False Positives

Fun with Dice in a Workshop for Management

and “data” are what most people use when they make decisions,
especially decisions that others see as hopelessly biased and idiotic.
The challenge is learning how to interpret facts and how to analyze data
so that are decisions are less likely to be blunders based on the many
biases and fallacies that can mislead all of us.

In a
training class on decision making that I was invited to do for managers
in one of my employer’s groups in China, I brought in a big bag of dice
to help local managers understand a serious example of self-deception in
leadership. In particular, I sought to illustrate why criticism of
employees for poor results seems to work better than praise for good
results. It’s an example where solid experience and significant data can
actually mislead and deceive..

Everybody in a group of
about 50 people were given three dice. I then explained their KPIs (Key
Performance Indicators–an important phrase in modern Bizspeak) for the
exercise: the company needs high scores. Everyone was asked to shake
their dice and roll them once, then record their score. The few with the
highest scores (e.g., a sum of 15 or higher) were brought up to the
front. A group with about the same number of people with the lowest
scores (e.g., less than 6) was also brought up to the front.

it was time for their performance review. I approached the high
performers and personally congratulated them. I shook each person’s
hand, thanked them for their amazing achievement, gave them gifts (a
candy bar) and cash incentives (a Chinese bill–real money), and praised
them as good examples for the rest of the company. The whole room then
joined me in loud applause for these high-achievers.

it was time for consequences for the low-performers. I shook my head,
grimaced, wagged my finger at them, and scolded them for their failure
in giving such disappointing results. They were a shame to the company,
and we might need to demote them or fire them if they didn’t shape up.

proper rewards and punishments having been meted out, the people in
these two outlier groups were given three more dice each and allowed to
roll again. Amazingly, the average score of the former top performers
now dropped significantly. Almost everyone in that team did more poorly
after receiving praise and rewards. But for the ones who had been
scolded and criticized, a notable improvement was observed. Almost all
of them showed significant gains in their scores. Wow, praise hurts and
criticism helps, right?

This pattern is fairly
reproducible, and coincides with the vast experience of many coaches,
bosses, generals, and leaders of all kinds: criticism and punishment
works better than praise; yelling works better than kindness. They have
solid experience to prove it, and they are often right, in a sense, but
also perhaps terribly wrong.

Obviously, the results
with the dice were not likely to be affected by praise or rewards (as
long as the participants behaved honestly). What was happening here is a
common statistical phenomenon that results in a great deal of
self-deception in many fields of life. The phenomenon is “regression to
the mean.” When there is a degree of randomness, as there is in much of
life, random trends that depart above or below the mean tend to come
back. Results that are extreme are often statistical outliers,
explainable by chance, that are not necessarily caused by the
explanations we try to concoct. It’s why athletes who make it to the
cover of famous sports magazines after a string of remarkable successes
tend to disappoint immediately after, leading to the “Sports Illustrated
jinx” which may not be a real jinx at all. It’s the reason why highly
intelligent women such as my wife tend to marry men who are less
intelligent, like certain bloggers around here. Since the correlation
between female and male intelligence in marriage is not perfect and
therefore involves some degree of randomness, the most intelligent
outliers among females will tend to marry men who are not such extreme
outliers themselves, and the probability is that they will tend to be
less intelligent. This works both ways.

Two Books That Inspired My Workshop

experiment with dice and other parts of my workshop were inspired in
part by two outstanding books that I recommend. The exercise with dice
was inspired by a story in Thinking Fast and Slow by Daniel
Kahneman (New York: Farrar, Straus and Giroux, 2011). I picked this up
for airplane reading a couple years ago and found a real gem that I have
applied in a variety of ways, though I still readily fall into many of
the fallacies of human thought that so easily beset us. The story that
motivated my dice exercise for management came from Chapter 17,
“Regression to the Mean,” pp. 175-176.

Kahneman, winner
of the Nobel Prize in economics, once taught Israeli air force
instructors about the psychology of effective training. He stressed an
important principle: that rewards for improved performance worked better
than punishment for mistakes. This is something that we employees tend
to understand easily, but is often a mystery to those dishing out the
punishments and rewards. One of the instructors challenged him and said
that this principle was refuted by his own extensive experience. When a
cadet performed exceptionally well and was praised, he would usually do
worse on the next exercise. But when someone performed poorly and was
criticized, he usually did better on the next run. This was a “a joyous
moment of insight” to Kahneman, who recognized an important application
of what he had been teaching for years about the regression to the mean.
The instructor had been looking for a cause-and-effect explanation to
natural, random fluctuations, and had developed an iron-clad theory that
was dead wrong. He had extensive real data, but had been deceived by a
failure to understand the impact of randomness. Real data + bad
statistics (or bad math) = bogus conclusions.

to the mean is one of several important principles Kahnema discusses.
Many have roots in mathematics. All have connections to human psychology
and the way our brains work. Kahneman is brilliant in illustrating how
often we make flawed decisions, and gives us some tools to overcome
these tendencies.

