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Estimating the Evidence
Episode 0: On Quantifying Skepticism

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[Editor’s Note: This episode introduces a series of 23 essays—each an episode—summarizing and evaluating Book of Mormon-related evidence from a Bayesian statistical perspective. See the FAQ at the end of this episode for details on methodology.]

 

The TLDR

Skepticism can’t be equated with doubt or unbelief. True skepticism is the need to thoroughly investigate all claims, regardless of their source. Our investigation of the Book of Mormon embraces this type of skepticism, allowing us to evaluate the strength of the evidence both for and against.

 

The Narrative

Imagine yourself in nineteenth-century New England, sitting at a thick wooden table, a hard chair cradling you as you sit, bent over a large Bible. That table, that chair, and that Bible are all contained in a one-room log cabin, its walls keeping the brisk autumn air at bay. Midmorning light pours through a nearby window, illuminating the words of the sacred text. The pages are well-worn from years of use, edges torn in spots from inexperienced hands. This was a family Bible, but you are the last of the family that remains, children and spouse claimed by years of hard winters.

Your eyes veer toward one verse on the page—Chapter 5, Verse 7 in the First Epistle of John. You whisper the words aloud to yourself:

“For there are three that bear record in heaven, the Father, the Word, and the Holy Ghost, and these three are one.”

As you read them you feel bitterness well up within you. For decades you had read these words and saw them as proof of something your parents and priests and teachers had vigorously taught, and that you’d vigorously believed—the creedal concept of the Trinity. The problem is that the verse shouldn’t have been there in the first place. You turn to another book, also on the table, not as thick as the Bible but thick enough: an 1807 edition of Charles Butler’s Horae Biblicae. You carefully flip to the words in that book that sparked the betrayal:

“The passage has been discovered in one manuscript only—the Codex Monteortianus, which is neither of sufficient antiquity, nor of sufficient integrity, to be entitled to a voice in the question of sacred criticism.” (p. 272)

In short, after hundreds of years of debate by biblical scholars, they reached the consensus that most of that scripture wasn’t a part of John’s original epistle. Everything after the word “record” was an insertion by some well-meaning scribe somewhere around the fifth century. Not only does John not witness that the members of the Godhood were one, they’re not the ones “bearing record” at all—it’s “the Spirit, the water, and the blood” from the next verse.

You consider yourself well-read, particularly on biblical history, but somehow this issue completely blindsided you. One of the main scriptural pillars of the Trinity now lays in metaphorical ashes at your feet. And if a scripture this important could have been this wrong for more than a thousand years, what other critical mistakes had scribes made over the centuries? What other beliefs or doctrines relied on error and falsehood? How could anyone take the doctrine of biblical inerrancy seriously in that light?

You feel your well of anger overflow. You think back to every old doubt that had ever plagued you—every outlandish scripture story, every overbearing pastor, every terrible argument—all of those spiritual thorns again pierce your flesh, deeper than they ever had before. All those years of study, all those hours on your knees, all the quiet words of comfort that you had given your family about a just and caring God—every scrap of it a fervent and holy waste.

You push yourself up from the hard chair and toss the Horae Biblicae into the hearth, where a fire still burns. You turn away from it before the flames begin licking the book’s leather binding. You leave the Bible open where it is, determined to never turn its pages again.

I know now for a surety that this is no God,” you tell yourself. “From this moment I am a dissenter from all religions, and would be content for all of them to die out.”

 

The Commentary

An Experience of Doubt

You’ve now been introduced to our skeptic, the person whose mind should theoretically be changed by evidence regarding the Book of Mormon. His pain and betrayal (though it could just as easily be her pain and betrayal) should be familiar to any person who has at some point felt faith. The losses we’ve experienced may not be as deep as his, and the specific issues we’ve struggled with are obviously different, but I don’t think anyone has gotten into adulthood without feeling at least a sliver of the doubt expressed by our skeptic.

For me, it was on my mission. I had a few hard questions for my mission president at various points (e.g., on the contradictions in material shared between 1 Nephi and the JST; on the criteria in D&C 76 for entry into the kingdoms of glory being odd and not mutually exclusive), but the question that gave me the most pause was one I never ended up asking him. We’d tracted into somebody one afternoon that recounted the question she’d often used to stump missionaries at her door: Why does D&C 132:39 say that David didn’t sin in having multiple wives, yet Jacob 2:24 criticizes him, in the name of the Lord, for his many wives and concubines? It seemed odd for God to disagree so thoroughly with one of his prophets about the same behavior from the same person. I wondered which scripture was right and which was wrong, because it didn’t seem possible for both to be right together.

I didn’t have an answer for her that day, and I didn’t while we were driving home either. Not as I lay awake that night, nor when I was in my personal study the next morning, poring through the Old Testament looking for something to dislodge this doctrinal logic puzzle. And the more I studied the more it became much bigger than a logic puzzle—this was existential. I’d had questions before, but this was the first time that a question truly bothered me. If I couldn’t climb over this hurdle, why bother climbing over anything else my mission had to throw at me? I was determined that if I couldn’t figure it out that day that I was going to call my mission president, and, as drastic as it sounds, if he couldn’t give me a solid answer, I was going to ask him to send me home.

