$30k challenge to Interpreter’s “Team Bayes”

[Dr Moore]

Update:

From the Dales: no indication of interest.
From John Gee: no indication of interest.
From Kyler Rasmussen: some response, followed by radio silence. Kyler seems content to label my challenge somewhere in between misleading and misguided. A shame; he's going to defeat himself I'm afraid.


Now I acknowledge that this subject matter can be head-spinning. Which might tempt readers to wonder if it all boils down to interpretation. Let me go on the record with a firm assertion that Mopologists adopting hard-hitting tools of math most certainly does not boil down to interpretation, or opinions, or "agreeing to disagree". In math, some things really are black and white.

Let me offer a little perspective on what's missing from the collective submissions by Team Bayes (anticipating KR's 23 Book of Mormon probability-smashing episodes will end up) and why it matters.

In summary form, what Team Bayes do with the 3 projects linked above is straightforward enough:

1. Identify a large number of "hits" that Joseph Smith made in his translation projects (Book of Mormon, Book of Abraham)
2. Assert that each of those hits are
(Second Amendment) specific
(2b) unlikely
(2c) independent of one another
3. Assign odds of Joseph making each of those hits, like an N-sided dice roll
4. Multiply all of those odds together to show astronomically "impossible" odds that Joseph could have guessed, like saying "I'm going to roll all all sixes 50 or 100 times in a row" and then doing it the first time
5. By implication, the impossibility of the guessing scenario leaves only one viable alternative: prophet

I think this is all clear enough to everyone.

Now, a reminder that my challenge is simple. A big cash prize for showing that step 4 was done properly, eg that the probability functions CAN be multiplied together because they are shown to be independent. That's it. This isn't a "nice to have" in probability multiplication. It's the most fundamental rule of probability multiplication. You have to show that each probability function is independent of the others. To show that, obviously, you have to know what the probability function looks like -- you have to have a valid statistical data set or a valid mathematical model of the process. Again, super basic stuff. Material that ANY CREDIBLE STATISTICIAN will say is 100% absolutely unavoidably necessary to show.

Without it, Team Bayes' works are garbage-in, garbage out. Because if they can't show probabilistic independence, guess what, no probability multiplication. No multiplication, no astronomical odds. No astronomical odds, no prophet-magic alternative. They have nothing but academically bankrupt rubbish.

Anyway, as I've said all along. Don't take my word for it. Go find a working statistician in ANY field, or a sitting professor of statistics, and ask them to take a good, hard look at the mathematical frameworks proposed by Team Bayes -- specifically, whether sufficient work was done to show variable independence. Ask for an opinion about whether satisfactory process variable validity in the Bayesian analysis. Ask for a clean bill of health on the math, and I'll shut up. Until then, there is only one thing to say about the works of Team Bayes: it's garbage. Maybe long-winded, fancifully presented garbage. But yes, useless garbage. Not "directionally right but specifically off by a few digits" -- directionally garbage too.

But rather than just rail at the utter lack of supporting rigor behind the eye-popping numbers in these papers, I'll go one step further and offer a starter clue. Just in case, you know, one of them accidentally forgot to check the user manual before jamming the gas pedal on his glimmering new Bayesian Bugatti?

For the Dales

This paper is actually not "...a Bayesian Statistical Analysis..." at all. Not once do the Dales construct a proper Bayesian probability of anything. All of the "Bayes factors" are just made up based on a finger-to-the-wind justification in 1 paragraph (or less) about why this or that feature of the culture would be more hard or less hard to guess.

So for starters, the paper should be retitled as "...a probability multiplication exercise..."
Truth in advertising, guys.

The Dales cannot multiply their probability factors, or "Bayes factors" as they call them, without showing independence between those factors.

I'll take the first 2 of their "Bayes factors" to illustrate what must be done.

Factor 1.1 -- Bayes factor of 0.02 -- "Fundamental level of political organization is the independent city-state"
Factor 1.2 -- Bayes factor of 0.02 -- "'Capital' or leading city-state dominates a cluster of other communities

The Dales multiply these Bayes factors together for combined factor of 0.0004, or 4 in 10,000 chances that Joseph could have correctly guessed these features of Mayan culture together in the Book of Mormon.

