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Estimating the Evidence
Episode 13: On Inverting Parallels

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[Editor’s Note: This is the thirteenth 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.]

 

The TLDR

It seems unlikely that the Book of Mormon could have so many examples of chiasmus if it was written by Joseph.

Chiasmus has been a mainstay of Book of Mormon apologetics for more than five decades, but the ease with which chiasmus can be found in just about any book has led some to doubt its utility as evidence for the Book of Mormon. Yet the raw amount of chiasmus in the book is truly prodigious, with hundreds of potential examples just within 1 Nephi. I use a measure of repetition as a proxy for the amount of chiasmus we might expect in the Book of Mormon and other texts. I show that, in that regard, the Book of Mormon is remarkably similar to biblical scripture, and an extremely poor fit for pseudobiblical works from Joseph’s time (p = 3.14 x 10-10). I also incorporate evidence that the Book of Mormon’s ancient poetic forms are distributed in a way that would be unlikely if such had appeared by chance or were a general feature of Joseph’s own writing (p = .000016). Chiasmus remains formidable evidence in the Book of Mormon’s favor.

Evidence Score = 14 (increasing the probability of an authentic Book of Mormon by 14 orders of magnitude)

 

The Narrative

When we last left you, our ardent skeptic, you had decided to set aside two conspicuous books from your collection, and press onward through the other tome that lay open on your table. You turn the pages almost absentmindedly—the story continued through a rather interesting tree-oriented allegory, as well as a very, very long prayer, followed by a set of brief entries by those who seemed to hold very little interest in contributing to the text. An odd choice of narrative structure, to be sure, but you give it little thought as it plods on, verse by verse and book by book.

As you keep reading, you barely notice the light outside beginning to dim, and it’s only reluctantly that you reach to light a nearby candle. The hours had been long, and as the candlelight dances on the page your eyes begin to play tricks, your mind forming shapes and patterns that you knew weren’t there. Your eyes squint involuntarily and you shake your head, and as you again find your place you discover a different sort of pattern—one you definitely hadn’t expected to find in this particular work. The words of the pattern almost jump off the page as you read on:

But men drink damnation to their own souls except they humble themselves and become as little children, and believe that salvation was, and is, and is to come, in and through the atoning blood of Christ, the Lord Omnipotent. For the natural man is an enemy to God, and has been from the fall of Adam, and will be, forever and ever, unless he yields to the enticings of the Holy Spirit, and putteth off the natural man and becometh a saint through the atonement of Christ the Lord, and becometh as a child, submissive, meek, humble, patient, full of love, willing to submit to all things which the Lord seeth fit to inflict upon him, even as a child doth submit to his father.

Like an image that resolves after long-crossed eyes, the pattern of words resolves into a strange structure, an inverted parallel, circling from humble to natural man and back again. The pattern gives your memory a palpable jog—you had heard of this sort of structure before, an obscure form of ancient poetry that had been described only a few years earlier by scholars an ocean away. To find it in the words of an uneducated farm boy was strange indeed.

You suppose that perhaps that farm boy might’ve heard of this structure, or perhaps that it occurred by chance, and content yourself with those thoughts for the moment, ready to move on with your reading. But only a couple chapters later, you’re somewhat surprised to find yet another example of an inverted parallel:

And now, because of the covenant which ye have made ye shall be called the children of Christ, his sons, and his daughters; for behold, this day he hath spiritually begotten you; for ye say that your hearts are changed through faith on his name; therefore, ye are born of him and have become his sons and his daughters.

One example was rather easy dismissed. Two, appearing so quickly, is much more difficult to ignore. You try your best to do so, though, pressing forward with the chapter. Only a few verses later, though, your eyes hit upon yet another such pattern:

And now it shall come to pass, that whosoever shall not take upon him the name of Christ must be called
by some other name; therefore, he findeth himself on the left hand of God. And I would that ye should remember also, that this is the name that I said I should give unto you that never should be blotted out, except it be through transgression; therefore, take heed that ye do not transgress, that the name be not blotted out of your hearts. I say unto you, I would that ye should remember to retain the name written always in your hearts, that ye are not found on the left hand of God, but that ye hear and know the voice by which ye shall be called, and also, the name by which he shall call you.

You turn your eyes away from the book as a sense of frustration fills your mind—these poetic structures seem to be taunting you wherever you turn in the book, and now that you see them, it seems impossible to unsee them. It seems unlikely that a book could be filled with such poetic structures by accident, and unlikelier still for them to have been placed with such prodigious frequency by any modern imitator.