Related to Kahneman’s work is another
math-oriented book which I relied on in my workshop on decision making,
and which I highly recommend: Jordan Ellenberg, How Not to be Wrong: The Power of Mathematical Thinking (New York: Penguin Press, 2014).

shows how basic mathematics can quickly expose many of the fallacies
that we make in our thinking and decision making. Some of his
discussions have application to matters that come up in discussions of
LDS religion and in evaluation of evidence to support or discredit a
theory. He decimates one of the classic “Texas sharpshooter” disasters
in religious circles, the utterly bogus methodology used in The Bible Code
in which the Hebrew text of the Old Testament was treated as a
miraculous, absolutely perfect text filled with hidden prophecies that
could be obtained by mathematically rearranging the letters of the text
in numerous different grid patterns and then searching for new words in
something of a hidden-word puzzle. With computerized tools, thousands of
grids could be formed to lay out the letters in new two-dimensional
patterns and then these patterns were searched to find all sorts of
modern topics.

There’s an old joke about a man in Texas
who took a rifle and fired a few dozen random rounds into the side of a
barn. Wherever the shots were clustered together, he painted a target
around them and then told people that he was a sharpshooter. Drawing
circles around spaced-apart Hebrew letters on, say, arrangement number
47, 356 and finding a hidden prophecy is analogous to the Texas

Further, the very premise of a perfect
text for the study is completely without logic. There are multiple
versions of the ancient Torah with obvious gaps and uncertainties (e.g., compare the Torah in the Dead Sea Scrolls to the version used today: there are differences).
Changing one letter in the text would through off the alignments on the
selected grid patterns that give mystical results, making the whole
exercise obviously bogus.

In “Dead Fish Don’t Read
Minds” (Chapter 7), Ellenberg warns of the dangers of amplifying noise
into false positives when we have the resources of Big Data to play
with. With numerous variables to explore and map, it is incredibly easy
to find some that seem to correlate. This was brilliantly illustrated in
a real but still somewhat tongue-in-cheek paper that managed to be accepted for presentation at the 2009
Organization for Human Brain Mapping in San Francisco, where UC Santa
Barbara neuroscientist Craig Bennett presented a poster called “Neural correlates of interspecies perspective taking in the post-mortem Atlantic Salmon: An argument for multiple comparison corrections.” (See discussion at Scientific American.) 
Basically, this paper reported statistical results from MRI brain
mapping taken in a dead fish as the fish was shown photos of people in
different emotional states. Dr. Bennett used the power of Big Data to
explore MRI signals from millions of positions and found a couple spots
in the fish’s neural architecture where the fluctuates corresponded well
with the emotional state shown in the photos. His paper was a clever
way of illustrating the dangers of using Big Data to find correlations
that really don’t mean anything, much like the work to find “smoking
guns” for Book of Mormon plagiarism by doing computer searches of short
phrases with hundreds of thousands of books to toy with.

is often critical of religion and believers, and probably with good
reason, and mocks some aspects of the Bible a time or two, but religious
people can learn much from his mathematically sound approach to

What Are the Odds of That? Actually, Unlikely Results are Guaranteed

many fallacies explored by Kahneman and Ellenberg can affect all of us
in our thinking and decision making. When it comes to apologetics,
Latter-day Saints can fall into related traps if we treat anything from
anywhere, anytime as potentially being a relevant parallel to the Book
of Mormon or other LDS works. Not every New World drawing of people in
two or more tones implies that we are looking at Nephites and Lamanites.
Not every drawing of a horse means we are looking at evidence for Book
of Mormon horses. And a place called Nehem on a map of Arabia is not
necessarily evidence that a name like Nahom existed anywhere in Arabia
in Lehi’s day. Those things can be random parallels. If they are
meaningful, there should be further data that can support the hypotheses
put forward. Such finds would be most meaningful if they are part of a
large body of information from multiple sources that can serve as
convergences useful in assessing the particular question at hand, such
as “Is the story of Lehi’s trail plausible? Could there have been a
place called Nahom where Ishmael was buried, with a fertile place like
Bountiful nearly due east?” Such questions can be framed in ways that do
not leave the infinite wiggle room of Bible Code explorations.
(It was such a question, in fact, that motivated Warren Aston to
undertake exploration in the Arabian Peninsula at great personal cost
with predetermined criteria for Bountiful, a target already drawn before
he ever touched the coast of Oman.)

When we are
exploring a hypothesis, false positives can easily result from errors in
thinking due to failure to understand randomness and regression to the
mean, as well as other mathematical and logical fallacies. A key element
in the field of statistics is recognizing that a random result can seem
to support a hypothesis when there is not actually a cause-and-effect
relationship. The science of statistics provides tools and tests to help
differentiate between what is random and what is real, though it
certainty is almost always elusive. Statistics gives us some tools to help reduce the risk of seeing things
that aren’t there, or to know when we might be missing something that
is (these topics involves the issues of “significance” and “power,” for example). Even for those trained in
statistics, there are abundant errors that can be made and false
conclusions made.

