Intro/FAQ ⎜ Episode 1 ⎜ Episode 2 ⎜ Episode 3 ⎜ Episode 4 ⎜ Episode 5 ⎜ Episode 6 ⎜ Episode 7 ⎜ Episode 8 ⎜ Episode 9 ⎜ Episode 10 ⎜ Episode 11 ⎜ Episode 12 ⎜ Episode 13 ⎜ Episode 14 ⎜ Episode 15 ⎜ Episode 16 ⎜ Episode 17 ⎜ Episode 18 ⎜ Episode 19 ⎜ Episode 20 ⎜ Episode 21 ⎜ Episode 22 ⎜ Episode 23
[Editor’s Note: This is the first 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.]
It seems unlikely that a young man of Joseph Smith’s limited education could produce a book the length of the Book of Mormon as a first-time author.
Joseph Smith is a definite outlier among the nineteenth-century’s great authors, even without considering the extraordinary content of the book itself. The estimated probability that someone of Joseph Smith’s age and education would publish a book the size of the Book of Mormon as their first work is p = .0006.
Evidence Score = 3 (beliefs adjusted 3 orders of magnitude toward authenticity)
Imagine yourself on a dark, cold night in New England, 1835. Your hearth dances with faint light from a dying fire, and you huddle next to it with a thick wool blanket, trying to keep warm. As you stare at the coals you find your eyes wandering to a Bible, open on the table to where you’d last been reading. Dust skirts the wrinkles of the paper, catching the light from the fire. You turn away quickly, the edge of your cheek twitching with the hint of a grimace.
As you sit, a muffled knock works its way through the heavy wood of the cabin door. A moment’s silence hangs in the air, and you hope that silence will keep, but the knock repeats—a more desperate knock this time.
"What is it?" you yell out grumpily toward the door. "You picked a cold night for visiting."
The voice of a young man responds with deference. "My apologies. I was told in the village that you had an interest in rare and unusual books. I have one that I think you might like to see."
Your eye edges again to the Bible on the table, and your exhaling breath turns to an audible sigh. "You’re mistaken, young sir. I’m not in the habit of entertaining booksellers on my doorstep, let alone at this late hour."
"Please", the voice says, quieter this time. "The night is cold, and I have no friends in this place. If you would allow me to warm myself by the fire a moment, it would help speed me on the road back to town."
You take another moment before pulling yourself off your hard wooden chair. You pull the door open and do your best to put on a more welcoming face. "Thank you", the young man says, though a creeping baldness at the edges of his dark hair tells you he’s not as young as he sounds. You move another chair by the fire and motion him to sit. He does, his eyes grateful. "The Lord bless you for your kindness."
You keep your eyes on him as he watches the coals, rubbing the chill from his hands. He doesn’t seem as keen to talk as a bookseller might be. "Well then," you say, "as long as you’re here you might as well pull out that book."
He looks back at you almost in surprise, but dutifully moves his stiff hands to his satchel. Those hands pull out a book, small but thick, its cover red in the light of the fire. You can’t quite read the title in the dim light. "And what is that?" You ask.
"This," he says, "is the Book of Mormon."
The words hold no meaning for you, but you listen as he tells you about the book. He says that it’s a volume of scripture, one that tells of the ancient inhabitants of the American continent and their visit by Christ following his resurrection. He says that the book is evidence that God has called a new prophet—a modern Moses—to restore the Church of Jesus Christ to the earth.
You can’t help but let out a chuckle at that last part. This Joe Smith wouldn’t be the first rabble-rousing prophet you’d heard of, and he wouldn’t be the last. Still, none of them had a book like this. You take the book in your hands, running your fingers the length of the spine. You open it and flip through the pages—hundreds of them filled with a tightly packed script. You know that writing such a thing would be no mean feat.
You close the book and face the young man, who you know can see your skepticism. “This Smith fellow, how old was he when this book was published?”
He eyes turn upward in thought. “That was five years ago now, which would have made him 24.”
“And where was he educated? Harvard? Princeton?”
The young man’s head gives a shake, and a laugh comes with it. “If you had ever seen him write you wouldn’t have asked. He saw enough school to learn his letters, but he didn’t learn them very well.”
“Hmm,” you say, continuing to run your fingers along the book’s spine. “I suppose it does seem unlikely that a young man with so little schooling could have written something like this.”
That last statement is the sort of thing I could imagine anyone saying to themselves the first time they encounter the Book of Mormon. Those that early missionaries approached on the American frontier certainly thought similar things. Judging by the arguments they make, many critics of the Book of Mormon think it rather strongly. Its why so many have searched for so long (and so unsuccessfully) for someone else on whom they can pin the book’s authorship. And phrased as it is above, I think it’s something everyone on all sides should be able to agree on—it does seem unlikely. The question is, is it actually unlikely, and how unlikely is it?
That’s a big question. I’m only going to tackle a part of that question here, and it’s the most basic part. Given Joseph’s age and education, how unexpected would it be for him to write a book the length of the Book of Mormon, with no prior history of publication (or of, you know, coherent and well-worded letters). As hopefully you know by now, given the introductory episode, we’re going to use Bayesian analysis to help answer that question.
Now, to clarify, when I talk about “length,” I mean it literally—we’re going to base our analysis on the word count within the Book of Mormon and within other nineteenth-century works—but I also mean something more than that. The Book of Mormon is much more than just a large collection of words. It’s a complex web of history, narrative, and sermon that gives it a deserved place in literature’s great epics. That narrative complexity is much more difficult to quantify than word count, but it’s a point on which few seriously contend, and it’s worth noting as we leave that complexity behind to focus on its raw size.
I know this is the first episode where I actually get into some Bayesian analysis, but I really recommend taking a glance at my FAQ in the introductory episode before you go much further. It should help you get your bearings on the type of analysis I’m trying to do here and what all these terms and formulas mean. I also know that no one ever clicks on links, so I’m going to try to take things slow here, but you can’t say I didn’t warn you.
First, we have to think clearly about the evidence we have at hand—in this case, the sheer size of the Book of Mormon along with Joseph’s age and education at the time it was published.
The Book of Mormon is about 268,163 words long, taking up 531 (very dense) pages in its current edition. You’re not likely to get through it in a breezy afternoon reading session. It was also the first written work he ever produced, which is relevant given that most authors have early projects that prepare them for their eventual masterpieces. Joseph Smith’s magnum opus came out of nowhere and, aside from scattered revelations (including the Joseph Smith Translation), sermons, and the relatively brief Book of Abraham, his writing career ended almost as quickly. We could potentially account for these additional works in his word count, but what we’re most interested in here is the debut production of an author. Similar analyses could be done for other aspects of an authors’ writings, such as lifetime composition, but that would be unlikely to help the critics’ case, given how unique Joseph’s writing career is in that regard. We’ll keep it simple and stick with the Book of Mormon itself.
The publication of the Book of Mormon was completed when Joseph Smith was 24, though its dictation took place when he was 23. We’ll go with 24 just for the sake of argument, though. It’s commonly claimed that Joseph Smith had three years of formal education, and if we’re trying to align it with an equivalent public school education today, that’s probably not far off. If we’re trying to be technical about it, though, there were seven distinct years in which he received some sort of schooling, including a season in high school when he was 20. We’ll stick with seven years of education for this particular analysis.
If you’re interested in a more in-depth discussion of additional literary characteristics (e.g., reading level; lifetime composition) of the works attributed to Joseph Smith, this one by Brian Hales is a fantastic place to start.
So that’s the evidence as we seem to have it, and on which reasonable people can likely agree. Now, what explanations do we have for that evidence?
Joseph Smith as author of the text—According to this theory, Joseph Smith was the sole author of the text and, having produced it, should be considered among the great literary talents of the nineteenth century.
The Book of Mormon as an authentic ancient text—If this theory is correct, Joseph Smith was not the author of the Book of Mormon. The book was instead written by two-dozen authors over a period of a thousand years, and was edited and abridged by an ancient scribe who made doing so his life’s work. There would be no reason to expect the length of the Book of Mormon to align with nineteenth-century literary works.
In addition to these two theories, many have made arguments over the years that some other individual, such as Sidney Rigdon, was the author of the text. Though the available primary evidence doesn’t align well with that theory (and arguments for Sidney’s authorship seem particularly weak), it would be possible to adjust my analysis for any given author by replacing Joseph’s age and education with theirs. As we’ll see, though, age and education don’t end up making much of a difference. Theories that suggest multiple nineteenth-century individuals collaborating to create the book have similar evidentiary problems, and would probably require a different analysis (comparing the Book of Mormon to other collaborative works of fiction, which might be a bit tougher to track down). I’ll be focusing this analysis on Joseph, and let others take up alternative torches if they so desire.
So, given those two competing theories and our background knowledge, how probable would we consider those hypotheses at first blush, before considering any of the evidence?
*Note: If we were doing a complete Bayesian analysis, we would spend more time trying to produce reasonable estimates for these values. But given that no one will ever agree on the likelihood of stuff like angels or seer stones, I’ve opted to use prior probabilities to demonstrate a type of faith journey. As we consider more evidence, both for and against the Book of Mormon, we can track how those beliefs change. Starting with a position of extreme skepticism and having the evidence alter that probability allows us to see that change in action.
PH—Prior Probability of Ancient Authorship—We start with the assumption that the probability of ancient authorship is low to the point of vanishing (1 in 1040, or p = 1.0 x 10-41).
PA—Prior Probability of the Alternative (Joseph Smith Authorship)—If we assume the probability of ancient authorship is low, then that means we’re assuming that the probability of Joseph Smith authoring the document is high (i.e., extremely close to 1, or, if you want to be a bit more precise, p = 1 – 1.0 x 10-41).
CH—Consequent Probability of Ancient Authorship—How likely would it be for the Book of Mormon to be its size if it was authored anciently? Well, if Joseph Smith didn’t write the Book of Mormon, then his own age and education aren’t relevant, so we can just leave those factors out. We would instead expect the length of the book to look much more like a collection of scriptural texts than a nineteenth-century work of fiction.
So how does the Book of Mormon compare to that type of collection? The Bible seems like a pretty useful reference in this case, and it makes sense to take a look at it at the level of individual books within the Bible and Book of Mormon (see Table 1 in the Appendix). The average book in the Book of Mormon has 17,989 words, which is obviously more than the Bible’s 11,943 words. However, the word count in the books of the Bible has quite a range, and the standard deviation is 12,352. That would put the Book of Mormon’s count well within a single standard deviation of the Bible’s average, which suggests that the Book of Mormon fits comfortably with what we’d expect for books of scripture.
We can go a step further, though, and estimate a more exact probability that the books of the Book of Mormon fall on the same distribution as the books of the Bible. Since the word counts of the books of the Bible and the Book of Mormon clearly don’t follow a normal distribution, that limits us a bit. But we can use a statistical test like the Independent Samples Mann-Whitney U Test to get what we need. When we conduct that particular test, the probability that the word count distribution differs between those sets of books is p = .535.
Now, that probability is likely too far on the low side—you could argue that the Book of Mormon is structured more like the Old Testament than the New (i.e., as weighted more heavily toward lengthy scribal abridgements than toward brief personal letters). If you only include the books of the Old Testament, the Book of Mormon would look even more similar to the Bible. But we’ll give the critics the benefit of the doubt and stick with our .535 value.
And that fits what would likely be our gut expectation here—if we had a volume of ancient scripture like the Book of Mormon, it wouldn’t be guaranteed to be the size the Book of Mormon actually is, but that sort of length wouldn’t be unexpected by any stretch.
