An Analytical Tool for the Study of Book of Mormon Chiasmus

In 2004, Boyd F. Edwards and W. Farrell Edwards published one of the more significant apologetic studies of the Book of Mormon in recent history. Their paper, titled "Does Chiasmus Appear in the Book of Mormon by Chance?" (BYU Studies 43:2, 2004), is a statistical analysis designed to determine whether Book of Mormon chiasmus was intentionally created by the author or is merely a chance occurrence. The paper is designed to rebut the argument of critics like Dan Vogel and Brent Metcalfe that chiasmus is likely to appear accidentally in any highly repetitive text.

There is definitely room for criticism of the Edwards and Edwards study, but that is not the purpose of this blog post. Rather, my purpose here is to bring to readers' attention the computer program that Edwards and Edwards developed for their study. This tool is available (along with helpful instructions) for download and use by the general public from the BYU Studies website. The function of the program is basically as follows. Say we have a proposed chiasm with five parallel elements, but that there are also other repeated words and phrases in the passage that do not participate in the chiasm. In order to determine the likelihood that a five-element chiasm would appear in the passage by chance, we can randomly rearrange all the repeated elements in the passage a particular number (R) of times and then determine how many of the random rearrangements include five-element chiasms. The result, divided by R, will give us the probability of intentionality (L) for the passage's chiastic structure. If we know the number (N) of opportunities for five-element chiastic structures to appear in the entire Book of Mormon, the program can also calculate the likelihood (P) that such a structure will appear at least once somewhere in the Book of Mormon.

Once you understand the concept, the Edwards and Edwards program is not difficult to use. the hardest part is to determine the values to be inputted. These values must be determined manually. Some time ago I had the pleasure of discussing with Robert Ramsey his proposed chiasm in Helaman 5. (See here for our discussion of it.) In order to illustrate how the Edwards and Edwards method works, I have applied it to the proposed Helaman 5 chiasm. In the image below I have highlighted all major repeated elements in the passage. Some of these are discarded, because they are repeated within the same section. Elements that are repeated within the same section do not "count", as far as the Edwards and Edwards method is concerned. So "the Earth" or "shown unto you", for example, are highlighted but don't get taken into consideration in the statistical analysis. The Edwards and Edwards method also ignores synonymy in favor of objective repetitions, for the reason that objective repetitions are more easily quantifiable.

Here, then, are the inputs that I used:

Chiastic elements: 5
Number of times each chiastic element appears : 3,4,2,2,3
Non-chiastic elements: 3
Number of times each chiastic element appears: 3,2,2
Number of random reorderings: 200000
Number of duplicate levels: 0

For reference, the chiastic elements included in the analysis were "Lamanites", "prison", "forth/slay", "durst not lay their hands upon them", and "burned/fire". The non-chiastic elements included in the analysis were "Nephi and Lehi", "fear", and "encircled about". The program returned the following result:

L = .33203
Margin of error = .00129

In other words, a random rearrangement of the elements in the passage will produce a comparable chiastic structure 33% of the time. That means that there may be an intentional chiasm here, but that from a statistical standpoint it might just be a freak accident. It should also be noted that this is the probability of intentionality within this single "opportunity". (By an "opportunity" I mean any section of text that has at least 5 repeated elements within close proximity of one another. In any text with many repeated elements, the elements might unintentionally have a chiastic ordering.) There are a probably dozens of opportunities in Helaman (the Edwardses estimate 956 such opportunities in the entire Book of Mormon) for an accidental chiasm of this length to emerge. If our L value for one opportunity is 33%, the P value over, say, ten opportunities would be greater than 98%.

That does not necessarily mean that the Helaman 5 chiasm is unintentional. The Edwardses' method takes into account only 4 of 15 of the criteria by which John Welch proposes we evaluate the strength of a chiasm. (They use the quantifiable ones; the rest are subjective). The case for intentionality in Helaman 5 could therefore be strengthened by application of Welch's 11 other criteria. But from a purely statistical standpoint, we are not compelled to accept the intentionality of this structure.