I’m not a statistician, but I did
have 10 hours of graduate level statistics and have frequently had to
rely on statistics to assess hypotheses. I even published a little paper
on a mathematical issue related to a statistical issue known as the
“collector’s problem.” The publication (peer-reviewed, but still lightweight, IMO) is J.D. Lindsay, “A New Solution for the
Probability of Completing Sets in Random Sampling: Definition of the
‘Two-Dimensional Factorial’,” The Mathematical
, 17: 101-110 (1992), which you can also read online
as a Web page or as a Word document. But what really
matters is that I am married to a statistician (M.Sc. degree in
statistics, now math teacher at an international school in
Shanghai)–what are the odds of that? Well, 100%, since that’s what

That reminds me of the many mistakes that
people on both sides of the debate can make as they argue probabilities.
It’s easy to see significance in something that happens by chance,
especially when we find something that did happen, possibly by chance,
and then try to make a case for how improbable that was. Richard Feynman
once joked to a class that one the way to campus that morning, he saw a
car with a specific license plate, ARW 357. “Of all the millions of license plates in the state, what was the chance that I would see that particular one tonight?” This fallacy of a posteriori
conclusions is an easy one to make. It’s inevitable that any particular
license plate will be rare, maybe even unique in all the world or at
least all the state. That odds of that happening are low–a priori,
before the event–but a posteriori, the odds are high, as in
100%. Making much of something because it is unusual is an error. But
again, today, much of the serious evidence being raised for Book of
Mormon plausibility is not of that nature.

Parallels occur
all over the place. Parallel words, themes, and motifs occur across
large bodies of literature, even when they are surely unrelated. I can
take any two texts and find some parallels. Within a sufficiently large
text, I can probably find parallel words and phrases that I can sketch
out as a chiasmus. If we scour all the names introduced in the Book of
Mormon, we should not be surprised to find a few might have apparent
connections to ancient languages. We might even not be shocked to find
an occasional one whose purported meaning might be construed to relate
well to its context. But when numerous names begin to have support and
offer useful new meaning for the text, when things like Hebraic
wordplays occur many times and in interesting, meaningful ways, then the
evidence can become more significant. When linguistic and
archaeological evidence bring about interesting and repeated
convergences, it may be time to take a deeper look at the evidence
rather than assuming it’s all chance.

unlikely findings are actually quite likely to happen. That truism,
however, is not an excuse to disregard meaningful bodies of evidence and
convergences that enlighten a text in question.

Progress in Avoiding False Positives

the risk of methodological fallacies is frequently and openly
considered among many LDS apologists, contrary to the allegations of
critics who sometimes seem blind to their own biases and methodological

For example, while chiasmus can and does occur
randomly, just as rhymes and other aspects of poetry can be found in
random text, there are reasonable criteria for evaluating the strength
of a chiasmus that can help screen random chaff from deliberately
crafted gems. The possibility of false positives was an important factor
in the analysis of John Welch as he explored the role of chiasmus in
scripture. Others build upon his foundation and even offered statistical
tools for evaluating chiasmus. It is still possible for something that
appears elegant, compact, and brilliantly crafted to be an unintended
creation, but we can speak of probability and plausibility in making
reasonable evaluations.

In the early days of LDS
apologetics, evidence of all kind was enthusiastically accepted. But
gradually, I see LDS writers becoming more nuanced and cautious. A prime
example of this is, in my opinion, Brant Gardner in his book, Traditions of the Fathers: The Book of Mormon as History
(Salt Lake City: Greg Kofford Books, 2015). He is fully aware of the
risk of fallacious parallels, but in evaluating the relationship between
a text and history, they must be considered. What matters is how they
are considered and what they data can plausibly support. On page 47
[visible in an online preview],
Gardner discusses an insight from William Dever, a prominent professor
of Near Eastern archaeology and anthropology at the University of
Arizona who has been excavating in the Near East for several decades:

Some form of comparison between text and history is always required to discern

Texts are always compared to archaeology and/or other texts. Sometimes
even artifacts require explanation by comparison or analogy to similar
artifacts from another culture. Comparisons must be made. The problem
cannot, therefore, reside in an absolute deficit in any methodology that
makes comparisons, but rather in the way the comparisons are made and
made to be significant. One important type of controlled parallel is
ethnographic analogy. Dever explains his version of this method:

aspect shared by both biblical scholarship and archaeology is a
dependence on analogy as a fundamental method of argument. . . .

challenge is to find appropriate analogues, those offering the most
promise yet capable of being tested in some way. Ethnoarchaeology is
useful in this regard, particularly in places where unsophisticated
modern cultures are still found superimposed, as it were, upon the
remains of the ancient world, as in parts of the Middle East. Analogies
drawn from life of modern Arab villages or Bedouin society can, with
proper controls, be used to illuminate both artifacts and texts, as many
studies have shown. [William G. Dever, What Did the Biblical Writers Know and When Did They Know It? What Archaeology Can Tell Us About the Reality of Ancient Israel (Grand rapids, Michigan: Eerdmans, 2001), pp. 77-78.]