Do the smell test -- would only 4 out of 10,000 authors guessing about ancient American cultures accurately describe the city-state with a leading city dominating a cluster of other cities? How many alternatives are there? Clearly something is wrong.

If the Dales sought to show independence, they'd have forced themselves to show their work on the Bayes factor math. Here's what it would look like.

For Factor 1.1
A = Mayan fundamental political organization is the city-state
B = Joseph identified the city-state as the fundamental political organization in the Book of Mormon

For Factor 1.2
C = Mayan leading city-state dominates a cluster of communities
D = Joseph identified that a leading city dominates a cluster of other communities in the Book of Mormon

With me so far?

Now, for each of these factors, the Dales failed to show their work. They just assigned a 1 in 50, or 0.02, probability factor to each. Here is the missing work:

For Factor 1.1 -- Bayesian probability factor

The probability of finding that the Maya followed a city-state model, given that Joseph guessed it in the Book of Mormon, is:
P(A|B) = [ P(B|A) * P(B) ] / P(A)
where
P(B|A) is the probability that Joseph would identify the city-state model, knowing that was the fundamental model
P(B) is the probability that Joseph would just guess the city-state model out of thin air
P(A) is the probability of finding the city-state model in Mayan culture

What are realistic assumptions for these Bayesian components?

For P(B|A), arguably 1, because if he knew the answer he'd have guessed the correct answer

Therefore, the Bayesian reduces to:
P(A|B) = P(B) / P(A)

For P(B), we have to judge what was in Joseph's mind. This will be a function of his environment, books he read, stories he heard, and his intelligence at assessing potential political models. Key question: what makes a "hit" for this? If the Book of Mormon contains the city-state regime, but also contains examples of small-city tribal, nomadic family tribal, and nation-state, is that a "hit" for B or not? What is the threshold of specificity or exclusivity? Indeed, the probability function of P(B) requires incredible scrutiny if any assumption is to be valid.
Conclusion: P(B) can range from 0.0 to 1.0, absent a crystal clear definition of specificity and exclusivity

For P(A), we would have to survey the extant literature to know what the other possible political models were (city-state, nation-state, nomadic family tribal, small-city tribal, pure communist theocracy, others?). Like B, what constitutes a "hit" for A or not? What is the threshold of specificity and exclusivity? Indeed, the probability function of P(A) requires incredible scrutiny if any assumption is to be valid.
Conclusion: P(A) can range from 0.0 to 1.0, absent a crystal clear definition of specificity and exclusivity

For Factor 1.2 -- Bayesian probability factor

The probability of finding that the Maya had dominant/leading a cities governing other communities, given that Joseph guessed it in the Book of Mormon, is:
P(C|D) = [ P(D|C) * P(D) ] / P(C)
where
P(D|C) is the probability that Joseph would identify leading cities governing others, knowing that was the fundamental model
P(D) is the probability that Joseph would just guess the governing leading city model out of thin air
P(C) is the probability of finding the leading city model in Mayan culture

What are realistic assumptions for these Bayesian components?

For P(D|C), arguably 1, because if he knew the answer he'd have guessed the correct answer

Therefore, the Bayesian reduces to:
P(C|D) = P(D) / P(C)

For P(D), we have to judge what was in Joseph's mind. This will be a function of his environment, books he read, stories he heard, and his intelligence at assessing potential political models. Key question: what makes a "hit" for this? If the Book of Mormon contains time periods in which the leading city model was present, but also contains examples of non-leading cities in the governance model, is that a "hit" for D or not? What is the threshold of specificity or exclusivity? Indeed, the probability function of P(D) requires incredible scrutiny if any assumption is to be valid.
Conclusion: P(D) can range from 0.0 to 1.0, absent a crystal clear definition of specificity and exclusivity

For P(C), we would have to survey the extant literature to know what the other possible leadership and city models were (democratic city-states, elected judges, non-city specific theocracy, etc). Like D, what constitutes a "hit" for C or not? What is the threshold of specificity and exclusivity? Indeed, the probability function of P(C) requires incredible scrutiny if any assumption is to be valid.
Conclusion: P(C) can range from 0.0 to 1.0, absent a crystal clear definition of specificity and exclusivity

So before we even begin to consider statistical independence, a fatal problem is evident in the Dales' process. Factors 1.1 and 1.2 have been estimated out of thin air without even so much as ONE SENTENCE of consideration about what constitutes a statistically valid data set. The Bayesian ratio can be simplified, but the simplified form leaves us with no useful information about the numerator or the denominator.

