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Estimating the Evidence
Episode Episode 15: On Trajectories of Truth

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[Editor’s Note: This is the fifteenth 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.]

 

The TLDR

It seems unlikely that an allegedly fraudulent text could become more plausible after decades of intense critical examination.

Over time, critics of the Book of Mormon have unearthed dozens of anachronisms and alleged historical errors within the book’s pages. In their turn, faithful scholars have demonstrated that most of those criticisms are unfounded, leading the book’s plausibility to increase substantially as the decades have passed. A recent analysis by Matt Roper concludes that, as of 2019, 70% of all the anachronisms identified in the book had been overturned by new archaeological and historical discoveries, with many more trending toward confirmation.

Building on that analysis, I ask just how unexpected that trajectory of confirmation is. Though we shouldn’t expect all of the book’s anachronisms to be overturned anytime in the near future, I estimate (using a reframing of current Book of Mormon evidence) that the probability of seeing that trajectory in a fraudulent text is p = 5.29 x 10-23. Even with a conservative estimate of the likelihood of seeing that trajectory in a true document, this evidence weighs heavily on the side of Book of Mormon authenticity.

Evidence Score = 20 (the evidence increases the probability of an authentic Book of Mormon by 20 orders of magnitude—a “critical strike” in the Book of Mormon’s favor)

 

The Narrative

When we last left you, our ardent skeptic, you had just awoken from a strangely informative dream. The winter night outside lay still and quiet, unmarred by anything that might disturb your sleep further, and you could tell that dawn still lay hours away. As unsettling as it had been being swallowed in the depths of an ash cloud, it doesn’t take long for sleep to once again overtake you.

It’s there, despite your best efforts, that another dream finds you. You open your eyes in annoyance, unsure of where you are or what scene lay in front of you. All you can tell for sure is that you’re no longer in New England, and that it’s no longer winter. A harsh sun beats down on you with a heavy, wet heat, your breath weighed down with an oppressive moisture that matches the sweat you now feel oozing from your pores. And you aren’t alone. Around you are dozens of others who stand shirtless, their bare backs exposed to the sun’s full rays, their hands busily wielding instruments of labor—shovels and picks—hurling them against the barren rock of an open-pit mine.

You watch as they work tirelessly, the blades of their shovels searching for something, but you’re not sure what. With the effort they’re exerting, you only get the sense that, whatever it is, it’s of tremendous worth.

After a moment you notice a flurry of activity off to your right. A dozen voices chatter excitedly in an unknown language, and a crowd gathers around something you can’t quite see. The laborers around you turn to look as well, and they immediately drop their shovels and turn to the source of the commotion. You follow, eager to see what the workers were able to find. You push your way through the crowd, and the men in your way seem to melt away as they let you pass. The crowd had formed a circle around two eager workers, who lay their prize on a stone slab before them.

The prize is…nothing special, as far as you can tell. A large clod of misshapen dirt that seems ready to fall apart in their hands. You can’t seem to understand why these hardened laborers would be so keen to celebrate its discovery, but keen they are. Two large men emerge from the crowd with hammers in their hands, with heads of iron, and with shafts nearly as tall as the men themselves. Their biceps twitch as they bring the hammers to the ready.

Surely one swing from those hammers will bash the clod into oblivion. But the crowd seems as eager as ever as the two raise the hammers high. The iron heads fall like lightning, a deep thud rising above the din, raising a cloud of dust. Yet as the dust settles, instead of crumbling, you see that the clod has barely moved. Undeterred, one worker raises their hammer again, letting it fall with the same crushing power. The other does the same, followed again by the first, their efforts setting a pounding rhythm against the energetic shouts of their fellow workers. With each strike the clod loses some dust here, an awkward protrusion there, but still it keeps its overall shape. The dust forms a cloud that makes it increasingly difficult to see, but after what seems like an age you see the swings of the laborers slow, their aching arms soon falling still and their hammers silent. As they catch their breath you can at last see the clod, but it’s a clod no longer—it’s a book—the same book that lay on the table back in New England, its seemingly fragile spine and soft pages no worse for the overwhelming wear they’d just endured. The other workers let out a fervent cheer as the book comes into full view, but no one stops to retrieve it from the slab. After a moment the workers return to their pounding, the heads of metal ringing against the book with the distinct clang of metallic copper.

That ringing fades, as do the crowd of men around you, and you awake again to the quiet of your cabin. This time you can see the hint of approaching dawn through the window. Your eyes turn to the table, where the book still lay open to where you’d been reading. This book may seem to you a dusty clod, you think, with the origin of that thought unclear, but it won’t remain that way forever. You may not live to see that evidence take full shape. But over time, as its critics swing away, the stronger that evidence will become.

You wonder at that thought—asking yourself whether it could possibly be true. Could any fraud such as this get more plausible the more it was examined and scrutinized?

 

The Introduction

The question of Book of Mormon authenticity can, at times, feel intractable and unknowable. Like a hydra, criticisms and unanswered questions lurk around every corner, and for every issue for which there’s a satisfying answer, two others seem ready to take its place, seeding doubt on all sides. Scholars and sources who seem so confident in some areas can, in others, do little more than encourage patience and faith. Those in the midst of a faith crisis may find that advice unsatisfying. Yet patience, it turns out, may indeed be on the Book of Mormon’s side.

As we considered last time, the archaeological evidence surrounding the Book of Mormon does little to convincingly settle the question one way or the other. But the trajectory of that evidence—how the state of such evidence has changed over time—may tell a different story. Critics have spent decades highlighting the book’s apparent weaknesses. Yet, line upon line, many of those criticisms have fallen by the wayside, the evidence turning unexpectedly in the Book of Mormon’s favor. Critics are decidedly slow to give the book any credit in these cases, and instead tend to move on to the next available line of attack. But if those past criticisms could be addressed, why not the ones we currently face? Why not the ones that will inevitably turn up in the future?

In this post, we build on some intriguing work tracking the criticisms leveled against the Book of Mormon over time, and how those criticisms have fared as additional evidence has come to light. We ask what that evidence could look like in the years to come. We then gauge how likely it is that a fraudulent work could show the “trajectory” we observe with the Book of Mormon.

