms. Using their (quite generous) estimates for the strength of those anachronisms, the overall probability of observing them, without taking the various correspondences into accounts, is the inverse of the product of the weights the Dales assigned to them. After making the minor change of removing the reference to missing DNA, that leaves us with p = 4.0 x 10-19.
Though that’s the value we’re going to be working with for our overall Bayesian calculations, it’s worth taking a bit to discuss an important question: if the Book of Mormon is authentic, why are there any anachronisms at all? Shouldn’t decades of archaeological effort have been able to accurately uncover everything important about Mesoamerican society and, if so, shouldn’t we be able to draw bright and complete lines from the Book of Mormon’s claims to those various peoples?
The short answer to those questions is no. Archaeology is far from an exact science—new discoveries happen all the time that can nullify previous anachronisms, with recent use of LiDAR in Mesoamerica being an excellent example. The picture of Mesoamerican life was very different even five years ago, and it so happened that those new discoveries aligned exceptionally well with the Book of Mormon. Even if the archaeology is accurate, there are other potential sources of error, particularly when it comes to our understanding of the Book of Mormon.
I think it’s instructive to consider what it would take for a piece of archaeological evidence to be confidently connected with the Book of Mormon. From what I can see, that process would have to include at least the following (error-prone) steps:
Knowing what you’re looking for. Modern assumptions about what the Book of Mormon means when it references iron or swine or horses or chariots can be exceptionally faulty, a fact proven time and again in trying to tie biblical scripture to history in the same way. Does a reference to iron require widespread metallurgy and smelting technology, or could iron refer instead to the manipulation of iron ore, including more small-scale mining activities? Does cattle refer to literal cows, or could it be a broader reference to domesticated livestock or other forms of movable property?
We can get a different example of this phenomenon in the Iliad, where many English translations have Greek horses eating "corn" many centuries before the Greeks could have ever imported corn into the Mediterranean. This isn’t a problem for Homer, since the original Greek word isn’t actually “corn,” and the English word can refer to many different varieties of grain. But since we can’t access the original Reformed Egyptian on the plates, and it’s hard to know the intent of its English translator(s), we shouldn’t expect easy resolutions to these kinds of anachronisms. If we don’t know what we’re looking for, we can’t know if we’ve successfully found it.
Surviving natural decay. Metal corrodes; wood decays; stone wears away. Though there are some contexts where this sort of decay is less applicable (e.g., in well-preserved tombs), there are all sorts of natural forces that can quickly destroy any evidence you might be looking for. This is a particular problem in the moisture-rich jungles of Mesoamerica, where metal tools exposed to the open air can be almost entirely corroded in a short period of time.
Surviving man-made destruction or alteration. Gold and silver are valuable commodities—even whole ontis of the stuff are going to be difficult to find if people have despoiled and repurposed it over the course of centuries. Even entire stone walls can be deconstructed and moved to new locations if need be. Place names can change, sometimes en masse, if new people move in or languages shift (which happens to be the case for the most of Mesoamerica). This sort of destruction isn’t always applicable (see the aforementioned well-preserved tombs), but it’s going to be hard to accurately document every aspect of a given culture if subsequent ones keep making off with the evidence or stomping it into the ground.
Digging in the right spot. Even if evidence survives those decay-related processes, it has to be found, and the finding doesn’t happen easily. Only a small fraction (on the order of 1%) of Mesoamerican sites have been excavated and, within those, only a portion of each site has received specific archaeological attention. It can be surprising what one can do with a limited sample size, but it wouldn’t be surprising for some (or perhaps many) aspects of Mesoamerican culture to escape that particular net.
Dating the find correctly. As much as radiocarbon dating and other forms of archaeological dating practices can feel like a precise, foolproof scientific process, that’s not always the case (and you could say that for just about any other precise, foolproof scientific process you could name). The error bars associated with these sorts of dating can be quite large and, on occasion, entirely incorrect. Since some of the Book of Mormon’s anachronisms have been found, just not at the proper time period, it’s conceivable that these are essentially anachronisms ‘in date only,’ and that the reason the evidence is missing is because it’s been improperly dated.
Interpreting the evidence. Once a piece of evidence has been found, we still require a flesh-and-blood human being to draw the connection between that evidence and the Book of Mormon. As formidable as archaeologists and other scholars can be, this is a subjective and interpretive effort that can be marred in any number of ways. Horses may just be a good example of this. There are examples of horse bones discovered in Mesoamerica, dated to the correct layers, but that have generally been interpreted by scholars as some form of post-Columbian contamination. Even the right evidence in the right place and the right time can still fail to make a dent in the archaeological record.
So, should we expect some anachronisms to be present in an authentic Book of Mormon? Out of the hundreds of claims that the Book of Mormon makes about its peoples, yes, we should expect some of them to fail to make it through that process. Each of the anachronisms included in our analysis could be plausibly explained through one (or more) of the factors listed above.
CA—Consequent Probability of a Fabricated Setting—How about if the Book of Mormon and its peoples were fabricated works of fiction? Should we expect there to be the parallels that we see? As we’ve already discussed in another episode, yes, we should expect some correspondences to exist, either on the basis of chance or based on the commonalities shared among many or most ancient societies. But there comes a point where correspondences become difficult to ignore, and the table above shows a goodly number where chance or shared characteristics seem inadequate explanations. How likely would it be for Joseph to just happen to pick a city-state/Suzerain political orientation for his description of Indigenous peoples, a form of politic far removed from his personal experience or of any handy historical model? Or for the rise and decline of his civilizations to almost perfectly align with the rise and decline of Olmec and Mayan civilization? Or for Joseph to be able to accurately describe intense volcanic activity of the type common to Mesoamerica? Or for Joseph to time a major drought in the exact period one likely occurred? These specific, detailed, and unusual correspondences could be multiplied several times over. None are necessarily impossible on their own, but together they quickly diminish the plausibility of a fabricated Book of Mormon.
And, yes, we should beware the possibility of parallelomania, where parallels can be multiplied to the point of near meaninglessness. But keep in mind that I’m being exceptionally conservative with the correspondences presented here. Sorenson’s list of over 400 correspondences has here become just shy of 50, with care being taken to choose correspondences that can be corroborated within the Maya, that are likely to be statistically independent, and that don’t match the sources Joseph would’ve had on hand. Even then, you could cut the number of correspondences in half and the evidence would still favor authenticity. The only way we can reasonably advantage the critical hypothesis is to do what we’ve done here, which is to make all of those correspondences as weak as possible.
Of course, when you do so, the likelihood of observing that many correspondences is still small—just not as small as that of our non-handicapped anachronisms, with p = 3.55 x 10-15, which is the value we’ll be using for our final Bayesian estimate.
PH = Prior Probability of the Hypothesis (our initial estimate of the probability of an authentic Book of Mormon, based on the evidence considered thus far, or p = 1—2.3 x 10-10)
CH = Consequent Probability of the Hypothesis (our estimate of the likelihood of seeing the anachronisms we do if the Book of Mormon took place in a Mesoamerican setting, or p = 4.0 x 10-19)
PA = Prior Probability of the Alternate Hypothesis (our initial estimate of the probability of a fabricated Book of Mormon including the observed correspondence, or 2.3 x 10-10)
CA = Consequent Probability of the Alternate Hypothesis (our estimate for the likelihood of seeing the correspondences we do if the Book of Mormon was fabricated, or p = 3.55 x 10-15)
PostProb = Posterior Probability (our new estimate of the probability of an authentic Book of Mormon)
|PH = 1—2.3 x 10-10|
|PostProb =||PH * CH|
|(PH * CH) + (PA * CA)|
|PostProb =||(1—2.3 x 10-10) * 4.0 x 10-19)|
|((1—2.3 x 10-10) * 4.0 x 10-19) + (2.3 x 10-10 * 3.55 x 10-15)|
|PostProb =||1—2.04 x 10-6|
Lmag = Likelihood Magnitude (an estimate of the number of orders of magnitude that the probability will shift, due to the evidence)
Lmag = log10(CH/CA)
Lmag = log10(4.0 x 10-19/3.55 x 10-15)
Lmag = log10(.0000113)
Lmag = -4
This result is a notable one, in that it’s the strongest evidence available to the critics out of everything we’ve considered so far. It’s important to emphasize, though, that what we’ve done here is in no way fair to the faithful position. Not only are we acting as if all of the positive evidence is as weak as possible, we’re failing to account for the interdependence of potential anachronisms and we’re leaving out a number of additional correspondences that’ve since been identified by the Dales. Anyone who would like to argue for a stronger evidence score here will have some serious explaining ahead of them.
But we’ll ignore, for the moment, all that statistical gerrymandering. Based on this analysis, those critical of the Book of Mormon could have reason for seeing these archaeological issues as a legitimate challenge to its authenticity. And though the faithful have their own reasons to be confident, they should acknowledge that the archaeological picture is not yet overwhelmingly on the Book of Mormon’s side. What that picture probably shouldn’t do, however, is form the sole basis for a rejection or acceptance of the Book of Mormon’s claims. These archaeological and historical battles have been fought for decades without a clear victor, and they’ll continue to be fought for decades to come—which just happens to be the subject of the next episode.
I have to be honest here: the sort of Bayesian analysis offered by the Dales, where rough weights are subjectively assigned to categories of evidence, is definitely not the ideal way to suss out the state of the archaeological evidence. I’ll maintain, however, that it remains the "best bad method" available to us given mortal restraints on time and/or omniscience. One could easily spend years conducting individual Bayesian-style analyses for each piece of archaeological evidence, as I’ve attempted to do with many other arguments regarding the Book of Mormon. And I would absolutely be open to a reasoned take on this sort of analysis from the critical side of things. If a critic decided to do so, however, they should be careful to apply a fortiori reasoning in favor of Book of Mormon authenticity, in which case I don’t see a way of making this a critical strike against the Restoration.
Next Time, in Episode 15:
In the next episode, we’ll continue on the theme of archaeological evidence for and against the Book of Mormon. Only instead of taking a look at how things stand at the moment, we’ll be analyzing the trajectory of that evidence over time—and where they’re likely to stand in the future.
Questions, ideas, and vows of revenge can be served cold on the plate of BayesianBoM@gmail.com or submitted as comments below.