Call that fatal mistake the first contribution to Garbage-In. This fatal mistake is repeated 131 times in the Dales' paper.

But let's assume the Dales realize the error of their ways, and lay out specific criteria for including and excluding hits in The Maya and in the Book of Mormon. Let's say they do that for all 131 correspondences, and then do the requisite work to assemble the probabilities of finding specific hits in the historical literature, as illustrated by P(A) and P(C) above. Great start, if not a ton of work. All of the Bayesian denominators are now properly accounted.

And in all likelihood, many of these factors will be statistically unrelated and practically independent. I think Kyler has been trying to make this point, and he's mostly right. You can safely make the assumption about various occurrences being independent if they are wholly unrelated.

(By the way, if the Dales had simply gotten this far and taken note, their contribution to the "guesswork" aspect of Joseph's translation projects would have been MASSIVE. But yeah, they didn't even try, in all the length of that paper.)

Even with all of the Bayesian denominators in hand, we still have the numerators to grapple with, in P(B) and P(D) above for instance, repeated 131 times. Specifically, how to think about the probability of Joseph guessing specific things. Every one of these numerators shares one CAUSAL relationship: what was in Joseph's bricolage? How do we even begin to know? What stories he heard? What things he read. What ideas he concocted? And how many variations of a specific "hit" idea are actually represented in his works? And this is where the test of statistical independence fails.

Look at it in formula form, because it will be more obvious.

The probability of both 1.1 AND 1.2 Bayes factors happening together looks like:

P(1.1 && 1.2) = [ P(B) * P(D) ] / X
where
X = the multiplied probability factors A and C, already determined from the data or a data model, of presumably independent historical occurences.

In other words, looking at the above, in order to validly multiply the Bayes factors for the Dales' hits 1.1 and 1.2, we have to multiply the probability functions for B and D. Both of these probability functions ARE the mind, or bricolage, of Joseph Smith. They are likely not independent of one another, and proving independence of any two is incredibly difficult for at least 2 reasons.

Reason #1: we cannot read Joseph's mind -- we actually have no way to know what ideas he'd heard, read, or imagined. We do know he was curious, imaginative, and pretty well read prior to the Book of Mormon translation.

Reason #2: we have to apply the same set of "hit" criteria as in the denominator analysis above -- how many "versions" of what comprises a "hit" and a "not hit" do we find in Joseph's translation processes, or other key events surrounding the restoration?

And unfortunately, without a durable control for parsing and separating B and D (repeated 131 times), we truly cannot say anything about independent probabilities of Joseph guessing anything.

So the Dales have their work cut out for them.

A similar analysis will apply to John Gee in his 4 idol names study, and to Kyler Rasmussen in his 23 evidences with multiplied probabilities to come. If such an analysis cannot be demonstrated, then what's left cannot be taken seriously as anything but misleading, lazy, garbage-in/garbage-out Mopologetic pornography.

Speaking of which, where the hell is Dr. Kyle Pratt by the way? I see from his vitae that he's published some fascinating research on a specific type of probability distribution, as well as prime numbers, so he should know the rules of probability multiplication like mixing ramen soup. Will Dr. Pratt be willing to weigh in publicly, since he provided the "peer review" for Kyler's upcoming 23-part Bayesian Book of Mormon proof series. Judging by the start Rasmussen is off to, it's abundantly clear he's about to put new sheen on the same type of garbage math-porn that his elder Team Bayes members have done. My question for Dr. Pratt is: do you really want your academically-pristine name stamped on this kind of lazy misleading stats garbage? It would be a shame to see such a promising career thrown away like that.

Can someone reach this Dr. Pratt? If so, actually I have just 1 question for Dr. Pratt. "If you're willing to put your good name in the affirmative question, then I will shut up right away. Question 1: Did Kyler Rasmussen adequately establish statistical independence among his 23 (I assume 23, based on 23 upcoming episodes) Bayesian conditionals, including that the component probabilities of those Bayesians are backed by estimable and valid data or data models?"