But that morning we got a knock on the door. It was our landlord who, along with her husband and three young children, were members of the church in humble circumstances. We lived in a studio apartment attached to their house, but they’d never come knocking this early before. I reluctantly put down my Bible and opened our screen door. She was frantic. Her youngest, Moses, just over a year old, had a high fever and wouldn’t settle. He had strange marks on his head and arms that she couldn’t explain, and she was worried that he was getting worse. Moses needed a blessing, and my companion and I were the ones to give it.

I wasn’t sure if I should give it, but her urgency left no room for quibbling. My companion anointed and I sealed. As I put my hands on his head and began the prayer, I felt the power of God flow tangibly through me into that little boy. His painful squirms immediately settled under my arms. He stopped crying. As we passed the boy through the door and back into the arms of our landlord, her eyes were wet with tears. I’ll let my mission journal take it from here:

“I did not return to studying the Old Testament. The phone rang five minutes later, and it was our landlord thanking us for the blessing. She remarked how Moses had shown an immediate and marked improvement, as well as how touched she’d been. I’d received my answer, and it hadn’t been received on my knees or in the scriptures, but instead came while fulfilling the duties of the priesthood.”

Of course, it wasn’t actually an answer to my question, but receiving that answer was suddenly much less important. The answer did come in time. But the point is that I know what it feels like to experience heart-wrenching doubt and see my way through to the other side.

That’s not what this episode is about, though. I’ve experienced doubt, and I’ve had my share of skepticism, but my question here is, when our skeptic says that he “knows of a surety there is no God”, is he actually expressing skepticism?

Skepticism as Unbelief

Judging by the behavior of some of the church’s critics, you might think so. I often hear them frame themselves as skeptics of the church’s truth claims, but I also hear many say, in no uncertain terms, that they know the church is false. They leave little to any room in their own minds or in their arguments for other alternatives.

Now, this does seem to align with how the word skepticism is commonly used. It’s usually defined as doubting the truth of something, and is treated as synonymous with disbelief and cynicism. However, that kind of perspective doesn’t jive with how philosophers and academics treat skepticism. According to those philosophers, skepticism is the theory that certain knowledge is impossible—that no amount of apparent evidence is sufficient to demonstrate absolute truth; there is always room for error and misinterpretation. We may use the term colloquially to mean disbelief in something, and our skeptic is certainly expressing disbelief, but true skepticism is an affirmation that all things are possible, no matter how unlikely they may seem.

The critics I’ve encountered spend quite a bit of time poking fun at Latter-day-Saint use of the term “know.” We hear the phrase “I know the church is true” a dozen times every first Sunday, and judging by testimony meetings you would think that Latter-day Saints themselves have no place in their hearts for skepticism, questioning, or doubt. Now, there are definitely some believers who think that way—who prefer to ignore hard questions and cling to unjustified certainty when faced with the specter of doubt. But every believer I know would admit readily that there’s a chance that they’re wrong about God, about the Book of Mormon, and about Joseph Smith—and they’re generally much more ready to do so than the critics I’ve met online.

Dennis Prager tells a story about a speaking assignment he received to a national atheist organization in the U.S. To them he asked the question: “How many of you have ever doubted whether you’re right about there being or not being a God?” Among that group of atheists, there wasn’t a hand to be seen. Their conviction in the lack of deity was nearly unanimous. Certainty, it seemed to him, was not the sole domain of the religiously devout.

Besides, I’ve always thought that such criticisms of testimony meetings have been a bit unfair. Critics mistake the genre of testimony meetings themselves—they’re meant to be a place not just to express confidence and build faith, but to give people a chance to share their experience—to literally testify to the things they’ve seen, heard, and felt. When someone says “I know the church is true”, they generally aren’t saying that they have special access to the metaphysical veracity of the truth claims of the church. They didn’t query God with a magical Boolean phrase that returned the answer “true.” Even if they did, it wouldn’t mean much. When that phrase gets said in testimony, what I hear is something like, “within the realm of my own experience (i.e., my knowledge), the church has proven reliable.” Given that I generally know these people and their experiences (or they’ve just finished relating a bunch of them), that statement gives me a pretty good sense of how the church, or church leaders, or God, have proven reliable. In that context, they’re not lying. They’re not pretending. They aren’t expressing false confidence. They’re testifying of the knowledge they have available to them. It doesn’t mean I have to buy into what they’re saying, but unless they’re specifically spouting known falsehoods, I’m in no real position to question their experience or their interpretation of it. It is what it is, even if mine doesn’t line up with it.