Appendix—Full Analysis of the Dale Correspondences
|1.01||Political||Independent City States||0.02||Combine 1.01, 1.02, 1.03, 1.25
set at .02
|In any city state setup, it’s probable that one city would come to dominate the others, that they could, at times form competing factions, and that city states would switch sides. I think it’s better to make this a single, much stronger correspondence.|
|1.02||Political||Capital Dominates Other City States||0.02||Combine 1.01, 1.02, 1.03, 1.25
set at .02
|1.03||Political||City States Switching Allegiances||0.1||Combine 1.01, 1.02, 1.03, 1.25
set at .02
|1.04||Political||Complex State Institutions||0.02||Remove||Conforms to biblical expectations.|
|1.05||Political||Many Cities Exist||0.1||Remove||Conforms to biblical expectations.|
|1.06||Political||City of Lamanai||0.02||Keep||See the episode on Nahom for the likelihood of guessing a three-syllable city. 1 in 50 is a quite conservative estimate here.|
|1.07||Political||Densely Settled Areas||0.1||Remove||Could have obtained from View of the Hebrews.|
|1.08||Political||Large-Scale Public Works||0.1||Remove||Could have obtained from View of the Hebrews.|
|1.09||Political||Rulers Live in Luxury||0.5||Combine 1.09, 1.10, 1.11, 1.12, 1.13, 1.14, 1.15, 1.28, 1.29, 1.30
set at .1
|All the aspects connected to the idea of a royal court would be interdependent. The idea of a luxurious royal court would conform to biblical expectations. Not all biblical kings would have elaborate thrones, or have competing political factions, political marriages, political feasts, and political gifts. Courts imitating each other wouldn’t necessarily have been described biblically, but that’s how most similar social organizations operate. Most of the fantasy novels that exist follow these tropes. Recommend combining and setting at .1.|
|1.1||Political||Elaborate Thrones||0.1||Combine 1.09, 1.10, 1.11, 1.12, 1.13, 1.14, 1.15, 1.28, 1.29, 1.30
set at .1
|1.11||Political||Royal Courts||0.1||Combine 1.09, 1.10, 1.11, 1.12, 1.13, 1.14, 1.15, 1.28, 1.29, 1.30
set at .1
|1.12||Political||Political Marriages||0.5||Combine 1.09, 1.10, 1.11, 1.12, 1.13, 1.14, 1.15, 1.28, 1.29, 1.30
set at .1
|1.13||Political||Political Feasting||0.1||Combine 1.09, 1.10, 1.11, 1.12, 1.13, 1.14, 1.15, 1.28, 1.29, 1.30
set at .1
|1.14||Political||Gifts to the King||0.5||Combine 1.09, 1.10, 1.11, 1.12, 1.13, 1.14, 1.15, 1.28, 1.29, 1.30
set at .1
|1.15||Political||Organized Political Factions||0.1||Combine 1.09, 1.10, 1.11, 1.12, 1.13, 1.14, 1.15, 1.28, 1.29, 1.30
set at .1
|1.16||Political||Foreigners Take Over||0.1||Combine 1.16 and 6.14
set to .1
|Agree that foreign takeovers are specific and detailed, though they would not be an unusual occurrence in ancient cultures. Would be interdependent with foreigners imposing a language and writing system.|
|1.17||Political||City Administrative Area||0.1||Change to .5||Most large centers in ancient times would have had administrative centres like this, so it wouldn’t be unusual. Recommend changing to .5.|
|1.18||Political||Separate Records for Reigns of Kings||0.02||Change to .1||Though this would have been unusual to a Joseph operating on a biblical model, these sorts of separate records wouldn’t have been unusual in ancient cultures. Recommend changing to .1.|
|1.19||Political||Native Leaders Incorporated||0.02||Change to .5||In describing conquering foreign lands, there are only two choices–install your own rulers or extract tribute from the current ones. Recommend changing to .5.|
|1.2||Political||Tribute Required||0.1||Remove||Conforms to biblical expectations.|
|1.21||Political||Limited Number of Important Patrilineages||0.02||Remove||Conforms to biblical expectations. Strong arguments that Lehi’s tribes follow the same pattern and structure as the tribes of Israel.|
|1.22||Political||King and King-Elect||0.5||Combine 1.22, 1.23,
set at .5
|To be more conservative, the correspondence could be to the overall structure of king, king-elect, and captains.|
|1.23||Political||Captains Serving Kings||0.5||Combine 1.22, 1.23,
set at .5
|1.24||Political||Family Dynasties||0.1||Remove||Conforms to biblical expectations.|
|1.25||Political||Kings Rule Over Subkings||0.5||Combine 1.01, 1.02, 1.03, 1.25
set at .02
|1.26||Political||“Seating” With Political Power||0.02||Change to .1||The concept of being “seated” is commonly applied to royalty.|
|1.27||Political||Separation of Civil and Religious Authority||0.5||Remove||Conforms to American sensibilities.|
|1.28||Political||Aspiring to Power||0.5||Combine 1.09, 1.10, 1.11, 1.12, 1.13, 1.14, 1.15, 1.28, 1.29, 1.30
set at .1
|1.29||Political||Courts Imitating Enemies||0.1||Combine 1.09, 1.10, 1.11, 1.12, 1.13, 1.14, 1.15, 1.28, 1.29, 1.30
set at .1
|1.3||Political||Courts Function as Great Households||0.5||Combine 1.09, 1.10, 1.11, 1.12, 1.13, 1.14, 1.15, 1.28, 1.29, 1.30
set at .1
|“Great households” wouldn’t necessarily imply the lack of a “palace”.|
|1.31||Political||Hidden Knowledge for Rulers||0.1||Change to .5||It’s unusual, but the specifics don’t necessarily match, and doesn’t apply to all candidates for high office in the Book of Mormon case.|
|1.32||Political||Abrupt Breaks in Dynasties||0.1||Remove||Changes in the ruling class are definitely not unusual, and the specifics don’t match (war in the case of the Maya, peaceful transition in the Book of Mormon).|
|1.33||Political||“Possession” of the Land||0.1||Remove||The word “possess” has different meanings in the two contexts.|
|2.01||Social||Ancient Cultural Origin||0.1||Change to .5||Coe doesn’t specify “when”, thus it’s neither specific or detailed. Only two real options here: ancient vs. recent origin.|
|2.02||Social||Interchange of Elite Ideas||0.02||Change to .5||Ideas and material goods would have been naturally interchanged among peoples in close contact, particularly among elites. Not unusual, not detailed, but the timeline of hundreds of years of exchange would be somewhat specific.|
|2.03||Social||Foreign Brides for Elites||0.1||Remove||Specifics don’t match, since it’s foreign husbands rather than foreign brides.|
|2.04||Social||Slavery Practiced||0.1||Remove||As stated, not unusual, nor actually detailed. Conforms to biblical expectations.|
|2.05||Social||Languages in Pockets||0.1||Keep|
|2.06||Social||Great Flood Narrative||0.1||Remove||Can be found in View of the Hebrews.|
|2.07||Social||Settlement by Seafarers||0.1||Combine 2.07 and 2.20,
set at .1
|Settlement by seafarers is interdependent with having ancestors from beyond the sea.|
|2.09||Social||Strong Class Distinctions||0.1||Remove||Conforms to biblical expectations.|
|2.1||Social||Human Sacrifice||0.1||Remove||Conforms to biblical expectations.|
|2.11||Social||Egyptian Cultural Correspondence||0.5||Keep|
|2.12||Social||Mobile Populations||0.1||Remove||Only two options for population movement: mobile and immobile, and mobile may have been more common.|
|2.13||Social||Extreme Inequality||0.5||Remove||Interdependent with class distinctions, conforms to biblical expectations.|
|2.14||Social||Marketplaces||0.1||Remove||Conforms to biblical expectations.|
|2.15||Social||People Driven from Homes||0.02||Remove||Conforms to biblical expectations (e.g., Babylonian conquest).|
|2.16||Social||Architectural Extravagance||0.02||Remove||Most of these details are interdependent with some of the political correspondences, and would conform to biblical expectations (e.g., Solomon’s temple)|
|2.17||Social||Large Northward Migrations||0.02||Remove||Two different cases of “land Northward” (central Mexico vs. Yucatan). Timing of the movement of refugees could still be specific and detailed if it corresponded with late Nephite warfare in Mormon/Moroni, but since there were multiple waves over a long stretch, it’s not specific or detailed.|
|2.18||Social||Constant Migrations||0.5||Remove||Conforms to biblical expectations.|
|2.19||Social||Cities Named After Founder||0.5||Remove||Conforms to biblical expectations.|
|2.2||Social||Ancestors From Beyond the Sea||0.1||Combine 2.07 and 2.20,
set at .1
|Settlement by seafarers is interdependent with having ancestors from beyond the sea.|
|2.21||Social||Poetic Repetition||0.02||Change to .5||As unusual as the Book of Mormon’s chiasmus is (as covered in a previous episode), we don’t have as much evidence of complex chiasms in the Popul Vuh, meaning the details don’t match, and we could find those examples in most literature.|
|2.22||Social||Corn Among Grains||0.1||Remove||Mentioned in View of the Hebrews.|
|2.23||Social||Multiple Wives/Concubines||0.1||Remove||Conforms to biblical expectations.|
|2.24||Social||Importance of Geneological Connection||0.02||Remove||Conforms to biblical expectations.|
|2.25||Social||Geneology Kept by Priests||0.02||Combine 2.25 and 2.31
Change to .1
|Genealogical records and lineage histories conform to biblical expectations, but having them kept by religious leaders is specific and unusual, though the details don’t match exactly.|
|2.26||Social||Homosexuality Practiced||0.5||Remove||Reference in the Book of Mormon too unclear to count as a specific parallel.|
|2.27||Social||Sacred or Prestige Language||0.02||Change to .5||The details don’t necessarily match, since it’s obviously not the same prestige language in both cases, and Coe makes it clear that it’s not necessarily an unusual practice (e.g., Latin, Coptic).|
|2.28||Social||Repopulating Abandoned Cities||0.1||Change to .5||Repopulating old or abandoned cities would have been a common practice in most ancient societies.|
|2.29||Social||World in Four Quarters||0.1||Remove||Conforms to biblical (and modern) expectations (e.g., Jeremiah 49:36).|
|2.3||Social||Facination with Ancient Culture||0.1||Change to .5||It’s specific, but not unusual (e.g., see the renaissance fascination with Greek and Roman thought).|
|2.31||Social||Lineage Histories||0.02||Combine 2.25 and 2.31
Change to .1
|Genealogical records conform to biblical expectations, but having them kept by religious leaders is specific and unusual, though the details don’t match exactly.|
|3.01||Religious||Central Role of Temples||0.1||Remove||Conforms to biblical expectations and is found in View of the Hebrews.|
|3.02||Religious||Strong Christian Elements||0.02||Change to .1||There would be some parallels that would fit with any religious tradition, so it may be specific and detailed, but not necessarily unusual.|
|3.03||Religious||Change in Cultic Traditions||0.1||Keep|
|3.04||Religious||Associating Temples with Hills||0.02||Remove||Considering the reference is to an Isaiah quote, it doesn’t count as a Book of Mormon parallel, and it conforms to biblical expectations.|
|3.05||Religious||Seers and Seer Stones||0.1||Remove||Conforms to Joseph’s own seership practices.|
|3.07||Religious||Belief in Resurrection||0.02||Remove||Conforms to Christian biblical expectations (Methodists, for instance, believe in a literal resurrection of Christ).|
|3.08||Religious||Belief in Baptism||0.02||Remove||Conforms to biblical expectations.|
|3.09||Religious||Walking in Straight Roads||0.1||Remove||Conforms to biblical language of a straight and narrow path.|
|3.1||Religious||Abiding by Covenants||0.02||Remove||Conforms to biblical expectations (it may have been ignored in modern Christianity, but it’s hard to escape anyone familiar with the bible).|
|3.12||Religious||Opposition in All Things||0.02||Keep|
|3.13||Religious||Pantheistic Religion||0.1||Remove||Conforms to biblical expectations for pagan religions.|
|3.14||Religious||Sorcery and Magic Practiced||0.1||Remove||Sorcery and magic are near universals throughout all ancient cultures.|
|3.15||Religious||Ritual of Renewal||0.02||Remove||Details don’t match entirely, with universe-wide renewal rather than being limited to the community.|
|3.16||Religious||Combining Priestly and Political Roles||0.5||Keep|
|3.17||Religious||Consulting Oracles||0.1||Remove||Conforms to biblical expectations.|
|3.18||Religious||Calendars Kept by Priests||0.1||Change to .5||Keeping of a calendar may be different from keeping a record.|
|3.19||Religious||Virtuous Persons “Confess”||0.02||Remove||Conforms to (New Testament) biblical practice, particularly James.|
|4.01||Military||Extreme Cruelty to Captives||0.1||Combine 4.01 and 4.11
set to .1
|Cannibalism would qualify as a form of extreme cruelty, and would be interdependent with those other forms.|
|4.03||Military||Walled Cities||0.5||Remove||Conforms to biblical expectations and is found in View of the Hebrews.|
|4.04||Military||Thick Clothing as Army||0.02||Keep|
|4.05||Military||Fighting with “Darts”||0.02||Remove||Darts were included among descriptions of biblical weapons in the old testament.|
|4.06||Military||Societies Destroyed by Warfare||0.02||Keep|
|4.08||Military||Raids to Take Captives||0.1||Remove||Conforms to early American expectations.|
|4.09||Military||Dressing to Inspire Fear||0.5||Remove||Details are given and don’t match, removing the correspondence.|
