Estimating the Evidence, Episode 8: On Very Long Boat Rides

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[Editor’s Note: This is the eighth 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 Nephi could have built and sailed a boat from the Arabian Peninsula to the New World.

Though some critics have labeled Nephi’s voyage as an impossibility, those perceptions are largely based on the assumption that Nephi had to have built a Renaissance-style sailing vessel, as if the Nina, Pinta, or the Santa Maria were Nephi’s only options. That assumption doesn’t hold, given a variety of demonstrated oceanic voyages that rely only on ancient technology. Given the success rate of those voyages, and a conservative estimate of 16,000 man-hours of available labor for Nephi and his family, I put the probability of him being to build a boat at p = .3085 and the probability of him being able to sail it the requisite 17,000 miles at p = .0265. The odds would have been stacked against Nephi, but not enough to drastically alter the Book of Mormon’s authenticity.

Evidence Score = -2 (reducing the probability of an authentic Book of Mormon by two orders of magnitude)

The Narrative

When we last left you, our ardent skeptic, you were following the desert adventures of a strange little family in a strange little book, one given to you by a stranger. You read on, curious where this tale will go next, with the narrative taking them from a desert burial to a further eight years wandering in the vast wilderness of what you presume is the Arabian peninsula. After that, though, it seems as though they find some peace, arriving at a lush coastal area they term Bountiful. But there can be no lasting peace for these tragic figures, and it’s there that the story turns once again from the amusing (and at times confusing) to the ridiculous.

The young lad you had conversed with the night before had told you that this book told the story of the ancestors of the native peoples of the American continent, and so far you’d wondered how on earth the story was going to get these characters from Jerusalem to the other side of the world. You aren’t sure what you were expecting, but it certainly wasn’t having this decidedly non-nautical family build a boat, and then to have them sail that boat across the vast seas. You sympathize with the mutinous behavior of the two rebellious (and eminently sensible) brothers presented by the narrative—their foolish brother would have the ocean kill them as surely as any sword-stroke.

You scoot your stool back from the table and go back to your small library on the opposite side of the cabin. After a moment’s rummaging you pull out a small but elegantly detailed world map—one of your prized possessions. Your eyes quickly find the Arabian peninsula, and then follow two different trails through the sea toward the Americas—one through the Atlantic passing around the horn of Africa, and the other through the vast Indian and Pacific Oceans. You shake your head and give a chuckle. The book would have this Nephi outdo Columbus several-fold, beating him to the continent by over 2000 years. It would almost be easier to believe that angels had carried them over, or that they had bred flying horses to make the journey. You put the map down and return to the still-open book on the table, aghast at the audacity of this Joe Smith. It seems unlikely that anyone could build a boat capable of carrying an entire family on such a transoceanic voyage, and even less likely that they could survive the journey.

The Introduction

The transoceanic voyage of Nephi and his family has always been considered among the most incredible claims of the book. Critics rightly point out that boat-making is difficult business and that seafaring is extremely hazardous—they generally align with the mainstream academic consensus that there was no oceanic contact with the Americas prior to Leif Erickson and his Viking comrades. Faithful scholars, for their part, point to the serious, but minority, scholarship contending that there was indeed contact, and a great deal of it, ranging from the Polynesians to the Japanese to the Egyptians to the Phoenicians. Though the validity of that research is out of our particular scope, the general question is a workable one from a Bayesian perspective. Given access to materials, (divinely given) expertise, a navigational instrument, and the timeframe outlined in the text, how likely would it be for a small group of people to build a boat capable of carrying 30-40 individuals halfway across the globe, and then to have them survive the journey?

The Analysis

The Evidence

The story of Nephi’s sailing and boat-building activities, as recorded in 1 Nephi 17-18, provides a number of important pieces of information pertinent to our estimates. Nephi smelted woodworking tools from ore available within the Bountiful site and built a boat capable of carrying approximately 40 individuals using wood from timber

available in the vicinity (nowhere does he say that ore was used in the construction of the boat itself). We know that he had help from Laman and Lemuel (following a rather shocking altercation between them and Nephi), and would’ve had reliable assistance from at least Sam and Zoram, if not the sons of Ishmael, meaning there was as least five sets of hands working on the boat. We get very few other specifics about the boat itself, except that the revelation-provided instructions for building the boat resulted in a craft that didn’t look like any of the boats that Nephi was already familiar with (though it likely had a sail).

There’s no direct indication of how long it took to build the boat. John Sorenson estimates that they had at least two years based on the timing of the destruction of Jerusalem and Lehi’s being told of that destruction in a vision in the New World. However, there’s no rule saying that the vision had to happen immediately after that destruction, and contrary to Sorenson’s suggestion, the site of Bountiful may have been relatively isolated from contact with trade caravans (and with associated news of Jerusalem’s destruction). Aside from that conjecture, the next hard and fast date provided by Nephi is 30 years after leaving Jerusalem, by which time he’s in the promised land and has put down enough roots in the New World to construct a temple, meaning that Nephi technically could have had as much as 20 years to complete his journey. For argument’s sake, though, we’ll assume that he only had two years with which to build the boat.

