Hi Billy! I've missed you! I was worried that COVID might've taken you away like a thief in the night, which would've grieved me deeply.

Billy Shears wrote: ↑Fri Oct 01, 2021 3:45 pm

Your first paragraph is exactly right. In this case, the proxy for chiasmus is the “inverted type-token ratio,” which is used by quantitative linguists to assess the working vocabulary of an author. It is simply the total number of words in a text divided by the number of unique words.

One works with what one has available. And calculating the TTR has the advantage of not taking me several lifetimes to do, which is what it would've taken to accurately count the number of chiasms in the Book of Mormon.

Billy Shears wrote: ↑Fri Oct 01, 2021 3:45 pm

It turns out that the D&C also has a small working vocabulary.

I make note of this, but I also don't make much of it. Maybe it's an indication that repetition is just a part of Joseph's (fake) revelatory process, and maybe it's an indication that the D&C wasn't originally composed in English. But I'm not sure it's an indication of either. The D&C is a different beast than the Book of Mormon entirely. As has been pretty easy to notice this year, the D&C employs quite a bit of apparently stock language when it comes to forming various blessings and mission calls. That sort of thing could quickly decrease working vocabulary, but it's also not something we really see in the Book of Mormon. There you have repetition in the form of chiasmus and parallelism and (often subtle) internal allusions, but you don't really get stock bits of language copied and pasted every other chapter.

Stuff like the D&C is why I think we need a deeper dive into the TTR and what drives it, both in the Book of Mormon and in comparative contexts. My essay may or may not stimulate that kind of effort, but a guy can hope. In the meantime, it serves as a decent barometer for what I see as the probability of Joseph or anyone else in the 19th century giving us the chiastic and parallelistic structures we see in the Book of Mormon.

Billy Shears wrote: ↑Fri Oct 01, 2021 3:45 pm

In Bayesian statistics, you ask “What is the probability you’d see this basket of evidence if hypothesis A is true? What is the probability you’d see this basket of evidence if hypothesis B is true?” In a continuous statistical model, “the probability of seeing this basket of evidence” is given by the

*height* of a probability distribution function (PDF)

*at a specific point corresponding to the evidence*, or by the

*height* of a likelihood function

*at a specific point corresponding to the evidence.*
However, that isn’t what Kyler does. Rather, he consistently uses the p-value from Fisher’s significance testing. This corresponds to the height of the

*cumulative distribution function* (CDF)—not to the height of the

*PDF*.

For anyone not up to speed with what these terms mean, a probability distribution function is a general term for any function that models how likely a set of events are. The cumulative distribution function, on the other hand, is a function adds up a set of probability values for a range of various outcomes. For instance, you could ask what the probability is that someone could have a child that's 6'7". In doing so, you could examine the probability distribution function for height, and then look at the number of children born where were exactly 6'7". That number would probably be pretty low. But it's also probably not the question you really care about. In that case, you really care about the more general question: what's the probability that someone could have a child 6'7"

*or higher*--in other words, instead of asking what the probability is of getting the exact result (6'7"), you're asking what the probability is that you could get a result similar to that (6'7" or above). When asking statistical questions in the social sciences and elsewhere, we generally are asking the latter kinds of questions, and the same goes for my explorations of Book of Mormon evidence. I'm usually asking what are the chances we'd get evidence

*as strong or stronger* than what we see, assuming the book was fraudulent as well as assuming the book was authentic. Chi-squares and t-tests and ANOVAs are pretty good at producing those sorts of probability estimates.

If I'm following Billy here, it seems that he would prefer that I instead produce estimates for the probability of producing the specific results that we see

*and only those specific results*, and that it's somehow inappropriate that I make use of stats that rely on cumulative functions. That would be pretty dumb. In fact, it would probably lead me to engage in the kind of sharpshooter fallacy that he's been accusing me of since the start of this essay series.

Chiasmus is a pretty good example here. If I took the kind of approach Billy suggests here, I could taken a look at the arrangement of Alma 36 and figured out the probability of producing a chiasm with exactly as many levels as we see. That probability would probably be pretty low. It would probably be more fair to the critics though, to estaimte the probability of seeing a chiasm with that many levels

*or higher*, as faithful scholars would probably been crowing just as loudly had that been the case. The cumulative probability function would then spit out a higher probability value, advantaging both the critics and common sense.

In short, Billy's critique here is incorrect (and a bit pedantic). If he would prefer that I use different probability values, he's always welcome to make alternative proposals (though the one he made a couple weeks ago ended up being a bit squishy). Until then, I think my approach works pretty well.

Thanks to Noel for letting me know about this thread (though I'm not in charge of moderating your comment, sadly). If you'd ever like me to comment on something, feel free to let me know.