work deals with the concept of “convergences” wherein multiple lines of
evidence, such as evidence from archaeology and from a text, come
together and support the historicity of a text in question. In spite of
the risk of fallacious parallels or false positives, convergences can be
strong and can create compelling cases for the historicity of a text.
Dever’s work is also relied on by John Sorenson in Mormon’s Codex,
where extensive correspondences between Mesoamerica and the Book of
Mormon in many different topical areas are explored. Gardner observes
his requirements for a convergence are more demanding than the criteria
in Sorenson’s approach. But I feel both authors are aware of the risk of
random parallels being mistaken as evidence, and are seeking to provide
a thorough methodology that combines multiple approaches to establish
meaningful though tentative connections that do more than just buttress
one point, but which also provide a framework that solves other problems
and makes more sense of the text. Convergences that are fruitful and
lead to new meaningful discoveries are the most interesting and
compelling, though there is always the risk of being wrong.

approach also draws upon wisdom from the field of linguistics, which
offers many analogies to the problems of evaluating the historicity of a
text based on parallels and convergences.

As a result
of my orientation, I suggest that we will be best served by an approach
applied with great success in the field of historical linguistics. Bruce
L. Pearson describes both the problem and the solution:

of words exhibiting similarities in both form and meaning may be
presumed to be cognates, given that the languages involved are assumed
to be related. This of course is quite circular. We need a list of
cognates to show that languages are related, but we first need to know
that the languages are related before we may safely look for cognates.
In actual practice, therefore, the hypothesis builds slowly, and there
may be a number of false starts along the way. But gradually certain
correspondence patterns begin to emerge. These patterns point to
unsuspected cognates that reveal additional correspondences until
eventually a tightly woven web of interlocking evidence is developed.
[Bruce L. Pearson, Introduction to Linguistic Concepts, 51]

linguistic methodology describes quite nicely the problem we have in
attempting to place the Book of Mormon in history. We cannot adequately
compare the text to history unless we know that it is history. We cannot
know that it is history unless we compare the text to history. We
cannot avoid the necessity of examining parallels between the text and

The problem with the fallacy of parallels is
that it doesn’t protect against false positives. What is required is a
methodology that is more recursive than simple parallels. We need a
methodology that generates the “tightly woven web of interlocking
evidence” that Pearson indicates resolves the similar issue for
historical linguists.

In my studies of foreign
language, I’ve often been intrigued by false cognates that can trick
people into imagining connections between languages that might not
exist. An interesting involves the English and Chinese words “swallow.”
In English “swallow” can be a noun involving the ingestion of food or
liquid and it can be a noun describing a particular bird. Something
similar happens in Chinese, where 燕 (yan, pronounced with a
falling tone) is the Chinese character for swallow, the bird, while the
same sound and nearly the same traditional character, 嚥, is the verb, to
swallow. The latter just adds a square at the left, representing a
mouth. It’s a cool parallel. If this kind of thing happened frequently,
or if there were, say, hundreds of ancient Chinese words that showed
connections to English, we might have a case for a systematic
relationship between the languages. But there really are not meaningful
connections between the languages apart from modern borrowed words and a
few rare occurrences that can be chalked up to chance. But exploring
parallels between languages is a vital area for research and study–it’s
how relationships between languages are established in the first place
and can help fill in huge gaps in the historical and archaeological
record. When the parallels become numerous and show patterns that begin
to make sense, it’s possible that two languages share historical
connections. To me, Gardner’s appeal to lessons from historical
linguistics makes sense. Parallels can be real and meaningful, or they
can be spurious. It’s a matter of exploring the data and being open to
convergences that enlighten and reveal useful new ways of understanding
the data.

In evaluating the Book of Mormon, I believe
LDS scholars today generally recognize that there is a risk of finding
impressive parallels to, say, ancient Mesoamerica or ancient Old World
writings that may be merely due to chance.

In my own
writings, I’ve often pointed to the risk that my conclusions are based
on chance, misunderstanding, and so forth, and use my blog as a tool to
get frequent input from critics. In spite of their repetitive dismissal
of all evidence as mere blindness, bias, and methodological fallacy on
our part, occasionally they engage with the data and provide some
helpful balance or even strong reasons to reject a hypothesis. It’s a
healthy debate. We don’t have all the answers, we are subject to biases
of many kinds, but there is still a great deal of exploration and
discovery to do that goes beyond finding random items and painting a
bullseye around it.

Sometimes the target was there
before the bullseye was there long before the bullet holes were
discovered, as in the Arabian Peninsula, which has long been a target
for criticism of the Book of Mormon before the field work was done that
helped us recognize just how many impressive hits had been scored by the
text in First Nephi.