 

The Introduction

Since the 1960s, critics and faithful scholars alike have had to grapple with the presence of chiasmus in the Book of Mormon and other Latter-Day Saint scripture. On the one hand, these and other structures characteristic of ancient literary works seem out of place in the writing of Joseph Smith or other nineteenth-century authors given the lack of knowledge they would have had of such structures and their lack of expertise in producing them. Faithful scholars have done a thorough job of documenting these structures and providing arguments for their validity and literary merit, most notably John Welch and Donald Parry. On the other hand, chiastic structures can appear unintentionally in almost any work of a certain length, leading many critics to dismiss chiasmus as either a fluke or as an unconscious characteristic of Joseph’s writing style.

The question, given this debate, is how unexpected chiasmus in the Book of Mormon is given its purported modern and ancient origins. Hopefully Bayesian analysis can help us uncover a few unique insights.

 

The Analysis

The Evidence

Chiasmus is a literary structure, common in ancient poetry, involving words, concepts, or ideas repeated in reverse order. Though scholars today have little trouble finding numerous examples of chiasmus in biblical contexts, as well as in ancient, archaic, and modern poetry, chiasmus itself wasn’t recognized or described in the modern era until the work of John Jebb and Thomas Boys in England in the 1820s. Since that time there’s been an explosion of scholarship that seems to find chiasmus around every literary corner, and the Book of Mormon has been no exception.

Very few would deny that chiasmus exists in the Book of Mormon. Many readers would be familiar with the extensive chiasm in Alma 36—what could effectively be described as the Book of Mormon’s chiastic crown jewel. Before starting my research for this episode, I’d known generally about chiasmus, but I wouldn’t have been able to identify many other specific cases besides Alma 36. When I looked into it, I was frankly a bit floored by the raw amount of chiastic examples that have been proposed over the years—over 280 potential examples just in 1 Nephi. It’s probably easier to count the verses that haven’t been implicated in a chiasmus than to count the ones that are.

Not all of these are classic examples of the poetic form. Some of the patterns are conceptual and span multiple chapters, and even multiple books. Others include variation or imperfection in the inversion pattern. Literary scholars have even found reason to doubt whether Alma 36 is an intentional chiasm, particularly since there are a number of important and repeated themes in the chapter that weren’t incorporated into the structure (and there’s little agreement on what ultimate form the structure takes). But there are plenty of strong examples that are more difficult to criticize, including some of the ones detailed above.

The question is whether it would be unusual to find chiasmus in a book like the Book of Mormon, if someone like Joseph Smith had written it. The general tack taken by the critics is to offer counter-examples of chiasmus in contexts where it was certainly not intended, from pseudobiblical works to Dr. Seuss to modern technical manuals. Many books have repeated elements, and with enough repetition it’s only a matter of time before a chiasmus presents itself on the basis of chance alone.

And that fact is worth emphasizing—chiasmus depends on repetition. Where repetition is found, chiasmus will follow. Consequently, where more repetition is found, you’ll be more likely to find chiasmus.

I’m not the first to realize that fact or to try to calculate the probability of encountering chiasmus in a given text by chance. Boyd and Farrell Edwards, a father and son duo of physics professors operating out of Utah State University, took up that problem in a paper published in BYU Studies in the mid 2000s. Specifically focusing on the chiasm in Alma 36, along with a few other prominent examples, they assessed how likely it would be for chiasmus of different levels to appear given an estimated amount of repetition of words or concepts, as well as the length of the text. Using their own proposed 9-level structure for Alma 36, they estimated the probability of those concepts appearing by chance in inverse-parallel order at p = .00000049. Assuming that each Alma 36-size section of the book represented an independent chance for that size of chiasmus to appear, that would mean the overall probability of that type of chiasm appearing at any point in the book is p = .00018. To them, this was a strong indication that Alma 36 was an intentional chiasm, rather than one that appeared accidentally.

Despite some criticism of their (and others’) handling of the chiasm in Alma 36, the statistical point still stands—it’s very unlikely that the ordering of elements in Alma 36 is accidental. Though this helps us place more confidence that Alma 36 has intentional poetic meaning, worthy of literary merit (a point further strengthened in a recent Interpreter article by Noel Reynolds), it doesn’t fully resolve the question of authenticity. Even though Joseph Smith likely knew little if anything about chiasmus, it’s difficult to rule out his intentional (if unknowing) creation of an inverted parallel in these or other isolated cases (though you could still argue that this intentionality is unexpected enough to count in the Book of Mormon’s favor—if you’re wondering how I’ll be exercising a fortiori reasoning in this episode, it’ll be by not incorporating this analysis into my probability estimates).

So we’ll be taking a different tack than did the Edwards. Rather than ask how likely it would be to find one specific chiasmus out of the hundreds in the Book of Mormon, we’ll consider whether we should expect to find those hundreds in the first place.