Skepticism as Doubt

So, back to skepticism. Say that our skeptic wasn’t expressing supreme confidence that God didn’t exist; say he was expressing doubt. Wouldn’t we be able to call that skepticism? Based on the words of one famed atheist, you would certainly think so:

“I think we ought always to entertain our opinions with some measure of doubt. I shouldn’t wish people dogmatically to believe any philosophy, not even mine.” —Bertrand Russell

Given how it’s used there you would think that doubt was an avoidance of all kinds of dogmatic belief. But that sort of approach doesn’t automatically apply to how doubt exists in the wild. Doubt hardly ever exists in a vacuum; it always exists in relation to some proposed truth. Yes, it’s a move away from certainty in that proposition. But, most of the time, it’s also a move toward some other, competing proposition. If my son sees a spot of brown liquid on the kitchen floor, he may shout “ICE CREAM!” with unbounded enthusiasm and bend down to lick it up. I, in contrast, may have my doubts (especially if I have dogs or potty-training toddlers in the house). If so, I’d probably rush over to prevent impending disaster. Why? Because if it’s not ice-cream, it’s probably something I’d rather he didn’t eat. As my doubt in it being ice-cream increases, so too does my belief that it’s something inedible. Doubt can imply belief as much as it implies disbelief.

This is particularly the case when it comes to doubt in the teachings of the church. The way I usually see it employed, doubt doesn’t just mean that a person is no longer certain about particular truth claims. It usually means that belief in a competing truth claim has superseded it. For whatever reason, they’ve become persuaded that the church is incorrect, along with a number of related propositions—such as that there’s nothing wrong with homosexual activity, that women should hold the priesthood, or that the Book of Mormon couldn’t possibly be literal. And here’s the kicker—that kind of doubt does a pretty good job of discouraging sincere investigation. Given its unknown origin, the spot on the floor doesn’t need a fair hearing—it needs to be obliterated. So, too, given doubt in the truth claims of the church, critics would generally be happy to see those beliefs go away. As is true of everybody, if they do investigate, they do so in service of supporting their currently held beliefs.

When we use the term doubt, it usually only points one way—doubt is something that critics have, and belief is something that faithful members have. That’s fine enough as a handy means of categorizing those with varying degrees of faith. But doubt is only skepticism when it serves as a double-edged sword—when individuals are doubtful of any and all truth claims including their own, not just the ones posed by the church.

Pure Skepticism, Undefiled

So, what is skepticism? By what characteristics can we recognize it and distinguish it from doubt and unbelief? The way I see it, skepticism is itself the tendency to investigate—an insistence on seeing and understanding for oneself, and, even then, to not be satisfied with how things appear at first (or second, or third, or fourth) glance. A true skeptic keeps digging, everywhere, and in all directions; if there’s nowhere else to dig they’ll start scratching at the walls.

Pure skeptics of this variety likely don’t exist. Everyone has limitations on their time and their patience. All of us have a threshold of “good enough.” Good enough to be sufficiently persuaded one way or another. Good enough that we can go on with our lives without constantly questioning every aspect of our existence. These limitations mean that our skepticism is necessarily lopsided. We tend to doubt the claims we disagree with and to accept uncritically the ones that support our own beliefs. We criticize new claims and let the old and familiar pass unscathed. And the fact that some people have more time and more patience means that some of us are more skeptical than others.

And this is where our “extreme skeptic” can actually deserve the term. It’s unrealistic to make our skeptic completely unbiased, but he can have an insatiable appetite for investigation. We can show them as much evidence as we have available and he’ll never reach a firm conclusion—our skeptic will just consider the claim as some degree of probable. And since we’re only considering one claim (the authenticity of the Book of Mormon), it doesn’t really matter that this skepticism is one-sided. It can approximate the doubt and unbelief of the critics without borrowing their implied (but certain) acceptance of alternative claims, or their tendency to dismiss competing evidence.

Can we quantify this sort of extreme skepticism? How high of a wall does Book of Mormon authenticity have to climb? Does it have a 1 in 100 chance of being true? 1 in 1000? I don’t think we need to be nearly as accommodating as that. We could take the advice of Dr. Richard Carrier (as discussed in the FAQ at the end of this episode) and give it a 1 in 1,000,000 chance of being true, but, as we’ll see, even that won’t be a particularly difficult bar to clear.

We could always go by the standard set by Wagenmakers, who conducted a Bayesian analysis of one particularly controversial claim that reared its head within psychology more than a decade ago. Dr. Daryl Bem, an experimental social psychologist with an otherwise sterling CV, put his lot in with parapsychology in his old age, claiming to have found evidence of extrasensory perception—of some people being able to detect the future. You may have caught his segment on Colbert called “Time-Travelling Porn” back in 2011. It may seem ridiculous on its face, but his methods were sound enough to merit publication in the field’s flagship journal, and his findings have since been replicated by researchers around the world. The probability that we’d observe those findings by chance currently stands at 1 in 1010—impressive enough that if it was any other topic we’d already be teaching it in textbooks.

But as we’ve heard many times before, extraordinary claims require extraordinary evidence, a statement with which I happen to agree. In their analysis of Bem’s study, Wagenmakers set the prior probability of paranormal events at 1 in 1020. (Wagenmakers apparently believes there’s a better chance of him being personally crushed by a meteor than of ESP being real.)