The most plausible reading of the text has Nephi and his family sailing through the Indian and Pacific oceans to reach Central America (based on a western landing as suggested by the placement of the land of first inheritance), meaning that he would’ve traveled 17,000 miles to reach their final destination. We’re told, though, that he did have a workable navigation instrument available to guide them along the way. We’re not going to worry much about how long it took them to sail, since we’ll be calculating probabilities based on distance travelled, but it could have taken them a year or more to travel that distance by sea.

The Hypotheses

We have two relatively straightforward hypotheses to consider this time around:

Nephi’s voyage is authentic—The story in the Book of Mormon reflects a real Nephi who built a real boat, which took his real family from the real Arabian peninsula to a real American continent. Really.

Nephi’s voyage is fictional—The story in the Book of Mormon reflects Joseph Smith’s imagination. There should be no more reason to expect that the story would conform to reality than to expect eagles to be able to carry hobbits off of erupting volcanos.

Prior Probabilities

PH—Prior Probability of an Ancient Voyage—At the moment, given the evidence we’ve considered so far, the Book of Mormon is still rather incredulous. Our current estimate for the probability of an authentic Book of Mormon stands at p = 2.41 x 10-28. Here’s a look at where we’ve been so far.

PA—Prior Probability of a Fictional Voyage—That would leave the still-formidable remainder of our probability for the hypothesis of modern authorship, which would stand at p = 1 – 2.41 x 10-28.

Consequent Probabilities

CH—Consequent Probability of Ancient Authorship—To get an estimate for this probability, we’re going to need to try to calculate how likely it would be for Nephi to pull off this voyage. We’re going to treat it in two parts: 1) the likelihood of being able to build a boat given the time available to him, and 2) the likelihood of surviving a 17,000-mile ocean journey using an improvised oceangoing vessel.

Building a Boat. To some critics, we’ve already arrived at something they perceive as impossible. The ever-reliable Zelph on a Shelf frames the impossibility of Nephi constructing a boat thusly: 1) A transoceanic vessel would require iron, which Nephi wouldn’t have been able to smelt; 2) transoceanic vessels require a rounded hull, which would require building a dry-dock, which would have taken too long to build; 3) creating rounded hulls would’ve required steaming and bending the boards, which would’ve required at least Renaissance-level ship-making facilities and a large amount of labor; 4) storing food for the long journey would’ve required being able to pickle food, which Nephi wouldn’t have been able to do.

To me, this framework reflects both a lack of imagination and ignorance of non-Western means of ocean travel. Just because popular art depicts Nephi and his family riding a Renaissance-style ship to the New World doesn’t mean that they necessarily would’ve had to do so. European explorers were far from the only ones travelling the open seas. We don’t need to look any farther than the expeditions of Thor Heyerdahl to get a sense of what would be possible. Within a few months, Thor and his small team constructed a large oceangoing raft using little more than a few balsa logs, with neither a rounded hull nor any variety of metal in sight. It was able to carry his crew and necessary supplies over 4,300 miles across the Pacific just drifting on the wind and the current. Sorenson and others have suggested that Nephi could’ve used a larger version of that type of vessel to take his family to the promised land, and given what Thor and others were able to accomplish, it certainly seems plausible.

And, of course, regarding their point on food storage, it turns out that dates and dried meat have a pretty impressive shelf life, which is what Nephi would’ve had available, and that’s not accounting for the possibility of their diet being supplemented by a bit of ocean fishing. It may have even been easier than usual to gather those supplies given the unexpectedly verdant nature of the proposed Bountiful site. That site also would’ve had the requisite copper ore available for Nephi’s woodworking tools, which is much easier to smelt than iron.

So how long would it have taken to build an ocean-going vessel capable of carrying the entire Lehite clan? Even though Nephi wouldn’t have used European methods for constructing the ship, we can assume that it might take about the same amount of raw labor (or less) to put the thing together. The best estimates I could find were for Viking sailing vessels, which not only were able to travel oceanic distances, but were largely constructed by non-specialists, warriors, and farmers who added their spare labor to the project when they could. The best guess of anthropologists have suggested it took as long as 40,000 hours of labor to build a ship capable of carrying 80 people. But a Danish team, working in the early 2000s and making use of ancient methods, was able to build one much faster. They estimate that it would have taken actual Vikings around 28,000 hours of labor to construct.