 

The Analysis

The Evidence

For this analysis, our evidence will be furnished by the years-long efforts of Matt Roper, a prolific research fellow formerly with the BYU Maxwell Institute. Sparked by a preliminary effort with archaeologist John Clark back in 2005, he took a look at every published criticism of the Book of Mormon dating back to 1830. Dividing these criticisms into three different time periods (1829-1844, corresponding to the life of Joseph Smith; 1845-1965, from Joseph’s death up to Matt Roper’s birth; and 1966-2019, from Roper’s birth up to the then-present), he then documented whether any of these criticisms had been "confirmed” (i.e., overturned) based on new information, as well as any anachronisms “trending” toward confirmation (where the anachronism hasn’t yet been confirmed, but the issues has become more favorable toward the Book of Mormon over time). He used that data to provide a sense of how the state of those criticisms has changed as the Book of Mormon and the issues surrounding it have received increasing scholarly attention.

I highly recommend heading over to the presentation itself to see the analysis. By the time of Joseph’s death in 1844, Roper identifies 89 items that critics suggested were anachronistic within the Book of Mormon. Critics were quick to point out that the Book of Mormon suggests a number of items that didn’t fit the contemporary consensus on indigenous peoples in the Americas, including pre-Columbian writing, earthquake and volcanic activity, a number of Book of Mormon names, and military details such as the inclusion of scimitars, javelins, and spears. Yet even at that early period some of those anachronisms had begun to crumble, with five of those items confirmed, mainly based on the tantalizing descriptions of Mesoamerican civilization that began to emerge in 1841.

By 1965, that overall picture hadn’t changed a great deal. An additional 61 criticisms had emerged during that time, making for 150 total. And though some of those anachronisms received confirmation in that 121-year period (17, for a total of 22), and a few more were “trending” (5), overall the idea of an authentic Book of Mormon looked rather bleak, with 123 anachronisms remaining unconfirmed.

Yet after 1966 things start to look quite different. New anachronisms didn’t slow down—in fact, they came in at a faster rate over those 54 years, with 55 additional items (a total of 205). But it’s as if the brakes came off when it came to seeing those anachronisms overturned. As the focus of Book of Mormon archaeology turned from a continental scale to a limited Mesoamerican geography, and as the Old World areas of Jerusalem and Arabia received more thorough attention by LDS and other scholars, 119 of those anachronisms were confirmed (141 total) with an additional 21 trending (26 total). All told, 70% of all the criticisms that have been put forward since 1829 had been overturned by 2019, with an additional 11% trending toward confirmation.

That’s quite the trajectory, and it doesn’t include the many impressive positive evidences in the Book of Mormon’s favor that have come to light over the same period (e.g., Early Modern English, stylometry, and chiasmus). Some may still point with skepticism to the 38 remaining unconfirmed anachronisms, but it’s fair to wonder what the future has in store for the items in that swiftly dwindling list, and if we should expect an alleged fraud to have seen so many criticisms overturned in so short a time.

As we do so, it’s important to ask what that trajectory tends to look like for real-life examples of forgery; say, for the Howard Hughes memoirs or for Elvis’s recently-debunked copy of the Book of Mormon or for the famed poems of Ossian. In short, the trajectory tends to look very much like the reverse of what we see in the Book of Mormon—initial acceptance and credence of the forgery, followed by a sometimes decades-long process of evidentiary discovery, one that culminates in mainstream rejection. In addition to furnishing a number of important insights about forgeries in general and in connection with the Book of Mormon, Senator Bob Bennett describes his first-hand experience with that trajectory in his book Leap of Faith:

There is an old saying: “Truth is the daughter of time.”…With most forgeries, the farther you get from its date of production, the clumsier it looks. In the case of the Book of Mormon, the farther we get from the date of its production, the better it looks.

The example of the poems of Ossian is an interesting one—a set of translations of purportedly ancient Gaelic poems written out in the eighteenth century. Despite some vocal critics, these poems were accepted as authentic by many in the mainstream. Most now generally conclude that the poems were largely fraudulent, though there is some rather convincing evidence that they were based in part on real archaic Gaelic stories. Importantly, though, that conclusion of limited authenticity didn’t come from its alleged anachronisms being overturned by new discoveries—as far as I can tell from my limited research, those criticisms remain very much in force, and continue to be added to.

Yet firmly outlining the trajectory of those criticisms is difficult, since no modern Ossian expert appears to have done what Roper has done with the Book of Mormon, and that’s not a venture I’d be inclined to devote my life to. And even then, Ossian and the Book of Mormon wouldn’t necessarily represent an apples-to-apples comparison—the Book of Mormon is a much broader work that provides many more opportunities to prove itself wrong (and then right). In the end, the only allegedly fraudulent work to which we might meaningfully compare the Book of Mormon may just be the Book of Mormon itself. We’ll get into that a bit more as we continue our analysis.

The Hypotheses

As usual, we’re going to be delving deep into two main hypotheses.

Anachronisms have been overturned due to the historical and archaeological evidence catching up with the statements made in the Book of Mormon—According to this theory, all of the anachronisms that have been put forward are based on the misunderstanding or (justifiable) lack of information on the part of critics, with new information coming to light and gradually overturning those anachronisms over time. The trajectory of confirmed items should thus mirror the trajectory of increasingly thorough and accurate archaeological examination taking place in presumed Book of Mormon areas.

Anachronisms have been overturned on the basis of chance—This hypothesis asserts that anachronisms are based on the Book of Mormon being a work of fiction, and that as such it should offer plenty of tell-tale anachronisms that would be traced to the misinformed imaginings of Joseph Smith. Some anachronisms may have been put forward by critics out of ignorance, and as such could be overturned by new information, but such instances should be rare, with confirmations occurring by chance as new information happens to coincidentally align with what the Book of Mormon posits. The trajectory of confirmed items should mirror what we observe for other known frauds or other examples of inaccurate ideas.

There is a third option worth discussing briefly: It’s possible that confirmations aren’t due to new information aligning with the Book of Mormon, but interpretations of the Book of Mormon changing to fit the available evidence. The move from a continental to a limited geography model is a good example of this—even if the Book of Mormon isn’t authentic, it would be easy for the number of confirmations to increase suddenly and dramatically just by finding a geography where the anachronisms no longer apply.

A good test for that idea is to look at anachronisms that apply specifically to Old World archaeology and geography. Faithful scholars can readily alter their view on where the Book of Mormon took place in the New World, but with the Old World anachronisms they’re pretty well stuck—we know where Jerusalem was, and the Book of Mormon describes travel through the Old World in sufficient detail that interpretations aren’t likely to change. By looking at these Old World anachronisms we can thus get a sense of whether the Book of Mormon’s move to a limited geography is creating a misleading picture of its trajectory.

