Did Chiasmus Appear in the Book of Mormon by Chance?
Transcript of the September 2003 BMAF Conference held at Thanksgiving Point
(references and text updated on 15 November 2007)
Did Chiasmus Appear in the Book of Mormon by Chance?
by Boyd F. Edwards:
Chiasmus is important because it bears on the authenticity of the Book of Mormon. There are qualitative aspects to the problem, but the essence of the problem and my approach to it as a physicist is quantitative. I'm grateful to Farrell Edwards, my insightful collaborator on this project, who is both my physics teacher and my father. I'm also grateful to Jack Welch for a number of helpful insights he's made along the way as we have striven to understand chiasmus in the Book of Mormon. I thank my wife, Nadine, and my daughter, Claire, for technical assistance and support.
I believe that chiasms in the Book of Mormon are truly one way that the language of the Book of Mormon speaks volumes. I welcome your questions both during and after the presentation. I also have printed copies of the paper written on the subject for anyone who is interested, as well as a few copies of the slides [1, 2].
The presentation is divided into four sections:
1- define chiasmus, give some historical background and learn how to approach the problem
2- discuss the tools that we have developed for the purposes of determining whether chiasms have appeared by chance. Or, more precisely stated, could they have appeared by chance or not?
3- discuss the application of these tools to particular chiasms in the Book of Mormon and elsewhere
4- discuss conclusions implied by our studies
Chiasmus is a Hebrew literary style in which two or more elements are stated and then restated in reverse order. Matthew 10:39 states
He that findeth his life (A) shall lose it (B):
and he that loseth his life (B) for my sake shall find it (A);
in the form of A - B - B - A. The way it's laid out on the page, A then B, then on the next line B then A, so that when you draw a line between the two A's, then again between the two B's, you get the letter 'X,' which is the Greek letter 'chi,' which is the root of the word 'chiasmus'.
Hebrew Biblical writers used chiasmus in their writing. One example in the book of Ezekiel has 12 literary elements that are stated and then restated in exactly the reverse order.
I was 13 years old when Jack Welch, then a graduate student at BYU and now the editor in chief of BYU Studies, published his discovery of chiasmus in the Book of Mormon in BYU Studies. I can still remember my father's excitement as he told me that an ancient Hebrew literary form had been discovered in the Book of Mormon, and that Joseph Smith apparently did not know about this form. I was fascinated by the evidence that this discovery gave to the authenticity of the Book of Mormon. It was a very significant event for me, and important to the development of my perception of the intellectual authenticity and robustness of the Book of Mormon.
Did chiasms appear in the Book of Mormon by chance? The short answer, for most of us when we first examined chiasmus in the Book of Mormon, is 'No'. It seems that there is no way that the beautiful, detailed chiasms in the Book of Mormon could have appeared there by chance. However, some argue just the opposite: The unidentified author of www.ldsmormon.com said, “The chiasms that Mormon researchers find all through the book are, in fact, the result of an incredible amount of repetition contained therein, and are well within the bounds of probability.” When I read this statement last summer, it struck me as wrong and irresponsible; and I set about the task of challenging this statement using my training as a statistical physicist.
To give you and idea what this author means by repetition, I'd like to point out a favorite chiasm of mine in King Benjamin's sermon (Mosiah 5:10-12). This chiasm has seven chiastic elements, and they are: 1- name, 2- called, 3- left hand of God, 4- I would that ye should remember, 5- I said/say, 6- blotted out, and 7- transgression/transgress. The message of the chiasm is that our own transgressions can cause the name of Christ to be blotted out from our hearts, but critics point out that elements that form part of this chiastic structure, such as the word 'name,' are repeated elsewhere in the chiasm. Such extra appearances of chiastic elements are the repetition spoken of by the anonymous author. Why should they be important? Well, if you pick out all of the words in that chiasm and you jumble them up and pull them out of a hat at random, your chances of happening upon a random chiastic ordering of the words are higher if there's extra repetition in the passage. Furthermore, there is an element 'hearts' that appears twice in the passage that does not participate in the seven-element chiastic structure. The word 'hearts' is called a non-chiastic element. If you jumbled up all the words at random, this word could easily have formed part of the chiastic structure, but, as you can see, it doesn't.
