Estimating the Evidence, Episode 7: On Three Consonants and a Turn

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[Editor’s Note: This is the seventh 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 Joseph could guess the name Nahom by chance alone, or that he could’ve gotten that location from a map.

The site of Nahom has been touted as solid archaeological evidence for the Book of Mormon, but it’s hard to know exactly how strong that evidence actually is. Could Joseph have guessed the name by chance? Could he have gotten the name from a contemporary map of Arabia? Some options are less likely than others. I estimate the odds that a Book of Mormon place name would match any of almost a hundred sites in the area around Nahom at just under 1 in 100 (p = .0097). By contrast, a liberal estimate of the likelihood that Nahom could have been gleaned from an available map is about 2 in 10,000 (p = .0001585). Regardless, Nahom provides meaningful—though far from overwhelming—evidence in the Book of Mormon’s favor.

Evidence Score = 2 (the probability of an authentic Book of Mormon increased by two orders of magnitude—though it could be as high as four if we apply somewhat less conservative requirements)

The Narrative

When last we left you, our nineteenth-century skeptic, you were applying your skeptical worldview to the opening chapters of the Book of Mormon. You’ve now somehow managed to push past your seething contempt for Nephi’s murderous ways, running your eyes swiftly from line to line. You skim over an odd dream filled with seemingly opium-driven nonsense, only to shruggingly read through a second recitation of the same dream. You ignore familiar passages from Isaiah that you’re pretty sure match word for word with those from your own volume of the King James, which still lays open and dusty a few feet away on the table. Your vow to never touch the tome again keeps you from checking that for the moment, but you know sooner or later your curiosity will get the best of you. You hope in the meantime that such blatant plagiarism is an isolated anomaly.

Despite those hiccups, there’s something undeniably fascinating with the tale of this troubled Hebrew family. The narrative of brother against brother is simplistic, almost cliché, but compelling nonetheless. You also can’t help but notice some admittedly nice touches. You recognize the association of valleys with strength, rather than mountains, as a thoughtful and poetic Arabic idiom. It does strike you as strange, though, that someone would put reference to a continually flowing spring in the Arabian wasteland south of Jerusalem.

It occurs to you, though, that such details could be this Joe Smith’s undoing. You doubt highly that said Smith had travelled much past the Ohio, let alone to the far side of the world. If he was putting details this specific into his tall tale it wouldn’t take much more than a good map to prove him wrong. And the absurd details don’t stop there. A few pages later you read about a burial in “a place which was called Nahom,” a few weeks’ travel south of Jerusalem. Was there indeed such a place? Could one then turn and find a way to cross the seemingly infinite desert sands, as the book described?

If not, Smith might as well place his literary head in a noose right now, since sooner or later such pronouncements would hang him. But if so…well, if such things could be verified, it seems unlikely that one could get such geographic details correct simply through pure luck.

The Introduction

When critics of the Book of Mormon state, unequivocally, that there is “absolutely no archaeological evidence for the Book of Mormon," there’s at least one piece of evidence that they’re flatly ignoring. I’m not sure how anyone could take a look at the well-attested studies of the Nehem site, which is in the exact spot the Book of Mormon says it should be, and call that anything but evidence. Critics are nevertheless quite aware of the need to deal with this evidence, and seem committed to one of two propositions: either Nahom itself is a lucky guess, or Joseph had access to specialized maps that, at the time, were only available in distant locations.

It’s hard to know at first glance how likely either of these options are. It’s not easy to look at a name like Nahom and know how easy it would be to match with a stroke of guesswork, and it’s even harder to know whether it would be possible for Joseph to spend weeks traveling to dig through library stacks without leaving incriminating evidence. But those sorts of problems are exactly what Bayesian analysis is there to help us with.

As I’ve hinted at above, there’s a ton of different aspects of Lehi’s journey that could be pertinent to a Bayesian analysis, from the consistent use of the terms up and down in reference to travel to Jerusalem, to attestation of Hebrew temples built outside of the Holy Land, to viable locations for the Valley of Lemuel and Nephi’s Bountiful. But none of those seem to highlight the potential accuracy of the Book of Mormon narrative in the way Nahom does. So, for the purposes of this episode, we’ll be sticking to those three special consonants and the two (somewhat less relevant) vowels sandwiched between them.