Methodological Error: Not Unique to Mormons

Fallacies of logic and math, of course, aren’t unique to believers.

it comes to the Texas sharpshooter fallacy and related problems with
false positives, the critics of Mormonism also have some particular
gifts in this area as they scour modern sources to support theories of
plagiarism or modern fabrication of the Book of Mormon. Examples of
improperly finding meaning from randomness coupled with serious
methodological flaws include computer-assisted database searching among
thousands of texts for short phrases found in common with the Book of
Mormon or allegedly pointing to implausible sources for the Book of
Mormon such as the The Late War Between the United States and Great Britain.
Naturally, texts written in imitation of the King James style score
highly with their abundance of such words as “thou” and “thee” instead
of “you,” but there is no substance to the claim of plagiarism.

in fact, is an increasing problem in the works of critics purporting to
explain the Book of Mormon by appeals to numerous other texts. An
excellent discussion of false positives from parallels in an anti-Mormon
work is found in “Finding Parallels: Some Cautions and Criticisms, Part One” by Benjamin L. McGuire in Interpreter: A Journal of Mormon Scripture 5 (2013): 1-59. In Part Two, he gets more heavily into the methodology of treating parallels.

is no doubt that there are many parallels, as there can be between any
two unrelated texts. One of my early essays on the Book of Mormon sought
to expose the problem of false positives for those claiming Book of
Mormon plagiarism by coming up with even stronger examples of parallels
than the critics were delivering. The result was my satirical essay, “Was the Book of Mormon Plagiarized from Walt Whitman’s Leaves of Grass?” (May 20, 2002, but slightly updated several times since then), which Brant Gardner kindly quotes from in The Book of Mormon as History
(2015, pp. 44-45). Based on the data alone, one can make a strong case
that the Book of Mormon borrowed heavily from Whitman’s 1855 work or at
least had a common source (perhaps Solomon Spaulding was plagiarized by
Whitman as well?). That’s ridiculous, of course–but the parallels show
just how easy one can be mislead by random parallels, coupled with a
little creativity and a dash of zeal. If those claiming plagiarism can’t
clearly outdo Whitman as a control, a reasonable case has not been

One of latest posts at Mormanity dealt with my
explorations of a hypothesis from Noel Reynolds about the possibility of
the Book of Moses and the brass plates sharing some common material.
Reynolds’ article includes a detailed discussion of what it takes to
determine the relationship between two texts. It begins with a
consideration of the requirements for one text to depend on another. He
is aware of the risk of random parallels and discusses the issues rather carefully, aware of risks and aware of the kind of evidence that is required to find meaningful parallels. He also offers a test case also in
the Book of Abraham. Does it depend on the Book of Mormon or visa versa?
Very little sign of relationship is evidence in that case. But further tests and more rigor is needed. It’s very tentative and speculative, but interesting. Not completely illogical methodology at all, though the results are controversial.

But just as
alleged evidence sometimes falls prey to the sharpshooter fallacy as it
is improperly used to buttress a theory, the sharpshooter fallacy can
easily be misapplied to dismiss legitimate, meaningful evidence. A
noteworthy example is found when Dr. Philip Jenkins, a professor of
history, dismisses the significance of the evidence for Nahom in the
Arabian Penninsula, an important but small piece of the body of evidence
related to the plausibility of Nephi’s account of his journey through
Arabia along the route we often call Lehi’s Trail. Jenkins has this to say as he dismisses this evidence:

One other critical
point seems never to have been addressed, and the omission is amazing,
and irresponsible. Apologists argue that it is remarkable that they have
found a NHM inscription – in exactly the (inconceivably vast) area suggested by the Book of Mormon. What are the odds!

By the way, the Arabian Peninsular covers well over a million square miles.

indeed, what are the odds? Actually, that last question can and must be
answered before any significance can be accorded to this find. When you
look at all the possible permutations of NHM – as the name of a person,
place, city or tribe – how common was that element in inscriptions and
texts in the Middle East in the long span of ancient history? As we have
seen, apologists are using rock bottom evidentiary standards to claim
significance – hey, it’s the name of a tribe rather than a place, so

How unusual or commonplace was NHM as a name element in
inscriptions? In modern terms, was it equivalent to “Steve” or to
“Benedict Cumberbatch”?

So were there five such NHM inscriptions
in the region in this period? A thousand? Ten thousand? And that
question is answerable, because we have so many databases of
inscriptions and local texts, which are open to scholars. We would need
figures that are precise, and not impressionistic. You might conceivably
find, in fact, that between 1000 BC and 500 AD, NHM inscriptions occur
every five miles in the Arabian peninsular, not to mention being
scattered over Iraq and Syria, so that finding one in this particular
place is random chance. Or else, the one that has attracted so much
attention really is the only one in the whole region. I have no idea.
But until someone actually goes out and does some quantitative analysis
on this, you can say precisely nothing about how probable or not such a
supposed correlation is.