Prior Probabilities

PH—Prior Probability of Ancient Authorship—For our initial estimate of the likelihood of anachronisms being overturned on the basis of an authentic Book of Mormon, we can see where we landed at the end of the last post. Even with the archaeological evidence giving the critics a minor reprieve, the overall likelihood of an authentic Book of Mormon continues to tip over into implied belief, at p = 1—2.04 x 10-6. Here’s where we stand so far:

PA—Prior Probability of Modern Authorship – In contrast, we can assign the remaining probability to the likelihood of anachronisms being overturned on the basis of chance, with p = 2.04 x 10-6.

Consequent Probabilities

We’ll get to our usual analysis in a bit, but before we do that we’ll need to attempt to fill in some of the gaps in Roper’s analysis. In his presentation he only gives us three data points, noting the numbers confirmed, unconfirmed, and trending in 1844, 1965, and 2019. Once he publishes the full paper we’ll be able to get much more detail in terms of when anachronisms were presented and subsequently overturned, but for the moment we’ll need to make some educated guesses. And with those guesses, we can try to answer what I see as one of the most interesting questions arising from Roper’s analysis: given the trajectories we see, how should we expect the picture of those anachronisms to change beyond 2019?

Inferring and Projecting Trajectories—To make those guesses, we’ll have to start by laying out a few assumptions about how the process of criticism and confirmation has worked in the Book of Mormon. Some of these aren’t likely to hold, but they’ll serve well enough to build a workable projection:

  1. Each unconfirmed anachronism has a chance to become confirmed. This chance is applied each year that an anachronism remains unconfirmed.
  2. The chance that an anachronism becomes confirmed differs depending on the time period the year appears in (i.e., 1829-1844; 1844-1965; 1966-2019), and is uniform within each time period.
  3. The rate that new anachronisms are presented differs depending on the time period, and, though generally uniform within each period, is somewhat smoothed at period boundaries for aesthetic purposes (I don’t apply that smoothing to confirmation rates, as that would disadvantage the critical position).
  4. Once confirmed, an anachronism cannot become unconfirmed. There are some exceptions to this (e.g., discovering that the bow and arrow was a relatively recent invention among ancient Indigenous societies), but we’ll ignore them for the purposes of this analysis.
  5. After 2019, rates of new anachronisms follow the same rate as in the 1966-2019 period (this assumption probably won’t hold—they have to slow down sometime, and probably already have—but we’re giving the critics the benefit of the doubt).
  6. After 2019, the chance of confirmation follows the same rate as in the 1966-2019 period (critics may not like this one, but that’s just tough cookies—we have every reason to assume that the confirmations are going to keep trucking as they have been, as evidenced by the recent confirmations produced by LIDAR and continued explorations of the Arabian peninsula).

Based on those assumptions, I created a year-by-year model of confirmed and unconfirmed anachronisms (ignoring any trending items for the sake of the critics), with fractional values of each kind allowed. I used the observed rates of new anachronisms in each time period (dividing the number of new anachronisms in each period by the number of years; e.g., dividing the 88 anachronisms identified between 1829-1844 by the 15 years in that period to produce a value of 5.867), and calculated confirmation probabilities using a guess-and-check process that reproduced the values provided by Roper. These values are provided in the table below.

Figure 1. Observed Parameters for a Projection of Confirmed Anachronisms
Period Rate of New Anachronisms/Year Annual Probability of Confirmation
1829-1844 5.867 0.007
1845-1965 0.504 0.001
1966-2019 0.981 0.025

To give you a sense of how that guess-and-check process worked, I’ll give you an example. Say that it’s 1830, with one year having passed since the publication of the Book of Mormon. Ignoring the silliness of allowing for fractional anachronisms, we’ll say that critics identified 5.867 anachronisms in that first year. However, let’s say that faithful scholars worked very hard, and had a 10% chance of confirming each of those 5.867 anachronisms. In our fractional world, that would mean that they would’ve confirmed a bit over half an anachronism, with .587 anachronisms overturned. That would leave a remaining 5.28 valid anachronisms. Then the next year, like clockwork, an additional 5.867 anachronisms are produced by critics, leaving a total of 5.867 + 5.28 = 11.15 valid anachronisms. The 10% chance of confirmation would then apply once again, resulting in an additional 1.115 anachronisms overturned, leaving 10.03 remaining valid criticisms. This process repeats until we hit 1844.

But that value of 10% probability of confirmation turns out to be too high—it leaves us with more anachronisms confirmed (46.07), and fewer unconfirmed (40.72), than in Roper’s analysis (5 and 83 respectively). The quickest way to fix that is to directly fiddle with the annual probability of confirmation, moving it down or up so that things land where they need to be to align with Roper. And for 1829-1844, that value happens to be 0.7%, or .007. This process is then repeated for the other two time periods.

When we plot the values in Table 1, we get the following figure:

Here we can see very clearly the stark change in trajectory occurring somewhere after 1965. Somebody around that time seems to have loosed the chains on a ravenous scholarly beast or three. The critics were very busy themselves, though, and we’ll continue to assume that their creativity knows no bounds. It’s this overall trajectory in the 1965-2019 that seems truly unexpected, rising from 15% confirmed to 70% confirmed in that 54-year span. We’ll be making use of that trajectory later in the analysis.

In terms of what’s going to happen in the future, it’s easy to take a look at Roper’s analysis and assume that all Book of Mormon anachronisms are going to be resolved in the near future. My projection gives us reason to be a bit cautious on that front. Assuming the anachronisms keep on coming, which they certainly might, the overall percentage of confirmed anachronisms could rise somewhat through the rest of this century, but might eventually flatten out at around the 90% mark. Anyone hoping for a Book of Mormon that conforms entirely to contemporary scientific consensus will be in for a long wait (possibly an eternal one).

And that, I think, is as it should be. If Book of Mormon authenticity was ever the received scientific consensus, that would be more than a little damaging to the role of faith. The Book of Mormon can be plausible, and unexpectedly so, but that evidence should never overwhelm individual choice and reason.

Old vs. New World anachronisms. As mentioned above, it’s also worth breaking down the proposed anachronisms by whether they make reference to items in the New World (e.g., metallurgy in the Americas), or in the Old (e.g., a reference to the “Land of Jerusalem”). If the increased plausibility of the Book of Mormon has come largely from relocating New World theories to a limited area in Mesoamerica, we should see nearly all of the confirmed anachronism coming from ones applicable to the New World, and almost none from the Old. But that’s not what we see, as shown in the table below. Based on my own coding, and excluding criticisms not attached to a general location (e.g., the plausibility of names, sea voyages, post-decapitation movement), there are 36 anachronisms that apply to the Old World. Of these, 33, more than 90%, have been confirmed, relative to 67% for the New World anachronisms. Only three such anachronisms remain unconfirmed: bows of fine steel, the presence of glass windows (to be dashed to pieces), and the presence of synagogues in Lehi’s day. It’s clear that the trajectory of confirmations we see for the Book of Mormon applies to the Old World just as much if not more than in the New, and that excluding New World anachronisms would hurt the critics more than it would help them.