The Analysis

The Evidence

When it comes to the location of Nahom, the facts are these: The Book of Mormon describes a location “which was called Nahom," a place where Lehi and his family bury Ishmael. This place, according to the book, is a long journey south-southeast of Jerusalem along a path near the Western coast of the Arabian peninsula. It is there, importantly, that they make a turn nearly east before arriving in a fertile coastal location, which they term Bountiful.

This described path generally aligns with the Frankincense trail, what is really a series of trails that snake through the arid, mountainous region on the west side of Arabia. The Frankincense trail makes a notable eastward turn a few hundred kilometers north of the southern coast, and follows what would’ve been the only practical path eastward through the desert in all of southern Arabia.

In 1997, archeologist Burkhard Vogt discovered an altar at a digsite in Yemen with an inscription of NHM. As the original written form of Hebrew did not include vowels, this inscription could have easily referred to a place called Nahom. This place lies close to the aforementioned eastern turn in the Frankinsence trail, and since this altar dated to 800 BC, it’s entirely plausible that Lehi and his party could have encountered this place on their journey through southern Arabia.

This Nahom, (or Nehem or Nehhm), was known to some outside of Arabia in the 1820s, but this knowledge wasn’t widely available. Maps containing reference to a town with that name, in that location, were only available at a few universities, the closest being Allegheny College, several hundred miles east of where Joseph lived or where he conducted his translation of the Book of Mormon. There is no evidence that he made a trip to any of these universities or would otherwise have access to maps detailed enough to contain reference to the relatively obscure settlement. Importantly, other than Jerusalem, none of the other places referenced in the Old World by the Book of Mormon (e.g., Shazer) are contained in those maps. If Joseph used any of those maps, he pulled only Nahom from them (though that would also be odd, since none of the available maps used Nahom as a spelling for the site), and nothing else.

Joseph also showed no knowledge that Nahom was a real place in Arabia at any point in his life. Joseph was keenly interested in archaeological evidence for the Book of Mormon, yet made no reference to Nahom as a place that could or would be confirmed as by archaeological efforts.

Scholars have also noted the potential for an interesting potential wordplay with the term Nahom, as the Hebrew meaning of the word is “mourning," which would fit well with the burial of Ishmael. Critics have noted, however, that the spelling of the actual site in Yemen uses a slightly different spelling (a hard h rather than a soft h). This doesn’t necessarily invalidate the wordplay (the spelling still could have reminded Nephi of the term), but we’ll give the critics the benefit of the doubt and not include the wordplay in our analysis (saving the concept of wordplay in the Book of Mormon for a later episode).

The Hypotheses

So, let’s take a look at our three hypotheses:

There was an authentic Lehi whose family visited the Nahom that corresponds with the present-day archaeological site—This theory is rather straightforward. The place name in the Book of Mormon is of ancient origin because ancient people recorded their visit.

Nahom is a place name invented by Joseph, and only corresponds to the present-day archaeological site due to chance alone—According to this theory, Joseph created the name as he would have created any other place name in the Book of Mormon, out of his own imagination. Based on this theory, we could assume that, due to chance, the name Nahom could have instead resembled any of the other allegedly invented names in the book.

Joseph chose the name of Nahom by inspecting available contemporary maps—This theory implies that the current evidence we have for the translation process is wrong, and that Joseph had certain resources available to him to help him obtain accurate information about ancient Arabia when piecing together his narrative. This would have involved a secret journey to a place with a map containing Nahom.

Why did the journey have to be secret? Couldn’t others have known about the journey and those resources and simply covered it up? Maybe, but it’s not a great maybe—as we’ve discussed previously, conspiracies are very very hard to maintain. Having to account for conspiracies would do the critics no favors, in this case or any other.

It’s also worth mentioning another, related theory. Rather than making up the name, it’s possible that Joseph could have pulled something similar to the name Nahum from the Bible, as is potentially the case for other (though far from all!) proper names in the Book of Mormon. Statistically, though, this theory is essentially indistinguishable from Joseph inventing the name—he would still be selecting the name basically at random from a large pool of potential options. The characteristics of Bible and Book of Mormon names probably aren’t identical, but they’re close enough that it wouldn’t matter for our analysis.