CA—Consequent Probability of Modern Authorship—Now how likely would it be for the Book of Mormon to be its size if it was the product of a single nineteenth-century author of Joseph Smith’s age and education? To figure that out we have to take a close look at some other nineteenth-century authors. I’m not the first to do so, but there may be a few things I can add to what’s come before.
To do that, I relied on this handy Wikipedia list of prominent literary works produced in each decade going back to 1500. It provides a useful sample of highly respected authors within Joseph Smith’s timeframe and, sure enough, Joseph Smith and the Book of Mormon are right there on the list. I took the 116 authors with works published between 1800 and 1860 and used their individual Wikipedia entries (supplemented by Encyclopedia Britannica, when necessary) to keep track of three things: how old they were when they published their first fictional work (of greater than 50 pages), how long that work was (in pages), and how many years of formal education they received (see Table 2 in the appendix).
Now, there are some limitations there to keep in mind. Because I was working with page counts rather than word counts, it was important to get a comparable page count for the Book of Mormon. The Book of Mormon’s pages are quite a bit denser than the average book. If it did have the average number of words per page (which readinglength.com calculates at about 306) it would have 876 pages instead of 531. I also didn’t have precise publication dates for the books, which meant I calculated age at publication by subtracting the birth year from the publication year for each author. Education was tricky as well—some entries didn’t include exact information on formal schooling (particularly for the female authors). I picked the lowest number of years I could justify based on the information available.
All told, it was a horrifically interesting Wiki-binge. A couple things stood out pretty clearly by the end. First, 24 is young for a first-time author, but not horrendously young, and even turned out to be the modal age. The average age at publication was 30, but there were some as young as 16. (In all of the following charts, the red bars indicate where Joseph and the Book of Mormon fall in the distribution of data.)
Second, many of the authors were university educated, and those who weren’t had the benefit of extensive private tutoring. None of them could be plausibly labeled as a country bumpkin. Even those with more spotty education were described as voracious readers as children and were recognized early for their precocious talents (very much in contrast to Joseph Smith). For those with private tutoring, I assumed (conservatively) they had the equivalent of a sixth-grade education.
It’s important to keep in mind, too, that the primary argument about Joseph Smith’s education isn’t that he was too uneducated to write a book. It’s that he didn’t have the very specific education required to produce some of the book’s more impressive (and ancient) literary features. Demonstrating that some other prominent authors had even less education than he did does nothing to counter that argument.
And if we just look at page counts, Joseph Smith is clearly exceptional as a first-time author. Only one comes close to matching his output, and that’s the incomparable Charles Dickens, who seemed to do little else other than write his brain to pieces. I should note, though, that Dickens was about the same age as Joseph at the time his first novel was published, and himself had an atrocious education.
Now, before any critics get too excited, it’s important to keep a few things in mind. Dickens was one of those precociously talented, voracious readers mentioned above. He also wrote his first novel in monthly installments as a serial, being paid for each installment, over a span of 20 months. That may sound quick, but it’s got nothing on Joseph’s 65 working days. Dickens was exceptional in his own right, in part due to a medium that incentivized producing a ton of material. I wouldn’t use him as proof that Joseph could’ve written the Book of Mormon.
Once I had that lovely little dataset, though, I used a form of outlier analysis using a measure called the Mahalanobis Distance to estimate how likely it is that Joseph Smith belonged in the group of nineteenth-century literary masters. When I conduct this sort of analysis in my research, I’m generally looking to see if there are any odd ducks in my data—anything that doesn’t seem to “fit” with the rest of what I’m looking at. The analysis shows me the probability that a particular case belongs to the same distribution of data as the rest of the cases in the dataset. Usually, if that probability is less than 1 in 1000, I’ll toss it aside so it doesn’t mess up the rest of my analyses.
All told, Joseph is a clear outlier. He was younger than average, had substantially less education than average, and, taking all that into account, produced a work far larger than anyone would have guessed. He had a Mahalanobis Distance of 17.5, which, when plugged into a chi-square test with three degrees of freedom (for the number of variables in the analysis), reveals a probability of p = .00055. In other words, we would expect about 55 in 100,000 first-time authors of his age and education to publish a work with the length of the Book of Mormon.
For those who are curious, there was only one other actual outlier in the analysis, but he was an outlier for a different reason. Johann David Wyss wrote his first novel, The Swiss Family Robinson, at the ripe age of 69. If you take out Joseph Smith, then Dickens himself becomes an outlier with a probability of p = .0002, but he makes somewhat less of a splash (p = .001) in a world where the Book of Mormon exists. None of our other candidates even comes close to being an outlier.
(And if it seems like it would be possible to fiddle with the analysis and change the results depending on which books we included, you’re right—it would. Which is why it’s important that I’m not hand-picking—or, if you prefer, cherry picking—which books make it in and which don’t. Basing my sample on Wikipedia entries helps avoid that kind of tom-foolery.)
We can do some further analyses to get a sense of which of those three characteristics—education, age, and length—are contributing most to Joseph’s outlier status. We can remove each of those variables from the analysis, one at a time, and see what happens to the probability when we do. As we might expect from the figures above, removing education and age doesn’t change much—in fact, the probability gets lower (p = .00016 and .00031 respectively). That means the Book of Mormon’s length is what’s setting it apart as an outlier. When we remove length from the analysis, it doesn’t seem like much of an outlier at all (p = .65). It turns out that considering his age and education actually worked a little in favor of the critics, which is a bit surprising given how often the faithful tend to play those things up.
Overall, however, it still seems quite unlikely that any nineteenth-century author would have produced a book with the length of the Book of Mormon as a first-time work. And my estimate, again, is a conservative one—the real probability is probably even lower than that. The power to detect outliers increases as the sample size increases, so odds are good the probability would decrease further if I considered more authors.
So what does all this mean for our beliefs about the Book of Mormon? Now we get to plug all those values into Bayes’ formula and see what happens:
PH = Prior Probability of the Hypothesis (1 in 1040 chance of ancient authenticity, or p = 1.0 x 10-41)
CH = Consequent Probability of the Hypothesis (the probability of an ancient collection of records being as long as the Book of Mormon, or p = .535)
PA = Prior Probability of the Alternate Hypothesis (1 – 1.0 x 10-41 chance of Joseph Smith as author, a very very high initial estimate)
CA = Consequent Probability of the Alternate Hypothesis (our estimate of the probability of a first-time nineteenth-century author publishing a book as long as the Book of Mormon, given his education and age, or p = .00055)
PostProb = Posterior Probability (the new probability of Book of Mormon authenticity)
|PH = 1.0 x 10-41|
|PostProb =||PH * CH|
|(PH * CH) + (PA * CA)|
|PostProb =||1.0 x 10-41 * .535|
|(1.0 x 10-41 * .535) + ((1-1.0 x 10-41) * .00055))|
|PostProb =||9.99 x 10-39|
We can also calculate the “likelihood magnitude,” or an estimate of how many orders of magnitude the probability changes when we consider this evidence.
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(.535/.00055)
Lmag = log10(972)
Lmag = 3
It may not look like much happened there. At first glance, you might think that we started with an incredibly small probability of an authentic Book of Mormon and ended up with an incredibly small probability of an authentic Book of Mormon. But after reviewing the evidence, our extreme skeptic would have increased his estimate of an authentic Book of Mormon almost a thousand-fold—a change of about three orders of magnitude. If we were dealing with someone less skeptical—say, someone who gave the Book of Mormon only a 1 in 100 chance of being ancient, just the length of the Book of Mormon alone could be enough to move them to over 90 in 100 odds that it was ancient. That’s not nothing. And that’s all before we even consider what’s actually in the book, or even how the book was translated.
Did I just use Wikipedia to prove that the Book of Mormon is ancient? No. It would be very easy for the actual content of the Book of Mormon to betray itself as a fraud. This is just one piece of a very large corpus of evidence, both scholarly and less so. But it shows how it would be reasonable for someone to pick up the Book of Mormon and get the sense that they should take it seriously. It sets the first block in a foundation of reasoned skepticism—not skepticism of the church’s truth claims (there’s plenty of that to go around), but a skepticism that questions the claim that the Book of Mormon is a modern artifact of nineteenth-century origin.
Just so I don’t give you the impression that my analyses are law, with each essay I’ll be taking a minute to more explicitly play the role of skeptic, discussing aspects that I think could be improved or that deserve a bit more investigation. In this case, if I was a critic, I’d wonder how the Book of Mormon stacked up against twentieth- and twenty-first-century authors, to know whether Joseph is still an outlier in that context. It’d also be useful to get a sample of amateur rather than professional authors—perhaps the book’s length could be attributable to his lack of taste or his unrefined literary sensibilities (though whether that supposition would line up with the book’s other qualities is a separate question). And of course, using actual word counts instead of estimated page counts would be helpful as well.
It’s worth noting, too, that considering things like reading level or lifetime composition has a real shot at making this type of evidence much, much stronger. It seems very unusual for someone to have produced so much by the age of 24 and then to write little else to compare to it. It wouldn’t take much to statistically compare authors’ lifetime trajectory of work, similar to how Brian Hales plotted them in his Interpreter article, but we’ll leave such questions for another time (or for others to tackle at their convenience).
Next Time, in Episode 2:
Next week, our skeptic will encounter Joseph’s multiple accounts of the First Vision, and we’ll estimate the probability of producing highly disparate and even contradictory accounts when telling a story years apart in different settings.
Questions, ideas, and sharp objects can be flung in the direction of BayesianBoM@gmail.com or submitted as comments below.