|4.1||Military||Stones and Slings||0.02||Remove||Conforms to biblical expectations.|
|4.11||Military||Cannibalism Practices||0.1||Combine 4.01 and 4.11
set to .1
|Cannibalism would qualify as a form of extreme cruelty, and would be interdependent with those other forms..|
|4.12||Military||Deliberate Destruction of Records||0.1||Remove||Timeframe of the destruction doesn’t match.|
|5.01||Geographic||Highlands and Lowlands||0.1||Keep|
|5.02||Geographic||Volcanic Activity||0.02||Combine 5.02 and 5.07,
set at .02
|Both volcanic activity and earthquakes would be correlated due to being on a faultline.|
|5.03||Geographic||Periods of Drought||0.02||Keep||Notable that this correspondence has been supported by drought data (https://journal.interpreterfoundation.org/let-there-be-a-famine-in-the-land/)|
|5.06||Geographic||Powerful Highland Culture||0.02||Keep|
|5.07||Geographic||Earthquakes Present||0.02||Combine 5.02 and 5.07,
set at .02
|Both volcanic activity and earthquakes would be correlated due to being on a faultline.|
|5.08||Geographic||Deforestation||0.1||Combine 5.08 5.09,
Set to .1
|Details don’t quite match up (though they don’t necessarily conflict), and deforestation and shipping of lumber would be interdependent to a degree.|
|5.09||Geographic||Forest Regrowth||0.02||Combine 5.08 5.09,
Set to .1
|Details don’t quite match up (though they don’t conflict necessarily), and deforestation and shipping of lumber would be interdependent to a degree.|
|5.1||Geographic||Precious Stones||0.02||Change to .5||Since we don’t have any details about the precious stones, and precious stones themselves would not be unusual, a conservative view would place this as merely specific, though the argument about the lack of diamonds/rubies/pearls is compelling.|
|5.12||Geographic||Perishable Writing Materials||0.1||Remove||Conforms to expectations of Joseph’s time period.|
|5.13||Geographic||Refined Gold||0.5||Remove||Strange to count this both as a positive and negative parallel.|
|6.01||Miscellaneous||Millions of Inhabitants||0.02||Keep|
|6.02||Miscellaneous||Calendars Kept||0.02||Remove||Conforms to biblical expectations.|
|6.03||Miscellaneous||Multiple Calendars||0.02||Remove||The Mayan calendars don’t conform to either 600BC or to the instituting of judges, so the details don’t match.|
|6.04||Miscellaneous||Beekeeping||0.1||Change to .5||The single mention at a very early timeframe makes it difficult to establish this as detailed.|
|6.05||Miscellaneous||Art Details||0.1||Remove||Conforms to biblical expectations.|
|6.06||Miscellaneous||Knowledge of Astronomy||0.02||Remove||Conforms to biblical expectations.|
|6.07||Miscellaneous||Presence of Writing||0.02||Remove||Conforms to biblical expectations.|
|6.08||Miscellaneous||Engraved Writing on Stone||0.1||Remove||Conforms to biblical expectations.|
|6.09||Miscellaneous||Many Books Present||0.02||Remove||Records kept in repositories would conform to biblical expectations, and the stone box point is covered later on.|
|6.1||Miscellaneous||Large-Scale Trade||0.1||Remove||Conforms to biblical expectations.|
|6.11||Miscellaneous||Many Merchants||0.5||Remove||Conforms to biblical expectations.|
|6.12||Miscellaneous||Roads and Causeways||0.1||Remove||Mentioned in View of the Hebrews.|
|6.13||Miscellaneous||Houses with Gardens||0.5||Keep|
|6.14||Miscellaneous||Foreigners Imposing Culture||0.02||Combine 1.16 and 6.14,
set to .1
|Settlers in Joseph’s day did try to teach new writing systems and cultures to Indigenous peoples. Would be interdependent with foreign incursions generally.|
|6.15||Miscellaneous||Writing Systems Change Over Time||0.1||Remove||It’s not clear that they’re talking about the same languages.|
|6.16||Miscellaneous||Buildings of Cement||0.02||Combine 6.16 and 6.17,
set at .02
|Agree that cement is an unusual and specific detail, but these two would definitely be interdependent.|
|6.17||Miscellaneous||Great Skill With Cement||0.02||Combine 6.16 and 6.17,
set at .02
|Agree that cement is an unusual and specific detail, but these two would definitely be interdependent.|
|6.18||Miscellaneous||Excellent Workmanship||0.02||Remove||Conforms to biblical expectations.|
|6.19||Miscellaneous||Goods Shipped by Sea||0.1||Keep|
|6.2||Miscellaneous||Books in Stone Boxes||0.02||Keep|
|6.21||Miscellaneous||Watchtowers||0.1||Remove||Conforms to biblical expectations.|
|6.22||Miscellaneous||Multiple Formal Entrances||0.5||Remove||Conforms to biblical expectations (e.g., Jerusalem)|
|6.23||Miscellaneous||Fine Fabrics||0.02||Remove||Conforms to biblical expectations.|
Hello! I was just wondering if the concept of “human-trophy taking” (https://en.wikipedia.org/wiki/Human_trophy_taking_in_Mesoamerica) is relevant to an analysis of correspondences between the Mayans and the Book of Mormon peoples. Just asking due to its relevance involving Lamanite practices of capturing women and children and sacrificing them to idol Gods (Mormon 4:14-15 & Mormon 4:21)
The concept of capturing enemies and sacrificing them for ritualistic (presumably religious) purposes (as suggested by the idea of sacrificing to idol gods) does seem to be both a correspondence and somewhat specific and detailed. That being said, I believe that the current evidence for Mayan sacrifice does typically involve male soldiers being sacrificed, not women and children, but I don’t think that precludes the importance of human trophy taking happening in warfare in religious context in both Nephite and Mayan societies or that in this instance, the sacrifice of Women and children to idol gods is still a reasonable possibility, even if it did happen more often to male soldiers. So does it still count as relevant evidence or is the case of human trophy taking in the Book of Mormon not nearly specific enough to be relevant to a significant degree to be included in an analysis?
Thanks Jeremy. I agree that these are useful correspondences. They would probably be captured within item 4.01, which includes extreme cruelty to captives and cannibalism, as well as item 3.06, religious bloodletting. At the very least the idea of trophy-taking probably wouldn’t be independent with those items, though incorporating those elements might strengthen those correspondences somewhat. I’m sure Bro. Gardner has some detailed opinions that are worth much more than mine.
One of the strengths of this series has been the clear-cut delineation of hypotheses by Dr. Kyler Rasmussen. In every episode and with every encounter, he proposes claims from both the critic and the supporter in a two-fold or one-hand-as-opposed-to-the-other-hand type of presentation of opposing hypothesis. Instead of brushing the critic’s claims, criticisms and suppositions under the proverbial rug, Dr. Rasmussen elucidates the points carefully and succinctly, –along with the supporters opposite viewpoint. I really like how well he has done this.
From my perspective, Dr. Rasmussen has bent over backwards to grant an effectual guarantee of fairness to the opposing side, and yet no reciprocal compromise has been evident from even one of the opposing side’s comments. As I continue reading each episode and the subsequent comments, the summation of all of these opposing comments has been illuminating to say the least.
For example, it appears to me from my humble perspective that if Billy Shears is so good at what he does that he should be able to do his own analysis which would be fully supportive of his own particular biases. I’ve noticed multiple times that Bruce Dale and Dr. Rasmussen have directly invited and even supplied challenge to Billy to do his own Bayseian analysis. Billy ignores or stonewalls each time the challenge is presented.
On a side note, I don’t know Billy Shears, but I do know is that Billy Shears claims to be a credentialed academic. Our humble Professor Shears’ answer that ” Because of my background in statistics, I find the flaws in your methodology more important and more interesting…” sounds a little disingenuous to me, or the classic line here: “Part of my profession is as an educator who explains complex things to lay audiences, and explaining the flaws in your methodology to a lay audience is an interesting challenge…” sounds even more contrived. If the topic is so fascinating that he can’t bear to leave it alone, and he is such an ingenious maestro in statistical analysis, why can’t he do his own Bayseian analysis? He could cherry-pick his own equations and biases to his heart’s content then.
The bottom line on Billy Shears doing his own analysis is this: Either he can’t, or he won’t.
If he can, then either he’s afraid of the outcome or afraid of the perusal afterwards, because he won’t even concede to begin the attempt. If he can’t do his own analysis, it’s either because he isn’t as able as he claims, or he never had the capability in the first place.
Repeating the obvious, “Either he can’t, or he won’t,” and there are obvious reasons for either.
If our 2019 Interpreter paper was “inconsequential”, why did you spend so much time attacking it back then…and now? And if Interpreter is an inconsequential journal, why are are spending so much time attacking Kyler’s work now?
Why did you feel it necessary to introduce a piece of misleading evidence in the discussion on Episode 7? Why have you not responded to two invitations to explain to us why introducing that false evidence was an honest mistake on your part, and not a deliberate lie?
Why are you determined to avoid discussing the evidence itself? Why are you determined to keep the focus on the methodology rather than the evidence itself? Why have you refused my repeated offer to send you a copy of Coe’s Ninth Edition?
If the many points of evidence linking the Book of Mormon to ancient Mesoamerica as described by Dr. Coe and cited in our Interpreter paper don’t actually exist, you can easily examine them and refute them, can’t you? And if the correspondences don’t exist, then there is no need for any statistical analysis, is there?
It shouldn’t take you long at all to check the correspondences. We have provided detailed citations between Coe’s book and the Book of Mormon in Appendix A that demonstrate these correspondences.
If we are making this up, it should be easy to show. And it should be easy for you to use a better Bayesian approach to examine the newly-revised, rebutted list of evidences.
If the evidence doesn’t actually exist, then you can publish or proclaim that fact to the world, without any need for statistical analysis (or cognitive psychologists, for that matter). You can expose Brian and me as frauds and Interpreter as third-rate journal.
However, if the correspondences do exist, then you and other critics have a real problem don’t you? You have to explain how Joseph Smith “guessed” all these points of evidence at a time when nothing (according to Dr. Coe) was known about ancient Mesoamerica.
Your actions speak much louder than your words, Billy. Your actions shout that you are afraid to examine the evidence.
You asked me several questions. Here are the answers.
If our 2019 Interpreter paper was “inconsequential”, why did you spend so much time attacking it back then…and now? Great question. There are two main reasons. First, your arguments are interesting and second, why somebody would be convinced such terrible arguments were valid is very interesting. Part of my profession is as an educator who explains complex things to lay audiences, and explaining the flaws in your methodology to a lay audience is an interesting challenge.
Why have you not responded to two invitations to explain to us why introducing that false evidence was an honest mistake on your part, and not a deliberate lie? What false evidence? I thought we were done with that discussion, and I thought I won the debate. Regarding cardinal directions, ancient people who lived on land thought in terms of the direction the sun came up and the direction it went down. And they got North and South by looking half-way between those points. If you lived in Egypt, you thought in terms of the direction the Nile flowed. That is why there are hundreds of references in the Bible to the cardinal directions, and zero references to intercardinal directions. Likewise with the Book of Mormon, with only one anomalous exception. Sometimes people associated north with the north star. Otherwise, they thought of directions in terms of local landmarks.
The reference I supplied explains this. Yes, the paper mentions two exceptions. First, in Polynesian languages people thought of directions in terms of wind direction, so Polynesian languages have terms for “southeast wind,” “northeast wind,” and the like. The second exception are the Inupiat Eskimos who had terms to distinguish the north/northeast wind and the north/northwest wind ;these differences had important meteorological implications. The reason these two exceptions exist are because of the unique geographies of living on islands or living near the arctic circle.