Which is fine; that kind of skepticism and doubt is his right. And whether it’s reasonable or not, we’ll do Wagenmakers one better and use an even higher ultra-skeptical bar—1 in 1040. In Bayesian terms, we’ll be using that as our starting prior probability—our initial guess at the likelihood of the Book of Mormon being an authentically ancient text.

 

Conclusion

In the episodes that follow, we’ll examine the most compelling evidence for and against the authenticity of the Book of Mormon. We’ll place it in front of our hypothetical skeptic, analyzing how likely we should be to observe that kind of evidence, and use Bayesian analysis to track how his beliefs change over time. What we’re looking for, ultimately, is whether the evidence we bring to bear can show that the Book of Mormon beats the odds—that the odds of it being produced by natural means (i.e., without angels and seer stones) are even less than 1 in 1040. If it does, even the most hardened skeptic should take notice, and somewhat more reasonable skeptics (e.g., those on the fence who give the Book of Mormon 50-50 odds), should be obliged to move their belief to the realm of firm confidence in the book’s authenticity.

We’ll also be interested in comparing different pieces of evidence, in the hopes of identifying the strongest (and weakest) evidence both for and against the Book of Mormon. To that end, we’ll be using our Bayesian analyses to give each piece of evidence a likelihood magnitude score (see the FAQ below for more details). In doing so, we’ll make use of the Wagenmakers standard of 1 in 1020. If a single piece of evidence is strong enough to clear that particular bar, that means it will have shifted the probability of the book’s authenticity by at least 20 orders of magnitude—representing a “critical strike” (think D&D) either for or against.

What these essays represent are essentially a series of mathematically grounded thought experiments, and it’s important to treat them as such. These aren’t intended to be the final answer proving the book true or false. Since no one else has really taken this sort of approach, I’m very much trodding on unbroken ground. This is an initial exploration, a first stab, and an invitation to others to improve on what I’m doing. I hope you’ll adopt the same spirit of skepticism I outline above, keeping in mind that all things are possible, that investigation is always worthwhile, and that such investigation won’t—and shouldn’t—end here.

 

Next Time, in Episode 1:

In the next episode, we’ll introduce our skeptic to the Book of Mormon, and estimate the probability of someone like Joseph Smith producing a work of its size as a first-time nineteenth-century author.

Questions, ideas, and unsolicited insults can be hurled toward BayesianBoM@gmail.com.

 

FAQ

What is this essay series?

This series summarizes a variety of evidence surrounding the Book of Mormon and evaluates it according to a Bayesian statistical perspective. In short, I take stuff that scholars have identified as either supporting the authenticity of that book (e.g., the Nahom inscription) or as undercutting it (e.g., the lack of Middle Eastern DNA in ancient America) and try to figure out how unexpected that evidence is. The less we’d expect to see that evidence in, for example, a nineteenth-century forgery, the more likely the book is to be ancient, and vice versa.

Given the noise of internet conversations and how people’s emotions are tied to the book, it can be difficult to get a sense of whether any of the evidence, on either side, is actually good. The Bayesian approach I use here is good for cutting through the rhetorical crud to see how valuable a piece of evidence is and why it’s valuable. It also gives us a way to compare evidence head-to-head and helps us focus on the wheat rather than the chaff. My goal is to be useful to both advocates and critics of the Book of Mormon as they look for clear thinking on the subject.

Sorry I…I wasn’t listening to any of that.

Okay…look, I don’t blame you for nodding off. I realize this can be heady stuff. I’m going to try to make this as approachable as I can, but I know I’m not always going to succeed. How about you ask the questions and we’ll see if we can get you on the right track.

Whatever. I got one for you. What’s a Bayesian?

Bayesian analysis is a mathematical summary of when and how your mind changes in response to new evidence. It takes your prior beliefs and background knowledge on a subject (expressed as the “prior probability” of something being true) and estimates how those beliefs should change based on available evidence (and how “unexpected” it is). If the evidence is more likely to be observed if the thing was true than if it was false (which represent “consequent” probabilities) than that would support the idea that the thing is true (i.e., it would increase your “posterior probability”).

Now, there’s a lot of ways that particular sentence could fall in your head, so here’s an example: Say you walk outside on a summer morning and wanted to figure out if it rained the night before. Based on your understanding of the climate of the area, you estimate that it rains on about a quarter of the nights in the summer, meaning that your starting odds are 1 in 4 that it rained last night (a “prior probability” of .25). The odds that it didn’t rain would be 3 in 4.

Say that as you walked onto the lawn, you discovered that the grass was wet. Would that change the likelihood of it having rained? To figure it out, we’ve got to calculate a few other probabilities. How likely would we be to observe a wet lawn if it rained the night before? Assuming the sun hasn’t had a chance to dry it, we’d probably be certain to have a wet lawn, given rain. So, the “consequent probability” of our hypothesis of rain would be 1.