Table 2. Breakdown of Roper’s Anachronisms by Geographic Location
Category Total Anachronisms # Confirmed (2019) %
New World 136 92 67.7%
Old World 36 33 91.7%
Other 28 15 53.6%

Overall, whether it’s in the Old World or the New, it’s difficult to imagine a fraudulent document making so many strides so quickly. Estimating just how difficult will require a little more thought (and more modeling!).

CH—Consequent Probability of Ancient Authorship—If the Book of Mormon is authentic, how likely are we to observe the trajectory of confirmations that we do? Answering that question is a bit trickier than it might appear. After all, critics might suggest that an authentic document should’ve seen far more confirmations on a much shorter timescale, rather than waiting 135 years for the confirmations to start rolling in. That’s certainly possible, but I don’t think it’s necessarily reasonable given how much the scholarly landscape has shifted in the decades since the Book of Mormon was published. After all, if the Book of Mormon had been completely consistent with an early 19th century understanding of archaeology, and been hailed by all contemporary scholars as perfectly accurate, it would’ve instead become less accurate over time as that understanding evolved. An authentic book describing ancient peoples would and should have disagreed quite strongly with how those peoples were viewed by the scholars of Joseph’s day.

So, as the hypothesis above describes, we should expect there to be an initial set of anachronisms, and for those anachronisms to be overturned proportional to an increased and accurate understanding of the ancient world. Is there a way, then, to get a sense for how that understanding has evolved over time? A complete picture is probably out of scope for this particular analysis, but we can make a rough guess by, say, tracking rates of published articles in relevant fields over time. The figure below shows the trajectory of confirmed Book of Mormon anachronisms from 1829 to the present, and then maps it alongside a count in Google Scholar of all the articles that mention “archaeology” in each year (as a ten-year moving average, to smooth the line a bit). This gives us a ballpark for how our understanding of the ancient world has improved over time.

What this shows is that work in the field of archaeology, and likely of anthropology and history as well, has been increasing exponentially since the Book of Mormon was published (with citations doubling about every 10-20 years, with blips in that pattern around WW2 and after 2010), with startling gains in productivity starting in the 1970s. Though we wouldn’t expect this to necessarily map exactly to the percentage of confirmed anachronisms in the Book of Mormon (especially since we only have solid data at our three data points at the moment), I think it’s reasonable to conclude that the data is broadly consistent with our hypothesis. Book of Mormon anachronisms started to be confirmed at a dramatic rate after 1965, as archaeological work exploded over that same time period, which is exactly what we’d expect from an authentic Book of Mormon.

So how do we translate that into a probability estimate? I think it’s important to weigh this particular estimate in favor of the critics. We could potentially justify setting this estimate at p = 1, based on the Google Scholar data, but we’ll be extremely conservative, and say that only 1 in 100 authentic documents would show a trajectory like the one we see for the Book of Mormon. That leaves us with an estimated likelihood of observing the evidence we do under this hypothesis at p = .01.

CA—Consequent Probability of Modern Authorship—So if that’s the sort of trajectory we might expect from an authentic document, what might be expected from a fraudulent one? Should we expect a majority of criticisms to eventually be overturned, like we see with the Book of Mormon?

It might help to start with a bit of a thought experiment. Take, for example, the theory that the earth is flat. Ponder in your heart for a moment the message that theory contains. Then make in your head a list of all the criticisms that have been brought to bear against that theory. There’s going to be a lot of criticisms, brought forward by noted experts, and they’re going to be both pointed and powerful. Now consider for a moment, what the odds would be that any of those criticisms might eventually be overturned—where the flat earthers will eventually be proven correct. How likely is it? How many of them would you expect to be overturned? Is it 70% of them? Given more time and more extensive knowledge of astronomy and geology, would you expect the percentage of overturned criticisms to rise over time, and in dramatic fashion?

My guess is that your answers to those questions are, respectively: exceptionally unlikely, none, no, and not in a million years.

But the flat earth example may not be the best one to use here—astronomy and physics can’t necessarily be compared to archaeology and history. Unfortunately, we don’t have a ton of fraudulent historical documents of the type and scale of the Book of Mormon to compare it to, and if there was I wouldn’t necessarily have the time to dig deep into the criticisms being leveled against them. As I suggested above, however, we can use the Book of Mormon itself as a comparison.

If doesn’t take much to turn an authentic book into a fraudulent one—all you have to do is change its purported setting. If, for instance, I took the Popul Vuh and claimed that it took place in Outer Siberia, I’d instantly have a fraud on my hands. I could then document all the various problems that could have been leveled against that theory, and track how many of those criticisms would have been overturned over time.

We can do that with the Book of Mormon. For most of the Book of Mormon’s history people had assumed that, say, a small, archaeologically insignificant drumlin in upstate New York was the site of a massacre of hundreds of thousands of people. We can state rather confidently now that such isn’t the case. But what if that was still the dominant theory? What if the faithful consensus was that the Book of Mormon took place predominantly in the central or northeast United States? Various people have tried and continue to try to make that argument, while others have leveled criticisms against it. By taking a look at those criticisms, we can get a sense for how the Book of Mormon would be faring if it was an incorrect or fabricated document.

If so, much of Roper’s analysis would still apply—the entire trajectory up to 1965 would apply just as much to that theory (which I label here as the “Original Assumptions” theory) as it would to the current consensus. It’s the period from 1966-2019 that would change. To figure out how it would change, I started by going through Roper’s set of anachronisms, conducting a cursory search to see how many of those anachronisms would still be in force if applied to the Indigenous peoples of ancient North America (you can see the Appendix for a list of which ones I see as confirmed under that theory). I then scanned through some additional criticisms that faithful scholars have applied to that theory as it’s generally argued today. If you’re curious, you can see the list of criticisms that scholars have applied specifically to one or more versions of the original assumptions theory in the table below.