Table 1. Scriptural Word Counts
|22||Song of Solomon||2658|
|B07||Words of Mormon||889|
Table 2. Early 19th Century Authors
|Author||Book||Years of Formal Schooling||Age at Publication||Pages||Comments|
|Joseph Smith||Book of Mormon||7||24||876|
|Maria Edgeworth||Castle Rackrent||7||32||176|
|Friedrich Schiller||Die Rauber||13||22||168|
|Francois Rene de Cautaubriand||Atala||10||33||160|
|Germaine de Stael||Could not locate.|
|Jane Porter||Thaddeus of Warsaw||—||26||267||No mention of formal education, but would have been tutored extensively.|
|Jean Paul||Gronlandische Prozesse||6||20||212|
|Charles Brockden Brown||Alcuin||6||27||106|
|Elizabeth Helme||Louisa; or the Cottage on the Moor||—||34||286||No mention of formal education, but would have been tutored extensively.|
|William Blake||Did not produce novel-length works|
|Jean-Baptiste Cousin de Grainville||Le Dernier Homme||10||59||400|
|Elizabeth Meeke||Count St. Blancard||—||34||100||No mention of formal education, but would have been tutored extensively.|
|Heinrick von Kleist||Die Familie Schroffenstein||9||26||114|
|Johann Wolfgang von Goethe||Gotz von Berlichingen||13||24||130|
|Percy Bysshe Shelley||Zastrozzi||13||18||138|
|Regina Maria Roche||The Maid of the Hamlet: A Tale||—||29||256||No mention of formal education, but would have been tutored extensively.|
|Lord Byron||Childe Harold’s Pilgrimage||15||23||128|
|Jane Austen||Sense and Sensibility||3||36||368|
|Johann David Wyss||Swiss Family Robinson||10||69||496|
|Carles Robert Maturin||The Fatal Revenge||10||27||448|
|René-Charles Guilbert de Pixérécourt||Could not locate.|
|William Wordsworth||The Borderers||15||27||140|
|E.T.A. Hoffmann||Fantasiestücke in Callots Manier||11||38||220|
|Mary Shelley||Frankenstein||—||21||288||No mention of formal education, but would have been tutored extensively.|
|Washington Irving||Letters of Jonathan Oldstyle||12||19||67|
|Alexander Pushkin||Ruslan and Ludmila||10||21||134|
|Thomas De Quincey||Confessions of an English Opium Eater||7||37||352|
|Clement Clarke Moore||Did not produce novel-length works|
|Alexander Griboyedov||Woe From Wit||12||28||204|
|James Fenimore Cooper||Precaution||11||31||317|
|Mary Russell Mitford||Watlington Hill||5||25||54|
|Alessandro Manzoni||Il Conte di Carmagnola||12||34||142|
|Alfred de Vigny||Éloa, ou La Sœur des Anges||11||27||62|
|Jane C. Loudon||The Mummy!||—||20||340|
|John James Audubon||Did not publish fiction.|
|Thomas Love Peacock||6||30||112|
|Victor Hugo||Han d’Islande||8||21||332|
|Carl von Clausewitz||Vom Kriege||3||50||142|
|Nikolai Gogol||Evenings on a Farm Near Dikanka||8||22||190|
|Honoré de Balzac||Les Chouans||10||30||204|
|Edgar Allen Poe||The Narrative of Arthur Gordon Pym of Nantucket||11||29||288|
|Alexis de Tocqueville||De la démocratie en Amérique (Vol. 1)||12||30||270|
|Karel Hynek Mácha||Maj||15||25||100|
|Mikhail Lermontov||A Hero of Our Time||9||25||208|
|Charles Dickens||The Pickwick Papers||8||24||848|
|Charles Darwin||The Voyage of the Beagle||10||30||448|
|Richard Henry Dana Jr.||Two Years Before the Mast||13||25||190|
|John Ruskin||The King of the Golden River||7||22||52|
|Thomas Babington Macaulay||Lays of Ancient Rome||12||42||148|
|Hans Christian Andersen||Did not produce novel-length works.|
|Søren Kierkegaard||Did not produce novel length works.|
|William Harrison Ainsworth||Rookwood||12||29||430|
|Alexandre Dumas||Captain Paul||—||36||108||"Did not have much of an education."|
|Domingo Faustino Sarmiento||Facundo||5||34||288|
|Benjamin Disraeli||Vivian Grey||11||22||348|
|Henry Wadsworth Longfellow||Hyperion||14||32||158|
|Charlotte Brontë||Jane Eyre||7||31||492|
|Emily Brontë||Wuthering Heights||3||29||416|
|Frederick Marryat||The Naval Officer||—||37||288||"Son of a merchant prince and member of parliament", so it’s likely he was well educated.|
|Anne Brontë||Agnes Grey||4||26||192|
|William Makepeace Thackeray||The Memoirs of Mr. C. J. Yellow-Plush||14||26||474|
|Francis Parkman||The Oregon Trail||16||24||178|
|Nathaniel Hawthorne||The Scarlet Letter||15||46||148|
|George Borrow||The Zincali||12||38||296|
|Elizabeth Gaskell||Mary Barton||6||38||464|
|Herman Melville||Typee: A Peep at Polynesian Life||7||27||368|
|Harriet Beecher Stowe||Uncle Tom’s Cabin||15||41||266|
|Matthew Arnold||The Strayed Reveller, and Other Poems||10||27||68|
|Charlotte Mary Yonge||Abbeychurch||—||21||268||Educated at home by her father studying latin, greek, french, Euclid, and algebra. Educated until she was 20.|
|Henry David Thoreau||A Week on the Concord and Merrimack Rivers||14||32||368|
|Walt Whitman||Franklin Evans||5||23||208|
|Bozena Nemcova||Origin (including birthdate and identity) under dispute.|
|Elizabeth Barrett Browning||The Seraphim, and Other Poems||—||32||384||Educated at home and tutored.|
|Fitz Hugh Ludlow||The Hasheesh Eater||14||21||228|
|Thomas Hughes||Tom Brown’s Schooldays||15||35||466|
|Gustave Flaubert||Rêve d’enfer||13||16||311|
|George MacDonald||Phantastes: A Fairie Romance for Men and Women||15||34||158|
|Aleksey Pisemsky||Nina; The Comic Actor; An Old Man’s Sin||6||30||184||Was also tutored at home for several years. Couldn’t find his first novel, but I could find his second published a year later.|
|Alexander Ostrovsky||Did not produce novel-length works|
|Ivan Goncharov||A Common Story||14||35||264|
|George Meredith||The Shaving of Shagpat||8||28||252|
|Wilkie Collins||Iolani, or Tahiti as It Was; a Romance||5||20||250|
|Mary Anne Evans||Adam Bede||11||30||608|
|Eduard Douwes Dekker||Max Havelaar: Or the Coffee Auctions of the Dutch Trading Company||3||40||352|
|Antanas Baranauskas||Did not produce novel-length works.|
|Ellen Wood||Danesbury House||—||46||298||No mention of education or tutoring.|
|Anthony Trollope||The Macdermots of Ballycloran||5||32||364|
|Charles Reade||Peg Woffington||16||29||106|
|Sheridan Le Fanu||The Cock and Anchor||4||31||384||Studied law at Trinity College. Was tutored previously (though ineffectively).|
|Charles Warren Adams||The Notting Hill Mystery||—||32||176||No mention of education. Couldn’t find a good page estimate for Velvet lawn, his first novel.|
|Nikolay Chernyshevsky||What Is to Be Done?||12||35||464|
|Mary Elizabeth Braddon||The Trail of the Serpent||—||25||496||"Was privately educated."|
|Jules Verne||Un prêtre en 1839||12||19||249|
|Théophile Gautier||Mademoiselle de Maupin||12||24||400|
|Fyodor Dostoevsky||Poor Folk||10||24||112|
|Lewis Carroll||Alice’s Adventures in Wonderland||5||33||192|
|Algernon Charles Swinburne||The Queen Mother and Rosamund||11||23||234|
|Karl Marx||The Holy Family||12||27||116|
|Bret Harte||Condensed Novels and Other Papers||7||29||332||"Formal schooling ended when he was 13"|
|Louisa May Alcott||Moods||—||33||178||Tutored by her father and Henry David Thoreau|
|Edward Everett Hale||The Brick Moon||14||47||232|
|R. D. Blackmore||Clara Vaughan||10||39||336|
|Comte de Lautréamont||Les Chants de Maldoror||8||18||342|
I’m starting to wonder if Joseph’s authorship is a nuance parameter. (May need to use marginalization). What I’d be more interested in is who else authored the book. Evidence should point to Moroni and Mormon, if not, I’d better figure out whom instead or else the analysis is incomplete.
Please forgive me, it’s so weird applying probability to faith questions for me. I thought I’d be really into it, but the more I think about it, the more uncomfortable I feel. Maybe it’s the old Ecclesiastes proverb that with an increase of knowledge comes an increase in sorrow… I love that book. Maybe it’s time to start attending Elder’s Quorum again…
“I’m starting to wonder if Joseph’s authorship is a nuance parameter.”
Agreed that the question of potential 19th century authorship is extremely important. This is especially the case because critics tend to jump around to whichever candidate isn’t under present investigation. If you present evidence against Joseph they’ll jump to Oliver or Sidney. If you present evidence against Oliver or Sidney, they’ll, almost in the same breath, jump back to Joseph, without much self-awareness of this lack of consistency.
I don’t think there’s any question that Joseph is the prime suspect here, and so these analyses will frame the critical hypotheses in that light. But we can absolutely consider other possibilities. A question we can ask in each case that I think gets to the heart of the matter is this: “is there anyone we can identify for whom this evidence wouldn’t be unexpected?” In the present case, particularly because age and education swayed the analysis so little, I have a hard time thinking of an experienced author among the potential candidates whom I’d expect to produce a book of the size and scope of the BofM.
There are a couple pieces of evidence we’ll talk about here where we might consider meaningful alternatives (e.g., the dictation evidence), and some where alternatives are explicitly considered (i.e., stylometry), but for the most part the faithful evidence is grounded in the words of the book itself rather than in its author, and would apply equally to any potential 19th century candidate (e.g., Early Modern English, chiasmus, archaeological and thematic evidence, onomasticon, etc.). Anyone who would want to solve the problem of the BofM by finding a non-ancient, non-Joseph alternative should recognize the limitations of that approach, and these limitations find expression in the inability (so far) for critics to be able to build consensus (or even a coherent proposal) for any of those alternatives.
“Maybe it’s time to start attending Elder’s Quorum again…”
As a currently service EQP, I’m under professional obligation to say that you indeed should! They need you!
KR: If they’re not, either their prior isn’t really at 1 in 400, or the evidence isn’t actually hitting them at p = .0006, or they’re taking into account more information than merely its length.
I have two points. First, the evidence really isn’t at the p = 0.0006 level. Your analysis that came up with that number is flawed (the sample data is not normally distributed). Second, I don’t think this really has any bearing on authorship (19th Century authors are not homogenous).
KR: Actually, it assumes that they follow a given distribution on each of those three variables, which is a much more reasonable assumption than saying that they’re homogeneous on those characteristics.
The Mahalanobis Distance is simply a well-defined number that comes out of the mathematical calculations. But when you plug this number into a chi-squared test, you are implicitly assuming the underlying distribution is normal. If the underlying distribution is NOT normal, then you are interpreting the results incorrectly. In this case, the underlying distribution is not normal. When dealing with the tail, this is a big deal. 1.9% of your sample (i.e. two observations out of 107) have a page count of over 847 pages. If the normal assumption that you are relying on when you invoked the chi-squared test were true, the probability of this happening would be 0.00000032%. Additionally, if ages were normally distributed with the sample variance, the chances of an author being 69 years old is 0.00035%. Yet in the data, 1% of the authors are that old.
And yes, the authors being homogenous is an implicit assumption in your model. If this model provides evidence at the p = 0.0006 level that Joseph Smith was not a 19th Century author, then we have similar evidence that Johann David Wyss and Charles Dickens weren’t 19th Century authors, either. Shouldn’t three extreme outliers in a set of only 106 data points indicate that there is a problem with how you are scoring these extreme outliers?
KR: Based on my experience we’d still be counting the BofM as an outlier even if we tried to use a different distribution.
If we use the actual distribution of the data rather than the normal distribution, the BoM is an outlier at the p = 0.01 level.
But does that really have any bearing? For example, what if our model had three categories of books:
1- Typical 19th Century books that were written to entertain, educate, and persuade.
2- 19th Century books that were written to resemble the Bible.
3- Authentic ancient books.
A book belonging the category 1 isn’t necessarily going to have a page length drawn from the same distribution as a book belonging to category 2. This is what I mean by homogeneity.
Based on page length, we can reject the BoM belonging to category 1 at the p = 0.01 level. The other half of your analysis shows the data are consistent with the BoM belonging to category 2. However, by only comparing the BoM to the Bible, your doesn’t give a good indication how likely it is to belong to category 3. To see how similar the BoM is to ancient books, we would need to compare it to a wide variety of ancient books to determine how well it fits into that set. You just compared it to one book.
All that said, this is a really fascinating analysis and I look forward to your next installment.
“Your analysis that came up with that number is flawed (the sample data is not normally distributed).”