Prior Probabilities

PH—Prior Probability of an Authentic Lehi—Based on where we left off last time, our prior probability for an authentic Book of Mormon is sitting at a still unlikely p = 2.12 x 10-30. Here’s where we’ve been thus far:

PA_1—Prior Probability of an Invented Nahom—It’s hard to know exactly how likely we might initially expect an invented Nahom to be relative to Joseph obtaining it from an existing map, but It’s clear that we should give the advantage to an invented Nahom, just in terms of parsimony. You need a lot fewer assumptions for Joseph to make up the name. He doesn’t even have to pack a bag, for heaven’s sake—he just has to sit there for a few seconds mulling it over. Based on that thinking, we’re going to divide the remaining probability by 10, and assign about 90% of it to an invented Nahom. That would leave us with a prior probability of p = .90.

PA_2—Prior Probability of a Map-Originated Nahom—With about 10% of the remaining probability, that means our initial estimate for a likelihood of a map-originated Nahom is p = 0.1 – 2.12 x 10-30.

Consequent Probabilities

CH—Consequent Probability of an Authentic Lehi—Our question here is, how likely would we be to observe evidence for an authentic Nahom given an authentic Lehi? Now, it was never guaranteed that evidence for Nahom would ever show up even if it was authentic—it’s possible the name for it could have changed, or that ruins for it could have been damaged, or that it just plain never caught the interest of archaeologists. But, given time and improved methods, we would certainly expect evidence of this kind to turn up eventually. I’m comfortable treating this evidence as perfectly compatible with an authentic Lehi, with a consequent probability of p = 1.

CA_1—Consequent Probability of an Invented Nahom—Here’s one case where the statistical problem at hand seems fairly straightforward. We have three Hebrew consonants, and all we appear to have to do is randomly select from the 22 consonants in the Hebrew language to try and guess each of those three. That probability all by itself is easy enough to calculate at p = .00009.

But matters are a little trickier than that. For one, Joseph wouldn’t have necessarily picked a name with three consonants. If you go through all 75 place names in the Book of Mormon (not counting Jerusalem), you discover that the number of consonants in the names varies from two to six—three is the most common, but it’s actually in the minority. That would mean multiplying the value above by .4667 to get the actual probability that a Book of Mormon place name would match NHM, with the resulting p = .000042. Here’s a table showing the distribution:

For these analyses I counted consonant sounds (e.g., sh; th) as a single consonant, double consonants (e.g., mm) as a single consonant, and I counted terminal silent h’s (e.g., as in “Antiparah”) as a separate consonant. If you feel that some other method would be more appropriate, feel free to let me know.

So that 4 in 100,000 chance is pretty low, and would constitute pretty strong evidence from a Bayesian standpoint. But that’s just the odds of guessing Nahom specifically. That brings up another important question—would Nahom be the only possible place where someone could have made a “nearly eastward turn” when in southwest Arabia? If not, then Nahom’s not the only potential target for a randomly generated place name, and we’ll need to increase our probability estimate accordingly. There are a bunch of different settlements relatively close to Nahom that could have just as easily substituted as a valid location for Ishmael’s burial, and that faithful scholars might have locked onto as a valid hit for the Book of Mormon.

What’s less clear is how big of a circle we would have to draw around Nahom to capture potentially valid sites, and I don’t think that’s something I could realistically determine as part of this essay. But we certainly can’t head too far north of Nahom, nor too far south—if the Frankincense trail is anything to go by, the path by Nahom is literally the only passable eastern trail in the entire peninsula—the wastes to the north are impassable, as is the rocky southern coastline. There’s no real east/west restriction that I can see, though—Lehi could’ve been essentially on the western coast itself and still made an eastward turn that cut through or near Nahom.

We’re going to be generous, as is our custom, and say that Joseph could have guessed at any location within 100 kilometers north and south of Nahom, as far west as the coast, and as far east as we can find any notable settlements in that range. (Want measurements in miles? Tough luck. I’m Canadian. Sorry.) We’ll use the most densely labeled map of the area from those available in 1830 (because they’re handy, not because they’d give a sense of what the area looked like in 600 BC), and make a list of all the labeled settlements within that range. That map has been included below, with the area of interest shaded. It gives us a list of 92 potential targets, for which we can calculate the odds of them being randomly guessed by Joseph, just as we did for Nahom (see the appendix for a table showing each). Once we do that, we can just sum those probabilities to get an estimate of how likely he would’ve been to hit any of those targets. That value happens to be p = .0097. Not as impressive as 4 in 10,000, but still somewhat difficult to pull off by chance alone.