We’ll also be considering the distribution of chiasmus in the book. One analysis by Carl Cranney divided various sections of the Book of Mormon into those that would’ve been delivered orally (i.e., its sermons) and those that would’ve been originally delivered via written text (i.e., in letters), and then counted the proportion of those sections that contained chiasmus and other forms of parallelism. As chiasmus is generally meant to be conveyed orally, one would expect sermons to be more likely to contain these poetic elements than written letters, which is exactly what Cranney found. Approximately 52% of the oral texts were implicated in parallelistic elements, while only about 14% of the written texts were. Though the sample of texts was relatively small (10 in each group), the difference was more than enough to reach statistical significance, at t(18) = 5.84, p = .000016. We’ll need to think through whether and how to incorporate this evidence into our overall estimate.

The Hypotheses

Chiasmus in the Book of Mormon is due to ancient writing patterns and techniques—According to this hypothesis, chiasmus is in the Book of Mormon because ancient authors put it there, either intentionally through the deliberate crafting of chiastic patterns or unintentionally as a consequence of ancient literary habits.

Now, hold on here, did I just say that unintentional chiasmus can still count in favor of the Book of Mormon? Yes, yes I did, and here’s why.

For one, when it comes to the question of authenticity, it doesn’t matter what the authors’ intention is—the only thing that matters is whether it’s ancient or modern. Lots of the evidence we’ve considered so far is unintentional, whether it’s the word pattern ratios used by particular authors or the Early Modern nature of syntax, grammar, and vocabulary. Unintentional patterns actually have the advantage of being more difficult to discover and recognize, and thus more difficult to fake.

For another, it’s clear that not all chiasmus is intentional, even in authentic ancient documents. It’s hard to imagine the author of Matthew, for example, taking the time to deliberately craft nearly 150 examples of chiasmus. As I’ve noted, chiasms could form purely on the basis of chance—chiasmus depends on repetition, and enough repetition, over time, will create chiastic patterns. But there are a lot of factors that serve to increase that repetition. For instance, some languages have a relatively limited vocabulary, and thus naturally feature more repetition, just by having fewer words to work with. There might also be other (non-chiastic) linguistic forms that also depend on repeated concepts, such as parallelism.

In addition, it’s possible that the chiasmus is intentional, but not the way we usually think. Chiasmus may not always require that an author take the time to deliberately put together each piece of the chiasmus, embedding within it deep poetic meaning. It might instead be formed simply on the basis of convention. Take periods, for example. When I put a period at the end of a sentence, sometimes I do so deliberately. But most of the time I put it there because modern writing conventions tell me that I should. The period has meaning, but only on the basis of agreed-upon (and usually unwritten) rules—rules that we learn and that eventually become ingrained in our writing style. I don’t have to take the time to think about the placement of my periods, and they usually don’t carry any broader poetic meaning. Most of the time, a period is just a period.

Something similar could apply to chiasmus. Perhaps, to ancient writers, a thought just didn’t sound right unless it was repeated in reverse order. If so, chiasmus would end up appearing very frequently throughout a text, and authors would be so practiced at it that they wouldn’t have to spend much time putting them together. There wouldn’t necessarily be any deeper literary meaning locked within, any more than we’d expect deeper meaning in commas or periods.

Between those three—chance, convention, and non-chiastic writing patterns—we have an explanation for the large frequency of chiasmus we find in both biblical scripture and the Book of Mormon. There would still be room for ancient authors to craft beautiful, meaningful chiasms, such as Alma 36. But many—if not most—would be there either unintentionally or without deliberate literary intent. And notably, if any of those sources of chiasm are specific to ancient writing, they would serve as a valid means of testing the book’s authenticity. In short, if the Book of Mormon is authentically ancient, it should have comparable rates of chiasmus to other authentically ancient works, such as the Bible.

So that is a roundabout way of forming our first hypothesis. What about the second?

Chiasmus in the Book of Mormon can be attributed to modern authorship—With this hypothesis, chiasmus could appear in the same general ways as they might with ancient authorship—that is, intentionally or unintentionally. If Joseph or someone else in the nineteenth century wrote the Book of Mormon, he would either do so intentionally or unintentionally, due to chance or convention. But in both cases we would expect a far lower frequency of chiasmus within the text compared to ancient sources. As unpracticed as Joseph would have been in creating chiasmus, it’s unlikely that he would be able to do so at such a prodigious rate, particularly when dictating the text. And it’s clear that chiasm is not a convention of modern writing, nor is modern writing characterized by the ancient literary patterns that could otherwise give rise to unintentional chiasms.

Because of this, if the Book of Mormon is a modern book, it should contain about as much chiasmus as other modern books, including books that attempt to replicate biblical style. Also, any examples of chiasmus or parallelism that we did find (either through chance or through the writer “having an ear” for biblical poetic forms) should be randomly distributed throughout the text. Anything else would be, dare I say it, unexpected.