In contrast, there is no evidence of people born and Raised in Jerusalem around the year 600 B.C. using a term like “nearly south-southeast,” nor is there a geographic reason why such a term would exist. I stand by what I said.
Why are you determined to avoid discussing the evidence itself? This question is built on a false premise. I am happy to engage in the actual evidence and have extensively done so.
Why are you determined to keep the focus on the methodology rather than the evidence itself? Because of my background in statistics, I find the flaws in your methodology more important and more interesting. After all, the statistics is how you came up with your ludicrous probability scores. Statistics is what drives how the evidence is scored and combined. This is fundamentally important for what you are doing.
Why have you refused my repeated offer to send you a copy of Coe’s Ninth Edition? As I’ve explained to you over and over and over, I already have a copy of Coe’s Ninth Edition. Why do you think I need a second copy in my library?
If the many points of evidence linking the Book of Mormon to ancient Mesoamerica as described by Dr. Coe and cited in our Interpreter paper don’t actually exist, you can easily examine them and refute them, can’t you? The question isn’t whether the “points of evidence” exist. The question is how they ought to be interpreted. But the answer is yes, I could easily refute the details of these correspondences and your assertion that they constitute strong evidence for authenticity. Of course I could. But I don’t see what the point of that would be.
However, if the correspondences do exist, then you and other critics have a real problem don’t you? The question isn’t whether the correspondences exist. The question is how they should be interpreted and what they actually imply. If they actually implied that the BoM is historical, why are you wasting your time presenting this information to the choir? Why not present your evidence to Dr. Coe’s peers in a mainstream journal?
See, now you’re just starting to call the arguments names. That’s a tactic I have a hard time respecting. It’d be one thing if such a term was backed up by the logic you’ve brought to bear. Readers can decide that for themselves, of course, but from where I sit that isn’t the case.
“I thought we were done with that discussion, and I thought I won the debate.”
This may be the area in which your personal bias is doing you the greatest disservice. I can assure you that the perception from many readers is very different from your own.
I wasn’t trying to be mean or win an argument via name calling. I was just trying to answer Bruce’s questions in a sincere and clear manner.
You said, “This may be the area in which your personal bias is doing you the greatest disservice.”
That’s fair, which is why I explained in relative detail why I still think “nearly south-southeast” is an anachronism and why I still think when read in context, the Cecil Brown paper supports my point.
“…there are hundreds of references in the Bible to the cardinal directions, and zero references to intercardinal directions.” “…there is no evidence of people born and Raised in Jerusalem around the year 600 B.C. using a term like ‘nearly south-southeast’.”
On the contrary, Billy, intercardinal directions were certainly familiar to biblical authors, but you may want to consult the NRSV for an accurate translation (I Ki 7:39, II Chron 4:10 “south-east” Hebrew hayemanit qedma). The Maya themselves had a more complex array of intercardinal directions than any other known culture. Moreover, long before the Maya, the Olmec had the magnetite compass (Dr Coe himself presenting the evidence for this), and it was used in laying out their great cities. Lehi & Nephi were even contemporaries of Thales of Miletus, who was well aware of the properties of lodestone (magnetite from Magnesia). We must not underestimate the knowledge and cleverness of ancient peoples.
You win! Your last comment is so funny that it would be churlish not to respond. 🙂 I have had professional disagreements with various colleagues over the years. We have aired our disagreements using the normal tools of scholarship: primarily by publishing peer-reviewed papers.
But I have never had a disagreement with anyone who offered to put me in touch with cognitive psychologists who can help me and the reviewers of our 2019 Interpreter article figure out how my son Brian and I could have written and published such a “terrible paper” (as you put it). That puts you in a class all by yourself.
Congratulations, you are sui generis.
And I am overwhelmed, deeply touched, moved to tears even, by your generous concern for me expressed thusly in your comment: “You (i.e., Bruce) should be interested in pursuing this [i.e. being interviewed by cognitive psychologists]—it has the potential to seriously improve your rational decision-making skills and improve the Interpreter’s peer review process.”
I was pretty sure I knew what “cognitive psychologists” do but I went ahead and looked it up, just to be certain. Sure enough: “Cognitive psychologists study the brain to understand how it works in order to develop treatment strategies for individuals with psychological disorders. For example, cognitive psychologists can use their knowledge of the brain to treat individuals with learning disorders.”
I graduated magna cum laude in a pretty demanding discipline (chemical engineering) and don’t seem to have any learning disorders. I have also held a variety of responsible administrative and management functions both professionally and in my church where any psychological disorders should have been obvious. But none were exposed.
Seriously, Billy, can’t you do better than that? Are you really reduced to casting baseless aspersions on people you disagree with?
Once again, I invite you, as Kyler has done repeatedly, please write your own paper. Explore our disagreements as scholars are supposed to do.
You say our Interpreter paper is “terrible”, and that our Bayesian methodology is the “worst choice”. Well, if there are other better choices in methodology, please use a better one to compare, as we have done, the correspondences between the Book of Mormon and Michael Coe’s Ninth Edition of The Maya. Then get your paper peer-reviewed and published. That is how honest scholarship works, Billy.
Speaking of honest scholarship, let me remind you and others of an exchange we had back in Episode 7. I had asked you provide a reference to support your claim that the ancients didn’t use intercardinal directions. You replied: “Please read Cecil Brown’s paper, “Where do Cardinal Direction Terms Come From?” in the journal Anthropological Linguistics, January 1983.”
Well, I did. I got Brown’s paper and read it carefully several times. Not only does Brown’s paper not support your claim, it supports exactly the opposite conclusion. The ancients did think in terms of intercardinal directions.
For those who may be masochistic enough to be reading this thread but don’t want to dig back into Episode 7, here is my response to Billy from that episode.
“You submitted the article by Brown to this discussion as proving your point that the ancients didn’t think in terms of intercardinal directions. Since the article says nothing of the kind, but rather supports exactly the opposite conclusion, I can think of only three possible reasons why you would do this.
You referenced the article either because:
1) you didn’t read it, but thought you could bluff your way through our discussion of this point by citing an obscure article that I either wouldn’t be able to find or wouldn’t take the time to read, or,
2) you did read it, but not carefully, and missed the 20 references to intercardinal directions in the article, or,
3) you did read it, saw the references to intercardinal directions, but decided to ignore them in an effort to win your point.
None of these explanations reflects well on you, Billy. Can you offer a more benign explanation? I do like to think well of people, especially people with whom I disagree. You are making that difficult for me.”
It has been almost two months since I asked you to provide a more benign explanation than any of those three possible explanations I provided.
I am still waiting. You are still making it very difficult for me to take you seriously.
I know many cognitive psychologists, and they’re very interesting people to talk to!
We could probably all use a good dose of humility when it comes to checking our biases and considering alternate assumptions. But Billy should probably be more concerned about pulling the beam out of his own eye in this case.
You asked me, “Seriously, Billy, can’t you do better than that? Are you really reduced to casting baseless aspersions on people you disagree with?”
You misunderstand. Cognitive biases are a real phenomenon and are a part of normal, healthy, human psychology. We all have our blind spots. I cited two top-tier psychologists (Daniel Kahneman and Steven Pinker) who both know that highly educated and accomplished people can be irrational in certain circumstances, especially when defending their pet ideas. The title of an article in Scientific American summarizes my point succinctly: “Smart People Believe Weird Things: Rarely does anyone weigh facts before deciding what to believe.” (https://www.scientificamerican.com/article/smart-people-believe-weir/)
Here is the reality of the situation:
You published a paper that concluded, “the cumulative weight of these correspondences, analyzed using Bayesian statistics, provides overwhelming support for the historicity of the Book of Mormon as an authentic, factual record set in ancient Mesoamerica.”
Scientists are superlatively interested in ancient texts that shine light on the factual reality of the ancient world. If you would have published your above conclusions in a legitimate and relevant peer-reviewed journal, it would be universally considered the most important article of the century in all of archeology.
However, your paper is being completely ignored outside of the narrow world of Mormon apologetics, and the answer as to why is obvious. There is no reason for any respectable journal to publish a response because this paper doesn’t merit a response.
To reiterate, I believe qualified scholars will *unanimously* agree with me: your methodology is fundamentally and irredeemably flawed. Consequently, there is no reason to write a response.
I’ve already suggested a way to prove that I’m wrong: just produce a single qualified scholar who will publicly defend you. Just one. If you can produce a single qualified expert who will commit to publicly evaluating my position, I’ll write a concise paper that lays it out. But if nobody takes your paper seriously, there is no reason to write a response.
Speaking of cognitive biases being “a real phenomenon,” here are five easy examples from your response, Billy:
Speaking more directly to example #5, if nobody except the anti-Mormon faction of the apologetics backwater in which we apparently all swim has taken notice, then how can that anti-Mormon faction make the rock-solid determination that the paper “doesn’t merit a response?” Oh, wait… could it be because of cognitive bias on the part of the anti-Mormon faction? Yeah, could be, but those in the faction (Billy Shears included) will never acknowledge their own biases, just discount those they disagree with because it is ALWAYS the opposite side that is biased.
And, I can’t help but point out this gem: “I believe qualified scholars will *unanimously* agree with me: your methodology is fundamentally and irredeemably flawed. Consequently, there is no reason to write a response.”
This seems a classic example of the post hoc ergo propter hoc fallacy. Nice job, but your cognitive bias probably won’t allow you to perceive it.
Finally, the following is nothing but hand-waving:
Why? Because you never take the time to define what a “qualified scholar” is. I could produce the names of the multiple scholars who did the peer review on the Dales’ paper (since I managed that process), but you would no doubt dismiss them as “unqualified” because, I suspect, they don’t agree with your conclusions. And, of course, because you’ve already dismissed Interpreter as an illegitimate and irrelevant journal. Much easier to simply wave the hand and dismiss any call for you, as a critic, to put up or shut up (as we used to say on the playground).
Those snippets you quoted are all true. Within the realms of archeology and anthropology, scientists are superlatively interested in authentic ancient manuscripts. Is Interpreter a legitimate and relevant peer-reviewed journal in the realm of identifying and authenticating “authentic, factual records set in ancient Mesoamerica”? I’m willing to be proven wrong here, but the answer is clearly no. Do journals like, say, “Ancient Mesoamerica” ever cite Interpreter? Of course not.
I already defined what a qualified scholar is. If somebody teaches Bayesian statistics at the graduate level, or has published specifically about Bayesian statistics in a legitimate journal about math or statistics, I would consider that qualified. Somebody who sometimes uses Bayesian analysis in engineering or psychology? No.
Kyler has pointed out that he is nothing if not an optimist. I am a lot older than Kyler, so perhaps I have more experience with reality than he does. Therefore I am less of an optimist. 🙂 But I am glad for Kyler’s optimism because it has motivated me to make one more optimistic invitation to you, Billy.
Our Interpreter paper from 2019 had some weaknesses, including the issue of independence of correspondences that you and Kyler have properly pointed out. Our upcoming paper will deal with the independence issue and several other important topics. That said, our 2019 Interpreter paper is, to my knowledge, the only study to date that compares evidence both for and against the Book of Mormon based on the work of an avowed skeptic of the Book of Mormon, Dr. Michael Coe.
Furthermore, our study analyzed, within a Bayesian statistical framework, this large body of evidence both for and against the Book of Mormon, so as to provide a quantitative answer to the question: “Is the Book of Mormon an authentic ancient document or is it a work of fiction?” Once again, I am not aware of anyone who has attempted to do something like that for the Book of Mormon.
As I mentioned in a previous comment, the existence (or not) of those correspondences is the critical issue here. And the existence (or not) of the correspondences is the issue you have declined to deal with for over two years.
How we weight the value of the evidence provided by each correspondence (or each negative point of evidence) is an important factor, but it is secondary. If you do not agree with our method of statistical analysis, then please propose and defend your own approach to weighting the evidence.