Table 3. Criticisms Presented by Faithful Scholars Against an “Original Assumptions” Model
# Type Feature Notes
1 Geography Cultural leader with continent-level influence Alma 22 requires that the King the Lamanites is able to send messengers throughout the entirety of his lands, extending from the Sea West to the Sea East, which in the Original Assumptions model would have to be the Pacific and Atlantic Oceans
2 Geography Messengers traveling continent-level distances Alma 22 requires that the King the Lamanites is able to send messengers throughout the entirety of his lands, extending from the Sea West to the Sea East, which in the Original Assumptions model would have to be the Pacific and Atlantic Oceans
3 Geography Narrow strip of mountainous wilderness close to southern Illinois The “head” of the Sidon river, which is identified in some models as the place where the Mississippi and Ohio rivers meet, needs to be located in a narrow strip of wilderness, as noted in Alma 22:27.
4 Geography Long-distance march from east sea to southern Illinois Alma 43:22 notes a Lamanite march from Antionum, which Alma 31:3 places near the “seashore”. In the relevant models this would have to be near the Atlantic, necessitating a march of at least 500 miles. There’s no evidence that armies of this period could feasibly travel this far.
5 Geography Southern Illinois as an important gateway to Independence Alma 43:22 requires that Manti, which is placed at the confluence of the Mississippi and Ohio rivers, be an important entrance to Zarahemla, placed in some models as Independence, Missouri. Going through Manti at that location would be a significant detour rather than a required gateway.
6 Geography Narrow neck south of Cumorah The Book of Mormon clearly places the Hill Cumorah north of the narrow neck of land, which cannot be squared with the Great Lakes narrow neck within these models.
7 Geography Lack of volcanic activity There was no known volcanic or earthquake activity in the U.S. region during the time specified.
8 Fauna Poisonous serpents at narrow neck There are no known poisonous serpents plausibly occupying the area around the narrow neck of land.
9 Military Swords There is a lack of sword-like objects used in battle by area peoples.
10 Military Headplates There is a lack of head-plate objects serving as feasible armor.
11 Technological Cement There is a lack of limestone mortar or any type of cement dating to the correct time period.
12 Geography Lack of mention of snow or cold climate in the New World Aside from a metaphorical reference by Nephi (who would have been familiar with snow and blizzards from the Old World) the Book of Mormon never mentions the type of snow or cold that would have seasonally characterized relevant U.S. areas.
13 Geography Columbus did not visit the contiguous United States A key feature of the theory is that the “promised land” is entirely within the contiguous United States, while in the Book of Mormon an explorer, usually labeled Columbus, is specifically said to have visited (and smote) descendents of the Lamanites in the promised land.
14 Cultural Two separate cultures living in close proximity The Book of Mormon requires two cultures, living adjacent to but separate from each other within a similar timeframe. The Adena and the Hopewell don’t fit these criteria.
15 Cultural Numerous cities within the dated timeframe I was unable to identify evidence of the numerous cities noted in the Book of Mormon between 200BC and 400AD.
16 Geography Lehi’s landing on the West coast Lehi’s landing is definitively identified as on the west coast, far from relevant areas.
17 Geography Metals in great abundance There is a lack of necessary ore deposits in relevant areas.
18 Geography Elevation differences between Manti, Nephi, and Zarahemla The locations for Manti, Nephi, and Zarahemla must have relative elevation differences, with Manti being the highest and Zarahemla being the lowest.
19 Geography Mississippi flowing northward The Sidon river is required to flow north from the narrow strip of wilderness, while the Mississippi, identified as the Sidon by some models, flows inexorably southward.
20 Technological Written languages There is no evidence for written languages among the Hopewell or Adena during the specified timeframe.
21 Demography Millions of people There is no evidence for the millions of people residing in the Hopewell and Adena areas during the specified timeframe.
22 Military Massive battles There is no evidence for massive battles occurring among the Adena or Hopewell during the specified timeframe.
23 Geography Launching Hagoth’s ship in the West Sea Hagoth’s ship launched in the west sea to explore new territory. If it was the Pacific, there’s no evidence that Hopewell culture extended that far westward. If it was Lake Michigan, they would’ve had to navigate Niagra Falls.
24 Technological Extensive deforestation It’s hard to characterize the lands of the Great Lakes or other relevant U.S. areas as having been extensively deforested, as indicated by the text.
25 Geography Jaredites in the land northward The Adena do not meet the criteria strongly suggested by the text that the Jaredites inhabited the land northward.
26 Technological Cereal agriculture The Great Lakes and other relevant areas lacked cereal agriculture until 1000AD (according to John Clark).
27 Military Fortifications within the appropriate timeframe The area’s fortifications date to after 1100AD (according to John Clark).
28 Technological Non-hunter gatherers There is no indication in the Book of Mormon of individuals following a hunter/gatherer lifestyle (aside from Enos’ hunting trip), whereas all the relevant U.S. areas can offer us are societies of hunter/gatherers.
29 Geography Sunken cities The geology and hydrology of the relevant U.S. areas aren’t suitable for that kind of catastrophic event.

By 2019, how many of those criticisms (including the ones outlined by Roper) would have been overturned if we were operating under those original assumptions? Well, it depends on whether we’re including the anachronisms that don’t specifically apply to a New World location (i.e., those that pertain to the Old World). Common sense should say that we should only include those that apply to the New World, since that’s what the “original assumptions” theory is about. That would mean we’re working with a smaller set of anachronisms (about 152 of them—see the Appendix for more detail). Even then, by my reckoning, only about 24% of those anachronisms would have been overturned, which aligns pretty well with the trajectory we see for the Book of Mormon pre-1965.

But we shouldn’t rule out those Old World anachronisms quite yet. What they represent is an opportunity to practice a fortiori reasoning. Remember that over 90% of those Old World anachronisms have been confirmed. Though we could justify removing them, keeping them in would strengthen the critics’ argument. It would also ensure that we’re making a liberal estimate of what we’d expect from fraudulent document, since it would include ideas and claims that the Book of Mormon makes that appear to be accurate. If you include those non-New World anachronisms, the proportion that are confirmed by 2019 under the “original assumptions” theory rises to about 38%. I went ahead and mapped that alongside our original projection, using the same “guess and check” methodology to determine the annual risk of each anachronism being confirmed under an “original assumptions” theory, both with and without Old World anachronisms included. You can see the result in the figure below.

However, that’s not all we’ll need to build our estimate. We’ll also need to get a sense of how much we might expect those trajectories to vary. Yes, we might see as much as 38% of anachronisms confirmed on average for a set of fraudulent documents, but how tight would the distribution be? If we had, say, 10,000 of them, would any of them get as high as 70%? If so, how many?