Few chiastic analysts, both in and out of the church, do their analysis responsibly. It is common to pick and choose the words that fit the chiastic pattern and to sweep the rest under the rug, such as the extra appearances of 'name' and the appearances of 'heart' in Mosiah 5:10-12. Doing so can mislead the unwary into erroneous conclusions about the significance and intentionality of chiasmus . Responsible analysts include all extra repetition in their analysis, including extra appearances of chiastic elements and appearances of nonchiastic elements.
The evidence of chiasmus supporting the authenticity of the Book of Mormon has also been called into question by those who argue that Joseph Smith actually knew about chiasmus. Sandra Tanner argues that it's conceivable that Joseph Smith learned about this style from his study of the Bible and employed it deliberately while writing, rather than translating, the Book of Mormon and other works. As evidence, she points out chiastic passages in the Doctrine and Covenants, which Joseph Smith published not as a translation of an ancient text but as a list of modern instructions. The best chiasm that we've been able to identify in the Doctrine and Covenants is D&C 88:34-39, a five-element chiasm, and at first glance it looks pretty good. Does Sandra Tanner have a point? Yes. Can we evaluate the likelihood that chiasms appear in the Doctrine and Covenants by chance? Yes. It's important to investigate claims of chiasmus in the Doctrine and Covenants because if they are likely to have appeared by chance, then their presence in the Doctrine and Covenants supplies no evidence that Joseph Smith knew about chiasmus. If they could have appeared by chance, then they don't help Sandra's case against chiasms in the Book of Mormon.
Our approach to the problem is, using a computer and mathematical statistics, to put each significant repeated literary element that appears in a passage on a separate slip of paper and jumble them all up in a hat, and then to pull these slips out one by one and to determine whether this random ordering is chiastic or not. We also take into account the fact that the longer the work in which the chiasm appears (such as the Book of Mormon for Mosiah 5:10-12), the greater the likelihood that a chiasm will appear somewhere at random in the work; the longer a monkey sits at a typewriter, the greater the likelihood that he will type out a sonnet. Our analysis tells us nothing about the identity of the authors in the Book of Mormon. This is not a wordprint analysis. It cannot, of itself, determine whether Joseph Smith wrote or translated the book. The analysis is also blind to the literary aspects of the book. And, it's not concerned at all about the meaning of words. All that our analysis does is to ask about the order in which words appear.
In performing this analysis, we employ seven basic rules to ensure uniform comparisons between chiasms in various works. Rule 2 helps to ensure reliable statistical results by requiring that the first and second instances of the same element be associated strongly, thus eliminating many weak pairings that are found in the literature. The other rules are listed in Refs. 1-3. We do not claim that these rules define what is and what is not a chiasm. All we're saying is that these rules help to ensure reliable statistical results.
For I am come to set a man at variance against his father,
and the daughter (a) against her mother (b),
and the daughter (a') in law against her mother (b') in law.
And a man's foes shall be they of his own household.
He that loveth (c) father or mother more than me is not worthy of me (d):
and he that loveth (c') son or daughter more than me is not worthy of me,(d').
And he that taketh not his cross, and followeth after me, is not worthy of me.
He that findeth his life (e) shall lose it (f):
and he that loseth his life (f') for my sake shall find it (e').