And yet, none of the highly credentialed quantitative specialists that’ve looked at this sees that as a fatal flaw. Your highly-trained legal mind (at least I recall that you’re a lawyer–apologies if I’m mistaken) sees a rule violation, and you’ve filed a motion to dismiss. Ours, who are used to seeing the statistical sausage get made, know that this is par for the course, and that these deviations don’t generally invalidate the statistical inference on offer.
“When dealing with the tail, this is a big deal.”
The normal distribution would also posit a tail there, just one that’s shaped a little differently. And not differently enough to dramatically alter our interpretation of the BofM’s data point.
“Shouldn’t three extreme outliers in a set of only 106 data points indicate that there is a problem with how you are scoring these extreme outliers?”
The 106 data points help inform us as to the state of the underlying distribution, and allow us to make some guesses as to what it looks like. Samples like that can often, as is the case when relying on randomness, capture unusual examples that don’t seem to fit the distribution. As you point out, though, outliers are outliers for a reason: Dickens because of his incentive structure, Wyss because of his unusual career path (becoming an author after spending his life as a well-educated pastor, who would’ve written a great deal), and the BofM because of…well, that’s the entire question under consideration.
The incentive structure is a good explanation for Dickens because there’s a clear causal connection between that structure and producing more pages. The structure would do the same for any author, to one degree or another. The ‘producing something like the bible’ explanation, though plausible on its face, lacks that clear causal connection. It certainly didn’t lead the authors of other pseudo-biblical works to write more pages. Why should it have done so with such certainty in Joseph’s case?
“All that said, this is a really fascinating analysis and I look forward to your next installment.”
Thanks Billy. I’ll look forward to continuing our conversation in a few days.
KR: And yet, none of the highly credentialed quantitative specialists that’ve looked at this sees that as a fatal flaw. Your highly-trained legal mind (at least I recall that you’re a lawyer–apologies if I’m mistaken) sees a rule violation, and you’ve filed a motion to dismiss. Ours, who are used to seeing the statistical sausage get made, know that this is par for the course, and that these deviations don’t generally invalidate the statistical inference on offer.
Is that an appeal to authority? In any case I am not an attorney. I am a “highly credentialed quantitative specialist” in my own right. But I’d rather keep this focused on the arguments themselves rather than on the strength of my C.V.
If I may tell a personal story, when I was in graduate school I found it remarkably easy, for example, to do a multivariate linear regression: if you could invert X-transpose-X (i.e. if the matrix X-transpose-X is non-singular), you could solve for a line through k-dimensional space that minimized the sum of squared errors. Using linear algebra, the formula to do this is one of the most elegant things in all of mathematics. That’s remarkable. However, that is the easy part. The hard part is figuring out what, if anything, the regression actually implies. The hard part if understanding the model’s validity.
This goes way past looking at the t-statistics of the betas and has little to do with R-squared. The key things I remember focusing on was whether the explanatory variables were independent and whether the error terms really were independent, identically distributed, and normally distributed. That is when words like autocorrelation, multicollinearity and heteroskedasticity entered my vocabulary. Any of these problems could cause our models and our confidence in them to be significantly misplaced. Anscombe’s Quartet illustrates the significance of this nicely.
It is the responsibility of the person who proposes a model to understand its implicit assumptions, to evaluate how likely they are to be true, to understand the implications, and to make the appropriate caveats.
I understand the pain of making sausage. In my presentations I often lead off with an image from the Simpsons of the Springfield Sausage Factory (it has a banner in front that reads, “Kids, come see how it is made!”) We have to do the best we can with the data we have. I get that. But we also need to understand the theory backing the models so that we can put in the appropriate caveats.
In this case, the Book of Mormon is an outlier. I am not contesting that. The question is whether it is an outlier at the p = 0.01 level or at the p = 0.0006 level. The other issue is the one involving homogeneity: what does a book being an outlier on this set imply? We agree that a serialized novel written by Charles Dickens is not homogenous with other books published in a single volume; we agree that Pickwick Papers being an outlier has no bearing on whether it is really 19th century literature.
The question is whether the Book of Mormon is homogenous with the typical books on this list, or whether it is like the Pickwick Papers and has a mundane explanation for being different. I don’t think it homogenous with the other books, which is why I’m leaving my odds at 1-to-400.
That said, I think this is a fascinating argument and I appreciate you sharing it.
“I am a “highly credentialed quantitative specialist” in my own right.”
Greetings fellow highly credentialed quantitative specialist! We who are about to analyze salute you!
“The question is whether it is an outlier at the p = 0.01 level or at the p = 0.0006 level.”
And that’s a fair thing to wonder. Kolmogorov-Smirnow test is significant (p = .015). Skewness is 1.3 and kurtosis is 2.9. So you’re right about the skew, but with that kurtosis, the normal distribution ends up overestimating the tail by quite a bit. Throwing the normal curve on the histogram suggests that’s the case. Happy to email it your way if you’re curious.
Finding the right distribution and trying to fit it is tough with just excel and my neutered SPSS, but, eyeballing it, I could see it being something like a chi-square with about 5 df. If you align the peak of that distribution with the peak of the histogram, that would put 876 pages at somewhere like chi-square = 20, which would be a p of around .001, which would split the difference between the two of us.
But we should really be dealing with this data at the word level instead of the page level, so until that gets fixed trying to fix the distribution is small beans.
“The question is whether the Book of Mormon is homogenous with the typical books on this list, or whether it is like the Pickwick Papers and has a mundane explanation for being different.”
I appreciate you coming at least that far with me–an acknowledgement that there’s something about the length of the BofM that doesn’t fit and that requires explaining. Getting critics even that far on any topic can be a challenge (and I know it can be a challenge on the other side as well). The key is identifying that alternate explanation (i.e., that he was trying to write something like the Bible) and seeing how much water it holds. It feels pretty leaky to me, but apparently your mileage is varying, and that’s fine.
KR: Greetings fellow highly credentialed quantitative specialist! We who are about to analyze salute you!
The pleasure is mine.
KR: And that’s a fair thing to wonder. Kolmogorov-Smirnow test is significant (p = .015). Skewness is 1.3 and kurtosis is 2.9. So you’re right about the skew, but with that kurtosis, the normal distribution ends up overestimating the tail by quite a bit.
I was originally surprised by the Kurtosis number, but when you consider how thin the tail is on the left, it makes more sense. After all, the normal distribution predicts that 5% of books have 11 pages or fewer.
KR: Finding the right distribution and trying to fit it is tough with just excel and my neutered SPSS, but, eyeballing it, I could see it being something like a chi-square with about 5 df. If you align the peak of that distribution with the peak of the histogram, that would put 876 pages at somewhere like chi-square = 20, which would be a p of around .001, which would split the difference between the two of us.
Does a continuous distribution that actually fits the data exist? Not necessarily. My p = 0.01 is based on the Empirical Distribution Function which has the advantage of actually fitting the data.
KR: But we should really be dealing with this data at the word level instead of the page level, so until that gets fixed trying to fix the distribution is small beans.
I’d also be interested in why this was limited to first books. That seems arbitrary. The big thing I want to see is a larger sample with more books.
KR: I appreciate you coming at least that far with me–an acknowledgement that there’s something about the length of the BofM that doesn’t fit and that requires explaining. Getting critics even that far on any topic can be a challenge (and I know it can be a challenge on the other side as well).
You’re welcome 🙂 I appreciate an analysis that has some bearing in actual data.
KR: The key is identifying that alternate explanation (i.e., that he was trying to write something like the Bible) and seeing how much water it holds. It feels pretty leaky to me, but apparently your mileage is varying, and that’s fine.
Even if we can’t identify a specific alternate explanation doesn’t mean that one doesn’t exist. Nor does it mean that that unknown explanation is unlikely. As an example, a few months ago I saw several points of light that were close together in a tight row, quickly moving in the night sky. It was clearly not an airplane and was unlike anything I’d ever seen. Somebody asked me what it was, and I said in jest, “It must be aliens. There is no other explanation.”
Really, there was another explanation and me not knowing what it was didn’t mean it didn’t exist and didn’t have a high probability of being the correct explanation. In this case, the correct explanation turned out to be that it was a set of SpaceX satellites that had just been launched and were in the process of being deployed.
“Does a continuous distribution that actually fits the data exist?”
If it’s discontinuous, then there’s probably a cliff at the 500 page mark, after which it drops off rapidly, which wouldn’t be great news for your tail.
“My p = 0.01 is based on the Empirical Distribution Function which has the advantage of actually fitting the data.”
It’s also has the advantage of being a bit of a cop-out, as I’d need to sample 10,000 more books to have a shot at replicating my original estimate. Maybe Stan’s got a good way to extract the metadata from Nineteenth Century Collections Online.
“Even if we can’t identify a specific alternate explanation doesn’t mean that one doesn’t exist.”
It’s good to know that even critics have a shelf upon which to stick their Zelphs. We’re in the no-shelf zone here! (Or at least everything on it has to be tagged and numbered.)
“I’d also be interested in why this was limited to first books.”
I’ll admit that there was an untested assumption that later works would generally be longer than initial ones, on the premise that authors build up to toward epic masterpieces, and that people who eventually write long, complex narratives generally have to cut their teeth on shorter, simpler ones. Brandon Sanderson is capable of delivering a Rhythm of War (1232 pages), but he first had to get out things like Elantris (492 pages) and Alcatraz verses the Evil Librarians (320 pages). It would be interesting to see if that assumption pans out for 19 century works.
KR: Brandon Sanderson is capable of delivering a Rhythm of War (1232 pages), but he first had to get out things like Elantris (492 pages) and Alcatraz verses the Evil Librarians (320 pages).
Rhythm of War is an interesting example. While it is a hefty book standing alone, it is only one book of a single epic story that will eventually be about 10,000 pages longer than the Book of Mormon. It could be argued that just as the books of the Book of Mormon should collectively count as one book, the books of the Stormlight Archive should count as one book, too.
When people publish shorter books earlier in their careers, is that because they weren’t up to the task of writing longer books without more practice, or is it driven by decisions of publishers who don’t want to risk publishing a more expensive long book on an unpublished author? Or is it driven by starving authors who need a royalty check and don’t have time to write longer books? If Dickens didn’t have the opportunity to publish his first book in a serial fashion, would it have been so long? Is Brandon Sanderson releasing the Stormlight Archive in serial fashion because he doesn’t yet have the experience to write a single book with 11,000 pages?
KR: If it’s discontinuous, then there’s probably a cliff at the 500 page mark, after which it drops off rapidly, which wouldn’t be great news for your tail.
If that’s the case, would it definitively prove that all books longer than 500 pages are really ancient scripture? The truth is there are lots of books the size of the Book of Mormon or longer. Models are not reality, but our models should account for the size of books that actually exist.
KR: It also has the advantage of being a bit of a cop-out, as I’d need to sample 10,000 more books to have a shot at replicating my original estimate.
It isn’t a copout. It is what the data indicates. You don’t need 10,000 or more books to prove your original estimate is valid. You just need a valid sample of data that indicates the right-hand tail is as thin as you seem to think.
Excluding the Book of Mormon, your data shows two very extreme outliers out of only 107 books. This needs to be accounted for. In broad categories the possibilities are:
1- Your assumptions are true and we stumbled upon a string of events that is less likely than winning the mega-lottery.
2- Like Joseph Smith, we have strong evidence that Dickens and Wyss weren’t really 19th Century authors.