To get at that question, I got to once again use my handy (and very amateur) Python programming skills and put together a program to simulate the trajectory of confirmed anachronisms over time (see the Appendix for the full code). Starting in 1965 with a certain set of anachronisms, the program simulated the percentage that would be confirmed by 2019 given 1) a particular rate of new anachronisms being presented and 2) a certain risk of each anachronism being confirmed each year. The program calculated and kept track of that final percentage. I then had the simulation repeat 10,000 times to produce a distribution of those percentages, tracking the highest recorded percentage, as well as the mean and standard deviation.

Overall, when I use the 38% value for our “original assumptions” theory, none of those 10,000 iterations reached anywhere near 70%. The highest value recorded was 51.2%, with a standard deviation of 3.1%. I repeated the simulation for all three of the projected trajectories in the above figure, and used them to produce the error bars that you can see at the 2019 mark, representing 95% confidence intervals. All told, the percentage we actually observe for the Book of Mormon is well outside of the values we’d expect from a fraudulent document, based on our liberal assumptions.

Just how far outside is it? How many fraudulent documents would we need in our population to find one that had a value of 70% confirmed? Based on my simulation data, 70% would be 10.3 standard deviations from our estimated mean of 38%, which, based on that z-score, would mean we would need 1.89 x 1022 of them. That would place the probability of any one document showing a value that high or higher at a cool p = 5.29 x 10-23. We’ll be using that value for our estimate of consequent probability.

Posterior Probability

We now have enough to build our final probability estimate.

PH = Prior Probability of the Hypothesis (our original estimate of the likelihood of the Book of Mormon being authentic, or p = 1—2.04 x 10-6)

CH = Consequent Probability of the Hypothesis (our estimated probability of authentic documents showing the trajectory of overturned anachronisms that we observe for the Book of Mormon, or p = .001)

PA = Prior Probability of the Alternate Hypothesis (our original estimate of the likelihood of a fraudulent Book of Mormon, or p = 2.04 x 10-6)

CA = Consequent Probability of the Alternate Hypothesis (the estimated probability that a fraudulent document would show the trajectory of overturned anachronisms that we observe for the Book of Mormon, or p = 5.29 x 10-23)

PostProb = Posterior Probability (our updated estimate of the probability of an authentic Book of Mormon)

PH = 1 — 2.04 x 10-6
PostProb = PH * CH
(PH * CH) + (PA * CA)
PostProb = (1 — 2.04 x 10-6 * .01)
((1 — 2.04 x 10-6) * .01) + (2.04 x 10-6 * 5.29 x 10-23)
PostProb = 1 — 1.08 x 10-26

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(.01 / 5.29 x 10-23)

Lmag = log10(1.89 x 1020)

Lmag = 20

 

Conclusion

Overall, though we should be a bit cautious about overinterpreting this result (it is, after all, based on the examination of a single document—the Book of Mormon itself), the confirmation trajectory we observe for the Book of Mormon weighs heavily in its favor—just enough to make it a “critical strike”, improving the probability of an authentic Book of Mormon by 20 orders of magnitude. We would absolutely not expect a fraudulent document to have so many of its criticisms overturned, and the fact that that’s the case for the Book of Mormon should be genuinely astounding. In my mind, the ball is in the court of the critics. To substantially alter this result, they would need to produce a known and verifiable hoax that has somehow become more plausible with increased scrutiny—and not just a little more plausible, but a lot more. In that task, I wish them the best of luck.

 

Skeptic’s Corner

Though critics might have their work cut out for them in terms of finding a known fraud with an outlook that’s improved over time (looking at how the criticisms of View of the Hebrews have fared over the years might be a decent place to start), there are a number of convenient ways to nitpick this particular analysis. The one that stands out most to me is the nature of my Python simulation. By necessity it assumes that the probability of confirmation remains static throughout the 1965-2019 time period—it’s a handy assumption, but real life often turns out to be quite a bit messier. Trying to incorporate a little more real-life statistical noise in those estimates would probably result in wider standard deviations, and thus a weaker overall evidence score. The problem is that without more fine-tuned year-by-year data on confirmed anachronisms, I don’t see an empirical basis for doing so.

That would be just one of a number of ways that Roper’s raw data would be useful in helping to improve this analysis. With it I’d be able to put together much better post-2019 projections, as well as get a better sense for what his bar is for judging anachronisms as “confirmed” or “trending”. I’ll cross my fingers that he’ll see this post and decide to make that data available.

The other concern would be my use of the “Original Assumptions” hypothesis as a way of estimating the trajectory of confirmation for a fraudulent work. I still maintain that it’s the best apples-to-apples comparison we have available, and that it gives a solid sense of how archaeological discoveries might overturn a limited number of anachronisms on the basis of chance. But in doing so we might be enacting the reverse of one of the problems I outline in the Evidence section—instead of changing our theory to fit the evidence, we’re changing our theory to a place where we know that it doesn’t fit. It may be that an Original Assumptions framework is a particularly bad example in the universe of potential frauds, and that placing it somewhere else (say, in the islands of the sea) would alter our conclusion. Those trying to do that, though, should keep in mind that many of those anachronisms would never have arisen in the first place if Joseph had set the Book of Mormon somewhere else, whereas essentially all of them would have applied to a 19th century understanding of Mesoamerica. You would need to be careful to only count an anachronism as overturned if 1) it would have been considered an anachronism based on an expert understanding of that area during Joseph’s era, and 2) new archaeological discoveries came about in that area which realigned that understanding to match the Book of Mormon.

Of course, it’s possible that I’m misrepresenting the Original Assumptions theory, and that I’m missing cases where the anachronisms associated with it have been overturned. The hope is that my inclusion of Old World anachronisms helps to cover my bases on that front, but I could be wrong. Don’t worry, though. I can already hear the thundering hoofbeats of a small army of OA supporters heading to the comment section to correct my profound ignorance.

 

Next Time, On Bayesian BofM:

When next we meet, we’ll be discussing the purported 19th century religious and cultural themes contained in the Book of Mormon, and weighing them against the ancient themes that scholars have located in the text.

Questions, ideas, and non-descript sandwich bags filled with baking soda can be mailed to BayesianBoM@gmail.com or submitted as comments below.