For over two years, you have successfully avoided any real engagement with the evidence summarized in our first paper. So once again, as I did over two years ago, I offer to send you a free copy of the Ninth Edition of The Maya so that you can check those 131 correspondences and see if we are making this all up or if those correspondences really do exist.
If they do not exist, then by all means expose us as a fraud.
You said, “As I mentioned in a previous comment, the existence (or not) of those correspondences is the critical issue here.”
Yes, you said that. However, you are absolutely, positively wrong about that. The issue is most assuredly NOT whether these correspondences exist. The issue is the following two things:
1- How likely are we to see the actual evidence we have under the hypothesis the BoM is an authentic ancient record?
2- How likely are we to see the actual evidence we have under the hypothesis the BoM is fiction?
A reasonable estimation of the ratio of those two things is the real issue. Your infatuation with counting correspondences and your system of scoring them are a flagrant abuses of statistics. You are causing Thomas Bayes to roll in his grave. I’ve explained this to you this before in detail. I’ve provided references. Yet you continue to ignore it.
“For over two years, you have successfully avoided any real engagement with the evidence summarized in our first paper. So once again, as I did over two years ago, I offer to send you a free copy of the Ninth Edition of The Maya so that you can check those 131 correspondences and see if we are making this all up or if those correspondences really do exist.”
This is the type of comment that makes me even less optimistic than you are. Two years ago I engaged with several of your so-called correspondences in detail. In doing so, I sometimes quoted extensively from the Ninth Edition of The Maya. In fact, I copied one of those comments here (see my comments titled “On Calendars, Part 1:” and “On Calendars, Part 2:” (my engagement of this correspondence was so extensive it didn’t fit into the 5,000 character limit per post and I needed to spread it across two posts).
Now you are refusing to acknowledge that I’ve engaged with the evidence. Further, you are refusing to even acknowledge that I obviously already own a copy of that book from which I quote.
Here is my offer to you. I’ll write a 2-3 page paper explaining why your methodology is fundamentally flawed. I’ll include my real name and a brief bio with my qualifications on the bottom. You choose a qualified expert at Bayesian statistics to critique my paper. It can be anybody you choose, but he needs to be qualified. By qualified, I’m imagining a Ph.D. in math or statistics who has published about Bayesian statistics in respectable journals with statistics as its primary focus, or a Ph.D. who teaches Bayesian statistics at the graduate level. And hopefully he’ll be near the middle of his career so that he is motivated to care about his academic reputation.
I’ll pay the expert you choose to review my paper. (I’m hoping he’ll do it for about $1,000). He’ll need to write a short report and give us permission to publish it on the Internet. The report needs to answer two questions. 1- In his professional opinion, is your methodology basically sound. 2- In his professional opinion, is my critique of your methodology basically valid. The scope of this is limited to methodology (i.e. are you right when you say, “the existence (or not) of those correspondences is the critical issue here”).
If he concludes you are basically right and I’m basically wrong, I’ll need to donate $1,000 to the charity of your choice. But if he concludes I am basically right and you are basically wrong, then *you* need to donate $1,000 to the charity of my choice.
What do you think? Do you *really* want me to expose you as a fraud?
This feels like an odd bet to make. His paper’s been published for all to see. You, as a credentialed expert, have made your views thoroughly known where anyone reading the paper can see. I’m sure you could find people who’d agree with you, but I’m not sure why you’d need to certify that fact.
In my estimation, the best way to move the conversation forward would be to contribute to it, officially and publically. Instead of a 2-3 pager, why don’t you put together a full paper? I’m sure Dialogue would be happy to publish it. Surely with your credentials that wouldn’t be a problem, and I imagine your thoughts here would survive peer review. That would feel quite a bit more open and worthwhile than what you’re attempting here.
Just a thought.
“This feels like an odd bet to make. His paper’s been published for all to see. You, as a credentialed expert, have made your views thoroughly known where anyone reading the paper can see. I’m sure you could find people who’d agree with you, but I’m not sure why you’d need to certify that fact.”
I was selected as an expert witness in a legal dispute involving several billion dollars. The two parties were under contract to have their dispute settled by arbitration. The arbitration was to be settled by a panel of three arbitrators, and the method for selecting the panel was clearly laid out in the contract.
Despite the fact the contract said disputes will be settled by arbitration, for over a year the case was tied up in court. The two parties were suing each other over who the three arbitrators will be.
I bring this up because it illustrates that in a real-world dispute, people have different views, philosophies, and biases. If your position is the least bit reasonable, it’s relatively easy to find people who will agree with your side or are likely to agree with your side.
The point of my proposed bet is not for me to find people who agree with me. Doing so would be beyond easy. The point is this: can Bruce find a single qualified expert who agrees with him and is willing to say so publicly? For purposes of my bet, the arbitration panel is one person hand-picked by Bruce. As long as the individual is in fact qualified to state an opinion, it can be *anybody* Bruce chooses. Can he find one expert–just one–who agrees with him? The scope here is just one narrow question: is his methodology (i.e. “the existence (or not) of those correspondences is the critical issue here”) valid?
“In my estimation, the best way to move the conversation forward would be to contribute to it, officially and publically. Instead of a 2-3 pager, why don’t you put together a full paper? I’m sure Dialogue would be happy to publish it.”
I won’t put together a full paper because there is no need to. Bruce’s basic methodology (i.e. counting specific, detailed, and unusual correspondences) is so fundamentally flawed it is self-refuting. Just as it is beneath the dignity of, say, the Journal of Anthropological Archaeology to respond, it is beneath the dignity of Dialogue to respond. Outside of the Interpreter’s bubble, nobody takes this seriously.
I’m genuinely interested in seeing if Bruce could find a single expert who thinks his methodology isn’t fundamentally flawed. Just one. I’m betting he can’t, am willing to pay money to get the question answered.
No thanks, Billy.
You want to focus on a methodology you think is flawed. But I don’t see why you are concerned about how to analyze evidence that you obviously don’t believe exists in the first place. If you are thinking we made up those 131 correspondences we cited in our Interpreter paper, then just say so and have done with it. If the evidence doesn’t exist, we are wasting time here.
I agree that almost any analytical methodology has limitations. The Bayesian method my son Brian and I applied in our Interpreter paper may indeed be the best choice among set of bad options. It may be the cleanest dirty shirt in the laundry. But before it was published, that paper went through one of the most rigorous and demanding reviews that I have ever experienced in 40 plus years of writing 300 plus research papers and 60 plus patents.
The review of our paper included an explicit review of the Bayesian analytical framework, and was judged satisfactory. But from my point of view, the most important quality control on the Bayesian statistics was provided by my son Brian, a Ph. D. biomedical engineer who uses Bayesian methods every day in his job at Siemens Medical Solutions.
So if you think our paper was flawed, I invite you to do better, as Kyler has suggested. Write your own paper on Michael Coe’s description of the culture, geography, warfare, religion, political structures, etc. of ancient Mesoamerica as compared with corresponding statements in the Book of Mormon. Use a better analytical methodology, get your paper peer-reviewed and published. Then maybe we can discuss this issue further.
Until then, I am done with this discussion on Episode 14…write whatever you want in reply. I am going to do more productive and useful things.
To be clear, the Bayesian method you and Brian applied in your Interpreter paper is not the best choice among a set of bad options. It is the worst choice. It isn’t the cleanest dirty shirt in the laundry. It is the dirtiest.
After the space shuttle Columbia disaster, an accident investigation board was convened to figure out what had happened. Ultimately the disaster was preventable, so how did the extraordinarily intelligent, well-educated, and motivated engineers at NASA allow this to happen? One of the board’s primary focuses had to do with NASA’s organizational issues, cultural issues, and decision-making processes.
I bring this up because your paper does raise a serious academic question that would be of interest to the scholarly community. How did something that aspires to be a respectable journal go through “one of the most rigorous and demanding reviews that you have ever experienced,” yet still ended up publishing such a terrible paper? What happened? If you and the reviewers would be willing to be interviewed by a team of cognitive psychologists and give them your correspondence from the review process, a fascinating case study in cognitive biases and group decision making could be made. You should be interested in pursuing this—it has the potential to seriously improve your rational decision-making skills and improve the Interpreter’s peer review process. If you’re interested, let me know and I’ll put you in contact with a cognitive psychologist who might be interested in leading the research.
Of course it’s possible that I’m wrong. I am not immune to biases. But if I am wrong, how could I be disabused of my incorrect opinion? Referring to Daniel Kahneman, an eminent expert on the psychology of decision-making, Steven Pinker said the following:
“Kahneman has observed that humans are never so irrational as when protecting their pet ideas. So he advocated a new method for resolving scientific controversies to replace the time-honored custom of the rivals taking turns moving the goalposts and talking trash in volleys of rejoinders and replies. In an “adversarial collaboration,” the disputants agree in advance on an empirical test that would settle the matter, and invite an arbiter to join them in carrying it out.” (Pinker, Steven. Rationality (p. 29))
That is basically the approach I was trying to take with my proposed bet. My hypothesis is that your methodology is so bad that you can’t find one qualified expert who will publicly defend it. If you don’t want to have the betting element to the deal, that’s fine. Just produce one qualified expert who will agree to read a concise paper about why your methodology is irredeemably flawed, and will then publicly opine on whether or not I’m right. If you can’t find an expert who has the free time to seriously consider this, then I would be willing to pay him for his valuable time.
If you have another idea for how we can engage in adversarial collaboration and resolve this, please let me know.
“It isn’t the cleanest dirty shirt in the laundry. It is the dirtiest.”
And yet in all your comments both here in and for the Dales’ paper, you’ve yet to propose an alternative.
The only alternative that I see would be to sit back and trust in the mainstream consensus (which, it turns out, aligns pretty well with the evidence score I’ve assigned here). My main issue with that approach is that it essentially ignores everything the BofM gets right about Mesoamerican culture, (not to mention the degree to which the BofM makes more sense if placed in a Mesoamerican setting, none of which are treated here). I prefer a method that allows us to take into account the evidence we see, as well as what hasn’t yet been observed.
“Just produce one qualified expert who will agree to read a concise paper about why your methodology is irredeemably flawed, and will then publicly opine on whether or not I’m right.”
I’ll just note here that all my essays were reviewed by a PhD-level probability theorist, and he generally agreed with my framing here. And I’ve conversed with him enough on the topic of Bayesian analysis to have a sense of how he’d feel about your arguments.
As to why he’s not coming forward to opine publicly on the topic, I suspect there’s two reasons: 1) I don’t think anyone is under the illusion that such opining would end your current pattern of rejoinders and replies, and 2) he would rather avoid devoting his life to responding to those with the …vigor…you’ve displayed here. Though I’ve enjoyed our tete-a-tete over the last few months, I completely understand why someone might decide that they had more important matters on their plate.
“If you have another idea for how we can engage in adversarial collaboration and resolve this, please let me know.”
I would settle for you presenting a serious alternative proposal for weighing all the archaelogical evidence for the Book of Mormon, both for and against, and working together to determine where and in what ways we agree and disagree. From there, we could see if there might be such adversarial arrangements that we both agree could settle the matter, and where we might instead have to settle to agree to disagree.
I appreciate very much the work you have done here and for your respectful treatment of our previous article. That said, I have several points of disagreement/concern that I wish to raise.
First, a casual reader of this article may come away with the impression that all the correspondences between the Book of Mormon and ancient Mesoamerica have been identified and dealt with in your analysis. But that is not correct.
As you mention, Sorenson identified 420 correspondences between the Book of Mormon and ancient Mesoamerica in his book Mormon’s Codex. Your article deals with only 131 of the correspondences, the ones we identified and analyzed in our previous Interpreter article.