Prior Probabilities

Here’s a reminder of where the evidence stands so far:

PH—Prior Probability of Ancient Authorship—Our initial estimate of probability of the Book of Mormon’s authenticity remains where we last left it, at a value that’s starting to get within striking distance of the tipping point of .5, p = .0000779.

PA—Prior Probability of Modern Authorship—Conversely, our estimate of the probability of modern authorship stands at p = .9999221.

Consequent Probabilities

CH—Consequent Probability of Ancient Authorship—So how likely would we be to observe the amount of chiasmus we do in the Book of Mormon if it’s truly ancient scripture? Well, the best way to figure that out would be to count the number of examples of chiasmus we find in the Book of Mormon, and then compare it to the number we find in ancient scripture, with the Bible being the obvious comparison. At first glance that seems like a doable thing to do—as we’ve noted, Jack Welch has devoted his life to documenting every known example of chiasmus in a variety of different sources, including the Book of Mormon and the Bible.

I even took a stab at making those comparisons, throwing each example and the number of levels of the chiasmus into a spreadsheet. But a few things became clear pretty quickly:


  1. Ain’t nobody got time for that. As an amateur analyst doing this in my spare time, extracting that kind of data in the time I allot for these episodes would’ve been damaging to my sanity. I managed to get through 1 Nephi and the book of Matthew, but that alone took hours; there were over 500 examples to go through in those two books alone. If I was a full-time researcher with a small army of starving students at my disposal it wouldn’t be that bad, but that wasn’t in the cards.
  2. The data itself is messy. Welch’s database is fastidious and extremely useful, but it’s hard to know how comparable these examples are. In the case of the Book of Mormon you have a number of different analysts analyzing the book, picking out examples based, in many cases, on their own idiosyncratic criteria, and who often disagree with each other about the exact form and extent of each chiasm. In the case of the Bible you have hundreds of people who have worked through the text with a fine-tooth comb without any consistent methodology. Welch has worked to establish a set of useful ways to separate the wheat from the chaff, but even those criteria need to be subjectively applied. A valid analysis would’ve required carefully reading through each example and trying to judge the quality of the chiasmus—an effort that could easily take several lifetimes and that would ultimately represent little more than my own opinion.
  3. The chiasmus database doesn’t cover more modern works from Joseph’s day. I might have been able to do something workable using the data I extracted from 1 Nephi and Matthew—it seems, for instance, that 1 Nephi has a surprising amount of chiasmus in comparison to the New Testament (see the figure below). But that wouldn’t have helped me when it came to the really interesting comparisons I needed to make down the road when testing the hypothesis of modern authorship. Some people have cherry-picked examples of chiasmus from, say, The Late War, but no one’s done the truly thorough search for chiasmus in modern books that’s been done for the Bible and the Book of Mormon. To conduct any sort of valid comparison I would’ve needed to do that myself, and I can think of better uses of my time than poring through the First Book of Napoleon looking for inverted parallels.

I thought I was up a creek for a while there, but a little perseverance led me down a more promising path. We can’t get a solid count of chiasmus for our analysis, but is there a way to estimate how much chiasmus we’d find? Better yet, is there an analysis we could use that doesn’t take a ton of time and that isn’t quite as subjective as the process of searching for chiasmus itself?

If we can’t access chiasmus, can we access the phenomenon that gives rise to it—the repetition of words, ideas, and concepts?

Turns out that we can. Quantitative linguists have long used a measure of repetition as a meaningful characteristic to distinguish between different forms of literature. That measure is the Type-Token Ratio (TTR), or the ratio of the total number of unique words in a text (types), to the total number of raw words in that text (tokens). It’s essentially a way to assess the working vocabulary of the author—the higher the vocabulary, the more unique words you’ll find relative to a text’s total word count. But it also works to measure repetition—the more repetitive a text is, the fewer unique words you’ll find. It’s also exceptionally easy to calculate if you have the software necessary to count the number of unique words in each text.

For example, 1 Nephi has a total word count of 25,126 as measured by WordCruncher, but only has 1,699 unique words. We can calculate the TTR by dividing the number of unique words by the total word count, which would be 1699/25126 = 0.07. You could compare that to a modern book, such as our good friend The Late War, which only has about twice the total word count (56,632), but over triple the number of unique words (5,749), creating a substantially higher TTR (0.10).

For our purposes here, though, we want higher TTR values to represent more repetition (which might indicate more chiasmus). To do that, we’re going to invert our TTR values to create an “Inverted TTR” measure. Doing this doesn’t change the results at all, it just helps it match what we’re actually trying to measure. In the cases above, we’d end up with values of 14.8 and 9.85 for 1 Nephi and The Late War, respectively, indicating that 1 Nephi shows more repetition than The Late War.