Now that brings us to another interesting problem—the relationship between the carrying capacity of a boat and how long it takes to build. We can’t just divide the number of hours in half to estimate the labor required for a ship that could carry 40 people. Some of that labor would be required of a ship of any size, such as the work needed to craft the necessary tools and lay out a worksite. On the other hand, smaller boats might require a lot less in terms of build quality in order to keep them afloat. Data on how long it took to build ancient boats is pretty hard to come by. If we wanted to, we could collect a whole bunch of data on modern carrying capacity and boat lengths to try to build a better estimate. But relying on modern data might just lead us further astray.

Instead, let’s just assume that a substantial amount of the required labor, say maybe 5,000 hours of the total 28,000, consisted of that sort of preparatory effort, after which additional labor was used to add carrying capacity. If so, then we can divide the remaining 23,000 hours by two, and then add 5,000 to estimate the labor required for a vessel capable of carrying Lehi’s family. All told, we might expect such a vessel to take about 16,500 hours to complete.

Did Nephi have that much time available to him? If we go by the two-year time limit, and an assumption of five laborers, we can start to make some guesses. Assuming that Lehi and his party were able to live a hunter/gatherer lifestyle in Bountiful, they would have had a substantial amount of free time beyond what was needed to maintain subsistence living, and their wives and other companions could have done a lot to allow them to spend their time building a boat. Even those in more agrarian societies often didn’t need to spend the entirety of their time in subsistence labor. For the sake of creating an estimate, we’ll say that those five laborers could spend 8 hours a day working on the boat for an average of 200 days per year, that would mean Nephi and his makeshift crew could have devoted about 16,000 hours to the construction of the ship—just about enough to build a ship of the required size.

To get a probability estimate here, we’ll also need to estimate the variability in boat construction time. Given differences in the design of the ship and expertise of the work involved, that variability is probably pretty large. But let’s assume that ship construction would have a pretty tight standard deviation relative to its mean, say around 1000 hours (the smaller the deviation the better it would be for the critics). That would mean that Lehi’s ship is half a standard deviation away from our estimated mean, and that 30.85% of ships that size would require 16,000 hours or less of labor.

You’ll notice that there was plenty of red text above. It’s worth remembering, though, that exactness isn’t the goal—what we’re trying to do is build a reasonable, conservative estimate, and I’m pretty confident that this fits the bill. These numbers are a way for us to get a broad sense of how unexpected this kind of boat-building feat would actually be, and I don’t see the values above as being particularly far off. If they are, it’s probably in a direction that would help the critics. I feel quite comfortable using p = .3085 as our estimate for this part of the analysis.

The Risks of Ocean Travel. Once Nephi had a workable boat at his disposal, he and his family still had to face the perils of extended ocean travel. It would’ve been by no means easy for him or anybody else to make it across two oceans, though one would have to assume that the availability of divine intervention could’ve made things substantially easier. As is our habit, though, we’re not going to assume divine intervention. We’ll assume that Nephi would’ve faced similar risks as any other traveler on the maiden voyage of a first-time sailing vessel.

We can get a sense of that risk by looking at the various drift voyages, similar to Heyerdahl’s Kon Tiki, that have been attempted in the Pacific. Some of those voyages were successful, and others, including Heyerdahl’s own, didn’t go quite as planned—with boats becoming damaged in severe storms or being run aground on reefs. If any of those had happened to Nephi it would have quickly spelled the end of his journey. As you can see in the table below, of the 11 voyages recorded, 5 of them ended earlier than hoped due to boat or navigation issues. This lets us calculate the risk of failure, similar to how risk per mile estimates are made in the context of modern transportation safety. To make the calculation, I divided those five failures by the total number of miles travelled to get a per-mile risk associated with that sort of ocean travel. By that reckoning, the probability that a voyage would fail would be just over 1 in 10,000 for each mile traveled.

Ship

Length (Miles)

Success?

Kon-Tiki

4,300

No

Seven Little Sisters I

6,301

Yes

Seven Littls Sisters II

7,457

Yes

Kantuta I

2,323

No

Kantuta II

2,323

Yes

Tahiti-Nui

4,470

No

Tahiti-Nui II & III

5,460

No

Tangaroa I

4,576

Yes

Tangaroa II

4,300

Yes

An-Tiki

3,000

Yes

Kon-Tiki II

2,323

No

Total

46,833

5 failures

Risk/Mile

.000106762

Now, keep in mind that this is probably an overestimate of the risk, given that the successful voyages probably could have gone quite a bit further than their final destination. Nevertheless, given that we’re dealing with a pretty small sample size, we’re going to assume that this risk is too low, and that the real risk for this type of voyage would be double what we estimate here, at about 2 in 10,000 per mile.