Although I had read Sorenson’s book twice, and knew about these additional correspondences, we limited our article to only those correspondences found in both the Book of Mormon and Coe’s book The Maya. The major purpose of our article was to address Coe’s very negative characterization of the Book of Mormon with facts from his own book, not to summarize and analyze all of the evidence supporting an ancient Mesoamerican setting for the Book of Mormon.
Since we limited ourselves to those 131 correspondences and your analysis is based largely on our article, less than one third of the known correspondences are treated in your current episode. Thus the totality of the evidence supporting an ancient Mesoamerican setting for the Book of Mormon is severely under-represented in Episode 14.
Second, while I agree with your generous approach to the skeptical position, I think you have gone too far here. Not all evidence is equally strong…or equally weak. But the assumption you made to get to your final result of a four orders of magnitude decrease in the authenticity of the Book of Mormon is that all supporting evidence is equally weak. In fact, it the very weakest likelihood we considered (0.5 for the converse hypothesis). While this approach may be useful as part of a sensitivity analysis, I don’t think it is valid to use this approach to arrive at your final conclusion, as you have done here.
Third, it is appropriate to deal carefully and conservatively with the independence of the positive correspondences in support of the Book of Mormon, as you have done. But I believe it is inappropriate not to deal the same way with the independence of the negative correspondences, those points of evidence that contradict the Book of Mormon. Unfortunately, you did not examine the negative correspondences to determine which of them might not be independent.
For example, the failure to find iron, brass, steel, copper and refined gold and silver in ancient Mesoamerica, all of which are counted as individual, independent negative correspondences in our analysis, can be subsumed under a single independent correspondence “lack of metallurgy”. Likewise the lack of sheep, goats, swine and cattle, can be subsumed under another correspondence “no domesticated food animals”.
Thanks for considering these points and for any comments you might choose to make in response.
Thanks for the comment Bruce. I really do have substantial respect for your previous article–it represents a tremendous amount of effort, and I’m doing little more than building a small hut on its shoulders.
“Thus the totality of the evidence supporting an ancient Mesoamerican setting for the Book of Mormon is severely under-represented in Episode 14.”
Completely agreed. Anyone who wants a full picture of Mesoamerican correspondences should absolutely turn to books like Mormon’s Codex and Traditions of the Fathers. All my essay helps to demonstrate is that even a minimalist reading of those correspondences suggests that chance would be insufficient to produce those connections.
“I think you have gone too far here.”
Yep. It’s much too far, and my estimate provides a greater advantage to the critics that is actually reasonable, and I hope the critics are able to recognize that.
“Unfortunately, you did not examine the negative correspondences to determine which of them might not be independent.”
Completely agreed. Any critic that attempts a serious counter-proposal here (and I think they should absolutely try to do that–though watching them try to exercise a fortiori reasoning on behalf of the restoration would be…entertaining) will very much need to keep the independence issue in mind when it comes to the negative evidence.
Thanks again Bruce!
On Calendars, Part 2:
In contrast, here are some quotes from Cole: “The Calendar Round of 52 years was present among all Mesomaericans, including the Maya, and is presumably of very great age. It consists of two permutating cycles. One is of 260 days, representing the intermeshing of a sequence of the numbers 1 through 13 with 20 named days…the 260-day count was fundamental…Meshing with the 260-day count is a “vague year” or Ha’b of 365 days…from this it follows that a particular day in the 260-day count, such as 1 K’an, also had a position in the Ha’b, for instance 2 Pop. A day designated as 1 Ka’n 2 Pop could not return until 52 Ha’b (18,980 days) had passed. This is the Calendar Round, and it is the only annual time count possessed by the highland peoples of Mexico….”
But for keeping track of history, the Mayans didn’t count Calendar Rounds, much less “vague years.” Rather, they used Long Counts. Quoting Coe:
“Instead of taking the Vague Year as the basis for the Long Count, the Maya and other peoples employed the turn, a period of 360 days. The Long Cycles are:
20 k’ins = 1 winal or 20 days
18 winals = 1 turn or 360 days
20 turns = 1 k’atun or 7,200 days
20 k’atuns = 1 bak’tun or 144,000 days
“Long Count dates inscribed by the Maya on their monuments consist of the above cycles listed from top to bottom in descending order of magnitude, each with its numerical coefficient, and all to be added up so as to express the number of days elapsed since the end of the last but one Great Cycle, a period of 13 bak’tuns the ending of which fell on the date 4 Ajaw 8 Kumk’u….”
Analysis: The Book of Mormon keeps track of history in months and years in a way that is indistinguishable from the Gregorian calendar, and is carefully calibrated so that Lehi leaving Jerusalem, the birth of Christ, and the death of Christ can all be reconciled with old-world history. In contrast, the Mayans kept track of historical days using Long Count days, which is really about counting up days since the end of the last “great cycle,” but rather than being “base 10” as we would count, they are counted using k’ins, winals, tuns, k’atuns, and bak’tuns. There is nothing in this that could be construed as months and years, nor could it easily be converted into lunar months and solar years.
Central to Mayan life were 260 day cycles. Central to Book of Mormon life were 7-day weeks.
The calendar in the Book of Mormon has nothing to do with the Mayan Calendar. This is very strong evidence that it is not based on Mesoamerican history. I score this a “likelihood ratio” of 50+.
I hate to wave away the effort you put into your well-structured prose, but these arguments simply don’t engage with the relevant scholarship on the issue. See, for example:
Must the Book of Mormon have used 260- or 360-day calendars in order to align with Mesoamerican practices? No, the Mayans used many calendars, including the 365-day solar calendar. The Hebrew lunar-solar calendar could’ve been compatible with how the Mayans kept track of time.
Could the Book of Mormon have been based on the 360-day calendar used in the Mayan Long Count? There’s disagreement on that, but notable faithful mesoamericanists seem to think it’s possible.
Does it make sense for the Mormon and other authors to have maintained the Hebrew calendar rather than universally adopt local calendrical practices? I think the answer to this is an obvious yes, given the importance to the Nephites of maintaining other Hebrew cultural traditions, and for the sake of consistency between Lehi’s and Mormon’s framing of time.
Is there no evidence that the Book of Mormon was influenced by mayan calendrical practices? Mark Wright, Brant Gardner, and John Sorenson seem to think that it was, particularly in terms of framing dates in terms of year-groupings of 400 and 20. And that certainly would comport with what we seem to see in the Caractors document.
In short, I see few reasons to count Book of Mormon calendrical pracitces as evidence against authenticity, and several reasons to see Joseph’s treatment of the calendar and of the scribes who took care of it as unusual.
But really, thanks for taking the time to spell out your thoughts here. These are exactly the kind of conversations that need to happen if we hope to garner any kind of consensus on Book of Mormon evidence (it’s a pipe-dream, I know, but I’m nothing if not an optimist).
On Calendars, Part 1:
Beyond the systematic bias I described earlier, the judgment on the correspondences is biased. As a specific example, in a comment about his paper, Bruce highlighted Correspondence 6.2 (“Calendar kept by day, month and year”) as being an especially strong hit and said, “the Book of Mormon is very much congruent with ancient Mesoamerican Indian cultures.”
To his (partial) credit, this is one of the correspondences Kyler rejected due to the shortcomings he identified. However, Kyler didn’t go far enough. To understand why, we need to understand what likelihood ratios mean—they are a comparison of how *likely* it is that we’d see the evidence that we see under the made-up hypothesis divided by how *likely* it is that we’d see the evidence we see under the authentic hypothesis. It isn’t enough to say there is something mentioned in both books that is “specific, detailed, and unusual.” The specific and detailed elements need to match in a way that is relatively unlikely for Joseph Smith to make up yet likely to be seen in an authentic record.
It turns out that the Maya and the Book of Mormon both talk extensively about calendars, and the details of these calendars fit very neatly into 19th century American Fiction and don’t fit at all in ancient Mayan history. Repeating my comments from the Dale’s paper on this:
The null hypothesis of the Book of Mormon is that it is a made-up account of a group of proto-Christian Jews who immigrated from Jerusalem to the New World in 600 B.C. These people brought their Jewish/Christian heritage with them, built a great civilization (as evidenced by the then well-known Moundbuilders who had once inhabited North America), and after 1,000 years they fell from grace and devolved into the “savages” that were discovered 1,000 years after that. Anything that is consistent with how Joseph Smith could have reasonably conceived of an epic story of a group of people who went from being pilgrims from Jerusalem to civilized Moundbuilders to savages over the course of thousands of years is completely consistent with this theory.
The Jewish calendar is based lunar months, solar years, and pays particular attention paid to the seasons (that is why Easter is the first Sunday after the first full moon after the Spring Equinox), and most importantly, seven-day weeks. This calendar eventually evolved into the Gregorian calendar which Joseph Smith used and is still used today.
Everything regarding dates and calendars in the Book of Mormon is consistent with this. They had seven-day weeks and kept the sabbath holy (e.g. Jarom 1:5, Mosiah 18:25, Alma 32:11). They had lunar months (Omni 1:21). Solar years were carefully counted, sometimes in unlikely ways (e.g. 3 Nephi 5:7). According to this counting, one can easily verify that Lehi left Jerusalem in 600 B.C., right before the fall of Jerusalem, that Jesus was then born on cue in 1 BC, and then died, was resurrected, and visited them 33 years later, right on cue. This all seems like it was written by somebody creating historical fiction that needed to calibrate with some events that were predefined and presumed to be historic. The counting is done exactly as somebody using a Gregorian calendar would do it.
This is a response to your parts 1 and 2, Billy:
“…for keeping track of history, the Mayans…used Long Counts”[360-day year tuns]
That is certainly correct, and John Sorenson long ago suggested that the tun-year common to all of Mesoamerica was the basis of the Book of Mormon calendar, while archeologist John E. Clark has said:
“A correspondence that has always impressed me involves prophecies in 400-year blocks. The Maya were obsessed with time, and they carved precise dates on their stone monuments that began with the count of 400 years, an interval called a baktun. Each baktun was made up of 20 katuns, an extremely important 20-year interval. If you permit me some liberties with the text, Samuel the Lamanite warned the Nephites that one baktun “shall not pass away before . . . they [would] be smitten” (Helaman 13:9). Nephi and Alma uttered the same baktun prophecy, and Moroni recorded its fulfillment. Moroni bids us farewell just after the first katun of this final baktun, or 420 years since the “sign was given of the coming of Christ” (Moroni 10:1). What are the chances of Joseph Smith guessing correctly the vigesimal system of timekeeping and prophesying among the Maya and their neighbors over 50 years before scholars stumbled onto it?” (Clark in JBMS, 14/2 :38-49,71-74).
Lord Yax Kuk Mo’, for example, apparently came from central Mexico to Copán, Honduras, with his warrior retinue, took over, and began to rule at the beginning of baktun 9 (8 Ahau 13 Ceh, 126.96.36.199.0 = 11 Dec 435 A.D.), and his dynasty continued to rule Copán until the end of baktun 9, four hundred Long Count years later, i.e., the dynasty ruled for one baktun (Schele & Freidel 1990:311-313).
“The calendar in the Book of Mormon has nothing to do with the Mayan Calendar”
The Book of Mormon calendar “fit very neatly into 19th century American Fiction and don’t fit at all in ancient Mayan history.”
“Lehi left Jerusalem in 600 B.C., right before the fall of Jerusalem, that Jesus was then born on cue in 1 BC, and then died, was resurrected, and visited them 33 years later, right on cue.”
It is true that the BofM does give three precise interlocking dates: The 600-year prophecy, Jesus’birth, and Jesus’death 33 years and 3 days later. And one could indeed account for them as a fictional accommodation to 19th century notions. What is remarkable, however, is that the absolute archeological date of King Zedekiah’s first year is 597 B.C., and 600 tuns later fits the best scholarly date for Jesus’ birth, the Fall of 5 B.C. 33 tuns later would be at Passover, right on cue. No other calendar fits the actual time constraints.