Now, whether or not we invert it, the TTR is a bit of a tricky measure. For one, our ratios are much lower for longer texts than for shorter ones. This makes intuitive sense—the longer the text is, the less likely you’ll be to run into unique words, even if the vocabulary is about the same. That issue means you can’t just compare the ratio for the Book of Mormon to, say, the Old Testament—since the Old Testament is more than twice as long, the values themselves aren’t comparable. But it turns out that the ratio does tend to follow a pattern. If you plot different portions of a text (of different sizes) by both the TTR and the overall word count, it tends to follow a logarithmic curve.

You can see what I mean in the figure above. In that figure I’ve calculated an inverted TTR for both Book of Mormon texts of various sizes (verses from 1 Nephi, and the different books themselves), and texts of biblical scripture (verses from Matthew, the books of the Gospels, the Pentateuch, and Isaiah and Jeremiah). I then let Excel draw a logarithmic line of best fit through each, which are the red and orange lines respectively. The higher a curve is on the graph, the more repetition occurs in the text (fewer unique words relative to the total word count). You’ll notice that the Book of Mormon texts and the biblical texts closely fit their respective lines, and, importantly, that they’re fairly close to each other. This means that, though there’s some variation (note that Leviticus, for example, has substantially more repetition than Isaiah; it’s also not a coincidence that Leviticus is famous for its prolific examples of chiasmus and parallelism), the Book of Mormon and the Bible have similar levels of repetition, suggesting that we should be about as likely to see chiasmus (whether intentional or unintentional) in both (interestingly, you’ll notice that the D&C, as well as the books of Moses and Abraham from the Pearl of Great Price also fit well with other books of scripture).

Getting a decent probability estimate out of that is a fairly straightforward procedure. I used a variation of a one-way Analysis of Variance (ANOVA) to see if there were substantial differences between the two sets of scriptural texts, the same way scientists test for differences in two different treatment groups in an experiment. ANOVA uses variation around means to test those differences—it calculates the mean for each group independent of each other (group means), as well as the mean for all observations regardless of group (the grand mean). The test compares how group means differ from each other relative to what we’d expect given how variable the observations are generally (around the grand mean), using an F-statistic to get a probability estimate for the hypothesis that the two groups are the same. I did the same thing, except instead of using means, I used the curves of best fit from the Excel chart. I calculated the variation of each group of texts (just the books, not individual chapters) around their respective lines, and compared it to the variation around a separate line of best fit (not shown in the figure) describing all the scriptural texts as if they were a single group. You can see the full list of works and their respective word count measures in the Appendix, along with the equations for those curves, and you can see the relevant calculations for the ANOVA below.

Book of Mormon — Bible ANOVA
Sum of Squares Within (SSW) 66.10 F (MSB/MSE)
Sum of Squares Total (SST) 69.43 1.21
Sum of Squares Between (SSB; SST – SSW) 3.33
Mean Square Between (MSB; SSB/(k-1)) 3.33 p
Mean Square Error (MSE; SSW/(N-k)) 2.75 0.28
k (number of groups) 2
N (number of observations) 26

Overall, not only do those lines of best fit seem close to each other, they actually are close in a statistical sense, with the probability that they belong to the same category estimated at p = .28; F(1,24) = 1.21. That’s the estimate we’re going to use for the consequent probability of ancient authorship.

CA—Consequent Probability of Modern Authorship—But how likely would we be to observe that level of repetition if the Book of Mormon was a modern text? Thankfully, we have plenty of examples of modern books that we can compare it to, including books from the nineteenth century that attempted to emulate a biblical style. You’ll see those examples plotted in the figure as well, including modern novels (e.g., Pride and Prejudice and Lord of the Rings) and a variety of pseudobiblical texts. Notice that none of them reach the same level of repetition that we see in the Bible and the Book of Mormon (the closest, interestingly enough, is Catcher in the Rye; also note that Joseph Smith—History fits very well with these modern texts). Based on this, it follows that we’d be less likely to see any kind of chiasmus or parallelism within these texts (though we’d still see some, particularly in the longer texts) than we would in the texts that are actually scriptural.

We can also do the same statistical test as above, comparing these modern texts, specifically the nineteenth-century pseudobiblical texts (of which there were 25, of varying lengths), to the Book of Mormon. How likely is it that the Book of Mormon belongs with these pseudobiblical texts? As you could probably tell by looking at the blue line of best fit, not very. In terms of the results of the statistical test, though, “not very” is a substantial understatement. It’s extremely unlikely that the books belong in the same category, with p = 3.14 x 10-10; F(1,38) = 71.1.