[Philo Sofee]

EXCELLENT Dr. Moore. I have a sincere question. I need some clarification if I may. If I am grasping the Beta Distribution accurately, this helps is take data and then estimate what probabilities we are dealing with. The 23 items KR is going to discuss then, can and ought to be put into a Beta Distribution so see what successful AND failure outcomes occur. (The Dale's 131 items most certainly are more than enough!) The more data we have, the more accurate our probabilities we can calculate realistically. 23 items seems to me to be enough to give us a good and solid start.

The Beta Distribution is said to correctly model a range of possible probabilities for an event but we simply HAVE to take BOTH the successes AND failures into account. The alpha number is used in the calculation for the number of successes, the beta is used for the number of failures. In order to make any meaningful distribution, the entire all encompassing enchilada simply HAS to be taken into the calculation. This full distribution is what helps us to be able to be flexible with the strengths of our beliefs. The distribution gives us a range of beliefs, not just a simple black and white true or false.

But that range must account for evidences that favor as well as disfavor the Book of Mormon, including former hits such that further scholarship has definitely demonstrated is not longer a "hit" in it's favor, such as the recently posted Sheum as bullseye I presented, Alma as an ancient Name, (now discovered as contemporary with Joseph Smith), the Liahona, not an ancient compass, but a modern Joseph Smith day "Coach Hand Warmer" (see RFM new podcast!) and the missing flora and fauna of Mesoamerica like Cheetahs, parrots, anteaters, monkeys, piranha's, Book of Abraham constrictor's, bananas, coconuts, etc., the Book of Mormon merely maintaining what was known in Joseph's neighborhood, or the Bible. All of this and more is not an option to perhaps use in a probability function or calculation, they all are a must in order to produce a valid Beta Distribution.

The key with the Beta Distribution is the gathering of more data which will give a corresponding stronger certainty ONLY if ALL facets of evidences have been accounted for, both pro and con.

In other words, it appears to me that "Team Bayes" is entirely missing and messing up one of the singular most important distribution in probability! Without it can they have any hope at all of giving a realistic Bayesian presentation of validity to the Book of Mormon? Could I please get anyone's thoughts on this. Thank you all.

[Dr Moore]

Philo, I don’t think beta distribution has relevance here.

Beta is one of many continuous functions used to model probability. Under specific conditions, beta collapses to a normal (Gaussian) distribution. It can be very useful, but first you have to know that the data you’re working with fits in a beta distribution model. That is likely not the case with any of the Mopologetic evidences, or correspondences. Or at least, you can’t assume this to be the case before gathering enough data.

To be able to assume anything about these Book of Mormon or Book of Abraham parallels and their related probability functions, the Mopologists first have to take their hits and properly frame them for statistical analysis: accurately define the criteria for hits, then establish a control set, and then evaluate whether there is enough positive data on top of the control to qualify as statistically significant.


The most we ever see in Mopologetic writings is step 1, followed by declaration of victory. You don’t see controls set up, probably because the control feels like a waste of time, probably because they’re all just looking for data to support a conclusion they “know” is right.

The missing hard work on controls involves taking the identical “hits” criteria for, say, Early Modern English or “attested ancient names” and just as vigorously looking at large amounts of other literature for the same.

I think they won’t do it, which is fine except that this means they cannot use probability analysis to support their conclusions. Trade offs. No free lunch.

[Kishkumen]

Mopologists have really done this to themselves. By insisting that their claims relate well to the way skeptics frame their questions, they step right into the trap that skeptics have laid for them. The more I reflect on all of this, the less sense any of it seems to make to me. If I were to apply the same tests to the likelihood of the historicity of Herakles/Hercules, the unfavorable results for some imagined species of Herakles belief would be absolutely predictable. The entire premise upon which the question is built has so many problems that it renders the whole exercise ridiculous.

But Mopologetics is equally ridiculous and makes itself the sacrificial lamb for these bizarre exercises.

[Analytics]

In other words, it appears to me that "Team Bayes" is entirely missing and messing up one of the singular most important distribution in probability! Without it can they have any hope at all of giving a realistic Bayesian presentation of validity to the Book of Mormon? Could I please get anyone's thoughts on this. Thank you all.