 

Appendix—List of Anachronisms

# Period Area Anachronism Confirmed by 1844 Confirmed by 1965 Confirmed by 2019 Confirmed Under Original Assumptions
1 1844 New Fortifications No No Yes No
2 1844 New Military Costumes No No Yes No
3 1844 New Armor No No Yes No
4 1844 New Swords No No Yes No
5 1844 Old Steel Swords (OW) No No Yes Yes
6 1844 New Steel Swords (NW) No No No No
7 1844 Old Scimitars (OW) No No Yes Yes
8 1844 New Javelins No No Yes No
9 1844 New Spears No No Yes Yes
10 1844 New Bow and Arrow Yes Yes No No
11 1844 Old Bow of Fine Steel (OW) No No No No
12 1844 New Slings No No Yes No
13 1844 New Large Armies No No Yes No
14 1844 New Large Army Casualties No No Yes No
15 1844 Other Post Decapitation Movement/Breathing No No No No
16 1844 Old Compass No No Yes Yes
17 1844 Old Rations No No Yes Yes
18 1844 Old Steel (OW) No No Yes Yes
19 1844 New Steel (NW) No No No No
20 1844 New Forges No No No No
21 1844 New Gold Money No No No No
22 1844 New Silver Money No No No No
23 1844 New Horse Pre-Columbian No Yes Yes Yes
24 1844 New Ass No No No No
25 1844 New Cow No No No No
26 1844 New Ox No No No No
27 1844 New Goat No No No No
28 1844 New Wild Goat No No No No
29 1844 Old Sacrifice not at Temple No No Yes Yes
30 1844 New Sheep No No No Yes
31 1844 Old Land of Jerusalem No Yes Yes Yes
32 1844 Old Bethlehem Part of Land of Jerusalem No Yes Yes Yes
33 1844 Old 3 Days Journey No No Yes Yes
34 1844 Old Not Much Fire No Yes Yes Yes
35 1844 Old Raw Meat No Yes Yes Yes
36 1844 Old Bountiful Site in Arabia No No Yes Yes
37 1844 New 600 Year Chronology No No Yes Yes
38 1844 Old Killing Laban No No Yes Yes
39 1844 Old Non Jerusalem Temples No No Yes Yes
40 1844 Old Jews Write in Egyptian No No Yes Yes
41 1844 Old Scripture in Egyptian No No Yes Yes
42 1844 Old Direction in Wilderness No Yes Yes Yes
43 1844 Old Non Levite Priests No No Yes Yes
44 1844 Old Metal Plates (OW) No Yes Yes Yes
45 1844 Old Israelite Writing on Metal No No Yes Yes
46 1844 New Metal Plates in NW No No No No
47 1844 New Pre-Columbian Writing Yes Yes Yes No
48 1844 Old Reformed Egyptian (OW) No Yes Yes Yes
49 1844 New Hiding Up Records No Yes Yes Yes
50 1844 New Inscribed Stone Monuments Yes Yes Yes No
51 1844 Other Sam No No Yes Yes
52 1844 Other Josh No No Yes Yes
53 1844 Other Gid No No Yes Yes
54 1844 Other Neas No No No No
55 1844 Other Ziff No No No No
56 1844 Other Money Names No No No No
57 1844 Other Rameumptum No No No No
58 1844 Other Kim No No No No
59 1844 Other Nephi No No Yes Yes
60 1844 Other Moroni No No No No
61 1844 Other Mormon No No Yes Yes
62 1844 Other Gadianton No No No No
63 1844 Other Day Night and Day No No Yes Yes
64 1844 New Sunken Cities No No Yes No
65 1844 New Great Tempest No No Yes Yes
66 1844 New Destruction by Fire No No Yes No
67 1844 New Whirlwind No No Yes Yes
68 1844 New Earthquake No No Yes No
69 1844 New Buildings Fall No No Yes No
70 1844 New Thick Darkness No No Yes No
71 1844 New Darkness Felt No No Yes No
72 1844 New Three Days of Darkness No No Yes No
73 1844 New Inability to Light Fire No No Yes No
74 1844 New Earth Closing Up No No Yes No
75 1844 New Earth Carried Up No No Yes No
76 1844 New Destruction at Time of Christ No No No No
77 1844 New Native Traditions No No No No
78 1844 New Civilization Yes Yes Yes Yes
79 1844 New Large Cities Yes Yes Yes No
80 1844 Old Glass (OW) No No No No
81 1844 New Arts No Yes Yes Yes
82 1844 New Astronomy No No Yes Yes
83 1844 New Archaeological Evidence No Yes Yes No
84 1844 New Chariots No No No No
85 1844 New Plausible Geography (NW) No No No No
86 1844 New Navigation No No No No
87 1844 New Wild Beasts No Yes Yes Yes
88 1965 New No Warfare No Yes Yes
89 1965 New No Wars of Conquest No Yes No
90 1965 New Swords Early No Yes No
91 1965 Old Scimitars (OW) No Yes Yes
92 1965 New Axes No Yes Yes
93 1965 New Bow and Arrow Early No Yes Yes
94 1965 New Shields No Yes No
95 1965 New Arm Shields No Yes No
96 1965 New Head Plates No Yes No
97 1965 New Breastplates No No No
98 1965 New Breastplates of Copper and Brass No Yes No
99 1965 New Wars of Extermination No Yes No
100 1965 New Elephants Pre-Columbian Yes No No
101 1965 New Pre-Columbian Christians No No No
102 1965 New Brass (NW) No Yes Yes
103 1965 New Iron (NW) No Yes No
104 1965 New Iron Working (NW) No Yes Yes
105 1965 New Iron Practical Use of (NW) No Yes No
106 1965 New Metal Money No Yes No
107 1965 New Chains No Yes No
108 1965 New Metallurgy (Early) No No No
109 1965 New Horse With Man No Yes Yes
110 1965 New Horse Book of Mormon Times No No No
111 1965 New Cattle No No No
112 1965 New Elephants Contemporary With Man No Yes Yes
113 1965 New Elephants in BM Times No No No
114 1965 Old Synagogues No No No
115 1965 Old River in a Valley No Yes Yes
116 1965 Old River into Red Sea No Yes Yes
117 1965 Old Timber No Yes Yes
118 1965 Old Ore No Yes Yes
119 1965 New Lehi Ocean Route No No No
120 1965 Other Length Jaredite Voyage No Yes Yes
121 1965 Other Pre-Columbian Sea Cross No Yes No
122 1965 New Feasts Custom Festivals No Yes Yes
123 1965 Old Jew Pre-Exilic Term Yes Yes Yes
124 1965 New Egyptian Language (NW) No No No
125 1965 New Egyptian Inscriptions (NW) No No No
126 1965 New Hebrew Language (NW) No No No
127 1965 New Hebrew Inscriptions (NW) No No No
128 1965 New NW Inscriptions/BM Names No No No
129 1965 New NW Inscriptions/BM Text No No No
130 1965 Other Alma No Yes Yes
131 1965 Other Deseret Yes Yes Yes
132 1965 Other Jarom No Yes Yes
133 1965 Other Zeniff No No No
134 1965 Old Honey Bees No Yes Yes
135 1965 Other Non-Biblical Hebrew Names No Yes Yes
136 1965 Other Egyptian Names Yes Yes Yes
137 1965 New Earthquakes in Mesoamerica No Yes No
138 1965 New Cities Identified No No No
139 1965 New Cement No Yes No
140 1965 New Snakes Hedge Way Yes Yes No
141 1965 New Machinery No No No
142 1965 Other Omni No Yes Yes
143 1965 Other Mosiah No Yes Yes
144 1965 Other Helaman No No No
145 1965 Other Ether No No No
146 1965 New Flocks No No No
147 1965 New Swine No No No
148 2019 New Daggers Yes No
149 2019 New Quivers Yes No
150 2019 New Fiery Darts Yes No
151 2019 New Set Time for Battle No No
152 2019 New BM Battle Remains Yes No
153 2019 New Trumpets Yes No
154 2019 New Cords Yes Yes
155 2019 New Ladders Yes No
156 2019 New Tents Yes Yes
157 2019 Old Bellows (OW) Yes Yes
158 2019 Old Brass Early (OW) Yes Yes
159 2019 New Brass Early (NW) No No
160 2019 New Abundance of Metal Ores Yes No
161 2019 New Gold Early No No
162 2019 New Silver Early No No
163 2019 New Copper Early No No
164 2019 New Lion-like Animals Yes Yes
165 2019 New Moths Yes Yes
166 2019 New Dragon-like Animals Yes No
167 2019 New Chickens Yes No
168 2019 New Dogs Yes Yes
169 2019 New New Names to Locations Yes Yes
170 2019 Old Much Fruit Yes Yes
171 2019 Old Wild Honey Yes Yes
172 2019 Old Mountain at Bountiful Yes Yes
173 2019 New Animal Sacrifice Yes Yes
174 2019 New Seantum’s Confession Yes Yes
175 2019 Other Jonas No No
176 2019 Other Timothy No No
177 2019 New Temples Yes Yes
178 2019 New Palaces Yes No
179 2019 New Barns Yes Yes
180 2019 New Pearls Yes Yes
181 2019 New Silk Yes Yes
182 2019 New Linen No No
183 2019 New Wheat No No
184 2019 New Barley Yes Yes
185 2019 New Corn Yes No
186 2019 New Grapes Yes No
187 2019 New Wine Yes No
188 2019 New Salt Yes No
189 2019 New Highways Yes No
190 2019 New Leprosy Yes Yes
191 2019 New Tools to Spin Yes Yes
192 2019 New Till Soil Yes No
193 2019 New Hoe Yes No
194 2019 New Thrash Yes No
195 2019 New Prune Yes Yes
196 2019 New Plow Yes No
197 2019 New Sickle Yes No
198 2019 New Tools to Work Beasts No No
199 2019 New Kings Yes No
200 2019 New Buildings Yes Yes
201 OA New Leader with continent-level influence No
202 OA New Traveling continent-level distances No
203 OA New Narrow strip of mountainous wilderness No
204 OA New Long-distance march to southern Illinois No
205 OA New Southern Illinois as a gateway No
206 OA New Narrow neck south of Cumorah No
207 OA New Lack of mention of snow or cold No
208 OA New Columbus did not visit No
209 OA New Two cultures living in close proximity No
210 OA New Lehi’s landing on the West coast No
211 OA New Elevation differences No
212 OA New Mississippi flowing northward No
213 OA New Launching Hagoth’s ship in the West Sea No
214 OA New Extensive deforestation No
215 OA New Jaredites in the land northward No
216 OA New Non-hunter gatherers No