Figure 1. A map of the area of Yemen containing Nahom, with a 200 km band highlighted.

CA_2—Consequent Probability of a Map-Originated Nahom—If guessing at a valid Nahom-like site is unlikely, do we do any better by positing Joseph’s access to a contemporary map of Arabia? Since it’s very hard to imagine what good data on this question would even look like (how many other examples of proposed forgeries that made secret use of contemporary maps come to mind?), we’re going to have to make some educated guesses about how likely each step in that process would be, doing our best to bias those estimates in the critics’ direction.

Based on my understanding of this theory, there are seven unusual features in it that you would have to account for to align it with the data we have. Just for fun, I’m going to call them the Seven Seals of the Nahom Bayesian Apocalypse.

First, you have to get Joseph to a place with one of the Nahom maps without any of his family or friends making note of the trip. Second, he would have to access the map without any of the staff at the library noting his presence. Third, you have to account for the fact that he would’ve made the several-hundred-mile jaunt only to select a single location from a single map as a way of providing credence to his story. Fourth, you have to account for the change in spelling as none of the contemporary maps spell it the same way Joseph did—if you’re copying from a map, why change the spelling? Fifth, since none of the maps included information on the eastward turn, you have to account for him getting the turn right. Sixth, the city he chose would need to have existed at the purported time of Lehi—there’s no guarantee that would’ve been the case for a randomly selected location from the map. And seventh, you need to account for Joseph never mentioning Nahom again—why work so hard if no one would ever realize that the name matched a real-world location?

None of these items are necessarily impossible, but they’re definitely unexpected, and all of them should be independent of the others. I’m going to throw some numbers out there and you can tell me how unreasonable they are if you so desire.

The First Seal. The closest map that I can see that anyone’s posited that he might have had access to is 173 miles (from Harmony—now Oakland–Pennsylvania to Philadelphia, where a medical school at the time had one of the maps). A secret trip would be hard to pull off, and it would get harder the longer he was away. At a pace of 4 miles an hour, walking 10 hours a day, that round-trip would’ve taken him a little over a week. If he had even a 5% chance of getting caught each day of that trip, then the odds of him getting away with it would be just over half (p = .63401), and that’s without him actually spending any serious amount of time studying in the library.

The Second Seal. It seems fair to suggest that a young man from the frontier showing up out of nowhere at Amherst College would’ve turned some heads, and Joseph was later famous enough that you would think his arrival would’ve been reported at some point later in his life. Libraries in this era often required subscriptions in order to let people check out books, and it’s hard to imagine some uptight college librarian letting some random farm kid peruse the map section. I’m going to set the probability of him getting noticed by library staff at a very generous 50%.

The Third Seal. If someone is taking the time to enter some serious study of the geography of the Arabian peninsula, I would expect that they would have more to show for the fruits of their labor than a single, obscure location. As far as I’m concerned, I would only expect that to happen 10% of the time at the very most.

The Fourth Seal. Why pull a real location for use in your narrative and then immediately obscure that location with a change in spelling? In what universe does that make sense? A probability of 10% seems exceedingly generous here.

The Fifth Seal. There are approximately 2000 kilometers of the Arabian peninsula where Joseph could have had Lehi make that turn. If we use the same 200 km leeway we used for an invented Nahom, that would give Joseph a 10% chance of putting that turn in a reasonable location.

The Sixth Seal. Names change, people move, languages shift. The odds that a small settlement would remain settled over a period of 2500 years and also retain the same name seems really low on its face. I’ll still be a very nice person and give a 10% chance that a site that he chose could be dated to the right timeframe.

The Seventh Seal. And lo, the seventh seal was opened, and we all agreed that we don’t always know what Joseph Smith was thinking. We can’t say that it’s impossible for him to have concealed knowledge of Nahom, but hopefully we can all agree that not everyone would’ve done so if they were in his shoes. I’m assigning a probability of 50% for this one.