Once we have that estimate, we can calculate the probability that Nephi would have survived his 17,000-mile voyage. If we assume that every mile would have an independent chance of failure, we can take the value of .000213525 (double our initial risk estimate), subtract it from 1, and then take it to the power of 17,000. That would mean that the probability of surviving that journey would be at least p = .026508. You can get a sense of how that probability changes over the length of the journey in the figure below:

Summary. With these two probabilities in hand—the probability of being able to build the boat with the available labor, and the probability of surviving the 17,000-mile voyage—we can calculate the overall consequent probability by multiplying the two values together. If you do that, you get an estimate of p = .008178. That’s a fairly low probability. It’s also far from impossible.

It’s also important to note that this probability hinges strongly on our estimates of per-mile risk of ocean travel. If we decided, for instance, not to double our risk estimate, the consequent probability would increase to p = .05. If somehow the risk is actually far greater than reflected in my list of ocean voyages, then Nephi’s chances start to sink considerably.

CA—Consequent Probability of Modern Authorship – So what should the probability be for being able to produce Nephi’s story assuming that it’s fictional? Obviously, people can make up whatever they want when producing fictional narratives, so you might think that the probability is p = 1. I think there’s a case to be made, though, that Joseph gets more right about boatbuilding and ocean travel than he should in a fictional narrative. A lot of fictional ocean-going tales are extremely fanciful affairs and, as is evident here, Joseph never strays into territory that’s completely implausible. Nevertheless, as is our habit, we’re going to give critics the benefit of the doubt on this (and many other) fronts. Our estimated consequent probability will be p = 1.

Posterior Probability

PH = Prior Probability of the Hypothesis (Our prior estimate of how likely it is that the Book of Mormon is authentic, or p = 2.41 x 10-28)

CH = Consequent Probability of the Hypothesis (The estimate of how likely it would be to build a boat and sail it to the New World, given what we know from the text and similar voyages, or p = .008178)

PA = Prior Probability of the Alternate Hypothesis (Our prior estimate of how likely is it that the Book of Mormon is a modern work of fiction, or p = 1 – 2.41 x 10-28)

CA = Consequent Probability of the Alternate Hypothesis (The estimate of how likely it would be to create Nephi’s stories within a fictional account, or p = 1)

PostProb = Posterior Probability (Our new estimate of the probability of an authentic Book of Mormon)

PH = 2.41 x 10-28

PostProb =

PH * CH

(PH * CH) + (PA * CA)

PostProb =

(2.41 x 10-28 * .008178)

((2.41 x 10-28) * .008178) + ((1 – 2.41 x 10-28) * 1)

PostProb =

1.97 x 10-30

Lmag = Likelihood Magnitude (an estimate of the number of orders of magnitude that the probability will shift, due to the evidence)

Lmag = log_10(CH/CA)

Lmag = log_10(.008178 / 1)

Lmag = log_10(.008178)

Lmag = -2

Conclusion

It’s pretty easy to see why critics would latch onto the idea that Nephi’s voyage was impossible. Most of the people reading this would likely laugh openly at the suggestion that they, themselves, would be able to build a boat and sail it across the ocean, particularly when they have in mind a Renaissance-era sailing vessel. But even conservative estimates suggest that it’s not nearly as implausible as it might seem at first glance. Assuming that Nephi had the available expertise (via revelation), he and his brothers likely had more than enough time to build a boat and would have had a fair shot at reaching the New World even in the absence of divine protection.

Skeptic’s Corner

To be fair to the critics on this one, very few of my estimates are based on hard data. It’s very hard to get a sense of things like the overall risk of ocean travel in ancient times, or how long it might have taken Nephi’s amateur crew to build a boat. There’s just too much we don’t know about the boat, about the route they travelled, about how much work they put in, or how many years they stayed at Bountiful, or any of a number of other important variables. In the end, that uncertainty is part of why this doesn’t make for great evidence against the Book of Mormon. Critics could potentially build a statistical case here that looks worse for the Book of Mormon, but it’s unlikely that such an estimate would be more reasonable or more grounded in hard data.

That said, there’s one particular thing that could change this picture somewhat, and that would be how the risk of ocean travel might change over the course of the journey. Here we’ve assumed that the risk is constant—that the risk at the first mile is about the same as the risk at the 17,000th mile. But that’s not necessarily true. It could be that the risk dramatically increases over time—that wear and tear accumulates on the boat, that supplies run low, or that cabin fever starts to set in. Projects like Hokulea show that this doesn’t have to be the case, and that if properly equipped ancient boats could stay on the water almost indefinitely. But if that risk does systematically increase, so too could the strength of this particular evidence. The problem, as with most everything else, would be in pinning down the details—at this point, those details remain slippery enough that the Book of Mormon can sail by relatively unscathed.

Next Time, in Episode 9:

When next we meet, we’ll be considering evidence from Royal Skousen and Stanford Carmack concerning the presence of Early Modern English within the Book of Mormon.

Questions, ideas, and blunt objects can be flung recklessly toward BayesianBoM@gmail.com or submitted as comments below.

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