3- Your basic model framework is valid, but the real underlying distribution has a long tail and/or is bimodal. This would indicate that these multiple outliers really aren’t that extreme after all.
4- There is some other flaw in the framework.
You can’t make up ad hoc rationalizations for why Pickwick Papers doesn’t fit into your model, but then rigorously insist that the BoM must fit.
KR: It’s good to know that even critics have a shelf upon which to stick their Zelphs. We’re in the no-shelf zone here! (Or at least everything on it has to be tagged and numbered.)
Touche, LOL. Historically, there have been things we don’t scientifically understand which could easily be explained by appeals to religious traditions. For example, consider Evolution. Darwin and his critics knew that evolution would have taken at least hundreds of millions of years to produce the complexity and diversity of life we now have. But according to 19th century science, if the sun was hundreds of millions of years old it would have burnt out by now. Further, if the earth was hundreds of millions of years old, all the land mass would have washed into the sea by now. But evolution predicted that somehow, the sun and earth must be very, very old.
In the 20th century, we figured out that the sun is actually burning nuclear fuel and has been around for billions of years. Likewise, we learned that plate tectonics regenerate landmass and that the earth is billions of years old, too. Evolution was vindicated. Zelf no longer needed that shelf.
Naturalism has a superlatively excellent track record, and betting that its success will continue seems a little bit different than religious faith.
“When people publish shorter books earlier in their careers, is that because they weren’t up to the task of writing longer books without more practice, or is it driven by decisions of publishers who don’t want to risk publishing a more expensive long book on an unpublished author?”
In my experience as an aspiring author, and in knowing quite a few people in this space, it’s generally the former. Authors dream about writing something on the scale of Stormlight, but that’s not where they start. They usually start with short stories, eventually have an idea for a relatively simple, cohesive novel, and then either expand from there (via sequels), or move onto more complex projects.
Paolini’s a good case to consider here. Eragon, his first effort, was pretty long (150k). But it’s only after Eragon became a success that the sequels really build things out (Eldest – 213k; Brisingr – 254k; Inheritance – 280k). That’s not because Eragon started out at 300k and the publisher threw it back (he needed a bit stronger of an editor for Eragon, to be honest). It’s because he was still developing as a writer, and needed confidence and experience to even consider expanding to that kind of scale.
It’s also worth remembering that the Inheritance Cycle was a decade-plus effort. Stormlight, by the end, will probably have taken Brandon 30 years.
“2- Like Joseph Smith, we have strong evidence that Dickens and Wyss weren’t really 19th Century authors.”
This would only apply if they also fit within the distribution of ancient scripture, which they don’t.
That’s part of the beauty and curse of the Bayesian approach. It works a bit like diffusion, pushing beliefs away from theories where the evidence doesn’t fit toward ones where they do. Dickens and Wyss get pushed away from both the idea that they match other 19th century authors and that they’re ancient (which is as it should be), and toward other explanations, as we’ve already discussed. The same isn’t true for the BofM, and soon enough this small note of evidence will be supported by a rather robust chorus.
“Naturalism has a superlatively excellent track record, and betting that its success will continue seems a little bit different than religious faith.”
And that bet (you could call it trust, built on a foundation of past experience), is almost the definition of a very low prior. Since you haven’t taken issue with where I’ve set mine, I’ll assume I’m modeling that bet adequately enough.
KR: This would only apply if they also fit within the distribution of ancient scripture, which they don’t.
Regarding the distribution of ancient scripture, I would think a valid likelihood ratio would be considering the same evidence in the numerator and the denominator, i.e. P(876 Pages|Modern)/P(876 Pages|Ancient).
In other words, find 100 ancient books, calculate the mean and sample variance, assume a normal distribution, etc.
What is your theoretical basis for dinging modern authorship because it has 876 pages but disregarding the total page count altogether for ancient authorship? The point of this is to compare how well the evidence fits under each hypothesis, not cherry pick evidence against modernity and compare it to different cherry picked evidence in favor of antiquity.
I’ve been thinking about the length of the Book of Mormon in the context of nineteenth century literature, and I hope you’ll indulge one more comment.
In 1687, Blaise Pascal wrote, “Je n’ai fait celle-ci plus longue que parce que je n’ai pas eu le loisir de la faire plus courte.” Since then others have made similar remarks. “I have already made this paper too long, for which I must crave pardon, not having now time to make it shorter.” Benjamin Franklin. “Not that the story need be long, but it will take a long while to make it short.” Henry David Threau. “I didn’t have time to write you a short letter, so I wrote you a long one.” Mark Twain.
When viewed as literature, the Book of Mormon has some excellent passages and storylines. However, if it would have been subject to some robust copyediting, it’s aggregate quality could be greatly improved which would have resulted in the overall length of the book becoming more consistent with its peers.
As Mark Twain quipped, “If he had left out [and it came to pass], his Bible would have been only a pamphlet.”
From the perspective of the Bayesian model, is the book being longer than its peers evidence that it’s an actual translation of an ancient text, or is it evidence that it was dictated over a short period of time and not subjected to the revisions it clearly needs?
Too often we ask questions based on a set of assumptions that are too limited. It is quite difficult to assess whether or not the Book of Mormon is a translation without discussing the nature of the translation. Your analysis assumes something about translation that is not based on any evaluation of the text. The nature of the language of the text (and in many cases, the need for editing) show the evidence that it really was dictated. However, once we accept (as all evidence indicates) that it was dictated, we are still left with the question of how or whether that dictation is related to an ancient text or a modern composition. By the way, it is also clear that it is based on a previously composed text. That is evidence, but not yet determinative of the type of previously composed text.
“is the book being longer than its peers evidence that it’s an actual translation of an ancient text, or is it evidence that it was dictated over a short period of time and not subjected to the revisions it clearly needs?”
This is something that an old mission buddy of mine brought up elsewhere, in connection with the idea that the BofM was self-published, and thus not subjected to copy-editing. It’s also an extension of my “amateur” idea in the skeptic’s corner. I agree that it’s an interesting niggle, but I could see it cutting both ways. If you don’t have an editor less is going to be cut, but you also have to pay by the page, which could serve to disincentivize length.
And if we tried to look at a sample of dictated texts…well, I’d have to assume that would result in dramatically shorter texts overall, given the extra effort and manpower involved.
Lots of fun things to think about!
And as Robert helpfully reminded us below, all those instances of “and it came to pass” are actually pretty expected on the whole!
It has been almost two years since we interacted. I hope you and your loved ones are well.
I had to smile at your comment. For me, this is a brand-new objection/point of view with regard to the Book of Mormon: that it was inadequately edited. 🙂
Really? I am assuming that you are serious. If so, what parts of the Book of Mormon do you suggest should have been left out by the editor? I am genuinely interested.
Under the hypothesis that it is the Book of Mormon is modern, the BoM is an outlier compared to the first books of other 19th Century authors with regards to word count. I’m making the simple observation that if it would have been written and edited with the same standards as its 19th Century peers, it would have been significantly shorter *and* would have taken longer to write.
As a few examples, Alexis de Tocqueville didn’t write, “And thus did the thirty and eighth year pass away, and also the thirty and ninth, and forty and first, and the forty and second, yea, even until forty and nine years had passed away, and also the fifty and first, and the fifty and second; yea, and even until fifty and nine years had passed away…And it came to pass that the seventy and first year passed away, and also the seventy and second year, yea, and in fine, till the seventy and ninth year had passed away; yea, even an hundred years had passed away.”
Jane Austen didn’t increase the page count of Sense and Sensibility by quoting nineteen chapters of the Bible in their entirety.
Charlotte Bronte didn’t write the phrase “and it came to pass” a thousand times.
Nice idea, but it doesn’t work. There was a very large body of literature of the period imitating the KJV, and “and it came to pass” is clearly modeled on the KJV language and could have been written in another way–but another way wouldn’t have signaled scriptural language to an audience of that time.
I have no idea what kind of evidences are coming in this series, but a close examination of the way “and it came to pass” functions in the text indicates that it has a very specific textual function (as do some other common linking phrases). That strongly suggests that it was not a stylistic addition, but one that had a reason to be there.
As for the fascinating string of empty dates, those also have reason and precedent in an ancient text. They are certainly foreign to our sensibilities, but that is the point. There are several elements of the construction of the text that do not respond to modern concepts. Those, I find, are more interesting that mere length.
Thanks for commenting Brant. I’m very glad to have you reading these, and I’ll be interested in your thoughts.
“Those, I find, are more interesting that mere length.”
I absolutely agree. Looking at length was a bit of a proof of concept for me, and though I think it’s a valid starting point, it’s probably the least compelling aspect of authenticity that comes to mind. There’s much more meat coming down the pike, though my lack of time and specific subject-matter expertise means that the analysis of its ancient characteristics stays at a bird’s eye level. If, at the end, you think there are characteristics that might be amenable to a deeper dive that would be great information to have.
My point on this is subtle and specific to the technical aspects of Kyler’s argument. If you will allow me to clarify, he assumes that in regards to number of pages, 19th century literature is homogenous and that page count has normal distribution with a mean of 261 pages and a standard deviation of 152 pages. He says the Book of Mormon has 876 pages, which means it is nearly 6 standard deviations above the mean. Based just on page count, this implies we can be 99.9%+ certain that the Book of Mormon is ancient.
That is the crux of his statistical argument. The point is obfuscated with the Bayesian calculations, Mahalanobis Distance outlier calculations, general analysis that has no bearing on the math, etc. But what I just said is really what’s driving his results. My point is that I disagree with the implied assumption that 19th century literature is homogenous and that page count is normally distributed. Perhaps the wordiness examples I’ve laid out are perfectly consistent with an ancient Book of Mormon. I’m simply stating that modern books (not necessarily the BoM) that “signal scriptural language,” plagiarizes Bible chapters by the dozen, are generally wordy, and are specifically designed to be weightily and comparable to the Bible shouldn’t be expected to have the same number of pages as more typical books.
I am NOT saying that the Book of Mormon is incompatible with ancient Mesoamerican books of scripture. I AM claiming that in and of itself, having lots of pages really isn’t extraordinarily strong evidence that the book is ancient.
Without attempting to divine his intent, length is a more useful argument about Joseph as an author rather than the Book of Mormon as ancient. If Joseph Smith were not seen as a viable author, that opens the door for a historical text. I agree that the logic is two steps removed. I will stay far away from math and statistics. I have no talent for either.
As you know, the alternate hypothesis, the one that I accept, is that the Book of Mormon is NOT a modern book. It is an authentic ancient document. According to this hypothesis, therefore, holding the Book of Mormon to “modern” standards of editing and writing is unreasonable and does not follow as a logical argument. But that is the argument you seem to be making.
If you think the Book of Mormon is a modern production, then your objection might be reasonable. But for me, the fact that the Book of Mormon does not read at all like any of the thousands of modern books I have read is a definite piece of evidence in its favor. It does not read at all like Dickens, or H. Rider Haggard, let alone L. Ron Hubbard (yes, I have read all these authors…and a lot more.)
BTW, scripture always quotes other scripture. Note how many times Christ quotes the Old Testament prophets. And Paul quotes Isaiah extensively, as do the books of the Qumran community and the Nag Hammadi manuscripts. So the fact that the Book of Mormon quotes a lot of other scripture, especially Isaiah, is simply another point in its favor, not a point against it…as you seem to believe.