It might be best to illustrate the Beta distribution with an example. Say we have a 10-sided die and want to find the probability of rolling a 6.

First, we need to collect some data. We roll the die 100 times and get nine 6’s. What does this tell us?

Fisher would have said we should start with the assumption that the probability of rolling a 6 is 1/10, and would have said nine 6’s out of 100 tries is broadly consistent with that, and would thus stick with the belief the probability is 1/10 (i.e. he would have failed to reject the null hypothesis).

A more modern approach would be set up a likelihood function. Setting this up is relatively arduous, but the concept is simple. It asks the question, for every X between 0 and 1, what is the probability we’d see the data that we do (i.e. nine 6’s and 91 non-6’s), if the true underlying probability of rolling a 6 is X. Once this likelihood function curve is established, we can use calculus to come up with the maximum likelihood estimator of what value of X is more likely than any other X to produce the data we see. We can also use calculus to look at the area under the curve, scale up the area so that it equals 1, and then say things like, “Given that we rolled the die 100 times and got nine 6’s, we can be 95% certain that the actual probability of rolling a 6 on any given roll is between 4.2% and 15.3%.”

This all has a Bayesian flavor because it deals with likelihood functions, and the approach invites collecting more data: if we gather more evidence by rolling the die more times, the likelihood function will get tighter and tighter around the true probability of rolling a 6.

The math to do all that is difficult. But it turns out that there is a statistical distribution called the Beta Distribution that almost has exactly the same shape as the likelihood function. The Beta distribution is very easy to parameterize. Just set alpha equal to the number of hits (i.e. to nine, because we rolled a 6 nine times), and beta equal to the number of misses (i.e. to 91, because we rolled 91 non-6’s). This results in a curve that gives a very good approximation for what the data indicates the true value of rolling a six is.

When dealing with the claims about the historicity of the Book of Mormon, I don’t think this application of the Beta distribution is applicable. The Book of Mormon is not true X percent of the time, and we are not trying to estimate the value of X. Rather, it is always true or always not true, and we are trying to figure out which it is.

[Gadianton]

Since Dr. Moore has re-emphasized the focus on variable independence, I returned to SR's complaints that it's impossible to show variable independence. Well, with the kind of invented data he's dealing with, it's impossible to show anything, but his way forward was with a real-world example of bad haircuts. Lem already brought the smack-down, showing that Covid and bad haircuts are very likely correlated -- in fact, i'll bet they were correlated in his mind, which is a result of coming up with examples too quickly -- due to the pandemic. SR pursued an exotic "mutual dependency on time".

I admit I had to look this up, but it turns out there is a pretty trivial way to prove independence, at least with real data.

Sample 50 people during the pandemic and determine if they had covid and if they got a bad haircut.

Let's say the results are in:

40 had bad cuts, and 10 had good cuts.
30 had covid, 20 didn't have covid.

So here is the big simple take-away: if covid and haircuts during pandemic are independent, then P(Covid | bad Cut) = P(Covid).

The probability of having covid given you had a bad cut, is equal to the probability of getting covid by itself.

3/5 people had covid. So expect that 3/5 people with bad cuts have covid, or, 3/5 * 40, which is 24.

For the hypothetical study, I don't know how many people surveyed both had covid and had a bad cut; what I do know, is if that number significantly deviates from 24, then covid and bad cuts are not independent.

So now it's a matter of applying the same logic to SR's witnesses and chiasmus, etc. except you have to show this for 29 variables each with each other, instead of 2.

[Dr Moore]

We can also use calculus to look at the area under the curve, scale up the area so that it equals 1, and then say things like, “Given that we rolled the die 100 times and got nine 6’s, we can be 95% certain that the actual probability of rolling a 6 on any given roll is between 4.2% and 15.3%.”

A confidence outcome only made possible in a properly controlled experiment, or controlled data gathering, exercise. Eg, you didn’t start by facing the die with a 6 showing up top and roll it the same way with a robotic tool 100 times. You didn’t put your finger on the scale of the science, in other words. Confidence, or even directionally informative analysis, doesn’t come by making up numbers that “seem reasonable” with long winded rationalizations about why the remaining steps don’t apply, backed by appeals to authority of other fringe authors who themselves make endless special pleadings and carefully dodge the data gathering burden.