Multiplying the probabilities of the Seven Seals together, you get an estimated probability of producing the evidence listed above at p = .0001585. We’re going to go ahead and use that as the consequent probability of a map-originated Nahom.

Posterior Probability

With those probabilities calculated, we see where our Bayesian analysis lands us.

PH = Prior Probability of the Hypothesis (our initial estimate of the probability of an authentic Lehi, based on prior analyses, or p = 2.12 x 10-30)

CH = Consequent Probability of the Hypothesis (the probability of observing the evidence we have given an authentic Lehi, which we set at p = 1)

PA_1 = Prior Probability of an Invented Nahom (our initial estimate of the probability of an invented Nahom, or p = .9)

CA_1 = Consequent Probability of an Invented Nahom (the probability that Joseph could have randomly matched the name of a settlement in the vicinity of Nahom, estimated at p = .0097)

PA_2 = Prior Probability of a Map-Originated Nahom (our initial estimate at how likely Joseph could have been to get the name of Nahom off of a contemporary map, which we set at p = .1 – 2.12 x 10-30)

CA_2 = Consequent Probability of a Map-Originated Nahom (the probability that Joseph could have accessed and used Nahom from a contemporary map while producing the evidence we observe, or p = .0001585)

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

PH = 2.12 x 10-30

PostProb =

PH * CH

(PH * CH) + (PA_1 * CA_1) + (PA_2 * CA_2)

PostProb =

(2.12 x 10-30 * 1)

((2.12 x 10-30) * 1) + (.9 * .0097) + ((0.1 – 2.12 x 10-30) * .0001585)

PostProb =

2.41 x 10-28

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 / ((PA_1 * CA_1) + (PA_2 * CA_2))

Lmag = log_10(1 / ((.9 * .0097) + ((0.1 — 2.12 x 10-30) * .0001585)))

Lmag = log_10(1 / (.00873 + .00001585))

Lmag = log_10(1 / .00875)

Lmag = log_10(114.34)

Lmag = 2

Conclusion

There are a couple things that I glean from this analysis. The first is that critics should clearly prefer an “invented Nahom” scenario to a “map-originated” one. It’s easy to think that Joseph might have had access to a map, but making it concrete helps show how unrealistic that scenario would’ve been. Joseph hitting on it by chance is a way simpler—and way more likely—explanation. The second is that the strength of Nahom as evidence relies on something that I haven’t seen much attention paid to in scholarly circles, and that’s the number of other appropriate locations that Joseph could have hit on instead of Nahom. If there are 92 appropriate locations (which I would think is the high end) it’s not nearly as strong as if the Nehem site is the only possible spot. If Nehem really is the only viable target, it would move the needle about 3.5 orders of magnitude instead of 2, which, given our scale, would make the evidence about 50 times more informative from a Bayesian standpoint.

But either way, the evidence for Nahom is useful, but it’s far from a silver bullet. It’s not likely that Nahom could’ve been hit on by chance, but it’s not a statistical impossibility either. Its true strength, in my opinion, is as part of the rich tapestry of Old World evidence, the majority of which is outside the scope of this episode. Joseph could’ve—and should’ve–run afoul of the Old World in dozens of ways, but he simply doesn’t. Cataloguing those ways would be a much bigger project than the efforts I’ve put forward here. For the moment, though, we can be content with knowing that Nahom moves us a little further in the direction of an authentic Book of Mormon.

Skeptic’s Corner

Critics should probably be content with letting Nahom sit at a 2—given some of the evidence we have coming down the pike, they’ll soon have much bigger fish to try and fry. But if there’s a potential weakness here, it’s in the assumption that Joseph could’ve chosen any random combination of Hebrew consonants when putting together names. We know, for instance, that those names aren’t random—they tellingly avoid the consonants F, Q, V, W, X, and Y, some of which would have been improper within Semitic language conventions. Perhaps Joseph, with a bit of Hebrew expertise at his disposal (which he isn’t likely to have had at the time), could have limited his search space to just valid consonant combinations, potentially improving his chances of getting a direct hit. It would take a deeper dive than I have time for here to search out a set with potentially thousands of valid combinations, but if critics are determined to whittle down the strength of this evidence, they may be obliged to try.