You and I have interacted a lot regarding my article “Joseph Smith: the World’s Greatest Guesser…” https://journal.interpreterfoundation.org/joseph-smith-the-worlds-greatest-guesser/
In that article, we cite 131 points of evidence, as reported by Dr. Michael Coe, that link the world described in the Book of Mormon with ancient Mesoamerica. There are actually hundreds of other points of evidence that link the Book of Mormon and ancient Mesoamerica that we did not include in our article.
We did not include these other points because Dr. Coe did not mention them in his various editions of The Maya, and we were focused on showing that his claim that “99% of the details in the Book of Mormon are false” was completely off base. If we can trust Coe’s mastery of the details of the world ancient Mesoamerica, then the Book of Mormon describes a world very much like that world.
One of these additional points of evidence is the use of the phrase “and it came to pass” in the Book of Mormon, which seems to offend your editorial sensibilities. 🙂 I do not have enough remaining characters to respond to this point in this comment, so I will post a second comment to deal with it.
BD: As you know, the alternate hypothesis, the one that I accept, is that the Book of Mormon is NOT a modern book. It is an authentic ancient document. According to this hypothesis, therefore, holding the Book of Mormon to “modern” standards of editing and writing is unreasonable and does not follow as a logical argument. But that is the argument you seem to be making. If you think the Book of Mormon is a modern production, then your objection might be reasonable….
What you need to remember is that Bayesian analysis really doesn’t have anything to do with how “specific, detailed, and unusual” a prospective correspondence is. Rather, it has to do with looking at the evidence from different paradigms. As you said in your paper, “[the Bayesian likelihood ratio] is the probability of the evidence assuming that the hypothesis is true divided by the probability of the evidence assuming that the hypothesis is false.”
To do this correctly, it doesn’t matter whether or not you or I personally believe hypothesis A or B. Rather, we need to step into each hypothesis and evaluate the likelihood of the evidence from that perspective.
The reasonableness of my objection has absolutely no bearing on whether I personally think the BoM is modern. All I was doing was evaluating the evidence assuming the hypothesis was true.
BD: So the fact that the Book of Mormon quotes a lot of other scripture, especially Isaiah, is simply another point in its favor, not a point against it…as you seem to believe….
My point wasn’t that excessively quoting scripture is evidence against the the BoM. My point is that *assuming it is modern*, excessively quoting the Bible helps explain the long page length and indicates it is not homogenous with other 19th Century books.
Whether the details of this are consistent with the hypothesis that it is ancient is another issue I did not address.
(The specifics of the quotes are very problematic for the ancient hypothesis, but that is a discussion for another day.)
With respect to your most recent interactions with me, you are both correct and incorrect.
First the correct part: I wrote that piece on the number of instances of “it came to pass” in the Book of Mormon for another purpose over six years ago. Either I made a mistake in my search then or the search engines are better now, because a search for the phrase now returns over 1400 instances in the Book of Mormon. Mea culpa for not checking.
By the way, you can search all of the scriptures and other church library materials without being a member or even opening an account by using this link:
However, my point with respect to Mark Twain remains correct. If all of those instances of “and it came to pass” had been eliminated by the editor, the Book of Mormon, 531 pages long now, would still have about 520 pages, definitely not a pamphlet. Not a great triumph for the editor.
I am still unclear about why you think the editing job on the Book of Mormon is inadequate. Could you please respond to that point?
On the other issue, strength of evidence in Bayes, you are incorrect.
As Kyler is showing us, different points of evidence, negative or positive, can affect the skeptical prior by different amounts, depending on the strength of the evidence. Kyler is rolling out this analysis using orders of magnitude, i.e., a log scale to evaluate the strength of evidence and how each set of new evidence affects his prior.
In the same way, in our “Greatest Guesser…” article we used three different strengths of evidence as summarized in this paper by Kass and Raftery from the literature (J. of the American Statistical Association, many thousands of citations).
In this highly-cited paper, these three different strengths of evidence are explicitly described as being both quantitative (again, log scale-based, see pg. 777 in the article) and also qualitative. Our evidence weighting approach involved a qualitative evaluation that was then converted to a quantitative or numerical value.
So, Billy, you are mistaken in your characterization of the Bayes approach to statistical evaluation. Different strengths of evidence are specifically included and allowed in the Bayesian approach.
Numbers matter. Quality of evidence matters. Specific, detailed and unusual is a higher quality evidence than just specific.
You said, “I am still unclear about why you think the editing job on the Book of Mormon is inadequate. Could you please respond to that point?”
The thing about Bayesian analysis is that it involves conditional probabilities. You have to be able to ask yourself two questions: “what is the probability we would see this evidence if it is ancient?” and “what is the probability we would see this evidence if it is modern.”
I never said the editing job of the Book of Mormon is inadequate. I said that *assuming it is modern*, the editing job is inadequate. That is an entirely different thing. You seem quite content that an ancient Mayan would inscribe “and it came to pass” thousands of times on gold plates. Maybe so, but that has no bearing on whether or not a modern editor would share Twain’s sensibilities on the issue.
BR: In this highly-cited paper, these three different strengths of evidence are explicitly described as being both quantitative (again, log scale-based, see pg. 777 in the article) and also qualitative. Our evidence weighting approach involved a qualitative evaluation that was then converted to a quantitative or numerical value. So, Billy, you are mistaken in your characterization of the Bayes approach to statistical evaluation.
Did you really just reference an article from the Journal of the American Statistical Association to argue that a Bayesian approach to evaluating evidence isn’t based on statistics?
BR: Numbers matter. Quality of evidence matters.
I couldn’t agree more.
Also to everyone (responding to one post was the easiest way to insert this)
A comment as moderator. We are at a point of diminishing returns on this particular topic. I suggest we pause and pick up again with the next in line. Arguments for or against are difficult to build on a single issue.
More on “And It Came to Pass”
Readers of the Book of Mormon will have noted, as did you and Samuel Clemens (aka Mark Twain), how often the phrase “and it came to pass” occurs. Twain had a bit of fun at Joseph Smith’s expense when he said that if Joseph Smith had left that phrase out of the Book of Mormon, the book “would have been only a pamphlet”. (“Roughing It” Chapter 16 pgs. 107-115)
Since I really like numbers, I decided to test Mr. Sam Clemens’ claim. By word search analysis, the phrase “And it came to pass” occurs 151 times in the 531 pages of the Book of Mormon, on average a bit less than one time for every three pages. There are another 18 occurrences of the phrase “came to pass”… not nearly the thousand times you claim.
In total, there are 1,418,073 characters (with spaces) in the text of the Book of Mormon. The phrase “And it came to pass” contains 19 characters including spaces, and the phrase “came to pass” contains 12 characters including spaces. If we multiply 151 x 19 and add it to 18 x 12 we get a total of 3,085 total characters (including spaces) used in the entire Book of Mormon to write these two phrases. This is 0.218% of the total characters in the book, or a bit more than 1 page out of the 531 pages in the book.
If these two phrases that so amused Mr. Twain (and apparently bother Billy Shears also) had been left out of the Book of Mormon, it certainly would not have “been only a pamphlet”. It would be about 1.2 pages shorter.
So there, Sam (and Billy). 🙂
On a more serious level, the Book of Mormon claims to be written by people with their linguistic and cultural roots in Palestine, circa 600 years before Christ, during the time of the prophet Jeremiah. In other words, it has roots in Old Testament times, places and cultures. The Old Testament has over 500 instances where the phrase “came to pass” is used—the New Testament uses the phrase over 100 times.
My point is that this is how the Hebrew people told their stories. The phrase “it came to pass” is always used in the context of telling a story, both in the Bible and the Book of Mormon. (The Book of Mormon is, in fact, told as a story from start to finish…it is not written as a text book or a theological treatise.) We should expect to find the phrase in an authentic Hebrew text…and we do.
What is even more interesting (at least to me) is that we find the phrase in the New World also. We don’t know yet exactly where the events recorded in the Book of Mormon happened, but a lot of evidence points toward southern Mexico and Central America, in the Maya heartland.
In the written Maya story of the creation and in the records of their dynasties (the reigns of their kings), as recorded on their stone stelae, a particular glyph is used very, very often. The glyph is translated (not by Latter-day Saints) as meaning “and then it happened”… which could certainly be rendered equally well as “and it came to pass”.
For an interesting account of how the Maya language was deciphered, you can watch “Breaking the Maya Code” on Netflix. This particular glyph and its translation are discussed at around 1 hour and 27 minutes into the film.
This may be just a coincidence, but it is interesting nonetheless, at least to me. Joseph could have left the phrase out, saved 1.2 pages of text, and perhaps have avoided some of Mr. Twain’s (and Billy Shear’s) sarcasm.
But if Joseph Smith really did translate the record of a people with Hebrew linguistic roots, the phrase should occur. It does indeed occur with considerable (even annoying?) frequency in the Book of Mormon…and in the Mayan records.
Apparently the ancient Maya don’t meet your editorial standards either, Billy. 🙂
BD: Since I really like numbers, I decided to test Mr. Sam Clemens’ claim. By word search analysis, the phrase “And it came to pass” occurs 151 times in the 531 pages of the Book of Mormon…
Are you surprised that the BoM only says “And it came to pass” 151 times? I am suspicious of that number–it does not ring true to me. I don’t have the BoM in a document I can easily search, but according to FAIR, the BoM says “And it came to pass” 1,404 times, not 151. Can you double-check you figures?
Actually, the Book of Mormon that we have is already highly edited, for the portion that constitues the large plates. If we had the whole record in print, it would be extremely long. We have numerous editorial insertions and places where the editor makes clear that he is summarizing information.
The narrative of the Book of Mormon simply does not read as some stream of consciousness word salad that Joseph Smith regurgitated
“Either the BoM is ancient, given its length, or it was written by Joseph Smith, given its length” is an obvious example of a false dilemma. Nothing will stop us from assigning numbers to any imagined disjunction and obtaining a result, but the result might be meaningless.
if there is a 53% probability a book its length is ancient, and a 47% probability that it’s length is 19th century, and supposing we rule out that Joseph Smith could have written it due to length, then the simplest alternative would be that somebody else in the 19th century wrote it. For instance, Mr. Spaulding.
Nothing stops me from proposing the following, “Either the book of Mormon was written by L. Ron Hubbard, given its length, or Joseph Smith, given its length” either. In fact, If there is a 10% chance that L. Ron wrote it, given its length (and I’ll bet it’s higher), then per your equation, it’s 90% likely that L. Ron wrote it, given how unlikely it is that Smith didn’t write it, per you.
Hi Igor! Thanks for posting.
“Nothing will stop us from assigning numbers to any imagined disjunction and obtaining a result, but the result might be meaningless.”
Imagination could definitely lead us in the wrong direction, and we have to be careful of that. That’s why I tried to collect a bit of data so that my estimates didn’t try to fly around the moon and back.
But even then, sometimes we won’t have clear data to guide us, so imagination will have to do. In those cases, we can hope that reason can keep us at least somewhat grounded, particularly if we try to bias our estimates against an authentic Book of Mormon.
“If there is a 10% chance that L. Ron wrote it, given its length (and I’ll bet it’s higher)”
I hope you’re not assigning a 10% chance to L. Ron. That would’ve been a remarkable feat for a person not yet living.
And that’s part of the point–our imagination should have limits. It should be guided and informed by reason and evidence, at least as much as possible. I’m not always going to succeed at that, but I don’t think people can fault me that much for giving it a shot.
I enjoyed reading The Narrative. It is an immersive way to kick off your analysis.