It’s a fair question, but one
that has been answered for many years. The NHM name turns out to be
exceedingly rare in the Arabian Peninsula. As far as we can tell, it is
only found in the general region associated with the ancient Nihm tribe.
It’s in the region required by the Book of Mormon, with a convergence
of data showing that this tribal name was there in Lehi’s day, in a
region associated with ancient burial sites, a region where one can go
nearly due east and reach a remarkable candidate for Nephi’s Bountiful.
It’s part of an impressive set of convergences pointing to plausibility
for the journey of Lehi’s trail. In light of the new body of evidence,
the task of critics has suddenly shifted from mocking the implausibility
of Nephi’s account to explaining how obvious it all is in light of the
knowledge that Joseph and his technical advisory team surely must have
found by searching various books and maps, all the time lacking any
evidence that such materials were anywhere near, and still being unable
to explain the motivation for plucking “Nehhm” or “Nehem” off a rare
European map amidst the hundreds of other names, ignoring every
opportunity to use the map for something useful. They also fail to
explain how any of these sources could have guided Joseph to fabricate
the River of Laman and Valley of Lemuel, the place Shazer, or the place
Bountiful, each with excellent and plausible candidates. Here appeals to
the Texas sharpshooter fallacy or any other fallacy miss the reality of
serious evidence and serious convergences that demand more than casual
dismissal and scenarios devoid of explanatory power.

Yes, it’s fair and important to worry about false positive (and false negatives) as we approach issues of evidence for the Book of Mormon, and against the Book of Mormon as well. Methodology, logic, and intellectual soundness are fair topics for debate. Let’s keep that in mind as we explore the issues and watch out for the many fallacies that can catch us on either side of the debate.

Author: Jeff Lindsay

156 thoughts on “False Positives

  1. Sorry Jeff. You didn't get this peer reviewed. It is not admissable if you don't get it peer reviewed.

    (I bit my tongue.)


  2. Jeff, I'm puzzled that you would write that chiasmus can and does occur randomly, etc.

    Has anyone argued that the obvious chiasmuses in the Book of Mormon "occur randomly"? My argument has always been that they're in the Book of Mormon because they're in the Bible, and the author of the BoM was imitating the Bible. This has nothing whatsoever to do with randomness.

    Glenn, I wish you could understand that secular academic peer review is not the enemy of LDS apologetics. It is, however, the enemy of bad apologetics, which is all the more reason apologists should pursue it.

  3. Orbiting,

    Do you have evidence for your assertion that chiasmus only appear in the BoM because the structures were copied from the Bible? Did this occur randomly? It seems to be that you are implying that Joseph Smith just read the Bible, and naturally produced chiasmus without thinking about it. Or if it was done intentionally then why was it never mentioned by Joseph Smith? I find it hard to believe that he intentionally put them in there and then forgot that he had done it.

    If it was something that "anyone familiar with the KJV in the 19th century could have done" then books like The Late War, which was written specifically to mimic the Bible, would have chiastic structures, much like those found in Deuteronomy 8 and Numbers 8. If "anyone" could have done it then we should find many examples of chiasmus in literature from the 1800's. And if it was so prevalent that random farmers could produce it then why did it slip past every academic who studied language and literature up until about the 1920's? So where is your evidence? You say "apologists are not operating in good faith" yet you produce no evidence to support your rather astounding assertions.

  4. Quantum, I'm saying that Joseph was very familiar with the sound of the KJV, and in writing the BoM he was trying to imitate that sound, and chiasmus is part of that sound, just like anaphora ("and it came to pass") is part of that sound, just like the cognate accusative ("he dreamed a dream") is part of that sound, and so on and on. In the course of trying to imitate the KJV's sound he naturally produced chiasmus (and many other biblical stylistic elements) without thinking about it.

    But no, I'm not saying he put chiasmus in the BoM deliberately. What he did deliberately was try to imitate the biblical style. Think of it this way. Your comment contains adverbs. Did you put those adverbs in your comment deliberately? No, what you were doing deliberately was trying to craft a response to my claims. That's what you were deliberately and consciously thinking about. The adverbs got in there unconsciously. And you could have used those adverbs even if you had never in your life heard the term adverb. You're confusing the use of language with the conscious use of language, and further confusing the use of rhetorical techniques with knowledge of the academic terms for those techniques.

    None of what I'm saying here is the least bit astounding. It's all rooted in our uncontroversial understanding of the way people acquire and use language.

    Consider this passage from the famous "Ain't I a Woman" speech of former-slave-turned-abolitionist Sojourner Truth:

    I have ploughed, and planted, and gathered into barns, and no man could head me! And ain't I a woman? I could work as much and eat as much as a man – when I could get it – and bear de lash as well! And ain't I a woman? I have borne thirteen chilern, and seen 'em mos' all sold off to slavery, and when I cried out with my mother's grief, none but Jesus heard me! And ain't I a woman?

    The repetition of the same word or phrase at the end of successive sentences is known as epistrophe. I seriously doubt that Sojourner Truth ever heard this term or studied classical rhetoric at all. Must we therefore conclude that she couldn't have used epistrophe in her speech? Of course not.

    Similarly, Smith's ignorance of the term chiasmus does not at all mean he couldn't have used chiasmus — no more than a child has to know the terms noun, verb, and direct object in order to use them in saying "I want a cookie." This sort of thing just comes naturally.

    Before I respond more specifically to your demand for evidence, let me ask you this:

    Do you believe Joseph knew how to read? If so, what is your evidence?

    After I have your answers, I'll be happy to go on.