To illustrate how our calculations are carried out, we determine the likelihood that Matthew 10:39 (the find, lose, lose, find example discussed above) could have appeared by chance in a larger work, Matthew 10:35-39, as shown in Example 5. In this passage there are three opportunities for chiastic structure. The first opportunity is the daughter, mother, daughter, mother structure (a, b, a, b) Is that a chiasm? No, because to be chiastic the order has to be reversed the second time and it's not reversed. The second opportunity is the loveth, worthy, loveth, worthy structure (c, d, c, d) which is also not chiastic for the same reason. The third opportunity is the find, lose, lose, find structure (e, f, f, e) noted above, and is chiastic. Thus, the number of chiastic opportunities is N = 3 and the number of chiastic elements per opportunity is n = 2. The next step is determining the likelihood that each opportunity would result in chiastic structure. To do so, take four slips of paper and write “a” on two of them and “b” on the other two. Throw them into a hat and draw them out in a random order. The six possible orders are (a, b, a, b), (b, a, b, a), (a, a, b, b), (b, b, a, a), (a, b, b, a), and (b, a, a, b). Only the last two of these six are chiastic. Hence the likelihood that each opportunity would result in chiastic structure is L = 2/6 = 1/3. So, you have a 33% chance of getting a valid two-element chiasm when drawing the four elements out of a hat. Since the likelihood that each opportunity would not result in chiastic structure is 2/3, and since N = 3, the likelihood that you would get chiastic structure by chance somewhere in Matthew 10:35-39 is P = 1 - (2/3)(2/3)(2/3) = 0.70. Accordingly, you have a 70% chance of getting at least one chiasm when randomly rearranging the elements of all three opportunities in Matthew 10:35-39.
The next step is to apply these tools to various words. Why do we consider the Book of Abraham? The same reason that we evaluate the Doctrine and Covenants. Some critics say regarding the Book of Abraham that Joseph probably incorporated chiasmus deliberately into the work. Here's the best chiasm we could find in the Book of Abraham (Abraham 3:26-38), a simple three-element chiasm, therefore the likelihood is 1/15, which is 0.067. So, there is a 6.7% chance that a single three-element chiasm, if rearranged randomly, would result in a chiastic structure. We went through the entire Book of Abraham and asked how many opportunities there would be for chiastic structure. After the calculations, what does that say? It says that if you take the Book of Abraham and jumble up its elements and ask what is the likelihood that any one of the opportunities for chiasm would have had that structure, we would have a 99% chance of that happening. What does that say? That says it's highly likely that the chiastic structure in the Book of Abraham occurs by chance. That doesn't say that it necessarily did occur by chance, but that it could have. The bottom line is that chiastic structure in the Book of Abraham cannot be used as evidence to say that Joseph Smith knew about chiasmus.
Regarding the Doctrine and Covenants, we examine the same simple five-element example that we identified before (D&C 88:34-39), which has a small likelihood L = 0.0011 of appearing by chance. Based just upon this value, you might have come to the wrong conclusion about its intentionality. But there are approximately 686 opportunities for chiastic structure with five elements in the Doctrine and Covenants. When we take that into account, then the overall likelihood of chiastic structure with five elements appearing by chance in the Doctrine and Covenants is about 52%. What does it say to have approximately a 50:50 chance of jumbling all the elements in the Doctrine and Covenants and having at least one chiasm come out? It says that such chiastic structure could have appeared by chance. This particular chiasm could have resulted by the random jumbling up of words. It's the same as the 50:50 chance of getting 'heads' when I flip a coin. Chiasmus in the Doctrine and Covenants could have happened by chance, and there's no evidence that it happened by design or that Joseph knew about chiasmus and incorporated it deliberately into the Doctrine and Covenants.
Now, back to the Book of Mormon. We can't put the entirety of Alma 36 on the screen, but what we have done is to summarize the chiastic structure we have used to come up with the conclusions we have reached. Critics point out that analysts have come up with different chiastic structures for Alma 36, saying that if these analysts can't agree on its chiastic structure, then this structure was probably not intentional in the first place. To these critics, this lack of consensus indicates that the alleged chiastic structure stems from the ingenuity of the analyst, not the author, and likely resulted by chance. To others, this lack of consensus indicates that the author of the chapter may have taken liberties with chiastic form.