An idea that came to mind is that I could do a statistical analysis that compares your episodes to other blog posts on related topics. I would likely be able to prove that by utilizing a narrative written in the second-person to help give context to your point, your style of laying out your ideas is distinctive, perhaps even unique.
However, demonstrating that your writing stile is distinctive would not constitute statistical evidence that your words were written with the help of a seer stone, much less that they are of ancient origin.
What you’ve really demonstrated here is that in terms of page count and the volume being subdivided into books, the Book of Mormon is more like the Bible and less like nineteenth-century literature. However, interpreting the Mahalanobis Distance as measuring how unlikely it would be for a nineteenth century author to have produced a book of the length of the Book of Mormon is simply a non sequitur. Likewise, interpreting this as powerful evidence of ancient authorship is also a non sequitur.
MY BAYESIAN ANALYSIS
CH: Presuming the Book of Mormon were ancient, what are the odds that it would be this size? You say the chances are high because in certain ways it resembles the Bible. But how many other ancient books are also like that? I would think the Bible is an anomaly and that most books that were written on clay tablets, scrolls, papyri, or bark paper were smaller. If that’s the case, a book that is 268,000 words long would be an anomaly and a book being that length would count against the Book of Mormon’s authenticity.
CA: Presuming the Book of Mormon were modern, what are the odds that it would be this size? The Book of Mormon anachronistically compares itself to the Bible (2 Nephi 29). Under this bracketed assumption, the author was deliberately trying to write something like the Bible. That fact that he succeeded (in terms of page length) is completely consistent with the hypothesis.
POSTERIOR: I’m tempted to say that since I’d expect an authentically ancient book to be smaller, in aggregate this counts as evidence against the Book of Mormon. But that wouldn’t really be fair because I haven’t done that analysis, and it wouldn’t be proper reasoning. If the book were ancient, that implies God’s hand in it, which would imply that the book is precisely as long as God wants it to be.
Consequently, the size of the book fits perfectly well with both hypotheses, and I don’t see this as counting as evidence in favor of or against the book’s authenticity. My odds remain at 1 to 400.
Thanks Billy. I hope you won’t mind me adapting from responses I’ve posted elsewhere (that you’ve likely also read).
“I would likely be able to prove that by utilizing a narrative written in the second-person to help give context to your point, your style of laying out your ideas is distinctive, perhaps even unique.”
Perhaps. But would that uniqueness itself be unique? If I sampled from the universe of blog posts and podcasts (which would be the proper point of comparison), I’d probably find a large host of different media that attempt to be unique in a similar fashion. This is why it’s important to have a well-defined variable and a proper sample to compare it to. In this case, there’s enough variability in approach that no blog post format would be truly unexpected.
There’s no one in the entire world who has identical DNA to mine. But that uniqueness is itself as common as the summer grass. It thus wouldn’t be enough for me to show that the Book of Mormon is different from other books. Good evidence should show that it’s different from what we’d have strong reason to expect the book to be–the stronger our expectation, the stronger the evidence.
“Interpreting the Mahalanobis Distance as measuring how unlikely it would be for a nineteenth century author to have produced a book of the length of the Book of Mormon is simply a non sequitur.”
I understand that it’s a little counter-intuitive to claim that something as mundane as length could somehow be evidence for it being ancient. But in this sort of Bayesian analysis, you don’t necessarily need a connection to the ancient world in order for it to count as evidence. You just need that evidence to be expected under one hypothesis and unexpected under the other. In this case, regardless of who wrote it, if we’re claiming that the Book of Mormon is a 19th century work of fiction, the book’s length in no way matches what we’d expect. That applies regardless, ultimately, of which 19th century individual (or even set of individuals) we’re claiming wrote it.
“I would think the Bible is an anomaly and that most books that were written on clay tablets, scrolls, papyri, or bark paper were smaller.”
See, I like where you’re going here. You’re testing the boundaries and seeing if my assumptions themselves are valid, and if there might be better assumptions that could be applied instead.
Hopefully we can agree that if the Book of Mormon is authentic, it’s not a single book, but a collection of many books, written by people who generally took a great deal of time to write them–again, similar to the Bible. We’d then have to be careful to compare the length of Book of Mormon to ones that are trying to do something similar. ‘All ancient documents’ is probably too broad a subset to work with. I’d probably agree that we could expand our subset to ancient scribal collections, and you’re free to do that, if you like. I wouldn’t expect them to look much different from what we see in the Bible.
And then, even if we looked at ‘all ancient documents’ that would be likely to increase our variability dramatically. And when variability increases, our ability to make strong statistical inferences decreases. The average might be much smaller, but the Book of Mormon would still be difficult to differentiate from the broad sea of book lengths we’d be likely to observe.
That’s not even to mention the bias we’d encounter for ancient documents that have actually survived. The ones that survive are generally those on materials more likely to survive, which generally have a limited size (e.g., tablets), so examining those documents would be very different proposition from examining all the documents that have actually been written.
“Under this bracketed assumption, the author was deliberately trying to write something like the Bible.”
This I’d definitely agree with. But a lot of people have tried to write something “like the Bible”. Most fail spectacularly. I’d expect the distribution of biblical imitators to look very much like the distribution of fiction authors more generally (and Stanford Carmack actually has a sample of psuedobiblical works that he uses for his analysis–they’re mostly quite short). If you’d like to collect some data showing otherwise I’d be happy to take a look at it.
“If the book were ancient, that implies God’s hand in it, which would imply that the book is precisely as long as God wants it to be.”
I like this point, because it’s a good way for you to practice a fortiori reasoning–in this case, biasing your analysis in favor of authenticity as much as possible. For my analyses, though, I strongly avoid invoking the power of God to explain away negative evidence (except in one very defined case, where I think it’s a minimally reasonable assumption). You don’t need to keep invoking it through. No need to pull your punches here.
“I understand that it’s a little counter-intuitive to claim that something as mundane as length could somehow be evidence for it being ancient. But in this sort of Bayesian analysis, you don’t necessarily need a connection to the ancient world in order for it to count as evidence. You just need that evidence to be expected under one hypothesis and unexpected under the other. ”
I get your point in theory. If an intrinsic, immutable feature of the first books of 19th Century authors was that their lengths are normally distributed with a mean of 225 pages and a standard deviation of 50 pages then sure, a book of 531 pages would extremely unlikely to belong to that set.
But I don’t believe the lengths of books aren’t driven by a random process that produces book lengths that fit that (or any other) distribution. That’s why I’m generally skeptical of this point. You might expect a priori that it would be about 250 pages because that’s how long the average book was. I might expect it to be 1,000 pages because that is how long the Bible is. But in both cases we are describing our own subjective guesses, not the forces that actually drove the length of the book.
In other words, there is a difference between saying *I subjectively guess* that the length of the Book is given by N(250,50) pages and saying *real-world stochastic forces* dictate that the book *will* have a length of N(250,50) pages.
It reminds me of Moby Dick, another long, unlikely book from 19th Century America. In terms of a big heavy book full of big heavy words, Moby Dick is an outlier. The book is an outlier not because a stochastic process caused it to be an outlier, but because Melville chose to write it this way. In his own words, “Since I have undertaken to manhandle this Leviathan, it behooves me to approve myself omnisciently exhaustive in the enterprise; not overlooking the minutest seminal germs of his blood, and spinning him out to the uttermost coil of his bowels. Having already described him in most of his present habitatory and anatomical peculiarities, it now remains to magnify him in an archæological, fossiliferous, and antediluvian point of view. Applied to any other creature than the Leviathan—to an ant or a flea—such portly terms might justly be deemed unwarrantably grandiloquent. But when Leviathan is the text, the case is altered. Fain am I to stagger to this emprise under the weightiest words of the dictionary. And here be it said, that whenever it has been convenient to consult one in the course of these dissertations, I have invariably used a huge quarto edition of Johnson, expressly purchased for that purpose; because that famous lexicographer’s uncommon personal bulk more fitted him to compile a lexicon to be used by a whale author like me. (Moby Dick, Chapter 104, Paragraph 2)
“But a lot of people have tried to write something “like the Bible”. Most fail spectacularly.”
I agree. But in this case, we have selected one that succeeded, and that isn’t a coincidence. The question, “what’s the probability that somebody like Joseph Smith wrote the BoM?” makes me think of questions like, “what’s the probability Beethoven wrote the ninth symphony?” Many have tried. Most have failed. Yet we still have the work.
Answering my question though, the probability that any given 24-year old kid from someplace like Palmyra could write something like BoM would be, say one in a hundred million. But the alternate hypothesis needs to be considered, too. What are the odds God would given golden plates to any-given 24-year old from someplace like Palmyra? The odds of *that* might be 40 billion to one.
These are reasonable thoughts, Billy.
“If an intrinsic, immutable feature…”
And that, I think, is one of the issues that prevents cogent discussion on questions like this. If evidence doesn’t count unless it commands that level of metaphysical certainty, then there’s no point even asking whether or not there’s evidence. I don’t see any practical difference between someone who will never believe and someone who will only believe once all relevant assertions are proven with the same precision as would be required of particle physics. Someone with an evidentiary bar that high is likely to miss a great many true things (or, more likely, will apply that bar only on a very selective basis).
“But I don’t believe the lengths of books aren’t driven by a random process that produces book lengths that fit that (or any other) distribution.”
I’ll assume the double-negative is a typo here. The world, however, is made of random processes. This is one of the things that struck me most when I actually started analyzing data as a psychologist. You might think that random processes aren’t driving things like attitudes toward revenge or pornography consumption or reaction times or anything else like that. But when you tabulate enough data, it’s pretty rare not to find something approximating a statistical distribution underlying all of those phenomena, and there’s no reason that book length should be any different. Melville choice of book length arbitrary. That choice was likely influenced by an innumberable number of stochastic processes that helped produce the book as we have it today.
Those influences could’ve worked on Joseph as well. We just wouldn’t expect them to.
“Many have tried. Most have failed. Yet we still have the work.”
In both Melville and Beethoven’s cases, we have considerably more than the work, and that’s the rub. Before Beethoven wrote his ninth symphony, he obviously wrote eight others, and had a well documented history of precocious musical talent and education leading up to that point.
If I had no idea who Beethoven was, and he came up to me and said, “I wrote a symphony”, I might be inclined, on the basis of probability alone, to be a bit skeptical. Symphonies, after all, are uncommon things. But if he did write it, he could quite easily furnish a bunch of evidence to support his claim: stuff like drafts of sheet music written in his hand, numerous prior musical works, and certificates from musical acadamies. That type of evidence would quickly and dramatically overwhelm my skepticism of his original claim, and I’d be forced to admit that he was correct.
It’s no different here–p = .0006 sounds like a small probability, but it wouldn’t take much hard evidence on the other side to just wipe it away. And with a 10^-41 prior, our skeptic barely takes notice–it’s just not enough, particularly on its own, to mean much of anything to him. But it is evidence, and it deserves to be weighed in along with everything else on offer.
Let me rephrase my point. Just as Stephen Covey said the map is not the territory, a statistical model is not reality. Every given model has some assumptions that are underpinning it. To the extent those assumptions are questionable, the model’s results are questionable.
I am NOT saying that evidence needs to be disregarded unless it meets an arbitrarily rigorous bar. Rather, I’m pointing out that in theory, your statistical results here might point to invalid assumptions backing your model rather than a valid rejection of modern authorship at the p = 0.0006 level. And to be clear, p = 0.0006 *is* extremely small. Juxtaposing it with an arbitrary and unreasonably low prior probability of 10^-41 prior is misdirection.