Book of Mormon — Pseudobiblical ANOVA
Sum of Squares Within (SSW) 84.83 F (MSB/MSE)
Sum of Squares Total (SST) 243.45 71.06
Sum of Squares Between (SSB; SST – SSW) 158.62
Mean Square Between (MSB; SSB/(k-1)) 158.62 p
Mean Square Error (MSE; SSW/(N-k)) 2.23 3.14 x 10-10
k (number of groups) 2
N (number of observations) 40

It’s fair to ask why the modern texts would have so little repetition. Yes, they don’t share the same conventions as ancient literature, and are unlikely to deliberately produce the chiasmus or parallelism we see in the biblical texts. But it’s more than that. As mentioned above, English is a high-vocabulary language. English is an eclectic and unusual mix of Germanic, Latin, and Scandinavian languages that has absorbed thousands of words of foreign origin over the centuries. We have words for everything, and usually a substantial number of words for each individual something. It’s not surprising that the modern texts, all written in English, would have a relatively large number of unique words, and that the biblical texts, written in relatively less-developed ancient Hebrew and Greek, would have relatively few.

But then what about the Book of Mormon, the D&C, and the Pearl of Great Price? This is a bit of conjecture on my part, so be warned. But it’s possible that such repetition is an indication that these texts weren’t actually composed in English. That would make fine enough sense if the books are authentic, but would be rather surprising if they were modern texts written by the decidedly uni-lingual (at the time) Joseph Smith.

Regardless, we have what we need to wrap up our analysis. Before we do, though, we’ll need to consider how to incorporate the findings from the Cranney article, which found that chiasmus and parallelism were much more likely to be found in Book of Mormon texts that would’ve been delivered orally than in its written texts. The main question here is one of independence—would we expect the frequency of chiasmus in a text (as indicated by the TTR) to be independent of how those texts are distributed within the text? Hopefully this is something on which reasonable people can agree—merely inserting more instances of chiasmus into a text should have nothing to do with putting those instances in the right spots and in the right context—in fact, doing so naively might lead to those instances being scattered indiscriminately through the text. If so, then these two pieces of evidence can be considered to be independent, and we can incorporate that evidence by multiplying the p-value calculated by Cranney (p = .000016) by the p-value for the TTR comparison that we’ve calculated here (p = 3.14 x 10-10). That would leave us with a final consequent probability estimate of p = 5.02 x 10-15.

Posterior Probability

PH = Prior Probability of the Hypothesis (our initial estimate of the likelihood of an authentic Book of Mormon, given the evidence we’ve considered so far, or p = .0000779)

CH = Consequent Probability of the Hypothesis (our initial estimate of the probability of modern authorship, given that earlier evidence, or p = .9999221)

PA = Prior Probability of the Alternate Hypothesis (our estimate of the probability of observing the amount of repetition we see in the Book of Mormon, if it represents authentic ancient scripture, or p = .28)

CA = Consequent Probability of the Alternate Hypothesis (our estimate of the likelihood of observing that repetition, if the book is a modern pseudobiblical text, or p = 5.02 x 10-15)

PostProb = Posterior Probability (our new estimate of the probability of an authentic Book of Mormon)

PH = .0000779
PostProb = PH * CH
(PH * CH) + (PA * CA)
PostProb = (.0000779 * .28)
(.0000779 * .28) + (.9999221 * 5.02 x 10-15)
PostProb = 1 – 2.3 x 10-10

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(.28/5.02 x 10-15)

Lmag = log10(5.57 x 1013)

Lmag = 14

 

Conclusion

That’s enough to place the chiasmus-related evidence into pole position alongside our other evidence—not a critical strike, by any means, but still prompting a substantial shift in favor of authenticity. And importantly, our view of the Book of Mormon has finally flipped on its head, moving from a still-small probability of .0000779 to a surprisingly confident .99999999977. Many faithful scholars have long seen chiasmus and other assorted ancient literary structures as formidable evidence on the side of the Book of Mormon, and this analysis does nothing to change that perception. Critics can chip away at individual examples of chiastic structure all they like, but the raw repetition (and distribution) undergirding those structures is both a good match for biblical scripture and thoroughly unexpected from the standpoint of modern authorship, especially from a young, first-time author.

 

Skeptic’s Corner

Since I’m the first person to mess around with the idea of using the TTR as a proxy-measure for chiasm and parallelism, it goes without saying that these results are tentative and exploratory. As interesting as these results may be, there would be a ton of ways to improve it. For one, I could repeat the analysis using all the books of the Bible rather than the select few I used here. I could also account for common words, such as articles and prepositions (e.g., “a”, “the”), or the unusual personal and place names in the Book of Mormon. Then I could look at removing all the different KJV quotations from the Book of Mormon to see what stands on its own, though this would be unlikely to help the cause of the critics (Isaiah is one of the least repetitious books that we analyzed, while Alma, which has relatively few quotations, has some of the most repetition). Do I think this would alter the analysis much? Probably not. But it would be a start toward making this a scholarly effort worthy of mainstream publication.