  5. About chiasmus in the Book of Mormon: at least some of the Book of Mormon chiasmus is something that would be trickier to copy from the Bible, because it is really long and elaborate. To the extent that I want to ask: does any known ancient Hebrew writing really use such elaborate chiasmus? Or is this a hypertrophied form that is unique to the Book of Mormon — in which case it might be interesting, but it wouldn't count so much as evidence of authenticity as an ancient Hebrew text.

    The other problem with such a gigantic Book of Mormon chiasm as the one in Alma is that it takes a bit of squinting to see the pattern. The chiasmic form only emerges, in the long text, if you assign the right subheadings to big chunks of verses. This supplies a considerable amount of wiggle room, and every element in the pattern can wiggle independently. If you don't take that wiggle room into account when you estimate the probability of the big chiasmic pattern occurring by chance, then simply because the pattern is long, you easily end up with an overwhelming likelihood that the pattern is real and deliberate. But if you think about how subjectively the verses were grouped and characterized, in order to define the pattern, you should really up the chance of randomness at each step quite a lot. The final probability that the long pattern is real then becomes awfully fuzzy, because small changes in the probability for each item make a big difference when they're multiplied thirty times. At the very least, though, one should say that the very existence of this big chiasm is a lot less clear cut than some apologists have made it out to be.

  6. About this latest post: I'm quite impressed. Jeff seems to have quite a good grasp of the subtleties of inductive argument; I reckon he knows enough to appreciate pitfalls in arguments as well as anyone. Professional expertise might help one to recognize pitfalls more quickly, but if you take a bit of time to think about the reasoning, then I'm pretty sure that Jeff's level of statistical awareness is quite sufficient to do the job. Expertise in statistics isn't as big a deal as some people think.

    People who don't do much math often seem to regard statistics as a black art. They know that if you don't follow certain arcane rules, your results will be invalid; but they have no idea why. On the other hand, they imagine that if you do follow the arcane rules, then your results will be guaranteed to be true, by the mystic power of statistics. They don't get the fact that statistics is just ordinary common sense, applied carefully. There are no rules so mystical that you can turn weak evidence into fact just by following the rules.

    So on the one hand I'm reassured that Jeff, at least, is quite able to handle methodological discussions about inference from evidence. But on the other hand I still have the concern that at least some apologists may not appreciate just how much of that kind of discussion needs to be done.

    A good example of what I mean is In my most recent comment before this one: the trickiness of quantitatively analyzing chiasmus. I've seen several Mormon apologists cite the high final probability estimate for deliberate chiasmus in Alma 36 that was claimed by one particular paper, as if citing that one paper was decisive. That's like counting somebody as Heavyweight Champion just because they showed up at the ring wearing shorts. Presenting a quantitative analysis is something, all right: it's like stepping into the ring. But that's just the beginning. You've got to go the distance. That can be tough.

    I'm sure that critics and skeptics of Mormonism are also often guilty of underestimating the work involved in really establishing even basic points. The fact is that, even though a bunch of amateurs on either side may have enough wit and knowledge to thresh this stuff out properly, we may well not have the time to slog through to the end.

    If that's true, then I think we should admit that, on either side, rather than kid ourselves about how strong a case we can make — for our against — in our spare time.

  7. @ Jack:
    "Not sure I could chalk Alma 36 up to an accident of cultural influence."

    That's what I said. If it's there, it's too big to be an accident. The thing is: it's really not so clear that it's there. It's a loose and subjectively identified pattern in a long text.

  8. One more point on the theme of how much attention the premises of inference really require.

    "You have to go the distance" doesn't necessarily mean that everyone has to "engage the material". If a hundred dense pages are all based on one flimsy premise that isn't properly established, then carefully reading all those pages would be a poor use of an amateur's limited time.

    In fact that's why things that might seem like mere preliminary details need so much careful attention. If you skimp on them, then no amount of detail built on top of them can make up for their flimsiness; if an opponent points out that flimsiness, you can't complain that they ignored all your other hard work. A skyscraper built on sand falls just as fast as a house.

  9. Like James, I'm also impressed with this post. Jeff is taking some big steps down the road that leads eventually to a better understanding of the Mormon scriptures.

    Maybe someday we'll see a similar post about the value of academic peer review. As I mentioned above, peer review is not the enemy of LDS apologetics — only of bad LDS apologetics.

    As for Alma 36, there's another question that never seems to get discussed: What in the world would be the purpose of a 39-level chiasmus in the first place?

    Techniques like chiasmus are used because they have certain effects on the reader/listener, such as making things more memorable. (Ditto, of course, for anaphora, alliteration, rhyme, rhythm, etc.) Which of the following is more memorable? This…

    We should all support one another, both individually and as a group.

    … or this:

    All for one and one for all!

    Clearly the latter is the one more likely to stick in the mind, and that's mostly because of its chiastic structure. Its chiastic structure has a clear and beneficial effect on the reader/listener. But I don't see how there could possibly be any such effect in the case of Alma 36. Even if it is a genuine chiasm — and not just a methodological artifact created via the clever use of ellipses — it's simply too big and loose and baggy to have any rhetorical effect. By the time you get to the end you've long since lost touch with the beginning. What, then, could possibly have been the point of creating it? This question applies whether its author was ancient or modern.