That doesn’t mean much, though. A wet lawn could be produced by things other than rain. We also have to calculate the probability of observing water on the lawn if didn’t rain the night before (the consequent probability of alternative hypotheses). If 80% of non-rain summer mornings have dew, for instance, that probability would be .8. There might be other things that could get the lawn wet (e.g., aliens flying down and sneezing on it), but those are unlikely enough that we can just ignore them for now.

To calculate how much a wet lawn should change our mind, we can plug those values (or ones derived from them) into the following equation:

Wait, we’re doing equations? You’re gonna make me MATH?!?

Yep. Suck it up, FAQ guy. The math’s not that hard; you’re going to be fine.

PH = Prior Probability of the Hypothesis (25% chance that it rained)
CH = Consequent Probability of the Hypothesis (100% chance of a wet lawn if it rained)
PA = Prior Probability of the Alternate Hypothesis (75% chance that it didn’t rain)
CA = Consequent Probability of the Alternate Hypothesis (80% chance of a wet lawn even if no rain)
PostProb = Posterior Probability (the new probability that it rained, having observed a wet lawn)

PostProb = PH * CH
(PH * CH) + (PA * CA)
PostProb = .25 * 1
(.25 * 1) + (.75 * .8)
PostProb = .29

So the wet lawn should increase the probability that it rained, but not by much—that’s as it should be, since wet lawns in the summer aren’t very diagnostic of rain (i.e., it’s pretty expected). But is there something that’s a better litmus test? Might there be some evidence that would increase the probability, not just by a little, but by a lot?

What if my two-year-old left his stuffed panda on the lawn, and it wasn’t just a little damp, but it was soaked. That’s still really likely to have occurred if it rained the night before, but much less likely if it didn’t rain (though not impossible—my two-year-old gets around). Knowing the history of the stuffed panda, I could estimate that it’s been dripping wet through non-rain causes for about 1% of its lifespan. Knowing that, we can revisit the equation. The prior probabilities remain the same, but we can change the consequent probability for the alternate hypothesis:

PostProb = .25 * 1
(.25 * 1) + (.75 * .01)
PostProb = .97

Our observation of a soggy panda means that the likelihood of rain is now a near certainty, making the panda useful for figuring out whether or not it rained. It’s certainly better than a wet lawn for that purpose. Now, you probably didn’t need an equation to figure that out. What the equation was helpful for, though, was clarifying our thinking about the rain and our evidence for it and making explicit some of our assumptions. If someone disagreed with us about whether it rained, they could see exactly how we came to that conclusion and where they needed to argue with us about it. That’s the sort of thing I want to do with evidence surrounding the Book of Mormon.

In general, you’ll see me take the following steps when evaluating a piece of Book of Mormon evidence:

  1. Provide a summary of the class of evidence being discussed. It’s important to lay out what the evidence is before trying to estimate how likely it would be to observe it.
  2. Detail hypotheses for how the evidence could come about based on faithful and critical perspectives. This is another important prerequisite for estimating the probability of observing the evidence. The “how” of the evidence is just as important as the what, and often a piece of evidence can go from impossible to probable just by altering assumptions about how it could be produced.
  3. Generate prior probabilities of how likely certain explanations are for the Book of Mormon. This one is generally pretty easy—I start by assuming angels and divine translation methods are nearly impossible (1 in 1040 odds, substantially lower than skeptics have applied to other sorts of strange ideas) and that more naturalistic explanations fill in the remaining probability. The prior probability of the hypothesis and the alternate must sum to 1, so whatever doesn’t get assigned to one prior probability has to go in another. As the series progresses, the posterior probability from each episode is used as the prior probability for the next one, mirroring a sort of faith journey as we consider each piece of evidence.
  4. Calculate the probability of observing the evidence if the hypothesis is true (e.g., if the Book of Mormon is ancient). If the evidence generally supports the Book of Mormon, this probability should be relatively high. If the evidence supports it being written in the nineteenth-century, this should be relatively low.
  5. Calculate the probability of observing the evidence if the alternate hypothesis is true (e.g., if the Book of Mormon is a modern forgery). Here, with evidence that supports the Book of Mormon, the probability should be very low, with evidence suggesting that it’s a modern production likely showing a high probability.
  6. Input the values into the equation to produce the posterior probability. Once I have the posterior probability, I can compare it with my prior probability of ancient authenticity and see how much the probability changed. The posterior probability can then become my new prior when it comes time to consider another piece of evidence.
  7. Calculate an “evidence score” that can be roughly compared with other types of evidence. In Bayesian analysis, it’s possible to get a measure of how strong a piece of evidence is using the probability estimates that the analysis generates. This is really useful, since it should help guide debate about which types of evidence are relatively strong and which are weak, separate from the question of whether the book should be considered authentic overall.

And that’s largely it. On occasion there are multiple alternative hypotheses to try to account for (e.g., Joseph could have guessed a certain fact or he might have instead found it in an existing book). If so, it gets slightly more complicated, but not by much.