 

TrajSim—Python Code

import random ##importing the needed python modules

import statistics

 

anach=149 ##total number of anachronisms in 1965

 

confirm=22 ##total number of anachronisms confirmed in 1965

 

## rate of anachronism increase = .984/year

## probability of confirmation (for OA model from 1965-2019, including old world) = .008625

 

iteration=0 ##declaring the iteration variable and setting its initial value

 

num_BoM=0 ##declaring a variable tracking the number of iterations where overturned anachronisms

##exceed the observed value for the BofM

 

final_percent=[] ##declaring a list variable tracking the final percentage of anachronisms overturned in

##each iteration

 

year=1965 ##declaring the year variable and setting it to its initial value

 

iterationnum=int(input(‘Iterations:’)) ##asking the user to input the number of iterations

rate_com=int(input(‘Rate (out of 10000):’)) ##asking the user to input the confirmation rate (86/10000)

 

while iteration<iterationnum: ##for each iteration

while year<2019: ##for each year in the iteration

rando1=random.randint(1,1000) ##rolling a random value to indicate whether a new anachronism

if rando1<=984: ##is added that year

anach+=1

unconfirm=anach-confirm ##calculating the number of unconfirmed anachronisms in each year

while unconfirm>0: ##iterating through each unconfirmed anachronism and giving it a chance to

rando2=random.randint(1,10000) ##become confirmed based on the inputted confirmation rate

if rando2<=rate_com:

confirm+=1 ##adding to the number of confirmed anachronisms

unconfirm-=1 ##decrementing the number of unconfirmed anachronisms that haven’t yet

else: ##been iterated through in that year

unconfirm-=1

percent=confirm/anach ##a running calculation of the percentage of confirmed anachronisms

year+=1

##print(‘Year: ‘,year,’ Anach: ‘,anach,’ Confirm: ‘,confirm,’ Percent: ‘,percent)

## optional print statement to check if the code is working

final_percent.append(percent) ##appending the percentage at the end of each iteration to the list

iteration+=1 ##incrementing the iteration counter

anach=149 ##resetting the number of anachronisms at the start of each iteration

confirm=22 ##resetting the number of confirmed anachronisms at the start of each iteration

year=1965 ##resetting year at the start of each iteration

for x in final_percent: ##code to track the number of iterations where the percentage exceed that

if x>0.7: ##observed for the BofM

num_BoM+=1

maximum=max(final_percent) ##calculating the highest final percentage recorded over all iterations

average=statistics.mean(final_percent) ## calculating the average percentage recorded

standarddev=statistics.stdev(final_percent) ##calculating the standard deviation of the percentages

print(‘Max: ‘,maximum,’ Num: ‘,num_BoM) ##printing the statistics recorded above

print(‘Mean: ‘,average,’ StDev: ‘,standarddev)

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