    The idea that Alma 36 contains a massive chiasmus that is an artistic writerly creation (as opposed to methodological artifact) makes about as much sense as the idea that the BoM is rife with actual EModE (as opposed to scattered bulletholes made by a Texas sharpshooter). These things serve nicely as a hammer for the apologist, because they support the argument that Joseph could not be the author. But we should remember that, in addition to serving the modern purposes of the apologist, such literary marvels must have served some ancient purpose of the author.

    At this point I guess the (bad) apologist might say this: The ancient writer's purpose was not to have a rhetorical effect on his ancient audience, but to conceal items in the text that, upon discovery some 1,500 or more years in the future, would confirm the faith of his modern audience. This is the point where the apologist starts preaching solely to the choir. This is the point where the apologist requires us to believe that, while Jeremiah was writing for an audience of 6th-century BCE Jews, Paul for an audience of 1st-century Christians, etc., Nephi and Mormon were writing specifically for an audience of modern Americans. We are being asked to believe something of this particular ancient text that is not true of any other ancient text that we know.

    Well, um, okay…. But if we grant all this, we might wonder why these ancient authors would not attempt to persuade their future audiences by providing less equivocal evidence. But at this point the (bad) apologist starts talking about how, yes, God wants us to believe, but doesn't want to make it too easy for us to believe, etc. — and at this point Gentiles like me simply throw up our hands and say, "There's just no reasoning with you guys. You move the goalposts, your claims are never falsifiable, and whatever it is that you're doing here, you're not arguing in good faith. You're more interested in shoring up your testimonies than in searching for truth."

    P.S. FWIW, a 21-level (but very loose and baggy) "chiasm" has been discovered/invented in The Late War — see here.

  10. Please, let's stop with the lame critical analysis by the critics, and stop harping on Alma 36. A good critical analysis must consider at least Mosiah 3:18-19, Mosiah 5:10-12, Alma 41:13-14, and Helaman 6:9-11. See various Welch publications for more, and Edwards and Edwards (2004) BYU Studies for stats.

    Also, orbitational analogizes from simple epistrophe to multi-level chiastic construction. Who thinks he's a reasonable analyst who's trying to check his biases in this case?

  11. Anon 12:05, I didn't analogize simple epistrophe to multi-level chiasmus. I used epistrophe to challenge a particular apologetic assumption: that one must know the technical term for a rhetorical figure in order to use that rhetorical figure.

    My argument about Alma 36 is that it's not a chiasmus at all — it's a methodological artifact created by the bogus method of (1) fishing in an expansive sea of text until finding a passage that (2) can be made to appear chiastic by strategically omitting non-chiastic portions of the text. Basically, Welch put his thumb on the scale. Any subsequent statistical analysis that fails to take this into account is meaningless.

    (1) above is basically Texas sharpshooter. (2) is just intellectually dishonest. It's basically saying, "This passage is chiastic…" without adding "…except where it's not." It's like James's used-car salesman saying "With its new tires, new brakes, and new paint job, this car is in great shape…" without adding "…except for the leaky head gasket and worn-out transmission."

    At any real academic journal this kind of stuff would be pointed out in peer review. That's why these arguments wind up only in pseudo-journals, like BYU Studies, where once again the thumb is on the scale.

    If the aim is to do things like better understand the Mormon scriptures and persuade the outside world of their value, then secular academic peer review is your friend, not your enemy.

    Peer review is the enemy only if the aim is to shore up the believer's testimony at all cost.

  12. Please stop with Alma 36. Okay, not analogizing in one sense, but you're equating epistrophe to production of 7-level chiasmus. They're wholly different. The normal human mind cannot produce the latter subconsciously.

  13. Okay, I'll stop with Alma 36. Will the apologists?

    The normal human mind cannot produce the latter [7-level chiasmus] subconsciously.

    Actually, I'm not so sure of that. There are plenty of examples of people spontaneously dictating some pretty complex stuff. In any case, Joseph Smith surely had an exceptional mind.

    If you'd like to show us the 7-level chiasmus you're referring to, feel free.

  14. If you google "Alma 36 chiasmus", the current sixth hit is the article in Dialogue by a guy named Wunderli, which points out a level of shakiness — in the very existence of this giant chiasm — that is disturbing to me. I'm not saying Wunderli has won the whole fight, but he certainly comes out swinging pretty hard for a few rounds. Maybe the chiasmus can somehow be salvaged, but after reading Wunderli's critque, I felt a bit annoyed that Mormon apologists hadn't been more up-front about how much scaffolding is needed to support this purported multi-level pattern.

    From the way I'd read apologists referring to Alma 36, I was expecting something almost like a sonnet, with the chiasmus building line after line. Instead it's really an overlay that you have to put onto the text, by declaring passages of varying length to be 'about' certain topics. Perhaps it's not sheer invention — though at the moment that's what I think it is — but it's definitely not the striking literary landmark that I felt led to expect.