All the math you’re doing looks extremely sketchy. Are you just making all this up?

You sound skeptical. Truth is, it depends. I try very hard not to just pull numbers out of the air. One of the ways I’m trying to add value here is by collecting data to help provide useful points of reference for Joseph Smith or the Book of Mormon. If good data isn’t available or isn’t feasible to collect myself then I’ll resort to making educated guesses about what that data might look like. For instance, if I’m comparing Joseph Smith to professional comedians (a surprisingly apt reference class when it comes to dictating large amounts of material), I’ll estimate what the mean and standard deviation might be for how long comedians take when memorizing an hour of material. I can then use that to estimate how unexpected Joseph’s apparent performance is within that context.

That sort of estimation is actually pretty common and is a lot more useful than you might think. My favorite example is Randall Munroe of xkcd fame. As part of his “what if” series (I highly recommend the hardcover version), he’ll engage in what’s called Fermi estimation to help him frame a problem. Need to know how much paint you’d need to paint the earth? Make guesses (rounded to the nearest order of magnitude) about how much paint you’d need in your house, and then extrapolate that to the surface area of the planet. You wouldn’t necessarily want to use those estimates to buy the paint, but they would generally put you in the right ballpark. We can get a surprising amount of traction using those sorts of guesses. Since my scoring system works with orders of magnitude anyway, we can tolerate a fair amount of error in the details. It is, as they say, better than nothing. And if I ever do pull a number purely out of my head, I’ll give you a heads-up by marking it in red.

So a Bayesian is a…I still don’t know what a Bayesian is, please help me.

Thomas Bayes is a dead old white guy who liked math and philosophy. He came up with a theorem to describe how probabilities change with new observations. There’s an entire branch of statistics that makes use of his theorem, and it’s been applied in a ton of different ways to solve important statistical problems in a variety of scientific fields.

The specific equations you see here have been adapted from Dr. Richard C. Carrier, a professional historian of the Early Roman/New Testament period (and a prominent atheist) who has worked to use Bayes’ theorem to answer intractable historical questions. He has put it to work in two volumes, one describing the utility of the Bayesian approach for the study of history, and one using it to examine the historicity of Jesus. Though I disagree with Dr. Carrier on (so many) particulars, I agree with him that Bayesian statistics are the best way to get to the heart of historical problems, including the problem of the Book of Mormon.

So…what’s a Book of Mormon?

Oh, you poor dear! You’re in the wrong corner of the Internet. Here’s a better one.

Okay Mr. Bayes Man, what makes you qualified to tell me what I should believe about the Book of Mormon?

Not much. I’m not a statistician or a mathematician. I’m not an expert in archaeology, anthropology, or history. I hold a PhD in experimental psychology and taught psych for a few years before taking a job in government. That means I’ve had some serious run-ins with Bayes, which has gained distinct prominence in psychology as it has floundered in its own statistical faith-crisis. My government work as a data analyst means that I like to play with numbers and abstract concepts that have real and severe human consequences.

For the sake of full disclosure, I’m an active and faithful member of the Church of Jesus Christ of Latter-day Saints, which means I’ve had serious run-ins with the Book of Mormon. And I’m a millennial on the internet, which means I’ve had serious run-ins with disaffected Latter-day Saints, their arguments, and the arguments intended to counter them. Those discussions have made me want to think through these arguments out loud and in the clearest way possible (i.e., using Bayes). Whether you’re persuaded by any of my musings is your own affair.

Wait, doesn’t being an active member make you a biased, dishonest hack?

I’m biased, for sure, but it’s a bias that you and I should be able to account for together now that it’s out in the open. How we’re going to do that is through a process called a fortiori argument. It’s similar to steel-manning (the opposite of straw-manning), and in the context of Bayesian analysis, means that anytime I have a choice between two reasonable positions or have a range of reasonable probabilities, I’m obligated to pick the one that disadvantages the Book of Mormon or makes it look least authentic.

Why? Because I know I’m going to be wrong to some degree or another. That’s just part of being human. But a fortiori reasoning will help me guarantee which direction I’m wrong. The case for the Book of Mormon should be at least as strong as my analysis suggests it is—if it’s biased, it’ll be biased on the side of it being a modern forgery. That’s why I’m starting from a position of extreme skepticism against the Book of Mormon. If I’m right, the Book of Mormon can take care of itself—it doesn’t need any help from me, and I won’t be doing it any favors if I try to coddle it. My standard for evidence should be as high or higher as that of almost any critic (well, any reasonable critic, though I’ve yet to see many in the wild).

Also, here’s a psychology PSA for you. I know the interwebz doesn’t tell you this, but bias, including confirmation bias, isn’t just something that exclusively afflicts faithful members of the church. It’s something that all of humanity is subject to, including progressives, atheists, naturalists, and scientists of all stripes. Same goes for cognitive dissonance. Whoever you are, you’re probably experiencing both those things right now (and, assuming we’re both human, it’s affecting your judgment just as much, if not more, than it is mine), and will continue to for the foreseeable future. Okay? Okay. PSA over.