The biggest limitation here, though, is the lack of an explicit connection between the TTR and the actual amount of Hebrew poetic structures in the text. The connection was assumed (with good reason) but not actually measured. A validation study that actually tries to count the number of poetic structures and correlating that with the TTR would be a vital step here, though it would take work that I didn’t have time for and likely will never have available.

It would also be worth looking a bit deeper into the question of the distribution of chiasms. Do biblical texts show the same relative distribution when comparing oral and written texts? If circumstances had allowed Joseph to somehow read up on chiasmus while he was writing the Book of Mormon, would he have known to stick those chiasms primarily within sermons? Both of these are valid questions. But for the moment we move on, content to have documented another means by which the Book of Mormon appears out of place in a nineteenth-century context.

 

Next Time, in Episode 14:

When next we meet, we’ll be digging into the archaeological arguments surrounding the Book of Mormon, both for and against.

Questions, ideas, and foreboding chills can be run down the spine of BayesianBoM@gmail.com or submitted as comments below. Bonus friend-points for anyone who can locate examples of chiasmus in this essay!

Many thanks to Stanford Carmack for use of his WordCruncher package containing the 25 pseudobiblical texts included in the analysis.



 

Appendix

Word Count Measures and Predicted and Residual Values for ANOVA Analyses

Source Book Unique Words Total Words TTR
(Inverted)
Within Between – BofM/Bible Between – BofM/Pseudo
Predicted Residual2 Predicted Residual2 Predicted Residual2
Bible Matthew 2130 23684 11.1 12.7 2.4 12.9 3.2
Bible Mark 1679 15166 9.0 10.5 2.0 10.7 2.7
Bible Luke 2398 25938 10.8 13.2 5.5 13.4 6.8
Bible John 1401 19094 13.6 11.5 4.3 11.8 3.4
Bible Genesis 2511 38263 15.2 15.6 0.1 15.8 0.4
Bible Exodus 2050 32686 15.9 14.5 2.0 14.8 1.3
Bible Leviticus 1430 24541 17.2 12.9 18.5 13.1 16.4
Bible Numbers 2084 32896 15.8 14.6 1.5 14.9 0.9
Bible Deuteronomy 2059 28352 13.8 13.7 0.0 13.9 0.0
Bible Isaiah 3118 37036 11.9 15.3 12.0 15.6 14.0
Bible Jeremiah 2619 42654 16.3 16.3 0.0 16.6 0.1
BofM 1 Nephi 1699 25126 14.8 14.1 0.5 13.2 2.4 10.4 19.1
BofM 2 Nephi 2352 29419 12.5 15.0 6.3 14.2 2.7 11.1 2.0
BofM Jacob 1026 9131 8.9 9.3 0.1 8.6 0.1 7.0 3.5
BofM Enos 358 732 2.0 3.3 1.5 2.9 0.8 2.6 0.3
BofM Jarom 267 1398 5.2 4.3 0.9 3.9 1.9 3.4 3.5
BofM Omni 349 1160 3.3 4.0 0.4 3.6 0.1 3.1 0.0
BofM Words of Mormon 234 857 3.7 3.5 0.0 3.1 0.3 2.8 0.8
BofM Mosiah 2095 31151 14.9 15.4 0.3 14.5 0.1 11.3 12.5
BofM Alma 3344 85032 25.4 23.3 4.7 22.3 10.0 16.8 74.8
BofM Helaman 1632 20402 12.5 12.9 0.2 12.1 0.2 9.6 8.4
BofM 3 Nephi 2006 28636 14.3 14.8 0.3 14.0 0.1 11.0 10.9
BofM 4 Nephi 404 1946 4.8 4.9 0.0 4.4 0.1 3.8 1.0
BofM Mormon 1178 9437 8.0 9.4 1.9 8.7 0.5 7.1 0.8
BofM Ether 1374 16627 12.1 11.9 0.1 11.1 1.0 8.9 10.4
BofM Moroni 862 6116 7.1 7.9 0.6 7.2 0.0 6.0 1.2
Pseudo Chronicle of the Kings of England 2789 16465 5.9 7.2 1.8 8.8 8.6
Pseudo The Book of Jasher 1935 19279 10.0 7.7 5.3 9.4 0.3
Pseudo American Chronicles 2878 17012 5.9 7.3 2.0 8.9 9.2
Pseudo The American Revolution 3563 56172 15.8 11.3 20.1 14.3 2.2
Pseudo The First Book of Napoleon 2999 22118 7.4 8.1 0.5 9.9 6.5
Pseudo History of Anti-Christ 2052 15057 7.3 7.0 0.1 8.5 1.4
Pseudo The Late War 5749 56632 9.9 11.3 2.1 14.3 19.9
Pseudo Chronicles of Eri 7103 131741 18.5 15.4 10.2 19.9 1.9
Pseudo The Epistles of Ignatius and Polycarp 2323 18058 7.8 7.5 0.1 9.2 1.9
Pseudo Sacred Roll 4520 61889 13.7 11.7 4.0 14.8 1.3
Pseudo The Healing of the Nations 8779 110871 12.6 14.4 3.2 18.6 35.8
Pseudo The New Gospel of Peace 3809 59162 15.5 11.5 16.3 14.6 0.9
Pseudo Book of Preferment 760 2731 3.6 3.8 0.0 4.4 0.6
Pseudo The French Gasconade Defeated 295 902 3.1 2.5 0.3 2.8 0.0
Pseudo Parable Against Persecution 186 402 2.2 1.9 0.1 2.1 0.0
Pseudo Chronicles of Nathan Ben Saddi 778 2999 3.9 3.9 0.0 4.5 0.5
Pseudo Samuel the Squomicutite 247 605 2.4 2.2 0.1 2.4 0.0
Pseudo The Book of America 653 2562 3.9 3.7 0.1 4.3 0.1
Pseudo Chapter 37th 251 611 2.4 2.2 0.1 2.4 0.0
Pseudo Chronicles of John 341 828 2.4 2.5 0.0 2.7 0.1
Pseudo The First Book of Chronicles, Chapter the Fifth 587 1830 3.1 3.3 0.0 3.7 0.4
Pseudo Chronicles of Andrew 1206 4790 4.0 4.6 0.4 5.5 2.2
Pseudo A Chronicle of the Chiefs of Muttonville 377 933 2.5 2.6 0.0 2.9 0.2
Pseudo Reformer Chronicles 295 680 2.3 2.3 0.0 2.5 0.1
Pseudo Chronicles of the Land of Gotham 374 1281 3.4 2.9 0.3 3.3 0.0