If the Mopologist establishment wants to move their arguments into the stats world and be perceived by history as anything more than fringe crackpots, then they need to stop making excuses for doing such horrific science. But again, don’t take my word for it. Go hire or find some professionals to help. Get a second AND third opinion.

[Analytics]

We can also use calculus to look at the area under the curve, scale up the area so that it equals 1, and then say things like, “Given that we rolled the die 100 times and got nine 6’s, we can be 95% certain that the actual probability of rolling a 6 on any given roll is between 4.2% and 15.3%.”

A confidence outcome only made possible in a properly controlled experiment, or controlled data gathering, exercise. Eg, you didn’t start by facing the die with a 6 showing up top and roll it the same way with a robotic tool 100 times. You didn’t put your finger on the scale of the science, in other words. Confidence, or even directionally informative analysis, doesn’t come by making up numbers that “seem reasonable” with long winded rationalizations about why the remaining steps don’t apply, backed by appeals to authority of other fringe authors who themselves make endless special pleadings and carefully dodge the data gathering burden.

If the Mopologist establishment wants to move their arguments into the stats world and be perceived by history as anything more than fringe crackpots, then they need to stop making excuses for doing such horrific science. But again, don’t take my word for it. Go hire or find some professionals to help. Get a second AND third opinion.

I think I see your point. However, statistical models can be coherently used to describe somebody's opinion about things that can't be evaluated in a scientifically controlled study. As a concrete example, as I'm typing this, I have a coin that I'm about to toss into the air and let fall onto the desk. What do you think the probability of it being a heads is? In this context, "the probability of it being a heads" is describing an actual real-world stochastic process that can be scientifically proven to have a Boolean distribution.

Now I've now flipped the coin. It is now either a heads or a tails. I know the answer, but you don't. What would you say the probability of it being a heads is now? You might say "the probability of it being a heads is 50%." However, this isn't talking about a real-world stochastic process, and there isn't a properly controlled experiment you can perform to justify that opinion. Rather, "the probability of it being a heads" is describing your own personal uncertainty about the nature of reality--the nature of which side of a coin on my desk is facing up.

That is coherent. In principle, it is fair to use the language and models of statistics to describe our subjective uncertainty about real world things that are uncertain but aren't literally stochastic in nature.

I remember a few decades ago a certain editor for FARMS Review said something to the effect of, "With all this new evidence in favor of the historicity of the Book of Mormon, it is getting harder and harder for critics to explain it away." While I think that is a hopelessly biased evaluation of the evidence, it is a coherent statement. If he were to take the evidence he is alluding to and put it into a Bayesian model, it will allow us to explicitly see how he weights the evidence and either be convinced or disabuse him of his biases, as the case may be.

In any case, these are all simply models. As George Box said, all models are wrong, but some are useful.

[Analytics]

The major problem with the Dales paper is not that they are using a Bayesian framework to evaluate the evidence, nor is it because they treat the "points of correspondence" as being statistically independent. The big problem is that the way they evaluate the evidence with a "specific, detailed and unusual" heuristic is arbitrary, unjustified, and performed in a hopelessly biased way. Issues of statistical independence and a biased process for selecting what to include in the study are secondary problems.

In principle, somebody could use a Bayesian approach to fairly determine the likelihood of the Book of Mormon being historical. The following two posts from the comment section of the Interpreter website is a good juxtaposition between somebody who does a superlatively poor job of evaluating the evidence and somebody who does a pretty good job:

Correspondence 6.2

The area of evidence examined here is the reckoning of time. Both the Book of Mormon peoples and the Maya reckoned time. So did the North American Indians on which Joseph Smith’s limited knowledge of Indians was probably based.

But the Book of Mormon peoples and the Maya had the same basic approach to reckoning time: a definite starting year, followed by succeeding days, months and years. The North American Indians had another approach as described in View of the Hebrews (see below).

Since the Book of Mormon approach to keeping the calendar is very similar (“similar” does not mean “identical”) to that used by the Maya, we count this as a strong point of evidence. In this point at least, Dr. Coe is wrong. In this important feature of the reckoning of time, the Book of Mormon is very much congruent with ancient Mesoamerican Indian cultures.