Next Time, in Episode 8:

When next we meet, our skeptic will consider the efforts of boatbuilding and the perils of a transoceanic voyage.

Questions, ideas, and embarrassing anecdotes can be related to BayesianBoM@gmail.com or submitted as comments below.

Appendix

Potential Nahom Turn Targets

#

Place Name

Consonants

Probability

1

Ala

1

6.1E-04

2

Ali

1

6.1E-04

3

Uddeie

1

6.1E-04

4

Affar

2

3.9E-04

5

Attal

2

3.9E-04

6

Cheiat

2

3.9E-04

7

Chula

2

3.9E-04

8

Demm

2

3.9E-04

9

Loheia

2

3.9E-04

10

Loma

2

3.9E-04

11

Matta

2

3.9E-04

12

Moor

2

3.9E-04

13

Rodda

2

3.9E-04

14

Saedie

2

3.9E-04

15

Sana

2

3.9E-04

16

Torr

2

3.9E-04

17

Tulla

2

3.9E-04

18

Zeiat

2

3.9E-04

19

Achraf

3

4.4E-05

20

Achraf

3

4.4E-05

21

Amram

3

4.4E-05

22

Aschiab

3

4.4E-05

23

Asfal

3

4.4E-05

24

Attual

3

4.4E-05

25

Autar

3

4.4E-05

26

Bahas

3

4.4E-05

27

Charit

3

4.4E-05

28

Charres

3

4.4E-05

29

Chobt

3

4.4E-05

30

Degro

3

4.4E-05

31

Dehan

3

4.4E-05

32

Deiban

3

4.4E-05

33

Dennub

3

4.4E-05

34

Dobber

3

4.4E-05

35

Doffir

3

4.4E-05

36

Dofian

3

4.4E-05

37

Elboon

3

4.4E-05

38

Gsuvie

3

4.4E-05

39

Habir

3

4.4E-05

40

Hakel

3

4.4E-05

41

Hamada

3

4.4E-05

42

Heiran

3

4.4E-05

43

Iirban

3

4.4E-05

44

Karn

3

4.4E-05

45

Mabian

3

4.4E-05

46

Mahamma

3

4.4E-05

47

Marabea

3

4.4E-05

48

Nehhm

3

4.4E-05

49

Nunra

3

4.4E-05

50

Rahab

3

4.4E-05

51

Sabca

3

4.4E-05

52

Salibe

3

4.4E-05

53

Sand

3

4.4E-05

54

Schibani

3

4.4E-05

55

Schirra

3

4.4E-05

56

Sjenned

3

4.4E-05

57

Tauasch

3

4.4E-05

58

Temah

3

4.4E-05

59

Tsibu

3

4.4E-05

60

Tureiba

3

4.4E-05

61

Uschech

3

4.4E-05

62

Woreda

3

4.4E-05

63

Wulled

3

4.4E-05

64

Zilleba

3

4.4E-05

65

Zobera

3

4.4E-05

66

Zobra

3

4.4E-05

67

Abrahun

4

1.0E-06

68

Belled Laa

4

1.0E-06

69

Bulsedi

4

1.0E-06

70

Dsjalie

4

1.0E-06

71

Elbattaba

4

1.0E-06

72

Hamdan

4

1.0E-06

73

Kahhlan

4

1.0E-06

74

Kalbeen

4

1.0E-06

75

Kankeban

4

1.0E-06

76

Kaukeban

4

1.0E-06

77

Limruch

4

1.0E-06

78

Machadra

4

1.0E-06

79

Menejre

4

1.0E-06

80

Mnakeb

4

1.0E-06

81

Sanhan

4

1.0E-06

82

Surdud

4

1.0E-06

83

Ben Zeren

5

1.8E-08

84

Dahhrjin

5

1.8E-08

85

Elfchams

5

1.8E-08

86

Hadsjar

5

1.8E-08

87

Hudsjera

5

1.8E-08

88

Muschwar

5

1.8E-08

89

Nedsjera

5

1.8E-08

90

Redsjum

5

1.8E-08

91

Sdjelledi

5

1.8E-08

92

Kasr El-Nad

6

1.2E-10

Overall

0.0097

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