To respond responsibly the critics on this issue, we calculated the chiastic structure of Alma 36 based on two different chiastic structures. The first is a simple eight-element structure with no extra repetition. The second is a ten-element structure that is similar to Welch and Parry's analysis and involves a couple of extra-appearances of chiastic elements. The likelihood that chiastic structure with eight elements could occur randomly in the book of Mormon is 0.018%, or about two hundredths of one percent, whereas the likelihood of ten-element structure is 0.0003%. The first result can be obtained from a mathematical equation because the chiastic form is simple, whereas the second result, because of the two extra appearances, requires an overnight computer simulation involving 400 million random rearrangements of the chiastic elements, drawing them as it were from a hat. Thus, no matter how you analyze Alma 36, the likelihood that it could have appeared by chance in the Book of Mormon is very small. Consequently, the lack of consensus about the specifics of the intended chiastic structure of Alma 36 really doesn't matter. What matters is that, to a high degree of certainty, this structure was incorporated intentionally in the Book of Mormon by the author of Alma 36.
In summary, our analysis yields an estimated likelihood of 52% that the chiastic structure D&C 88:34-39 could have appeared by chance in the Doctrine and Covenants, and a likelihood of 0.02% that the eight-element chiastic structure of Alma 36 could have appeared by chance in the Book of Mormon. Thus, chiasmus could easily have appeared in the Doctrine and Covenants by chance, whereas it's highly unlikely that chiasmus could have appeared in the Book of Mormon by chance. Stated another way, the statistical evidence indicates with 99.98% certainty that chiasmus appears in the Book of Mormon by design. Our statistical study supplies reliable evidence of intentional chiasmus in the Bible and in the Book of Mormon, but no evidence of chiasmus in the Doctrine and Covenents, the Book of Abraham, and in a letter of Joseph Smith to his wife Emma that has also been touted as evidence that he knew about chiasmus .
Did chiasmus appear in the Book of Mormon by chance? Not likely, according to our calculations. Our results do not establish that the Book of Mormon is a translation of an ancient document, but do establish that the chiastic structure in Alma 36 likely did not occur by chance. Furthermore, our results do not rule out the possibility that Joseph Smith knew about the chiastic style when translating the Book of Mormon. However, our results do rule out chiasms in the Doctrine and Covenants as evidence that Joseph Smith knew about chiasmus.
I greatly admire the poetic elegance and mathematical symmetry of chiasmus in the Book of Mormon. I'm happy to report that attempts have failed to dismiss its chiasms as groups of words that happened to fall into chiastic order by chance. For me, the real value of chiasmus in the Book of Mormon is the insights they give into the hearts of the authors. Alma 36 was lovingly constructed, as Jack Welch has pointed out, by Alma the Younger, some 20 years after his miraculous conversion, for the purpose of teaching his sons. It's nice to know that chiastic analysis helps to confirm what I already knew to be true, namely, that Book of Mormon is true. I know of no more powerful way that the language of the Book of Mormon speaks volumes.
 Does chiasmus appear in the Book of Mormon by chance?,” B. F. Edwards and W. F. Edwards, BYU Studies 43, no. 2, 103 (2004); http://byustudies.byu.edu/chiasmus/.
 “Response to Earl Wunderli's critique of Alma 36 as an extended chiasm,” B. F. Edwards and W. F. Edwards, Dialogue: A Journal of Mormon Thought 39, no. 3, 164 (2006); full account at Dialogue Paperless, http://www.dialoguejournal.com, E-paper #1 (2006).
 “Does Joseph's letter to Emma of 4 November 1838 show that he knew about chiasmus?,” B. F. Edwards and W. F. Edwards, Dialogue Paperless, http://www.dialoguejournal.com, E-paper #4 (2006).