What’s the quickest and most effective way to tell you how wrong you are?

As I said before, you’re probably right that I’m wrong. (Though, to be fair, you should keep in mind that you could also be mistaken about how or why I’m wrong.) I’m going to be wrong on a number of issues here, both big and small. That’s just part and parcel of this kind of exploratory, thought-experiment approach—one that’s going to take me into a lot of intellectual areas I’m not trained in or even all that comfortable in. But I don’t think being wrong should stop me from trying to work these things through. As my good friend Karl G. once said, “Only those who have courage to make mistakes ever learn worthwhile lessons and truths.”

That’s why I’m absolutely open to constructive feedback or thoughts on how to improve my estimates. Odds are good that I’ll be revisiting episodes as new information or innovative arguments come to light, so any insights are appreciated. You can comment on the episodes in this series, or, as I state at the end of every one, you can email me at BayesianBoM@gmail.com. I look forward to thoroughly ignoring your unsolicited abuse.

What are you even doing, dude? Angels and miracles and seer stones? Why are you defending all this supernatural mumbo jumbo? It’s way worse than just “unlikely.” It’s impossible. Science has proven that all that garbage doesn’t exist, hasn’t it?

Are you a scientist?

Um, no. But…

Well, I am, and I know a lot of other scientists as well. And sure, there’d be quite a few that would agree with your assessment, but most of them (the intellectually honest ones) understand that nothing’s ever proven, and there’s always room in a mysterious universe for things we don’t quite know–at least not yet.

Wait, it’s not like I’m a real person actually asking you these questions. I’m you! Does that make me a scientist after all? I’m…I’m super confused.

Our atheist friend Dr. Carrier is a good example. As he says in Proving History:

“There is always some small probability that I’m wrong about there being no supernatural causes or phenomena…Even claims with a very low prior probability can still turn out to be true–and not only true, but supremely credible–because the consequent probabilities can still diverge enough to overcome even the smallest prior. In other words, when the evidence really is good enough, even the incredibly improbable becomes likely." (p. 55)

If there’s reason to believe the Book of Mormon is ancient (and there is), then there’s very good reason to keep your mind open to “all that garbage.”

What’s with your scoring system?

It may seem a little strange, but it works, and it helps avoid some of the problems associated with probability. In Bayesian analysis, you can get a sense of how strong a piece of evidence is by calculating the likelihood ratio, which you do by dividing the probability of observing the evidence if the hypothesis if true by the probability of observing it if it’s false. This value corresponds to how the prior probability will change after considering the evidence: if the ratio is 100, the prior probability will generally increase 100-fold, meaning this sort of evidence should change our minds more than if the ratio is 2. You can get a sense of how likelihood ratios are applied by taking a look at this article.

Likelihood ratios are all well and good when the ratios are 2 or 10 or 50. It’s going to get a little awkward when the ratios are in the billions or quintillions or even more. So instead of using a likelihood ratio, we’ll be using what could be termed a likelihood magnitude. The value corresponds to the order of magnitude of the likelihood ratio. If the ratio is 10, the magnitude would be 1, since it would be changing the prior probability by one order of magnitude (e.g., from p = .001 to p = .01). If the ratio is 100, the magnitude would be 2, and so on. An example of a similar scale is the Richter Scale, which measures the energy released by earthquakes. In the Richter scale, if you have an earthquake with a magnitude of 2, it’s not twice as powerful as an earthquake with a magnitude of 1, it’s 10 times more powerful. As with the Richter Scale, using a likelihood magnitude will let us compare evidence with a broad range of different strengths with manageable numbers.

It also helps us better conceptualize what’s happening with the prior probability as we consider different types of evidence. Probabilities can be arbitrarily small (as they approach zero), but they can’t be arbitrarily large—they can just get really close to 1. Given that we’re starting with very small probabilities (1 in 1040) that means the probability of the Book of Mormon being true will increase by billions of billions on the way to, say, 50/50 odds (probability of .5), but even infinite amounts of evidence can only ever make it twice as probable from there. It makes evidence at the start of our faith journey seem more informative than stuff at the end, when nothing’s really changed along the way.

When we use likelihood magnitude values, we can get a sense of what’s going on. As the probability increases beyond .5, the order of magnitude of the probability is still changing, but it’s the order of magnitude of the alternative hypothesis. As the likelihood of an authentic Book of Mormon increases, the likelihood of the alternative (that it was written in the nineteenth century) decreases. A likelihood magnitude of 3 could increase the probability of an authentic Book of Mormon by a small amount in the relative sense (from p .99 to p = .99999), but the probability of the alternative hypothesis is becoming a thousand times smaller (from p = .01 to p = .00001). As this happens, we can continue to refer to the probability of an authentic Book of Mormon using the format p = 1 – (probability of modern authorship), with the likelihood magnitude resulting in order of magnitude changes in the probability of modern authorship as it decreases.