Imagine an openminded skeptic in your story with a reasonable yet highly skeptical prior 399-to-1 against the Book of Mormon’s authenticity. He takes a Fisherian approach rather than a Bayesian one. Presuming he had all of the books you listed on his library shelf and was familiar with their authors and page counts, would he flip through the Book of Mormon and immediately say, “My null hypothesis was that the Book of Mormon was modern, and I set alpha equal to a very skeptical 0.0025. But based on page count, I set p = 0.0006 and soundly reject the null hypothesis. The BoM is probably ancient!”
I don’t think an openminded person with that level of skepticism and that information would come to that conclusion. This smell test makes me think there is a flaw in your model; it makes me think one or more underlying assumptions are probably false.
What are the underlying assumptions in your model? The basic assumptions are that the set of 19th century books are homogenous with regards to age, education level, and page count, and that the page counts of books belonging to that set are normally distributed with a constant mean and variance. Further, your model assumes that the Book of Mormon either belongs to that set or is an ancient authentic record.
The histogram of number of pages you presented strongly suggests that page count is not normally distributed—rather, it shows the distribution is skewed significantly to the right with a long, fat tail. This by itself invalidates your results.
Further, I don’t think it is reasonable to assume that the BoM is either homogenous with other 19th Century books or is of ancient origins. Everything about the book is unique including how it was written, the style, and what the author claimed about it. Given this uniqueness, I don’t find it reasonable to presume it will be statistically homogenous with other 19th Century books.
I’m all in favor of looking at all the evidence. I’m also in favor of understanding the assumptions that underpin statistical models and evaluating how likely they are to be true.
Once again, good thoughts Billy, and I’m happy you’re having them.
“To the extent those assumptions are questionable, the model’s results are questionable.”
Agreed, though there’s a difference between ‘questionable’ (which will be inescapable in this kind of exploratory exercise) and ‘questionable in ways that would substantially alter the conclusion’.
” And to be clear, p = 0.0006 *is* extremely small.”
Not in the grand scheme. Things that unlikely happen all the time. It’s small enough to give us substantial confidence that the BofM doesn’t belong in the same distribution as the other books, but given the number of books that have ever been published (100 million or so), books like the BofM are going to show up rather regularly (at a rate of about 138/year over the last 400 years of publishing history). It makes a bit of a splash when we’re trying to base our beliefs in terms of probability, but we could easily be wrong.
“I don’t think an open-minded person with that level of skepticism and that information would come to that conclusion.”
If they’re not, either their prior isn’t really at 1 in 400, or the evidence isn’t actually hitting them at p = .0006, or they’re taking into account more information than merely its length. I’d guess all three apply to the imaginary skeptic in your head.
If the quantitatively based skeptic had ONLY the length information to go by, he’d have to conclude (though not by much) that the BofM fit better with the biblical books than the 19th century works. If that doesn’t then translate into an assumption of authenticity, it’s because there are other things and other information affecting his prior.
“The basic assumptions are that the set of 19th century books are homogenous with regards to age, education level, and page count”
Actually, it assumes that they follow a given distribution on each of those three variables, which is a much more reasonable assumption than saying that they’re homogeneous on those characteristics.
“The histogram of number of pages you presented strongly suggests that page count is not normally distributed.”
Not perfectly normal, no. It’s got a bit of positive skew, and it’s left-censored (as I literally censored on the left by not counting those with less than 50 pages), and has at least one obvious outlier. It’s a good thing these kinds of analyses are generally robust to violations of normality.
Based on my experience we’d still be counting the BofM as an outlier even if we tried to use a different distribution.
“Further, your model assumes that the Book of Mormon either belongs to that set or is an ancient authentic record.”
This is the most pertinent assumption, for sure–that if the BofM is a 19th century fictional work, it should fall on the same distribution as these other 19th century fictional works. We’ve already talked about alternate assumptions, though, and how the BofM would still probably be an odd duck under those assumptions.
If you believe the BofM is long because it somehow had to be (e.g., because Joseph’s chosen genre required it), and you don’t have any particular data to back that up, then it might be appropriate to handicap yourself to account for that assumption. For instance, you could assume that 1 in 10 or 1 in 100 people in Joseph’s position would’ve chosen that genre and implemented it in the way that he did. You’ll see me do similar things on occasion to further handicap the faithful position as we move forward.
For the meantime, though, the surface characteristics of Joseph as an author are strange enough (including for the characteristics we haven’t considered, like prior interest and lifetime composition), that I’m comfortable that an evidence score of 3 remains a conservative estimate. Joseph and his pattern of authorship are definitely not what we’d expect, and in ways that can’t be accounted for by the uniqueness inherent to all authors and their respective works.
One other point: if you’re defining books “like the Bible” to mean “long books”, then you’ve just made yourself an exceptionally circular argument, and I’m not sure how reasonable that would be.
As a non-intellectual, I find your analysis fascinating. Critics will be critics (even sympathetic critics) regardless of evidence and data, nevertheless Joseph’s role as translator is credited over and over by sincere and legitimate scholars. The Book of Mormon speaks for itself and any who sincerely study this book find all else secondary to the “burning within” as evidence of its validity and truth. Thank you for your depth and study…you have enlightened me as one striving to be faithful to the teachings of this sacred record.
Thanks Kody! Glad you’re finding it useful so far.
I have read Episode 0 and Episode 1 and look forward to reading all of your work. (I especially appreciate the cheekiness in Episode 0. Hope to read more of it. :)).
I thought I would respond now and, very probably, later in my reading of your work as I have something (I hope) useful to contribute.
As you point out, Bayesian analysis is an appropriate tool to evaluate many aspects of the Book of Mormon. Thank you for referencing the earlier work done by my son Brian and I focusing on Bayesian analysis of correspondences between the Book of Mormon and The Maya by Michael Coe.
The question we sought to address in that paper was whether or not the Book of Mormon was a work of fiction and how likely each of Joseph Smith’s “guesses” (aka fact claims) were if the book is a work of fiction. As you also correctly point out, the independence of correspondences was not dealt with in that article–we assumed that all the correspondences were independent.
You may be interested to know that Brian and I have written another article, this time focusing on whether or not correspondences with the Book of Mormon as reflected in all nine editions of Coe’s book increase with time or not. That paper is currently under review for possible publication in BYU Studies.
This latest paper is not focused on Bayesian analysis, although we do make some use of Bayesian methods. However, one of the Appendices is devoted to the independence of correspondences.
In that Appendix, we proposed a total of 10 overarching independent correspondences composed of 94 different sub-correspondences. In effect, we removed 84 correspondences (and their associated Bayesian likelihoods) from the evaluation by combining them with other correspondences.
Taking this much more restrictive approach to the independence of correspondences than we took in our previous paper, we identified a total of seventeen (17) specific correspondences, twenty-one (21) positive and thirty-four (34) strong correspondences. (Using the three weights of evidence as described in our previous paper.)
The overall probability that these correspondences are the result of a long series of lucky guesses by Joseph Smith can be estimated as (0.5) to the 17th power x (0.1) to the 21st power x (0.02) to the 34th power = 1.31 x 10 to the -84th power.
As before, our skeptical prior hypothesis was that the Book of Mormon is a work of fiction with odds of a billion to one that this statement is true. Also, as in our previous paper, we admit all 18 of the facts counted against the Book of Mormon at their maximum evidentiary value of 50.
We then computed posterior odds that the Book of Mormon is a work of fiction as 1.31 x 10-84 x 10 to the 9th power x (50) to the 18th power = 4.98 x 10 to the -45th power, approximately 1 in a billion, billion, billion, billion, billion.
That is…no change in the conclusion. The Book of Mormon is not a work of fiction to a very, very high degree of certainty.
I really look forward to reading the rest of your episodes. As you conclude in Episode 1, the Book of Mormon was quite a writing debut for Joseph Smith. It surely was.
Thanks Bruce! It’ll be great to have your thoughts on these.
“You may be interested to know that Brian and I have written another article, this time focusing on whether or not correspondences with the Book of Mormon as reflected in all nine editions of Coe’s book increase with time or not.”
I very much look forward to this. You might be interested in Episode 15, where I take a potentially similar look at how criticisms against the book have fared over time. It’s possible we converged on some similar findings and conclusions. If you’d be interested in an advance look just let me know and I’ll send it your way.
“However, one of the Appendices is devoted to the independence of correspondences.”
It’ll be very interesting to compare notes, then, as I do a similar re-analysis of your correspondences in Episode 14. I end up with a list of 48 correspondences that I feel are independent, so if you landed on an even more restrictive list that’ll be great fodder for discussion.
Cheers, and best of luck to you and Brian!
Yes, I would be delighted to take a look at anything you want to send my way. This is fun! 🙂
Once we get the reviewers’ comments back on our current paper, I would like to send it to you for your comments. I want to make this next paper as strong as possible, and I am sure you will have some valuable input.
The Book of Mormon is something else, isn’t it?
Always happy to review.
As for sending you the draft episodes, if you could send me an email at BayesianBoM@gmail.com I’ll make sure those come your way. I believe I’ve tried to contact you before without success, so I just want to make sure I can get it to the right spot.
I hope you’ve been well since we last corresponded.
Since you are expanding and refining your analysis, I’d like to give you a little bit of constructive feedback. For example, your correspondence 1.21 is called “limited number of important patrilineages.” You said this correspondence was highly unlikely and got a likelihood score of 0.02.
The reason why patrilineages was included in the analysis was *because* it is mentioned in both the BoM and in The Maya. And you considered this to be an exceptional hit–a piece of evidence that shows Joseph was an exceptionally good guesser.
What would be helpful to get your point across would be to list 50 different hypothetical ways that the BoM and the Maya could both mention patrilineages, and explain why 49 would be misses but how the one that Joseph actually “guessed” would be correct.
Remember: if the BoM would NOT have mentioned anything about patrilineages you wouldn’t have counted that as a miss. Rather, you would have excluded it from the analysis. So there must be something that distinguishes mentions of patrilineages that are hits from mentioning them that are misses.
If you could explain that in a convincing way, your scoring system would seem justifiable.
Your comparison with the Bible was particularly weak, since, unlike the Book of Mormon, the Bible contains such a diversity of genres. In my own statistical analysis of the Bible and Book of Mormon for FARMS in 1984, I concentrated on the narrative genre, and was able to achieve substantive, meaningful results: http://premormon.com/resources/r003/003Smith.pdf .
As a result of the systematic work of Carmack & Skousen, the whole question of Joseph’s possible authorship is thrown into a cocked hat. Nor could any 19th century author be credited in any case. The presence of the archaic grammar and vocabulary of Early Modern English makes that impossible. This indicates a pre-existing manuscript of some sort, and that authorship of a Book of Mormon pseudepigraphon or translation from actual plates must be thrown back at least a century or more before Joseph Smith.
You’re correct Robert. I definitely wouldn’t claim that these would match any sort of specialist analysis, particularly for the biblical comparison. I think it makes the point clearly enough, though. A more thorough analysis would only change the result if it could somehow demonstrate that the length of the BofM doesn’t fit into expectations of ancient scripture. My findings, limited though they are, suggest that would be a tough sell.
Plus, since a more thorough analysis based on genre would probably show that the BofM is a closer match for what we would expect scripture, sticking with my rough estimate is just another small way to throw the critics a bone.
Thanks for reading!