 

Values for Modern Non-Pseudobiblical Books

Book Unique Words Total Words TTR (Inverted)
A Separate Peace 6418 54050 8.4
The Outsiders 3898 49444 12.7
Catcher in the Rye 4206 74193 17.6
Pride and Prejudice 6323 122880 19.4
Officer’s Daughter 11308 140245 12.4
Sense and Sensibility 7265 119893 16.5
A Tale of Two Cities 10778 137137 12.7
Adventures of Tom Sawyer 7896 71122 9.0
The Hobbit 6911 96072 13.9
The Lion, The Witch, and The Wardrobe 3520 39166 11.1
Harry Potter and the Sorcerer’s Stone 6185 77883 12.6
Twilight 8507 119270 14.0

 

Additional Word Count Measures Used in Figure

Book Chapter Distinct Word Count Word Count TTR (Inverted)
1 Nephi 1 265 907 3.42
2 252 879 3.49
3 254 1066 4.20
4 316 1262 3.99
5 231 761 3.29
6 86 202 2.35
7 245 992 4.05
8 278 1221 4.39
9 98 259 2.64
10 285 918 3.22
11 275 1315 4.78
12 217 860 3.96
13 314 1896 6.04
14 282 1283 4.55
15 330 1485 4.50
16 371 1632 4.40
17 507 2523 4.98
18 305 1216 3.99
19 335 1291 3.85
20 237 697 2.94
21 306 955 3.12
22 345 1506 4.37
Matthew 1 173 473 2.73
2 207 619 2.99
3 192 387 2.02
4 224 557 2.49
5 317 1081 3.41
6 241 794 3.29
7 228 626 2.75
8 271 773 2.85
9 291 837 2.88
10 298 919 3.08
11 261 668 2.56
12 337 1168 3.47
13 351 1367 3.89
14 261 721 2.76
15 280 785 2.80
16 241 688 2.85
17 248 620 2.50
18 275 869 3.16
19 246 719 2.92
20 244 779 3.19
21 339 1126 3.32
22 286 828 2.90
23 286 833 2.91
24 336 1047 3.12
25 264 995 3.77
26 426 1625 3.81
27 400 1359 3.40
28 182 421 2.31
D&C and
Pearl of Great Price
D&C 4721 111912 23.71
Moses 1230 12540 10.20
Abraham 769 5506 7.16
Joseph Smith-History 1290 6071 4.71
PoGP 2411 26045 10.80

 

Equations for Curves of Best Fit

Bible 0.1696(X)^.4282
BofM 0.2154(X)^.4125
Psuedo 0.2153(X)^.362
BofM/Bible 0.1757(X)^.4266
BofM/Psudo 0.1992(X)^.3906
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