(It’s also worth pointing out that the likelihood magnitude works a bit differently between .1 and .9. It might seem like it would only take a magnitude of 1 to move the probability from .1 to .9, but it actually takes two—one to go from .1 to .5, and another to go from .5 to .9.)

Based on the likelihood magnitude, I score each piece of evidence on a 20-point scale (it can go higher than that, but 20 is high enough), where each point is analogous to an order of magnitude change in the probability of the Book of Mormon being ancient. A score of 20 can be thought of as a critical strike, like in D&D. It represents evidence so strong that it has the potential to move someone from extreme skepticism (a 1 in 1020 shot of the BofM being true—the bar proposed by secular psychologists skeptical of paranormal phenomena) to implied acceptance (p > .5) all by itself. And a -20 should do the same for the critical end—it should be really hard to maintain belief in the face of a -20 piece of evidence.

The cool part is, a piece of evidence will have very close to the same score no matter what prior you start with. If a piece of evidence moves someone from .00001 to .001, it will move someone (approximately) from .9 to .999. That means critics and faithful members can use the same scale and it’ll mean about the same thing (which is the mark of a good scale to begin with). Keep in mind, though, that these scores aren’t the end-all, be-all when it comes to Book of Mormon authenticity. They’re just another way to frame the strengths and weaknesses of various types of evidence, helping to put the rest of the Bayesian analysis in context.

But how do you deal with the problem of statistical independence?

That’s a pretty good question. Did you come up with that one all on your own, FAQ guy?

I didn’t think it was possible to condescend to yourself, but you just did.

Fine, I’m sorry. This really is a great question, and it’s the one that’s most commonly leveled against this kind of Bayesian analysis. In fact, you can find me leveling it in the comments of this Interpreter article. For instance, say that I wanted to find the probability that I would both vote for Donald Trump AND that I would contract COVID. To do that, I might take the proportion of people in the United States who voted for Trump (i.e. 47.5%, otherwise known as not me), and the proportion of people who’ve contracted COVID (about 3% at the time of writing) and then multiply those values together, ending up with a value of 1.4%. But in doing so, I’d be assuming that those values are independent—that voting for Trump has nothing to do with contracting COVID. And that turns out to not be the case. We could point out, for one, that Trump voters are less likely to wear masks than non-Trump voters, but a bigger factor would be that Trump voters tend to live in socially disconnected rural areas, substantially decreasing their likelihood of contracting the virus. Thus, someone’s odds of contracting COVID depend on (or, at least can be predicted based on) whether they voted for Trump; knowing the outcome of one of them changes the probability I should use for the other, and in ways that are very hard to calculate.

This gets to be a problem when it comes to some Book of Mormon evidence. Take, for example, the probability that the witnesses to the Book of Mormon would recant their testimony. I could (and eventually will) try to calculate the probability that any given witness would recant, and then use that to calculate the probability that none of the eleven witnesses would do so (by, say, subtracting that value from 1, and then taking it to the 11th power—that is, multiplying each witness’ value together). But there’s a potential independence issue there. The probability that one witness recants could depend on whether the other witnesses recant; if one did, it’s possible that the others would’ve felt more free to do so. Multiplying those values together might thus leave us with a misleading probability estimate, one that unfairly advantages an authentic Book of Mormon.

So how would I deal with that problem? By assuming that some proportion of that likelihood is independent of the others, and instead try to estimate that value. And in the case of the witnesses, there’s a plausible framing for that independent chance to recant. Even if all the others stayed quiet, each would’ve still had plenty of opportunity and motivation to take back their sworn statements. Each would’ve thus had some chance, independent of the others, of being the first to recant. As long as we are clear about what we’re estimating, and what assumptions we’re making, the dependence that does exist isn’t necessarily an issue.

There will be a few different cases where I take that approach, assuming that certain probabilities are independent of each other (at least functionally so). When I do I try to state it explicitly. I’ve also tried to limit myself to pieces of evidence that I firmly believe are independent of each other (e.g., there should be no connection between the presence of chiasmus in the book and the likelihood of the witnesses maintaining their testimonies), and I’m prepared to toss out evidence where I end up concluding that it’s not independent (particularly if it favors authenticity). But these are ultimately subjective judgments, and others could justifiably see things differently. The important part, I hope, is that I’m doing my best to think this issue through, keeping it in the back of my mind as I go along, and keeping you informed when it has a chance to alter my conclusions.

Your essays are boring, can you just tell me what the 20s are so we can call it a day?

I’d love to, but that wouldn’t be much fun, and it’s hard to tell for sure which are the best kinds of evidence until I think it all the way through. I can make guesses as to where the 20s are lurking in the sea of apologetic evidence (Brian Stubbs analysis on Uto Aztecan is probably pretty up there, as is Skousen and Carmack’s work on Early Modern English), but sometimes evidence ends up being…well…unexpectedly unexpected. We’ll just have to go on this journey together and see where the dice land.

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