Even more impressive is the correlation unknown to the Bible of the weights & measures in Alma 11 with the Israelite-Egyptian system of weights & measures used in Israel & Judah in the 8th and 7th centuries B.C. (Contemporary with Lehi & Nephi). Non-LDS archeologists have only been able to reconstruct that system in the last 50 years from extensive finds of standardized limestone weights with Egyptian hieratic designations. Why are Israelites and Jews using Egyptian hieratic on their weights? Probably because Egypt was the neighboring great power with whom they did a lot of trade.
Thanks for the detailed reply. Helaman 13:9 giving a prophesy of 400 years is interesting, but it’s important to remember that a baktun is NOT 400 years. A baktun is 144,000 days, which is about 394 years and 3 months. If the Samuel had prophesied 394 years rather than an even 400, THAT would be interesting. As it is, this seems like data mining with round numbers to make something fit better than it really does.
In detail this can’t be a rounding error. If Samuel would have actually said “1 baktun shall not pass away until they be smitten” and this was merely rounded to 400 years in the translation process, then Samuel’s prophesy would have failed–the judgment didn’t come until about 6 years after 1 baktun.
Likewise, in Moroni 10:1, Moroni said “more than 420 years have passed away.” In long-count cycles “more than 420 years” is actually “more than” 1 baktun, 1 katun, 6 winals, 2 kins, and 5 days. For a people obsessed with time, rounding this to 1 baktun and 1 katun is not a hit. So, “what are the chances of Joseph Smith guessing correctly the vigesimal system of timekeeping and prophesying among the Maya and their neighbors over 50 years before scholars stumbled onto it?” Pretty low. If he would have guessed it correctly that would be impressive, but he did not.
You said, “What is remarkable, however, is that the absolute archeological date of King Zedekiah’s first year is 597 B.C., and 600 tuns later fits the best scholarly date for Jesus’ birth, the Fall of 5 B.C. 33 tuns later would be at Passover, right on cue.”
I don’t see how old-world events corresponding to a new-world calendar system has much to do with the BoM. Indeed, according to the BoM we know Jesus wasn’t born in the Fall of 5 B.C., we know he was born in 1 B.C.
But anyway, this is the level of analysis that is needed here and I thank you for engaging with it. If the calendar system implied by the BoM fits better with the Mayan calendar than with the Gregorian calendar, that is evidence in favor of the BoM. But if the calendar system fits better with the Gregorian system, it is evidence of modernity.
You stated: “Helaman 13:9 giving a prophesy of 400 years is interesting, but it’s important to remember that a baktun is NOT 400 years. A baktun is 144,000 days, which is about 394 years and 3 months.” Then later: “I don’t see how old-world events corresponding to a new-world calendar system has much to do with the BoM. Indeed, according to the BoM we know Jesus wasn’t born in the Fall of 5 B.C., we know he was born in 1 B.C.”
I can easily understand why you would not have spent a lot of time trying to understand the meaning of “year” in the Book of Mormon, but please understand that your responses to Bob reflect that lack of understanding rather than an actual issue. There are different definitions of what a “year” is, and either the lunar year (used in Israel) or the Mesoamerican tun-year were both shorter–and close enough that either system’s “year” fits the known dating based on our modern understanding of calendars.
As Bob noted, the Book of Mormon year fits better with the Mesoamerican tun, or the Old World’s lunar calendar.
While counted numbers have some suggestion of a base 10 system (it was printed in English, of course), there are a large number of significant years that do not fit base-10 expectations, but do fit rather nicely with the base-20 assumption (the Mesoamerican system).
“If the calendar system implied by the BoM fits better with the Mayan calendar than with the Gregorian calendar, that is evidence in favor of the BoM.”
Thank you. That is exactly the point I was making, although you completely misunderstood Dr Clark’s point about using tun-years, not Gregorian years, to understand the BofM dates. There is thus no need for rounding or imprecision. The 360-day tun-year accommodates all your objections and requirements, and fits archeological reality like a glove. Do the math.
Does this mean that the dates that modern editors have added to the chapter headings are off, because the editors incorrectly thought “year” meant solar year and not 360-day tuns?
I’ll answer for Robert. Yes, they are off. They (as did you) assumed a solar year.
Yes. I began systematically inserting tun-year dates into the BofM in 1984, with the first edition of my Book of Mormon Critical Text (published by FARMS), and included an appendix with all the dates in a spreadsheet.
The LDS Church began inserting generic solar year dates in the 1920 edition of the BofM.
I was accused of making an “unsubstantiated claim of bias” in regards to the Dale & Dale paper, so for the interested reader, I’d like to go ahead and substantiate it.
In this episode, Rasmussen claims that the Dales limiting their work to correspondences and anachronisms that could be found specifically in the Maya is “commendable.” I disagree—this is a systematic bias that by itself would be enough to discredit the entire endeavor (but it’s also mainly a mute point, because as far as I can tell, not a single one of the so-called correspondences has a likelihood ratio as strong as what they claim).
Why is this a systematic bias? Because a book about the Maya simply shouldn’t be expected to talk about things that aren’t a part of Mayan history or culture. It shouldn’t be expected to say things like, “The Mayans weren’t Christians. The Mayans didn’t record records on gold plates. The Mayans didn’t divide their society into a group of white Nephites and dark Lamanites. The Mayans didn’t quote Isaiah in their sacred books…”
Because the Maya talks about positive things rather than negative things, the methodology is fundamentally biased towards finding positive correspondences.
That is my hypothesis. Can it be tested? Yes. We can apply their methodology to a book that everybody concedes isn’t about the Maya. If their methodology is valid, their methodology should conclusively prove that the book really isn’t about the Maya. If their methodology is invalid, it could indicate that it is likely the non-Mayan book *is* about the Maya.
Here is the test. When the Dales applied their methodology to View of the Hebrews, the positive correspondences outweighed the negative ones. Using a pure frequentist approach, their methodology of selecting evidence and their weighting of the evidence indicates that we can be 98.46% certain that View of the Hebrews is about the Mayan. That is what *their* analysis of the evidence *they* selected says!!! The likelihood of View of the Hebrews being about the Maya is 98.46%.
It’s important to keep in mind that the View of the Hebrews is only 227 pages long. If it were 800 pages long and the ratio between positive and negative correspondences persisted, we would be 99.99996% sure the book was Mayan.
Since we know the View of the Hebrews really isn’t about the Maya, this proves their methodology of selecting and weighting evidence is flawed. They obfuscate this fact by multiplying the likelihood ratio by an arbitrarily high skeptical prior, but this is irrelevant to the point—irrespective of the a priori belief, the likelihood of View of the Hebrews being Mayan is 0%, not 98.46%. A methodology that indicates View of the Hebrews is likely Mayan is fundamentally and systematically flawed.
“Rasmussen claims that the Dales limiting their work to correspondences and anachronisms that could be found specifically in the Maya”
It’s a good thing that they didn’t do this, and that I didn’t say that they did. They limited themselves to correspondences that could be found there, but their anachronisms were a different bag. Of course we wouldn’t expect The Maya to discuss specific Book of Mormon issues, but we should expect Coe to in articles he’s written and interviews he’s conducted about the BofM, which is where the majority of their negative correspondences were drawn.
“Using a pure frequentist approach, their methodology of selecting evidence and their weighting of the evidence indicates that we can be 98.46% certain that View of the Hebrews is about the Mayan.”
This is, of course, a dramatic misinterpretation of their probability estimates (and represents the most common mistake that I saw freshman Psychology students making about p values). What their p = .015 represents is the probability of observing those correspondences if the text has no connection with The Maya, which is a very different proposition. As is plain from my previous analyses, p = .015 would ultimately give us a very weak evidence score, and it would certainly fail to overcome even a sympathetic prior.
But even then, we could rightly ask if there really is NO connection between View of the Hebrews and the Maya, and if it really is raw chance producing those correspondences. The fact that View of the Hebrews provides a (mostly inaccurate) description of ancient peoples living in the same time period and that shared (distant) cultural origins suggest that some of those correspondences were not due to blind guesses, but reflect real similarities between the two cultures. In which case, that p value is absolutely doing its job, and it’s entirely our fault if we fail to look for better explanations for why those correspondences exist (as your accusation of bias implicitly fails to do).
When it comes to the Book of Mormon both the Dales and I have worked pretty hard to examine and account for those alternate explanations (e.g., borrowing from the Bible or from View of the Hebrews or from his understanding of mound builder cuture), so your complaint has little to no bearing on what I’ve done here.
“It’s important to keep in mind that the View of the Hebrews is only 227 pages long.”
Now this is a claim that actually has some substance to it–the idea that longer books that favor certain kinds of correspondences systematically overestimate the probability of producing them by chance, when compared to smaller books, assuming the ratio of negative to positive correspondences remained constant. That’s an idea worth examining.
Of course, the assumption that the ratio would remain constant may not hold. If Ethan Smith left behind his (poorly conducted) research on Indigenous peoples and just started to pontificate incoherently for another 600 pages, would that ratio hold? Probably not. It certainly wouldn’t have helped Spaulding any to continue to pontificate in his manner–making the same adjustment for him would have substantially weakened his already troubled case even further.
But really, this problem is akin to saying that we should be careful about increasing our sample size, because increasing sample sizes for a biased method could increase confidence in bad conclusions. That’s true, as far as it goes, but also doesn’t negate the common sense consensus that larger sample sizes are generally to be preferred over smaller ones. If the Dales had somehow limited themselves to only 1st and 2nd Nephi, the first thing that critics would’ve done would’ve been to insist that they analyze the claims made in the rest of the book. And, as discussed above, the results for View of the Hebrews are automatically evidence of bias, and may only represent such to one who has already decided that the Book of Mormon is fraudulent. In fact, the comparison between the BofM and View of the Hebrews, even when adjusting for differences in book length, suggest that there’s something very special about the correspondences we observe in the former.
I of course meant to say that the results for View of Hebrews *aren’t* automatically evidence of bias. Carry on.
“[What Billy said above] is, of course, a dramatic misinterpretation of their probability estimates (and represents the most common mistake that I saw freshman Psychology students making about p values). What their p = .015 represents is the probability of observing those correspondences if the text has no connection with The Maya, which is a very different proposition. As is plain from my previous analyses, p = .015 would ultimately give us a very weak evidence score, and it would certainly fail to overcome even a sympathetic prior.”
With all due respect, where do you come up with this?
Allow me to quote from the paper “Bayes Factors” by Kass and Raftery, the paper with 7,600 citations to date that Bruce cited (and I’ll note that this paper has almost nothing to do with the Dales’ actual methodology). That paper says:
“The Bayes factor is a summary of the evidence provided by the data in favor of one scientific theory, represented by a statistical model, as opposed to another. Jeffreys (1961, app B) suggested interpreting B10 in half-units on the log10 scale. Pooling two of his categories together for simplification, we have:
log(B) Evidence against H0
0 to 1/2 Not worth more than a bare mention
1/2 to 1 Substantial
1 to 2 Strong
> 2 Decisive
Probability itself provides a meaningful scale defined by betting, and so these categories are not a calibration of the Bayes factor, but rather a rough descriptive statement about standards of evidence in scientific investigation.” (page 777)
That’s what the authoritative literature says.
The log of the Dales’ Bayes factor is 1.8, which on that scale is “strong”, and closer to “decisive” than it is to being merely “substantial.”
This means that according to the Dales Methodology as implemented by the Dales, the evidence provided by the data constitutes “Strong” evidence that View of the Hebrews is of Mayan origins.
If you really think a log of a Bayes factor of 1.8 is “very weak”, you ought to write a paper refuting how Kass and Raftery suggest Bayes factors should be interpreted.
You seem to have a strange penchant for rule following, and from what I can see of your perspective, the less applicable or substantive the rule, the better.