Here is correspondence 6.2 from Appendix A in the paper.

6.2 Calendar kept by day, month and year
Coe’s standard: “The Maya Long Count, which will be explained in greater detail in Chapters 3 and 9, is an absolute, day-to-day calendar which has run like some great clock from a point in the mythical past (p. 25). “The Maya New Year started with 1 Pop, the next day being 2 Pop, etc. The final day of the month, however, carried not the coefficient 20, but a sign indicating the ‘seating’ of the month to follow” (p. 64). “Maya learning as well as ritual was in their [the Maya priests’] hands. Among them were ‘computation of the years, months, and days, the festivals and ceremonies’” (p. 243).

Book of Mormon correspondence: See Alma 10:6; Alma 49:1; 3 Nephi 1:1; 3 Nephi 2:7‒8; 3 Nephi 8:5.

Analysis of correspondence: Specific and detailed. Both the Book of Mormon peoples and the peoples described in The Maya kept calendars by day, month and year. The keeping of calendars is also unusual. The Indian peoples of eastern North America did not keep calendars, and were focused on the passing of the seasons. How did Joseph Smith “guess” that any Indians kept an absolute calendar by day, month and year? Likelihood = 0.02.

For comparison, here is negative Correspondence 7 from View of the Hebrews, showing how different the North American Indian approach to reckoning time was from that of the Maya…and the Book of Mormon peoples.

Negative correspondence 7 from View of the Hebrews. Indians used a lunar calendar and had no name for a year

Coe’s standard: The Maya kept their calendars by day, month, and year. They kept multiple calendars. “The Maya Long Count … is an absolute, day-to-day calendar which has run like some great clock from a point in the mythical past” (p. 25). “How the 260 day calendar even came into being is an enigma. … Meshing with the 260-day count is a ‘Vague Year’ or Ha’b of 365 days. … Within the Ha’b, there were 18 named ‘months’ of 20 days each” (p. 64).

“View of the Hebrews” correspondence: See p. 61. “They count time after the manner of the Hebrews. They divide the year into spring, summer, autumn and winter. They number their year from any one of those four periods, for they have no name for a year … and count the year by lunar months.”

Analysis of correspondence: This calendaring system is specific, detailed, and unusual (to Americans in the early 1800s) for both books, but the calendaring systems are not in agreement. Likelihood = 50.0.

OK, comments or rebuttal, anyone?

Billy Shears responded:

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 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.

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 [less than .02].

[Dr Moore]

The major problem with the Dales paper is not that they are using a Bayesian framework to evaluate the evidence, nor is it because they treat the "points of correspondence" as being statistically independent. The big problem is that the way they evaluate the evidence with a "specific, detailed and unusual" heuristic is arbitrary, unjustified, and performed in a hopelessly biased way.

Yes, I would agree the arbitrary, unscientific heuristics are fatal for each of the data points argued by the Dales. However, I am also aware that merely by condescending to arguing any of their 131 points, it amounts to pig wrestling in the end. No one will be convinced. That may be the home turf for many folks on this board, but it isn't where my 25+ years of education and professional experience are strongest.

So I chose to mark this challenge by statistical independence, and that was a deliberate decision. Statistical independence is math, where any argument must be reduced to math and data to have validity, where there are tradeoffs for convenience and error that all have well-developed mathematical constructs, and you can't avoid one thing without incurring the wrath of another. Arguing for statistical independence avoids pig wrestling by staying out of polemics, personal bias, spiritual witness or subjectivity about how a particular piece of correspondence makes you feel inside. I am simply choosing to fight my battle on familiar turf.

But it might be worth mentioning that I am also highly confident you and I will agree that you cannot argue for statistical independence between two or more conditional probability functions if the data backing those functions is too limited (N=1 or 2) to be meaningful or if the process for collecting affirmative and non-affirming data is not carefully defined and consistently performed.

In fact I doubt we would disagree at all in terms of what's wrong with the Team Bayes' papers, or even with the hierarchy of problematic assumptions. I simply chose to approach this challenge from a place that, to my mind, is most easily arbitrated by the math and least easily mucked up by poor analogies and special pleadings.