And the issue here is applicability. Kass and Raftery’s suggestion for interpreting log likelihood ratios (which is all it is, a suggestion) pertains rather clearly to a quantitative research context. Having lived in that world for a long time, I can say that their suggestion fits that context pretty well. It corresponds to something like a p value of .01 or .001 in frequentist terms, which would indeed be considered “strong” or “decisive” when considering a particular research result.
But there are other contexts where a p of .001 would get you laughed out of the room. One of those is physics, where they would much prefer something on the order of 6 or 9 sigma. They can insist on p values that small because the precision of their measurement allows for it, and the rigor of their theories demands it. A log likelihood ratio of 2 would be completely insufficient when trying to establish the reality of gravitational waves or the existence of the multiverse.
Is the context of historical Bayesian analysis different from the context inhabited by Kass and Raftery? Most assuredly yes. And the issues that characterize it are very different from those that characterize physics. It lives in a world of 1) very low initial prior probability estimates, 2) a lack of precision (at least in the case of efforts like those of Carrier or an exercise like this essay), and 3) attempts to evaluate and classify large sets of competing evidence.
If one’s initial prior probability is on the order of 1 in a million (Carrier’s) or 1 in 10^-41 (mine), a likelihood magnitude of 2 isn’t going to get you very far. In that context, a 2 is neither strong nor decisive.
If one is making an imprecise guess as to the probability of a particular result, and one has no particular basis for choosing between a 1 in 100 or 1 in 1,000,000 probability (as is the case for Joseph hitting on such vividly accurate details of volcanic destruction), or when analytic decisions can swing a result by many orders of magnitude, then a likelihood of magnitude of 2 is little more than rounding error. In that context, a 2 is neither strong nor decisive.
When attempting to summarize many different pieces of research and evidence in a meta-analytic manner (as is the case with the Dales or or with my project generally), that too changes the context. In past meta-analyses where I’ve combined the results of 100+ studies, an individual result of .01 or .001 amounts to a drop in the bucket. In the Dales’ analysis of View of the Hebrews, where you have 15 positive correspondences on one hand and 9 negative correspondences on the other, a p of .016 could be essentially wiped out by the addition of a single negative correspondence. In that context, a likelihood magnitude of 2 is the farthest thing from strong or decisive.
In short, and in answer to your question, I “come up with this” by engaging in such activities as “thinking” and “observing”. In an exploratory effort like this one in which I’m very much breaking new ground, those are just about the only tools at my disposal. At this point, the best context I have for judging the strength of an evidence score is to look through the list of scores my analyses have produced, and in that context, a 2 is nothing to write home about.
The Dales’ adaptation of Kass and Raftery’s Bayes factors is yet another exercise in thinking and observing, and though it might break the rules you have in your head, from where I sit it’s resulted in a flawed but nonetheless workable method (and the best bad one we have) for sifting through large amounts of qualitative evidence.
I know that you’re capable of similar degrees of thought and observation, but the pattern of conversations we’ve had so far suggests that you’re only willing to bring those to bear in service of your own worldview. The fact that I was willing to snip out more than 100 orders of magnitude that would otherwise have weighed in the BofM’s favor should be evidence enough that I’m not following in your footsteps.
Thanks Billy. I’ve exceeded my response limit, so the stage is yours if you feel like it.
“You seem to have a strange penchant for rule following…”
It’s not about following the rules. It’s about thinking in a coherent manner.
“But there are other contexts where a p of .001 would get you laughed out of the room. One of those is physics, where they would much prefer something on the order of 6 or 9 sigma….”
That is plainly false. If a physicist runs an experiment 1,000 times and gets the predicted results *only* 999 times, physicists aren’t going to laugh you out of the room. They’ll demand even more conclusive evidence for the reasons you cite, but they won’t deny that this is very strong evidence.
Probabilities, likelihoods, and odds have intrinsic meaning. You seem to think they are arbitrary ways of keeping score in math games. That isn’t true.
“Is the context of historical Bayesian analysis different from the context inhabited by Kass and Raftery? Most assuredly yes. And the issues that characterize it are very different from those that characterize physics. It lives in a world of 1) very low initial prior probability estimates, 2) a lack of precision (at least in the case of efforts like those of Carrier or an exercise like this essay), and 3) attempts to evaluate and classify large sets of competing evidence. If one’s initial prior probability is on the order of 1 in a million (Carrier’s) or 1 in 10^-41 (mine), a likelihood magnitude of 2 isn’t going to get you very far. In that context, a 2 is neither strong nor decisive.”
Your point here is plainly false. Odds mean the same thing, regardless of context. Regarding Richard Carrier, what in the heck are you talking about? Carrier says, “the prior probability [or P(h|b)] that Jesus was historical can be no more than 1 in 3 or 33% (which translates into prior ‘odds’ against h of 2 to 1)” (Carrier, Richard. On the Historicity of Jesus, p. 296).
1- There is nothing intrinsic about historical Bayesian analysis that requires “very low initial prior probability estimates.” In fact, such numbers are both arbitrary and meaningless.
2- I agree that this world “lacks precision,” but that isn’t a rationalization to redefine what probabilities mean. Your point here is a total non sequitur.
3- Likewise, working with large sets of competing evidence isn’t a valid reason to disregard or redefine what probabilities mean.
“In short, and in answer to your question, I “come up with this” by engaging in such activities as ‘thinking’ and ‘observing’.” The quality of your thoughts and observations in this topic are exceptionally poor.
“I know that you’re capable of similar degrees of thought and observation, but the pattern of conversations we’ve had so far suggests that you’re only willing to bring those to bear in service of your own worldview. The fact that I was willing to snip out more than 100 orders of magnitude that would otherwise have weighed in the BofM’s favor should be evidence enough that I’m not following in your footsteps.”
The thing is, every statistical model is based on a series of assumptions. To the extent *any* of those assumptions aren’t true, the results of the model are invalid. You systematically fail to acknowledge the specific assumptions your models are based on, much less analyze how well they hold. The fact is that if a highly educated and experienced practitioner such as myself looks at what the implicit assumptions are, basically every single one of them is obviously, patently false. The model is junk, beginning to end.
Your comment about how conservative and reasonable you think you are being by “snipping out more than 100 orders of magnitude” reminds me of a friend I knew several years ago. He invited me over to his house and explained that he had a plan to get rich. He was going to get six people to join his multi-level marketing scheme over the next month. They were each going to get six more over the next month, then they would all get six more the next month, etc. He then adjusted it out of being “conservative” and assumed these “down line” people were *only* going to get only 2 or 3 people each month rather than 6. Based on these “ultra conservative” assumptions, he calculated that in five years, he’d have an income of $10 million a year. I told him he was nuts. He responded, okay, let’s assume I *only* make 1/20th of what my model forecasts. That’s still $500,000 a year! I told him the same thing I’m telling you now: his model was fundamentally flawed, and the adjustments he was making out of feigned “conservativeness” didn’t address the fundamental issues.
It turns out that I was right. He ended up losing several thousand dollars and went broke.
I’m content to let most of this stand, but I’ll respond briefly to the bit about Carrier.
In Proving History, Carrier notes several different potential priors, including a 1 in a million prior, and specifically indicates that it would be an appropriate prior to use for theistic hypotheses.
He does set a 1 in 3 prior for a historical Jesus, but his one for a supernatural Jesus is much, much, lower.
Kyler has honored my son Brian and me by basing this episode in part on our earlier work. I want to make a couple of things clear about that work.
First, we did our analysis specifically to address Dr. Michael Coe’s claim that “99% of the details in the Book of Mormon are false”. We were not trying to “prove” any particular location in the Americas as the location for the events described in the Book of Mormon.
Well, if Dr. Coe is correct in his statement about the Book of Mormon (a book that Coe read just once, decades ago), then there are hundreds of details regarding the world of ancient Mesoamerica in Coe’s Ninth Edition that are also false. In hundreds of cases, what the Book of Mormon says about a particular ancient world located somewhere on the American continent agrees remarkably well with what Coe wrote about ancient Mesoamerica.
To put it bluntly, Coe didn’t know beans (or even maize) about the Book of Mormon, or he could not have made such a claim. It is remarkable that none of the critics of our earlier article mustered the intellectual honesty to concede that Coe’s assertion about the Book of Mormon was itself obviously wrong.
Second, the numerical likelihoods assigned to each correspondence in our previous work were not pulled out of a hat. Those values (2, 10 and 50 for the hypothesis that the Book of Mormon is a work of fiction and 0.5, 0.1 and 0.02 for the converse hypothesis that it is an authentic ancient record) came from a highly-cited (7,600 citations to date) paper in the Journal of the American Statistical Association. (Reference below.) The values represent approximate midpoints in a range of likelihoods described qualitatively as well as quantitatively in that paper.
Thus it is incorrect to state that Bayesian analysis requires extensive numerical support for each piece of evidence. It does not. Bayesian likelihoods are frequently described as “rational betting odds”. As long as we apply the same standards to evidence both for and against the hypothesis, Bayesian analysis using qualitative descriptions of the evidence is fully justified.
Robert E. Kass and Adrian E. Raftery, “Bayes Factors,” Journal of the American Statistical Association 90, no. 430 (1995): 777, doi:10.2307/2291091.
For the record, in principle I have no problem with simplifying the math with likelihood ratios and with bucketing them the way you did.
However, I strenuously disagree with your last point: it is not sufficient to “apply the same standards to evidence both for and against the hypothesis;” I can assure you that the Kass and Raftery paper you reference does not make this claim. The standards need to represent the actual likelihood of the evidence under both hypotheses—you can’t make up an arbitrary standard that has nothing to do with likelihood and say it is okay because you are applying it to both sides.
According to that paper, the Bayes factor categories are a way of interpreting the results of a statistical model. They are not representations of how subjectively specific, detailed, and unusual you find evidence to be.
Quoting from the paper, “The Bayes factor is a summary of the evidence provided by the data in favor of one scientific theory, represented by a statistical model, as opposed to another.”
Thanks Bruce. Just one thought here.
Though your intent may have been neutral in terms of geography, clearly Coe and The Maya aren’t. It’s not really possible to do this sort of analysis without grounding it in a specific place, people, time period, and culture, and there’s no mistaking where and when and to whom these specific correspondences are pointed.
I agree, though, that your article doesn’t directly address the question of geography, as it doesn’t actually test and compare different geographic models. It would be interesting to conduct a similar analysis for alternate theories of Book of Mormon geography, and next week’s essay actually touches on that a bit.
I don’t normally comment but I need to vent on this one. As someone who is very on the side of the Book of Mormon is authentic, I understand what I am about to say is biased, but it is also sincere.
This is rough analysis for me. For one I am bummed that a change in like 3 subjective assumptions can change a Bayesian Analysis by a factor of like 114. It really shows me what we are dealing with is the “best bad” form of measuring the evidence.
I feel like there were some overly pulled punches. For one, with so many correspondences excluded because of biblical connections, nothing was done to take those biblical connections from the the test books. How poorly would View of the Hebrews faired if any correspondences that are biblical were taken out?
I felt this way when the witnesses were given an evidence factor score of 8. The limitations of Bayesian analysis just felt unable to adequately describe the power of the witnesses (who are know for their honesty and integrity) that never denied such an unbelievable claim.
Although I do appreciate Kyler attempting keep his analysis a fair fight. This would be a boring (and less credible for neutral readers) series if the authenticity was absolutely blowing fabrication out of the water at p=1-10^-million.
Kyler, thank you for the great work. I really enjoy tuning in each week for a fun new episode on Book of Mormon thought
Thanks for the comment Carter. I feel ya, for sure. Taking the biblical correspondences out of View of the Hebrews would change that comparison, for sure. I personally find a lot of these correspondences to be pretty dang mind-blowing, and this evidence is definitely a critical strike within the bounds of my own head-canon. I’m glad you’re enjoying the series, and the fact that you’re perceiving what I’m doing as unfair to the faithful position shows me that I’m on the right track.